MEASUREMENT OF THE HIGGS BOSON COUPLINGSUSING THE W W ∗ → ℓνℓν FINAL STATE

A Dissertation submitted in partial fulfillment of
the requirements for the Degree of Doctor of Science
11/08/2014

CERN-THESIS-2014-151

Keisuke Yoshihara

Graduate School of Science, The University of Tokyo

July 2014

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Copyright⃝2014
by Keisuke Yoshihara
All Rights Reserved

Abstract
The discovery of a Higgs boson with a mass of approximately 125 GeV was reported by
the ATLAS and CMS collaborations in July 2012 [1, 2], which has opened up a new era inunderstanding the nature of electroweak symmetry breaking and possibly completing theStandard Model of particle physics. The center of physics analysis is property measurementof the Higgs boson, which allows us to investigate underlying physics beyond the Standard
Model. This thesis presents measurements of the Higgs couplings in the H→ W W ∗ → ℓνℓν
final state, using the full Run-I pp collision data recorded by the ATLAS at the LHC, cor√√
responding to 4.5 fb−1 of s = 7 TeV data collected in 2011 and 20.3 fb−1 of s = 8
TeV data collected in 2012. The H→ W W ∗ → ℓνℓν is one of the most sensitive channels
to the coupling measurement through both gluon-gluon fusion (ggF) and vector boson fusion (VBF) production processes. The analysis adopted several enhanced techniques on
the background estimation to attain a substantially better sensitivity to the measurement;
the study of the W +jets process, being one of the most important backgrounds, is fully
described. The coupling strength is represented by signal strength µ that is defined as theratio of cross section times branching fraction in data to that in theoretical prediction. The
result presented in this thesis supersedes the previous measurement [3, 4], owing to optimizations of selection of physics objects and improvements of the modeling of backgrounds.
The observed excess of the inclusive production is about 6 σ that is large enough to claim
the discovery of the H→ W W ∗ decay, and the corresponding signal strengths for individual
production processes are:+0.23
µggF =1.15+0.18−0.18 (stat.)−0.19 (syst.),+0.32µVBF+VH =1.36+0.41−0.45 (stat.)−0.24 (syst.).

Furthermore the couplings to fermions and weak bosons are each extracted, introducing
coupling scale factors κF for fermions and κV for weak bosons. The measured scale factors
are:
+0.07
+0.08
κV =1.08+0.11−0.11 = 1.08−0.08 (stat.)−0.07 (syst.),
+0.24
+0.22
κF =1.00+0.32−0.24 = 1.00−0.18 (stat.)−0.15 (syst.).

which are consistent with the values predicted by Standard Model.
iiiAcknowledgement
This thesis would not have been materialized without the help from many people who gave
their support in diﬀerent ways.
First and foremost, I would like to express my sincere gratitude to my supervisor
Prof. T. Kawamoto for providing a great opportunity to participate in the ATLAS experiment and for the continuous support of my research and of my life at CERN. His
guidance helped me in all the time of research and writing of this thesis. I could not haveimagined having a better advisor.
My sincere thanks also goes to Dr. T. Masubuchi, who has supported me throughout my research with his patience and knowledge while allowing me the room to work in
my own way. I have worked very closely with him over three years having sleepless night,
in particular in the discovery phase. The discovery of the Higgs boson is irreplaceable
memory. I would also like to thank Prof. T. Kobayashi, Prof. S. Asai, Prof. J. Tanaka, andProf. Y. Enari for leading our group and giving enormous advices about how to conduct
research and about how to survive in large collaboration represented by the ATLAS group.
I am deeply grateful to all members involved in “Team W +jets”, Prof. J. Kroll, Dr. J. Alison, Dr. C. Mills, Dr. D. Schaefer, Dr. L. Galtieri, T. Kishimoto, Dr. O. Arnaez, andC. Lester for continuous and long discussions on this topic. They have made lots of meaningful suggestions and have given me ideas to improve my works. I would like to add one
more special thanks to Prof. J. Kroll again who will be my supervisor at University of Pennsylvania in the near future for his proof reading of this thesis, and for making lots of suggestions on it. I am very much indebted to ATLAS-Higgs HW W organizers during my stayat CERN : Dr. T. Masubuchi, Dr. C. Mills, Prof. J. Kroll, Prof. C. Hays, Prof. B.D. Micco,
Dr. T.M. Hong, Dr. M. Chelstowska, Prof. P. Savard, and Prof. J. Qian, and editorial board
members, Prof. D. Froidevaux, Prof. A. Nisati, Prof. J. Baptiste, Prof. B. Malaescu, andProf. R. Teuscher, and (co-) editors of supporting documentations with total > 1000 pages,
Dr. L. Ma, Dr. M. Chelstowska, J.M. Miguens, Dr. R. Polifka, Dr. L. Yuan, Dr. D. Schaefer,
Prof. C. Hays, D.C. Hall, Dr. J. Griﬃths, Dr. P.J. Hsu, S. Gadatsch, Dr. C. Mills for theircontinuous eﬀorts on this analysis!

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I would also like to thank all other members, including secretaries in the University of Tokyo and ICEPP, Prof. S. Komamiya, Prof. H. Sakamoto, Prof. N. Kanaya,
Prof. K. Terashi, Prof. T. Namba, Prof. K. Nakamura (KEK), Prof. T. Mashimo, Prof. I. Ueda,
Prof. T. Nakamura (KEK), Dr. S. Yamamoto, Dr. Y. Kataoka, Dr. Y. Takashi, Dr. K. Hanawa,
Dr. T. Kubota (Melbourne), Masako Shiota, Ritsuko Anbiru, Yoshie Tezuka, Yoko Takemoto, and Akiko Miyazono, and the same-grade (or younger) colleagues, Yuki Fuji, Shingo
Kazama, Akira Miyazaki, Yuichi Sasaki, Yohei Yamaguchi, Yoichi Ninomiya, Aine Kobayashi,
Masahiro Morinaga, Yuto Minami, and Takashi Goto for supportive and friendly atomosphere.
On a more personal note, I would like to thank my room mates in Thoiry, France,
Yutaro, Andrew, Nil, and Bastian for sharing a precious time with me! I am also very
thankful for “my lovely friends”, Katarina and Filip for making me happy and making
my Europe life fulfilling, especially travelling Amalfi, Sorrento, and Capri together was so
wonderful!! I would also like to thank Kohei who was always my playmate in Geneva andhe is still my young star!!
Last but not least, I would like to thank my family: my parents for giving birth tome at the first place and infinite supports, and my wife’s parents for all support, ... And ofcourse my wife, Seiko, for all her love and support!

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Executive Summary
The Standard Model of particle physics (SM) is a fundamental and elegant theory of elementary particles and their interactions. It has been tested in various aspects by many
experiments, and has been accomplished as a local gauge invariant theory. In the SM there
was a theoretical obstacle when considering mass of weak bosons, since all particles in thetheory are massless. In 1960’s it has been demonstrated by R. Brout, F. Englert, and
P. Higgs that the weak bosons acquire their own mass interacting with a scalar boson, socalled the Higgs boson, through the Brout-Englert-Higgs (BEH) mechanism [5–7]. However
the Higgs boson had not been observed for more than 50 years. In July 2012 the ATLAS
and CMS collaborations reported the discovery of new particle consistent with the Higgs
boson predicted by the SM [1, 2]. In the SM the BEH mechanism must be responsible formass of weak bosons, but the discovery of the Higgs boson via gluon-gluon fusion (ggF)
process also implies the presence of Yukawa coupling, namely couplings to fermions. Thus,
as a next step, measurements of the Higgs boson couplings to fermions and weak bosons
are of special importance.
From the beginning of the LHC experiment, the H→ W W ∗ → ℓνℓν channel led Higgs
boson search due to the large branching fraction of H→ W W ∗ . In fact this channel wasmost sensitive to the search in the mass region of 114< mH < 158 GeV that was not excluded by previous experiments. Also this channel was sensitive to other scenarios (i.e.
non-SM scenarios) represented by fermiophobic scenario [8, 9], 4th generation scenario [10],and no Higgs boson scenario [11] in early 2011. Even after the discovery of the Higgs bosonwith a mass of approximately 125 GeV in 2012, this channel continues to lead eﬀorts to themeasurement of the couplings to fermions and weak bosons.
This thesis presents the latest measurement of the Higgs couplings using W W ∗ → ℓνℓν
final state through the ggF and VBF production processes. The most crucial part of theanalysis is background estimation because the analysis suﬀers from many backgrounds.
Most of the SM processes such as W W and top (tt̄, W t) production processes enter a signal
region as backgrounds. One of the most significant backgrounds is W +jets background,
where a W boson produced in association with a jet that is misidentified as a lepton. Since
the large uncertainty on this background makes it an important limitation to the experimental sensitivity, the study of systematic uncertainty on this background is a crucial partof the analysis.

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Author’s Contribution
Since early 2011, I have been an active member of the H→ W W ∗ → ℓνℓν analysis groupin the ATLAS collaboration. I spent three years at CERN that taught me the importanceof being “on the ground” in the large collaboration. During my stay at CERN, I had achance to contribute to the discovery of the Higgs boson, which is one of the best andirreplaceable experiences. Since the discovery, I have stayed in this analysis to study andmeasure the Higgs boson couplings to fermions and weak bosons.
My main contributions to the collaboration are as follows:• I have studied cavern background (e.g. neutrons) to the TGC detector that is a subsystem of the ATLAS Muon Spectrometer (for qualification for the ATLAS authorship).
I measured the rate of such backgrounds comparing to simulation. This study is very
important since the contamination of the backgrounds increases the trigger rate significantly. More details can be found in the cavern background note [12] (ATLASInternal).
• I have studied performance of leptons (electrons and muons). I have been responsible
for the leptons in the analysis group as a contact person since early 2011. I haveparticularly worked closely with e/gamma group to study eﬃciency for electron identification focusing on the eﬃciency for the low ET electron that is quite important for
the low mass (mH < 140 GeV) Higgs analysis because the sub-leading lepton in the
final state tends to have lower ET . The studies of leptons are described in Chapter 4.
More details can be found in the electron performance paper [13, 14] and H→ W W ∗object note [15] (ATLAS Internal).
• I have worked extensively on extending and improving a data-driven technique for
the W +jet estimate. The rate of hadronic jets misidentified as leptons may not be
accurately described in the simulation, because these events are due to rare fragmentation processes or interactions with the detector. This background is therefore
determined from data using control samples dominated by the W +jets events. The
W +jets background is described in Chapter 6. Furthermore the detailed study of thesample composition of the misidentified lepton can be found in Appendix B. Moredetails can be found in the H→ W W ∗ background note [16] (ATLAS Internal).
• I have contributed to introducing same sign control region method (SS CR) for thenormalization of diboson backgrounds (W Z/ZZ/W γ/W γ ∗ ). In particular I havedeveloped a dedicated correlation model between the signal region and the control
region. The SS CR is described in Chapter 7. More details can be found in the
H→ W W ∗ background note [16] (ATLAS Internal).
• I am leading eﬀorts to documenting object selection and background estimation as aco-editor of the object note [15] and background note [16] for a paper being preparedfor publication.

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Thesis Organization
This thesis is organized as follows:
Chapter1 Introduction:
Physics motivations and goals of this thesis are presented starting from a basic introduction to the SM and Higgs boson physics.
Part I: Experimental Apparatus and Physics Object- Chapter 2 LHC and ATLAS Detector:
The LHC and ATLAS detector are briefly summarized.
- Chapter 3 Event and Object Reconstruction:
Event and object reconstruction for all physics objects including triggers used in
the analysis are summarized.
- Chapter 4 Determination of Lepton Selection:
Reconstruction and important studies of leptons are summarized including the
optimization and systematic uncertainties.
Part II: Analysis for the Measurement of the Higgs Boson Couplings- Chapter 5 H→ W W ∗ → ℓνℓν Analysis:
The H→ W W ∗ → ℓνℓν analysis is briefly summarized.
- Chapter 6 Fake Backgrounds:
A data-driven technique for the W +jets/QCD backgrounds estimation called
fake factor method is described. The systematic uncertainties on those backgrounds are summarized.
- Chapter 7 Modeling of Same Sign Backgrounds:
An introduction to the Same Sign Control Region (SS CR) is given. Systematic
uncertainties on this control region are briefly summarized. Also the correlation
model of signal region and this control region is discussed.
Part III: Result and Conclusion- Chapter 8 Results:
Results of the couplings of the Higgs boson are presented. Also some compatibility tests are made.
- Chapter 9 Conclusion:
Concluding remarks.
For those who want to grasp shortly the outline of the whole contents in this thesis, pleasego through Chapter 1 Introduction, Chapter 5 H→ W W ∗ → ℓνℓν Analysis, Chapter 8 Results, and Chapter 9 Conclusion.
For those (I assume LHC colleagues) who want to get the whole procedure of specific topics,
please go to Chapter 4 Determination of Lepton Selection, Chapter 6 Fake backgrounds,
and Chapter 7 Modeling of Same Sign Backgrounds.
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Contents
1 Introduction
1.1 The Standard Model and Mass of Gauge Bosons . . . . . . . . . . . . . . .
1.1.1 Spontaneous Symmetry Breaking . . . . . . . . . . . . . . . . . . . .
1.1.2 Brout-Englert-Higgs Mechanism . . . . . . . . . . . . . . . . . . . .
1.1.3 Glashow-Weinberg-Salam Model . . . . . . . . . . . . . . . . . . . .
1.2 The Standard Model Processes as ‘Backgrounds’ . . . . . . . . . . . . . . .
1.3 Higgs Phenomenology at the LHC . . . . . . . . . . . . . . . . . . . . . . .
1.3.1 Higgs Production Processes . . . . . . . . . . . . . . . . . . . . . . .
1.3.1.1 ggF Higgs production process . . . . . . . . . . . . . . . . .
1.3.1.2 VBF Higgs production process . . . . . . . . . . . . . . . .
1.3.1.3 VH and ttH Higgs production processes . . . . . . . . . . .
1.3.2 Higgs Decay Processes . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3.2.1 Decay into weak bosons . . . . . . . . . . . . . . . . . . . .
1.3.2.2 Decay into fermions and γγ . . . . . . . . . . . . . . . . . .
1.3.2.3 Total width and branching fractions . . . . . . . . . . . . .
1.4 History of Higgs Search . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.5 Coupling Measurements using the H→ W W ∗ → ℓνℓν . . . . . . . . . . . . .

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Experimental Apparatus and Physics Objects

2 LHC and ATLAS Detector
2.1 Large Hadron Collider . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.1 Proton injector chain . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.2 LHC parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.3 Pileups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 ATLAS Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.2 Inner Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.3 Calorimeters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.4 Muon Spectrometer . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.5 Magnet system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.6 Trigger system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Luminosity monitoring . . . . . . . . . . . . . . . . . . . . . . . . . .

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3 Event and Object Reconstruction
3.1 Lepton Triggers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.1 Electron triggers . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.2 Muon triggers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.3 Oﬀ-line triggers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.4 Trigger eﬃciency . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Tracks and vertices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.1 Track reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.2 Vertex reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3 Jets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.1 Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.2 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.3 Jet vertex fraction . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.4 Heavy flavor tagging . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.5 Jet Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4 Missing Transverse Energy and Momentum . . . . . . . . . . . . . . . . . .
miss reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.1 ET
3.4.2 pmissreconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . .
T

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4 Determination of Lepton Selection
4.1 Electrons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.1 Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.2 Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.3 Isolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.4 Energy scale and resolution . . . . . . . . . . . . . . . . . . . . . . .
4.2 Muons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.1 Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.2 Isolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.3 Momentum scale and resolution . . . . . . . . . . . . . . . . . . . . .
4.3 Tag-and-Probe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.1 Tag and probe definition . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.2 Background evaluation and systematic uncertainties . . . . . . . . .
4.3.3 Eﬃciencies and scale factors . . . . . . . . . . . . . . . . . . . . . . .
4.4 Optimization Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4.1 General Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4.2 Signal and background eﬃciencies . . . . . . . . . . . . . . . . . . .
4.5 Electron Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.5.1 Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.5.2 Isolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.5.3 Vertex Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.6 Muon Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.6.1 Isolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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4.8

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4.6.2 Vertex Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . .
Additional Selection Eﬃciency . . . . . . . . . . . . . . . . . . . . . . . . .
4.7.1 Electron isolation and vertexing parameter . . . . . . . . . . . . . .
4.7.2 Muon isolation and vertexing parameter . . . . . . . . . . . . . . . .
Summary of Lepton Selection and Uncertainties . . . . . . . . . . . . . . . .
4.8.1 Electron Selection and Eﬃciency . . . . . . . . . . . . . . . . . . . .
4.8.2 Muon Selection and Eﬃciency . . . . . . . . . . . . . . . . . . . . .

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Analysis for the Measurement of the Higgs Boson Couplings

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5 H→ W W ∗ → ℓνℓν Analysis
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2 Analysis Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3 Monte Carlo Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4 Event Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4.1 Pre-selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4.2 ggF 0-1 jet Diﬀerent Flavor Selection . . . . . . . . . . . . . . . . . .
5.4.3 ggF 0-1 jet Same Flavor Selection . . . . . . . . . . . . . . . . . . .
5.4.4 VBF Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.5 Background Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.5.1 ggF 0-1 jet analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.5.2 VBF analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.5.3 Background Summary . . . . . . . . . . . . . . . . . . . . . . . . . .
5.6 Systematic Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.6.1 Experimental systematic uncertainty . . . . . . . . . . . . . . . . . .
5.6.1.1 Lepton . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.6.1.2 Jet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.6.1.3 Missing transverse energy . . . . . . . . . . . . . . . . . . .
5.6.2 Theoretical systematic uncertainty . . . . . . . . . . . . . . . . . . .
5.6.2.1 Systematic uncertainty on the Higgs boson production . . .
5.6.2.2 Systematics on the Standard Model W W production . . .

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6 Fake Backgrounds
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2 Fake Factor Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2.1 Signal and Control Samples . . . . . . . . . . . . . . . . . . . . . . .
6.2.2 Fake Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.3 Anti-id Lepton Definitions and Overlap Removals . . . . . . . . . . . . . . .
6.3.1 Anti-id Electron Definition . . . . . . . . . . . . . . . . . . . . . . .
6.3.2 Anti-id Muon Definition . . . . . . . . . . . . . . . . . . . . . . . . .
6.3.3 Overlap Removal Procedure in W +jets/QCD estimation . . . . . . .
6.4 Z+jet Fake Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.4.1 Feature of Z+jet Fake Factor . . . . . . . . . . . . . . . . . . . . . .

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6.4.2Z+jet selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.4.2.1 Z → ℓℓ selection . . . . . . . . . . . . . . . . . . . . . . . .
6.4.2.2 Diboson veto procedure . . . . . . . . . . . . . . . . . . . .
6.4.2.3 Fake factor Measurement . . . . . . . . . . . . . . . . . . .
6.4.3 Systematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.4.3.1 Sample dependence . . . . . . . . . . . . . . . . . . . . . .
6.4.3.2 Lepton contamination in Z+jet sample . . . . . . . . . . .
6.4.3.3 Trigger bias and pileup uncertainty . . . . . . . . . . . . .
Correction Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.5.1 OS W +jets versus SS W +jets . . . . . . . . . . . . . . . . . . . . .
6.5.2 Correction Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.5.2.1 OS/Z and SS/Z correction factors . . . . . . . . . . . . . .
6.5.2.2 SS/OS correction factor . . . . . . . . . . . . . . . . . . . .
6.5.3 Data Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
W +jets Control Sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.6.1 Control Sample Definition . . . . . . . . . . . . . . . . . . . . . . . .
6.6.2 Run Dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
QCD Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.7.1 QCD in the Fake Factor Method . . . . . . . . . . . . . . . . . . . .
Summary of the W +jets Systematic Uncertainty . . . . . . . . . . . . . . .

154
154
156
156
160
161
161
163
163
163
164
164
166
166
171
171
176
177
177
177

7 Modeling of Same Sign Backgrounds
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.2 Dibosons backgrounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.2.1 Theoretical Uncertainties on Dibosons . . . . . . . . . . . . . . . . .
7.2.2 Conversion Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.3 W +jets Correlation Model . . . . . . . . . . . . . . . . . . . . . . . . . . . .

181
181
187
187
189
191

III

193

6.5

6.6

6.7
6.8

Result and Conclusion

8 Results
8.1 Signal Extraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.1.1 ggF 0-1 jet Signal Region . . . . . . . . . . . . . . . . . . . . . . . .
8.1.2 VBF Signal Region . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.2 Fitting Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.2.1 Profile Likelihood . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.2.2 Test statistic and p-values . . . . . . . . . . . . . . . . . . . . . . . .
8.2.3 Normalization Factors . . . . . . . . . . . . . . . . . . . . . . . . . .
8.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.3.1 ggF 0-1 jet Result . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.3.2 VBF Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.3.3 Combined Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.3.4 Signal Profiling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
xii

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195
195
195
200
200
202
203
204
204
204
206
207

8.4

8.3.5 Coupling Fits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.3.6 Summary of Observables . . . . . . . . . . . . . . . . . . . . . . . . .
Compatibility of Signal Strength . . . . . . . . . . . . . . . . . . . . . . . .
8.4.1 Comparison of Individual Measurements . . . . . . . . . . . . . . . .
8.4.2 Comparison to Previous Analysis . . . . . . . . . . . . . . . . . . . .
8.4.3 Comparison to CMS . . . . . . . . . . . . . . . . . . . . . . . . . . .

208
211
212
212
213
214

9 Conclusion

215

A Additional Materials for H→ W W ∗ → ℓνℓν Analysis
A.1 ggF 2-jet analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A.1.1 Event Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A.1.2 Background Estimation . . . . . . . . . . . . . . . . . . . . . . . . .
A.2 7 TeV (2011) analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A.2.1 Physics Object . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A.2.2 ggF analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A.2.3 VBF analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

217
217
217
218
220
220
221
221

B Additional Studies for Fake Backgrounds
B.1 Di-jet Fake Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.1.1 Electron Fake Factors . . . . . . . . . . . . . . . . . . . . . . . . . .
B.1.2 Muon Fake Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.1.3 Systematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.1.3.1 Sample dependence . . . . . . . . . . . . . . . . . . . . . .
B.1.3.2 Lepton contamination in di-jets sample . . . . . . . . . . .
B.1.3.3 Trigger bias . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.1.3.4 Pileup uncertainty . . . . . . . . . . . . . . . . . . . . . . .
B.1.4 Z+jet vs Di-jet Fake Factors . . . . . . . . . . . . . . . . . . . . . .
B.1.4.1 Comparison of systematic uncertainties . . . . . . . . . . .
B.1.4.2 Compatibility of fake factors . . . . . . . . . . . . . . . . .
B.2 OS/SS Asymmetry and Flavor Composition . . . . . . . . . . . . . . . . . .
B.2.1 OS/SS Asymmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.2.2 Flavor Composition in W +charm Production . . . . . . . . . . . . .
B.2.3 Flavor Composition in W + bb̄ Production . . . . . . . . . . . . . . .
B.2.4 Flavor Composition in Inclusive W +jets Production . . . . . . . . .
B.2.4.1 Flavor composition in electron channel . . . . . . . . . . .
B.2.4.2 Flavor composition in muon channel . . . . . . . . . . . . .
B.3 W +jets Shape Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.4 Triggered Fake Correction . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.4.1 Triggered Anti-id Electron Definition . . . . . . . . . . . . . . . . . .
B.4.2 Triggered Anti-id Muon Definition . . . . . . . . . . . . . . . . . . .
B.4.3 Fake Factors for Triggered Anti-id Leptons . . . . . . . . . . . . . .
B.4.4 W +jets Control Sample for Triggered Anti-id Leptons . . . . . . . .
B.5 QCD Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

223
223
223
225
227
228
229
230
231
232
232
233
235
235
236
237
240
240
241
247
249
249
250
250
252
254

xiii

B.5.1 QCD Subtraction from W +jets Control Sample . . . . . . . . . . . . 254
B.5.2 QCD Correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256
B.5.3 QCD Control sample . . . . . . . . . . . . . . . . . . . . . . . . . . . 259
C Additional Material for Modeling of Same Sign Backgrounds
263
C.1 Heavy Flavor Cross Section Variations . . . . . . . . . . . . . . . . . . . . . 263
D Additional materials for Results
D.1 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
D.1.1 ggF Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
D.1.2 VBF Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

xiv

267
267
267
267

Chapter 1

Introduction
The Higgs boson was the final piece of the puzzle in the Standard Model of particle physics(SM). On 4th July 2012, the ATLAS and CMS collaborations announced that they hadeach observed a new particle, most likely “the SM Higgs boson”, with a mass of approximately 125 GeV [1, 2]. The discovery implies that we finally reached a portal of new era inunderstanding the nature of electroweak symmetry breaking and possibly completing theSM. The major focus of physics analysis at the LHC now is therefore the measurement of
the properties of the Higgs boson including mass [17], spin-parity [18], and couplings [4]. In
this thesis, the measurements of the couplings using the H→ W W ∗ → ℓνℓν final state are√presented with the full Run-I pp collision data corresponding to 20.3 fb−1 of s = 8 TeV
and 4.5 fb−1 of 7 TeV, recorded by the ATLAS at the LHC. There are some advantages tousing the H→ W W ∗ → ℓνℓν channel as follows:• a large branching fraction of H → W W ∗ (∼22 %),• leptonic final state (W W ∗ → ℓνℓν) allows for rejecting a large amount of QCD.
Those advantages make this channel sensitive to the coupling measurements via ggF and
VBF (see Section 1.3.2), even with the limited data set in Run-I. The remainder of thischapter is a brief introduction to the SM and the Higgs physics, which will provide an ideaof how the analysis can be important.

1.1

The Standard Model and Mass of Gauge Bosons

The SM is a relativistic quantum field theory that incorporates three (out of four) fundamental interactions in nature: electromagnetic, weak, and strong interactions. The threeinteractions are described in a local gauge symmetry based on SU(3)⊗SU(2)⊗U(1), where
all interactions are propagated via massless gauge bosons. Nevertheless it is well-known
fact that the symmetry must be broken since weak vector bosons have their own masses,
so the question is what endows them with masses. The answer can be given by introducing
the Brout-Englert-Higgs (BEH) mechanism [5–7] in the electroweak theory. In this section,a brief introduction to the electroweak theory and BEH mechanism is given.
1

2

1.1.1

1.1 Introduction

Spontaneous Symmetry Breaking

The global U(1) symmetry is a simple example of the Spontaneous Symmetry Breaking(SSB) [19–22]. The U(1) transformation of a complex field ϕ can be expressed as:
ϕ(x) → eiα ϕ(x),(1.1)

where α is a constant and hence a global parameter that is independent of space-time, andthat introduces a global symmetry. The Lagrangian of this complex scalar field is expressed
as follows:
L = ∂µ ϕ∂ µ ϕ∗ − V,
V (ϕ) = µ2 ϕϕ∗ + λ(ϕϕ∗ )2 ,(1.2)

where ϕϕ∗ is a mass term with a mass µ, and (ϕϕ∗ )2 term symbolizes a four-point configuration for the self interaction of the field ϕ with a coupling constant λ. The potential has
a parabola-shape with µ2 > 0.
For the SSB, the sign of the mass term is however chosen negative (µ2 < 0), which ends
up with a Mexican hat (or wine bottle) potential. In this case the ground state (i.e. vacuum)
can be defined as ϕ(x) = v, and the local maximum of the potential at ϕ(x) = 0 is unstable.
The field will condense into a stable ground state that is not an unique ground state forthis system. The minima of this system are then degenerate, in other words, there exists
many states with the same vacuum energy. The diﬀerent orientations in the complex plane
define diﬀerent states, and applying the U(1) transformation to any of the vacuum states
will rotate it to a diﬀerent orientation, describing a diﬀerent physical state. To analyze
the Lagrangian, it is necessary to define a perturbative expansion around the ground state.
This can be achieved by writing ϕ as:
1
ϕ(x) = √ (v + η(x) + iξ(x)),
2

(1.3)

√
2
where v = ( −µλ ) is a non-zero value of the ground state (vacuum expectation value), andwhere η(x) and ξ(x) are real fields while ϕ(x) is a complex field. When this expression isplugged into the Lagrangian, the Lagrangian is rewritten as follows:1
1
L = (∂µ η)2 − (λv 2 )η 2 + (∂µ ξ)2 − 0 · ξ 2 + · · · .
2
2

(1.4)

The Lagrangian now shows that there is a mass term with a positive coeﬃcient for theη field, with a mass given by m2η = λv 2 . There is however no mass term for the ξ field. The
particle associated with this massless field is called a “Goldstone boson”, that always shows
up in the SSB of a global symmetry. The Goldstone boson can be interpreted as a freedom
in the ground state plane. This was demonstrated by J. Goldstone, and the existence of
the Goldstone boson in the (global) SSB is referred to as Goldstone theorem [23, 24].

1.1 Introduction

1.1.2

3

Brout-Englert-Higgs Mechanism

The Goldstone bosons that appeared upon the breaking of a global symmetry, however,will not be found in spontaneously broken “local” symmetry, meaning that the Goldstone
theorem breaks down in the local symmetry. The Brout-Englert-Higgs mechanism (referred
to as Higgs mechanism) gives an idea of how the SSB works in the local gauge symmetry, andof how a field with a non-zero ground state can be a source of massive gauge bosons [25,26].
The cornerstone in the BEH mechanism is the assumption of a new scalar field, the BEH
field, whose non-zero vacuum expectation value locally breaks the U(1) gauge symmetry of
the Lagrangian. This is implemented in the Lagrangian in a similar fashion for the caseof global symmetry breaking. The Lagrangian for ϕ4 theory with the simple Abelian U(1)gauge symmetry is:1
L = Dµ ϕDµ ϕ∗ − µ2 ϕϕ∗ − λ(ϕϕ∗ )2 − F µν Fµν ,4(1.5)
Dµ = ∂µ + iqAµ ,where F µν Fµν is the kinetic term for the gauge field. The gauge field Aµ interacts withthe field ϕ in such a way that the Lagrangian is invariant under the gauge transformationsof ϕ(x) → q iα(x) ϕ(x) and Aµ → Aµ + 1q ∂µ α(x). Then a mass term would break the gauge
invariance of the Lagrangian. In the BEH mechanism ϕ(x) is the BEH field satisfyingµ2 < 0, so that the potential has the Mexican hat shape. To analyze the Lagrangian ina perturbative expansion, it is, as in the global U(1) symmetry case, necessary to expand
around a variable field that is small for perturbations around the ground state. Therefore
the field can be again written out, similar to the global symmetry case:1
ϕ(x) = √ (v + ρ(x) + iξ(x)),(1.6)
2where v is vacuum expectation value, and ρ(x) and ξ(x) are real scalar fields. Plugging this
into the Lagrangian gives:1
1
L = (∂µ ρ)2 − λv 2 ρ2 + (∂µ ξ)2
2
2
(1.7)
1
1
+ qvAµ ∂ µ ξ + q 2 v 2 Aµ Aµ − F µν Fµν + · · · .
2
4
2
2
µ
The term q v Aµ A shows that the gauge field Aµ has become massive, due to its
interaction with the constant part of the BEH field. The term λv 2 ρ2 also represents that
one of the components in the BEH field ρ(x) is massive, while the other component ξ(x)seems to be a massless Goldstone mode, like in the global case. ξ(x) is however not aphysical particle but it arises from a freedom to pick up a gauge. Looking at the term
including the ξ field, one can rewrite it as:
1
1
L = (∂µ ξ)2 + qvAµ ∂ µ ξ + q 2 v 2 Aµ Aµ ,
2
2
1
1
1
µ
= q 2 v 2 [Aµ + (∂µ ξ)]2 = q 2 v 2 A′ µ A′ ,
(1.8)
2
qv
2
1
where Aµ → A′µ = Aµ + ∂µ ξ.
qv

4

1.1 Introduction

This choice of gauge (Aµ → A′µ ) is referred to as ‘unitary gauge’ [27, 28]. Then the
Lagrangian becomes:111µL = (∂µ ρ)2 − λv 2 ρ2 + q 2 v 2 A′ µ A′ − F µν Fµν
2
2
4
1 2 ′ ′µ 2
12′′µ
+ q vA µ A ρ + q A µ A ρ − λvρ3 − λρ4 .
2
4

(1.9)

The Lagrangian now clearly shows that there is a massive gauge field (the third term),
and that the BEH field has one massive component (the second term). There are no masslessparticles in this theory, and the field ξ(x) has completely disappeared from the Lagrangian.
With a similar treatment it is possible to expand the BEH mechanism to the SU(2)⊗U(1)symmetry of the electroweak theory.
One can notice the presence of interaction terms (A′ µ A′ µ ρ, A′ µ A′ µ ρ2 , ρ3 , and ρ4 ) that
correspond to the self-couplings of the scalar massive boson (shown by dashed line with H)
and its couplings to the gauge boson A′ µ (shown by wavy line) as shown in Figure 1.1.

Figure 1.1: Schematic view of the self-interactions of the scalar massive boson (dashedline, ρ field in the text but is referred to as “H” in this figure) and its interactions with thegauge bosons (wavy line) in the U(1) gauge theory.

The discussion here is still in the context of the U(1) symmetry, but the scalar massive boson corresponds to the Higgs boson when considering the Glashow-Weinberg-Salam(GWS) theory discussed in Section 1.1.3. Only the term A′ µ A′ µ ρ is relevant to the measurement currently performed at the LHC. The others will be subjects of the High Luminosity LHC(HL-LHC) [29] in the near future.

5

1.1 Introduction

1.1.3

Glashow-Weinberg-Salam Model

The theories, namely the SSB and BEH mechanism, are applicable to the Glashow-WeinbergSalam (GWS) model [30–32] that describes the electroweak interactions. The Lagrangian
for the GWS theory is written as:
L = (Dµ ϕ)† (Dµ ϕ) − V (ϕ),
ii⃗µ.
Dµ = ∂µ + g ′ Y Bµ + g⃗τ · W
2
2(1.10)

where Y denotes hypercharge. The kinetic term (F µν Fµν ) is not shown here. In the presenceof the gauge fields, the fields are transformed into the unitary gauge, so that the field canbe written as:()
1
0ϕ(x) = √.
(1.11)
2 v + h(x)The only diﬀerence from the U(1) gauge theory is that the BEH field is now a SU(2)doublet. V (ϕ) term will again obtain the mass term for the massive scalar boson and theself-interactions. And (Dµ ϕ)† (Dµ ϕ) term will give rise to the masses of the gauge bosons
and their interactions with the massive scalar. (Dµ ϕ)† (Dµ ϕ) term finally leads to:
1
1
h2
µ
µ
(Dµ ϕ)† (Dµ ϕ) = (∂µ h)2 + mW 2 W + µ W − + g 2 W + µ W − (vh + )
2
2
2
2
1
1
h
2
+ mZ 2 Zµ Z µ + (g 2 + g ′ )Zµ Z µ (vh + ),2
4
2

(1.12)

where mW 2 = 14 g 2 v 2 and mZ 2 = 41 (g 2 + g ′ 2 )v 2 denote masses of the W and Z bosons. As
illustrated in Figure 1.2, the couplings of the massive scalar boson to the W W and ZZ canbe then expressed as ghW W ∝ g · mW ∝ m2W /v and ghZZ ∝ g · mZ / cos θW ∝ m2Z /v wherecos θW indicates ‘Weinberg angle’ defined as the ratio of those masses, mW /mZ . It is now
clear that the couplings to the gauge bosons are proportional to the squared mass of eachgauge boson (m2W or m2Z ). The ghW W and ghZZ (referred to in general as ‘Feynman rules’)are used for the calculation of the matrix element M for individual decay width (or crosssections) of the Higgs boson.
Recently the ATLAS and CMS also reported their discovery of the Higgs decay into
fermionic channels [33–35], meaning that the BEH mechanism can also give rise to massesof the fermions. The formalization will not be presented here but it can be found, forinstance, in [36, 37].

6

1.2 Introduction

Figure 1.2: Schematic view of the scalar massive boson (H) interactions with the weakgauge bosons in the GWS theory.

1.2

The Standard Model Processes as ‘Backgrounds’

In the last 50 years, the SM predictions have been tested and well-verified by many experiments, as can be seen in the electroweak global fit [38] that includes more than 20
experimental input parameters. It is no exaggeration to say that the result of the global
fit including the Higgs mass measured by the ATLAS and CMS, is exactly our current
understanding of the SM.
At the LHC, the cross section measurements of several important benchmark SM production processes have been performed since 2010. Given that a huge amount of the SMprocesses can contribute as ‘backgrounds’ to the Higgs analyses, and that the cross sectionof the Higgs production is smaller than that of the SM processes, further cross checks ofthe cross sections for these SM production processes at new energy scale at the LHC is
obviously meaningful.
The most relevant cross section measurements, namely the measurements using a similarphase space (possibly opposite sign dilepton final state) to that used in the H→ W W ∗ → ℓνℓν
analysis, are summarized below:√• “Measurement of the W W production in s = 7 TeV pp collisions with the ATLAS
detector and limits on anomalous gauge couplings” [39, 40]”,• “Measurement of the tt̄ production cross-section using eµ events with b-tagged jets√in pp collisions at s = 7 and 8 TeV with the ATLAS detector” [41],• “Measurement of the cross section for associated production of a top quark and a W√
boson at s = 8 TeV with the ATLAS detector” [42],• “Measurement of the t-channel single top-quark production cross section in pp colli√
sions at s = 7 TeV with the ATLAS detector” [43],1.2 Introduction

7• “Measurement of the W → ℓν and Z/γ ∗ → ℓℓ production cross sections in proton√
proton collision at s = 7 TeV with the ATLAS detector” [44],√• “Measurement of the low-mass Drell-Yan diﬀerential cross section at s = 7 TeV
using the ATLAS detector” [45],√• “Measurements of the W γ and Zγ Production in pp collisions at s = 7 TeV with
the ATLAS Detector at the LHC” [46],√• “Measurement of W Z Production in Proton-Proton Collisions at s = 7 TeV with
the ATLAS Detector” [47],√• “Measurement of ZZ production in pp collisions at s = 7 TeV with the ATLAS
detector and limits on anomalous ZZZ and ZZγ couplings” [48].
In addition to those described above, measurements of production (or diﬀerential) crosssection of the W/Z processes in association with heavy flavors are also important for understanding the W +jets “background” in the analysis due to large fraction of W +heavy
flavors.
• “Measurement of diﬀerential production cross-sections for a Z boson in association
with b-jets in 7 TeV proton-proton collisions with the ATLAS detector” [49],• “Measurement of the production of a W boson in association with a charm quark in√
pp collisions at s = 7 TeV with the ATLAS detector” [50],• “Measurement of the cross-section for W boson production in association with b-jets√in pp collisions at s = 7 TeV with the ATLAS detector” [51].
It is very impressive and evident that theoretical predictions (all calculated at the NLO
or higher order) and experimentally measured cross sections, are in good agreement for
all the SM processes as shown in Figure 1.3. Our understanding on the SM processes at√
s = 7 and 8 TeV including the description of Monte Carlo samples are good enough toproceed measurements of the Higgs boson properties. In the analysis, the SM backgrounds
are independently evaluated by defining dedicated “control” regions where we normalize
individual backgrounds to data. The background estimation techniques and expected yieldsof the backgrounds in the signal region are presented in detail in Chapter 5.

8

1.2 Introduction

Status:Standard Model Total Production Cross Section Measurements July 2014
pp

σ = 95.35 ± 0.38 ± 1.3 hackb (data)

Jets R=0.4
Dijets R=0.4

σ = 86.87 ± 0.26 + 7.56 − 7.2 nb (data)

NLOJet++, CT10 (theory)

L dt[fb−1 ]
8×10

COMPETE RRpl2u 2002 (theory)total
σ = 563.9 ± 1.5 + 55.4 − 51.4 nb (data)R

0.1 < pT < 2 TeV|y |<3.0−8

Reference
ATLAS-CONF-2014-040

4.5

ATLAS-STDM-2013-11

4.5

JHEP 05, 059 (2014)

W

σ = 94.51 ± 0.194 ± 3.726 nb (data)

0.035

PRD 85, 072004 (2012)

Z

σ = 27.94 ± 0.178 ± 1.096 nb (data)

0.035

PRD 85, 072004 (2012)

4.6
20.3
4.6
20.3

arXiv:1406.5375 [hep-ex]

4.7

ATLAS-CONF-2012-157

4.6
20.3
4.8
20.3
2.0
20.3
4.6
13.0
4.6
20.3

PRD 87, 112001 (2013)

20.3

ATL-PHYS-PUB-2014-009

20.3

ATLAS-CONF-2014-038

20.3

ATLAS-CONF-2014-038|y |<3.0, y ∗ <3.0

NLOJet++, CT10 (theory)

0.3 < mjj < 5 TeV

FEWZ+HERA1.5 NNLO (theory)

total
FEWZ+HERA1.5 NNLO (theory)

total

tt̄

total

tt−chan
total

WW+WZ

σ = 182.9 ± 3.1 ± 6.4 pb (data)

top++ NNLO+NNLL (theory)σ = 242.4 ± 1.7 ± 10.2 pb (data)

top++ NNLO+NNLL (theory)σ = 68.0 ± 2.0 ± 8.0 pb (data)
NLO+NLL (theory)
σ = 82.6 ± 1.2 ± 12.0 pb (data)
NLO+NLL (theory)

σ = 72.0 ± 9.0 ± 19.8 pb (data)
MCFM (theory)

total

WW
total

H ggF
total

Wt
total

WZ
total

ZZ
total

σ = 51.9 ± 2.0 ± 4.4 pb (data)
MCFM (theory)

σ = 71.4 ± 1.2 + 5.5 − 4.9 pb (data)
MCFM (theory)

ATLAS Preliminary√s = 7, 8 TeV
Run 1

σ = 19.0 + 6.2 − 6.0 + 2.6 − 1.9 pb (data)
LHC-HXSWG (theory)σ = 25.4 + 3.6 − 3.5 + 2.9 − 2.3 pb (data)
LHC-HXSWG (theory)σ = 16.8 ± 2.9 ± 3.9 pb (data)
NLO+NLL (theory)σ = 27.2 ± 2.8 ± 5.4 pb (data)
NLO+NLL (theory)σ = 19.0 + 1.4 − 1.3 ± 1.0 pb (data)
MCFM (theory)σ = 20.3 + 0.8 − 0.7 + 1.4 − 1.3 pb (data)
MCFM (theory)σ = 6.7 ± 0.7 + 0.5 − 0.4 pb (data)
MCFM (theory)
σ = 7.1 + 0.5 − 0.4 ± 0.4 pb (data)
MCFM (theory)

H VBF

σ = 2.6 ± 0.6 + 0.5 − 0.4 pb (data)tt̄W

σ = 300.0 + 120.0 − 100.0 + 70.0 − 40.0 fb (data)tt̄Z

σ = 150.0 + 55.0 − 50.0 ± 21.0 fb (data)

LHC-HXSWG (theory)

total

MCFM (theory)

total

LHC pp√s = 7 TeV
TheoryData
stat
stat+syst

LHC pp√s = 8 TeV
TheoryData
stat
stat+syst

HELAC-NLO (theory)total

10−5 10−4 10−3 10−2 10−1 1

arXiv:1406.5375 [hep-ex]
arXiv:1406.7844 [hep-ex]
ATLAS-CONF-2014-007

ATLAS-CONF-2014-033
ATL-PHYS-PUB-2014-009
ATL-PHYS-PUB-2014-009
PLB 716, 142-159 (2012)
ATLAS-CONF-2013-100
EPJC 72, 2173 (2012)
ATLAS-CONF-2013-021
JHEP 03, 128 (2013)
ATLAS-CONF-2013-020

101 102 103 104 105 106 1011 0.5 1 1.5 2

σ [pb]

data/theory

Figure 1.3: Detailed summary of several SM total and fiducial production cross section
measurements, corrected for leptonic branching fractions, compared to the corresponding
theoretical expectations [52]. All theoretical expectations were calculated at NLO or higher.
The W and Z vector-boson inclusive cross sections were measured with 35 fb−1 of integrated
luminosity from the 2010 data set. All other measurements were performed using the2011 data set or the 2012 data set. The dark-color error bar represents the statisticaluncertainty. The lighter color error bar represents the full uncertainty, including systematics
and luminosity uncertainties. The data/theory ratio, luminosity used and reference for eachmeasurement are also shown. Uncertainties for the theoretical predictions are quoted fromthe original ATLAS papers [53].

1.3 Introduction

1.3

9

Higgs Phenomenology at the LHC

In this section the Higgs production and decay are briefly described. Our best knowledge
on them has been well summarized in detail in the Yellow Report [54–56].

1.3.1

Higgs Production Processes

At the LHC, four major production modes are accessible, the gluon-gluon fusion (ggF),
the vector boson fusion (VBF), the production in association with a vector boson (VH),
and the production in association with a pair of top/bottom quarks (ttH/bbH). From theanalysis point of view, our main focus in Run-I was on the measurement of the ggF and
VBF modes because of their large cross sections.

1.3.1.1

ggF Higgs production process

The dominant production mode at the LHC is the ggF as illustrated in Figure 1.4.

Figure 1.4: Diagram contributing to the ggF production at the LO.

The largest contribution comes from the top quark because of the largest Yukawa coupling. Since the ggF cross section makes up approximately 90 % of the total production
cross section, the discovery of the Higgs boson with a cross section which is consistent with
the SM expectation would indicate the existence of the ggF production. Hence the discovery had indirectly confirmed that the Higgs boson couples to fermions. The ggF crosssection has been calculated up to the next-to-next-to-leading order (NNLO) in QCD [57–62].
Furthermore the NNLO calculation has been improved by resumming the soft-gluon contributions up to next-to-next-to leading logarithm (NNLL) [63]. The theoretical calculation of
the ggF process is available at the NNLO+NNLL including the NLO EW correction [64,65].
More details can be found in [66–68]. The uncertainty on the cross section has two primary
origins from uncalculated higher-order QCD radiative correction (QCD scale) and from ourlimited knowledge of the parton distribution functions (PDFs) that are of order ∼ 10 % in
total.

10
1.3.1.2

1.3 Introduction
VBF Higgs production process

The second dominant SM Higgs boson production mode at the LHC is the VBF process as
illustrated in Figure 1.5.

Figure 1.5: Diagrams of t-, u-channel contributions to the VBF production at the LO.

The VBF process is typically associated with two jets in the forward and backward
regions of the detector. The s-channel qq → qqH production contribution is suppressed
after requiring the presence of the two jets, so-called VBF selection requirements. The VBF
process provides information about the direct coupling to weak gauge bosons. Experimental
observation of the VBF production would therefore imply that the Higgs boson is responsible
for the SSB in the GWS theory as discussed in Section 1.1. Since the LO matrix element
contains only EW vertices, the LO calculation is already a good approximation. The
approximate NNLO QCD correction [69] and the full NLO corrections for the QCD andEW [70–72] are also applied to the LO calculation.
1.3.1.3

VH and ttH Higgs production processes

The other modes at the LHC are the VH and ttH processes as illustrated in Figure 1.6.

Figure 1.6: Diagrams of the VH process (top left) and the ttH process (bottom) at theLO. The top right is an example of an EW correction to the ggF production (gg → HZ).

11

1.3 Introduction

In the VH process, the presence of a vector boson provides triggerable leptons (or neutrinos as missing transverse energy) in event. This is especially crucial in the search for
H → bb̄ decay due to the huge bb̄ background at the LHC, making it unrealistic to trigger
on the b-jets from the Higgs boson decay. It is also important to search and measure the
VH production in other decay channels, such as the W H → W W W and ZH → ZZZchannels, because the Higgs boson can couple purely to either the W or Z boson that canallow us to study the custodial symmetry [73, 74]. In the ttH process, the Higgs boson canpurely couple to top quarks via ttH vertex, meaning that the production rate can provide
relevant information on the top Yukawa coupling.

LHC HIGGS XS WG 2013

pp → H (NNLO+NNLL QCD + NLO EW)

10pp → qqH (NNLO QCD + NLO EW)

1

pp → WH (NNLO QCD + NLO EW)

102

σ(pp → H+X) [pb]σ(pp → H+X) [pb]

102

pp

pp

→H
+X

→

at

H+

Xa

10

pp

pp → ZH (NNLO QCD + NLO EW)

10-1

LHC HIGGS XS WG 2012√
In summary, the cross sections of the production modes at s = 8 TeV and the in√clusive cross sections at s = 7 TeV, 8 TeV, and 14 TeV are shown in Figure 1.7.

pp → tt H (NLO QCD)

→

H+
Xa

t

t

s=1
4

s=8

TeV

TeV

s=7
Te
V

s = 8 TeV
-2

10

120

122

124

126

128

130

MH [GeV]

1

100

150

200

250
300
MH [GeV]Figure 1.7: Production cross section of the SM Higgs boson for each mode at√(left) and s dependence (right) as a function of mH [75].

1.3.2

Higgs Decay Processes

1.3.2.1

Decay into weak bosons√s = 8 TeV

The general expression of the two-body diﬀerential width is expressed as:
dΓ
|M|2
=
|pf |S,dΩ
32π 2 M

(1.13)

where √
M, |pf |, and S denote the matrix element, the momentum of produced particles( 12 mH ( 1 − 4m2f /m2H )), and the number of identical particles, respectively. The S is equal
to 1 for the H → W W decay and 2 for the H → ZZ decay. The complete matrix element(that is obtained from ‘Feynman rules’ as discussed in Section 1.1.3) is written as follows:∑
iMH→W W =igmW gµν ϵ1λ ∗µ ϵ2ρ ∗ν
(1.14)λ,ρ12

1.3 Introduction

where ϵ denotes the helicity states of the W boson, and λ and ρ are corresponding indicesof ϵ. Using the Equations 1.13 and 1.14, the partial decay width for the two on-shell W W
can be written as:∫dΓΓH→W W = dΩ ,dΩ√(1.15)
g 2 mH 3
mW 2
mW 2
mW 2
=
1−4
(1 − 4+ 12).
64π mW 2
mH 2
mH 2
mH 2
Given that the mass of the Higgs boson is about 125 GeV, it is necessary to take into
account the case that one of the weak bosons or both are oﬀ-shell. This case has been
calculated, for example, in [76], and has been simulated by HDECAY [77] that provides
proper oﬀ-shell W W decays and includes the complete NLO QCD and EW corrections.
1.3.2.2

Decay into fermions and γγ

The SM Higgs boson has other decay channels as well. In the H → γγ decay [78], thedecay is possible only through W boson or (top) quark loop processes, since the photon ismassless gauge boson. Similar to the H → γγ decay, the H → gg decay is also possible
through quark loop. In the fermionic decays, the decay width is determined based on the
Yukawa coupling that is proportional to the squared mass of fermions, so that the decay
is dominated by bottom quark pairs because the light Higgs boson (e.g. mH = 125 GeV)
cannot go into top quark pairs. The partial width is obtained as follows:√
4m2f
g 2 Nc2
ΓH→f f =mH mf 1 − 2 ,(1.16)
32πm2WmH
where Nc denotes the number of colors that is equal to three for quarks and one for leptons.
1.3.2.3

Total width and branching fractions

The total width of the Higgs boson is computed by putting together all the partial widths.
Figure 1.8 shows the total width as a function of the mass of the Higgs boson. The total
width blows up around 160 GeV that is the threshold of the (two on-shell) W W production.
At mH =125 GeV, the total width is about 4 MeV that makes it diﬃcult to directly measure
the width due to detector, while around 600 GeV, the width is order of 100 GeV. The
branching fraction (BR) is defined as fraction with respect to the total width, i.e. Γi /Γtot(i: individual channels). The BRs for individual channels between mH = 120-130 GeV are
also shown in Figure 1.8. It shows that the BR of the H→ W W ∗ is 22 % at mH = 125 GeV.
It is also clear that the branching fraction to the W W strongly depends on the mass of the
Higgs boson. This implies that the signal strength (defined as the ratio of σ×BR in data
to that in the SM expectation) has also dependence on the mass. 1
The mass of the Higgs boson is determined by other high resolution channels H → γγ and H →ZZ ∗ → 4ℓ because the H→ W W ∗ → ℓνℓν channel is not sensitive to the mass measurement due to worse
mass resolution (i.e. two neutrinos in the final state).
1

13

102
10
1

LHC HIGGS XS WG 2013

LHC HIGGS XS WG 2010

103

Higgs BR + Total Uncert

ΓH [GeV]

1.4 Introduction
1
bb
WW
gg

10-1

ττ
cc
ZZ

10-2

γγ

10-1
10-3

Zγ

-2

10

µµ

100

200

300

500

1000

10-4
120 121 122 123 124 125 126 127 128 129 130

MH [GeV]MH [GeV]Figure 1.8: Total width of the SM Higgs boson (left) and branching fractions for individual
channels (right), as a function of mH [75].

1SMWW → l± νqq

10

+

10-1

s = 8TeV

τ+τ-

WW → l± νqq

1 VBF H → τ+τ±-

WH → l νbb-

WW → l νl ν

WW → l+νl ν+-

ZZ → l l qq

10-1

+-

ZZ → l l qq

LHC HIGGS XS WG 2012

s = 7TeV

σ × BR [pb]10

LHC HIGGS XS WG 2011

σ × BR [pb]At the end of this section, the σ×BR is shown in Figure 1.9 that provides more straightforward information about the size of the Higgs boson signal for each decay channel. Given
the Higgs mass of approximately 125 GeV, the W W → ℓ+ νℓ− ν (shown in blue) has thethird largest signal yield. One needs to consider that the fact that the W W → ℓ± νq q̄
channel suﬀers from a huge amount of the backgrounds, and that the τ τ channel will decay
further hadronically or leptonically. Hence the W W → ℓ+ νℓ− ν channel will be better thanthose channels in the signal/background ratio.

-

ZZ → l+l νν

+-ZZ → l l νν+- +-ZZ → l l l l

10-2
-3

10

10-4 100+- +-H → τ+τ+ZH → l l bb
γγ
l = e, µ
VBF H → τ+τν = νe,νµ,ντ
WH → l± νbb
q = udscb

150

200

ZZ → l l l l

10-2

250
MH [GeV]10-3
10-4 100-

ZH → l+l bb
l = e, µν = νe,νµ,ντ
q = udscb

150γγ
ttH → ttbb

200

250
MH [GeV]Figure 1.9: The SM Higgs boson production cross section times branching fraction at√
s = 7 TeV (left) and 8 TeV (right) as a function of mH [75].

14

1.4 Introduction

1.4

History of Higgs Search

The Higgs search has a long history since the BEH mechanism was proposed in 1964 [79].
The mass of the Higgs boson had been constrained by many theoretical considerations,however it could not be specified by theories. The first experimental limit on the Higgs
mass was made by LEP [80] and SLD [81] in mass plane of W boson and top quark. The
two dimensional mass plane allowed for an indirect measurement of the Higgs mass because
the Higgs boson can contributes to measured quantities of W boson and top quark via loop
corrections. LEP and SLD measured W boson mass whereas they deduced top quark massfrom electroweak measurements. This indirect measurement was updated making stronger
constraint by LEP2 [82] and Tevatron [83, 84] with the direct measurement of the mass of
top quark from the Tevatron. The constraint from these indirect measurements is shownin Figure 1.10.

July 2010

80.5

6

LEP2 and Tevatron (prel.)
LEP1 and SLD

mLimit = 158 GeVJuly 2010

Theory uncertainty∆αhad =
(5)

50.02758±0.00035
0.02749±0.00012
incl. low Q2 data4

∆χ2

mW [GeV]

68% CL

80.4

3
2

80.3

mH [GeV]
114
300
150

∆α

1

1000
175

0

mt [GeV]200

Excluded30

Preliminary

100

300

mH [GeV]Figure 1.10: (Left): Indirect constraints on the Higgs mass in the W boson mass and top
quark mass plane obtained from the LEP, Tevatron, and SLD. The shaded band represents
the SM relationship for the masses as a function of mH . The arrow labeled ∆α shows thevariation of this relation with one of the SM parameters that gives an additional uncertainty
to the band. (Right): Direct search and indirect constraints on the Higgs mass in the ∆χ2(from the global fit) and mH plane. The line is the result of the fit using data at the Z pole,and the direct determinations of mt , mW and ΓW . The band represents uncertainty on
theory due to higher order corrections. The yellow band represents the 95% CL exclusion
limit on mH from the LEP (up to 114.4 GeV) and Tevatron (158-175 GeV) in July 2010[85].
In parallel the direct searches were also performed using the Higgs production in association with a vector boson (VH mode) by the LEP/LEP2. In 2000, the LEP2 finally15

1.4 Introduction

obtained a lower limit of mH > 114.4 GeV. After the shutdown of the LEP2, the lead in the
Higgs searches was taken by the Tevatron. As the analyzed Tevatron luminosity accumulated, the CDF [86] and D0 experiments [87] at the Tevatron started excluding a range ofthe Higgs masses between 156 GeV and 177 GeV. The constraint on the Higgs mass fromthese direct measurements is also shown in Figure 1.10.

10

Local p

95% CL Limit on µ0

In 2010, the LHC turned on and started data-taking with the center of mass energyof 7 TeV. The ATLAS and CMS experiments had each accumulated ∼ 5 fb−1 in 2011. By
the end of 2011 the ATLAS excluded a range of the Higgs masses between 131 GeV and 237
GeV, and between 251 GeV and 453 GeV [1], and eventually in July 2012, the discovery
of a new boson that was most likely the SM Higgs boson was reported by the ATLAS and
CMS. Figure 1.11 shows 95% CL upper limit on the signal strength µ and local p0 value as afunction of mH . The largest excess over the background prediction can be seen around mH= 125 GeV. The discovery opened up new era in understanding the nature of electroweak
symmetry breaking. The center of physics analysis is moving from “the search for the Higgs
boson” to “the measurement of its properties”. The measurement allows for investigating
underling physics beyond the Standard Model.

ATLAS 2011 - 2012

± 1σ

s = 7 TeV: ∫ Ldt = 4.6-4.8 fb

± 2σ

-1

s = 8 TeV: ∫ Ldt = 5.8-5.9 fb

Observed
Bkg. Expected-1

1

CLs Limits

-1

10

110

150

200

300

400

500

mH [GeV]ATLAS 2011 - 2012

Obs.
Exp.
±1 σ

s = 7 TeV: ∫ Ldt = 4.6-4.8 fb-1
s = 8 TeV: ∫ Ldt = 5.8-5.9 fb

-1

0σ
1σ
2σ

1
10-1
10-2
10-3
10-4
10-5
10-6
10-7
10-8
10-9
10-10
10-11

110

3σ
4σ
5σ
6σ

115

120

125

130

135

140

145 150mH [GeV]Figure 1.11: Results of the Higgs boson search using H → γγ, H → ZZ ∗ → 4ℓ, and
H→ W W ∗ → ℓνℓν channels [1]. (Left): Observed 95% CL upper limit (solid line) on thesignal strength as a function of mH and the expectation (dashed line) under the backgroundonly hypothesis. The dark and light shaded bands show the plus/minus one sigma andplus/minus two sigma uncertainties on the background-only expectation. (Right): Observed
local p0 (solid line) as a function of mH in the low mass range. The dashed curve shows the
expected local p0 under the hypothesis of a SM Higgs boson signal at that mass with its
plus/minus one sigma band. The horizontal dashed lines indicate the p-values corresponding
to significances of 1 to 6 sigma.

16

1.5

1.5 Introduction

Coupling Measurements using the H→ W W ∗ → ℓνℓν

The H→ W W ∗ → ℓνℓν channel had played a leading role in the Higgs search since theturn-on of the LHC, and contributed to the discovery. Even after the discovery the
H→ W W ∗ → ℓνℓν analysis is leading eﬀorts on the property measurements. For example, the spin-0 nature of the new boson has been tested in the H→ W W ∗ → ℓνℓν channel bycomparing with a spin-2 model that can be separated from the spin-0 by dilepton kinematics
because the spin-2 makes larger angle between the leptons in the final state [88]. Also the
H→ W W ∗ → ℓνℓν provided the first measurement of the Higgs couplings to weak bosons [3].
The updated analysis presented in this thesis aims at measuring the couplings moreaccurately. The precise measurement is possible only in understanding of all the Standard
Model processes, since the analysis suﬀers from many backgrounds such as Standard Model
W W , top (tt̄, W t), W +jets and other diboson (W Z, ZZ, W γ (∗) ), referred to as “other V V ”,
backgrounds. One of the most significant backgrounds is the W +jets background, wherea W boson produced in association with a jet that is misidentified as a lepton, due to its
large systematic uncertainty (that was 40-60%), making it an important limitation to theexperimental sensitivity. The previous analysis [3] was thus optimized making the W +jets
background as small as possible, however it was found that the analysis was limited by large
statistical uncertainty as shown in Table 1.1.
Table 1.1: Leading uncertainties on the signal strength µ in the previous analysis [3].
Category
Statistical
Theoretical
Theoretical
Experimental
Experimental
Experimental
Others
Total

SourceObserved data
Signal yield and acceptanceW W normalization
Objects and DY estimation
MC statistics
W +jets estimation
luminosity, other backgrounds

Uncertainty, up (%)
+21
+15
+12
+9
+7
+5
+6
+32

Uncertainty, down (%)
−21
−11
−12
−8
−7
−5
−6
−29

To improve the statistics in a given integrated luminosity, the analysis presented inthis thesis employs looser lepton selection as suggested by the lepton optimization (seeChapter 4), but the looser selection increases the W +jets and other V V backgrounds bymore than a factor of two. Figure 1.12 shows distribution of transverse mass mT of the
dilepton system (for the 0-jet analysis) that is used as a final discriminant in this analysis.
As can be seen in this figure, the W +jets (light blue) and other V V (magenta) are now
the second largest backgrounds (the largest is Standard Model W W background). Several
improvements have been made on the modeling of these backgrounds, such as Z+jets fakefactor method and SS CR method, in order to reduce the systematic uncertainties on thesebackgrounds. These new methods are described in detail in Chapter 6 and 7.

17

Events / 10 GeV

1.5 Introduction
900
800
700

s = 8 TeV, ∫ Ldt = 20.3 fb-1
H→WW*→lνlν + 0 jetsWWtt *Z/γ →llW+jet

SM (sys ⊕ stat)
Other VV
Single Top
Z/γ *→τ τ
QCD
H [125 GeV]

600
500
400
300
200
100
50

100

150

200

250

300

mtrack-clj[GeV]
T

Figure 1.12: Transverse mass of the dilepton system (mT ) [89] for 0-jet analysis. mT isused as final discriminant in the analysis.

The goal of this thesis is to perform more precise measurements of the Higgs couplings
represented by signal strength µ that is defined as the ratio of cross section times branching
fraction in data to that in theoretical prediction given by:µ=(σ · BR(H→ WW∗ → ℓνℓν)) data,(σ · BR(H→ WW∗ → ℓνℓν)) Theory(SM)(1.17)

where σ is cross section of the Higgs production and BR(H→ W W ∗ → ℓνℓν) is branching
fraction of the Higgs decay into W W ∗ → ℓνℓν. Assuming that there is no contribution
from beyond the Standard Model (BSM) particles that can couple to the Higgs boson, thesignal strength is expected to be unity, while if there exists the BSM particle, one can see a
deviation on the signal strength. The results presented in this thesis supersede the previous
measurement by > 50% on the experimental sensitivity. The large improvement is achieved
owing to optimizations of selection of physics objects (see Chapter 4) and better modelingof the W +jets and V V backgrounds (see Chapter 6, 7).
The signal strength is measured for the individual processes µggF and µVBF , optimizing
the analysis to each production process. The comparison of individual signal strengths ismeaningful because the coupling strengths of these production processes are diﬀerent. The
ggF production includes the Higgs coupling with top quark (or bottom quark), namely
Yukawa coupling, as well as the coupling with weak bosons. While the VBF production
contains only electroweak (EW) vertices in the leading order, thus the VBF indicates thecouplings with purely weak bosons. Eventually the coupling to fermions and weak bosons
are each extracted by introducing new parameterization of the coupling strengths (κF andκV ). The results of these coupling strengths are also shown and discussed in Chapter 8.

18

1.5 IntroductionPart I

Experimental Apparatus andPhysics Objects

19Chapter 2

LHC and ATLAS Detector
2.1

Large Hadron Collider

The Large Hadron Collider (LHC) [90, 91] is a superconducting hadron accelerator outsideof Geneva, Switzerland. The machine was installed in the existing 27 km tunnel that was
initially constructed in 1984-1989 for the Large Electron-Positron (LEP) experiment [80]by European Organization for Nuclear Research (CERN). Four main experiments [92] were
installed in four interaction points (IPs) located between 50 m and 150 m underground as
shown in Figure 2.1.

Figure 2.1: Locations of the four main experiments (ALICE, ATLAS, CMS, and LHCb) at
the LHC [93]. They are located between 50m and 150m underground. The SPS, the final
link in the pre-acceleration chain, and its connection tunnels to the LHC are also shown.

21

22

2.1 LHC and ATLAS Detector

The ATLAS [94–97] and the CMS [98] are general purpose detectors designed to survey
the new energy scale, targeting searches for a Higgs boson and beyond the Standard Model(BSM) particles in addition to precision measurements of the Electroweak Symmetry Breaking (EWSB). The LHCb [99] experiment is dedicated to study CP violation through heavy
flavor physics. The ALICE [100] is an experiment focused on the physics of strongly interacting matter and the quark −gluon plasma at an extreme energy density and temperature
through heavy ion collisions at the LHC.

2.1.1

Proton injector chain

The LHC is only the final stage of a series of machines used to accelerate the protons to increasingly higher energies. The protons are initially obtained from ionized hydrogen atoms,
and are accelerated away from the bound electrons by electric fields, forming into bunches.
The protons start their journey to the LHC in a linear particle accelerator (LINAC2), where
they are accelerated up to 50 MeV. The beam is then fed into the first circular accelerator P roton Synchrotron Booster (PSB). The P roton Synchrotron (PS) then raises thebeam energy from 1.4 GeV to 25 GeV. From the PS the bunched beam is injected into theSuper P roton Synchrotron (SPS). The beam energy is then increased to 450 GeV in the
SPS. The beam from the SPS is finally injected into the LHC [101]. The injector chain issummarized in Figure 2.2.

Figure 2.2: The proton injector chain for the LHC at CERN [102].

23

2.1 LHC and ATLAS Detector

2.1.2

LHC parameters

The LHC is the most powerful tool for particle physics research, and is designed to collide√
proton beams at s = 14 TeV with a maximum instantaneous luminosity of 1034 cm−2 s−1 .
√It can also collide heavy (Pb) ions at s = 2.8 TeV per nucleon with a peak luminosity of
10−27 cm−2 s−1 . During 2010 and 2011 the energy of proton beams circulated in opposite
directions was 3.5 TeV, producing collisions at a center-of-mass energy of 7 TeV. In 2012,
the energy was increased to 4 TeV per beam, producing collisions at 8 TeV. The beam
structure is composed of proton bunches, nominally with 115 billion protons in each. A
bunch train is composed of 36 bunches with 50 ns bunch spacing, after which there is a 345
ns gap before the next bunch train. In total, there were 1380 colliding bunches in each in
the LHC ring. The beam parameters are summarized in Table 2.1.2.
Table 2.1: The LHC proton beam parameters [103].

Proton energy [GeV]
Bunch spacing [ns]Number of bunches
Number of particles per bunch
Peak luminosity [cm−2 s−1 ]Magnetic field on the dipoles [T]Beam current [A]Bunch length [cm]Transverse beam size at IP [µm]
Crossing angle at IP [µrad]

2.1.3

Design2012 Run

7000
25
2808
1.15×1011
1.0×1034
8.33
0.582
7.55
16.7
285

4000
50
1380
∼ 1.7 × 1011
7.7 × 1033
4.76
0.369
≥9
19
290

PileupsDue to the high instantaneous luminosity, there are approximately 20 (9) expected interactions, inelastic scatterings, per bunch crossing in 2012 (2011) [104]. This eﬀect is calledpileup and is classified into two categories, In-time pileup and Out-of-time pileup. The Intime pileup accounts for multiple interactions in the same bunch crossing. The additional
interactions are mostly caused by soft collisions and are not interesting in most of physics
analyses. The Out-of-time pileup accounts for overlaps of electronic signals between bunch
crossings. Both pileups can be a common issue in physics analysis. In the H→ W W ∗ → ℓνℓν
analysis, Drell-Yan background is, for instance, increased by a factor of >3 in same flavor
miss )(ee and µµ) channels due to worse energy resolution of missing transverse energy (ETmisscaused by the higher pileup in 2012. Hence the objects (lepton, jet, and ET etc) used in
the analysis must be robust against the pileups, and the eﬀect of pileups must be corrected
to obtain the physical quantities. (See Section 3.2.2)

24

2.2 LHC and ATLAS Detector

2.2

ATLAS Detector

2.2.1

Overview

The ATLAS (A T oroidal Lhc ApparatuS) detector is a multipurpose detector and is designed to cover almost 4π rad in solid angle for providing excellent physics performance inthe diﬃcult environment of the LHC. The size of the detector is over 25 m in height andabout 44 m in length as shown in Figure 2.3.

Figure 2.3: Cut-away view of the ATLAS detector and subsystems [105]. The dimensionsof the detector are over 25 m in height and about 44 m in length. The overall weight of thedetector is approximately 7000 tons.
The ATLAS employs a right-handed coordinate system with its origin at the interaction
point (IP). The beam direction defines the z-axis, the positive x-axis points from the IP
toward the center of the LHC ring and the positive y-axis points upwards. Cylindrical coordinates (r, ϕ) are used in the transverse plane and the pseudo-rapidity η is defined insteadof the polar angle θ as η = −ln tan(θ/2).
The ATLAS detector is made up of a barrel region and two endcaps, with each region consisting of several detector subsystems. Closest to the IP is the Inner Detector(ID) [106,107], which consists of two silicon detectors, the Pixel Detector [108] and the Semi-

25

2.2 LHC and ATLAS Detector

Conductor Tracker (SCT) [109–111], and the Transition Radiation Tracker (TRT) [112–114],
all immersed in a 2 T magnetic field provided by a superconducting solenoid magnet. The
ID is surrounded by barrel and endcap liquid argon electromagnetic (EM) calorimeters. The
EM calorimeters are surrounded by hadronic calorimeters. In the barrel region, the Tile
Calorimeter is composed of steel and scintillating tiles, with a central barrel and two extended barrel regions, And the endcap region (|η| > 1.5) is covered by the Hadronic Endcap
Calorimeter (HEC) based on liquid argon. Furthermore the forward region (3.2 < |η| < 4.9)
is covered by a liquid argon Forward Calorimeter (FCal). The calorimeters are surroundedby the Muon Spectrometer (MS) that is relied on the air-core toroid magnet system. Theη coverages and typical resolutions of each subsystem are summarized in Table 2.2.
Table 2.2: The η coverage and typical resolution of each subsystem in the ATLAS detector [96].
Detector component
Tracking
EM calorimeter
Hadronic calorimeterbarrel and endcap
forward

Muon spectrometer

2.2.2

Typical Resolution
σpT /pT = 0.05√× pT (GeV) ⊕ 1%
σE /E = 10/ E(GeV) ⊕ 0.7%

η coverage
Precision
Trigger
0.0 < |η| < 2.5
0.0 < |η| < 3.2 0.0 < |η| < 2.5√
σE /E = 50/√E(GeV) ⊕ 3%
σE /E = 100/ E(GeV) ⊕ 10%
σpT = 10% at pT = 1 TeV

0.0 < |η| < 3.2
3.1 < |η| < 4.9
0.0 < |η| < 2.7

0.0 < |η| < 3.2
3.1 < |η| < 4.9
0.0 < |η| < 2.4

Inner Detectors

In order to measure the momentum of charged particles and to determine the location ofprimary and secondary vertices (that are originated from heavy flavor and τ decays) against
a high occupancy environment expected in every event at the LHC, a good spatial resolution is crucial. For this purpose the ID consists of three independent but complementary
subsystems (Pixel, SCT, and TRT) that are all immersed in a superconducting solenoid
magnet. The layout of the ID in the barrel region is illustrated in Figure 2.4.
The precision tracking detectors (the Pixel and the SCT) cover the region |η| < 2.5.
In the barrel region they are arranged on concentric cylinders around the beam axis whilein the endcap they are mounted on disks perpendicular to the beam axis. The highest
granularity is achieved around the vertex region using the Pixel that is the closest detector
to the IP. The Pixel is segmented in r-ϕ and z with typically three layers crossed by eachtrack. All pixel sensors that consist of 80.4 million readout channels, have a minimum pixel
size in r-ϕ × z of 50×400 µm2 . The typical spatial resolutions are 10 µm in r-ϕ and 115µm in the longitudinal direction that is z for the barrel and r for the endcap region.

26

2.2 LHC and ATLAS Detector

Figure 2.4: Cut-away view of the ATLAS inner detector system [105] that consists of
the Pixel, SCT, and TRT in the barrel region, being crossed by one high-energy particle(red-line).
The SCT is the second innermost detector that consists of eight strip layers (four spacepoints) crossed by each track. The SCT module consists of two layers of silicon strip sensors
with a strip pitch of 80 µm. The two layers in each module are rotated by ±20 mrad eachother to measure both coordinates, r-ϕ and z. The typical spatial resolutions per moduleare 17 µm in r-ϕ and 580 µm in the longitudinal direction that is z for the barrel and r forthe endcap region. The total number of readout channels in the SCT is approximately 6.3
million.
The TRT is the outermost detector that consists of a barrel (|η| < 1.0) and two endcaps(1.0 < |η| < 2.0) modules. The TRT uses transition radiation (TR) that is in generalemitted by a particle when it comes across a boundary of two media with diﬀerent indicesof refraction. The probability of the TR emission is proportional to the lorentz boost factor(γ) that is sensitive to a mass of the incident particle. The barrel contains 73 layers (144 cm
long gas-filled straw tubes) that are oriented parallel to the beam axis, whereas the endcap
contains 160 layers (37 cm long gas-filled straw tubes) that are arranged radially in wheels.
Typically 36 hits per track are provided by the TRT, which enables to perform precision
tracking up to the region |η| = 2.0. Also the TRT can be used for the electron identification
distinguishing electrons from heavier particles. The TRT provides r-ϕ information with an2.2 LHC and ATLAS Detector

27

accuracy of 130 µm per straw. The total number of TRT readout channels is approximately
0.35 million.
In summary, the combination of the inner detector system gives very robust patternrecognition and high precision in both r-ϕ and z. The TRT also contributes significantly tothe momentum measurement by the large number of hits and longer measured track length.
The achieved spatial resolution of charged particles in r-ϕ is typically σpT /pT = 0.05 % pT
⊕ 1 % in |η| < 2.5. And the vertex reconstruction is accurate enough (typically 15 µm inr-ϕ) to observe secondary vertices that are mostly enhanced by the innermost layer of the
Pixel (called B-layer). The configuration of the inner detector system with its η coverage
is summarized in Figure 2.5.

Figure 2.5: Schematic view of a quarter-section of the ATLAS inner detector system [105],
showing each subsystem, Pixel, SCT, and TRT with their active dimensions. The IP is
located at (r, ϕ) = (0, 0).

2.2.3

Calorimeters

The calorimeter system is designed to measure the energy of electrons, photons, andhadrons. The system covers the range up to |η| < 4.9, and it consists of mainly two typesof calorimeters: electromagnetic (EM) and hadronic calorimeters that are sensitive to theelectromagnetic and hadronic interactions, respectively. A cut-away view of the calorimetersystem is shown in Figure 2.6.
All calorimeters are so-called sampling calorimeters made of absorbers and active sensors. When an incident particle hits the absorber inside a calorimeter, the particle interacts
with the absorber generating a shower. A part of energies from the shower is then “sam-28

2.2 LHC and ATLAS Detectorpled” by the sensors. The energy of the full shower can be inferred and determined fromthe “sampled” energy. The calorimeter system must provide good containment for thoseshowers to limit energy leakages, called “punch-through”, into the muon system. To satisfy
this requirement a total thickness of the calorimeter can be an important consideration.
Together with a large η coverage up to |η| < 4.9, it must be ensured to reconstruct physics
miss objects.
objects, particularly jet and ET

Figure 2.6: Cut-away view of the calorimeter system [105].
The EM calorimeter consists of a barrel (|η| < 1.475) and two endcaps (1.375 < |η| <3.2) with a transition region (1.37 < |η| < 1.52). The EM calorimeter is a lead-liquidargon detector (LAr) with accordion-shaped absorbers (lead) and electrodes (kapton) in
a combination with liquid argon as active medium providing uniform coverage in ϕ andfast readout. In the barrel region, the EM calorimeter is segmented in depth into threelongitudinal layers varying granularity as shown in Figure 2.7.
The first (innermost) layer has a finest granularity in η that is used for the precision measurement of the EM showers discriminating photons from π 0 s. The largest energy
deposit can be observed in the second layer that has a thickness of ∼ 16 X0 . The thirdlayer is mainly used for distinguishing the EM and hadronic showers. For the regions of|η| < 1.8, a presampler detector that provides a measurement of the energy lost in frontof the EM calorimeters, is also placed to correct for the energy for better performance inenergy resolution. In the endcap region, the calorimeter is segmented into two longitudinallayers with a coarse lateral granularity. With this configuration, a total thickness of >22
radiation lengths (X0 ) in the barrel and of >24 X0 in the endcap is achieved.
The hadronic calorimeters surround the EM calorimeters. The hadronic calorimeter(Tile HCal) in the range of |η| < 1.7 uses steel as absorber material and scintillating tiles as2.2 LHC and ATLAS Detector

29

active media. The scintillation photons are guided to photomultiplier tubes by wavelengthshifting fibres. The granularity of the hadronic calorimeters is coarser than that of the EM
calorimeter because the hadronic showers are typically wider than the EM showers. In theendcap region, the Hadronic Endcap Calorimeters (HEC) are placed and they cover theregion 1.5 < |η| < 3.2 with the LAr active media. With this configuration, a total thicknessof >10 interaction lengths (λ) that is suﬃcient to reduce the “punch-through” events, isachieved. Figure 2.9 shows interaction lengths as a function of |η|.

Figure 2.7: Sketch of an accordion-shaped barrel module of the EM calorimeter [105]. The
granularity in η and ϕ of the cells of each of the three layers and of the trigger towers is
also shown.

Figure 2.8: Cumulative amount of material (in units of radiation length) in front of the
EM calorimeters and in the EM calorimeters themselves for the barrel (left) and endcaps(right) regions as a function of |η| [105].

30

2.2 LHC and ATLAS Detector

Figure 2.9: Cumulative amount of material (in units of interaction length) in front of
the EM calorimeters, in the EM calorimeters themselves, in hadronic calorimeters, and thetotal amount of material in front of the active layer of muon spectrometer (light blue), asa function of |η| [105].
The calorimeter system also keeps its coverage at higher η region (3.1 < |η| < 4.9)
provided by the forward calorimeter (FCal). The aim of covering the high η region is totrigger the VBF topology (See Section 1.3.1) that has two forward/backward jets in event.
The first layer is dedicated to the measurement of the EM showers while the second andthird layers are dedicated to the hadronic showers. This is achieved by constructing last
two layers with tungsten instead of steel.

2.2.4

Muon Spectrometer

The outermost detector in the ATLAS is the Muon Spectrometer (MS) system. The systemcovers the range of |η| < 2.7 and it consists of two precision tracking chambers, two trigger
chambers and air-core toroid magnet system. The layout of the MS is shown in Figure 2.10.
The muon tracks are reconstructed using precision chambers that consist of three layersof the Monitored Drift Tubes (MDT) and the Cathode Strip Chambers (CSC). The momenta are then measured from the deflection of the muon trajectory in the magnetic field
generated by the air-core toroid system. Since the precision chambers require a wide time
window of about 700 µs, the MS system needs to have independent trigger chambers toprovide fast responses to issue muon triggers. Hence the MS system also has such trigger
chambers that consist of three layers of the Resistive Plate Chambers (RPC) and threelayers of the Thin Gap Chambers (TGC). The TGC and RPC provide the ATLAS level-1
triggers with correct bunch crossing in every 25 ns. The TGC and RPC are also used tomeasure the muon trajectories in ϕ coordinate.

2.2 LHC and ATLAS Detector

31

Figure 2.10: The ATLAS muon spectrometer [115].

2.2.5

Magnet system

The magnet system in the ATLAS detector consists of four superconducting magnets. A
superconducting solenoid is placed parallel to the beam axis, and is designed to provide
the ID with a 2 T axial field that is enough to bend and measure momenta of charged
particles from around the IP. The solenoid is also designed to be as thin as possible to reduce the unnecessary material (that corresponds to 0.66 X0 ) in front of the EM calorimeter.
There are also three large air-core toroidal magnets that lie outside the calorimeterbut in the MS. One is dedicated to the barrel and the others to the endcaps. These magnets are placed concentrically behind the calorimeter and produce a 0.5 T toroidal fieldin the barrel and 1 T in the endcap. Each of three magnets consists of eight coils thatare arranged radially and symmetrically around the beam axis. In the barrel region, eachcoil is immersed in their own cryostat whereas in the each endcap the coils are housed all
together in a single but large cryostat. The bending power can be tunable by rotating thecoil systems in the endcap with respect to the system in the barrel. Each endcap is now
rotated 22.5 degrees to be optimal and to provide the radial overlap.

2.2.6

Trigger system

The trigger system is of crucial importance to the physics analyses at the LHC. During the
LHC running, a bunch of protons collide inside the ATLAS every 25 ns. Neither the dataacquisition system nor the resources for doing oﬀ-line analysis are capable of handling suchamounts of data. Therefore a trigger system is required to select only rare processes ofprimary interest to the physics analyses to be written to disk and analyzed further oﬀ-line.
In general those interesting events are characterized by large momentum transfer in the32

2.2 LHC and ATLAS Detector

miss ).
hard process, namely high pT jets, leptons, and large missing transverse energy (ETFigure 2.11 shows cross sections of primary processes in pp collisions.

√Figure 2.11: Cross section as a function of s in pp collision [116]. The cross sections arecalculated either at NLO or NNLO QCD correction, using MSTW2008 parton distributions,with the exception of the total hadronic cross section which is based on parametrization of
the Particle Data Group. The discontinuity in some of the cross sections at 4 TeV is dueto the switch from pp̄ to pp collisions.
Roughly speaking, the ggF process (σggH ) is produced with the probability of 1/1010√
at s = 8 TeV in pp collisions. Hence the order of 1010 soft pp collisions have to be rejected by triggering and oﬀ-line analysis. In the current trigger system, the order of 105 -106
reduction has been achieved by the trigger system, meaning that W/Z events (σW/Z ) aremostly recorded by the (lepton) trigger system for physics analysis.
The trigger system consists of three levels of event selection: Level-1(L1), Level-2(L2),and Event Filter (EF) where the L2 and EF form the High-Level Trigger (HLT). A schematic

2.2 LHC and ATLAS Detector

33

overview of the trigger system is shown in Figure 2.12.
The L1 trigger performs as an initial event selection. The L1 is hardware-based and it
uses limited information from a subset of detectors to look for signatures: the RPC and
TGC for high pT muons, and all the calorimeter systems with a low granularity for elecmiss and large total transverse
trons/photons, jets, and τ , selecting an event with large ET
energy. The L1 sends information about those triggered signatures with their coordinate in
ϕ and η to the L2. The information about the coordinate is called Regions − of − Interest(ROI). The maximum L1 acceptance that can be handled by the detector readout is 75 kHZ ,and the L1 decision must reach the front-end electronics within 2.5 µm after corresponding
bunch crossing is occurred. All data selected by the L1 are held in the Readout Buﬀers(ROB) until they are processed by the L2.

Figure 2.12: Block diagram of the ATLAS trigger system [94].

The L2 trigger is software-based and it uses the ROI information, energy, and the typeof signatures, and provides more sophisticated selections based on the full detector information that was not available in the L1 such as reconstructed track information from the
ID and better information on energy deposition etc, to reduce the event rate to below 3.5
kHZ , with an average event processing time of approximately 40 ms.
The EF performs as the final oﬀ-line selection on the events that passed the L2 selection to further select events down to a rate which can be recorded for subsequent oﬀ-line
analysis. It reduces the event rate to approximately 200 HZ , with an average event processing time of order four seconds.

34

2.2.7

2.2 LHC and ATLAS Detector

Luminosity monitoring

Besides the main detector, there are two luminosity detectors in the ATLAS: Beam Condition Monitor (BCM) and LUminosity measurement using Cherenkov Integrating Detector(LUCID). They measure instantaneous/integrated luminosities and calibrate data quantity
recorded by the ATLAS.
The LUCID, located at z = ± 17 m from the IP, consists of twenty aluminum tubes
surrounding the beampipe. The LUCID performs online luminosity monitoring of the instantaneous luminosity and beam conditions by counting inelastic pp scatterings since the
LUCID is based on the principle that the number of pp scattering in a bunch crossing is
proportional to the number of particles detected in this detector. This holds true even whenmost of the detected particles originate from secondary interactions.
The BCM, located at z = ± 1.84 m from the IP, consists of four small diamond sensors arranged around the beampipe in a cross pattern on each side of the IP. The BCM
performs bunch-by-bunch luminosity measurement in the ID by counting in-time and outof-time collisions, and by distinguishing particles in pp collisions from beam-backgroundparticles using timing information. The BCM also provides a beam-abort signal when the
beam losses start to risk damaging the ID.

Chapter 3

Event and Object Reconstruction
Since the H→ W W ∗ → ℓνℓν analysis is binned in jet multiplicity, obtaining robust jet definition against pileup jets is crucial. In addition, as the Higgs signature contains two genuine
isolated high pT leptons and two neutrinos in the final state, leptons and missing transverse
miss ) are also key objects regardless of the Higgs production process. Furthermore
energy (ETb-tagging is of special importance to reduce/control the top backgrounds (tt̄, single top)that are dominant in the ≥1 jet analysis.
In this chapter lepton triggers are firstly presented since any events used in the analysis
are collected with those triggers. The reconstruction of the physics objects, except for leptons (See Chapter 4), used in the analysis are then briefly summarized, starting from thereconstruction of tracks and vertices that are primary objects for the reconstruction of all
miss ).
the other physics objects (electrons, muons, jets, and ET

3.1

Lepton Triggers

This section focuses on lepton triggers since the analysis relies on those trigger. The overall
trigger system is summarized in Section 2.2.6. In the analysis, luminosity prescaled triggers
referred to as “supporting triggers” [117, 118], are also used but they are only for themodeling of the W +jets/QCD backgrounds. Hence the detail of those triggers are presented
in Chapter 6.

3.1.1

Electron triggers

At the Level 1 trigger (L1), e/gamma objects are identified by making use of trigger
tower [119] as illustrated in Figure 3.1. The trigger tower consists of the calorimeter cellswith a reduced granularity of ∆η × ∆ϕ = 0.1×0.1. The towers are used for measuring thetransverse energy ET in the clusters (with a precision of the order of ∼ 1 GeV) that areformed by identifying local maxima using a sliding window algorithm [119] based on a 4×4
group of trigger towers. A trigger is fired if the central 2×2 trigger towers contain at least
one pair of neighboring towers with a combined energy that satisfies a certain threshold.
35

36

3.1 Event and Object Reconstruction

Finally the positions of the triggered e/gamma objects, referred to as Region of Interests(ROI), are determined and the ROI information is sent to the Level 2 trigger (L2).

Figure 3.1: Schematic view of trigger tower [105].
At the L2, fast calorimeter and tracking reconstruction algorithms that are mostly thesame as the oﬀ-line electron reconstruction described in Section 4.1.1 but using only thehighest ET seed cluster in the second layer, are used. Finally at the EF, the full oﬀline reconstruction and identification algorithms described in Section 4.1.1 and 4.1.2, areapplied.

3.1.2

Muon triggers

At the L1 trigger, an initial selection based on the reduced granularity information from asubset of the detectors is made. The transverse momentum of muons are roughly estimatedfrom the hit patterns along the muon trajectory using only trigger chambers, the RPC in
the barrel and the TGC in the endcap. The muons from the limited pT measurements
are classified into six pT categories, and the position information and hit patterns, namely
ROIs, based on the classification are sent to the L2.
At the L2, muons are further selected using fast L2 muon algorithms. The candidates
from the L1 are refined by using both the trigger and precision chambers. The trajectory of the candidate is identified by fast fitting, while the pT is reconstructed by Look
Up Tables (LUT) to achieve reasonable resolution in suﬃciently short time allowed at theL2. Subsequently the reconstructed tracks in the ID are combined with the tracks reconstructed by the precision chambers, to refine the track parameters. Finally at the EF, thefull oﬀ-line reconstruction algorithm with the isolation requirement, is applied as describedin Section 4.2.1.

37

3.1 Event and Object Reconstruction

3.1.3

Oﬀ-line triggers

The data sample used in the analysis was collected with primary electron and muon triggers√
in 2011 with center mass energy of s = 7 TeV and integrated luminosity of 4.5 fb−1 , and√2012 with center mass energy of s = 8 TeV and integrated luminosity of 20.3 fb−1 . For
the diﬀerent flavor (eµ,µe) analysis, all electron and muon triggers are “OR”-ed, and forthe same flavor (ee,µµ) analysis, either electron or muon triggers are used.
In 2012 the dilepton triggers are “OR”-ed because of their gain in acceptance, thedilepton trigger thresholds also allow for the loosening of the lepton pT thresholds from 25
GeV → 22 GeV for the leading lepton. In the ee and µe channels, however, the dilepton
trigger thresholds are too high for any contribution to events with a sub-leading electron
below 15 GeV. Table 3.1 presents combined gain from lowering the leading and sub-leading
lepton pT when dilepton triggers are included (for both cut selections, reference point issame cut but with single lepton trigger).
Table 3.1:
Signal eﬃciency gains from adding dilepton triggers. Eﬃciency gains arecomputed for the ggF Higgs signal in 0 jet analysis.
Channelee channelµµ channeleµ channelµe channel

pT >25,10
2.6%
9.0%
1.6%
2.1%

pT >22,10
9.1%
18.5%
8.3%
8.2%

While no dilepton triggers are considered in 2011 due to the fact that the trigger threshold is lower than the leading lepton pT requirement, retaining a high trigger eﬃciency. Table 3.2 shows all the triggers used in the analysis. The definitions of the triggers are changed
through the years 2011 and 2012 according to the LHC running conditions, in other words,
the increasing luminosity and therefore worsening pileup conditions.
For electron triggers, numbers after EF e in the trigger names mean pT threshold values
that are set to give an eﬃciency of 90 % relative to the trigger plateau eﬃciency at the given
threshold value in the EF in units of GeV. vh denotes a cut on the hadronic core isolation(< 1 GeV) at the L1. This is similar to the hadronic leakage cut (see Section 4.1.2) but as
it uses a fixed energy cut, it causes an ineﬃciency at very high pT (pT > 300 GeV). The i
after vh indicates a cut on the track isolation at the EF (Ptcone20/pT < 0.1). The T before
vh denotes a change of the ET threshold from 2EM7VH to 2EM10VH at the L1 in 2011,
but it does not imply anything in 2012. The L2StarB trigger was added during the 2012
data taking in order to recover the eﬃciency in the endcap. Finally medium, medium1, andloose1 denote the tightness of the electron identification. For medium1, additional cuts (onshower shapes and tracking variables) are applied to medium.

38

3.1 Event and Object Reconstruction

For muon triggers, the suﬃxes medium and tight are added for triggers seeded by
MU11 and MU15, respectively. The i on EF mu24i tight indicates a cut on the track isolation at the EF (Ptcone20/pT < 0.12). The EFFS on EF mu18 tight mu8 EFFS indicatesthat additional muons are searched for by “full-scan” information rather than relying on
only the ROI information. This results in no L1 seed for the second (or third) muon as canbe seen in Table 3.2.
Table 3.2: Trigger setup for 2011 and 2012 analysis. The definitions of the triggers arechanged through the years 2011 and 2012 according to the LHC running conditions.
Primary single lepton triggers in 2011
Oﬄine trigger
EF e20 mediumelec
EF e22 medium
EF e22vh medium1
muon
EF mu18 MG
EF mu18 MG medium

L1 seed
EM14
EM16
EM16VH
MU10
MU11

Primary single lepton and dilepton triggers in 2012
Oﬄine trigger
L1 seedEF e24vhi medium1
EM18VHelec
EF e60 medium1
EM30
EF 2e12Tvh loose1
2EM10VH
EF 2e12Tvh loose1 L2StarB
2EM10VH
EF mu24i tight
MU15
muon
EF mu36 tight
MU15
EF mu18 tight mu8 EFFS
MU15
elec-muon
EF e12Tvh medium1 mu8
EM10VH MU6

3.1.4

Period
B-J
K
L-M
B-I
J-M

PeriodA-L
A-L
A-L
D - L (data only)
A-L
A-L
A-L
A-L

Trigger eﬃciency

The trigger eﬃciencies have been measured using tag-and-probe method (see Section 4.3.1),
and have been found to be ∼90 % for electrons, and ∼90 % (∼70 %) for muons in theendcap (barrel). Any diﬀerences between data and simulation in eﬃciency are corrected
for by calculating scale factors (SF) for individual leptons. Using the individual SFs, theper-event SF is also calculated as follows:
SF =

lead
sub
1 − (1 − ϵlead) × (1 − ϵsub)Eﬀ data
M C × SF
M C × SF
=
,
lead
sub
Eﬀ M C
1 − (1 − ϵM C ) × (1 − ϵM C )

(3.1)

sub
where ϵlead
M C and ϵM C are trigger eﬃciencies for the leading and sub-leading leptons, and
lead
sub
SF
and SFare individual scale factors for the leading and sub-leading leptons. The

3.2 Event and Object Reconstruction

39‘OR’ing of the dilepton triggers increases the complexity of the eﬃciency calculation as
follows:Eﬀ = ϵsingle + ϵdi−lep − ϵsingle · ϵdi−lep= (ϵs1 + ϵs2 − ϵs1 ϵs2 ) + (ϵd1 ϵd2 ) − (ϵs1 + ϵs2 − ϵs1 ϵs2 ) · (ϵd1 ϵd2 ),

(3.2)
(3.3)

where ϵsingle and ϵdi−lep are the per-event eﬃciencies from the single lepton triggers anddilepton triggers. The superscripts s and d denote the single lepton trigger and dilepton
trigger, and the subscripts 1 and 2 denote the leading and sub-leading leptons. Using thesesymbols, the uncertainty on the per-event eﬃciency is expressed as:(∆Eﬀ)2 = [σ1s (1 − ϵs2 )(1 − ϵdi−lep ) + σ1d ϵd2 (1 − ϵsingle )]2(3.4)+ [σ2s (1 − ϵs1 )(1 − ϵdi−lep ) + σ2d ϵd1 (1 − ϵsingle )]2 ,(3.5)

d is the uncertainty, for instance, on either e12Tvh medium1 or mu8 in eµ final state.
where σ1,2In order to reduce the complexity, a simplification is made for events that are triggered byboth single lepton and dilepton triggers. For those events, the uncertainties for the single
lepton triggers are used. And for events that fire only the dilepton triggers, the uncertainties
for the dilepton triggers are applied. In practice the events that have the leading lepton
pT = 22-25 GeV, are not accessible by the single lepton triggers because of its trigger
plateau threshold (pT > 25 GeV). Therefore the uncertainties for the dilepton triggers are
considered for those events. The uncertainties are treated as uncorrelated between theleading and sub-leading leptons when the leptons fire diﬀerent triggers while are treated ascorrelated when the leptons fire the same trigger.

3.2

Tracks and vertices

3.2.1

Track reconstruction

Track reconstruction [120–123] is based on two algorithms referred to as “inside-out” and“outside-in” algorithms. The former starts the reconstruction from the innermost detector,
namely the Pixel, whereas the latter from the outermost detector, the TRT.
inside-out algorithm: In the inside-out algorithm, the track reconstruction starts fromforming track-seeds using all three layers of the Pixel and the first layer of the SCT. Simultaneously a fast primary vertex search is performed to further constrain the seeds. Thenthe seeds provide directional information to build roads for the further search of associatedhits in the remaining layers of the SCT to one track candidate. However the seeded trackfinding results in a very high number of track candidates. Many of these track candidates
share silicon hits including fake tracks that do not originate from one single particle. In
the second stage, the ambiguities between real and fake tracks are resolved by placing ascore on the track quality [124] with more sophisticated fitting that includes global χ2 andKalman filter algorithms [125]. In the final stage, the tracks reconstructed in the silicondetectors are extended into the TRT by associating extra hits in the TRT. The tracks are40

3.2 Event and Object Reconstruction

refitted with the additional hits in the TRT and compared to the silicon-only tracks inthe fitting score. If the score is improved by the TRT hits, then the extended track istaken, otherwise the original silicon-only track is taken instead as a real track. The tracks
reconstructed by the inside-out algorithm are required to have pT > 400 MeV and |η| < 2.5.
back-tracking algorithm:
After the inside-out algorithm, the outside-in algorithm
referred to as the back-tracking, is also performed. The back-tracking algorithm is a track
search starting from segments reconstructed in the TRT. The algorithm is designed to reconstruct secondaries that are defined as particles produced in the interactions of primaries.
Since heavy flavor/τ decays and photon conversions have secondaries, it is crucial to identify
those tracks in this algorithm. If there are no tracks associating to the silicon detectors,
the tracks are classified as the TRT-standalone tracks.

3.2.2

Vertex reconstruction

Primary vertices are then reconstructed using the reconstructed tracks based on the ‘vertex
finding’ algorithm [126]. Firstly the algorithm selects the reconstructed tracks that arecompatible with tracks originated from the interaction point (IP). Then a vertex seedis obtained from a global maximum in the z position of the reconstructed tracks at thebeamline. An iterative χ2 fit is then performed using the seed and the nearby tracks. Eachtrack carries a weight that is a measurement of its compatibility with the fitted vertex
depending on the χ2 . Bad χ2 tracks, defined as more than 7 σ far from the vertex, areused again to seed a new vertex and the whole procedure is repeated until no unassociatedtracks are left. Each primary vertex is finally required to have more than two associatedtracks.
Reconstruction eﬃciency
The vertex reconstruction eﬃciency depends on the pileups. The eﬃciency decreases withthe higher pileup because of an increased number of fake tracks, which results in the worse
resolution of the vertex position, namely an increased number of fake vertices. Figure 3.2
shows the vertex reconstruction eﬃciency and fake probability as a function of the average
number of interactions per bunch crossing, referred to as < µ >, that is from the calorimeterreadout including both in-time and out-of-time pileups (see also Section 2.1.3). The reconstruction eﬃciency for the robust selection with having more than two associated tracks(shown in green) is higher by ∼ 5 % thanks to the smaller contamination of the fake tracks
in the denominator sample. Hence the analysis also requires more than two associatedtracks when defining the vertex.
NPV and < µ > rescaling
Since it is hard to generate the < µ > distribution correctly in simulation, the diﬀerence
between data and MC in the µ is corrected by ‘< µ >-rescaling’. As illustrated in Figure 3.3, the < µ >-rescaling also improves the NPV distribution.

3.2 Event and Object Reconstruction

41

The remaining diﬀerence is further corrected for by reweighting the < µ > distribumiss andtion to data. These corrections aﬀect most of the physics objects such as leptons, ET
jets. The impact of the scaling in the analysis is further discussed in Section 8.3.2

Figure 3.2:
The vertex reconstruction eﬃciency (left) and fake probability (right) asa function of µ in minimum bias MC sample. These are shown both using default track
selection (blue, dashed) and with robust track requirements (red, solid). The reconstruction
eﬃciency with the robust track requirements is shown for reconstructible interactions (green,
dot-dased), defined as having at least two stable charged primary particles with |η| < 2.5
and pT > 400 MeV [122].

Figure 3.3: NPV distribution before (left) and after (right) the < µ >-rescaling. Since
the number of interactions per crossing (< µ >) is highly correlated with NPV, the NPV
distribution can be improved by the µ-rescaling. The remaining diﬀerence in < µ > isfurther corrected for by another reweighting referred to as ‘pileup reweighting’.

42

3.3 Event and Object Reconstruction

3.3

Jets

3.3.1

Reconstruction

Jets used in the analysis are reconstructed from the topological clusters (topo-clusters) using
the anti-kt algorithm [127] that is designed to form jets by an iterative sorting algorithm.
Jets defined by the algorithm are not influenced by soft QCD radiations. The jet finding
procedure starts from a creation of the topo-clusters that are built from the calorimeter
cells with a large energy deposit above a certain threshold. The cells neighboring the seeded
topo-cluster are added iteratively to the cluster. The anti-kt algorithm is then applied to the
topo-cluster to form an “anti-kt jet”. This can be expressed as Equation 3.6 by introducing
a distance parameter dij between the objects.
−2
dij = min(p−2T,i , pT,j )

2
∆Rij
,
R2

(3.6)

where pT,i is a transverse momentum of object i, and R is a distance parameter that is set
to be 0.4 in the analysis. The algorithm iteratively calculates the dij values looking for thesmallest dij . Once the smallest is found, both objects i and j are combined. The calculationis repeated until finding the final smallest dij that corresponds to pT,i . This means that theobject i is stable and is defined as a jet.

3.3.2

Calibration

The topo-clusters are reconstructed at the EM energy scale. Hence the clusters need tobe calibrated/scaled to ‘jet energy scale (JES)’, using the local cluster weighting (LCW)
method. The LCW can classify the topo-clusters as either electromagnetic or hadronic
based on the measured energy density and the longitudinal shower depth since hadrons aresupposed to have a lower energy density and a longer shower depth in the EM calorimetercompared to electrons. The jet energy corrections are derived according to this classificationfrom the truth jets that are generated from single charged/neutral pion in simulation, andthat are reconstructed using the same anti-kt algorithm. The correction is further weighted
by pileup correction, etc accordingly, to get the final jet energy correction [15].
To derive the systematic uncertainties on the JES the jet pT in data is compared tothe one in simulation by exploiting the pT balance between the jet pT and the pT of areference object as follows:refjet ref∆(JES) = < pjet
T /pT >data / < pT /pT >M C ,(3.7)

Firstly, di-jets events are exploited to test the pT balance between a central jet (|η| <0.8)
and a forward jet (0.8< |η| <4.5) (referred to as ‘di-jet η-intercalibration’). After theintercalibration, γ+jet and Z+jet events are exploited as references to test the direct pTbalance (DB), and to evaluate the uncertainties in the region |η| >1.2. Finally events wherea system of low pT jets recoils against a high pT jet are used to calibrate jets up to the TeV
scale. The low pT jets are required to be within |η| <2.8 while the leading jet is within

43

3.3 Event and Object Reconstruction|η| <1.2. In addition to the main JES uncertainties discussed above, other uncertainties
are also evaluated:• pileup (in-time and out-of-time) uncertainty,• close-by-jet uncertainty that accounts for the presence of non-isolated jets,• jet flavor composition uncertainty to accounts for the diﬀerence in response between
gluon and quark jets,• heavy flavor response that accounts for the diﬀerence in energy scale for b-jet,• diﬀerent pileup simulation sample (PYTHIA6.4 vs PYTHIA8) [128, 129]) in the jet calibration,

0.1
0.09
0.08

anti-kt R = 0.4, LCW+JES + in situ correction

ATLAS Preliminary

Data 2012, s = 8 TeV
η = 0.0

0.07
0.06
0.05

Total uncertainty
Absolute in situ JES
Relative in situ JES
Flav. composition, inclusive jets
Flav. response, inclusive jets
Pileup, average 2012 conditions

0.04

Fractional JES uncertainty

Fractional JES uncertainty

Figure 3.4 shows the total JES uncertainty for 2012 as a function of η (pT = 40 GeV)
and as a function of pT (|η| = 0). The uncertainty at the lowest pT is ∼4% and at thehighest η is ∼7%. The impact on the final result is discussed in Chapter 8.
0.1
0.09
0.08

0.04

0.02

0.01

0.01
102

2×102

103
2×103
jet
p [GeV]T

Total uncertainty
Absolute in situ JES
Relative in situ JES
Flav. composition, inclusive jets
Flav. response, inclusive jets
Pileup, average 2012 conditions

0.05

0.03

30 40

jet

0.06

0.02

20

ATLAS Preliminary

Data 2012, s = 8 TeV
p T = 40 GeV

0.07

0.03

0

anti-kt R = 0.4, LCW+JES + in situ correction

0

-4

-3

-2

-1

0

1

2

3

4
η

Figure 3.4: Fractioal jet energy scale systematic uncertainty components as a function ofpT for anti-kt jets at |η|=0.0 (left) and as a function of η for anti-kt jets at pT = 40 GeV
with R=0.4 calibrated using the LCW+JES calibration sheme. The total uncertainty (allcomponents summed in quadrature) is shown as a filled blue region. Average 2012 pileup
conditions were used, and topology dependent components were taken from inclusive di-jets
sample [130].

3.3.3

Jet vertex fraction

Even after pileup correction (namely pileup subtraction [131, 132]) in the jet calibration, alarge amount of pileup jets remain non-negligible, which results in the increased number ofreconstructed jets. In order to further reject the pileup jets, tracking information is used
to calculate a discriminant variable referred to as jet vertex fraction (JVF).
The JVF is defined for each jet as the ratio of the scalar pT sum of the tracks (pT > 500

44

3.3 Event and Object ReconstructionMeV) associated with the jet from the primary vertex (PV) with the largest
scalar pT sum of all associated tracks from all primary vertices:∑ 2
pT , to the∑
JVF = ∑

trackk(PV0 )
k pT∑∑
trackll(PV0 ) + n≥1 ( l ptrack(PVn ))
l pT
T

,

(3.8)

∑ 2
where PV0 is the primary vertex (PV) with the largest
pT of constituent tracks, andPVn (n ≥ 1) corresponds to primary vertices from other smaller pp interactions in theevent. In other words the JVF is the fraction of pT from tracks associated with the PV
from the hardest pp collision in event. Figure 3.5 shows JVF distribution. The JVF =0 indicates that all associated tracks originate from pileup vertices, while the JVF = 1
indicates that all associated tracks originate from the hard-scatter vertex. The JVF = -1 isassigned to jets which do not have associated tracks. A cut on the JVF (|JVF| > 0.5 is usedin the analysis for jets with 25 < pT < 50 GeV and |η| < 2.4) can help to reduce the pileup
jets, but enhance jets from hard scattering, which depends on the number of reconstructedprimary vertices in the event.

Figure 3.5: JVF distribution for hard scatter (blue) and pileup (red) jets with 20 ≤ pT < 50
GeV in simulated Z → ee events. The JVF = 0 indicates that all associated tracks originate
from pileup vertices, while the JVF = 1 indicates that all associated tracks originate fromthe hard-scatter vertex. The JVF = -1 is assigned to jets which do not have associatedtracks [131].

3.3 Event and Object Reconstruction

3.3.4

45

Heavy flavor tagging

In the analysis it is essential to identify b-jets eﬃciently, namely high b-tagging eﬃciency
for real b-jets while retaining the misidentification eﬃciency for c and light flavors at low
rate. The suﬃcient performance of the b-tagging allows to reduce top backgrounds and to
define dedicated top control region. The b-tagging is performed based on the multivariate (MVA) tagging algorithm referred to as MV1 algorithm [133, 134]. The MV1 uses all
available information that is sensitive to the b-jet identification such as vertexing parameters (transverse impact parameter significance d0 /σd0 and longitudinal impact parameterz0 ) [135], secondary vertices [136] that generate displaced tracks, and topology of weakb− and c−hadron decays, as input. The b-tagging eﬃciency is derived from tt̄ events inthe dilepton decay channel classifying the final states into four channels, two lepton flavor
channels (eµ and ee + µµ channels) and two jet bins (two jets and three jets channels).
The MV1 can exploit the per-event flavor correlations between the possible combinationsof two or three jets (for two jets case: b-jet vs b-jet, b-jet vs non b-jet, non b-jet vs nonb-jet), taking into account the pT dependence. Finally four channels are combined and all
single systematic variations are treated as fully correlated in the combination, except for
the theory uncertainty for which 50% correlation is assumed due to the diﬀerent eﬀect ineach channel. For the H→ W W ∗ → ℓνℓν analysis, 85% eﬃciency operating point is chosen
to maximize the rejection of top backgrounds.
The uncertainties on the b-jet identification that potentially change the flavor composition, are decomposed into 6 uncorrelated components using eigenvector method [15]instead of varying each source of uncertainties. The eigenvector method can reduce thenumber of variations (108 variations) to the handleable numbers (10 variations). For eachsource of uncertainties one covariance matrix is constructed with dimension corresponding
to the number of bins (10 bins) and the total covariance matrix is obtained as a sum ofthese individual component matrices. The eigenvectors which solve the total covariancematrix can be seen as “directions” in which independent variations are carried out. This
leads to the 6 uncorrelated parameters related to the b-jet tagging in the final fit. The total
uncertainty is between 2-9%.

3.3.5

Jet Selection

The jet selection used in the analysis is summarized below:- |η| < 4.5,
- pT > 25 GeV for |η| < 2.4 and pT > 30 GeV for |η| ≥ 2.4,
- |JV F | > 0.5 for jet with pT < 50 GeV and |η| < 2.4,
- b-jet: MV1 algorithm (85% operating point) for the same jets but with pT > 20 GeV.

46

3.4 Event and Object Reconstruction

3.4

Missing Transverse Energy and Momentum

Due to the presence of two neutrinos in the final state and the inability of the ATLAS
detector to detect them, the missing transverse energy is an important observable for themiss and pmiss have been developed and used for diﬀerent
analysis. Two types of variables ETTpurposes in the analysis.

3.4.1

ETmiss reconstruction

miss reconstruction [137] uses energy deposits in the calorimeters and muons reconThe ET
structed in muon spectrometer (MS) as follows:
miss, calo
miss, µmissEx(y)= Ex(y)+ Ex(y),(3.9)

where each term is calculated as the negative vector sum of the reconstructed and calibrated
objects in the region |η| < 4.5. The muon term accounts for all muons that include segment
tagged (ST) muons (see Section 4.2.1) to recover the contribution from low pT muons. The
calo term includes all physics objects reconstructed in the calorimeters, namely electrons,
photons, hadronically decaying τ leptons, and jets, as well as energy deposits not associatedwith any such objects, referred to as ‘soft term’. Splitting the calo term the Equation 3.9
can be rewritten as:
miss, µmiss, softTermmiss, jets
miss, τmiss, γ
miss, emiss,
) + Ex(y)+ Ex(y)+ Ex(y)+ Ex(y)+ Ex(y)Ex(y)= (Ex(y)√missET= (Exmiss )2 + (Eymiss )2 ,(3.10)(3.11)

where each term in the calo term is calculated in that order, which allows to avoid any
double counting of those objects. The soft term is calculated from the topological clusters (see Section 3.3.1) and tracks not associated to other parent objects, subtracting any
overlap between the topological clusters and tracks, and the energy losses for muons in
the calorimeters. The uncertainties on each term such as energy scale and resolution are
miss calculation [137].
calculated and propagated to the ET
miss is strongly dependent on the pileup conditions. The
The performance of the ET
degradation of the performance due to the pileups can be serious issue in most of analyses.
In 2012 the H→ W W ∗ → ℓνℓν analysis also suﬀers from the higher pileups, which results
in a factor of 3-5 increase of the Z/DY backgrounds. It is clear that the increased Z/DY
backgrounds make the analysis insensitive in ee and µµ channels without solving the issue,
or at least improving the situation. Indeed the situation has been much improved by introducing a cut on new variable referred to as frecoil (see Section 5.4.3). The cut reduces the
Z/DY backgrounds significantly and they remain very small in the signal region.
miss side, the jet term and soft term are recalculated using primary
Also from the ET
vertex information to suppress the degradation of the performance. For the jet term, thejet vertex fraction (JVF) (see Section 3.3.3) is applied to each jet, which makes the jet3.4 Event and Object Reconstruction

47

term more robust against the pileups. Similarly for the soft term, the fraction of pT fromtracks matched to the soft term, referred to as ‘soft term vertex fraction (STVF), has been
miss is not
calculated to mitigate the impact of the pileups. In the analysis the STVF ET
used but instead the pmiss(see Section 3.4.2) is used.
T

3.4.2

pmiss
reconstructionT

miss has dependence on the pileups, the missing transverse momentum pmiss [138]Since the ETT
has been considered for the analysis because of its little dependence on the pileups. Thepmiss
is calculated from the reconstructed tracks defined in Section 3.2.1 with the quality
Tcuts shown in Table 3.3. Regardless of the quality cuts above, all electron and muon tracks
calculation.
defined in Table 3.4 are taken into account in the pmiss
T

Table 3.3: Definition of tracks used in the pmiss
calculation.
T
Quality cuts for track selection· track pT > 500 MeV (all tracks associated to primary vertices)· |η| < 2.5 that corresponds to the coverage of inner detector (ID)· |d0 | < 1.5 mm (d0 : transverse impact parameter w.r.t. primary vertex)· |z0 sin θ| < 1.5 mm (z0 : longitudinal impact parameter w.r.t. primary vertex)· Number of Pixel hits ≥ 1· Number of SCT hits ≥ 6

Table 3.4: Definition of lepton tracks used in the pmiss
calculation.
T
Electron track selection
cluster > 10 GeV· ET· |η| < 2.47
· cut-based Medium++ identification (see Section 4.1.2)· |z0 sin θ| < 1.5 mm (z0 : longitudinal impact parameter w.r.t. primary vertex)· lower pT electron is removed if ∆R(electron, electron) < 0.10
· electron is removed if ∆R(electron, jet) < 0.30
Muon track selection· pT > 6 GeV· |η| < 2.50
· Staco muons (see Section 4.2.1)· |z0 sin θ| < 1.5 mm (z0 : longitudinal impact parameter w.r.t. primary vertex)

In addition, anti-id leptons used for data-driven W +jets background estimate (see Section 6.3.1 and 6.3.2) are considered since the anti-id leptons particularly anti-id electrons

48

3.4 Event and Object Reconstruction

cannot pass the selection for electron track by definition because of the requirement of
cut-based Medium++ veto. Without including the anti-id leptons in the calculation, theW +jets background is significantly (30-40 %) underestimated in the signal region. The
impact of the anti-id correction on pmiss
and mT distributions are shown in Figure 3.6.
T
Furthermore tracks that correspond to bremsstrahlung photons subsequently converting
into e+ e− pairs inside the inner detector (or earlier), are removed if the tracks are within
the electron cone defined as ∆R (electron, track) < 0.05, excluding the electron track itself, while no bremsstrahlung cut is applied to muons because the bremsstrahlung photons
cannot convert into muons.

Figure 3.6: pmiss
and mT distributions showing the impact of anti-id correction on the
T
miss
pT
calculation. Without including the anti-id correction, about 30-40% underestimateof the data-driven W +jets backgrounds is expected.
The pmissdefined above is however only used in the same flavor (ee,µµ) analysis. In
T
jetCorr
addition to the pmissa new missing transverse momentum referred to as pmiss,isTTalso defined by replacing all tracks in jet cone (∆R(jet, tracks)<0.4) and electron tracks
with the reconstructed objects defined in Section 3.3.1 and 4.1.1 as expressed below:∑ ∑ j,k∑jetCorrpmiss,= −pmiss+(pT (trk) − pjT (cal)) +(plT (trk) − plT (cal)) (3.12)
TT
j (jet)kl (ele)jwhere pj,kT (trk) and pT (cal) in the second term indicate all tracks associated to jet j andjet j reconstructed in the calorimeter, and plT (trk) and plT (cal) in the third term indicate
electron track l and electron l calibrated in the calorimeter, respectively.
jetCorr
Since mis-measured tracks that make a longer tail at higher pmiss,still remainTnon-negligible, further removals are applied in the following order:jet• track is removed if ∆R(track, jet) < 0.40 with jet pT > 10 GeV and ptrk
T > 1.4 · pT ,• track is removed if the track with ptrk
T > 100 GeV does not match to any reconstructedobjects.

3.4 Event and Object Reconstruction49

For events that do not have jets, the jet replacement is not made by definition, namely
jetCorr
the pmiss,is identical to the pmiss
definition. In addition to the robustness against
TT
miss, jetCorr
the pileups, the pT
also shows its better performance in resolution as shown in
miss, jetCorr
Figure 3.7, so that the pT
is also used to reconstruct a final discriminant dilepton
mT for the signal extraction.

miss andFigure 3.7:
Comparison of missing transverse energy resolution between ET
miss, jetCorr
miss
miss
miss
pT
in (ET - truth ET / truth ET ) (left) and in dilepton (mT - truth
mT / mT ) (right) distributions.

50

3.4 Event and Object Reconstruction

Chapter 4

Determination of Lepton Selection
Leptons are important ingredients in the H→ W W ∗ → ℓνℓν analysis. In order to maximize the analysis sensitivity, lepton selection must be optimized. The eﬃciencies for those
optimized leptons are then measured using tag-and-probe method, in order to correct forthe mis-modeling in simulation. In this chapter the reconstruction of leptons are firstly
presented. The lepton optimization is then discussed. Finally lepton selection criteria andcorresponding lepton eﬃciencies are summarized.

4.1

Electrons

4.1.1

Reconstruction

Central electrons (|η| < 2.5) are reconstructed based on the energy deposited in the EM
calorimeter, being associated to the reconstructed tracks in the inner detectors (ID) [139]. 1
The electron reconstruction starts with a creation of seed clusters having a transverse
energy ET > 2.5 GeV. The seed clusters are searched for by a sliding − window algorithm [119] in the middle layer of the EM calorimeter that has the largest radiation length(X0 > 16), using a window size of 3×5 in units of 0.025×0.025 in η × ϕ space.
The reconstructed tracks with ET > 1 GeV that is larger than the default track pT(namely 400 MeV) for taking into account the energy losses at material surface, are thenloosely matched to the seed clusters satisfying ∆η(cl, track) < 0.05. In√
case that several
tracks are matched to the same cluster, the one with the smallest ∆R = ∆η 2 + ∆ϕ2 distance to the cluster is chosen. After the loose matching, the electron tracks, in most of thecases the TRT-standalone tracks defined in Section 3.2.1, are refit by an optimized electron
track fitter, referred to as the Gaussian Sum Filter (GSF) algorithm [140] that is a non-linear
generalization of the Kalman filter [125]. With the GSF, the electron track parameters willOn the other hand the associated track is not required for forward electrons (2.5 < |η| < 4.9) becauseof the ID coverage (|η| < 2.5), and those electrons are not used in the analysis.
1

51

52

4.1 Determination of Lepton Selection

be more accurately determined by accounting for the non-linear bremsstrahlung eﬀects. 2
The electron cluster is then rebuilt using a larger number of clusters, 3×7 (5×5) longitudinal towers in the barrel (endcaps), in order to determine the cluster energy summing
four diﬀerent contributions: energy deposit in the material in front of the EM calorimeter,
energy deposit in the cluster, external energy deposit outside the cluster (lateral leakage),and energy deposit beyond the EM calorimeter (longitudinal leakage). The four-momentum
is finally computed using information from both the final cluster and the best track matchedto the original seed cluster. The electron energy is given by the cluster energy. The ϕ andη directions are taken from the corresponding track parameters at the vertex, except for
the TRT-standalone tracks for which the cluster-based directions are used.

4.1.2

Identification

Even after the reconstruction, the purity of real electrons is still very low and it suﬀers
from a huge amount of non-real electrons that originate from hadrons, photon conversions,and semi-leptonic decays of heavy flavors. A suﬃcient rejection of those backgrounds, while
retaining high eﬃciency for real electrons, is therefore crucial. 3 The electron identification
plays an important role against those backgrounds. Figure 4.1 shows two examples of theshower shape variables used in the identification.
10-1

1

ATLAS Preliminary

ATLAS Preliminary

Simulation

Simulation

Isolated electrons

Isolated electrons

10-1

Hadrons

10-2

Hadrons

Non-isolated electrons

Non-isolated electrons

Background electrons

Background electrons

10-2
10-3
10-3
10-4

10-5
-0.02

10-4

0

0.02

0.04

0.06

0.08

0.1

Rhad1

10-5
0

0.005

0.01

0.015

0.02

0.025

wη2

Figure 4.1: Comparison of shower shape variables between isolated electrons and “background” electrons in simulation. The left (right) figure shows Rhad1 (Wη2 ) distribution
over inclusive ET . The contribution from real electrons is labeled as “Isolated” electrons.
Conversions and electrons from semi-leptonic decays of heavy flavors are referred to as“Background” and “Non-Isolated” electrons, respectively [141].
2

Note that the GSF electrons are only available in the 2012 analysis.
In the H→ W W ∗ → ℓνℓν analysis the misidentified electrons result in either W +jets/QCD or W + γ
background that potentially limits the experimental sensitivity.
34.1 Determination of Lepton Selection

53

The hadronic leakage variable Rhad1 is used that is defined as the ratio of the longitudinal energy leakage into the first layer of the hadronic calorimeter to the total energy
deposited in the EM calorimeter, to discriminate real electrons from hadrons. The lateral
shower width in the second layer of the EM calorimeters, referred to as Wη2 , is also useful
to separate real electrons from hadrons as the hadronic shower generally tend to be wider
than the EM shower. In total there are 22 discriminating variables used as input for theidentification. All discriminating variables are summarized in Table 4.1.
For the identification, there are two types of identifications: cut-based and likelihood
identifications. The cut-based identification [14,142], which is based on rectangular cuts onthese variables, has been used for identifying electrons in 2011. The identifications tight,
medium, and loose are subsets of each other. With increasing tightness, more variables
are added. On the other hand, in order to deal with the higher pileup condition in 2012,
likelihoods techniques have been also developed [143]. The likelihoods are one of the multivariate (MVA) techniques that are used extensively in physics analyses to separate signal
from background, since they allow the simultaneous evaluation of several properties. The
likelihoods are chosen because of its simplicity in construction. The likelihoods make useof signal and background probability density functions (PDF) of discriminating variables.
Based on these PDFs that are obtained from data, an overall probability is calculated forthe event or object to be signal(-like) or background(-like). The signal and backgroundprobabilities for a given electron are combined into a discriminant on which a cut is made.
The choice of the cut value determines the signal eﬃciency/background rejection of thelikelihood.
The identification operating point for electrons has been optimized (see Section 4.4)
for each ET bin due to the fact that the background composition highly depends on ET .
Both likelihood and cut-based identifications are used in the H→ W W ∗ → ℓνℓν analysis.
The very tight identification that is the tightest operating point in the likelihoods, hasbeen designed/optimized to have roughly the same signal eﬃciency as the cut-based tightbut to have better rejection against hadrons and conversions. For the lower ET (ET < 25
GeV), the very tight is preferred to cope with a large amount of the W +jets/QCD backgrounds that arise from the electron misidentification, whereas the cut-based medium withsome additional cuts is preferred to keep the signal eﬃciency as high as possible, since theW +jets/QCD backgrounds remain small in high ET (ET > 25 GeV).

4.1.3

Isolation

In order to further reject hadrons, two types of isolations: track isolation and calorimeter
isolation, are used. The isolations are good discriminants for the background rejection evenafter the identification because they are uncorrelated with the identification variables, so a
substantial improvement is expected from the isolations.
Calorimeter isolation: The calorimeter isolation is defined as the sum√of the transverse energy ET deposited in the calorimeter cells in a cone size of ∆ R (= ∆η 2 + ∆ϕ2 )54

4.1 Determination of Lepton Selection
Table 4.1: Definition of electron discriminating variables [14, 141, 142].

Type
Hadronic leakage

Description· Ratio of ET in the first layer of the hadronic calorimeterto ET of the EM cluster in the range of |η| < 0.8 and |η| > 1.37
· Ratio of ET in the hadronic calorimeter to ET of the EM clusterin the range of |η| > 0.8 and |η| < 1.37

Variable name
Rhad1
Rhad

Third layer of
EM calorimeter· Ratio of the energy in the third layer to the total energy

f3

Middle layer of
EM calorimeter· Lateral shower width in the second layer in 3×5 cells· Ratio of the energy in 3×3 cells over the energy in 3×7 cells
centered at the electron cluster position· Ratio of the energy in 3×7 cells over the energy in 7×7 cells
centered at the electron cluster position

Wη2
Rϕ· Shower width in overall strips within ∆η × ∆ϕ ∼ 0.0625×0.2
corresponding typically to 20 strips in η
· Ratio of the energy diﬀerence between the largest and second
largest energy deposits in the cluster over the sum ofthese energies· Ratio of the energy in the strip layer to the total energy

Wstot

Strip layer ofTrack quality

TRT

Track-cluster
matching

Conversion

Rη

Eratiof1· Number of hits in the B-Layer (the innermost layer of the Pixel)· Number of hits in the Pixel detector· Number of total hits in the Pixel and SCT detectors· Transverse impact parameter· Significance of transverse impact parameter defined as
the ratio of d0 and its uncertainty· Momentum lost by the track between the perigee [126]and the last measured point divided by original momentum

Nblayer
NpixelNSid0
σd0· Total number of hits in the TRT· Ratio of the number of high-threshold hits to the total numberof hits in the TRT

NT RT
FHT

· ∆η between the cluster position in the first (strip) layer
and the extrapolated track· ∆ϕ between the cluster position in the middle layer
and the extrapolated track· Defined as ∆ϕ2 but the track momentum is rescaled to thecluster energy before extrapolating the track to the middle
layer of the calorimeter· Ratio of the cluster energy to the track momentum∆η1· Veto electron candidates matched to reconstructed
photon conversions

∆p/p

∆ϕ2
∆ϕRes

E/p
!isConv

4.1 Determination of Lepton Selection

55= 0.3 around the electron, excluding the contribution of the electron itself. In 2011 thecell-based algorithm [144] (Etcone) has been used, whereas in 2012, the algorithm has been
replaced with the new algorithm [145] based on topological cluster (topoEtcone). Figure 4.2 shows a comparison of the Etcone and topoEtcone isolations where signal (red)events are collected with the Z tag-and-probe, and backgrounds (green) are collected withEF g20 etcut trigger that enhances QCD or γ+jet like events. The signal and backgrounddefinitions will be described later on in Section 4.3.

Figure 4.2: Isolation distributions for Etcone (left) and topoEtcone (right) divided by ET
with a cone size of ∆R = 0.3 for electrons that pass the cut-based tight with ET > 15
GeV. The signal (real) electrons collected with Z tag-and-probe and background electrons
collected with EF g20 etcut trigger are shown as red and green, respectively.
The isolation energy for topoEtcone is computed by summing the energy of uncalibrated
topological clusters with only positive energy deposited in the cone around the electron,
which acts as a noise suppression keeping only the cells with an energy deposit coherently
spread over neighboring cells [145]. The isolation energy is corrected for the leakage andcorrected on event by event basis for energy deposits from the underlying event [146]. Figure 4.3 shows signal eﬃciency versus background rejection for the Etcone and topoEtcone.
The performance of the Etcone gets worse in increased pileup (µ > 20) environment,
whereas the topoEtcone is more robust against the pileup and is better in the backgroundrejection for a given signal eﬃciency. It is also found that the smaller cone size is betterat higher signal eﬃciency (namely high ET ), while the larger is better at the lower signal
eﬃciency (namely low ET ).
Track isolation: The track isolation is defined as the sum of the transverse momentum of the tracks with pT >400 MeV (900 MeV in 2011) in a given cone ∆R around theelectron, excluding the contribution of the electron itself. The tracks must come from theprimary vertex and be of good quality satisfying at least four hits in the Pixel and SCT detectors, which makes the track isolation better than the calorimeter one in the backgroundrejection and in robustness against the pileup. Figure 4.4 shows a comparison of the track56

4.1 Determination of Lepton Selection

isolation between 2011 and 2012.
signal VS bkg rejection Efficiency
0.8

0.7

0.7
background Ef fi ciency

background Ef fi ciency

signal VS bkg rejection Efficiency
0.8

0.6
0.5
0.4

0.6
0.5
0.4
0.3

0.3

etcone20 (<mu> > 20 )etcone30 (<mu> > 20 )etcone40 (<mu> > 20 )etcone20 (<mu> <= 20 )etcone30 (<mu> <= 20 )etcone40 (<mu> <= 20 )

0.2
0.1

0.8

0.85

0.9

etcone20 (<mu> > 20 )etcone30 (<mu> > 20 )etcone40 (<mu> > 20 )etcone20 (<mu> <= 20 )etcone30 (<mu> <= 20 )etcone40 (<mu> <= 20 )

0.2
0.1
0
0.95

1
signal Efficiency

0.8

0.85

0.9

0.95

1
signal Efficiency

Figure 4.3: Signal eﬃciency versus background rejection for Etcone (left) and topoEtcone(right) for electrons that pass the cut-based tight with ET > 20 GeV. The cone size is
explicitly labeled as etconeXX (XX = 20, 30, and 40) where XX = 20, for instance, denotes
a cone size of ∆R = 0.2. The topoEtcone is more robust against the pileups regardless ofthe cone size, and is better in the rejection.

Figure 4.4: Isolation distributions for Ptcone for 2011 (left) and 2012 (right) divided by
ET with a cone size of ∆R = 0.3 for electrons that pass the cut-based tight with ET > 15
GeV. The signal (real) electrons collected with Z tag-and-probe and background electrons
collected with EF g20 etcut trigger are shown as red and green, respectively.
Also the performance of the track isolation in 2012 is improved compared to that in 2011
in the background rejection as shown in Figure 4.5. This is due to the lower pT thresholdfor each track from 900 MeV to 400 MeV in the isolation energy calculation. Since thetrack isolation is the best discriminant against the W +jets/QCD backgrounds, the lepton
optimization (see Section 4.4) rather relies on it. The signal eﬃciency for the isolations at
actual operating points in the analysis are presented in Section 4.7.

57

4.1 Determination of Lepton Selection

background rejection Efficiency

signal VS bkg rejection Efficiency
0.8
0.7
0.6
0.5
0.4

ptcone20 (2012)
ptcone30 (2012)
ptcone40 (2012)
ptcone20 (2011)
ptcone30 (2011)
ptcone40 (2011)

0.3
0.2
0.1
0

0.8

0.85

0.9

0.95

1
signal Efficiency

Figure 4.5: Signal eﬃciency versus background rejection for Ptcone for electrons that pass
the cut-based tight with ET > 20 GeV. The cone size is explicitly labeled as ptconeXX(XX = 20, 30, and 40) where XX = 20, for instance, denotes a cone of ∆R = 0.2. The
topoEtcone is more robust against the pileup regardless of cone size, and is better in the
background rejection.

4.1.4

Energy scale and resolution

Electron energy scale and resolution [119] are determined from the Z → ee or J/ψ → ee
resonances. The mis-calibration is defined as the diﬀerence in energy response between dataand simulation, and is parametrized as follows:
Eidata = Eimc (1 + αi ),(4.1)

where Eidata and EiM C are the electron energy in data and simulation for a given η regioni, and αi represents the deviation from the optimal calibration. For Z and J/ψ decays, theeﬀect of electron mis-calibration on the invariant mass is expressed as:
C
MC
mdata
= mM
ij
ij (1 + αij ) ∼ mij (1 +αi + αj
),
2

(4.2)

where mij is the invariant mass for a pair of reconstructed electrons, and αij is the induced
shift on the mass peak in given η bins i and j. The second order terms are neglected byassuming that the angle between the two electrons is known.
The energy resolution is parametrized under the assumption that the resolution curve
is well modeled in simulation as follows:ab
σE= √ ⊕ ⊕ c,
E
E E

(4.3)

where a, b, and c denote the sampling term, the noise term, and a constant term, respectively. The constant term is determined by fitting the invariant mass using a Breit-Wigner
convoluted with a Crystal Ball function. The intrinsic width of the Z or J/ψ is fixed andthe experimental resolution is described by the Crystal Ball.

58

4.2 Determination of Lepton Selection

The total uncertainty on the energy scale is <0.05 %, and the total uncertainty on
the energy resolution is at most <0.5 %, so the scale and resolution uncertainties are notour concern due to the fact that the uncertainty on the identification and isolation is muchlarger (∼ a few percent level).

4.2

Muons

4.2.1

Reconstruction

The muon reconstruction [147–150] is performed using both Muon Spectrometer (MS) andInner Detector (ID). The configuration of the MS and ID is described in Section 2.2.4 andSection 2.2.2, respectively. The triggering and coordinate measurement are provided by
the RPC in the barrel (|η| < 1.05) and by the TGC in the endcap (1.0 < |η| < 2.4). The
precision momentum measurement with a typical resolution of < 3 % over a wide pT range
and up to 10 % at pT = 1 TeV in the transverse plane is performed by the MDT in |η| <2.0 and by the CSC up to |η| < 2.7. An independent measurement of the muon momentum
is also performed up to |η| < 2.5 by the ID that provides coordinate measurements withhigh resolution for the track reconstruction inside the solenoid magnet. The reconstruction is performed according to the available information provided by the ID and MS (andcalorimeter). The following three are the most relevant algorithms:
stand-alone (SA) muons:the muon trajectory is reconstructed using only MS information. The direction of flight and the vetexing parameter (impact parameter) of themuon with respect to the interaction point (IP) are determined by extrapolating the MS
track back to the beam axis, taking into account the energy loss in the calorimeters.
combined (CB) muons: the muon trajectory is reconstructed independently in the
MS and ID. The statistical combination of the track parameters of the SA and ID muontracks is performed using the covariance matrices. The combined measurement improves
the momentum resolution and reduces the fake tracks including secondaries from heavy
flavor decays. This type of muons has the highest purity than other types of muons.
segment-tagged (ST) muons: the muon track is identified by the ID if the track extrapolated to the MS is associated with at least one track segment in the MDT or CSC.
The ST muons can recover the reconstruction eﬃciency of in particular the low pT muonssince the ST muons cannot be identified as CB muons.
The three types of muons are reconstructed based on Staco [151] algorithm and they are
relevant to the analysis. (There is another algorithm referred to as MuID [152] that provides muons refit by full hit information from the MS and ID.) In addition, there is anothertype of muons referred to as ‘calorimeter-tagged (CaloTag) muons’. The CaloTag muons
do not use the MS but instead use the calorimeter assuming that the muon candidate is aminimum ionizing particle (MIP). The CaloTag has the lowest purity than any others but
recovers the reconstruction eﬃciency in the region which is not covered by the MS. Given
that large fake background in the analysis, the CaloTag is not considered for now.

59

4.2 Determination of Lepton Selection

4.2.2

Isolation

Similar to the electron isolations described in Section 4.1.3, a substantial improvement is
expected from the isolations in the analysis.
Calorimeter isolation:
The calorimeter isolation is also used to reject background
dominated by the muons from heavy flavor decays. For the calorimeter isolation, a pileup
correction has been developed [15]. The correction is derived from the Z tag-and-probe
method (see Section 4.3.1). The isolation median distribution for ‘probe’ muons is fit using
a quadratic function of the number of primary vertices (NPV) in event. The functional
form can be seen in Equation 4.4.
coneXX
coneXX
ET,corrected= ET− a[η] NP2 V − b[η] NP V − c[η](4.4)

etcone40 (GeV)

etcone30 (GeV)

where a, b, and c are discrete functions of η which are obtained from the fitting the median
distribution as a function of NPV in bins of η. The ‘median’ is chosen rather than ‘mean’ toaccount for the non-gaussian tails on the isolation. To account for a decrease of the vertex
reconstruction eﬃciency at the higher NPV, there is a small quadratic term included in
the equation. The Etcone versus NPV can be seen in Figure 4.6. The diﬀerence in slope
between 2011 and 2012 is mainly due to the application of the noise suppression in 2012,
as well as the change of the muon definition through the years 2011 and 2012.
5
ATLAS Data, STACO combined
4
3

10
8

ATLAS Data, STACO combined

6
4

2

2011

1

2011

2

2012
0
0

5

10

15

20

25

30

2012
35

40

nVtx

0
0

5

10

15

20

25

30

35

40

nVtx

Figure 4.6: Quadratic calorimeter isolation corrections for 2011 and 2012. The diﬀerencein slope between 2011 and 2012 is mainly due to the application of the noise suppression in2012, as well as the change of the muon definition through the years 2011 and 2012. The
left and right figures show Etcone30 (∆R = 0.3) and Etcone40 (∆R = 0.4), respectively.
Track isolation: For muons the track isolation defined in Section 4.1.3 is also used. The
isolation eﬃciencies are presented later in Section 4.7.

4.2.3

Momentum scale and resolution

Muon momentum resolution and scale are determined from Z → µµ, J/ψ → µµ, andΥ → µµ resonances. A fractional momentum resolution is parametrized by the quadratic

60

4.3 Determination of Lepton Selection

sum of two terms:

σpT= a ⊕ b · pT ,
pT

(4.5)

where a is a constant term to account for the eﬀect of multiple scattering, and b indicatesthe intrinsic resolution from the spatial resolution of the detectors and any residual misalignment. When the momentum scale “s” is taken into account, the equation is rewritten
as follows:
C
C
pCor
= pM
· s(η)(1 + ∆a(η)G(0, 1) + ∆b(η)G(0, 1)pM
(4.6)
T
T
T ),
where G(0, 1) denotes a random seed with mean 0 and width 1, and the correction factorss(η), ∆a(η), and ∆b(η) are derived for a given η region. The correction of the muon
momentum is computed as the average of the ID and MS momentum correction weighted by
the inverse square of their resolution. The correction is determined by fitting the invariant
mass distribution using the template derived from the Z → µµ in simulation. It is foundthat the total uncertainty on the momentum scale correction is <0.2 %.

4.3

Tag-and-Probe

The eﬃciency is not measured as a single quantity but is factorized into individual eﬃciencies such as those related to triggers, reconstructions, identifications, and isolations:
ϵtotal = ϵrec. × ϵid. × ϵadd. × ϵtrig. ,(4.7)

where ϵtotal is the total eﬃciency of lepton, ϵrec. is the reconstruction eﬃciency given thepresence of the clusters (see Section 4.1.1), ϵid. is the identification eﬃciency with respect
to the reconstructed leptons, ϵadd. is the eﬃciency for additional cuts such as isolations andimpact parameters with respect to the reconstructed and identified leptons, ϵtrig. is trigger
eﬃciency with respect to fully identified leptons used in the analysis.
For the purpose of measuring those individual eﬃciencies from data, the tag-and-probe
method has been extensively used to select clean and unbiased samples from well-known
resonances. The most popular and widely used sample at the LHC is Z → ℓℓ resonancedue to its fairly large statistics even at lower pT (pT > 10 or 15 GeV) and its simplicity oftriggering without any bias. The tag-and-probe method can be further extended to much
lower pT (pT > 7 GeV for electrons and > 6 GeV for muons) with J/ψ → ℓℓ resonance eventhough the available statistics are quite limited due to the triggering with low pT leptons.
The tag-and-probe is also used to collect signal sample for the lepton optimization
where the eﬃciencies are measured for leptons with pT > 10 GeV that corresponds to the
lepton pT threshold used in the H→ W W ∗ → ℓνℓν analysis.

4.3.1

Tag and probe definition

As an example of the tag-and-probe method, one can consider the eﬃciency for electron
identification using Z → ee decays in which there are exactly two oppositely charged elec-

4.3 Determination of Lepton Selection

61

trons. One of the two electrons is firstly chosen as “tag”electron with very strict selection criteria. The other that passes minimal selection criteria is then considered as a“probe”electron candidate used for the eﬃciency measurement. Table 4.2 summarizes selection criteria for those electrons for identification eﬃciency measurement. Note that thedefinition of the probe changes according to the individual measurements.
Table 4.2: Definition of tag and probe electrons.
Tag electron selection in 2012cluster > 20 GeV· ET· |η| < 2.47 (excluding crack region 1.37 < |η| < 1.52)· track quality cut· cut-based Tight++ identification (see Section 4.1.2)· |d0 /σd0 | < 3 (d0 : transverse impact parameter w.r.t. primary vertex)· |z0 sin θ| < 0.4 mm (z0 : longitudinal impact parameter w.r.t. primary vertex)· Ptcone40/pT < 0.06 (track isolation with ∆R = 0.4)
· topoEtconeEt30/ET < 0.16 (calorimeter isolation with ∆R = 0.3)
· lower ET electron is removed if ∆R(electron, electron) < 0.10
· EF e24vhi medium1 || EF e60 medium1
Probe electron selection in 2012 (for identification eﬃciency)
cluster > 10 GeV· ET· |η| < 2.47 (excluding crack region 1.37 < |η| < 1.52)· track quality cut· (targeting) identification for numerators OR no identification for denominators· lower ET electron is removed if ∆R(electron, electron) < 0.10
· no trigger requirement

The primary single lepton triggers (EF e24vhi medium1 and EF e60 medium1) are used
to collect events from Z → ee, and are imposed on only tag candidates. While the triggers
are not required for probe candidates to avoid possible trigger bias from the requirements,
such as medium1, i (Ptcone20/pT < 0.10), and ET > 24 GeV on EF e24vhi medium1, thatmake the triggers tighter than the probe definition, otherwise the biased probes will end
up with higher eﬃciency in the measurement. Similarly the primary dilepton triggers suchas EF 2e12Tvh loose1 is not used in the measurement due to loose1 that also causes bias
on the probe definition.
It is possible that the probe candidates also pass the tag selection criteria at some rate,
turning the probe into another tag. This is not the case for the probes with ET < 25 GeV
since the trigger plateau threshold for the primary single electron trigger EF e24vhi medium1(ET = 25 GeV) is above the ET requirement for the probes. In other words, the tag andprobe are defined exclusively due to the trigger requirement in event. While if the probe
passes tag’s selection criteria with ET < 25 GeV, all possible tag and probe combinations

62

4.3 Determination of Lepton Selection

are taken into account, so more than one pair of the tag and probe electrons in event areconsidered for the measurement.

4.3.2

Background evaluation and systematic uncertainties

In order to ensure that the probes are likely real electrons from Z bosons, an invariant massmee for an oppositely charged pair of the probe and tag electrons is required to be within
the Z mass window defined as |mZ − mee | < 10 GeV. The cut on the invariant mass mee
significantly increases the purity of Z → ee events. However, even after the window cut,background electrons represented by hadrons faking electrons, electrons from heavy flavor
decays, and photon conversions (see Section 4.1.2), still contaminate mainly in the probe
samples. In case of the Z → ee tag-and-probe, the background electrons are dominated by
the W +jet background where a jet is misidentified as a probe electron. At smaller rate,
there also exists the QCD background, namely double fake background, where another jet
is also misidentified as a tag electron paired with the jet faking probe. Figure 4.7 showsmee distributions with probe ET = 10-15 GeV and ET = 25-30 GeV before identification
requirements.

Figure 4.7: Invariant mass mee distributions for pairs of the probe and tag electrons, where
no identification cut is applied to the probe electrons. The ET cut is applied to the probe
electrons: 10-15 GeV (left) and 25-30 GeV (right).
The backgrounds significantly increase with lower probe ET . Given that the eﬃciency
measurement is made in a region |mZ − mee | < 10 GeV, the signal-background ratio S/B
is less than 50 % for the probe ET = 10-15 GeV, so the backgrounds must be subtracted as
properly as possible using signal and background templates (or combined fits of backgroundand signal analytical models to data). For the signal template, Z → ee events are generated
in simulation. In order to avoid selecting undesired pairs of tag and probe electrons insimulation, for instance a pair of a jet faking probe and a tag from Z → ee, and theother electron from Z → ee is out of acceptance, generator-level information is also used
to select electrons originating only from Z → ee decays when forming the template. For

63

4.3 Determination of Lepton Selection

the background template, probes are chosen with two additional requirements that enhance
jets/photons faking electrons and significantly reduce real electrons from Z decays:• cut-based loose++ veto• same charge as the tag electron
Both signal and background templates are normalized to data simultaneously in theregion 60 < mee < 120 GeV. The normalized background are then subtracted from datawhen counting the number of probes for the eﬃciency.
In order to assess systematic uncertainties on the background estimation, several variations are considered:• isolation requirements for tag electrons are varied to Ptcone20/pT < 0.10 that is identical to the isolation cut on the trigger. The variation can change the compositionof the backgrounds between the W +jets and QCD backgrounds since the tighter isolation on tag electron possibly reduce the QCD background but enhance more theW +jet background in the background template. So the variation results in the shapevariation for the background template.
• Z mass range is also varied to be wider |mZ −mee | < 20 GeV and to be narrower |mZ −mee | < 5 GeV, which potentially increases/decreases the background contaminationin the signal region used for the measurement. The wider mass range is more sensitive
to the background mis-modeling.
• fit range for the signal and background templates are varied to be 70 < mee < 140
GeV, keeping χ2 /ndof value reasonable (less than 4). The variation can change theoverall normalization of the background template.
All those uncertainties are added in quadrature to compute the total systematic uncertainty.

4.3.3

Eﬃciencies and scale factors

The eﬃciency is finally measured using the selected probes as the fraction of them. For theidentification eﬃciency, only acceptance cuts (ET > 10 GeV and |η| < 2.47) are applied to
the reconstructed electrons for denominators, whereas the identification cut is also added
to the denominator selection criteria for numerators. Then the eﬃciency can be written as
follows:
ϵdata
id. =
ϵMC
id. =

bkg
data
− Nrec.+id.
Nrec.+id.
data − N bkg
Nrec.
rec.
MC
Nrec.+id.
,
MC
Nrec.

,

(4.8)
(4.9)

64

4.4 Determination of Lepton Selection

where Nrec. is the number of denominators and Nrec.+id. is the number of numerators. The
background subtraction is not made to the simulated Z → ee events but the generatorlevel matching like the signal template is applied to select real electron pairs. Finally any
diﬀerence in eﬃciency between data and simulation are corrected for by taking the ratio of
those eﬃciencies as scale factor:(i,j)

data(i,j)

SFid. = ϵid.

MC(i,j)/ϵid.

(where i : ET bin, j : η bin).

(4.10)The eﬃciencies and corresponding scale factors are evaluated as a function of ET and η, andall scale factors from the individual measurements (reconstruction, identification, isolationetc) are put together for the final electron eﬃciency used in the analysis.

1

Efficiency

Efficiency

Figure 4.8 shows eﬃciencies for electron identification comparing with both cut-based
and likelihood identifications. The eﬃciency for the VeryTight likelihood is very close tothat for the cut-based Tight++.

0.95
0.9
0.85

0.6

0.9

0.8

|η| < 2.47

0.75

0.65

0.95

0.85

0.8

0.7

1

LooseLLH
2012
ATLAS Preliminary= 20.3 fb∫sL= dt8 TeV
Z→ ee
-1

0.75

LooseLLH, MC

0.7

VeryTightLLH

0.65

VeryTightLLH, MC

0.6

10 20 30 40 50 60 70 80 90 100
ET [GeV]|η| < 2.47
Loose
2012
LooseLLH
ATLAS Preliminary
Multilepton
Medium-1
L dt = 20.3 fb
Tight
VeryTightLLH
s = 8 TeV Z→ ee∫

10 20 30 40 50 60 70 80 90 100
ET [GeV]Figure 4.8: Comparison of likelihood identification eﬃciency between data and simulation
as a function of ET (left) and identification eﬃciency for the various cut-based and LH
identifications as a function of ET (right) [153].

4.4

Optimization Strategy

4.4.1

General Strategy

In order to maximize the experimental sensitivity, lepton optimization has been performed
focusing on identifications, isolations, and impact parameters. Since the W +jets background is significant in the signal region and has relatively large systematic uncertainty,
the optimization criteria below, are defined explicitly including the eﬀect of the W +jets

65

4.4 Determination of Lepton Selection
systematics on the significance:NSigsignif = √,NSig + NBkg(non−Wjet) + NBkg(Wjet) + ∆2(non−Wjet) + ∆2Wjet(4.11)

where NSig is signal yield, NBkg(non−Wjet) is total background yield without W +jets, NBkg(Wjet)
is W +jets yield, ∆i(non−Wjet) is the impact of the total backgrounds without W +jets(NBkg (non − Wjet)×σnon−Wjet ), and ∆Wjet is the impact of the W +jets background (NBkg (Wjet)×
σWjet ). These yields and uncertainties are obtained from the previously published results [3],adding several improvements that have been considered for this updated analysis such as
dilepton triggers and lowering lepton pT (plead= 22 GeV and psubT
T = 10 GeV). Equation 4.11
can be rewritten to be more complete form as:
signif = √ϵ × NSig
ϵ × (NSig + NBkg(non−Wjet) ) + f × NBkg(Wjet) + Unc(ϵ, f)2 + Corr(ϵ, f),(4.12)
Unc(ϵ, f)2 =(ϵ × σ(non−Wjet) NBkg(non−Wjet) )2 + (f × σWjet NBkg(Wjet) )2 ,m
∑ j ∑Nik )2 ,Corr(ϵ, f)2 =(Ni ×i(4.13)(4.14)j̸=k

where(I) ϵ is a ratio of the signal (either signal or non-Wjet) eﬃciency at the selection point
being considered to the pre-optimized eﬃciency,(II) f is a ratio of the background (W +jets) eﬃciency at the selection point being considered to the pre-optimized background eﬃciency that approximates the ratio of the
W +jets fake factors,(III) σWjet is uncertainty on the W +jets, and σ(non−Wjet) is uncertainty on the non-Wjet.
The non-Wjet uncertainty is defined for each background,(IV) Unc(ϵ, f) is total background uncertainty where the W +jets is scaled by f , and the
non-Wjet is scaled by ϵ,(V) Corr(ϵ, f) is correlation term between signal regions 4 as a function of ϵ and f , whichmakes the optimization more realistic. In this term i denotes either W +jets or nonWjet background, j is index of each signal region, and m is the number of signal
region. Without this term, the systematic uncertainty will end up with zero whensplitting into infinite number of signal regions.
4the signal region is split into two mℓℓ bins (10 < mℓℓ < 30, 30 < mℓℓ < 55 GeV), and four psubbins
T(10-15,15-20, 20-25, 25- GeV).

66

4.4 Determination of Lepton Selection

The significance is computed in two-dimensional map of isolation variables “Etcone vsPtcone” for each signal region. The two-dimensional optimization is useful as it can take into
account the correlation automatically between the isolations. The computed significancesfor each signal region are finally combined and the optimal operating point is extracted forthe analysis. The optimization is made for each sub-leading lepton pT (psubT ) bin because thesubimpact of the W +jets background is strongly dependent on pT . At lower psub
T , the W +jets
background increases rapidly, while the W +jets background remains small at higher psub
T .
This optimization procedure is extremely powerful as it can simulate well-approximatedanalysis sensitivity without full machinery, while taking into account the correlation between
the isolations (as well as the correlation between the signal regions). This optimization procedure is applied to both electron and muon optimizations. Given that eµ and µe channels
are the most sensitive channels in the analysis, only those two channels (µe for electrons,
and eµ for muons) are considered in the optimization.
There is one limitation in this method due to the fact that all background processes
except for the W +jets are considered as true-lepton backgrounds. This assumption is notaccurate for some background like the W + γ background where photon is faking electron.
In practice, since the conversion rate is like neither ϵ nor f , it would be better to reduce theconversion background as much as possible. This will be a crucial point when considering
the identification for higher pT (see Section 4.5.1).

4.4.2

Signal and background eﬃciencies

To define ϵ and f , it is necessary to measure signal and background eﬃciencies for eachisolation operating points. The eﬃciencies are measured using signal and background samples. The definition of the samples are summarized in Table 4.3.
The signal eﬃciency is measured in data using Z tag-and-probe method (see Section 4.3.1) with a narrow Z mass range defined as |mℓℓ − mZ | < 10 GeV in order tosuppress the contamination of background leptons (No background subtraction made in
the optimization).
The background eﬃciency is measured in data using multijet/QCD-enriched samples
collected with e/gamma and MCP supporting triggers that are also used in the di-jets fakefactor evaluation (see Section B.1). To further reduce the contamination of true leptons
from Z → ℓℓ or W → ℓν decays, a event veto referred to as ‘EW veto’ is applied to thebackground samples. The EW veto is defined as:• |mℓℓ − mZ | > 15 GeV for leptons from Z → ℓℓ decays• mT (lep, Emiss
T ) < 30 GeV for leptons from W → ℓν decays
The background contamination is negligibly small after the EW veto. Measured signal
eﬃciency and background rejection are shown for each psub
T bin (10-15, 15-20, 20-25, 25-) in67

4.5 Determination of Lepton Selection

Table 4.3: Definition of signal and background samples.
Electron selection in 2012cluster > 10 GeV· ET· |η| < 2.47 (excluding crack region 1.37 < |η| < 1.52)· track quality cut· being considered identification (see Section 4.1.2)· |d0 /σd0 | < 3 (d0 : transverse impact parameter w.r.t. primary vertex)· |z0 sin θ| < 1.0 mm (z0 : longitudinal impact parameter w.r.t. primary vertex)· overlap removals (see Section 6.3.3)· Signal: EF e24vhi medium1, EF e60 medium1, and EF 2e12Tvh loose1 triggers· Background:EF g24 etcutEF g20 etcut, EF e11 etcut, and EF e5 etcut triggers· being considered isolation selection (Etcone and Ptcone)
Muon selection in 2012
· pT > 10 GeV· |η| < 2.50
· track quality cut· |d0 /σd0 | < 3 (d0 : transverse impact parameter w.r.t. primary vertex)· |z0 sin θ| < 1.0 mm (z0 : longitudinal impact parameter w.r.t. primary vertex)· overlap removals (see Section 6.3.3)· Signal: EF mu24i tight, EF mu36 tight, and EF mu18 tight mu8 EFFS triggers· Background:EF mu6 and EF mu15 triggers· being considered isolation selection (Etcone and Ptcone)

Figure 4.9 and 4.10. ϵ and f are finally computed by taking the ratio of the two operating
points, being scanned operating point and Moriond operating point.

4.5

Electron Optimization

4.5.1

Identification

The identification optimization is made by comparing either the (Very) Tight likelihood or
cut-based Medium++, to the cut-based Tight++ in a given isolation operating point. The
signal eﬃciency ratio ϵ in Equation 4.11 can be expressed explicitly including identificationand isolation terms as follows:
ϵ=

eﬀ op
eﬀ op
eﬀ op
sub
iso
id
∼
×
pre
pre ,
eﬀ pre
eﬀ
eﬀ
iso
sub
id

(4.15)

where superscript ‘op’ is a selection operating point being considered and ‘pre’ is the selection operating point used in the previous result. Only sub-leading lepton is considered68

4.5 Determination of Lepton Selectionin the low ET optimization, and muon eﬃciencies are fixed. Similarly, f can be written as
follows:
f=

eﬀ op
eﬀ op
eﬀ op
sub
id
iso
.
pre ∼
pre ×
eﬀ subeﬀ id
eﬀ preiso(4.16)

Note that the correlation between the identification and isolation is not taken into account in the Equations above. Since it is diﬃcult to make signal sample without the identification requirement as discussed in Sections 4.3.1 and 4.4.2. For the identification term,
signal and background eﬃciency ratios is obtained from the identification eﬃciency measurement, by taking the ratio of “being considered” identification eﬃciency to the cut-based
Tight++ eﬃciency. Measured signal and background ratio is summarized in Table 4.4. The
numbers are calculated taking into account the small eﬀects caused by the diﬀerence in input
variables. 5
Table 4.4: Signal eﬃciency and background eﬃciency ratio for electron identification.
Signal eﬃciency ratio w.r.t. cut-based Tight++
ET [GeV] LH Tight/ Tight++ LH Very Tight/ Tight++
10-15
1.18
1.03
15-20
1.13
1.03
20-25
1.12
1.02
25-

Medium++/ Tight++
1.19
1.14
1.12
1.11

Background eﬃciency ratio w.r.t. cut-based Tight++
ET [GeV] LH Tight/ Tight++ LH Very Tight/ Tight++ Medium++/ Tight++
10-15
1.09
0.83
1.59
1.16
0.89
1.59
15-20
20-25
1.16
0.87
1.55
251.605|d0 /σ − d0 | cut is not included in the cut-based. This is explicitly added in the cut-based Tight++ toperform fair comparison. Also the cut-based Medium++ is modified to include conversion flag and B-Layer
hit requirements at |η| > 2.37. With this additional η requirement full η acceptance used in the analysis iscovered.

69

0.82240.84740.86750.88340.89600.90600.9146

0.78380.82040.84520.86520.88110.89360.90350.91200.73670.78120.81770.84240.86230.87800.89040.90030.90870.3 0.6153

0.66130.73390.77840.81460.83930.85910.87450.88680.89650.90470.61210.65790.73020.77440.81040.83490.85450.86990.88200.8916

0.89980.60820.65380.72570.76940.80520.82940.84880.86390.87590.88550.89350.25 0.6033

0.35 0.8333

0.83090.81810.78040.74570.71580.68810.65950.63250.60450.57810.55270.8206

0.78330.74890.71940.6922

0.66400.63710.60980.58370.55860.83590.82310.78640.75250.72330.69650.66840.64180.61470.58900.56470.3 0.8383

0.8256

0.78910.75550.72670.70010.6726

0.64630.61940.59400.57010.84090.8282

0.79240.75940.73090.70450.67760.65200.62560.6006

0.57730.84320.83080.79580.76330.73540.70920.68270.6576

0.63220.60800.58520.25 0.8464

0.64840.71950.76280.79820.82210.84130.85620.86800.87740.88520.59770.64240.71280.75570.79070.81420.83300.84760.85940.86860.87620.2 0.5897

0.63380.70320.74550.77990.80260.82120.8356

0.84700.85590.86340.57950.62280.69070.73220.76580.84010.84740.56730.60990.67610.71660.74940.7712

0.78870.80240.81300.82130.82820.59440.6582

0.69730.72890.74980.76670.77980.78990.79780.80440.15 0.8710

0.53290.57280.63390.67130.70170.72170.73770.75020.75970.76700.77330.1 0.5081

0.54600.60410.63970.66840.68720.70220.71400.72280.72940.47800.5136

0.56820.60130.62770.64480.6586

0.6696

0.67770.68380.44020.47290.52270.55280.57690.59210.60450.61430.62150.62700.63160.90670.46580.49230.51350.52700.53780.54650.55290.5576

0.56160.05 0.9190

0.89940.42180.91250.89550.87930.86780.85550.84440.83420.82500.81680.80840.3597

0.39680.41950.43750.44880.45780.46500.47060.47440.47750.93310.92750.91340.90040.89080.88100.8716

0.86370.85630.84950.84320.33500.78810.80610.82030.83150.83420.80010.76840.84990.83790.80480.77360.74710.72290.69800.67410.65110.62870.60730.2 0.8547

0.84310.81090.78050.75490.73170.70770.6846

0.6626

0.64150.62120.86070.84970.81880.78970.76560.74290.7201

0.69800.67760.6577

0.63840.86550.85460.82490.79760.77470.75270.73100.71050.69120.67270.65460.86070.83250.8062

0.78490.76410.74350.72410.70630.68950.87850.86890.84230.81710.79730.77740.75850.74100.72480.70960.69440.73510.1 0.8873

0.87830.85400.83110.81390.7956

0.77830.76230.74780.73490.72100.68900.89480.88680.86450.84360.82810.81150.79630.78210.76920.75760.74530.87960.86090.74100.84730.71560.83280.68970.81940.66530.80680.64070.79520.61730.78520.59510.67250.77480.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22

pTcone40/Et

pTcone40/Et

0.35 0.7483

0.74940.82910.82790.87720.90790.92800.94100.95000.95640.96130.96470.96730.74710.82650.87570.90630.92640.93930.9482

0.9546

0.95940.96280.96540.3 0.7454

0.82460.87850.87370.90920.90410.92940.9241

0.94240.93700.95150.94590.95800.95230.96290.95700.96630.9604

0.96890.96290.74340.82240.87130.9016

0.92150.93430.9432

0.9494

0.9541

0.95740.95990.74110.81980.86850.8986

0.91840.93100.93970.94590.9506

0.95380.95620.81630.8646

0.89440.91410.9266

0.9352

0.94130.94580.94900.95130.25 0.7380

topoEtCone30/Et

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22

0.78080.74320.70880.6731

0.63870.60920.58170.54800.52090.49880.47330.74750.71340.67850.64450.6154

0.58870.55620.52900.50700.48140.74980.71570.68090.64680.61850.59180.56000.53330.5116

0.48680.3 0.7901

0.75370.72040.68590.65180.62430.59840.56740.54180.79280.75640.72390.69060.65690.63010.60460.57400.55000.53020.50580.79630.25 0.8021

0.76070.72850.69600.6627

0.63630.61150.58090.55810.53990.51590.76840.73780.70720.67540.64950.62510.59530.57320.5562

0.53330.35 0.7847
0.78700.52130.49690.73320.81100.85890.88850.90780.92020.92870.9346

0.93900.9421

0.94440.80710.77420.74440.71610.68550.66000.63670.6092

0.58830.57240.2 0.7271

0.80430.85170.88080.89990.91200.92030.92610.93040.93340.93550.2 0.8133

0.78080.75170.7242

0.69400.66960.64760.62200.6026

0.58680.56660.71970.79600.84270.87150.89020.90200.91010.91570.91990.92260.92470.81950.78970.76180.73550.70680.6844

0.66230.63830.62080.60610.58640.70870.55030.78400.61150.82980.85790.87610.88750.89540.90080.90470.90740.90930.82730.77380.74830.72080.70020.68050.65840.64250.62900.81250.83980.85730.86820.87580.88080.88440.88680.88870.15 0.8339

0.7986

0.76800.80710.78500.76070.73510.71650.69870.6782

0.66380.65140.67440.74570.78870.81510.83170.84210.84930.85390.85730.85950.86120.84160.81640.79510.77270.74860.73280.71610.69790.68510.67430.66270.1 0.6479

0.71610.7571

0.78230.79810.80770.81430.81860.82170.82370.82510.1 0.8521

0.82880.80870.78890.76800.75370.73900.72390.71220.70330.6936

0.61190.67610.71460.73790.75240.76100.76710.77080.77360.77530.77660.86480.84310.82570.80790.79090.78080.76680.75600.74550.73700.72930.56420.62320.6586

0.67950.69240.70010.70530.70850.71090.71230.71330.84740.7971

0.78810.58490.60290.61390.62040.62480.62760.62950.6307

0.63150.05 0.8981

0.86170.55360.88460.87410.86250.84970.84240.83190.82570.81990.81560.81100.46350.48940.50420.51270.51790.52150.5236

0.52510.52590.52660.91790.90740.89890.88960.88070.87530.86750.86410.86020.85670.85280.15 0.6945

0.05 0.5016
0.42020.87840.83310.81870.80980.78040.77270.63790.76610.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22

pTcone30/Et

pTcone30/Et

0.35 0.7794

0.77990.87310.9167

0.94150.95630.9656

0.97200.97630.97940.9816

0.98330.87250.91600.94080.9556

0.96490.97130.97550.97860.98070.98240.77870.87180.91520.93990.95470.96390.97030.97450.9776

0.97970.98130.3 0.7779

0.87080.91410.93880.95350.96280.9691

0.9732

0.97630.97840.98000.77690.86970.91290.93750.9521

0.96130.9676

0.97170.9747

0.97680.97840.77550.86800.91110.93570.95030.95940.9656

0.96970.97270.9747

0.97630.25 0.7737

topoEtCone30/Et

topoEtCone30/Et

0.78580.7391

0.66360.05 0.3928

topoEtCone30/Et

0.74100.66580.15 0.5528

0.35 0.7483

0.74640.69810.65470.62080.57940.54740.51600.48090.45140.41560.39050.69990.65720.6246

0.58320.5512

0.52100.48650.45700.4212

0.39860.74950.70180.66040.6277

0.58630.5556

0.52540.49090.46200.42690.4055

0.3 0.7527

0.7062

0.66480.63280.59130.5606

0.53110.49650.46830.43440.41430.75460.70810.66730.63780.5976

0.56750.53800.50470.47710.44440.42560.75640.71120.67170.64340.60450.57560.54740.51480.48710.45700.43820.25 0.7577

0.86600.90890.93330.94780.95680.96300.96710.97000.97200.97360.71500.67550.64720.60890.58130.55430.52290.49650.47020.4526

0.77110.86310.90570.93000.94430.95330.95940.96330.96620.96820.96970.75960.71750.6786

0.65100.61390.58820.56120.53170.50530.4796

0.46390.2 0.7678

0.85930.90160.92580.93990.94880.95470.9586

0.96140.96330.96480.2 0.7646

0.72320.68490.65850.62270.5976

0.57120.54240.51730.49150.47650.76270.85360.89550.91940.93330.94200.94780.9516

0.95440.9561

0.95750.76900.72820.69180.66790.63340.60830.58250.5556

0.53230.50850.49340.75580.84580.88720.91060.92420.93270.9384

0.94200.9446

0.94630.94770.77280.69680.67360.64030.61580.59130.56560.54490.52290.83410.87480.89770.91100.91910.9246

0.92800.93040.93200.93320.15 0.7797

0.73320.74260.70750.68610.65600.63340.6114

0.59130.57250.55300.54110.73110.81750.85720.87940.89220.90000.90510.90830.91050.91190.91300.78970.75390.72000.69990.67480.65410.63470.61640.6001

0.58380.5756

0.1 0.7089

0.79240.83060.85170.86380.87120.87590.87890.88090.88210.88310.1 0.8010

0.76960.73890.72070.69680.6792

0.66480.64850.63400.6196

0.61640.67700.7562

0.79220.81190.82310.82980.83400.83660.83830.83940.84020.80980.78150.75270.7376

0.71690.70180.68990.67610.66600.65220.65030.63070.70390.73670.75450.76450.77030.77400.77610.77750.77850.77920.82860.77780.76400.74640.73320.72440.71250.70620.6962

0.69490.65590.67110.67950.68440.68740.68920.69030.69100.69150.05 0.8462

0.80160.62730.82420.80290.79350.77780.76840.76330.75520.75020.74200.7407

0.52160.5446

0.55670.56330.56710.56940.57070.5716

0.57210.57240.87820.85940.84310.83680.82550.82110.81800.81230.80980.80540.80480.15 0.7456

0.05 0.5626
0.4680

topoEtCone30/Et

0.66750.6175

topoEtCone30/Et

0.62110.35 0.6195

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22

pTcone30/Et

pTcone30/Et

0.89420.95690.9794

0.99400.99600.99700.99770.9981

0.99830.95670.97930.9891

0.99390.99580.99690.99750.99790.99820.99840.9566

0.97910.98890.99370.9956

0.99670.99730.99770.99800.99820.3 0.8937

0.95640.97890.9887

0.99350.9954

0.99650.9971

0.99750.99780.99790.89350.9561

0.97870.9884

0.99320.9951

0.99620.99680.99720.9974

0.9976

0.89320.95580.97830.98800.99280.99470.99580.9964

0.99680.99700.99720.35 0.8940
0.89390.25 0.8928

0.98920.99850.73290.68330.64400.60230.56500.5262

0.49250.4606

0.42820.39550.36360.68490.64560.60430.56700.52880.4956

0.46390.43170.39930.36790.68690.64790.60680.56980.53250.4996

0.46850.43710.4056

0.3 0.7358

0.68780.64960.60930.57280.53630.50440.47430.4436

0.41240.38160.73810.69040.65290.6136

0.57790.54220.51150.48220.45300.4236

0.39430.74110.69490.65840.62000.58520.55080.52060.4922

0.46370.43520.40660.35 0.7339
0.73530.25 0.7443

0.95530.97780.98750.99230.99420.99520.99580.99620.99650.9966

0.8922

0.95470.97710.98680.9916

0.9934

0.99450.99510.9954

0.99570.99580.2 0.8914

0.9537

0.97610.98580.99050.9924

0.9934

0.99400.9944

0.9946

0.99480.8901

0.9524

0.97470.98430.98900.99080.99180.9924

0.9927

0.99300.88810.9502

0.97240.98190.98650.98830.98930.98980.99020.99040.99050.9464

0.9684

0.97780.98240.98420.98510.9856

0.98590.98610.98630.15 0.7672

0.87900.9401

0.96170.97090.9754

0.9771

0.97800.97850.97880.97890.97900.86890.92900.95010.95900.96320.96480.9656

0.96610.96640.96650.96660.85050.90880.92910.9374

0.94130.94280.9435

0.94390.9441

0.94430.94430.81620.87140.89030.89780.90130.90250.90310.90350.90360.90370.90380.80100.81740.82380.82650.82750.82800.82820.82840.82840.82850.05 0.8393

0.66910.68170.68650.68840.68910.68940.68960.68970.68970.68980.87110.15 0.8848
0.1

0.50910.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22

topoEtCone30/Et

topoEtCone30/Et

4.5 Determination of Lepton Selection

0.05 0.7513
0.62880.37440.69800.66280.62580.59130.55770.52820.50160.47460.44790.42110.74790.7026

0.6684

0.63270.59950.56730.54010.51480.48970.46560.44090.2 0.7507

0.7066

0.67310.63970.60830.57770.5516

0.52850.50450.48290.45990.99310.1

0.75500.71240.68050.64830.61950.59090.56620.54570.52440.50470.48490.76010.71880.68890.6584

0.63240.60550.58240.56430.54580.52920.51250.72810.69980.67110.64810.62480.60330.58830.5724

0.55840.77680.74010.71420.68890.66740.64660.62910.6166

0.60320.59140.57950.78620.75270.72960.70790.6896

0.67170.65670.64610.63600.62710.61670.80030.77070.75090.73250.71680.66880.66100.81880.79250.7761

0.76310.75120.74050.73170.7266

0.72130.71670.71150.81630.8024

0.79370.78490.77830.77200.76850.76420.76090.75710.85330.84450.83990.83530.83170.82820.82620.82420.82260.82010.70210.69070.68300.67550.54490.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22

pTcone30/Et

pTcone30/Et

Figure 4.9: Electron signal eﬃciency (left) and background rejection (right) after theidentification applied in µe channel. Top of them are for 10-15, 2nd for 15-20, 3rd for 20-25,
and the bottom for > 25 GeV.

0.35 0.7234

0.72410.72410.7386

0.77610.80610.82550.83940.85020.85990.86830.72340.72340.73790.77540.80530.82460.83840.84920.85880.86720.72250.72410.72250.72250.73680.77430.80410.82340.83720.84790.85750.86590.72140.72140.72140.73580.77310.80290.82210.83590.84670.85620.86440.72000.72000.72000.73430.77150.80110.82020.83400.84460.85410.86230.71840.71840.3

0.92160.88890.87330.86010.84640.83040.81590.92260.92260.90910.89020.87490.86180.84830.83250.81830.92400.92400.91080.89220.87710.86420.85100.83550.82150.8071

0.3 0.9251

0.92510.9251

0.91220.89390.87900.86650.85340.83810.82440.81040.92670.92670.92670.91410.89630.88180.86950.85680.84180.82840.81470.92810.90800.80100.8036

0.71840.73270.76980.79920.81820.83190.84250.85190.86010.92810.91600.89860.88450.87240.85990.84550.83260.81920.73070.7676

0.79690.81580.82930.83990.84920.85720.25 0.9298

0.92810.71640.92980.92980.91820.90130.88740.8756

0.86350.84950.83690.82400.71340.71340.72760.76430.79330.81210.82550.83590.84510.85310.93200.93200.93200.92080.90440.89110.87970.86810.85460.84240.82980.2 0.7096

0.70960.7096

0.72370.76010.78900.80750.82070.83100.84010.84800.2 0.9344

0.93440.93440.92360.90770.89480.88370.87250.85990.84840.83650.70430.70430.70430.71820.7542

0.78280.80100.81410.82420.83320.84090.93680.93680.93680.92650.91140.89890.88840.87800.86600.85500.84370.69770.69770.69770.71150.74700.7751

0.79300.80590.81580.82450.83210.9396

0.9396

0.93960.92990.91580.90410.89420.88430.87310.86270.85210.68870.68870.70230.73720.7646

0.78210.79470.80430.81280.81990.15 0.9429

0.94290.94290.93400.92060.90950.90050.89110.88070.87090.86110.6756

0.6756

0.6756

0.68880.72280.74950.76640.77850.78780.79590.80280.94680.94680.94680.93870.92650.91630.90780.89920.88970.88060.87210.1 0.6584

0.65840.65840.67120.70380.72940.74560.75710.76580.77340.78000.1 0.9504

0.95040.9504

0.94300.93180.92250.91480.90730.89890.89080.88350.63330.63330.63330.6456

0.67620.70060.71580.72630.73450.74150.74750.95530.95530.95530.9486

0.93860.93070.92370.91730.91040.90350.89730.5976

0.5976

0.59760.60910.63750.65990.67380.68310.69050.69690.70230.96100.96100.95550.94710.94070.93480.92940.92340.91760.91260.54790.54790.5581

0.5836

0.60330.61540.62360.63000.63550.64020.05 0.9678

0.96100.96780.96780.96340.95690.95150.9471

0.94320.93900.93440.93070.47750.47750.48610.50730.52350.53340.54000.54520.5496

0.5532

0.97490.97490.97490.97180.96750.96370.96080.95790.9551

0.9522

0.94970.47750.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22

pTcone40/Et

pTcone40/Et

0.8331

EtCone30/Et

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22

0.88920.88920.88610.86230.84050.82170.80310.78440.76490.74580.72730.89080.88770.86420.84280.82430.80600.7876

0.76860.74970.73170.89260.88950.86650.84540.82720.80930.79120.77260.75430.7366

0.3 0.8946

0.8946

0.89160.86900.84830.83050.81290.79520.77700.75910.74200.89700.89700.89400.87190.85170.83430.81710.79990.78220.76470.89950.89950.89670.87510.85550.83860.82190.8052

0.78810.77130.75510.90250.89980.87880.85980.84350.82730.8112

0.79480.7786

0.76320.90570.90570.90310.88290.8646

0.84880.83320.81790.80220.78670.77190.35 0.8326

0.83310.84550.88430.90610.91860.92770.93470.9402

0.94430.94760.83260.84500.88370.90540.91790.92700.93400.9394

0.94350.94680.83180.83180.84420.88290.90460.91700.92610.93300.9384

0.9426

0.94580.3 0.8310

0.83100.84330.88200.90350.91600.92500.93190.93730.94140.94460.82980.82980.84210.88060.90220.9146

0.92350.93040.93580.93980.94300.82850.82850.84080.87920.9006

0.91300.92190.92870.93400.93800.94110.82690.83910.87740.89870.91100.91980.9266

0.93190.93590.93890.25 0.9025

0.82480.82480.83700.87510.89630.90850.91730.92400.92920.93310.93600.2 0.8219

0.82190.25 0.8269

0.35 0.8908
0.89260.74810.92540.92930.93220.2 0.9094

0.90940.90690.88750.86990.85490.84010.82550.81070.79600.78200.81810.81810.83020.86780.88860.90050.90910.91560.92050.92430.9271

0.91340.91340.91100.89270.87600.86170.84780.83400.82000.80630.79320.81250.81250.8246

0.86170.88220.89400.90230.90870.91360.91710.91980.91770.91770.91550.89820.88250.86920.85620.84340.83030.81760.80570.83410.87190.89290.90500.91370.92040.80520.81710.85370.87380.88530.89340.89960.90430.90770.91020.15 0.9230

0.92300.92100.90480.89010.87770.86560.85400.84210.83050.79400.79400.80570.84150.86100.87210.88000.88580.89030.89350.89580.92880.92880.92690.91220.89890.88770.87680.86650.85590.84570.83610.1 0.7778

0.77780.78910.82370.84250.85300.86050.86600.87010.87310.87510.1 0.9352

0.93520.93350.92040.9086

0.89870.88920.88000.87090.86200.85380.75290.75290.76370.79660.81440.82430.83110.83620.83980.84240.8442

0.94250.94250.94100.92960.91950.91110.90310.89520.88750.88020.87330.71430.71430.72440.75490.77100.78000.78610.7904

0.7936

0.79570.79720.95080.94960.94030.93200.92530.91870.91230.9061

0.66340.69040.70420.71180.71690.72040.72290.72460.72570.05 0.9604

0.95080.65430.96040.95950.95230.94600.94090.93590.93120.92680.92290.91910.56020.56770.58950.60040.60610.60980.61240.61420.61530.6161

0.97100.97100.97040.96520.96080.95750.95430.9511

0.94810.9457

0.94330.15 0.8052

0.05 0.6543
0.56020.89530.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22

pTcone30/Et

pTcone30/Et

0.85590.85590.90310.93050.94450.95420.96090.96550.96900.9717

0.97380.85540.90270.93000.94400.95370.96030.96500.96850.9711

0.97320.85490.90210.9294

0.9434

0.95310.95970.96430.96780.97050.97250.85430.85430.90140.9287

0.94270.95230.95890.96350.96700.9696

0.97160.85360.85360.90070.92780.94180.95140.95800.9626

0.96600.96860.97060.85260.8526

0.8996

0.92680.94070.95030.95680.96130.96480.96730.96930.35 0.8554
0.30.90050.81970.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22

0.85490.25 0.8515

EtCone30/Et

EtCone30/Et

0.92160.92400.71640.05 0.5479

EtCone30/Et

0.92160.35 0.9226

0.71340.25 0.7164

0.15 0.6887

0.91180.91180.81160.79020.91310.89380.87160.85360.83400.8144

0.79340.77350.75260.73220.91450.91450.89570.87380.85620.83690.81770.79710.77780.75730.7376

0.3 0.9160

0.91600.89750.87620.85890.84010.82130.8012

0.78230.76240.74310.91760.9176

0.89960.87880.86200.84370.82550.80600.78770.76830.74980.91930.91930.9016

0.88130.86510.84740.82970.81090.79320.77460.75660.35 0.9131

0.25 0.9216

0.89230.86970.85140.83140.77000.74870.72800.85150.89840.92550.93930.94890.95540.95990.96320.96580.96770.92160.90450.88470.86910.85200.83500.81680.79980.78190.76480.85020.85020.89700.92390.93770.9472

0.95370.9581

0.96140.96400.96580.92390.92390.90750.88850.87360.85730.84100.82360.80720.79010.77390.2 0.8484

0.84840.8951

0.92200.93570.9451

0.95150.95590.95920.9616

0.96350.2 0.9265

0.92650.91070.89280.87850.86300.84760.83120.8156

0.7996

0.78430.84600.84600.89250.91920.93280.9422

0.94840.95270.95590.95830.92930.92930.91430.89740.88390.86930.85490.83980.82540.8106

0.79650.84270.84270.88890.91540.92890.9381

0.9442

0.9484

0.95150.95390.95550.93280.91850.90270.88990.87630.86300.84910.83570.82220.80910.88370.90990.92320.93220.9382

0.94220.9452

0.9474

0.94890.15 0.9368

0.93280.83800.93680.92370.90910.89750.88530.87320.86050.84870.83670.82520.83060.83060.87570.90150.91440.92320.92890.93280.93550.9376

0.93900.94150.94150.92940.91610.90580.89470.88390.87260.86230.85170.84180.1 0.8192

0.81920.86340.88840.90090.90930.91480.91830.92090.92270.15 0.8380

0.96010.92400.1 0.9467

0.94670.93580.92400.91510.90540.89610.88640.87750.86870.86060.80010.80010.84270.86680.8786

0.88630.89140.8946

0.89680.89850.89950.9526

0.9526

0.94330.93300.92550.91740.90970.90170.89480.88790.88150.76730.76730.80740.82970.84040.84740.85180.85450.85640.85770.85850.95920.95920.9516

0.94330.93740.93110.92500.91890.91400.90890.90440.70970.74570.76520.77430.7801

0.7836

0.78580.7872

0.7882

0.78880.96680.96070.95450.95020.94580.94140.93720.93400.9306

0.92800.60590.63510.65040.6572

0.6614

0.66390.66530.66620.66690.6673

0.9762

0.9721

0.96830.9656

0.96290.96040.95800.95630.95450.95320.05 0.7097
0.6059

EtCone30/Et

EtCone30/Et

4.5 Determination of Lepton Selection

0.05 0.9668
0.97620.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22

pTcone30/Et

pTcone30/Et
0.91220.90450.88370.86580.80780.78620.90550.88490.86740.84910.82980.8106

0.78940.76860.74650.72660.90620.88590.86880.85080.83180.81280.79210.77170.75040.7306

0.3 0.9144

0.90710.88730.87050.85280.83440.81580.79570.77580.75490.73560.91530.90820.88900.87260.85530.83740.81930.79980.78070.76040.74150.91670.90960.89080.87480.85810.84080.82340.80450.78610.76670.91140.89330.87790.86180.84530.82870.81050.79290.77430.75700.92000.91340.89590.88120.86570.85020.83470.81720.80040.78320.76680.2 0.9216

0.91530.89870.88470.8902

0.94330.96940.98050.98640.98980.99190.99430.99500.9956

0.9431

0.96920.98040.98630.9897

0.99180.9931

0.9941

0.99480.99540.88990.94300.96910.98020.98610.98950.9916

0.99290.99390.9946

0.99520.3 0.8897

0.94280.96890.98000.98590.98930.99130.9927

0.99370.9944

0.99500.8894

0.94250.9686

0.97970.9856

0.98900.99100.9924

0.9934

0.9941

0.99460.8892

0.94220.96830.97940.98530.98860.9907

0.99200.99300.99370.99430.94180.96790.97900.98490.98820.99030.9916

0.9926

0.99330.99380.25 0.9183

0.8884

0.94140.96740.97850.98440.98770.98980.9911

0.99200.9927

0.99330.2 0.8879

0.35 0.8900

0.25 0.8888

0.9933

EtCone30/Et

EtCone30/Et

70

0.35 0.9130
0.91370.84700.87010.82730.85570.84100.82470.76490.80880.74250.79270.72200.74840.77760.94090.96690.97790.98370.98710.98910.9904

0.9914

0.9921

0.99260.88720.94010.96610.9771

0.98290.98630.98830.98960.99050.99120.99160.92410.91810.90240.88940.87560.86210.84840.83340.81860.80350.78950.88630.93920.96510.9761

0.98180.98510.98710.98840.98930.98990.99040.92630.92060.90590.89400.88140.86880.85590.84200.82840.81480.80220.93780.9636

0.97450.98020.98350.98540.98670.98750.98810.98850.92400.91030.89900.88770.87610.86440.85250.84060.82870.81780.9612

0.97200.97770.98080.98270.98390.98470.98530.83490.15 0.8850

0.15 0.9293

0.88290.93550.98570.93200.92700.91450.90450.89430.88400.87400.86420.85390.84390.1 0.8793

0.93170.9571

0.9677

0.9732

0.97630.97810.97920.97990.98040.98070.1 0.9352

0.93050.91950.91110.90220.89350.88510.87700.86870.86070.87260.92430.94920.9596

0.96490.96770.96940.97030.97090.9714

0.9716

0.93970.93570.92620.91910.91190.90470.89800.89180.88530.87940.87410.85810.90870.9326

0.9424

0.9472

0.94980.9511

0.95190.95240.95280.95300.94440.94080.93300.92740.92220.91720.91240.90780.90330.89900.8956

0.87120.89300.90160.90560.90760.90860.90920.90960.90980.90990.94690.94090.93700.93310.92970.92680.92410.92110.91870.91670.7697

0.78680.79310.79580.79710.79770.79800.7982

0.7984

0.79840.9574

0.95370.9511

0.9491

0.9476

0.94600.9447

0.94330.9422

0.94130.05 0.8235
0.72950.05 0.9499
0.95960.85360.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22

pTcone30/Et

pTcone30/Et

Figure 4.10: Muon signal eﬃciency (left) and background rejection (right) after the identification applied in µe channel. Top of them are for 10-15, 2nd for 15-20, 3rd for 20-25,
and the bottom for > 25 GeV.

71

4.5 Determination of Lepton Selection
Trigger bias

The eﬃciency loss from “medium1” identification on EF e12Tvh medium1 mu8 dilepton trigger, needs to be taken into account when comparing the likelihood and cut-based identifications because the likelihood identification is not a subset of the “medium1”. This isparticularly important in the low ET , 10-25 GeV optimization since the likelihood is considered.
While there is no “medium1” bias from the single lepton triggers such as EF e24vhi medium1
and EF e60 medium1 because the cut-based identifications, which are a subset of “medium1”,
are used above 25 GeV. In order to include the loss from the triggers in the optimization,
the loss can be quantitatively evaluated using Z tag-and-probe method in data for the signal eﬃciency and using multijet/QCD samples in data for the background eﬃciency.

1.8
VTLH+Iso+Imp (signal)
1.6
VTLH+Iso+Imp && Medium (signal)
1.4
s = 8 TeV,

1.2

∫ L dt = 20.7 fb

-1

1
0.8

Electron Background Efficiency

Electron Signal Efficiency

Figure 4.11 shows the signal and background eﬃciencies with/without the cut-based
Medium++ requirement, assuming that Medium++ ∼ medium1. The change in the signal
eﬃciency caused by the cut-based Medium++ is also summarized in Table 4.5.
0.01
0.009

VTLH+Iso+Imp (background)

0.008
VTLH+Iso+Imp && Medium (background)

0.007
0.006

s = 8 TeV,

0.005

∫ L dt = 20.7 fb

-1

0.004
0.003

0.6

0.002

0.4

0.001
10

12

14

16

18

20

22
24
Electron ET [GeV]

0

10

12

14

16

18

20

22
24
Electron ET [GeV]

Figure 4.11: Plots show the comparison of electron eﬃciencies in data for Very Tight
likelihood and the AND of the Very Tight likelihood and cut-based Medium++ after isolations, impact parameters, and exactly two leptons requirements. The left and right plots
are signal and background eﬃciencies as a function of ET , respectively. About 5 % loss canbe seen depending on ET in 10-25 GeV. For the ET > 25 GeV, the bias is not expected
since the cut-based Medium++ is a subset of medium1.

Other bias
In addition to the loss caused by the trigger, the variables which has been further addedin the likelihood (but not in the cut-based Tight++ or Medium++) have to be taken
into account in the optimization. In fact, there are several new variables included in thelikelihood such as ∆p, ∆ϕRes , σd0 (see Section 4.1.2). Especially evaluating the impact of d0

72

4.5 Determination of Lepton Selection

Table 4.5: Table shows expected event loss caused by medium1 on EF e12Tvh medium1 mu8
for each ET bin. The event loss is not expected below 15 GeV by definition because eventsare collected with only single muon triggers. Also the event loss is not expected above 25
GeV since the likelihood is not considered.
ET [GeV]
10-15
15-20
20-25
25-

expected event loss from “medium1”
0.0%(by definition)
0.92%
0.79%
0.0%(by definition)

significance is important because it is one of the variables that has less correlation among
other variables. In order to make a fair comparison between the Very Tight likelihood andthe cut-based Tight++ in the signal and the background eﬃciency, the d0 significance inthe likelihood is taken into account in the optimization. The numbers in Table 4.4 arealready corrected for the d0 significance.
Identification optimization
The comparisons of the significances between the identifications are made in the 2-D map
taking into account any bias discussed above. Table 4.6 and Figure 4.12 are the results foreach ET bin.
Table 4.6: Comparison of Electron identification in significance for each ET bin. The
significance is calculated in a given isolation operating point (optimal operating point) inµe channel for 10-25 GeV, and in eµ+µe channels for 25- GeV.
ET [GeV]
10-15
15-20
20-25
> 25

Very Tight LH
0.418
0.733
0.851
Medium++1.778

Tight++
0.359
0.701
0.841
Tight++
1.730

For 10-25 GeV, the improvements from the likelihood identification in significance in µe
channel are ∼ 15 % in 10-15 GeV, ∼ 3 % in 15-20 GeV, and ∼ 1 % in 20-25 GeV at the
optimal isolation operating point, which results in 1.5 % improvement in overall ET . For
25- GeV, the cut-based Medium++ is considered since the W +jets background is smaller.
The improvement from the cut-based Medium++ in significance in eµ+µe channels are ∼2.8 % in 25- GeV.
In order to avoid non-negligible increase of the W + γ background with the cut-based

73

0.40600.41570.41540.41510.41180.40680.4016

0.39520.38910.38310.40680.41650.41630.41600.41280.40790.4026

0.39640.39020.38430.40750.41730.41710.41690.41370.40880.40340.39710.39100.38530.3 0.3950

0.40800.4176

0.41750.41740.41420.40930.40390.39770.39150.38580.39520.40820.41800.41800.41780.4146

0.40980.4046

0.39840.39220.3866

0.39490.40800.41800.41800.41790.41470.40990.40470.39880.39280.38720.40780.41800.41810.41800.41490.41020.40510.39930.39350.38790.39450.40750.41790.41800.41810.41530.41080.40570.40040.39470.38920.2 0.3940

0.40700.41750.4176

0.41780.41510.41070.40580.4006

0.3952

0.39340.40650.41690.41720.41780.41490.41070.40590.40110.39590.39090.40380.41430.41520.41600.41310.40920.40470.40010.39510.39020.40080.4111

0.41200.41310.41030.4066

0.40230.39790.39340.38870.39440.25 0.3948

0.15 0.3877

0.35240.34830.35340.35010.34690.34150.33580.32940.32250.31570.34890.35420.35100.34790.3427

0.33690.33050.3236

0.31690.3105

0.3 0.3391

0.34970.35510.35200.34900.34380.33830.33180.32490.31810.31170.33960.35020.35590.35290.34990.34470.33920.33290.32610.31930.31300.34030.34890.34570.3402

0.33450.32800.32120.31440.30790.30930.25 0.3410

0.35110.35700.35410.35120.34580.34040.33410.32750.32080.35170.35770.35480.35190.3466

0.34130.33500.3286

0.32200.31580.34150.35220.35840.35550.35280.34790.3427

0.33650.33040.32410.31790.38990.2 0.3414

0.35220.35870.35600.3536

0.34880.34370.33770.33180.32560.39080.34200.35290.3596

0.35700.3546

0.34980.34480.33910.33330.32750.32140.34120.15 0.3395

0.35210.35870.35640.35420.34950.34470.33930.33370.3281

0.32230.35050.35730.35510.35340.34850.34390.33900.33350.32840.31450.3226
0.32290.3196

0.39620.40650.40720.40850.40570.40230.39850.39450.39030.38600.33700.34780.35470.35290.3513

0.34680.34250.33810.33300.32830.39000.40060.4016

0.40380.40110.39790.39430.39060.38700.38270.1 0.3333

0.34400.35140.35010.34950.34510.34090.3367

0.33210.32780.36730.37990.39050.39180.39410.3916

0.38880.38570.38230.37900.37510.32580.33680.34450.34350.34310.33900.33530.3316

0.32720.32320.31820.35640.36850.37890.3801

0.38250.38020.37770.37470.37140.36840.36500.3174

0.33600.3354

0.33540.33150.32800.32440.32030.31670.31250.35100.36100.36240.36490.3631

0.36110.35880.35630.35370.35070.05 0.3034

0.32810.31370.32140.32090.32100.31790.31500.31210.30860.30530.30190.32730.3367

0.33870.34110.33970.3377

0.33610.33400.33160.32920.28450.29400.30120.30160.30170.29910.2966

0.29430.29150.28820.2856

0.32260.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22

pTcone40/Et

pTcone40/Et

0.67680.70400.71610.71800.7156

0.71190.70730.69940.69310.68780.68100.70510.71730.71940.71700.71330.70880.70130.69490.68940.6826

0.67820.70540.71740.71950.71710.71360.70900.70170.69530.69000.68340.3 0.6786

0.70600.71820.72030.71780.71450.71020.70300.69700.69190.68540.67870.70590.71840.72080.71830.71520.71100.70380.6982

0.69340.68670.67880.70620.71850.72110.71860.7156

0.71150.7042

0.69890.69450.68790.35 0.6779

0.25 0.6797

topoEtCone30/Et

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22

0.65920.35 0.6603
0.66070.68230.6921

0.69340.68960.68250.67620.6677

0.66100.65460.64730.68330.69350.69490.69100.68400.67790.6696

0.66280.65660.64940.68380.69390.69540.69180.68540.67940.6712

0.66440.65820.65140.3 0.6617

0.68480.69510.69670.69310.68710.6814

0.67350.66680.66070.6541

0.66210.68540.69590.69780.69420.68850.68300.67530.6692

0.66310.65650.66250.68590.6966

0.69880.69530.68970.68450.67690.67120.66610.65970.25 0.6636

0.70760.72020.72330.72120.71810.71400.70680.7016

0.69750.69110.68780.69870.70110.69760.69220.68700.6796

0.67400.6691

0.66280.67930.70730.72000.72380.72190.71880.71500.70840.70350.6996

0.69330.66330.68740.69870.70180.69850.69340.68850.6816

0.67610.67170.66530.2 0.6788

0.70660.71930.72320.72120.71830.71480.70870.70420.7002

0.69440.2 0.6637

0.68790.69950.70250.69930.69420.6896

0.6832

0.67830.67380.66790.67750.70590.71870.72280.72120.71880.71500.70930.70530.70150.69570.66260.68790.69940.70320.70050.69590.69110.68510.68080.6766

0.67480.70310.71680.72080.71920.71710.71400.70860.70500.70140.69620.66050.69790.70170.69920.69530.69110.68550.6816

0.67780.67230.69810.71240.71650.71520.71360.71080.70560.70230.69900.69500.15 0.6557

0.68600.68130.69380.69770.69560.69220.68850.68350.67980.67670.6722

0.66190.69030.70430.70860.70740.70650.70390.69930.69630.69340.68990.64900.67440.68730.69120.68930.68690.68340.67880.67530.6726

0.66870.1 0.6516

0.67970.69340.69840.69790.6972

0.69490.69120.68840.68600.68300.1 0.6387

0.66370.67630.68070.67940.6772

0.67420.67080.66780.6652

0.6617

0.6366

0.66380.67780.68270.68310.68370.68130.67870.67600.67340.67100.62350.64790.6606

0.66550.6652

0.66430.66140.65880.65580.65350.65050.61370.64160.65580.6612

0.66190.66240.65990.65770.65580.65330.65100.60400.64180.64640.64660.64570.64280.64080.6382

0.63600.63330.61040.62490.63020.63050.63100.62890.6276

0.62610.62480.62320.05 0.5760

0.62870.60010.61300.61720.61730.61670.61410.61270.61080.60920.60700.56280.57620.5811

0.58200.58270.58130.58080.57990.57870.57710.53080.55320.56550.57010.57090.57040.5691

0.56850.56690.5656

0.56360.15 0.6697

0.05 0.5836
0.53810.67070.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22

pTcone30/Et

pTcone30/Et

0.82370.35 0.8238

0.84310.84940.85180.8506

0.84930.84720.84420.84320.84950.85200.85090.84950.84760.84460.84210.83860.83650.82380.84320.84970.85220.85100.84980.84790.84490.84240.83900.83700.3 0.8239

0.84340.84990.85250.85130.85000.84820.84520.84270.83940.83760.82390.84340.84980.85270.85170.85050.84860.84570.84330.84020.83850.82370.84330.84990.85290.85200.85100.84920.84640.84400.84110.83940.84330.84980.85280.85190.85100.84940.84670.84440.84200.84040.82290.84280.84930.85240.85160.85090.84920.84670.84440.84200.84070.2 0.8226

0.84250.84900.85220.85150.85080.84920.84680.84460.84220.82180.8416

0.84830.85160.85110.85030.84870.84650.84450.82030.84010.84670.85000.84950.84870.84720.84500.84330.81630.84470.84810.84790.84730.84600.84440.84290.84110.84000.15 0.8147

0.83570.83810.83390.81550.83500.84150.84490.84520.84470.84360.84220.84090.83930.83870.81170.83070.1 0.8106

0.83000.83660.84000.84020.84000.83940.83820.83700.83550.83540.1 0.8071

0.82620.80250.82140.82770.83120.83160.83150.83110.83010.82930.82790.82780.79940.81740.78800.25 0.8234

0.15 0.8183

0.79130.84160.83820.8358

topoEtCone30/Et

topoEtCone30/Et

0.3472

0.33830.38330.3168

topoEtCone30/Et

0.33660.35 0.3377

0.1 0.3774
0.05 0.3396

topoEtCone30/Et

topoEtCone30/Et

0.39280.35 0.3936

0.8366

0.84190.84300.82890.82580.83670.84200.84320.84010.83720.83400.82950.82630.82140.81810.83710.84250.84380.84080.83800.83480.83020.82710.82230.8191

0.3 0.8187

0.83750.84300.84440.84140.83860.83540.83090.82790.82310.82010.81880.8376

0.84320.84490.84200.83930.83610.83170.82880.82430.82140.81870.83770.84340.84520.84250.83990.83690.83270.83000.82560.82280.83800.84360.84530.84270.84050.83760.83370.83110.82720.81850.83780.84350.84540.84310.84110.83840.83470.83210.82840.82620.84080.2 0.8182

0.83750.84330.84550.84340.84150.83900.83560.83310.82940.82730.84230.84090.81740.83680.84280.84520.84350.84170.83930.83630.83400.83040.82840.84130.84000.84160.84400.84240.84080.83860.83600.83380.83050.82870.83980.84230.84130.83990.83800.83590.83400.83120.83660.83910.83860.83750.83580.83400.83230.82980.82890.83220.83490.83460.83380.83270.83100.82940.82710.82670.81830.82420.82730.82740.82670.82580.82430.82320.82120.82100.81810.80590.81170.81450.81490.81440.81390.81270.81190.81040.81020.78650.79170.7946

0.79520.79520.79510.79430.7936

0.79250.79230.7591

0.76370.76620.76690.76740.76750.76710.7666

0.76580.76570.35 0.8181
0.81840.25 0.8187

0.05 0.7730

0.80910.81530.81850.81900.81890.81880.81780.81630.81630.7896

0.7952

0.7984

0.79870.79880.79900.7984

0.79810.7972

0.79710.05 0.7696

0.7476

0.76210.76700.76980.77020.77080.77100.77060.77050.77000.77010.74420.83980.83690.83340.82080.81730.82480.82960.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22

pTcone30/Et

pTcone30/Et

1.7294

1.76131.77191.7756

1.77691.77671.77611.77541.77451.7736

1.76131.77191.7756

1.77691.77671.77611.77541.77461.77361.77271.76131.77191.7756

1.77691.77671.7762

1.77551.77471.77371.77280.3 1.7292

1.7612

1.77181.7756

1.77691.77671.7762

1.77561.77471.77381.77291.7292

1.7612

1.77181.7756

1.77691.77681.77631.77571.77491.77411.7732

1.72910.25 1.7290

1.76111.77181.77561.77701.77681.77641.77581.77501.7742

1.7734

1.76101.77171.77551.77691.77681.77641.77581.77511.77441.7736

1.72881.76081.77151.7754

1.77681.77671.77641.77581.7752

1.77451.77380.35 1.7293
1.72930.2 1.7284

1.7726

topoEtCone30/Et

topoEtCone30/Et

4.5 Determination of Lepton Selection

0.35 1.6834

1.68341.71381.71381.72411.72811.72981.72991.72991.72971.7293

1.72881.72841.6833

1.71381.72411.72801.72971.72991.72991.72971.7293

1.72881.7284

0.3 1.6832

1.71371.72401.72801.72971.72991.72991.72971.7293

1.72891.72841.6832

1.71361.72391.72791.72961.72991.72991.72971.7293

1.72891.68300.25 1.6829

1.71351.72381.72781.72961.72981.72981.72961.7293

1.72891.72851.71331.72371.72771.7294

1.72971.72971.72961.7293

1.72891.72851.68271.71311.72351.72751.72931.72951.72961.7294

1.7292

1.72881.72851.72411.72811.72981.73001.73001.72971.7293

1.72881.7284

1.72851.77390.2 1.6823

1.71271.7231

1.7272

1.72891.7292

1.72931.7292

1.72891.7286

1.7283

1.72791.75991.77061.7746

1.77611.77611.77581.77541.77491.77441.77381.68181.7122

1.72251.7266

1.7284

1.72871.72881.72871.72851.7283

1.72801.72701.75901.76971.77361.7752

1.77531.77501.77471.77431.77391.7734

1.68101.7113

1.72161.72571.72751.72781.72791.72791.72771.72750.15 1.7254

1.76051.77111.77511.77651.77651.7762

1.77571.77511.77451.7273

1.7573

1.76801.77201.77361.77371.77351.77331.77301.77261.77220.15 1.6794

1.70971.71991.72401.72581.7262

1.7263

1.7263

1.7262

1.72601.72581.72261.75431.76491.76891.77051.77081.77071.77051.7702

1.76991.7696

1.67671.70681.71701.72111.72281.7232

1.72341.72341.72331.72311.72300.1 1.7174

1.74881.7593

1.76331.76491.7651

1.7651

1.76501.76481.76461.76430.1 1.6719

1.70171.71181.71571.71751.71791.7181

1.7181

1.71801.71791.71781.7076

1.73861.74881.75271.7542

1.75451.75451.75451.75431.7542

1.75401.66301.6922

1.70201.70581.70751.70791.70811.70811.70811.70801.70791.6891

1.71901.72871.7324

1.73391.7342

1.7342

1.7342

1.73411.73401.73391.64581.6834

1.68701.68851.68891.68901.68911.68911.68901.68901.6803

1.6892

1.6925

1.69371.69401.6941

1.6941

1.69401.69391.69380.05 1.6119

1.67411.63831.64671.64991.65121.65151.65171.65171.65171.65171.65161.60371.61111.61381.61481.61511.61511.6152

1.61511.61511.61501.54401.56691.57391.5765

1.5775

1.57781.57791.57801.57801.57801.57790.05 1.6524
1.57940.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22

pTcone30/Et

pTcone30/Et

Figure 4.12: Comparison of the identifications in 2-dimensional map. Top three plots arecomparison of the Very Tight likelihood (left) and Tight++ (right) for ET = 10-15 GeV(top), 15-20 GeV (2nd), and 20-25 GeV (3rd) in µe channel. Bottom plots are comparisonof the modified Medium++ (left) and Tight++ (right) for ET > 25 GeV in eµ+µe channels.

74

4.5 Determination of Lepton Selection

Medium++, the conversion flag and B-Layer hit in the inner detector are additionallyrequired on the top of the cut-based Medium++, at high η (|η| >2.37) to cover full η
acceptance. 6 The gain from the modified Medium++ in the signal eﬃciency is ∼ 10 %,while retaining the W + γ rejection similar to the cut-based Tight++. The comparison of
the cut-based Medium++ and Tight++ in significance is also found in Figure 4.12 and in
Table 4.6. Also the comparison in cutflow between the modified Medium++ and Tight++
above 25 GeV for eµ channel is found in Tables 4.9 and 4.10. From the table it is clear thatthe rate of the W + γ background does not change much between the two identifications.
The final electron identification criteria as a function of ET are found in Table 4.7.
Table 4.7: Electron identification as a function of ET .
ET [GeV]
10-15
15-20
20-25
> 25

4.5.2

Electron identification
Very Tight LH
Very Tight LH
Very Tight LH(Modified) cut-based Medium++

Isolation

The isolation optimization is of crucial importance since the isolations are the most powerful
discriminants against the W +jets background. The electron isolations are particularly
important since most of the W +jets backgrounds originate from non-prompt electrons
rather than non-prompt muons. Since the previous publication, there has also been a
lot of improvements considered to mitigate the impact of the W +jets background. The
optimization is therefore made step by step verifying the impact of each improvement thatcan be seen as a change of the optimal operating points.
• step1: the same configuration as previous publication but adding dilepton triggers
and lowering ET ,• step2: change from Di-jet fake factor to Z+jets fake factor (see Chapter 6)• step3: add mll split and SS CR method (see Chapter 7)
The first item is just a statistical improvement, which is roughly 10 % in total. The
second and third items are more important in terms of the W +jets background because
they can change the isolation operating points to be looser than those for the previous analysis. More specifically, for the second item, the change from the di-jet fake factor to theZ+jets fake factor in 10-25 GeV are taken into account, which implies the total systematic
uncertainty on the W +jets background is reduced from 45 % to 20-45 % depending on ET .
6

Both are already required in full η region by default in the cut-based Tight++. Also this eﬀect is taken
into account in Table 4.4.

75

4.5 Determination of Lepton Selection

The Z+jets fake factor has a big impact in 10-20 GeV, while it has less impact in ET > 20
GeV due to large EW contamination and statistical uncertainty in the measurement. The
Z+jets fake factor is discussed in detail in Chapter 6. For the third item, mll split at 30
GeV in signal region and the SS CR method are taken into account. Briefly the SS CR is
one of the control regions in which the non-WW dibosons (W + γ (∗) /W Z/Z +γ (∗) /ZZ) normalization is determined from same sign data but subtracting out the W +jets backgroundthat is pre-dominant background in this region. The step-by-step changes in significance areverified and shown in Figure 4.13. 7 At the second and third steps, the optimal operating
points are apparently moved to be looser due to smaller impact of the W +jets background.
A summary of isolation cuts is found in Table 4.8. The optimization suggests thatthe analysis should rely on the track isolation rather than the calorimeter isolation because
the track isolation is more powerful in the background rejection while keeping higher signal
eﬃciency. There is however an upper limit on the cut value on the track isolation due tothe trigger isolation (Ptcone20/pT < 0.10) on EF e24vhi medium1. The track isolation istherefore set to be a subset of the trigger isolation at higher pT .
Table 4.8: Electron isolation and impact parameters as a function of ET .
ET [GeV]
10-15
15-20
20-25
25-

7

topoEtcone30
topoEtConeCor30/ET <0.20
topoEtConeCor30/ET <0.24
topoEtConeCor30/ET <0.28
topoEtConeCor30/ET <0.28

ptconePtcone40/pT <0.06
Ptcone30/pT <0.08
Ptcone30/pT <0.10
Ptcone30/pT <0.10|d0 /σd0 |3333|z0 sin θ|
0.4 mm
0.4 mm
0.4 mm
0.4 mmNote that the cut-based Tight++ is used in the step-by-step optimization for ET = 10-25 GeV but the
optimal points are finally chosen from the Figure 4.12 with the optimal identification defined in Table 4.7.

blinding
lepton pT
Scale factors
OS leptons
mℓℓ > 12, 10 GeV
Z veto (for ee, µµ)
Scale factors
miss > 45, 25 GeVET,relZ validation region (incl)
Top validation region (incl)
Scale factors
0j: jet veto
0j: ∆ϕℓℓ,MET > 1.57
0j: pT,ℓℓ >45,30 GeV
0j: mℓℓ < 50 GeV
0j: ∆ϕℓℓ < 1.8
0j: mℓℓ < 30 hipt
0j: mℓℓ > 30 hipt
0j: mℓℓ < 30 lowpt
0j: mℓℓ > 30 lowpt
0j: 0.75 · mH ≤ mT ≤ mH
0j: Z validation region
Scale factors
0j: W W control region
0j: W W Old control region
0j: W W validation region
Scale factors
1j: one jet
1j: SMT veto
1j: b-jet veto
1j: Z → ττ veto
1j: mℓℓ < 50 GeV
1j: ∆ϕℓℓ < 1.8
1j: mℓℓ < 30 hipt
1j: mℓℓ > 30 hipt
1j: mℓℓ < 30 lowpt
1j: mℓℓ > 30 lowpt
1j: 0.75 · mH ≤ mT ≤ mH
1j: Z validation region
Scale factors
1j: W W control region
Scale factors
1j: Top control region
448.31 ± 6.38
878.60 ± 8.62
24.92 ± 1.56
221.68 ± 4.71
216.24 ± 4.67
176.26 ± 4.24
106.60 ± 3.52
102.62 ± 3.46
37.21 ± 2.15
19.72 ± 1.40
40.31 ± 2.22
5.38 ± 0.65
29.79 ± 1.80
376.80 ± 5.90

217.81 ± 1.59 3595.25 ± 14.71
331.59 ± 1.95 5698.50 ± 18.56
10.65 ± 0.36
139.54 ± 3.05

2354.36 ± 11.95
2325.18 ± 11.88
1961.45 ± 10.91
545.47 ± 5.72
515.08 ± 5.55
165.10 ± 3.15
278.71 ± 4.08
36.05 ± 1.46
35.23 ± 1.45
220.08 ± 3.66
3644.76 ± 14.90
709.74 ± 6.57
895.84 ± 7.41
653.82 ± 6.33
915.42 ± 7.42
910.34 ± 7.40
844.39 ± 7.09
821.00 ± 6.99
185.03 ± 3.30
162.09 ± 3.08
51.36 ± 1.73
86.97 ± 2.27
11.29 ± 0.81
12.47 ± 0.85
52.32 ± 1.76
1485.36 ± 9.46
403.87 ± 4.91
64.34 ± 2.12

123.24 ± 1.23
122.29 ± 1.23
111.56 ± 1.17
93.60 ± 1.07
88.62 ± 1.04
34.66 ± 0.65
34.68 ± 0.66
11.84 ± 0.38
7.43 ± 0.30
51.86 ± 0.80
160.66 ± 1.40

15.96 ± 0.45
0.11 ± 0.04
0.00 ± 0.00

61.32 ± 0.84
61.02 ± 0.83
56.81 ± 0.80
56.55 ± 0.80
45.24 ± 0.72
39.97 ± 0.67
15.96 ± 0.42
16.42 ± 0.43
4.60 ± 0.23
2.99 ± 0.18
21.55 ± 0.50
104.38 ± 1.09

0.03 ± 0.01

4.15 ± 0.23

8.69 ± 0.87

46.71 ± 1.84

142.47 ± 3.36
141.15 ± 3.35
132.37 ± 3.23
129.14 ± 3.19
48.28 ± 2.09
43.19 ± 2.02
19.66 ± 1.44
14.47 ± 1.07
7.07 ± 0.87
1.98 ± 0.32
15.55 ± 1.22
307.11 ± 4.79

33.15 ± 1.59
40.28 ± 1.87
30.07 ± 1.61

917.75 ± 8.92
878.60 ± 8.62
878.60 ± 8.62

335.30 ± 1.96 5707.86 ± 18.57
331.59 ± 1.95 5698.50 ± 18.56
331.59 ± 1.95 5698.50 ± 18.56

2.53 ± 0.62

9.44 ± 1.19

37.58 ± 2.38
37.43 ± 2.38
34.89 ± 2.30
34.26 ± 2.27
17.18 ± 1.59
16.02 ± 1.54
9.24 ± 1.16
3.47 ± 0.73
3.07 ± 0.69
0.24 ± 0.17
6.22 ± 0.98
76.30 ± 3.44

7.65 ± 1.12
11.52 ± 1.38
8.19 ± 1.15

89.20 ± 3.79
87.95 ± 3.77
72.34 ± 3.41
55.16 ± 2.98
53.39 ± 2.92
22.27 ± 1.87
7.49 ± 1.14
22.04 ± 1.86
1.59 ± 0.50
14.47 ± 1.52
139.39 ± 4.74
19.69 ± 0.92
22.45 ± 1.01
16.72 ± 0.89

0.93 ± 0.35

2.91 ± 0.59

4.84 ± 0.50

32.84 ± 1.27

13.65 ± 1.27 84.40 ± 1.99
13.57 ± 1.26 83.46 ± 1.98
12.65 ± 1.22 78.55 ± 1.91
12.34 ± 1.20 76.47 ± 1.89
7.49 ± 0.93 21.18 ± 0.98
7.18 ± 0.91 18.32 ± 0.93
3.83 ± 0.65
6.13 ± 0.56
1.63 ± 0.45
8.65 ± 0.64
1.73 ± 0.46
1.97 ± 0.27
0.00 ± 0.00
1.57 ± 0.27
1.63 ± 0.43
7.26 ± 0.58
30.13 ± 1.88 161.30 ± 2.72

4.37 ± 0.66
5.61 ± 0.75
4.68 ± 0.69

42.95 ± 2.05 81.55 ± 1.88
42.60 ± 2.04 78.96 ± 1.85
34.68 ± 1.85 65.45 ± 1.69
25.17 ± 1.57 24.59 ± 1.02
24.74 ± 1.56 23.00 ± 0.99
9.01 ± 0.94
5.59 ± 0.48
3.16 ± 0.54
8.34 ± 0.61
11.96 ± 1.10
6.13 ± 0.52
0.62 ± 0.24
2.94 ± 0.34
5.50 ± 0.72
9.38 ± 0.63
67.01 ± 2.55 135.40 ± 2.40

149.81 ± 4.87 63.53 ± 2.68 217.23 ± 3.13
270.49 ± 6.57 111.56 ± 3.58 403.23 ± 4.24
8.31 ± 1.21
2.04 ± 0.54 13.65 ± 0.82

298.92 ± 6.90 120.08 ± 3.69 404.84 ± 4.25
270.49 ± 6.57 111.56 ± 3.58 403.23 ± 4.24
270.49 ± 6.57 111.56 ± 3.58 403.23 ± 4.24

0.39 ± 0.05

1.53 ± 0.07

6.84 ± 0.16
6.69 ± 0.15
6.28 ± 0.15
6.08 ± 0.15
2.44 ± 0.09
1.66 ± 0.08
0.47 ± 0.04
0.72 ± 0.06
0.30 ± 0.03
0.17 ± 0.02
0.44 ± 0.04
39.38 ± 0.34

1.44 ± 0.11
0.70 ± 0.05
0.48 ± 0.04

7.98 ± 0.22
6.73 ± 0.21
3.79 ± 0.17
1.68 ± 0.12
1.49 ± 0.11
0.33 ± 0.05
0.73 ± 0.08
0.19 ± 0.03
0.24 ± 0.06
0.45 ± 0.06
35.00 ± 0.37

1896.54 ± 15.61

340.37 ± 6.48

3014.38 ± 19.67
2660.71 ± 18.46
673.69 ± 9.32
647.94 ± 9.14
138.13 ± 4.38
126.88 ± 4.21
39.96 ± 2.43
66.14 ± 3.06
9.46 ± 1.08
11.32 ± 1.15
34.55 ± 2.18
4452.00 ± 23.85

82.49 ± 3.29
159.90 ± 4.40
128.68 ± 3.94

304.86 ± 6.21
298.02 ± 6.14
275.06 ± 5.91
55.57 ± 2.74
54.41 ± 2.71
16.39 ± 1.56
29.75 ± 1.99
3.49 ± 0.65
4.77 ± 0.72
16.12 ± 1.47
412.13 ± 7.18

17.74 ± 0.29 18328.05 ± 48.69
93.32 ± 0.55 31618.50 ± 64.06
0.92 ± 0.07 16079.82 ± 45.70

93.92 ± 0.55 31659.81 ± 64.10
93.32 ± 0.55 31618.50 ± 64.06
93.32 ± 0.55 31618.50 ± 64.06

532.56 ± 3.43

122.29 ± 1.78

879.74 ± 5.18
806.34 ± 5.05
249.29 ± 3.64
239.44 ± 3.61
50.39 ± 1.69
47.24 ± 1.68
14.04 ± 0.49
26.04 ± 1.20
3.55 ± 1.03
3.61 ± 0.24
12.90 ± 0.47
1336.93 ± 6.13

52.73 ± 0.94
87.77 ± 1.23
68.29 ± 1.09

41.47 ± 2.51

16.04 ± 1.47

705.72 ± 10.61
702.89 ± 10.59
653.83 ± 10.19
556.61 ± 9.55
260.46 ± 5.73
32.58 ± 1.98
2.59 ± 0.55
16.10 ± 1.39
3.63 ± 0.68
10.26 ± 1.10
2.18 ± 0.50
4575.36 ± 36.04

27.63 ± 2.04
6.41 ± 1.00
2.83 ± 0.65

175.17 ± 1.97 2034.39 ± 21.00
172.85 ± 1.96 1387.93 ± 18.32
159.90 ± 1.65
63.88 ± 4.75
33.12 ± 0.75
14.92 ± 1.50
32.38 ± 0.74
1.20 ± 0.48
10.01 ± 0.41
0.00 ± 0.00
17.17 ± 0.54
0.03 ± 0.03
2.18 ± 0.19
0.63 ± 0.35
3.02 ± 0.23
0.54 ± 0.32
8.96 ± 0.39
0.16 ± 0.13
234.07 ± 2.69 17221.42 ± 59.24

1828.81 ± 7.40 3010.73 ± 24.75
2948.07 ± 9.55 23594.73 ± 73.56
1278.06 ± 5.36
105.68 ± 4.35

2950.44 ± 9.55 23612.59 ± 73.58
2948.07 ± 9.55 23594.73 ± 73.56
2948.07 ± 9.55 23594.73 ± 73.56

42.15 ± 3.07

42.93 ± 2.53

254.08 ± 6.55
246.82 ± 6.42
203.89 ± 5.61
198.26 ± 5.47
86.26 ± 3.46
51.95 ± 2.51
12.20 ± 1.16
11.35 ± 1.19
15.94 ± 1.39
12.45 ± 1.26
15.69 ± 1.39
1098.58 ± 12.75

78.43 ± 3.01
60.90 ± 2.79
37.46 ± 2.10

547.65 ± 8.66
479.90 ± 7.98
297.77 ± 5.88
128.09 ± 3.85
99.89 ± 3.40
14.72 ± 1.32
23.15 ± 1.49
36.72 ± 2.15
25.30 ± 1.73
44.05 ± 2.22
2229.07 ± 18.52

2585.75 ± 16.63

972.21 ± 9.01

5911.79 ± 25.21
5468.24 ± 24.20
2757.46 ± 17.21
2592.40 ± 16.63
768.56 ± 9.06
463.91 ± 6.66
139.80 ± 3.58
221.08 ± 4.52
50.93 ± 2.46
52.10 ± 2.24
133.19 ± 3.43
13255.33 ± 46.69

984.17 ± 8.41
1251.11 ± 9.38
921.17 ± 8.02

5638.11 ± 26.90
4880.11 ± 24.57
2934.32 ± 15.22
883.78 ± 8.38
805.57 ± 7.90
243.44 ± 4.34
368.52 ± 5.01
119.38 ± 3.51
74.23 ± 2.49
319.16 ± 4.89
24118.25 ± 64.56

1060.32 ± 13.40 28271.47 ± 58.95
4195.40 ± 25.90 68933.81 ± 103.42
207.52 ± 7.47 17835.55 ± 46.94

4245.61 ± 26.02 69094.06 ± 103.52
4195.40 ± 25.90 68933.81 ± 103.42
4195.40 ± 25.90 68933.81 ± 103.42

Signal [125 GeV]WWW Z/ZZ/W γ
Wγ
W γ∗
WZ
ZZ
tt̄
Single Top
Z+jetsW +jets
Total Bkg. Observed Data/MC
352.61 ± 2.01 5813.28 ± 18.74 2113.36 ± 13.82 729.45 ± 10.75 332.49 ± 6.05 854.91 ± 6.19 196.51 ± 0.75 32099.93 ± 64.52 3013.26 ± 10.97 28773.58 ± 84.01 11242.09 ± 37.76 83055.50 ± 115.36
335.65 ± 1.96 5723.46 ± 18.60 1816.44 ± 12.56 581.08 ± 9.62 244.80 ± 5.30 811.50 ± 6.04 179.06 ± 0.72 31757.35 ± 64.20 2985.79 ± 10.87 23870.63 ± 78.33 6518.01 ± 30.71 72671.68 ± 108.73

Table 4.9: Event yields and predictions for eµ channel with the cut-based Tight++ in ET > 25 GeV. Only statisticaluncertainties are shown in this table.

76
4.5 Determination of Lepton Selection

blinding
lepton pT
Scale factors
OS leptons
mℓℓ > 12, 10 GeV
Z veto (for ee, µµ)
Scale factors
miss > 45, 25 GeVET,relZ validation region (incl)
Top validation region (incl)
Scale factors
0j: jet veto
0j: ∆ϕℓℓ,MET > 1.57
0j: pT,ℓℓ >45,30 GeV
0j: mℓℓ < 50 GeV
0j: ∆ϕℓℓ < 1.8
0j: mℓℓ < 30 hipt
0j: mℓℓ > 30 hipt
0j: mℓℓ < 30 lowpt
0j: mℓℓ > 30 lowpt
0j: 0.75 · mH ≤ mT ≤ mH
0j: Z validation region
Scale factors
0j: W W control region
0j: W W Old control region
0j: W W validation region
Scale factors
1j: one jet
1j: SMT veto
1j: b-jet veto
1j: Z → ττ veto
1j: mℓℓ < 50 GeV
1j: ∆ϕℓℓ < 1.8
1j: mℓℓ < 30 hipt
1j: mℓℓ > 30 hipt
1j: mℓℓ < 30 lowpt
1j: mℓℓ > 30 lowpt
1j: 0.75 · mH ≤ mT ≤ mH
1j: Z validation region
Scale factors
1j: W W control region
Scale factors
1j: Top control region
473.54 ± 6.57
923.49 ± 8.86
25.65 ± 1.56
241.86 ± 4.96
235.99 ± 4.92
190.82 ± 4.43
115.31 ± 3.67
111.26 ± 3.62
40.78 ± 2.26
22.17 ± 1.51
42.73 ± 2.29
5.58 ± 0.67
33.02 ± 1.92
412.01 ± 6.24

249.39 ± 1.87 3823.94 ± 15.18
382.24 ± 2.30 6057.42 ± 19.14
14.24 ± 0.53
147.94 ± 3.14

2509.95 ± 12.34
2478.78 ± 12.27
2089.64 ± 11.27
581.73 ± 5.91
549.14 ± 5.73
176.48 ± 3.25
297.18 ± 4.22
38.42 ± 1.51
37.06 ± 1.49
234.27 ± 3.78
3882.26 ± 15.39
760.92 ± 6.81
949.17 ± 7.63
691.12 ± 6.51
971.22 ± 7.65
965.96 ± 7.63
896.05 ± 7.31
871.50 ± 7.21
196.98 ± 3.41
172.52 ± 3.18
54.64 ± 1.78
92.33 ± 2.33
12.25 ± 0.84
13.30 ± 0.89
56.11 ± 1.83
1576.77 ± 9.76
426.71 ± 5.05
68.29 ± 2.18

135.80 ± 1.36
134.74 ± 1.35
122.52 ± 1.28
101.34 ± 1.14
96.06 ± 1.11
37.63 ± 0.71
37.72 ± 0.69
12.54 ± 0.40
8.17 ± 0.32
55.96 ± 0.86
176.55 ± 1.54

18.56 ± 0.54
0.89 ± 0.19
0.45 ± 0.14

71.65 ± 1.02
71.26 ± 1.02
66.00 ± 0.97
65.61 ± 0.96
51.23 ± 0.81
45.25 ± 0.75
17.98 ± 0.47
18.73 ± 0.49
5.23 ± 0.26
3.31 ± 0.20
23.71 ± 0.54
121.12 ± 1.31

1.26 ± 0.28

5.15 ± 0.32

9.18 ± 0.88

47.42 ± 1.85

147.78 ± 3.43
146.24 ± 3.42
137.01 ± 3.30
133.94 ± 3.27
50.72 ± 2.16
45.38 ± 2.08
21.42 ± 1.52
14.40 ± 1.07
7.57 ± 0.89
1.99 ± 0.31
16.04 ± 1.24
316.73 ± 4.88

36.03 ± 1.68
43.69 ± 1.96
32.72 ± 1.70

965.66 ± 9.17
923.49 ± 8.86
923.49 ± 8.86

386.33 ± 2.31 6067.38 ± 19.16
382.24 ± 2.30 6057.42 ± 19.14
382.24 ± 2.30 6057.42 ± 19.14

2.53 ± 0.62

10.44 ± 1.25

42.23 ± 2.54
42.09 ± 2.53
39.50 ± 2.45
38.88 ± 2.43
19.74 ± 1.73
18.43 ± 1.67
10.77 ± 1.27
3.83 ± 0.77
3.55 ± 0.74
0.27 ± 0.17
6.59 ± 1.01
86.28 ± 3.67

8.65 ± 1.19
12.99 ± 1.47
9.47 ± 1.24

99.12 ± 4.02
97.85 ± 4.00
79.37 ± 3.59
59.90 ± 3.12
58.22 ± 3.07
24.25 ± 1.97
8.61 ± 1.22
23.75 ± 1.95
1.61 ± 0.51
16.14 ± 1.62
155.28 ± 5.03
20.74 ± 0.94
23.78 ± 1.04
17.72 ± 0.92

1.04 ± 0.35

3.02 ± 0.54

5.19 ± 0.52

32.47 ± 1.26

14.16 ± 1.17 84.58 ± 1.98
14.05 ± 1.16 83.47 ± 1.97
13.05 ± 1.11 78.25 ± 1.90
12.82 ± 1.11 76.22 ± 1.88
7.56 ± 0.85 20.98 ± 0.97
7.20 ± 0.83 18.08 ± 0.92
3.96 ± 0.62
6.23 ± 0.56
1.51 ± 0.38
8.32 ± 0.63
1.73 ± 0.40
1.98 ± 0.27
0.00 ± 0.00
1.54 ± 0.25
1.84 ± 0.43
7.14 ± 0.58
30.05 ± 1.70 161.40 ± 2.71

5.11 ± 0.71
6.19 ± 0.78
5.03 ± 0.70

48.40 ± 2.15 85.95 ± 1.93
47.92 ± 2.14 83.14 ± 1.90
38.77 ± 1.93 68.65 ± 1.73
27.95 ± 1.63 25.66 ± 1.04
27.47 ± 1.61 23.98 ± 1.01
10.35 ± 1.00
5.83 ± 0.49
4.04 ± 0.62
8.71 ± 0.62
12.39 ± 1.07
6.40 ± 0.53
0.68 ± 0.26
3.04 ± 0.35
6.57 ± 0.80
9.81 ± 0.64
77.27 ± 2.72 142.47 ± 2.46

167.16 ± 5.17 67.25 ± 2.54 221.02 ± 3.15
302.87 ± 6.98 116.60 ± 3.35 409.28 ± 4.25
8.56 ± 1.23
1.93 ± 0.47 14.19 ± 0.84

333.28 ± 7.31 126.09 ± 3.48 410.97 ± 4.26
302.87 ± 6.98 116.60 ± 3.35 409.28 ± 4.25
302.87 ± 6.98 116.60 ± 3.35 409.28 ± 4.25

0.41 ± 0.05

1.48 ± 0.07

6.81 ± 0.16
6.63 ± 0.16
6.21 ± 0.15
6.02 ± 0.15
2.43 ± 0.10
1.67 ± 0.08
0.45 ± 0.04
0.73 ± 0.06
0.31 ± 0.03
0.18 ± 0.03
0.47 ± 0.04
39.00 ± 0.34

1.53 ± 0.11
0.74 ± 0.05
0.50 ± 0.04

8.39 ± 0.22
7.08 ± 0.21
4.03 ± 0.18
1.81 ± 0.13
1.60 ± 0.12
0.35 ± 0.05
0.81 ± 0.09
0.19 ± 0.03
0.25 ± 0.06
0.49 ± 0.06
36.99 ± 0.38
56.94 ± 1.08
90.12 ± 1.30
69.17 ± 1.12

1991.60 ± 16.13

357.02 ± 6.72

577.48 ± 3.25

128.92 ± 1.60

44.20 ± 2.70

21.10 ± 3.82

757.47 ± 12.72
754.92 ± 12.71
703.54 ± 12.32
601.32 ± 11.74
275.80 ± 6.33
34.68 ± 2.11
2.81 ± 0.58
17.00 ± 1.49
3.70 ± 0.70
11.16 ± 1.18
2.49 ± 0.57
4901.25 ± 40.76

30.24 ± 2.18
9.46 ± 2.91
5.71 ± 2.81

183.04 ± 1.88 2162.69 ± 23.07
180.74 ± 1.87 1475.75 ± 19.65
167.17 ± 1.78
74.62 ± 6.37
34.94 ± 0.79
19.52 ± 3.47
34.09 ± 0.78
4.96 ± 3.12
10.56 ± 0.44
3.81 ± 3.09
18.36 ± 0.57
0.18 ± 0.15
2.21 ± 0.19
0.63 ± 0.35
2.96 ± 0.23
0.33 ± 0.24
9.48 ± 0.41
1.18 ± 0.87
245.14 ± 2.17 18340.71 ± 66.11

3165.37 ± 20.34 944.06 ± 4.23
2794.27 ± 19.08 864.15 ± 4.06
709.28 ± 9.66 260.60 ± 2.34
682.56 ± 9.48 249.90 ± 2.29
145.30 ± 4.53
53.08 ± 1.09
133.47 ± 4.36
49.44 ± 1.04
42.20 ± 2.50
15.20 ± 0.53
69.76 ± 3.17
27.24 ± 0.75
9.72 ± 1.12
2.97 ± 0.34
11.79 ± 1.20
4.03 ± 0.34
35.78 ± 2.24
14.49 ± 0.63
4677.29 ± 24.65 1437.20 ± 5.21

85.23 ± 3.38
166.41 ± 4.55
134.17 ± 4.07

318.45 ± 6.41
311.02 ± 6.33
286.44 ± 6.09
58.83 ± 2.83
57.60 ± 2.80
17.21 ± 1.60
31.73 ± 2.07
3.88 ± 0.68
4.79 ± 0.74
17.14 ± 1.53
429.61 ± 7.40

18.12 ± 0.29 19249.52 ± 50.35 1954.88 ± 6.19 3204.51 ± 27.87
94.73 ± 0.56 33207.34 ± 66.23 3156.72 ± 7.92 25176.50 ± 82.99
0.97 ± 0.07 16887.43 ± 47.25 1380.69 ± 5.15
111.89 ± 4.64

95.33 ± 0.56 33249.80 ± 66.27 3159.23 ± 7.92 25195.85 ± 83.01
94.73 ± 0.56 33207.34 ± 66.23 3156.72 ± 7.92 25176.50 ± 82.99
94.73 ± 0.56 33207.34 ± 66.23 3156.72 ± 7.92 25176.50 ± 82.99

40.16 ± 3.02

49.14 ± 2.60

272.55 ± 6.66
265.50 ± 6.53
224.65 ± 5.76
218.77 ± 5.62
92.64 ± 3.59
56.43 ± 2.59
13.65 ± 1.20
12.32 ± 1.20
17.27 ± 1.44
13.18 ± 1.31
17.04 ± 1.41
1231.74 ± 13.37

87.84 ± 3.09
69.66 ± 2.88
43.76 ± 2.20

606.74 ± 9.00
530.87 ± 8.28
325.86 ± 6.08
137.47 ± 4.00
107.29 ± 3.54
16.09 ± 1.38
25.92 ± 1.57
39.28 ± 2.25
26.00 ± 1.75
47.73 ± 2.30
2495.55 ± 19.43

2730.90 ± 17.11

1030.31 ± 9.90

6258.45 ± 26.61
5791.03 ± 25.58
2931.14 ± 18.66
2758.00 ± 18.08
814.52 ± 9.54
491.91 ± 6.76
149.92 ± 3.72
233.05 ± 4.57
53.48 ± 2.33
55.46 ± 2.36
141.96 ± 3.55
14140.99 ± 50.93

1057.20 ± 8.72
1328.51 ± 10.06
976.66 ± 8.71

6022.73 ± 28.89
5213.15 ± 25.94
3134.54 ± 16.26
947.80 ± 9.22
864.34 ± 8.75
264.93 ± 5.47
395.54 ± 5.21
127.15 ± 3.64
76.72 ± 2.53
342.82 ± 5.1425805.28 ± 71.30

1147.08 ± 13.67 29853.48 ± 61.73
4661.44 ± 26.97 73182.90 ± 111.84
207.66 ± 7.43 18761.27 ± 48.45

4715.11 ± 27.10 73353.02 ± 111.94
4661.44 ± 26.97 73182.90 ± 111.84
4661.44 ± 26.97 73182.90 ± 111.84

Signal [125 GeV]WWW Z/ZZ/W γ
Wγ
W γ∗
WZ
ZZ
tt̄
Single Top
Z+jetsW +jets
Total Bkg. Observed Data/MC
417.39 ± 2.55 6179.52 ± 19.33 2198.02 ± 14.05 786.25 ± 11.20 346.66 ± 5.73 866.68 ± 6.20 198.44 ± 0.76 33702.40 ± 66.70 3227.70 ± 8.27 30384.46 ± 92.93 12039.60 ± 38.94 87731.71 ± 123.45
399.22 ± 2.50 6089.92 ± 19.19 1899.32 ± 12.81 638.24 ± 10.11 255.42 ± 4.95 824.03 ± 6.06 181.63 ± 0.73 33367.90 ± 66.38 3198.65 ± 8.21 25505.74 ± 87.81 7319.03 ± 32.17 77380.57 ± 117.27

Table 4.10: Event yields and predictions for eµ channel with the cut-based Medium++ in ET > 25 GeV. Only statisticaluncertainties are shown in this table.

4.5 Determination of Lepton Selection77

0.21400.21820.21380.2054

0.19850.19110.18420.17730.17050.16410.15830.21950.21500.20680.19990.19240.18550.17860.17180.16540.15960.22030.21610.20780.20110.19370.18670.17980.17300.16660.16080.3 0.2172

0.22140.21730.20910.20240.19510.18820.18120.17430.16790.16210.21820.22240.21850.21040.20370.19630.18950.18260.17570.16930.16350.21940.22370.22010.21210.20540.19790.19100.18420.17740.17090.16510.22500.22150.21360.20680.19940.19250.18570.17910.17270.16690.35 0.2153
0.21620.25 0.2207

0.41500.41640.41570.41000.40120.39070.38240.37250.36450.35750.34990.41170.41730.41650.41100.40240.39270.38440.37450.36650.35950.35220.3 0.4132

0.38890.38030.37020.36230.3552

0.34740.41830.41290.40430.39500.38690.37730.36940.36250.35540.42010.41980.41470.40610.39710.38920.37980.37250.36550.35840.42140.42130.41650.40810.39910.3916

0.38230.37540.36940.36230.42450.42470.42010.4116

0.40290.39540.38620.37930.37350.3666

0.41840.42550.42620.42240.41420.4056

0.39850.38980.38300.37770.37060.42050.42780.42880.42500.41690.40850.4016

0.39330.3871

0.38180.37520.4056

0.39780.39230.38710.38050.22310.21510.20850.20140.19460.18780.18140.17510.16930.22750.22450.21680.21050.20340.19670.19000.18370.17760.17180.22490.22960.22690.21920.21300.20580.19920.19260.18640.18050.17470.22570.23040.22790.22050.21450.20740.20100.19460.18860.18280.17710.23110.22890.22170.21610.20900.20270.19680.19080.18540.17960.15 0.4208

0.22650.23150.2296

0.22280.21750.21070.20470.19910.19340.18840.18290.1 0.2264

0.22430.22000.21320.20730.20200.19670.19190.42140.43000.43110.4206

0.41280.42210.43120.43280.4301

0.42280.4156

0.40910.40180.3966

0.39190.43020.43290.43030.42820.4236

0.41710.41120.40450.3996

0.39560.39040.41880.42840.43180.42940.42300.41770.41200.40580.40120.3976

0.39300.38560.23150.23040.18650.1 0.4147

0.42430.42780.42610.4206

0.41570.4106

0.40580.40170.39830.39400.22350.22910.22880.22310.21910.21280.20740.2026

0.19750.19290.18780.40780.41750.42150.42080.41670.41330.40850.40460.40050.39750.39390.22080.22650.22690.22190.21860.21270.20750.20280.19790.19380.18930.39980.41570.41520.41190.40870.40400.40090.39730.3944

0.39110.22000.22090.21650.21360.20850.20410.20010.19580.19200.18820.05 0.3871

0.41080.39880.40440.40390.40080.3981

0.39390.3916

0.38880.38670.38400.21010.21140.20850.20600.2016

0.19780.19450.19100.18720.18420.36190.37350.37950.38010.37840.37610.37350.37220.36990.36810.36570.20470.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22

pTcone40/Et

pTcone30/Et

0.26530.27270.27230.26560.26000.25300.24620.23910.23200.22510.27400.27350.26700.26140.25430.24760.24050.23330.22650.22010.27480.2746

0.26800.26250.25570.24890.24180.23460.22770.22140.3 0.2683

0.27580.27570.26930.26380.25700.25040.24320.23590.22910.22270.26920.2766

0.27680.27050.26500.25820.2516

0.2446

0.23740.23040.22410.27030.27780.27830.27200.2666

0.25960.25300.2461

0.23900.23210.22580.27900.27950.27330.26780.26090.25430.24740.24050.23370.22740.26730.25 0.2714

0.21870.27250.28000.28080.2746

0.26930.26270.25620.24930.24280.23610.22980.27310.28070.28180.27580.27090.26440.25800.25120.24470.23830.23210.27460.28250.28380.27770.27280.26630.26000.25340.24710.24090.23470.27480.2826

0.28390.27830.2736

0.26710.26100.25470.24850.2426

0.23650.27850.27420.25590.24980.24420.23820.15 0.2744

topoEtCone30/Et

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22

0.35 0.2665

0.2

0.39930.41880.25 0.4175
0.2

0.40810.41540.22630.2

0.41390.41420.22300.05 0.2143

topoEtCone30/Et

0.40930.35 0.4108

0.22200.15 0.2262

0.53990.55280.55520.55050.54140.55450.55740.55280.5436

0.5321

0.52290.5116

0.50250.49450.48580.55550.55830.55380.54500.53430.52500.51380.50470.49670.48830.3 0.5445

0.55730.5604

0.55600.54700.53680.52790.51690.50800.5001

0.49190.54570.55880.56200.55800.54900.53910.53040.51970.51140.50340.49520.54700.25 0.5495

0.56010.56370.56010.55120.54130.53300.52230.51450.50770.49950.56390.56760.56420.55520.54550.5371

0.52650.51870.51210.55040.56470.56910.5666

0.55780.54830.54030.53030.5226

0.51650.50830.55280.56720.57190.56930.5606

0.55120.54340.53390.52680.52070.51300.55350.56950.57410.57250.56440.55560.54750.53840.5321

0.52610.51830.55370.57020.57540.57380.56600.55800.55060.54200.53600.5306

0.52320.35 0.5417

0.2

0.54270.15 0.5511

0.53000.52040.50890.5001

0.49200.48310.50410.28240.28400.2676

0.26170.56780.57420.57270.5656

0.55820.55140.54370.53800.53330.52710.27350.28150.28320.27810.27410.26780.26220.25690.25120.24600.24020.54730.56410.57120.56990.56290.55690.55040.54300.53770.53350.52800.1 0.2719

0.27990.28230.27780.27480.2686

0.26310.25800.25270.24790.24230.1 0.5404

0.55690.56390.56340.55740.55180.54590.54020.5354

0.5314

0.52630.26680.27520.27820.27410.27140.26560.26060.25590.25090.24630.24100.52940.5456

0.55300.5536

0.54910.54540.53970.53520.53030.52670.52230.26150.26990.27330.26970.2676

0.26210.25730.25280.24800.24380.23930.5166

0.53390.54230.54270.53900.53540.52970.52590.52160.51800.51400.25950.26320.25990.25800.25330.24930.24550.24140.23750.23370.05 0.4972

0.51470.5236

0.52370.52010.51690.5116

0.50880.50530.50270.49930.24500.24850.24640.24470.24070.2371

0.23410.23060.22690.22380.46070.47750.48630.48760.48550.48270.47940.47780.47490.4726

0.46950.05 0.2515
0.2375

topoEtCone30/Et

topoEtCone30/Et

4.5 Determination of Lepton Selection

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22

pTcone40/Et

pTcone30/Et

0.33660.35 0.3377

0.34720.35240.34830.35340.35010.34690.34150.33580.32940.32250.31570.30930.34890.3542

0.34890.35100.34570.34790.3402

0.3427

0.33690.33050.3236

0.31690.31050.33830.33180.32490.31810.31170.33920.33290.32610.31930.31300.33830.3 0.3391

0.34970.35510.35200.34900.34380.33960.35020.35590.35290.34990.34470.34030.33450.32800.32120.31440.30790.25 0.3410

0.35110.35700.35410.35120.34580.34040.33410.32750.32080.35170.35770.35480.35190.3466

0.34130.33500.3286

0.32200.31580.34150.35220.35840.35550.35280.34790.3427

0.33650.33040.32410.31790.31450.2 0.3414

0.35220.35870.35600.3536

0.34880.34370.33770.33180.32560.3196

0.34200.35290.3596

0.35700.3546

0.34980.34480.33910.33330.32750.32140.15 0.3395

0.35210.35870.35640.35420.34950.34470.33930.33370.3281

0.32230.35050.35730.35510.35340.34850.34390.33900.33350.32840.3226

0.34680.34250.33810.33300.32830.3412

topoEtCone30/Et

topoEtCone30/Et

78

0.65920.35 0.6603
0.66070.68230.6921

0.69340.68960.68250.67620.6677

0.66100.65460.64730.68330.69350.69490.69100.68400.67790.6696

0.66280.65660.64940.68380.69390.69540.69180.68540.67940.6712

0.66440.65820.65140.3 0.6617

0.68480.69510.69670.69310.68710.6814

0.67350.66680.66070.6541

0.66210.68540.69590.69780.69420.68850.68300.67530.6692

0.66310.65650.66250.68590.6966

0.69880.69530.68970.68450.67690.67120.66610.65970.68780.69870.70110.69760.69220.68700.6796

0.67400.6691

0.66280.66330.68740.69870.70180.69850.69340.68850.6816

0.67610.67170.66530.2 0.6637

0.68790.69950.70250.69930.69420.6896

0.6832

0.67830.67380.66790.66260.68790.69940.70320.70050.69590.66050.68600.69790.70170.69920.69530.69110.68550.6816

0.67780.67230.68130.69380.69770.69560.69220.68850.68350.67980.67670.67220.25 0.6636

0.15 0.6557

0.69110.68510.68080.67660.67070.33700.34780.35470.35290.35130.32290.64900.67440.68730.69120.68930.68690.68340.67880.67530.6726

0.66870.1 0.3333

0.34400.35140.35010.34950.34510.34090.3367

0.33210.32780.3226

0.1 0.6387

0.66370.67630.68070.67940.6772

0.67420.67080.66780.6652

0.66170.32580.33680.34450.34350.34310.33900.33530.3316

0.32720.32320.31820.62350.64790.6606

0.66550.6652

0.66430.66140.65880.65580.65350.65050.60400.62870.64180.64640.64660.64570.64280.64080.6382

0.63600.63330.60010.61300.61720.61730.61670.61410.61270.61080.60920.60700.55320.56550.57010.57090.57040.5691

0.56850.56690.5656

0.56360.05 0.3034

0.31740.32810.33600.3354

0.33540.33150.32800.32440.32030.31670.31250.31370.32140.32090.32100.31790.31500.31210.30860.30530.30190.05 0.5760

0.28450.29400.30120.30160.30170.29910.2966

0.29430.29150.28820.28560.53080.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22

pTcone40/Et

pTcone30/Et

Figure 4.13: Step-by-step isolation optimization: isolation map at the first step (top), at
the second step (middle), and at the third step (bottom) in µe channel. As examples, only
ET = 10-15 (left) and 15-20 GeV (right) are shown where the impact of the W +jets are
relatively large.

4.5 Determination of Lepton Selection

4.5.3

79

Vertex Requirements

The electron track impact parameter resolutions are significantly improved in 2012 due tothe new Gaussian Sum Filter (GSF) algorithm based on a non-linear generalization of the
Kalman Fitter, where the error distributions in the track reconstruction are approximatedas weighted gaussian sums. After the loose matching between tracks and electromagnetic
clusters, the candidate electron or photon conversion tracks above 1 GeV in the event arerefit with the GSF algorithm (see Section 4.1.1).
While in the 2011 reconstruction, there is no special treatment applied to the electron
tracking. All tracks are fit using a pion particle hypothesis. An electron can lose a significant amount of its initial energy due to bremsstrahlung eﬀects when interacting with thematerial in the inner detector and surrounding infrastructure. The lack of special treatment
results in poorly determined track parameters, particularly in the bending plane, and a significant dependence of electron tracking parameters on the amount of material encountered.
The optimization of vertex parameters, namely d0 significance and z0 impact parameters, benefits by the GSF improvements. In addition, the cut on z0 is changed into a cut
on z0 sin θ to take into account the fact that more forward tracks have a longer projection
on the z-axis and thus a larger uncertainty. The diﬀerence of this change is significant at
higher η as shown in Figure 4.14. Also d0 significance and z0 sin θ distributions just after
the isolations are shown in Figure 4.15. After the isolation, both vertexing parameters do
not work well as good discriminants because most of background electrons originated fromlight flavors such as charged/neutral pions are rejected by the isolations.

Figure 4.14: Comparison of z0 and z0 sin θ impact parameters in |η| > 2.0, where the red
is prompt electrons and the green is non-prompt (hadron background) electrons.

80

4.6 Determination of Lepton Selection

d0sig_Sig

z0sin_Sig

0.07
0.06

d0sig(sig)

0.16

d0sig(bkg)0.14

z0sinθ(sig)z0sinθ(bkg)

0.12

0.05

0.1

0.04

0.08
0.03
0.06
0.02

0.04

0.01

0.02

0
0

1

2

3

4

5

6

7

8

9

0
0

10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Figure 4.15: d0 significance and z0 sin θ after isolation cuts. Red and blue solid lines arereal and background electrons, respectively.

For the d0 significance and z0 parameter optimizations, the same procedure as theidentification or isolation is applied. In order to assess the eﬀect of pile-up, the optimization
was made in the beginning of 2012, with the variations of the average mu (< µ >). From
Figure 4.16, it was found that the vertexing parameters are robust against high pileups,
and that the optimal point does not change between low and high < µ >.
sensitivity scan for impact parameters1.02385

1.02224

1.01455

1.01052

1.00828

1.006631.00592

1.00403

1.00418

1.00325

1.003311.00334

1.00128

1.00131.06

91.02503

1.02326

1.01661

1.01255

1.010291.00862

1.00791

1.00601

1.00615

1.005221.00527

1.005311.00428

1.00431.02484

1.024111.01851.01439

1.012111.010431.00971

1.00781.00794

1.007

1.00706

1.007091.00606

1.00608

1.02824

1.02809

1.023421.0192

1.01686

1.015161.014421.01355

1.01371.01382

1.01388

1.01391

1.01286

1.01288

8

1.05

7

10
1.02047

1.01973

1.012631.00934

1.007231.00609

1.021611.02071.021421.02161.01466

1.011311.009191.00804

1.01661

1.013211.01105

1.00989

1.02479

1.02559

1.02153

1.01805

1.01583

1.014641.03155

1.04486

1.035811.03239

1.02865

1.02633

1.04927

1.04884

1.04471

1.042161.05027

1.05902

1.06171.05699

1.054221.04461

1.05785

1.06095

1.058111.00347

1.016131.01846

1.015421.00565

1.00399

1.00424

1.00327

1.00332

1.00335

1.00126

1.00129

1.00761.00592

1.00944

1.00775

1.006171.0052

1.00524

1.00801

1.00703

1.007071.00528

1.004221.00425

1.007111.00605

1.00608

1.01418

1.013541.01381.01388

1.01392

1.013961.01287

1.01291

1.026211.02572

1.043171.04261

1.02503

1.02529

1.04187

1.042141.02537

1.025421.025451.02433

1.02436

1.0422

1.04225

1.04229

1.0411

1.04113

1.055191.05451

1.05496

1.0552

1.05527

1.05532

1.05535

1.05535

1.055391.055

1.01451.05591.05645

1.05685

1.01527

1.01572

1.01599

1.05707

1.05713

1.05718

1.0572

1.0572

1.05724

1.016191.01626

1.016311.01634

1.01634

1.01636

1.06

9
1.05

8
7

1.04

6

1.04

6
1.03502

1.038431.03441.02995

1.027481.02682

1.02604

1.025141.02529

1.025411.02547

1.02551.024411.024431.04838

1.052021.05092

1.04604

1.04338

1.04385

1.04301

1.04204

1.04219

1.042311.04237

1.04241.04124

1.04127

1.05437

1.06178

1.06375

1.05839

1.05551

1.05597

1.05503

1.05524

1.05538

1.05551

1.05556

1.05561.05562

1.05565

1.03

5
4

1.02

3

5
4

1.03

1.02

3
1.049431.062131.064421.06104

1.05778

1.058221.05853

1.05871.05881.05891

1.05896

1.05899

1.05901

1.05904

1.00704

1.01964

1.02105

1.017641.01665

1.017

1.017311.017441.01751

1.01761

1.017641.01767

1.01769

1.0177

1.01

2
1

d0sig

d0sig

sensitivity scan for impact parameters
10

0.2

0.4

0.6

0.8

1

1.2

1.4
z0sin

2
1

0.2

0.4

0.6

0.8

1

1.2

1.01

1.4
z0sin

Figure 4.16: Significance in 2-dimensional map of vertexing parameters for electrons. The
left and the right show significances with < µ >< 20 and < µ >> 20, respectively.

According to the updated isolation and identification operating points, the impact parameters optimization is also repeated. Since the Very Tight likelihood already includes
d0 significance as input to create the PDFs, the optimization of the d0 significance is justa confirmation whether or not further cut on the d0 significance on the top of the likelihood works better. The updated 2-D map in d0 significance versus z0 sin θ is shown in
Figure 4.17. It is found that further cut on the d0 significance works better. A summaryof impact parameter cuts is also found in Table 4.8.

81

|d0sig/d0|

4.6 Determination of Lepton Selection

10 1.0158 1.0247 1.0240 1.0230 1.0221 1.0217 1.0213 1.0208 1.0206 1.0204 1.0205 1.0205 1.0205 1.0205 1.0205
9 1.0159 1.0251 1.0243 1.0234 1.0225 1.0221 1.0217 1.0213 1.0210 1.0209 1.0209 1.0209 1.0209 1.0209 1.0209
8 1.0163 1.0258 1.0251 1.0243 1.0233 1.0230 1.0227 1.0222 1.0220 1.0219 1.0219 1.0219 1.0219 1.0219 1.0219
7 1.0168 1.0264 1.0258 1.0250 1.0242 1.0239 1.0236 1.0231 1.0229 1.0228 1.0228 1.0228 1.0228 1.0228 1.0229
6 1.0173 1.0271 1.0266 1.0259 1.0250 1.0247 1.0245 1.0241 1.0239 1.0238 1.0238 1.0238 1.0238 1.0238 1.0238
5 1.0180 1.0284 1.0281 1.0274 1.0267 1.0264 1.0261 1.0258 1.0257 1.0255 1.0255 1.0255 1.0255 1.0256 1.0256
4 1.0177 1.0282 1.0282 1.0278 1.0272 1.0269 1.0266 1.0263 1.0261 1.0260 1.0260 1.0261 1.0261 1.0261 1.0261
3 1.0172 1.0290 1.0293 1.0289 1.0283 1.0281 1.0279 1.0276 1.0275 1.0273 1.0274 1.0274 1.0274 1.0274 1.0274
2 1.0105 1.0231 1.0235 1.0233 1.0229 1.0227 1.0225 1.0223 1.0221 1.0220 1.0220 1.0220 1.0220 1.0221 1.0221
1 0.9569 0.9732 0.9744 0.9744 0.9743 0.9742 0.9741 0.9740 0.9738 0.9738 0.9738 0.9738 0.9738 0.9738 0.9738
0.2
0.4
0.6
0.8
1
1.2
1.4
|z0sinθ|Figure 4.17: Significance in 2-dimensional map of vertexing parameters for electrons.

4.6

Muon Optimization

4.6.1

Isolation

The procedure of muon optimization is the same as the electron optimization. In orderto verify all the changes from the previous analysis, the step-by-step optimization is also
made as shown in Figure 4.18. For muons, the optimization suggests that the calorimeter
isolation should be tightened as well as since the identification is not applied to the muon
selection. The cut value on the calorimeter isolation is only about 50 % compared to theone for electrons. Also as discussed in the electron optimization, note that there is anupper limit on the cut value on the track isolation to be a subset of the trigger isolation(Ptcone20/pT < 0.12) on EF mu24i tight. A summary of muon isolation selection is foundin Table 4.11.
Table 4.11: Muon isolation and impact parameters as a function of pT .
pT [GeV]
10-15
15-20
20-25
25-

Etcone30
EtConeCor30/pT <0.06
EtConeCor30/pT <0.12
EtConeCor30/pT <0.18
EtConeCor30/pT <0.30

ptconePtcone40/pT <0.06
Ptcone30/pT <0.08
Ptcone30/pT <0.12
Ptcone30/pT <0.12|d0 /σd0 |3333|z0 sin θ|
1.0 mm
1.0 mm
1.0 mm
1.0 mm0.3498

0.34980.34980.32580.30280.28710.27380.26010.24460.23220.2206

0.35170.35170.32780.30490.28920.27590.26220.2466

0.23430.22260.35460.35460.33100.30790.29220.27890.26520.24970.23720.22540.3 0.3569

0.35690.35690.33350.3106

0.29490.28180.26790.25230.23980.22810.36010.36010.36010.33700.31440.29880.28550.27170.25600.24340.23170.36280.36280.36280.34040.31800.30250.28920.27540.25980.24740.23550.35 0.3517
0.35460.25 0.3663

0.65190.65450.65360.64770.6404

0.63210.62300.61310.60300.59320.65270.65540.65460.64890.64180.63370.62470.61500.60510.59540.65360.65630.65580.65030.64330.63540.62670.61710.6075

0.3 0.6546

0.65460.65730.65710.65180.64500.63720.62870.61940.61000.60080.65570.65570.65840.65840.65340.64690.63930.63110.62210.61280.60390.65690.65690.65970.66000.65520.64900.6417

0.63380.62510.61620.60750.65360.25 0.6582

0.59800.36630.36630.3446

0.32230.30680.29340.2796

0.26410.2516

0.23960.6582

0.66100.66170.65730.65140.6444

0.63680.62850.61990.61150.37060.3706

0.34920.32730.31200.29870.28500.26940.25680.24480.65950.65950.6624

0.66340.65940.65390.64720.64000.63200.62390.61580.2 0.3752

0.37520.37520.35420.33250.31710.30360.29010.2751

0.26270.25070.2 0.6608

0.66080.66380.6652

0.66170.65650.65030.64350.63600.62820.6206

0.37940.37940.37940.35890.33790.32270.3096

0.29650.2816

0.26910.2572

0.66200.66200.66500.6671

0.66390.65920.65340.64710.6401

0.63280.62570.38430.38430.38430.36470.34480.33010.31730.30420.28950.27710.2651

0.66280.66580.66840.66580.66160.65630.65050.64400.63730.63080.38970.38970.37160.35210.33760.32550.31240.29790.28540.27360.15 0.6635

0.66280.66350.6666

0.66970.6676

0.66390.65910.65390.64800.64200.3956

0.3956

0.3956

0.37860.3606

0.34680.33460.32190.30780.29520.2844

0.66300.66300.66620.66990.6686

0.6654

0.66130.65680.65170.64640.64110.39940.39940.39940.38350.3666

0.3536

0.34220.33050.31730.30520.2951

0.6611

0.66110.66430.66870.66800.66550.66210.65820.65390.64920.64470.40390.40390.40390.38930.37370.36280.35170.34100.32930.31810.30850.65620.65620.65950.66450.6646

0.66290.66020.65700.65330.64950.64570.40720.40720.40720.39500.38190.37290.36300.35330.34200.33130.32280.64650.64980.65550.65630.65530.65330.65070.64780.64490.64200.40800.39790.38860.38070.37320.36550.35690.34750.34020.05 0.6283

0.64650.40800.62830.63150.63780.6391

0.63870.6374

0.63550.63350.63150.62930.40020.4002

0.39350.38870.38370.37880.37300.36680.35990.35430.59350.59350.59660.60290.60460.60480.60400.60280.60150.60020.59870.05 0.4080
0.40020.1

0.63600.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22

pTcone40/Et

pTcone30/Et

0.40750.40750.40750.37500.34610.32710.31120.29500.41020.41020.37770.34860.32970.31370.29750.27930.26500.2516

0.41430.41430.38200.35250.33330.31740.30110.28280.26840.25480.3 0.4176

0.4176

0.4176

0.38530.35600.33670.32090.30430.28580.27140.25780.42230.42230.42230.39000.36080.34150.32550.30890.29020.2756

0.42620.42620.4262

0.39470.36540.34620.33000.31330.29480.28020.26640.82210.80880.79030.77220.75360.73510.71620.43130.40040.37100.3516

0.33510.31830.29980.28510.27120.25 0.8237

0.81910.43130.82370.82670.81390.79590.77820.76000.74180.72340.70560.68910.43780.43780.43780.40680.37750.3582

0.34170.32490.30610.29120.27710.82850.82850.83160.81950.80210.78480.76700.74930.73130.71390.69770.44460.44460.4446

0.41380.38440.36470.34780.33110.31300.29810.28410.83360.83360.83690.82570.80880.79210.77500.75780.74030.72340.70750.45100.45100.45100.42050.3916

0.37180.35530.33900.32070.3057

0.29160.83910.83910.84250.83240.81630.8002

0.78360.76700.75010.73380.45880.45880.45880.42890.40100.38150.3651

0.34850.33030.31530.30090.84410.84760.83860.82350.80830.79240.77670.76050.74480.73030.46750.43910.41100.39150.37550.35870.34050.32510.31090.15 0.8501

0.84410.46750.85010.85370.84580.83160.81720.80210.78730.77200.75710.74340.47740.47740.47740.44990.42310.40380.38740.37080.3527

0.33690.32360.85480.85480.85870.85220.83940.82620.8122

0.7986

0.78450.77070.75780.1 0.4842

0.48420.48420.45770.43170.41300.39730.38170.36450.34910.33640.1 0.8578

0.85780.86170.85700.84580.83390.82130.80870.79580.78320.77150.49300.49300.49300.46760.44230.42600.41010.39540.3796

0.36490.35260.85710.85710.86120.85830.84900.83870.82760.81630.80470.79350.78310.50120.50120.50120.47850.45570.44120.42620.41210.3961

0.38150.37030.84960.85400.85330.84590.83760.82810.81810.80810.79900.79020.50770.50770.48700.46850.45450.44200.43000.41700.4032

0.39290.05 0.8303

0.84960.83030.83470.83610.83070.82410.81640.80830.8006

0.79350.78640.5026

0.5026

0.48680.47450.46360.45430.44390.43340.42230.41350.78650.78650.79080.79330.78990.78540.77990.77370.76780.76270.75760.35 0.4102
0.41430.25 0.4313
0.2

0.15 0.4675

0.05 0.5077
0.5026

0.27690.2626

0.2492

EtCone30/Et

0.1

EtCone30/Et

0.65190.35 0.6527

0.37060.15 0.3897

EtCone30/Et

EtCone30/Et

4.6 Determination of Lepton Selection

0.26200.80340.80340.80600.69190.67280.80590.8084

0.7936

0.77370.75450.73510.71550.69570.67660.65900.80870.81130.79680.77720.75820.73890.71950.69990.6811

0.66370.3 0.8117

0.81170.81440.80040.78100.76220.74310.72400.70460.68590.66870.81520.81520.81800.80430.78530.76680.74790.72910.70990.69150.67450.69810.68130.35 0.8059
0.80870.8191

0.2

0.79090.77070.75130.73170.71200.65500.71850.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22

pTcone40/Et

pTcone30/Et

0.56280.35 0.5654

0.56280.56280.53100.50330.48430.46720.4486

0.42690.4092

0.39230.56540.56540.53370.5061

0.48720.47010.45160.42980.41220.39530.56930.56930.56930.53810.5102

0.49130.47430.45590.43410.41650.39940.3 0.5725

0.57250.57250.54140.51390.49500.47830.45970.43780.42020.40340.57690.57690.57690.54610.51910.50040.48350.46500.44310.42540.40860.58050.58050.35 0.9447

0.9431

0.9431

0.9476

0.94530.93520.92310.90980.89550.88020.86500.85040.94470.9492

0.94720.93720.92540.91220.89820.88310.86810.85370.93960.92790.91500.90120.88640.87160.85750.9464

0.94640.95090.94920.3 0.9482

0.94820.95290.95150.94210.93070.91800.90440.88990.87550.86160.95030.95030.95500.95400.94500.93390.92140.90820.89400.87980.86620.95270.95270.95740.95690.94820.93760.92540.91250.89870.88480.87150.58050.55080.52390.50550.48860.47010.44850.43120.58520.58520.55640.52970.51130.49430.47590.45450.43700.42010.25 0.9553

0.95530.96010.96000.95180.94160.92980.91740.90400.89060.87770.59100.59100.59100.5624

0.53630.51830.50140.48330.46190.44440.42730.95800.95800.96290.96330.95570.94590.93450.92260.90970.89670.88420.2 0.5970

0.59700.59700.56900.54310.43570.2 0.9607

0.96070.96570.96680.95980.95050.93980.92830.91600.90350.89150.60230.60230.60230.57500.55000.53210.51570.49850.4782

0.46120.4446

0.96330.96330.96840.97040.96400.95530.94510.93420.92260.91080.89930.6086

0.6086

0.6086

0.5822

0.55880.5416

0.52580.5086

0.48880.47190.45530.96520.9704

0.97320.9676

0.95960.95010.94000.92900.91790.61520.61520.59080.56780.55100.53590.51890.49940.4826

0.46640.15 0.9672

0.96520.9672

0.97250.9761

0.97120.96390.95510.94590.93570.92540.91560.62210.62210.62210.59900.57800.56200.54690.53050.51160.49470.4801

0.96740.9674

0.97280.9774

0.9736

0.96720.9594

0.9511

0.94200.93270.92360.62540.62540.62540.60370.58390.56890.55490.54000.52250.50640.49280.96510.96510.97050.9762

0.97350.9681

0.96130.95390.94590.93760.9296

0.62880.62880.62880.60870.59020.57800.56440.55080.53540.5206

0.50790.95800.95800.96350.97020.96880.9646

0.95890.95250.94550.93830.93140.62930.62930.62930.61220.5967

0.58680.57460.56220.54730.5332

0.94280.94830.95630.62470.60990.59910.59020.58090.57100.55970.54730.53780.05 0.9137

0.94280.62470.60510.60510.59480.58950.58370.57770.56990.5616

0.55230.54490.85790.25 0.5852

0.15 0.6152
0.1

0.05 0.6247
0.60510.52500.50800.49010.46970.45250.4141

EtCone30/Et

EtCone30/Et

82

0.52210.1

0.90720.95590.95300.9484

0.94300.93720.93150.92590.91370.91910.92790.92850.9266

0.92310.91900.91470.91050.90620.85790.86290.87160.87300.87210.86990.86690.86370.86080.85780.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22

pTcone40/Et

pTcone30/Et

Figure 4.18: Step-by-step isolation optimization: isolation map at the first step (top), at
the second step (middle), and at the third step (bottom) in eµ channel. As examples, only
pT = 10-15 (left) and 15-20 GeV (right) are shown where the impact of the W +jets are
relatively large.

83

4.7 Determination of Lepton Selection

4.6.2

Vertex Requirements

For muons, the d0 significance is particularly important since it is very sensitive to muons
from heavy flavor decays that make longer tail in transverse direction, and that are notrejected much by the isolations. Since those background muons are dominant source of the
fake background like the W +jets, the d0 significance needs to be tightened.
While the z0 sin θ is less sensitive to those background muons because the backgroundmuons do not produce longer tail on beam axis. 8 Figure 4.19 shows d0 significance andz0 sin θ distributions after the isolations, where red and blue solid lines are real and background muons, respectively.
z0sin_Sig

d0sig_Sig
0.1

0.08

d0sig(sig)0.12

z0sinθ(sig)d0sig(bkg)0.1

z0sinθ(bkg)

0.08
0.06
0.06
0.04
0.04
0.02

0
0

0.02

1

2

3

4

5

6

7

8

9

10

0
0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Figure 4.19: d0 significance and z0 sin θ after isolation cuts. Red and blue solid lines arereal and background muons, respectively. Even after the isolations, d0 is still sensitive tomuons from heavy flavor decays, while z0 sin θ is less sensitive to those backgrounds.

The muon vertexing parameters are also optimized. In order to take into account thecorrelation between the impact parameters and isolations, the optimization is made justafter isolation cuts. Figure 4.20 is the result of the optimization.
The optimization suggests that d0 significance is very sensitive in the analysis, while theanalysis is less sensitive to the z0 sin θ. For the z0 , the looser operating point (|z0 sin θ| < 1mm) than the electron’s one is taken as a cut value. A summary of impact parameter cutsis also found in Table 4.11.

4.7

Additional Selection Eﬃciency

After evaluating the identification eﬃciency, the eﬃciency for all additional selections thatare specific for each physics analysis, is also measured using the Z tag-and-probe. The
8

Strictly speaking, secondaries make longer tails in both transverse and beam direction but it is harder
to discriminate the secondaries from primary particles using z0 impact parameter.

84|d0sig/d0|

4.7 Determination of Lepton Selection

10 1.1772 1.2034 1.2082 1.2100 1.2109 1.2115 1.2119 1.2122 1.2124 1.2125 1.2125 1.2126 1.2126 1.2126 1.2126
9 1.1774 1.2036 1.2085 1.2103 1.2112 1.2118 1.2122 1.2125 1.2127 1.2128 1.2129 1.2129 1.2129 1.2129 1.2130
8 1.1776 1.2040 1.2089 1.2107 1.2117 1.2122 1.2127 1.2129 1.2131 1.2132 1.2133 1.2133 1.2134 1.2134 1.2134
7 1.1780 1.2044 1.2094 1.2112 1.2121 1.2128 1.2132 1.2134 1.2136 1.2137 1.2138 1.2138 1.2139 1.2139 1.2139
6 1.1783 1.2049 1.2099 1.2118 1.2127 1.2134 1.2138 1.2140 1.2142 1.2143 1.2144 1.2144 1.2145 1.2145 1.2145
5 1.1788 1.2055 1.2105 1.2124 1.2134 1.2140 1.2144 1.2147 1.2149 1.2150 1.2150 1.2151 1.2151 1.2151 1.2151
4 1.1791 1.2059 1.2111 1.2129 1.2139 1.2145 1.2149 1.2152 1.2154 1.2155 1.2155 1.2156 1.2156 1.2156 1.2156
3 1.1793 1.2062 1.2113 1.2131 1.2141 1.2147 1.2151 1.2153 1.2155 1.2156 1.2157 1.2157 1.2157 1.2157 1.2158
2 1.1781 1.2051 1.2101 1.2118 1.2127 1.2132 1.2136 1.2138 1.2140 1.2141 1.2141 1.2142 1.2142 1.2142 1.2142
1 1.1486 1.1778 1.1830 1.1847 1.1855 1.1860 1.1863 1.1865 1.1867 1.1867 1.1868 1.1868 1.1868 1.1868 1.1869
0.2
0.4
0.6
0.8
1
1.2
1.4
|z0sinθ|Figure 4.20: Significance in 2-dimensional map of vertexing parameters for muons.

eﬃciency can be written as follows:
ϵdata
add. =
ϵMC
add. =

bkg
data
Nrec.+id.+add.
− Nrec.+id.+add.
bkg
data
Nrec.+id.
− Nrec.+id.
MC
Nrec.+id.+add.
MC
Nrec.+id.

,,(4.17)(4.18)

where Nrec.+id. is the number of denominators and Nrec.+id.+add. is the number of numerators. The identification must be required for both the numerator and denominator totake into account the correlation between the identification and additional selection whenmeasuring the eﬃciency for the additional selection. As is done for the identification, thescale factor is also evaluated as a function of pT to correct for possible mis-modeling insimulation.

4.7.1

Electron isolation and vertexing parameterFor electrons, the followings are considered as additional selection:• calorimeter isolation (topoEtcone30/ET )• track isolation (Ptcone40/pT for 10-15 GeV and Ptcone30/pT for pT > 15 GeV)• longitudinal impact parameter (|z0 sin θ| < 0.4 mm)• transverse impact parameter significance (|d0 /σd0 | < 3)

85

4.7 Determination of Lepton Selection• conversion flag and B-Layer hits at 2.37 < |η| < 2.47 for pT > 25 GeV (see Section 4.5.1),
Figure 4.21 shows comparison of data and simulation in isolation distributions. The
overall agreement looks reasonable except for lower tail of the calorimeter isolation. Given
that the calorimeter isolation cut is made at higher tail (topoEtcone30/ET < 0.20 or higher
depending on ET ), the diﬀerence in eﬃciency between data and simulation ends up small
but the small mis-modeling is corrected for by scale factor.

Figure 4.21: Comparison of calorimeter isolation (left) and track isolation (right) distributions between data and simulation. Both data and simulation are collected with Z
tag-and-probe method, and are normalized to unit area.
Figure 4.22 shows invariant mass mee (tag and probe pairs) distributions with probe pT= 10-15 GeV after the identification where the background is modeled with same sign events
as defined in Section 4.3.1. Even for denominator samples, the background contaminationis less than 3 %. The contamination remains much smaller (∼0.5 %) in the numerator.
Zee Invariant Mass : 10 GeV - 15 GeV
Events / ( 1 )Events / ( 1 )Zee Invariant Mass : 10 GeV - 15 GeV

250

200

200
180
160
140
120

150

100
80

100
60
40

50

20
0
65

70

75

80

85

90

95

100

105

110
115
Mee GeV

0
65

70

75

80

85

90

95

100

105

110
115
Mee GeVFigure 4.22: Invariant mass mee distributions with probe pT = 10-15 GeV before (left) andafter (right) passing all additional selections. Here green and light blue line show expectedsignal and background, respectively.

86

4.7 Determination of Lepton Selection

Figure 4.23 shows the eﬃciency and corresponding scale factor. In overall, the eﬃciency
is well modeled in simulation, which results in less than 2 % deviation from unity on thescale factor. The bump at pT = 25 GeV is due to the requirements of conversion flagand B-Layer hits at 2.37 < |η| < 2.47 for pT > 25 GeV (see Section 4.5.1). To assess theuncertainty on the scale factor, two systemtic uncertainties are considered:• Z mass range is varied to be wider |mZ − mee | < 20 GeV and to be narrower |mZ −mee | < 5 GeV to see the background fluctuation that is ≲ 1 % eﬀect.

1.2

Scale Factor

Efficiency• pileup dependence is also evaluated by varying < µ > (< µ >≥ 20 and < µ >< 20).
The vertexing parameter resolution is expected to decrease with increased pileups.
Also isolation energy is expected to increase with higher pileups.

data (20.7 fb-1)
Full sim
AFII

1.1
1

1.04

Full sim (20.7 fb-1)
1.02

AFII (20.7 fb-1)
1

0.9
0.8

0.98

0.7

0.96
10

20

30

40

50

60

10

20

30

Electron Et GeV

40

50

60

Electron Et GeV

Figure 4.23: Electron eﬃciency for all the additional selections (left) and corresponding
scale factors (right) as a function of pT . Conversion bit and B-Layer requirements are also
taken into account above 25 GeV.
Table 4.12 summarizes the uncertainties on the scale factor for individual components.
Table 4.12: Electron additional selection scale factor and corresponding uncertainties.
ET
10-15
15-20
20-25
25-30
30-35
35-40
40-45
45-50

scale factor
1.01691.00420.99920.99140.98970.99080.9911
0.9922stat.
0.00750.00350.00180.00140.00100.00080.00070.0009bkg variation
0.01060.00400.00260.00200.00130.00090.00090.0011pile-up0.00900.00700.00700.00600.00500.00500.00500.005087

4.8 Determination of Lepton Selection

4.7.2

Muon isolation and vertexing parameter

For muons, the followings are considered as additional selection:• calorimeter isolation (Etcone30/ET )• track isolation (Ptcone40/pT for 10-15 GeV and Ptcone30/pT for pT > 15 GeV)• longitudinal impact parameter (|z0 sin θ| < 1.0 mm)• transverse impact parameter significance (|d0 /σd0 | < 3)
Figure 4.24 shows invariant mass mµµ (tag and probe pairs) distributions with probe
pT = 10-15 GeV after the identification where the background is modeled with same sign
events as well. For denominator samples, the background contamination is less than 1 %and is smaller for numerator samples.
Events / ( 1 )Zµµ Invariant Mass : 10 GeV - 15 GeV

Events / ( 1 )Zµµ Invariant Mass : 10 GeV - 15 GeV

16000

12000

16000

20000

14000

18000

14000

10000

12000
8000

10000

6000

8000
6000

4000

4000
2000

2000
0
65

70

75

80

85

90

95

100

105

110
115
Mee GeV

0
65

70

75

80

85

90

95

100

105

110
115
Mee GeVFigure 4.24: Invariant mass mµµ distributions with probe pT = 10-15 GeV before (left) andafter (right) passing all additional selections. Here green and light blue line show expectedsignal and background, respectively.
Figure 4.25 shows the eﬃciency and corresponding scale factor. In overall, the eﬃciency
is well modeled in simulation except for the lowest pT muons. This is due to the mismodeling of the calorimeter isolation. The systematic uncertainty is evaluated in the same
way as is done for electrons, and is summarized in Table 4.13.

4.8

Summary of Lepton Selection and Uncertainties

4.8.1

Electron Selection and Eﬃciency

The optimized electron definition used in the analysis is summarized in Tables 4.14.
The eﬃciency for electrons that pass all the optimized selection criteria, with respect totruth electrons from the Higgs signal sample, is shown in Figure 4.26. The overall eﬃciency
is ∼ 70 %. Finally all electron systematics that are relevant to the analysis are summarizedin Table 4.15.

4.8 Determination of Lepton Selection
1.4

Scale Factor

Efficiency

88

1.3
1.2
1.1

s = 8 TeV,

∫ L dt = 20.7 fb

-1

1

1.04
s = 8 TeV,

1.02

∫ L dt = 20.7 fb

-1

1
0.98

0.9

0.96

0.8
0.94

0.7

data (2012)

0.6

MC12 (Full sim Powheg)

0.5

data/mc(Full sim)
0.92
0.9

10

20

30

40

50

60

10

20

30

40

Muon Pt GeV

50

60

Muon Pt GeV

Figure 4.25: Muon eﬃciency for all the additional selections (left) and corresponding scale
factors (right) as a function of pT .

Table 4.13: Muon additional cuts scale factor and corresponding uncertainties.
pT
10-15
15-20
20-25
25-30
30-35
35-40
40-45
45-50

scale factor
0.95430.98140.99090.9934
0.99390.99380.9941
0.9942

stat.
0.00460.00230.00100.00050.00040.00030.00020.0002

bkg variation
0.02210.00740.00230.00080.00070.00050.00030.0003pile-up
0.01000.00900.00600.00500.00500.00500.00500.0050

Table 4.14: Electron selection as a function of ET . ∆R for isolations is set to be 0.3,
except for track isolation for 10-15 GeV in which ∆R = 0.4 is used. “CBL” refers to
the conversion flag and B-Layer hit requirements extended to all η (within the electron
acceptance coverage).
ET GeV
10-15
15-20
20-25
> 25

PID
Very Tight LH
Medium++with “CBL”

Cal Iso (∆R<0.3)
cal /E < 0.20
ΣETT
cal /E < 0.24
ΣET
T

Trk Iso (∆R<0.3)
Σptrk
T /ET < 0.06
Σptrk
T /ET < 0.08

cal /E < 0.28
ΣET
T

Σptrk
T /ET < 0.10

Vertexd0 /σd0 < 3.0,
z0 sin θ < 0.4 mm

89Selection Efficiency in Truth

Selection Efficiency in Truth

4.8 Determination of Lepton Selection

1.6
1.4

Updated Electron Selection

1.2

Moriond 2013 Electron Selection

1
0.8

1.6
1.4

Updated Electron Selection

1.2

Moriond 2013 Electron Selection

1
0.8

0.6

0.6

0.4

0.4

0.2

0.2

0

-2

-1

0

1

0
10

2
Electron η

15

20

25

30

35

40
45
50
Electron p GeV
T

Figure 4.26: Electron selection eﬃciencies with respect to truth electrons for a 125 GeV
Higgs signal versus η (left) and pT (right). Only statistical uncertainty is shown.
Table 4.15: Updated electron selection eﬃciencies and total uncertainties (relative) for a
125 GeV Higgs signal sample. All uncertainties are added in quadrature. (Not included
energy scale and resolution).
ET
10-15
15-20
20-25
25-30
30-35
35-40
40-45
45-

4.8.2

Total eﬀ.
0.412
0.619
0.668
0.755
0.770
0.796
0.798
0.813

Iso. unc.
0.016
0.009
0.008
0.007
0.007
0.006
0.006
0.006

ID+Rec. unc.
0.016
0.024
0.027
0.014
0.005
0.003
0.002
0.002

Total unc.
0.022
0.025
0.028
0.016
0.009
0.007
0.006
0.006

Muon Selection and Eﬃciency

The optimized muon definition used in the analysis is summarized in Tables 4.16.
Table 4.16: Muon selection as a function of pT . ∆R for isolations is set to be 0.3, except
for track isolation for 10-15 GeV in which ∆R = 0.4 is used.
pT GeV
10-15
15-20
20-25
> 25

Cal Isocal /p < 0.06
ΣETT
cal /p < 0.12
ΣETT
cal /p < 0.18
ΣETT
cal /p < 0.30
ΣET
T

Trk IsoΣptrk
T /pT < 0.06
Σptrk
T /pT < 0.08
Σptrk
T /pT < 0.12

IP
d0 /σd0 < 3.0,
z0 sin θ < 1.0 mm

90

4.8 Determination of Lepton Selection

1.6
1.4

Updated Muon Selection

1.2

Moriond 2013 Muon Selection

1
0.8

Selection Efficiency in Truth

Selection Efficiency in Truth

The eﬃciency for muons that pass all the optimized selection criteria, with respect totruth muons from the Higgs signal sample, is shown in Figure 4.27. The overall eﬃciency
is ∼ 70 %. Finally all electron systematics that are relevant to the analysis are summarizedin Table 4.17.
1.6
1.4

Updated Muon Selection

1.2

Moriond 2013 Muon Selection

1
0.8

0.6

0.6

0.4

0.4

0.2

0.2

0

-2

-1

0

1

2

Muon η

0
10

15

20

25

30

35

40

45
50
Muon p GeV
T

Figure 4.27: Muon selection eﬃciencies with respect to truth muons for a 125 GeV Higgs
versus η (left) and pT (right). Only statistical uncertainty is shown.

Table 4.17: Updated muon selection eﬃciencies and total uncertainties (relative) for a 125
GeV Higgs signal sample. All uncertainties are added in quadrature. (Not included energy
scale and resolution).
pT
10-15
15-20
20-25
25-30
30-35
35-40
40-45
45-

Total eﬀ.
0.574
0.808
0.904
0.924
0.932
0.942
0.943
0.944

Iso. unc.
0.027
0.012
0.007
0.006
0.006
0.005
0.005
0.005

ID+Rec. unc.
< 0.005< 0.005< 0.005< 0.005< 0.005< 0.005< 0.005< 0.005

Total unc.
< 0.027< 0.013< 0.009< 0.008< 0.008< 0.007< 0.007< 0.007

Part II

Analysis for the Measurement of
the Higgs Boson Couplings

91Chapter 5

H→ W W ∗→ ℓνℓν Analysis
The H→ W W ∗ → ℓνℓν (ℓ = e, µ) analysis is particulary sensitive to the coupling measurement via gluon fusion (ggF) and vector boson fusion (VBF) production processes. This isdue to: (1) the second largest branching fraction to W W ∗ for the SM Higgs boson with amass of mH = 125 GeV, and (2) the dilepton decay mode of the W pair (W W → ℓνℓν)that occurs in 5 % of W W events, allows Higgs candidates to be identified with a good (10% or better) signal-to-background ratio (S/B).
In this chapter the overview of the H→ W W ∗ → ℓνℓν analysis is presented starting fromsignature of H→ W W ∗ → ℓνℓν and analysis classification as an “Introduction (Section 5.1)”.
After the introduction, the following topics are discussed: “Analysis Strategy (Section 5.2)”,“Monte Carlo Simulation (Section 5.3)”, “Event Selection (Section 5.4)”, “Background Estimation (Section 5.5)”, and “Systematic Uncertainties (Section 5.6)”. Since the modelingof the W +jets background is diﬀerent from other backgrounds, the W +jets background isseparately discussed in next Chapter 6. Furthermore the diboson (other V V ) backgrounds
are also discussed separately after the W +jets background in Chapter 7 as the modeling of
the diboson backgrounds is deeply related to the W +jets background.

5.1

Introduction

A typical signature of the H→ W W ∗ → ℓνℓν for the ggF and VBF production processes is
illustrated in Figure 5.1. Regardless of the Higgs boson production processes, the signature
contains two genuine isolated high pT leptons from W boson decays and a large missing
miss ) from two neutrinos in the final state. In the ggF production
transverse energy (ETprocess, there is no jet in the final state in the leading order (LO) but possibly there is one
jet (or two jets) that arises from initial state gluon radiation. On the other hand, the VBF
signature is characterized by two forward/backward jets in the final state, making a highinvariant mass (mjj ) and a large rapidity gap (∆yjj ) as illustrated in Figure 5.2.

93

5.1 H→ W W ∗ → ℓνℓν Analysis

94

Figure 5.1: Typical signature of the Higgs boson in the H→ W W ∗ → ℓνℓν analysis. Two
miss in the W W → ℓνℓν final state. The left is topology
genuine high pT leptons and large ETof the ggF process where one jet can arise from initial state gluon radiation. The right is
topology of the VBF process that is characterized by two forward jets.

Sub-leading Jet Rapidity

Correlation of Jet Rapidity (Y)
4

220

3

200
180

2

160
1

140

0

120
100

-1

80
-2

60

-3

40

-4

20
-4

-3

-2

-1

0

1
2
3
4
Leading Jet Rapidity

0

Figure 5.2: Correlation of forward/backward jets rapidities in the VBF production process.
The goal of the analysis is to measure the signal strength defined in Equation 1.17.
In order to measure individual signal strengths for each production process (i.e. µggF andµVBF ), the analysis is optimized for each process by separating into bins of jet multiplicity.
The 0-1 jet analysis is designed to select H→ W W ∗ events from the ggF process. The
0-1 jet analysis is referred to in the following as “ggF 0-jet” and “ggF 1-jet” analyses.
The 2-jets analysis aims at selecting H→ W W ∗ events mainly from the VBF process while5.1 H→ W W ∗ → ℓνℓν Analysis

95

containing some H→ W W ∗ events from the ggF process as background (denoted as “VBF
analysis”). Since the contribution from the ggF process remains non-negligible in the 2-jet
analysis, the “ggF 2-jets” analysis is also defined to be orthogonal to the VBF analysis.
Similarly the contribution of the VBF process remains non-negligible (∼ 10%) in the ggF
1-jet analysis. The VBF 1-jet is however not treated as separated analysis but the VBF
signal is profiled as one of free parameters when performing the statistical analysis (See
Section 8.3.4).
In order to maximize the experimental sensitivity to the measurement, the analysis
is further separated into four lepton flavor channels (ee, µµ, eµ, µe) as listed in Table 5.1,
where eµ channel is defined as events that have a leading electron and a sub-leading muon,
while µe channel as events that have a leading muon and a sub-leading electron.
Table 5.1: Analysis classification for 2011 and 2012 data set.
Year (luminosity)
2011 (4.5 fb−1 )2012 (20.3 fb−1 )ggF 0-jetee, µµ, eµ, µe
ee, µµ, eµ, µe

ggF 1-jetee, µµ, eµ, µe
ee, µµ, eµ, µe

ggF 2-jets
eµ, µeVBF (Njet ≥ 2)ee, µµ, eµ, µe
ee, µµ, eµ, µe

The same flavor channel (ee, µµ) has very diﬀerent background composition from thediﬀerent flavor channel (eµ, µe). In particular the Z/DY process is significant backgroundin the same flavor while this background remains small in the diﬀerent flavor. It is also
worth noting that the diﬀerent flavor is further split into eµ and µe channels because thebackground composition and shape are diﬀerent, in particular the W +jets background. In
the eµ channel, the W +jets is dominated by fake muons from heavy flavor decays, whereas
in the µe channel the W +jets is mainly due to fake electrons that overlapping with charged
or neutral pions. One more note is that the ggF 2-jet analysis is only considered for the2012 diﬀerent flavor due to little sensitivity to the same flavor (and the 2011 analysis).
Table 5.2 summarizes expected significance to show contributions from individual analyses. The largest contribution is from the ggF 0-1 jet diﬀerent flavor analysis, and the same
flavor addes only ∼ 6% to the sensitivity. In comparison to the ggF 0-1 jet diﬀerent flavor
analysis, it is also clear that the 2011 and ggF 2-jet analyses (see Appendix A) have lesssensitivity. Therefore the remainder of this chapter focuses on the main analyses, namely
ggF 0-1 jet (2012) and VBF (2012).
On the other hand, the final results presented in Chapter 8 also include the remaining
analyses (i.e. 2011 and ggF 2-jets) to fully exploit the sensitivity of this analysis. Adding
small contributions, for example from the 2011 analysis, is particularly important for the
VBF analysis, since the significance is not large enough to claim the VBF observation.

5.2 H→ W W ∗ → ℓνℓν Analysis

96

Table 5.2: Expected local significance (in sigma) based on p0 in a given Higgs mass
hypothesis mH = 125 GeV for individual analyses: diﬀerent flavor (DF) and same flavor(SF) ggF 0-jet, ggF 1-jet, ggF 2-jets, and VBF analyses. The ggF 2-jets analysis is only
considered for 2012 diﬀerent flavor data set. The results will be presented in detail in
Chapter 8.

ggF 0-jetggF 1-jetggF 2-jet
VBF

DF (2012)
3.50
2.39
1.25
2.02

SF (2012)
1.25
0.94
1.18

DF (2011)
1.34
0.92
0.79

SF (2011)
0.65
0.44
0.36

Last comment on the selection of physics objects, the optimization of the physics objects
is made focusing on the ggF 0-1 jet analysis due to the largest sensitivity of this analysis. In
order to easily keep orthogonality across the analyses, the ggF 2-jets and VBF analyses also
use the same physics objects as used in the ggF 0-1 jet analysis. This is quite importantin the combination of all the analyses, otherwise it is hard to avoid any double counting of
the Higgs signals.

5.2

Analysis Strategy

The analysis starts from data set with two oppositely signed leptons splitting into four lepmiss ) corresponding
ton flavor channels (ee, µµ, eµ, µe). The missing transverse energy (ETto the two neutrinos is then imposed, except for the VBF diﬀerent flavor analysis. 1 The
composition of this data set as a function of jet multiplicity (after selection requirement of
the analysis-dependent missing transverse energy) is illustrated in Figure 5.3.
The background composition is strongly dependent on lepton flavor and jet multiplicity.
Numerous background processes contribute to this data set, including top (tt̄ and W t),
SM W W , Z/γ ∗ → ℓℓ, W Z, W γ (∗) , ZZ, and W +jets/QCD. These can be grouped into
categories based on the properties of the final state which allows these events to pass thesignal region selection.
- The tt̄, W t, and SM W W have two W bosons in the final state, similar to the signal.
The presence of jets, especially those tagged as b-jets, is used to discriminate against
top, and properties of spin correlation are used to reduce W W .
- Z/γ ∗ → ee/µµ, which is relevant mostly to the same flavor analysis, has a high crossmiss and M
miss issection but can be rejected through ETℓℓ requirements, because ET
1
miss
miss
In the VBF diﬀerent flavor analysis, no requirement of ET
is optimal because the ET
rejects alarge amount of signal as well as backgrounds. One can imagine that the dominant background processes
miss
miss
miss
(e.g. W W and tt̄ processes) have real ET, and the backgrounds with no ETor softer ET
spectrum(e.g. Drell-Yan and QCD processes) are not as important in the VBF diﬀerent flavor analysis.

5.2 H→ W W ∗ → ℓνℓν Analysis

97

Events

45000
40000
35000

s = 8 TeV, ∫ Ldt = 20.3 fb-1
H→WW*→eνµ ν/ µ νeν

WWtt *Z/γ →llW+jet
H [125 GeV]

SM (sys ⊕ stat)
Other VV
Single Top
Z/γ *→τ τ
QCD

30000

Events

70000

50000

60000
50000

s = 8 TeV, ∫ Ldt = 20.3 fb-1
H→WW*→eνeν/ µ νµ νWWtt *Z/γ →llW+jet
H [125 GeV]

SM (sys ⊕ stat)
Other VV
Single Top
Z/γ *→τ τ
QCD

40000

25000
20000

30000

15000

20000

10000
10000

5000
0

2

4

6

8

10

0

2

4

6

8

N jets10
N jets160 ×10

Events

70000
60000

s = 8 TeV, ∫ Ldt = 20.3 fb-1
H→WW*→eνµ ν/ µ νeν

WWtt *Z/γ →llW+jet
H [125 GeV]

SM (sys ⊕ stat)
Other VV
Single Top
Z/γ *→τ τ
QCD

Events

3

80000

140
120

50000

100

40000

80

30000

60

20000

40

10000

20
0

2

4

6

8

10
N jetss = 8 TeV, ∫ Ldt = 20.3 fb-1
H→WW*→eνeν/ µ νµ ν

0

2

4

WW
tt *
Z/γ →llW+jet
H [125 GeV]

6

SM (sys ⊕ stat)
Other VV
Single Top
Z/γ *→τ τ
QCD

8

10
N jetsFigure 5.3: Jet multiplicity distributions after the dilepton pre-selection and analysisspecific missing transverse energy selection for the diﬀerent flavor (left) and same flavor(right) lepton pairs. The top pair of plots shows the background composition for the ggF
diﬀerent flavor (top left) and the ggF same flavor analyses. The bottom pair shows theequivalent for the VBF analysis.
mainly produced through mis-measurement of momenta. This is primarily the eﬀectof relatively poor resolution for soft jets and particles, which can produced by pileupinteractions as well as the primary one.
- Two or more real leptons are produced by the Z/γ ∗ → τ τ and “Non-W W ” diboson
processes W Z, W γ (∗) , and ZZ. These have a smaller cross section but more signal-likekinematics because of their asymmetric lepton pT particularly in the case of W γ (∗) .
- Finally W +jets/QCD also pass the signal region selection under the rare condition
that a jet is misidentified as an isolated lepton. The W +jets is particularly importantbackground since it has similar kinematics to the signal, the size of this backgroundis large, and the uncertainty on the fake rate is large.
The lepton flavor and jet multiplicity dependent selections are applied to cope withthose individual backgrounds. The main purpose of these selections is to reject a hugeamount of Z/γ ∗ → τ τ , Z/γ ∗ → ee/µµ as well as top backgrounds. In the VBF analysis, forinstance, several selection requirements based on the VBF specific topology (e.g. mjj and5.2 H→ W W ∗ → ℓνℓν Analysis

98∆yjj ) are imposed. 2 Furthermore the selection requirements of the dilepton kinematics
are imposed to deal with the largest SM W W background and to extract the signal basedon spin correlations as illustrated in Figure 5.4.

Figure 5.4: Spin correlation in the (H →)W W ∗ system. The two leptons from the Higgs
boson tend to make small lepton angle due to angular momentum (or helicity) conservation,
while the two leptons from the SM W W process tend to make larger angle.
In comparison to the SM W W process, the two leptons from the signal tend to makesmaller opening angle due to the fact that the Higgs boson is a spin-0 particle [88]. The
spin-0 particle produces correlations between the two leptons based on V-A structure ofelectroweak interaction in the W W ∗ system leading the two leptons in the same direction.
Hence certain cuts on the dilepton kinematics such as those ∆ϕℓℓ and mℓℓ can descriminate
the signal from the continuum SM W W background eﬃciently. The comparison of signal
and SM W W in ∆ϕℓℓ distribution is illustrated in Figure 5.5. The signal tends to havesmall ∆ϕℓℓ , whereas the SM W W does not.

Figure 5.5: Comparison of ∆ϕℓℓ distributions between the signal (red) and SM W W (blue).
Spin correlation in the (H →)W W ∗ system leads to small opening angle in ∆ϕℓℓ .
2Strictly, the mjj and ∆yjj are not imposed but are used as input variables of the BDT analysis.

5.3 H→ W W ∗ → ℓνℓν Analysis

99

Due to the presence of the two neutrinos in the final state and worse energy resolution of
the missing transverse energy compared to leptons or photons, it is diﬃcult to make a narrow
peak of the Higgs boson from decay products. Instead of invariant mass, transverse mass ofthe dilepton system (mT ) that also have mass information, is used as a final discriminant
to extract the signals. The mT [89] is defined as:√ℓℓ + E miss )2 − |pℓℓ + E miss |2 ,(5.1)
mT = (ET
T
T
T
miss
miss
where pℓℓ
T is vector sum of pT of the two leptons,√ and E T (ET ) is vector (scalar) sum
miss . Also E ℓℓ can be rewritten as E ℓℓ =
of ET
T
T
system.

ℓℓ
2
2
|pℓℓ
T | + mℓℓ where pT is pT of the dilepton

jetCorr
For all the ggF analyses, mT based on pmiss,(see Section 3.4.2) is used as aT
miss, jetCorr
discriminating variable. Making use of pT
for the mT improves the resolution ofthis observable. To obtain signal strength (µ), the mT distribution is fit using the binned
likelihood L (see Section 8.2), in which all the signal and control regions, and all the systemtatic uncertainties (experimental uncertainties and theoretical uncertainties), treated as
nuisance parameters (NP), are put together.

The VBF analysis uses a Boosted Decision Trees (BDT) technique. The final signal
region is defined by a cut on the BDT value, and is subdivided into bins by BDT score.
The BDT analysis has a higher expected sensitivity compared to the cut-based analysis,
because it can benefit from knowledge of the correlations between all variables (see Section 5.4.4). To obtain signal strength the BDT score is fit using the binned likelihood, inwhich all the signal and control regions as well as systematics are put together.

5.3

Monte Carlo Simulation

In this analysis many processes of the SM contribute to the signal regions as backgrounds.
For the modeling of signal and backgrounds, the Monte Carlo (MC) event generators areused [154]. The MC generators are built up by a few main steps: “Hard process” and“Parton shower and Hadronization”. The first step is simulating the hard process. This
step is responsible for the simulation and calculation of the matrix element based on the
fixed order perturbation theory. The Parton Distribution Functions (PDFs) describe partons coming into the process and the perturbation theory gives a probabilistic distributionof the outgoing partons. The second step is parton showering evolution that starts fromthe hard process and works downwards to a lower momentum scale at which perturbation
theory breaks down, namely the lower cut-oﬀ threshold. Subsequently to the parton shower
process, hadronization is simulated. The hadronization takes account of the confinement ofa system of partons into hadrons, which are seen in the detector. All the MC generators
used in the analysis are listed in Table 5.3. For example, “Alpgen [155]”+“Herwig [156]”
denotes the generator that uses Alpgen for the hard process and Herwig for the parton
shower and hadronization.

100

5.3 H→ W W ∗ → ℓνℓν Analysis

The signal production includes the dominant ggF production process, the VBF production process, and W H/ZH process. Other small contributions from the ttH and bbH
are neglected. The contribution from H → τ τ in the signal region is explicitly investigated,
and it is found to be negligible. For most processes, separate programs are used to generate
the hard scattering and parton showering/hadronization. Pythia [128], Pythia8 [129] or
Herwig [156] is used for the parton shower/hadronization modeling. 3 The ggF Higgs
boson pT spectrum in Powheg [158] is tuned to agree with the prediction from HqT [159].
Finite heavy quark mass eﬀects in the ggF production process are also included [160].
For the background processes, the following generators are used:- Continuum W W is modeled in Powheg. The small contribution from quark box
diagram, which is not included in P owheg, is explicitly added by using gg2VV [161].
For ggF+2jet and VBF analyses, W W +jets is modeled in Sherpa because the 2nd
jet in Powheg is not well modeled. The W W process with six electroweak couplings
is modeled in Sherpa. This process is more important for the VBF analysis due todiagrams associated with two forward jets.
- tt̄ process is modeled in Powheg. In 8 TeV, dilepton filter sample is generated toincrease statistics, while the filter is not applied to 7 TeV sample. The relevant
single-top production channels (s-channel, t-channel and W t) are included.
- The inclusive Z/γ ∗ (Z/DY ) process is generated with a dilepton invariant mass
greater than 10 GeV. Low mass DY background is more important in this analysis because of the requirement of Z mass veto. To enhance statistics, a dilepton filter requiring at least one pT > 20 GeV lepton and two pT > 7 GeV leptons
in |η| < 3.0 is imposed. Furthermore, VBF filter requiring at least two jets withpT > 15 GeV, |η| < 5.0, mjj > 200 GeV, and ∆yjj > 2.0, sample is generated for
VBF analysis. This QCD Z+jets is modeled in Alpgen. In addition, electroweak
Z+jets process, which has no QCD coupling, is modeled in Sherpa.
- W +jets process modeled in Alpgen is only used for the evaluation of fake factor
systematic uncertainties and for the subtraction from the QCD control region.
- For the W Z (∗) and W γ ∗ processes, interference between the Z (∗) and the γ ∗ is included, and the boundary between the samples is at mℓℓ = 7 GeV. For the W γ ∗ ,Sherpa is used with a lower invariant mass cut of mℓℓ > 2mℓ depending on decay ofγ ∗ . For W Z (∗) , Powheg is used. To remove overlap with Sherpa sample, the eventswith mZ/γ∗ < 7 GeV are removed from sample. A dilepton filter requiring at least
two charged leptons with pT > 5 GeV and |η| < 2.7 is also applied in Powheg W Z (∗)
sample. The Z (∗) Z (∗) → 4ℓ samples are modeled in Powheg and generated withan invariant mass cut of mℓℓ > 4 GeV. Electroweak W Z and ZZ processes with six
electroweak couplings are generated in Sherpa.
3

And the JIMMY [157] is used for the underlying event modeling.

5.3 H→ W W ∗ → ℓνℓν Analysis

101- W γ process is modeled in Alpgen. Kinematic criteria are also applied in the generation of W (→ ℓν)γ events (the photon must have pT > 8 GeV and be separated fromthe charged lepton by ∆R > 0.25and W (→ ℓν)γ ∗ (→ ℓ′ ℓ′ ) events (at least two leptons
have pT larger than 5 GeV and |η| < 3 for the ee and µµ case, and |η| < 5 for the τ τcase).
- Zγ (the photon pT > 7 GeV) is generated by Sherpa.
For the Parton Distribution Function (PDF), the CT10 PDF set [162] is used for the
Powheg, Sherpa and gg2VV samples, and CTEQ6L1 [163] is used for the Alpgen, AcerMC, Pythia8 and several Sherpa (in 7 TeV) samples, except for the Alpgen Z/γ ∗sample that is reweighted to the MRSTMCal [164] PDF set. Acceptances and eﬃciencies
are obtained for most processes from a full simulation [165] of the ATLAS detector using
GEANT4 [166], including pileup simulation.
Table 5.3: MC generators and corresponding cross sections (given for mH = 125 GeV)
used to model the signal and background processes. The quoted cross section includes thebranching ratio assuming the leptonic decay (e, µ, τ ) of W/Z bosons.
Process
ggF H → W W
VBF H → W W
W H/ZH H → W W
q q̄/g → W W
gg → W W
QCD W W + 2 jets
EW W W + 2 jetstt̄ dileptonic
tW/tb leptonic
tqb leptonic
inclusive W
inclusive Z/γ ∗ (mll ≥ 10GeV )EW Z/γ ∗W (Z/γ ∗ )W (Z/γ ∗ )(m(Z/γ ∗ ) < 7 GeV)
Z (∗) Z (∗) → 4l(2l2ν)
EW W Z + 2 jets
EW ZZ + 2 jets (4l, llνν)Wγ
Zγ(pγT > 7GeV )Generator
Powheg [167]+Pythia8 [129]Powheg [168]+Pythia8
Pythia8 (Pythia6)
Powheg +Pythia6
gg2WW [161]+Herwig [156]SherpaSherpaPowheg [169]+Pythia6
Powheg [169]+Pythia6
AcerMC [170]+Pythia6 [128]Alpgen [155]+Herwig
Alpgen [155]+Herwig
SherpaPowheg +Pythia8
SherpaPowheg +Pythia8
SherpaSherpaAlpgen [155]+Herwig
Sherpaσ · Br(8TeV) (pb)
0.435
36 · 10−3
25 · 10−3
5.68
0.20
0.568
0.039
26.6
4.17
28.4
37 · 10316.5 · 103
5.36 (inc. t-ch)
12.7
12.2
0.73(0.50)
13 · 10−3−573 · 10 (12 · 10−4 )369
163

σ · Br(7TeV) (pb)
0.341
28 · 10−3
21 · 10−3
4.68
0.14
0.027
18.6
3.15
20.7
31 · 10314.9 · 103
2.26
10.8
10.6
0.64(0.42)
8.5 · 10−3
−553 · 10 (8.8 · 10−4 )313-

5.4 H→ W W ∗ → ℓνℓν Analysis

102

5.4

Event Selection

5.4.1

Pre-selection

The trigger selection, object selection, and overlap removals are common for all analyses.
The analysis uses single and dilepton triggers (see Section 3.1) to collect dilepton sample,
and selects isolated leptons (see Section 4.8) and reconstructed jets (see Section 3.3.5)
for analysis categorization. The overlap removals (see Section 6.3.3) are then required toprioritize the physics objects (lepton and jet) in case of a high proximity of two objects.
The pre-selection that is also common for all analyses is applied after the overlap removals.
- exactly two opposite sign leptons,- plead> 22 GeV, psublead> 10 GeV,T
T- mℓℓ > 10 (12) GeV for eµ + µe (ee + µµ) lepton channel,- |mℓℓ − mZ | > 15 GeV for ee + µµ,

s = 8 TeV, ∫ Ldt = 20.3 fb-1
H→WW*→lν lν
KS Prob = 0.0%

Data

SM (sys ⊕ stat)

WW

Other VV
Single Top
Z/ γ *→ττtt*
Z/ γ →ll
W+jet

QCD
H [125 GeV]

Events / 5 GeV

1013
1012
1011
1010
109
108
107
106
105
104
103
102
10
1
10-1
-2
10
1.4
1.2
1
0.8
0.6

Data / SM

Data / SM

Events / 5 GeV

where the lower mℓℓ cut aims at rejecting low mass resonance of J/ψ and Υ decays as well
as QCD background, and the fourth cut aims at rejecting Z/γ ∗ → ℓℓ resonance. After themiss is imposed. Figures 5.6, 5.7, and 5.8 present
pre-selection, the analysis-dependent ET
the understanding of the objects after the pre-selection requirement where the backgrounds
are normalized to the SM cross section. The agreement of data/SM is acceptable at thisstage. The yellow band represents statistical uncertainty on simulation, the occasional
discrepancies are covered by the relevant systematics which are not applicable at this stage.

50

100

150

200

250
p

T,lead lep

300
[GeV]

1013
1012
1011
1010
109
108
107
106
105
104
103
102
10
1
10-1
-2
10
1.4
1.2
1
0.8
0.6

s = 8 TeV, ∫ Ldt = 20.3 fb-1
H→WW*→lν lν
KS Prob = 0.0%

20

40

60

80

Data

SM (sys ⊕ stat)

WW

Other VV
Single Top
Z/ γ *→ττtt*
Z/ γ →ll
W+jet

QCD
H [125 GeV]

100 120 140 160 180 200pT,sublead lep[GeV]

Figure 5.6: Leading lepton pT (left) and sub-leading lepton pT (right) after the preselection for all lepton flavors combined. The Data/ SM shows the ratio of data to thetotal background where yellow band represents the statistical uncertainty. No systematic
uncertainty is displayed.

5.4 H→ W W ∗ → ℓνℓν Analysis

103

400 ×10s = 8 TeV, ∫ Ldt = 20.3 fb-1
H→WW*→lν lν
KS Prob = 0.0%

Data

SM (sys ⊕ stat)

WW

Other VV
Single Top
Z/ γ *→ττtt*
Z/ γ →ll
W+jet

Events / 0.2

10
1010
109
108
107
106
105
104
103
102
10
1
10-1
-2
10
1.4
1.2
1
0.8
0.6

QCD
H [125 GeV]

350
300

s = 8 TeV, ∫ Ldt = 20.3 fb-1
H→WW*→lν lν
KS Prob = 0.0%

Data

SM (sys ⊕ stat)

WW

Other VV
Single Top
Z/ γ *→ττtt*
Z/ γ →ll
W+jet

QCD
H [125 GeV]

250
200
150
100
50
Data / SM

Data / SM

Events / 5 GeV

3

11

50

100

150

200

250
p

T,lead jet

300

1.4
1.2
1
0.8
0.6
-4

-3

-2

-1

0

1

2

3

4
η

[GeV]

lead jetData

SM (sys ⊕ stat)

WW

Other VV
Single Top
Z/ γ *→ττtt*
Z/ γ →ll
W+jet

Events / 5 GeV

1013
1012
s = 8 TeV, ∫ Ldt = 20.3 fb-1
1011
1010 H→WW*→lν lν
109 KS Prob = 0.0%
108
107
106
105
104
103
102
10
1
10-1
-2
10
1.4
1.2
1
0.8
0.6
0
50
100

QCD
H [125 GeV]

Data / SM

Data / SM

Events / 5 GeV

Figure 5.7: Leading jet pT (left) and η (right) after the pre-selection for all lepton flavors
combined. The Data/ SM shows the ratio of data to the total background where yellow
band represents the statistical uncertainty. No systematic uncertainty is displayed.

150

200

250

miss,track,Clj
[GeV]
ET

1013
SM (sys ⊕ stat)
Data
1012
Other VVWW1011
s = 8 TeV, ∫ Ldt = 20.3 fb-1
Single Top
tt
10
*
10
Z/ γ *→ττ
Z/ γ →ll
H→WW*→lν lν
9
W+jet
QCD
10
KS Prob = 0.0%
H [125 GeV]
108
7
10
106
105
104
103
102
10
1
10-1
-2
10
1.4
1.2
1
0.8
0.6
0
20 40 60 80 100 120 140 160 180 200[GeV]
E missT

jetCorr
miss (right) distributions after the pre-selection (m )Figure 5.8: pmiss,(left) and ETℓℓT
for all lepton flavors combined. The Data/ SM shows the ratio of data to the total background where yellow band represents the statistical uncertainty. No systematic uncertainty
is displayed.

5.4 H→ W W ∗ → ℓνℓν Analysis

104

5.4.2

ggF 0-1 jet Diﬀerent Flavor Selection

ggF 0-jet Diﬀerent Flavor
The selection criteria in the 0-jet analysis exploit the dilepton kinematics resulting fromspin correlations present in the H→ W W ∗ → ℓνℓν (See Section 5.1). In addition to thepre-selection described in Section 5.4.1, the following requirements are imposed:
miss, jetCorr> 20 GeV,- pT- The opening angle between the dilepton system and the transverse missing energy,∆ϕℓℓ,E miss , is required to be larger than π/2 to remove potential pathological eventsT
miss is pointing in the direction of the lepton pair (this criteria is morein which the ET
than 99 % eﬃcient for signal),- The transverse momentum of the dilepton system, |pℓℓ
T | > 30 GeV,
- The invariant mass of the dilepton system, mℓℓ < 55 GeV,
- The dilepton opening angle in the transverse plane, ∆ϕℓℓ < 1.8 radians.

1600
1400
1200

s = 8 TeV, ∫ Ldt = 20.3 fb-1
H→WW*→eνµ ν/ µ νeν + 0 jetsWWtt *Z/γ →llW+jet
H [125 GeV]

SM (sys ⊕ stat)
Other VV
Single Top
Z/γ *→τ τ
QCD

1000

Events / 0.13 rad

Events / 10 GeV

Figure 5.9 shows mℓℓ distribution after pℓℓ
T requirement and ∆ϕℓℓ distribution after mℓℓ
requirement. The signal has lower mℓℓ and ∆ϕℓℓ due to the spin correlation. Also it isclearly presented that the ∆ϕℓℓ is a good discriminant against Z/DY → τ τ which is thelargest background after pre-selection requirement.
400
350
300

200

600

150

400

100

200

50
100

150

200

250
mll [GeV]WW
tt *Z/γ →llW+jet
H [125 GeV]

SM (sys ⊕ stat)
Other VV
Single Top
Z/γ *→τ τ
QCD

250

800

50

s = 8 TeV, ∫ Ldt = 20.3 fb-1
H→WW*→eνµ ν/ µ νeν + 0 jets

0

0.5

1

1.5

2

2.5

3
∆φ [rad]llFigure 5.9: mℓℓ distribution after pℓℓ
T requirement (left) and ∆ϕℓℓ distribution after mℓℓ
requirement (right). The signal has lower mℓℓ and ∆ϕℓℓ due to the spin correlation in the
H→ W W ∗ → ℓνℓν.
Figure 5.10 shows sub-leading lepton pT , mℓℓ , ∆ϕℓℓ , and mT distributions after ∆ϕℓℓ
requirement. The remaining backgrounds are dominated by the W W , non-W W dibosons(other V V ), and W +jets backgrounds, and these backgrounds are strongly dependent on
sub-leading lepton pT and mℓℓ . The W W (both W s are on-shell) tends to be in high pT
while the other V V and W +jets backgrounds tends to be in low pT region. The other5.4 H→ W W ∗ → ℓνℓν Analysis

105

300
250

s = 8 TeV, ∫ Ldt = 20.3 fb
H→WW*→eνµ ν/ µ νeν + 0 jets
-1

SM (sys ⊕ stat)
Other VV
Single Top
Z/γ *→τ τ
QCD

WW
tt *
Z/γ →llW+jet
H [125 GeV]

200

Events / 10 GeV

Events / 1 GeV

V V and W +jets can be further separated in mℓℓ since the contribution from other V V
backgrounds are mostly in lower mℓℓ , while the W +jets background is mostly in higher
mℓℓ , so the split in mℓℓ and sub-leading lepton pT helps the analysis discriminate thosebackgrounds eﬃciently. The signal region is split in mℓℓ (10-30, 30-55) and psub
T (10-15,
15-20, 20-) into 6 sub-regions. Figures 5.11 and 5.12 show mT distributions and Table 5.4
shows expected signal and background counts for each sub-divisions (but psub
T = 15-20 and
20- are combined).
900
800
700

s = 8 TeV, ∫ Ldt = 20.3 fb
H→WW*→eνµ ν/ µ νeν + 0 jets
-1

WW
tt *
Z/γ →llW+jet
H [125 GeV]

SM (sys ⊕ stat)
Other VV
Single Top
Z/γ *→τ τ
QCD

600
500

150
400
300

100

200
50
100
10

15

20

25

30

35

Events / 0.13 rad

p

40
45
[GeV]

300

s = 8 TeV, ∫ Ldt = 20.3 fb
H→WW*→eνµ ν/ µ νeν + 0 jets
-1

WW
tt *
Z/γ →llW+jet
H [125 GeV]

SM (sys ⊕ stat)
Other VV
Single Top
Z/γ *→τ τ
QCD

250

150

200

250
mll [GeV]

500
450

s = 8 TeV, ∫ Ldt = 20.3 fb
H→WW*→eνµ ν/ µ νeν + 0 jets
-1

400
350

WW
tt *
Z/γ →llW+jet
H [125 GeV]

SM (sys ⊕ stat)
Other VV
Single Top
Z/γ *→τ τ
QCD

300

200

250

150

200
150

100

100

50
0

100

T,sublead lep

400
350

50

Events / 10 GeV

5

50
0.5

1

1.5

2

2.5

3
∆φ [rad]
ll

50

100

150

200

250

300

mtrack-clj[GeV]
T

Figure 5.10: Sub-leading lepton pT (top left), mℓℓ (top right), ∆ϕℓℓ (bottom left), and mT(bottom right) distributions after ∆ϕℓℓ requirement.

5.4 H→ W W ∗ → ℓνℓν Analysis

106

Table 5.4: Expected event counts in the 8 TeV ggF 0-jet analysis. Percentages are thefraction of the total background. The W +jets and QCD are from data-driven estimate.
H
41
46
14
10
32
36
10
6

All Bkg.
330
632
172
117
300
543
152
107

S/B
0.125
0.073
0.081
0.085
0.105
0.066
0.063
0.060

WW
228 (69%)489 (77%)
54 (31%)54 (46%)194 (65%)410 (76%)
39 (25%)39 (37%)

50
45
40
35

s = 8 TeV, ∫ Ldt = 20.3 fb-1
H→WW*→eνµ ν + 0 jetsWWtt *Z/γ →llW+jetVV
50 (15%)33 (5%)
59 (34%)10 (9%)
57 (19%)33 (6%)
64 (42%)17 (15%)

Events / 10 GeV

Events / 10 GeV

eµ mℓℓ < 30, psublead> 15
Teµ mℓℓ > 30, psublead
> 15
T
< 15
eµ mℓℓ < 30, psubleadTeµ mℓℓ > 30, psublead< 15
Tµe mℓℓ < 30, psublead> 15
Tµe mℓℓ > 30, psublead> 15
Tµe mℓℓ < 30, psublead< 15
Tµe mℓℓ > 30, psublead< 15
TSM (sys ⊕ stat)
Other VV
Single Top
Z/γ *→τ τ
QCD
H [125 GeV]30tt̄
18 (6%)
43 (7%)
5 (3%)
7 (6%)
15 (5%)
35 (6%)
3 (2%)
5 (4%)(W )t
11 (3%)
25 (4%)
2 (1%)
4 (3%)
9 (3%)
20 (4%)
2 (1%)
2 (2%)

Z+jets3 (1%)
4 (1%)
4 (2%)
2 (2%)
5 (2%)
3 (1%)
5 (3%)
3 (3%)

W +jets
18 (5%)
35 (6%)
43 (25%)39 (34%)21 (7%)
41 (8%)
40 (26%)41 (39%)s = 8 TeV, ∫ Ldt = 20.3 fb-1
H→WW*→eνµ ν + 0 jetsWWtt *Z/γ →llW+jet

SM (sys ⊕ stat)
Other VV
Single Top
Z/γ *→τ τ
QCD
H [125 GeV]

140
120

QCD
0.9 (0.3%)
1.2 (0.2%)
4.3 (2.5%)
0.8 (0.7%)
0.5 (0.2%)
0.8 (0.1%)
0.6 (0.4%)
0.0 (0.0%)

100
80

25

60

20
15

40

10
20

5
50

100

150

200

250

300

50

100

150

200

90
80
70

s = 8 TeV, ∫ Ldt = 20.3 fb-1
H→WW*→eνµ ν + 0 jetsWWtt *Z/γ →llW+jet

SM (sys ⊕ stat)
Other VV
Single Top
Z/γ *→τ τ
QCD
H [125 GeV]

60
50

80
70

30

20

20

10

10
200

250

300

mtrack-clj
[GeV]
T

WW
tt *
Z/γ →llW+jet

SM (sys ⊕ stat)
Other VV
Single Top
Z/γ *→τ τ
QCD
H [125 GeV]

50
40

150

s = 8 TeV, ∫ Ldt = 20.3 fb-1
H→WW*→eνµ ν + 0 jets

60

30

100

300

90

40

50

250

mtrack-clj[GeV]T
Events / 10 GeV

Events / 10 GeV

mtrack-clj
[GeV]
T

50

100

150

200

250

300

mtrack-clj[GeV]
T

Figure 5.11: mT distribution for each sub-divisions in the 0-jet eµ channel: psub
T = 10-15
sub
GeV and mℓℓ > 30 GeV (top left), pT > 15 GeV and mℓℓ > 30 GeV (top left), psub
T =10-15 GeV and mℓℓ < 30 GeV (bottom left), psub
>
15
GeV
and
m
<
30
GeV
(bottomℓℓTright).

107

50
45
40
35

s = 8 TeV, ∫ Ldt = 20.3 fb
H→WW*→µ νeν + 0 jets

-1

WW
tt *
Z/γ →ll
W+jet

Events / 10 GeV

Events / 10 GeV

5.4 H→ W W ∗ → ℓνℓν Analysis

SM (sys ⊕ stat)
Other VV
Single Top
Z/γ *→τ τ
QCD
H [125 GeV]

30
25

120
100

s = 8 TeV, ∫ Ldt = 20.3 fb
H→WW*→µ νeν + 0 jets

-1

WW
tt *
Z/γ →llW+jet

SM (sys ⊕ stat)
Other VV
Single Top
Z/γ *→τ τ
QCD
H [125 GeV]

80
60

20
40

15
10

20

5
50

100

150

200

250

300

50

100

150

200

90
80
70

s = 8 TeV, ∫ Ldt = 20.3 fb
H→WW*→µ νeν + 0 jets

-1

WW
tt *
Z/γ →llW+jet

SM (sys ⊕ stat)
Other VV
Single Top
Z/γ *→τ τ
QCD
H [125 GeV]

60
50

250

300

mtrack-clj[GeV]T
Events / 10 GeV

Events / 10 GeV

mtrack-clj
[GeV]
T
80
70
60

s = 8 TeV, ∫ Ldt = 20.3 fb
H→WW*→µ νeν + 0 jets

-1

WW
tt *
Z/γ →llW+jet

SM (sys ⊕ stat)
Other VV
Single Top
Z/γ *→τ τ
QCD
H [125 GeV]

50
40

40
30

30
20

20

10

10
50

100

150

200

250

300

mtrack-clj
[GeV]
T

50

100

150

200

250

300

mtrack-clj[GeV]
T

Figure 5.12: mT distribution for each sub-divisions in the 0-jet µe channel: psub
T = 10-15
sub
GeV and mℓℓ > 30 GeV (top left), pT > 15 GeV and mℓℓ > 30 GeV (top left), psub
T =10-15 GeV and mℓℓ < 30 GeV (bottom left), psub
>
15
GeV
and
m
<
30
GeV
(bottomℓℓTright).

5.4 H→ W W ∗ → ℓνℓν Analysis

108
ggF 1-jet Diﬀerent Flavor

The selection of events satisfying the pre-selection (see Section 5.4.1) and containing exactly
one selected jet is similar to the 0-jet analysis. In addition to the pre-selection, the following
requirements are imposed:
miss, jetCorr- pT> 20 GeV,- b-jet veto: there should be no jet in the event with pT > 20 GeV tagged as originatingfrom a b-quark using the MV1 algorithm [133, 134] with an 85% eﬃcient operating
point,- The τ τ invariant mass, mτ τ , is reconstructed using the approximation that the neutrinos are collinear with the visible products of the corresponding τ decays, and assumingthat the leptons arise from Z → τ τ decays. If the energy fractions xτ1 and xτ2 carriedby the putative visible decay products are positive (the collinear approximation does
not always yield good solutions) and the invariant mass of the hypothetical τ τ system
satisfies mτ τ > mZ − 25 GeV, the event is rejected,- Max mT (W ) > 50 GeV 4 is required to reject the QCD and Z/γ ∗ → τ τ backgrounds,- The event must pass the same cuts on mℓℓ and ∆ϕℓℓ as those of the 0-jet analysis.

1400
1200
1000

s = 8 TeV, ∫ Ldt = 20.3 fb-1
H→WW*→eνµ ν/ µ νeν + 1 jet

WWtt *Z/γ →llW+jet
H [125 GeV]

SM (sys ⊕ stat)
Other VV
Single Top
Z/γ *→τ τ
QCD

800

Events / 0.13 rad

Events / 5 GeV

Figure 5.13 shows Max mT (W ) distribution after b-jet veto requirement and ∆ϕℓℓ distribution after mℓℓ requirement. The mT (W ) cut removes most of the QCD backgroundthat has a large (∼ 40%) uncertainty because it originates from the rare event of a jet faking
a lepton. Similar to the 0-jet analysis, the signal has lower ∆ϕℓℓ due to the spin correlation.
300
250

s = 8 TeV, ∫ Ldt = 20.3 fb-1
H→WW*→eνµ ν/ µ νeν + 1 jet

WWtt *Z/γ →llW+jet
H [125 GeV]

SM (sys ⊕ stat)
Other VV
Single Top
Z/γ *→τ τ
QCD

200
150

600
100

400

50

200
0

20

40

60

80 100 120 140 160 180 200
MaxmlT,clj [GeV]

0

0.5

1

1.5

2

2.5

3
∆φ [rad]llFigure 5.13: Max mT (W ) distribution after b-jet veto requirement (left) and ∆ϕℓℓ distribution after mℓℓ requirement (right). The signal has lower mℓℓ and ∆ϕℓℓ due to the spincorrelation.
4

The Max mT (W ) is the maximum of the two transverse masses formed with each charged lepton andthe missing transverse energy. For W decays, mT has a Jacobian distribution with an edge at mT = mW .
Backgrounds such as QCD (multijet) production tend to have lower mT (W ).

5.4 H→ W W ∗ → ℓνℓν Analysis

109

80
70
60

s = 8 TeV, ∫ Ldt = 20.3 fb-1
H→WW*→eνµ ν/ µ νeν + 1 jet

SM (sys ⊕ stat)
Other VV
Single Top
Z/γ *→τ τ
QCD

WW
tt *
Z/γ →llW+jet
H [125 GeV]

50

Events / 10 GeV

Events / 1 GeV

Figure 5.14 shows sub-leading lepton pT , mℓℓ , ∆ϕℓℓ , and mT distributions after ∆ϕℓℓ
requirement. In comparison to the 0-jet analysis, the top backgrounds are larger, otherwise
the background composition is similar to the 0-jet analysis. Similar to the 0-jet analysis,
the signal region is split in mℓℓ (10-30, 30-55) and psub
T (10-15, 15-20, 20-25) into 6 subregions. Figures 5.15 and 5.16 show mT distributions and Table 5.5 shows expected signal
and background counts for each sub-divisions (but psub
T = 15-20 and 20- are combined).
450
350

30

200
100
50
15

20

25

30

35

160
s = 8 TeV, ∫ Ldt = 20.3 fb-1
H→WW*→eνµ ν/ µ νeν + 1 jet

40
45
[GeV]

WW
tt *
Z/γ →llW+jet
H [125 GeV]

SM (sys ⊕ stat)
Other VV
Single Top
Z/γ *→τ τ
QCD

100

100

150

200

250
mll [GeV]

200
180

s = 8 TeV, ∫ Ldt = 20.3 fb-1
H→WW*→eνµ ν/ µ νeν + 1 jet

160
140

WW
tt *
Z/γ →llW+jet
H [125 GeV]

SM (sys ⊕ stat)
Other VV
Single Top
Z/γ *→τ τ
QCD

120
100

80

80

60

60

40

40

20
0

50

T,sublead lep

Events / 10 GeV

10

p

120

SM (sys ⊕ stat)
Other VV
Single Top
Z/γ *→τ τ
QCD

150

10

140

WW
tt *
Z/γ →llW+jet
H [125 GeV]

300
250

5

s = 8 TeV, ∫ Ldt = 20.3 fb-1
H→WW*→eνµ ν/ µ νeν + 1 jet

400

40

20

Events / 0.13 rad

500

20
0.5

1

1.5

2

2.5

3
∆φ [rad]

50

100

150

200

250

300

mtrack-clj
[GeV]
T

ll

Figure 5.14: Sub-leading lepton pT (top left), mℓℓ (top right), ∆ϕℓℓ (bottom left), and mT(bottom right) distributions after ∆ϕℓℓ requirement.

Table 5.5: Expected event counts in the 8 TeV ggF 1-jet analysis. Percentages are thefraction of the total background. The W +jets and QCD are from data-driven estimate.
eµ mℓℓ < 30, psublead> 15
Teµ mℓℓ > 30, psublead> 15
Teµ mℓℓ < 30, psublead< 15
Teµ mℓℓ > 30, psublead< 15
Tµe mℓℓ < 30, psublead> 15
Tµe mℓℓ > 30, psublead> 15
Tµe mℓℓ < 30, psublead< 15
Tµe mℓℓ > 30, psublead
< 15
T

H
21
25
5
4
17
20
3
3

All Bkg.
151
309
47
51
133
265
37
38

S/B
0.140
0.081
0.113
0.073
0.132
0.077
0.089
0.069

WW
64 (42%)144 (47%)
13 (27%)16 (31%)56 (42%)122 (46%)
9 (25%)
11 (29%)VV
23 (15%)19 (6%)
11 (23%)
4 (8%)
24 (18%)20 (8%)
12 (32%)5 (13%)tt̄
38 (25%)86 (28%)8 (17%)
11 (22%)31 (23%)73 (27%)5 (14%)
8 (21%)(W )t
15 (10%)33 (11%)
3 (6%)
4 (8%)
12 (9%)
27 (10%)2 (4%)
3 (7%)

Z+jets1 (0%)
9 (3%)
2 (3%)
3 (6%)
2 (1%)
7 (3%)
2 (4%)
1 (4%)

W +jets
10 (6%)
17 (5%)
9 (20%)
11 (22%)8 (6%)
16 (6%)
8 (20%)
10 (26%)QCD
0.7 (0.5%)
0.9 (0.3%)
1.7 (3.6%)
1.1 (2.1%)
0.5 (0.4%)
0.8 (0.3%)
0.2 (0.5%)
0.1 (0.3%)

5.4 H→ W W ∗ → ℓνℓν Analysis

1412

s = 8 TeV, ∫ Ldt = 20.3 fb
H→WW*→eνµ ν + 1 jet

-1

WW
tt *
Z/γ →ll
W+jet

Events / 10 GeV

Events / 10 GeV

110

SM (sys ⊕ stat)
Other VV
Single Top
Z/γ *→τ τ
QCD
H [125 GeV]

10
8

70
60
50

30

4

20

2

10
100

150

200

250

WW
tt *
Z/γ →ll
W+jet

300

50

100

150

200

14
12

s = 8 TeV, ∫ Ldt = 20.3 fb
H→WW*→eνµ ν + 1 jet

-1

WW
tt *
Z/γ →llW+jet

SM (sys ⊕ stat)
Other VV
Single Top
Z/γ *→τ τ
QCD
H [125 GeV]

10

35
30

20
15

4

10

2

5
150

200

250

300

mtrack-clj[GeV]T

s = 8 TeV, ∫ Ldt = 20.3 fb
H→WW*→eνµ ν + 1 jet

-1

WW
tt *
Z/γ →llW+jet

SM (sys ⊕ stat)
Other VV
Single Top
Z/γ *→τ τ
QCD
H [125 GeV]

25

6

100

300

40

8

50

250

mtrack-clj[GeV]T
Events / 10 GeV

Events / 10 GeV

mtrack-clj
[GeV]
T
16

SM (sys ⊕ stat)
Other VV
Single Top
Z/γ *→τ τ
QCD
H [125 GeV]

40

6

50

s = 8 TeV, ∫ Ldt = 20.3 fb
H→WW*→eνµ ν + 1 jet

-1

50

100

150

200

250

300

mtrack-clj[GeV]
T

Figure 5.15: mT distribution for each sub-divisions in the 1-jet eµ channel: psub
T = 10-15
sub
GeV and mℓℓ > 30 GeV (top left), pT > 15 GeV and mℓℓ > 30 GeV (top left), psub
T =10-15 GeV and mℓℓ < 30 GeV (bottom left), psub
>
15
GeV
and
m
<
30
GeV
(bottomℓℓTright).

108

s = 8 TeV, ∫ Ldt = 20.3 fb
H→WW*→µ νeν + 1 jet

-1

WW
tt *
Z/γ →ll
W+jet

111

Events / 10 GeV

Events / 10 GeV

5.4 H→ W W ∗ → ℓνℓν Analysis

SM (sys ⊕ stat)
Other VV
Single Top
Z/γ *→τ τ
QCD
H [125 GeV]

6

60
50

s = 8 TeV, ∫ Ldt = 20.3 fb
H→WW*→µ νeν + 1 jet

-1

WW
tt *
Z/γ →ll
W+jet

40
30

4

20

2

10
50

100

150

200

250

300

50

100

150

200

14
s = 8 TeV, ∫ Ldt = 20.3 fb
H→WW*→µ νeν + 1 jet

-1

WW
tt *
Z/γ →llW+jet

SM (sys ⊕ stat)
Other VV
Single Top
Z/γ *→τ τ
QCD
H [125 GeV]

10
8

250

300

mtrack-clj[GeV]T
Events / 10 GeV

Events / 10 GeV

mtrack-clj
[GeV]
T

12

SM (sys ⊕ stat)
Other VV
Single Top
Z/γ *→τ τ
QCD
H [125 GeV]

40
35
30

s = 8 TeV, ∫ Ldt = 20.3 fb
H→WW*→µ νeν + 1 jet

-1

WW
tt *
Z/γ →llW+jet

SM (sys ⊕ stat)
Other VV
Single Top
Z/γ *→τ τ
QCD
H [125 GeV]

25
20

6

15

4

10

2

5
50

100

150

200

250

300

mtrack-clj
[GeV]
T

50

100

150

200

250

300

mtrack-clj[GeV]
T

Figure 5.16: mT distribution for each sub-divisions in the 1-jet µe channel: psub
T = 10-15
sub
GeV and mℓℓ > 30 GeV (top left), pT > 15 GeV and mℓℓ > 30 GeV (top left), psub
T =10-15 GeV and mℓℓ < 30 GeV (bottom left), psub
>
15
GeV
and
m
<
30
GeV
(bottomℓℓTright).

5.4 H→ W W ∗ → ℓνℓν Analysis

112

5.4.3

ggF 0-1 jet Same Flavor Selection

The selection criteria in the same flavor (ee, µµ) analysis is essentially the same as the different flavor analysis. Nevertheless one needs to more seriously consider a large contribution
from resonance decay of Z/γ ∗ → ℓℓ. The Z/γ ∗ → ℓℓ background increased by a factor ofmiss ) compared tothree in 2012 due to worse resoulution of missing transverse energy (ET2011. The worse resolution arises from higher pileup in 2012 that aﬀects soft term of themiss calculation. The increased Z/γ ∗ → ℓℓ background makes the analysis very diﬃcult,ET
so that the analysis has little sensitivity. Therefore, to suppress the Z/γ ∗ → ℓℓ background,the following cuts are required in addition to the diﬀerent flavor selection:
miss > 40 GeV,
- ET,rel- |pmiss| > 35 GeV,T
- frecoil < 0.1.
miss is considered in the same flavor analysis as a missing transverse energy
Note that ET,rel
miss ). The E miss is projection onto the axis defined by the nearest object:variable (ET
T,rel

miss
miss
ET,rel= ET· sin ∆ϕmiss
= ET(∆ϕ < π/2),(∆ϕ > π/2),

(5.2)
(5.3)

miss and the nearest hard object (lepton or jet). This
where ∆ϕ is the angle between the ET
variable is sensitive to the mis-measured object, thus has an advantage of reducing themiss is only considered for the same flavor analyQCD and Z/γ ∗ → ℓℓ backgrounds. The ET,relsis because it also rejects substantial signals. The risk of reducing the signals is still optimal
due to a huge amount of Z/γ ∗ → ℓℓ background in the analysis. Furthermore track-based
miss . The combination helps to further|pmiss| is also required in a combination with ET,relT
miss .
reduce the Z/γ ∗ → ℓℓ background since the |pmiss| has less correlation with ET,rel
T

The Z/γ ∗ → ℓℓ background is still large after the |pmiss| requirement, so a special cut
Tbased on soft hadronic recoil, referred to as frecoil , is made to further reject the Z/γ ∗ → ℓℓ
background. The missing transverse energy in the Z → ℓℓ events is in principle due tomiss ) because no neutrino exists in the event to balance themis-measured objects (fake ET
dilepton system, so the two leptons must be balanced by a hadronic recoil system. In fact
the soft jets below the analysis jet threshold play a role in the recoil system since the jetveto, in particular for the 0-jet analysis, ensures that this recoil is not reconstructed as thejet used in the analysis. The frecoil is defined as:∑| soft jets |JVF| · p⃗T |frecoil =
.
(5.4)
pℓℓ
T
The frecoil variable measures the strength of the recoil system relative to the dilepton system,with the pT of the soft jets weighted by the jet vertex fraction (JVF) to reduce the eﬀects

5.4 H→ W W ∗ → ℓνℓν Analysis

113

of soft jets from pileup. The soft recoil system is reconstructed as the vector sum pT ofsoft jets with pT > 10 GeV and |η| < 4.5 in the transverse quadrant opposite the dilepton
system (3π/4 < ∆ϕ(ℓℓ, soft-jets) < 5π/4) as illustrated in Figure 5.17.

Figure 5.17: Schematic view of soft hadronic recoil system. The hadronic recoil system is reconstructed in the transverse quadrant opposite the dilepton system (3π/4 <∆ϕ(ℓℓ, soft-jets) < 5π/4).
The frecoil can be extended to the 1-jet analysis by substituting the pT of the dileptonand “jets (pT > 25 GeV)” system for the pT of the dilepton system in the denominator of
extended . Figure 5.18 shows thesethe frecoil definition. This modified variable is labeled frecoil
variables and their discriminating power against Z/γ ∗ → ee/µµ and other processes, including the signal.
For the same flavor analysis, the signal region is split neither in mℓℓ nor psub
T unlike
the diﬀerent flavor analysis. Only lepton flavor split (ee, µµ) is used for final result since
the statistics in the signal region is quite limited. Table 5.6 shows expected signal andbackground counts for the 0-jet and 1-jet same flavor analysis.
A cut on frecoil = 0.1 after all signal region selection except for ∆ϕℓℓ and |pmiss| obtainsT
90 % rejection against Z/γ ∗ → ℓℓ background while retaining 60-70 % signal (or nonZ/γ ∗ → ℓℓ background), so the contribution from the Z/γ ∗ → ℓℓ background ends up verysmall (< 10 %) compared to W W (or top) background in the end of cutflow. The frecoil
extended are used for the data-driven Z/γ ∗ → ℓℓ background estimation by measurand frecoil
ing those cut eﬃciencies in data in relevant Z control regions. The data-driven Z/γ ∗ → ℓℓ
background estimation is discussed in Section 5.5.1. Figures 5.19 and 5.20 show sub-leading
extended ) requirement.
lepton pT , mℓℓ , ∆ϕℓℓ , and mT distributions after frecoil (or frecoil

5.4 H→ W W ∗ → ℓνℓν Analysis

10-1

Ratio

10-2
1.2
1
0.8
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
f recoil

Entries normalized to 1

low Mll SF SR
diboson, top, W+jets and Z→ττ
Z→ ee/ µµH[125]

1

1

low Mll SF SR
diboson, top, W+jets and Z→ττ
Z→ ee/ µµH[125]

10-1

10-2
1.2
1
0.8
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
1j
f recoil

Ratio

Entries normalized to 1

114

extended variable in the 1-jet
Figure 5.18: frecoil variable in the 0-jet analysis (left) and frecoil
analysis (right) for the signal, Z/γ ∗ → ℓℓ background, and non-Z/γ ∗ → ℓℓ backgrounds(i.e. top, W + jets, Z → τ τ , W W and other diboson backgrounds). For the frecoil events
pass all signal regions selection except for |pmiss|, ∆ϕℓℓ and frecoil itself, to allow for moreTℓℓstatistics. The pT > 30 GeV threshold boosts the dilepton system, creating the shapeextended events pass all signal region selection except for ∆ϕdiﬀerence visible. For the frecoilℓℓextended itself.
and frecoil

Table 5.6: Expected event counts in the 8 TeV ggF 0-1 jet analysis. Percentages are thefraction of the total background.
ggF 0-jet same flavor signal region

ee
µµ

H
25
46

All Bkg.
406
680

S/B
0.062
0.067

WW
283 (70%)505 (74%)VV
34 (8%)
34 (5%)tt̄
16 (4%)
24 (4%)(W )t
12 (3%)
19 (3%)

Z+jets24 (6%)
58 (8%)

W +jets
38 (9%)
41 (6%)

QCD
0.2 (0.0%)-0.1 (-0.0%)VV
17 (11%)
12 (5%)tt̄
37 (24%)57 (23%)(W )t16 (10%)26 (10%)Z+jets9 (6%)
20 (8%)

W +jets
8 (5%)
9 (4%)

QCD
0.0 (0.0%)-0.0 (-0.0%)

ggF 1-jet same flavor signal region

ee
µµ

H
10
17

All Bkg.
159
249

S/B
0.060
0.068

WW
71 (45%)124 (50%)

90
80
70

s = 8 TeV, ∫ Ldt = 20.3 fb-1
H→WW*→eνeν/ µ νµ ν + 0 jets

SM (sys ⊕ stat)
Other VV
Single Top
Z/γ *→τ τ
QCD

WW
tt *
Z/γ →llW+jet
H [125 GeV]

60

Events / 10 GeV

100

500
450
400
350
250

40

200

30

150

20

100

10

50
10

15

20

25

30

35
p

120

s = 8 TeV, ∫ Ldt = 20.3 fb-1
H→WW*→eνeν/ µ νµ ν + 0 jetsWWtt *Z/γ →llW+jet
H [125 GeV]

40
45
[GeV]

50

100

150

200

WW
tt *
Z/γ →llW+jet
H [125 GeV]

SM (sys ⊕ stat)
Other VV
Single Top
Z/γ *→τ τ
QCD

100

SM (sys ⊕ stat)
Other VV
Single Top
Z/γ *→τ τ
QCD

250
mll [GeV]

T,sublead lep

160
140

s = 8 TeV, ∫ Ldt = 20.3 fb-1
H→WW*→eνeν/ µ νµ ν + 0 jets

300

50

5

Events / 0.13 rad115

Events / 10 GeV

Events / 1 GeV

5.4 H→ W W ∗ → ℓνℓν Analysis

300
250

s = 8 TeV, ∫ Ldt = 20.3 fb-1
H→WW*→eνeν/ µ νµ ν + 0 jetsWWtt *Z/γ →llW+jet
H [125 GeV]

SM (sys ⊕ stat)
Other VV
Single Top
Z/γ *→τ τ
QCD

200

80

150

60

100

40
50

20
0

0.5

1

1.5

2

2.5

3
∆φ [rad]
ll

50

100

150

200

250

300

mtrack-clj[GeV]
T

Figure 5.19: Sub-leading lepton pT (top left), mℓℓ (top right), ∆ϕℓℓ (bottom left), and mT(bottom right) distributions after frecoil requirement for 0-jet same flavor analysis.

5.4 H→ W W ∗ → ℓνℓν Analysis

40
35
30

s = 8 TeV, ∫ Ldt = 20.3 fb-1
H→WW*→eνeν/ µ νµ ν + 1 jet

SM (sys ⊕ stat)
Other VV
Single Top
Z/γ *→τ τ
QCD

WW
tt *
Z/γ →llW+jet
H [125 GeV]

25

Events / 10 GeV

Events / 1 GeV

116

180
160
140

s = 8 TeV, ∫ Ldt = 20.3 fb-1
H→WW*→eνeν/ µ νµ ν + 1 jet

WWtt *Z/γ →llW+jet
H [125 GeV]

SM (sys ⊕ stat)
Other VV
Single Top
Z/γ *→τ τ
QCD

120
100

20

80

15

60
10

40

5
10

15

20

25

30

35

Events / 0.13 rad

p

40
45
[GeV]

80
70
60

s = 8 TeV, ∫ Ldt = 20.3 fb-1
H→WW*→eνeν/ µ νµ ν + 1 jet

50

100

150

200

250
mll [GeV]

T,sublead lep

WWtt *Z/γ →llW+jet
H [125 GeV]

SM (sys ⊕ stat)
Other VV
Single Top
Z/γ *→τ τ
QCD

50

Events / 10 GeV

5

20

90
80
70

s = 8 TeV, ∫ Ldt = 20.3 fb-1
H→WW*→eνeν/ µ νµ ν + 1 jet

WWtt *Z/γ →llW+jet
H [125 GeV]

SM (sys ⊕ stat)
Other VV
Single Top
Z/γ *→τ τ
QCD

60
50

40
40
30

30

20

20

10

10

0

0.5

1

1.5

2

2.5

3
∆φ [rad]
ll

50

100

150

200

250

300

mtrack-clj[GeV]
T

Figure 5.20: Sub-leading lepton pT (top left), mℓℓ (top right), ∆ϕℓℓ (bottom left), and mT
extended requirement for 1-jet same flavor analysis.
(bottom right) distributions after frecoil

5.4 H→ W W ∗ → ℓνℓν Analysis

5.4.4

117

VBF Selection

The VBF analysis employs multivariate analysis (MVA) based on Boosted Decision Tree
(BDT) technique to fully exploit distinct VBF topology. A decision tree is a collection ofcuts designed to classify events as signal-like or background-like. A given signal event iscorrectly identified if it is placed in a signal-dominated leaf, and vice-versa for background
events. After the initial tree is built, another tree is grown to better separate the signal
and background events that were misidentified by the first tree. This proceeds iteratively
until there is a collection of a specified number of trees, in a process known as boosting.
A weighted average is taken from all these trees to form a BDT output discriminant withvalues ranging between -1 and 1.
In this analysis, the BDT is trained using both diﬀerent flavor (eµ, µe) and same flavor(ee, µµ) data set, since most of non-Z/γ ∗ → ℓℓ backgrounds are insensitive to lepton flavor,
and adding extra same flavor specific variables did not oﬀer a significant gain. On the other
hand, training with all flavor channels gains in statistics of training samples. The BDT istrained with events that satisfy sub-leading lepton pT (psub
T ) > 15 GeV, but applied to allsubevents (pT > 10 GeV) when fitting to the BDT output. A couple of cuts are made for the
VBF analysis before the BDT training after the pre-selection described in Section 5.4.1:- No missing transverse energy requirement for the diﬀerent flavor channel,
jetCorr
miss > 45 GeV are imposed for the same flavor
while pmiss,> 40 GeV and ET
Tchannel,- b-jet veto (see Section 5.4.2),- Z → τ τ veto (see Section 5.4.2),- CJV (Central Jet Veto): Events that have jets with pT > 20 GeV, lying between thetwo forward jets in η are rejected.
- OLV( (Outside
Lepton Veto): The two charged leptons must have rapidities Y (=)
E+pz
1
2 ln E−pz ) that are between the tagging jets’ rapidities.
The additional requirements above allow for having sample that is similar to the signal
region in phase space. The data set that passes the criteria above are used to create the
BDT with the following eight variables:: The total transverse momentum ptot
- ptot,track,jetCorr
T ,T
miss, jetCorr ∑ jetsl1
l2
the magnitude of pT +pT +pT+ pT , suppresses events with significant
soft gluon radiation that recoils against the two leptons and two jets system. For
the missing transverse energy, jet-corrected track-based missing transverse energy
miss, jetCorr
pT
is used.
- ∆yjj : The signal is characterized by a separation of the two tagging jets in rapidity,- mjj : invariant mass of the tag jets (mjj ),5.4 H→ W W ∗ → ℓνℓν Analysis

118

centrality- ηlep: It quantifies the exact positions of the leptons with respect to the twotagging jets in the η plane:

centrality
ηlep
=

∑

OLVℓn =

n=0,1

∑

2·

n=0,1

|ηℓn − η̄|,|ηj0 − ηj1 |(5.5)

centrality> 1 indicates awhere η̄ = (ηj0 + ηj1 )/2 is the average η of the two tag jets. ηlep
event that have outside leptons.
∑ℓ,j Mℓj : The sum of the invariant mass of lepton and jet pairs. The VBF signal
makes large opening angle between jet and lepton,- mℓℓ : The invariant mass of dilepton system,- ∆ϕℓℓ : The opening angle of leptons in the ϕ plane,- mT : The transverse mass of dilepton system. For the missing transverse energy,
jetCorr
jet-corrected track-based missing transverse energy pmiss,is used.
T
First five are variables specific for the VBF analysis, and last three that are related tothe spin correlation are common variables to the ggF analysis. Key input variables after
pre-selection are shown in Figure 5.21 for the diﬀerent flavor channel, and Figure 5.22 forthe same flavor channel.
The BDT output distribution (BDT score) is then fit to get final result. The binninghas been optimized for maximal expected significance while keeping reasonable MC statistics in each bin. The chosen configuration is four bins with boundaries at [−0.48, 0.3, 0.78]
over the range of [−1, 1]. The bin with the lowest BDT score contains the majority ofbackground (> 90%) and thus substantially smaller signal to background ratio. Hence it
is negligible in terms of total significance and is excluded from the BDT fit, which also
ensures orthogonality with the ggF 2-jets analysis. Table 5.7 shows expected signal andbackground counts in each bin of BDT, and Figure 5.23 shows corresponding BDT bins.
Table 5.7: Expected yield in each bin of BDT for the diﬀerent flavor and same flavor
channels (No normalization factors (NFs) are applied).
eµ + µe
Bin 1
Bin 2
Bin 3
ee + µµ
Bin 1
Bin 2
Bin 3

vbf+vh [125 GeV]

ggf [125 GeV]WWW Z/ZZ/W γ

tt̄

Single Top

Z → ℓℓ+jets

Z → τ τ +jets

W +jets/QCD

Total Bkg.(+ggf)

4.27 ± 0.10
4.23 ± 0.09
3.12 ± 0.07

3.03 ± 0.07
1.25 ± 0.05
0.40 ± 0.03

5.99 ± 0.28
2.06 ± 0.16
0.53 ± 0.07

2.53 ± 0.49
0.75 ± 0.28
0.06 ± 0.06

11.52 ± 0.40
2.36 ± 0.18
0.33 ± 0.07

2.14 ± 0.18
0.37 ± 0.05
0.09 ± 0.03

0.19 ± 0.12
0.00 ± 0.00
0.00 ± 0.00

4.30 ± 0.59
0.29 ± 0.07
0.07 ± 0.04

5.31 ± 1.23
0.69 ± 0.43
0.01 ± 0.02

35.20 ± 1.25
8.14 ± 0.49
1.61 ± 0.16

2.22 ± 0.07
2.47 ± 0.07
1.74 ± 0.06

1.48 ± 0.05
0.62 ± 0.03
0.18 ± 0.02

3.53 ± 0.22
1.14 ± 0.12
0.26 ± 0.05

0.89 ± 0.22
0.30 ± 0.15
0.02 ± 0.02

7.24 ± 0.32
1.51 ± 0.14
0.25 ± 0.06

1.24 ± 0.14
0.31 ± 0.07
0.05 ± 0.02

25.54 ± 2.26
4.56 ± 0.57
0.63 ± 0.19

1.94 ± 0.35
0.31 ± 0.08
0.01 ± 0.01

1.15 ± 0.55
0.28 ± 0.19
0.00 ± 0.00

43.48 ± 2.39
9.20 ± 0.66
1.42 ± 0.21

119

800
700
600

s = 8 TeV, ∫ Ldt = 20.3 fb-1
H→WW*→eνµ ν/ µ νeν + ≥ 2j

SM (sys ⊕ stat)

WW

Other VVtt
Z/γ *→ll

Single top

500

Z/γ *→τ τ

W+jet

ggF

VBF (× 50)

Events / 0.4

Events / 5 GeV

5.4 H→ W W ∗ → ℓνℓν Analysis

400

300
250

s = 8 TeV, ∫ Ldt = 20.3 fb-1
H→WW*→eνµ ν/ µ νeν + ≥ 2j

200

SM (sys ⊕ stat)

WW

Other VVtt
Z/γ *→ll

Single top
Z/γ *→τ τ

W+jet

ggF

VBF (× 50)

150

300

100

200
50

100
0

20

40

60

80

100

120

140

0

1

2

3

4

5

6

7

100

s = 8 TeV, ∫ Ldt = 20.3 fb-1
H→WW*→eνµ ν/ µ νeν + ≥ 2j

SM (sys ⊕ stat)

WW

Other VVtt
Z/γ *→ll

Single top
Z/γ *→τ τ

W+jet

ggF

VBF (× 50)

Events / 4.3 GeV

Events / 25 GeV

120

80

8

∆ Y jjP tot[GeV]T, jet corr.

100
80

s = 8 TeV, ∫ Ldt = 20.3 fb-1
H→WW*→eνµ ν/ µ νeν + ≥ 2j

SM (sys ⊕ stat)

WW

Other VVtt
Z/γ *→ll

Single top
Z/γ *→τ τ

W+jet

ggF

VBF (× 50)

60

60
40
40
20

20
0

500

1000

1500

2000

2500

mjj [GeV]

50

100

150

200

250

300

mT, jet corr. [GeV]

Figure 5.21: Distributions of ptot,track,jetCorr, ∆yjj , mjj , and mT in diﬀerent flavor channelTafter all pre-selection. The VBF signal is scaled by 50 times larger.

5.4 H→ W W ∗ → ℓνℓν Analysis

500
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s = 8 TeV, ∫ Ldt = 20.3 fb-1
H→WW*→eνeν/ µ νµ ν + ≥ 2j

SM (sys ⊕ stat)

WW

Other VVtt
Z/γ *→ll

Single top
Z/γ *→τ τ

W+jet

ggF

VBF (× 50)

Events / 0.4

Events / 5 GeV

120

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s = 8 TeV, ∫ Ldt = 20.3 fb-1
H→WW*→eνeν/ µ νµ ν + ≥ 2j

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SM (sys ⊕ stat)

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Z/γ *→ll

Single top
Z/γ *→τ τ

W+jet

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VBF (× 50)

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SM (sys ⊕ stat)

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s = 8 TeV, ∫ Ldt = 20.3 fb-1
H→WW*→eνeν/ µ νµ ν + ≥ 2j

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∆ Y jjP tot[GeV]T, jet corr.

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H→WW*→eνµ ν/ µ νeνSM (sys ⊕ stat)

WW

Other VV
Single toptt
Z/γ *→ll

Z/γ *→τ τ

W+jet

ggF

VBF

Events / 0.5

Events / 0.5

Figure 5.22: Distributions of ptot,track,jetCorr, ∆yjj , mjj , and mT in same flavor channelTafter all pre-selection. The VBF signal is scaled by 50 times larger.

70
60
50

40

40

30

30

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10

-1 -0.8 -0.6 -0.4 -0.20

0.2 0.4 0.6 0.8

1BDT

s = 8 TeV, ∫ Ldt = 20.3 fb-1
H→WW*→eνeν/ µ νµ ν

-1 -0.8 -0.6 -0.4 -0.2

0

SM (sys ⊕ stat)

WW

Other VV
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W+jet

ggF

VBF

0.2 0.4 0.6 0.8

1

BDT

Figure 5.23: BDT score for the eµ+µe (left) and ee+µµ (right) channels after the BDT> −0.48 cut. The MC is unblinded. The grey band contains only statistical uncertainties.

5.5 H→ W W ∗ → ℓνℓν Analysis

5.5

121

Background Estimation

In order to determine expected background yield in the signal region, some backgrounds
are normalized to data in dedicated control regions, and other background normalizations
are taken directly from MC cross section, except for the W +jets/QCD and the same flavor
Z+jets backgrounds. These backgrounds are evaluated in data-driven methods.

5.5.1

ggF 0-1 jet analysis

Figure 5.24 shows schematic view of the extraction of the main backgrounds in the ggF
0-jet analysis.

Figure 5.24: Schematic view of the extraction of the main backgrounds for ggF 0-jet
analysis. Signal region is defined as “∆ϕℓℓ < 1.8 and mℓℓ < 55 GeV. Several backgrounds
are normalized to data in dedicated control regions.
In the ggF 0-jet analysis, W W , Z/γ ∗ → τ τ , and Same Sign (SS) control regions are defined.
The SS control region is used to extract the normalization of the “non-W W ” dibosons(V V ). Other significant background is the W +jets background. The W +jets backgroundis estimated by a data-driven method called fake factor method (see Chapter 6). Making useof the data-driven method is essential for this background, since it may not be accurately
modeled by simulation. For the same flavor channel (ee, µµ), the Z/γ ∗ → ℓℓ background isalso of special importance, which is discussed in this section.

122

5.5 H→ W W ∗ → ℓνℓν Analysis

Figure 5.25 shows schematic view of the extraction of the main backgrounds in the ggF
1-jet analysis.

Figure 5.25: Schematic view of the extraction of the main backgrounds for the ggF 1-jet
analysis. Signal region is defined as “∆ϕℓℓ < 1.8 and mℓℓ < 55 GeV. Several backgrounds
are normalized to data in dedicated control regions. Several backgrounds are normalized
to data in dedicated control regions.
In the ggF 1-jet analysis, the top control region is added, since the contribution from the
top background is large. Otherwise the strategy of the background estimation is the same as
the ggF 0-jet analysis. In the remaining section, each background estimation is described.
W W backgroundThe background from continuum W W ∗ → ℓνℓν production is the most important background in the analysis since it has the same final state (W W ∗ → ℓνℓν) and more than 10times larger cross section than the Higgs signal cross section. The W W background isnormalized using a control region which is defined to be orthogonal to the signal region
but to be similar to the signal region in phase space. In order to define the control region,
topological selection criteria, namely mℓℓ and ∆ϕℓℓ are changed from the signal region definition described in Section 5.4.2:
0-jet• 55 < mℓℓ < 110 GeV,

5.5 H→ W W ∗ → ℓνℓν Analysis

123• ∆ϕℓℓ < 2.6 radians,
1-jet• mℓℓ > 80 GeV,• no ∆ϕℓℓ cut applied,
where the ∆ϕℓℓ cut intends to reduce the remaining Z/γ ∗ → τ τ contribution at high ∆ϕℓℓ
for the 0-jet analysis but is not applied to the 1-jet analysis since the Z/γ ∗ → τ τ vetorequirement already rejects most of the Z/γ ∗ → τ τ . It is worth noting that the sub-leading
lepton pT is set to be psublead> 15 GeV for the W W control region to avoid the large
T
W +jets contamination from events with 10 < psublead< 15 GeV.
T
The normalization factor (NF) is derived from this control region. The NF is evaluatedsubtracting contribution from other backgrounds, and taking the ratio of the remaining
data events to the W W yield predicted by MC. Since there is no significant diﬀerence
between the eµ and µe channels and no physical reason to separate eµ and µe channels,
the combined diﬀerent flavor channel (eµ+µe) is used to derive the NF. As Z/γ ∗ → ℓℓ
contamination in the W W control region is large for the same flavor channels, The same
normalization factor is applied to all lepton flavor channels (ee, µµ, eµ, µe). The resulting
NFs are 1.22 ± 0.03(stat.) for 0-jet and 1.05 ± 0.05(stat.) for 1-jet, and is listed along withother NFs in Table 5.11.
The signal and control regions are fit simultaneously and the W W normalization is
extrapolated from the control region to the signal region as extrapolation factor α (NSR =αNCR ). The theoretical uncertainties on the extrapolation factor α is the main source of systematic uncertainty on the W W background. The theoretical uncertainties are evaluated,varying the renormalization and factorization scales for QCD scale uncertainty, comparing diﬀerent PDFs for PDF uncertainty, and comparing the extrapolation factors between
generators for underlying/parton shower (UEPS) and matrix element modeling. These uncertainties (referred to as QCD scale, PDF, UEPS, and matching) are evaluated for eachsignal region, namely the same sub-leading lepton pT and mℓℓ configuration. In orderto reduce the theoretical uncertainties, the control region is defined closely to the signal
region in mℓℓ . The mℓℓ boundary between signal and control region is optimized to keep
both signal and control region acceptance, while ensuring similar kinematics in both regions.
For the W W background mT shape variations are also evaluated as shape systematic uncertainty. The uncertainties on the W W background will be further discussed in
Section 5.6.2.2 since they have large impact on the measured signal strength.
jetCorr
Figure 5.26 and 5.27 show kinematic distributions (mℓℓ , mT , pmiss,, and subT
leading lepton pT ) of the W W control region for 0-1 jet analysis. Overall agreement between
data/MC looks reasonable and the purity of the W W control region is 70% level for 0-jet
and 40% for 1-jet.

5.5 H→ W W ∗ → ℓνℓν Analysis

1000
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jetCorr
Figure 5.26: mℓℓ (top left), mT (top right), pmiss,(bottom left), and sub-leadingT
lepton pT (bottom right) distributions in the W W control region for 0-jet analysis.

125

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5.5 H→ W W ∗ → ℓνℓν Analysis

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Figure 5.27: mℓℓ (top left), mT (top right), pmiss,(bottom left), and sub-leadingT
lepton pT (bottom right) distributions in the W W control region for 1-jet analysis.

126

5.5 H→ W W ∗ → ℓνℓν Analysis

Z/γ ∗ → τ τ background
The Z/γ ∗ → τ τ background that is sub-dominant background in the signal region is estimated using MC but the cross section is normalized to data in an appropriate Z/γ ∗ → τ τcontrol region. In order to define the Z/γ ∗ → τ τ control region, some selection criteriasuch as those Z/γ ∗ → τ τ veto, mℓℓ , and ∆ϕℓℓ are changed from the signal region definition
described in Section 5.4.2:
0-jet• mℓℓ < 80 GeV,• ∆ϕℓℓ > 2.8 radians,
1-jet• mℓℓ < 80 GeV,
• revert Z/γ ∗ → τ τ veto.
The purity of this control region is ∼ 90% and 0.5% of the total Z/γ ∗ yield originatesfrom the Z/γ ∗ → ℓℓ (ℓ = e, µ) component. The normalization factors (NF) are calculated, subtracting small contribution from other processes in the control region, and taking
the ratio of background-subtracted data to MC cross section. Since there is no significant
diﬀerence between the eµ and µe channels and no physical reason to separate eµ and µe
channels, the combined diﬀerent flavor channel (eµ+µe) is used to derive the NF. AlthoughZ/γ ∗ → τ τ is negligible in the same flavor channels, the NF derived from the diﬀerent
flavor dateset is applied to all lepton flavor channels (ee, µµ, eµ, µe). The resulting NFs are
1.01 ± 0.02(stat.) for 0-jet and 1.07 ± 0.04(stat.) for 1-jet, and is listed along with other NFs
in Table 5.11.
Similar to the W W background, the uncertainties on the Z/γ ∗ → τ τ extrapolationfrom the control region to the signal region is evaluated from the variations of the PDF,
QCD scale, UEPS (underlying event/parton shower) and matching (matching of parton
shower to the matrix element). The total uncertainty that is dominated by the scale uncertainty is 8% for 0-jet and 12% for 1-jet.
jetCorr, and subFigure 5.28 and 5.29 show kinematic distributions (mℓℓ , mT , pmiss,Tleading lepton pT ) of the Z/γ ∗ → τ τ control region for 0-1 jet analysis. Overall agreement
between data/MC looks reasonable.

127

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5.5 H→ W W ∗ → ℓνℓν Analysis

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Figure 5.28: mℓℓ (top left), mT (top right), pmiss,(bottom left), and sub-leadingT
lepton pT (bottom right) distributions in the Z/γ ∗ → τ τ control region for 0-jet analysis.

5.5 H→ W W ∗ → ℓνℓν Analysis

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Figure 5.29: mℓℓ (top left), mT (top right), pmiss,(bottom left), and sub-leadingT
lepton pT (bottom right) distributions in the Z/γ ∗ → τ τ control region for 1-jet analysis.

5.5 H→ W W ∗ → ℓνℓν Analysis

129

Z/γ ∗ → ℓℓ background
The Z/γ ∗ → ℓℓ background (Z/DY ) arises mainly from mis-measured objects or associatedsoft pp collisions in event. This background is significant in the same flavor analysis. The
soft hadronic recoil variable (frecoil ) described in Section 5.4.3, shows a clear diﬀerence inshape between the Z/DY and all other processes that have neutrino(s) in the final state(i.e. true missing transverse energy), including the signal as shown in Figure 5.18. Based on
soft hadronic recoil, a data-driven technique called “Pacman method” has been developed
for the Z/DY background estimation. For the Z/DY background estimate, the data-driven
procedure is essential because frecoil uses very soft jets (pT > 10 GeV) which may not be
accurately modeled in simulation. The Pacman method is illustrated in Figure 5.30.

Figure 5.30: Schematic view of the Pacman method for the Z/DY background estimate.
In the Pacman method, the eﬃciency of frecoil cut for Z/DY (green box) and non-Z/DY(blue box) events are independently measured in data. The Z/DY eﬃciency is calculated
in the same flavor (SF) Z mass peak, |mℓℓ − mZ | < 15 GeV (see green box in Figure 5.30).
The purity of Z/DY events in this region is only ∼ 50%, thus the non-Z/DY contribution
must be subtracted. The Z/DY eﬃciency is written as follows:
non-Z/DY

ϵ

Z/DY

=

N 0Zpeak− ϵZpeakSF× N (non-Z/DY)Zpeak
SF

Zpeak
NSF
− N (non-Z/DY)Zpeak
SF

,

(5.6)

where N 0Zpeak
is the number of events that pass frecoil cut in the same flavor Z peak,
SF
Zpeak
NSF
is the number of events before applying frecoil cut in the same flavor Z peak, andN (non-Z/DY)Zpeak
is the number of non-Z/DY events in the same flavor Z peak. The
SF
normalization of the non-Z/DY contribution, N (non-DY)Zpeak, is taken from the MC crossSFsection (but including data normalizations for W W , top and Z/γ ∗ → τ τ from the control
non-Z/DY
regions), and has an associated uncertainty of ∼ 10%. The non-Z/DY eﬃciency, ϵZpeak ,is measured in data using diﬀerent flavor data set in the Z peak. The non-Z/DY eﬃciency
in the Z peak is written as:
non-Z/DY

ϵZpeak

=N 0Zpeak
DF
Zpeak
NDF

.

(5.7)

5.5 H→ W W ∗ → ℓνℓν Analysis

130
where DF denotes diﬀerent flavor.

One can write the Z/DY background in the signal region (red box in Figure 5.30)
as:
SR
SR
N0(Z/DY)SR
SF = N0SF − N0(non-Z/DY)SF .

(5.8)

Similarly one can write the Z/DY background in the signal region before the frecoil cut
using ϵZ/DY (green box) and ϵnon-Z/DY (blue box) as:
N0(Z/DY)SR
N0(non-Z/DY)SR
SR
SF
SF
=
N
−
.
SF
ϵZ/DY
ϵnon-Z/DY(5.9)

Then solve for N0(Z/DY)SR
SF using Equations 5.8 and 5.9 as:
Z/DY
N0(Z/DY)SR×
SF = ϵ

non-Z/DY × N SR
N 0SR
SF − ϵSF.
ϵZ/DY − ϵnon-Z/DY(5.10)

ϵnon-Z/DY is the cut eﬃciency for non-Z/DY events in the low mℓℓ signal region (bluebox), and is obtained from the frecoil data distribution of diﬀerent flavor events that pass fullsame flavor selection. One can derive the cut eﬃciency for the non-Z/DY using diﬀerent
flavor data set since the relative fractions of each non-Z/DY process in the signal region
are the same between diﬀerent flavor and same flavor due to flavor universality.
non-Z/DY

The systematic uncertainties on ϵnon-Z/DY and ϵZpeak
to account for the uncertainties
on the extrapolation from the diﬀerent flavor control sample to the same flavor signal region
are evaluated, comparing several MC generators and data. The systematic uncertainties
are then added in quadrature to the statistical uncertainty on the measured non-Z/DY
eﬃciency. The same procedure is also applied to ϵDY to account for the extrapolation fromthe Z-peak control sample to the low mℓℓ signal region. Figure 5.31 shows a comparison of
Z/DY recoil shapes between Z peak and low mℓℓ regions in MC.
Table 5.8 summarizes the systematic uncertainties on the cut eﬃciencies for the 0-jet
and 1-jet analyses. One can expect a final uncertainty on the Z/DY background of ∼ 50%,
dominated by the extrapolation uncertainty on ϵDY .
W +jets/QCD background
The W +jets background arises from events that have one fully identified lepton and one
jet faking an identified lepton. Similarly the QCD background arises from events that have
two jets faking identified leptons. Since the fake backgrounds are diﬃcult to model insimulation, the data-driven method called “fake factor method” has been developed. The
fake factor method is further discussed in detail in Chapter 6. This data-driven method
is employed to both ggF and VBF analyses. The size of these backgrounds is very large
in the signal region in particular in the region that contains sub-leading lepton with pT <

Entries normalized to 1

5.5 H→ W W ∗ → ℓνℓν Analysis

0.3

131

Z→ee/µ µ FullSim
Alpgen+Herwig low m ll
Alpgen+Herwig Z peak

0.25

Alpgen+Pythia low m ll
Alpgen+Pythia Z peak

0.2

0.15
0.1

Ratio

0.05
0
1.2
7.35% +/- 5.04% = 1.5σ
32.24% +/- 8.46% = 3.8σ1
0.8
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
f recoilFigure 5.31: Comparison of Z/DY recoil shapes for the 0-jet between same flavor Z peakand signal low mℓℓ regions events in MC.
Table 5.8: Z/DY and non-Z/DY eﬃciencies and uncertainties, used to estimate the Z/DY
background in the 0-jet signal region with the Pacman method.
Sources
ϵnon-DY
DF → SF extrapolation
statistical uncertainty
total uncertainty
non-DYϵZpeakDF → SF extrapolation
statistical uncertainty
total uncertainty
DYϵZ peak → low mℓℓ extrapolation
statistical uncertainty
total uncertainty
estimated DY yield in SF SR
statistical uncertainty
total uncertainty

0-jet
0.69 ± 0.01
0.8%
1.8%
1.9%
0.68 ± 0.02
1.9%
2.5%
3.1%
0.14 ± 0.05
32%
9.4%
38%
88 ± 43
15%
49%

1-jet
0.64 ± 0.02
1.2%
3.0%
3.2%
0.66 ± 0.03
2.4%
3.9%
4.5%
0.13 ± 0.04
16%
16%
32%
26 ± 1229%
45%

15 GeV, which results in large impact on the final fit, so a sophisticated modeling of thesebackgrounds is very important.

5.5 H→ W W ∗ → ℓνℓν Analysis

132
V V backgroundThe non-W W backgrounds (W Z/ZZ ∗ /W γ (∗) /Zγ (∗) ) contribute to the signal region. Thesebackgrounds are normalized in Same Sign control region by subtracting the W +jets background which is sub-dominant in this region. The SS control region is further discussed in
Chapter 7.
Top backgroundTop quark events (tt̄ and single top process W t) are a significant background to the 0-1 jetanalysis as shown in Table 5.4 and 5.5.
Top background in the 0-jet analysis
The top background in the 0-jet analysis is estimated using the jet-veto survival probability (JVSP) method [16, 171]. Pre-selected sample that passes pre-selection described in
jetCorr
Section 5.4.1 and some additional cuts, pmiss,> 20 GeV and ∆ϕℓℓ < 2.8, is used.
T
The top background in the signal region after the jet veto cut is given by:Exp
Ntop,0j= (Ndata − Nnon-top ) × P2Exp ,(5.11)

where Ndata is the total number of events in data after pre-selection and Nnon-top is contributions from non-top backgrounds in the pre-selected data sample (Ndata ). P2Exp isa data-driven fraction of top events which pass the jet veto in the pre-selected sample.
Assuming that a tt̄ event has two b-quarks and there is no correlation between the twob-quarks, the P2 can be expressed as:
P2 = P12 ,(5.12)

where P1 is a single jet veto survival probability that can be obtained from a control sample
requiring at least one b-jet. P2Exp is then written using P1 as:
P2Exp = P2MC × (P1Btag,data 2) ,P1Btag,MC(5.13)

where superscript “Btag” indicates that P1 is measured in b-tagged control region, andP2MC is a fraction of top events that pass the jet veto. The top background in the signal
region is rewritten using Equations 5.11 and 5.13 as:Exp
Ntop,0j= (Ndata − Nnon-top ) × (P1Btag,data )2 ×

P2MC
(P1Btag,MC )2.

(5.14)The eﬃciency for the remaining requirements on pℓℓ
T , mℓℓ ,and ∆ϕℓℓ is taken from simulation. The ratio of the resulting prediction to the one from simulation alone is 1.11 ±0.02(stat.). This ratio is applied as a correction to the predicted top background.

5.5 H→ W W ∗ → ℓνℓν Analysis

133
P2MC
Btag,MC 2(P1)

The total systematic uncertainty on the ratio term

is 8% in which exper-

imental uncertainties contribute about 7% that is mostly coming from the jet energy scaleand resolution, and in which theoretical uncertainties contribute about 4.5% including thePDF, QCD scale, UEPS, and matching uncertainties.
Top background in the 1-jet analysis
The top background in the 1-jet analysis is estimated using the b-tagged control region
that can be expressed as:
data,1j−CR
Ntop
data,1j−SR
MC,1j−SR
Ntop= Ntop× MC,1j−CR ,Ntop(5.15)

1j−SR
1j−CR
where Ntop
is the number of top background in the signal region and Ntop
is thenumber of top background in the control region that contains at least one b-jet, otherwise
passes the same requirements as the signal region. When introducing the b-tagging eﬃciency(ϵtag ) and ineﬃciency (1 − ϵtag ), the ratio N 1j−SR /N 1j−CR is given by:
1j−SR
Ntop

=
1j−CR

Ntop

1j−CR
1 − ϵtagϵ1j−CRtag.

(5.16)

data,1j−SR
Substituting Equation 5.16 into Equation 5.15, the Ntop
is expressed as:

data,1j−SR
data,1j−CR
Ntop= Ntop×

1 − ϵMC,1j−CR
tagϵMC,1j−CRtag.

(5.17)

In practice the eﬃciency is not measured using MC but measured in data because theMC eﬃciency leads to large experimental uncertainty coming from mis-tagging eﬃciency,
jet energy scale, and jet energy resolution. To reduce the uncertainty one can measure theb-tagging eﬃciency using tt̄ events in data. The data-driven method is so-called tag-andprobe method where randomly chosen one b-jet is defined as “tag”. Making use of the otherjet as “probe” does not make any bias in jet composition. Substituting MC eﬃciency fordata eﬃciency, the equation above can be expressed as:
data,1j−CR
Ntop
data,1j−SR
Ntop= data,2j−CR
× (1 − ϵdata,2j−CR
× fcorr ),tag
ϵtag
× fcorr
C,1j−CRϵMtagfcorr = M C,2j−CR ,ϵtag(5.18)(5.19)In this formalization, the experimental uncertainty on the MC eﬃciency is mostly canceled by taking the ratio, thus the systematic uncertainty is dominated by the theoreticaluncertainties on fcorr . The theoretical uncertainty is evaluated by comparing several MC

5.5 H→ W W ∗ → ℓνℓν Analysis

134

samples, and it is found that the theoretical uncertainty propagated to the final measured
top events is ∼ 4%.

1200
1000

s = 8 TeV, ∫ Ldt = 20.3 fb-1
H→WW*→eν µν / µν eν + 1 jet

800

Data

SM (sys ⊕ stat)

WW

Other VV
Single Top
Z/ γ *→ττtt*
Z/ γ →ll
W+jet
H [125 GeV]

QCD

Events / 10 GeV

Events / 10 GeV

jetCorr
Figure 5.32 shows mℓℓ , mT , pmiss,, and sub-leading lepton pT distributions forT
1-jet analysis. Overall agreement between data/MC looks reasonable and the purity of the
top control region is 90% level. The normalization factor (NF) is also calculated in thedata,1j−SR
signal region as the ratio of estimated top events (Ntop) to the predicted top events
MC,1j−SR(Ntop), which is 1.03 ± 0.03(stat.).
1000
900
800

s = 8 TeV, ∫ Ldt = 20.3 fb-1
H→WW*→eν µν / µν eν + 1 jet

700

Data

SM (sys ⊕ stat)

WW

Other VV
Single Top
Z/ γ *→ττtt*
Z/ γ →ll
W+jet
H [125 GeV]

QCD

600
500

600

400
400

300
200

200

Data / SM

Data / SM

100
1.4
1.2
1
0.8
0.6
50

100

150

200

1.4
1.2
1
0.8
0.6

250

50

100

150

200

250

800
700

s = 8 TeV, ∫ Ldt = 20.3 fb-1

H→WW*→eν µν / µν eν + 1 jet

600

Data

SM (sys ⊕ stat)

WW

Other VV
Single Top
Z/ γ *→ττtt*
Z/ γ →ll
W+jet
H [125 GeV]

QCD

Events / 1 GeVEvents / 5 GeV

900

300

[GeV]
mtrack-clj
Tmll [GeV]

500

500
450
400

s = 8 TeV, ∫ Ldt = 20.3 fb-1
H→WW*→eν µν / µν eν + 1 jet

350

Data

SM (sys ⊕ stat)

WW

Other VV
Single Top
Z/ γ *→ττtt*
Z/ γ →ll
W+jet
H [125 GeV]

QCD

300
250

400

200
150

200

100

100

50

1.4
1.2
1
0.8
0.6
0

Data / SM

Data / SM

300

50

100

150

200
miss,track,Clj

ET

250
[GeV]

1.4
1.2
1
0.8
0.6
5

10

15

20

25

30

35
p

40

T,sublead lep

45

[GeV]

jetCorr
Figure 5.32: mℓℓ (top left), mT (top right), pmiss,(bottom left), and sub-leadingT
lepton pT (bottom right) distributions in the top control region for 1-jet analysis.

5.5 H→ W W ∗ → ℓνℓν Analysis

5.5.2

135

VBF analysis

Figures 5.33 shows schematic view of the extraction of the main backgrounds in the VBF
analysis.

Figure 5.33: Schematic view of the extraction of the main backgrounds for the VBF
analysis. Some backgrounds are normalized to data in dedicated control regions.

Top background
The top background is estimated using MC but the cross section is normalized to data ina b-tagged control region. The control region requires exactly one b-tagged jet, in order tomake the flavor composition of tag jets closer to the one in the signal region. The control
region is defined for each bin in the BDT score, but due to the lack of data statistics,
the two bins with the highest BDT score share a combined normalization factor (NF).
The resulting NFs from diﬀerent flavor data set are 1.50±0.14(stat.) for the lowest bin
and 1.34±0.38(stat.) for the highest two bins, and the NFs from same flavor data set are
1.67±0.20(stat.) for the lowest bin and 0.31±0.54(stat.) for the highest two bins. Figure 5.34 shows kinematic distributions for diﬀerent flavor top control region.
The theoretical uncertainties are evaluated for the standard sources: the QCD scale,the PDF, the UEPS, and the matching using diﬀerent MC generators. The uncertainties
are derived for each bin of the BDT score. The total theoretical uncertainties for each bin
are 10%, 12%, and 21% for each bin, that are dominated by the UEPS uncertainty, whileother uncertainties are relatively small.

5.5 H→ W W ∗ → ℓνℓν Analysis

1000
900
800

s = 8 TeV, ∫ Ldt = 20.3 fb-1

H→WW*→eν µν / µν eν + ≥ 2j

700

Data

SM (sys ⊕ stat)WW
tt
Z/ γ *→ll

Other VV
Single top
Z/ γ *→ττ

W+jet

ggF

Events / 0.4

Events / 5 GeV

136

600
s = 8 TeV, ∫ Ldt = 20.3 fb-1

500

H→WW*→eν µν / µν eν + ≥ 2j

400

VBF

Data

SM (sys ⊕ stat)WW
tt
Z/ γ *→ll

Other VV
Single top
Z/ γ *→ττ

W+jet

ggF

VBF

600
500

300

400
200

300
200

100

1.4
1.2
1
0.8
0.6
0

Data / SM

Data / SM

100

20

40

60

80

100

120

140

1.4
1.2
1
0.8
0.6
0

1

2

3

4

5

6

7

350
300

s = 8 TeV, ∫ Ldt = 20.3 fb-1
H→WW*→eν µν / µν eν + ≥ 2j

Data

SM (sys ⊕ stat)WW
tt
Z/ γ *→ll

Other VV
Single top
Z/ γ *→ττ

W+jet

ggF

Events / 4.3 GeV

Events / 25 GeV

400

VBF

250

8

∆ Y jjP tot
T, jet corr. [GeV]

200

120
100

s = 8 TeV, ∫ Ldt = 20.3 fb-1
H→WW*→eν µν / µν eν + ≥ 2j

Data

SM (sys ⊕ stat)WW
tt
Z/ γ *→ll

Other VV
Single top
Z/ γ *→ττ

W+jet

ggF

VBF

80
60

150
40
100
20

1.4
1.2
1
0.8
0.6
0

Data / SM

Data / SM

50

500

1000

1500

2000

2500

mjj [GeV]

1.4
1.2
1
0.8
0.6
50

100

150

200

250

300

mT, jet corr. [GeV]

Figure 5.34: Distributions of ptot,track,jetCorr, ∆yjj , mjj , and mT in diﬀerent flavor top
Tcontrol region after all pre-selection.

5.5 H→ W W ∗ → ℓνℓν Analysis

137

Z/γ ∗ → τ τ background
The Z/γ ∗ → τ τ background is estimated using MC but the cross section is normalized todata in an appropriate Z/γ ∗ → τ τ control region. In order to define the Z/γ ∗ → τ τ control
region, some selection criteria such as those Z/γ ∗ → τ τ veto and mℓℓ are changed like the
ggF analysis from the signal region definition described in Section 5.4.2:• mℓℓ < 80 GeV,
• revert Z/γ ∗ → τ τ veto,• BDT score > -0.48.
The cuts above increase the purity of the control region. The normalization factor (NF) is
calculated using combined lepton flavor channels (ee, µµ, eµ, µe) due to lack of statistics.
The resulting NF is 0.9±0.3(stat.). The systematic uncertainties are evaluated for standard
sources: the PDF, the QCD scale, the UEPS, and the matching variations. Given the large
statistical uncertainty (30%), the extrapolation uncertainty is negligible.
Z/γ ∗ → ℓℓ background
The Z/γ ∗ → ℓℓ (Z/DY ) background is only relevant to the same flavor analysis. Thisbackground is estimated using a data-driven method, so-called ABCD method. Table 5.9
summarizes all regions used in the ABCD method.
Table 5.9: Summary of the regions used for the Z/DY estimation technique used in the
SF channel of the VBF BDT analysis.

Region A(Signal Region)

Region C

missET> 45 GeVmℓℓ < 75 GeV

missET> 45 GeV|mℓℓ − mZ | < 15 GeV

Region B

Region D

miss
25 GeV < ET
< 45 GeVmℓℓ < 75 GeV

miss
25 GeV < ET
< 45 GeV|mℓℓ − mZ | < 15 GeV

miss control region, referred to as
The Z/DY shape is derived in data using a low ET
miss cut“Region B”. The Z/DY is normalized in the signal region (Region A) using the ET5.5 H→ W W ∗ → ℓνℓν Analysis

138

eﬃciency calculated from data in the Z peak (Region C and D). The Z/DY estimate ineach BDT score bin i is given by:
B,i
NSR,i
Z/DY = NiZ/DY ·

NC
Z/DY
ND
Z/DY

· fnon-closure ,(5.20)

where NZ/DY = (Ndata − Nnon-Z/DY MC ), and fnon-closure is the non-closure factor from MC
miss cut eﬃciencies between Z peak and the low mthat represents the diﬀerence in ETℓℓ(mℓℓ < 75 GeV) region, defined as:
fnon-closure =NA /NB.
NC /ND(5.21)

Due to lack of events in data in the last BDT bin of Region B, a common normalization
is used for the last two bins. The resulting NFs are 1.13 ± 0.14 for −0.48 < BDT < 0.3 and0.79 ± 0.23 for 0.3 < BDT < 1.0 The systematic uncertainties are evaluated by varying the
QCD, the PDF, the UEPS, and the matching that is ∼ 11% in total.
W +jets/QCD background
The W +jets/QCD backgrounds are estimated using the same data-driven method as is
employed in the ggF 0-1 jet analysis.
V V background
For V V backgrounds fully MC-based estimation is employed since they remain small in thesignal region. These backgrounds can be validated in the Same Sign region.
W W background
The W W background are categorized into processes containing only electroweak vertices“EW W W ” and those containing a QCD vertex “QCD W W ”. Even though the crosssection of QCD W W is much larger than that of EW W W , the contribution is compatible
in the VBF phase space. The W W control region is not established due to large top
background in a potential W W enriched region, thus the W W background is predictedby purely MC. The systematic uncertainty on the production cross section is evaluated byvarying the QCD scale, the PDF, the UEPS, and the matching that is in total less than 2%.
ggF backgroundThe ggF process is an important background in the VBF analysis, since the cross sectionof the ggF process is 10 times higher than that of the VBF. The systematic uncertainty isevaluated by varying the QCD scale using the MCFM generator, that is ∼ 30% uncertainty.
The ggF uncertainty is further discussed in Section 5.6.2.1.

5.5 H→ W W ∗ → ℓνℓν Analysis

5.5.3

139

Background Summary

All significant sources of backgrounds are normalized using either fully data-driven estimatesor the data in appropriate control regions. The W W , top, Z/γ ∗ → τ τ , and V V (W γ (∗) ,W Z, and ZZ) backgrounds are estimated using control regions in which one signal region
criterion is reversed and others are loosened or dropped. The W +jets/QCD backgrounds
are estimated using the fake factor method, which is discussed in Chapter 6. The Z/γ ∗ → ℓℓ
background is estimated using a fully data-driven method based on Z/γ ∗ -enriched and depleted regions. The background treatment is summarized in Table 5.10, and the set of
all CR-derived normalization factors used in the analysis is summarized in Table 5.11.
Table 5.10: Methods of background estimation used in the 8 TeV analysis. The estimation
procedures for various background processes are given in four categories: normalized using
a control region (CR); data-driven estimate (Data); normalized using the MC (MC); andnormalized using the MC, but validated in a control region (MC+VR). The “(eµ+µe)”
indicates that the control region is defined in diﬀerent flavor data set instead of same flavor
data set for reasons of purity and/or statistics.
ChannelNjet = 0
eµ+µe
ee+µµ
Njet = 1
eµ+µe
ee+µµ
Njet ≥ 2
eµ+µe
VBF
eµ+µe
ee+µµ

WW

Top

Z/γ ∗ → τ τ

Z/γ ∗ → ℓℓ

W +jets/QCDVVCR
CR (eµ+µe)

CR
CR (eµ+µe)

CR
CR (eµ+µe)

MC
Data

Data
Data

CR
MC+VR

CR
CR (eµ+µe)

CR
CR (eµ+µe)

CR
CR (eµ+µe)

MC
Data

Data
Data

CR
MC+VR

MC

CR

CR

MC

Data

MC+VR

MC
MC

CR
CR

CR (eµ+µe +ee+µµ)
CR (eµ+µe +ee+µµ)

MC
Data

Data
Data

MC+VR
MC+VR

Table 5.11: Normalization factors evaluated from control regions. Only statistical uncertainties are quoted. The VBF top NF is shown only for highest two bins.

WW
topZ/γ ∗ → τ τVVNjet = 01.22 ± 0.03(stat.)1.11 ± 0.02(stat.)1.01 ± 0.02(stat.)0.93 ± 0.07(stat.)Njet = 1
1.05 ± 0.05(stat.)1.03 ± 0.03(stat.)
1.07 ± 0.04(stat.)0.96 ± 0.12(stat.)

VBF (eµ+µe)
1.34±0.38(stat.)0.90±0.30(stat.)-5.6 H→ W W ∗ → ℓνℓν Analysis

140

5.6

Systematic Uncertainties

5.6.1

Experimental systematic uncertainty

5.6.1.1

LeptonSystematic uncertainties related to electrons, except for uncertainties of isolation and impact
parameter eﬃciencies, are summarized in Table 5.12. The eﬃciency of all additional cuts,(i.e. calorimeter isolation, track isolation, vertexing parameters, adding conversion bit
and B-Layer at high η in > 25 GeV) is also measured to correct possible mis-modelingin simulation. These additional cuts are a source of additional systematic uncertainties
which is estimated with the Z tag-and-probe method and the final systematic uncertainty
is presented in Section 4.8.
Table 5.12: Summary of electron systematic uncertainties. [119, 153]
Source of uncertainty
Electron Eﬃciency
Electron Energy Scale
Electron Energy Resolution

Size of uncertainty
reconstruction: 0.1 - 1.0 % depending on ET and η
identification: 0.2 - 2.7 % depending on ET and η∼ 0.4 % depending on ET and η (except for crack region)
about 1 % depending on ET and η

An additional uncertainty is applied to photons misidentified as electrons. The electronfrom converted photon arises from W γ events that are sub-dominant background in the
0-1 jet analysis. Table 5.13 summarizes the uncertainty to account for the mis-modeling ofthese electrons.
Table 5.13: Systematic uncertainty on converted electron as a function of pT .
ET
10-15
15-20
20-

Uncertainty
25%
18%
5%

Systematic uncertainties related to muons, except for uncertainties of isolation andimpact parameter eﬃciencies, are summarized in the Table 5.14. Similar to the electrons,
the systematic uncertainty due to additional cuts is evaluated using the Z tag-and-probe
method and the final systematic uncertainty is presented in Section 4.8.
5.6.1.2

Jet

Jet systematic uncertainties are mostly relevant to the higher jet multiplicity analyses suchas the ggF 2-jet and VBF analyses. Three sources of systematics are mainly considered: jet5.6 H→ W W ∗ → ℓνℓν Analysis

141

Table 5.14: Summary of muon systematic uncertainties. [147]Source of uncertainty
Muon Eﬃciency
Muon Energy Scale
Muon Energy Resolution

Size of the uncertainty< 0.46 % depending on pT and η< 0.50 % depending on pT and η
less than 1 % depending on pT and ηenergy scale/resolution (JES/JER), jet vertex fraction (JVF), and pileup. Also dedicatedsystematics for b-tagging is presented below.
Jet energy calibration uncertainties
The JES systematics are evaluated as a function of jet pT and η that are at most 7%
as shown in Section 3.3.1. The largest uncertainty on JES is coming from η modeling,which is ∼ 13% in the ggF 2-jet analysis, but the uncertainty gets smaller in the otheranalyses. The JER is an additional source of uncertainty and is added as uncorrelated
source. The JER has some impact on the ggF 2-jet but otherwise it has less impact. The
final impact on µ will be discussed in Section 8.3.2.
JVF uncertainty
The systematic uncertainty due to the application of JVF in the jet selection has beenstudied. The uncertainty is found to be negligible in case of signal and for any backgroundestimation, the uncertainty can be canceled in usage of control regions. The most potentially sensitive selection is the Central Jet Veto (CJV) in the VBF analysis. A dedicatedstudy shows a negligible eﬀect of ∼ 0.5%.
Pileup uncertainty
The systematic uncertainty due to increased pileup especially in 2012 is evaluated by varyingµ rescaling (see Section 3.2.2), pileup related JES uncertainties, and systematic uncertainties that can migrate across jet bins. The impact of µ scaling variation is at most 4% on the
ggF 2-jet analysis that is compatible with statistical fluctuation. The variation of pileup
related JES uncertainties aﬀects ∼ 2% on the ggF 2-jet analysis but has less impact on theother analyses. The eﬀect of jet bin migration is also checked and found to be < 1% that issmaller than theory uncertainty on the ggF cross section, thus the uncertainty is neglectedin the ggF analysis, while for the VBF analysis, the jet bin migration uncertainty of 1% is
explicitely added because the theory uncertainty on the VBF production process is smaller
than that on the ggF production process.
b-tagging uncertainty

5.6 H→ W W ∗ → ℓνℓν Analysis

142

The uncertainties related to b-jet identification eﬃciency are decomposed into 6 uncorrelated components using so called eigenvector method (see Section 3.3.4). The 6 decomposedcomponents of the uncertainty are ranging between 0.01%-0.6%, 0.01%-0.4%, 0.01%-0.7%,
0.6%-1.5%, 0.2%-4.8%, and 1.1%-7.8%. In addition, for the misidentified light or c-jets
as a b-jets, the uncertainties are determined varying ±1σ as a function of pT and η. The
uncertainty (1σ) on the light flavor is 9%-15% in the region |η| < 1.1, and 9%-19% at higherη bin, and the uncertainty on the c-jet is 6%-14% that is given in inclusive η range.
5.6.1.3

Missing transverse energy

miss,CAL
Calorimeter-based missing transverse energy (ET)
miss,CAL
The calorimeter missing transverse energy ET
that is only relevant to the ggF 01 jet same flavor analysis, is composed of all hard objects present in the event as well as
the remaining part referred to as a “soft term” (see Section 3.4.1). The object related sysmiss,CAL
tematic variations are propagated into the ET. The only systematic source specificmiss,CAL
to the ET
calculation is the soft term systematic uncertainty. In order to derive
miss,CAL
miss,CAL
the systematic uncertainty on the soft term of the ET, the ET
direction isdecomposed into longitudinal and perpendicular directions with respect to the direction
miss,CALof the hard component of the ET. The systematic uncertainties are obtained fromsmearing and scaling both of these components, and those variations are treated as fully
miss > 45 GeV cut (ggF 0-1 jet same
correlated uncertainties. The total uncertainty of ET,rel
miss (or E miss ) is detailed in [15].
flavor analysis) is 17%. The systematic uncertainty on the ET
T,relTrack-based missing transverse momentum (pmiss)
T
Similar to calorimeter missing transverse energy, the pmiss
is composed of all hard obTmiss,CAL
ject (electron, muon, and jet) and soft track term (see Section 3.4.2). As is the ET
case, the systematic uncertainties on the soft track term are derived in Z → µµ events bydecomposing pmiss
direction into longitudinal and perpendicular directions, and by comparT
jetCorr
ing several generators to account for the modeling of parton shower. For the pmiss,,T
an additional uncertainty is considered to account for tracks inside hard jets, which is as
jetCorra function of pT and η. The total uncertainty on the pmiss,is ∼ 5% and all thoseTvariations are treated as fully correlated uncertainties. The systematic uncertainty on the
jetCorrpmiss,
is detailed in [15].
T

5.6.2

Theoretical systematic uncertainty

Theoretical uncertainties (QCD scale, PDF, and modeling of underlying event and parton
shower) are considered as uncertainties on cross sections of signal and background processes.
The uncertainties on the Higgs signal are of special importance because of their large impact
on the final result. Also the uncertainties on the W W production are important, since theW W is the largest and irreducible background in the main (ggF 0-1 jet) analysis. For theW W background in the ggF 0-1 jet analysis, the uncertainties are assigned on extrapolation

5.6 H→ W W ∗ → ℓνℓν Analysis

143

from the control region to the signal region, since the cross section of the W W backgroundis normalized to data in the control region, while in the ggF 2-jets and VBF analyses, theuncertainty is considered on cross section rather than the extrapolation because the W W
control region is not defined. In the remaining sections, uncertainties on both signal andW W productions are discussed, and others are detailed in [172].
5.6.2.1

Systematic uncertainty on the Higgs boson production

For the ggF analysis, since the analysis is separated into bins of jet multiplicity (0,1, ≥2),the signal cross section is calculated in each jet bin at the generator level to match thebest available calculations of the veto eﬃciency of first and second jets. The uncertainty
on the veto eﬃciencies to account for higher order corrections are 12% for the first jet and
14% for the second jet. These are treated as fully correlated to account for the jet bin
migrations. For the signal acceptance the following variations are considered as theoreticaluncertainties :- QCD scale,- PDF model uncertainties,- underlying event and parton shower modeling (UEPS),- mathcing of matrix element calculation to the parton shower.
These uncertainties are calculated in each signal regions and are summarized in Table 5.15. For the QCD scale, variations of renormalization and factorization scales ranging-50% to 200% are evaluated. The PDF uncertainties are evaluated for acceptances relative to the inclusive cross section, whereas others are calculated within jet bins. Diﬀerent
matching schemes of matrix element to the parton shower modeling are also calculatedusing generators with the same parton shower model (Herwig), which gives an estimate of
the uncertainty due to the choice of matching scheme.
For the VBF process, the uncertainties on the signal acceptance (PDF, UEPS, QCD
scale, matching) are also calculated. The uncertainty on the UEPS is 3.4%, the PDF
uncertainty is 4.0%, the QCD scale is 3.0%, and the matching is 4.2%. To account forthe diﬀerence among BDT bins, the BDT shape uncertainties are also evaluated and aresummarized in Table 5.16. The uncertainties on those production processes are detailedin [172].

5.6 H→ W W ∗ → ℓνℓν Analysis

144

Table 5.15: Theoretical uncertainties in the ggF acceptance of each signal region. PDF
uncertainties are evaluated for acceptances relative to the inclusive cross section, whereas
others are calculated within jet bins. When the sign of an uncertainty is parenthesised,
this means that the uncertainty is not statistically significant. In these cases, the statisticaluncertainty on the generator diﬀerence is given, and the sign of the generator diﬀerence isparenthesised.

0-jet
1-jet

0-jet

1-jet

≥2-jetmll(GeV)

psublead
T,l
(GeV)

Scale

12–55
12–55

> 10
> 10

1.4%
1.9%

10–30
10–30
10–30
30–55
30–55
30–55
10–30
10–30
10–30
30–55
30–55
30–55
10–55

10–15
15–20
> 20
10–15
15–20
> 20
10–15
15–20
> 20
10–15
15–20
> 20
> 10

2.6%
1.3%
1.0%
1.5%
1.5%
3.5%
3.7%
9.0%
3.5%
5.7%
3.4%
1.4%
18%

PDF
MSTW 68% CL
ee/µµ channels
1.9%
3.2%
1.8%
2.8%
eµ/µe channels
1.8%
3.2%
1.9%
3.2%
1.9%
3.2%
1.8%
3.3%
1.9%
3.3%
1.9%
3.3%
1.7%
2.9%
1.7%
2.9%
1.8%
2.7%
1.7%
3.0%
1.9%
3.3%
1.8%
2.8%
2.0%
2.2%

UEPS
Pythia Herwig

NLO-PS
matching+1.6%(−)1.5%

+6.4%
+2.1%

−2.5%
(−)1.4%−1.7%(+)2.4%−2.2%(+)2.0%(−)2.5%−1.9%+2.9%(+)3.8%(+)2.1%(+)3.2%(+)2.6%(−)1.9%(−)1.7%

+5.7%
+4.9%
(−)1.6%+5.5%(+)2.4%−2.4%+10.8%(+)3.9%(+)2.0%+11.4%+13.5%(−)1.8%(+)1.7%

−3.5%
−2.9%
(−)1.4%−3.8%−2.5%(−)1.3%−3.8%(+)3.6%(−)1.9%−6.8%+6.7%(+)1.7%−4.5%

Table 5.16: Theoretical uncertainties on the VBF Higgs production process, on the overall
normalization in BDT (BDT norm.) and the BDT shape. µF and µR denote the variationsof renormalization and factorization scales that are varied ranging [-50%, 200%].
Source
Scale
PDF
UEPS
Matching

DescriptionµF , µR in Powheg + Pythia
CT10 and NNPDF
Pythia v.s. Herwig
Powheg v.s. aMC@NLO

BDT norm.
0.5%
4.0%
3.4%
4.2%

BDT shape[1%, 3%, 3%]< 2.0%[0.2%, 1.8%, 11%]-

5.6 H→ W W ∗ → ℓνℓν Analysis
5.6.2.2

145

Systematics on the Standard Model W W production

For the ggF 0-1 jet analysis, the W W background is normalized in the diﬀerent flavor
control region that is separated from the signal region at mℓℓ = 55 GeV. The followings are
considered as the uncertainties on the extrapolation parameter α from the control region
to the signal region:- QCD scale,- PDF model uncertainties,- underlying event and parton shower modeling (UEPS),- mathcing of matrix element calculation to the parton shower,- EW corrections.
Table 5.17 summarizes the uncertainties on the extrapolation for NLO q q̄, qg → W W
processes. Note that the diﬀerent flavor control region is also used in the same flavor
analysis but the extrapolation uncertainties are separately calculated.
Table 5.17: Scale, UEPS, matching, higher order EW correction, and PDF uncertainties on
the W W extrapolation parameters α for the NLO q q̄, qg → W W processes. The correlationsin the UEPS and matching uncertainties are shown explicitly, including the signed diﬀerencein the comparison. The diﬀerent flavor (DF) signal regions are divided into 10 < mℓℓ < 30(“SR1”) and 30 < mℓℓ < 55 (“SR2”). The uncertainties on the uncertainties are also shown
but only central values are used as the uncertainties.
psublead[GeV]T
10 − 1515 − 20

20−

10−

αi
DF (SR1)
α0j
DF (SR2)
α0j
DF (SR1)
α1j
DF (SR2)
α1j
DF (SR1)
α0j
DF (SR2)
α0j
DF (SR1)
α1j
DF (SR2)
α1j
DF (SR1)
α0j
DF (SR2)
α0j
DF (SR1)
α1j
DF (SR2)
α1j
SF (SR)
α0j
SF (SR)
α1j

Scale0.73 ± 0.59
0.69 ± 0.63
3.1 ± 1.1
3.2 ± 1
1.2 ± 0.53
0.83 ± 0.46
1.6 ± 1
1.5 ± 0.83
0.72 ± 0.41
0.76 ± 0.29
1 ± 0.7
1.3 ± 0.48
0.77 ± 0.23
0.81 ± 0.38

UEPS
2.2 ± 0.29
1.5 ± 0.3
−2.4 ± 0.54
−2 ± 0.5
1.7 ± 0.26
1 ± 0.23−3 ± 0.5−3 ± 0.41−1.9 ± 0.2−2.4 ± 0.14
−3.6 ± 0.33
−3.1 ± 0.23
−1.2 ± 0.12
−2.3 ± 0.18

Matching
0.44 ± 0.4
0.49 ± 0.41
−3.4 ± 0.74
1.9 ± 0.68
0.9 ± 0.36
1 ± 0.32
0.7 ± 0.7
2.4 ± 0.56
3.1 ± 0.28
3.9 ± 0.2
5.3 ± 0.46
5.6 ± 0.32
2.4 ± 0.16
3.8 ± 0.25

EW corr
1.2 ± 0.33
0.82 ± 0.34
−0.85 ± 0.6−0.9 ± 0.56
0.69 ± 0.3
0.47 ± 0.26
−1.5 ± 0.57
−1.6 ± 0.46
−0.25 ± 0.23
−0.4 ± 0.16
−2.8 ± 0.38
−2.7 ± 0.26
0.14 ± 0.13
−2.1 ± 0.21

PDFs
0.96
0.79
0.55
0.55
0.79
0.68
0.48
0.45
0.61
0.67
0.62
0.62
1.1
0.86

Total
2.8
2.1
5.4
4.5
2.6
2
3.9
4.5
3.8
4.8
7.1
7.1
2.9
5.1

146

5.6 H→ W W ∗ → ℓνℓν Analysis

The scale uncertainties are evaluated by varying the renormalization and factorization
scales in aMC@NLO by a factor of two. The PDF uncertainties are evaluated comparing
CT10 PDFs to the MSTW2008 and NNPDF2.3 PDFs. The UEPS uncertainty is evaluated by comparing the extrapolation parameter for the P owheg+P ythia6 to that forP owheg+P ythia8 and P owheg+Herwig. The Matching uncertainty is from comparison of Powheg +Herwig to MC@NLO+Herwig. The uncertainty on the EW correction
is evaluated by comparison of the extrapolation with the NLO correction to the higher
order calculation. The total uncertainty on the extrapolation varies 2.0-7.1%. For the
gg → W W process, the relative uncertainty (∆α) on the extrapolation (which is only 5.5%
contribution in total W W cross section) is estimated to be 0.5% for 0-jet and 3.1% for 1-jet.
For the W W background, a shape uncertainty of the mT distribution is also considered with three sources: the QCD scale, the UEPS, and the matching. The PDF shape
uncertainties are small relative to those three, thus not included here. The shape uncertainties are considered for all subdivisions ([mℓℓ < 30, mℓℓ > 30] ⊗ [psublead: 10 − 15, 15 −T
20, 20−] ⊗ [0 − jet, 1 − jet]), 12 variations for each source of uncertainty. For each mT
shape comparison, envelopes are constructed by dividing one distribution by the other.
Figure 5.35 shows mT shape uncertainties, as an example, for the 0-jet low mℓℓ (mℓℓ < 30)
signal region. The final shape weights are made continuous by performing a piecewise linear interpolation which is visualized by looking at the bands themselves for each source of
uncertainty. The variations are minimal at lower mT (100-120 GeV), whereas they increaseat higher mT tail, which is up to ∼ 15%.
For the VBF analysis, the uncertainties for the QCD scale are separately evaluatedfor the production processes with zero (EW W W +2jets) or two QCD (QCD W W +2jets)
vertices. In the former case a flat uncertainty of 10% is assigned, and in the latter case theuncertainty is 27%. The PDF uncertainties are at most 4 %, and the interference between
processes is found to be negligible. An additional uncertainty is taken from the diﬀerencesamong several generators to cover remaining uncertainties, the UEPS, and the matching,which are in total [14%, 8%, 12%] for each BDT bin.

5.6 H→ W W ∗ → ℓνℓν Analysis

147

Figure 5.35: UEPS, matching, and scale envelopes for the 0-jet 10 < mℓℓ < 30 GeV signal
region. The linear envelope shows the global weight which parametrizes the three envelopes
added in quadrature. However, a piecewise linear interpolation is used for each individual
source of uncertainty instead of the linear envelope. The top left is for sub-leading lepton
pT = 10-15, top right for pT = 15-20, bottom left for pT = 20-, and bottom right for pT =10- just for reference.

148

5.6 H→ W W ∗ → ℓνℓν Analysis

Chapter 6

Fake Backgrounds
6.1

Introduction

Events in which W bosons are produced in association with jets give rise to background to
W W events when the jet is misidentified as a lepton. The rate at which jets are misidentified
as leptons may not be accurately described in simulation. A data-driven method to estimate
this background is employed [173]. In this method, the QCD background can be similarly
estimated as events in which two jets are misidentified as leptons. A description of the Fake
Factor Method for predicting the W +jets/QCD backgrounds is presented in this chapter.

6.2

Fake Factor Method

6.2.1

Signal and Control Samples

In the Fake Factor Method, three samples are defined exclusively: signal sample (Nid+id ),W +jets control sample (Nid+anti−id ), QCD control sample (Nanti−id+anti−id ).
The signal sample Nid+id is identical to what is used in the standard analysis. In otherwords the sample is defined as events containing two fully identified leptons in data. It canalso be rewritten, explicitly including the W +jets and the QCD backgrounds as:
QCD
W+jet
EW
Nid+id = Nid+id+ Nid+id+ Nid+id

(6.1)

QCD
W+jet
EW is
where Nid+id
is the QCD background, Nid+id
is the W +jets background, and Nid+id
all other backgrounds including the Higgs signal itself. The signal regions defined in theanalysis is a subset of Nid+id samples.
In order to estimate the W +jets background in the signal sample, the W +jets control
sample is defined using an alternative lepton definition that enhances jets misidentified as
leptons. Objects passing this alternative lepton definition are referred to in the following
as anti-id objects. Events containing one fully identified lepton and one anti-id object
constitute the W +jets control sample. These events are otherwise required to pass the fullW W event selection, where the anti-id object is treated as if it were a fully identified lepton.

149

150

6.3 Fake Backgrounds

The W +jets control sample is expressed as:
QCD
W+jet
EW
Nid+anti-id = Nid+anti-id+ Nid+anti-id+ Nid+anti-id

(6.2)

QCD
W+jet
EW
where Nid+anti-id
is the QCD background, Nid+anti-id
is the W +jets background, and Nid+anti-id
is all other backgrounds including the Higgs signal itself in the W +jets control sample.
QCD
EW
Contaminations of Nid+anti-id
and Nid+anti-id
are normally small depending on jet bins andlepton flavors but those backgrounds are subtracted from the W +jets control sample when
predicting the W +jets background in the signal sample.
Similarly the QCD backgrounds are also estimated from data using events containing
two anti-id objects. The two anti-id objects constitute the QCD control sample as:
QCD
W+jet
EW
Nanti-id+anti-id = Nanti-id+anti-id+ Nanti-id+anti-id+ Nanti-id+anti-id

(6.3)

QCD
W+jet
where Nanti-id+anti-id
is the QCD background, Nanti-id+anti-id
is the W +jets background, andEW
Nanti-id+anti-id
is all other backgrounds including the Higgs signal itself in the QCD control
W+jet
EW
sample. Contaminations of Nanti-id+anti-id
and Nanti-id+anti-id
are normally small dependingon jet bins and lepton flavors but those backgrounds are similarly subtracted from the QCD
control sample when predicting the QCD background in the signal sample.

6.2.2

Fake Factor

The W +jets background is estimated from the W +jets control sample by applying an
extrapolation factor, referred to in the following as a fake factor, which relates the W +jets
control sample to the W +jets background in the signal sample (or which relates the QCD
control sample to the QCD background in the W +jets control sample). The fake factor isexpressed as:
Nidfl ≡(l = e or µ).
(6.4)
Nanti-id
The fake factor, fl , is independently defined for both electrons and muons, and it measures the ratio of the rate at which jets pass the full lepton identification requirements, tothe rate at which they pass the anti-id requirement but fail the full lepton identification
requirements. This fake factor is not exactly a fake rate and cannot be interpreted as aprobability because the numerator samples are not a subset of the denominator samples(but the numerators and denominators are defined exclusively as shown in Table 6.2, 6.1,
6.4, and 6.3). The fake factor is measured in data using either di-jets or Z+jets events.
The W +jets background in the signal sample is then calculated by scaling the number of
events in the W +jets control sample using the measured fake factor:
W+jet
W+jet
Nid+id= fl × Nid+anti-id
QCD
EW= fl × (Nid+anti-id − Nid+anti-id− Nid+anti-id
),

(6.5)
(6.6)

QCD
EW
where Nid+anti-id is subtracted out using simulation and Nid+anti-id is subtracted using
Nanti-id+anti-id events. The QCD subtraction from the W +jets control sample is discussed
in detail in Section 6.7.

6.3 Fake Backgrounds

6.3

Anti-id Lepton Definitions and Overlap Removals

6.3.1

Anti-id Electron Definition

151

The id electron (numerator) and anti-id electron (denominator) definitions are shown in
Table 6.1 and 6.2. The optimization procedure for id electrons can be found in Chapter 4.
The denominator selection is defined by loosening isolation cuts and reverting the identification such that prompt electrons from W and Z bosons are suppressed, and that thecontribution from misidentified jets is enhanced.
Table 6.1: Definition of the id electron (numerator).
Identified Electron
Author 1 or 3 (default algorithm of electron reconstruction [14])pT > 10 GeV|η| < 2.47, excluded crack region (1.37 < |η| < 1.52)|z0 sin θ| < 0.4 mm, |d0 /σd0 | < 3
topoEtCone30Corr/ET < 0.20 , PtCone40/pT < 0.06 (10-15 GeV)
topoEtCone30Corr/ET < 0.24 , PtCone30/pT < 0.08 (15-20 GeV)
topoEtCone30Corr/ET < 0.28 , PtCone30/pT < 0.10 (20- GeV)
VeryTight Likelihood (10 − 25 GeV)
Medium++ with conversion bit and b-layer requirement (25− GeV)

Table 6.2: Definition of the anti-id electron (denominator).
Anti-id Electron
Author 1 or 3 (default algorithm of electron reconstruction [14])pT > 10 GeV|η| < 2.47, excluded crack region (1.37 < |η| < 1.52)|z0 sin θ| < 0.4 mm, |d0 /σd0 | < 3
SCT + N P ixel ≥ 4
Nhits
hits
topoEtCone30Corr/ET < 0.30
PtCone30/pT < 0.16
Fails isEM Medium++
Fails the identified electron

6.3.2

Anti-id Muon Definition

The id muon and anti-id muon definitions are shown in Table 6.3 and 6.4. The optimization procedure for id electrons can be found in Chapter 4. The denominator selection is

152

6.3 Fake Backgrounds

defined by loosening isolation cuts and removing d0 significance such that prompt muons
from W and Z bosons are suppressed, and that the contribution from misidentified jets isenhanced.
Table 6.3: The definition of id muon (numerator).
Identified Muon Definition
STACO Combined MuonpT > 10 GeV|η| < 2.5|z0 sin θ| < 1 mm, |d0 /σd0 | < 3
EtCone30Corr/pT < 0.06 , PtCone40/pT < 0.06 (10-15 GeV)
EtCone30Corr/pT < 0.12 , PtCone30/pT < 0.08 (15-20 GeV)
EtCone30Corr/pT < 0.18 , PtCone30/pT < 0.12 (20-25 GeV)
EtCone30Corr/pT < 0.30 , PtCone30/pT < 0.12 (25- GeV)

Table 6.4: The definition of anti-id muon (denominator).
Anti-id Muon Definition
STACO Combined MuonpT > 10 GeV|η| < 2.5|z0 sin θ| < 1 mm
d0 Impact Parameter Requirements Removed
EtCone30Corr/pT < 0.15 (10-15 GeV)
EtCone30Corr/pT < 0.25 (15-20 GeV)
EtCone30Corr/pT < 0.30 (20- GeV)
Track isolation cuts Removed
Fails the identified muon selection

6.3.3

Overlap Removal Procedure in W +jets/QCD estimation

The proper overlap removal between leptons and jets is of crucial importance for W +jets/QCD background estimations since the anti-id objects are less isolated. The anti-id objects
are often overlapping with the jets defined in Section 3.3.1 (pT > 25 (30) GeV for |η| < (≥)2.4). The procedure of overlap removals for standard analyses and for W +jet /QCD control
samples is summarized in Table 6.5 and 6.6, where id denotes id objects and anti-id
denotes anti-id objects.

153

6.3 Fake Backgrounds

Table 6.5: Summary of overlap removals in standard analysis.

dR (µ(id), e(id)) < 0.1
dR (e(id), e(id)) < 0.1
dR (e(id), jet) < 0.3
dR (µ(id), jet) < 0.3

Overlap removals in standard analysis
electron is removed if it overlaps with muon
electron is removed if it overlaps with higher ET electron
jet is removed if it overlaps with electronmuon is removed if it overlaps with jet

Table 6.6: Summary of overlap removals in W +jet /QCD control sample.

dR (µ(id), e(id)) < 0.1
dR (µ(id), e(anti-id)) < 0.1
dR (µ(anti-id), e(id)) < 0.1
dR (µ(anti-id), e(anti-id)) < 0.1
dR (e(id), e(id)) < 0.1
dR (e(anti-id), e(anti-id)) < 0.1
dR (e(anti-id), e(id)) < 0.1
dR (e(id), jet) < 0.3
dR (e(anti-id), jet) < 0.3
dR (µ(id), jet) < 0.3
dR (µ(anti-id), jet) < 0.3

Overlap removals in W +jet /QCD control sample
electron is removed if it overlaps with muon
electron is removed if it overlaps with muon
electron is removed if it overlaps with muon
electron is removed if it overlaps with muon
electron is removed if it overlaps with higher ET electron
electron is removed if it overlaps with higher ET electron
electron is removed if it overlaps with higher ET electron
jet is removed if it overlaps with electron
jet is removed if it overlaps with electronmuon is removed if it overlaps with jet
jet is removed if it overlaps with muon

In the W +jet /QCD estimate, the overlap removals for denominators are added. Notethat µ-jet overlap removal is not symmetric between the anti-id and the id objects. An
identified muon overlapping with a jet is removed in the W +jet /QCD control sample tokeep consistency with standard analysis. It is found that the eﬀect of this incompatibility is
negligible in the W +jet /QCD control sample. In same flavor analysis, soft jets are definedwith lower threshold (jet pT > 10 GeV). If the jet is overlapping with the identified electronor the anti-identified electron/muon, the jet is removed from the jet counting. Without thisprocedure, the jet would be double counted since the jet is already counted as the anti-id
muon in the W +jet /QCD control sample. Similarly, in VBF analysis, central jets aredefined with lower threshold (jet pT > 15 GeV, |η| < 2.5). If the central jet is overlappingwith the identified electron or the anti-identified electron/muon, the central jet is removed
from the jet counting. Without this procedure, the central jet veto eﬃciency would behigher in the W +jet /QCD control sample since the jet is already counted as the anti-id
muon in the W +jet /QCD control sample.

154

6.4 Fake Backgrounds

6.4

Z+jet Fake Factors

For the fake factor, Z+jets sample has been considered, instead of the di-jets sample.
Making use of the Z+jets sample for the fake factor has never been tried because themeasurement in general requires large statistics. As one can imagine, Z+jet production
cross section is much smaller than the di-jets (QCD) cross section. Nevertheless fairly large
Z boson statistics have been available at the LHC, which makes the Z+jets fake factor
possible. The procedure of the Z+jets fake factor measurement is summarized below.

6.4.1

Feature of Z+jet Fake Factor

The fake factor is measured using Z+jets sample. There are several advantages to using
the Z+jets sample below:- no trigger bias is expected in the measurement since the triggers (see Section 6.4.2)
are fired by leptons from Z → ℓℓ decays,- jet flavor composition in the Z+jets sample is expected to be similar to that in
the W +jets sample (gq ′ → Zq ′ vs gq ′ → W q ′′ ), 1 which results in small sample
dependence compared to that on the di-jets fake factor,- jet kinematics like jet pT in the Z+jets are expected to be similar to those in the
W +jets because the center-of-mass energy of W and Z events is approximately identical,
Nevertheless there are a couple of limitations in the Z+jets fake factor measurement:- statistics are limited (Z boson production cross section is small and the rate at whichjets are misidentified as leptons is also small), in particular numerator statistics,- larger EW contamination from diboson backgrounds, W γ (∗) /W Z/Zγ (∗) /ZZ in theZ+jets sample.
Hence the systematic uncertainty on the Z+jets fake factor must be scrutinized comparing
to the uncertainty on the di-jets fake factor. This is extensively discussed in Section B.1.4.
Also the jet flavor composition is discussed in detail in Section B.2.

6.4.2

Z+jet selection

6.4.2.1

Z → ℓℓ selection

For electrons, in order to gain in acceptance, “medium” electron is defined by loosening
fully identified electron selection criteria shown in Table 6.1. In particular the electron
identification is loosened from the VeryTight likelihood to the cut-based Medium++, which
results in 10 % improvement in single electron acceptance. The leading electron ET is set to1

It means heavy flavor versus light flavor. One can imagine that heavy flavor composition is very diﬀerent
from the W +jets because of the W +charm process. This is true and is discussed further in Section B.2.

155

6.4 Fake Backgrounds

be 25 GeV without di-electron trigger, 2 EF 2e12Tvh loose1, since the gain in acceptancefrom the di-electron trigger lowering lepton ET is less than 10 %. In addition lowering
electron ET can increase the contamination of third electrons from W γ (∗) /Zγ (∗) decays in
the Z+“fake electron” sample, in particular photon conversions from the Zγ, in Z+fake
electron sample.
For muons, “medium” muon is also defined but is identical to the fully identified muonshown in Table 6.3. The leading muon pT is lowered to be 22 GeV with the di-muon trigger,
EF mu18 tight mu8 EFFS, since the gain in acceptance is substantial (∼15-20 %), due tothe extended η coverage from the di-muon trigger in the central region (see Section 4.2.1).
Since leptons from Z → ℓℓ decays are triggered by primary single/di-muon triggers,
trigger bias is not expected in the fake factor measurement. After leptons selection, jetcleaning and overlap removals that are identical to those used in the standard analysis, areapplied. Independently numerators and denominators for the fake factor calculation are
also defined as shown in Table 6.1, 6.2, 6.3, 6.4, with proper overlap removal proceduresummarized in Section 6.3.3. The lepton selection for Z → ℓℓ reconstruction is summarizedin Table 6.7.
Table 6.7: lepton selection for Z → ℓℓ reconstruction.
leptonelectron
muon

plead
T [GeV]25
22

triggers
EF e24vhi medium1, EF e60 medium1
EF mu24i tight, EF mu36 tight, EF mu18 tight mu8 EFFS

Pairs of two oppositely signed same flavor leptons are then selected to reconstruct Z
bosons as shown in Figure 6.1.
zmumu_spectrum

10

10

109

s = 8 TeV,

∫ L dt = 20.7 fb

W+jet
W+X
Zg*
top

Data
ZZ
Zg
WW

-1

108

Entries

Entries

zee_spectrum

109

107

106

106

105

105

104

104

103

103

102

102

1

∫ L dt = 20.7 fb

20

40

-1

108

107

10

s = 8 TeV,

W+jet
W+X
Zg*
top

Data
ZZ
Zg
WW

1010

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40

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100

120

140

160

180
200
Mee [GeV]

1

0

60

80

100

120

140

160

180
200
Mµµ [GeV]

Figure 6.1: Invariant mass distributions for Z → ee (left) and Z → µµ (right) after
Z → ℓℓ selection. The Z+jets contribution is not explicitly shown but they can been seenas the diﬀerence between data and all other backgrounds. To suppress the contaminationof diboson backgrounds, the Z mass window selection is applied later.

2

the standard analysis uses EF 2e12Tvh loose1 trigger as well with the leading lepton pT > 22 GeV.

156

6.4 Fake Backgrounds

After Z → ℓℓ reconstruction, invariant mass of the two leptons are required to be within
the Z mass window defined as 81 GeV < Mℓℓ < 107 GeV. However there is still a substantial
diboson contamination in the Z+jets sample, in particular in Z+numerator sample, evenmiss ) distributions forafter the cut on the Z mass window. Figure 6.2 shows mT (lepton, ET
electrons and muons.

250

s = 8 TeV,∫

L dt = 20.7 fb

mtNo_muon_numerator
W+jet
W+X
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mtNo_electron_numerator

240
220
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20

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180

200

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140

150

120
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100

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60

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40
20

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20

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80
100
120
140
electron Numerator MTW [GeV]

0
0

60

80

100
120
140
muon Numerator MTW [GeV]

miss ) distributions for electron channel (left) and for muon
Figure 6.2: The mT (lep, ET
channel (right) after Z mass window selection where “METRefFinal” is used as missing
ET . The jacobian peak from W boson can be clearly seen around 80 GeV. At the high mT
region, W Z background is dominated in electron and muon channel. Further mT selectionis therefore needed to reduce the contamination of these background.

6.4.2.2

Diboson veto procedure

In order to further reduce the remaining contamination, ZZ and W Z veto cuts are applied,defining “loose” leptons that do not pass any identification and isolation requirements but
do pass lepton pT > 7 GeV:
- ZZ veto: event is vetoed if there is another pair of oppositely signed same flavor
leptons is within Z mass peak, |MZ − Mℓℓ | < 15 GeV,
- W Z veto: event is vetoed if there is an associated W boson candidate satisfying
miss ) > 30 GeV.
mT (lep,ET
The W Z veto is optimized to make the total uncertainty on the fake factor smallest as
shown in Table 6.8, 6.9 by varying mT cuts.
6.4.2.3

Fake factor Measurement

After ZZ and W Z veto, the fake factors are measured by taking the ratio of the numberof numerators to the number of denominators as a function of pT as shown in Figure 6.3.
The fake lepton pT distributions in Z+numerator and in Z+denominator control samples
are shown in Figure 6.4 and Figure 6.5 by comparing two cases, mT > 30 GeV and > 100
GeV.

157

6.4 Fake Backgrounds

Table 6.8: Comparison of EW systematic uncertainty and statistical uncertainty varying
mT cuts from 20 GeV to 50 GeV in electron channel. The EW systematic uncertainty blows
up rapidly while the statistical uncertainty goes down, when going to looser mT veto cut.
It is found that mT > 30-40 GeV is optimal.
stat. ± EW syst.
10 < ET < 15
15 < ET < 20
20 < ET < 25
ET > 25mT > 20
21.1 ± 9.9 %41.8 ± 18.7 %52.1 ± 18.8 %38.0 ± 23.7 %mT > 30
17.6 ± 10.5 %34.0 ± 19.2 %52.1 ± 24.8 %29.6 ± 23.1 %mT > 40
15.5 ± 10.2 %40.1 ± 27.8 %45.2 ± 25.4 %22.1 ± 20.2 %mT > 50
15.5 ± 10.9 %28.2 ± 20.1 %72.5 ± 50.6 %20.5 ± 22.5 %Table 6.9: Comparison of EW systematic uncertainty and statistical uncertainty varying
mT cuts from 20 GeV to 50 GeV in muon channel. The EW systematic uncertainty blows
up rapidly while the statistical uncertainty goes down, when going to looser mT veto cut.
It is found that mT > 30-40 GeV is optimal.
mT > 20
12.1 ± 2.3 %20.6 ± 4.1 %37.3 ± 8.9 %31.4 ± 13.2 %mT > 30
10.2 ± 2.6 %17.9 ± 5.1 %28.6 ± 8.9 %34.1 ± 21.0 %

0.08
0.07

No EW subtraction

0.06
s = 8 TeV,
0.05

EW subtraction∫ L dt = 20.7 fb-1
EW subtraction UP

Muon Fake Factor

Electron Fake Factor

stat. ± EW syst.
10 < pT < 15
15 < pT < 20
20 < pT < 25
pT > 25mT > 409.4 ± 3.0 %17.3 ± 7.0 %24.2 ± 9.4 %25.1 ± 18.4 %mT > 50
9.3 ± 3.3 %16.6 ± 8.1 %28.1 ± 14.6 %32.4 ± 31.8 %0.4
No EW subtraction

0.35

EW subtraction

0.3
s = 8 TeV,
0.25

∫ L dt = 20.7 fb

EW subtraction UP-1
EW subtraction DOWN

EW subtraction DOWN

0.04

0.2

0.03

0.15

0.02

0.1

0.01

0.05

0
10

20

30

40

50

60

70

80
90
100
Electron ET [GeV]

0
10

20

30

40

50

60

70

80
90
100
Muon p [GeV]T

Figure 6.3: The Z+jets fake factor as a function of pT in electron channel (left) and muonchannel (right). The red dots are the fake factor before the EW subtraction, the blue dots
are after the EW subtraction, and the others (light blue and magenta) are the variationsof the EW subtraction. Since the statistics are very small above 25 GeV, all pT bins above
25 GeV are merged.

158

6.4 Fake Backgrounds

500
s = 8 TeV,

400

∫ L dt = 20.7 fb

mt30_electron_numerator_pt
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mt100_electron_numerator_pt

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mt100_electron_denominator_pt

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∫ L dt = 20.7 fb

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140
electron Numerator pT [GeV]

mt30_electron_denominator_pt
W+jet
W+X
Zg*
top

25000

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100
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140
electron Numerator pT [GeV]

ZZ
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WW

Entries

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0

20000
18000

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Zg
WW

14000
12000

15000

10000
8000

10000

6000
4000

5000

2000
0
0

20

40

60

80
100
120
140
electron Denominator pT [GeV]

0
0

60

80
100
120
140
electron Denominator pT [GeV]

Figure 6.4: Comparison of electron ET distributions after applying various mT veto. The
left two plots show ET distribution for the numerator (top left) and for the denominator(bottom left) after applying mT > 100 GeV veto. The right two plots show ET distribution
for the numerator (top right) and for the denominator (bottom right) after applying mT >30 GeV veto. In order to reduce real lepton contaminations in the Z+jets control sample,
in particular in Z+numerator sample, the mT > 30 GeV is applied before measuring the
fake factors. The remaining backgrounds are dominated by Zγ in lower ET whereas are
dominated by W Z/W γ ∗ in higher ET .

159

6.4 Fake Backgrounds

500
s = 8 TeV,

∫ L dt = 20.7 fb

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∫ L dt = 20.7 fb

60

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100
120
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mt30_muon_denominator_pt
W+jet
W+X
Zg*
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ZZ
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Entries

0
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2500

2500

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1500

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WW

1500
1000
1000
500

500
0
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20

40

60

80

100
120
140
muon Denominator pT [GeV]

0
0

60

80

100
120
140
muon Denominator pT [GeV]

Figure 6.5: Comparison of muon pT distributions after applying various mT veto. The
left two plots show pT distribution for the numerator (top left) and for the denominator(bottom left) after applying mT > 100 GeV veto. The right two plots show pT distribution
for the numerator (top right) and for the denominator (bottom right) after applying mT >30 GeV veto. In order to reduce real lepton contaminations in the Z+jets control sample,
in particular in Z+numerator sample, the mT > 30 GeV is applied before measuring the
fake factors. The remaining backgrounds are dominated by W Z/W γ ∗ .

160

6.4 Fake Backgrounds

Finally the η dependence of the fake factor from the di-jet measurement is injected to theZ+jet fake factors by taking the ratio of the pT dependent fake factors:
Z+jetsZ+jetsf(p= (fpZ+jets/fpdi-jets) × f(p
,
T
T
T ,η)
T ,η)

(6.7)

0.045

0.0 < |η| 1.0

0.04
EF_e5_medium1(EF_e5_etcut) :

0.035
0.03
0.025

s = 8 TeV,∫

L dt = 0.2413(0.0124) pb

1.0 < |η| 2.0-1

2.0 < |η| 2.5

EF_g24_etcut :s = 8 TeV,

∫ L dt = 2.084 pb

Muon Fake Factor

Electron Fake Factor

As is hard to take the η dependence directly from the Z+jets sample due to poor statistics,
this approach (1D fake factor → 1D×1D fake factor) is the best way to make the shape on
the W +jets background more accurate. The injected η dependence is shown in Figure 6.6.
0.45
EF_mu15 :

0.3
0.25

-1

0.02

0.2

0.015

0.15

0.01

0.1

0.005

0.05

0
10

20

30

40

50

60

70

80
90
100
Electron p [GeV]T

0.0 < |η| 1.0

0.4
0.35

0
10

s = 8 TeV,∫

L dt = 22.72 pb

1.0 < |η| 2.0-1

2.0 < |η| 2.5

EF_mu6 :s = 8 TeV,

20

∫ L dt = 0.941 pb

30

40

-1

50

60

70

80
90
100
Muon p [GeV]T

Figure 6.6: Plots show η dependence of fake factors taken from the di-jet enriched sample
for electrons (left) and for muons (right). The fake factors tend to increase more than afactor of 2-3 at endcap region (2.0 < |η| <2.5) because of detector geometry. The dependence is injected to the Z+jets fake factors to obtain more accurate shape estimate for the
W +jets background.

6.4.3

Systematics

Systematic uncertainty associated with the fake factor measurement is the dominant sourceof uncertainty on the W +jets background. The fake factor uncertainty is divided into thefollowing sources:- The potential diﬀerence in fake factor between the Z+jets and W +jets is considered as
sample dependence uncertainty. This is estimated by comparing the two fake factors
in simulation. 3 This is the dominant systematic uncertainty on the fake factor.
- The uncertainty related to the third lepton contamination from diboson processes suchas those W γ (∗) /W Z/Zγ (∗) /ZZ in the Z+jet sample. This is estimated by varying
the diboson subtractions.
These are each described in more detail below.
3

The diﬀerence are in fact corrected for by correction factors based on simulation. The uncertainty on thecorrection factor as sample dependence is then evaluated by comparing several generators (see Section 6.5).

161

6.4 Fake Backgrounds
6.4.3.1

Sample dependence

0.04

W+jets(MC)-Z+jet(MC) /Z+jet(MC)Electron Fake Factor

The fake factor is measured in the Z+jet sample and is applied to the W +jets control
sample (Nid+anti−id ). Diﬀerences in jet kinematics and heavy flavor fraction may cause thefake factor to be diﬀerent in these two samples. A systematic uncertainty account for thissample dependence. This uncertainty is evaluated in simulation by comparing the two fakefactors.
For electrons, the W +jets background is dominated by light-flavor (for instance, charged
pion track overlapping with neutral pion cluster in EM calorimeter), and the contributionof heavy flavor is found to be small. The flavor composition is studied in detail, which isfound in Section B.2. Figure 6.7 shows the comparison of the electron fake factors between
the Z+jets and W +jets in simulation, (flZ+jet − flW+jets )/flZ+jet as a function of ET . The
fractional diﬀerence from the two samples is found to be ∼ 20 %.

0.035
W+jets fake factor (Alpgen Pythia6)
0.03
Z+jets fake factor (Alpgen Pythia6)

0.025
0.02
0.015

1
0.8

W+jets (Alpgen Pythia6)

0.6
0.4
0.2
0
-0.2
-0.4

0.01
-0.6
0.005
0
10

-0.8
20

30

40

50

60

70

80
90
100
Electron p [GeV]

-1
10

T

20

30

40

50

60

70

80
90
100
Electron p [GeV]T

Figure 6.7: Comparison of electron fake factors between the Z+jets and W +jets samples (left). The fractional diﬀerence between the Z+jets and W +jets electron fake factors(right). The yellow band represents the sample dependence expected from the di-jets fakefactor, while the pink band represents the sample dependence expected from the Z+jets
fake factor. The sample dependence for the Z+jet fake factor is ∼ 20 % that is only 50 %of that for the di-jet fake factor.
For muons, W +jets background is dominated by heavy flavor (for instance, (semi)leptonic decay of charm or bottom meson from Wc and Wbb /Wcc processes). The eﬀect oflight flavor is found to be smaller than that of heavy flavor, depending on pT range. The
flavor composition is studied in detail, which is found in Section B.2. Figure 6.8 shows
the comparison of the muon fake factors between the Z+jets and W +jets in simulation,(flZ+jet −flW+jets )/flZ+jet as a function of pT . The fractional diﬀerence from the two samples
is found to be ∼ 20 %.
6.4.3.2

Lepton contamination in Z+jet sample

The Z+jet sample enhances jets misidentified as leptons. However there is still real lepton
contamination from diboson processes such as those W γ (∗) /W Z/Zγ (∗) /ZZ in the Z+jets

162
0.5

W+jets(MC)-Z+jet(MC) /Z+jet(MC)Muon Fake Factor

6.4 Fake Backgrounds

0.45
W+jets fake factor (Alpgen Pythia6)

0.4
0.35

Z+jets fake factor (Alpgen Pythia6)

0.3
0.25
0.2
0.15

1
0.8
0.6
0.4
0.2
0
-0.2
-0.4

0.1

-0.6

0.05

-0.8

0
10

20

30

40

50

60

70

-1
10

80
90
100
Muon p [GeV]

W+jets (Alpgen Pythia6)
20

30

40

50

60

70

T

80
90
100
Muon p [GeV]T

Figure 6.8: Comparison of muon fake factors between the Z+jets and W +jets samples(left). The fractional diﬀerence between the Z+jets and W +jets muon fake factors (right).
The yellow band represents the sample dependence expected from the di-jets fake factor,
while the pink band represents the sample dependence expected from the Z+jets fake factor.
The sample dependence for the Z+jet fake factor is ∼ 20 % that is only 50 % of that forthe di-jet fake factor.

0.035

mT > 20 GeV
mT > 30 GeV
mT > 40 GeV
mT > 50 GeV

0.03
0.025

s = 8 TeV,

Fake Factor

Fake Factor

sample. The lepton contamination from those events will bias the fake factor measurement.
To reduce this bias, the EW veto (ZZ and W Z veto defined in Section 6.4.2.2) is applied to
the Z+jets sample. The EW veto rejects 80 % of real lepton contamination, while retaining
70-80 % of the Z+jets sample. It has been checked that the EW veto does not bias thefake factor as shown in Figure 6.9.

∫ L dt = 20.7 fb

-1

0.02

0.4
0.35
0.3
s = 8 TeV,
0.25

mT > 20 GeV
mT > 30 GeV
mT > 40 GeV
mT > 50 GeV∫ L dt = 20.7 fb

-1

0.2
0.015
0.15
0.01

0.1

0.005
0
10

0.05
20

30

40

50

60

70

80
90
100
Electron p [GeV]
T

0
10

20

30

40

50

60

70

80
90
100
Muon p [GeV]T

Figure 6.9: The Z+jets fake factor as a function of pT in various mT cuts to see thestability of the fake factors in electron channel (left) and muon channel (right) separately.
Since the statistics are very small above 25 GeV, all pT bins above 25 GeV are merged.

The remaining dibosons contribution is subtracted from the observed data using simulation. Figure 6.3 shows the estimated fake factor with/without the EW background163

6.5 Fake Backgrounds

subtraction. The uncertainty due to the level of residual EW background is evaluated byvarying the overall diboson cross sections by ±10%. The 10 % is set to be conservative
compared to the uncertainties on the cross section evaluated for individual diboson processes [172]. The EW uncertainty accounts for uncertainties associated with those dibosons
cross sections, and the modeling of simulated leptons from those dibosons satisfying thedenominator selection. The EW uncertainty is in general smaller at lower lepton pT , while
it increases rapidly at higher pT .
6.4.3.3

Trigger bias and pileup uncertainty

The trigger bias is not expected in the Z+jets measurement since electrons and muons usedin the Z → ℓℓ reconstruction are defined to be tighter than trigger requirement. Also thepileup dependence appeared in the di-jets measurement is mostly cancelled out as can beseen in Equation 6.7, and the remaining uncertainty is expected to be less than a few %.
Since the pileup uncertainty is much smaller than other uncertainties, the uncertainty is
not included in the total systematic uncertainty.

6.5

Correction Factors

6.5.1

OS W +jets versus SS W +jets
W+jet(OS)In the previous publication, the W +jets background in the signal region (Nid+id) was
estimated using the W +jets control sample (Nid+anti-id ) and fake factor obtained from diincl. ) as:
jets sample (fdi−jets
W+jet(OS)Nid+idW+jet(OS)

incl.
incl.
= fW
+jets · Nid+anti-id = fdi−jets ·

incl.
fW
+jets
incl.
fdi−jets

W+jet(SS)

Similarly the W +jets estimate in same sign region (Nid+id
W+jet(SS)

Nid+idW+jet(SS)

incl.
incl.
= fW
+jets · Nid+anti-id = fdi−jets ·W+jet(OS)Nid+anti-id(6.8)) is expressed as:

incl.
fW
+jets
incl.
fdi−jets

W+jet(SS)

Nid+anti-id(6.9)

incl. ), assuming
The same sign region was used as a validation region for the fake factor (fdi−jetsf incl.

+jets
the ratio of the fake factors ( fWincl.
) is unity and the deviation from unity is accounted fordi−jets

as the sample dependence systematic uncertainty.
The di-jets fake factor is replaced with the Z+jets fake factor when the Z+jets fake factor
W+jet(OS)is introduced. The W +jets background in signal region (Nid+id) is otherwise estimatedin the same way as:
W+jet(OS)Nid+idW+jet(OS)

incl.
incl.
= fW
+jets · Nid+anti-id = fZ+jets ·

incl.
fW
+jets
incl.
fZ+jets

W+jet(OS)Nid+anti-id(6.10)

164

6.5 Fake Backgrounds

incl.
fW
+jets W+jet(SS)W+jet(SS)
W+jet(SS)
incl.
incl.
Nid+id= fW +jets · Nid+anti-id = fZ+jets · incl. Nid+anti-id
fZ+jets(6.11)

However these Equations are not accurate because the W +jets fake factor is diﬀerent between OS and SS. The W +jets fake factor is therefore split into OS and SS, and the ratios,
OS
incl.
SS
incl.
fW
+jets /fZ+jets and fW +jets /fZ+jets , are evaluated as “correction factors” in simulation.
The Equations 6.10 and 6.11 can be then expressed as:
W+jet(OS)Nid+idW+jet(SS)

Nid+idW+jet(OS)

OS
incl.
= fW
+jets · Nid+anti-id = fZ+jets ·W+jet(SS)

SS
incl.
= fW
+jets · Nid+anti-id = fZ+jets ·

OS
fW
+jets
incl.
fZ+jets
SS
fW
+jets
incl.
fZ+jets

Nid+anti-id

W+jet(OS)(6.12)

W+jet(SS)(6.13)

Nid+anti-id

In this approach, the sample dependence is evaluated for OS and SS separately by comparing
several generators that accounts for how well the correction factors are understood. The
Equations 6.12 and 6.13 are new procedures used for the W +jets background estimate.

6.5.2

Correction Factors

6.5.2.1

OS/Z and SS/Z correction factors

0.04
0.035

Di-jet fake factor (Pythia8)

0.03

OS W+jets fake factor (Alpgen Pythia6)

0.025

Muon Fake Factor

Electron Fake Factor

To obtain the W +jets predictions in OS and SS separately, the two correction factors,
OS
incl.
SS
incl.
fW
+jets /fZ+jets and fW +jets /fZ+jets , in Equations 6.12 and 6.13 are independently computed in simulation. Figure 6.10 and 6.11 show the OS W +jets and SS W +jets fake factors
comparing with the di-jets and Z+jets fake factors.
0.5
0.45

Di-jet fake factor (Pythia8)

0.4
OS W+jets fake factor (Alpgen Pythia6)

0.35
0.3

Z+jets fake factor (Alpgen Pythia6)

0.02

Z+jets fake factor (Alpgen Pythia6)

0.25
0.2

0.015

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0.005
0
10

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80
90
100
Electron p [GeV]
T

0
10

20

30

40

50

60

70

80
90
100
Muon p [GeV]T

Figure 6.10: Comparison of the fake factors among the OS W +jets, di-jets, Z+jets samples
in electron channel (left) and muon channel (right). Alpgen+Pythia6 sample is used for
the OS W +jets and Z+jets fake factors, while Pythia8 is used for the di-jets fake factor.
And Figure 6.12 shows direct comparison of the OS W +jets and SS W +jets fake factors
in simulation. It is found that the SS W +jets fake factors are more than 20 % higher than

165

0.04
0.035

Muon Fake Factor

Electron Fake Factor

6.5 Fake Backgrounds

Di-jet fake factor (Pythia8)

0.03

SS W+jets fake factor (Alpgen Pythia6)

0.025

0.5
0.45

Di-jet fake factor (Pythia8)

0.4
SS W+jets fake factor (Alpgen Pythia6)

0.35
0.3

Z+jets fake factor (Alpgen Pythia6)

0.02

Z+jets fake factor (Alpgen Pythia6)

0.25
0.2

0.015

0.15
0.01
0.1
0.005
0
10

0.05
20

30

40

50

60

70

0
10

80
90
100
Electron p [GeV]

20

30

40

50

60

70

T

80
90
100
Muon p [GeV]T

Figure 6.11: Comparison of the fake factors among the OS W +jets, di-jets, Z+jets samples
in electron channel (left) and muon channel (right). Alpgen+Pythia6 sample is used for
the OS W +jets and Z+jets fake factors, while (mu-filtered) Pythia8 is used for thedi-jets fake factor.

0.04
0.035

Muon Fake Factor

Electron Fake Factor

the OS W +jets fake factors. The diﬀerence in the fake factors arises from the diﬀerence inthe flavor composition, which is discussed in detail in Section B.2.

OS W+jets (Alpgen Pythia6)

0.03

SS W+jets (Alpgen Pythia6)

0.025

Inclusive W+jets (Alpgen Pythia6)

0.02

0.5
0.45
OS W+jets (Alpgen Pythia6)
0.4
0.35

SS W+jets (Alpgen Pythia6)

0.3

Inclusive W+jets (Alpgen Pythia6)

0.25
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70

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100
Electron p [GeV]
T

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40

50

60

70

80
90
100
Muon p [GeV]T

Figure 6.12: Comparison of the fake factors between the OS W +jets and SS W +jets
samples in electron channel (left) and muon channel (right). Alpgen+Pythia6 sample isused for the OS W +jets and SS W +jets fake factors.

Using individual fake factors in Figures 6.10, 6.11, and 6.12, the correction factors,
OS
incl.
SS
incl.
fW
+jets /fZ+jets and fW +jets /fZ+jets , are computed. Figure 6.13 shows the correction facOSincl.
tors. fW
+jets /fZ+jets is quite consistent with unity (, namely no correction) within theSS
incl.
statistical uncertainty for both electrons and muons, whereas fW+jets /fZ+jets is 25 % correction for electrons and 40 % correction for muons.
Since the Alpgen+Pythia6 generator is well validated in data (see Figure B.9), theAlpgen+Pythia6 is used to derive the central value of the correction factors. The sam-

166
1

W+jets - Z+jet /Z+jet

W+jets - Z+jets /Z+jets

6.5 Fake Backgrounds

0.8
0.6
0.4
0.2

1
0.8
0.6
0.4
0.2

0

0

-0.2

-0.2

-0.4

-0.4
OS Wjet - Zjet / Zjet (Alpgen Pythia6)

-0.6
-0.8
-1
10

OS Wjet - Zjet / Zjet (Alpgen Pythia6)-0.6
SS Wjet - Zjet / Zjet (Alpgen Pythia6)

20

30

40

50

60

70

80
90
100
Electron p [GeV]T

SS Wjet - Zjet / Zjet (Alpgen Pythia6)

-0.8
-1
10

20

30

40

50

60

70

80
90
100
Muon p [GeV]
T

OS
incl.
Figure 6.13:
Deviation of correction factors from unity, (fW+jets /fZ+jets ) − 1 andincl.
SS(fW +jets /fZ+jets ) − 1, for electrons (left) and muons (right). Yellow band represents 30% correction as reference, and does not indicates something special. The diﬀerence between OS and SS arises from the diﬀerence in the flavor composition that is discussed in
Section B.2.

ple dependence is then evaluated by comparing with other generators with diﬀerent ME
and parton shower modeling such as those Alpgen+Herwig and Powheg+Pythia8 .
Tables 6.10 and 6.11 show the comparison of the correction factors between generators foreach pT bin. Generally the correction factors are consistent within statistical fluctuations,and they do not have dependence much on ME and parton shower modelings.
To deal with statistical fluctuations on the correction factors, the comparison is finallymade by merging pT bins. The resulting systematic uncertainties and correction factors are
summarized in Table 6.12. The correction factor in OS is quite consistent with the unity
within the statistical uncertainty meaning that they do not change the W +jets predictionin OS. On the other hand, the correction factor in SS is not consistent with the unity within
the statistical uncertainty but the unity (no correction) is still covered by the systematic
uncertainty.
6.5.2.2

SS/OS correction factor

In addition to the two correction factors, the W +jets fake factor ratio, SS/OS ratio, is also
computed using the W +jets simulation to see the direct diﬀerence in the two fake factors.
Figure 6.14 shows the deviation of the SS/OS ratio from the unity. Also the generator
comparison of the ratio is found in Table 6.13. Note that the SS/OS correction factor is
not used in the analysis but is of special interest to see pT dependence.

6.5.3

Data Validation

The correction factors derived from simulation are validated in the low pT W W controlℓℓregion, defined as 10 < psub
T < 15 GeV, 55 < Mℓℓ < 110 GeV after pT cut. The high purityof the W +jets is guaranteed in SS, whereas the W W contamination is substantial in OS.

167

6.5 Fake Backgrounds

Table 6.10: Comparison of correction factors between generators for electrons.
OS
incl.
fW
+jets /fZ+jets

10 < ET < 15
15 < ET < 25
ET > 25
ET average

Alpgen+Pythia6
1.09 ± 0.12
1.04 ± 0.31
0.95 ± 0.06
0.99 ± 0.05

Alpgen+Herwig
0.95 ± 0.16
0.72 ± 0.13
0.86 ± 0.07
0.86 ± 0.06

Powheg+Pythia8
0.87 ± 0.09
0.62 ± 0.08
0.87 ± 0.10
0.80 ± 0.06

SS
incl.
fW
+jets /fZ+jets

10 < ET < 15
15 < ET < 25
ET > 25
ET average

Alpgen+Pythia6
1.30 ± 0.16
1.12 ± 0.15
1.31 ± 0.11
1.25 ± 0.08

Alpgen+Herwig
1.13 ± 0.24
0.95 ± 0.22
1.11 ± 0.11
1.09 ± 0.09

Powheg+Pythia8
1.21 ± 0.13
0.57 ± 0.09
1.09 ± 0.14
0.95 ± 0.06

Table 6.11: Comparison of correction factors between generators for muons.
OS
incl.
fW
+jets /fZ+jets

10 < pT < 15
15 < pT < 25
pT > 25
pT average

Alpgen+Pythia6
0.97 ± 0.12
0.93 ± 0.11
1.14 ± 0.18
1.00 ± 0.08

Alpgen+Herwig
1.72 ± 0.28
1.21 ± 0.21
0.84 ± 0.17
1.12 ± 0.12

Powheg+Pythia8
1.17 ± 0.13
1.23 ± 0.17
1.50 ± 0.36
1.21 ± 0.10

SS
incl.
fW
+jets /fZ+jets

10 < pT < 15
15 < pT < 25
pT > 25
pT average

Alpgen+Pythia6
1.35 ± 0.19
1.43 ± 0.24
1.52 ± 0.35
1.40 ± 0.14

Alpgen+Herwig
1.19 ± 0.26
1.68 ± 0.46
0.63 ± 0.20
0.93 ± 0.15

Powheg+Pythia8
1.23 ± 0.15
1.52 ± 0.25
1.95 ± 0.62
1.33 ± 0.13

168

6.5 Fake Backgrounds

Table 6.12:
Corrections factors and corresponding systematic uncertainties. Alpgen+Pythia6 is used to derive the central value and the systematic uncertainty is evaluated by comparing with other generators. The systematic uncertainty accounts for thediﬀerence in the flavor composition among samples.
OS
incl.
fW
+jets /fZ+jets
0.99 ± 0.05(stat) ± 0.19(syst)
1.00 ± 0.08(stat) ± 0.21(syst)

1

SS W+jets - OS W+jets /OS W+jets

SS W+jets - OS W+jets /OS W+jets

electrons
muons

0.8
0.6
0.4
0.2
0
-0.2
-0.4
-0.6

SS W+jet - OS W+jet / OS W+jet (Alpgen Pythia6)

-0.8
-1
10

SS
incl.
fW
+jets /fZ+jets
1.25 ± 0.08(stat) ± 0.30(syst)
1.40 ± 0.14(stat) ± 0.47(syst)

1
0.8
0.6
0.4
0.2
0
-0.2
-0.4
-0.6

SS W+jet - OS W+jet / OS W+jet (Alpgen Pythia6)

-0.8
20

30

40

50

60

70

80
90
100
Electron p [GeV]

-1
10

20

30

40

50

T

60

70

80
90
100
Muon p [GeV]TSS
OS
Figure 6.14: Deviation of the SS/OS ratio from unity, (fW+jets /fW +jets ) − 1, for electrons(left) and muons (right). Yellow band represents 30 % correction as reference, and does notindicates something special. The diﬀerence between OS and SS arises from the diﬀerencein the flavor composition that is discussed in Section B.2.

It is hard to say something conclusive from this validation due to the limited statistics inSS but the agreement of data/simulation looks improved with the corrections as shown in
Figure 6.15. Given that the correction factors for OS are ∼ 1, the correction factors do notchange pictures much in OS.
Another data/simulation comparison is made using the SS/OS ratio in the low pT W W
control region. The W +jets fake factors for OS and SS in data can be directly computedby using Nid+anti-id and Nid+id samples as follows:
EW(OS)QCD
QCD
OS− Nid+id)/(Nid+anti-id− Nid+anti-id − Nid+anti-id)

EW(SS)QCD
QCD
SS− Nid+id)/(Nid+anti-id− Nid+anti-id − Nid+anti-id
)

OS
OS
fW
+jets = (Nid+id − Nid+id

SS
SS
fW
+jets = (Nid+id − Nid+id

EW(OS)(6.14)EW(SS)(6.15)

EW and N EW
where Nid+id
id+anti−id include all other backgrounds except for the W +jets/QCD
backgrounds.

169

6.5 Fake Backgrounds

Table 6.13: Comparison of correction factors between generators.
SS
OS
fW+jets /fW +jets for electrons

10 < ET < 15
15 < ET < 25
ET > 25

Alpgen+Pythia6
1.19 ± 0.14
1.07 ± 0.14
1.37 ± 0.11

Alpgen+Herwig
1.19 ± 0.28
1.32 ± 0.33
1.29 ± 0.12

Powheg+Pythia8
1.39 ± 0.12
0.93 ± 0.14
1.24 ± 0.14

SS
OS
fW
+jets /fW +jets for muons

10 < pT < 15
15 < pT < 25
pT > 25

Alpgen+Pythia6
1.39 ± 0.17
1.53 ± 0.23
1.33 ± 0.27

Alpgen+Herwig
0.68 ± 0.16
1.39 ± 0.39
0.75 ± 0.22

Powheg+Pythia8
1.05 ± 0.10
1.24 ± 0.17
1.30 ± 0.35

To extract pure W +jets component, other contributions such as those QCD and EW backgrounds are subtracted from data. The SS/OS ratio is then computed by taking the ratioof the two fake factors. The ratio can be a good quantity for the validation because there
is no room for the Z+jets fake factor.
The comparison of the SS/OS ratio between data and simulation is found in Table 6.14.
The SS/OS ratios in data are consistent with those in MC within the large uncertainty thatis dominated by W W background subtraction in OS and by statistical uncertainty in SS.
Table 6.14: The data/MC comparison of the SS/OS ratio in the low pT WW control
region, where the Alpgen+Pythia6 is used and only stat uncertainty is taken into accountfor MC. The uncertainty is dominated by the other background contamination and thestatistical uncertainty in data.

electrons
muons

Data
0.82 ± 0.30
2.22 ± 0.79

MC
1.19 ± 0.14
1.39 ± 0.17

170

6.5 Fake Backgrounds

h0ww

90
80
70

s = 8 TeV,
H → WW(*)∫ L dt = 20.7 fb-1→µνeν/eνµν

60

Data

SM(MCstat+ Wjet Syst.)

mH = 125 GeV(ggf)mH = 125 GeV(vbf)WW

W + jets DD (e-fake)W + jets DD (mu-fake)W + jets DD (triggerd-fake)

QCD DDZ/γ +jets

Wγ

WZ/ZZ

Wγ *

tt

Entries

Entries

h0ww

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s = 8 TeV,
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single top

20
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Wγ *

tt

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MT_TrackHWW_Clj [MeV]

3

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150

h0ww

90
s = 8 TeV,
H → WW(*)∫-1

L dt = 20.7 fb→µνeν/eνµν

60

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SM(MCstat+ Wjet Syst.)

mH = 125 GeV(ggf)mH = 125 GeV(vbf)WW

W + jets DD (e-fake)W + jets DD (mu-fake)W + jets DD (triggerd-fake)

QCD DDZ/γ +jets

Wγ

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Wγ *

Entriesh0ww
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W + jets DD (triggerd-fake)

QCD DD

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MT_TrackHWW_Clj [MeV]

3

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35

tt

s = 8 TeV,
H → WW(*)∫-1

L dt = 20.7 fb→µνeν/eνµν

single top

Data

SM(MCstat+ Wjet Syst.)

mH = 125 GeV(ggf)mH = 125 GeV(vbf)WW

W + jets DD (e-fake)W + jets DD (mu-fake)W + jets DD (triggerd-fake)

QCD DDZ/γ +jets

Wγ

WZ/ZZ

Wγ *

tt

single top

30

50

25

40

20

30

15

20

10

10

5
×10
200
250
300
MT_TrackHWW_Clj [MeV]

3

0
50

W + jets DD (e-fake)W + jets DD (mu-fake)

25

30

70

mH = 125 GeV(vbf)WWsingle top

4080SM(MCstat+ Wjet Syst.)

mH = 125 GeV(ggf)

30

50

0
50

Data

100

150

×10
200
250
300
MT_TrackHWW_Clj [MeV]

3

0
50

100

150

Figure 6.15: The low pT W W validation region defined as 10 < psub
T < 15 GeV, 55 < Mℓℓ <100 GeV after pℓℓ
cut.
The
top
plots
are
beforecorrections
andthe bottom plots are afterT
corrections.

6.6 Fake Backgrounds

6.6

W +jets Control Sample

6.6.1

Control Sample Definition

171

Data-driven W +jets control sample (Nid+anti−id ) is used to obtain the W +jets predictionin the signal region (Nid+id ) multiplying the fake factors as discussed in Section 6.2. The
W +jets control sample is defined as events that have one id lepton and one anti-id lepton. The control sample is collected with the primary triggers that are used in the standard
analysis (see Table 3.2): EF e24vhi medium1, EF e60 medium1, EF 2e12Tvh loose1, andEF e12Tvh medium1 mu8 for ee and eµ+µe channels, and EF mu24i tight, EF mu36 tight,
EF mu18 mu8 EFFS, and EF e12Tvh medium1 mu8 for µµ and eµ+µe channels. Neverthelessthere is a small bias on the W +jets control sample when using those triggers due to somerequirements on the triggers such as medium1 and i. This is further discussed in the next
Section B.4.
There is also a contribution from multiple anti-id lepton events that have one id
lepton and more than one anti-id leptons, to the W +jets control sample. It is possible toinclude such multiple anti-id lepton events by replacing one of the anti-id leptons withreconstructed jet when treating the other anti-id lepton as fake lepton. The contributionof the multiple anti-id lepton events to the control sample was investigated, and was foundto be < a few % in 0 jet bin, < 10 % in 1 jet bin, and ∼ 20 % in 2 jet bin. Given thelarge systematic uncertainty on the fake factor (30-40 %) and small impact of the W +jets
background in the VBF signal region, the events are not taken into account as the W +jets
control sample in the current analysis scheme.
Kinematic distributions of the W +jets control sample is investigated by splitting into
low pT and high pT (sub-leading pT > 15 GeV) and by overlaying the expectation from theW +jets simulation for shape comparison. The shape modeling of the W +jets backgroundis further discussed in Section B.3. The higher Z+jets contamination (20-30 %) is expectedin µµ channel but otherwise the purity of the W +jets background in the control sample ismore than 90 % depending on the cut stage or signal region.
Figure 6.16 and 6.17 show kinematic distributions after pℓℓ
T cut in 0 jet for µe andeµ channels, respectively. In terms of the shape modeling, data shows reasonable agreement with simulation even though statistics in simulation in low pT eµ channel is limited.
After ∆ϕℓℓ cut, the EW contamination will be negligible, less than a few %, in µe andeµ channels. Figure 6.18 and 6.19 show kinematic distributions after b-veto requirementin 1 jet for µe and eµ channels, respectively. After ∆ϕℓℓ cut, the EW contamination will
be negligible, less than a few %, in µe and eµ channels. Nevertheless the QCD contamination remains in lower MAX mT (W ) distribution in eµchannel, which will be correctly
subtracted using the QCD control sample (Nanti−id+anti−id . The detailed procedure of the
QCD subtraction from the W +jets control sample is presented in Section 6.7.

172

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h0ww

9000
8000
7000

s = 8 TeV,
H → WW(*)∫ L dt = 20.7 fb

-1

→µνeν

6000

Data

SM(MCstat)mH = 125 GeV

WW

W+jets MC (Normalized)

Z/ γ +jets

Wγ

WZ/ZZ/Wγ *ttsingle top

Entries

Entries

h0ww

25000
s = 8 TeV,

20000

H → WW(*)∫ L dt = 20.7 fb

-1

→µνeν

Data

SM(MCstat)mH = 125 GeV

WW

W+jets MC (Normalized)

Z/ γ +jets

Wγ

WZ/ZZ/Wγ *ttsingle top

15000

5000
4000

10000
3000
2000

5000

1000
×10
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MT_TrackHWW_Clj [MeV]

3

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8000
7000

0.5

1

1.5

2

2.5

3
DPhill []

h0ww

9000
s = 8 TeV,
H → WW(*)∫ L dt = 20.7 fb

-1

→µνeν

6000

Data

SM(MCstat)mH = 125 GeV

WW

W+jets MC (Normalized)

Z/ γ +jets

Wγ

WZ/ZZ/Wγ *ttsingle top

Entries

Entries

h0ww

0
0

10000
s = 8 TeV,

8000

5000

H → WW(*)∫ L dt = 20.7 fb

-1

→µνeν

Data

SM(MCstat)mH = 125 GeV

WW

W+jets MC (Normalized)

Z/ γ +jets

Wγ

WZ/ZZ/Wγ *ttsingle top

6000

4000
4000

3000
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2000

1000
×10
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MT_TrackHWW_Clj [MeV]

3

0
50

100

150

0
0

0.5

1

1.5

2

2.5

3
DPhill []Figure 6.16:
Kinematics of the W +jets control sample for µe channel in 0 jet afterℓℓpT requirement. The top plots are mT (left) and ∆ϕℓℓ (right) in high pT . The bottom
plots are mT (left) and ∆ϕℓℓ (right) in low pT . The expectation from the W +jets simulation is also shown for comparison.

173

6.6 Fake Backgrounds

h0ww

3500
3000
2500

s = 8 TeV,
H → WW(*)∫ L dt = 20.7 fb

-1

→eνµν

Data

SM(MCstat)mH = 125 GeV

WW

Entries

Entriesh0ww

W+jets MC (Normalized)

Z/ γ +jets

3500

s = 8 TeV,Wγ

WZ/ZZ/Wγ *3000

H → WWttsingle top

4000

(*)

∫ L dt = 20.7 fb

-1

→eνµν

Data

SM(MCstat)mH = 125 GeV

WW

W+jets MC (Normalized)

Z/ γ +jets

Wγ

WZ/ZZ/Wγ *ttsingle top

2500
2000
2000
1500
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1000

1000

500

500
×10
100 120 140 160 180 200
MAXmT_TrackHWW_Clj [MeV]

3

0
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20

40

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1000
s = 8 TeV,
800

50

100

150

200

h0ww

H → WW(*)∫ L dt = 20.7 fb

-1

→eνµν

Data

SM(MCstat)mH = 125 GeV

WW

W+jets MC (Normalized)

Z/ γ +jets

Wγ

WZ/ZZ/Wγ *ttsingle top

Entries

Entries

h0ww

×10
250
Mll [MeV]

3

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0

1400
s = 8 TeV,

1200
H → WW(*)∫ L dt = 20.7 fb

-1

→eνµν

1000

600

Data

SM(MCstat)mH = 125 GeV

WW

W+jets MC (Normalized)

Z/ γ +jets

Wγ

WZ/ZZ/Wγ *ttsingle top

800
600

400

400
200
200
×10
100 120 140 160 180 200
MAXmT_TrackHWW_Clj [MeV]

3

0
0

20

40

60

80

×10
250
Mll [MeV]

3

0
0

50

100

150

200

Figure 6.17:
Kinematics of the W +jets control sample for eµ channel in 0 jet afterℓℓpT requirement. The top plots are mT (W )(MAX) (left) and Mℓℓ (right) in high pT . The
bottom plots are mT (W )(MAX) (left) and Mℓℓ (right) in low pT . The expectation from theW +jets simulation is also shown for comparison.

174

6.6 Fake Backgrounds

h0ww

4500
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3500
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-1

→µνeν

3000

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SM(MCstat)mH = 125 GeV

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Z/ γ +jets

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WZ/ZZ/Wγ *ttsingle top

Entries

Entries

h0ww

18000
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14000

H → WW(*)∫ L dt = 20.7 fb

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Data

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W+jets MC (Normalized)

Z/ γ +jets

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WZ/ZZ/Wγ *ttsingle top

12000

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DPhill []

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1600

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Entries

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h0ww

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H → WW(*)∫ L dt = 20.7 fb

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W+jets MC (Normalized)

Z/ γ +jets

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WZ/ZZ/Wγ *ttsingle top

2500

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3

0
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100

150

0
0

0.5

1

1.5

2

2.5

3
DPhill []Figure 6.18: Kinematics of the W +jets control sample for µe channel in 1 jet after b-vetorequirement. The top plots are mT (left) and ∆ϕℓℓ (right) in high pT . The bottom plots
are mT (left) and ∆ϕℓℓ (right) in low pT . The expectation from the W +jets simulation is
also shown for comparison.

175

6.6 Fake Backgrounds

h0ww

3500
s = 8 TeV,

3000
H → WW(*)∫ L dt = 20.7 fb

-1

→eνµν

2500

Data

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WW

W+jets MC (Normalized)

Z/ γ +jets

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WZ/ZZ/Wγ *ttsingle top

Entries

Entries

h0ww

4500
4000
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3500
H → WW(*)∫ L dt = 20.7 fb

-1

→eνµν

3000

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SM(MCstat)mH = 125 GeV

WW

W+jets MC (Normalized)

Z/ γ +jets

Wγ

WZ/ZZ/Wγ *ttsingle top

2500

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1000
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W+jets MC (Normalized)

Z/ γ +jets

Wγ

WZ/ZZ/Wγ *ttsingle top

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3

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×10
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3

0
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100

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200

Figure 6.19: Kinematics of the W +jets control sample for eµ channel in 1 jet after b-vetorequirement. The top plots are mT (W )(MAX) (left) and Mℓℓ (right) in high pT . The
bottom plots are mT (W )(MAX) (left) and Mℓℓ (right) in low pT . The expectation from theW +jets simulation is also shown for comparison.

176

6.6 Fake Backgrounds

6.6.2

Run Dependence

The stability of the W +jets control sample against run period is investigated by comparing
the yield of the control sample for each lepton flavor channel through 2012 data taking.
Figure 6.20 shows the yield of the control sample per pb−1 versus period for OS events.
The comparisons are made after the jet veto requirement for 0 jet, after the one jet requirement for 1 jet, and after two jet requirement for 2 jet. No significant run dependence isobserved, and it is found that the yield is stable within the run period used in the analysis.
Any deviation arises from the pileup eﬀect, change in trigger configuration, and change inperformance of jet reconstruction.

4.5
4

s = 8 TeV

3.5

∫ Ldt = 20.7 fb

3

Number of W+Jets CR/pb -1

Number of W+Jets CR/pb -1

It is worth noting the fact that the acceptance of the sub-leading muon, namely eµ orµµ channel, increases with higher jet multiplicity. This is because the larger contributionof fake leptons from tt̄ events in the control sample. In practice the contribution is not
subtracted from the control sample as it is from real fake lepton. To do this, only leptonic
decays of tt̄ events with two real leptons in the final state are subtracted from the control
sample.

after 0jet (OS,ee-ch)after 0jet (OS,µ µ -ch)-1

after 0jet (OS,eµ -ch)after 0jet (OS,µ e-ch)

2.5
2
1.5

1.6
s = 8 TeV
1.4
1.2

∫ Ldt = 20.7 fb-1

1

after 1jet (OS,ee-ch)after 1jet (OS,µ µ -ch)after 1jet (OS,eµ -ch)after 1jet (OS,µ e-ch)

0.8
0.6
0.4

1

0.2

0.5
Peri

P
P
P
P
P
P
P
T
P
P
od A eriod B eriod C eriod D eriod E eriod G eriod H eriod I eriod J eriod L otal

Number of W+Jets CR/pb -1

0

1.8

2.4
2.2
2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0

s = 8 TeV

∫ Ldt = 20.7 fb

-1

Peri

0

Peri

P
P
P
P
P
P
P
T
P
P
od A eriod B eriod C eriod D eriod E eriod G eriod H eriod I eriod J eriod L otal

after 2jet (OS,ee-ch)after 2jet (OS,µ µ -ch)after 2jet (OS,eµ -ch)after 2jet (OS,µ e-ch)

P
P
P
P
P
P
P
T
P
P
od A eriod B eriod C eriod D eriod E eriod G eriod H eriod I eriod J eriod L otal

Figure 6.20: OS W +jet control region yields per pb−1 as a function of run period.
The yields are shown after the jet veto requirement, one jet requirement, and two jets
requirement for each channel.

177

6.8 Fake Backgrounds

6.7

QCD Estimation

6.7.1

QCD in the Fake Factor Method

As an extension of the fake factor method, it is possible to obtain data-driven QCD background estimation. The data-driven QCD estimation uses the QCD control sample definedas events that have two anti-id leptons (Nanti−id+anti−id ). For these events, the fake factor
based on the di-jets sample is applied twice to obtain the QCD prediction in the signal
region (Nid+id ):QCD
NQCD Bkg = f 2 × Nanti-id+anti-id,(6.16)
QCD
where f is the di-jets fake factor and Nanti-id+anti-id
is the number of QCD events with two
leptons satisfying the anti-id definition, and where the EW contamination is not explicitly
shown. The QCD enters the W +jet control sample when one of the jets satisfies id lepton
QCD
definition and the other satisfies the anti-id lepton definition (Nid+anti−id). The QCD in
the W +jets control sample is in principle double counted because there are two possiblecombinations (id + anti-id versus anti-id + id), which can be explicitly expressed as:
QCD
QCD
Nid+anti-id= 2 × f × Nanti-id+anti-id,(6.17)The QCD contamination in the W +jet prediction is finally written by combining the above
Equations 6.16 and 6.17, and Equation 6.5 as:
QCD in W+jets
QCD
QCD
Nid+id= f × Nid+anti-id= 2 × f 2 × Nanti-id+anti-id= 2 × NQCD Bkg .

(6.18)

Note that the formulation above ignores the fact that the QCD factor factor can be quite
diﬀerent from the Z+jets (or di-jets) fake factor due to the diﬀerence in flavor compositionand jet pT , which will be addressed in Section B.5.2.

6.8

Summary of the W +jets Systematic Uncertainty

The W +jets/QCD backgrounds are estimated in a data-driven way using the fake factor
method. The W +jets fake factor is derived in Z+jets sample, and the W +jets control sample is constructed by events that have one identified lepton and one anti-identified lepton.
The fake factors are applied to the W +jets control sample to obtain the W +jets predictionin the signal region. The Z+jets fake factor may not be accurate due to the diﬀerence inthe jet flavor composition between the Z+jets and W +jets sample. A dedicated correction
factors are evaluated separating into OS and SS to correct the diﬀerence in the flavor composition. The correction factors are further applied to obtain the final W +jets prediction in
the signal region (OS) and SS region. The systematic uncertainties on the fake factors areevaluated by varying EW contamination in the Z+jets sample and by comparing the correction factors using several generators (central value is derived in Alpgen + P ythia6). The
systematic uncertainties on the fake factors are summarized in Table 6.15 and Figure 6.21.

178

6.8 Fake Backgrounds

Table 6.15: Summary of systematic uncertainties (quoted as percentages) on the Z+jets
fake factor measurement. Same-sign and opposite-sign uncertainties are quoted separately
because the correction factor uncertainties diﬀer. For the correction factor uncertainties,
the statistical, correlated systematic, and uncorrelated systematic components quoted inTable 7.5 are summed in quadrature.

electrons

muons

stat.

EW syst.

10 < pT < 1518

11

15 < pT < 2034

19

20 < pT < 25

52

25

pT > 25

30

23

corr.
factor
20
25
20
25
20
25
20
25

total
29 (OS)
32 (SS)
44 (OS)
46 (SS)
61 (OS)
63 (SS)
43 (OS)
45 (SS)stat.

EW syst.

10

3

18

5

29

9

34

21

corr.
factor
22
35
22
35
22
35
22
35

total
25 (OS)
37 (SS)
29 (OS)
40 (SS)37 (OS)
46 (SS)46 (OS)
53 (SS)179

0.03
OS W+jets (Alpgen+Pythia6)

0.025

0.02

Z+jets (Alpgen+Pythia6)

s = 8 TeV,

∫ L dt = 20.3 fb-1Corrected Z+jets Data (20.3 fb-1)
Statistical Uncertainty

Electron Fake Factor

Electron Fake Factor

6.8 Fake Backgrounds

0.03
SS W+jets (Alpgen+Pythia6)

0.025

0.02

Z+jets (Alpgen+Pythia6)

s = 8 TeV,

∫ L dt = 20.3 fb-1Corrected Z+jets Data (20.3 fb-1)
Statistical Uncertainty+ EW contamination

0.015

0.01

0.01

0.005

0.005

20

30

40

50

60

70

0.35
OS W+jets (Alpgen+Pythia6)

0.3

Z+jets (Alpgen+Pythia6)

0.25

s = 8 TeV,

∫ L dt = 20.3 fb-1Corrected Z+jets Data (20.3 fb-1)
Statistical Uncertainty

0.2

0
10

80
90
100
Electron ET [GeV]

Muon Fake Factor

010Muon Fake Factor+ EW contamination

0.015+ Sample Composition (OS/Z)+ Sample Composition (SS/Z)

20

30

40

50

60

80
90
100
Electron ET [GeV]

0.35
SS W+jets (Alpgen+Pythia6)

0.3
0.25

Z+jets (Alpgen+Pythia6)

s = 8 TeV,

Corrected Z+jets Data (20.3 fb-1)∫ L dt = 20.3 fb-1

Statistical Uncertainty+ EW contamination

0.2+ EW contamination

70+ Sample Composition (SS/Z)+ Sample Composition (OS/Z)

0.15

0.15

0.1

0.1

0.05

0.05

0
10

20

30

40

50

60

70

80
90
100
Muon p [GeV]
T

0
10

20

30

40

50

60

70

80
90
100
Muon p [GeV]T

Figure 6.21: Summary of fake factor and corresponding systematics for OS electrons (topleft), SS electrons (top right), OS muons (bottom left), and SS muons (bottom right). The
correction factors summarized in Table 6.15 are applied to data Z+jets fake factor. All
systematic uncertainties are added in quadrature.

180

6.8 Fake Backgrounds

Chapter 7

Modeling of Same Sign
Backgrounds
7.1

Introduction

The “non-W W ” dibosons (V V ) such as those W γ, Zγ, W γ ∗ , W Z, Zγ ∗ , and ZZ, are thesecond largest backgrounds in the signal region. The Same Sign (SS) events that pass thesame selection criteria as the signal region but are required to be same signed two leptons,
provide a good validation region for those backgrounds, since the SS events are dominatedby V V (and W +jets) backgrounds. Adding the SS region to the simultaneous fit as anothercontrol region allows the fit to obtain more robust predictions of those backgrounds. The
same sign control region (SS CR) is designed to set the summed normalization of all theV V backgrounds. The SS CR is built from events that pass all the signal region cuts up tothe ∆ϕℓℓ with the same charge requirement.
The γ, γ ∗ , or Z in those diboson processes equally produces a lepton of either charge
relative to the charge of the lepton from the W . The normalization and kinematic distributions for the SS region from these V V backgrounds are thus identical in the diﬀerent lepton
flavor channels (eµ+µe) final states to the signal region (OS) in a good approximation.
Since the phase space of the signal and control regions is identical, potential extrapolation
uncertainties are negligible compared to other sources of uncertainties, thus the extrapolation uncertainties on the SS CR are not considered unlike W W or top control regions.
While in the same lepton flavor channels (ee+µµ), the SS populations are not identical to
the OS, for instance W Z process. The SS CR is therefore used only for diﬀerent lepton
flavor channels (eµ+µe).
Another dominant process which contributes to the SS region is the W +jets background with one fake lepton. Its contribution is not symmetric between SS and OS as
discussed in Section 6.5. The W +jets background needs to be predicted separately for the
SS region and signal region. Dedicated corrections factors to both the OS and SS W +jets
prediction have been introduced and described in Section 6.5. The W +jets background is
181

182

7.1 Modeling of Same Sign Backgrounds

subtracted from the SS data to obtain a collective normalization factor for the V V backgrounds. Tables 7.1 and 7.2 show the expected and observed event yields in the Njet = 0
and = 1 channels, respectively.
Table 7.1: The expected and observed event yields in the SS control region in the Njet = 0
channel. The W +jets background is estimated using the data-driven method. The H → τ τcontribution is included in the “Signal” column, and the “NF” column illustrates the ratioof the “data-non-V V ” to the V V .
eµ+µe
eµ
µe

Signal [125 GeV]
2.14 ± 0.39
1.27 ± 0.29
0.87 ± 0.26

W Z/ZZ/W γ
348.67 ± 8.51
156.76 ± 5.36
191.91 ± 6.62

Wγ
173.13 ± 7.46
67.05 ± 4.57
106.08 ± 5.90

W γ∗
115.32 ± 3.77
56.32 ± 2.53
59.01 ± 2.79

WZ
56.39 ± 1.61
31.51 ± 1.18
24.88 ± 1.08

ZZ
3.83 ± 0.14
1.88 ± 0.10
1.94 ± 0.10

Z+jets
20.86 ± 2.60
7.51 ± 1.56
13.35 ± 2.08

W +jets
162.86 ± 4.38
76.04 ± 4.02
86.82 ± 1.73

Total Bkg.
541.11 ± 9.95
246.06 ± 6.91
295.04 ± 7.15

Observed
531
272
259

Data/MC
0.98 ± 0.05
1.11 ± 0.07
0.88 ± 0.06

NF
0.96 ± 0.08
1.16 ± 0.13
0.81 ± 0.10

Table 7.2: The expected and observed event yields in the SS control region in the Njet = 1
channel. The W +jets background is estimated using the data-driven method. The H → τ τcontribution is included in the “Signal” column, and the “NF” column illustrates the ratioof the “data-non-V V ” to the V V .
eµ+µe
eµ
µe

Signal [125 GeV]
1.93 ± 0.35
1.00 ± 0.25
0.93 ± 0.25

W Z/ZZ/W γ
120.32 ± 4.35
57.30 ± 2.80
63.02 ± 3.32

Wγ
53.18 ± 3.58
19.37 ± 2.14
33.81 ± 2.87

W γ∗
30.02 ± 2.12
16.19 ± 1.52
13.82 ± 1.47

WZ
34.29 ± 1.27
20.11 ± 0.98
14.18 ± 0.80

ZZ
2.84 ± 0.12
1.63 ± 0.09
1.21 ± 0.08

Z+jets
13.96 ± 5.93
2.16 ± 0.92
11.80 ± 5.86

W +jets
58.49 ± 2.71
31.87 ± 2.48
26.61 ± 1.09

Total Bkg.
200.06 ± 7.86
96.24 ± 3.88
103.82 ± 6.83

Observed
193
104
89

Data/MC
0.96 ± 0.08
1.08 ± 0.11
0.86 ± 0.11

NF
0.93 ± 0.14
1.12 ± 0.20
0.75 ± 0.20

The normalization factor (NF) is obtained from the ratio of the “data-non-V V ” to the
expected V V yield predicted by simulaion. The resulting NF is taken from the eµ+µechannel and it is 0.96 ± 0.07 (stat.) and 0.93 ± 0.13 (stat.) in the Njet = 0 and = 1 channels, respectively. Figures 7.1 and 7.2 show the mℓℓ , ∆ϕℓℓ , mT and pℓℓ
T distributions for
the 0-jet eµ+µe eµ and µe channels, and the corresponding distributions for the 1-jet are
shown in Figures 7.3 and 7.4. The dedicated NFs have been applied to the V V background.
In the following sections the systematic uncertainties on W +jets and V V backgrounds
are discussed. The treatment of the uncertainty on the W +jets background is a bit complicated, since the correlation between OS and SS regions needs to be taken into account.
In practice the W +jets systematics due to flavor composition are split into correlated anduncorrelated uncertainties. On the other hand the uncertainties on V V backgrounds arecommon between OS and SS since they are uncertainties on production cross section. A
special treatment is also required for the W γ background because this background arises
from conversion (photon faking electron), so a dedicated systematic uncertainty to accountfor the conversion modeling is specially introduced for the W γ background.
In the simultaneous fit, the relative contributions of the individual V V processes are stillallowed to float under gaussian constraint within the uncertainty on their cross sections.

183

400
350
300

s = 8 TeV, ∫ Ldt = 20.3 fb-1
H→WW*→eν µν / µν eν + 0 jets

250

Data

SM (sys ⊕ stat)

WW

Other VV
Single Top
Z/ γ *→ττtt*
Z/ γ →ll
W+jet
H [125 GeV]

QCD

Events / 1 GeVEvents / 5 GeV

7.1 Modeling of Same Sign Backgrounds

100

40

50

20
Data / SM

60

1.4
1.2
1
0.8
0.6
50

100

150

200

250
p

30

Data

SM (sys ⊕ stat)

WW

Other VV
Single Top
Z/ γ *→ττtt*
Z/ γ →ll
W+jet
H [125 GeV]

T,lead lep

300

s = 8 TeV, ∫ Ldt = 20.3 fb-1
H→WW*→eν µν / µν eν + 0 jets

25

Data

SM (sys ⊕ stat)

WW

Other VV
Single Top
Z/ γ *→ττtt*
Z/ γ →ll
W+jet
H [125 GeV]

1.4
1.2
1
0.8
0.6
5

10

15

20

25

30

[GeV]

40
35

H→WW*→eν µν / µν eν + 0 jets

100

150

QCD

QCD

35
p

Events / 5 GeV

Data / SM120

s = 8 TeV, ∫ Ldt = 20.3 fb-1

80

200

Events / 10 GeV

140

20

40

T,sublead lep

45

[GeV]

300
250

s = 8 TeV, ∫ Ldt = 20.3 fb-1
H→WW*→eν µν / µν eν + 0 jets

200

Data

SM (sys ⊕ stat)

WW

Other VV
Single Top
Z/ γ *→ττtt*
Z/ γ →ll
W+jet
H [125 GeV]

QCD

150

15

100

10
50

Data / SM

Data / SM

5
1.4
1.2
1
0.8
0.6
50

100

150

200

250
[GeV]
mτtrack,Clj
τ

1.4
1.2
1
0.8
0.6
0

50

100

150

200
miss,track,Clj

ET

250
[GeV]

Figure 7.1: Kinematic distributions for same sign control region : plead(top left), psubTT (topmissright), mτ τ (bottom left), and ET (bottom right).

184

300
250

s = 8 TeV, ∫ Ldt = 20.3 fb-1
H→WW*→eν µν / µν eν + 0 jets

200

Data

SM (sys ⊕ stat)

WW

Other VV
Single Top
Z/ γ *→ττtt*
Z/ γ →ll
W+jet
H [125 GeV]

QCD

Events / 10 GeV

Events / 5 GeV

7.1 Modeling of Same Sign Backgrounds

400
350
300

s = 8 TeV, ∫ Ldt = 20.3 fb-1
H→WW*→eν µν / µν eν + 0 jets

250

Data

SM (sys ⊕ stat)

WW

Other VV
Single Top
Z/ γ *→ττtt*
Z/ γ →ll
W+jet
H [125 GeV]

QCD

200

150

150

100

100

1.4
1.2
1
0.8
0.6
0

50
Data / SM

Data / SM

50

20

40

60

80

100

120

140

1.4
1.2
1
0.8
0.6

160

50

100

150

200

250

100
90
80

s = 8 TeV, ∫ Ldt = 20.3 fb-1
H→WW*→eν µν / µν eν + 0 jets

70

Data

SM (sys ⊕ stat)

WW

Other VV
Single Top
Z/ γ *→ττtt*
Z/ γ →ll
W+jet
H [125 GeV]

QCD

60

mll [GeV]

Events / 10 GeV

Events / 0.13 rad

P llT [GeV]50300
s = 8 TeV, ∫ Ldt = 20.3 fb-1

250

H→WW*→eν µν / µν eν + 0 jets

200

Data

SM (sys ⊕ stat)

WW

Other VV
Single Top
Z/ γ *→ττtt*
Z/ γ →ll
W+jet
H [125 GeV]

QCD

150

40
100

30
20

50

1.4
1.2
1
0.8
0.6
0

Data / SM

Data / SM

10

0.5

1

1.5

2

2.5

3

∆ φ [rad]
ll

1.4
1.2
1
0.8
0.6
50

100

150

200

250

300

[GeV]
mtrack-clj
T

Figure 7.2: Kinematic distributions for same sign control region : pℓℓ
T (top left), mℓℓ (topright), ∆ϕℓℓ (bottom left), and mT (bottom right).

185

70
60

s = 8 TeV, ∫ Ldt = 20.3 fb-1
H→WW*→eν µν / µν eν + 1 jet

50

Data

SM (sys ⊕ stat)

WW

Other VV
Single Top
Z/ γ *→ττtt*
Z/ γ →ll
W+jet
H [125 GeV]

QCD

Events / 1 GeVEvents / 5 GeV

7.1 Modeling of Same Sign Backgrounds

40

50
45
40

s = 8 TeV, ∫ Ldt = 20.3 fb-1
H→WW*→eν µν / µν eν + 1 jet

35

Data

SM (sys ⊕ stat)

WW

Other VV
Single Top
Z/ γ *→ττtt*
Z/ γ →ll
W+jet
H [125 GeV]

QCD

30
25

30

20

20

15
10

Data / SM

5

1.4
1.2
1
0.8
0.6
50

100

150

200

250
T,lead lep

300

30
25

s = 8 TeV, ∫ Ldt = 20.3 fb-1
H→WW*→eν µν / µν eν + 1 jet

20

Data

SM (sys ⊕ stat)

WW

Other VV
Single Top
Z/ γ *→ττtt*
Z/ γ →ll
W+jet
H [125 GeV]

1.4
1.2
1
0.8
0.6
5

QCD

50

5

10

200

250

300

[GeV]
mτtrack-clj
τs = 8 TeV, ∫ Ldt = 20.3 fb-1

40

20

150

25

H→WW*→eν µν / µν eν + 1 jet

10

100

20

30

35

40

T,sublead lep

45

[GeV]

60

30

50

15

p

15

1.4
1.2
1
0.8
0.6
0

10

[GeV]

Data / SM

Data / SM

Events / 10 GeVp

Events / 5 GeV

Data / SM

10

1.4
1.2
1
0.8
0.6
0

50

100

Data

SM (sys ⊕ stat)

WW

Other VV
Single Top
Z/ γ *→ττtt*
Z/ γ →ll
W+jet
H [125 GeV]

150

QCD

200
miss,track,Clj

ET

250
[GeV]

Figure 7.3: Kinematic distributions for same sign control region : plead(top left), psubTT (topmissright), mτ τ (bottom left), and ET (bottom right).

186

45
40

s = 8 TeV, ∫ Ldt = 20.3 fb-1
H→WW*→eν µν / µν eν + 1 jet

35

Data

SM (sys ⊕ stat)

WW

Other VV
Single Top
Z/ γ *→ττtt*
Z/ γ →ll
W+jet
H [125 GeV]

QCD

30

Events / 10 GeV

50

100
90
80

50
40

15

30

10

20

5

10

20

40

60

80

100

120

140

H→WW*→eν µν / µν eν + 1 jet

Data

SM (sys ⊕ stat)

WW

Other VV
Single Top
Z/ γ *→ττtt*
Z/ γ →ll
W+jet
H [125 GeV]

1.4
1.2
1
0.8
0.6

160

50

100

150

200

250

45
40

s = 8 TeV, ∫ Ldt = 20.3 fb-1
H→WW*→eν µν / µν eν + 1 jet

35

Data

SM (sys ⊕ stat)

WW

Other VV
Single Top
Z/ γ *→ττtt*
Z/ γ →ll
W+jet
H [125 GeV]

QCD

30

mll [GeV]

Events / 10 GeV

Events / 0.13 rad

P llT [GeV]

50

70
60

s = 8 TeV, ∫ Ldt = 20.3 fb-1
H→WW*→eν µν / µν eν + 1 jet

50
40

20

30

15

Data

SM (sys ⊕ stat)

WW

Other VV
Single Top
Z/ γ *→ττtt*
Z/ γ →ll
W+jet
H [125 GeV]

QCD

20

10

10
Data / SM

5
Data / SM

80

25

1.4
1.2
1
0.8
0.6
0

QCD

60

20

1.4
1.2
1
0.8
0.6
0

s = 8 TeV, ∫ Ldt = 20.3 fb-1

70

25

Data / SM

Data / SM

Events / 5 GeV

7.1 Modeling of Same Sign Backgrounds

0.5

1

1.5

2

2.5

3

∆ φ [rad]
ll

1.4
1.2
1
0.8
0.6
50

100

150

200

250

300

[GeV]
mtrack-clj
T

Figure 7.4: Kinematic distributions for same sign control region : pℓℓ
T (top left), mℓℓ (topright), ∆ϕℓℓ (bottom left), and mT (bottom right).

7.2 Modeling of Same Sign Backgrounds

7.2

Dibosons backgrounds

7.2.1

Theoretical Uncertainties on Dibosons

187

The non-W W diboson (V V ) processes that include W γ/Zγ, W γ ∗ /W Z, ZZ/Zγ ∗ , and Zγ,
are the second largest backgrounds in the signal region. The size of these backgrounds
increases at lower sub-leading lepton pT and lower mℓℓ . For 0-jet diﬀerent flavor signal
regions, the sum of V V backgrounds is normalized to data in the SS CR. For individual
V V components, the theoretical uncertainties on NLO cross sections are evaluated by comparing to MCFM [174] generator at truth level.
W γ/Zγ backgrounds
The uncertainties and correction factor referred to as “k-factor” on the W γ backgroundare evaluated for each jet bin. The procedure of the calculation is described in [175]. For
the W γ production, there are infrared divergences at low photon pT that must be regularized with a minimum pT cut at generator level. Also there are collinear divergences thatarise from photons close to the other objects like lepton or jet. These are avoidable divergences by defining minimum ∆R cut. The cuts imposed at generator level are summarized
as follows :- pγT > 8 GeV,
- ∆R(ℓ, γ) > 0.25,- ∆R(jet, γ) > 0.1,√
where ∆R is defined as ∆ϕ2 + ∆η 2 . The comparison of Alpgen to MCFM is made after
these cuts are imposed. The k-factor is calculated for inclusive sample, which is 1.15, andthe diﬀerence in normalization for each jet bin is taken as theoretical uncertainty, which
is 11% for the 0-jet, 53% for the 1-jet, and 100% for the ≥2-jet. The large uncertainty on
the ≥1-jet bins is due to the fact that the MCFM is an NLO generator that is not able tocompute the uncertainty directly for σ≥2jet , so the uncertainty on the 1-jet bin is evaluatedas a fractional diﬀerence between σ≥2−jet and σ≥1−jet . An additional PDF uncertainty of
3.1% is also considered for this process. The Zγ background can also contributes to bothsignal region and SS CR, but it requires one lepton is out of acceptance, so the size of thisbackground is small compared to the W γ background. The Zγ background is thus treatedas a part of Z+jets backgrounds in the analysis. For the W γ background the additional
uncertainty is considered to account for conversion modeling (photon faking electron). The
conversion is discussed a bit more in the next Section.
W γ ∗ /W Z backgrounds
The W γ ∗ /W Z processes lead to the same final state. These processes are each defined byseparating in mℓℓ at 7 GeV, high mass sample is called W Z process and low mass sample iscalled W γ ∗ process. The W Z background is generated by Powheg and W γ ∗ background188

7.2 Modeling of Same Sign Backgrounds

is generated by Sherpa with ≤ 1 parton included in the matrix element. The dedicated kfactor is calculated for Sherpa comparing to MCFM generator at truth level. However the
MCFM is unstable in the region mγ ∗ < 0.5 GeV, the k-factor is calculated above mγ ∗ > 0.5
GeV (and up to 7 GeV). The mγ ∗ dependent k-factor is shown in Figure 7.5.

Figure 7.5: Invariant mass of the γ ∗ for Sherpa W γ ∗ and Zγ ∗ comparing to the MCFM
in the region 0.5 < mγ ∗ < 7 GeV (W γ ∗ ) and 0.5 < mγ ∗ < 4 GeV (Zγ ∗ ) after dilepton
selection. The ratio plots below show the resulting k-factors that are independent of mγ ∗ .
The resulting k-factor is 0.94±0.07. In addition to the k-factor, jet bin dependent correction
factors are calculated for normalization, which are summarized in Table 7.3.
Table 7.3: The jet bin dependent correction factors, C, applied to the W γ ∗ sample, andmultiplied by the k-factor. Relative scale uncertainties are shown.
Njets
0
1
≥2

C
0.905 ± 6.5%
1.09 ± 30%
1.95 ± 26%

k-factor × C
0.854 ± 9.9%
1.03 ± 31%
1.84 ± 27%

The W γ ∗ background is validated in a dedicated validation region (VR), which is discussed
in Appendix C.
Zγ ∗ /ZZ backgrounds
The Zγ ∗ /ZZ processes lead to the same final state. These processes are each definedby separating in mℓℓ at 4 GeV, high mass sample is called ZZ process and low mass sample
is called Zγ ∗ process. The ZZ background is generated by Powheg and Zγ ∗ background189

7.2 Modeling of Same Sign Backgrounds

is generated by Sherpa with ≤ 1 parton included in the matrix element. Similar to W γ ∗ ,the dedicated k-factor is calculated for Sherpa comparing to the MCFM generator at truthlevel. The mγ ∗ dependent k-factor is also shown in Figure 7.5. The resulting k-factor is
0.88 ± 0.048. This background is only ∼ 1% contribution in the SS CR, but Zγ ∗ is more
important when deriving fake factor for the W +jets background using the Z+jets sample(see Chapter 6).

7.2.2

Conversion Modeling

The W γ background may not be accurately modeled in simulation, since this backgroundarises from conversion (photon faking electron). A dedicated validation region, Zγ validation region (VR), is defined to investigate the modeling of the conversion. The Zγ validation
region is composed of the events with Z → µµ in association with final state photon radiation. Instead of reconstructed photons, reconstructed electrons are used for the Z → µµγ
reconstruction. Correlation of invariant mass between mµµe and mµµ is shown in Figure 7.6(left).

180

102

EventsM µ µ γ [ GeV]

M µµ VS M µµγ
200

1400
1200

s = 8 TeV, ∫ Ldt = 20.7 fb-1
H→WW*→lν lν

160

1000

140

SM (stat)

Data
WW
ZZ
Wγ

WZ
Zγ
*

Wγ
Single Top
W+jet

*

Z/ γ
ggF [125 GeV]

800

120

600
10

100

400

80

40
20
0

0

20

40

60

80

100

120

140

160 180 200
M µ µ [GeV]1

Data / SM200

MllvsMllg_0
Entries
7617
Mean x
66.16
Mean y
114.1
RMS x
22.73
RMS y
34.32

60

1.4
1.2
1
0.8
0.6
0

0.5

1

1.5

2

2.5

3

TightBit

Figure 7.6: Correlation of invariant mass between mµµγ (x-axis) and mµµ (y-axis).
A cut of |mµµe − mz | < 15 GeV is imposed to reduce W γ ∗ /W Z backgrounds as well
as Z → µµ+jet background, where a jet is misidentified as an identified electron, but toenhance converted electrons, which results in ∼ 90% purity of Zγ VR. To further increase
the purity of the Zγ events, the electrons are classifed into three regions using b-layer andconversion flag requirements in the electron identification as :- Tight Bit 0 : fail both b-layer and conversion flag requirements,- Tight Bit 1 : fail either b-layer or conversion flag requirement,- Tight Bit 2 : pass both b-layer and conversion flag requirements,
where “Tight Bit 2” is identical to the electron used in the standard analysis. Only electrons
that satisfy “Tight Bit 0” are used as Zγ VR, which is almost 100% pure with the Z → µµγ

1907.3 Modeling of Same Sign Backgrounds

100

SM (stat)

Data
WW
ZZ
Wγ

s = 8 TeV, ∫ Ldt = 20.7 fb-1
H→WW*→lν lν

WZ
Zγ
*

*

Z/ γ
ggF [125 GeV]80

WγSingle Top
W+jet

Events / 0.2

120

120
100

60

60

40

40

20

20

1.4
1.2
1
0.8
0.6
10

s = 8 TeV, ∫ Ldt = 20.7 fb-1
H→WW*→lν lνSM (stat)

Data
WW
ZZ
Wγ

WZ
Zγ
*

Wγ
Single Top
W+jet

*

Z/ γ
ggF [125 GeV]80

Data / SM

Data / SM

Events / 2 GeV

events as shown in Figure 7.6 (right). Figure 7.7 shows electron pT and η distribution in
Zγ VR.

20

30

40

50

60

70

p

T,electron

80

1.4
1.2
1
0.8
0.6
-3

-2

-1

0

1

2

3
η

[GeV]

electron

Figure 7.7: Kinematic distributions in the Zγ VR : electron pT distribution (left) and η
distribution (right). A mis-modeling depends on electron pT rather than electron η.

A mis-modeling on the conversion depends on electron pT rather than η, thus the systematic uncertainty is derived as a function of electron pT . The conversion systematic uncertainties are summarized in Table 7.4, which includes the agreement of data/simulationfor other “Tight Bit” regions, but the numbers in the “Tight Bit 0” row are taken as the
final systematics, since the contamination of ZZ background is about 40% in the “Tight
Bit 2”. The resulting systematic uncertainties vary 5-25% as a function of pT .

Table 7.4: Comparison of normalization factor (data/simulation) as a function of electron
pT in the Zγ enriched region. Only statistical uncertainty is displayed. The systematic
uncertainty due to the conversion mis-modeling is taken from the numbers in the “Tight
Bit 0”(Zγ VR).
Tight Bit
Tight Bit 2 (pass both)Tight Bit 1 (fail b-layer)
Tight Bit 1 (fail conversion flag)
Tight Bit 0 (fail both)

10-15
1.35 ± 0.19 (stat)0.90 ± 0.26 (stat)0.66 ± 0.12 (stat)0.75 ± 0.07 (stat)15-20
1.13 ± 0.19 (stat)
1.13 ± 0.26 (stat)0.72 ± 0.15 (stat)0.82 ± 0.07 (stat)201.09 ± 0.12 (stat)
1.11 ± 0.13 (stat)0.64 ± 0.06 (stat)0.95 ± 0.03 (stat)7.3 Modeling of Same Sign Backgrounds

7.3

191

W +jets Correlation Model

Since the W +jets contamination in the SS region is 30 % for both 0-jet and 1-jet channels,
it is essential to subtract the contamination correctly when the non-W W dibosons (V V ) arenormalized in the SS region. As discussed in Chapter 6, the W +jets prediction in SS region
diﬀers from the prediction in signal region (OS) due to the diﬀerent flavor composition.
Some compositions should be common between SS and OS, and the others should be uniquein OS, since any SS events arise from quark charge flip or gluon splitting. As an example,
the flavor composition of electron fake and muon fake is illustrated in Figure 7.8.

Figure 7.8: Schematic comparison of the flavor composition. The left figure shows theflavor composition in each sample (OS, SS, and OS-SS) for electrons. The right figure
shows the same for muons. The correlated uncertainties are computed by taking the ratio
SS /N OS ) using numbers in Tables B.5 and B.6of number of denominators (NdendenFrom Figure 7.8, it is found that the unique component is mainly from W +charm andW +light for electrons, and is mostly from W +charm for muons. It is well justified that every
processes appearing in SS has OS counterpart, but some fraction of OS is unique becauseof the OS/SS asymmetry caused by W +charm process etc. ( See Section B.2 ) The SS
events can be therefore considered as correlated component, whereas the unique component(i.e. OS-SS component) can be considered as uncorrelated component between OS and SS.
The uncertainty on the W +jets backgroud should be also separated into correlated anduncorrelated uncertainties. The relationship of correlated and uncorrelated components, or
the relationship of correlated and uncorrelated uncertainties, can be give by :
2
OS 2
OS
OS 2
σOS
= ∆(OS/Z)2 = ρ2 · (σcorr) + (σuncorr)2 + (σstat
) ,

(7.1)

2
SS 2
SS 2
σSS
= ∆(SS/Z)2 = (σcorr) + (σstat
) ,

(7.2)

192

7.3 Modeling of Same Sign Backgrounds

where ∆(OS/Z) and ∆(SS/Z) are uncertainties on the correction factors, OS/Z and SS/Z
(see Section 6.5), and where ρ, σcorr , and σuncorr are the fraction of correlated component,
the correlated uncertainty, and the uncorrelated uncertainty, respectively. What is needed
as an additional input is the ρ parameter that can be computed by taking the ratio of the
SS /N OS . The denominator ratio can be a good representation
number of denominators, Nden
denof the ρ. This approach can be simply justified by Equations below :f OS = f SS ·

OS−SS
SS
Nden
OS-SS Nden
+
f
·
.
OS
OS
Nden
Nden

(7.3)

The three superscripts, “OS”, “SS”, and “OS-SS”, can be replaced with “total”, “corr”,
and “uncorr”, respectively in this model. The Equation above can be then rewritten as
follows :corr
Nden
N uncorrf total = f corr · total+ f uncorr · den
(7.4)
total
Nden
Nden
The computed ρ is 0.48 for electrons and is 0.38 for muons. Also the resulting correlated
and uncorrelated uncertainties, σcorr and σuncorr , are summarized in Table 7.5. Note thatthe statistical uncertainty on the flavor composition is eventually added in quadrature to
the uncorrelated uncertainty.
Table 7.5:
Corrections factors and corresponding systematic uncertainties. Alpgen+Pythia6 is used to derive the central value and the systematic uncertainty is evaluated by comparing with other generators. The systematic uncertainty covers the diﬀerencesamong generators. In the second row the systematic on the OS correction factor is shown
splitting into the systematic components that are correlated and uncorrelated with the SS
correction factor systematic and the part. (Further study is found in Appendix C.1.)

electrons
muons

OS
incl.
fW
+jets /fZ+jets
0.99 ± 0.05 (stat) ± 0.19 (syst)± 0.11 (corr) ± 0.16 (uncorr)
1.00 ± 0.08 (stat) ± 0.21 (syst)± 0.13 (corr) ± 0.17 (uncorr)

SS
incl.
fW
+jets /fZ+jets
1.25 ± 0.08 (stat) ± 0.30 (syst)

1.40 ± 0.14 (stat) ± 0.47 (syst)

The calculated uncertainties are treated as separated nuisance parameters in the simultaneous fit. In this case, the correlated uncertainty on OS W +jets background (SR) can
be constrained by the SS W +jets background. In other word a part of the W +jets systematics is canceled because the W +jet background is determined in the SS region, while theother uncertainties are left because all the other uncertainties such as EW contamination,
statistical uncertainty etc are treated as fully correlated between OS and SS. Similarly the
improvement on the V V background is not expected to be large (only statistical improvement), since all the uncertainties are fully correlated between OS and SS. Therefore the SS
CR improves the W +jets systematics rather than V V systematics. The procedure of thestatistical analysis is further discussed in next Chapter 8.

Part III

Result and Conclusion

193Chapter 8

Results
8.1

Signal Extraction

8.1.1

ggF 0-1 jet Signal Region

For the signal extraction the transverse mass of dilepton system mT is used as final discriminant:√ℓℓ + E miss )2 − |pℓℓ + E miss |2 ,mT = (ET
(8.1)
T
T
T
√
ℓℓ can be rewritten as E ℓℓ =22where ET|pℓℓ
T
T | + mℓℓ . For the missing transverse energy
miss (and E miss ), track-based pmiss, jetCorr is used because of its higher resolution thanET
T
T
miss and better in the signal separation from backgrounds. Figure 8.1
calorimeter based ET
shows the mT distribution after all selections and before performing the fit (pre-fit) for 0-jet
and 1-jet analyses where all lepton flavors, sub-leading lepton pT bins (psublead
10-15, 15-20,
T
20- GeV), and mℓℓ bins (mℓℓ < 30, mℓℓ > 30 GeV) are combined, and Figures 8.2 and 8.3
are the same distributions for the 0-jet and 1-jet analyses but are split into lepton flavors,
where the Data/SM ratios include signal yields predicted by the Standard Model (µ = 1).
The data excess is observed in both 0-jet and 1-jet mT distributions. More quantitative
discussions introducing the statistical tool are made in Section 8.3.1.

8.1.2

VBF Signal Region

For the signal extraction the BDT score is used as final discriminant. The last bin (highest
score bin) is the most sensitive to the VBF signal, but last three bins are used as the signal
region for the VBF signal extraction. Figure 8.4 shows BDT score before performing thefit (pre-fit) for diﬀerent flavor channel and same flavor channels in the VBF analysis. The
data excess is observed at the high BDT score. More quantitative discussions introducing
the statistical tool are made in Section 8.3.2.

195

196

Events / 10 GeV

8.1 Results
1000
900
800

s = 8 TeV, ∫ Ldt = 20.3 fb

-1

Data

SM (sys ⊕ stat)

WW

Other VV
Single Top
Z/ γ *→ττtt*
Z/ γ →ll
W+jet

H→WW*→lν lν + 0 jets

700

QCD
H [125 GeV]

600
500
400
300
200

Data / SM

100
1.4
1.2
1
0.8
0.6
50

100

150

200

250

300

Events / 10 GeV[GeV]
mtrack-clj
T

400
350
300

s = 8 TeV, ∫ Ldt = 20.3 fb
H→WW*→lν lν + 1 jet

-1

Data

SM (sys ⊕ stat)

WW

Other VV
Single Top
Z/ γ *→ττtt*
Z/ γ →ll
W+jet

250

QCD
H [125 GeV]

200
150
100

Data / SM

50
1.4
1.2
1
0.8
0.6
50

100

150

200

250

300

[GeV]
mtrack-clj
T

Figure 8.1: mT distribution for all flavor channels (eµ+µe+ee+µµ) combined for the 0-jet
analysis (top) and 1-jet analysis (bottom) after all selections and before performing thefit (pre-fit). The Data/SM ratio includes signal yields predicted by the Standard Model(µ = 1). The yellow band includes both statistical and systematic uncertainties.

197

140
120

s = 8 TeV, ∫ Ldt = 20.3 fb-1
H→WW*→eν eν + 0 jets

Data

SM (sys ⊕ stat)

WW

Other VV
Single Top
Z/ γ *→ττtt*
Z/ γ →ll
W+jet

100

Events / 10 GeV

Events / 10 GeV

8.1 Results

QCD
H [125 GeV]

80

300
s = 8 TeV, ∫ Ldt = 20.3 fb-1

250

H→WW*→µν µν + 0 jets

Data

SM (sys ⊕ stat)

WW

Other VV
Single Top
Z/ γ *→ττtt*
Z/ γ →ll
W+jet

200

QCD
H [125 GeV]

150

60
100
40
50

Data / SM

Data / SM

20
1.4
1.2
1
0.8
0.6
50

100

150

200

250

1.4
1.2
1
0.8
0.6

300

50

100

150

200

400
350
300

s = 8 TeV, ∫ Ldt = 20.3 fb-1
H→WW*→eν µν + 0 jets

Data

SM (sys ⊕ stat)

WW

Other VV
Single Top
Z/ γ *→ττtt*
Z/ γ →ll
W+jet

250

QCD
H [125 GeV]

250

300

[GeV]
mtrack-clj
T

Events / 10 GeV

Events / 10 GeV[GeV]
mtrack-clj
T

200

300
s = 8 TeV, ∫ Ldt = 20.3 fb-1

250

H→WW*→µν eν + 0 jets

Data

SM (sys ⊕ stat)

WW

Other VV
Single Top
Z/ γ *→ττtt*
Z/ γ →ll
W+jet

200

QCD
H [125 GeV]

150

150

100

100
50

Data / SM

Data / SM

50
1.4
1.2
1
0.8
0.6
50

100

150

200

250

300

[GeV]
mtrack-clj
T

1.4
1.2
1
0.8
0.6
50

100

150

200

250

300

[GeV]
mtrack-clj
T

Figure 8.2: mT distribution for all flavor channels (ee, µµ, eµ, µe) for the 0-jet analysis
after all selections and before performing the fit (pre-fit). The Data/SM ratio includes
signal yields predicted by the Standard Model (µ = 1). The yellow band includes both
statistical and systematic uncertainties.

198

60
s = 8 TeV, ∫ Ldt = 20.3 fb-1

50

H→WW*→eν eν + 1 jet

Data

SM (sys ⊕ stat)

WW

Other VV
Single Top
Z/ γ *→ττtt*
Z/ γ →ll
W+jet

40

Events / 10 GeV

Events / 10 GeV

8.1 Results

QCD
H [125 GeV]

80
70
60

s = 8 TeV, ∫ Ldt = 20.3 fb-1
H→WW*→µν µν + 1 jet

Data

SM (sys ⊕ stat)

WW

Other VV
Single Top
Z/ γ *→ττtt*
Z/ γ →ll
W+jet

50

QCD
H [125 GeV]

40

30

30

20

20
10
Data / SM

Data / SM

10

1.4
1.2
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250

1.4
1.2
1
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300

50

100

150

200

140
120

s = 8 TeV, ∫ Ldt = 20.3 fb-1
H→WW*→eν µν + 1 jet

Data

SM (sys ⊕ stat)

WW

Other VV
Single Top
Z/ γ *→ττtt*
Z/ γ →ll
W+jet

100

QCD
H [125 GeV]

250

300

[GeV]
mtrack-clj
T

Events / 10 GeV

Events / 10 GeV[GeV]
mtrack-clj
T

80

120
s = 8 TeV, ∫ Ldt = 20.3 fb-1

100

H→WW*→µν eν + 1 jet

Data

SM (sys ⊕ stat)

WW

Other VV
Single Top
Z/ γ *→ττtt*
Z/ γ →ll
W+jet

80

QCD
H [125 GeV]

60

60
40
40
20

Data / SM

Data / SM

20
1.4
1.2
1
0.8
0.6
50

100

150

200

250

300

[GeV]
mtrack-clj
T

1.4
1.2
1
0.8
0.6
50

100

150

200

250

300

[GeV]
mtrack-clj
T

Figure 8.3: mT distribution for all flavor channels (ee, µµ, eµ, µe) for the 1-jet analysis
after all selections and before performing the fit (pre-fit). The Data/SM ratio includes
signal yields predicted by the Standard Model (µ = 1). The yellow band includes both
statistical and systematic uncertainties.

199

Events / 0.5

8.1 Results

100
90
80

s = 8 TeV, ∫ Ldt = 20.3 fb-1
H→WW*→eν eν / µν µν

70

Data

SM (sys ⊕ stat)WW
tt
Z/ γ *→ll

Other VV
Single top
Z/ γ *→ττ

W+jet

ggF

VBF

60
50
40
30
20

Data / SM

10
1.4
1.2
1
0.8
0.6
-1 -0.8 -0.6 -0.4 -0.20

0.2 0.4

0.6 0.8

1

Events / 0.5

BDT

70
60

s = 8 TeV, ∫ Ldt = 20.3 fb-1

H→WW*→eν µν / µν eν

50

Data

SM (sys ⊕ stat)WW
tt
Z/ γ *→ll

Other VV
Single top
Z/ γ *→ττ

W+jet

ggF

VBF

40
30
20

Data / SM

10

1.4
1.2
1
0.8
0.6
-1 -0.8 -0.6 -0.4 -0.20

0.2 0.4

0.6 0.8

1

BDT

Figure 8.4: BDT score for diﬀerent flavor channel (top) and same flavor channel (bottom)
after all selections and before performing the fit (pre-fit). The Data/SM ratio includes
signal yields predicted by the Standard Model (µ = 1). The yellow band includes only
statistical uncertainty, and no systematic uncertainty is displayed.

200

8.2 Results

8.2

Fitting Procedure

8.2.1

Profile Likelihood

In the ggF analysis, each mT distribution is firstly remapped to give a flat signal distribution
across the full 0 < mT < ∞ range where the mT distribution is binned into 10 bins for the
0-jet analysis and into 6 bins for the 1-jet analysis. The remapping is motivated by the wide
variation of signal and background shapes in the various signal region. For example, theV V backgrounds typically populate lower mT , while the top and W W background entersat high mT . In the VBF analysis, the highest 3 bins in the BDT score are used instead ofthe mT distribution where no remapping is made.
The statistical analysis is performed using the likelihood function. The likelihood function condenses all details of the analysis into a single equation from the minimal set of
information required to describe the analysis. A likelihood is constructed using the strengthparameters. Both signals and backgrounds are equally parametrized in the likelihood as:

exp
L(µ, µb ) = P (N |µs + µb bexp
SR ) × P (M |µb bCR ),

(8.2)

exp
where bexp
SR and bCR are expected background yields in the signal and control region predicted
in simulation, and where µ and µb are the signal and background strength parameter, and
M and N represent measured yield in signal region and control region. The expected signal
and background yields can be allowed to vary within the relevant systematic uncertainties
when introducing nuisance parameters θ. The nuisance parameters represent systematic
uncertainties, and they are constrained by the probability density functions N (θ̃|θ) (e.g.
Gaussian, and Poisson), where θ̃ represents an auxiliary measurement related to the nuisance parameter θ.

Expanding this simple likelihood to the complete form used in the analysis, a product over lepton flavors and jet multiplicity is explicitly written. Furthermore a productover the bins of final discriminant (mT bins for the ggF and BDT bins for the VBF) isalso present. The strength parameters µb are applied to the W W , V V , and diﬀerent flavor
Z/DY → τ τ and same flavor Z/γ ∗ →ee/µµ backgrounds in the 0-jet and 1-jet analyses, aswell as the top background in the 1-jet and 2-jet analyses. The other backgrounds which
do not have floating strength parameters, for instance, data-driven W +jets/QCD estimates
are added to the Poisson expectations. The full likelihood can be written as:

201

8.2 Results

Nlep NpT Nmℓℓ Njet Nbin

⃗ ={L(µ, θ)∏ ∏ ∏ ∏ ∏
i

j

k

l

P (Nijklm |µsSR
ijklm +

m

Nlep Njet NCR

×{

∏∏ ∏
o

Nθ
∏

×{

p

Nbg
∑

µb bSR
ijklmn )}

n
Nbg−1

CR
P (Mopq |µsCR
opq + (µb )q bopq +

q

∑

bCR
opqr )}(8.3)

r

N (θ˜s |θs )},swhere Nlep is the number of lepton flavors (ee, µµ, eµ, µe), NpT the number of sub-leading
lepton pT (10-15,15-20,20-) bins, Nmℓℓ the number of mℓℓ bins (mℓℓ <30, mℓℓ >30), Njet the
number of jet multiplicity, Nbin the number of bins in final discriminant, NCR the numberof control regions (W W , V V , top, Z/γ ∗ → τ τ , and Z/γ ∗ → ℓℓ), Nθ the number of nuisance parameters, and Nbg the number of types of backgrounds (W W , top, W +jets, V V ,Z/γ ∗ → τ τ , Z/γ ∗ → ℓℓ, etc) where “bg-1” in the second term indicates that it does notinclude the background itself being considered. s denotes the Higgs signal and b denotes the
background. sSR and sCR (or bSR∑and bCR ) are used according to the region being considered. µb does not appear in the Nbg−1 term since only the background being consideredis scaled in its control region. The product over mℓℓ and sub-leading lepton pT is explicitly
written out to emphasize the 3D fit (bins of sub-leading lepton pT ⊗ mℓℓ ⊗ mT ) used in
the 0-1 jet diﬀerent flavor analysis. The signal contamination in the control region is also
taken into account in this formalization. Since the signal (µ) is also treated as a floating
parameter, the change in signal yield can aﬀect µb .
The signal and background expectations are functions of the nuisance parameters. These
functions are parametrized such that the response of s and b to∏each θ is factorized∏
from thenominal value of the expected rate, s0 (or b0 ) namely s = s0 ×
ν(θ) (or b = b0 ×ν(θ)),
where ν(θ) depends on systematic source, type of the ν(θ), that is νstat (θ), νflat (θ), andνshape (θ). The statistical uncertainty is constrained by the Poisson probability given by:

P (θ̃|λ(θ)) =(λ(θ))θ̃exp(−λ(θ)).
θ̃!

(8.4)

For example, an uncertainty σb0 on an expected yield b0 , θ̃ and νstat (θ) are θ̃ = λ = b20 /σb20
and νstat (θ) = θ (b = b0 ·θ). The systematic uncertainties on the W +jets/QCD backgrounds
or theoretical uncertainties on the background normalization, are also constrained by the
Poisson probability. For flat systematics that do not change the mT or BDT shape (e.g.
overall systematics like luminosity, cross sections, etc), ν(θ) takes the form νflat (θ) = κθ ,where κ is determined by measuring µflat at θ = ±1. In this case the θ is constrained by
the Gaussian probability and κθ distributes log-normally. For shape systematics that canpotentially change the mT or BDT shape, the shape variation is firstly separated into a flat

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8.2 Resultscomponent (νflat (θ)) and purely shape component (νshape (θ)), such that varying pure shapecomponent of s or b has no eﬀect on the expected rate. The flat component is treated as aflat systematic uncertainty, and the pure shape component uses vertical linear interpolation
to estimate the variation (e.g. W W shape systematic uncertainty, see Section 5.6.2). The
shape component is distributed as νshape (θ) = 1 + ϵθ, satisfying νshape (θ < −1ϵ ) = 0. ϵ isdetermined by measuring νshape (θ) at θ = ±1 with Gaussian constraint, and the same θis shared between νshape (θ) and νflat (θ). The treatment of each nuisance parameter in thisanalysis is detailed in [176].

8.2.2

Test statistic and p-values

For statistical computations (e.g. compatibility test for data vs background-only or background+signal hypothesis), the profile likelihood ratio test statistic q̃µ is used [177]. First
the profile likelihood ratio is constructed as:ˆ⃗ˆL(µ,θ(µ))
µ̂ ≥ 0, L(µ̂,θ)⃗ˆ
λ̃(µ) =
(8.5)
ˆ

⃗ˆ
L(µ,θ(µ))
µ̂ < 0ˆ⃗ˆL(0,θ(0))

ˆ
ˆ
ˆ
⃗ˆ
⃗ˆ
where µ̂ and θ⃗ are the parameters that maximize the likelihood, and θ(0)and θ(µ)
are theconditional maximum likelihood of θ⃗ given a strength parameter of 0 or µ. Using the profile
likelihood ratio, the test statistic q̃µ is given by:ˆ⃗ˆL(µ,θ(µ))
−2lnµ̂ < 0 ,{ˆL(0,θ̂(0))−2 ln λ̃(µ) µ̂ ≤ µ
ˆ
q̃µ =
=
(8.6)
⃗ˆ

0 ≤ µ̂ ≤ µ ,−2 ln L(µ,θ(µ))
0µ̂ > µˆ⃗L(µ̂,θ)0µ̂ > µ .
The modified frequentist method CLs is used to compute 95% confidence intervals on thesignal strength parameter µ. In this case the test statistic is one sided with the constraint
0 < µ̂ < µ. The test statistic q̃µ can be computed for θ̂µ (or θ̂0 ) that maximizes thelikelihood for background+signal (or background-only) hypothesis. The p-value pµ (or pb )is derived from the sampling distribution f (q̃µ |µ, θ̂µ ) (or f (q̃µ |0, θ̂0 )) given by:
∫ ∞
pµ =

f (q̃µ |µ, θ̂µ )dq̃µq̃µ,obs∫ q̃µ,obs

pb =∞f (q̃µ |0, θ̂0 )dq̃µ

(8.7)
(8.8)

CLs is then constructed as the ratio of p-values, CLs = pµ /1 − pb . The 95% CL upper limiton µ is the solution to CLs = 0.05. For computing statistical significance, the backgroundonly p-value is computed from the test statistic q0 , with a diﬀerent constraint µ̂ > 0:

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8.2 Results

∫ ∞
p0 =

f (q0 |0, θ̂0 )dq0

(8.9)

q0,obs

One can extract the statistical significance Z from p0 by translating from the gaussian tailprobability Z = Φ−1 (1 − p0 ), where Φ−1 is the quantile of the standard Gaussian. Asymptotic formulae are employed to approximate the sampling distributions. This procedure iscovered in [178].

8.2.3

Normalization Factors

As a validation of the fitting for this analysis, comparisons of the background normalization
factors (NF) are made between pre-fit and post-fit, namely before and after the fit. Table 8.1
shows the post-fit NFs comparing to the pre-fit NFs. The post-fit NFs are compatible withthe pre-fit NFs within the uncertainty. The large uncertainty on the W W 1-jet NF is dueto the large subtraction of top background. Similarly the large uncertainty on the V V 0-jet
and V V 1-jet NFs are due to the large subtraction of the W +jets background. The W +jets
systematics (20-60%) are propagated to the uncertainties on the V V NFs.
Table 8.1: Comparison of the Normalization factors (NF) before and after the fitting.
NF

pre-fitpost-fit

W W 0-jet

1.22±0.10

1.22

W W 1-jet

1.06±0.23

1.11

top 0-jet

1.08±0.08

1.02

top 1-jet

1.04±0.07

1.03

Z/γ ∗ → τ τ 0-jet

1.00±0.02

0.99

Z/γ ∗ → τ τ 1-jet

1.06±0.04

1.05

V V 0-jet

0.92±0.18

0.99

V V 1-jet

0.96±0.25

0.88

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8.3 Results

8.3

Results

8.3.1

ggF 0-1 jet Result

Statistical tests for the ggF 0-1 jet analysis are performed. Figure 8.5 shows p0 curve. The
p0 is the given probability for the background-only scenario. The solid curve is observed p0
and the dashed curve is expected p0 in the presence of the SM Higgs boson with a givenmH , where the cross section is normalized to the Standard Model cross section. In caseof no signal, the solid line should fluctuates around 0σ line. The observed significance at
mH = 125 GeV is 4.61 σ (4.25 σ expected). The excess of events is quantified as signal
strength µ. Figure 8.5 also shows signal strenth as a function of mH .

Figure 8.5: Results of p0 significance (left) and signal strength µ (right) for the ggF 0-1
jet analysis. (Left) The solid line represents observed significance as a function of mH .
The dashed line represents expected significance for a given mH . (Right) The solid line
represents observed signal strength µ and shaded cyan band represents 1σ error band.
The observed µ value for mH = 125 GeV is:
+0.32
+0.20
+0.24
µobs
0−1jet = 1.14−0.27 = 1.14−0.20 (stat.) −0.19 (syst.),(8.10)

where the measurement with an accuracy of ∼ 30% is achieved. The uncertainties on thesignal strength are categorized and listed in Table 8.2. The leading uncertainties are thestatistical uncertainty on the signal region and the uncertainty on the signal yield andacceptance. The uncertainties on the backgrounds and objects are dominated by the W W
extrapolation, the W +jets systematics, and the Z/γ ∗ → ℓℓ systematics for same flavor
analysis.

8.3.2

VBF Result

Statistical tests for the VBF signal are performed by taking into account the ggF signal asa part of background. Figure 8.6 shows p0 curve and signal strength µ as a function of mH .
The observed significance at mH = 125 GeV is 4.08. σ (2.92 σ expected).

205

8.3 Results

Table 8.2: Leading uncertainties on the signal strength µ for the ggF 0-1 jet analysis.
The statistical uncertainties on the control regions are included in the each backgroundsystematic uncertainty.
Category

SourceUncertainty, up (%)

Uncertainty, down (%)

Statistical

Signal region statistics

+13

−13

Theoretical

Signal yield and acceptance

+14

−11

Theoretical

W W extrapolation

+11

−11

Experimental

W +jets systematics+7−7

Theo./Exp.

Z/γ ∗ → ℓℓ systematics+6−6

Theo./Exp.

V V systematics+4−4

Experimental

Luminosity+4−3

OthersOther bkg. and object

+7

−6

+28

−24

Total

Figure 8.6: Results of p0 significance (left) and signal strength µ (right) for the VBF
analysis. (Left) The solid line represents observed significance as a function of mH . The
dashed line represents expected significance for a given mH . (Right) The solid line represents
observed signal strength µ and shaded cyan band represents 1σ error band.
The observed µ value for mH = 125 GeV is:
+0.63
+0.53
+0.35
µobs
VBF = 1.58−0.53 = 1.58−0.53 (stat.) −0.30 (syst.),(8.11)

206

8.3 Results

where the measurement with an accuracy of ∼ 40% is achieved. The uncertainties on thesignal strength are categorized and listed in Table 8.3. The total uncertainty is dominatedby the statistical uncertainty on the signal region.
Table 8.3: Leading uncertainties on the signal strength µ for the VBF analysis.
Category

SourceUncertainty, up (%)

Uncertainty, down (%)

Statistical

Signal region statistics

+30

−30

StatisticalControl region statistics

+17

−16

Theoretical

Signal yield and acceptance

+15

−09

OthersOther bkg. and object (e.g. JES/JER)

+17

−17

+41

−39

Total

8.3.3

Combined Result

Statistical tests for the combined analysis including 2011 and 2012 ggF 2-jet analyses, areperformed. Figure 8.7 shows p0 curve and signal strength µ as a function of mH . The
observed significance at mH = 125 GeV is 5.81 σ (5.51 σ expected). The observed µ value
for mH = 125 GeV is:
+0.24
+0.16
+0.18
µobs
Comb = 1.15−0.22 = 1.15−0.16 (stat.) −0.15 (syst.).

(8.12)

Figure 8.7: p0 significance (left) and signal strength µ (right) for the combination. The
red solid line represents expected p0 and signal strength assuming the SM Higgs boson witha mass of mH = 125 GeV.

8.3 Results

8.3.4

207

Signal Profiling

The measurement of the signal strengths for combined analysis do not give direct information on the relative contributions of the diﬀerent production mechanism. Furthermore
fixing the ratios of the production cross sections for the various processes to the values
predicted by the Standard Model may conceal diﬀerences between data and theoreticalpredictions, therefore the signal strengths of diﬀerent production processes contributing to
the H→ W W ∗ decay channel are determined by profiling signals for individual production
processes. Two signal strength parameters, µggF and µVBF+VH = µVBF = µVH , are introduced where the H→ W W ∗ → ℓνℓν decay branching fraction is fixed to the nominal value
and is treated as common parameter, and cross section ratio (σVBF /σVH ) is still fixed to thevalues predicted by the Standard Model. This should be reasonable approach as both the
VH and VBF production processes are similar. The eﬀect of the fixed ratios is negligibly
small since the contamination of the VH process to the ggF or VBF signal region is lessthan 1%. The two parameters scale the theoretical prediction to those observed for a givenmH (here mH is fixed to be 125 GeV). Figure 8.8 shows likelihood contours in the µggF andµVBF+VH plane for mH = 125 GeV.

Figure 8.8: Likelihood contours in the µggF and µVBF+VH plane for mH = 125 GeV.
The best-fit values to data and the 68% (solid) and 95% CL (dotted), as well as the SM
prediction (1,1) are explicitly shown.
The best-fit µ values for mH = 125 GeV are:

208

8.3 Results

+0.23
+0.18
µggF = 1.15+0.30−0.26 = 1.15−0.18 (stat.)−0.19 (syst.),
+0.45
+0.32
µVBF+VH = 1.36+0.55−0.47 = 1.36−0.41 (stat.)−0.24 (syst.).

(8.13)

Here one may realize the fact that the best-fit value of µComb is the same as µggF . For theµComb , both ggF and VBF signals are treated as the same signal, whereas for the µggF they
are treated independently in the fit. In other words the fit model is diﬀerent between thetwo cases, thus it does not make sense to consider the relation between the two.
The signal strength ratio (µVBF+VH /µggF ) can be also a good observable due to thefact that there is no assumption made on the Higgs boson branching ratio, so the ratio
gives direct information about the ratio of the Higgs production cross section. The best-fit
ratio for mH = 125 GeV is calculated as:
+0.43
+0.36
µVBF+VH /µggF = 1.18+0.56−0.49 = 1.18−0.40 (stat.)−0.28 (syst.).

8.3.5(8.14)

Coupling Fits

In the measurements of the signal strength µ, the production and decay modes cannot betreated independently [179, 180]. However it is possible to deal with both production anddecay modes more consistently in leading order (LO) [56] based on the following assumptions.
- The signals observed in the diﬀerent search channels originate from a single narrow
resonance with a mass of 125 GeV. The case of several, possibly overlapping, resonances in this mass region is not considered.
- The width of the assumed Higgs boson near 125 GeV is neglected, i.e. the zerowidth approximation is used. Hence the product σ × BR(X → H → V V ) can be
decomposed in the following way for all channels including fermion channels:
σ × BR(X → H → V V ) =σ X · ΓV V,
ΓH

(8.15)

where σX , ΓV V , and ΓH represent the production cross section through the initialstate X, the partial decay width into the final state V V , and the total width of the
Higgs boson.
- Only the Standard Model particles contributes to the total decay width, namely the
BSM contributions are not considered.
- Only modifications of couplings strengths, i.e. of absolute values of couplings, aretaken into account, while the tensor structure of the couplings is assumed to be thesame as in the Standard Model, in other words, the Higgs boson is assumed to be a
CP-even scalar as in the Standard Model. This assumption has been tested [18, 181]by the ATLAS and CMS experiments.

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8.3 Results

The LO-motivated coupling scale factors κj are defined in a way that the cross section σjand the partial width Γj (associated with the Standard Model particle j) scale with thefactor κ2j when compared to the corresponding SM prediction [56, 179]. For example one
can consider the case of gg → H → W W :σ × BR(gg → H → W W ) = σSM (gg → H) · BRSM (H → W W ) ·κ2g · κ2W.
κ2H

(8.16)In the fits the eﬀective scale factor κg for gg → H process can be decomposed into more
fundamental coupling scale factors κt and κb , since the ggF produces the Higgs boson
through t-quark or b-quark loop:

κ2g =

tt
tb
bb
+ κ2t · σggH
κ2t · σggH
+ κt κb · σggH
tt
tb
bb
σggH
+ σggH+ σggH,(8.17)= 1.06 · κ2t − 0.07 · κt κb + 0.01 · κ2b .
where interference term κt κb is explicitly included. Similarly the VBF cross section can be
expressed as:
W W + κ2 · σ ZZ
κ2 · σVBFZVBF
κ2VBF = W W,
W + σ ZZ
σVBF
VBF

(8.18)=0.74 · κ2W + 0.26 · κ2Z .
Also the total decay width scale factor κH is expressed as:

κ2H =

∑

kj2 ΓSM
jj
ΓSM
H

,

jj=W W,ZZ,bb̄,···= 0.57 · κ2b + 0.22 · κ2W + 0.09 · κ2g + 0.06 · κ2τ + 0.03 · κ2Z + 0.03 · κ2c .

(8.19)

A simplification made by assuming common coupling scale factors κF for all fermions andκV for all vector boson as:κF = κt = κb = κτ = κg ,
κV = κW = κZ .

(8.20)As only Standard Model particles are considered in this model, the ggF process depends
directly on the fermion scale factor κ2F . Using this simplification the Equation 8.16 can be
rewritten as:
σ × BR(gg → H → W W ) ∼κ2F · κ2V.
0.75 · κ2F + 0.25 · κ2V(8.21)

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8.3 Results

Similarly the VBF production mode is written as:
σ × BR(qq ′ → qq ′ H → W W ) ∼κ2V · κ2V.
0.75 · κ2F + 0.25 · κ2V(8.22)

Figure 8.9 shows the correlation of the coupling scale factors κF and κV .

Figure 8.9: Likelihood contours in the κV and κF plane for mH = 125 GeV. The best-fit
values to data and the 68% (solid) and 95% CL (dotted), as well as the SM prediction (1,1)
are explicitly shown.
The low sensitivity to the high values of κF is due to the functional behavior of the ggF
yield shown in Equation 8.21. The σ × BR(gg → H → W W ) is in fact κF independent inthe κF → ∞. The sensitivity to the high κF is therefore driven by µVBF+VH that rapidly
vanishes in the κF → ∞, due to the increase of the total width (0.75 · κ2F + 0.25 · κ2V ) andthe consequent reduction of the W W branching fraction.
The best-fit values of κV and κF are:
+0.07
+0.08
κV = 1.08+0.11−0.11 = 1.08−0.08 (stat.)−0.07 (syst.),
+0.24
+0.22
κF = 1.00+0.32−0.24 = 1.00−0.18 (stat.)−0.15 (syst.).

(8.23)

Similar to the signal strength ratio, the κF /κV ratio (referred to as λF V in [180]) canbe also a good observable (i.e. no assumption made on the total width). The best-fit value
for mH = 125 GeV is calculated as:

211

8.3 Results

+0.22
+0.23
κF /κV = 0.93+0.31−0.24 = 0.93−0.18 (stat.)−0.15 (syst.).

8.3.6(8.24)

Summary of Observables

In summary, the measured and presented physical quantities related to the Higgs boson
couplings are summarized in Table 8.4. All the observables discussed above are compatible
with the values predicted by the Standard Model.
Table 8.4: Summary of measured physical quantities related to the Higgs couplings: µ, κ,and λ.
Observables

ValuesµggF+0.23
1.15+0.18−0.18 (stat.)−0.19 (syst.) (see Section 8.3.4)µVBF+VH+0.32
1.36+0.41−0.45 (stat.)−0.24 (syst.) (see Section 8.3.4)µVBF+VH /µggF+0.36
1.18+0.43−0.40 (stat.)−0.28 (syst.) (see Section 8.3.4)

κV

+0.08
1.08+0.07−0.08 (stat.)−0.07 (syst.) (see Section 8.3.5)

κF

+0.22
1.00+0.24−0.18 (stat.)−0.15 (syst.) (see Section 8.3.5)

λF V (= κF /κV )+0.22
0.93+0.23−0.18 (stat.)−0.15 (syst.) (see Section 8.3.5)

The observables related to the ggF production process start being limited by the systematic uncertainties, in particular the uncertainties related to the signal yields (e.g. QCD scale
and PDF, as well as the jet-bin-uncertainties) and uncertainties related to the backgroundestimation. However it is still possible to reduce the uncertainty on the W W normalization
with more statistics, and the uncertainty on the W W extrapolation by defining a closer control region to the signal region. Also the W +jets background that is reducible backgroundwill be reduced by tightening the lepton selection. Therefore the increased statistics will
give substantial improvements to the ggF analysis, but even incorporating those improvements the measurement will be again reaching the limit on the signal uncertainty which is∼ 20% in total. The higher order calculation of the signal cross section, especially higher
order QCD correction is thus necessary in the future measurement.
On the other hand, the observables related to the VBF production process are still
dominated by the statistical uncertainty. The impact of the signal uncertainty is relatively
small compared to the ggF analysis due to no QCD vertices in the leading order. Thus theanalysis with the higher statistics obviously improves the measurement (presumably up to∼ 15% due to the uncertainty on the signal) in the future.

212

8.4 Results

8.4

Compatibility of Signal Strength

8.4.1

Comparison of Individual Measurements

Observed Signal Strength µ

The combined signal strength is decomposed into the individual channels to see the compatibility. The individual measurements are summarized in Table 8.5 (observed and expected)
and Figure 8.10 (observed). All the individuals are compatible within their uncertainties.

3.5
3

Combined signal strength

2.5
2
1.5
1
0.5
0
-0.5
-1

201 201 201 201 201 201 201 201 201 201 201 201 201 201 201 201 201 201 201 201 201 201
2 0-j 2 0-j 2 0-j 2 1-j 2 1-j 2 1-j 2 01 2 01 2 01 2 2-j 2 VB 2 VB 2 VB 1 0-j 1 0-j 1 0-j 1 1-j 1 1-j 1 1-j 1 01 1 01 1 01
et
et
et
et
et
et
et
et (D et (S et (D et (D et (S et (D -jet
-je
-je
-je
-je
-je
F
F
F
F)
F)
F+S (DF) t (SF) t (DF+ (DF) (DF) (SF) (DF+S (DF) (SF) (DF+S (DF) (SF) (DF+S t (DF) t (SF) t (DF+F+S F)
F)
SF)
SF)
F)
F)
F)
F)
F)

Figure 8.10: Observed signal strength for individual and combined (band) analyses.
Table 8.5: Observed and expected signal strength for individual analyses: diﬀerent flavor(DF), same flavor (SF), and combined (DF+SF). The central value of the expected signal
strengths are set to be µ = 1 for mH = 125 GeV.
ChannelDF(obs)SF(obs)DF+SF(obs)DF(exp)SF(exp)DF+SF(exp)2012 0-jet

1.41+0.44−0.37

0.22+0.81−0.78

1.27+0.41−0.34

1.00+0.38−0.32

1.00+0.84−0.79

1.00+0.36−0.312012 1-jet

1.21+0.58−0.47

0.37+1.10−1.03

1.04+0.53−0.43

1.00+0.53−0.44

1.00+1.20−1.10

1.00+0.50−0.412012 0-1 jet

1.32+0.34−0.30

0.35+0.62−0.61

1.19+0.32−0.27

1.00+0.30−0.26

1.00+0.66−0.63

1.00+0.28−0.25

2012 2 jet

1.22+0.96
−0.85

-

-

1.00+0.94
−0.85

-

-

2012 VBF

1.25+0.66−0.54

2.52+1.31−1.05

1.58+0.63−0.53

1.00+0.67−0.55

1.00+1.13−0.87

1.00+0.59−0.49

2011 0-jet

0.61+0.71−0.67

1.40+1.40−1.40

0.75+0.69−0.63

1.00+0.76−0.68

1.00+1.36−1.25

1.00+0.70−0.632011 1-jet

2.20+1.50−1.20

0.17+2.00−1.70

1.70+1.30−1.00

1.00+1.17−1.01

1.00+1.89−1.61

1.00+1.04−0.90

2011 0-1 jet

1.00+0.67−0.60

0.89+1.20−1.10

0.99+0.61−0.55

1.00+0.63−0.58

1.00+1.07−1.00

1.00+0.57
−0.53

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8.4 Results

8.4.2

Comparison to Previous Analysis

A comparison of the signal strengths to the previous analysis [3] is made, even though bothanalyses use the same data set recorded in 2011-2012. Table 8.6 shows the comparison of
the signal strength presented in this thesis to the previous one.
Table 8.6: Comparison of signal strengths between the two analyses.
The analysis presented here

Previous analysisµggF

1.15±0.30 (∆µ/µ = 25%)0.82±0.36 (∆µ/µ = 44%)µVBF+VH

1.36±0.55 (∆µ/µ = 40%)1.66±0.79 (∆µ/µ = 47%)

Many improvements are incorporated into this analysis. For example, another 50% of
data is added from trigger/lepton optimization. The individual improvements for the ggF
analysis are summarized in Table 8.7. The total improvement on significance is > 50%.
Table 8.7: List of improvements made for the ggF analysis since previous results. Notethat some of those numbers are outdated.
Improvements

Z (Exp.)∆Z/Zprev. (%)

Previous Results

2.80

-

Increase MC Statistics

2.84

1.3%

Lepton optimization, Add dilepton trigger

3.04

8.5%

Updates on W +jets systematics

3.15

12.5%

miss )→m (pmiss, jetCorr )mT (ET
T T

3.43

22.5%

Doubling the mT bins

3.62

29.2%

Add low psubleadbin (10-15 GeV)
T

3.73

33.2%

Add SS CR method for V V backgrounds

3.87

38.2%

Updated b-tagging eﬃciency

3.93

40.3%

miss optimization
ET

4.23

51.1%

Add ggF 2-jet analysis

4.36

55.7%

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8.4.3

8.4 Results

Comparison to CMS

It is interesting to compare the result with other H→ W W ∗ analysis. The most relevant
way is to compare with the CMS H→ W W ∗ result [182]. Figure 8.11 shows 2-dimensional
contours, “κv versus κf ” and “µggF versus µVBF ”. Table 8.8 shows comparison of theobserved signal strength µ in the CMS to that in the ATLAS. The CMS obtained slightly
lower µ values but both are well agreed within the uncertainty.

Figure 8.11: Likelihood profiles on µggF and µVBF,VH at 68% (solid) and 95% CL (dotted).
The expected (black) and observed (red) distributions for mH = 125.6 GeV are shown.
(This figure is taken from [182].)

Table 8.8:
Comparison of the CMS results to the ATLAS (presented in this thesis):
observed σ/σSM (µ) and significance for each category at mH = 125 GeV. The CMS result
is taken from [182].
Category

σ/σSM (CMS)

exp./obs. (CMS)σ/σSM (ATLAS)

exp./obs. (ATLAS)

ggF Category

0.76+0.21−0.21

5.2/4.0 σ

1.15+0.30−0.26

4.6/5.0 σ

VBF Category

0.62+0.58−0.47

2.1/1.3 σ

1.36+0.55−0.47

2.5/3.4 σChapter 9

Conclusion
On 4th July 2012, the ATLAS and CMS collaborations announced that they had each observed a Higgs boson with a mass of approximately 125 GeV. The discovery opened up a
new era in understanding the nature of electroweak symmetry breaking. The major focus ofphysics analysis at the LHC now is the measurement of the properties of the Higgs boson.
In this thesis, the measurements of the couplings using the H→ W W ∗ → ℓνℓν final state√
are presented with the full Run-I pp collision data corresponding to 20.3 fb−1 of s = 8
TeV and 4.5 fb−1 of 7 TeV, recorded by the ATLAS at the LHC. The H→ W W ∗ → ℓνℓν
channel is sensitive to the coupling measurement through gluon-gluon fusion (ggF) andvector boson fusion (VBF) production processes. The precise measurement is possible onlyin understanding all the Standard Model processes, since the analysis suﬀers from manybackgrounds. The analysis adopted several enhanced techniques on the background estimation to attain a substantially better sensitivity of the measurement.
The result presented in this thesis supersedes the previous measurement in accuracy,
owing to optimizations of selection of physics objects and improvements of the modeling of
backgrounds. The observed excess of the inclusive production for mH = 125 GeV is about 6
σ that is large enough to claim the discovery of the H→ W W ∗ decay, and the corresponding
signal strengths for individual production processes are:+0.23
µggF =1.15+0.18−0.18 (stat.)−0.19 (syst.),+0.32µVBF+VH =1.36+0.41−0.45 (stat.)−0.24 (syst.).

Furthermore the coupling to fermions and weak bosons are each extracted, introducing κFand κV . The measured κV and κF are:
+0.07
+0.08
κV =1.08+0.11−0.11 = 1.08−0.08 (stat.)−0.07 (syst.),
+0.24
+0.22
κF =1.00+0.32−0.24 = 1.00−0.18 (stat.)−0.15 (syst.).

215

216

.0 Conclusion

The measured couplings via these production processes are consistent with the Standard
Model prediction. 1
The observables related to the ggF analysis (e.g. µggF ) start being limited by systematic
uncertainties. However it is still possible to reduce the uncertainty on the W W normalization with more statistics, and the uncertainty on the W W extrapolation by defining acloser control region to the signal region. Also the W +jets background will be reducedby tightening the lepton selection. Therefore the increased statistics will bring substantial improvements. Without having higher order calculation of the QCD correction on thesignal production, the analysis will eventually be reaching the limit on the signal uncertainty which is ∼ 20%. On the other hand, the observables related to the VBF analysis(e.g. µVBF ) is still limited by the statistical uncertainty. Therefore the analysis with thehigher statistics obviously achieves better measurement (presumably up to 15% due to theuncertainty on the signal) in the future.
In the Run II (2015-2018) we expect ∼100 fb−1 of 13-14 TeV data set. This corresponds to 10 times higher statistics of the Higgs boson signal when taking into account theincreased signal production cross section. Therefore it might be interesting to look into
other Higgs production processes and decay modes (e.g. bbH/ttH → bb̄ or γγ). Also it
might be interesting to continue to perform: (1) search for the BSM Higgs boson predictedin the MSSM [183–187] and (2) search for the invisible decay of the Higgs boson [188].

1

The final published numbers may be slightly diﬀerent from the numbers in this thesis.

Appendix A

Additional Materials for
H→ W W ∗→ ℓνℓν Analysis
A.1

ggF 2-jet analysis

A.1.1

Event Selection

The ggF production still present signal yield in 2-jet bin. A dedicated selection for the 2-jet
analysis based on the events orthogonal to the VBF and VH analyses is required. Since
the contribution from same flavor channel is tiny, only diﬀerent flavor (eµ+µe) channel isconsidered. The selection of events satisfying the preselection and containing at least two
selected jets is similar to the 0-1 jet analysis. In addition to the preselection described in
Section 5.4.1, the followings are required:
jetCorr• pmiss,> 20 GeVT• b-jet veto (see Section 5.4.2)• Z → τ τ veto (see Section 5.4.2)• Non-VBF(VH) selection:- VBF cut-based veto: fail of either ∆Yjj > 3.6, mjj > 600 GeV, CJV or OLV,
- VBF BDT veto: fail of either CJV, OLV or BDT score > −0.48,- VH veto: fail of either ∆yjj < 1.2 or |mjj − 85 GeV| < 15 GeV,
• The event must pass the same cuts on mℓℓ and ∆ϕℓℓ as well as 0-jet analysis.
The selection must be orthogonal to other analyses since the priority of VBF (and VH) is
high. Table A.1 shows fraction for each Higgs production after all signal region criteria. As
can be seen in this table, the contribution from other production modes (VBF and VH) is 25% even after VBF and VH veto applied. Table A.2 shows expected signal and backgroundcounts for the 2-jet analysis.
217

A.1 Additional Materials for H→ W W ∗ → ℓνℓν Analysis

218

Table A.1: The expected number of events and fraction for each production mode (ggF,
VBF and VH) after all signal region selection criteria.
Production process
Number of events
Signal composition [%]ggF
34.04 ± 0.25
74.9

VBF
6.88 ± 0.11
15.1

VH
4.53 ± 0.29
10.0

Table A.2: The expected number of signal and background counts for the 2-jet analysis.
Missing ET
at least two jets
b-jet vetoZ → τ τ veto
Non-VBF
VH vetomℓℓ < 55 GeV∆ϕℓℓ < 1.8

A.1.2

Signal H → W W
415.89 ± 3.80
119.95 ± 2.65
61.95 ± 2.07
42.19 ± 1.52
38.33 ± 1.52
31.57 ± 1.12
18.45 ± 0.76
12.62 ± 0.72

WW8107.26 ± 12.27
963.67 ± 4.15
693.58 ± 3.49
401.23 ± 2.66
390.09 ± 2.63
351.23 ± 2.50
53.83 ± 0.98
39.13 ± 0.83

W Z/ZZ/W γ
1246.34 ± 10.92
264.16 ± 4.97
174.73 ± 3.99
98.76 ± 3.07
97.64 ± 3.06
86.98 ± 2.91
21.85 ± 1.51
16.20 ± 1.35

tt̄
57508.99 ± 28.96
49665.85 ± 27.19
2621.99 ± 6.29
1640.11 ± 4.98
1623.59 ± 4.95
1457.22 ± 4.70
229.06 ± 1.86
181.54 ± 1.65

Single Top
5328.11 ± 6.72
2814.62 ± 4.90
317.98 ± 1.80
197.01 ± 1.41
193.97 ± 1.38
172.12 ± 1.29
25.87 ± 0.51
21.08 ± 0.42Z(τ τ ) +jets
12798.86 ± 46.85
2204.29 ± 22.39
1502.96 ± 17.59
417.81 ± 9.28
412.64 ± 9.24
368.31 ± 8.78
228.01 ± 6.80
78.78 ± 4.00

W +jets
2475.16 ± 20.28
704.93 ± 11.79
228.37 ± 6.82
126.12 ± 4.98
124.03 ± 4.93
107.47 ± 4.64
30.03 ± 3.68
15.31 ± 3.04

QCD
756.48 ± 3.53
194.40 ± 1.73
117.46 ± 1.39
68.99 ± 1.01
67.80 ± 1.00
62.36 ± 0.96
52.22 ± 0.89
41.64 ± 0.80

Total Bkg.
88677.83 ± 66.05
56927.25 ± 39.61
5729.99 ± 22.96
2967.64 ± 12.60
2926.46 ± 12.52
2619.57 ± 11.87
648.25 ± 8.31
397.41 ± 5.68

Background Estimation

Figures A.1 shows schematic view of the extraction of the main backgrounds in the ggF
2-jet analysis.

Figure A.1: Schematic view of the extraction of the main backgrounds for the ggF 2-jets
analysis. Some backgrounds are normalized to data in dedicated control regions.

A.1 Additional Materials for H→ W W ∗ → ℓνℓν Analysis

219

Top background
The top background is estimated using MC and is normalized in a high mℓℓ control region.
For the high mℓℓ control region the following selection criteria are added in addition to thepreselection described in Section 5.4.1:
jetCorr• pmiss,> 20 GeV,T• b-jet veto (see Section 5.4.2),• Non-VBF(VH) selection,• mℓℓ > 80 GeV.
The purity of this control region is ∼ 70% and the remaining contamination is mostly
W W background. Similar to the signal region, the b-jet veto is applied to the control
region, which allow for cancelling b-tagging related systematic uncertainties. The resulting normalization factor is 1.07 ± 0.03(stat.). For the systematics, the shape systematic
uncertainty is evaluated by comparing several generators in truth level, in addition to theexperimental and theoretical uncertainties that are small compared to the uncertaities on
the b-tagged control region for the 1-jet. The resulting shape systematic uncertainty is at
most 4 % level.
Z/γ ∗ → τ τ background
The Z/γ ∗ → τ τ background is estimated using MC and is normalized in a Z/γ ∗ → τ τcontrol region that is defined as:
jetCorr• pmiss,> 20 GeV,T• b-jet veto (see Section 5.4.2),• Non-VBF(VH) selection,• mℓℓ < 70 GeV,• ∆ϕℓℓ > 2.8 radians.
The definition and procedure of systematic evaluation for the Z/γ ∗ → τ τ control region
is mostly the same as the 0-1 jet analysis. The resulting normalization factor is 1.07 ±0.03(stat.).
W +jets/QCD background
The W +jets/QCD backgrounds are estimated using the same data-driven method as is
employed in the ggF 0-1 jet analysis.

A.2 Additional Materials for H→ W W ∗ → ℓνℓν Analysis

220
V V background

For V V backgrounds fully MC-based estimation is employed since they remain small in thesignal region. These backgrounds can be validated in Same Sign region.
W W background
The W W background is estimated using MC prediction. The W W control region is notestablished due to large top contamination in potential W W enriched region, and the sizeof this background is not large compared to the 0-1 jet analysis.

A.2

7 TeV (2011) analysis

In the previous sections only 8 TeV (2012) analysis is discussed. The addition of 7 TeV(2011) analysis incorporating all improvements made in the 8 TeV analysis, improves thesensitivity on the measurement. For the 7 TeV analysis, the following lepton flavor andjet-bin channels are considered :• eµ+µe and ee+µµ Njet = 0 and = 1 ggF-enriched,• eµ+µe and ee+µµ Njet ≥ 2 VBF-enriched.

A.2.1

Physics Object

Physics objects for the 7 TeV analysis basically follow those for 8 TeV analysis but there
are some diﬀerences due to changes in running condition, namely pileup condition. The
diﬀerent pileup condition induces changes in trigger and physics objects :• trigger:
1. single lepton (e and µ) triggers,
2. period dependent thresholds,• electrons:
1. non-GSF,
2. cut-based identification (tight++),3. tight isolation and impact parameter requirements (suppress W +jets/QCD contributions);
For the 7 TeV analysis, only single lepton triggers are used, since the trigger thresholdin 2011 is lower than that in 2012, and the lower threshold allows for making the same
lepton pT configuration as 2012 (leading lepton pT > 22 GeV and sub-leading lepton pT >10 GeV), while keeping high eﬃciency. The electron definition is slightly tightened due tothe fact that the GSF electron is not available in 2011 that reduces background electron,
mainly jet faking electron. The MC generators and processes used in the 7 TeV analysis
are summarized in Table 5.3.

A.2 Additional Materials for H→ W W ∗ → ℓνℓν Analysis

A.2.2

221

ggF analysis

The event selection of the 7 TeV analysis follows that of the 8 TeV, except for frecoil thatis set to be looser in 2011 due to lower level of pileup and lower contamination of Z/γ ∗background, otherwise the event selection is identical. Background estimation also follow
the procedures used in the 8 TeV analysis. One exception is the treatment of same sign
backgrounds, namely the W +jets/QCD and non-W W diboson (V V ) backgrounds. In the
7 TeV analysis the W +jets background is estimated using fake factor from di-jets enrichedsample, while the 8 TeV analysis using the fake factor from the Z+jets enriched sample.
This is due to the lack of the Z+jets statistics in the 7 TeV analysis. Furthermore thesame sign (SS) control region is not used for the V V background estimate in the 7 TeV
analysis due to the limited statistics in SS region, so the SS region is used only for purposeof validation of those backgrounds. The background treatment for the 7 TeV analysis islisted in Table A.2.2, along with that for the VBF analysis.
Table A.3: Background treatment listing for the 7 TeV analysis. The estimation proceduresfor various background processes are given in four categories : normalized using a control
region (CR); data-driven estimate (Data); normalized using the MC (MC); and normalizedusing the MC, but validated in a control region (MC+VR). The “(eµ+µe)” indicates thatthe control region is defined in diﬀerent flavor data set instead of same flavor data set forreasons of purity and/or statistics.
ChannelNjet = 0
eµ+µe
ee+µµ
Njet = 1
eµ+µe
ee+µµ
Njet ≥ 2
eµ+µe
VBF
eµ+µe
ee+µµ

A.2.3

WW

Top

Z/γ ∗ → τ τ

Z/γ ∗ → ee/µµ

W +jets/QCDVVCR
CR (eµ+µe)

CR
CR (eµ+µe)

CR
CR (eµ+µe)

MC
Data

Data
Data

MC+VR
MC+VR

CR
CR (eµ+µe)

CR
CR (eµ+µe)

CR
CR (eµ+µe)

MC
Data

Data
Data

MC+VR
MC+VR

MC

CR

CR

MC

Data

MC+VR

MC
MC

CR
CR

CR (eµ+µe +ee+µµ)
CR (eµ+µe +ee+µµ)

MC
Data

Data
Data

MC+VR
MC+VR

VBF analysis

For the 7 TeV analysis, the BDT trained for 8 TeV is applied to the 7 TeV data set due tohigher statistics in 8 TeV. There are also additional benefits to this apart from the resulting
increased sensitivity, such as being able to take the same theoretical uncertainties as for the
8 TeV analysis and to facilitate the combination of the two analyses. No changes are madeto the event selection and background estimation, except for doing a counting experiment(namely one bin in the signal region) instead of a fit to BDT score (3 bins in signal region)
as is done for the 8 TeV BDT analysis due to a lack of statistics in the signal region.

222

A.2 Additional Materials for H→ W W ∗ → ℓνℓν Analysis

Appendix B

Additional Studies for Fake
Backgrounds
B.1

Di-jet Fake Factors

Di-jets sample is extensively used for fake background estimations even for other methods
such as ‘Matrix Method’. However the di-jets fake factor is not mainly used for the W +jets
estimation in this analysis because it is found that the Z+jets fake factor has smaller
uncertainty. Nevertheless the di-jet fake factor is still partially used in this analysis for the
QCD estimation and W +jets triggered fake correction that are discribed in Section 6.7 and
B.4.

B.1.1

Electron Fake Factors

The fake factors are measured in data using a di-jet control sample. For electrons, the di-jet
control sample is collected with the e/gamma supporting triggers:- EF g24 etcut (2.084 pb−1 ),- EF e5 etcut (12.4 nb−1 ),- EF e5 medium1 (241.3 nb−1 ),where EF g24 etcut (EF e5 etcut) supporting trigger requires a reconstructed EM cluster with transverse energy ET above 24 (5) GeV but makes no requirement on the electron identification, and where EF e5 medium1 trigger requires a reconstructed electron withtransverse energy ET above 5 GeV that satisfies the medium1 electron identification requirements. Due to their large trigger rates, the e/gamma supporting triggers are heavily
pre-scaled.
The EF e5 etcut and EF e5 medium1 triggers are used below ET = 20 GeV, while theEF g24 etcut is used above ET = 20 GeV. The following basic quality cuts are required:
miss cleaning, primary vertex quality cut, and LAr veto. The presence of electrons
GRL, ET
from W or Z bosons in the di-jet sample will bias the calculation of the fake factor. To
223

224

B.1 Additional Studies for Fake Backgrounds

suppress this contamination, events used in the fake factor calculation are required to thefollowings:- away side jet with pT > 15 GeV,
- ∆ϕ(electron, jet) > 0.7,
and events are vetoed if they satisfy the followings:
miss ) > 30 GeV,
- mT (electron, ET- |MZ − Mℓℓ | < 13 GeV,

109
8

10

Data

EF_e5_medium1(EF_e5_etcut) :s = 8 TeV,

107

∫

W+jet
L dt = 0.2413(0.0124) pb

-1

Z+jet

s = 8 TeV,
5

10

1011

1010

EF_e5_medium1(EF_e5_etcut) :109

s = 8 TeV,8

EF_g24_etcut :106

Entries

Entries

where electrons are either id or anti-id.
The remaining W and Z contributions referred to as ‘EW contamination’, are subtracted
from the di-jet sample using simulation. This contribution has been validated by comparing
the data/simulation agreement in the Z peak. The di-jet pT distributions for numeratorsand denominators with W and Z contaminations are shown in Figure B.1. There is no
EW contamination in ET < 20 GeV due to the lack of EF e5 etcut and EF e5 medium1 insimulation sample but the eﬀect is covered by systematic uncertainty.

non-WW Diboson∫ L dt = 2.084 pb

-1

10
10

top

106

W+jet

EF_g24_etcut :

7

WW

∫

Data

L dt = 0.2413(0.0124) pb

s = 8 TeV,

-1

Z+jet
non-WW Diboson∫ L dt = 2.084 pb

WW

-1

top

105

104

104

103

103
102

102

10
1
10

10
20

30

40

50

60

70
80
90
100
electron Numerator pT [GeV]

1
10

20

30

40

50

60
70
80
90
100
electron Denominator pT [GeV]

Figure B.1: Di-jet pT distributions for electron numerators (left) and electron denominators(right) collected with e/gamma supporting triggers. W and Z contaminations are also
illustrated but the contributions are negligibly small at the end of the selection.

To avoid a possible bias due to trigger threshold, the fake factors for 10-20 GeV electrons
is calculated by a combination of supporting triggers (EF e5 etcut and EF e5 medium1).
The electrons satisfying the identified electron selection are collected with the EF e5 medium1
trigger, while the sample of electrons satisfying the electron denominator definition are collected with the EF e5 etcut trigger. The fake factor is then computed after correcting thedenominator sample for the pre-scale of the EF e5 etcut and EF e5 medium1 triggers. Making use of this combination increases the number of id objects and decreases the statisticaluncertainty significantly. Measured di-jets fake factors for electrons as a function of ETand η (1D and 2D) are shown in Figure B.2. Note that the sutracted EW contamination islarger at higher ET whereas it remains small at lower ET .

225

0.025

Electron Fake Factor

Electron Fake Factor

B.1 Additional Studies for Fake Backgrounds

No EW subtraction

EF_e5_medium1(EF_e5_etcut) :0.02
s = 8 TeV,

∫ L dt = 0.2413(0.0124) pb-1

EW subtraction

EF_g24_etcut :0.015
s = 8 TeV,

EW subtraction 20% DOWN

∫ L dt = 2.084 pb

-1

0.035
0.03

ATLAS Internal

0.025

s = 8 TeV,

dijet (No subtraction)∫ L dt = 2.084 pb

-1

0.02

EW subtraction 20% UP

0.015

0.01

0.01
0.005
0.005

20

30

40

50

60

70

100
90
80
70

0.0040± 0.0003

0.0047± 0.0004

0.0083± 0.0007

60
50
40
30
20
10
0

0
-2.5

80
90
100
Electron ET [GeV]Electron pT [GeV]Electron pT [GeV]

0
10

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2
2.5
Electron η

100
90
80
70

0.0021± 0.0002

0.0026± 0.0003

0.0056± 0.0006

0.0034± 0.0003

0.0045± 0.0003

0.0074± 0.0006

0.0055± 0.0003
0.0064± 0.0005
0.0086± 0.0007
0.0064± 0.0003

0.0056± 0.0004
0.0058± 0.0005
0.0060± 0.0006
0.0045± 0.0003

0.0127± 0.0008
0.0139± 0.0011
0.0142± 0.0014
0.0148± 0.0008

60
50

0.0053± 0.0003

0.0066± 0.0004

0.0096± 0.0007

0.0070± 0.0004
0.0071± 0.0005
0.0086± 0.0007
0.0064± 0.0003

0.0070± 0.0004
0.0065± 0.0005
0.0060± 0.0006
0.0045± 0.0003

0.0140± 0.0008
0.0145± 0.0011
0.0142± 0.0014
0.0148± 0.0008

0.5

1

1.5

2

40
30
20
2.5

Electron η

10
0

0.5

1

1.5

2

2.5

Electron η

Figure B.2: The di-jets fake factor as a function of pT (top left) and as a function of η
(top right) in electron channel. The red points show the fake factor before the subtractionof the EW contamination in the di-jet data sample. The blue points show the fake factor
after the subtraction and the change in fake factor by varying the amount of EW contamination by ± 20%. The top right plot shows the eta dependence before the subtraction of
the EW contamination in the di-jet data sample. The bottom left and right plots show
the 2-dimensional fake factor as functions of pT and η before the subtraction of the EW
contamination (left) and after the subtraction (right).

B.1.2

Muon Fake Factors

The fake factors are measured in data using a di-jet control sample. For muons, the dijet control sample is collected with the Muon Combined Performance (MCP) supporting
triggers:- EF mu6 (0.941 pb−1 ),- EF mu15 (22.72 pb−1 ),- EF g24 etcut (2.084 pb−1 ),where EF mu15 (EF mu6) supporting trigger requires a reconstructed muon with transverse
energy above 15 (6) GeV but makes no requirement on the muon impact parameters or

226

B.1 Additional Studies for Fake Backgrounds

isolations, and where EF g24 etcut supporting trigger requires a reconstructed EM clusterwith transverse energy ET above 24 GeV but makes no requirement on the presence of amuon. Due to their large trigger rates, the MCP supporting triggers are heavily pre-scaled
but the available luminosity is normally larger than e/gamma supporting triggers.
The EF mu6 trigger is used below pT = 15 GeV and the EF mu15 is used above pT =15 GeV. The fake factor calculation has been cross checked with the e/gamma supporting
miss cleaning,
trigger, EF g24 etcut. The following basic quality cuts are required: GRL, ET
primary vertex quality cut, and LAr veto. The presence of muons from W or Z bosons in
the di-jet sample will bias the calculation of the fake factor. To suppress this contamination,
events used in the fake factor calculation are required to the followings:- away side jet with pT > 15 GeV,
- ∆ϕ(muon, jet) > 0.7,
and events are vetoed if they satisfy the followings:
miss ) > 30 GeV,
- mT (muon, ET- |MZ − Mµµ | < 13 GeV,

1010
10

108
107

Data

EF_mu15 :9

s = 8 TeV,∫

L dt = 22.72 pb

W+jet

-1

EF_mu6 :s = 8 TeV,

610

∫ L dt = 0.941 pb-1

Entries

Entries

where muons are either id or anti-id.
The remaining W and Z contributions referred to as ‘EW contamination’, are subtracted
from the di-jet sample using simulation. This contribution has been validated by comparing
the data/simulation agreement in the Z peak. This contribution has been validated bycomparing the data/simulation agreement in the Z peak and high mT . The di-jet pT
distributions for numerators and denominators with W and Z contaminations are shownin Figure B.3.
1011

109

non-WW Diboson

108

EF_mu6 :WW107

s = 8 TeV,

top

106

10

∫

L dt = 22.72 pb∫ L dt = 0.941 pb

W+jet

-1

Z+jet
non-WW Diboson
-1

WW
top

105

104

104

103

103

102

102

10
1
10

s = 8 TeV,

Z+jet

5

Data

EF_mu15 :

1010

10
20

30

40

50

60

70
80
90
100
muon Numerator pT [GeV]

1
10

20

30

40

50

60

70
80
90
100
muon Denominator pT [GeV]

Figure B.3: Di-jet pT distributions for muon numerators (left) and muon denominators(right) collected with MCP supporting triggers. W and Z contaminations are also illustrated but the contributions are negligibly small at the end of the selection.

To avoid a possible bias due to trigger threshold, the fake factors for 10-15 GeV muons
have been calculated in a data set triggered by the EF mu6 trigger. Measured di-jets fake227

B.1 Additional Studies for Fake Backgrounds

0.6

0.5

0.4

No EW subtraction

EF_mu15 :s = 8 TeV,

Muon Fake Factor

Muon Fake Factor

factors for muons as a function of pT and η (1D and 2D) are shown in Figure B.4. Notethat the sutracted EW contamination is larger at higher pT whereas it remains small at
lower pT .

∫ L dt = 22.72 pb

EW subtraction-1

EW subtraction 20% DOWN

EF_mu6 :s = 8 TeV,

0.3

∫ L dt = 0.941 pb

EW subtraction 20% UP

-1

0.4

20

30

40

50

60

70

90
80
0.1329± 0.0055

0
-2.5

80
90
100
Muon ET [GeV]100

0.1737± 0.0069

0.2905± 0.0212

70

50

20
10
0

0.1166± 0.0034

0.1910± 0.0095

0.0996± 0.0024
0.1059± 0.0015
0.1068± 0.0009
0.1260± 0.0025

0.1148± 0.0026
0.1217± 0.0016
0.1243± 0.0009
0.1496± 0.0026

0.1900± 0.0073
0.1721± 0.0040
0.1727± 0.0023
0.2081± 0.0060

0.5

1

1.5

2

40
30
20
2.5

Muon η

-1.5

-1

-0.5

0

0.5

1

1.5

2
2.5
Muon η

80

60

0.1007± 0.0030

-2

90

50

30

-1

100

60

40

dijet (No subtraction)∫ L dt = 22.72 pb

0.1

Muon pT [GeV]

Muon pT [GeV]s = 8 TeV,

0.2

0.1

70

ATLAS Internal
0.5

0.3

0.2

0
10

0.6

10
0

0.1294± 0.0054

0.1691± 0.0068

0.2807± 0.0208

0.0991± 0.0030

0.1146± 0.0034

0.1873± 0.0094

0.0988± 0.0024
0.1054± 0.0015
0.1066± 0.0009
0.1242± 0.0024

0.1138± 0.0026
0.1213± 0.0016
0.1241± 0.0009
0.1476± 0.0026

0.1882± 0.0073
0.1713± 0.0040
0.1724± 0.0023
0.2050± 0.0060

0.5

1

1.5

2

2.5
Muon η

Figure B.4: The di-jets fake factor as a function of pT (top left) and as a function of η
(top right) in muon channel. The red points show the fake factor before the subtractionof the EW contamination in the di-jet data sample. The blue points show the fake factor
after the subtraction and the change in fake factor by varying the amount of EW contamination by ± 20%. The top right plot shows the eta dependence before the subtraction of
the EW contamination in the di-jet data sample. The bottom left and right plots show
the 2-dimensional fake factor as functions of pT and η before the subtraction of the EW
contamination (left) and after the subtraction (right).

B.1.3

Systematics

Systematic uncertainty associated with the fake factor measurement is the dominant sourceof uncertainty on the W +jets /QCD background. The fake factor uncertainty is divided
into the following sources:- The diﬀerence in fake factor between the di-jet and W +jets samples. This is estimatedby comparing the two fake factors: di-jets and W +jets fake factors in simulation. This

228

B.1 Additional Studies for Fake Backgrounds
is the dominant systematic uncertainty on the fake factor.
- The eﬀect of pileups on the fake factor due to diﬀerent run conditions during datataking. This is estimated by studying the fake factor as a function of < µ > (Average
number of interactions per bunch crossing).
- The uncertainty associated to the real lepton contamination from W/Z events in the
di-jet samples. This is estimated by varying the W/Z subtraction in the di-jet samples.

These are each described in more detail below and final uncertainty on the di-jets fakefactor is summarized in Table B.1 and B.2
Table B.1: Summary of the fake factor uncertainties in 15 - 20 GeV bin for electrons. The
individual contributions are added in quadrature to obtain total uncertainty.
Sourceη range
Fake Fator
Sample Dependence
Statistical Error
Pile-Up Error
EW-Contamination
Total Uncertainty|η| < 1.0
0.0086
60.0%
8.1%
10.4%
2.4%
61.4%

Electron
1.0 < |η| < 2.0 2.0 < |η| < 2.47
0.00600.0142
60.0%
60.0%
10.0%
9.8%
4.4%
7.7%
2.3%
0.8%
61.0%
61.3%

Table B.2: Summary of the fake factor uncertainties in 15 - 20 GeV bin for muons. The
individual contributions are added in quadrature to obtain total uncertainty.
Sourceη range
Fake Factor
Sample Dependence
Statistical Error
Pile-Up Error
EW-Contamination
Total Uncertainty

B.1.3.1|η < 1.0
0.102
40.0%
0.8%
10.3%
0.8%
41.3%

Muon
1.0 < |η| < 2.0
0.119
40.0%
0.8%
7.0%
0.8%
40.6%

2.0 < |η| < 2.5
0.163
40.0%
1.3%
5.4%
0.9%
40.4%

Sample dependence

The fake factor is measured in the di-jet sample and is applied to the W +jets control
sample (Nid+anti−id ). Diﬀerences in jet kinematics and heavy flavor fraction may cause the229

B.1 Additional Studies for Fake Backgrounds

0.04

W+jets(MC)-Di-jet(MC) /Di-jet(MC)Electron Fake Factor

fake factor to be diﬀerent in these two samples. A systematic uncertainty accounts for thissample dependence. This uncertainty is evaluated in simulation by comparing the two fakefactors.
For electrons, W +jets background is dominated by light flavor (for instance, charged
pion track overlapping with neutral pion cluster in EM calorimeter) and the contributionof heavy flavors is found to be small. The flavor composition is studied in detail, which
is found in Section B.2. Figure B.5 shows the comparison of electron fake factors between
the di-jet and W +jets in simulation, (fldi−jet − flW+jets )/fldi−jet as a function of ET . The
fractional diﬀerence from the two samples is found to be ∼ 60%.

0.035
Di-jet fake factor (Pythia8)
0.03
W+jets fake factor (Alpgen Pythia6)

0.025
0.02
0.015

1
0.8

W+jets (Alpgen Pythia6)

0.6
0.4
0.2
0
-0.2
-0.4

0.01
-0.6
0.005

-0.8

0
10

20

30

40

50

60

70

80
90
100
Electron p [GeV]

-1
10

20

T

30

40

50

60

70

80
90
100
Electron p [GeV]T

Figure B.5: Comparison of electron fake factors between the di-jets and W +jets samples(left). The fractional diﬀerence between the two fake factors (right). The overlaid yellow
band is a 40 % uncertainty as a reference. A 60 % uncertainty is assigned in overall ET .

For muon, W +jets background is dominated by heavy flavor (for instance, (semi)leptonic decay of charm or bottom meson from Wc and Wbb /Wcc processes). The eﬀectof light flavor is found to be smaller than that of heavy flavor, depending on pT range.
The flavor composition is studied in detail, which is found in Section B.2. Figure B.6
shows the comparison of muon fake factors between the di-jet and W +jets in simulation,(fldi−jet − flW+jets )/fldi−jet as a function of pT . The fractional diﬀerence is found to be∼ 40%.
B.1.3.2

Lepton contamination in di-jets sample

The di-jet sample enhances jets misidentified as leptons. However there is still real lepton
contamination from W and Z bosons in the di-jet sample. The lepton contamination from
W/Z events will bias the fake factor measurement. To reduce this bias, the EW veto isapplied to the di-jet sample. The EW veto rejects 80-90 % of W/Z contamination, while
retaining more than 90 % of the di-jet samples. It has been checked that the EW veto does
not bias the fake factor.
The remaining W/Z contribution is subtracted from the observed data using simulation.
The normalizations of the W/Z contributions are obtained from dedicated control samples

230
0.5

W+jets(MC)-Di-jet(MC) /Di-jet(MC)Muon Fake Factor

B.1 Additional Studies for Fake Backgrounds

0.45
Di-jet fake factor (Pythia8)

0.4
0.35

W+jets fake factor (Alpgen Pythia6)

0.3
0.25
0.2
0.15

1
0.8

0.4
0.2
0
-0.2
-0.4

0.1

-0.6

0.05

-0.8

0
10

20

30

40

50

60

70

80
90
100
Muon p [GeV]T

W+jets (Alpgen Pythia6)

0.6

-1
10

20

30

40

50

60

70

80
90
100
Muon p [GeV]T

Figure B.6: Comparison of muon fake factors between the di-jets and W +jets samples(left). The fractional diﬀerence between the two fake factors (right). The overlaid yellow
band is a 40 % uncertainty as a reference. A 40 % uncertainty is assigned in overall pT .

that are defined as |mll −mZ | < 13 GeV for Z bosons and as mT > 30 GeV for W bosons. It
is found that the evaluated normalization factors (Ndata /Nsimulation per W/Z) are close tounity. Figure B.2 and B.4 show the estimated fake factor with/without the EW backgroundsubtraction. The uncertainty due to the level of residual EW background is evaluated byvarying the normalization factors by ±20%. This uncertainty accounts for uncertainties
associated with the W and Z cross sections, and the modeling of simulated leptons from
W and Z bosons satisfying the denominator selection. The uncertainty is found to be
negligible at lower pT .
For electrons, the uncertainty for ET < 20 GeV cannot be evaluated due to the lack ofsimulation samples. The uncertainty is instead taken from the next pT bin where higher
EW contamination is expected. This approach is very conservative but the impact of thisuncertainty is still negligibly small compared to the sample dependence.
B.1.3.3

Trigger bias

For electrons, the etcut triggers are used to select electron denominators, and the medium1
triggers are used to select fully identified electrons. The etcut triggers are highly prescaled, but are expected to be no bias from the triggers since only ET cut is applied to
the reconstructed EM cluster. The fully identified electron selection is normally tigher
than medium1 but the bias remains in ET < 25 GeV where Very Tight LH identification
is used. The bias is evaluated by adding the cut-based Medium++ to the Very Tight LH
identification, and it is found that the bias is at most ∼ -5 % (see Section 4.5.1). This is anegligible bias comapred to the sample dependence uncertainty (40-60 %). The uncertainty
is thus not included in the fake factor systematics.
For muons, the EF mu6 and EF mu15 triggers are used to measure the fake factor. Since
they do not make any requirements on the impact parameters or isolations, they are unbiased with respect to both muon numerator and denominator definitions. The trigger bias

231

B.1 Additional Studies for Fake Backgrounds

on the muon fake factor is thus expected to be negligible, and is not included in the fakefactor systematics.
B.1.3.4

Pileup uncertainty

100
90

ATLAS Internal

80

s = 8 TeV,

70

0.0841± 0.1504∫

electron pT [GeV]

electron pT [GeV]

The systematic due to variations in the fake factor from diﬀering levels of pileup is investigated by calculating the fake factor in a high pileup and low pileup di-jet samples.
The di-jet sample has been divided into two subsets based on < µ > (average number ofinteractions per crossing). If the number of interactions is above (below) twenty, the eventis classified as the high (low) pileup sample. The results are shown in Figures B.7. As
expected, the fake factors decrease with increased pileups. This is primarily due to theincrease in isolation energy from the higher event activity in the high pileup events. The
level of systematic uncertainty is at most 10 % depending on pT and η.

-1

L dt = 2.084 pb

0.1387± 0.1309

0.0600± 0.1473

60
50
40
30
20
10
0

100
90

ATLAS Internal

80

s = 8 TeV,

70

0.0543± 0.1239

0.0876± 0.1215

0.0381± 0.1308

0.0443± 0.1003

0.0125± 0.0928

0.0081± 0.1099

0.0805± 0.0862
0.0292± 0.1052
0.0629± 0.0890
0.0018± 0.0511

0.0515± 0.0932
0.0636± 0.1149
0.0283± 0.1038
0.0067± 0.0571

0.0635± 0.0919
0.0364± 0.11080.0542± 0.1040
0.0488± 0.0514∫ L dt = 2.084 pb

-1

60
50

0.0710± 0.11300.0203± 0.1104

0.0133± 0.1287

0.1311± 0.0942
0.0489± 0.1285
0.1036± 0.1124
0.0029± 0.0600

0.0837± 0.1149
0.1061± 0.1286
0.0443± 0.1173
0.0109± 0.0676

0.1048± 0.1152
0.0630± 0.1379
0.0766± 0.11000.0845± 0.0582

0.5

1

1.5

2

40
30
20
10
0

2.5

0.5

1

1.5

2

2.5

100
90

ATLAS Internal

80

s = 8 TeV,

70

0.0863± 0.0818∫-1

L dt = 22.72 pb

0.0137± 0.0791

ηmuon pT [GeV]muon pT [GeV]η

0.0657± 0.1394

100
90

ATLAS Internal

80

s = 8 TeV,

70

0.0576± 0.0756

0.0096± 0.0709

0.0554± 0.1316

0.0102± 0.0557

0.0327± 0.0560

0.0576± 0.0964

0.0569± 0.0465
0.0447± 0.0315
0.0646± 0.0237
0.0091± 0.0868

0.0524± 0.0443
0.0398± 0.0295
0.0439± 0.0214
0.0122± 0.0678

0.0422± 0.0773
0.0051± 0.0508
0.0324± 0.0362
0.0260± 0.1363

60

60

50

50

40
30
20
10
0

0.0180± 0.0633

0.0509± 0.0628

0.0848± 0.1031

0.0888± 0.0510
0.0693± 0.0350
0.1033± 0.0261
0.0144± 0.1017

0.0840± 0.0492
0.0630± 0.0332
0.0698± 0.02400.0192± 0.0782

0.0637± 0.0859
0.0113± 0.0591
0.0538± 0.0413
0.0428± 0.1651

0.5

1

1.5

2

40
30
20
2.5
η

10
0

∫ L dt = 22.72 pb

0.5

-1

1

1.5

2

2.5
η

Figure B.7: Pileup dependence (relative) uncertainty on the di-jets fake factor for electrons(top) and for muons (bottom). The fake factor is measured in data with high pileup (left)
and low pileup (right).

232

B.1 Additional Studies for Fake Backgrounds

B.1.4

Z+jet vs Di-jet Fake Factors

Comparisons of the Z+jets and the di-jets fake factors in both data and simulation are
made to see the compatibility between the fake factors, and to obtain the pT threshold on
the Z+jets fake factor. As discussed above, the Z+jet fake factor has shown its better
performance than the di-jet fake factor in terms of sample dependence systematic uncertainty. Nevertheless it is not obvious that the Z+jets fake factor is still better at higher pT
region where larger statistical uncertainty and EW uncertainty are expected. Considering
two points below, the pT threshold on the Z+jets fake factor is determined:
1. size of total systematic uncertainty,
2. reliability and compatibility,
B.1.4.1

Comparison of systematic uncertainties

The systematic uncertainties on the Z+jets fake factor is compared to the uncertainty on
the di-jets fake factor. Table B.3 and B.4 show the comparison of the total and individual
systematic uncertainties.
Table B.3: Comparison of systematic uncertainty on the di-jet and Z+jets fake factor inelectron channel.
stat. ± EW syst. ± sample dependence (total) %10 < pT < 15
15 < pT < 20
20 < pT < 25
pT > 25di-jet2.9 ± 1.9 ± 60.0 (60.1) %5.0 ± 1.9 ± 60.0 (60.1) %3.9 ± 1.9 ± 60.0 (60.1) %3.6 ± 4.2 ± 60.0 (60.1) %Z+jets
17.6 ± 10.5 ± 20.0 (28.6) %34.0 ± 19.2 ± 20.0 (43.8) %52.1 ± 24.8 ± 20.0 (61.1) %29.6 ± 23.1 ± 20.0 (42.5) %Table B.4: Comparison of systematic uncertainty on the di-jet and Z+jets fake factor inmuon channel.
stat. ± EW syst. ± sample dependence (total) %10 < pT < 15
15 < pT < 20
20 < pT < 25
pT > 25di-jet1.1 ± 1.8 ± 40.0 (40.1) %0.5 ± 1.8 ± 40.0 (40.1) %0.9 ± 1.8 ± 40.0 (40.1) %1.6 ± 4.2 ± 40.0 (40.2) %Z+jets10.2 ± 2.6 ± 20.0 (22.6) %17.9 ± 5.1 ± 20.0 (27.3) %28.6 ± 8.9 ± 20.0 (36.0) %34.1 ± 21.0 ± 20.0 (44.8) %For electrons, the total systematic uncertainty on the Z+jets is smaller than the uncertainty on the di-jets in overall pT range, assuming 20 % sample dependene as shown in
Figure 6.7. For muons, the total systematic uncertainty on the Z+jets is smaller than theuncertainty on the di-jets in pT < 25 GeV, while they are compatible in pT > 25 GeV,
assuming 20 % sample dependence as shown in Figure 6.8.

233

B.1 Additional Studies for Fake Backgrounds
B.1.4.2

Compatibility of fake factors

0.045
0.04

Z+jets Fake Factor in data (Syst. included)

0.035
0.03

Multi-jets/QCD Fake Factor in data (Syst. included)

Muon Fake Factor

Electron Fake Factor

The Z+jets and di-jets fake factors are compared using both data and simulation. Figure B.8 shows the comparison of the Z+jets and di-jets fake factors in data and simulation.
It is found that the Z+jets fake factor is compatible with di-jet fake factor in data, whereas
they are not in simulation, even though they are not expected to be compatible due tosample dependence.
0.4
0.35

Z+jets Fake Factor in data (Syst. included)

0.3
Multi-jets/QCD Fake Factor in data (Syst. included)

0.25

0.025
0.2
0.02
0.15

0.015

0.1

0.01

0.05

0.005
20

30

40

50

60

70

0.04
0.035
Di-jet fake factor (Pythia8)
0.03
Z+jets fake factor (Alpgen Pythia6)

0.025

0
10

80
90
100
Electron ET [GeV]

20

30

50

60

70

80
90
100
Muon p [GeV]

0.5
0.45
Di-jet fake factor (Pythia8)

0.4
0.35

Z+jets fake factor (Alpgen Pythia6)

0.3

0.02

40

T

Muon Fake Factor

Electron Fake Factor

0
10

0.25
0.2

0.015

0.15
0.01
0.1
0.005
0
10

0.05
20

30

40

50

60

70

80
90
100
Electron p [GeV]
T

0
10

20

30

40

50

60

70

80
90
100
Muon p [GeV]T

Figure B.8: Comparison of Z+jets fake factor and di-jet fake factor for electrons (left)
and muons (right) in data (top) and simulation (bottom). Data fake factors include both
statistical uncertainty and systematic uncertainty, while simulated fake factors include only
statistical uncertainty in simulation. Alpgen+Pythia6 generator is used for Z+jets simulation, and Pythia8 (or mu-filtered Pythia8) is used for di-jets simulation.

Figure B.9 shows the comparison of data and simulated fake factors in Z+jets anddi-jets samples.
In overall the agreement on data/simulation looks better in the Z+jets fake factor. The
Z+jets fake factor in data is consistent with that in simulation, while the di-jets fake factor
does not well. This is probably due to the fact that the parton shower modeling in di-jets
simulation (Pythia8) is imperfect, while the parton shower modeling is better in Z+jets

234
0.045
0.04

Multi-jets/QCD Fake Factor in data (Syst. included)

0.035
0.03

Multi-jets/QCD Fake Factor in mc (Stat. included)

Muon Fake Factor

Electron Fake Factor

B.1 Additional Studies for Fake Backgrounds
0.4
0.35

Multi-jets/QCD Fake Factor in data (Syst. included)

0.3
Multi-jets/QCD Fake Factor in mc (Stat. included)

0.25

0.025
0.2
0.02
0.15

0.015

0.1

0.01

0.05

0.005
20

30

40

50

60

70

0.045
0.04

Z+jets Fake Factor in data (Syst. included)

0.035
0.03

0
10

80
90
100
Electron ET [GeV]

Z+jets Fake Factor in mc (Stat. included)

20

30

40

50

60

70

80
90
100
Muon p [GeV]T

Muon Fake Factor

Electron Fake Factor

0
10

0.4
0.35

Z+jets Fake Factor in data (Syst. included)

0.3
Z+jets Fake Factor in mc (Stat. included)

0.25

0.025
0.2
0.02
0.15

0.015

0.1

0.01

0.05

0.005
0
10

20

30

40

50

60

70

80
90
100
Electron ET [GeV]

0
10

20

30

40

50

60

70

80
90
100
Muon p [GeV]T

Figure B.9: The comparison of data and simulated fake factors in di-jets (top) and Z+jets(bottom) samples. Data fake factors include both statistical uncertainty and systematic
uncertainty, while simulated fake factors include only statistical uncertainty in simulation.
Alpgen+Pythia6 generator is used for Z+jets simulation, and Pythia8 (or mu-filtered
Pythia8) is used for di-jets simulation.

simulation (Pythia6).

1

In summary, Z+jets fake factor is feasible and is better for the analysis, even at higher
pT range when all pT bins above 25 GeV are merged. The Z+jets fake factor is therefore
used in overall pT range with 4 bins (10-15, 15-20, 20-25, 25- GeV).

1

Unfortunately no other di-jet simulation sample available for now.

B.2 Additional Studies for Fake Backgrounds

B.2

235

OS/SS Asymmetry and Flavor Composition

Motivated by the diﬀerence between the OS W +jets fake factor and SS W +jets fake factor,
flavor composition studies are performed based on MC to understand behaviors in fakefactors. Not only the diﬀerence between the OS W +jets and the SS W +jets, the flavor
compostion also explains any diﬀerences in fake factors among samples such as the di-jet,the Z+jets, OS W +jets, and SS W +jets. In this section, OS/SS asymmetry is introduced
first, the flavor composition for each sample is then shown.

B.2.1

OS/SS Asymmetry

It is well known the fact that there is a charge asymmetry in W +jets production in pp
collision. This is because a u-quark tends to be in the initial state rather than a d-quark.
However the OS/SS asymmetry is not exactly the same as the charge asymmetry. Figure B.10 shows typical tree level diagram in W +jets production.

Figure B.10: Tree level diagram for qg → W q ′ production.
In this diagram, the W +jet tends to be opposite sign (OS) regardless of the initial state
quark in ME level. The W + is always produced in association with d-quark (ug → W + d),
whereas the W − is always produced in association with u-quark (dg → W − u) in the context
of first generation. Similary the W +charm (sg → W c and sg → W cg) goes in OS even if
it associates with final state gluon. On the other hand, the W + bb̄ can equally go into OS
and SS because b-quark (or b̄-quark) always comes from gluon splitting. Figure B.11 shows
typical tree level diagrams in W +charm and W + bb̄ productions.
Extending the discussion above to the analysis, the situation will be more complicatedsince quarks can be observed as jets. The situation will be much more complicated when considering reconstructed fake leptons (id or anti-id leptons) since it is not obvious whether
or not these leptons can keep track of the final state quark charge, namely jet charge. A

236

B.2 Additional Studies for Fake Backgrounds

Figure B.11: Tree level diagram for qg → W q ′ production. Tree level diagram for q q̄ →W + g(→ bb̄) production.

quark charge flip (for instance, OS → SS or vice versa) can happen when the quark goes
into fake lepton. In addition the probability of the charge flip strongly depends on thetightness of lepton selection. It is therefore essential to understand the feature of quark
charge flip when the OS/SS asymmetry in the W +jets production is considered.

B.2.2

Flavor Composition in W +charm Production

A simple test is made to learn the OS/SS asymmetry using W +charm samples (Alpgen+Pythia6 W cN p0 − W cN p4). All tree level diagrams (ME level) included in the
W +charm samples are found in [155]. The W +charm process should tend to be OS unless there are charge flipped quarks or quarks from gluon splitting. Figure B.12 shows pT
distributions for anti-id leptons splitting into OS and SS. In muon channel, the OS/SS
asymmetry can be seen as the asymmetry in normalization, meaning that the normalization in OS is about 10 times higher than that in SS. The anti-id muons in OS are mostly
from leptonic decay of charm mesons, whereas the anti-id muons in SS are mostly fromgluon splitting in which the OS/SS ratio is expected to be unity. On the other hand, mostof the anti-id electrons are from gluon splitting, as a result, the asymmetry is less clear
compared to muon case. The diﬀerence between the anti-id muon and anti-id electron is
explained by the fact that the tightness of lepton selection is quite diﬀerent between them.
In fact the definition of the anti-id electron is looser than that of the anti-id muon, sothat the anti-id electrons tend to be more “real” jets (or fragments of jets) rather than“real” leptons.

B.2 Additional Studies for Fake Backgrounds

B.2.3

237

Flavor Composition in W + bb̄ Production

Another simple test is made to learn the case that the OS/SS is symmetric using W + bb̄
samples (Alpgen+Pythia6 W bbN p0 − W bbN p3). All tree level diagrams (ME level) included in the W + bb̄ samples are found in [155]. The W + bb̄ process should tend to besymmetric in OS and SS as far as the b-quarks from the gluon splitting go into fake leptons.
Figure B.13 shows pT distributions for anti-id leptons splitting into OS and SS. In muonchannel, most of the anti-id muons are from leptonic decay of b-mesons which makes thecomposition symmetric between OS and SS within stat uncertainty. On the contrary there
is an asymmetry from light flavor component such as those charged kaon and charged pionin electron channel. The asymmetry is from the process shown in Figure B.10 in association
with an additional final state gluon (ug → W d + g(→ bb̄)).

From the simple tests above, it is worthwhile summarizing several things:- SS events are always produced by either gluon splitting or quark charge flip,- anti-id muons are mostly from leptonic decay of heavy flavor mesons if heavy flavor
mesons exist in event,- anti-id electrons are mostly from a fragment of gluon or quark jet rather than
leptonic decay of heavy flavor mesons in event,- the diﬀerence between electrons and muons is related to the tightness of the lepton
selection,- the OS/SS asymmetry is caused by not only W +charm, but also light flavors (charged
pions and kaons) that is clearly shown in electrons.

238

others (with truth lepton)
othersπ +/- (with truth lepton)
π +/kaon (with truth lepton)kaon
c-jet (leptonic)
c-jet (hadronic)
b-jet (leptonic)
b-jet (hadronic)
stat. unc. on others (with truth lepton)
stat. unc. on others
stat. unc. on π +/- (with truth lepton)
stat. unc. on π +/stat. unc. on kaon (with truth lepton)
stat. unc. on kaon
stat. unc. on c-jet (leptonic)
stat. unc. on c-jet (hadronic)
stat. unc. on b-jet (leptonic)
stat. unc. on b-jet (hadronic)

6000
5000
4000
3000
2000

Entries

Entries

B.2 Additional Studies for Fake Backgrounds

400
300
200
100

40

50

60

photon/ π0 (with truth lepton)
photon/ π0π+/- (with truth lepton)
π+/kaon (with truth lepton)kaon
c-jet (leptonic)
c-jet (hadronic)
b-jet (leptonic)
b-jet (hadronic)
stat. unc. on photon/ π0 (with truth lepton)
stat. unc. on photon/ π0
stat. unc. on π+/- (with truth lepton)
stat. unc. on π+/stat. unc. on kaon (with truth lepton)

18000
16000
14000
12000
10000
8000

stat. unc. on kaon
stat. unc. on c-jet (leptonic)
stat. unc. on c-jet (hadronic)
stat. unc. on b-jet (leptonic)
stat. unc. on b-jet (hadronic)

6000
4000

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photon/ π0 (with truth lepton)
photon/ π0π+/- (with truth lepton)
π+/kaon (with truth lepton)kaon
c-jet (leptonic)
c-jet (hadronic)
b-jet (leptonic)
b-jet (hadronic)
stat. unc. on photon/ π0 (with truth lepton)
stat. unc. on photon/ π0
stat. unc. on π+/- (with truth lepton)
stat. unc. on π+/stat. unc. on kaon (with truth lepton)

14000
12000
10000
8000
6000

stat. unc. on kaon
stat. unc. on c-jet (leptonic)
stat. unc. on c-jet (hadronic)
stat. unc. on b-jet (leptonic)
stat. unc. on b-jet (hadronic)

4000
2000

2000
0
10

others (with truth lepton)
othersπ +/- (with truth lepton)
π +/kaon (with truth lepton)kaon
c-jet (leptonic)
c-jet (hadronic)
b-jet (leptonic)
b-jet (hadronic)
stat. unc. on others (with truth lepton)
stat. unc. on others
stat. unc. on π +/- (with truth lepton)
stat. unc. on π +/stat. unc. on kaon (with truth lepton)
stat. unc. on kaon
stat. unc. on c-jet (leptonic)
stat. unc. on c-jet (hadronic)
stat. unc. on b-jet (leptonic)
stat. unc. on b-jet (hadronic)

500

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90
100
Electron Denominator pT [GeV]

0
10

20

30

40

50

60
70
80
90
100
Electron Denominator pT [GeV]

Figure B.12: Flavor composition as a function of anti-id lepton pT in W +charm process(Alpgen+Pythia6). The top left is for anti-id muon in OS and the top right is foranti-id muon in SS. The OS composition is dominated by leptonic decay of charm mesons,
whereas the SS composition is dominated by a fragment of gluon splitting. The bottom
left is for anti-id electron in OS and the bottom right is for anti-id electron in SS.
Both the OS and SS compositions are dominated by a fragment of gluon splitting or nonleptonic decay of charm mesons. The leptonic decay event is defined as the event that hasa truth lepton around heavy flavor quark/meson/baryon. Otherwise, the event is classified
as hadronic decay.

239

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2500
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Entries3000

others (with truth lepton)
othersπ +/- (with truth lepton)
π +/kaon (with truth lepton)kaon
c-jet (leptonic)
c-jet (hadronic)
b-jet (leptonic)
b-jet (hadronic)
stat. unc. on others (with truth lepton)
stat. unc. on others
stat. unc. on π +/- (with truth lepton)
stat. unc. on π +/stat. unc. on kaon (with truth lepton)
stat. unc. on kaon
stat. unc. on c-jet (leptonic)
stat. unc. on c-jet (hadronic)
stat. unc. on b-jet (leptonic)
stat. unc. on b-jet (hadronic)

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photon/ π0 (with truth lepton)
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π+/kaon (with truth lepton)kaon
c-jet (leptonic)
c-jet (hadronic)
b-jet (leptonic)
b-jet (hadronic)
stat. unc. on photon/ π0 (with truth lepton)
stat. unc. on photon/ π0
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stat. unc. on π+/stat. unc. on kaon (with truth lepton)

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othersπ +/- (with truth lepton)
π +/kaon (with truth lepton)kaon
c-jet (leptonic)
c-jet (hadronic)
b-jet (leptonic)
b-jet (hadronic)
stat. unc. on others (with truth lepton)
stat. unc. on others
stat. unc. on π +/- (with truth lepton)
stat. unc. on π +/stat. unc. on kaon (with truth lepton)
stat. unc. on kaon
stat. unc. on c-jet (leptonic)
stat. unc. on c-jet (hadronic)
stat. unc. on b-jet (leptonic)
stat. unc. on b-jet (hadronic)

2500

photon/ π0 (with truth lepton)
photon/ π0π+/- (with truth lepton)
π+/kaon (with truth lepton)kaon
c-jet (leptonic)
c-jet (hadronic)
b-jet (leptonic)
b-jet (hadronic)
stat. unc. on photon/ π0 (with truth lepton)
stat. unc. on photon/ π0
stat. unc. on π+/- (with truth lepton)
stat. unc. on π+/stat. unc. on kaon (with truth lepton)

3000
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stat. unc. on kaon
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Figure B.13: Flavor composition as a function of anti-id lepton pT in W + bb̄ process(Alpgen+Pythia6). The top left is for anti-id muon in OS and the top right is foranti-id muon in SS. THe anti-id muons are dominated by leptonic decay of b-mesons
in both OS and SS. The contribution of the b-mesons is quite symmteric between the OS
and SS. The bottom left is for anti-id electron in OS and the bottom right is for anti-id
electron in SS. Both OS and SS are dominated by a fragment of final state u/d quark or
gluon. The OS/SS asymmetry in the light flavors is caused by gq → W q ′ +g(→ bb̄) diagram.
The leptonic decay event is defined as the event that has a truth lepton around heavy flavor
quark/meson/baryon. Otherwise, the event is classified as hadronic decay.

240

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B.2.4

Flavor Composition in Inclusive W +jets Production

B.2.4.1

Flavor composition in electron channel

Figure B.16 shows comparison of flavor composition between OS and SS in W +jets sample.
The light flavors (pions and kaons) are dominant components for both OS and SS in the
denominator sample. The contribution from leptonic decay of c-mesons is also not negligible(∼ 30 %) in the OS numerator sample due to the W +charm production that induces apart of the OS/SS asymmetry. Furthermore, the OS/SS asymmetry also arises from lightflavors (charged pions and kaons) due to the main W +jets diagram (qg → W q ′ ) shown in
Figure B.10. While the contribution from leptonic decay of b-mesons and neutral pions(π 0 → γγ) , referred to as ‘neutral components’, is symmetric between OS and SS. In otherwords, the “relative” contribution from the neutral components is larger in SS.
The fake factors for each component are also shown in Figure B.14, where a large
hierarchy from the quark type can be seen. The largest fake factor comes from the leptonic
decay of b-mesons, and the light flavor fake factors tends to be smaller. Moreover it isfound that the fake factors for each component are identical regardless of fake lepton charge,
which means that any diﬀerences in inclusive fake factors (for instance, OS W +jets versus
SS W +jets) can be fully explained by the diﬀerences in flavor composition. The number ofdenominators and numerators in OS and SS are found in Table B.5. The relatively larger
contribution from the neutral components leads to larger SS W +jets fake factor.
Figure B.17 shows comparison of flavor composition between the OS W +jets and Z+jets
sample. The light flavor compositions in the Z+jets sample are similar to those in the
OS W +jets sample. The diﬀerence between the two samples is the composition in heavy
flavor. A larger charm contribution can be seen in the OS W +jets composition becauseof W +charm process, whereas a larger bottom contribution can be seen in the Z+jet
composition. As a result, total heavy flavor contribution (b-mesons and c-mesons) in theZ+jets sample is similar to that in the OS W +jets, which makes the Z+jets fake factor
close to the OS W +jets fake factor. The similar light flavor/heavy flavor ratio between
the two samples implies that the flavor compositions in both samples are dominated by themain diagram (qg → W g ′ or qg → Zq) shown in Figure B.10.
Table B.5:
channel.

OS
Nden
Nnum
Fake Factor
SS
Nden
Nnum
Fake Factor

Number of denominators and numerators for each component in electron

c-quarks
12689±193
1147±600.09±0.004
c-quarks1188±69148±270.12±0.03

b-quarks
390±47318±380.81±0.13
b-quarks433±50289±410.66±0.13

charged pions
661085±1239
3097±92
0.0046±0.0002
charged pions
297028±895
1576±72
0.0053±0.0003

neutral pions
67080±695
2112±1200.031±0.002
neutral pions
67069±696
2250±126
0.033±0.002

kaons
287728±776
783±460.0027±0.0002
kaons
119766±521
379±360.0031±0.0003

total1028972±1630
7457±173
0.0072±0.0002
total
485484±1250
4642±157
0.0095±0.0003

241

10
OS W+jets fake factor (b quark leptonic decay)
SS W+jets fake factor (b quark leptonic decay)
OS W+jets fake factor (c quark leptonic decay)

1

SS W+jets fake factor (c quark leptonic decay)
OS W+jets fake factor (s quark)
SS W+jets fake factor (s quark)

Electron Fake Factor

Electron Fake Factor

B.2 Additional Studies for Fake Backgrounds
10
OS W+jets fake factor (b quark leptonic decay)
Z+jets fake factor (b quark leptonic decay)
OS W+jets fake factor (c quark leptonic decay)

1Z+jets fake factor (c quark leptonic decay)
OS W+jets fake factor (s quark)Z+jets fake factor (s quark)

10-1

10-1

OS W+jets fake factor (u/d quark)

OS W+jets fake factor (u/d quark)

SS W+jets fake factor (u/d quark)Z+jets fake factor (u/d quark)

OS W+jets fake factor (π0/gamma)

OS W+jets fake factor (π0/gamma)

SS W+jets fake factor (π0/gamma)

-2

10

-2

10

inclusive W+jets fake factor

Z+jets fake factor (π0/gamma)
Z+jets fake factor

OS W+jets fake factor

OS W+jets fake factor

SS W+jets fake factor
-3

10

-3

50

60

70

80

90
100
Electron p [GeV]

10

T

50

60

70

80

90
100
Electron p [GeV]T

Figure B.14: Comparison of electron fake factors for each component (Alpgen+Pythia6).
The left plot is the comparison of OS W +jets fake factor and SS W +jets fake factor in eachcomponent. The right plot is the comparison of OS W +jets fake factor and Z+jets fakefactor in each component. There is a large hierarchy in fake factor from quark types (inorder of b-quark > c-quark > light-quark). The fake factors are identical in each component
regardless of fake lepton charge. The inclusive fake factor is close to the light flavor fakefactor since the inclusive sample is dominated by light flavors. The larger b-quark fakefactor and nueutral pion fake factor lead to larger SS fake factor at the end.

B.2.4.2

Flavor composition in muon channel

Figure B.18 shows comparison of flavor composition between OS and SS in W +jets sample.
Regardless of charge, the heavy flavors (charm and bottom) are dominant components inboth the denominator and numerator samples except for the lowest pT bin. The light flavors
are also enhanced in the numerator sample due to d0 impact parameter and track isolation
requirements that are not required for the denominator sample but are required for thenumerator sample. Particularly the d0 impact parameter is sensitive to the heavy flavors as
discussed in Section 4.6.2. Similarly to the electron case, the OS/SS asymmetry arises from
leptonic decay of c-mesons in W +charm process as well as light flavors. On the other handthe contribution from leptonic decay of b-mesons and “others”(muons from calorimeter
including pion decay in-flight) is symmetric between OS and SS in normalization. In otherwords, the “relative” contribution from the neutral components is larger in SS.
The fake factors for each component are also shown in Figure B.15, where a large
hierarchy from the quark type can be seen. The largest fake factor is from the light flavors
and the fake factors from the leptonic decay of heavy flavor mesons are smaller. Moreover
the fake factors for each component are roughly consistent between OS and SS (and between
OS W +jets and Z+jets). So the similar discussion to the electron case can be applied tothe muon case. The number of denominators and numerators in OS and SS are found in
Table B.6. From Table B.6 it is found that OS fake factor is smaller than SS fake factor
because of the higher charm fraction in OS, which has a lower fake factor than all the others.
Figure B.19 shows comparison of flavor composition between the OS W +jets and Z+jets

242

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OS W+jets fake factor (b quark leptonic decay)
SS W+jets fake factor (b quark leptonic decay)
OS W+jets fake factor (c quark leptonic decay)
SS W+jets fake factor (c quark leptonic decay)
OS W+jets fake factor (s quark)

1

Muon Fake Factor

Muon Fake Factor

sample. The light flavor compositions in the Z+jets sample are similar to those in the OS
W +jets sample. The diﬀerence between the two samples is mainly from the compositionin heavy flavor. A larger charm contribution can be seen in the OS W +jets because of the
W +charm process, whereas a larger bottom contribution can be seen in the Z+jet sample.
As a result, total heavy flavor contribution in the Z+jets sample is also similar to that in
the OS W +jets, which makes the Z+jets fake factor close to the OS W +jets fake factor.
OS W+jets fake factor (b quark leptonic decay)
Z+jets fake factor (b quark leptonic decay)
OS W+jets fake factor (c quark leptonic decay)
Z+jets fake factor (c quark leptonic decay)
OS W+jets fake factor (s quark)

SS W+jets fake factor (s quark)Z+jets fake factor (s quark)
OS W+jets fake factor (u/d quark)
OS W+jets fake factor (u/d quark)
SS W+jets fake factor (u/d quark)Z+jets fake factor (u/d quark)

OS W+jets fake factor (others)

10-1

10-1

SS W+jets fake factor (others)

OS W+jets fake factor (others)

inclusive W+jets fake factor

Z+jets fake factor (others)

OS W+jets fake factor

Z+jets fake factor
OS W+jets fake factor

SS W+jets fake factor

50

60

70

80

90
100
Muon p [GeV]

50

60

70

80

T

90
100
Muon p [GeV]T

Figure B.15: Comparison of muon fake factors for each component (Alpgen+Pythia6).
The left plot is the comparison of OS W +jets fake factor and SS W +jets fake factor ineach component. The right plot is the comparison of OS W +jets fake factor and Z+jets
fake factor in each component. There is a large hierarchy in fake factor from quark types(in order of light-quark > b-quark > c-quark). The fake factors are mostly identical in eachcomponent regardless of fake lepton charge. The inclusive fake factor is close to the fakefactor in heavy flavor since the inclusive sample is dominated by heavy flavors. The larger
fraction of c-quark in OS which has smaller fake factor than any other components, leads
to SS fake factor higher than OS fake factor.

Table B.6: Number of denominators and numerators for each component in muon channel.
OS
Nden
Nnum
Fake Factor
SS
Nden
Nnum
Fake Factor

c-quarks29859±298
1866±750.06±0.01
c-quarks
2420±95240±330.10±0.02

b-quarks6067±181
544±540.09±0.01
b-quarks6314±186
747±670.11±0.01

charged pions
4118±136
1024±74
0.25±0.02
charged pions
2345±106417±510.18±0.03

kaons
3056±95580±460.19±0.02
kaons
1510±75
231±360.15±0.02

others5661±200
1186±930.20±0.02
others
5949±2091104±890.19±0.02

total
48761±434
5200±157
0.107±0.004
total
18538±322
2739±131
0.147±0.008

243

photon/π0 (with truth lepton)
photon/π0
π+/- (with truth lepton)
π+/kaon (with truth lepton)kaon
c-jet (leptonic)
c-jet (hadronic)
b-jet (leptonic)
b-jet (hadronic)
stat. unc. on photon/π0 (with truth lepton)
stat. unc. on photon/π0
stat. unc. on π+/- (with truth lepton)
stat. unc. on π+/stat. unc. on kaon (with truth lepton)
stat. unc. on kaon
stat. unc. on c-jet (leptonic)
stat. unc. on c-jet (hadronic)
stat. unc. on b-jet (leptonic)
stat. unc. on b-jet (hadronic)

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B.2 Additional Studies for Fake Backgrounds

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photon/π0 (with truth lepton)
photon/π0
π+/- (with truth lepton)
π+/kaon (with truth lepton)kaon
c-jet (leptonic)
c-jet (hadronic)
b-jet (leptonic)
b-jet (hadronic)
stat. unc. on photon/π0 (with truth lepton)
stat. unc. on photon/π0
stat. unc. on π+/- (with truth lepton)
stat. unc. on π+/stat. unc. on kaon (with truth lepton)
stat. unc. on kaon
stat. unc. on c-jet (leptonic)
stat. unc. on c-jet (hadronic)
stat. unc. on b-jet (leptonic)
stat. unc. on b-jet (hadronic)

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photon/π0 (with truth lepton)
photon/π0
π+/- (with truth lepton)
π+/kaon (with truth lepton)kaon
c-jet (leptonic)
c-jet (hadronic)
b-jet (leptonic)
b-jet (hadronic)
stat. unc. on photon/π0 (with truth lepton)
stat. unc. on photon/π0
stat. unc. on π+/- (with truth lepton)
stat. unc. on π+/stat. unc. on kaon (with truth lepton)
stat. unc. on kaon
stat. unc. on c-jet (leptonic)
stat. unc. on c-jet (hadronic)
stat. unc. on b-jet (leptonic)
stat. unc. on b-jet (hadronic)

2500

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×103
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photon/π0 (with truth lepton)
photon/π0
π+/- (with truth lepton)
π+/kaon (with truth lepton)kaon
c-jet (leptonic)
c-jet (hadronic)
b-jet (leptonic)
b-jet (hadronic)
stat. unc. on photon/π0 (with truth lepton)
stat. unc. on photon/π0
stat. unc. on π+/- (with truth lepton)
stat. unc. on π+/stat. unc. on kaon (with truth lepton)
stat. unc. on kaon
stat. unc. on c-jet (leptonic)
stat. unc. on c-jet (hadronic)
stat. unc. on b-jet (leptonic)
stat. unc. on b-jet (hadronic)

200

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Figure B.16: Comparison of flavor composition between OS and SS in W +jet sample(Alpgen+Pythia6). The top left is for id electron in OS and the top right is for id
electron in SS. The bottom left is for anti-id electron in OS and the bottom right is foranti-id electron in SS. The anti-id is dominated by light flavor components in both OS
and SS. The OS/SS asymmetry can be seen in leptonic decay of c-mesons, charged pion,and kaon components whereas leptonic decay of b-mesons and neutral pion components are
symmetric between OS and SS in normalization. Neverthless a relative contribution of theb-mesons and the neutral pions is higher in SS which makes SS fake factor higher than OS
fake factor.

244

photon/π0 (with truth lepton)
photon/π0
π+/- (with truth lepton)
π+/kaon (with truth lepton)kaon
c-jet (leptonic)
c-jet (hadronic)
b-jet (leptonic)
b-jet (hadronic)
stat. unc. on photon/π0 (with truth lepton)
stat. unc. on photon/π0
stat. unc. on π+/- (with truth lepton)
stat. unc. on π+/stat. unc. on kaon (with truth lepton)
stat. unc. on kaon
stat. unc. on c-jet (leptonic)
stat. unc. on c-jet (hadronic)
stat. unc. on b-jet (leptonic)
stat. unc. on b-jet (hadronic)

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B.2 Additional Studies for Fake Backgrounds

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photon/ π0π+/- (with truth lepton)
π+/kaon (with truth lepton)kaon
c-jet (leptonic)
c-jet (hadronic)
b-jet (leptonic)
b-jet (hadronic)
stat. unc. on photon/ π0 (with truth lepton)
stat. unc. on photon/ π0
stat. unc. on π+/- (with truth lepton)
stat. unc. on π+/stat. unc. on kaon (with truth lepton)

400

300

200

stat. unc. on kaon
stat. unc. on c-jet (leptonic)
stat. unc. on c-jet (hadronic)
stat. unc. on b-jet (leptonic)
stat. unc. on b-jet (hadronic)

100

500
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450

photon/π0 (with truth lepton)
photon/π0
π+/- (with truth lepton)
π+/kaon (with truth lepton)kaon
c-jet (leptonic)
c-jet (hadronic)
b-jet (leptonic)
b-jet (hadronic)
stat. unc. on photon/π0 (with truth lepton)
stat. unc. on photon/π0
stat. unc. on π+/- (with truth lepton)
stat. unc. on π+/stat. unc. on kaon (with truth lepton)
stat. unc. on kaon
stat. unc. on c-jet (leptonic)
stat. unc. on c-jet (hadronic)
stat. unc. on b-jet (leptonic)
stat. unc. on b-jet (hadronic)

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photon/ π0 (with truth lepton)
photon/ π0π+/- (with truth lepton)
π+/kaon (with truth lepton)kaon
c-jet (leptonic)
c-jet (hadronic)
b-jet (leptonic)
b-jet (hadronic)
stat. unc. on photon/ π0 (with truth lepton)
stat. unc. on photon/ π0
stat. unc. on π+/- (with truth lepton)
stat. unc. on π+/stat. unc. on kaon (with truth lepton)

60000
50000
40000
30000

stat. unc. on kaon
stat. unc. on c-jet (leptonic)
stat. unc. on c-jet (hadronic)
stat. unc. on b-jet (leptonic)
stat. unc. on b-jet (hadronic)

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Figure B.17: Comparison of flavor composition between OS W +jets sample and Z+jets
sample (Alpgen+Pythia6). The top left is for id electron in OS W +jets and the top
right is for id electron in Z+jets sample. The bottom left is for anti-id electron in
OS W +jets sample and the bottom right is for anti-id electron in Z+jets sample. The
fraction of light flavor components (pions and kaons) in Z+jets sample is similar to thatin OS W +jets sample. A larger charm contribution is seen in OS W +jets because of the
W +charm process whereas a larger bottom contribution is seen in Z+jet sample due to thefact that the electron PID strongly enhances the b-quark composition.

245

others (with truth lepton)
othersπ+/- (with truth lepton)
π+/kaon (with truth lepton)kaon
c-jet (leptonic)
c-jet (hadronic)
b-jet (leptonic)
b-jet (hadronic)
stat. unc. on photon/π0 (with truth lepton)
stat. unc. on photon/π0
stat. unc. on π+/- (with truth lepton)
stat. unc. on π+/stat. unc. on kaon (with truth lepton)
stat. unc. on kaon
stat. unc. on c-jet (leptonic)
stat. unc. on c-jet (hadronic)
stat. unc. on b-jet (leptonic)
stat. unc. on b-jet (hadronic)

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B.2 Additional Studies for Fake Backgrounds

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c-jet (leptonic)
c-jet (hadronic)
b-jet (leptonic)
b-jet (hadronic)
stat. unc. on photon/π0 (with truth lepton)
stat. unc. on photon/π0
stat. unc. on π+/- (with truth lepton)
stat. unc. on π+/stat. unc. on kaon (with truth lepton)
stat. unc. on kaon
stat. unc. on c-jet (leptonic)
stat. unc. on c-jet (hadronic)
stat. unc. on b-jet (leptonic)
stat. unc. on b-jet (hadronic)

2000

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500
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others (with truth lepton)
othersπ+/- (with truth lepton)
π+/kaon (with truth lepton)kaon
c-jet (leptonic)
c-jet (hadronic)
b-jet (leptonic)
b-jet (hadronic)
stat. unc. on photon/π0 (with truth lepton)
stat. unc. on photon/π0
stat. unc. on π+/- (with truth lepton)
stat. unc. on π+/stat. unc. on kaon (with truth lepton)
stat. unc. on kaon
stat. unc. on c-jet (leptonic)
stat. unc. on c-jet (hadronic)
stat. unc. on b-jet (leptonic)
stat. unc. on b-jet (hadronic)

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others (with truth lepton)
othersπ+/- (with truth lepton)
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c-jet (hadronic)
b-jet (leptonic)
b-jet (hadronic)
stat. unc. on photon/π0 (with truth lepton)
stat. unc. on photon/π0
stat. unc. on π+/- (with truth lepton)
stat. unc. on π+/stat. unc. on kaon (with truth lepton)
stat. unc. on kaon
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Figure B.18: Comparison of flavor composition between OS and SS in W +jet sample(Alpgen+Pythia6). The top left is for id muon in OS and the top right is for id muon
in SS. The bottom left is for anti-id muon in OS and the bottom right is for anti-id
muon in SS. The anti-id is dominated by heavy flavor components in both OS and SS
except for the lowest pT bin. The OS/SS asymmetry can be seen in leptonic decay of cmesons, charged pion, and kaon components whereas leptonic decay of b-mesons and others
components are symmetric between OS and SS in normalization. Neverthless a relative
contribution of the b-mesons and others is higher in SS which makes SS fake factor higher
than OS fake factor.

246

others (with truth lepton)
othersπ+/- (with truth lepton)
π+/kaon (with truth lepton)kaon
c-jet (leptonic)
c-jet (hadronic)
b-jet (leptonic)
b-jet (hadronic)
stat. unc. on photon/π0 (with truth lepton)
stat. unc. on photon/π0
stat. unc. on π+/- (with truth lepton)
stat. unc. on π+/stat. unc. on kaon (with truth lepton)
stat. unc. on kaon
stat. unc. on c-jet (leptonic)
stat. unc. on c-jet (hadronic)
stat. unc. on b-jet (leptonic)
stat. unc. on b-jet (hadronic)

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Entries

B.2 Additional Studies for Fake Backgrounds

250
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others (with truth lepton)
othersπ+/- (with truth lepton)
π+/kaon (with truth lepton)kaon
c-jet (leptonic)
c-jet (hadronic)
b-jet (leptonic)
b-jet (hadronic)
stat. unc. on photon/π0 (with truth lepton)
stat. unc. on photon/π0
stat. unc. on π+/- (with truth lepton)
stat. unc. on π+/stat. unc. on kaon (with truth lepton)
stat. unc. on kaon
stat. unc. on c-jet (leptonic)
stat. unc. on c-jet (hadronic)
stat. unc. on b-jet (leptonic)
stat. unc. on b-jet (hadronic)

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others (with truth lepton)
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c-jet (leptonic)
c-jet (hadronic)
b-jet (leptonic)
b-jet (hadronic)
stat. unc. on others (with truth lepton)
stat. unc. on others
stat. unc. on π +/- (with truth lepton)
stat. unc. on π +/stat. unc. on kaon (with truth lepton)
stat. unc. on kaon
stat. unc. on c-jet (leptonic)
stat. unc. on c-jet (hadronic)
stat. unc. on b-jet (leptonic)
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others (with truth lepton)
othersπ +/- (with truth lepton)
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b-jet (hadronic)
stat. unc. on others (with truth lepton)
stat. unc. on others
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stat. unc. on π +/stat. unc. on kaon (with truth lepton)
stat. unc. on kaon
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stat. unc. on b-jet (hadronic)

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Muon Denominator pT [GeV]

Figure B.19: Comparison of flavor composition between OS W +jets sample and Z+jets
sample (Alpgen+Pythia6). The top left is for id muon in OS W +jets and the top right isfor id muon in Z+jets sample. The bottom left is for anti-id muon in OS W +jets sample
and the bottom right is for anti-id muon in Z+jets sample. The fraction of non-heavy
flavor components (pions and kaons) in Z+jets sample is similar to that in OS W +jets
sample. A larger charm contribution is seen in OS W +jets because of the W +charmprocess whereas a larger bottom contribution is seen in Z+jet sample.

247

B.3 Additional Studies for Fake Backgrounds

B.3

W +jets Shape Modeling

It is not obvious that the data-driven W +jets background defined as events that have one
id lepton and one anti-id lepton scaled by the dedicated fake factor, can model kinematic
shapes of the W +jets background correctly. To validate the shapes of the data-driven
W +jet background, comparisons of the kinematic distributions are made using the W +jets
simulation.
Figures B.20 and B.21 show the comparisons of the kinematic distributions where black
dots are the W +jets prediction in simulation and red dots are the data-driven W +jets
prediction. Since the statistics of the W +jets simulation are quite limited due to its verylarge cross section, some high cross section weight events with large statistical uncertainty
can be seen in simulation, while the data-driven prediction has suﬃcient statistics. This is
one of the reasons why the data-driven method is preferred for the W +jets prediction. In
overall, the kinematic shapes of the data-driven W +jets prediction look reasonable.
1000
s = 8 TeV,

800

H → WW(*)

1400

W+jets(Lep+Lep) OS∫ L dt = 20.7 fb

-1

1200

W+jets(Lep+Den) OS→µν eν /eν µν

1000

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H → WW(*)

W+jets(Lep+Lep) OS∫ L dt = 20.7 fb-1

W+jets(Lep+Den) OS→µν eν /eν µν

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subleadLepPt [MeV]900
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700
600

H → WW(*)

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W+jets(Lep+Lep) OS∫ L dt = 20.7 fb-1

s = 8 TeV,

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W+jets(Lep+Den) OS→µν eν /eν µν

H → WW(*)

W+jets(Lep+Lep) OS∫ L dt = 20.7 fb-1

W+jets(Lep+Den) OS→µν eν /eν µν

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MET_TrackHWW_Clj [MeV]

DEtall []Figure B.20: Comparison of the data-driven W +jets and W +jets simulation in kinematic
shapes for eµ+µe channel. Alpgen+Pythia6 sample is used for the W +jets simulation,and data-driven W +jets control sample is scaled by the dedicated Z+jets fake factor.

248

B.3 Additional Studies for Fake Backgrounds

800
700
600

s = 8 TeV,
H → WW(*)

W+jets(Lep+Lep) OS∫ L dt = 20.7 fb

1200

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s = 8 TeV,

W+jets(Lep+Den) OS→µν eν /eν µν

1000

500

H → WW(*)

W+jets(Lep+Lep) OS∫ L dt = 20.7 fb-1

W+jets(Lep+Den) OS→µν eν /eν µν

800

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MT [MeV]Figure B.21: Comparison of the data-driven W +jets and W +jets simulation in kinematic
shapes for eµ+µe channel. Alpgen+Pythia6 sample is used for the W +jets simulation,and data-driven W +jets control sample is scaled by the dedicated Z+jets fake factor.

B.4 Additional Studies for Fake Backgrounds

B.4

249

Triggered Fake Correction

There exists a small bias on the W +jets control sample with the current definition ofanti-id leptons (see Section 6.3.1 and 6.3.2). This is because the anti-id electron isorthogonal to the trigger selection due to medium1, and because the trigger selection is nota superset of the anti-id muon due to diﬀerent isolation requirements. To correct for thebias, triggered anti-id lepton (triggered denominator) that can pass trigger selection isadditionally and exclusively defined. Events that contain one triggered anti-id lepton and
one id lepton are then added to the W +jets control sample. The contribution from thetriggered W +jets background is ∼10 % in overall, and it is dependent on the signal region.
The definition of the triggered anti-id leptons (triggered denominator) are summarized
below.

B.4.1

Triggered Anti-id Electron Definition

In the standard analysis, the following triggers are used in electron channel: EF e24vhi medium1,
EF e60 medium1, EF 2e12Tvh loose1, and EF e12Tvh medium1 mu8, where “medium1” iscompatible with isEM Medium++ and “i” indicates track isolation, Ptcone20/pT < 0.10.
Nevertheless (non-triggered) anti-id electron defined in Table 6.2 cannot pass the trigger
selection due to the requirement of isEM Medium++ veto (and looser track isolation) in
the anti-id electron. To correct for this bias, triggered anti-id electron is defined byrequiring isEM Medium++ and by loosening other cuts as shown in Table B.7.
Table B.7: Definition of the triggered anti-id electron (triggered electron denominator).
Triggered Anti-id Electron
Author 1 or 3
pT > 15 GeV|η| < 2.47, excluded crack region (1.37 < |η| < 1.52)|z0 sin θ| < 1.2 mm, d0 /σ(d0 ) < 9
SCT + N P ixel ≥ 4
Nhits
hits
isEM Medium++
Ptcone and Etcone cuts Removed
Fails the identified electron

Isolation cuts are removed from the triggered anti-id electrons to make the definition as
loosened as possible. Otherwise the EW contamination is too large to define the W +jets
control sample (W +triggered anti-id sample). The bias therefore still remains on the
W +jets control sample due to the trigger isolation. To avoid the trigger isolation bias on the
W +jets control sample, events that pass only dilepton triggers to which trigger isolation is
not imposed are used to collect the W +jets control sample (W +triggered anti-id sample).
The remaining bias from ineﬃciency of the di-leton triggers (ORing single/dilepton
versus only dilepton trigger) is expected to be negligible, at most < a few % that is simply

250

B.4 Additional Studies for Fake Backgrounds

computed as “0.10 (triggered anti-id contribution in total) × 0.20 (ineﬃciency of the
dilepton trigger)”.

B.4.2

Triggered Anti-id Muon Definition

In the standard analysis, the following triggers have been used in muon channel: EF mu24i tight,
EF mu36 tight, EF mu18 mu8 EFFS, and EF e12Tvh medium1 mu8, where “i” indicates track
isolation, Ptcone20/pT < 0.12. Nevertheless (non-triggered) anti-id muons shown in Table 6.4 sometimes do not pass the EF mu24i tight trigger because there is no track isolation
requirement in the anti-id muon definition. To correct for this bias, triggered anti-id
muon is defined by changing Etcone cut to Ptcone cut as shown in Table B.8. The bias isthen completely removed from the W +jets control sample (W +triggered anti-id sample).
Table B.8: Definition of the triggered anti-id muon (triggered muon denominator).
Triggered Anti-id Muon Definition
STACO Combined MuonpT > 25 GeV|η| < 2.5
d0 Impact Parameter Requirements Removed|z0 sin θ| < 1 mm
Ptcone30/pT < 0.12
Fails the identified muon selection

B.4.3

Fake Factors for Triggered Anti-id Leptons

The fake factors for the triggered anti-id lepton is measured by using the di-jets sample.
In practice the procedure of the fake factor measurement is the same as what is used for
non-triggered anti-id leptons as described in Section B.1. It is also possible to use theZ+jets sample for the fake factor measurement. The larger uncertainty on the di-jets fakefactor than that on the Z+jets fake factor does not matter much since the contribution of
the triggered anti-id leptons to the W +jets control sample is not large. Also the triggeredanti-id leptons are mainly used for the QCD estimation where the di-jets fake factor isessential.
The fake factor increases with the triggered anti-id lepton because the number ofdenominators (Nanti−id ) decreases due to tighter lepton definition. This can be seen in thecomparison of the denominator pT distributions (non-triggered versus triggered anti-id)
as shown in Figure B.22. Also dedicated fake factors for the triggered anti-id lepton (1D
and 2D) and corresponding EW uncertainty (2D) are shown in Figure B.23 for electrons
and in Figure B.24 for muons. According to the decrease of the number of denominators,
resulting fake factor increase by roughly a factor of 10, depending on pT bin.

251

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B.4 Additional Studies for Fake Backgrounds∫ L dt = 2.084 pb

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Electron pT [GeV]Electron Fake Factor

Figure B.22: Di-jet pT distributions for non-triggered (left) and triggered electron denominators (right) collected with e/gamma supporting triggers. W and Z contaminations arealso illustrated but the contributions are negligibly small at the end of the selection.

No EW subtraction

EF_e5_medium1(EF_e5_etcut) :0.4
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0.0821± 0.0088

0.0800± 0.0082

0.0833± 0.0066

0.1058± 0.0078

0.0719± 0.0058

0.0859± 0.0055
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0.0622± 0.0066
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0.0961± 0.0066
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0.1115± 0.0073
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0.0519± 0.0901
0.0230± 0.11190.0473± 0.0958
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0.0184± 0.0925
0.0080± 0.1193

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Figure B.23: 1D (top left) and 2D fake factors (top right) for triggered anti-id electrons.
And the EW contamination systematic uncertainties (bottom) for triggered anti-id electrons. The EW contamination is not evaluated below 20 GeV due to the lack of e5 triggers
in MC. The uncertainty on 15-20 bin is thus taken from next bin (higher bin).

252
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EF_mu15 :s = 8 TeV,

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Muon pT [GeV]

Muon Fake Factor

B.4 Additional Studies for Fake Backgrounds∫ L dt = 22.72 pb

EW subtraction-1

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EF_mu6 :s = 8 TeV,

1.5

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EW subtraction 20% UP

-1

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0.2640± 0.0191

0.3227± 0.0239

0.1991± 0.0332

0.2575± 0.01050.2935± 0.01200.3136± 0.0225

0.2610± 0.0076
0.0941± 0.0014
0.0977± 0.0008
0.1178± 0.0023

0.3280± 0.0092
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0.3893± 0.0184
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0.1568± 0.0021
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0.0359± 0.0401
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0.0074± 0.0109
0.0021± 0.0247

0.0418± 0.0677
0.0209± 0.0346
0.0087± 0.0191
0.0025± 0.0408

60
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Figure B.24: 1D (top left) and 2D fake factors (top right) for triggered anti-id muons.
And the EW contamination systematic uncertainties (bottom) for triggered anti-id muons.

B.4.4

W +jets Control Sample for Triggered Anti-id Leptons

In addition to the fake factor, dedicated W +jets control sample is also defined as events
that have one triggered anti-id lepton and one id lepton. The statistics of the control
sample for the triggered anti-id is smaller than that for the non-triggered anti-id due
to its small contribution to the W +jets control sample. Also the EW contamination, inparticular the W γ background, is relatively larger due to the fact that the tighter lepton
definition enhaces more either ture electrons or conversions rather than jets misidentified
as leptons. The remaining contribution needs to be subtracted from the control sample to
avoid double counting of the EW background. Figure B.25 shows kinematic distributionsof the W +jets control sample for the triggered anti-id leptons.

253

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B.4 Additional Studies for Fake Backgrounds

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2.5

3
DPhill []Data

SM(MCstat)mH = 125 GeVWWZ/γ +jets

Wγ

WZ/ZZ/W γ *ttsingle top

50

100

2

40

80
30
60
20

40

10

20
×10
250
Ptll [MeV]

3

0
0

50

100

150

200

×10

3

0

60

80

100

120

140

160

180

200

220 240
MT [MeV]Figure B.25: Kinematic distributions of the W +jets control sample for the triggeredanti-id leptons. The statistics of the control sample is smaller and the EW contaminationin the control sample is larger compared to the W +jets control sample for the non-triggeredanti-id leptons.

254

B.5 Additional Studies for Fake Backgrounds

B.5

QCD Estimation

B.5.1

QCD Subtraction from W +jets Control Sample

Before having a QCD prediction, it is necessary to subtract the QCD contamination fromthe W +jets control sample. The W +jets control sample can be written as:
W+jet
QCD
EW
Nid+ anti-id = Nid+anti-id + Nid+ anti-id + Nid+ anti-id .

(B.1)

To obtain the pure W +jets prediction in the signal region, the QCD and EW backgrounds
are subtracted oﬀ, and the Z+jets (or di-jets) fake factor is applied as:
W +jet
W+jet
Nid+id= f · Nid+anti-id
(
)
QCD
EW
= f · Nid+anti-id − Nid+anti-id − Nid+anti-id

(B.2)
(B.3)

EW
where Nid+anti−id
is obtained from simulation. Using Equation 6.17 to substitute for
QCD
Nid+anti-id , the QCD contribution to the W +jets control sample can be evaluated using
the data driven QCD estimate with two anti-id leptons (Nanti−id+anti−id ). However the
fake factor can be quite diﬀerent between the W +jets and QCD backgrounds due to thediﬀerences in the jet pT spectrum and flavor composition. Hence the fake factor appeared in
Equation 6.17 is labelled as f ′′ instead of f . The pure W +jets prediction is then expressedas:)(
W +jet
QCD
′′
EW
(B.4)
Nid+id = f · Nid+ anti-id − 2 × f × Nanti-id+anti-id − Nid+anti-id

Since the electron and muon fakes are separated in the analysis, the QCD contaminationmust be subtracted independently from the id µ + anti-id electron sample and id electron+ anti-id µ sample, etc. f ′′ depends on the anti-id definition as well as the presence ofother lepton in the event because the presence of the other lepton can dramatically change
the jet flavor composition. One can rewrite f ′′ as:f ′′ = c′′ near-sideaway-side anti-id

× f,

(B.5)

where the near-side refers to the anti-id lepton definition to which the fake factor isapplied, and the away-side refers to the other lepton in the event, meaning that ceµ , forinstance, refers to a anti-id muon and id electron in the event. Since there are triggered
and non-triggered anti-id definitions as well as id definitions, a diﬀerent correction isrequired for each lepton definition and away-side lepton definition. The procedure to split
the electron and muon fakes by subtracting the QCD contribution, for example, from theW +jets with electron fake is given as:()
W+jet electron fake
QCD
′′ µ
EW
Nid
=
f
·
N
−c
×f
×N
−N
id µ+ anti-id ee
id µ+ anti-id e , (B.6)µ+predicted-id eanti-id µ +anti-id e
W+jet electron fakewhere Nidµ+predicted-id e is the pure W +jets contribution with electron fake to the signal
region. The µ and e terms are reversible when predicting the amount of W +jets backgroundB.5 Additional Studies for Fake Backgrounds

255

QCD
with the muon fake. The Nanti-idµ+anti-id e is the events with a pair of two anti-id leptons.
Note that the order does not indicate the leading and sub-leading lepton but indicateselectron and muon fakes. Also when correcting the f to the OS or SS fake factor to accountfor diﬀerences in jet flavor composition for fake leptons with the same charge as the W andopposite charge of the W , it is important to apply these corrections to the subtraction of
QCD as well.
QCD
In the QCD subtraction from the W +jets control sample, the Nanti-idµ+anti-id e term isused twice. Once to subtract from the electron fakes, and once to subtract from the muon
fakes, which accounts for the double counting of the QCD contamination in the W +jets
control sample. To summarize, the correction term is either for an electron or muon, and theelectron or muon can be for a triggered anti-id or a non-triggered anti-id definition. The
away-side lepton can be either lepton flavor, and either id, anti-id, or triggered anti-id.
Combining these together, there are 2×2 × 2 × 3 =24 diﬀerent correction terms defined.
QCD
At the end, the Nanti-idµ+anti-id e term is once more used to predict the QCD backgroundin the signal region by modifying Equation 6.16 as:
QCD
W+jet
EW,MC
Nid+id= f ′ · f ′′ · (Nanti-id+anti-id − Nanti-id+anti-id− Nanti-id+anti-id
)

(B.7)

where f ′ refers to the di-jets fake factor corrected for the presence of an away-side id lepton,
and f ′′ referes to the di-jets fake factor corrected for the presence of an away-side anti-id
lepton. Schematic view of those fake factor measurements is illustrated in Figure B.26.

Figure B.26: Schematic view of di-jets fake factor measurements for the data-driven QCD
estimate. f ′ refers to the di-jets fake factor corrected for the presence of an away-side id
lepton (left). f ′′ refers to the di-jets fake factor corrected for the presence of an away-side
anti-id lepton (right).

256

B.5.2

B.5 Additional Studies for Fake Backgrounds

QCD Correction

The di-jets fake factors, f ′ and f ′′ , for the QCD subtraction/prediction are dependence
on the away-side lepton flavor and lepton definition due to the change in the jet flavor
composition. The requirements on the away-side object can greatly enhance the heavy
flavor contributions. Hence the correction factors, c′ and c′′ , that are derived in simulation,must be determined for each away-side lepton condition.
QCD
Looking at Nid+anti-id, for example, one realize that one id lepton biases the other jetthat ends up as a anti-id lepton, so one can label the fake factor of the second jet as:′

away-side id
f ′ = cnear-side
· f,

(B.8)

where f is the di-jets fake factor that is the ratio of the total count of id leptons (N ), to
the total count of anti-id leptons (D) in di-jets sample in data. When requirements areplaced on away-side object in the event, the composition of the N and D samples changes,
which are referred to as N bias and Dbias . The c can be then rewritten as:c=

1 N bias·.
f Dbias(B.9)

The N bias and Dbias can be split into three flavor components, c-quark, b-quark and lightflavor (LF). Then the c can be further rewritten as:c=bias + N bias + N bias
1 NLF
c
b
· bias,f DLF + Dbbias + Dcbias(B.10)

bias (D bias ) is the number of light flavor jet faking id lepton (anti-id lepton)
where NLF
LF
with away-side lepton, Ncbias (Dcbias ) is the number of c-quark jet faking id lepton (anti-id
lepton) with away-side lepton, Nbbias (Dbbias ) is the number of c-quark jet faking id lepton
bias , estimated(anti-id lepton) with away-side lepton. Each component is, for example NLF
by introducing the jet ratio as:
bias
NLF= NLF ·

away−side
JLF
jet−unbiased
JLF= NLF · ξLF ,(B.11)

where ξLF is the ratio of the number of LF jets with away-side id or anti-id requirement to
the number of LF jets without away-side requirements. The above is for the LF component
bias and D bias into N
but one can also factorize Nc,bc,b · ξc,b and Dc,b · ξc,b .
c,b
ξ physically corresponds to the change in jet composition after requiring one id oranti-id lepton in an event. ξ = 1 means no change, and ξ larger or smaller than 1 means
an increase or decrease, respectively, of that flavor jet. Plugging Equation B.11 for all
flavors into Equation B.10, the equation can be written as:c=

1 NLF · ξLF + Nb · ξb + Nc · ξc·,
f DLF · ξLF + Db · ξb + Dc · ξc

(B.12)

where NLF , Nb , Nc , DLF , Db , Dc , ξLF , ξb , and ξc are measured in the di-jets simulation.
The largest uncertainty comes from using an away-side muon due to the limited muon MC

257

B.5 Additional Studies for Fake Backgroundsξ (Change in jet fraction)

statistics. ξLF , ξb , and ξc for an away-side electron are shown in Figure B.27, and ξ averaged
over all jet pT is summarized in Table B.5.2. Due to the poor statistics, the ξ averaged overjet pT is used.
ξb
6

ξc

4

ξLF

2
0
0

50

100
Jet PT

×103

Figure B.27: The change in the awayside jet fractions for an awayside electron as a functionof the jet pT . An ξ = 1 indicates no change, and being larger than 1 indicates an increasein that jet flavor. The bottom (green), charm (red), and light flavor (black) jets.

Table B.9: Awayside jet corrections (ξ) from a numerator and denominator for the electron
and muon. ξ is change in bottom, charm, and LF jets averaged over all jet pT by having
an awayside muon or electron numerator or denominator. ξ = 1 means no change in jet
composition.
Lepton definition
FlavorMean (ξ)
bottomcharm
Light Flavor (LF)
Electron Numerator
3.0 ± 0.5
1.1 ± 0.2
0.94 ± 0.01
Electron Denominator1.15 ± 0.03 1.05 ± 0.01
0.995 ± 0.002
0.928 ± 0.004
Electron Triggerable Denominator 3.40 ± 0.11 1.13 ± 0.04
Muon Numerator
8.0±0.2
1.18±0.04
0.82±0.005
Muon Denominator
7.0±0.1
1.26±0.01
0.82±0.002
The largest systematic uncertainty on the correction (c) arises from varying the b-quarkand c-quark fractions up and down by 50% and the simulation statistical uncertainties. The
uncertainties and correction factors for the electron are shown in Figure B.28, and uncertainties for the correction factors and f used in the analysis are in Table B.10 for 10 GeV
correction factors. All uncertainties are added in quadrature to get the total uncertainty
on the QCD background.
It is found that the correction factors for some of the anti-id leptons are very similar
each other as shown in Figure B.29. The diﬀerence in the correction factors, for example,
between triggered anti-id muon and non-triggered anti-id muon is less than 5 %. Hence
it is possible to make a simplification to reduce the number of correction factors. To reduceB.5 Additional Studies for Fake Backgrounds

4

Dijet FF bias Correction (c)Dijet FF bias Correction (c)258Total Errorb XS errorξ MC stat error
Stat Uncertainty

3
2
1
0
0

20

40

1

0.5

×103
60
80
100
Electron PT

00

Total Errorb XS errorξ MC stat error
Stat Uncertainty

20

40

×103
60
80 100Electron PT

Figure B.28: QCD correction to the fake factor for flavor composition. The correction
for the non-triggereable denominator (left) and triggered denominator (right) electrons inevents with a muon numerator. The uncertainties from each component are shown and isdominantly the b-cross-section for the non-triggereable denominator.

Table B.10: Ralative uncertainties on f and the QCD correction factors for 10-15 GeV
leptons in the diﬀerent flavor.

Sourcesb-XS
c-XS
jet pT
MC Statξ StatPileupEW Contamination
Total

Uncertainties
cµe anti-id trig cµe anti-id
0.00
0.32
0.04
0.04
0.20
0.20
0.21
0.21
0.10
0.06
0.10
0.10
0.05
0.05
0.33
0.45

ceµ
0.03
0.00
0.20
0.03
0.25
0.10
0.05
0.34

the very large number of corrections, the away-side id lepton is used for both the away-side
id and away-side anti-id leptons as:′′′

away-side anti-id
away-side id
cnear-side= cnear-side.

(B.13)The one exception is the eﬀect of the away-side non-triggered electron on the muon, which
is roughly 10% diﬀerent as shown in Figure B.29. For the non-triggered electron on muon,
its own correction factor is used.

259

4
3.5

Away Muon Denominator3
2.5

Away Muon Numerator

2
1.5

Dijet FF bias Correction (c)Dijet FF bias Correction (c)B.5 Additional Studies for Fake Backgrounds

1.4
1.2
1
0.8
0.6

1

0.4

0.5

0.2

0
0

Awayside Id Electron
Awayside Non-Triggerable Electron Anti-Id

10

20

×10
30 40 50 60 70 80 90 100
Non−Triggerable Anti−Id Electron P T

00

Awayside Triggerable Electron Anti-Id

10

20

30

40

50

60

70

80

×10
90 100
Muon P T

Figure B.29: QCD corrections comparing the eﬀect of an awayside id lepton (red) andan away-side anti-id lepton (black and green). The eﬀect of an awayside anti-id vs an
away-side id lepton is small except for the non-triggerable electron anti-id eﬀect on the
muon.

miss region (max m (W ) <20
Finally the correction factors are validated in data using low ET
TGeV). The comparison of the correction factors between data and simulation is found in
Table B.11.

Table B.11: QCD correction terms derived in data from the max mT (W ) < 20 GeV. The
simulation is corrected for the diﬀerence in dilepton and single lepton triggers. The QCD
uncertainties are the sum in quadrature of all the systematics, and the data uncertainties
are statistical only.

Correction Termcµe anti-idceµµce anti-id trig

B.5.3

Channel
eµ
eµ
µe

data
2.33 ± 0.17
1.07 ± 0.10
1.75 ± 0.10

simulation
2.1±0.9
1.2±0.4
1.6±0.7

QCD Control sample

Data-driven QCD control sample (Nanti−id+anti−id ) is used to obtain the QCD prediction/subtraction in the signal region (Nid+id ) multiplying the fake factors as discussed in
Section 6.7.1. The QCD control sample is defined as events that have two anti-id leptons.
The control sample is collected with the primary triggers that are used in the standard
analysis (see Table 3.2): EF e24vhi medium1, EF e60 medium1, EF 2e12Tvh loose1, andEF e12Tvh medium1 mu8 for ee and eµ+µe channels, and EF mu24i tight, EF mu36 tight,
EF mu18 mu8 EFFS, and EF e12Tvh medium1 mu8 for µµ and eµ+µe channels.

260

B.5 Additional Studies for Fake Backgrounds

The trigger acceptance for QCD control sample is diﬀerent from the W +jets control
sample due to the isolation and identification that is cut on in the trigger. Most of the
W +jets control sample trigger on the generally higher pT lepton from the W for which theoﬄine requirements are tighter than the trigger’s. The W +jets control sample then uses
a non-triggerable anti-id definition to predict W +jets in the signal region. On the other
hand, the QCD control sample has both leptons coming from jets, which means that both
leptons need a looser isolation or identification to extrapolate into the signal region. The
dilepton triggers make looser requirements on the leptons. Therefore the QCD events aremainly accepted through the dilepton triggers, which use the triggered anti-id definitionsummarized in Section B.4.
The purity of the QCD control sample is very high over all jet multiplicity bins. The
contamination of the EW backgrounds are subtracted out, and additionally the W +jets
simulation is subtracted to remove event in which the prompt lepton from the W satisfies
the anti-id definition.
h0ww

h0ww
×10

25000
s = 8 TeV,

20000

H → WW(*)∫-1

L dt = 20.7 fb→µνeνSM(MCstat)mH = 125 GeV

WW

W + jets (MC)Z/γ +jets

Wγ

WZ/ZZ/W γ *ttsingle top

Entries

Entries

3

Data

140
s = 8 TeV,
120
H → WW(*)∫-1

L dt = 20.7 fb

→µνeν

100

15000

Data

SM(MCstat)mH = 125 GeV

WW

W + jets (MC)Z/γ +jets

Wγ

WZ/ZZ/W γ *ttsingle top

80
60

10000

40
5000
20
×10
200
250
300
MT_TrackHWW_Clj [MeV]

3

0
50

100

150

0.5

1

1.5

2

2.5

3
DPhill []

h0ww

7000
6000

s = 8 TeV,

5000

H → WW(*)∫ L dt = 20.7 fb

-1

→µνeν

Entries

Entries

h0ww

0
0

Data

SM(MCstat)20000

mH = 125 GeV

WW

18000

W + jets (MC)Z/γ +jets

Wγ

WZ/ZZ/W γ *ttsingle top

s = 8 TeV,

16000
14000

H → WW(*)∫ L dt = 20.7 fb

-1

→µνeν

Data

SM(MCstat)mH = 125 GeV

WW

W + jets (MC)Z/γ +jets

Wγ

WZ/ZZ/W γ *ttsingle top

12000

4000

10000
3000

8000

2000

6000
4000

1000

2000
×10
200
250
300
MT_TrackHWW_Clj [MeV]

3

0
50

100

150

0
0

0.5

1

1.5

2

2.5

3
DPhill []Figure B.30: Kinematics of the QCD control sample for µe channel after Mℓℓ requirement.
The QCD events are represented as data events - all other simulations. The top plots aremT (left) and ∆ϕℓℓ (right) in high pT . The bottom plots are mT (left) and ∆ϕℓℓ (right) in
low pT .

261

B.5 Additional Studies for Fake Backgrounds

h0ww
40000

s = 8 TeV,

20000
H → WW(*)∫ L dt = 20.7 fb

-1

→eνµν

Data

SM(MCstat)mH = 125 GeV

WW

W + jets (MC)Z/γ +jets

Wγ

WZ/ZZ/W γ *ttsingle top

Entries

Entries

h0ww
25000

35000
30000

s = 8 TeV,
H → WW(*)∫ L dt = 20.7 fb

-1

→eνµν

25000

Data

SM(MCstat)mH = 125 GeV

WW

W + jets (MC)Z/γ +jets

Wγ

WZ/ZZ/W γ *ttsingle top

15000
20000
10000

15000
10000

5000
5000
×10
100 120 140 160 180 200
MAXmT_TrackHWW_Clj [MeV]

3

0
0

20

40

60

80

12000
10000

50

100

150

200

h0ww

s = 8 TeV,
H → WW(*)∫ L dt = 20.7 fb

-1

→eνµν

Data

SM(MCstat)mH = 125 GeV

WW

Entries

Entries

h0ww

×10
250
Mll [MeV]

3

0
0

45000
40000

W + jets (MC)Z/γ +jets

Wγ

WZ/ZZ/W γ *

35000

tt

single top

30000

8000

s = 8 TeV,
H → WW(*)∫ L dt = 20.7 fb

-1

→eνµν

Data

SM(MCstat)mH = 125 GeV

WW

W + jets (MC)Z/γ +jets

Wγ

WZ/ZZ/W γ *ttsingle top

25000
20000

6000

15000

4000

10000
2000

5000
×10
100 120 140 160 180 200
MAXmT_TrackHWW_Clj [MeV]

3

0
0

20

40

60

80

×10
250
Mll [MeV]

3

0
0

50

100

150

200

Figure B.31: Kinematics of the QCD control sample for eµ channel after Mℓℓ requirement.
The QCD events are represented as data events - all other simulations. The top plots aremT (W )(MAX) (left) and Mℓℓ (right) in high pT . The bottom plots are mT (W )(MAX)(left) and Mℓℓ (right) in low pT .

262

B.5 Additional Studies for Fake Backgrounds

Appendix C

Additional Material for Modelingof Same Sign Backgrounds
C.1

Heavy Flavor Cross Section Variations

It is not obvious that the W +jets fake factors are stable against parton distribution functions (PDFs) for heavy flavor. In order to check the stability against the heavy flavor crosssection, the cross section of the W +charm and W +bb̄ processes is each varied from 50% to200% as shown in Figure C.1 and C.2. The resulting diﬀerences are less than 20% and are
well covered by the systematic uncertainty on the correction factors currently assigned.

263

264

0.04
0.035

Muon Fake Factor

Electron Fake Factor

C.1 Additional Material for Modeling of Same Sign Backgrounds

OS W+jets (Alpgen Pythia6)

0.03

OS W+jets (Alpgen Pythia6) W+Charm X-Sec × 2

0.025

OS W+jets (Alpgen Pythia6) W+Charm X-Sec × 0.5

0.5
0.45
OS W+jets (Alpgen Pythia6)

0.4
OS W+jets (Alpgen Pythia6) W+Charm X-Sec × 2

0.35

OS W+jets (Alpgen Pythia6) W+Charm X-Sec × 0.5

0.3

0.02

0.25
0.2

0.015

0.15
0.01
0.1
0.005
0
10

0.05
20

30

40

50

60

70

0
10

80
90
100
Electron p [GeV]

20

30

40

50

60

70

0.04
0.035

OS W+jets (Alpgen Pythia6)

0.03

OS W+jets (Alpgen Pythia6) W+bb X-Sec × 2

0.025

OS W+jets (Alpgen Pythia6) W+bb X-Sec × 0.5

0.5
0.45
OS W+jets (Alpgen Pythia6)

0.4
OS W+jets (Alpgen Pythia6) W+bb X-Sec × 2

0.35

OS W+jets (Alpgen Pythia6) W+bb X-Sec × 0.5

0.3

0.02

80
90
100
Muon p [GeV]T

Muon Fake Factor

Electron Fake Factor

T

0.25
0.2

0.015

0.15
0.01
0.1
0.005
0
10

0.05
20

30

40

50

60

70

80
90
100
Electron p [GeV]
T

0
10

20

30

40

50

60

70

80
90
100
Muon p [GeV]T

Figure C.1: Comparison of the fake factors varying the heavy flavor cross section by
50% or 200%. No strong dependence on the heavy flavor cross section is observed and thevariations are well covered by the systematic uncertainty currently assigned on the W +jets
correction factors. Alpgen+Pythia6 sample is used.

265

1
0.8

W+Charm XsecUP (Alpgen Pythia)

0.6

W+Charm XsecDown (Alpgen Pythia)

0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
-1
10

20

30

40

50

60

70

80
90
100
Electron p [GeV]

W+charm UP(DOWN) f.f. - W+jets f.f.) / W+jets f.f.

W+Charm UP(DOWN) f.f. - W+jets f.f.) / W+jets f.f.

C.1 Additional Material for Modeling of Same Sign Backgrounds

1
0.8

W+Charm XsecUP (Alpgen Pythia)

0.6

W+Charm XsecDown (Alpgen Pythia)

0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
-1
10

20

30

40

50

60

70

1
0.8

W+bb XsecUP (Alpgen Pythia)
W+bb XsecDown (Alpgen Pythia)

0.6
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
-1
10

20

30

40

50

60

70

80
90
100
Electron p [GeV]
T

80
90
100
Muon p [GeV]T

W+bb UP(DOWN) f.f. - W+jets f.f.) / W+jets f.f.

W+bb UP(DOWN) f.f. - W+jets f.f.) / W+jets f.f.

T

1
0.8

W+bb XsecUP (Alpgen Pythia)
W+bb XsecDown (Alpgen Pythia)

0.6
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
-1
10

20

30

40

50

60

70

80
90
100
Muon p [GeV]T

Figure C.2: Relative diﬀerence of the fake factors varying the heavy flavor cross section by
50% or 200%. No strong dependence on the heavy flavor cross section is observed and thevariations are well covered by the systematic uncertainty currently assigned on the W +jets
correction factors. Alpgen+Pythia6 sample is used.

266

C.1 Additional Material for Modeling of Same Sign Backgrounds

Appendix D

Additional materials for Results
D.1

Results

D.1.1

ggF Results

The mT distributions of each signal region (mℓℓ :[10-30, 30-55] ⊗ psub
T :[10-15, 15-] ⊗ flavor:[eµ,µe])
for ggF 0-jet and ggF 1-jet diﬀerent flavor analyses are shown in Figure D.1, D.2, D.3, andD.4. Also Table D.1 and D.2 show full cutflow for diﬀerent flavor and same flavor channels
comparing observed data to expected signal and background counts.

D.1.2

VBF Results

Table D.3 show full cutflow for diﬀerent flavor and same flavor channels comparing observed
data to expected signal and background counts.

267

268

80
70
60

s = 8 TeV, ∫ Ldt = 20.3 fb-1
H→WW*→eν µν + 0 jets

Data

SM (sys ⊕ stat)

WW

Other VV
Single Top
Z/ γ *→ττtt*
Z/ γ →ll
W+jet

50

Events / 10 GeV

Events / 10 GeV

Bibliography

QCD
H [125 GeV]

180
160

s = 8 TeV, ∫ Ldt = 20.3 fb-1
H→WW*→eν µν + 0 jets

140

Data

SM (sys ⊕ stat)

WW

Other VV
Single Top
Z/ γ *→ττtt*
Z/ γ →ll
W+jet

100

30

80
60
40

10
Data / SM

20

1.4
1.2
1
0.8
0.6
50

100

150

200

250

1.4
1.2
1
0.8
0.6

300

50

100

150

200

100
90

s = 8 TeV, ∫ Ldt = 20.3 fb-1
H→WW*→eν µν + 0 jets

70

Data

SM (sys ⊕ stat)

WW

Other VV
Single Top
Z/ γ *→ττtt*
Z/ γ →ll
W+jet

QCD
H [125 GeV]

60

250

300

[GeV]
mtrack-clj
T

Events / 10 GeV

Events / 10 GeV[GeV]
mtrack-clj
T

80

QCD
H [125 GeV]

120

40

20

Data / SM

200

100
80

s = 8 TeV, ∫ Ldt = 20.3 fb-1
H→WW*→eν µν + 0 jets

Data

SM (sys ⊕ stat)

WW

Other VV
Single Top
Z/ γ *→ττtt*
Z/ γ →ll
W+jet

QCD
H [125 GeV]

60

50
40

40

30
20

20

Data / SM

Data / SM

10
1.4
1.2
1
0.8
0.6
50

100

150

200

250

300

[GeV]
mtrack-clj
T

1.4
1.2
1
0.8
0.6
50

100

150

200

250

300

[GeV]
mtrack-clj
T

Figure D.1: mT distribution for each sub-divisions in the 0-jet eµ channel : psub
T = 10-15
GeV and mℓℓ > 30 GeV (upper left), psub
>15
GeV
and
m
>
30
GeV
(upperleft),
psub
ℓℓ
T
T =
sub
10-15 GeV and mℓℓ < 30 GeV (lower left), pT >15 GeV and mℓℓ < 30 GeV (lower right).

269

50
45
40

s = 8 TeV, ∫ Ldt = 20.3 fb-1
H→WW*→µν eν + 0 jets

35

Data

SM (sys ⊕ stat)

WW

Other VV
Single Top
Z/ γ *→ττtt*
Z/ γ →ll
W+jet

Events / 10 GeV

Events / 10 GeV

Bibliography

QCD
H [125 GeV]

30

140
120

s = 8 TeV, ∫ Ldt = 20.3 fb-1
H→WW*→µν eν + 0 jets

Data

SM (sys ⊕ stat)

WW

Other VV
Single Top
Z/ γ *→ττtt*
Z/ γ →ll
W+jet

100

25

80

20

60

15

20
Data / SM

5
1.4
1.2
1
0.8
0.6
50

100

150

200

250

1.4
1.2
1
0.8
0.6

300

50

100

150

200

[GeV]
mtrack-clj
T

90
80

s = 8 TeV, ∫ Ldt = 20.3 fb-1

70

H→WW*→µν eν + 0 jets

Data

SM (sys ⊕ stat)

WW

Other VV
Single Top
Z/ γ *→ττtt*
Z/ γ →ll
W+jet

60

QCD
H [125 GeV]

250

300

[GeV]
mtrack-clj
T

Events / 10 GeV

Events / 10 GeV

QCD
H [125 GeV]

40

10

Data / SM

160

50

100
80

s = 8 TeV, ∫ Ldt = 20.3 fb-1
H→WW*→µν eν + 0 jets

Data

SM (sys ⊕ stat)

WW

Other VV
Single Top
Z/ γ *→ττtt*
Z/ γ →ll
W+jet

QCD
H [125 GeV]

60

40
40

30
20

20

Data / SM

Data / SM

10
1.4
1.2
1
0.8
0.6
50

100

150

200

250

300

[GeV]
mtrack-clj
T

1.4
1.2
1
0.8
0.6
50

100

150

200

250

300

[GeV]
mtrack-clj
T

Figure D.2: mT distribution for each sub-divisions in the 0-jet µe channel : psub
T = 10-15
GeV and mℓℓ > 30 GeV (upper left), psub
>15
GeV
and
m
>
30
GeV
(upperleft),
psub
ℓℓ
T
T =
sub
10-15 GeV and mℓℓ < 30 GeV (lower left), pT >15 GeV and mℓℓ < 30 GeV (lower right).

270

s = 8 TeV, ∫ Ldt = 20.3 fb-1

16
14

H→WW*→eν µν + 1 jet

Data

SM (sys ⊕ stat)

WW

Other VV
Single Top
Z/ γ *→ττtt*
Z/ γ →ll
W+jet

12

Events / 10 GeV

18

QCD
H [125 GeV]90
80

s = 8 TeV, ∫ Ldt = 20.3 fb-1

70

H→WW*→eν µν + 1 jet

50

8

40

6

30

4

20

2

10

1.4
1.2
1
0.8
0.6
50

100

150

200

250

Data

SM (sys ⊕ stat)

WW

Other VV
Single Top
Z/ γ *→ττtt*
Z/ γ →ll
W+jet

60

10

Data / SM

Data / SM

Events / 10 GeV

Bibliography

1.4
1.2
1
0.8
0.6

300

50

100

150

200

H→WW*→eν µν + 1 jet

Data

SM (sys ⊕ stat)

WW

Other VV
Single Top
Z/ γ *→ττtt*
Z/ γ →ll
W+jet

20

Events / 10 GeV

s = 8 TeV, ∫ Ldt = 20.3 fb

25

-1

QCD
H [125 GeV]

H→WW*→eν µν + 1 jet

20

5

10

150

200

250

300

[GeV]
mtrack-clj
TData

SM (sys ⊕ stat)

WW

Other VV
Single Top
Z/ γ *→ττtt*
Z/ γ →ll
W+jet

40

10

100

s = 8 TeV, ∫ Ldt = 20.3 fb-1

50

30

50

300

60

15

1.4
1.2
1
0.8
0.6

250

[GeV]
mtrack-clj
TData / SM

Data / SM

Events / 10 GeV[GeV]
mtrack-clj
T

30

QCD
H [125 GeV]QCD
H [125 GeV]

1.4
1.2
1
0.8
0.6
50

100

150

200

250

300

[GeV]
mtrack-clj
T

Figure D.3: mT distribution for each sub-divisions in the 1-jet eµ channel : psub
T = 10-15
GeV and mℓℓ > 30 GeV (upper left), psub
>15
GeV
and
m
>
30
GeV
(upperleft),
psub
ℓℓ
T
T =
sub
10-15 GeV and mℓℓ < 30 GeV (lower left), pT >15 GeV and mℓℓ < 30 GeV (lower right).

271

14
12

s = 8 TeV, ∫ Ldt = 20.3 fb-1
H→WW*→µν eν + 1 jet

Data

SM (sys ⊕ stat)

WW

Other VV
Single Top
Z/ γ *→ττtt*
Z/ γ →ll
W+jet

10

Events / 10 GeV

Events / 10 GeV

Bibliography

QCD
H [125 GeV]

70
60

s = 8 TeV, ∫ Ldt = 20.3 fb-1
H→WW*→µν eν + 1 jet

Data

SM (sys ⊕ stat)

WW

Other VV
Single Top
Z/ γ *→ττtt*
Z/ γ →ll
W+jet

50

30

4

20

2

10

1.4
1.2
1
0.8
0.6
50

100

150

200

250

1.4
1.2
1
0.8
0.6

300

50

100

150

200

14
s = 8 TeV, ∫ Ldt = 20.3 fb
H→WW*→µν eν + 1 jet

-1

Data

SM (sys ⊕ stat)

WW

Other VV
Single Top
Z/ γ *→ττtt*
Z/ γ →ll
W+jet

10

QCD
H [125 GeV]

8

300

40
35
30

s = 8 TeV, ∫ Ldt = 20.3 fb-1
H→WW*→µν eν + 1 jet

Data

SM (sys ⊕ stat)

WW

Other VV
Single Top
Z/ γ *→ττtt*
Z/ γ →ll
W+jet

25

QCD
H [125 GeV]

20

6

15

4

10

2

5
Data / SM

Data / SM

250

[GeV]
mtrack-clj
T

Events / 10 GeV

Events / 10 GeV[GeV]
mtrack-clj
T

12

QCD
H [125 GeV]

40

6

Data / SM

Data / SM

8

80

1.4
1.2
1
0.8
0.6
50

100

150

200

250

300

[GeV]
mtrack-clj
T

1.4
1.2
1
0.8
0.6
50

100

150

200

250

300

[GeV]
mtrack-clj
T

Figure D.4: mT distribution for each sub-divisions in the 1-jet µe channel : psub
T = 10-15
GeV and mℓℓ > 30 GeV (upper left), psub
>15
GeV
and
m
>
30
GeV
(upperleft),
psub
ℓℓ
T
T =
sub
10-15 GeV and mℓℓ < 30 GeV (lower left), pT >15 GeV and mℓℓ < 30 GeV (lower right).

272
Bibliography591.34 ± 1.78
781.70 ± 2.25
289.34 ± 1.17
70.54 ± 0.82

789.33 ± 2.26
781.70 ± 2.25
781.70 ± 2.25

Signal [125 GeV]
851.34 ± 2.69
815.21 ± 2.6411340.06 ± 14.51
11321.85 ± 14.50
11321.85 ± 14.50

WW11523.52 ± 14.62
11378.76 ± 14.53

1490.91 ± 12.12
2041.01 ± 13.99
591.84 ± 7.60
148.36 ± 3.52
NFs applied
735.86 ± 8.35
733.42 ± 8.34
569.33 ± 7.36
349.37 ± 6.02
349.37 ± 6.02
320.74 ± 5.80
320.74 ± 5.80
145.25 ± 3.97
175.49 ± 4.22
78.37 ± 2.72
323.93 ± 5.79
995.33 ± 10.00
326.20 ± 5.79
289.10 ± 5.46
171.12 ± 4.04
110.24 ± 3.26
115.44 ± 3.02
NFs applied
98.77 ± 2.79
98.77 ± 2.79
48.69 ± 1.93
NFs applied
492.04 ± 6.43
419.22 ± 5.95
363.05 ± 5.53
273.89 ± 4.89
138.06 ± 3.70
138.06 ± 3.70
118.27 ± 3.42
118.27 ± 3.42
31.06 ± 1.82
87.21 ± 2.89
41.28 ± 1.98
116.23 ± 3.40
663.88 ± 7.66
176.36 ± 3.97
109.54 ± 3.10
69.29 ± 2.43
126.15 ± 3.06
NFs applied
126.15 ± 3.06
126.15 ± 3.06
73.34 ± 2.43
49.19 ± 1.99
58.95 ± 2.18

2149.80 ± 14.51
2041.01 ± 13.99
2041.01 ± 13.99

Other VV
4806.33 ± 21.81
4290.11 ± 20.45

4.28 ± 0.38
4.28 ± 0.38
26.71 ± 0.56
16.96 ± 0.47
21.45 ± 0.51

192.93 ± 1.17
166.05 ± 1.03
141.18 ± 0.94
119.78 ± 0.77
100.25 ± 0.59
100.25 ± 0.59
87.25 ± 0.49
87.25 ± 0.49
13.89 ± 0.19
73.36 ± 0.45
48.81 ± 0.37
1.91 ± 0.35
225.66 ± 1.31
74.30 ± 0.69
52.65 ± 0.61
31.57 ± 0.48
4.28 ± 0.38

28.25 ± 0.43
28.25 ± 0.43
0.56 ± 0.18

322.34 ± 1.08
321.93 ± 1.07
272.65 ± 0.90
232.51 ± 0.68
232.51 ± 0.68
208.81 ± 0.64
208.81 ± 0.64
42.90 ± 0.27
165.91 ± 0.57
133.57 ± 0.46
2.14 ± 0.39
386.65 ± 1.38
169.30 ± 0.71
158.62 ± 0.64
128.64 ± 0.60
82.39 ± 0.48
49.79 ± 0.54

9121.65 ± 13.02
11321.85 ± 14.50
4951.87 ± 9.59
598.37 ± 3.44
NF = 1.22
7094.13 ± 12.68
7088.89 ± 12.68
5674.72 ± 11.35
1666.01 ± 6.12
1666.01 ± 6.12
1498.84 ± 5.81
1498.84 ± 5.81
184.45 ± 2.02
1314.38 ± 5.44
658.19 ± 3.84
2.47 ± 0.21
7214.82 ± 11.60
3873.77 ± 9.38
3562.40 ± 9.01
2994.43 ± 8.29
2179.35 ± 7.09
2056.20 ± 6.84
NF = 1.22
1948.64 ± 6.66
1948.64 ± 6.66
1111.45 ± 5.04
NF = 1.06
2781.31 ± 7.38
2430.73 ± 6.86
2285.49 ± 6.65
1683.65 ± 5.71
491.15 ± 3.07
491.15 ± 3.07
422.03 ± 2.85
422.03 ± 2.85
47.66 ± 0.95
374.37 ± 2.69
144.85 ± 1.67
1.00 ± 0.13
2961.14 ± 7.41
1368.80 ± 5.18
1042.27 ± 4.54
726.45 ± 3.80
1159.92 ± 4.75
NF = 1.06
1159.92 ± 4.75
1159.92 ± 4.75
347.02 ± 2.72
244.87 ± 2.23
304.55 ± 2.55

tt̄59889.72 ± 28.84
59380.15 ± 28.72
NF = 1.05
62291.28 ± 30.18
62214.96 ± 30.16
62214.96 ± 30.16
NF = 1.05
37927.21 ± 23.54
62214.96 ± 30.16
25385.75 ± 19.26
45582.02 ± 25.85
NF = 1.09
822.98 ± 3.52
814.95 ± 3.50
732.84 ± 3.32
141.18 ± 1.45
141.18 ± 1.45
132.69 ± 1.41
132.69 ± 1.41
20.08 ± 0.54
112.61 ± 1.30
39.92 ± 0.77
0.59 ± 0.09
871.96 ± 3.57
516.23 ± 2.79
487.52 ± 2.71
426.30 ± 2.53
186.12 ± 1.67
217.93 ± 1.81
NF = 1.09
216.46 ± 1.81
216.46 ± 1.81
187.29 ± 1.68
NF = 1.03
8138.04 ± 10.76
1599.27 ± 4.80
1528.02 ± 4.69
1095.34 ± 3.96
294.00 ± 2.05
294.00 ± 2.05
266.64 ± 1.95
266.64 ± 1.95
32.98 ± 0.68
233.66 ± 1.83
75.59 ± 1.04
1.36 ± 0.14
8967.03 ± 11.45
4508.62 ± 8.01
3592.30 ± 7.15
1960.89 ± 5.28
827.09 ± 3.46
NF = 1.03
827.09 ± 3.46
827.09 ± 3.46
6599.58 ± 9.73
4674.09 ± 8.17
5783.48 ± 9.11

Single Top
5748.70 ± 7.26
5703.64 ± 7.21
NF = 1.05
5936.77 ± 7.15
5930.55 ± 7.15
5930.55 ± 7.15
NF = 1.05
4365.61 ± 6.12
5930.55 ± 7.15
2659.49 ± 4.72
3663.46 ± 5.45
NF = 1.09
408.04 ± 2.03
406.11 ± 2.03
364.25 ± 1.88
79.31 ± 0.85
79.31 ± 0.85
75.21 ± 0.81
75.21 ± 0.81
9.89 ± 0.29
65.32 ± 0.76
21.41 ± 0.47
0.47 ± 0.07
434.15 ± 2.08
261.27 ± 1.58
248.42 ± 1.53
220.22 ± 1.38
119.90 ± 1.03
120.17 ± 1.19
NF = 1.09
119.48 ± 1.14
119.48 ± 1.14
83.73 ± 0.80
NF = 1.03
2238.43 ± 4.32
546.78 ± 2.34
522.81 ± 2.27
384.21 ± 1.95
109.78 ± 1.09
109.78 ± 1.09
101.00 ± 1.00
101.00 ± 1.00
11.84 ± 0.38
89.16 ± 0.93
29.40 ± 0.61
1.83 ± 0.43
2495.32 ± 4.62
1197.11 ± 3.13
964.07 ± 2.76
612.86 ± 2.18
266.92 ± 1.52
NF = 1.03
266.92 ± 1.52
266.92 ± 1.52
1707.21 ± 3.67
1434.80 ± 3.31
1485.23 ± 3.41
182.73 ± 20.80
564.81 ± 35.13
18.02 ± 2.27
23.27 ± 7.15

573.68 ± 35.18
564.81 ± 35.13
564.81 ± 35.13

Z → ℓℓ + γ/jets
2535.47 ± 88.71
907.92 ± 37.06

44632.41 ± 88.77
44603.03 ± 88.74
44603.03 ± 88.74
NFs applied
12055.96 ± 45.16
44603.03 ± 88.74
1045.55 ± 12.89
1157.16 ± 14.39

Z → τ τ + γ/jets
52129.75 ± 95.82
44756.46 ± 88.89

2331.82 ± 19.04
3726.42 ± 30.39
851.95 ± 9.59
538.20 ± 10.51

3715.91 ± 30.57
3726.42 ± 30.39
3726.42 ± 30.39

W +jets
3545.57 ± 49.47
6237.25 ± 39.43

599.99 ± 3.54
2176.42 ± 6.10
46.30 ± 1.35
122.17 ± 1.37

2228.36 ± 6.17
2176.42 ± 6.10
2176.42 ± 6.10

QCD
7857.39 ± 10.74
3447.42 ± 7.51

68075.88 ± 61.28
132579.07 ± 106.94
35550.77 ± 28.43
51833.00 ± 33.06

132868.28 ± 107.11
132579.07 ± 106.94
132579.07 ± 106.94

Total Bkg.
148036.45 ± 145.55
136101.72 ± 111.32

16410
16326
9334
3411
3411
2642
2642
614
2028
1129
531
48505
6123
5032
4057
2780
3255

69244
13567536392
51833

136013135675135675Observed
1575571429261.01 ± 0.01
1.00 ± 0.01
1.01 ± 0.01
1.12 ± 0.02
1.12 ± 0.02
1.13 ± 0.02
1.13 ± 0.02
1.13 ± 0.05
1.13 ± 0.03
1.20 ± 0.04
1.00 ± 0.05
1.05 ± 0.01
1.00 ± 0.01
1.00 ± 0.01
1.00 ± 0.02
1.01 ± 0.02
1.02 ± 0.02

1.02 ± 0.00
1.02 ± 0.00
1.02 ± 0.01
1.00 ± 0.00

1.02 ± 0.00
1.02 ± 0.00
1.02 ± 0.00

Data/MC
1.06 ± 0.00
1.05 ± 0.00

1.01 ± 0.02
1.01 ± 0.02
0.93 ± 0.03

16311.04 ± 40.85
16249.16 ± 40.76
9266.07 ± 22.79
3052.66 ± 14.08
3052.66 ± 14.08
2345.06 ± 10.30
2345.06 ± 10.30
543.42 ± 6.62
1801.63 ± 7.89
937.70 ± 5.78
528.86 ± 7.67
46278.81 ± 88.17
6122.08 ± 16.47
5022.73 ± 12.28
4054.34 ± 10.46
2753.08 ± 8.67
3177.38 ± 14.21

2711
2711
1381

1.01 ± 0.01
1.01 ± 0.01
1.01 ± 0.01
1.02 ± 0.02
1.06 ± 0.03
1.06 ± 0.03
1.10 ± 0.03
1.10 ± 0.03
1.13 ± 0.08
1.09 ± 0.04
1.22 ± 0.06
1.01 ± 0.08
1.03 ± 0.01
1.01 ± 0.01
1.01 ± 0.01
1.01 ± 0.02
1.00 ± 0.02

236.82 ± 2.67
230.25 ± 2.66
27.86 ± 1.83
12.39 ± 1.71
12.39 ± 1.71
9.17 ± 1.63
9.17 ± 1.63
5.66 ± 1.55
3.51 ± 0.51
0.82 ± 0.60
5.49 ± 0.67
1196.29 ± 4.74
27.12 ± 1.21
2.22 ± 0.90
-0.58 ± 0.87
-0.29 ± 0.72
6.08 ± 0.53

2682.75 ± 9.33
2682.75 ± 9.33
1487.25 ± 5.91

20595
10854
7365
4573
1655
1655
1128
1128
196
932
407
193
25759
7763
5863
3477
2646

1.00 ± 0.02
1.00 ± 0.02
1.01 ± 0.01
1.00 ± 0.01
1.00 ± 0.01

1334.92 ± 12.62
1333.39 ± 12.57
1054.39 ± 8.76
426.61 ± 6.16
426.61 ± 6.16
277.65 ± 5.02
277.65 ± 5.02
163.11 ± 4.13
114.54 ± 2.85
132.73 ± 2.90
173.78 ± 4.23
2014.69 ± 22.54
466.62 ± 5.90
399.15 ± 4.78
237.47 ± 3.69
154.95 ± 2.98
298.43 ± 4.32

1.98 ± 0.48
1.98 ± 0.48
0.95 ± 0.1220357.52 ± 37.14
10776.32 ± 32.94
7266.84 ± 24.00
4489.10 ± 15.78
1568.55 ± 10.40
1568.55 ± 10.40
1028.91 ± 6.18
1028.91 ± 6.18
173.04 ± 3.27
855.87 ± 5.25
334.85 ± 3.44
191.09 ± 4.49
24919.82 ± 43.22
7716.09 ± 13.20
5822.78 ± 10.07
3438.76 ± 7.77
2641.72 ± 11.97

2646
2646
9741
6717
7934

5562.51 ± 31.74
5527.12 ± 31.66
782.68 ± 11.70
349.94 ± 7.80
349.94 ± 7.80
12.31 ± 1.59
12.31 ± 1.59
6.10 ± 1.10
6.21 ± 1.16
2.34 ± 0.67
2.74 ± 0.82
33159.70 ± 78.58
637.09 ± 9.95
25.60 ± 1.97
1.58 ± 0.57
0.35 ± 0.28
339.47 ± 7.61

182.42 ± 3.08
182.42 ± 3.08
53.96 ± 1.47

334.25 ± 2.22
268.17 ± 2.00
62.35 ± 0.98
31.70 ± 0.77
18.61 ± 0.59
18.61 ± 0.59
6.06 ± 0.39
6.06 ± 0.39
3.07 ± 0.27
2.99 ± 0.28
0.54 ± 0.19
2.95 ± 0.25
672.07 ± 3.18
13.12 ± 0.51
0.35 ± 0.20
0.08 ± 0.18
12.81 ± 0.43

2641.72 ± 11.97
2641.72 ± 11.97
9649.97 ± 17.07
6715.10 ± 12.27
7946.34 ± 12.65

115.77 ± 15.75
115.02 ± 15.74
59.99 ± 10.24
27.85 ± 4.47
27.85 ± 4.47
18.45 ± 2.37
18.45 ± 2.37
8.88 ± 1.68
9.57 ± 1.67
3.92 ± 1.09
19.38 ± 2.50
391.87 ± 28.61
13.79 ± 2.01
8.33 ± 1.57
3.79 ± 1.15
2.46 ± 0.92
23.66 ± 8.04

662.57 ± 12.00
534.83 ± 10.58
476.35 ± 7.17
310.95 ± 5.50
128.61 ± 4.00
128.61 ± 4.00
88.02 ± 2.89
88.02 ± 2.89
38.34 ± 2.06
49.67 ± 2.02
39.94 ± 1.73
62.15 ± 2.60
878.37 ± 15.33
192.68 ± 4.69
110.39 ± 3.41
67.40 ± 2.64
152.06 ± 3.07

12.81 ± 0.43
12.81 ± 0.43
66.08 ± 0.97
12.32 ± 0.40
15.65 ± 0.45

9.14 ± 1.71
9.14 ± 1.71
0.66 ± 0.37
62.47 ± 13.54
53.43 ± 12.54
40.33 ± 11.15
18.85 ± 5.39
5.82 ± 1.31
5.82 ± 1.31
4.56 ± 1.17
4.56 ± 1.17
1.26 ± 0.60
3.30 ± 1.01
0.80 ± 0.44
4.75 ± 1.18
113.38 ± 15.97
2.79 ± 0.84
1.06 ± 0.51
0.75 ± 0.41
15.42 ± 8.67
15.42 ± 8.67
15.42 ± 8.67
8.27 ± 4.55
5.32 ± 4.17
3.01 ± 1.82

152.06 ± 3.07
152.06 ± 3.07
127.60 ± 5.67
90.46 ± 3.85
107.77 ± 4.20

105.87 ± 4.21
105.87 ± 4.21
0.52 ± 0.31
NFs applied
5648.41 ± 28.58
4923.90 ± 26.48
1988.44 ± 17.23
690.52 ± 10.62
382.53 ± 7.85
382.53 ± 7.85
22.33 ± 1.93
22.33 ± 1.93
6.83 ± 1.09
15.50 ± 1.60
2.44 ± 0.69
0.83 ± 0.37
8168.62 ± 33.20
256.61 ± 5.88
2.79 ± 0.68
1.05 ± 0.36
81.35 ± 3.52
NFs applied
81.35 ± 3.52
81.35 ± 3.52
720.87 ± 10.78
204.04 ± 5.62
187.71 ± 5.74

Table D.1: Full cutflow for the 8 TeV ggF Njet = 0 and = 1 eµ+µe signal and control regions. Uncertainties are statistical
only. The Data/MC ratio does not include signal yields.
lepton pT
Scale factors
OS leptons
mℓℓ > 10, 12 GeV
Z veto (SF)
Scale factors
miss,(track)E> [40], (20)T,[rel],(clj)
Z VR (incl)
miss > 40 GeV
Z VR (incl), ET,rel
Top VR (incl)
Scale factors
0j: jet veto
0j: ∆ϕℓℓ,M ET > 1.57
0j: pT,ℓℓ >30 GeV
0j: mℓℓ < 55 GeV
miss,track
0j: ET,rel> 40 GeV (SF)0j: ∆ϕℓℓ < 1.8
0j: frecoil < 0.1 (SF)0j: low pT
0j: high pT
0j: 0.75 · mH ≤ mT ≤ mH
0j: SSCR
0j: Z VR
0j: Z VR (E miss )T,rel
0j: Z VR (pT,ℓℓ )
miss,track
0j: Z VR (ET,rel)
0j: Z VR (frecoil )
miss,track
0j: W W CR (no SF ET,rel)
Scale factors
0j: W W CR
0j: W W CR (SF frecoil )0j: W W VR
Scale factors
1j: one jet
1j: b-jet veto
1j: Max lepton-MT (DF)1j: Z → τ τ veto (DF)1j: mℓℓ < 55 GeV
miss,track
1j: ET,rel> 35 GeV (SF)1j: ∆ϕℓℓ < 1.8
1j: frecoil < 0.10 (SF)1j: low pT
1j: high pT
1j: 0.75 · mH ≤ mT ≤ mH
1j: SSCR
1j: Z VR
miss )
1j: Z VR (ET,rel
1j: Z VR (E miss,track )T,rel
1j: Z VR (frecoil )
miss,track
1j: W W CR (no SF ET,rel)
Scale factors
1j: W W control region
1j: W W control region (SF frecoil )
miss,track
1j: Top CR (no SF ET,rel)
1j: Top CR
1j: Top CR (SF frecoil )lepton pT
Scale factors
OS leptons
mℓℓ > 10, 12 GeV
Z veto (SF)
Scale factors
miss,(track)ET,[rel],(clj) > [40], (20)Z VR (incl)
miss > 40 GeV
Z VR (incl), ET,rel
Top VR (incl)
Scale factors
0j: jet veto
0j: ∆ϕℓℓ,M ET > 1.57
0j: pT,ℓℓ >30 GeV
0j: mℓℓ < 55 GeV
miss,track
0j: ET,rel> 40 GeV (SF)0j: ∆ϕℓℓ < 1.8
0j: frecoil < 0.1 (SF)0j: low pT
0j: high pT
0j: 0.75 · mH ≤ mT ≤ mH
0j: SSCR
0j: Z VR
miss )
0j: Z VR (ET,rel
0j: Z VR (pT,ℓℓ )
miss,track
0j: Z VR (ET,rel)
0j: Z VR (frecoil )
miss,track
0j: W W CR (no SF ET,rel)
Scale factors
0j: W W CR
0j: W W CR (SF frecoil )0j: W W VR
Scale factors
1j: one jet
1j: b-jet veto
1j: Max lepton-MT (DF)1j: Z → τ τ veto (DF)1j: mℓℓ < 55 GeV
miss,track
1j: ET,rel> 35 GeV (SF)1j: ∆ϕℓℓ < 1.8
1j: frecoil < 0.10 (SF)1j: low pT
1j: high pT
1j: 0.75 · mH ≤ mT ≤ mH
1j: SSCR
1j: Z VR
miss )
1j: Z VR (ET,rel
miss,track
1j: Z VR (ET,rel)
1j: Z VR (frecoil )
miss,track
1j: W W CR (no SF ET,rel)
Scale factors
1j: W W control region
1j: W W control region (SF frecoil )
miss,track
1j: Top CR (no SF ET,rel)
1j: Top CR
1j: Top CR (SF frecoil )11799.62 ± 14.92
11742.00 ± 14.89
9216.56 ± 13.18
4075.19 ± 8.78
2525.43 ± 6.92
1021.82 ± 4.41
284.44 ± 2.40
NF = 1.22
3247.40 ± 8.66
3243.99 ± 8.66
3000.77 ± 8.34
1252.63 ± 5.39
1093.77 ± 5.05
1064.88 ± 4.98
783.77 ± 4.29
72.09 ± 1.29
711.69 ± 4.09
347.80 ± 2.85
0.95 ± 0.13
1626.34 ± 5.57
784.30 ± 4.27
704.91 ± 4.06
578.44 ± 3.69
419.83 ± 3.15
801.34 ± 4.32
NF = 1.22
584.37 ± 3.70
428.54 ± 3.18
706.87 ± 4.06
NF = 1.06
1122.13 ± 4.74
981.51 ± 4.40
981.51 ± 4.40
981.51 ± 4.40
354.63 ± 2.65
295.28 ± 2.42
267.79 ± 2.30
189.85 ± 1.95
22.99 ± 0.67
166.86 ± 1.83
59.43 ± 1.09
0.22 ± 0.06
653.93 ± 3.53
291.34 ± 2.43
213.39 ± 2.09
147.38 ± 1.74
385.61 ± 2.76
NF = 1.06
269.58 ± 2.31
185.36 ± 1.92
139.60 ± 1.75
80.50 ± 1.30
71.68 ± 1.26

850.52 ± 2.55
828.40 ± 2.54
770.61 ± 2.17

288.42 ± 1.13
57.79 ± 1.31
7.19 ± 0.57
26.97 ± 0.47

0.56 ± 0.21
0.44 ± 0.19
10.55 ± 0.34
5.65 ± 0.24
4.14 ± 0.19

77.13 ± 0.74
66.47 ± 0.66
66.47 ± 0.66
66.47 ± 0.66
57.87 ± 0.51
42.62 ± 0.43
38.57 ± 0.41
23.15 ± 0.28
4.37 ± 0.10
18.78 ± 0.26
15.97 ± 0.22
0.76 ± 0.26
18.71 ± 0.75
3.17 ± 0.40
1.78 ± 0.31
0.65 ± 0.19
0.92 ± 0.29

7.02 ± 0.20
4.28 ± 0.18
0.47 ± 0.16

171.45 ± 0.67
171.23 ± 0.67
160.75 ± 0.65
146.88 ± 0.58
120.94 ± 0.53
117.00 ± 0.53
74.77 ± 0.42
13.07 ± 0.15
61.70 ± 0.40
58.27 ± 0.34
0.89 ± 0.24
20.75 ± 0.61
2.26 ± 0.25
1.63 ± 0.23
1.25 ± 0.22
0.80 ± 0.19
20.38 ± 0.25

WW11968.71 ± 15.03
11829.38 ± 14.94

Signal [125 GeV]
913.38 ± 2.99
879.86 ± 2.95

30.30 ± 1.31
19.63 ± 1.02
28.63 ± 1.40
14.11 ± 0.95
11.52 ± 0.88

193.64 ± 3.57
164.97 ± 3.28
164.97 ± 3.28
164.97 ± 3.28
79.44 ± 2.41
49.72 ± 1.84
44.91 ± 1.75
29.73 ± 1.43
6.92 ± 0.72
22.81 ± 1.23
11.30 ± 0.92
22.73 ± 1.44
1527.66 ± 7.70
515.72 ± 4.62
380.63 ± 3.94
246.13 ± 3.14
46.91 ± 1.65

44.34 ± 1.50
30.67 ± 1.24
44.63 ± 1.56

366.46 ± 5.08
363.49 ± 5.07
316.87 ± 4.78
182.73 ± 3.88
109.99 ± 2.81
107.69 ± 2.79
71.52 ± 2.25
19.64 ± 1.31
51.88 ± 1.82
32.52 ± 1.57
57.91 ± 2.32
2447.66 ± 8.35
879.61 ± 5.42
804.77 ± 5.18
681.70 ± 4.75
482.83 ± 3.95
64.57 ± 1.96

642.13 ± 6.66
4895.68 ± 12.97
1652.23 ± 7.94
71.22 ± 2.31

7748.74 ± 18.53
7564.33 ± 18.00
2668.65 ± 12.48

Other VV
10290.00 ± 24.00
9779.67 ± 22.96

tt̄
60864.97 ± 29.01
60378.04 ± 28.89
NF = 1.05
63360.16 ± 30.36
63107.21 ± 30.30
49903.22 ± 26.94
NF = 1.05
18651.80 ± 16.46
13203.99 ± 13.87
5358.01 ± 8.83
18435.23 ± 16.39
NF = 1.09
419.48 ± 2.51
416.93 ± 2.50
395.56 ± 2.44
109.55 ± 1.28
99.39 ± 1.22
96.47 ± 1.20
40.86 ± 0.78
6.27 ± 0.30
34.59 ± 0.72
10.89 ± 0.40
0.19 ± 0.05
173.32 ± 1.59
102.15 ± 1.24
95.63 ± 1.20
83.88 ± 1.12
36.26 ± 0.74
83.01 ± 1.12
NF = 1.09
69.28 ± 1.02
29.28 ± 0.66
132.10 ± 1.41
NF = 1.03
3648.34 ± 7.19
718.43 ± 3.21
718.43 ± 3.21
718.43 ± 3.21
224.16 ± 1.79
191.55 ± 1.65
177.45 ± 1.59
97.17 ± 1.18
14.15 ± 0.44
83.02 ± 1.09
22.93 ± 0.57
0.39 ± 0.07
1874.64 ± 5.23
945.26 ± 3.66
747.25 ± 3.26
408.93 ± 2.41
333.42 ± 2.19
NF = 1.03
243.08 ± 1.87
129.58 ± 1.37
2956.73 ± 6.50
1765.23 ± 5.01
1289.21 ± 4.29

Single Top
5846.84 ± 7.32
5804.62 ± 7.28
NF = 1.05
6047.50 ± 7.27
6026.80 ± 7.26
4761.06 ± 6.41
NF = 1.05
2046.97 ± 4.21
1265.75 ± 3.41
563.14 ± 2.21
1620.44 ± 3.64
NF = 1.09
211.99 ± 1.38
211.57 ± 1.38
202.05 ± 1.33
64.22 ± 0.78
58.92 ± 0.73
57.44 ± 0.68
30.99 ± 0.50
4.41 ± 0.19
26.58 ± 0.47
8.31 ± 0.28
0.31 ± 0.11
92.31 ± 1.01
55.08 ± 0.79
51.41 ± 0.75
44.89 ± 0.63
23.71 ± 0.43
48.70 ± 0.67
NF = 1.09
39.98 ± 0.60
21.33 ± 0.44
61.21 ± 0.69
NF = 1.03
966.67 ± 2.88
242.13 ± 1.63
242.13 ± 1.63
242.13 ± 1.63
83.52 ± 1.04
71.81 ± 0.86
67.35 ± 0.82
43.37 ± 0.65
5.85 ± 0.28
37.52 ± 0.58
10.68 ± 0.35
0.30 ± 0.27
545.44 ± 2.18
256.97 ± 1.45
201.96 ± 1.24
128.95 ± 1.01
100.28 ± 0.87
NF = 1.03
73.99 ± 0.75
44.25 ± 0.57
731.11 ± 2.40
525.19 ± 2.01
376.34 ± 1.71
16192345.92 ± 8112.88
16162912.14 ± 8112.57
1835968.42 ± 2031.24
NFs applied
41142.35 ± 264.49
14326943.72 ± 7854.16
311269.08 ± 1030.37
2830.42 ± 67.36
NFs applied
31818.84 ± 235.84
29252.31 ± 223.43
6862.84 ± 101.33
4900.17 ± 34.13
661.66 ± 14.81
649.95 ± 14.72
90.37 ± 5.26
21.97 ± 2.53
68.40 ± 4.61
64.29 ± 4.54
0.23 ± 0.1811055491.90 ± 6875.07
250892.95 ± 918.49
33172.47 ± 385.89
3198.08 ± 135.29
434.59 ± 60.68
1678.83 ± 66.70
NFs applied
123.32 ± 21.44
6.29 ± 1.63
70.51 ± 19.15
NFs applied
8334.16 ± 113.12
6867.41 ± 100.84
7464.26 ± 109.63
7464.26 ± 109.63
3466.06 ± 24.07
198.40 ± 8.79
197.91 ± 9.20
26.18 ± 2.95
8.05 ± 1.26
18.13 ± 2.67
13.65 ± 2.53
0.00 ± 0.00
2413668.33 ± 3258.62
49491.46 ± 423.51
1694.06 ± 102.52
224.22 ± 44.89
1342.06 ± 67.71
NFs applied
52.69 ± 17.37
9.14 ± 8.51
1308.84 ± 46.66
47.06 ± 9.36
24.03 ± 13.09

Z → ℓℓ + γ/jets
16567081.31 ± 8163.91
16225683.08 ± 8120.74

0.39 ± 0.29
0.26 ± 0.26
0.21 ± 0.21
NFs applied
279.44 ± 6.16
240.81 ± 5.66
240.81 ± 5.66
240.81 ± 5.66
167.80 ± 4.68
1.75 ± 0.51
1.50 ± 0.49
0.85 ± 0.35
0.17 ± 0.17
0.68 ± 0.30
0.00 ± 0.00
0.02 ± 0.02
317.73 ± 6.59
8.08 ± 0.96
0.39 ± 0.21
0.23 ± 0.14
2.55 ± 0.58
NFs applied
0.23 ± 0.23
0.23 ± 0.23
38.57 ± 2.45
0.47 ± 0.22
0.33 ± 0.19

684.27 ± 10.37
621.31 ± 9.88
21.05 ± 1.79
8.70 ± 1.13
0.28 ± 0.20
0.28 ± 0.20
0.11 ± 0.11
0.00 ± 0.00
0.11 ± 0.11
0.11 ± 0.11
0.00 ± 0.00
1356.92 ± 16.09
27.97 ± 2.10
1.97 ± 0.51
0.18 ± 0.18
0.00 ± 0.00
9.69 ± 1.21

48995.52 ± 93.36
48934.46 ± 93.31
47132.54 ± 91.55
NFs applied
1062.35 ± 13.00
1801.91 ± 18.06
41.80 ± 2.56
83.10 ± 3.85

Z → τ τ + γ/jets
55564.19 ± 99.41
49080.33 ± 93.44

14.19 ± 0.84
9.29 ± 0.61
40.54 ± 3.38
16.73 ± 1.99
9.94 ± 1.60

177.59 ± 6.71
137.07 ± 5.80
137.07 ± 5.80
137.07 ± 5.80
73.11 ± 4.32
37.49 ± 1.98
30.27 ± 1.77
17.39 ± 1.31
6.63 ± 0.84
10.76 ± 1.00
11.17 ± 0.97
13.77 ± 1.23
2821.04 ± 59.90
89.91 ± 9.01
20.93 ± 2.00
11.90 ± 1.21
31.37 ± 1.67

34.57 ± 1.72
22.19 ± 1.13
22.41 ± 0.91

503.98 ± 11.14
492.62 ± 10.79
396.06 ± 6.67
250.57 ± 5.27
133.48 ± 3.34
122.28 ± 3.17
78.54 ± 2.46
33.80 ± 1.70
44.75 ± 1.78
53.17 ± 1.98
41.54 ± 1.94
10385.52 ± 102.39
272.74 ± 17.17
109.53 ± 7.37
40.82 ± 2.38
21.87 ± 1.43
77.87 ± 2.94

836.17 ± 14.18
14299.23 ± 124.89
401.40 ± 20.17
196.69 ± 6.68

18826.16 ± 148.73
22169.52 ± 144.80
7870.28 ± 73.28

W +jets
21993.57 ± 162.28
18535.11 ± 152.08

0.03 ± 0.01
0.02 ± 0.01
2.54 ± 0.17
-0.00 ± 0.06
0.04 ± 0.03

12.77 ± 0.37
10.23 ± 0.32
10.23 ± 0.32
10.23 ± 0.32
7.79 ± 0.28
0.20 ± 0.05
0.17 ± 0.05
0.02 ± 0.03
0.01 ± 0.01
0.02 ± 0.02
0.00 ± 0.01
-0.05 ± 0.04
65.40 ± 0.92
1.45 ± 0.14
0.05 ± 0.04
0.00 ± 0.02
0.59 ± 0.08

0.07 ± 0.02
0.04 ± 0.02
0.06 ± 0.02

29.22 ± 0.60
25.84 ± 0.57
2.60 ± 0.29
1.98 ± 0.27
0.53 ± 0.24
0.46 ± 0.24
0.04 ± 0.23
-0.13 ± 0.22
0.17 ± 0.04
-0.05 ± 0.22
0.14 ± 0.04
143.34 ± 1.66
3.15 ± 0.30
0.02 ± 0.17
-0.15 ± 0.14
-0.08 ± 0.11
0.39 ± 0.05

45.04 ± 0.72
235.20 ± 1.98
5.12 ± 0.34
6.15 ± 0.26

6901.81 ± 8.46
2429.08 ± 5.10
2193.88 ± 4.70

QCD
11913.82 ± 11.20
7998.49 ± 9.04

684.08 ± 17.71
397.50 ± 8.93
5246.56 ± 47.41
2449.28 ± 11.11
1783.09 ± 14.06

14734.75 ± 113.90
9362.56 ± 101.38
9959.41 ± 110.12
9959.41 ± 110.12
4456.50 ± 25.24
846.20 ± 9.70
787.34 ± 9.98
404.57 ± 4.26
64.76 ± 1.89
339.80 ± 3.82
129.15 ± 3.14
37.38 ± 1.92
2421474.16 ± 3259.19
51600.19 ± 423.66
3258.67 ± 102.69
1167.74 ± 45.13
2242.78 ± 67.85

896.32 ± 21.91
538.60 ± 4.04
1038.00 ± 19.72

37281.66 ± 236.56
34628.06 ± 224.15
11197.81 ± 102.05
6770.54 ± 35.22
2158.02 ± 16.31
2099.45 ± 16.17
1096.19 ± 7.62
158.03 ± 3.59
938.16 ± 6.73
517.04 ± 5.95
101.27 ± 3.03
11071717.30 ± 6875.86
253017.95 ± 918.68
34940.71 ± 386.02
4627.85 ± 135.45
1418.99 ± 60.92
2764.40 ± 66.96

68502.00 ± 265.96
14365170.93 ± 7855.20
320312.60 ± 1030.65
23527.68 ± 69.93

16356025.43 ± 8114.88
16324885.54 ± 8114.50
1959714.62 ± 2034.90

Total Bkg.
16745523.40 ± 8166.24
16389088.72 ± 8122.81

651
371
5441
2457
1791

15333
9892
9892
9892
5123
959
888
467
64
403
143
34
2476415
51512
3319
1149
2057

863
526
998

38015
35425
11656
6785
2197
2127
1108
159
949
510
89
11014687
253043
34951
4623
1419
2637

70601
14366535
32030724022

16519905
16379188
2012653

Observed
17068931
16554616

0.95 ± 0.04
0.93 ± 0.05
1.04 ± 0.02
1.00 ± 0.02
1.00 ± 0.03

1.04 ± 0.01
1.06 ± 0.02
0.99 ± 0.01
0.99 ± 0.01
1.15 ± 0.02
1.13 ± 0.04
1.13 ± 0.04
1.15 ± 0.05
0.99 ± 0.13
1.19 ± 0.06
1.11 ± 0.10
0.91 ± 0.16
1.02 ± 0.00
1.00 ± 0.01
1.02 ± 0.04
0.98 ± 0.05
0.92 ± 0.03

0.96 ± 0.04
0.98 ± 0.04
0.96 ± 0.04

1.02 ± 0.01
1.02 ± 0.01
1.04 ± 0.01
1.00 ± 0.01
1.02 ± 0.02
1.01 ± 0.02
1.01 ± 0.03
1.01 ± 0.08
1.01 ± 0.03
0.99 ± 0.05
0.88 ± 0.10
0.99 ± 0.00
1.00 ± 0.00
1.00 ± 0.01
1.00 ± 0.03
1.00 ± 0.05
0.95 ± 0.03

1.03 ± 0.01
1.00 ± 0.00
1.00 ± 0.00
1.02 ± 0.01

1.01 ± 0.00
1.00 ± 0.00
1.03 ± 0.00

Data/MC1.02 ± 0.00
1.01 ± 0.00

Table D.2: Full cutflow for the 8 TeV ggF Njet = 0 and = 1 ee+µµ signal and control regions. Uncertainties are statistical
only. The Data/MC ratio does not include signal yields.

273
Bibliography

274
Bibliography

ggF [125 GeV]
4.59 ± 0.08
3.03 ± 0.06
1.21 ± 0.04
0.36 ± 0.02
1.56 ± 0.04

W +jets
3.82 ± 0.85
3.38 ± 0.81
0.43 ± 0.26
0.01 ± 0.02
0.44 ± 0.26

W +jets
1.24 ± 0.51
0.99 ± 0.47
0.28 ± 0.19
-0.03 ± 0.02
0.25 ± 0.19

ggF [125 GeV]
2.20 ± 0.05
1.48 ± 0.04
0.56 ± 0.03
0.16 ± 0.01
0.72 ± 0.03

EW Z → τ τ +jets
0.15 ± 0.08
0.05 ± 0.05
0.09 ± 0.05
0.00 ± 0.00
0.09 ± 0.05

VH [125 GeV]
0.06 ± 0.04
0.06 ± 0.04
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00

EW Z → τ τ +jets
0.66 ± 0.20
0.18 ± 0.09
0.36 ± 0.15
0.12 ± 0.09
0.48 ± 0.17

VH [125 GeV]
0.10 ± 0.05
0.08 ± 0.05
0.02 ± 0.02
0.00 ± 0.00
0.02 ± 0.02

QCD
0.16 ± 0.04
0.16 ± 0.04
-0.00 ± 0.00
-0.00 ± 0.00
-0.00 ± 0.00

WW4.94 ± 0.25
3.53 ± 0.22
1.14 ± 0.12
0.26 ± 0.05
1.40 ± 0.13

QCD
2.11 ± 0.17
1.84 ± 0.16
0.27 ± 0.06
0.00 ± 0.00
0.27 ± 0.06

WW
8.58 ± 0.33
5.99 ± 0.28
2.06 ± 0.16
0.53 ± 0.07
2.60 ± 0.18

tt̄
19.07 ± 0.61
16.97 ± 0.59
1.85 ± 0.14
0.26 ± 0.05
2.10 ± 0.15

Data/MC
1.14 ± 0.15
0.90 ± 0.15
1.87 ± 0.51
4.06 ± 1.71
2.23 ± 0.51

Single Top
3.52 ± 0.27
3.16 ± 0.27
0.29 ± 0.04
0.07 ± 0.02
0.37 ± 0.04

Observed
57
37
14
6
20

Data/MC
1.29 ± 0.16
1.12 ± 0.17
1.68 ± 0.47
5.61 ± 2.41
2.12 ± 0.50

Single Top
2.11 ± 0.22
1.83 ± 0.21
0.24 ± 0.06
0.04 ± 0.01
0.28 ± 0.06

Observed
72
52
14
6
20

tt̄
12.04 ± 0.48
10.67 ± 0.47
1.18 ± 0.11
0.19 ± 0.05
1.37 ± 0.12

Total Bkg.(+ggF)
55.80 ± 2.42
46.38 ± 2.33
8.35 ± 0.63
1.07 ± 0.14
9.42 ± 0.64

W Z/ZZ/W γ
1.21 ± 0.27
0.89 ± 0.22
0.30 ± 0.15
0.02 ± 0.02
0.32 ± 0.15

Total Bkg.(+ggF)
49.89 ± 1.40
40.94 ± 1.31
7.48 ± 0.47
1.48 ± 0.15
8.95 ± 0.50

W Z/ZZ/W γ
3.35 ± 0.57
2.53 ± 0.49
0.75 ± 0.28
0.06 ± 0.06
0.82 ± 0.28

Table D.3: Event yields in the VBF BDT eµ+µe (top) and ee+µµ (bottom) signal region. The Data/MC ratio does notinclude signal yields.

VBF [125 GeV]
11.52 ± 0.14
4.19 ± 0.09
4.21 ± 0.09
3.12 ± 0.07
7.33 ± 0.11

Z → τ τ +jets
4.16 ± 0.53
3.85 ± 0.52
0.26 ± 0.06
0.06 ± 0.04
0.32 ± 0.07

Z → τ τ +jets
2.03 ± 0.32
1.74 ± 0.32
0.28 ± 0.08
0.01 ± 0.01
0.29 ± 0.08

VBF [125 GeV]
6.38 ± 0.11
2.17 ± 0.06
2.47 ± 0.07
1.74 ± 0.06
4.21 ± 0.09

EW Z → ℓℓ+jets
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00eµ+µe
≥2j: Fit region≥2j: −0.48 <BDT< 0.30
≥2j: 0.30 <BDT< 0.78
≥2j: 0.78 <BDT< 1.0≥2j: 0.30 <BDT< 1.0

Z → ℓℓ+jets
0.02 ± 0.02
0.02 ± 0.02
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00

EW Z → ℓℓ+jets
0.55 ± 0.14
0.42 ± 0.12
0.08 ± 0.04
0.05 ± 0.05
0.13 ± 0.07

ee+µµ
≥2j: Fit region≥2j: −0.48 <BDT< 0.30
≥2j: 0.30 <BDT< 0.78
≥2j: 0.78 <BDT< 1.0≥2j: 0.30 <BDT< 1.0

Z → ℓℓ+jets
29.18 ± 2.25
24.61 ± 2.18
4.21 ± 0.54
0.36 ± 0.11
4.57 ± 0.55

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