Doctoral Dissertation
博士論文

Search for heavy diboson resonances decaying into semi-leptonic√
final states in 139 fb−1 of s = 13 TeV pp collisions with the
ATLAS detector(ATLAS測定器において収集した重心系エネルギー13 TeVの陽子陽子衝突データ139 fb−1を使った、セミレプトニック終状態を持つ弱ボソン共鳴の探索）

A Disseration submitted for the Degree of Doctor of Philosophy
January 2020

令和２年１月博士（理学）申請
Department of Physics, Graduate School of Science
The University of Tokyo東京大学大学院理学系研究科物理学専攻
Masahiro Yamatani
山谷 昌大

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Abstract
This thesis represents searches for heavy new resonances decaying into dibosons (W W , W Z and ZZ) in
semi-leptonic
final states (ννqq, `νqq and ``qq) using proton-proton collision data at a center-of-mass energy√of s = 13 TeV. The data, corresponding to an integrated luminosity of 139 fb−1 , were recorded with the
ATLAS detector between years 2015 and 2018 at the Large Hadron Collider. The searches are performed in
final states in which one vector boson decays leptonically (a pair of electrons or muons, a pair of neutrinos,
and a pair of an electron (muon) and a neutrino), and the associated W boson or the other Z boson decays
hadronically. Several new ideas are introduced to improve the sensitivity e.g. Track-CaloCluster (TCC),
which is particle-flow algorithm to achieve better jet substructure performance for high-pT jet, Variableradius (VR) track-jet b-tagging for the boosted Z → bb reconstruction and machine learning (ML) based
analysis. No evidence for the production of heavy resonances is observed. Upper bounds on the production
cross sections of heavy resonances times their decay branching ratios to W W , W Z and ZZ are derived in themass range from 300 to 5000 GeV, within the context of Standard Model extensions with a heavy vector triplet
or warped extra dimensions. Production processes of gluon-gluon-fusion, Drell-Yan or vector-boson-fusion
are considered, depending on the assumed model.

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To my loving wife Tomomi, and my dear child Naoya.

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Acknowledgements
I wish to express my deepest gratitude to my supervisor, Professor Masaya Ishino, who adequately guided
and encouraged me to be professional. Without his support, I could not pass the defence in 2020. I also
would like to thank my local supervisors, Dr. Tatsuya Masubuchi and Dr. Takuya Nobe, for helping me with
V V semi-leptonic analysis and insightfull discussions about an angular analysis and a TCC jet study. I am
grateful to Associate Professor Tatsuo Kawamoto, who was my supervisor for the first four years of my PhD
course, for his support and encouragement.
I would like to thank the academic researchers at the University of Tokyo, Dr. Yuji Enari for giving
delicious cuisines, Dr. Koji Terashi for giving insightfull advisies, Associate Professor Yasuyuki Okumura forgiving me a ride when I missed the last bus, Professor J. Tanaka and Associate professor Ryo Sawada forgiving me a chance to use a quantum annealing system, and Dr. Tomoyuki Saito for inviting me to CERN
relay race. I also would like to express my appreciation to people in ATLAS V V semi-leptonic group.
I am thankfull to my thesis committee members, Yutaka Ushiroda, Koichi Hamaguchi, Susumu Shimoura,
Toshinori Mori and Taku Gunji, for their insightful discussions, hard questions during the defence, and joining
the defence by video conferencing in this difficult situation with COVID-19.
I really enjoyed my student life with all the ICEPP members. In particular, I would like to express myrespectful gratitude to the ICEPP secretaries, Masako Shiota, Yumi Kase, Michiko Takemoto and Sonoko
Kaneko for supporting my research life. During my six years at ICEPP, I was able to focus on my research
thank to their huge support.
I wish to thank I-Han Chiu for doing desk lunch together, Yuya Kano for an air show in France, Shota
Nakaura for inviting me to your wedding ceremony in Lucerne, Naoki Nagakura for playing football together
in Tokyo, Yuichi Nishizawa for chatting idly via SNS, Masahiko Saito for Berlioz’s Symphonie Fantastique,
Tomohiro Yamazaki for giving a moderate break, Yi-Ling Yang for talking on my way to CERN from SaintGenis-Pouilly.
Finally, the deepest appreciation goes to my family for supporting me all my life.

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Contents
Abstractiii

Acknowledgementsvii

1

Introduction
1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 The Standard Model of Particle Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3 Limitations of the Standard Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.4 BSM Models and The Interpretation Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.4.1 Heavy Vector Triplet Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.4.2 RS Graviton and Radion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.4.3 Signal Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.5 Heavy Resonance Searches using Early Run2 Data . . . . . . . . . . . . . . . . . . . . . . . .
1.5.1 Upper limits on the cross-section times branching ratio . . . . . . . . . . . . . . . . .
1.5.2 Upper limits on coupling strengths . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.6 Search for heavy diboson resonances in semi-leptonic final states . . . . . . . . . . . . . . . .

1
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2
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2

Experimental Setup
2.1 The Large Hadron Collider . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 The ATLAS Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.1 Coordinate System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.2 Inner Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.3 Calorimeter System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.4 Muon System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.5 Trigger and Data Acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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3

Data and Monte Carlo Simulated Samples
3.1 Data Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Simulation of pp collisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.1 Factorization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.2 The fixed-order partonic cross-section . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.3 Parton showering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.4 Hadronization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.5 Detector Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.6 Pile-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3 Monte Carlo Simulated Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.1 Background samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.2 Signal Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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4

Object Reconstruction and Particle Identification
4.1 Tracks and Vertices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.1 Track Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.2 Vertex Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Topological cluster . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.1 Topo-cluster formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.2 Topo-cluster kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3 Jets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.1 Jets Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.2 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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4.3.3 Pile-up Jet Tagging and Suppression . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.4 Jet selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.5 Flavor tagging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Leptons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4.1 Electrons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4.2 Muons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Missing ET . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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5

Track-CaloClusters (TCCs)
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2 TCCs algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2.2 Matching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2.3 Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3 Jet reconstruction and performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3.1 Jet reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3.2 Jet substructure performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4 Boson Tagger Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.5 Boson Tagging Efficiency SF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.5.1 Signal Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.5.2 Background Rejection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.5.3 Systematic uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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6

Event Selection
6.1 Strategy to the SR orthogonalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2 Event Cleaning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.3 Trigger requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.4 Categorization of production processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.5 Reconstruction and identification of the V → qq decay . . . . . . . . . . . . . . . . . . . . . .
6.5.1 W/Z → J candidates (merged category) . . . . . . . . . . . . . . . . . . . . . . . . . .
6.5.2 W/Z → jj candidates (resolved category) . . . . . . . . . . . . . . . . . . . . . . . . .
6.6 Event selections of individual leptonic channels . . . . . . . . . . . . . . . . . . . . . . . . . .
6.6.1 0-lepton: ZV → ννqq . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.6.2 1-lepton: W V → `νqq . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.6.3 2-lepton: ZV → ``qq . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.7 Signal efficiencies and mass resolutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.8 Control region definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.9 Summary of Signal and Control Regions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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7

Background Estimations
7.1 Z + jets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.2 W + jets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.3 ttbar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.4 Multi-jet Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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8

Systematic Uncertainty
8.1 Experimental Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.2 Theoretical Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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9

Statistical Interpretation
9.1 Likelihood function definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.2 Hypothesis Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.2.1 Discovery of a positive signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.2.2 Signal exclusion and Upper limit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.2.3 Asymptotic Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.3 Fit inputs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.4 Signal Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.5 Nuisance parameters: normalization and systematic uncertainties . . . . . . . . . . . . . . . .
9.5.1 Smoothing and Symmterization of Systematic Uncertainties . . . . . . . . . . . . . . .

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4.5

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9.5.2
9.5.3

Pruning of the Systematic Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . 103
Pull and Impact of nuisance parameters . . . . . . . . . . . . . . . . . . . . . . . . . . 103

10 Results
10.1 Search for X → W W/ZZ signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10.1.1 Post-fit distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10.2 Test of background-only hypothesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10.3 Interpretations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10.3.1 Results for spin-0 Radion models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10.3.2 Results for spin-1 HVT models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10.3.3 Results for spin-2 Graviton models . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10.4 Impact of systematic uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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11 Conclusion

116

A Search for X → W Z signal

117

B Yields Table, Pulls and Correlation
122
B.1 Background only Fit results for the X → W Z search . . . . . . . . . . . . . . . . . . . . . . . 122
B.2 Background only Fit results for the X → W W/ZZ search . . . . . . . . . . . . . . . . . . . . 127
C Impact of systematic uncertainties

133

References

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List of Figures
1.1(a) The reconstructed invariant mass distributions of the two photons decaying from candidate
Higgs boson and (b) The observed p0 values from the combination of channels in the ATLAS
experiment [1]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 Representive Feynman diagrams for the production of heavy resonances X with their decays
into a pair of vector bosons. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3 The measurements of the e+ e− → q q̄ cross-section from LEP close to the Z resonance at LEP.
The solid and dashed lines show before and after ISR correction, respectively [22]. . . . . . .
1.4 One-loop correction to the Higgs boson mass by (a) a fermion f and (b) a scalar particle S. .
1.5 Observed and expected 95% CL (confidence level) upper limits on the W 0 cross-section times
branching ratio to W Z for the HVT model. Expected limits for individual channels and their
combination are shown for the (a) DY and (b) VBF production mechanisms. The limits forthe combined channels for the (c) DY and (d) VBF production mechanisms are also shown,along with predictions for HVT models A, B, and C [51] . . . . . . . . . . . . . . . . . . . . .
1.6 Observed and expected 95% CL upper limits on the GKK cross-section times branching ratioto (a) W W and (b) ZZ for the Bulk RS model. Expected limits and their combination for
individual channels and their combination are shown, along with (c), (d) predictions for Bulk
RS model with k/M¯P l = 1 [51]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.7 Observed and expected 95% CL upper limits on the scalar cross-section times branching ratio
for the heavy scalar model. Expected limits for individual channels and their combination
are shown for the (a) ggF-W W , (b) VBF-W W , (c) ggF-ZZ and (d) VBF-ZZ production
mechanisms [51]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.8 Observed and expected 95% CL upper limits on the V 0 cross-section times branching ratio toV V , V H, and lepton–antilepton states for (a) W 0 , (b) Z 0 , and (c) V 0 production, along thepredictions for HVT Model A [51]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . √. . . .
1.9 Upper limits on the production cross section times branching ratio to two photons at s =13 TeV of the lightest KK graviton as a function of its mass mG∗ for k/MPl = 0.1. For
mG∗ > 2500 GeV, the observed and expected limits are determined with pseudo-experiments
shown by the blue solid and dashed lines, respectively. Predictions are shown for the RS1model, where the grey shaded band represents the PDF uncertainty [52]. . . . . . . . . . . .
1.10 Observed 95% CL exclusion contours in the HVT parameter space {gH , gf } for resonances ofmass 3, 4, and 5 TeV for the combination of (a) V V , and (b) V V +V H+lv/ll channels. The
areas outside the curves are excluded, as are the filled regions which show the constraints fromprecision EW measurements [51]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8

(a) Overview of the LHC, including the ALICE, ATLAS, CMS and LHCb experiment [54].
(b) A schematic view of the CERN accelerator complex [55]. . . . . . . . . . . . . . . . . . .
Total Integrated Luminosity and Data Quality in 2015-2018 [60]. . . . . . . . . . . . . . . . .
An overview of the ATLAS detector [62]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Sketch of the barrel region of the ATLAS inner detector [61]. . . . . . . . . . . . . . . . . . .
Overview of the ATLAS calorimeter system [61]. . . . . . . . . . . . . . . . . . . . . . . . . .
Schematic drawing of the ATLAS muon spectrometer. . . . . . . . . . . . . . . . . . . . . . .
(a) Cross-section of the barrel muon system perpendicular to the beam axis (non-bending
plane) and (b) cross-section of the muon system in a plane containing the beam axis (bending
plane) 2.7b. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The ATLAS TDAQ system in Run 2 with emphasis on the components relevant for triggering[73] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1
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10

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3.1

3.2
4.1

4.2
4.3
4.4
4.5

4.6
4.7
5.1
5.2

Sketch of a hadron-hadron collision simulated by a Monte-Carlo event generator [76]. The
hard collision is represented by the largest red blob which is surrounded by tree-like structure
describing Bremsstrahlung as simulated by parton showers. The purple blob represents asecondary hard scattering. The light green blobs represent parton-to-hadron transitions anddark green blobs indicate hadron decays, while yellow lines indicate soft proton radiation. . .
Number of Interactions per Crossing [60]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Created topo-clusters in the first module (FCAL0) of the FCAL calorimeter displayed on adimensionless grid using the polar angle θ and the azimuthal angle φ. Figure 4.1a and 4.1bshow cells satisfying |EM| > 4 and |EM| > 2, respectively. All clusterd cells with the outlineof topo-clusters are shown in Figure 4.1c. Clusters which do not contain a seed cell from thismodule are seeded in other modules. Not colored cells inside a topo-cluster correspond to anegative signal, while cells shaded grey are not part of a topo-cluster themselves [116]. . . .
(Left) 1-prong background QCD jet, dominated by collinear (blue) and soft (green) radiation.
(Right) 2-prong W/Z → qq jet resolved into two subjets, dominated by collinear (blue), soft
(green), and collinear-soft (orange) radiation emitted from the two subjets [122]. . . . . . . .
.
and eβ=1
Phase space defined by the measurement of the energy correlation functions eβ=132The phase space is divided into 1- and 2-prong regions with a boundary corresponding to the)3 which is explored based on the power counting method [122]. . . . . . .
∼ (eβ=1
curve eβ=123Ratio of the EM+JES jet response in data to that in the nominal MC event generator as afunction of jet pT for Z-jet, γ-jet, and multijet in situ calibrations [132]. . . . . . . . . . . . .
A schematic illustration of the path of an electron through the detector. The hypothetical
path of an electron is shown with the red trajectory. A photon, depicted with the dashed
red trajectory, is produced by the interaction of the electron with the material in the tracking
system [140]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Electron isolation efficiencies for the various WPs as a function of the probe lepton pT using
ggF NWA Higgs with m = 3 TeV samples. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Muon isolation efficiencies for the various WPs as a function of the probe lepton pT using ggF
NWA Higgs with m = 3 TeV samples. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

24
26

31
33
33
35

38
40
42

The fraction of different TCCs classes as a function of (a) the TCC η and (b) the TCC pT [149]. 45
The schematic demonstrating of the TCC objects reconstruction. Details on the exact reconstruction procedure are provided in the text [149]. . . . . . . . . . . . . . . . . . . . . . . . . 46
5.3 A comparison of the mass response, Rrm , for jets built with all TCCs, all TCCs after trimmingand only combined TCCs.[149]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
5.4 The (a) TCC jet pT pseudo-response with respect to trimmed topo-cluster jets and (b) ηresidual for both topo-cluster and TCC jet [149]. . . . . . . . . . . . . . . . . . . . . . . . . . 48
5.5 The distributions of jet inputs for (a) topo-clusters, (b) all TCCs and (c) only combined TCCs
in η-φ plane. [149]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
5.6 A comparison of the mass response for jets built from topo-clusters (black circles), all-TCCs(red squares) and combined-TCCs (green triangles) for 700 GeV < pT < 800 GeV in Figure reffig:MassResponse1 and for 2.1 TeV < pT < 2.5 TeV in Figure 5.6b. [149] . . . . . . . . . . . . 49
5.7 A comparison of the D2 residual for jets built from topo-clusters (black circles), all-TCCs (redsquares) and combined-TCCs (green triangles). [149] . . . . . . . . . . . . . . . . . . . . . . . 50
5.8 A comparison of the fractional jet mass (a) and D2 (b) resolution for topo-cluster jets (solid
black lines), jets built using all-TCC objects (dash-dotted red lines) and jets built using only
combined-TCC objects (dashed green lines), as a function of truth-jet pT . The TCC definitions
are seen to outperform at high pT , particularly for D2 [149]. . . . . . . . . . . . . . . . . . . . 50
5.9 D2 distribution of quark- and gluon-induced jets derived from Z+jets, separated by 200 <pT < 650 (a) and 650 < pT < 2500 (b). In low pT region (b), quark-induced jets have a tail inhigher D2 and causing the difference from gluon-induced jets. The difference is getting small
in high pT region (b) due to boost of jets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
5.10 Optimal D2 thresholds as a function of quark-induced jet fraction. Jet mass window cut
assuming naive boson tagger is applied. A quark fraction dependency observed at low masssignal, but not at high mass signal as expected. . . . . . . . . . . . . . . . . . . . . . . . . . . 51

xiv
5.11 The upper cut on (a) D2 and (b) jet mass window cut i.e. the upper and lower boundary of
the mass of the W -tagger as a function of jet pT . Corresponding values for Z-tagger are shownin (c) and (d). The optimal cut values for maximum significance are shown as solid markers
and the fitted function as solid lines. Working points from V V → JJ is also shown as dashedlines as a reference. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(β=1)
5.12 Efficiencies of the mJ and D2
requirements as functions of the large-R jet pT for the V → J
tagging for (a) the W boson and (b) the Z boson. . . . . . . . . . . . . . . . . . . . . . . . .
5.13 (a) Signal efficiency and (b) background rejection comparison between TCC jet tagger and
LCTopo jet tagger. Red points show the result of the TCC boson tagger optimized for the VV
semi-leptonic analysis. Blue points correspond to the boson tagger with LCTopo jet, optimized
to keep 50% signal efficiency over the full range of the jet pT . . . . . . . . . . . . . . . . . . .
5.14 A comparison of the observed data and predicted MC distribution of the leading pT large-R jet(TCC jet) in the event for the (a) W boson and (b) top quark selections in a sample enrichedin lepton-plus-jets tt̄ events. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.15 The post-fit distribution of the large-R jet mass in (a) D2 failed, mass failed, (b) D2 passed,
mass failed, (c) D2 failed, mass passed and (d) D2 passed, mass passed for W-boson selection.
5.16 The post-fit distribution of the large-R jet mass in (a) D2 failed, mass failed, (b) D2 passed,
mass failed, (c) D2 failed, mass passed and (d) D2 passed, mass passed for top-quark selection.
5.17 The signal efficiency on W-boson jet for the boson tagger as a function of the large-R jet pT
in (a) D2 failed, mass failed, (b) D2 passed, mass failed, (c) D2 failed, mass passed and (d)D2 passed, mass passed. In the bottom panel, the boson tagging efficiency SF are shown. . .
5.18 The signal efficiency on top-quark jet for the boson tagger as a function of the large-R jet pT
in (a) D2 failed, mass failed, (b) D2 passed, mass failed, (c) D2 failed, mass passed and (d)D2 passed, mass passed. In the bottom panel, the boson tagging efficiency SF are shown. . .
Illustration of the selection flow and signal regions of the X → V V search. The VBF category
is targeted for VBF production whereas the ggF/DY category is for the rest. Three signal
regions (high purity, low purity and resolved) are selected for each category based on the
V → qq reconstruction. The 0-lepton channel does not consider resolved selection. For final
states with hadronic decaying Z bosons, the three signal regions in the ggF/DY category areeach further split into tagged and untagged according to the b-tagging information of jets fromZ → qq decays. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2 4-momentum of the Jet1 used as RNN input for VBF (red) and ggF (blue) a scalar signal in
2-lepton channel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.3 (a) RNN score distributions for the signal models considered for this search; (b) The fractionof signal events passing the requirement on the RNN score. . . . . . . . . . . . . . . . . . . .
6.4 Comparison of distributions of input variables for the RNN between data and MC. (Top)
Leading jet. (Bottom) Sub-leading jet. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.5 Comparison of distribution of RNN score between data and MC. The peak around score=0.5
corresponds to events with no small-R jets, which are categorized into ggF/DY category. . . .
6.6 Large-R jet (a) mass and (b) D2 distributions before boson tagging in 0-lepton channel. . . .
6.7 Observed and expected distributions of the three variables used to reject QCD background.
miss
miss miss
These are pmiss(left), min(∆φ(ET, j )) (middle), and ∆φ(ET, pT ) (right) following theTselections from top to bottom. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.8 Comparison of the reconstructed invariant mV V between before and after the dijet mass correction in (a) 1-lepton and (b) 2-lepton. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.9 Comparison of distributions for relative boson pT between 1 TeV Radion signal and backgroundin (a) `νqq merged ggF and (b) `νqq merged VBF categories. . . . . . . . . . . . . . . . . . .
6.10 The dilepton mass window cut efficiencies for signal in (a) electron and (b) muon channesl. .
6.11 Selection acceptance times efficiency for the X → ZV → ννqq signal events from MC simulations as a function of the resonance mass for (a) ggF/DY and (b) VBF production, combining
HP and LP signal regions.The light blue band represents the total statistical and systematic
uncertainties for the radion model, and the total uncertainties are similar for the other signal
models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

53
54

54
55
57
58
59
60

6.1

62
64
65
66
66
67
69
70
71
73

75

xv
6.12 Selection acceptance times efficiency for the X → W V → (eν/µν/τ ν)qq signal events from
MC simulations as a function of the resonance mass for (a) ggF/DY and (b) VBF production,
combining all SRs of both ggF/DY and VBF categories of both resolved and merged analyses.
Signal contributions from W → τ ν decays are included in the efficiency calculation. The light
blue band represents the total statistical and systematic uncertainties for the radion model,
and the total uncertainties are similar for the other signal models. The “bump” structurearound 800 GeV is due to the falling off of the resolved analysis. . . . . . . . . . . . . . . . .
6.13 Selection acceptance times efficiency for the X → ZV → ``qq signal events from MC simulations as a function of the resonance mass for (a) ggF/DY and (b) VBF production, combining
all SRs of both ggF/DY and VBF categories of both resolved and merged analyses.The light
blue band represents the total statistical and systematic uncertainties for the radion model,
and the total uncertainties are similar for the other signal models. The decreases in efficiencies
for resonance masses above approximately 2.5 TeV are due to the merging of electrons fromthe highly boosted Z → ee decays. The “bump” structure around 800 GeV is due to the falling
off of the resolved analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.14 The sckematic view of SR and CR. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.1
7.2
7.3

7.4

7.5
7.6

7.7
7.8

Background compositions for each lepton channel in all SRs. . . . . . . . . . . . . . . . . . . .
Observed and expected distributions of transverse mass of the leptons and jets from the W Z
resonance decay in (a) ggF merged HP ZCR, (b) ggF merged LP ZCR, (c) VBF merged HP
ZCR, (d) VBF merged LP ZCR, (d) ggF resolved ZCR and (e) VBF resolved ZCR. . . . . . .
Observed and expected distributions of invariant mass of the leptons and jets from the ZZ
resonance decay in (a) ggF merged HP tagged ZCR, (b) ggF merged HP untagged ZCR, (c)ggF merged LP tagged ZCR, (d) ggF merged LP untagged ZCR, (e) VBF merged HP ZCR,(f) VBF merged LP ZCR, (g) ggF resolved tagged ZCR, (h) ggF resolved untagged ZCR and(i) VBF resolved ZCR. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Observed and expected distributions of invariant mass of lνqq from the W Z resonance decayin (a) ggF merged HP tagged WCR, (b) ggF merged HP untagged WCR, (c) ggF merged
LP tagged WCR, (d) ggF merged LP untagged WCR, (e) VBF merged HP WCR, (f) VBF
merged LP WCR, (g) ggF resolved tagged WCR, (h) ggF resolved untagged WCR and (i)VBF resolved WCR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Observed and expected distributions of invariant mass of lνqq from the W W resonance decay(a) ggF merged HP WCR, (b) ggF merged LP WCR, (c) VBF merged HP WCR, (d) VBF
merged LP WCR, (d) ggF resolved WCR and (e) VBF resolved WCR. . . . . . . . . . . . . .
Observed and expected distributions of invariant mass of lνqq from the W Z resonance decayin (a) ggF merged HP tagged TCR, (b) ggF merged HP untagged TCR, (c) ggF merged LP
tagged TCR, (d) ggF merged LP untagged TCR, (e) VBF merged HP TCR, (f) VBF merged
LP TCR, (g) ggF resolved tagged TCR, (h) ggF resolved untagged TCR and (i) VBF resolved
TCR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Observed and expected distributions of invariant mass of lνqq from the W W resonance decayin (a) ggF merged HP TCR, (b) ggF merged LP TCR, (c) VBF merged HP TCR, (d) VBF
merged LP TCR, (d) ggF resolved TCR and (e) VBF resolved TCR. . . . . . . . . . . . . . .
missObserved and expected distributions of (a) ET, (b) pT,`ν , (c) p`T , (d) transverse mass of themissleptons and jets from the W Z resonance decay, (e) ∆φ between a lepton and ET
and (f) ∆ηmisswith estimated multi-jet . . . . . . . . . . . . . . . . . . . . . . .
between a lepton and ET

76

76
77
79
81

82

83
84

85
86
89

8.1

The comparison of recontructed mV V distributions between nominal and alternative V + jets
samples in (a) Merged ggF, (b) Merged VBF, (c) Resolved ggF, and (d) Resolved VBF categories. 94

9.1

Examples of the invariant VV mass fit with a Gaussian function (1- and 2- lepton) and transverse mass fit with a Landa function (0-lepton). (a); ggF merged region, mass = 3 TeV in
1-lepton (b) ggF merged region , mass = 3 TeV in 0-lepton. . . . . . . . . . . . . . . . . . . . 102
The HVT signal mass resolution as a function of mass fit with a straight line in (a) ggF merged
1-lepton and (b) ggF merged 0-lepton channel. . . . . . . . . . . . . . . . . . . . . . . . . . . 102

9.2

10.1 Postfit distributions in all (left) control regions and (right) signal regions of the W W/ZZ
analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

xvi
10.2 Postfit distributions of the invariant mass in the llqq (a) GGF merged HP ZZ Tag SR (b) GGF
merged HP ZZ Untag SR (c) GGF merged LP ZZ Tag SR (d) GGF merged LP ZZ Untag SR(e) GGF resolved ZZ Tag SR (f) GGF resolved ZZ Untag SR (g) VBF merged HP ZZ SR (h)VBF merged LP ZZ SR (i) VBF resolved ZZ SR. . . . . . . . . . . . . . . . . . . . . . . . . .
10.3 Postfit distributions of the invariant mass in the lνqq (a) GGF merged HP WW SR (b) GGF
merged LP WW SR (c) GGF resolved LP WW SR (d) VBF merged HP WW SR (e) VBF
merged LP WW SR (f) VBF resolved LP WW SR. . . . . . . . . . . . . . . . . . . . . . . . .
10.4 Postfit distributions of the transverse mass in the ννqq (a) GGF merged HP ZZ Tag SR (b)GGF merged HP ZZ Untag SR (c) GGF merged LP ZZ Tag SR (d) GGF merged LP ZZ Untag
SR (e) VBF merged HP ZZ SR (f) VBF merged LP ZZ SR. . . . . . . . . . . . . . . . . . . .
10.5 Scan of p0 as a function of the resonance mass of (a) ggF Radion, (b) VBF Radion, (c) DY HVTW’, (d) VBF HVT W’, (e) ggF Graviton and (f) VBF Graviton with three lepton channels
combined. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10.6 95% CL upper limit on cross section times branching ratio of Radions produced via (a) ggF
and (b) VBF decaying to W W/ZZ pair, with all three lepton channels combined. . . . . . . .
10.7 95% CL upper limit on cross section times branching ratio of HVT W 0 produced via (a) DY
and (b) VBF decaying to W Z pair, with all three lepton channels combined. . . . . . . . . .
10.8 Observed 95% CL exclusion contours in the HVT parameter space {gH , gf } for resonances ofmass 2, 4 and 5 TeV for the combination of (a) V V channel, and (b) V V channel with thefilled regions which show the constraints from precision EW measurements. The dot A, B in
the plots indicate Model A and Model B, respectively. . . . . . . . . . . . . . . . . . . . . . .
10.9 95% CL upper limit on cross section times branching ratio of Graviton produced via (a) ggF
and (b) VBF decaying to W W/ZZ pair, with all three lepton channels combined. . . . . . . .
A.1 Postfit distributions in all (left) control regions and (right) signal regions of the W Z analysis
A.2 Postfit distributions in the llqq (a) GGF merged HP WZ SR (b) GGF merged LP WZ SR(c) GGF resolved WZ SR (d) VBF merged HP WZ SR (e) VBF merged LP WZ SR (f) VBF
resolved WZ SR. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A.3 Postfit distributions in the `νqq (a) merged HP W Z VBF SR and (b) Merged LP W Z VBF
SR (c) Resolved W Z VBF SR. Fit is performed using data from all W Z regions. . . . . . . .
A.4 Postfit distributions in the ννqq(a) merged HP W Z VBF SR, (b) merged LP W Z VBF SR.
Fit is performed using data from all W Z regions. . . . . . . . . . . . . . . . . . . . . . . . .

106
107
108
110
111
112

113
114
117
118
119
120

B.1 Pull distributions for the nuisance parameters (a) Jet relevant NPs (b) Other experimantalNPs (c) Theory NPs (d) XS NPs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
B.2 Correlation matrix for the nuisance parameters for the final W Z GGF+VBF, HP+LP+Res,Tag+Untag,
0+1+2-lepton fit using data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
B.3 Pull distributions for the nuisance parameters (a) Jet relevant NPs (b) Other experimantalNPs (c) Theory NPs (d) XS NPs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
B.4 Correlation matrix for the nuisance parameters for the final W W/ZZ GGF+VBF, HP+LP+Res,Tag+Untag,
0+1+2-lepton fit using data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

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List of Tables
1.1
1.2
1.3

A table of the SM bosons and their properties [18] . . . . . . . . . . . . . . . . . . . . . . . .
A table of the SM elementary particles (fermions) and their properties [18] . . . . . . . . . .
List of benchmark signal models. Predictions of cross-section σ, branching ratio BR (X →W W/W Z/ZZ), and intrinsic width divided by the resonance mass Γ/m for the given hypothetical new particle at m = 500 GeV and 3 TeV are summarized. . . . . . . . . . . . . . . . .
√Selected LHC parameters for pp collisions at s = 13 TeV in 2015–2018. The best accelerator
performance during normal physics operation are shown. In 2017, the LHC was run in twomodes: standard 25 ns bunch train operation and ’8b4e’ denoting a pattern of eight bunches
separated by 25 ns followed by a four bunch-slot gap. The peak instantaneous luminosity of
16 × 1033 cm−2 s−1 in 2017 is part of the 8b4e period [56]. . . . . . . . . . . . . . . . . . . . .

16

4.1
4.2
4.3
4.4
4.5

Summary of small-R jet selection and calibration . . . . . . . . . . . . . . . . . . . . . . . . .
Summary of large-R jet selection and calibration . . . . . . . . . . . . . . . . . . . . . . . . .
Summary of VR track jet selection. No calibration is available for VR track jets. . . . . . . .
Summary of electron selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Summary of muon selections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

36
36
37
40
43

5.1

A list of normalization factors to be decided in fit. . . . . . . . . . . . . . . . . . . . . . . . .

56

6.1

A summary of signal region event selection. These regions are split into VBF and ggF(DY)
categories as described in Section 6.4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
Cutflow for HVTWZ DY (VBF) signals with 600 GeV and 2000GeV in 0-lepton. . . . . . . . 70
Summary of selection criteria used to define the signal region (SR), W +jets control region (WCR) and tt̄ control region (tt̄ CR) for merged 1-lepton channel. . . . . . . . . . . . . . . . . . 71
The list of selection cuts in the resolved analysis for the W W and W Z signal regions (SR),W + jets control region (WR) and tt̄ control region (TR). More details of the object definitions
can be found in Section 4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
Cutflow for HVTWZ DY (VBF) signals with 600 GeV and 2000GeV in 1-lepton Merged category. 72
Event selection summary for merged analysis in 2-lepton channel. . . . . . . . . . . . . . . . . 74
Event selection summary for resolved analysis in 2-lepton channel. . . . . . . . . . . . . . . . 74
Cutflow for HVTWZ DY (VBF) signals with 600 GeV and 2000GeV in 2-lepton Resolved
category. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
Numbers of signal regions in each leptonic channel and of control regions for different diboson
final states. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

2.1

6.2
6.3
6.4
6.5
6.6
6.7
6.8
6.9
7.1
7.2
7.3
7.4
7.5

8.1
8.2

3
3
9

Summary of normalization factors for Z+jets. . . . . . . . . . . . . . . . . . . . . . . . . . . .
Summary of normalization factors for W +jets. . . . . . . . . . . . . . . . . . . . . . . . . . .
Summary of normalization factors for tt̄. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Definitions of "inverted" leptons used in multi-jet control region . . . . . . . . . . . . . . . . .
The fit is done in various WCRs, in order to obtain the corresponding scale factors for MJ
templates: ggF resolved WCR for the W W → lvqq selection, ggF resolved untagged WCR
for the W Z → lvqq selection, ggF resolved tagged WCR for the W Z → lvqq selection, VBF
resolved WCR for the W W → lvqq selection, and VBF resolved WCR for the W Z → lvqq
selection. Post-fit event yields for electroweak processes and MJ contributions are shown. The“SF” column shows the corresponding normalization scale factors for electroweak processes
from the fit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

80
87
87
88

Summary of evaluated ratio and extrapolation uncertainties for Z + jets . . . . . . . . . . . .
Summary of evaluated ratio and extrapolation uncertainties for W + jets . . . . . . . . . . . .

95
96

90

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8.3

Summary of evaluated ratio and extrapolation uncertainties for tt̄

9.1

Summary of the regions entering the likelihood of the fit models to search for heavy resonances
decaying to ZZ and W W in semileptonic final states. “X” indicates that the shape of the final
discriminant is taken into account in the fit. “One bin” implies that a single bin without any
shape information is used in the corresponding fit region and “–” means that the region is notpresent in the fit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
Summary of the regions entering the likelihood of the fit models to search for heavy resonances
decaying to ZW in semileptonic final states. “X” indicates that the shape of the final discriminant is taken into account in the fit. “One bin” implies that a single bin without any shapeinformation is used in the corresponding fit region and “–” means that the region is not present
in the fit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

9.2. . . . . . . . . . . . . . .

96

10.1 The expected background events with breakdowns from individual sources in 6 W W and 15
ZZ SRs compared with the data. The backgrounds are estimated from a background-only
simultaneous fit to all W W and ZZ SRs and their corresponding CRs. . . . . . . . . . . . . . 109
10.2 Ranking of the nuisance parameter impact on the best-fit µ value on ggF Radion with m(X) =600 GeV and σ(pp → X) × BR(X → V V ) = 0.01 pb, ggF Radion with m(X) = 2000 GeV
and σ(pp → X) × BR(X → V V ) = 0.002 pb, VBF Radion with m(X) = 600 GeV andσ(pp → X) × BR(X → V V ) = 0.01 pb and VBF Radion with m(X) = 2 TeV and σ(pp →X) × BR(X → V V ) = 0.002 pb, corresponding to approximately the expected median upper
limits at these two mass values. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
A.1 The numbers of observed data events in the 19 W Z SRs are compared with the expectedbackground events with breakdowns from individual sources. The backgrounds are estimatedfrom a background-only simultaneous fit to all W Z SRs and their corresponding CRs. The
uncertainties on the estimated backgrounds combine statistical and systematic contributions.
B.1 Fitted values of background normalization factors in the W Z region. . . . . . . . . . . . . . .
B.2 Postfit yield in the `νqq W Z WCR in the (top) GGF Untag, (middle) GGF Tag, and (bottom)
VBF regions from a simultaneous fit in all W Z regions . . . . . . . . . . . . . . . . . . . . . .
B.3 Postfit yield in the `νqq W Z TCR in the (top) GGF Untag, (middle) GGF Tag and (bottom)
VBF regions from a simultaneous fit in all W Z regions . . . . . . . . . . . . . . . . . . . . . .
B.4 Postfit yield in the ``qq W Z CR in the (top) GGF and (bottom) VBF regions from a simultaneous fit in all W Z regions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.5 A summary of exclusion limits for HVT W 0 from W Z fit. . . . . . . . . . . . . . . . . . . . .
B.6 A summary of exclusion limits for HVT VBF W 0 from W Z fit. . . . . . . . . . . . . . . . . .
B.7 Fitted values of background normalization factors in the W W ZZ region. . . . . . . . . . . .
B.8 Postfit yield in the `νqq W W ZZ WCR in the (top) GGF and (bottom) VBF regions from asimultaneous fit in all W W ZZ regions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.9 Postfit yield in the `νqq W W ZZ TCR in the (top) GGF and (bottom) VBF regions from asimultaneous fit in all W W ZZ regions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.10 Postfit yield in the ``qq W W ZZ ZCR in the (top) GGF Untagged, (middle) GGF Tagged and(bottom) VBF regions from a simultaneous fit in all W W ZZ regions . . . . . . . . . . . . . .
B.11 A summary of exclusion limits for Radion from W W/ZZ fit. . . . . . . . . . . . . . . . . . .
B.12 A summary of exclusion limits for Radion VBF from W W/ZZ fit. . . . . . . . . . . . . . . .
B.13 A summary of exclusion limits for RSG from W W/ZZ fit. . . . . . . . . . . . . . . . . . . . .
B.14 A summary of exclusion limits for RSG VBF from W W/ZZ fit. . . . . . . . . . . . . . . . . .

121
122
123
123
124
125
126
127
128
128
129
129
131
131
132

C.1 Ranking of the nuisance parameter impact on the expected exclusion limits on ggF HVT W’
with m(X) = 600 GeV and σ(pp → X) × BR(X → W Z) = 0.01 pb, ggF HVT W’ withm(X) = 2000 GeV and σ(pp → X) × BR(X → W Z) = 0.002 pb, VBF HVT W’ withm(X) = 600 GeV and σ(pp → X) × BR(X → W Z) = 0.01 pb and VBF HVT W’ withm(X) = 2 TeV and σ(pp → X) × BR(X → W Z) = 0.002 pb. . . . . . . . . . . . . . . . . . . 133
C.2 Ranking of the nuisance parameter impact on the expected exclusion limits on ggF Graviton
with m(X) = 600 GeV and σ(pp → X)×BR(X → V V ) = 0.01 pb, ggF Graviton with m(X) =2000 GeV and σ(pp → X) × BR(X → V V ) = 0.002 pb, VBF Graviton with m(X) = 600 GeV
and σ(pp → X) × BR(X → V V ) = 0.01 pb and VBF Graviton with m(X) = 2 TeV andσ(pp → X) × BR(X → V V ) = 0.002 pb. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

1Chapter 1

Introduction
1.1 Overview

0

3500

ATLAS

Local pEvents / 2 GeV

The discovery of a new scalar particle with a mass of approximately 125 GeV by the ATLAS and CMS
collaborations at the Large Hadron Collider (LHC) in the year 2012 [1, 2] represents a major milestone in
the understanding of electroweak symmetry breaking. Figure 1.1 shows the distribution of reconstructedinvariant mass of diphoton candidates and the combined results of observed local p0 values as a functionof candidate particle mass in the ATLAS experiment. The particle was identified as a scalar boson, andsubsequent studies have shown that the properties of the new particle are consistent with the expectationsof the last missing piece of the Standard Model (SM), Higgs boson.

Data
Sig+Bkg Fit (mH=126.5 GeV)

3000

1500
1000

s=7 TeV, ∫ Ldt=4.8fb-1

500

s=8 TeV, ∫ Ldt=5.9fb-1

200100
100
0
-100
-200
100

110

H→γ γ

120

130

140

150

160

s = 8 TeV: ∫ Ldt = 5.8-5.9 fb

-1

120

130

(a)

140

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
110

Obs.
Exp.
±1 σ

s = 7 TeV: ∫ Ldt = 4.6-4.8 fb-1

Bkg (4th order polynomial)

2500
2000

Events - Bkg

ATLAS 2011 - 2012

3σ
4σ
5σ
6σ

115

120

125

130

150
160
mγ γ [GeV]

135

140

145 150mH [GeV](b)

Figure 1.1: (a) The reconstructed invariant mass distributions of the two photons decaying from candidate Higgs
boson and (b) The observed p0 values from the combination of channels in the ATLAS experiment [1].

Nevertheless, the SM is not the ultimate theory of particle physics since it cannot fully explain underlying
problems such as Dark Matter and Hierarchy problem, and therefore we need the extensions of the SM which
predict new particles. Motivated by hierarchy and naturalness arguments [3], several new physics models areproposed, such as the Extended Gauge Model (EGM) [4], Extra Dimensions [5, 6], and Technicolor models [7,8]. They predict new heavy resonances which decay into a pair of vector bosons V V (V = W, Z) which canbe discovered in the modern technology of particle physics experiments. For instance, a heavy W -like vectorboson is predicted by the extended gauge model, and the extra dimension models predict spin-2 Kaluza-Klein(KK) excitations of graviton.
This thesis presents searches for new heavy diboson resonances (X → W W , ZZ or W Z, collectively
denotedas X → V V ), using pp collision data collected with the ATLAS detector at a center-of-mass energy√of s = 13 TeV in years 2015-18 corresponding to an integrated luminosity of 139 fb−1 . The search utilizes
the semi-leptonic final states of the heavy diboson resonances, where one of the boson pair decays leptonicallyand the other decays hadronically. It takes advantages of a larger branching ratio from a hadronic vectorboson decay and smaller background yields from a leptonic vector boson decay. Therefore the analysis cansearch for a broader range of the resonance mass from 300 GeV to 5 TeV, while full hadronic (leptonic)
analysis can only search for higher (lower) mass regions. Figure 1.2 shows production modes considered inthis analysis: gluon-gluon-fusion (ggF), Drell-Yan (DY) and vector-boson-fusion (VBF).

2

Chapter 1. Introduction

g

V

q

V′

q/q ′′

q

V′

V′

X

X

g

V

(a) gluon-gluon fusion

q¯′

V

V

(b) Drell-Yan

X

q′

V
q′

(c) vector-boson fusion

5 their decays into a
Figure 1.2: Representive Feynman q/q
diagrams
for the production of heavy resonances X with′′qpair of vector bosons.

This thesis is organized
as follows. Z/W
Chapter 1 gives an overview of the theoretical background and motivaZ/W
tions for heavy diboson resonances search in semi-leptonic final states. Chapter 2 describes the experimental
X Hadron Collider (LHC) and the ATLAS detector. Chapter 3 describes the
setup, which includesZthe Large
Z
accumulated data sample and Monte Carlo simulated samples to model
the signals and background events.
q/q ′′q
The details of the object definitions are found in Chapter 4. The details of the Track-Calo Cluster, which arestudiesq ′ for improvement of signal sensitivities,
are found in Chapter 5. Event selection and categorizationq′
are summarized in Chapter 6. Strategy on the background estimation ′is discussed in Chapter 7 as well asV
V ′ are discussed
data/MC comparison studies. Systematic uncertainties
in Chapter 8. After the discussion
about the statistical treatment in Chapter 9, results are presented in Chapter 10. Finally, a summary of theXVwork presented is given in Chapter 11.
V

1.2 qThe Standard ModelW ofq′ Particle Physicsq′

The Standard Model (SM) of particle physics [9–11] is a relativistic field theory in which the interactions
between the elementary particles (fermions) are described as the exchange of the force-mediating particles(gauge bosons) derived by imposing local gauge symmetries on the natural world. The SM is based on
SU (3)c × SU (2)L × X
U (1)Y gauge symmetry group, where the SU (3)c symmetry defines strong interactions
and SU (2)L × U (1)Y symmetry expresses the electroweak interactions. The bosonic gauge fields define thespin-one force-mediating particles and the spin-half 5elementary particles are described by fermionic Weyl
fields. ¯′ZqThe simplified lagrangian for the SM can be described as:

41
LSM = − Fµν F µν
4
/ + h.c+ iψ̄ Dψ

(1.1)

+ |Dµ φ|2 − V (φ)+ ψi yij ψj φ + h.c.
The first term of Equation 1.1 is the scalar product of the field strength tensor Fµν , corresponding to kinetic
terms of force-mediating particles. Under the requirement of the local gauge invariance, the interactions
between the elementary particles arise from the kinetic terms of elementary particles described in the second
term of Equation 1.1. The third term corresponds to kinetic term of Higgs field and Higgs potential, which
explain how massive force-mediating particles acquire their mass. Massive force-mediating particles, W ±and Z bosons, are obtained by introducing the scalar filed called the Higgs filed [12–15]. The Higgs field
has a nonzero Vacuum Expectation Value (VEV) which breaks SU (2)L × U (1)Y to U (1)EM symmetry. The
unbroken U (1)EM symmetry is identified as electromagnetism. Finally, the mass of elementary particles is3

1.2. The Standard Model of Particle Physics

acquired by introducing the last term of Equation 1.1, Yukawa coupling terms, which involve the coupling ofelementary particles to the Higgs boson, and thus particles obtain their mass.
All of the SM particles are listed in Table 1.1-1.2. Weak interaction involves all fundamental particles,
while electromagnetic interaction of quantum electrodynamics (QED) does not affect neutrinos since they
are electronically neutral. In the case of the strong interaction of quantum chromodynamics (QCD), only
the quarks receive the interaction because of their color charge. Quarks are never observed as free particles
due to asymptotic freedom, a feature of QCD [16, 17]. Therefore quarks are always confined to bound statescalled hadrons.
Table 1.1: A table of the SM bosons and their properties [18]Particle

Q

Symbolspin

massgauge symmetryforce

Vector bosons
photonW bosonZ boson
Gluon

γ
W±
Z
g

0
±1
0
0

1
1
1
1

0
80.4 GeV
91.2 GeV
0

Higgs

H

0

0

125 GeVSU (2)L × U (1)YSU (2)L × U (1)YSU (2)L × U (1)YSU (3)c

Electromagnetism
Weak
Weak
StrongScalar bosons-- (Origin of particle mass)

Table 1.2: A table of the SM elementary particles (fermions) and their properties [18]Particle

Symbol

Q

spin

mass

strongInteraction

electromagnetic
Interaction

weakInteraction

X

X
X
X
X
X
X

Leptons
electronelectron neutrino
muon
muon neutrinotau
tau neutrino

e
νe
µ
νµ
τ
ντ

-1
0
-1
0
-1
0

1/2
1/2
1/2
1/2
1/2
1/2

0.51 MeV<0.2 eV105.6 MeV
<0.2 eV1776 MeV<0.2 eV

X
X

Quarksdownupstrangecharembottom
top

d
u
s
c
b
t

-1/3
+2/3
-1/3
+2/3
-1/3
+2/3

1/2
1/2
1/2
1/2
1/2
1/2

4.7 MeV
2.2 MeV
96 MeV
1.3 GeV
4.2 GeV173 GeV

X
X
X
X
X
X

X
X
X
X
X
X

X
X
X
X
X
X

The SM has been highly successful in predictions. One of the most successful predictions is the Higgs
boson, discovered in 2012 by the ATLAS and CMS collaborations [1, 2] at the Large Hadron Collider (LHC) as
introduced in Section 1.1. The level of agreement between the background-subtracted data and the expected
Higgs boson signal in Figure 1.1a indicates the observed excess is a signal from Higgs boson decay. Afterthe discovery of Higgs boson, the analysis of the data collected at the LHC has led to the observations ofvarious production modes and decay channels predicted by the SM, and it was found that the measurements
are consistent with the SM prediction [19–21].
There are 18 free parameters in the SM of particle physics: the masses of nine elementary particles, thethree coupling constant describing the strengths of the gauge interactions, vacuum expectation value and themass of the Higgs boson, and the three mixing angles and the CP-violating phase of Cabibbo-KobayashiMaskawa (CKM) matrix. These parameters cannot be determined by the SM itself and we need to put themby hand.
An example of the SM measurements and predictions is the mass and width measurement of the Z boson
performed at the LEP collider, which was operated at center-of-mass energies close to the Z mass from 1989
to 1995 [22]. Figure 1.3 shows the measurements of the Z resonance at LEP. From this, the mass and widthof the Z boson are determined to be mZ = 91.1875 ± 0.0021 GeV and ΓZ = 2.4952 ± 0.0023 GeV. Since thetotal width of the Z boson can be represented as the sum of the particle decay widths for all its decay modes,
the number of light neutrino generations can be obtained by the measured particle decay widths for all of its

4

Chapter 1. Introduction

decay modes except for neutrinos. The obtained number of light neutrino generations is determined to beNν = 2.9840 ± 0.0082 and it indicates the observed data is consistent with three neutrino generations.

Figure 1.3: The measurements of the e+ e− → q q̄ cross-section from LEP close to the Z resonance at LEP. The
solid and dashed lines show before and after ISR correction, respectively [22].

1.3 Limitations of the Standard Model
Although the SM can provide several predictions, it is also known that there are some critical issues thatcannot be explained within the SM framework. This section describes some of the open questions indicating
the new physics beyond the SM.

Gravity
As described in Section 1.2, the SM does not include the gravitational interaction. The quantization of gravity
faces difficulty at the Planck scale (1019 GeV) due to the nonrenormalizability of gravity. There are several
potential candidates of the quantum gravity theory like the string theory and the loop quantum gravity.

Dark Matter
Many experimental observations suggest a fraction of the Universe consisting of luminous matter is quite
small [23, 24]. The most significant evidence for that is the velocity distributions of stars orbiting around agalactic center. According to our observations of a spiral galaxy, most of the luminous mass is located in thecenter, and we can calculate the tangential velocity of a star outside the central region based on that,Gm
mv 2∼ 2 M (r),
r
r

(1.2)

where M (r) is the total mass within a radius r of a galaxy, and the tangental velocity should decrease as
r−1/2 . However, the observed velocity of the stars is not consistent with the calculated ones, implying thatthe mass of a galaxy has a significant non-luminous component.
The non-luminous component, things composing the remaining parts of the Universe, are called Dark
Matter and Dark Energy. They constitute nearly 95% (68% for Dark Energy and 27% for Dark Matter) of
the Universe according to the Standard Model of Cosmology [25]. Dark Matter is expected to be weaklyinteracting with the SM particles and massive since it interacts gravitationally and is not detected directly
yet. Weakly interacting massive particles model (WIMP) is a good candidate for Dark Matter. The WIMP
density becomes consistent with the production at the thermal equilibrium if its mass is between 10 GeV and
10 TeV.

5

1.4. BSM Models and The Interpretation Strategy

Hierarchy problem
As seen from discussions in previous sections, the SM contains several problems and it seems that the physics
beyond the Standard Model of particle physics (BSM) exists. From this point of view, the SM can be regarded
as the low energy effective theory with the cutoff scale of ΛUV , and the BSM emerges beyond the energy
scale.
Experimentally we know that the Higgs boson mass is 125 GeV [19]. When calculating the Higgs boson
mass mH , it receives large radiative corrections due to the coupling with other particles. Figure 1.4 shows
one-loop correction to the Higgs boson mass from a fermion and a scalar particle. The correction from fermion

(a)

(b)

Figure 1.4: One-loop correction to the Higgs boson mass by (a) a fermion f and (b) a scalar particle S.

couplings is described as∆m2H = −|λf |2 2
Λ + ...
8π 2 UV(1.3)

where λf is a coupling constant to fermion f and ΛUV is the cutoff scale. If we assume the BSM includes
gravity, the cutoff scale ΛUV would be at the Planck scale and this brings up the hierarchy problem. In thiscase, the correction to the Higgs boson mass is extremely high (∼ 1019 GeV), which is about 17 orders ofmagnitude larger than Higgs boson mass. The theory is said to have a naturalness [3] problem since the
Higgs boson mass and its correction must be at most of the same order to obtain the Higgs boson mass 125
GeV. The SM fermions are less affected by the ΛUV cutoff since the dependency on ΛUV is logarithm andnot quadratic due to the chiral symmetry.
One of the solutions is preparing a counterterm to cancel the correction by introducing a new scalar filed
S. The correction is described as∆m2H =λS[Λ2 − 2m2S log(Λ2UV /mS ) + ...].
16π 2 UV

(1.4)

Comparing Equation 1.3 and 1.4, one sees that the large corrections can be cancelled out. Generally, thissolution is obtained by adding a new symmetry. Supersymmetry [26–31] can achieve this kind of cancellation
by suggesting a symmetry between fermions and bosons. If each SM fermion has a corresponding boson, theΛUV contribution can be canceled.
The other option is introducing a new phenomenon between the cutoff scale ΛUV and the Planck scale
so that we don’t need to apply the cutoff scale ΛUV up to the Planck scale. The Extended gauge symmetry
model assumes an additional gauge symmetry to introduce new particles [4]. Composite Higgs model istrying to avoid the hierarchy problem by regarding the Higgs boson as a composite particle, referring to theparticles like neutron and proton in the context of QCD theory [32]. Extra dimension theory is also a possible
solution [33]. These models predict a TeV-scale new particle and it is one of the biggest motivations to search
for new particles at the LHC.

1.4 BSM Models and The Interpretation Strategy
Many kinds of BSM models have been proposed to avoid the hierarchy problem. BSM models like an extended
gauge symmetry, Minimal Composite Higgs Model, and Bulk Randall-Sundrum Model predict heavy particles
that could decay into diboson final states. This section introduces the models predicting new particles that

6

Chapter 1. Introduction

decay into diboson final states and can be explored by the ATLAS experiment. The interpretation strategies
for each model are also discussed in this section.

1.4.1 Heavy Vector Triplet Models
In this section, BSM models predicting spin-1 new particles are discussed. First, two kinds of BSM models
are introduced as benchmark models in this analysis: Extended Gauge Symmetry and Minimal Composite
Higgs Model. Then the Heavy Vector Triplet (HVT) model, a phenomenological framework for describing
spin-1 new particles, is introduced. Finally, the strategy for the signal interpretation is discussed.
Extended Gauge Symmetry
The Extended Gauge Symmetry model describes the new vector particles emerging from the symmetry
breaking of SU (2)1 × SU (2)2 × U (1)Y to SU (2)L × U (1)Y symmetry throughout a linear σ-model [4]. Herethe additional gauge group SU (2)2 symmetry is considered in addition to the SM gauge group symmetry
SU (2)1 × U (1)Y . The electric charge operator is defined as Q = T3 + Y /2 + T30 where T30 accounts for the
additional gauge SU (2)2 symmetry . To achieve the spontaneous symmetry breaking, the scalar field Φ(T3 = 21 , Y = 0, T30 = 21 ) is introduced as a quartet in addition to the SM Higgs doublet H (T3 = 12 , Y =1, T30 = 0). The bosonic part of the Lagrangian is
L=−

1
1
a
W a W aµν − 2 W2µν
W2aµν + Dµ H † Dµ H + Tr(Dµ Φ† Dµ Φ) − V(H, Φ),
4g12 1µν 1
4g2

where a=1,2,3. The potential V is defined so that H and Φ have vacuum expectaion values.




0
f 0
hHi =
, hΦi =
.
v
0 f

(1.5)

(1.6)

The VEV of scalar field Φ breaks SU (2)1 × SU (2)2 gauge symmetry to the SM SU (2)L gauge symmetry.
The mass terms of gauge bosons are obtained from the kinetic term of Φ. After the specific field redefinition,
we can obtain a new vector triplet V and the SM W boson fields. The kinetic mixing between V and W is
obtained from the kinetic term of W2 and it leads to the decay of V into the SM diboson resonance.
Minimal Composite Higgs Model
The fundamental idea of the Minimal Composite Higgs Model (MCHM) [32] is based on technicolor (TC) [7,8] in which Higgs arises as a composite pseudo-Nambu-Goldstone boson (PNGB). The electroweak symmetry
breaking (EWSB) arises from a strongly interacting new sector, similarly as the chiral symmetry breaking in
QCD. Due to the different EWSB mechanism from the SM, TC models need no fundamental scalar particle
which is the cause of the hierarchy problem. The problems of TC are that they can not pass the electroweak
precision tests (EWPT) at LEP and SLAC colliders, mainly for their large contribution to the Peskin-Takeuchi
S parameter [34] allowed by the experimental data.
The MCHM can account for these problems and contributions to electroweak precision observables are
below experimental bounds. In the MCHM, the Higgs boson arises as a composite PNGB with a symmetry
breaking of a global SO(5) symmetry to an SO(4) subgroup. The top loop effects trigger EWSB dynamicallyand the Higgs field acquires a VEV, breaking SO(4) down to the custodial SO(3) group. Originally the
MCHM is a four-dimensional (4D) conformal field theory (CFT) with Higgs as a composite PNGB of astrongly coupled sector. Since it is a theory of strong dynamics, we cannot determine the values of parameterin the effective Lagrangian for the SM fields. Considering AdS/CFT correspondance [35–37], we can obtainthe corresponding five dimensional (5D) AdS theory that leads to the same effective Lagrangian as the original
4D model. By working on the 5D AdS model, the precise parameter values of the effective Lagrangian canbe computed and it leads to the compatible predictions with the electroweak precision tests. The existenceof heavy vector resonances with electroweak quantum numbers are also predicted by this model.
Interpretation strategy for HVT Models
In this analysis, a simplified model called the HVT model, is introduced to provide a phenomenologicalparameterization of a broad set of explicit models such as Extended Gauge Symmetry and Minimal Composite
Higgs Model.

7

1.4. BSM Models and The Interpretation Strategy

The HVT model introduces a heavy vector triplet which corresponds to the new heavy vector particles
V 0 (W 0± and Z 0 ) predicted by BSM. In the HVT model, gq , gl and gH correspond to the coupling strengths
between the new vector triplet and the quark, lepton and Higgs fields. The triplet also interacts with SM W
and Z bosons by the equivalence theorem [38–40]. To capture the features of several kinds of models, the newcoupling gV is introduced. The gV parametrizes the interaction strength between the heavy vectors and W/Zbosons and is related to other coupling constants as follows. The Higgs coupling and the universal fermion
coupling are gH = gV cH and gf = g 2 cF /gV , where g is the SM SU (2)L gauge coupling. cH(F ) parameters isa free parameter that can be fixed in explicit models. Generally, cH(F ) is of order one.
In the HVT model, a real vector Vµa (a=1,2,3) are considered in addition to the SM vector bosons. The
additional neutral and charged heavy vector particles are defined byVµ± =Vµ1 ∓ iVµ2√
, Vµ0 = Vµ3 .
2

(1.7)

The dynamics of the new vector are described by a simple phenomenological Lagrangian:m2
1
LV = − D[µ Vν]a D[µ V ν]a + V Vµa V µ a42↔
g2+ igV cH Vµa H † τ a Dµ H +cF Vµa JFµ agVggµ+ cV V V abc Vµa Vνb D[µ V ν]c + gV2 cV V HH Vµa V µ a H † H − cV V W abc W µνa Vµb Vνc .
2
2

(1.8)

The kinetic and mass term of V are contained in the first line. The second line contains direct interaction of
V with the Higgs current↔

iH † τ a Dµ H = iH † τ a Dµ H − iDµ H † τ a H,

(1.9)

and with the SM left-handed fermionic currents
JFµa =Xf¯L γ µ τ a fL ,(1.10)fwhere τ a = σ a /2. The Higgs current term involves the V interaction with the SM vectors and with the Higgs
boson. Therefore the V decay into bosonic channel is controlled by the coefficient cH . On the other hand,the coefficient cF describes the direct interaction with fermions. The fermionic current is responsible for the
Drell-Yan (DY) production and fermionic decays. To take into account the more general situation, cF , auniversal coupling of V to fermions, are generalized tocF V · JF → cl V · Jl + cq V · Jq + c3 V · J3 .

(1.11)The third line of Equation 1.8 contains 3 new operators involving cV V V , cV V HH and cV V W . However, they
do not contribute directly to V decays and single production processes since none of them contains verticesof one V with SM fields. Therefore the phenomelogy of interest is described by the five parameters cH , cF ,cl , cq , c3 and the mass term mV . The coupling gV represents the typical strength of V interactions and thedimensionless coefficients "c" parametrize the departures from the typical size of order one. In the case of
the fermion couplings, one extract factor of g 2 /gV2 is introduced. This feature is common to all the explicit
heavy vector triplet models we are interested in and the cF ’s are of order one.
By tuning the HVT parameters, several kinds of BSMs such as Extended Gauge Symmetry and Minimum
Composite Higgs Model can be treated. In this analysis, three explicit parameter sets are chosen as spin-1
new particle benchmarks. The first two correspond to Extended gauge symmetry and Minimum Composite
Higgs model, which are produced by DY mechanism. The first DY beanch mark is the weakly coupled model
describing the Extended Gauge Symmetry model. In this case gV = 1 and the fermion coupling is assumed
to univeral (gf = gq = gl ). This model is referred to as Model A in this thesis. The second DY scenario
reproduces the phenomenology of a strongly coupled model as Minimum Composite Higgs Model. This modelis called Model B in this thesis. gV = 3 is adopted in the model. For the DY processes, the branching ratios
for decays into individual SM diboson channels are about 2% in Model A, whereas 50% in Model B. As
the extreme case, the third model called Model C, is designed to study the rare process of VBF production
mode. In this model the couplings are set to gH = 1 and gf = 0. The interpretation can be done for eachresonance mass and the two-dimensional parameter space consisting of coupling constants defined above.
Signal samples for the HVT (both DY and VBF) are generated with MadGraph5 (MG5) [41] interfaced to8Chapter 1. Introduction

Pythia 8.

1.4.2 RS Graviton and Radion
In this section, BSM models predicting new spin-0/2 particles are discussed. The strategy for the interpretation is also discussed.
Bulk Randall-Sundrum Model
Models with large compactified extra dimension provide an alternative solution to the hierarchy problem[5, 6]. In these models, the effective four-dimensional Planck scale MPl is determined by the fundamental(4+n)-dimensional Planck scale M and the geometry of the extra dimensions. The relation is described by2MPl= M n+2 Vn , where Vn is the volume of the extra dimensions. The large hierarchy between the weak scale
and the fundamental scale of gravity can be eliminated if Vn is large enough. Unfortunately, the large extra−1/ndimension introduces a new hierarchy, namely between the compactification scale µc = Vn
and M .
Randall-Sundrum model [33] is one of higher dimensional scenarios that can solve the hierarchy problem
with small extra dimensions. This model consists of a spacetime with a single S 1 /Z2 1 orbifold extra dimension(−π ≤ φ ≤ π with φ and −φ identified) and two 4-dimensional branes localized at both φ = 0 ("UV/Planck"brane) and φ = π ("IR/TeV" brane). The resulting spacetime metric is
ds2 = e−2krc |φ| ηµν dxµ dxν − rc2 dφ2 ,(1.12)

where rc is the radius of the compactifed dimension, k is a curvature scale which is assumed to be of orderof M , and xµ are Lorentz coordinates on the four-dimensional surface of constant φ. By exploring thefour-dimensional effective field theory based on Eq 1.12, we can see
2
MPl
=


M3 
1 − e−2krc π .
k(1.13)

This tells that MPl depends only weakly on rc in the large krc limit and M is compatible with MPl as
fundamental scale. The large hierarchy between TeV physical mass scales and fundamental Planck massscales are generated by the exponential geometric factor appearing in the metric. This model assumes all SM
particles are localized on the "IR/TeV brane" and KK (Kaluza-Klein) gravitation is predicted at the TeV
scale. Since KK graviton is also assumed to be localized near the "IR/TeV brane", the entire SM particles
have TeV scale coupling to KK graviton. However, the original Randall-Sundrum model leads to the large
contributions to flavor changing neutral current (FCNC) and observables related to electroweak precision
tests, which is forbidden by experimental observations.
To avoid these problems, "Bulk" RS model, in which the SM fields are allowed to propagate in the extra
dimension, had been proposed [42–45]. In this model, 1st and 2nd generation fermions are localized near
"UV/Planck brane" so that the contributions to FCNC and electroweak precision tests are suppressed. On
the other hand, KK graviton is still localized near the "IR/TeV brane" so that the coupling of KK graviton
to light fermions are highly suppressed.
RadionThe problem of the RS model is that it lacks the mechanism of determining the value of rc dynamically.
Radion is a bulk scalar which provides the mechanism of generating a potential to stabilize the value of rc[46]. The bulk action with the five-dimensional bulk scalar fields Φ is1
Sb = a
2

Z

4

Z φ

dx

√

dφ G GAB ∂A Φ∂B Φ − m2 Φ2 ,(1.14)−φ

where GAB with A, B = µ, φ. We can also consider the interactions of scalar fields Φ on "IR/TeV brane" and"UV/Planck brane". The interaction terms on branes cause Φ to develop a φ-dependent vacuum expectation
value


Φ(φ) = e2σ Aeνσ + Be−νσ ,(1.15)
1 A space obtained by identifications that have fixed points. A circle of raidus r with the identification φ ∼ −φ in this case.
c91.5. Heavy Resonance Searches using Early Run2 Datapwhere ν = 4 + m2 /k 2 . Putting this back into the scalar field action and integrating over φ, an effective fourdimensional potential VΦ (rc ) is obtained and it leads to the minimum value of rc . Therefore the compactified
radius rc is stabilized. This mechanism for stabilizing rc is caused by the presence of a φ-dependent vacuum
bulk field and causes the radion field Φ to acquire a mass term and couplings to SM fields [47–49].
Interpretation strategy for Bulk RS graviton
In the bulk RS model described, both gravity and SM fields can propagate into the warped extra dimension
and it leads to a tower of KK excitations of gravtion GKK and SM fields. The couplings of GKK to lightfermions are suppressed by virtue of avoiding constraints from FCNC and electroweak precision tests. The
spin-2 KK gravitons GKK is produced dominantly via gluon-gluon fusion (ggF). The coupling strength
depdends on k/MPl , where MPl is the reduced Planck mass [50]. Consequently both the production crosssection and decay width of the GKK scale as the square of k/MPl . Typically the value of k/MPl is of orderone. In the interpretation, k/MPl = 1 is used so the only free parameter is mass of GKK
Interpretation strategy for Radion
The couplingstrength of the radion field to SM fields depends on the model parameter ΛR =
q

p

(g) ×

M53
k3

ke−kπrc
where M5 is the 5-dimensional Plank mass [47–49], kπrc = 35, and ΛR = 3 TeV. The sizeof the extra dimension defined as kπrc , is another parameter of the model. The coupling of the radion tofermions is proportional to the mass of the fermion while it is proportional to the square of the mass forbosonic fields. This leads to the dominant decay mode for the radion to be a pair of bosons when the radion
mass above ∼ 1 TeV. Both the production cross-section for the radions and the total width scale like ∼ 1/Λ2R .

1.4.3 Signal Parameters
Finally, signal parameters used in the interpretation are summarized in Table.1.3
Table 1.3: List of benchmark signal models. Predictions of cross-section σ, branching ratio BR (X →W W/W Z/ZZ), and intrinsic width divided by the resonance mass Γ/m for the given hypothetical new particle at m = 500 GeV and 3 TeV are summarized.
Model

Spin

Radion (kπrc = 35,
ΛR = 3 TeV)
Model A
HVT

Model B

Model C(VBF)
Bulk RS GKK(k/M Pl = 1.0)

R → WW
R → ZZ
W0 → WZ
Z0 → W W
W0 → WZ
Z0 → W W
W0 → WZ
Z0 → W W
GKK → W W
GKK → ZZ012m = 500 GeV
σ [pb]
BR
1.96 (3.5 × 10−3 )in ggF (VBF)
327
157
–
–
0.036
0.023
17.2 (0.46)
in ggF (VBF)

0.39
0.19
0.028
0.027
–
–
0.50
0.46
0.43
0.23

Γ/m
0.001
0.027
–
0.00400.037

σ [fb]

m = 3 TeV
BR

1.38 (5.5 × 10−3 )in ggF (VBF)
79
36
5.5
2.5
1.61 × 10−3
1.04 × 10−3
0.47 (1.6 × 10−2 )in ggF (VBF)

Γ/m

0.44
0.22

0.03

0.020

0.025

0.47

0.031

0.50

0.0033

0.20
0.10

0.062

1.5 Heavy Resonance Searches using Early Run2 Data
This section presents the results of the previous round of searches for the new heavy resonance decaying√
into diboson final states. ATLAS Run-2 data sample correponding to 36.1 fb−1 of pp collisions at s=13
TeV collected by the ATLAS detector in 2015-2016 is used [51]. Interpretation results of the spin-1 HVTmodel, spin-2 Bulk RS model, and a spin-0 new heavy scalar are presented. Based on the number of charged
leptons, the semi-leptonic analysis is split into three analysis channels: 0-lepton (ZZ/ZW → ννqq), 1-lepton(W W/W Z → `νqq) and 2-lepton (ZZ/ZW → ``qq) channels. Here `, ν and q denote the charged lepton (eor µ), neutrino, and quark (u, d, c, s, b), respectively. Section 1.5.1 shows upper limits on cross-section times
branching ratio as a function of new boson mass using combined searches performed in the VV channels
including the semi-leptonic channel; W Z → qqqq, lνqq, lνll; W W → qqqq, lνqq, lνlν; and ZZ → qqqq, ννqq,
llqq, llνν, llll. In addition, exclusion contour of signal parameters is also discussed for the HVT models in
Section 1.5.2. Detailed event selection and statistical methodology can be found in Refs [51].

10

Chapter 1. Introduction

1.5.1 Upper limits on the cross-section times branching ratio

104

Observed 95% CL limit
Expected 95% CL limit
Exp. lvqq
Exp. llqq
Exp. vvqq
Exp. lllv
Exp. qqqq

ATLAS
s = 13 TeV, 36.1 fb-1

3

10

102
10

σ(pp → W’ → WZ) [fb]σ(pp → W’ → WZ) [fb]Figure 1.5 shows the upper limits on the cross-section times branching ratio of W 0 for the HVT model. For
DY category, the lower limit on the m(W 0 ) is 3.6 TeV in the weakly coupled HVT Model A and approximately
4 TeV in the strongly coupled HVT Model B. On the other hand, the lower limit does not reach to an expected
theory curve for VBF production at all, and therefore there is room for exploring new particles produced via
VBF production mode. In high m(W 0 ) region of both DY and VBF categories, lνqq and ννqq channels havedominant lower limits, while llqq channel shows better constraints at low m(W 0 ) region. The full leptonic
channel (lllν) presents the best performance at low m(W 0 ) region. The full hadronic channel (qqqq) indicatesthe compatible sensitivity with `νqq and ννqq channels in high m(W 0 ) region, but it can search for onlym(W 0 ) greater than ∼ 1 TeV. In contrast to these situations, the semi-leptonic channels can probe the fullrange of m(W 0 ) by compensating shortages of each channel, and therefore the channel could be the goodprobe for exploring new physics.

1
10−1

104

ATLAS

Observed 95% CL limits = 13 TeV, 36.1 fb-1

Expected 95% CL limit

10

Exp. lvqq
Exp. llqq

102

Exp. vvqq
Exp. lllv

3

10
1
10−1

DY HVT W’ → WZ (qqqq + vvqq + lvqq + llqq + lllv)

0.5

1

1.5

2

2.5

3

3.5

4 4.5 5m(W’) [TeV]VBF HVT W’ → WZ (vvqq + lvqq + llqq + lllv)

0.5

1

1.5

104

ATLAS

Observed 95% CL limits = 13 TeV, 36.1 fb-1

Expected 95% CL limit
Expected ± 1σ

310Expected ± 2σ
HVT model A

2

HVT model B

10

10
1
10−1

2.5

3

3.5
4
m(W’) [TeV](b)σ(pp → W’ → WZ) [fb]σ(pp → W’ → WZ) [fb]

(a)

2

104

ATLAS

Observed 95% CL limits = 13 TeV, 36.1 fb-1

Expected 95% CL limit

3

Expected ± 1σ

2

HVT model C

10

Expected ± 2σ

10

10
1

DY HVT W’ → WZ (qqqq + vvqq + lvqq + llqq + lllv)

0.5

1

1.5

2

2.5

(c)

3

3.5

4 4.5 5m(W’) [TeV]10−1

VBF HVT W’ → WZ (vvqq + lvqq + llqq + lllv)

0.5

1

1.5

2

2.5

3

3.5
4
m(W’) [TeV](d)Figure 1.5: Observed and expected 95% CL (confidence level) upper limits on the W 0 cross-section times branchingratio to W Z for the HVT model. Expected limits for individual channels and their combination are shown for the(a) DY and (b) VBF production mechanisms. The limits for the combined channels for the (c) DY and (d) VBF
production mechanisms are also shown, along with predictions for HVT models A, B, and C [51]Figure 1.6 shows the upper limits on the cross-section times branching ratio of GKK for the Bulk RS model.
For GKK → W W search, the `νqq outperforms both full leptonic and full hadronic channels over the fullrange of m(GKK ). For GKK → ZZ search, the ννqq channel has strong constraints at high m(GKK ) region
and the llqq channel shows better constraints at low m(GKK ) region. The lνqq channel does not contributeto this search. As in the case of HVT searches, the semi-leptonic channel demonstrates the outstanding
sensitivity to GKK in all m(GKK ) region. The lower limit on the m(GKK ) is 1.9 TeV in GKK → W W and
1.7 TeV in GKK → ZZ.

11

Observed 95% CL limits = 13 TeV, 36.1 fb-1

Expected 95% CL limit

3Exp. lvqq

10Exp. lvlv

102

σ(pp → Gσ(pp → G→ ZZ) [fb]

ATLAS

KK

104

KK

→ WW) [fb]1.5. Heavy Resonance Searches using Early Run2 Data

Exp. qqqq

10
1
10−1
0.5

104

ATLAS

Observed 95% CL limits = 13 TeV, 36.1 fb-1

Expected 95% CL limit
Exp. llqq

310Exp. vvqq
Exp. llll

102

Exp. qqqq

10
1
10−1

GKK → WW (qqqq + lvqq + lvlv)

1

1.5

2

2.5

3

3.5

4

4.5

5

0.5

GKK → ZZ (qqqq + vvqq + llqq + llvv + llll)

1

1.5

2

2.5

3

3.5

m(G ) [TeV]KKExpected 95% CL limit

KK

Expected ± 1σ

102σ(pp → Gσ(pp → G→ ZZ) [fb]Observed 95% CL limits = 13 TeV, 36.1 fb-1

KK→ WW) [fb]

ATLAS

Expected ± 2σ
Bulk RS, k/MPl = 1.0

10
1

0.5

5

(b)

103

10−1

4.5
KK

(a)

104

4

m(G ) [TeV]

104

ATLAS

Observed 95% CL limits = 13 TeV, 36.1 fb-1

Expected 95% CL limit

103

Expected ± 1σ

102

Bulk RS, k/MPl = 1.0

Expected ± 2σ

10
1
10−1

GKK → WW (qqqq + lvqq + lvlv)

1

1.5

2

2.5

3

3.5

4

4.5

5

0.5

GKK → ZZ (qqqq + vvqq + llqq + llvv + llll)

1

1.5

2

2.5

m(G ) [TeV]

3.5

4

4.5

5

m(G ) [TeV]

KK

(c)

3

KK

(d)

Figure 1.6: Observed and expected 95% CL upper limits on the GKK cross-section times branching ratio to (a)W W and (b) ZZ for the Bulk RS model. Expected limits and their combination for individual channels and their
combination are shown, along with (c), (d) predictions for Bulk RS model with k/M¯P l = 1 [51].

12

Chapter 1. Introduction

104

ATLAS

σ(pp → Scalar → WW) [fb]σ(pp → Scalar → WW) [fb]Figure 1.7 shows the upper limits on the cross-section times branching ratio for the heavy scalar model.
`νqq and ννqq channels are dominant in high m(scalar) region, while llqq channel shows better constraints
in low m(scalar) region.

Observed 95% CL limits = 13 TeV, 36.1 fb-1

Expected 95% CL limit

103

Exp. lvqq
Exp. lvlv

2

10

Exp. qqqq

10
1
10−1

104

ATLAS

Observed 95% CL limits = 13 TeV, 36.1 fb-1

Expected 95% CL limit

103

Exp. lvqq
Exp. lvlv

2

10

10
1
10−1

ggF Scalar → WW (qqqq + lvqq + lvlv)

0.5

1

1.5

2

2.5

3

VBF Scalar → WW (lvqq + lvlv)

0.5

1

1.5

2

2.5

m(Scalar) [TeV]

(b)

ATLAS

Observed 95% CL limits = 13 TeV, 36.1 fb-1

Expected 95% CL limitσ(pp → Scalar → ZZ) [fb]σ(pp → Scalar → ZZ) [fb]

(a)

104

Exp. llqq

103

Exp. vvqq
Exp. llll

102

Exp. qqqq

10
1
10−1

3

m(Scalar) [TeV]

104

ATLAS

Observed 95% CL limits = 13 TeV, 36.1 fb-1

Expected 95% CL limit

103

Exp. llqq
Exp. vvqq

102

Exp. llll

10
1
10−1

ggF Scalar → ZZ (qqqq + vvqq + llqq + llvv + llll)

0.5

1

1.5

2

2.5

3

VBF Scalar → ZZ (vvqq + llqq + llvv + llll)

0.5

1

1.5

m(Scalar) [TeV]

(c)

2

2.5

3

m(Scalar) [TeV](d)Figure 1.7: Observed and expected 95% CL upper limits on the scalar cross-section times branching ratio for theheavy scalar model. Expected limits for individual channels and their combination are shown for the (a) ggF-W W ,(b) VBF-W W , (c) ggF-ZZ and (d) VBF-ZZ production mechanisms [51].

V V + V H combined results of observed and expected 95% CL upper limits on the cross-section times
branching ratio for HVT, Bulk RS and heavy scalar models are also discussed in Refs [51]. The upper limits
on HVT Model A combined V V , V H and V 0 → ``/`ν decay modes are shown in Figure 1.8. Combined limits
exclude HVT Model A up to approximately 4.5 TeV due to stronger dileptonic decay mode.
For the original RS Graviton model with k/MPl = 0.1, Figure 1.9 shows the limits on the cross-section
times branching ratio to two photons as a function of the resonance mass. The RS model with k/MPl = 0.1
is excluded for mG∗ below 4.1 TeV, and this is one of the motivations of searching for the Bulk RS model
discussed in Section 1.4.2.

1.5.2 Upper limits on coupling strengths
Constraints on the coupling strengths to both quarks and bosons (gq , gH ) are also provided in the context of
HVT models. The constraints are shown in Figure 1.10. In the shaded region, the limits are not valid sinceresonance would have a width greater than 5% of their mass. This is a region where the width of resonancewould exceed the experimental m(V V ) resolution, and an assumption of the narrow-width approximation is
not valid anymore. The area outside the curves is excluded for each mass point. The resonance couplings to
V V and V H decreases as the gH coupling approaches zero, and production of the resonance tends to zero as
the gf couplings approach zero. This is why the constraints become weak when the couplings for both gH
and gf decrease. By combining V V +V H+lv/ll channels, only smaller couplings for gf are not excluded as

13

104

ATLAS

σ(pp → Z’ → WW + ZH + ll) [fb]σ(pp → W’ → WZ + WH + lv) [fb]1.5. Heavy Resonance Searches using Early Run2 Data

Observed 95% CL limits = 13 TeV, 36.1 fb-1

Expected 95% CL limit
Expected ± 1σ

103

Expected ± 2σ

102

HVT model A

10
1
10−1
0.5

1.5

2

2.5

3

3.5

4

4.5

5

Observed 95% CL limits = 13 TeV, 36.1 fb-1

Expected 95% CL limit

103

Expected ± 1σ

102

HVT model A

Expected ± 2σ

10
1
10−1

DY HVT W’ → WZ + WH + lv

1

ATLAS

104

DY HVT Z’→ WW + ZH + ll

0.5

1

1.5

2

2.5

m(W’) [TeV]

3

3.5

4

4.5

5

m(Z’) [TeV]

(a)

(b)

95% CL Upper Limit on σ × B [fb]Figure 1.8: Observed and expected 95% CL upper limits on the V 0 cross-section times branching ratio to V V ,V H, and lepton–antilepton states for (a) W 0 , (b) Z 0 , and (c) V 0 production, along the predictions for HVT ModelA [51].

103

102

10

Observed CLs limit
Expected CLs limit
Expected ± 1σ
Expected ± 2σpp→G*→γ γATLAS
s = 13 TeV, 36.7 fb-1
Spin-2 Selection
G*→γ γ , k / MPl = 0.10
Observed CLs limit
from pseudo-exp.
Expected CLs limit
from pseudo-exp.

1

10−1
10−2

500 1000 1500 2000 2500 3000 3500 4000 4500 5000
mG* [GeV]√
Figure 1.9: Upper limits on the production cross section times branching ratio to two photons at s = 13 TeV ofthe lightest KK graviton as a function of its mass mG∗ for k/MPl = 0.1. For mG∗ > 2500 GeV, the observed andexpected limits are determined with pseudo-experiments shown by the blue solid and dashed lines, respectively.
Predictions are shown for the RS1 model, where the grey shaded band represents the PDF uncertainty [52].

14

Chapter 1. Introduction

ATLAS 3 TeV
EW fits 3 TeV

1
0.8
0.6
0.4

ATLAS

f

Observed

Fermion coupling g

Fermion coupling gfdescribed in Figure 1.10b. This motivates a search for a heavy vector like particle produced via VBF, whichcorresponds to HVT model C (gf = 0) discussed in Section 1.4.1.

s = 13 TeV
36.1 fb-1
V’ → VV
4 TeV

0.2

3 TeV

B
2 TeV

0
−0.2
−0.4
−0.6
−0.8
−1
−3

ATLAS 5 TeV
EW fits 5 TeV

0.8

ATLAS

0.6

s = 13 TeV
36.1 fb-1
V’ → VV+VH+lv+ll

0.4
0.2

Observed

B

0
−0.2
−0.4

A

A

−0.6

Γ
m > 5%−2

ATLAS 4 TeV
EW fits 4 TeV

1

−0.8
−1

0

1

2

3

Higgs and vector boson coupling g

H

(a)

−1
−3

−2

−1

0

1

2

3

Higgs and vector boson coupling gH(b)

Figure 1.10: Observed 95% CL exclusion contours in the HVT parameter space {gH , gf } for resonances of mass
3, 4, and 5 TeV for the combination of (a) V V , and (b) V V +V H+lv/ll channels. The areas outside the curves
are excluded, as are the filled regions which show the constraints from precision EW measurements [51].

1.6 Search for heavy diboson resonances in semi-leptonic final states
As introduced briefly in the previous section, the semi-leptonic channel of heavy resonances search has thegood sensitivity to new particles over broader range of resonance mass. Furthermore, only this analysis
searches for VBF production mode, and most of the resonance mass parameters are not excluded yet. There
are still motivations to improve the sensitivity of all mass regions. In ggF production mode, lower mass region
is excluded for most of the benchmark models. Hence sensitivity improvements for higher mass region are
getting more important. Since the semi-leptonic analysis could be the significant indicator of new physics,
the analysis improvement is surely helpful and the author contributed to that by introducing several ideas,
which are discussed in Section 5 and 6 in details.
The author introduced several new ideas to improve the sensitivity e.g. Track-Calo Cluster (TCC), which
is a particle-flow algorithm for high-pT jet to achieve better jet substructure resolution, variable-radius (VR)track-jet b-tagging for the boosted Z → bb reconstruction, machine-learning (ML) based analysis. The
author contributed in the ATLAS collaboration to these developments, in particular the optimization ofboson tagging criteria and the calibration of TCC jets.
In the semi-leptonic analysis, the invariant-mass (for 1-lepton and 2-lepton channels) and transverse mass(for the 0-lepton channel) reconstructed by the final-state boson candidates are used as a final discriminant,and an excess against the estimated SM background is explored. When the resonance mass is significantly
greater than the W/Z boson mass, the hadronically decaying W/Z boson from new particle X is highly
boosted. Therefore the resulting quark pair can be collimated so that each of quark can not be identified
separately. To handle this situation, each lepton channel analysis is split into two categories based on
the different jet reconstruction techniques: (1) merged category with large-radius jet and a boson-tagging
technique using jet substructure and (2) resolved category with the "standard" small-radius jets. In the
0-lepton channel, only merged category is considered. The merged category is further split into high-purity
and low-purity regions based on the efficiency of boson tagging. In addition, in the case of the reconstructionof Z → q q̄ candidate, all categories are separated into the bottom-quark enriched subcategory (b-tagged) andthe other (untagged). Thus a large-radius jet is used to reconstruct the final discriminant in merged analysis,
while two separate small-radius jets are used for resolve analysis.
Dominant SM backgrounds of this analysis are W and Z bosons production in association with jets
(W +jets and Z + jets, or collectively denoted as V +jets), top-quark production (both top-quark pair, tt̄,and single top-quark), non-resonant diboson production (W W ,W Z and ZZ), and multijet production. The
modeling of these background processes are validated by the dedicated control region. The defined control
regions are also used for statistical analysis to estimate the background. In all lepton channels and bothmerged and resolved categories, events are further categorized into subcategories based on the event topology
consistent with VBF and ggF/DY categories, respectively.

15

Chapter 2

Experimental Setup
2.1 The Large Hadron Collider√
The Large Hadron Collider (LHC) [53] is a proton-proton collider with a center-of-mass energy s = 13 TeV
and a design luminosity of 1034 cm−2 s−1 . The LHC is also able to accelerate lead ions and produce ion-ion
and ion-proton collisions. The main LHC ring of a circumference of 26.7 km is located underground (between
70m and 140m) near Geneva, Switzerland. The collisions take place at four interaction points (IP) for the
ALICE, ATLAS, CMS and LHCb experiments. The schematic overview of the LHC is shown in Figure 2.1a.

Geneva
CERN
LHCb

CMS

ALICE

ATLAS

LHCb

ATLAS

PS
BOOSTER

SPS

CMS

LHC

(a)

ALICE

~100 m(b)

Figure 2.1: (a) Overview of the LHC, including the ALICE, ATLAS, CMS and LHCb experiment [54]. (b) A
schematic view of the CERN accelerator complex [55].

The LHC has two beam pipes and proton beams are circulating in opposite directions, clockwise andanti-clockwise, with an energy of 6.5 TeV. Before injecting into the LHC ring, protons are accelerated to450 GeV by the acceleration chain which is a system of boosters: the LINAC2, Proton Synchrotron Booster(PSB), Proton Synchrotron (PS) and Super Proton Synchrotron. Figure 2.1b shows the overview of a seriesof accelerators.
The accelerated proton beams are directed by 1232 superconducting dipole magnets consist of niobiumtitanium super-conductors which provides a magnetic field of up to 8.3 Tesla. The maximum field strengthis necessary to bend protons with an energy of 7 TeV. They are operated at an extremely low temperatureof 1.9 Kelvin to keep enough margin from the critical point. Furthermore, 392 quadrupole magnets are used
to focus the proton beams and dedicated insertion magnets are used to focus the beams into the collision
points. The proton acceleration is performed by superconducting radio frequency (RF) cavities, 8 modules
per beam, operating at a frequency of 400 MHz and an accelerating gradients of 5.5 MV m−1 [53]. During
Run 2 the LHC was running with the number of bunches per beam up to nb = 2544 and the number ofprotons per bunch Nb = 1.15 × 1011 with a bunch spacing of 25 ns. The selected typical parameters for eachyear with standard 25 ns bunch train operation are summarized in Table 2.1.

16

Chapter 2. Experimental Setup√
Table 2.1: Selected LHC parameters for pp collisions at s = 13 TeV in 2015–2018. The best accelerator
performance during normal physics operation are shown. In 2017, the LHC was run in two modes: standard 25
ns bunch train operation and ’8b4e’ denoting a pattern of eight bunches separated by 25 ns followed by a fourbunch-slot gap. The peak instantaneous luminosity of 16 × 1033 cm−2 s−1 in 2017 is part of the 8b4e period [56].
Parameter
Maximum number of colliding bunch pairs (nb )Bunch spacing (ns)Typical bunch population (101 1 protons)β∗ (m)
Peak luminosity (1033 cm−2 s−1 )Peak number of inelastic interactions/crossing (< µ >)Luminosity weighted mean inelastic interactions/crossing (< µ >)Total delivered integrated luminosity (fb−1 )

2015
2232
25
1.1
0.8
5
16
13
4.0

2016
2208
25
1.1
0.4
13
41
25
38.5

2017
2544/1909
25/8b4e1.1/1.2
0.3
16
45/60
38
50.2

2018
2544
25
1.1
0.3-0.25
19
55
36
63.4

Luminosity Determination
Luminosity measurements at the LHC are crucial since it directly relates to the production rate of physicalprocesses. In ATLAS, luminosity information is provided by several detectors. The LUCID-2 (LUminosity
Cerenkov Integrating Detector) [57], which is upgraded to cope with all beam conditions and luminosity
ranges during Run 2, is able to provide the primary bunch-by-bunch luminosity information, both online
and offline. Measurements from other detectors such as calorimeters and BCM (beam condition monitor)
diamond detectors can be found in Refs. [57, 58].
The LUCID-2 consists of two simple rings of 16 PMTs (Photomultipliers) placed at approximately z =±17 m from the interaction point, one ring per side, with the quartz window working as a Cherenkov radiator.
In addition, four quartz fiber-bundles coupled to PMTs are installed 1.5 m away from the beam pipe. In
order to convert the raw signals from the PMTs to a luminosity, several luminosity algorithms requiring hits
information are used: BiEventORA in 2015, BiHitOR in 2016 and 2017 [56]. Since most of PMTs stopped
working in 2018, a single PMT on the C-side was used for the baseline luminosity estimate.
Based on the number of hit counts, a visible interaction rate per bunch crossing µvis , which is proportional
to the instantaneous luminosity, is evaluated [59]. Then, the per-bunch instantaneous luminosity can be
written as:
Lb =µvis fr
,
σvis

(2.1)

where fr is the LHC revolution frequency (11245 Hz for protons), and a calibration constant corresponding
to the visible cross-section σvis is evaluated by vdM (van der Meer) scans [56, 58, 59]. In terms of beam LHC
parameters, the per-bunch instanteneous luminosity can also be wrriten as:
Lb =fr n1 n2P P ,2π x y(2.2)

PP
where n1 (n2 ) is the number of protons in the beam-1 (2), and x and y are the convolved beam sizes in
the horizontal and vertical planes.
vdM scans, the beam separation is varied in individually horizontal
PIn the P
and vertical direction to obtain x and y , and to scan µvis . Combining Equations 2.1 and 2.2 gives σvis
followingP P
2π x ymax,(2.3)
σvis = µvis
n1 n2
wehre µmax
vis is the maximal visible rate extracted in the vdM scan. The measurements are complemented
by the four-diamond BCM sensors on each side of interaction points using similar formalism. Given theseparameters, the instantaneous luminosity is obtained as L = nb Lb . The expected events number of a traget
process is then calculated as Nprocess = σprocess L. Here L is the time-integrated luminosity of L. Figure 2.2
shows the total integrated luminosity in Run-2.

2.2 The ATLAS Detector
The ATLAS detector [61] at the LHC is a multipurpose particle detector with an approximately 4π coveragein solid angle. It consists of an inner detector, electromagnetic and hadronic calorimeters, and a muon

17

160

ATLAS
140 Preliminary120

LHC Delivered
ATLAS Recorded100

s = 13 TeV
Delivered: 156 fb-1
Recorded: 147 fb-1
Physics: 139 fb-1

Good for Physics

80
60
40

2/19 calibration

Total Integrated Luminosity fb-1

2.2. The ATLAS Detector

20
0'15 ul '15 an '16 ul '16 an '17 ul '17 an '18 ul '18
J
J
J
J
Jan
J
J
J

Month in Year
Figure 2.2: Total Integrated Luminosity and Data Quality in 2015-2018 [60].

.
spectrometer. The schematic view of the ATLAS detector is shown in Figure 2.3.
The inner detector (ID) for tracking covers the pseudorapidity range |η| < 2.5 and is immersed by a 2 T
magnetic field provided by a solenoid. The inner detector is composed of silicon pixel, silicon microstrip, andtransition-radiation tracking detectors. An innermost pixel layer inserted at a radius of 3.3 cm has been usedsince 2015.
Lead and liquid argon (LAr) electromagnetic sampling calorimeters provide electromagnetic (EM) energy
measurements and the position of the electromagnetic showers with |η| < 3.2. The LAr sampling calorimeters
are also used to measure hadronic showers in the endcap (1.5 < |η| < 3.2) and electromagnetic and hadronic
showers in the forward regions (3.1 < |η| < 4.9). Hadronic calorimeters cover the central pseudorapidity
range (|η| < 1.7). The end cap and forward regions are instrumented with LAr calorimeters for both the EM
and hadronic energy measurements up to |η| = 4.9.
The muon spectrometer (MS) surrounds the calorimeters and covers the pseudorapidity range |η| < 2.7.
The MS features three large air-core toroidal superconducting magnet systems with eight coils each (between
2.0 and 6.0 Tm). In the MS, Precision tracking chambers cover up to |η| = 2.7 and fast detectors for triggering
cover up to |η| = 2.4.

2.2.1 Coordinate System
The ATLAS experiment adopts a right-handed coordinate system. The origin lies at the IP and the positive
x-axis direction points to the center of the LHC and the positive y-axis points upwards. The x-y plane isused for transverse measurements and the z-axis points along the beamline by definition. In addition to acartesian coordinate, polar coordinates are also used. The azimuthal angle φ is defined in the x-y plane and ismeasured from the y-axis. The polar angle θ is defined in the y-z plane and is measured from the z-axis. The
pseudorapidity is defined as η = − ln tan θ2 , which is invariant under Lorentz-transformations. The angularpdistance ∆R is also used and is defined as ∆R = ∆η 2 + ∆φ2 .

2.2.2 Inner Detector
The ATLAS Inner Detector (ID), shown in Figure 2.4, is designed for providing position measurements ofcharged particles in the range |η| < 2.5. In order to provide the track measurements, the ID is immersed ina 2 T magnetic field generated by the central solenoid which has a length of 5.3 m with a diameter of 2.5
m. The ID consists of three different technologies of silicon pixel, silicon micro-strip (SCT) and straw tube
transition radiation tracker (TRT) detectors. It is composed of a cylindrical barrel region arranged aroundthe beam pipes (|η| < 1.5), and two end-caps for 1.5 < |η| < 2.5. A detailed description of the inner detector
can be found at [61].

18

Chapter 2. Experimental Setup

Figure 2.3: An overview of the ATLAS detector [62].

The pixel detector [63] has four-barrel layers at radii of 33, 50.5, 88.5 and 122.5 mm and three disks ineach of the end-caps at |z|=495, 580 and 650 mm. From Run 2, the insertable B-layer (IBL) is introduced as
the innermost layer [64, 65]. The typical pixel size is 50 µm (r − φ)× 250 µm (z) for IBL and 50 µm (r − φ)×400 µm (z) for the outer barrel and disk layers.
The SCT [66] consists of four double strip layers at raddi of 299, 371, 443 and 514 mm, spanning |z| <746 mm, complemented by nine wheels in each of the end-caps with 854 mm < |z| < 2720 mm. A typical
strip of a barrel SCT sensor has a 80 µm pitch and 128 mm length running approximately along the z-(r-)
direction for the barrel (end-caps). Each module consists of a double-sided sensor with a stereo angle of 40
mrad. The information from the two sides of each layer can be combined to provide a three-dimensional
position measurement referred to as a space-point.
The silicon detectors are complemented by the outer volumes of the inner detectors furnished with theTRT [67]. The TRT extends track reconstruction radially up to a radius of 1082 mm. It is comprised ofapproximately 300 000 straw tubes and covers the pseudorapidity range of |η| < 2.0. Each straw tube only
provides two-dimensional position information with a position resolution of approximately 130 µm. Starw
tubes in the barrel region (|z| < 712 mm) run along the z-direction providing (r, φ) information, while forend-caps (848 mm<|z|<2710 mm) they run in the radial direction providing (z, φ) information.

2.2.3 Calorimeter System
The ATLAS calorimeter system [68, 69] is degined for providing good measurements for electromagnetic
and hadronic showers. Figure 2.5 shows the sckematic view of the ATLAS calorimeter system. The ATLAS
calorimeters have a highly granular lateral and longitudinal segmentation. It covers |η| < 4.9 and is composedof the electromagnetic (EM) calorimeter and the hadronic calorimeter. The EM calorimeter can be used for
precision measurement of electrons and photons, by requiring the matching between the inner detector. The
misshadronic calorimeter also provides the information for jet reconstruction and ET
measurements.
The EM calorimeter is a high-granularity liquid-argon sampling carolimeter (LAr) with accordion-shaped
Kapton electrodes and lead absorber plates over its full coverage. The EM calorimeter is divided into one
barrel (EMB; |η| < 1.475) and two end-cap (EMEC; 1.375 < |η| < 3.2) components. The barrel calorimeteris separated by a small gamp (4 mm) at z = 0. The each end-cap calorimeter comprised two coaxial wheels.
An outer wheel covers 1.375 < |η|, 2.5 and an inner wheel covers the 2.5 < |η| < 3.2. The radiation lengthsof the EM calorimeter is > 22X0 in the barrel and > 24X0 in the end-caps. In the region of |η| < 1.8,
a presampler detector is mounted to correct for the energy lost by electrons and photons upstream of thecalorimeter. The barrel presampler covers |η| < 1.52, while the end-cap presampler covers 1.5 < |η| < 1.8.

2.2. The ATLAS Detector

Figure 2.4: Sketch of the barrel region of the ATLAS inner detector [61].

Figure 2.5: Overview of the ATLAS calorimeter system [61].

19

20

Chapter 2. Experimental Setup

The hadronic calorimeters comprises the three distinct sections. The central section covers the barrel
region (|η| < 0.8) and two extended barrel regions (0.8 < |η| < 1.7). It is a sampling calorimeter instrumented
with scintillator tile/steel calorimeters and referred to as Tile calorimeter. Each barrel region is divided
azimuthally into 64 modules. The two hadronic end-cap calorimeters (HEC; 1.5 < |η| < 3.2) feature liquidargon/copper calorimeter modules instrumented as an independent wheel per end-cap. The HEC is built from
32 identical wedge-shaped modules and is located directly behind the end-cap electromagnetic calorimeterwith sharing the same LAr cryostats. Each wheel is divided into two segments in-depth, for a total of four
layers per end-cap. The two forward calorimeters (FCAL; 3.1 < |η| < 4.9) are instrumented with liquidargon/copper and liquid-argon/tungsten modules for electromagnetic and hadronic energy measurements,
respectively. The FCAL is integrated into the end-cap cryostats and consists of three modules in each endcap. The first module is made of copper and is designed for electromagnetic measurements. On the other
hand, the rest of the two modules are made of tungsten thus measure the energy of hadronic interactions.
More details of the calorimeter read-out structures, absorption characteristic, inactive material distributions, and cell signal formation can be found in Ref. [61].

2.2.4 Muon System
The ATLAS Muon Spectrometer (MS) is desgined to detect charged particle going through the calorimeters
and to measure their transverse momentum with an uncertainty varying from 3% at 100 GeV to about 10%
at 1 TeV. It also provides a trigger for muons with varying transverse momentum thresholds down to a few
GeV. A detailed description of the muon spectrometer and its expected performance can be found at [61, 70].
The measurement of muon momentum is performed by using the track curvature in a toroidal magnetic fields.
The main component of the magnetic field is always perpendicular to the muon track so that the transverse
momentum resolution is approximately independent of η over the whole acceptance. The magnetic filed isgiven by three toroids, one is the "barrel" (|η| < 1.1) and one for each "end-cap" (1.1 < |η| < 2.7), with afiled integral between 2 and 8 Tm. The muon curvature is measured using three precision chamber stations
positioned along its track. The precision measurement requires each station to detect the muon with anaccuracy of 50 µm. The schematic drawing of the muon spectrometer is shown in Fig 2.6.
End cap toroid

BEE chamber

Barrel toroid coil

End cap chambers
Large barrel chambers
Small barrel chambers

Feet

Figure 2.6: Schematic drawing of the ATLAS muon spectrometer.

.
The precision momentum measurement is performed by Monitored Drift Tube chambers (MDT’s) [61]and Cathode Strip Chambers (CSC’s) [61]. The MDT’s cover the pseudorapidity range |η| < 2.7 (except in
the innermost end-cap layer where their coverage is limited to |η| < 2.0). These chambers are comprised ofthree to eight layers of drift tubes with an absolute pressure of 3 bar. Each tube is 30 mm in diameter andhas an anode wire of 50 µm diamter. The coordinate in the plane perpendicular to the wires, measured by
the MDT is referred to as the precision or bending coordinate. The gas mixture used is 93% Ar and 7% CO2

212.2. The ATLAS Detector

with a small admixture of water vapor. The total drift time is about 700 ns [71, 72] and the space resolution
is 80 µm per tube, or about 35 µm per chamber.
In the end-cap inner region, for 2.0 < |η| < 2.7, The CSC’s are used because of their capability to copewith higher background rates and time resolution. The CSC’s are multiwire proportional chambers withcathode planes. The cathode planes are segmented into strips in orthogonal directions to multiwires andthe coordinate is obtained measuring the induced-charge distribution. Typical resolution obtained with thisread-out shceme is about 50 µm.

(a)

(b)

Figure 2.7: (a) Cross-section of the barrel muon system perpendicular to the beam axis (non-bending plane) and(b) cross-section of the muon system in a plane containing the beam axis (bending plane) 2.7b.

The trigger system of the MS is composed of two different chamber technologies: Resistive Plate Chambers(RPC’s) [61] in the barrel region and Thin Gap Chambers (TGC’s) [61] in the end-cap regions. The trigger
system in the barrel consists of three concentric cylindrical layers of RPC’s around the beam axis. The two
inner chambers provide the low-pT trigger while the outer most layer contributes to the high-pT trigger in
combination with the inner chambers. The RPCs also provide the coordinate along the MDT wires that is
not measured by the MDT chambers.
Similarly in the end-cap two TGC doublets and one triplet are installed close to the middle station andprovide the low-pT and high-pT trigger signals. The TGC’s also measure the coordinate of the muons andthis coordinate is referred to as the second, or non-bending coordinate. For this purpose, TGC chambers arealso installed close to the MDTs in the inner layer of the end-cap (EL). Fig 2.7a and 2.7b give cross-sectionsof the MS system in the planes transverse to, and containing, the beam axis.

2.2.5 Trigger and Data Acquisition
The ATLAS Trigger and Data Acquisition (TDAQ) system [73] for selecting events of interest are shownin Figure 2.8. It consists of a hardware-based first-level trigger (L1) and a software-based high-level trigger(HLT). Based on information from a subset of detectors, interesting proton-proton collisions are identified
and the corresponding detector outputs are recorded to the permanent storage.
The L1 trigger searches for high transverse momentum muons, electrons, photons, jets and τ -leptons
decaying into hadrons, as well as large missing and total transverse energy. The event rate is reduced fromthe 40 MHz bunch crossing rate to below 100 kHZ. It decides within 2.5 µs whether or not events should be
kept, to satisfy the 400 reduction factor. The L1 trigger decision is made by the Central Trigger Processor(CTP) which receives inputs from the L1 calorimeter (L1Calo) and L1 muon (L1Muon) triggers sub-systems.
Region-of-interest (RoI) is defined by the L1 trigger. The RoI has calorimeter clusters with high transverse
energy, ET , or muon tracks in the muon chambers.
After the L1 trigger acceptance, events are buffered in the Read-Out System (ROS) and processed by the
HLT based on algorithms implemented in software. The event rate is further reduced to an average of ∼ 1
kHz. The HLT utilizes the detector information including fine-granularity calorimeter information, precision
measurements from the muon spectrometer and tracking information from the ID. In order to reduce the22Chapter 2. Experimental Setup

Calorimeter detectors
TileCalMuon detectors

Level-1 Calo

Endcapsector logic

JEP (jet, E)
CMX

Barrelsector logic

MUCTPI

L1TopoCTPCTPCORE

Level-1 Accept

Preprocessor
nMCM
CP (e,γ,τ)CMX

Detector
Read-Out

Level-1 Muon
FE

FE

ROD

ROD

...

FE

ROD

DataFlow
Read-Out System (ROS)

Level-1

Central Trigger
RoI

Fast TracKer(FTK)

Pixel/SCTCTPOUT

High Level Trigger(HLT)
AcceptData Collection Network

Data Storage

Processors O(28k)

Event
Data

Tier-0Figure 2.8: The ATLAS TDAQ system in Run 2 with emphasis on the components relevant for triggering [73].
time consumed by the HLT to reconstruct the event and make a decision, the selection of particle candidates
by the HLT is performed at each step.
The goal of L1 and HLT trigger is to select interesting proton-proton collisions by identifying one ormore particles of a given type and a given threshold of transverse energy or momentum. For example, muon
triggers are meant to select events with one or more muons in the detector. The configuration of the trigger
is controlled by the ’trigger menu’ and the menu compositions and trigger thresholds are optimized for the
LHC running conditions.

23

Chapter 3

Data and Monte Carlo Simulated Samples
3.1 Data Samples
This analysis is performed using the proton-proton collision data collected between years 2015 and 2018
corresponding to an integrated luminosity of 139 fb−1 . The uncertainty on the integrated luminosity is
1.7% [74], obtained using the LUCID-2 Cherenkov detector [57] for the primary luminosity measurements.
The integrated luminosity is 36.2 fb−1 in 2015-16, 44.3 fb−1 in 2017 and 58.5 fb−1 in 2018, respectively.

3.2 Simulation of pp collisions
Describing and simulating the final states occuring from pp-collisions provided by the LHC is very complicatedand thus is the very challenging task. In this section, a brief review of the description and the simulationof pp-collisions performed by Monte Carlo (MC) simulation is given. MC simulated events are used forthe background modeling, evaluation of the signal acceptance, optimization of event selection, estimation ofsystematic uncertainties and the statistical analysis. The Monte Carlo simulated event generation is split
into several steps as shown in Figure 3.1. All steps are performed within the ATLAS software framework
ATHENA [75].

3.2.1 Factorization
Since the different energy scales of the hard interaction are involved, it is impossible to calculate the crosssection for a certain process in a pp collision directly. Making use of the factorization theorem [77], thecalculation can be broken down into a high-energy part that can be described by perturbation theory anda low-energy part that is calculated by tunable models. According to the factorization theorem, the crosssection for a scattering process pp → n can be written as
XZ Z 1
σpp→n =
dxi dxj fi (xi , µ2F )fj (xj , µ2F )σ̂ij→n (xi , xj , s, µ2F ),
(3.1)
i,j

0

where the sums run over all partonic constituents of the protons p, s is the square of the center-of-massenergy, and σ̂ij→n (xi , xj , s, µ2F ) is the partonic cross-section for the final state n from partons of type i andj. The function fi (xi , µ2F ) and fj (xj , µ2F ) are the parton distribution function (PDF) which describes the
propability density that a parton i with a fraction x of the longitudinal momentum of the proton is found at
the factorization scale µF . Since the PDFs can not be derived from the perturbation theory, they are obtained
experimentally. ATLAS uses the PDFs obtained from the Les Houches Accord PDF Interface library [78].

3.2.2 The fixed-order partonic cross-section
The partonic cross-section σ̂ij→n (xi , xj , s, µ2F ) introduced in the previous section is perturbatively calculable
when µF is reasonably large to allow for a perturbative treatment of QCD. The partonic cross-section canbe expanded in powers of the strong coupling constants:Z12
σ̂ij→n (xi , xj , s, µF ) = dΦn |Mij→n (Φn ; µF )|2 ,
(3.2)
2ŝ
where Mij→n is the matrix element for the production of the final state, Φn is phase space, and ŝ = xi xj s.
The matrix element can be computed based on the QCD and EW theory, with the truncated fixed-order

24

Chapter 3. Data and Monte Carlo Simulated Samples

Figure 3.1: Sketch of a hadron-hadron collision simulated by a Monte-Carlo event generator [76]. The hard collision
is represented by the largest red blob which is surrounded by tree-like structure describing Bremsstrahlung as
simulated by parton showers. The purple blob represents a secondary hard scattering. The light green blobs
represent parton-to-hadron transitions and dark green blobs indicate hadron decays, while yellow lines indicate
soft proton radiation.

perturbative expansion (shown as a large red blob in Fig 3.1). While the fixed-order calculation can cover
the most of the phase space, it is also significantly important to calculate the higher-order terms since thisanalysis searches for the phase spaces where the SM backgrounds have much smaller cross-section. For the
event generator, the matrix element of each process is calculated at leading order (LO) or next-to-leading order(NLO) accuracy in perturbation theory. There are several kinds of event generators available in ATHENA,
such as Powheg [79], Sherpa [80], and aMC@NLO [81].

3.2.3 Parton showering
The hard process from the event generation is then processed via two steps, the parton showering and parton
hadronization. The parton shower (PS) approximation is the approach to provide the calculations of emissions
in soft and collinear regions of phase space to compensate the higher-order effects. The concept of parton
showering is based on gluons splitting into quark anti-quark pairs or partons radiating gluon bremsstrahlung(red lines in Figure 3.1).
The partons showering assumes the cross-section for final states n with an additional parton radiation
can be approximately factorized into the original cross-section as:
dσn+1 = dσn

X αS dti→jk

2π t

dzPi→jk (z, φ),(3.3)

where the indices i, j are parent parton before and after the splitting, k is the emitted parton with momentum
fraction z, and t is the invariant mass of the parton i. Pi→jk is the DGLAP splitting functions [82–84]

25

3.2. Simulation of pp collisions
calculated as:
Pq→qg

=

Pq→gq

=

Pg→gg

=

Pg→qq̄

=1 + z2,1−z
1 + (1 − z)2,CFzz 4 + a + (1 − z)4CA,z(1 − z)CF

TR (z 2 + (1 − z))2 .

(3.4)
(3.5)
(3.6)
(3.7)

The Casimir operators, CF = (Nc2 − 1)/2Nc and CA = Nc , depend on the number of colors and TR = 1/2.
As seen from the Eq.3.3, dσn+1 can diverge in the limit of soft and collinear emission (e.g. z → 0). The
divergences are technically avoided by introducing a cutoff below which no further parton emission is allowed.
Usually, the transverse momentum of the partons is used as a cutoff and the showering is stopped once thedecreasing parton energy scale is lower than a cutoff scale ∼ 1 GeV.
The parton shower technique is an iterative process of parton splitting until no partons with momentum
above a cutoff are produced. This recursive process is described by the probability of emitting an extra
parton at each step, referred to as the Sudakov form factor [85]:
X Z T dt0 Z
αs
dz Pi→jk (z) ,(3.8)
Si = 1 − exp −
0
t
2π
t
j,k

where T is the maximum possible virtuality and the starting point for the shower. The initial-state radiation(ISR) is simulated similarly but needs more complicated procedure since the parent parton is coming fromthe non-perturbative PDFs and developed shower does not result in hard scatter. Therefore the ISRs take abackward evolution approach in which the evolution starts with the parton from the hard interaction withincreasing momentum fraction and each of the resulting parton is then evolved forward. The iteration stops
when a cutoff is reached. The double-counting between the fixed-order matrix element calculation and theparton showering are resolved by the matching algorithms such as CKKW [86] and MLM [87].

3.2.4 Hadronization
The resulting partons from the parton shower then conform color singlet hadrons, a process referred to as
hadronization (light-green blobs in Figure 3.1). The most common model is "Lund string model" [88] which
describes the interaction between the combinating partons by a string being stretched between parton pairs.
Given a quark-antiquark pair, the string can be regarded as a uniform color-flux between them. As thepartons move apart with increasing distance, the potential energy reaches a threshold and then the string
breaks down to a new quark-antiquark pair. This process is repeated until only on-shell mesons remain.
These hadrons decay further into stable particles (dark-green blobs in Figure 3.1). The hadronization
cannot be calculated due to its non-perturbative energy scale. Therefore the simulation of the hadronization
relies on phenomenological models in which several free parameters are to be derived from experiments, andsets of the parameters are referred to as MC generator tunes. The EvtGen program [89] is used for propertiesof the bottom and charm hadron decays. "The underlying event", interactions and activities of the proton
remnants, are also added.

3.2.5 Detector Simulation
After the generation of simulated events, the interaction of particles with the detector’s material and thedetector responses are simulated using the GEANT4 framwork [90]. The generated particles pass throughthe simulated ATLAS detector and the hits in the detector are converted to detector response during a step ofdigitization. The same reconstruction algorithms are used for data and simulated events, therefore the outputof the simulation is identical to that of the ATLAS detector. This reconstruction method, referred to as full
simulation (FULLSIM), is expensive in terms of computation, and this is a limiting factor for the productionof large numbers of simulated events. To reduce the computation time, several simplified approaches havebeen developed at the cost of accuracy. The ATLFAST2 simulation uses FULLSIM for the inner detector
and the muon system but is provided with simplified geometry and showering in the calorimeter [91].

26

Chapter 3. Data and Monte Carlo Simulated Samples

3.2.6 Pile-up
Since multiple protons interact in each bunch crossing, Pile-up events need to be considered additionallyfor the events of interest. The rate of pile-up is represented by Rinel = Lσinel , where σinel is the inelastic
cross section taken to be 80 mb for 13 TeVcollisions [92]. With this measurement, the average number ofinteractions per bunch crossing is defined asµ=Lσinel
.
nb fr

(3.9)

600
ATLAS Online, 13 TeV
500∫Ldt=146.9 fb-1

2015: <µ> = 13.4
2016: <µ> = 25.1
2017: <µ> = 37.8
2018: <µ> = 36.1
Total: <µ> = 33.7

400
300
200

2/19 calibration

Recorded Luminosity [pb-1/0.1]

Additional proton-proton collisions occurring in the same bunch-crossing as the hard process of interest arereferred to as in-time pile-up. On the other hand, additional collisions occurring from other bunch crossing iscalled as out-of-time pile-up. The average number of interactions per bunch crossing between in 2015 and 2018is shown in Figure 3.2. In order to account for the possible difference between Monte Carlo simulated samples

100
0
0

10

20

30

40

50

60

70

80

Mean Number of Interactions per Crossing
Figure 3.2: Number of Interactions per Crossing [60].

and the actual Data, the correction for pileup is applied to the simulated samples by event reweighting [93].
For the simulation of pile-up events, multiple proton-proton collisions within each bunch crossing are overlaid
to each event by Pythia8 [94].

3.3 Monte Carlo Simulated Samples
3.3.1 Background samples
W/Z + jets
Events containing W or Z bosons with associated jets are simulated using the Sherpa 2.2.1 [95] generator.
Matrix elements are calculated for up to 2 partons at NLO and 4 partons at LO using the Comix [96]and OpenLoops [97] matrix element generators and merged with the Sherpa parton shower [98] using the
ME+PS@NLO prescription [99]. The NNPDF3.0NNLO PDF set with αs = 0.118 is used [100]. The W /Z
+ jets events are normalized to the next-to-nect-to-leading order (NNLO) cross-sections [101].
tt̄ and single-t
The tt̄ and single-top events are generated with the Powheg-Box [79] generator with the NNPDF3.0NLO
PDF sets in the matrix element calculation. The top quarks are decayed using MadSpin [102] preserving
all spin correlations, while for all processes the parton shower, fragmentation, and the underlying event are
simulated using Pythia 8 with the A14 tune set [103]. The top mass, mt , is set to 172.5 GeV. The crosssections of tt̄ and single-top are known to NNLO in QCD including re-summation of next-to-next-to-leading27

3.3. Monte Carlo Simulated Samples

logarithmic (NNLL) soft gluon terms [104, 105]. The parameter Hdamp to regulate the high-pT radiation in
the Powheg is set to 1.5mt for a good data/MC agreement at high pT region [106].
DibosonThe diboson processes (W W , W Z and ZZ) are generated with Sherpa 2.2.1 [95] generator which uses thematrix element at NLO accuracy in QCD for up to one additional parton and at LO accuracy for up to
three additional parton emissions. The electroweak production of diboson processes (W W jj, W Zjj andZZjj) are considered in `νqq channel and are neglected in ``qq and ννqq channel due to the extremely small
contributions.

3.3.2 Signal Samples
Signal samples are produced with MadGraph5 (MG5) [41] event generator and the Pythia 8 parton shower
program with NNPDF3.0NNLO PDF set and A14 tune. The RS Graviton samples are generated withk/M̄Planck = 1 and the radion samples are generated with kπrc =35 and ΛR =3 TeV. The HVT model A
signal samples are generated with gH = −0.56 and gF = −0.551 . Model B interpretation will be performed
assuming the same signal shape as the model A because the difference on the width in the model B from A
is smaller than the detector resolution. Another set of HVT signal samples is generated in the model C with
gH = 1 and gF = 0 for the generation of resonances produced via VBF. Masses of diboson resonances arevaried from 300 GeV to 6 TeV for each scenario.

1 HVT Model A is inspired by weekly coupled extensions of the SM gauge group and it predicts g

H ∼ gF ∼ −g

2 [107].

28

Chapter 4

Object Reconstruction and Particle
Identification
4.1 Tracks and Vertices
4.1.1 Track Reconstruction
Charged-particles leave energy-deposits when passing through the Inner Detector (ID). Combining the information of the energy-deposits clustered as hits, charged-particle trajectories are reconstructed and referred
to as tracks. The reconstructed tracks give several kinds of information about charged-particle to be usedin the physics analysis. There are two tracking strategies [108]; an inside-out track reconstruction and an
outside-in tracking. The former is the main track reconstruction strategy targeting primary charged particles
produced in the hard-scatter interaction or originating from decays of short-lived particles, while the later isthe complemental procedure designed to reconstruct tracks of decays of long-lived particles or photon conversions where fewer hits are found in the silicon detector. This tracking strategy is decided based on theefficiency and acceptance difference between silicon pixel, SCT and TRT.
Inside-out track reconstruction
The inside-out strategy follows a sequence of modules. First, clusters are defined by a connected component
analysis (CCA) [109] which groups pixels and strips with a charge over a given threshold. From these clusters,
three-dimensional representations of the silicon detector measurements called space-point are created. In the
pixel detector, each cluster provides one space-point, while the SCT needs to combine both sides of a strip
layer to obtain a three-dimensional measurement. Energy deposits from multiple particles can contributeto one cluster in a dense environment, where the neighboring charged particles are separated by only a few
pixels. In this case, a neural network (NN) clustering algorithm [110] is used to identify the merged clusters
created by multiple charged particles. The NN clustering algorithm uses the following information as inputs:
a fixed-size matrix of the charge collected in each pixel of the candidate cluster, a fixed-size vector of sevenelements with the longitudinal size of the pixels in the matrix to label the long pixels, layer number andlayer type (barrel or endcap), the angles of incidence φ and θ of the candidate charged particle with respect
to the sensor surface, and η of the pixel module (only if no track candidate is available yet). The cluster
judged as merged is split into multiple clusters based on the cluster positions obtained from the NN clustering
algorithm.
After the space-point creation, the collection of space-point is processed for creating track seeds. Trackseeds are composed of sets of three space-points, and there are three types of seed types considered: SCTonly, Pixel-only and mixed-detectors seeds, represeinting the order of purity. One additional space-pointcompatible with the investigating seed is required for the improvement of the purity. With the chosen seeds,
track candidates are formed by using a combinational Kalman filter [111] in which additional space-points
from the remaining layers of the pixel and SCT detectors are checked if compatible with the preliminary
trajectory. If more than one compatible space-point exists on the same layer, the filter creates multiple track
candidates.
Resulting track candidates are then processed for the ambiguity solving. In the ambiguity solving, a
track score [112] is calculated for each track candidate to describe the real trajectories of particles from theunderlying physics event. The track score calculation is mainly affected by simple measures of the track
quality, which includes the resolution and expected cluster multiplicities in the different subdetectors, the29

4.2. Topological cluster

number of 1 holes and the χ2 of the track fit. Tracks with bad score or failing certain track criteria are regarded
as rejected tracks and not used in further processing. If there is a cluster which is shared between multiple
track candidates and not identified as merged by a neural network clustering algorithm, the ambiguity solver
assigns the cluster to the track with the highest score and the cluster is removed from the remaining track
candidates. The remaining track candidates are then scored again and returned to the list of track candidates
in descending order.
Finally, the track extension from the silicon detector into the TRT is performed. If the track is within
the TRT acceptance (|η| < 2.0), measurements in the TRT are used for the track extension and it leads tobetter momentum resolution.
Outside-in track reconstruction
The inside-out tracking assumes a lot of hits existing in the silicon detector. The outside-in tracking is used
when the number of hits in the silicon detector is not enough to create track candidates. It starts with asegment finding in the TRT. Since the TRT consists of straw tubes, three-dimensional space-points cannot
be defined. Therefore the r-φ plane is used in the barrel region and the z-φ plane is used in the end-cap
region. The trajectories of charged-particles are extracted by using Hough transformation [113] and thentraced back into the silicon detector for reconstructing tracks. The outside-in tracking does not refer to hitsalready used in the inside-out track reconstrcution.

4.1.2 Vertex Reconstruction
The position of the inelastic proton-proton collisions are identified by vertex, which is reconstructed by theiterative vertex finding algorithm [114] based on the reconstructed tracks. The vertex with the largest scalarsum of p2T of the associated tracks is defined as the primary vertex. The vertex reconstruction consists ofvertex finding and vertex fitting. First, a seed position of the first vertex is selected based on tracks whichpass the following criteria:• pT > 500 MeV; |d0 | < 4 mm; σ(d0 ) < 5 mm; σ(z0 ) < 10 mm;• At least four hits in the SCT detector;• At least nine silicon (SCT or pixel) hits;• No pixel holes.
Here d0 and z0 represent the transverse and longitudinal impact parameter of tracks with respect to thecenter of the luminous region, and σ(d0 ) and σ(z0 ) correspond to the uncertainties, respectively. The trackpT threshold is raised from 400 MeV to 500 MeV to reduce average event size on disk during Run 2. The
transverse position of the seed is fixed at the position of beam-spot and the longitudinal position is definedby using the z-coordinates of tracks. The beam-spot coordinate is determined by position distribution ofvertices reconstructed by the looser definition [115]. The fitting is performed to determine the best positionof the vertex. The vertex fitting utilized tracks only compatible with the seed. After the vertex position
is determined, tracks that are regarded as not associated with the vertex are removed and to be used inother vertex reconstruction. This procedure is repeated until all of the tracks are assigned to vertices or no
additional vertex can be found in the remaining list of tracks.

4.2 Topological cluster
4.2.1 Topo-cluster formation
Three-dimensional topological clustering of individual calorimeter cell provides the way of reconstructing
signals from hadrons. The topological cell clusters, called as topo-cluster, have shape and location informationand is established as a well-performing calorimeter signal definition for jet reconstruction. The creation of
topo-cluster follows spatial signal-significance patterns generated by particle showers [116].
The cluster formation is based on the ratio of the cell signal to the average noise in this cell:
EM
ζcell
=

EM
Ecell
,
EM
σnoise1 A hole is defined as an expected but missing hit on silicon detectors based on the particle trajectory.

(4.1)

30

Chapter 4. Object Reconstruction and Particle Identification

EM
EM
where Ecellis the cell signal and σnoiseis the average noise in this cell. Both of them are measured on
the electromagnetic (EM) scale, which is calibrated by an electron testbeam for LAr and a 137 Cs-based
calibration system for Tile calorimeter [117, 118]. Therefore the energy deposited by electrons and photons isreconstructed correctly in the EM scale, while the signal from hadrons are not due to the non-compensating
character of the ATLAS calorimeters.
Topo-clusters are formed by a sequence of seeding and collecting steps, called as a growing-volume algoEM
rithm [116]. In the seeding algorithm, the three respective signal thresholds S, N, P in terms of σnoise,cellareused to control series of seeding and collection stages:
EM|Enoise,cell|>EM
Sσnoise,cell→EMζnoise,cell> S (primary seed threshold, default S = 4);

(4.2)

EM
|Enoise,cell|>EM
N σnoise,cell→EMζnoise,cell> N (threshold for growth control,

(4.3)

EM
|Enoise,cell|>EM
P σnoise,cell→EMζnoise,cell> P (principal cell filter,

default N = 2);

default P = 0).

(4.4)

EM
First, all cells with ζcell> S are selected and forms a proto-cluster, as shown in Figure 4.1a. The cells
EMEMneighboring a proto-cluster satisfying ζcell> N and ζcell> P are then merged to the proto-cluster. The
EM
EM
cells with ζcell > S and ζcell > N are presented in Figure 4.1b. If a particular neighboring cell is also aseed cell, the two proto-clusters are merged. If a cell is neighboring two different proto-clusters, the two
proto-clusters are merged. This procedure is iteratively repeated until the the last set of neighbouring cells
EMEMsatisfying ζcell> P , but not the one with ζcell> N , is collected. Cells with negative signal are also consideredin the clustering procedure to cancel out positive fluctuations originating from pile-up and electronic noise.
Figure 4.1c shows the created topo-clusters. The resulting clusters are calibrated to correct for thedifference of energy response between electromagnetic particles (labeled with EM) and hadrons with the local
hadronic cell weighting (LCW) scheme (labeled with LCW) [116]. The calibrated clusters are then provided
as input to a jet reconstruction algorithm as massless particles. More details of topo-cluster formation,
including treatment of negative cells and cluster splitting, can be found at [116].

4.2.2 Topo-cluster kinematics
The created topo-clusters contain a lot of information for signal characterisation. The cluster directions(ηclus , φclus ) are calculated as,
PNcell
ηclus

=

φclus

=

i=1

geo
EM
wcell,i· |Ecell,i| · ηcell,iPNcell,geo
EM
i=1 wcell,i · |Ecell,i |PNcell geo
EM
i=1 wcell,i · |Ecell,i | · φcell,i,PNcell geo
EM
i=1 wcell,i · |Ecell,i |

(4.5)
(4.6)

geo
where Ncell is the number of cells in the cluster, and wcell,iare the geometrical signal weights [116]. The
cluster directions are reconstructed with respect to the center of the ATLAS detector. Using the cell signals
EMand the geometrical signal weights, the total cluster signal amplitude Eclus
is calculated as

EM
Eclus
=

N
cell
X

geo
EM
wcell,i
Eclus,i
,

(4.7)

i=1

and it reflects the correct signal contribution from all cells. When using these topo-clusters as input to jetreconstruction, they are interpreted as massless pseudo-particle. The energy and momentum can be described
as
EM
EM
Pclus
=Eclus· (1, sin θclus cos φclus , sin θclus sin φclus , cos θclus )EM ~ EM= Eclus, Pclus .

Here θclus is the polar angle calculated from (ηclus , φclus ).

(4.8)

31

4.2. Topological cluster

ATLAS simulation 2010
|tan θ| × sin φ|tan θ| × sin φ

ATLAS simulation 2010
E [MeV]

Pythia 6.425
dijet event

5

10

0.05

E [MeV]

Pythia 6.425
dijet event

5

10

0.05

104

104

0

0
3

3

10

10

-0.05

-0.05
102

-0.05

0

102

0.05
|tan θ| × cos φ

-0.05

0

(a)

0.05
|tan θ| × cos φ(b)|tan θ| × sin φ

ATLAS simulation 2010
E [MeV]

Pythia 6.425
dijet event

5

10

0.05
104
0
3

10

-0.05
102

-0.05

0

0.05
|tan θ| × cos φ(c)Figure 4.1: Created topo-clusters in the first module (FCAL0) of the FCAL calorimeter displayed on a dimensionless grid using the polar angle θ and the azimuthal angle φ. Figure 4.1a and 4.1b show cells satisfying |EM| > 4 and|EM| > 2, respectively. All clusterd cells with the outline of topo-clusters are shown in Figure 4.1c. Clusters which
do not contain a seed cell from this module are seeded in other modules. Not colored cells inside a topo-cluster
correspond to a negative signal, while cells shaded grey are not part of a topo-cluster themselves [116].

32

Chapter 4. Object Reconstruction and Particle Identification

4.3 Jets
4.3.1 Jets Reconstruction
Calorimeter jets are formed by performing the anti-kT algorithm [119] with topological clusters as the input.
It iteratively merges the neighboring topo-clusters based on the distance defined as


−2
2
2
dij = min p−2
,
p
(4.9)
T,i T,j ∆Rij /R ,diB
where ∆Rij =

= p−2
T,i ,

(4.10)q
2 + ∆φ2 . η∆ηiji(j) , φi(j) , and pT,i(j) are respectively the pseudo-rapidity, azimuth andijtransverse momentum of the topo-cluster i(j). R is the radius parameter of the jet to reconstruct. If
dij < diB , a topo-cluster j is merged to a topo-cluster i and is removed from the list of remaining topoclusters for the jet reconstruction.
In this thesis, small-R jets with R = 0.4 and large-R jet with R = 1.0 are used to reconstruct W/Z → qq
candidates and the forward jets coming from VBF signal production mode. After the jet reconstruction, thetrimming algorithm [120], which reconstructs kT sub-jets with R = 0.2 within a jet and substructs them
if their pT fraction is less than 0.05, is applied to large-R jets to reduce the effect of pile-up, initial-stateradiation (ISR) and the underlying event. Large-R jets built with only topological clusters are called as
LCTopo jets. In the case of this analysis, in order to achieve more signal sensitivity at higher mass regions,clusters formed by TCC algorithm are used to define large-R jets (TCC jets). The more details of TCC jet
are discussed in Chapter. 5.
Track jets
Track jet is reconstructed from charged-particle tracks reconstructed in the inner detector (ID). The same
jet reconstruction procedure is applied to tracks to reconstruct track jets. In this thesis, the variable-radius(VR) track jet [121] is used to identify b-quark-induced jets. VR track jets adopt pT dependent cone size
defined as:
Reff (pT,i ) =ρpT,i(4.11)

for building track-jets with anti-kt algorithm. ρ = 30 GeV and upper and lower limit of cone size are set
to Rmax = 0.4 and Rmin = 0.02. Collinear VR track jets are possible, however their interplay with the
track-association for b-tagging is not ensured. Therefore, events are removed if they have a pair of VR trackjets i,j which satisfies the following requirement,∆Rij < min (Reff,i , Reff,j ) ,(4.12)

where the indices i, j run on all VR track jets with pT > 5 GeV and number of track > 1. The jets satisfying
pT > 10 GeV and |η| < 2.5 are considered in this analysis.

Jet substructure variable
For large-R jets, the window cut on the reconstructed jet mass is one of the strongest discriminant since jetsfrom W/Z → qq signals have peaks around W/Z-boson masses. In addition to that, the jet substructure
variable D2 is used to separate W/Z → qq jets and background QCD jets. Figure 4.2 shows skematic viewof 1-prong (background QCD) and 2-prong (W/Z → qq) jets. Jets originating from W/Z → qq jet tend tohave two localized energy distributions, while background QCD jets seems to have 1-prong jet substructure.
From this, different energy distribution is expected and the D2 is defined so that the jet substructure can bequantified.

33

4.3. Jets

Figure 4.2: (Left) 1-prong background QCD jet, dominated by collinear (blue) and soft (green) radiation. (Right)
2-prong W/Z → qq jet resolved into two subjets, dominated by collinear (blue), soft (green), and collinear-soft(orange) radiation emitted from the two subjets [122].

The D2 is reconstructed by the energy correlation functions based on energies and pair-wise angles of the
sub-constituents [122–124]. The energy correlation functions are defined as:
eβ=1
2

=

eβ=1
3

=

1 X
pT,J ij
1 X
pT,J

pT,i pT,j ∆Rij ,(4.13)

pT,i pT,j pT,k ∆Rij ∆Rjk ∆Rki .

(4.14)

ijk

Here the summation
runs over the jet constituents e.g. topo-clusters for the usual small (large)-R jets,Xand pT,J =pT,i . The behavior of the energy correlation function depends on soft and collinear QCDicontributions. Exploring the impact of each contribution, we can see the 1- and 2-prong jets can be separated
by the boundary eβ=1
∼ (eβ=1)3 [122] as shown in Figure 4.3, and therefore the D2 is defined as
3
2
(β=1)

D2

= eβ=1/(eβ=1)3 .
3
2(4.15)The jet mass window cut and D2 cut are applied to large-R jets to extract jets from W/Z → qq signals inthis analysis.

Figure 4.3: Phase space defined by the measurement of the energy correlation functions eβ=1
and eβ=1. The phase23
β=1
space is divided into 1- and 2-prong regions with a boundary corresponding to the curve e3 ∼ (eβ=1)3 which is
2
explored based on the power counting method [122].

34

Chapter 4. Object Reconstruction and Particle Identification

4.3.2 Calibration
The jet is calibrated in several steps [125]. The effects of pile-up on jet calibration is reduced by an area-based
subtraction method [126], which utilizes the average energy density in the η × φ plane. The jet energy scale(JES) calibration is applied to correct the reconstructed jet energy to the particle jet energy [127]. The scale
factors are derived from isolated jets in inclusive dijet events which are selected by requring back-to-backtwo jets passing the jet trigger. A correction in η is also applied to resolve the bias made by the energy scalecalibration. Dependence of the jet energy scale on longitudinal and transverse features of the jet is correctedsequentially by the global sequential corrections [128]. Finally, the in situ corrections are applied to accountfor differences between data and MC in the jet pT measurements, using γ/Z+jet and multijet balance [129].
Small-R jets
A series of calibration procedures are applied to small-R jets to restore the JES to that of particle jets (referred
to as "truth jets") for compensating effects which are not fully described by topo-cluster level calibration. The
JES calibration comprises of the following steps: origin correction, jet area-based pile-up correction, residual
pile-up correction, absolute MC-based calibration, global sequential calibration, residual In situ calibration.
First, the four-momentum of jets are corrected by the origin correction so that jets point to the hardscatter primary vertex instead of the center of the detector, without affecting the jet energy constant. The
η resolution of jets is improved by this correction.
The origin correction is followed by the two pile-up corrections to address the energy contamination fromboth in-time and out-time pile-up: jet area-based pile-up correction, residual pile-up correction. The areabased pile-up correction [130] is applied to remove the per-event pile-up contribution to the pT of each jet
according to its area. This correction is based on the median pT density ρ of jets in the η-φ plane, which is
calculated by all jets reconstructed from topo-clusters using the kT algorithm with radius parameter R = 0.4,
and the jet area A. Since the pT density, taken to be ρ/A, does not fully describe the pile-up, the corrected
jet pT still shows some pile-up dependence on NPV , the number of reconstructed primary vertices (PV),and µ, the average number of interactions per bunch crossing. Therefore a residual pile-up correction is
introduced additionally. In the second pile-up correction, the residual pT dependence is measured as thedifference between the reconstructed jet pT and truth jet pT . The residual pT dependence on NPV and µ is
found to be reasonably linear and independent of one another. The pile-up corretion can be descirbed as:
pcorr= precp− ρ · A − α · (NPV − 1) − β · µ,TT

(4.16)

where α and β denotes coefficients of linear fits for NPV and µ dependency.
Next, the absolute MC-based calibration corrects the reconstructed jet four-momentum to the particlelevel energy scale and accounts for biases in the jet η reconstruction. The correction is based on the inverseof the average energy response R = hEjet /Etruth i as a function of the reconstructed jet ηreco and the truth
jet energy Etruth , and the average difference between the true η truth and the origin-corrected jet η reco in binsof the detector η and Etruth , respectively. The energy response is derived from the simulated di-jet eventsfrom PYTHIA.
After the previous jet calibrations, a remaining dependence of the JES on longitudinal and transversefeatures of the jet, mainly coming from fluctuations in the jet particle composition and the distribution ofenergy within the jet (e.g. quark- and gluon-induced jets), are observed. The resolution of JES is further
improved by the global sequential calibration (GSC) [131] utilizing five observables from the calorimeter andmuon spectrometer (MS), and the inner detector (ID). For each of five observable, jet four-momentum iscorrected by the inverted energy response as a function of ptruthand |ηreco |, following the procedure of theTabsolute MC-based calibration. The dependence of the jet response on each observable is removed while
keeping the overall energy scale at the EM + JES. Corrections for each observable are applied independently
since no improvement was observed from including such correlations or altering the sequence of the corrections.
Finally, residual In situ calibration is applied to account for differences in the jet response between
data and MC simulation. It consists of two calibration steps: the η-intercalibration, three other in-situ
calibrations [132]. Both calibrations rely on the difference of a probe jet response against other reference
objects. The η-intercalibration corrects the jet energy scale of forward jets to that of well-measured central
jets using dijet events. In three other in situ calibrations, the average response of central jets is corrected bythose of well-measured reference objects. Due to the limitation of statistics, it uses Z boson from Z + jets,
photon from γ+jets, and multijet systems depending on a targeting jet pT range for the calibration. The
combined data-to-simulation ratio of the in-situ response as function of the jet pT is shown in Figure 4.4.
The derived factors are applied to data.

35
1.1

ATLAS
-1
s = 13 TeV, 3.2 fb
anti-kt R = 0.4, EM+JES

1.05

R

Data

/R

MC

4.3. Jets

1
0.95
Z−jet
γ −jetMultijet

0.9
0.85

Total uncertainty
Statistical component

0.8
20 30

102

2×102

103 2×103
pjet [GeV]T

Figure 4.4: Ratio of the EM+JES jet response in data to that in the nominal MC event generator as a functionof jet pT for Z-jet, γ-jet, and multijet in situ calibrations [132].

Large-R jets
In the case of standard large-R jets (LCTopo jets), only the absolute MC-based calibration is applied to correct
their average reconstructed calorimeter jet energy scale and η to those of the truth jet. Since the motivationof using large-R in this analysis is to reconstruct the jet mass accurately and precisely for high-pT region,
the jet mass calibration is added as a last step where the correction is derived based on the MC simulationof dijet events, as well as the jet energy correction [133]. The derived correction factor is parametrized in jet
pT , η, and mass, and applied according to variables of the jet..
The MC-based calibration is followed by In situ calibration based on the jet pT balance techniques using
Z boson, photon, and multijet systems depending on a targeting jet pT range, as well as the case of small-R
jets. In situ mass calibration uses the calorimeter-to-tracker response double-ratio method, referred to as
Rtrk method [129], which relies on the tracker for providing an independent measurement of the jet mass scale
and its associated uncertainty. The measurement is performed after applying the in situ energy calibration
since it changes the jet mass scale.
However, only Rtrk method is applied to consider pT scale uncertainty for TCC jets and In situ calibration
is not included. Since D2 and mass of TCC jets are used in this analysis we need to estimate D2 and massscale uncertainties. The evaluation of these uncertainties are discussed in Chapter. 5.

4.3.3 Pile-up Jet Tagging and Suppression
To separate hard-scatter and pile-up jets, the Jet Vertex Tagger (JVT) algorithm [134] which utilizes thevertex information is applied to small-R jets. The JVT is defined as output of a two-dimensional likelihood
which is based on the corrected Jet Vertex Fraction (corrJVF) and RpT . The RpT is designed to describe thecharged energy fraction in the jet, and defined as:
P trkkp(PV0 )
RpT = k T jet,(4.17)
pT
where PV0 denotes the hard-scatter vetex. The corrJVF is the modified version of JVF, which is originallydefined as:
P trkkp(PV0 )JVF = P trkl k T,(4.18)P
pT (PV)l pT (PV0 ) +This variable is defined as the ratio of the scalar sum of the pT of all tracks associated with PV0 and thesum of the pT of all matched tracks originating from any vertex, and used in Run1 analysis to mitigate
pile-up jet contamination.
The problem of the original JVF is that its discriminant power shows the pile-up
Pdependency due topT (PV) term in the denominator. To reduce this dependency, the corrJVF is defined36

Chapter 4. Object Reconstruction and Particle Identification

with

P

pT (PV) devided by the total number of pile-up tracks per event nPV
trk :
trkk
k pT (PV0 )P
corrJVF = PPtrkl
pT (PV)/(κ · nPVl pT (PV0 ) +trk )Here κ = 0.01 is the scaling factor determined by correlation with
For this thesis,P.

(4.19)

pT (PV) and nPV
trk .

• JVT > 0.59 for pT < 120 GeV and |η| < 2.4• JVT > 0.11 for pT < 120 GeV and 2.4 < |η| < 2.5
are applied to small-R jets for suppressing the pile-up jets.

4.3.4 Jet selection
Small-R jets are used to reconstruct W/Z → qq candidates resulting well separated Signal jets, and to selectthe forward jets coming from vector-boson fusion VBF jets. Large-R jet is used to reconstruct high-pT
W/Z → qq candidates. The variable-radius (VR) track jet [121] is used to identify b-quark-induced jetsin the merged analysis. Selection criteria of Small-R jet, Large-R jet and VR track jet are summarized inTable 4.1–4.3.
Table 4.1: Summary of small-R jet selection and calibration

Jet reconstruction parameters
Parameter
Valuealgorithm
anti-kT
R-parameter
0.4
input constituent Topological-cluster calibrated with EM scale
Selection requirements
Signal jet
VBF jetObservable
Requirement
pT>30 GeV
|η|
<2.5
< 4.5
JVT
> 0.59 for pT <120 GeV and |η| < 2.4> 0.11 for pT <120 GeV and 2.4 < |η| < 2.5(Medium working point)

Table 4.2: Summary of large-R jet selection and calibration

Jet reconstruction parameters
Value
anti-kT
1.0
TrackCaloCluster
Selection requirements
Observable
RequirementpT>200 GeV
|η|
<2.0
mass
> 50 GeV
SmoothedWZTagger
ObjectWorking point
W /Z-boson tagger Significance-based working point (See Section.5)
Parameteralgorithm
R-parameter
input constituent

37

4.3. Jets
Table 4.3: Summary of VR track jet selection. No calibration is available for VR track jets.

Jet reconstruction parameters
Parameter
Valuealgorithm
anti-kT
R-parametermax(0.02, min(0.4, 30/(jet pT [GeV])))
input constituent
ID TrackParticles
Observable
Requirement
pT>10 GeV|η|<2.5

4.3.5 Flavor tagging
Since the decay length of a b-quark reaches up to several millimetres (cτ ∼ 450 µm), it results in a displacement of the decay products with respect to the primary vertex. Combining the information of the displaced
vertex (secondary vertex) and the displaced tracks, b-tagging algorithm can identify b-jets with a good degree of accuracy [135]. The MV2 algorithm, which consists of a boosted decision tree (BDT), is the defaultb-tagging algorithm. It is trained with 24 input variables obtained from several algorithms including IP3D,
SV and JetFitter, discussed below.
Impact parameter-based Algorithm: IP2D, IP3D
The IP2D and IP3D algorithms [135] is based on a likelihood ratio using impact parameter informationof tracks associated with the jet. IP3D relies on the transverse impact parameter d0 , its error σ(d0 ), andlongitudinal impact parameter z0 , while IP2D does not use longitudinal information. Probability distributionfunctions (PDF) for b- and light-flavor jets are obtained from Monte Carlo simulated samples.
Secondary vertex-based Algorithm: SV
The SV algorithm [135] is designed to reconstruct the secondary vertex (SV) from tracks associated withthe jet. The algorithm starts with forming two-track pairs built from tracks associated with the jet and far
enough from the primary vertex. Vertices that are judged as originating from the decays of other long-lived
particles such as Ks or Λ, photon conversions or hadronic interaction with material are rejected. Remaining
two-track vertices are required to pass the set of qualification. Then a single secondary vertex is build fromall tracks from the vertices, based on χ2 fit.
Decay chain reconstruction: JetFitter
The JetFitter [136] algorithm exploits the topological structure of weak b- and c-hadron decays inside thejet. It assumes the primary vertex and the b- and c-hadrons lie on a common line and the line is found by a
Kalman filter, as well as their position on the line with the PV approximating the b-hadron flight direction.
Multivariate Algorithm: MV2
The MV2 use input variavles obtained from several flavor tagging algorithm discussed above. The full list of
input variables can be found at [135]. The MV2c10 is a discriminant which is trained with b-jets as signal
and a mixture of of 90% light-flavor jet and 10% c-jets as background.

Jet flavour tagging selection
Two different jet collections are used for b-tagging. The small-R jets (“signal” jet in Table 4.1) are used in the
resolved category. The VR track jets are used in the merged category. The efficiency working point showing
the best sensitivity to our benchmark signals is used in each category. Jets originating from b quark are called“b-jets” regardless of tagged or not, and those selected by b-tagging algorithm are “b-tagged jets”.

38

Chapter 4. Object Reconstruction and Particle Identification

4.4 Leptons
4.4.1 Electrons
Reconstruction
The reconstruction of electron candidates is performed by matching localized clusters of energy deposits
in the electromagnetic calorimeter and charged-particle tracks reconstructed in the inner detector (ID).
Electromagnetic-energy (EM) clusters are formed by a sliding-window algorithm [137]. First, a fixed-size ofwindow corresponding to 3 × 7 in units of ∆η × ∆φ = 0.075 × 0.175 (5 × 5 in units of ∆η × ∆φ = 0.125 × 0.125
for endcaps) is slided over the detector to search for electron cluster "seeds", which is identified as longitudinal
towers 2 with total cluster energy within the window greater than 2.5 GeV. Given a set of the cluster "seeds",
EM clusters are formed around them using a clustering algorithm [138]
The reconstructed EM clusters are then matched to tracks extrapolated from the ID to the middle EMlayer, using the distance in η − φ plane. In order to account for energy loss of charged particle in material, afitting procedure with an optimized Gaussian-sum filter (GSF) [139] is applied to reconstructed tracks whichhave at least four silicon hits and that are loosely matched to EM clusters. The EM cluster that is associatedwith the reconstructed track is considered as the electron. A schematic illustration of the path of an electron
through the detector is shown in Figure 4.5.
hadronic calorimeter

third layer∆η×∆φ = 0.05×0.0245

second layer∆η×∆φ = 0.025×0.0245

first layer (strips)

electromagnetic
calorimeterη∆η×∆φ = 0.0031×0.098

presamplerφ

TRT (73 layers)
SCT
beam axis

pixelsbeam spotd0
insertable B-layer

Figure 4.5: A schematic illustration of the path of an electron through the detector. The hypothetical path of anelectron is shown with the red trajectory. A photon, depicted with the dashed red trajectory, is produced by theinteraction of the electron with the material in the tracking system [140].

If more than a track matches the cluster, the track considered to be the primary electron track is selected,
based on the distance in η and φ from the cluster, the number of hits in the silicon detectors, and the numberof hits in the innermost silicon layer. If the selected track matches to a secondary vertex and has no pixel
hits, then the object is classified as a photon.
Identification
A fraction of electron candidates originate from hadronic jets or converted photon and they are referred to as
fake. To reject them and select prompt electrons effectively, a likelihood-based (LH) identification is applied
similarly to the electron LH identification [141, 142]. The LH utilizes a set of measurements from the tracking
system and the calorimeter system such as hadronic leakage, energy deposits in EM calorimeter, TRT highthreshold hits and track-cluster mathcing [142]. For each electron candidate, a discriminant dL is formed as:
dL =2 every cell within across all EM-calorimeter layers

LS.
LS + LB(4.20)

39

4.4. Leptons
The electron LH, LS(B) , is defined as
LS(B) (x) =nY

PS(B),i (xi ),(4.21)

i=1

where the x is the vector of input variables. PS,i (xi ) is the signal probability distribution function (PDF) for
qunatity i at value xi and PB,i (xi ) is the background (e.g. hadronic jets or converted photons) PDF. The
PDFs of both signal and background are modeled using the simulated events of Z → ee and dijet respectively.
In order to account for inaccuracies in the detector description and the modelling of the shower shapes, somecorrections derived from data are applied to the input variables in the MC simulation. The discriminantof the electron LH identification, dL , determines if an electron candidate is accepted. Based on dL , theLH-identification operating points, referred to as Loose, Medium and Tight, are defined [142]. The operating
points provide the vaious prompt-electron signal efficiencies and background rejection factors. For instance,
the identification efficiencies for a signal (background) electron with ET = 40 GeVare 95(0.4)%, 93(0.2)%,
and 83(0.1)% for the Loose, Medium, and Tight operating points, respectively.
Isolation
Electron candidates ogiriginate from the prompt electrons in signal processes such as the decay of W and Z,
or from background processes such as semileptonic decay of heavy quarks, hadrons misidentified as leptons
and photons. Since the characteristic signature of the prompt electron is represented by a smaller activity intheir surroundings, isolation from other objects would be important variable.
Two kinds of isolation variables are considered [140]. The calorimeter-based isolation, ETcone0.2 , is definedas the energies of all topological clusters within the cone size of ∆R = 0.2 around the candidate electron.
The energy deposited by the electron candidate itself is substracted by removing cells in a rectangular cluster
size ∆η × ∆φ = 0.125 × 0.175 around it. The energy leakage from the electron candidate outside this fixedrectangular area and the contributions from pile-up are corrected.
, is defined as the sum of the transverse momenta of the tracks foundThe track-based isolation, pvarcone0.2
T
within a cone size of ∆R = min (10 GeV/pT [GeV], Rmax = 0.2) aligned with the electron track. Tracks are
required to have pT >1 GeV and to satisfy loose vertex association qualification defined in Section 4.1.2. The
candidate’s track is excluded as well as the calorimeter-based isolation. Some requirements on the numberof hits and the longitudinal impact parameter are applied to achieve better isolation performance.
As in the case of the electron identification, several operating points are set for the electron isolation [142].
In this analysis two operating points are used:< 0.15.
/pelectron• FCLoose: ETcone0.2 /pelectron< 0.2 and pvarcone0.2
TTT• FixedCutHighPtCaloOnly: ETcone0.2 < max(0.015 × pelectron, 3.5 GeV).
T
The efficiencies of the various operation points have been measured by the tag-and-probe method using
Z → `` candidates. Figures 4.6 shows the electron isolation efficiencies for the operation points as a functionof the probe lepton pT using ggF Narrow width assumption (NWA) Higgs signal with 3 TeV. LooseTrackOnly
and TightTrackOnly seems to have a comparable behavior and in the low pT region FixedCutTightTrackOnly
has lower efficiency than LooseTrackOnly isolation point. However these operation opints are no longer
supported by Isolation and Fake Forum (IFF) group of ATLAS experiment. For 3 TeV signal, the efficiencies
of FCLoose are extremely low due to the smaller angular separation of the calo-cluster information. Therefore
we decided to apply FCLoose isolation to only electons with pT < 100 GeV for the sake of the high pT electron
efficiency. The number of background events is not increased even if we do not require any isolation cuts at
pT > 100 GeV.
Calibration
The energy calibration of electron is performed by two kinds of methods: a Monte Carlo based calibration andIn-situ corrections. A Monte Carlo based calibration [143] corrects the cluster energy to the truth electronenergy based on multivariate analysis (BDT). The BDT uses the following observables as input variables:
uncalibrated energy, the ratio of the energies in the first two layers of the caloirmeter, the cluster barycenterin η, and the cluster barycenter inη and φ in the calorimeter frame.
An in-situ correction [143] is then applied to remove residual mis-modeling in the energy scale and resolution. The energy miscalibration is parametrized by the electron energies in data and simulation, with thedeviation from optimal calibration in a given η region labeled i. The relative energy resolution is parametrized

40

Chapter 4. Object Reconstruction and Particle Identification

Figure 4.6: Electron isolation efficiencies for the various WPs as a function of the probe lepton pT using ggF NWA
Higgs with m = 3 TeV samples.

by the sampling term related to shower fluctuations in the calorimeter and modeled by simulation, the electronic noise term measured in calibration runs.
Electron selection
Two types of electron definition [141] are used in this analysis according to the number of charged-lepton. In
2-lepton channel, Loose electron is used to select Z → e+ e− candidate. In 1-lepton channel, Tight electron
is used to select W → eν candidate and Loose electron is used to veto events with additional leptons. In
0-lepton channel, Loose electron is used to veto events with leptons. The looser isolation working point [142]based on the ID track variable only is preferable to keep high signal efficiency at the very high-pT region,
where two electron candidates are closed by each other. The definitions of the Tight and Loose electrons are
summarized in Table 4.4.
Table 4.4: Summary of electron selection

Definition
Pseudorapidity range
Transverse momentum
Track to vertex association
Identification
Isolation

Loose

Tight
|η| < 2.47

pT > 7 GeV> 30 GeV

Loose
FCLoose at pT < 100 GeV
and no isolation requirement at > 100 GeV

Tight
FixedCutHighPtCaloOnly|d0 (σ)| < 5|∆z0 sin θ| < 0.5 mm

Efficiency correction
The efficiency of the electron reconstruction, identification, and isolation in simulated events can be different
than in data. These kinds of differences are corrected by applying the scale factors derived from Z → ee andJ/ψ → ee events to the simulated events. The scale factors are defined as the ratio of the efficiency in data
to the efficiency in simulated event. Usually, the scale factors are functions of the electron kinematics, suchas pT and η [141].

4.4. Leptons

41

4.4.2 Muons
Reconstruction
Both the inner detector (ID) and the muon spectromter (MS) provide measurements for muon reconstruction [144]. The track reconstruction algorithm in the ID is same as the one described in 4.1.1. In the MS,muon reconstruction first searches for hits inside each muon chamber. Then, muon track candidates are built
by fitting hits found in each MS sub-detector. The fit starts with the segments generated in the middle layersof the detector where more hits can be expected. For the segments, criteria based on hit multiplicity and fit
quality are required.
Based on the information provided by the ID and the MS, four muon types are defined in following order.
• Combined (CB) muons: the combined track is created by a global fit with tracks reconstructed in the
ID and the MS. An outside-in pattern recognition in which muons are first reconstructed in the MS andthen extrapolated to an ID track, is applied. An inside-out recognition is performed as a complementary
approach for better reconstruction efficiency.
• Segment-tagged (ST) muons: If an extrapolation from track in the ID matches at least one local track
segment in the MDT or CSC chambers, the track is identified as the muon.
• Calorimeter-tagged (CT) muons: A track in the ID is classified as a muon if it is matched to an energy
deposit in the calorimeter compatible with a minimum-ionizing particle.
• Extrapolated (ME) muons: the muon trajectory is reconstructed based only on the MS track. ME
muons are aimed to extend the acceptance for muon reconstruction into the region 2.5 < |η| < 2.7,
which is not covered by the ID.
About 90% of muons are reconstructed as CB.
Identification
Quality requirements are required to improve the purity of reconstructed muons. For CB tracks, the following
variables are used:• q/p significance: the difference between the charge-to-momentum ratios of the muons measured in the
ID and MS.
• ρ0 : the difference between the transverse momentum measurements in the ID and MS divided by thepT of the combined track.
• Reduced χ2 of the combined track fit
Muon tracks are required to have at least one pixel hit, at least five SCT hits and fewer than three pixelor SCT holes. According to these variables, several identification working points are defined. In this thesis,
the following identification working points are used.
• Medium: Only CB and ME tracks are used. CB tracks are required to have ≥ 3 hits in at least two
MDT layers, except for tracks in the |η| < 0.1. ME tracks need to have at least three MDT/CSC layers,
and are used only in 2.5 < |η| < 2.7. To remove the fake muons from hadrons, a loose requirement on
the compatibility between ID and MS measurements is imposed. The q/g significance is required toless than seven.
• Loose: All muon types are used. CT and ST muons are restricted to the |η| < 0.1 region. All Medium
muons are included by definition.
More details of the working points and their efficiency measurements can be found in [144].
Isolation
Both calorimeter-based and track-based isolation variables are used to select muons produced from the decay
cone0.2of heavy particles, as well as an electron. The calorimeter-based isolation, ET, is defined as the energiesof all topological clusters within the cone size of ∆R = 0.2 around the candidate muon. The track-based
isolation, pvarcone0.3, is defined as the sum of the transverse momenta of the tracks found within a cone sizeTof ∆R = min (10 GeV/pT [GeV], Rmax = 0.3) aligned with the muon. Tracks are required to have pT >1

42

Chapter 4. Object Reconstruction and Particle Identification

GeV and to satisfy loose vertex association qualification. Contributions from pile-up and the underlying eventare corrected based on the ambient energy-density technique [130].
As in the case of the electron, several operating points are also set for the muon isolation [142]. In thisanalysis two operating points are used:varcone0.3• FCLoose: ETcone0.2 /pµT < 0.3 and pT/pµT < 0.15.

• FixedCutTightTrackOnly: pvarcone0.3/pµT < 0.06.
T
Figures 4.7 shows the muon isolation efficiencies for the operation points as a function of the probe lepton
pT using ggF NWA Higgs signal with 3 TeV. In contrast to the electron isolation, the efficiency of FCLoose
does not decrease at high pT region. However, FCLoose isolation is applied to only muons with pT < 100
GeV for the sake of the high pT muon efficiency and the harmonization of lepton isolation between electrons
and muons.

Figure 4.7: Muon isolation efficiencies for the various WPs as a function of the probe lepton pT using ggF NWA
Higgs with m = 3 TeV samples.

Calibration
The muon momentum calibration is applied to correct mis-modeling coming from the imperfect understandingof the magnetic field inside the detector. Using the formula in Ref [145], the muon transverse momentum iscorrected as:
P1
MC,Det n
pMC,Det+ n=0 sDet)
Cor,Detn (η, φ)(pTT
pT=,(4.22)
P2
MC,Det m−1
Det
1 + m=0 ∆rm (η, φ)(pT)
gm
where gm is normally distributed random variables ranging from 0 to 1, and pMC,Det
and pCor,Det
are theT
T
Det
Detmuon transverse momenta before and after the correction. The terms ∆rm (η, φ) and sn (η, φ) describe themomentum resolution smearing and the scale corrections, respectively. The resolution and scale correction
coefficients are obtained by a template fit on J/ψ → µµ and Z → µµ events. The correction is applied in
η-φ regions. Knowledge of the magnetic field is reflected in the sDetn (η, φ).
Muon selection
Two types of muon definition are used in this analysis. In 2-lepton channel, Loose muon is used to selectZ → µ+ µ− candidate. In 1-lepton channel, Tight muon is used to select W → µν candidate, and Loosemuon is used to veto events with additional leptons, as well as electrons. In 0-lepton channel, Loose muon isused to veto events with leptons, as well as electrons. Looser working points are chosen to keep high signal
efficiency at the very high-pT region, where two muon candidates are closed by each other. The definitionsof the Tight and Loose muons are summarized in Table 4.5.

43

4.5. Missing ET
Table 4.5: Summary of muon selections

Criteria
Pseudorapidity range
Transverse momentum
d0 Significance Cut
z0 CutSelection Working Point
Isolation Working Point

Loose

Tight
|η| < 2.5

pT > 7 GeV|d0 (σ)| < 3|z0 sin θ| < 0.5 mm

Loose
FCLoos at pT < 100 GeV
and no isolation requirement at > 100 GeV

pT > 30 GeV
MediumFixedCutTightTrackOnly

Efficiency corrections
As in the case of electrons, scale factors of the efficiencies for simulated events are derived and applied
similarly to the electron case. Details can be found in [144].

4.5 Missing ET
Production of invisible particle such as neutrinos are detected by using momentum imbalance in the transverse
plane, referred to as a missing transverse momentum [146]. The missing transverse momentum consists of two
components. The first is reconstructed objects such as electrons, muons, photons, and jets. The second is soft
terms, which are charged-particle tracks not matched to the reconstructed objects. The missing transverse
momentum components are then given by
X
X
miss
Ex(y)
=−
px(y),i −px(y),j .
(4.23)i∈{hard objects}j∈{soft terms}

The set of observables constructed from ETmiss is(4.24)=(Exmiss , Eymiss ),q|ETmiss | = (Exmiss )2 + (Eymiss )2 ,=tan−1 (Eymiss /Exmiss ).

(4.26)

ETmiss=ETmissφmiss(4.25)

Here the multiple inclusions of the same signal in all objects are removed [146]. We can calculate the modulus
and the direction in the transverse plane in terms of the azimuthal angle φ, via the vector ETmiss .
The scalar sum of all transverse momenta from the objects contributing to the missing transverse momentum reconstruction is given by
X
X
ΣET =
pT,i +
pT,j .
(4.27)i∈{hard objects}j∈{soft terms}

This provides the information for estimating the hardness of the hard-scatter event in the transverse plane.

44

Chapter 5

Track-CaloClusters (TCCs)
5.1 Introduction
Jet substructure variables play a crucial role in discriminating boosted W/Z → qq bosons from non-resonant
jet in W/Z + jetsbackground. In the previous analyses [147, 148], we used calorimeter-clusters as inputs of
D2 calculation, which exploits the exceptional energy resolution of the ATLAS calorimeter [116]. However,jets highly collimate in the event with much higher energy and its substructure can not be resolved becauseof degraded angular resolution in the calorimeter. In the simple example of a hadronically decaying vectorboson W/Z → qq, the distance between the two quarks get closed as the parent particle becomes moreenergetic, following the approximation ∆R ≈ 2mV /pVT 1 where ∆R is the distance between two quarks in
η–φ plane. To provide the better jet substructure performance, the new jet input technique, referred toas Track-CaloClusters (TCCs) [149], had been developed. In the TCCs algorithm, a TCC is defined by
combining the information of tracks and individual energy deposited in the calorimeter. Then the TCCs areused to reconstruct the large-R jets. By combining information from the calorimeter and tracking detectors,
the precision of jet substructure techniques can be improved for a wide range of energies. As a consequence,
better boson tagging performance can be achieved.

5.2 TCCs algorithm
5.2.1 Motivation
As described briefly in previous section, the fundamental problem of calorimeter-clusters is the limited angularresolution in the highly boosted large-R jet . In the range of pT with greater than about 1 TeV, small numbersof calorimeter-clusters are created due to the insufficient granularity while the energy resolution is excellent.
On the other hand, the tracking detector has excellent angular resolution and good reconstruction efficiency
at very high energy [150], while its energy resolution degrades because of less curved tracks by magnetic
field. Since tracks and calorimeter-clusters have complimentary behavior as described above, we expect tomaximally exploits the strengths of individual detectors to improve jet substructure performance. This is thebasic idea of TCCs and the algorithm is developed to improve the jet substructure performance in different
energy regimes, reflected in their four-vector construction and energy sharing procedures. In the energy
sharing of the TCCs approach, only the relative track momenta are considered to spatially redistribute theenergy measured in the calorimeter. In short, the distinctive feature of the TCCs algorithm is that it uses
the spatial coordinates of the tracker and the energy scale of the calorimeter.

5.2.2 Matching
Track-cluster matching criterion is defined in order to build 4-vector jet inputs (TCCs) from track andtopo-cluster information. The matching procedure attempts to match every good quality track to every
topo-cluster following two steps. First, the uncertainty on the track extrapolation is compared to the topocluster width. If the track extrapolation uncertainty is larger than the width of the topo-cluster, the track
is removed from the matching procedure. Second, with thep remaining tracks, a track-cluster pair is defined22
as matched if their angular separation satisfies ∆R < σcluster+ σtrack
where σcluster is the topo-cluster
width and σtrack is the track extrapolation uncertainty. Since the uncertainty on track extrapolation reduces
significantly at high pT , the second matching criterion becomes ∆R < |σcluster | in high pT limit. In extremely
1 m2 ∼ 2p · p ∼ p
2
2
2
1
2
T,1 pT,2 ∆R1,2 = z(1 − z)pT,V ∆R1,2 , where z is the fraction of the parent energy retained by the daughter
V
quark.

45

5.2. TCCs algorithm

102
10

ATLAS
Simulation Preliminary

Fraction

Fractionhigh pT range, particles decaying from highly boosted particle such as W boson tend to fall within a single
topo-cluster. By matching tracks to this high energetic topo-cluster and defining multiple TCCs, the TCCs
can resolve the hidden topo-cluster substructure originating from two regions of energy corresponding to thetwo quarks decaying from the vector boson. The TCC objects fall into three categories. First, tracks withthe primary vertex and matched to topo-clusters are referred to as combined TCCs. Topo-clusters without
matched tracks and tracks from the primary vertex not matched to cluster, are referred to as neutral andcharged TCCs, respectively. While tracks from pileup vertices matched to topo-clusters are not used inbuilding TCC objects. Figure 5.1 shows the resulting fractions of neutral, charged and combined TCCs.
W 0 → W Z → qqqq events with a W 0 mass of 1 TeV are used. The combined TCCs become the dominantchargedneutral

WZ → qqqq, M = 1000 GeV
pTCC>10 GeV

combined

102
10

T

1

1

10−1

10−1

10−2

10−2

10−3

10−3

10−4−4

−3

−2

−1

0

1

2

3

4

10−40

ATLAS
Simulation Preliminary

charged

WZ → qqqq, M = 1000 GeV
|<2.5
|pTCC
η

combined

10

20

TrackCaloCluster η [rad]

(a)

30

40

50

neutral

60

70

80

90 100TrackCaloCluster p [GeV]T(b)

Figure 5.1: The fraction of different TCCs classes as a function of (a) the TCC η and (b) the TCC pT [149].

scenario at TCCs pT greater than 5 GeV since highly energetic topo-clusters are likely from the hadronicallydecaying W/Z boson and thus close to tracks.

5.2.3 Reconstruction
After matching tracks and topo-clusters, we need to build the actual TCC 4-vectors with dedicated energy
sharing algorithm. In this section some of the energy sharing examples are shown with the actual energy
sharing equation. Figure 5.2 shows the schematic view of the track-cluster matching examples. When referringto the figure, 1 refers to TCC object 1, c1 refers to topo-cluster c1 and t1 refers to track t1 . The first case isa direct single match between a track and a topo-cluster, refered to as 1 . The topo-cluster energy and thetrack directions are directly used to form a single TCC:
TCC 1 = (pcT1 , η t1 , φt1 , mc1 = 0).

(5.1)

In the case of topo-clusters without any matched tracks, such as 2 , the topo-cluster 4-vector is directly used:
TCC 2 = (pcT7 , η c7 , φc7 , mc7 = 0).

(5.2)

It is same for tracks which does not match any topo-clusters, such as 3 :TCC 3 = (ptT6 , η t6 , φt6 , mt6 = 0).

(5.3)

In complicated cases, there is a match between multiple tracks and a single cluster, multiple topo-clusters
and a single track and multiple topo-clusters with multiple tracks as in the case of 6 and 7 . One track
originating from a primary vertex creates the exactly one TCC object by definition and the angular coordinates are measured by the track. However, the scale coordinates must consider the energy sharing between
the different matches. Two tracks matching a single topo-cluster, such as the case of 4 and 5 , is a simple
example which need energy sharing. The TCC 4-vectors are defined as:
!
ptT2
ptT2
c2
t2
t2
c2

, η , φ , m
 =0 ,(5.4)
TCC 4 = pTpT ptT2 + ptT3
pT ptT2 + ptT3

46

Chapter 5. Track-CaloClusters (TCCs)

c3
4

t4
5

1
t1

t2

HCAL

2

7

6

3

ECAL

t3
t6

t5

SOLENOID

H Clusters
EM Clusters

INNER DETECTOR

TracksFigure 5.2: The schematic demonstrating of the TCC objects reconstruction. Details on the exact reconstruction
procedure are provided in the text [149].

TCC 5 =

pcT2

!
ptT3
ptT3
t3
t3
c2

, η , φ , m
 =0 .
pT ptT2 + ptT3
pT ptT2 + ptT3

(5.5)



pa is the 4-vector corresponding to a given particle a. pT pa + pb means the pT of the 4-vector sum of aand b.
Generally speaking, the TCC energy sharing algorithm considers the case where a seed track τ matched
to a set of topo-clusters Cτ . The notation Xy represents the set of objects of type X matched to a given
object y, where X is either C for topo-clusters or T for tracks. Furthermore, each topo-cluster c ∈ Cτ canalso be matched to a set of tracks Tc . Since the energy sharing procedure needs to consider several patternsof multiple matching between track (s) and topo-cluster (s), we need to introduce three general concepts ofpT fractions. First, the energy scale of the TCC object resulting from the seed track τ must be contributedby each matched cluster c ∈ Cτ , weighted by the pT fraction out of the all matched clusters. The fraction fτc
is defined as
fτc =

"
pT

pcT
X

#.

(5.6)

k

p

k∈Cτ

Second, each cluster c ∈ Cτ can also contribute to other TCC objects such as the case of 4 , 5 , 6 and 7 , so
its contribution to the TCC object should be also weighted by the pT fraction of the seed track τ comparedτto all other tracks matched to the cluster c. The fraction Fc,t
is
τ
Fc,t
=

"
pT

pτT
#.
X
pt ftc

(5.7)

t∈Tc

Notice that the pT fraction ftc is applied to those tracks t ∈ Tc to account for the weighted contributionof tracks t matched to multiple clusters, and this is the third pT fraction concept. In calculating the third
fraction ftc , tracks from any vertex are considered, while the seed track τ must be originating from theprimary vertex.

47

5.3. Jet reconstruction and performance

Applying these definitions to the actual building of TCC object built from the seed track τ , the final
4-vector becomes
X
X
pτT
pc
τ
#
pc fτc Fc,t
pc " T
(5.8)
Mτ =
=
X

pcT
X
t
#
"
c∈Cτ
c∈Cτ
p
pT
pk


X
pT t∈Tc
k∈C
p
pk 
T

τ

k∈Ct

Using the 4-vector Mτ definced as above, the final TCC 4-vector is
TCCτ = (pT [Mτ ], η τ , φτ , m[Mτ ]).

(5.9)

The pT and mass of the TCC 4-vector is defined by the 4-vector sum Mτ , taking into account of the energy
sharing between multiple tracks and clusters. The mass is zero when only one topo-cluster is matched to theseed track, and non-zero if at least two topo-clusters are matched to the seed track. This formula handles all
matching cases including examples shown in this section.

5.3 Jet reconstruction and performance
5.3.1 Jet reconstruction

Relative Number of Events

Large-R jets are built from anti-kt algorithm [119] with a distance parameter R = 1.0. Different sets of
TCC objects can be used as the jet inputs to the large-R jet reconstruction. We consider two selections of
TCC inputs: all-TCCs and only combined-TCCs, where all TCCs include both neutral and charged TCCs
in addition to combined TCCs. All-TCCs is used in this analysis based on the performance studies of massand D2 resolution, as discussed in Section 4.3.1.
A comparison of three types of large-R jets built from TCCs is presented in Figure 5.3. Each type of
the TCC jets is matched to the corresponding truth jet and is used at the uncalibrated scale for this study.
The jet inputs are compared using the jet mass response, Rrm = mTCC jet /mmatched truth jet . Comparing
distributions of the untrimmed and trimmed TCC jets built from all TCCs, the trimming algorithm [151] isfound to be able to improve the jet mass response significantly. On the other hand, jets built from combined
TCCs shows good mass response without trimming.
0.2
0.18
0.16

ATLAS Simulation Preliminarys=13 TeV
anti kT R=1.0, WZ → qqqq
jet

0.14

jet

|η |<2.0, p >200 GeV
T

All TCCs (not trimmed + not calibrated)

0.12

All TCCs (trimmed + not calibrated)
Combined TCCs (not trimmed + not calibrated)

0.1
0.08
0.06
0.04
0.02
0
0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Mass response

Figure 5.3: A comparison of the mass response, Rrm , for jets built with all TCCs, all TCCs after trimming andonly combined TCCs.[149].

The pT 2 pseudo response, comparing pT of TCC jets with topo-cluster jets, is shown in Figure 5.4a. The
reference topo-cluster jet is trimmed and not calibrated. Since all types of TCC jets are at the same calibration
scheme to topo-cluster jet, the distribution is to be peaked around 1. For the small shift to smaller pT , itcomes from the removal of pileup topo-clusters matching tracks from pileup primary vertices. Comparing
trimmed all TCCs and not trimmed combined TCCs shows the pileup contribution is well controlled andtopo-clusters coming from the hard scattering are retained by the TCC algorithm.
2 Pseudo-response where the reference jet is a different reconstructed jet definition. This is useful when comparing TCC jets
against the standard topo-cluster jet definition.

48

Chapter 5. Track-CaloClusters (TCCs)

0.4

Relative Number of Events

Relative Number of Events

Figure 5.4b shows the η residual distribution for the three jet definitions. Topo-cluster jet shows a betterη residual than TCC jets due to the well-known centroid of the high energy topo-clusters. However, the aimof TCC jets is improving the jet substructure and the impact of a bit larger η uncertainties is negligible inthis analysis.

ATLAS Simulation Preliminary
0.35
0.3

s=13 TeV
anti kT R=1.0, WZ → qqqq
jet

jet

|η |<2.0, p >200 GeV
T

0.25
0.2
0.15

All TCCs (not trimmed + not calibrated)
All TCCs (trimmed + not calibrated)
Combined TCCs (not trimmed + not calibrated)

0.4
ATLAS Simulation Preliminary
0.35
0.3

0.05
0.6

0.8

1

1.2

comb

)

All TCCs (trimmed + not calibrated)
Combined TCCs (not trimmed + not calibrated)

T

0.15

0.05
0.4

LC Topo (trimmed + calibrated + m

jet

0.2

0.1

0.2

jet

|η |<2.0, p >200 GeV

0.25

0.1

0
0

s=13 TeV
anti kT R=1.0, WZ → qqqq

0−0.1 −0.08−0.06−0.04−0.02 0T(a)

0.02 0.04 0.06 0.08 0.1
η residualp pseudo response(b)Figure 5.4: The (a) TCC jet pT pseudo-response with respect to trimmed topo-cluster jets and (b) η residual forboth topo-cluster and TCC jet [149].

The distributions of three kinds of jet inputs in η-φ plane are shown in Figure 5.5. TCC jets (Figure 5.5b
and 5.5c) show an additional kt subjet of size Rsub = 0.2 denoted by grey region within each of the twolarge-R jets demarcated by a blue circle. The total number of jet inputs to jet reconstruction is significantly
suppressed by the combined TCCs.

5.3.2 Jet substructure performance
The jet substructure variables, jet mass, and D2 , are used in the boson tagging to extract two quarks from
W/Z → qq. A comparison of the mass response for LCTopo jets built from topo-clusters only, all-TCCs, andcombined-TCCs is shown in Figure 5.6. Figure 5.6a is for 700 GeV < pT < 800 GeV, and Figure 5.6b is for
2.1 TeV < pT < 2.5 TeV. At high pT as seen in Figure 5.6b, the peak of the all-TCCs and combined-TCCs
jets are larger than one, however, this is because they are not calibrated and not a problem. Therefore, theperformance of these jets is seen to be similar.
A comparison of D2 residual, RdD2 for jets built from different jet inputs is shown for 700 GeV < pT <800 GeV in Figure 5.7a and for 2.1 TeV < pT < 2.5 TeV in Figure 5.7b. Better D2 residual distribution isobserved for both all-TCCs and combined-TCCs jets. In addition, the TCC jets remain centered around zero
while topo-clusters jets shift towards larger D2 . However, the combined-TCCs jet has a long tail, indicating
the missing of relevant energy contributions from track-cluster matches. The distribution of Topo-cluster jetschanges dramatically when changing the pT by an order of magnitude.
Figure 5.8 shows the comparison of mass and D2 resolutions of jets built from topo-clusters, all-TCCs
and combined-TCCs as a function of jet pT . A resolution metric is defined using the Inter-Quantile Range(IQR) of the distribution width. Qx is the x% of quantile boundary. For instance, Q50 means the median.
To account for the resolution of the response and the residual distribution, two kinds of IQR definitions are
used:
IQRr

=

IQRd

=

1 Q84 (Rr ) − Q16 (Rr ),2
Q50 (Rr )
1
Q75 (Rd ) − Q25 (Rd )2(5.10)(5.11)

These definitions correspond to half of a 68% window for the mass resolution, and half of 50% window for
the D2 resolution. The difference of the definitions come from the distribution to use: the response Rr or the
residual Rd . The resolution shown in Figure 5.8 is presented by using IQRr . For ptruth> 2 TeV, the massT
resolution of all-TCCs jets outperforms the topo-cluster jet, but shows the sligtly worse resolution for mostof the ptruth
range below that. All-TCCs jets are seen to be superior to the topo-cluster jets over the entireT49

5.3. Jet reconstruction and performance

AntiKT10 Jets
TopoClusters

5

ATLAS Simulation Preliminary

W' 2000 GeV - TopoClusters

6

φ

φ

ATLAS Simulation Preliminary

AntiKT10 Jets
Combined TCCs
Charged TCCs
Neutral TCCs

5

mjet1=159 GeV

4

4

3

3

2

W' 2000 GeV - All TCCs

6
mjet1=127 GeV2
mjet2 =145 GeV

mjet2 =161 GeV

1

1

0
−4

−3

−2

−1

0

1

2

3

0
−4

4

η

−3

−2

−1

(a)

0

1

2

3

4

η

(b)

φ

ATLAS Simulation Preliminary W' 2000 GeV - Combined TCCs
6

AntiKT10 Jets
Combined TCCs

5

mjet1=83 GeV

4
32
mjet2 =63 GeV

1
0
−4

−3

−2

−1

0

1

2

3

4

η

(c)

0.3

Relative Number of Events

Relative Number of Events

Figure 5.5: The distributions of jet inputs for (a) topo-clusters, (b) all TCCs and (c) only combined TCCs in η-φplane. [149].

ATLAS Simulation Preliminary
0.25

s=13 TeVLC Topo (trimmed + calibrated + m

anti kT R=1.0, WZ → qqqq

All TCCs (trimmed + not calibrated)

jet

jet

|η |<2.0, p >200 GeVT

0.2

jet, truth

700 GeV < p

T

comb

)

Combined TCCs (not trimmed + not calibrated)< 800 GeV

0.15
0.1

0.14

ATLAS Simulation Preliminary

0.12

anti kT R=1.0, WZ → qqqq

s=13 TeVLC Topo (trimmed + calibrated + m

T0.1

jet, truth

2100 GeV < p

T

comb

)

All TCCs (trimmed + not calibrated)

jet

jet

|η |<2.0, p >200 GeV

Combined TCCs (not trimmed + not calibrated)< 2500 GeV

0.08
0.06
0.04

0.05
0
0

0.02
0.5

1

1.5

2

2.5

3

0
0

0.5

1

1.5

Mass response

(a)

2

2.5

3

Mass response(b)Figure 5.6: A comparison of the mass response for jets built from topo-clusters (black circles), all-TCCs (redsquares) and combined-TCCs (green triangles) for 700 GeV < pT < 800 GeV in Figure reffig:MassResponse1 andfor 2.1 TeV < pT < 2.5 TeV in Figure 5.6b. [149]

50

0.2
0.18
0.16

ATLAS Simulation Preliminarys=13 TeV
anti kT R=1.0, WZ → qqqq
|η |<2.0, p >200 GeVTjet, truth

700 GeV < p

T

comb

)

All TCCs (trimmed + not calibrated)

jet

jet

0.14

LC Topo (trimmed + calibrated + m

Combined TCCs (not trimmed + not calibrated)< 800 GeV

0.12
0.1
0.08
0.06

Relative Number of Events

Relative Number of Events

Chapter 5. Track-CaloClusters (TCCs)

0.2

0.5

1

1.5

2

jet, truth
T)

Combined TCCs (not trimmed + not calibrated)< 2500 GeV

0.12
0.1
0.08
0.06
0.02

0

T

2100 GeV < p

comb

All TCCs (trimmed + not calibrated)jet|η |<2.0, p >200 GeV

0.14

0.04

−0.5

LC Topo (trimmed + calibrated + m

anti kT R=1.0, WZ → qqqq
jet

0.02
−1

s=13 TeV

0.16

0.04
0
−1.5

ATLAS Simulation Preliminary

0.18

0
−1.5

2.5

−1

−0.5

0

0.5

1

1.5

D2 residual

22.5

D2 residual

(a)

(b)

Figure 5.7: A comparison of the D2 residual for jets built from topo-clusters (black circles), all-TCCs (red squares)
and combined-TCCs (green triangles). [149]0.3

Jet D2 resolution

Fractional jet mass resolution

ptruthranges. Although the mass and D2 resolutions of all types of jets degrade with increasing ptruth
, the
T
T
degradation of D2 of all-TCCs jets are highly suppressed. According to the parformance studies discussed
above, we descided to use All TCCs as default jet inputs.

ATLAS Simulation Preliminary
0.25

s=13 TeV
anti kT R=1.0, WZ → qqqq
jet

jet

|η |<2.0, p >200 GeV
T

0.2

0.7
ATLAS Simulation Preliminary
0.6

s=13 TeV
anti kT R=1.0, WZ → qqqq

0.5

jet

jet

|η |<2.0, p >200 GeV
T

0.4

0.15
0.3
0.1

0.2
LC Topo (trimmed + calibrated + m

0.05

comb

)

LC Topo (trimmed + calibrated + m

0.1

All TCCs (trimmed + not calibrated)
Combined TCCs (not trimmed + not calibrated)

0

500

1000

1500

2000

)

Combined TCCs (not trimmed + not calibrated)

2500

0

500

1000

1500

Truth jet p [GeV]

2000

2500

Truth jet p [GeV]

T

(a)

comb

All TCCs (trimmed + not calibrated)T(b)

Figure 5.8: A comparison of the fractional jet mass (a) and D2 (b) resolution for topo-cluster jets (solid black lines),
jets built using all-TCC objects (dash-dotted red lines) and jets built using only combined-TCC objects (dashedgreen lines), as a function of truth-jet pT . The TCC definitions are seen to outperform at high pT , particularly
for D2 [149].

5.4 Boson Tagger Optimization
Designed to extract the jet substructure originating from two quarks from W/Z → qq, the boson tagger
performance is also sensitive to the source of background. For example, jets in W/Z + jets background aredominated by single quark-induced jets, while the jets in QCD multi-jet are dominated by gluon-induced
jets, In our analysis, W/Z + jets background is the dominant background. On the other hand, the otheranalysis such as V V → JJ [152] suffers from QCD multi-jet background. Therefore we need to optimize
the boson tagger depending on the dominant background in each analysis. In this section, the effect of thequark/gluon fraction in the background on the optimal working point of the W/Z tagger is discussed first.
Then, the boson tagger optimized for the VV semi-leptonic analysis is described in detail.

51

5.4. Boson Tagger Optimization
Effect of quark/gluon fraction

Figure 5.9 shows D2 distributions of both quark- and gluon-induced jets, devided by low- and high-pT range.A
The shape difference is observed especially in lower pT region, and it might lead to the different optimized
D2 thresholds for boson tagger.

(a)

(b)

Figure 5.9: D2 distribution of quark- and gluon-induced jets derived from Z+jets, separated by 200 < pT < 650(a) and 650 < pT < 2500 (b). In low pT region (b), quark-induced jets have a tail in higher D2 and causing thedifference from gluon-induced jets. The difference is getting small in high pT region (b) due to boost of jets

In order to estimate the impact of D2 difference, the quark/gluon fraction in the Z+jets background isvaried in the range of 0% to 100% (overall normalization is not changed) and the optimal D2 threshold to
G → ZZ → llqq signal is checked as a function of that, as shown in Figure 5.10. A fixed jet mass window cut(70 GeV< mJ <110 GeV) is applied in this study. The quark/gluon fraction significantly affects the optimal
D2 threshold at low-pT region. Looser cut on D2 is preferred if the quark-jet fraction is closed to one. On
the other hand, the dependency of the optimal threshold on the quark/gluon fraction becomes to be small at
high-pT region, since both quark- and gluon-jets have a similar D2 distributions at that region as shown in
Figure 5.9b. Due to this quark/gluon fraction dependency, we need to use the W/Z boson tagger optimized
for VV semileptonic analysis, where W/Z+jets with quark-induced jets are the dominant backgrounds.

Figure 5.10: Optimal D2 thresholds as a function of quark-induced jet fraction. Jet mass window cut assuming
naive boson tagger is applied. A quark fraction dependency observed at low mass signal, but not at high masssignal as expected.

52

Chapter 5. Track-CaloClusters (TCCs)

Optimization
A two-dimensional optimization of the jet mass and D2 is performed at pT > 200 GeV. A jet mass window
and D2 thresholds are scanned simultaneously in each pT bin for each W 0 → W Z and W 0 → W W signal,
respectively. Then, the ones showing the highest sensitivity to the signals is selected, as shown by dots in
Figure 5.11. The definition of the significance is
s 




b2
σ 2 (n − b)n(b + σ 2 )− 2 ln 1 +,(5.12)
Z = 2 n ln 2
b + nσ 2σb(b + σ 2 )which is based on the asymptotic formula for the distribution of profile likelihood test statistics. Here s
and b are the number of signal and background events (n = s + b), and σ is the statistical uncertainty ofbackground MC events (to avoid extreme selection in the region of lack of MC statistics). F Figure 5.11
shows the optimized thresholds on D2 and jet mass as a function of pT . The solid lines show the fit results.
Figure 5.12 shows the efficiency of the optimized W/Z taggers to W - and Z-induced jets as a function of
pT . The taggers are optimized to achieve about 40-50% efficiency at the lowest-pT , region, about 60 % at theintermediate pT , range and about 70% at the highest-pT , region.
Signal efficiency and background rejection compared with the previous working point with topo-cluster
jet are shown in Figure 5.13. TCC jet tagger achieved higher signal efficiency while keeping better or similar
background rejection to topo-cluster jet tagger at highest-pT , region.

5.5 Boson Tagging Efficiency SF
In this analysis, pT , mass and D2 of the TCC jet are used in the event selection for better signal sensitivity
and we need to estimate the scale factors (SFs) which describe the difference of data and MC simulationand the systematic uncertainties of them. The TCC jet pT is equivalent to the LCTopo jet pT in thefirst approximation. Therefore the Rtrk method [153], in which the possible mis-modeling is estimated bycomparing the TCC jet pT and the associated track jet pT , can be used in the estimation of the jet pT scale
uncertainty. However, it is not the case for D2 and mass scale uncertainty, because these variables highly
depend on the tracks information due to the TCCs algorithm [149]. To take into account D2 and mass scale
uncertainty as well as pT , boson tagging efficiency (fraction) scale factors are estimated in a data sample
enriched in semi-leptonic tt̄ events for signal and W/Z +jets for a background. Since the boson tagging utilizes
D2 and mass window cut, their uncertainties should be included in boson tagging scale factor uncertainty.
In our analysis the events with a large-R jet are categorized into four specific regions according to both D2
and jet mass cut results of the boson tagger. All of the defined regions are to be used as inputs of statisticalanalysis and the boson tagging SFs must be estimated for each of these regions including events mitigation
between them. The detailed definitions of signal region and background control region are discussed in 6.9.
We consider the three kinds of SFs: boson tagging SFs for W -boson, top-quark and single q/g background.
The estimated SFs for W -boson is also used for Z-tagger since the boson tag efficiency is similar and the SFs
for both W - and Z-tagger should be same.

5.5.1 Signal Efficiency
Event selection
For the boson tagging efficiency SF of large-R jets originating from W -boson and top-quark, a sample ofdata enriched in semi-leptonic tt̄ is used. The inclusive sample of events is further split into two exclusive
subsamples, enriched in W -boson jets and top-quark jets by using the angular distance between a b-tagged jet
and the large-R jet. Only the muon channel is used for the sake of purity of the target process. The selection
for the semi-leptonic tt̄ event is performed in a similar manner to Ref. [154]. Both data and MC simulated
events are required to pass an single muon trigger. The event selection is split into two steps: Leptonic top
selection, large-R jet from W /top candidate selection.
• Leptonic top selection– Require one muon candidate with pT > 30 GeV and |η| < 2.5 satisfying the Medium identification
criteria defined in Ref.[144].
– Events containing additional muons with pT > 25 GeV are rejected.

53

3
2.5

Jet mass [GeV]

Jet D25.5. Boson Tagging Efficiency SF

s=13 TeV, W-Tagger
VVSemileptonic Max significance2

VVJJ Max significance

1.5

150
140

s=13 TeV, W-Tagger

130

VVSemileptonic Max significance120

VVJJ Max significance

110
100
90

1

80
70

0.5

60
0

500

1000

1500

50

2000
2500
Jet pt [GeV]500

Jet mass [GeV]

Jet D22000
2500
Jet p [GeV](b)3
s=13 TeV, Z-Tagger
VVSemileptonic Max significance

2

1500

T

(a)

2.5

1000

VVJJ Max significance

1.5

150
140

s=13 TeV, Z-Tagger

130

VVSemileptonic Max significance120

VVJJ Max significance

110
100
90

1

80
70

0.5

60
0

500

1000

1500

(c)

2000
2500
Jet pt [GeV]

50

500

1000

1500

2000
2500
Jet p [GeV]T(d)Figure 5.11: The upper cut on (a) D2 and (b) jet mass window cut i.e. the upper and lower boundary of the massof the W -tagger as a function of jet pT . Corresponding values for Z-tagger are shown in (c) and (d). The optimal
cut values for maximum significance are shown as solid markers and the fitted function as solid lines. Working
points from V V → JJ is also shown as dashed lines as a reference.

54

1.6
1.4

s = 13 TeVm(J) cut( β=1)
m(J) + Dcut

W tagger2

1.2
1

Signal efficiency

Signal efficiency

Chapter 5. Track-CaloClusters (TCCs)

1.6
1.4

0.6

0.6

0.4

0.4

0.2

0.2
1000

1500

2000

2500

2

1
0.8

500

m(J) cut( β=1)
m(J) + D
cut

1.2

0.8

0

s = 13 TeV
Z tagger

0

500

1000

1500

p (J) [GeV]

2500

p (J) [GeV]

T

(a)

2000
T

(b)
(β=1)

requirements as functions of the large-R jet pT for the V → J
Figure 5.12: Efficiencies of the mJ and D2
tagging for (a) the W boson and (b) the Z boson.

(a)

(b)

Figure 5.13: (a) Signal efficiency and (b) background rejection comparison between TCC jet tagger and LCTopo
jet tagger. Red points show the result of the TCC boson tagger optimized for the VV semi-leptonic analysis. Blue
points correspond to the boson tagger with LCTopo jet, optimized to keep 50% signal efficiency over the full rangeof the jet pT .

55

5.5. Boson Tagging Efficiency SF– At least one topo-cluster based small-R jet (preselected by pT > 20 GeV, |η| < 2.5 and the loose
quality criteria defined in Ref.[155]) is required to have pT > 25 GeV and ∆R(muon, jet) < 1.5 toensure the topology is consistent with a tt̄ event.
– The missing transeverse momentum is required to be greater than 20 GeV .
miss– The scaler sum of ET
and the transverse mass of the leptonically decaying W boson candidate
missmust satisfy ET + mW
T > 60 GeV.

• Large-R jet from W /top candidate selection– The higest-pT large-R jet with a radius parameter of 1.0 with pT > 200 GeV and |η| < 2.0 is used
to study the boson tagging efficiency SF.
– The large-R jet is required to be well-separated from the semileptonic top-quark decay by requring∆R > 1.5 between the large-R jet and the small-R jet close to muon.
– The angular separation between the muon and the large-R jet is requird to be ∆φ > 2.3.

14000
12000

s = 13 TeV, 80 fb-1
Trimmed anti-k t R =1.0 jets
∆ R (large-R jet, b -jet) > 1.0
p > 200 GeV
T

10000
8000
6000

Data 2015+2016+2017
t t (top)t t (W )t t (other)Single Top (W )Single Top (other)W + jets
VV , Z + jets
Total uncert.
Stat. uncert.
t t modelling uncert.

Events / 5 GeV

Events / 5 GeV

After the event selection, the sample is divided into two subsamples for the efficiency measurement of W boson and inclusive top-quark jets. The b-tagged fixed-cone track-jet with a radius parameter of 0.2 is used
to separate them. The sample satisfying ∆R(b-tagged jet, large-R jet) <1.0 is categorized into "top-quark
selection", otherwise "W -boson selection". The large-R jet mass distributions of events after W -boson jets
and top-quark jets selection are shown in Figure 5.14.

Data 2015+2016+2017
t t (top)t t (W )t t (other)Single Top (W )Single Top (other)W + jets
VV , Z + jets
Total uncert.
Stat. uncert.
t t modelling uncert.

2500
2000
1500

s = 13 TeV, 80 fb-1
Trimmed anti-k t R =1.0 jets
∆ R (large-R jet, b -jet) < 1.0
p > 350 GeV
T

1000
4000
500

1.5

60

80

100 120 140 160 180 200 220 240

1
0.5
60

80

100 120 140 160 180 200 220 240
Leading large-R jet mass [GeV](a)Data/Pred.

Data/Pred.

2000

1.5

60

80

100 120 140 160 180 200 220 240

6080

100 120 140 160 180 200 220 240
Leading large-R jet mass [GeV]

1
0.5

(b)

Figure 5.14: A comparison of the observed data and predicted MC distribution of the leading pT large-R jet (TCCjet) in the event for the (a) W boson and (b) top quark selections in a sample enriched in lepton-plus-jets tt̄ events.

Truth labeling
In order to estimate the SF for the target processes such as W boson and top quark, the selected large-R jet
must be identified from which processes does the jet come. The truth label of the large-R is obtained by theMC generator information including truth jet mass and number of b-hadrons associated with the jet. Basedon that, large-R jets are labeled as "W ", "top", and "other".
Signal efficiencies measurements
The four regions including both signal and control regions are defined by the boson tagger results based on
the D2 and mass window cut. Events passing both mass and D2 cuts are selected in the high-purity (HP)
SR. Events passing mass window cut but failing D2 cut are used in the low-purity (LP) SR. Events passing
D2 cut but failing mass window cut are selected in the HPCR. Events failing both mass and D2 cuts areused in the LPCR. Therefore we need to estimate the boson tagging efficiency SFs for each of these regions,
respectively. In order to convolute the effect of D2 and mass scale uncertainty to the boson tagging efficiency

56

Chapter 5. Track-CaloClusters (TCCs)

SF, the event migration between the four regions needs to be considered. For this reason, we estimate eachof these efficiency SFs simultaneously.
The number of signal-like events in data which would be categorized into one of these regions is obtained from a simultaneous chi-square template fit of "signal" and "background" templates. The "signal"/"background" labeling is performed based on the truth labels defined above. In W boson (top quark)
selection, the signal template is composed of events with "W (top)" large-R jets from tt̄ and single-top
processes. In both selections, events other than signal templates are merged as the background template
to increase the fit stability. Therefore, we have different components of signal and background templates
according to types of the boson tagging SF to estimate.
For the SF for W boson, the signal template is composed of W -boson from tt̄ and single top processes,
while top quark from both tt̄ and single top processes comprise the signal template in top quark efficiency
measurement. In each of efficiency measurements, MC simulated processes without processes described above
are regarded as background and they compose the merged background template. The normalization of eachtemplate is allowed to float freely in the fit. The fit is performed using distributions of the leading largeR jet mass to make better signal and background separation. The total normalization of the backgroundcomponent is allowed to float and is extracted in the fit. The floating parameters to be decided in the fit arelisted in Table 5.1.
Table 5.1: A list of normalization factors to be decided in fit.
Name
µ1signalµ2signalµ3signalµ4signalµbkg

Normalization factor of signal (W/Top) in D2 failed & Mass failed region (LPCR)
Normalization factor of signal (W/Top) in D2 passed & Mass failed region (HPCR)
Normalization factor of signal (W/Top) in D2 failed & Mass passed region (LPSR)
Normalization factor of signal (W/Top) in D2 passed & Mass passed region (HPSR)
Normalization factor of background (common in all regions)

The signal efficiency (fraction) for each region in data can be extracted asdata =

regionNfittedsignalall regions
Nfittedsignal,(5.13)

regionwhere Nfitted
signal means the number of fitted signal events in one of each cateogry (HPSR, LPSR, HPCR,
all region
LPCR), and Nfitted
signal means the number of fitted signal events in all regions. These values are comparedto the signal efficiencies evaluated in MC simulation,

MC =regionNsignalall regions
Nsignal.

(5.14)The efficiencies are obtained in both data and simulations as a function of the large-R jet pT . The post-fit
large-R jet mass distributions are shown in Figure 5.15 for W -bosons and 5.16 for inclusive top-quarks. The
discrepancy between data and fitted MC events are observed. This comes from the shift of the TCC jet mass.
Since the TCC jet is not calibrated, this effect is expected.
The boson tagging efficiency SF, the ratio of signal efficiencies in the data to signal efficiencies in theMC simulation, is shown in Figures 5.17 for W -bosons and 5.18 for inclusive top-quarks. The dominant
uncertainties come from tt̄ modeling. For W boson selection, the mass failed region (a) and (b) have large
uncertainty due to the small fraction of W boson jets. Since these large-R jets with large systematic uncertainty are sub-dominant, its impact on our analysis would be small. On the other hand, in the top-quark
selection, the mass passed region (c) and (d) show relatively large fluctuations since most of the top-quark
jets fail the mass window cut. For the jet pT larger than the range of the plot, the values of the highest bin
is used with additional high-pT extraction uncertainty, which is evaluated by comparing different generators.
The derived SFs are applied to the MC simulated events according to the jet labelling and the boson
tagging result.

5.5.2 Background Rejection
The similar measurement to W -boson and top-quark jet need to be performed for the background jet (e.g.
W/Z+jets). The behavior of the background jet for the boson tagger is studied in two sets of events to cover57

5.5. Boson Tagging Efficiency SF

2000

Events / 10 GeV

Events / 10 GeV

1000

Data

s = 13 TeV, 80 fb-1

tt signal
background1500

lepton+jets selection
Trimmed anti-k t R =1.0 TCC jets
W tagger (to W): m + D 2
LP CR: m failed, D 2 failed
200 GeV < p T < 250 GeV

1000

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background600

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W tagger (to W): m + D 2
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200 GeV < p T < 250 GeV

400
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200 GeV < p T < 250 GeV

500

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tt signal

2000

background

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Events / 10 GeV(b)background
lepton+jets selection
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200 GeV < p T < 250 GeV

1500
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(a)

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s = 13 TeV, 80 fb-1

800

1.50
1
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400
mJ [GeV](d)

Figure 5.15: The post-fit distribution of the large-R jet mass in (a) D2 failed, mass failed, (b) D2 passed, massfailed, (c) D2 failed, mass passed and (d) D2 passed, mass passed for W-boson selection.

58

1000

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Events / 10 GeV

Chapter 5. Track-CaloClusters (TCCs)

Data

s = 13 TeV, 80 fb-1

tt signal

800

non-tt background600

lepton+jets selection
Trimmed anti-k t R =1.0 TCC jets
W tagger (to Top): m + D 2
LP CR: m failed, D 2 failed
350 GeV < p T < 400 GeV

400

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s = 13 TeV, 80 fb-1

tt signal
non-tt background400

lepton+jets selection
Trimmed anti-k t R =1.0 TCC jets
W tagger (to Top): m + D 2
HP CR: m failed, D 2 passed
350 GeV < p T < 400 GeV

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(a)

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non-tt background400

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LP SR: m passed, D 2 failed
350 GeV < p T < 400 GeV

200

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s = 13 TeV, 80 fb-1

tt signal

400

non-tt background
lepton+jets selection
Trimmed anti-k t R =1.0 TCC jets
W tagger (to Top): m + D 2
HP SR: m passed, D 2 passed
350 GeV < p T < 400 GeV

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Data/MC

Data/MC

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1.50
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mJ [GeV](d)

Figure 5.16: The post-fit distribution of the large-R jet mass in (a) D2 failed, mass failed, (b) D2 passed, massfailed, (c) D2 failed, mass passed and (d) D2 passed, mass passed for top-quark selection.

59

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PowhegPythia8
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200
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Trimmed anti-k t R =1.0 TCC jets
W tagger (to W): m + D 2
LP CR: m failed, D 2 failed

1.2

Data/MC

Signal efficiency (∈sig)

1.2

Data/MC

5.5. Boson Tagging Efficiency SF

200
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W tagger (to W): m + D 2
HP CR: m failed, D 2 passed

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Total uncert.

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Data/MC

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selection

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(a)

-1

PowhegPythia8

0.6

T

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Data

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s = 13 TeV, 80 fb
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selection

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s = 13 TeV, 80 fb
1 lepton+jets
selection

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Trimmed anti-k t R =1.0 TCC jets
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PowhegPythia8
Total uncert.

0.6
0.4
0.2
400

500

600

400
500
600
Leading large-R jet p [GeV]T(d)Figure 5.17: The signal efficiency on W-boson jet for the boson tagger as a function of the large-R jet pT in (a)D2 failed, mass failed, (b) D2 passed, mass failed, (c) D2 failed, mass passed and (d) D2 passed, mass passed. In
the bottom panel, the boson tagging efficiency SF are shown.

60

1.2
1
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s = 13 TeV, 80 fb-1
lepton+jets selection
Trimmed anti-k t R =1.0 TCC jets
W tagger (to Top): m + D 2
LP CR: m failed, D 2 failed

Data
PowhegPythia8
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0.6
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Data/MC Top background efficiency (∈top bkg)

Data/MC Top background efficiency (∈top bkg)

Chapter 5. Track-CaloClusters (TCCs)

1.2

0.8

Trimmed anti-k t R =1.0 TCC jets
W tagger (to Top): m + D 2
HP CR: m failed, D 2 passed

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T

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Data/MC Top background efficiency (∈top bkg)

Data

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LP SR: m passed, D 2 failed

800

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s = 13 TeV, 80 fb
1 lepton+jets
selection

PowhegPythia8

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-1

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selection

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selection

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PowhegPythia8
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0.6
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Leading large-R jet p [GeV]T(d)Figure 5.18: The signal efficiency on top-quark jet for the boson tagger as a function of the large-R jet pT in (a)D2 failed, mass failed, (b) D2 passed, mass failed, (c) D2 failed, mass passed and (d) D2 passed, mass passed. In
the bottom panel, the boson tagging efficiency SF are shown.

5.5. Boson Tagging Efficiency SF

61a broad kinematic range. For large-R jets with pT from 450 GeV to 3000 GeV, multi-jet events are used to
study a mixture of light-quark and gluon jets. For pT from 200 GeV to 300 GeV, the γ+jet sample is used to
study quark jets. Using these sample provides a means to probe the behavior of quark- and gluon-enriched
regions of phase space separately. As in the case of the study of W -boson and top-quark jets, the backgroundrejection is quantified in both data and MC simulation.
Event selection
The multi-jet events are selected by a single-jet trigger based on a single large-R jet with an online requirementof ET > 360 GeV during 2015 data taking and 420 GeV from 2016 to 2017. Then at least one large-R jet
is required to have pT > 450 GeV. For γ+jet selection, events are selected with a single-photon trigger
which requires loose quality photon with ET > 120 GeV in 2015 and 140 GeV in 2016 to 2017. The photon
candidates are required to be within |η| < 2.5 and satisfy both the identification and the isolation criteria of
the tight working points defined in Ref [156]. Furthremore, large-R jets are required to have pT > 200 GeV,
|η| < 2.0 and ∆φ(jet, γ) > π2 . Then events with at least one photon with ET > 150 GeV are selected toensure that the trigger efficiency reaches plateau.
The normalization of selected multi-jet and γ+jet event is derived from data after the selection discussed
above. First the contributions from hadronically decaying W -boson and top-quarks are subtracted from data.
Then, the remaining simulated samples are normalized to the background-subtracted data.
Background rejection measurements
The background rejection 1/bkg is measured for the boson tagger. This measurement is performed in boththe multi-jet and γ+jet topologies as a function of the large-R jet pT . Because of the purity of the target
processes, the approach in this measurement is simpler than the signal efficiencies measurements. Using
the signal-substracted data, the normalization of the multi-jet and γ+jet samples is performed and thebackground efficiency is calculated directly for the four regions. The derived SFs are applied to the MC
simulated events coming from W/Z + jets processes.

5.5.3 Systematic uncertainty
Various systematic uncertainty sources, such as MC generator differences, cross-section uncertainty, jet momentum and resolution uncertainties are propagated to the efficiency measurement. The propagation ofsystematic uncertainty is performed by repeating the fit procedure with templates varied by each systematic
uncertainty. The difference of measured SF between the nominal and the varied templates is regarded as
the corresponding SF uncertainty. Estimated SF uncertainties are combined by quadrature-sum with pruning systematic source with the uncertainty less than 5% of the total uncertainty. Large-R jet pT scale, tt̄
modeling, b-tagging SF uncertainty, and high-pT extrapolation uncertainties are considered at the end ofprunning. The correlation between the four regions is considered by definition. For background measurement
uncertainty, γ+jets is used in 500 < GeV, multi-jet result is used in 500 > GeV due to the limitation of
statistics. In the high-pT region, the highest bin of each measurement is used with additional uncertainty
derived from Herwig/Sherpa showering modeling and detector variations. Possible difference between W and Z- tagger is also considered by taking the difference of signal efficiency.

62

Chapter 6

Event Selection
The event selection of the main analysis for heavy W W/W Z/ZZ resonances in semi-leptonic final states
is presented in this chapter. The event selection has been optimized to maximize signal sensitivities. As
described in Section 6.2 and 6.3, a set of preselection including event cleaning and trigger requirements is
applied first. At the beginning of the main selection, the leptonic decaying boson candidate V` is selectedaccording to the number of charged-leptons and events are categorized into three channels: 0-lepton (V` = Z,
Z → νν), 1-lepton (V` = W , W → lν), 2-lepton (V` = Z, Z → ll). For each channel, a VBF and ggF/DY
categorization is applied as described in Section 6.4. Then a hadronically decaying vector boson candidate
Vh is selected in each event. First the merged V → J identification is tried and if it fails the resolved V → jj
identification is applied, as described in Section 6.5. Several signal regions (SRs) are defined to enhance signal
sensitivities in all mass ranges. V` W and V` Z selections are independently analyzed by using different mass
window cut for W and Z, however these selections have large overlap. Illustration of the selection flow andsignal regions are summarized in Figure 6.1.

X → VV → VVhselection flow schematic

2-lepton

0-lepton

1-lepton

Leptonic V selection

Event categorization
VBF Cat.

ggF/DY Cat.
Signal regions

Signal regions
High purity

Pass

Low purity

Pass

Vh selection
MergedFailResolved

Pass

Vh selection
Resolved

Fail
To control
region selection

Vh selection
MergedHigh purity
Low purity

Pass

Z → qqTaggedUntagged
TaggedUntaggedFail

Vh selection
Resolved
Fail

Pass

Resolved

TaggedUntagged

To control
region selection

Figure 6.1: Illustration of the selection flow and signal regions of the X → V V search. The VBF category istargeted for VBF production whereas the ggF/DY category is for the rest. Three signal regions (high purity, lowpurity and resolved) are selected for each category based on the V → qq reconstruction. The 0-lepton channel
does not consider resolved selection. For final states with hadronic decaying Z bosons, the three signal regions in
the ggF/DY category are each further split into tagged and untagged according to the b-tagging information ofjets from Z → qq decays.

6.1. Strategy to the SR orthogonalization

63

6.1 Strategy to the SR orthogonalization
In VBF and ggF/DY categories of 0-, 1- and 2-lepton channels, events are checked if they pass each of both
SRs and CRs selection. When an event fails a given selection, it is tested on the next selection according to
the following order. Evens failing all of the selection are discarded and not used in the analysis. The orderof selection is as follows:• VBF categories– Merged high-purity signal region(s)– Merged low-purity signal region(s)– Resolved signal region(s)– Merged high-purity control region(s)– Merged low-purity control region(s)– Resolved control region(s)• ggF/DY categories– Merged high-purity signal region(s)– Merged low-purity signal region(s)– Resolved signal region(s)– Merged high-purity control region(s)– Merged low-purity control region(s)– Resolved control region(s)The order of event selection is most important in the transition region from 500 ≤ mX ≤ 800 GeV, where thehadronically decaying W/Z boson is reconstructed as both two small-R jets and one large-R jet. By switching
the order of "Merged" and "Resolved" category, about 5% of events go to "Resolved" from "Merged". The
prioritization was studied and this "merged-then-resolved" scheme is found to maximize the sensitivity since
the most of two small-R jets are getting overlapped and a large-R jet can observe the hadronic decay more
precisely in the intermediate-mass region.

6.2 Event Cleaning
To maintain the good data quality, the following event-level requirements are applied to the collected data.
Events not listed in GRL (Good Run List) files, which contain the list of luminosity blocks approved for the
ATLAS analysis, are discarded. Events affected by the recovery of SCT’s single event upset (SEU)-induced
bit flips [157] are also rejected. To remove the effect of the coherent noise burst over a large region of Liquidargon calorimeter [158], events within a time window of a burst are not used since energy measurements
are corrupted in these events. Furthermore, corrupted data due to the non-optimal algorithm of Tile forrejecting problematic events are also discarded. Events are required to have a primary vertex with at least
two associated tracks as defined in Section 4.1.2. The additional veto is applied to 2015 to 2016 data tosuppress the events with calorimeter saturation problems [159].

6.3 Trigger requirements
miss
The data was collected by the unprescaled single-lepton or ET
triggers with the lowest thresholds, according
miss
to number of charged lepton in each channel. 0-lepton channel uses ET
trigger which is available from
miss
miss
miss
ET = 150 GeV. Since ET trigger efficiency reaches to the plateau at ET∼ 250 GeV, 0-lepton channel
missdoes not cover the region of mV V < 500 GeV. In 1-lepton channel the single lepton or ET
triggers are used.
The single electron triggers need to be satisfied in the electron sub-channel. The single muon triggers are
miss
miss
required in the events with W -boson pT reconstructed by muon and ET, pT,µν , below 150 GeV and the ET
triggers are required in the events with pT,`ν above 150 GeV in muon sub-channel to recover inefficiency ofmuon trigger due to the lack of detector coverage. In 2-lepton channel, single-electron or single-muon triggers
are used. In all sub-channels, trigger efficiencies with regard to signal region are greater than 90% in therange of mass above 300 GeV. At the lowest target mass points, mV V = 300 GeV, the trigger efficiencies are

64

Chapter 6. Event Selection

about 70% in µνqq, 85% in eνqq, and greater than 90% in llqq channel, respectively. Trigger efficiency scale
factors are applied to the simulated events to compensate for the possible data/MC difference on the lepton
misstrigger efficiency. For ET
trigger, scale factors are applied to take into account the data/MC difference inthe range of between 150 GeV and 250 GeV. The trigger efficiency SF is not applied above 250 GeV because
the efficiency is ∼ 100%. The total integrated luminosity is 139 fb−1 and this corresponds to about 95% ofrecorded luminosity as shown in Figure 2.2.

6.4 Categorization of production processes
The event selection for VBF and ggF/DY categorization is applied at the beginning of the analysis sinceideally the VBF process results in two additional reconstructed jets, referred to as VBF-tag jets. These jets
are typically well separated in pseudorapidity and have large dijet invariant mass.
In this analysis, a Recurrent Neural Network (RNN) [160] is adopted to classify the VBF and ggF/DY
event topologies. The RNN uses four-momentum kinetic variables (pT , η, φ, E) of up to two small-R jets indecreasing order of pT as the RNN’s input parameter. Figure 6.2 shows the leading jet kinematics. The
kinematics for the sub-leading jet (Jet2) are similar to the leading jet. The VBF-jet topology is quite clear
and we expect to have VBF jets in the forward region of the detector with higher energy with respect to theusual extra jets we have in the other physics processes.

(a)

(b)

(c)

(d)

Figure 6.2: 4-momentum of the Jet1 used as RNN input for VBF (red) and ggF (blue) a scalar signal in 2-lepton
channel.

To avoid overlapping with V → qq candidate jets, small-R jets with an angular separation of ∆R < 1 withthe leading large-R jet are removed from the VBF candidates jets. If large-R jets do not exist in the event,65

6.5. Reconstruction and identification of the V → qq decay

a pair of small-R jets with its invariant mass closest to W (Z) mass is removed. Events with no small-R jets
left are automatically classified as ggF/DY events. The efficiency for VBF events is significantly improvedby the RNN, while keeping contamination from ggF/DY low.
The training of RNN is performed to separate VBF and ggF/DY signal events. Though the RNN score
distributions depend on the assumed model of a heavy resonance and its mass, these small differences areovershadowed by the large differences between the VBF and ggF/DY processes. Since the kinematics of VBF
candidate jets are independent from the number of charge leptons, the RNN trained with the 1 TeV scalar
resonance in the X → ZZ → ``qq decay is applied to the three leptonic channels, the three resonance models
and for all resonance masses. Based on signal sensitivity studies, events with RNN score > 0.8 are selected
as the VBF category, and remaining events are categorized as the ggF/DY category. Figure 6.3 (a) compares
the RNN score of simulated events of various signal models considered in this search. Figure 6.3 (b) shows
the fraction of simulated signal events passing the RNN score requirement for different signal models.

(a)

(b)

Figure 6.3: (a) RNN score distributions for the signal models considered for this search; (b) The fraction of signal
events passing the requirement on the RNN score.

Comparison of distributions of input variables for the RNN between data and MC are shown in Fig 6.4.
The modeling of RNN scores between data and MC are shown in Fig 6.5. In general, the input variables andoutput scores are reasonably well modeled.

6.5 Reconstruction and identification of the V → qq decay
Two quarks from a hadronicaly decaying boson result in two energy deposits and the distance between them
depend on their momentum. Therefore the V → qq decay can be either reconstructed from two resolved
small-R jets (V → jj) or one merged large-R jet (V → J).

6.5.1 W/Z → J candidates (merged category)Merged category is dedicated to high resonance masses, i.e. mV V > 500 GeV. When the resonance mass getshigher, the hadronic W/Z boson is highly boosted so that the resulting two quarks can often be reconstructed
as a large-R jet. This merged category requires at least one large-R jet, with the assumption that the one
with the highest-pT is assumed to be from V → q q̄ decay. Finally, the selected large-R jet is asked to betagged as W/Z boson, based on the boson tagger discussed in Section 5.4.
Events are divided into four categories (HPSR, LPSR, HPCR and LPCR) based on the results of massand D2 cuts of the boson tagger, as described in Section 5.5.1. The detailed description of HPCR and LPCR
can be also found in Section 6.8. Figure. 6.6 shows large-R jet mass and D2 distributions before the boson
tagging in 0-lepton channel. Comparing HVT W 0 1.6 TeV signal (red line) and MC backgrounds indicatesthese variables have strong separation power.
Directions of two quarks tend to be perpendicular to a longitudinally-polarized W/Z boson, while tobe horizontal in a transversely-polarized W/Z boson. This causes a higher D2 variable for a transverselypolarized W/Z boson. Since the W/Z-boson tagger is optimized using longitudinally-polarized W/Z bosons,∫Ldt = 139 fb

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−5

−4

−3

−2

−1

0

VBF sub-leading jet p [GeV]

VBF sub-leading jet E [GeV]

2

3

4

∫Ldt = 139 fb-1

s = 13 TeV

ZV→ν ν qq, Before Boson tag VCR, WZ

(f)

(g)

5

−4

−3

−2

−1

0

Events / 0.02

∫Ldt = 139 fb

107

-1

1

(h)

Data
W+jetsZ+jetsTop Quarks
SM Diboson
Stat
Stat+Shape
Stat+Syss = 13 TeV

ZV→ν ν qq, Before Boson tag VCR, WZ

106
105
104
103
102
10
1
−1

(Data-Bkg)/Bkg

10

0.4
0.2
0
−0.2
−0.4
0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

3

4

0.9

Data
W+jetsZ+jetsTop Quarks
SM Diboson
Stat
Stat+Shape
Stat+Sys

2

3

4

VBF sub-leading jet φFigure 6.4: Comparison of distributions of input variables for the RNN between data and MC. (Top) Leading jet.
(Bottom) Sub-leading jet.

108

2

0.4
0.2
0
−0.2
−0.4

VBF sub-leading jet η

T

(e)

1

(Data-Bkg)/Bkg

101(Data-Bkg)/Bkg

10(Data-Bkg)/Bkg

102

10

400 600

1

104
103

200

0

107

102

0.4
0.2
0
−0.2
−0.4

−1

VBF leading jet φ

103

0

−2

(d)

104

4

0.4
0.2
0
−0.2
−0.4

−3

(c)

105

4

2

Data
W+jetsZ+jetsTop Quarks
SM Diboson
Stat
Stat+Shape
Stat+Sys

0.4
0.2
0
−0.2
−0.4

VBF leading jet ηTEvents / 20 GeV

107

600

VBF leading jet p [GeV]

Events / 0.32

400 600

Events / 0.4

200

0.4
0.2
0
−0.2
−0.4

(Data-Bkg)/Bkg

103

102

(Data-Bkg)/Bkg

103

0

s = 13 TeV

104

103

0.4
0.2
0
−0.2
−0.4

-1

105

103

0.4
0.2
0
−0.2
−0.4

∫Ldt = 139 fb

ZV→ν ν qq, Before Boson tag VCR, WZ

104

(a)
Events / 80 GeV

Data
W+jetsZ+jetsTop Quarks
SM Diboson
Stat
Stat+Shape
Stat+Sys

107

104

VBF leading Jet E [GeV](Data-Bkg)/Bkg

Data
W+jetsZ+jetsTop Quarks
SM Diboson
Stat
Stat+Shape
Stat+Syss = 13 TeV

Events / 0.32

107

Events / 0.4

108

Events / 20 GeV

Chapter 6. Event Selection(Data-Bkg)/Bkg(Data-Bkg)/Bkg

Events / 80 GeV

66

1

RNN Score

Figure 6.5: Comparison of distribution of RNN score between data and MC. The peak around score=0.5 corresponds to events with no small-R jets, which are categorized into ggF/DY category.

67

106

∫

Ldt = 139 fb-1

s = 13 TeV

ZV→ν ν qq, Before Boson tag, WZ

105(Data-Bkg)/Bkg

Events / 0.12

107

Data
W’ m(1600)
W+jetsZ+jetsTop Quarks
SM Diboson
Stat
Stat+Shape
Stat+Sys

108
107

103

103

102

102

10

10

0.4
0.2
0
−0.2
−0.4
100

120

140

160

180

Data
W’ m(1600)
W+jetsZ+jetsTop Quarks
SM Diboson
Stat
Stat+Shape
Stat+Syss = 13 TeV

ZV→ν ν qq, Before Boson tag, WZ

104

80

-1

106

104

60

∫

Ldt = 139 fb

105

200

(Data-Bkg)/Bkg

Events / 4 GeV

6.5. Reconstruction and identification of the V → qq decay

0.4
0.2
0
−0.2
−0.4
0

1

2

3

(a)

4

5

D2

m(J) [GeV](b)

Figure 6.6: Large-R jet (a) mass and (b) D2 distributions before boson tagging in 0-lepton channel.

the tagger may not be sufficient for transversely-polarized W/Z bosons. To keep our analysis modelindependent as much as possible, LPSR with higher D2 is used in addition. This LPSR also contributes
to the sensitivity of longitudinally-polarized signals.
In Z → q q̄ selection, events are further divided into tagged and untagged categories as well as resolved
category. Since the b-tagging can not be applied to large-R jets directly, two leading VR track jets ghostassociated to the large-R jet are used. If both of VR track jets are b-tagged, events are used in tagged
sub-category. Otherwise, events are selected in untagged sub-category. The efficinecy of double b-tagging on
Z → bb signal is ∼10% while ∼1% on the background.

6.5.2 W/Z → jj candidates (resolved category)
Resolved category is important for the resonance mass below about 1 TeV. This category is applied in 1missand 2-lepton channels. 0-lepton channel does not use resolved category due to ET> 250 GeV cut. In thiscategory, events are required to contain at least two signal jets with |η| < 2.5.
Z → q q̄ candidates
Z → bb̄ makes up 21% of Z → q q̄ signal events, while events with 2 b-jets are rare in the W/Z + jets processthat forms the dominant background. In order to exploit this feature, events are further split into tagged
category with two b-tagged jets and untagged category with less than two b-tagged jets. In tagger cateogry,
two b-tagged signal jets in events are used to reconstruct the hadronic Z. untagged cateogry uses the two jetswith the highest-pT , regardless of their b-tagged status.
W → q q̄ candidates
No enhancement of b-tagged jets is expected in W → q q̄ decay, thus no b-tagging selection is applied and that
two signal jets with the highest-pT are selected. If both selected jets are b-tagged, the event is discarded. The
VBF category also does not adopt b-tagging selection since there is no significant sensitivity improvement
expected due to the statistical limitation.
Kinematic cuts
After selecting V → q q̄ candidates, the leading jet of the two is required to have pT > 60 GeV and thesubleading jet is required to have pT > 45(30) GeV in the 1-lepton (2-lepton) channel. Tighter cut on thesubleading jet is preferred in 1-lepton channel for further multijet background rejection. Finally the dijet
mass m(jj) is used to maximize the sensitivity. The selected two jets are required to satisfy 78(68) < m(jj) <105(98) GeV for the consistency with the hadronically decaying Z(W ) boson. Events failing the dijet mass

68

Chapter 6. Event Selection

window cut are used in the control regions discussed in 6.8. The analysis for W → q q̄ and Z → q q̄ channels
are performed separately.

6.6 Event selections of individual leptonic channels
As described in Section 6.5, the selection of hadronic decaying V boson is common to all three channels.
On the other hand, the selection of leptonic decaying V boson is specific to individual leptonic channels anddescribed below.

6.6.1 0-lepton: ZV → ννqq
miss
As described in 6.5.2, 0-lepton channel employs only merged category due to its high ET
threshold. A νν
misspair from a Z boson decay is chosen by requiring no Loose lepton and ET> 250 GeV. To reduce QCD mulmiss
tijet and non-collision backgrounds, events are required to satisfy pmiss> 50 GeV, min(∆φ(ET, j )) > 0.4
Tmiss missmissand ∆φ(ET, pT ) < 1.0, where pmissisthetrack-based
missing
momentum,min(∆φ(E,j))
isthe minT
T
miss
miss missimum azimuthal angle difference between ET
and small-R jets, and ∆φ(ET, pT ) is the azimuthalangle
missdifference between ET
and pmissT .
Figure 6.7 shows that the QCD multijet backgrounds are highly suppressed by these selections. Only
statistical uncertainty is included in the plots. The large discrepancy between the observed data and thesimulated events are coming from multijet and non-collision backgrounds. Before the anti-QCD cuts (topfigures), most of multijet and non-collision backgrounds dominated at the lowest pmiss
region. The backT
missground rejection is achieved by the cut on pmiss
andmin(∆φ(E,j))(top-bottom:
g-i).
Small
non-collisionTT
miss missbackground is found at high-∆φ(ET, pT ) region. The cut on it and large-R jet mass cut m(J) > 50 GeV
can reduce the remaining non-collision background more (bottom: j-l). The fraction of the multijet and noncollision backgrounds is negligibly small after the anti-QCD cuts. The event selection of 0-lepton channle issummarized in Table 6.1. Validation region (VR) is defined in Section 6.8.

Reconstruction of mZV
miss
For the final discriminant, we use the transverse mass mT reconstructed by ET
and the large-R jet,q
J + E miss )2 − (~~ miss )2 ,pJT + E
(6.1)
mT = (ETT
T
J
and p~JT are the transverse energy and momentum of the large-R jet.
where ET

Table 6.1: A summary of signal region event selection. These regions are split into VBF and ggF(DY) categories
as described in Section 6.4.

Selection
Number of Loose leptons
miss
ET
miss
pT
miss
min(∆Φ(ET,small-R jets))miss miss
∆Φ(ET
,pT )
Number of large-R jets
D2 cutW/Z mass window cut
Numb. of associated VR track jets b-tagged

SR
HP

VR
LP

HP

LP
0
> 250 GeV
> 50 GeV> 0.4<1≥ 1 large-R jets

pass
fail
pass
fail
pass passmJ > 50 GeV, fail mass window cut
For Z → J: ≤ 1 (= 2) for untagged (tagged) category

The cutflow for HVT signal yields without cross-section normalization are summarized in Table 6.8.

6.6.2 1-lepton: W V → `νqq
1-leton channel requires events containing a W → `ν candidate. The identification requires exactly one Tight
miss
lepton. To suppress the multijet background, ET> 100 (60) GeV and pT,`ν > 200 (75) GeV are appliedin merged (resolved) category.

69

6.6. Event selections of individual leptonic channels

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

(k)

(l)

Figure 6.7: Observed and expected distributions of the three variables used to reject QCD background. These are
miss
miss
pmiss
(left), min(∆φ(ET, j )) (middle), and ∆φ(ET, pmiss) (right) following the selections from top to bottom.
T
T

70

Chapter 6. Event Selection
Table 6.2: Cutflow for HVTWZ DY (VBF) signals with 600 GeV and 2000GeV in 0-lepton.
ggF/DY

Signal

600 GeVVBF
2000 GeV

600 GeV

2000 GeV

45000
44233
44232
44158
43995
39742
37873
ggF/DY VBF
37075
439
3205
41
4700
55
17913
218
8337
102

150000102215100212
41483
39876
33205
32624
ggF/DY VBF
17889
5531
1129
297
2111
606
5758
2595
2534
1066

15000013654513641013043412890410015699784
ggF/DY
VBF
60425
38063
5467
3564
7638
4704
23473
16758
12394
8479

Selection
Generated
Preselection
TriggermissET> 250 GeV
pmiss
> 50 GeVT
missmin∆Φ(ET,small-R jets) >0.4 GeV
miss miss∆Φ(ET,pT ) < 1.0
RNN categorization
Number of large-R jets ≥ 1
Merged HP CR
Merged LP CR
Merged HP SR
Merged LP SR

90000
77151
76822
48258
46817
43520
43443
ggF/DY VBF
35921
330
2436
22
4575
34
16401
169
6982
50

Reconstruction of mW V
1-lepton channel uses the W V system mass mW V , reconstructed by lepton, neutrino and the hadronicallydecaying boson candidate. The neutrino momentum in z-direction, pz , is obtained by assuming that themass of the lepton and neutrino system is the PDG value of W boson mass [18]. This constraint leads to aquadratic equation and pz is taken as either the real component of the complex solutions or the one with thesmaller absolute value of the two real solutions.
In the resolved category, the W (Z) mass constraint is imposed on the dijet system in the W (Z) → q q̄channel. The kinetic variables of the corrected dijet system are
pcorr
T,jj

= pT,jj ×

mcorr
jj

= mW (Z) ,mW (Z)
,
mjj

(6.2)
(6.3)

0.3
0.25

Nomalized number of events

Nomalized number of events

where mjj and mW (Z) are the reconstructed invariant mass of the hadronically decaying W/Z boson and theW/Z boson mass value taken by PDG (Particle Data Group) [18], respectively. The mW V is reconstructed byusing these corrected variables and the resolution is improved by 20% for signal samples with negligible shape
distortion of background samples. Figure 6.8 shows the comparison between before and after the correctionin 1- and 2-lpeton channels. Since the signal sensitivity improvement is not found in the merged categorys = 13 TeV
1-lepton, Res GGF, Radion 300 GeV
before correction

0.2

after correction

0.15
0.1

0.45

s = 13 TeV

0.4

2-lepton, Res GGF, RSG 300 GeV

0.35

before correction

0.3

after correction

0.25
0.2
0.15
0.1

0.05

0.05
0
200

300

400

500

600

700

800

900

1000

0
200

300

400

500

m(VV) [GeV]

(a)

600

700

800

900

1000

m(VV) [GeV](b)

Figure 6.8: Comparison of the reconstructed invariant mV V between before and after the dijet mass correction in(a) 1-lepton and (b) 2-lepton.

due to the trimming algorithms as defined in Section 4.3.1, we do not constrain the large-R jet mass.

71

6.6. Event selections of individual leptonic channels

Table 6.3: Summary of selection criteria used to define the signal region (SR), W +jets control region (W CR) andtt̄ control region (tt̄ CR) for merged 1-lepton channel.

Selection
Num of Tight leptons
Num of Loose leptons
miss
ET
pT,`ν
Num of large-R jets
D2 cutW/Z mass window cut
Numb. of associated VR track jets b-taggedmin (pT,`ν , pT,J ) /mWV
Num of b-tagged jets outside of large-R jet
Pass VBF selection

W → lν

W/Z → J
Topology cut
Top-quark veto

W CR (WR)tt̄ CR (TR1)
HP
LP
HP
LP
1
0
> 100 GeV
> 200 GeV
≥1
pass fail pass
fail
pass
fail
pass pass fail
fail
pass
pass
For Z → J: ≤ 1 (= 2) for untagged (tagged) category> 0.35(0.25) for DY/ggF (VBF) category0≥1
no (yes) for DY/ggF (VBF) category
HP

SR

LP

Merged category
In the merged category, the relative boson pT cut is introduced:• min(pT,`ν , pT,J )/mWV > 0.35 (0.25)

0.18
0.16

s = 13 TeV

Nomalized number of events

Nomalized number of eventsfor DY(VBF) category. The optimal threshold does not depend on signal mass point and signal models(spin-0,-1 and -2). Figure 6.9 shows the relative boson pT distributions of signal and background in merged
category.

Background
Rad_1000

Merg GGF

0.14
0.12
0.1
0.08
0.06

0.16

s = 13 TeV

0.14

Merg VBF

0.12
0.1
0.08
0.06

0.04

0.04

0.02

0.02

0
0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Background
RadVBF_1000

0
0

0.1

0.2

0.3

Min p ratio

0.5

0.6

0.7

0.8

Min p ratio

T

(a)

0.4

T

(b)

Figure 6.9: Comparison of distributions for relative boson pT between 1 TeV Radion signal and background in(a) `νqq merged ggF and (b) `νqq merged VBF categories.

In order to suppress tt̄ background, the event is removed if there is at least one b-tagged jet with ∆R(btagged jet, large-R jet) > 1.0. About 70% of the remaining tt̄ backgrounds are removed by this cut. Event
selection for the merged category is summarized in Table 6.3.
Resolved category
Events failing the merged category are analyzed in the resolved category. The following topological cuts areapplied to enhance the event of which two high-pT bosons are back-to-back in the x-y plane:miss• ∆φ(l, ET) < 1.5• ∆φ(j1, j2) < 1.5• ∆φ(l, j1(2)) > 1.

72

Chapter 6. Event Selection

Table 6.4: The list of selection cuts in the resolved analysis for the W W and W Z signal regions (SR), W +jets control region (WR) and tt̄ control region (TR). More details of the object definitions can be found in
Section 4.

cuts

Number of Tight leptons
Number of Loose leptons
W → lν
miss
ET
pT,`ν
Number of small-R jets
Leading jet pT
Subleading jet pT
W/Z → jj
Z → q q̄W → q q̄Num. of b-tagged jets
∆φ(j, l)miss
∆φ(j, ET)
Topology cuts ∆φ(j, j)miss∆φ(l, ET)min (pT,`ν , pT,jj ) /mW V
Top veto
Number of additional b-tagged jets
Pass VBF selectionSR

W CR (WR)tt̄ CR (TR1)10> 60 GeV> 75 GeV≥2> 60 GeV> 45 GeV
78. < mjj < 105.Gev 50. < mjj < 68. GeV or
50 < mjj < 150Gev
68. < mjj < 98.Gev
105. < mjj < 150. GeV
For Z → jj: ≤ 1 (= 2) for untagged (tagged) category
> 1.0
> 1.0
< 1.5
< 1.5
> 0.35(0.25) for DY/ggF (VBF) category0≥1
no (yes) for DY/ggF (VBF) categorymiss• ∆φ(j1(2), ET> 1.0• min(pT,`ν , pT,jj )/mWV > 0.35(0.25) for DY/ggF(VBF) category
As in the merged category, the relative boson pT cut is applied:• min(pT,`ν , pT,jj )/mWV > 0.35 (0.25).
Finally, the event with additional b-tagged jets not associated to the W/Z in the event is rejected to suppresstt̄ background as well as the merged category. Event selection for the merged category is summarizedin Table 6.4. The cutflow for HVT signal yields without cross-section normalization are summarized inTable 6.5. Only the merged category is shown since 1-lepton channel has better sensitivity in higher mass
range where the most of events are categorized into the merged cateogry.
Table 6.5: Cutflow for HVTWZ DY (VBF) signals with 600 GeV and 2000GeV in 1-lepton Merged category.
SignalGenerated
Preselection
Only 1 lepton
RNN categorization≥ 1 large-R jet
missET> 100GeV
pT,`ν > 200GeV
pT ratio
LP Untagged TCR
LP Tagged TCR
LP Untagged WCR
LP Tagged WCR
LP Untagged SR
LP Tagged SR
HP Untagged TCR
HP Tagged TCR
HP Untagged WCR
HP Tagged WCR
HP Untagged SR
HP Tagged SR

ggF/DY600 GeV
90000
47818
45751
ggF/DY
VBF
30368
295
21045
205
20390
196
19288
196
88
1
11
714
3
131
2199
25
371
201
2
22
463
8
80
6306
76
991

2000 GeV
Selection
80000
40133
38666
ggF/DY
VBF
37484
457
35238
422
34105
407
29324
395
361
3
71
2196
36
459
4660
76
668
961
9
177
1840
30
377
11166
181
1874

VBF
600 GeV

2000 GeV

15000073136
70240
ggF/DY
VBF
24307
9042
15349
5173
13574
4320
10469
4308
99
29
11
496
213
49
972
528
134
215
91
32
1041
112
242
7088
1673
1096

15000090316
86434
ggF/DY
VBF
45930
32704
41653
29621
40809
29027
18355
23126
215
254
48
1135
1804
255
2959
4365
442
597
578
73
1041
1678
242
7088
9969
1096

73

6.6. Event selections of individual leptonic channels

6.6.3 2-lepton: ZV → ``qq
The Z → ll candidates are selected by requiring two isolated same-flavor leptons (electrons or muons)satisfying Loose criteria defined in Section 4.4.1 and 4.4.2. The lepton pT threshold is optimized to achieve
better signal sensitivity. Both leading and sub-leading leptons are required to have pT > 30 GeV. The
optimized lepton pT cut also makes a better fake leptons reduction compared to the previous round ofanalysis [148].
For muon pairs, opposite charges are required. Electron pairs are not required to have opposite charges
since electrons are more susceptible to charge mis-identification due to the conversions of photons frombremsstrahlung. The reconstructed dilepton invariant mass is then required to be consistent with the Zboson mass. Fixed mass window cut is applied to electrons while pT,ll dependent mass window cut is applied
to muons:
83 GeV <mee< 99 GeV,(6.4)(85.6 − 0.0117pT,µµ ) GeV <mµµ< (94.0 + 0.0185pT,µµ ) GeV,

(6.5)

1.4

Efficiency

Efficiency

which was optimized from the 2015+16 analysis [148]. The signal efficiencies for the Z → `` boson mass
window cut are shown in Figure 6.10.

s = 13 TeV

1.2

Electron channel, mll cut efficiency

1.4

s = 13 TeV

1.2

Muon channel, mll cut efficiency

1

1

0.8

0.8

0.6

0.6

0.4

0.4

0.2

0.2

0

200

400

600

800

1000 1200 1400 1600

0

200

400

600

800

p (ll) [GeV]

1000 1200 1400 1600
p (ll) [GeV]

T

T

(a)

(b)

Figure 6.10: The dilepton mass window cut efficiencies for signal in (a) electron and (b) muon channesl.

Reconstruction of mZV
The mZV is reconstructed by the selected two leptons and the hadronically decaying boson candidate (Alarge-R jet or two small-R jets). The dijet mass is corrected by imposing W/Z mass constraint as with
1-lepton channel. Furthermore, the Z-mass constraint is also imposed on the dimuon system by the same
equation,
pcorr
T,µµ

= pT,µµ ×

mcorr
µµ

= mZ .

mZ
,
mµµ

(6.6)
(6.7)

This correction compensates the poor muon momentum resolution at the very high-pT region and improves
the mZV resolution significantly. Since the electron pT is measured by the EM calorimeter, this constraint is
not applied in the electrons pair because of the better momentum resolution at high-pT region.
Merged category
In the marged category, events are required to have at least one large-R jet. Events are further required tosatisfy• min(pT,ll , pT,J )/mZV > 0.35(0.25)
in DY/ggF(VBF) category as well as 1-lepton channel. Summary of the llqq event selections in the merged
category is found in Table 6.6.

74

Chapter 6. Event Selection
Table 6.6: Event selection summary for merged analysis in 2-lepton channel.

Z → ``

HP
Number of Loose leptons
Same flavor
Subleading lepton pT

Topology cut

LP

HP

HP

tt̄ CR (TR2)LPyesdilepton invariant mass

W/Z → JZ CR (ZR)
LP
2

SR

Selection

Opposite sign
Num of large-R jets
D2 cutW/Z mass window cut
Numb. of associated VR track jets b-taggedmin (pT,ll , pT,J ) /mW V
Pass VBF selectionno> 30 GeV
83 < mee < 99Gev
76 < meµ < 106 GeV−0.01170pT,ll + 85.63 < mµµ < 0.01850pT,ll + 94.00GeVFor µµ channel only
–
≥1
pass
fail
pass
fail
pass
fail
pass pass
fail
fail
pass
pass
For Z → J: ≤ 1 (= 2) for untagged (tagged) category> 0.35(0.25) for the DY/ggF (VBF) categoryno (yes) for the DY/ggF (VBF) category

Resolved category
The ZV → lljj candidates are selected from the events rejected in the merged category. Two small-R ’signal’jets are required to have a dijet invariant mass which is consistent with a V → q q̄ decay. The relative bosonpT cut is also applied,• min(PT,ll , pT,jj )/mZV > 0.35
in both ggF/DY(VBF) category. The definitions of SR and CRs for 2-lepton channel in the resolved category
are summarized in Table 6.7.
Table 6.7: Event selection summary for resolved analysis in 2-lepton channel.

Selection

Z → ``Z CR (ZR)
2

SR
Number of Loose leptons
Same flavor
Subleading lepton pT
dilepton invariant mass

Opposite sign
Num of signal small-R jets
Leading jet pT
Subleading jet pT
W/Z → jj
Z → q q̄W → q q̄Num. of b-tagged jets
Topology cut min (pT,ll , pT,J ) /mW V
Pass VBF selection

tt̄ CR (TR2)yesno> 30 GeV
83 < mee < 99GeV
76 < meµ < 106 GeV−0.01170pT,ll + 85.63 < mµµ < 0.01850pT,ll + 94.00GeVFor µµ channel only–2
> 60 GeV> 30 GeV
78. < mjj < 105.GeV
50. < mjj < 68. GeV or
50 < mjj < 150GeV
68. < mjj < 98.GeV
105. < mjj < 150. GeV
For Z → jj: ≤ 1 (= 2) for untagged (tagged) category> 0.35(0.25) for the DY/ggF (VBF) categoryno (yes) for DY/ggF (VBF) category

The cutflow for HVT signal yields without cross-section normalization are summarized in Table ??. Only
the resolved category is shown since 2-lepton channel has better sensitivity in lower mass range where themost of events are categorized into the resolved cateogry. For 2 TeV signal, number of events in Resolved
SR/ZCR are significantly small since most of events are categorized as Merged.

6.7 Signal efficiencies and mass resolutions
Signal selection efficiencies depend on the signal model, the production process, and the mass of heavy
resonances. Figures 6.11, 6.12 and 6.13 show the acceptance times efficiency (A × ) of the signal events from
MC simulations as a function of the resonance mass for (a) ggF/DY and (b) VBF production, combining all
SRs of both ggF/DY and VBF categories of both resolved and merged analyses. The A ×  curves are mostly
determined by the merged analyses and the resolved analyses contribute only at the low mass region, up to
approximately 1 TeV.
Large differences in A ×  for different resonances are the results of the different spins. The spin-0
radions are produced with isotropic angular distributions for both ggF and VBF production, while the spin-1

756.8. Control region definitions
Table 6.8: Cutflow for HVTWZ DY (VBF) signals with 600 GeV and 2000GeV in 2-lepton Resolved category.

SignalGenerated
Preselection
Lepton pT
mll
Same flavor
RNN categorization
Two signal jets
Leading jet pT
pT ratio
Resolved CR
Resolved SR

ggF/DY600 GeV
89000
44008
38384
31830
31753
ggF/DY VBF
28862
350
28742
343
21135
302
760
27
5823
86

2000 GeV
Selection
75000
42628
40651
35463
35322
ggF/DY VBF
18384
194
18383
194
13162
175
45
1
15
1

VBF
600 GeV

2000 GeV

150000
70068
56960
48580
48562
ggF/DY
VBF
37462
12405
36704
12141
7347
7396
319
559
1758
2683

150000
78682
74744
65501
65459
ggF/DY
VBF
26870
12121
26776
12082
3788
5629
19
55
18
132

HVT resonances and spin-2 RS gravitons are produced more centrally (more forward) for ggF/DY (VBF)
production. These different angular distributions lead to different efficiencies of the pT ratio requirement.
missMoreover, the angular requirements between jets and ET
in the 0-lepton channel are more efficient for DY
production of HVT resonances than for ggF production of radion and graviton due to the difference in thecolor factors between the initial-state quarks and gluons.

Figure 6.11: Selection acceptance times efficiency for the X → ZV → ννqq signal events from MC simulations as afunction of the resonance mass for (a) ggF/DY and (b) VBF production, combining HP and LP signal regions.The
light blue band represents the total statistical and systematic uncertainties for the radion model, and the total
uncertainties are similar for the other signal models.

6.8 Control region definitions
The control regions (CRs) are defined in order to estimate the dominant backgrounds in this analysis: Z+jets ,W + jets and tt̄. The CRs are used in the fit in addition to SRs to give a constraint to the normalizationof each background process. The CRs for each background are defined in which the background becomesmost dominant e.g. Z + jets for 2-lepton and W + jets and tt̄ for 1-lepton. The sckematic view of SR/CR
relation is shown in Figure 6.14. The dedicated CRs are used commonly for all of 0-, 1- and 2-lepton channels.
However, the independent CRs for resolved/merged, b-tagged/untagged, HP/LP, and VBF/ggF categories
are employed to take into account for possible mis-modeling of the background modeling caused by each
event selection. In addition, the possible mis-modeling between the number of charged-lepton is considered
as a systematic uncertainty as discussed in Section 8.2.

76

Chapter 6. Event Selection

Figure 6.12: Selection acceptance times efficiency for the X → W V → (eν/µν/τ ν)qq signal events from MC
simulations as a function of the resonance mass for (a) ggF/DY and (b) VBF production, combining all SRsof both ggF/DY and VBF categories of both resolved and merged analyses. Signal contributions from W → τ ν
decays are included in the efficiency calculation. The light blue band represents the total statistical and systematic
uncertainties for the radion model, and the total uncertainties are similar for the other signal models. The “bump”
structure around 800 GeV is due to the falling off of the resolved analysis.

Figure 6.13: Selection acceptance times efficiency for the X → ZV → ``qq signal events from MC simulations as
a function of the resonance mass for (a) ggF/DY and (b) VBF production, combining all SRs of both ggF/DY
and VBF categories of both resolved and merged analyses.The light blue band represents the total statistical andsystematic uncertainties for the radion model, and the total uncertainties are similar for the other signal models.
The decreases in efficiencies for resonance masses above approximately 2.5 TeV are due to the merging of electrons
from the highly boosted Z → ee decays. The “bump” structure around 800 GeV is due to the falling off of theresolved analysis.

6.9. Summary of Signal and Control Regions

77

W + jets CR (WCR) and Z + jets CR (ZCR)
W +jets background is the main background in 1-lepton channel, while 0- and 2-lepton channels are dominatedby Z + jets background. The mass sideband of the hadronically decaying W (Z) boson candidate is used as
the W + jets CR (WR) and Z + jets CR (ZCR) in 1- and 2-lepton channels, respectively. Events passing themass window cut are used as SRs as described in 6.6.1, 6.6.2 and 6.6.3. In the merged category, the mass
sideband is defined using the mass window cut of the W/Z boson tagger, while the resolved category requires
50 GeV < mjj < 62 GeV or 105 GeV < mjj < 150 GeV in order to avoid possible migration of signal events
due to poor mjj resolution.

tt̄ CR (TCR)tt̄ background is the sub-dominant background in 1- and 0-lepton channels. Especially, the fraction oftt̄ background is increased in b-tagged regions. The TCRs are defined in 1-lepton channel by requiring atleast one additional b-tagged jet in each region.

ννqq sideband validation region(VR)The mass sideband region in 0-lepton channel is used as the validation region (VR). The VR is used tovalidate the background estimation derived from 1-/2-lepton CRs by checking data and MC consistency in
0-lepton channel. The possible different phase spaces between 0- and 1/2-lepton channels are also studied inthis region. Therefore the VRs are not used in the final results.

Figure 6.14: The sckematic view of SR and CR.

6.9 Summary of Signal and Control Regions
Finally, there are 10 SRs in the 0-lepton channel, 15 SRs each in the 1-lepton and 2-lepton channel with a
total of 40 SRs. These SRs are not exclusive since overlapping mass windows are used to select hadronic
decays of the W and Z bosons. Counting in terms of the diboson final states of resonance decays, there are
6 SRs for W W , 15 for ZZ and 19 for W Z. SRs in each diboson final state are orthogonal. Table 6.9 shows
the breakdowns in each leptonic channel for different diboson final states.

78

Chapter 6. Event Selection

Table 6.9: Numbers of signal regions in each leptonic channel and of control regions for different diboson final
states.

VV
final state
WW
ZZ
WZ

Signal regions
VBF category
ggF/DY category
0-lep. 1-lep. 2-lep.
0-lep. 1-lep. 2-lep.
0
3
0
0
3
0
2
0
3
4
0
6
2

3

3

2

6

3

Control regions
W + jets Z + jets

tt̄

6
−

−
9

6
−

9

6

9

79

Chapter 7

Background Estimations
The dominant background processes depend on the required number of charged-lepton and the signal regions. The background compositions for each lepton channel in all SRs are shown in Figure 7.1. The main
background processes are W +jets, tt̄ and non-resonant diboson in 1-lepton channel. In 2-lepton channel,
Z+jets and non-resonant diboson are the major backgrounds (tt̄ is also the source of the background in thetagged SRs). In 0-lepton channel, the main background processes are Z+jets, W +jets, tt̄ and non-resonant
diboson. These backgrounds are modeled by the MC simulation first, and the normalizations are evaluatedFigure 7.1: Background compositions for each lepton channel in all SRs.

by various control regions (CRs) defined in Section 6.8. In 1-lepton channel there are non-negligible multi-jet
contributions due to a jet misidentified as lepton. A dedicated data-driven method is used to estimate thecontribution from multi-jet background, as described in Section 7.4.
In this section, distributions of final discriminant i.e. the invariant mass of diboson resonances, comparing
data and MC simulated sample are shown in the CRs. The CRs are also used to control the normalizationof the corresponding backgrounds in the global profiled likelihood fit (Section 9) and all plots shown here are
before the profiled likelihood fit (prefit). Since the MC simulation is not perfect in SRs/CRs, some difference
between data and MC is expected in the prefit distributions. The uncertainty band includes both statisticaluncertainties and systematic uncertainties which are described in details in Section 8.

7.1 Z + jets
ZCRs are defined as the mass sideband of hadronically decaying W (Z) boson candidate and are used tocontrol normalizations of Z + jets background in signal regions of all three channels (See Section 6.8). The
comparison of distributions of final discriminant (invariant mass of the W Z system) between data and MC in
different ZCRs for W Z analysis are shown in Figure 7.2. Besides, Figure 7.3 shows data and MC comparisonof the final discriminant (invariant mass of the ZZ system) in different ZCRs. The ZZ analysis has more CRs
than the W Z analysis due to b-tagging categorization for extracting Z → bb. Overall, reasonable agreementwith MC predictions is observed in all regions.
As shown in Figure 7.3a–7.3c, in merged b-tagged categories, the overall normalization of the MC sample isabout 20% lower than data, while it is about 5% higher than data in untagged categories in Figure 7.3b–7.3d.
The observation can be explained by the modeling of the fraction of Z+heavy-flavor jets, where the fractionof Z+hevay-flacor jets in Sherpa MC can be about 20% lower than the observed data [161]. In order to80

Chapter 7. Background Estimations

handle different normalization between b-tagged and untagged categories, we use the separate normalization
factors for Z + jets in the final fit. The resolved category shows the similar feature (Figure 7.3g–7.3h). In thetagged region the normalization differs by about 20%, while the good agreement is observed in the untagged
regions.
As seen from Figure 7.2a and 7.2b, the background normalization is differenet between HP and LP (LPshows the higher background prediction). In order to handle different normalization between HP and LP
categories, we use the separate normalization factors for Z + jets as well as W + jets and tt̄ in the final fit.
In VBF categories, the MC simulated events overestimate the data by 5 (20%) for the resolved (merged)
channels. In order to absorb the possible mismodeling on the RNN score distribution, we use the different
normalization factors for Z + jets in VBF categories. Finally, nomalization factor for Z + jets are listed inTable.7.1.
Table 7.1: Summary of normalization factors for Z+jets.
Nuisance Parameter

SampleCategory

SigXsecOverSM
norm_Zmerged_HP_ggF_tagged
norm_Zmerged_LP_ggF_tagged
norm_Zmerged_HP_ggF_untagged
norm_Zmerged_LP_ggF_untagged
norm_Zmerged_HP_ggF
norm_Zmerged_LP_ggF
norm_Zmerged_HP_VBF
norm_Zmerged_LP_VBF
norm_Zresolved_ggF_tagged
norm_Zresolved_ggF_untagged
norm_Zresolved_ggF
norm_Zresolved_VBF

SignalZ+jetsZ+jetsZ+jetsZ+jetsZ+jetsZ+jetsZ+jetsZ+jetsZ+jetsZ+jetsZ+jetsZ+jetsAll regions
ggF HP merged tagged
ggF LP merged tagged
ggF HP merged untagged
ggF LP merged untagged
ggF HP merged
ggF LP merged
VBF HP merged
VBF LP merged
ggF resolved tagged
ggF resolved untagged
ggF resolved
VBF reolsved

Notes
X → Z(→ qq)V only"""
X → W (→ qq)V only"

X → Z(→ qq)V only"
X → W (→ qq)V only

7.2 W + jets
WCRs are defined as the mass sideband of hadronically decaying W (Z) boson candidate and are used toconstrain normalizations of W + jets background in signal regions of all three channels (See Section 6.8).
The selection for the W + jets background control region in the `νqq channel is summarized in Section 6.6.2.
Comparison of distributions of the final discriminant (invariant mass of the W Z system) between data andMC in different WCRs are shown in Figure 7.4. In addition, Figure 7.5 shows data and MC comparison of
the final discriminant (invariant mass of the W W system) in different WCRs. In 1-lepton analysis, the W Z
analysis has more CRs than the W W analysis due to b-tagging categorization for extracting Z → bb.
In general, the reasonable agreement with MC predictions is observed. As shown in Figure 7.4a, 7.4c
and 7.4g in the tagged region, WCRs are enriched by tt̄ contribution, especially in the lower-mass regionof less than 1 TeV. The plots imply the different normalization factors for tagged and untagged categories
and those for ggF and VBF categories as well as ZCRs. As with Z+jets normalizations, we use separate
normalization factors for them in the final fit. Nomalization factor for W +jets are listed in Table 7.2.

7.3 ttbar
TCRs are defined by requiring an additional b-tagged jet for each SRs in 1-lepton channel and used toconstrain normalizations of tt̄ background in signal regions of all three channels (See Section 6.8). The
selection for the tt̄ background control region in the `νqq channel is summarized in Table 6.3 and 6.4.
Comparison of distributions of the final discriminant (invariant mass of the W Z system) between data andMC in different TCRs are shown in Figure 7.6. In addition, Figure 7.7 shows data and MC comparison of
the final discriminant (invariant mass of the W W system) in different TCRs.
In general good agreement between data and MC is observed. In the resolved category, about 5% overestimation is found in ggF region, while VBF regions show very good agreement. In the merged category,
about 10% (20%) overestimation is also found in ggF (VBF) category. No significant difference is observed
between tagged and untagged regions, in both resolved and merged categories.

81

Data
W+jetsZ+jetsTop Quarks
SM Diboson
Stat
Stat+Shape
Stat+Sys

106
105

∫

Ldt = 139 fb-1

Events / 500 GeV

Events / 500 GeV

7.3. ttbar

s = 13 TeV

ZV→llqq, ZCR Tag HP, WZ

104
103

106
105

∫

Ldt = 139 fb

-1

Data
W+jetsZ+jetsTop Quarks
SM Diboson
Stat
Stat+Shape
Stat+Syss = 13 TeV

ZV→llqq, ZCR LP, WZ

104
103

102

102

10

10

1

1

10−1

10−1

(Data-Bkg)/Bkg(Data-Bkg)/Bkg

107

0.4
0.2
0
−0.2
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500

1000

1500

2000

2500

3000

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0
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mllJ [GeV]

(b)

105

∫Ldt = 139 fb-1

Events / 500 GeV

Events / 500 GeV

(a)

104

3000

mllJ [GeV]

Data
W+jetsZ+jetsTop Quarks
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Stat
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Stat+Syss = 13 TeV

ZV→llqq, ZCR Tag HP, VBF WZ
103

105
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∫Ldt = 139 fb

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(d)

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Stat
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107
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3000

mllJ [GeV](c)

Ldt = 139 fb

2500

s = 13 TeV

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5

10

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s = 13 TeV

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104
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0.4
0.2
0
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(Data-Bkg)/Bkg(Data-Bkg)/Bkg

10

0.4
0.2
0
−0.2
−0.4
500

1000

1500

mlljj [GeV]

(e)

2000

2500

3000

mlljj [GeV](f)

Figure 7.2: Observed and expected distributions of transverse mass of the leptons and jets from the W Z resonancedecay in (a) ggF merged HP ZCR, (b) ggF merged LP ZCR, (c) VBF merged HP ZCR, (d) VBF merged LP ZCR,(d) ggF resolved ZCR and (e) VBF resolved ZCR.

104

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103

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Stat
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Stat+Sys

106
105∫Ldt = 139 fb-1

Events / 500 GeV

Chapter 7. Background Estimations

Events / 500 GeV

Events / 500 GeV82

s = 13 TeV

ZV→llqq, ZCR Untag HP, ZZ

104
103

102

105

4

10

∫Ldt = 139 fb

-1

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103

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102

10

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2000

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107
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-1

500

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104

2000

2500

(c)

105

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-1

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103

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102

102

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3000

mllJ [GeV](b)
Events / 500 GeV

Events / 500 GeV

(a)

6

3000

0.4
0.2
0
−0.2
−0.4

mllJ [GeV]

Events / 500 GeV

1000(Data-Bkg)/Bkg

10

0.4
0.2
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500

−1

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(Data-Bkg)/Bkg(Data-Bkg)/Bkg

10−1

105
104

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ZV→llqq, ZCR LP, VBF ZZ

3

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102
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(Data-Bkg)/Bkg

500

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Events / 300 GeV

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10

-1

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104

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(e)

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(d)

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0.4
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(Data-Bkg)/Bkg

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10−1

s = 13 TeV

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105
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(g)

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500

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0.2
0
−0.2
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500

1000

1500

mlljj [GeV]

(h)

2000

2500

3000

mlljj [GeV](i)Figure 7.3: Observed and expected distributions of invariant mass of the leptons and jets from the ZZ resonancedecay in (a) ggF merged HP tagged ZCR, (b) ggF merged HP untagged ZCR, (c) ggF merged LP tagged ZCR,(d) ggF merged LP untagged ZCR, (e) VBF merged HP ZCR, (f) VBF merged LP ZCR, (g) ggF resolved tagged
ZCR, (h) ggF resolved untagged ZCR and (i) VBF resolved ZCR.

83

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WV→lν qq, ggF WZ HP Untag WCR,
105
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Events / 500 GeV

106

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7.3. ttbar

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(g)

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1
10−1(Data-Bkg)/Bkg(Data-Bkg)/Bkg

1000

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3

500

500

(e)
Events / 300 GeV

Events / 300 GeV

6

Ldt = 139 fb

3000

0.4
0.2
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−0.4

m(lνJ) [GeV]

(d)

107

2500

Events / 300 GeV

500(Data-Bkg)/Bkg(Data-Bkg)/Bkg

10(Data-Bkg)/Bkg

1
−1

0.4
0.2
0
−0.2
−0.4
500

1000

1500

m(lνjj) [GeV]

(h)

2000

2500

3000

m(lνjj) [GeV](i)Figure 7.4: Observed and expected distributions of invariant mass of lνqq from the W Z resonance decay in (a)ggF merged HP tagged WCR, (b) ggF merged HP untagged WCR, (c) ggF merged LP tagged WCR, (d) ggF
merged LP untagged WCR, (e) VBF merged HP WCR, (f) VBF merged LP WCR, (g) ggF resolved tagged WCR,(h) ggF resolved untagged WCR and (i) VBF resolved WCR

84

6

10

∫

Ldt = 139 fb-1

Events / 500 GeV

Data
W+jetsZ+jetsTop Quarks
SM Diboson
Stat
Stat+Shape
Stat+Sys107
s = 13 TeV

WV→lν qq, ggF WW HP WCR,
105
104

107
106

102

10

10

1

1

10−1

10−1

1000

1500

2000

2500

3000

Data
W+jetsZ+jetsTop Quarks
SM Diboson
Stat
Stat+Shape
Stat+Syss = 13 TeV

WV→lν qq, ggF WW LP WCR,

104
103

500

-1

10

102

0.4
0.2
0
−0.2
−0.4

∫

Ldt = 139 fb

5

103(Data-Bkg)/Bkg(Data-Bkg)/Bkg

Events / 500 GeV

Chapter 7. Background Estimations

0.4
0.2
0
−0.2
−0.4
500

1000

1500

2000

m(lνJ) [GeV]106∫Ldt = 139 fb

-1

Data
W+jetsZ+jetsTop Quarks
SM Diboson
Stat
Stat+Shape
Stat+Syss = 13 TeV

WV→lν qq, VBF Merged HP WCR,
104
103

105

∫Ldt = 139 fb

-1

Data
W+jetsZ+jetsTop Quarks
SM Diboson
Stat
Stat+Shape
Stat+Syss = 13 TeV

WV→lν qq, VBF WW LP WCR,
104
103
102

10

10

1

1

−1

−1

10

0.4
0.2
0
−0.2
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500

1000

1500

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2500

3000

(Data-Bkg)/Bkg

10(Data-Bkg)/Bkg

106

102

0.4
0.2
0
−0.2
−0.4
500

1000

1500

2000

m(lνJ) [GeV]∫

Ldt = 139 fb

-1

3000

(d)
Events / 300 GeV

Events / 300 GeV

108

2500

m(lνJ) [GeV]

(c)

107

3000

(b)
Events / 500 GeV

Events / 500 GeV

(a)

105

2500

m(lνJ) [GeV]

Data
W+jetsZ+jetsTop Quarks
SM Diboson
Stat
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Stat+Syss = 13 TeV

WV→lν qq, ggF WW Res TCR,

106
105
4

10

107
106
105

∫

Ldt = 139 fb

-1

Data
W+jetsZ+jetsTop Quarks
SM Diboson
Stat
Stat+Shape
Stat+Syss = 13 TeV

WV→lν qq, VBF WW Res WCR,

104
103

103

102

102
10
10
1

1

10−1

0.4
0.2
0
−0.2
−0.4
500

1000

1500

2000

2500

3000

(Data-Bkg)/Bkg(Data-Bkg)/Bkg

10−1

0.4
0.2
0
−0.2
−0.4
500

1000

1500

m(lνjj) [GeV]

(e)

2000

2500

3000

m(lνjj) [GeV](f)

Figure 7.5: Observed and expected distributions of invariant mass of lνqq from the W W resonance decay (a) ggF
merged HP WCR, (b) ggF merged LP WCR, (c) VBF merged HP WCR, (d) VBF merged LP WCR, (d) ggF
resolved WCR and (e) VBF resolved WCR.

85

5

10

∫Ldt = 139 fb

-1

Data
W+jetsZ+jetsTop Quarks
SM Diboson
Stat
Stat+Shape
Stat+Syss = 13 TeV

WV→lν qq, ggF WZ HP Tag TCR,
104
103

107
6

10

∫Ldt = 139 fb-1

s = 13 TeV

WV→lν qq, ggF WZ HP Untag TCR,

105
104

Events / 500 GeV

106

Events / 500 GeV

Events / 500 GeV

7.3. ttbar

Data
W+jetsZ+jetsTop Quarks
SM Diboson
Stat
Stat+Shape
Stat+Sys

103

102

106
105

∫Ldt = 139 fb

-1

Data
W+jetsZ+jetsTop Quarks
SM Diboson
Stat
Stat+Shape
Stat+Syss = 13 TeV

WV→lν qq, ggF WZ LP Tag TCR,
104
103
102

102
10

10
10
1

−1

10

−1

10

1000

1500

2000

2500

3000

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m(lνJ) [GeV]107∫Ldt = 139 fb

-1

3000

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WV→lν qq, ggF WZ LP Untag TCR,
105
4

10

Data
W+jetsZ+jetsTop Quarks
SM Diboson
Stat
Stat+Shape
Stat+Sys

2000

103
102

104

-1

3000

(c)
Data
W+jetsZ+jetsTop Quarks
SM Diboson
Stat
Stat+Shape
Stat+Sys

105∫Ldt = 139 fb

2500

m(lνJ) [GeV](b)
Events / 500 GeV

Events / 500 GeV

(a)

106

2500

0.4
0.2
0
−0.2
−0.4

m(lνJ) [GeV]

Events / 500 GeV

500

0.4
0.2
0
−0.2
−0.4

(Data-Bkg)/Bkg

10

0.4
0.2
0
−0.2
−0.4

(Data-Bkg)/Bkg(Data-Bkg)/Bkg

1

1

−1

s = 13 TeV

WV→lν qq, VBF WZ HP TCR,

103

Data
W+jetsZ+jetsTop Quarks
SM Diboson
Stat
Stat+Shape
Stat+Sys

105
104∫Ldt = 139 fb-1

s = 13 TeV

WV→lν qq, VBF WZ LP TCR,

103

102

102

10

10

10
1

1

10−1

10−1

1500

2000

2500

3000

500

1000

1500

2000

m(lνJ) [GeV]

Events / 300 GeV

Events / 300 GeV

105

∫

-1

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SM Diboson
Stat
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Stat+Syss = 13 TeV

WV→lν qq, ggF WZ Res Tag TCR,

104
103

1500

2000

107
106

∫

Ldt = 139 fb

-1

2500

3000

(f)

s = 13 TeV

WV→lν qq, ggF WZ Res Untag TCR,

105

Data
W+jetsZ+jetsTop Quarks
SM Diboson
Stat
Stat+Shape
Stat+Sys

104

106
105

∫Ldt = 139 fb

-1

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W+jetsZ+jetsTop Quarks
SM Diboson
Stat
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Stat+Syss = 13 TeV

WV→lν qq, VBF WZ Res TCR,
104
103
102

102

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m(lνJ) [GeV]

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(e)

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3000

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m(lνJ) [GeV]

(d)

106

2500

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1000

0.4
0.2
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−0.4

1
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0.4
0.2
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1000

1500

m(lνjj) [GeV]

(g)

2000

2500

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(Data-Bkg)/Bkg

500(Data-Bkg)/Bkg(Data-Bkg)/Bkg

0.4
0.2
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(Data-Bkg)/Bkg

1
10−1

0.4
0.2
0
−0.2
−0.4
500

1000

1500

m(lνjj) [GeV]

(h)

2000

2500

3000

m(lνjj) [GeV](i)Figure 7.6: Observed and expected distributions of invariant mass of lνqq from the W Z resonance decay in (a)ggF merged HP tagged TCR, (b) ggF merged HP untagged TCR, (c) ggF merged LP tagged TCR, (d) ggF merged
LP untagged TCR, (e) VBF merged HP TCR, (f) VBF merged LP TCR, (g) ggF resolved tagged TCR, (h) ggF
resolved untagged TCR and (i) VBF resolved TCR

86

106

∫

Ldt = 139 fb-1

Events / 500 GeV

Data
W+jetsZ+jetsTop Quarks
SM Diboson
Stat
Stat+Shape
Stat+Sys107
s = 13 TeV

WV→lν qq, ggF WW HP TCR,

5

10

104

106

102

102

10

10

1

1

10−1

10−1

1000

1500

2000

2500

3000

-1

s = 13 TeV

WV→lν qq, ggF WW LP TCR,

104
103

500

∫

Ldt = 139 fb

105

10

0.4
0.2
0
−0.2
−0.4

Data
W+jetsZ+jetsTop Quarks
SM Diboson
Stat
Stat+Shape
Stat+Sys

107

3(Data-Bkg)/Bkg(Data-Bkg)/Bkg

Events / 500 GeV

Chapter 7. Background Estimations

0.4
0.2
0
−0.2
−0.4
500

1000

1500

2000

m(lνJ) [GeV]104

Events / 500 GeV

Data
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s = 13 TeV

WV→lν qq, VBF WW HP TCR,

3

10

∫Ldt = 139 fb
104

10

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WV→lν qq, VBF WW LP TCR,

10

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-1

3

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102

500

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0.2
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WV→lν qq, ggF WW Res TCR,

Events / 300 GeV

Events / 300 GeV∫

106

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3000

(d)

108
107

2500

m(lνJ) [GeV]

(c)

-1

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(b)

(Data-Bkg)/Bkg(Data-Bkg)/Bkg

Events / 500 GeV(a)∫Ldt = 139 fb

2500

m(lνJ) [GeV]

Data
W+jetsZ+jetsTop Quarks
SM Diboson
Stat
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Stat+Syss = 13 TeV

105
4

10

3

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5

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-1

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WV→lν qq, VBF WW Res TCR,
4

10

103
102

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10
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1

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0.4
0.2
0
−0.2
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1000

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(Data-Bkg)/Bkg(Data-Bkg)/Bkg

10−1

0.4
0.2
0
−0.2
−0.4
500

1000

1500

m(lνjj) [GeV]

(e)

2000

2500

3000

m(lνjj) [GeV](f)

Figure 7.7: Observed and expected distributions of invariant mass of lνqq from the W W resonance decay in (a)ggF merged HP TCR, (b) ggF merged LP TCR, (c) VBF merged HP TCR, (d) VBF merged LP TCR, (d) ggF
resolved TCR and (e) VBF resolved TCR.

87

7.4. Multi-jet Background
Table 7.2: Summary of normalization factors for W +jets.
Nuisance Parameter

SampleCategory

SigXsecOverSM
norm_Wmerged_HP_ggF_tagged
norm_Wmerged_LP_ggF_tagged
norm_Wmerged_HP_ggF_untagged
norm_Wmerged_LP_ggF_untagged
norm_Wmerged_HP_ggF
norm_Wmerged_LP_ggF
norm_Wmerged_HP_VBF
norm_Wmerged_LP_VBF
norm_Wresolved_ggF_tagged
norm_Wresolved_ggF_untagged
norm_Wresolved_ggF
norm_Wresolved_VBF

Signal
W +jets
W +jets
W +jets
W +jets
W +jets
W +jets
W +jets
W +jets
W +jets
W +jets
W +jets
W +jets

All regions
ggF HP merged tagged
ggF LP merged tagged
ggF HP merged untagged
ggF LP merged untagged
ggF HP merged
ggF LP merged
VBF HP merged
VBF LP merged
ggF resolved tagged
ggF resolved untagged
ggF resolved
VBF resolved

Notes
X → Z(→ qq)V only"""
X → W (→ qq)V only"

X → Z(→ qq)V only"
X → W (→ qq)V only

Table 7.3: Summary of normalization factors for tt̄.
Nuisance Parameter

SampleCategory

Notes

SigXsecOverSM
norm_TTbarmerged_HP_ggF_tagged
norm_TTbarmerged_LP_ggF_tagged
norm_TTbarmerged_HP_ggF_untagged
norm_TTbarmerged_LP_ggF_untagged
norm_TTbarmerged_HP_ggF
norm_TTbarmerged_LP_ggF
norm_TTbarmerged_HP_VBF
norm_TTbarmerged_LP_VBF
norm_TTbarresolved_ggF_tagged
norm_TTbarresolved_ggF_untagged
norm_TTbarresolved_ggF
norm_TTbarresolved_VBF

Signal
tt̄
tt̄
tt̄
tt̄
tt̄
tt̄
tt̄
tt̄
tt̄
tt̄
tt̄
tt̄

All regions
ggF HP merged tagged
ggF LP merged tagged
ggF HP merged untagged
ggF LP merged untagged
ggF HP merged
ggF LP merged
VBF HP merged
VBF LP merged
ggF resolved tagged
ggF resolved untagged
ggF resolved
VBF resolved

X → Z(→ qq)V only"""
X → W (→ qq)V only"""
X → Z(→ qq)V only"
X → W (→ qq)V only

7.4 Multi-jet BackgroundThe backgrounds containing the real lepton from W/Z decay (tt̄, W/Z + jets, diboson, single-t) are modeledwith the MC simulated events. The multi-jet background contributes via two different sources: fake leptons1
or semileptonic decay of heavy flavor jet. The rate of fake leptons is about 10−3 to 10−4 while the crosssection of multi-jet background is significantly larger than that of W/Z+jets. Therefore we need to estimate
the non-negligible contribution from multi-jet background. However, the same approach is not applicablefor multi-jet background. Since multi-jet backgrounds are poorly modeled in the simulation, a data-driven
template method is used to estimate the multi-jet background in the 1-lepton channel. The contributionof multi-jet background is negligible in the 0- (as discussed in Section 6.6.1) and 2- (becuase of requiring 2
charged-leptons from Z boson) lepton channels.
Multi-jet template extraction
The template shape of the multi-jet background is extracted from data using multi-jet-enriched control regions(MJCRs) which are defined by requiring the same event selections to the SR/WCRs in 1-lepton resolved
category but the different lepton ID and isolation. The MJCRs is used to extract the MJ template that isused for SR/WCRs. The requirements of the inverted leptons to define MJCR are summarized in Table 7.4.

For the electron channel in which the misidentified electron comes from hadron-jet fake and heavy-flavor
decay, events with one electron failing Tight but passing Medium identification operation points (see Section 4.4.1) are used.
1 This contribution could be from particles mistaken as electrons originating from jets

88

Chapter 7. Background Estimations
Criterion
ElectronMuon

signal lepton

inverted lepton
MediumID
Tight!TightCalo Isolation
FixedCutHighPtCaloOnly FixedCutHighPtCaloOnly
ID
MediumMedium!FixedCutTightTrackOnly
Track Isolation FixedCutTightTrackOnly
pvarcone0.3/pT < 0.07∗
T*Only applied to events with pT,`ν < 150 GeV

Table 7.4: Definitions of "inverted" leptons used in multi-jet control region

For the muon channel in which the misidentified muon mainly comes from the heavy-flavor decay, the
MJCR is required to have muon passing a relaxed, but failing the tight isolation requirement. As describedin Section 6.3, two different triggers are used in the muon channel. For events with transverse momentum ofmiss
W → µν greater than 150 GeV, ET
trigger is used, while events with W -boson pT of less than 150 GeV arerecorded by single muon trigger. The isolation requirements in the muon trigger result in the different multijet shape templates between the two samples. Therefore, the muon channel is divided into two sub-channels
for multi-jet estimation.
Pre MJ template fit
The multi-jet contribution is estimated by using the template shapes extracted from data in a multi-jet
enriched control region. First, the MJ template is obtained by subtracting the contribution from otherbackground processes in the MJCRs, based on MC predictions. Systematic variations of the MC predictions
are later applied as a source of systematic uncertainty.
Second, the normalization factors for both the multi-jet and the electroweak components are obtained
missby a fit (“pre-MJ-fit”) on the ET
distribution in the WCRs. Templates for the multi-jet contributions are
estimated separately depending on the lepton flavor (e or µ). In the fit, the multi-jet component is left free
to float. The normalization of the other backgrounds are constrained to reasonable ranges according to their
expected normalization within the statistical uncertainties. Z+jets and diboson are fixed in the fit since
their contributions are small. W +jets and top quark are combined as one component in the fit because of
their similarity of shapes. Both electron and muon channels are used in the pre-MJ-fit. The normalization
scale factors are shared by the same background components in the fit, while the electron and muon MJCR
templates have separate scale factors.
Third, the obtained scale factors for MJCR are applied to the corresponding templates and the scaled
MJCR templates are used in the analysis, with uncertainties obtained from the pre-MJ-fit.
In principle, for each final WCR and SR used in the 1-lepton analysis, a corresponding MJ templateshould be derived. Due to tight cuts, some MJ regions suffer from low statistic. By comparing the MJ shapes
between VBF and ggF region, it is found that the shapes of MJ template are consistent within the statisticaluncertainty. Therefore the MJ templates are obtained using ggF+VBF combined regions.
Extraction of multi-jet background normalizations
The extracted normalization factor is applied to MJVR templates in WCRs, for various kinematic variables,
misssuch as ET, W transverse mass, lepton pT , and the invariant mass, as shown in Figure 7.8. The multi-jet
contribution in muon channel with pT,`ν > 150 GeV is consistent with zero, hence neglected in the final fit.
In general, good consistency between data and background estimation is observed. The yields and extracted
normalization factors are summarized in Table 7.5.

89

7.4. Multi-jet Background

(a)

(b)

(c)

(d)

(e)

(f)

miss
Figure 7.8: Observed and expected distributions of (a) ET, (b) pT,`ν , (c) p`T , (d) transverse mass of the leptons
miss
miss
and jets from the W Z resonance decay, (e) ∆φ between a lepton and ET
and (f) ∆η between a lepton and ET
with estimated multi-jet

90

Chapter 7. Background Estimations

Table 7.5: The fit is done in various WCRs, in order to obtain the corresponding scale factors for MJ templates:
ggF resolved WCR for the W W → lvqq selection, ggF resolved untagged WCR for the W Z → lvqq selection, ggF
resolved tagged WCR for the W Z → lvqq selection, VBF resolved WCR for the W W → lvqq selection, and VBF
resolved WCR for the W Z → lvqq selection. Post-fit event yields for electroweak processes and MJ contributions
are shown. The “SF” column shows the corresponding normalization scale factors for electroweak processes fromthe fit.

SampleYield

SF

ggF Resolved WW WCR
Top quarks & W +jets
645040 ± 1972
Z+jets & SM Dibosons
24075
Multi-jet (electron)
24156 ± 1225
Multi-jet (muon)
35528 ± 924

1.00
fixed
3.97
9.02

ggF Resolved WZ Untag WCR
Top quarks & W +jets
644690 ± 1981
Z+jets & SM Dibosons
24076
Multi-jet (electron)
24367 ± 1233
Multi-jet (muon)
35529 ± 921

1.00
fixed
3.87
8.75

ggF Resolved WZ Tag WCR
Top quarks & W +jets
71237 ± 688
Z+jets & SM Dibosons
519
Multi-jet (electron)
596 ± 449
Multi-jet (muon)
1197 ± 222

1.03
fixed
0.09
0.29

VBF Resolved WW WCR
Top quarks & W +jets
19032 ± 364
Z+jets & SM Dibosons
1092
Multi-jet (electron)
1426 ± 214
Multi-jet (muon)
1281 ± 157

0.93
fixed
0.24
0.31

VBF Resolved WZ WCR
Top quarks & W +jets
21342 ± 392
Z+jets & SM Dibosons
1112
Multi-jet (electron)
1414 ± 230
Multi-jet (muon)
1281 ± 157

0.94
fixed
0.23
0.31

91

Chapter 8

Systematic Uncertainty
Systematic uncertainties impact sensitivities for target signal models through their effects on backgroundestimations, signal selection efficiencies, and the distributions of mass discriminants. The sources of these
uncertainties are classified into mainly two groups: (a) Experimental uncertainties related to the detector
and reconstruction performance and (b) Theoretical uncertainties associated with the MC modeling of bothbackground and signal processes. In this section the source and the size of uncertainties are discussed.

8.1 Experimental Uncertainties
Luminosity
The uncertainty on the integrated luminosity for the 2015+2016 dataset is 2.1%, 2.4% for the 2017 dataset,and 2.0% for the 2018 data. The uncertainty for the combined run-2 dataset (2015-2018) is 1.7% [74]. The
combined uncertainty is applied to all simulated samples including both backgrounds and signal samples.
Pileup reweighting
The uncertainty associated with the pileup reweighting is included by considering a variation in the pileup
reweighting of MC. It covers the uncertainty on the ratio between the predicted and measured inelastic crosssection in the fiducial volume defined by MX > 13 GeV where MX is the mass of the non-diffractive hadronicsystem [162].
Trigger
Systematic uncertainties on the efficiency of the electron or muon triggers are evaluated with the tag and probe
method using Z → ll events in data and simulation [144, 163]. It is applied to the MC simulated samples.
miss
The ET
trigger uncertainty arises from the estimation on scale factor which contains two contributions:
statistics and the efficiency discrepancy between MC samples (tt̄ and W + jets) [164]. Small corrections areapplied to the simulation to better model the performance seen in data. These corrections have associateduncertainties on the order of 1% and uncertainties on the lepton triggers efficiencies are found to be negligible.
Muons/Electrons reconstruction and identification
The systematic uncertainties related to electrons and muons are estimated based on the difference between
data and simulation [141, 144]. Identification and reconstruction efficiencies are measured with the tag andprobe method using Z → ll events in data and simulation. Scale factor and its uncertainty of lepton isolation
efficiency are derived by tag and probe method as well. Energy and momentum scales are measured with Z
mass distribution shape. These uncertainties are considered in the analysis but their impacts are very small.
Uncertainties on the lepton energy (or momentum) scale and resolution, especially for muon momentum
resolution (3%), are also taken into account.
Small-R Jet Energy Scale and Resolution Uncertainty
The jet energy scale and resolution of the small-R jets are measured in situ by calculating the response
between MC and data in various bins of kinematic phase space [165]. There are roughly 100 kinds of welldefined systematic uncertainty sources. This thesis uses simplified groups of the uncertainty sources, which
are grouped into about 20 categories considering each correlation. For jets with |η| < 2.5, the total relative
uncertainty on the jet energy scale varies in the range 1-4% for pT > 20 GeV. The jet energy resolution

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uncertainty ranges from 10-20% for jets with pT ∼ 20 GeV to less than 5% for jets with pT > 200 GeV. They
also affect the merged regime because they are included in the calculation of the missing transverse energy.
Large-R Jet Energy Scale and Resolution Uncertainty
The large-R jet energy scale uncertainties are considered as one of the dominant uncertainties in this analysis.
The pT of the large-R jet can be approximated to be equivalent with calorimeter-jet pT , since the track
measurements enter the calculation of TCC jet pT as only "pT ratio". The uncertainty on the pT scale ofthe large-R jet is evaluated by comparing the ratio of the large-R jet pT to track-jet pT using dijet data andsimulation, which is called as Rtrk method [129, 153]. The precision on the relative jet energy scale is 1–2%
for 200 GeV < pT < 2 TeV, while that on the mass scale is 2–10%. The jet energy resolution uncertainty
is estimated to be approximately 2%. In addition to this “Baseline” uncertainty, the uncertainties on track
measurements (“Tracking”), the difference between Pythia and Sherpa dijet simulations (“Modelling”) andstatistical uncertainty of dijet data (“TotalStat”) are considered. In order to take into account the possible
difference between TCC and calorimeter-jet pT , the difference between TCC jet and calorimeter-jet pT in
dijet data and simulation is additionally considered as “Closure” uncertainty. As a pT resolution uncertainty,
jet pT is smeared by Gaussian with 2% width.
W/Z-tagging efficiency SF Uncertainty(β=1)

For the evaluation of mass and D2
scale uncertainties, the efficiency of W/Z-tagging based on cuts
(β=1)
on jet mass and D2
is estimated in data using the control sample and corrected by comparing it withsimulation, as described in Sec. 5.5. The efficiency of W/Z-induced jet signal is estimated by tt̄ control sample,
while the efficiency on single-q/g background is estimated by the dijet sample. The effects of experimental
and theoretical uncertainties on the efficiency SF is studied. By taking the double ratio (ratio of efficiencies(β=1)
between data and simulation), the uncertainties which are not related to jet mass and D2
scale/resolution
are canceled out. The efficiency SF and uncertainties on it are estimated in each of (1) pass mass and pass
(β=1)
(β=1)
(β=1)
D2
(HP SR), (2) pass mass and fail D2(LP SR), (3) fail mass and pass D2(HP CR) and (4)(β=1)
fail mass and fail D2(LP CR) regions, which are used to define SR and CR in our analysis (Sec. 6.5.1),
and correlation between four regions are correctly taken into account. The measurement is extrapolated tohigher-pT region with additional uncertainties estimated from simulations. The efficiency for backgroundlarge-R jets from light-quarks or gluons is estimated using dijet and γ+jets samples.
B-tagging systematics
The systematic uncertainties on the efficiencies for tagging b-jets and for mis-tagging light-flavor jets are
considered. They are evaluated as uncertainties on the scaling factor to take account for possible disagreementof the b-tag efficiency between data and MC. Scale factors and corresponding systematic uncertainties are
divided into several components like b-, c- and light-flavor-induced jets, based on several measurements [166].
The total uncertainties are 1–10%, 15–50%, and 50–100% for b-jets, c-jets, and light-flavour jets respectively.
Missing transverse energy
The missing transverse energy is calculated using physics objects, such as muons, electrons, taus, photons,
and jets. Therefore, all of the systematic errors on these objects, e.g. the jet energy scale, are propagated tomissuncertainty. In addition, there is an uncertainty called the "Soft Term", from the unassociated tracks.
ET
The resolution and scale of this soft term are varied within their errors to evaluate their contribution to thetotal uncertainty [167].
Track missing transverse energy
As discussed in Section 6.6.1, a very loose cut on pmiss
is applied for the event cleaning in 0-lepton channel.
T
on
the
total
background yield is estimated by varying the pmiss
The impact of possible mismodeling of pmiss
TTvalue by ±2% and found to be negligible.

8.2. Theoretical Uncertainties

93

8.2 Theoretical Uncertainties
Several theoretical uncertainties are considered to take into account the possible mis-modeling of the normalizations of diboson and single top-quark backgrounds, the shapes of the mass discriminant distributionsof background processes, and the signal acceptances. They are estimated by comparing the choices of event
generators, PDFs, parton shower models, underlying event tunes, etc. For the dominant backgrounds suchas W + jets, Z + jets and tt̄, only uncertainties on the shapes of discriminant variables matter since theirnormalizations are controlled by the dedicated CRs.
Uncertainties in the modeling of tt̄
For tt̄, an uncertainty on the shape of discriminants used in the fit are derived comparing the default
Powheg [79]+Pythia8 [94] sample with the distribution obtained using aMC@NLO [81]+Pythia8 as
an alternative sample. The normalizations of the alternative samples after the event selections are scaled to
the nominal sample and the difference between alternative generators is regarded as the shape uncertainty on
the distribution of final discriminant. The shape difference is found to be approximately 4% in merge signal
regions, doubling the value in the resolved analysis. Additional systematic uncertainties are also evaluatedby comparing the nominal sample showered with Pythia8 [94] to one showered with Herwig [168], and arefound to be between 2 and 5%.
W/Z+jets modeling uncertainty
W/Z+jets modeling uncertainty is also considered as well as tt̄ modeling uncertainty by comparing thenominal Sherpa samples with samples produced using MadGraph5. The resummation scale and theCKKW matching scale in the nominal samples are also varied. In addition, a matrix element and parton
shower variations are considered by comparing the nominal Sherpa samples with MadGraph+Pythia
samples.
The evaluated shape differences are stored as weights in the mV V spectrum and evaluated for each of
the individual signal/control regions during the final fit. To reduce the effects of statistics, noticeably in thetails of distributions, all signal and control regions among the resolved/merged and ggF/VBF categories are
merged in the calculation of the shape uncertainties.
The shape systematic uncertainty is typically smaller than 10%, with the Sherpa-Madgraph comparison
reaching 25% in the merged ggF WZ untagged signal regions for the `νqq channel. The comparison ofrecontructed mV V distributions between Sherpa and Madgraph W/Z+jets samples are shown in Figure 8.1.

Uncertainties on the modeling of single-t, diboson
Estimations of background contributions from diboson and single-t rely on MC prediction since it is notpossible to define a dedicated control region to control its modeling. For diboson process, the cross-section
uncertainty is estimated to be 10% [95, 169], using Sherpa samples. Furthermore, renormalization andfactorization scale and PDF variations contribute to the uncertainty on the diboson normalization with an
impact of 6%. A contribution from electroweak production is also evaluated with Madgraph+Pythia8 forthe diboson normalization. A conservative uncertainty of 50% is considered and the impact on the ggF/DY
analysis is negligible. Single-t process is a minor component in our analysis. For the cross-section of single t
process, conservative 20% uncertainty is considered.
Uncertainty on modeling multi-jet backgroundAs described in Sec. 7.4, the multi-jet (MJ) background template is obtained from dedicated control regionswith reverted electron identification or muon isolation requirement. The shape uncertainty of the multijet
background is estimated according to the following uncertainties. The normalization of the backgroundprocesses could affect the extracted MJ template shape. This systematic uncertainty is evaluated by varying
the normalization factors for tt̄ and W +jets processes, and the resulting difference in MJ template shape istaken as the systematic uncertainty. They are found to be a few percent to up to 15%.
Extrapolation uncertainty on background normalization in the 0-lepton channel
In the 0-lepton channel, it is not possible to define pure control regions for W +jets, Z+jets and tt̄. The
normalization factors for these backgrounds are obtained from the 1-lepton (for W +jets and tt̄) and 2-lepton

94

Events / GeV

Events / GeV

Chapter 8. Systematic Uncertaintys = 13 TeV
104
10

Merg GGF

Nominal (Sherpa)

3

Alternative (Madgraph)102

s = 13 TeV
Merg VBF

Alternative (Madgraph)

10

10

10−1

1

10−2

10−1
500
2
1.5
1
0.5
0
500

1000

1500

2000

2500

3000
m(VV) [GeV]

1000

1500

2000

2500

3000

m(VV) [GeV]

10−3
500
2
1.5
1
0.5
0
500

1000

1500

Events / GeV

Events / GeV

10

2500

3000

1000

1500

2000

2500

3000

m(VV) [GeV](b)s = 13 TeV
Res GGF

2000

m(VV) [GeV]

(a)

105

Nominal (Sherpa)

1

Ratio

Ratio

102

103

Nominal (Sherpa)

4

Alternative (Madgraph)

104
10

3

s = 13 TeV
Res VBF

Nominal (Sherpa)
Alternative (Madgraph)

102

103
10
102
1
10

10−1

2 500
1.5
1
0.5
0 500

1000

1500

2000

2500

3000

m(VV) [GeV]

1000

1500

(c)

2000

2500

3000

m(VV) [GeV]

Ratio

Ratio

1

10−2
2 500
1.5
1
0.5
0 500

1000

1500

2000

2500

3000

m(VV) [GeV]

1000

1500

2000

2500

3000

m(VV) [GeV](d)Figure 8.1: The comparison of recontructed mV V distributions between nominal and alternative V + jets samplesin (a) Merged ggF, (b) Merged VBF, (c) Resolved ggF, and (d) Resolved VBF categories.

95

8.2. Theoretical Uncertainties(for Z+jets) channels, and extrapolated to the 0-lepton channel. Such extrapolations can introduce additional
systematic uncertainties due to different phase space in the different lepton channels. As an illustration, thenormalization for W +jets in 0-lepton channel can be written as:
Nbkg,0−lep===

Nbkg,0−lep,MC · µbkg,1−lep
Nbkg,1−lepWCR,data
Nbkg,0−lep,MC ·Nbkg,1−lepWCR,MC
Nbkg,0−lep,MC
Nbkg,1−lepWCR,data ·Nbkg,1−lepWCR,MC

(8.1)
(8.2)
(8.3)
(8.4)

The factor Nbkg,0−lep,MC /Nbkg,1−lepWCR,MC could be model dependent, given the large phase space difference
among different channels. Therefore, it is necessary to study associated uncertainties due to such cross channel
extrapolation.
This effect can be studied by comparing the ratio of event yields for alternative sample to that for nominal
sample in each W (Z)+jets and tt̄ prediction between 0 and 1(2) lepton channel. We define a double ratio as:
1−lep (2−lep)

R=

0−lep
NAlternative
MC /NAlternative MC
1−lep (2−lep)

0−lep
NNominal
MC /NNominal MC

(8.5)

.

and this double ratio R is studied for W +jets, Z+jets and tt̄, in each signal region. The extrapolation
uncertainty is evaluated by the double ratio, defined as the absolute value of R − 1.
Z+jets background yield ratio between 0- and 2-lepton channel
The extrapolation uncertainties for Z+jets are estimated by comparing the nominal Sherpa samples andalternative MadGraph samples, as summarized in Table 8.1 for ggF and VBF categories, respectively.
Non-negligible extrapolation uncertainty for Z+jets should be considered, especially for ggF categories.
Table 8.1: Summary of evaluated ratio and extrapolation uncertainties for Z + jets

Z + jets ggF
Sherpa ratio
Madgraph ratio
Extrapolation uncertainty [%]Z + jets VBF
Sherpa ratio
Madgraph ratio
Extrapolation uncertainty [%]

HPSR
0.317
0.358
12.9
HPSR
0.565
0.537
5.0

HPCR
0.23
0.261
13.5
HPCR
0.414
0.371
10.4

LPSR
0.284
0.329
15.8
LPSR
0.546
0.532
2.6

LPCR
0.267
0.31
16.1
LPCR
0.477
0.454
4.8

W +jets background yield ratio between 0- and 1-lepton channel
The extrapolation uncertainties for W +jets are studied by comparing the nominal Sherpa samples andalternative MadGraph samples, as summarized in Table 8.2 for ggF and VBF categories, respectively.
tt̄ background yield ratio between 0- and 1-lepton channel
The extrapolation uncertainties for tt̄ are studied by comparing the nominal Powheg+Pythia8 samples
and alternative aMC@NLO samples, as summarized in Table 8.3, for ggF and VBF categories, respectively.

96

Chapter 8. Systematic Uncertainty

Table 8.2: Summary of evaluated ratio and extrapolation uncertainties for W + jets

W + jets ggF
Sherpa ratio
Madgraph ratio
Extrapolation uncertainty [%]W + jets VBF
Sherpa ratio
Madgraph ratio
Extrapolation uncertainty [%]

HPSR
0.397
0.374
5.8
HPSR
0.355
0.3502
1.4

HPCR
0.458
0.377
17.7
HPCR
0.362
0.3022
16.5

LPSR
0.576
0.511
11.3
LPSR
0.429
0.4246
1.0

LPCR
0.435
0.371
14.7
LPCR
0.361
0.285230.0

Table 8.3: Summary of evaluated ratio and extrapolation uncertainties for tt̄

W + jets ggF
Sherpa ratio
Madgraph ratio
Extrapolation uncertainty [%]W + jets VBF
Sherpa ratio
Madgraph ratio
Extrapolation uncertainty [%]

HPSR
0.551
0.467
15.2
HPSR
0.34
0.419
23.2

HPCR
0.697
0.53
24.0
HPCR
0.403
0.366
9.2

LPSR
0.727
0.616
15.3
LPSR
0.386
0.501
29.8

LPCR
0.857
0.688
19.7
LPCR
0.49
0.522
6.5

8.2. Theoretical Uncertainties

97

Signal Uncertainties
For possible mis-modeling of signal generators, uncertainties on signal acceptances are estimated for the
choice of the parton distribution function, the modeling of the initial- and final-state radiations. The PDF
uncertainties are studied by taking the acceptance difference due to internal PDF error sets and the difference
between the choice of PDF sets. The uncertainty from ISR/FSR modeling is estimated by varying parametersin the tunes used and applied to the HVT, the RS Graviton and Radion models. These uncertainties,
calculated in several resonant mass points, are retrieved for each model, production and decay and considered
as conservative. Those uncertainties on the signal acceptance are included in the fit. The PDF uncertainties
were evaluated to be under 5% for all models. ISR/FSR uncertainties ranges from 2% in the HVT model
merged regime to about 11% in the VBFHVT model in resolved regime.

98

Chapter 9

Statistical Interpretation
For the extraction of background normalizations and the signal strength of the hypothetical signal processes,
the search utilizes the statistical treatment using a combined profile likelihood fit to binned discriminants inall categories and regions simultaneously. The binning of the discriminant for each region is determined basedon the signal mass resolution, as described in Section 9.4. In the likelihood function definition, the signal
strength is assigned as the parameter of interest (POI) and the systematic uncertainties and the backgroundnormalization factors are assigned as nuisance parameters (NPs). The nuisance parameters are either free
to float, or constrained using Gaussian terms. Constructed likelihood function is then used to calculate thep-value for the discussion of discovery and signal exclusion.

9.1 Likelihood function definition
A binned likelihood function is defined as the product of Poisson probability terms,

Y
YY
sig ~
bkg ~
~ =
fk (θk0 |θk ),L(µ, θ)Pois nobs
|µ
·
n
(
θ)
+
n
(
θ)
ci
ci
ci
c

i

(9.1)

k

where a signal strength parameter µ multiplies the expected signal yield for a given benchmark set of parambkg
eters nsig
represents the backgroundci in each histogram bin i of the discriminant from channel c, and nci
content for bin i from channel c.
The effect of the systematic uncertainties on the signal and background predictions is introduced by a
~ The NPs affect the mean value of Poisson probability terms by shifting
set of nuisance parameters (NP) θ.
sigbkg
nci and nci with the constraints from the asigned prior distribution. The term fk (θk0 |θk ) represents theset of constraints on θ~ from auxiliary measurements θk0 , which include systematics normalization and shape
uncertainties in the signal and background models, and include the statistical uncertainties of the simulated
bin content. Each of NPs is parametrized by Gaussian or log-normal priors. The latter one, the log-normal
prior, is used for normalization uncertainties in order to keep a positive likelihood. Therefore the expected
numbers of signal and background events in each bin are regarded as functions of θ. For a normally distributed
θ, the rates in each category are log-normally distributed. MC statistical uncertainty is parametrized by
Poisson distribution.
~ is therefore a function of µ and θ.
~ The nominal fit of the likelihood
The likelihood function, L(µ, θ),function 9.1 is performed in terms of µ and θ~ by maximizing the likelihood function with respect to all parameters. The maximized function is referred to as the maximized log-likelihood value, MLL. Maximizing the
likelihood with floating µ corresponds to signal+background fit, and fixing µ = 0 corresponds to background
only fit.

9.2 Hypothesis Testing
To test a hypothesized value of µ the profile likelihood ratio
λ(µ) =

ˆL(µ, θˆµ )L(µ̂, θ̂)

,

(9.2)

ˆ
is considered, where µ̂ and θ̂ are the parameters that maximise the likelihood and θ̂µ are the nuisanceparameter values that maximise the likelihood for a given µ. The test statistic qµ is then constructed99

9.2. Hypothesis Testingaccording to the profile likelihood ratio:qµ = −2 ln λ(µ),(9.3)

This test statistic is used to measure the compatibility of the background-only model with the observed data
and to extract upper limits derived with the CLs method [170, 171]. The limit set on µ is then translated intoa limit on the signal cross-section times branching ratio, using the theoretical cross-section and branchingratio for the given signal model.

9.2.1 Discovery of a positive signal
The defined test statistic with µ = 0:(−2 ln λ(0) (µ̂ ≥ 0)q0 =0(µ̂ < 0)(9.4)

is used to discuss the discovery of a new signal. We don’t consider the case µ̂ < 0 as evidence against thebackground-only hypothesis, since our signal models do not lead to a decrease in the data and the data is
expected to contain the signal event. This type of upward fluctuation of the data is dealt with the NPs in
this analysis.
The p0 -value is calculated asZ ∞p0 =f (q0 |0)dq0 ,
(9.5)
q0obs

where q0obs is the value of q0 observed with data, and f (q0 |0) denotes the pdf of the statistics q0 underassumption of the background-only hypothesis (µ = 0). If p0 is below the certain value, the background-only
hypothesis is rejected. Conventionally, a significant excess is declared if the p0 -value is greater than 3σ, anda discovery is declared when the p0 -value reaches 5σ.

9.2.2 Signal exclusion and Upper limit
If the methodology of the previous section can not reject the background-only hypothesis, the test statistic
qµ is then used to exclude a given signal model and to establish an upper limit on the signal strength µ. We
redefine(−2 ln λ(µ) (µ̂ ≤ µ)
qµ =
.
(9.6)
0
(µ̂ > µ)Here the test statistic is set to qµ = 0 for µ̂ > µ since it is not a part of the rejection region of the test. The
higher value of qµ represents more incompatibility between the data and the hypothesized value of µ. As in
the case of discovery, the p-value is defined asZ ∞pµ =f (qµ |µ0 )dqµ ,
(9.7)
obs
qµ

where qµobs is the value of qµ observed with data, and f (qµ |µ0 ) is the pdf of qµ under the assumption of the
hypothesis µ0 . The confidence level (CL) for signal plus background hypothesis (µ = 1) is defined as
Z ∞CLs+b =f (qµ |1)dqµ ,
(9.8)
obs
qµ

If the value of CLs+b is below 1 − α, we can conclude the value of µ is said to be excluded at α CL. However,this definition is sometimes too aggressive to exclude a signal model properly, especially for signal models
with small sensitivity. To avoid the wrong excluding, the different CL,
CLs =

CLs+b
CLb

(9.9)

100

Chapter 9. Statistical Interpretation

is introduced, whereZ qµobsf (qµ |0)dqµ .

CLb =(9.10)−∞The greater CLb means more compatibility between the data and the background-only hypothesis (µ = 0).
Since CLb is always less than 1, CLs is always larger than CLs+b . It allows the exclusion results to be moreconservative and to be protected from background fluctuations by considering compatibility between the data
and background-only hypothesis. Upper limits on the signal strength at confidence level α are obtained byscanning the value of µ for which CLs is equal to 1 − α.

9.2.3 Asymptotic Formulas
According to the Wald’s theorem [172], the test statistic can be approximated as:qµ = −2 ln λ(µ) =√(µ − µ̂)2
+
O(1/
N ).
σ2

(9.11)

Here N represents the data sample size, and µ̂ follows a Gaussian distribution with a mean µ0 and standard
deviation σ. The standard deviation σ of µ̂ is estimated by the Asimov data set [170] corresponding √to astrength µ0 which gives µ̂ = µ0 . When the data sample size N is significantly large so that the O(1/ N )term can be neglected, one finds the test statistic is written as:−2 ln λA (µ) ∼(µ − µ0 )2= Λ.
σ2(9.12)

Therefore, with the Asimov data set, the distribution of f (qµ |µ0 ) can be characterized by the noncentrality
parameter Λ. The deviation σ is obtained asσ2 =(µ − µ0 )2,qµ,A(9.13)

where qµ,A = −2 ln λA (µ).
Using the validity of the asymptotic approximation discussed above, the p-value of the hypothesized µ
can be decribed in a simple way. For instance, in upper limit calculation the test statistic can be written as:((µ−µ̂)2µ̂ < µσ2
qµ =.
(9.14)
0µ̂ > µFollowing the discussion of Ref. [170] based on Equation (9.14), the simple expression of the p-value for the
hypothesized µ is obtained:√
pµ = 1 − Φ( qµ ),(9.15)

where Φ is the cumulative distribution function for the Gaussian distribution. Thanks to this approximation,
we can estimate the p-value by only one fit.

9.3 Fit inputs
The analysis uses many kinds of fit inputs which are arranged as the product of channel, category, regime
and region for a binned likelihood function 9.1. The channel refers to the analysis with different numbersof leptons in the final states (0-lepton, 1-lepton and 2-lepton). The category refers to the selection for
VBF or ggF signal. The regime refers to the merged and resolved jet analysis objects used in selection andthe region refers to signal (SR) and control regions (CR) which normally consist of subregions of different
properties. The merged regimes of both SR and CR are further split into high-purity (HP) and low-purity(LP) subregions based on the result of the boosted boson tagging. For Z → qq selection in the ggF category(SRWZ in 1-lepton channel and SRZZ in 0- and 2-lepton channels), signal and control regions in both merged
and resolved regimes are further split into untagged (0 or 1 b-tagged jet) and tagged subregions (exactly 2 btagged jets) according to the number of b-tagged jets. For 0-lepton channel, only merged regime is considered101

9.3. Fit inputs(see Section 6.6.1). For each of the final regions, the input to the likelihood is the invariant mass (for 1-leptonand 2-lepton channels) or transverse mass (for the 0-lepton channel) distribution of the V V system.
In the fit of Equation 9.1, resonance signal, W +jets, Z +jets, tt, single-top, diboson and multijet processes
are considered. The detailed description of these processes can be found at Section 3.3.1 and 7. Since whether
or not applying Z → bb tagging depends on the target signal model and the lepton channels, two different fit
configurations are used:• ZZ + W W , to probe for heavy spin-0 and spin-2 gravitons;• ZW , to probe for heavy charged spin-1 vectors (W 0± );The complete list of regions used in each fit model are shown in Tables 9.1–9.2.
Spin-0 and Spin-2 fit model (X → ZZ/W W )Regions

Merged HP
TaggedUntagged
0-lepton

ggF

SR

VBF

SR

ggF

X

X

Merged LP
TaggedUntagged
X

Resolved
TaggedUntagged

X

–

X

X

–

SR
WCR
TopCR

X
One binOne binX
One binOne binX
One binOne bin

VBF

SR
WCR
TopCR

X
One binOne binX
One binOne binX
One binOne bin

ggF

SR
ZCR

VBF

SR
ZCR

1-lepton

2-leptonX
One binX
One binX
One binX
One binX
One binX
One binX
One binX
One binX
One bin

Table 9.1: Summary of the regions entering the likelihood of the fit models to search for heavy resonances decaying
to ZZ and W W in semileptonic final states. “X” indicates that the shape of the final discriminant is taken into
account in the fit. “One bin” implies that a single bin without any shape information is used in the corresponding
fit region and “–” means that the region is not present in the fit.

Spin-1 fit model (X → ZW )Regions

0-lepton

Merged HP
TaggedUntagged

Merged LP
TaggedUntagged

Resolved
TaggedUntagged

ggF

SR

X

X

–

VBF

SR

X

X

–

ggF

SR
WCR
TopCR

VBF

SR
WCR
TopCR

X
One binOne binX
One binOne binX
One binOne binSR
ZCR

X
One binX
One binX
One binSR
ZCR

X
One binX
One binX
One bin

1-lepton

ggF
2-lepton
VBF

X
One binOne binX
One binOne binX
One binOne binX
One binOne binX
One binOne binX
One binOne bin

Table 9.2: Summary of the regions entering the likelihood of the fit models to search for heavy resonances decaying
to ZW in semileptonic final states. “X” indicates that the shape of the final discriminant is taken into account in
the fit. “One bin” implies that a single bin without any shape information is used in the corresponding fit region
and “–” means that the region is not present in the fit.

102

Chapter 9. Statistical Interpretation

9.4 Signal Resolution

χ2 / ndf
69.12 / 35
Constant 0.02372 ± 0.00027
Mean
2996 ± 1.8
Sigma
143.5 ± 2.5

0.025

0.02

Normalised entries

Normalised entries

The appropriate binning of VV invariant mass distribution is determined based on the expected signal mass
resolution. The MC simulated HVT signal is used to estimate the mass resolution for each mass point
separately in for ggF and VBF production and merged and resolved regions. The mass distribution is fit with
20)
dedicated functions. The one and two lepton channels use a Gaussian function, f (m) = A exp( (m−m),
2σ 2where σ is taken as the resolution. In the zero lepton channel, a Landau function is used to fit the transverse
mass distribution. The estimated scale parameter is used as an estimate of the resolution. Figure 9.1 showssome examples of these fits.

χ2 / ndf
639 / 122p00.07841± 0.00069
p1−2911 ± 1.8
p2140.7 ± 1.3

0.018
0.016
0.014
0.012

0.015

0.01
0.008

0.01

0.006
0.004

0.005

0.002
0
0

0
1000

2000

3000

4000

5000
6000
VV Mass [GeV]

0

1000

2000

3000

(a)

4000
5000
6000
VV Transverse Mass [GeV](b)

Figure 9.1: Examples of the invariant VV mass fit with a Gaussian function (1- and 2- lepton) and transverse mass
fit with a Landa function (0-lepton). (a); ggF merged region, mass = 3 TeV in 1-lepton (b) ggF merged region ,mass = 3 TeV in 0-lepton.

χ2 / ndf
546.4 / 15
p00.03683 ± 0.001064
p1
35.91± 2.719

220
200

width

width

The width of each mass peak is then plotted as a function of the resonance mass and fit with a straightline. Some examples of the fit results are shown in Figure 9.2. With the parameterized resolution, the binedges are chosen such that the bins are larger than the mass resolution. In addition, it requires that the
number of background events in the bin is non-zero, and that the relative statistical uncertainty on thenumber of background events in the bin is less than 10%.

180

180

160

160

140

140

120

120

χ2 / ndf
367.6 / 13
p00.04433 ± 0.00137
p1
12.05 ± 2.911

200

100

100

80

80

60

60
40
40
20
20

1000

2000

3000

(a)

4000

5000
Mass [GeV]

500

1000

1500

2000

2500

3000

3500

4000
Mass [GeV](b)

Figure 9.2: The HVT signal mass resolution as a function of mass fit with a straight line in (a) ggF merged 1-leptonand (b) ggF merged 0-lepton channel.

9.5 Nuisance parameters: normalization and systematic uncertainties
In addition to background processes, all the systematic uncertainties denoted in Section 8 also enter the
profile likelihood fit as nuisance parameters (NPs). Two different types of nuisance parameters are used:9.5. Nuisance parameters: normalization and systematic uncertainties

103

floating parameters and parameters with priors. In general, a prior probability distribution is assigned to thesystematic uncertainties. On the other hand, for the most significant backgrounds, the floating parameteris assigned to the normalization since the analysis is designed to constrain them by the dedicated control
regions. The normalization factores for the background contributions are discussed and summarized in
Section 7. Furthermore, there are several extra nuisance parameters which correspond to the uncertainties
on the acceptance or normalization of signal or a certain background component, as discussed in Section 8.2.
The statistical uncertainties for the total background MC samples in each bin are taken into account in
the profile likelihood as an extra nuisance parameter. This is performed by using a light weight version of
the Barlow-Beeston method [173] as implemented in HistFactory [174]. The additional nuisance parameters
for the statistical uncertainty is completely uncorrelated across bins. For the sake of fit stability, bins withthe relative statistical uncertainty less than 1% are ignored in the fit.

9.5.1 Smoothing and Symmterization of Systematic Uncertainties
When estimating systematic uncertainties, there is the possibility to have unsmooth distribution with unphysically large fluctuations due to low MC statistics. This may lead to artificial problems in the fit. In
order to remove such issues, a smoothing procedure composing the following steps is applied to all systematic
variation distribution in all regions.
• Rebin distributions with relative integral statistical error > 5% into a single bin.
• In all of local extrema, the smallest one is identified as a fluctuation and iteratively merged with theneighboring bin until only four local extrema remain.
• Rebin distributions until < 5% statistical uncertainty remain in each bin.
The up/down variations are sometimes in the same directions with respect to the nominal distribution.
In this case, a symmetrization procedure is performed. For up/down systematic variations, if there are morethan 3 bins in the same direction with respect to nominal, the variation is averaged by replacing the variation−|, where bnom is the nominal bin content, and b+ /b− are the original
bin content by bnew
= bnom ± |b+ −b±2
up/down variation bin content. For variations in a region, if the integral of the difference of the up/down
variation is twice that of the other up/down variation, the same procedure is applied to the variation.

9.5.2 Pruning of the Systematic Uncertainties
This analysis consider several kinds of the systemtic uncertainties. However, some of them have a negligible
effect on the final result. In addition, low MC statistics can cause large fluctuations on systematic templates,
which lead to artificial variations in the fit. To remove such effects, a Prunning procedure is applied to remove
uncertainties with negligible effects on the results. Pruning is performed as follows:• Neglect the normalization uncertainty for a given sample in a region if either of the following is true:– the variation is less than 1%;– both up and down variations have the same sign.
• Neglect the shape uncertainty for a given sample in a given region if the following is true:– not one single bin has a deviation over 1% after the overall normalization is removed;– if only the up or the down variation is non-zero and passed the previous pruning steps.
The list of pruned uncertainties is regularly checked to ensure that this is behaving as expected.

9.5.3 Pull and Impact of nuisance parameters
In order to investiage how far a nuisance parameter θ needs to be varied from its expected value θ0 whilefinding MLL, the "Pull" is defined as
Pull(θ) =θ̂ − θ0.
σθ(9.16)

When the pull average is zero with a standard deviation close to 1, we can say the corresponding NP is fine.
If this is not the case, further investigation is required. The expected value of a nuisance parameter and104

Chapter 9. Statistical Interpretation

its assumed standard deviation will be based on an auxiliary measurement or MC studies as discussed in
Section 8.
The impact of a nuisance parameter on signal sensitivities are studied by evaluating the variation of POI(parameter of interest) when fixing a nuisance parameter shifted from its expected value by ± one standard
deviation and keeping other parameters being float. The impact helps to investigate how much our parameterof interest varies when the nuisance parameter is changed.

105

Chapter 10

Results
This section presents the results of the search for new heavy diboson resonances decaying into semi-leptonic
final states, which are obtained from the combined fit of all three lepton channels with the fit configuration
described in Sec. 9. Background only fit (see Section 9.2) results for two different selections are shown:
X → W Z with W Z → ``qq, `νqq, ννqq and X → W W/ZZ with W W → `νqq and ZZ → ``qq, ννqq. In
general, no significant deviations from the post-fit SM predictions are observed. Then the interpretation
results for several benchmark BSM signal models are discussed.

10.1 Search for X → W W/ZZ signal
W W/ZZ background-only fit results are summarized in this section. All regions of the W W/ZZ analysis ofthree lepton channels are included in the fit. Background estimation is derived from a simultaneous fit inboth signal and control regions. All experimental and statistical uncertainties are included. Results of thesearch for W Z analysis can be found in Appendix A since most of the regions are largely overlapped withW W/ZZ analysis.

10.1.1 Post-fit distributions1010

s = 13 TeV, 139 fb

108
107

ZCR

WCR

109

107
106

TCR

105

105

104

104

103

103

102

102

10

10

2-lepton

1-lepton

Data
Z+jetsDibosonTop PairW+jetsSingle-t
MultijetUncertainty

0-lepton

1

VBF HP
VBF LP
VBF Resolved
GGF HPGGF LPGGF Resolved

VBF HP
VBF LP
VBF Resolved
GGF HPGGF LPGGF Resolved

VBF HP
VBF LP
VBF Resolved
GGF HP Tag
GGF LP Tag
GGF Resolved Tag
GGF HP Untag
GGF LP Untag
GGF Resolved Untag

0.9

Prefit/Postfit Data/Postfit

1

1.1

1.4
1.2
1
0.8
0.6

s = 13 TeV, 139 fb-1

1081
Prefit/Postfit Data/Postfit

1010

1.1
1
0.9
1.4
1.2
1
0.8
0.6

VBF HP
VBF LPGGF HP Tag
GGF LP Tag
GGF HP Untag
GGF LP Untag

106

Data
Z+jetsDibosonTop PairW+jetsSingle-t
MultijetUncertainty

VBF HP
VBF LP
VBF Resolved
GGF HPGGF LPGGF Resolved

10-1

VBF HP
VBF LP
VBF Resolved
GGF HP Tag
GGF LP Tag
GGF Resolved Tag
GGF HP Untag
GGF LP Untag
GGF Resolved Untag

9

EventsEventsEvent yields in each signal/control region are summarized in Figure 10.1. Good agreement between observed
data and post-fit predictions is observed in both control regions and signal regions. The final discriminantvariable in the signal regions are shown in Figures 10.2-10.4. No significant deviations from the post-fit
predictions are indicated. Table 10.1 shows the post-fit estimated background event yields from different
sources in all W W/ZZ SRs compared with the number of the observed events in data.

Figure 10.1: Postfit distributions in all (left) control regions and (right) signal regions of the W W/ZZ analysis.

Data
Z+jetsDibosonttbar
W+jetsSingle-t
Uncertainty

104

s=13 TeV, 139 fb-1
ZZ 2-lepton
ggF/DY merged HP

103

Data
Z+jetsDibosonttbar
W+jetsSingle-t
Uncertainty

104

s=13 TeV, 139 fb-1
ZZ 2-lepton
ggF/DY merged LP

103

102

102

10

10

1

1

10−1

10−1

Events / 30 GeV

Chapter 10. Results

Events / 30 GeV

Events / 30 GeV

106

s=13 TeV, 139 fb-1
102

ZZ 2-lepton
ggF/DY merged HP b-tagged

Data
Z+jetsDibosonSingle-tttbar
W+jets
Uncertainty

10

1000

1500

2000

2500

1.4
1.2
1
0.8
0.6
500

1000

1500

2000

2500

800

1000

Data
Z+jetsDibosonttbar
Single-t
W+jets
Uncertainty

s=13 TeV, 139 fb-1
ZZ 2-lepton
ggF/DY merged LP b-tagged

1200

1400

1600

(c)

Data
Z+jetsDibosonttbar
Single-t
W+jets
Uncertainty

105

s=13 TeV, 139 fb-1
104

1800

m(llJ) [GeV](b)
Events / 20 GeV

Events / 30 GeV

600m(llJ) [GeV]

(a)

102

1.4
1.2
1
0.8
0.6

3000

m(llJ) [GeV]ZZ 2-lepton
ggF/DY resolved

103

Events / 20 GeV

1.4
1.2
1
0.8
0.6
500

10−1

Data/Postfit

Data/Postfit

Data/Postfit

1104

s=13 TeV, 139 fb-1
103

ZZ 2-lepton
ggF/DY resolved b-tagged

102

Data
Z+jetsDibosonttbar
Single-t
W+jets
Uncertainty

10
102
10
10

1

1
1

10−1

1.4
1.2
1
0.8
0.6
800

1000

1200

1400

1600

1800

1.4
1.2
1
0.8
0.6

2000

400

600

800

600

800

Data
Z+jetsDibosonttbar
Single-t
W+jets
Uncertainty

s=13 TeV, 139 fb-1
ZZ 2-lepton
VBF merged HP

1000

1200

10

(f)

Data
Z+jetsDibosonttbar
Single-t
W+jets
Uncertainty

s=13 TeV, 139 fb-1
102

1400

m(lljj) [GeV](e)
Events / 30 GeV

Events / 30 GeV

400m(lljj) [GeV]

(d)

102

1.4
1.2
1
0.8
0.6

1000 1200 1400 1600 1800 2000m(llJ) [GeV]ZZ 2-lepton
VBF merged LP

Events / 20 GeV

600

Data/Postfit

10−1

Data/Postfit

Data/Postfit

10−1

104

Data
Z+jetsDibosonttbar
Single-t
W+jets
Uncertainty

s=13 TeV, 139 fb-1
103

ZZ 2-lepton
VBF resolved

102

10

10
1

1
1

10−1

1.4
1.2
1
0.8
0.6
600

800

1000

1200

1400

1600

10−1

Data/Postfit

Data/Postfit

Data/Postfit

10−1

1.4
1.2
1
0.8
0.6
600

800

1000

1200

m(llJ) [GeV]

(g)

1400

1600

1800

1.4
1.2
1
0.8
0.6
400

600

800

1000

m(llJ) [GeV]

(h)

1200

1400

1600
m(lljj) [GeV](i)Figure 10.2: Postfit distributions of the invariant mass in the llqq (a) GGF merged HP ZZ Tag SR (b) GGF
merged HP ZZ Untag SR (c) GGF merged LP ZZ Tag SR (d) GGF merged LP ZZ Untag SR (e) GGF resolved ZZ
Tag SR (f) GGF resolved ZZ Untag SR (g) VBF merged HP ZZ SR (h) VBF merged LP ZZ SR (i) VBF resolved
ZZ SR.

107

Data
W+jetsttbar
DibosonSingle-t
Z+jets
Uncertainty

s=13 TeV, 139 fb-1
WW 1-lepton
ggF/DY merged HP

104

Events / 60 GeV

105

105

s=13 TeV, 139 fb-1

104

WW 1-lepton
ggF/DY merged LP

103

103

102

102

10

10

1

1

10−1

10−1
Data/Postfit

Data/Postfit

Events / 60 GeV

10.1. Search for X → W W/ZZ signal

1.4
1.2
1
0.8
0.6
500

1000

1500

2000

2500

3000

3500

4000

Data
W+jetsttbar
DibosonSingle-t
Z+jets
Uncertainty

1.4
1.2
1
0.8
0.6
500 1000 1500 2000 2500 3000 3500 4000 4500 5000m(lvJ) [GeV]m(lvJ) [GeV]

6

(b)

10

s=13 TeV, 139 fb-1

105

WW 1-lepton
ggF/DY resolved

Data
W+jetsttbar
MultijetSingle-t
DibosonZ+jets
Uncertainty

104

Events / 70 GeV

Events / 40 GeV

(a)
104

Data
W+jetsttbar
DibosonSingle-t
Z+jets
Uncertainty

s=13 TeV, 139 fb-1
103

WW 1-lepton
VBF merged HP

102

3

10

10

102
10

1
1
10−1

Data/Postfit

Data/Postfit

10−1

1.4
1.2
1
0.8
0.6
400

600

800

1000 1200 1400 1600 1800 2000

1.4
1.2
1
0.8
0.6
500

1000

1500

2000

m(lvjj) [GeV]

(d)

104

Data
W+jetsttbar
DibosonSingle-t
Z+jets
Uncertainty

s=13 TeV, 139 fb-1
WW 1-lepton
VBF merged LP

Events / 40 GeV

Events / 70 GeV

3000m(lvJ) [GeV]

(c)

103

2500

105

s=13 TeV, 139 fb-1
104

WW 1-lepton
VBF resolved

103

Data
W+jetsttbar
Single-t
MultijetDibosonZ+jets
Uncertainty

102
102
10
10
1
1

1.4
1.2
1
0.8
0.6
500

10−1

Data/Postfit

Data/Postfit

10−1

1000

1500

2000

2500

3000

1.4
1.2
1
0.8
0.6
400

600

800

1000

m(lvJ) [GeV](e)1200 1400

1600 1800m(lvjj) [GeV](f)

Figure 10.3: Postfit distributions of the invariant mass in the lνqq (a) GGF merged HP WW SR (b) GGF merged
LP WW SR (c) GGF resolved LP WW SR (d) VBF merged HP WW SR (e) VBF merged LP WW SR (f) VBF
resolved LP WW SR.

108

Data
Z+jetsW+jetsttbar
DibosonSingle-t
Uncertainty

105

s=13 TeV, 139 fb-1
ZZ 0-lepton
ggF/DY merged HP

104

105

102

10

10

1

1

10−1

10−1

1000

1500

2000

2500

3000

ZZ 0-lepton
ggF/DY merged LP

104

102

1.4
1.2
1
0.8
0.6
500

3500
mT(vvJ) [GeV]

1.4
1.2
1
0.8
0.6
500

1000

1500

103

ZZ 0-lepton
ggF/DY merged HP b-tagged

Data
ttbar
Z+jetsW+jetsDibosonSingle-t
Uncertainty

103

10

1

1

10−1

10−1

1.4
1.2
1
0.8
0.6
600 800 1000 1200 1400 1600 1800 2000 2200 2400
mT(vvJ) [GeV]ZZ 0-lepton
ggF/DY merged LP b-tagged

1.4
1.2
1
0.8
0.6
500

1000

1500

ZZ 0-lepton
VBF merged HP

Data
Z+jetsW+jetsttbar
DibosonSingle-t
Uncertainty

2000

Data
Z+jetsttbar
W+jetsDibosonSingle-t
Uncertainty

2500
mT(vvJ) [GeV]

104

Data
Z+jetsW+jetsttbar
DibosonSingle-t
Uncertainty

s=13 TeV, 139 fb-1
103

ZZ 0-lepton
VBF merged LP

102

10

10

1

1

10−1

10−1

Data/Postfit

Data/Postfit

102

3500
mT(vvJ) [GeV](d)Events / 70 GeV

Events / 70 GeV

(c)

103

3000

s=13 TeV, 139 fb-1

10

s=13 TeV, 139 fb-1

2500

102

Data/Postfit

Data/Postfit

102

2000

(b)

Events / 40 GeV

Events / 40 GeV(a)s=13 TeV, 139 fb-1

Data
Z+jetsW+jetsttbar
DibosonSingle-t
Uncertainty

s=13 TeV, 139 fb-1

103

Data/Postfit

Data/Postfit

103

Events / 40 GeV

Events / 40 GeV

Chapter 10. Results

1.4
1.2
1
0.8
0.6
600

800

1000 1200 1400 1600 1800 2000 2200
mT(vvJ) [GeV]

(e)

1.4
1.2
1
0.8
0.6
600

800

1000

1200

1400

1600

1800 2000
mT(vvJ) [GeV](f)

Figure 10.4: Postfit distributions of the transverse mass in the ννqq (a) GGF merged HP ZZ Tag SR (b) GGF
merged HP ZZ Untag SR (c) GGF merged LP ZZ Tag SR (d) GGF merged LP ZZ Untag SR (e) VBF merged
HP ZZ SR (f) VBF merged LP ZZ SR.

2-lepton (ZZ)

1-lepton (W W )0-lepton (ZZ)

ChannelResolved

MergedResolved

MergedResolved

MergedResolved

MergedMerged0.01 ± 0.00
0.77 ± 0.01
0.01 ± 0.00
2.34 ± 0.02
04.68 ± 0.03

00.13 ± 0.01
0.27 ± 0.01

HP
LP

Tag
Untag
Tag
Untag

24819 ± 213
60269 ± 309
443515 ± 2444

529 ± 35
1384 ± 56
11365 ± 271

HP
LP

HP
LP

Tag
Untag

LP

HP

LP

HP

Merged134 ± 187669 ± 635
261 ± 34
16450 ± 1353

168 ± 18369 ± 33

HP
LP

recon.

Tag
Untag
Tag
Untag

W + jets

Signalregions

V → qq85.3 ± 6.2
3299 ± 43
138 ± 85923 ± 52
1323 ± 28
42747 ± 174

86.8 ± 6.04
170 ± 81566 ± 34

463 ± 61096 ± 912479 ± 43

8.3 ± 0.58
24.5 ± 1.2
526 ± 11266 ± 61
14276 ± 757
556 ± 645023 ± 387

228 ± 18411 ± 24

Z + jets
51.7 ± 1329.5 ± 50.28 ± 0.03
4.27 ± 0.1
0.31 ± 0.03
10.2 ± 0.2
114 ± 11111 ± 2

21.1 ± 2.5361 ± 35
12.8 ± 1.5
279 ± 28160 ± 141775 ± 133

ggF/DY category

0.08 ± 0.01
0.84 ± 0.08
17 ± 0.8

9.65 ± 1.89
9.9 ± 2.01
72.5 ± 13.6

4917 ± 345
3951 ± 296
16787 ± 1451

VBF category

13885 ± 282
11048 ± 197
126009 ± 1935

141 ± 41151 ± 46582 ± 338

101 ± 132317 ± 273
67.4 ± 9.2
1771 ± 218

ggF/DY category

320 ± 26225 ± 214061 ± 160

VBF category

436 ± 506009 ± 461
341 ± 3928517 ± 1442

ggF/DY category

103 ± 2475 ± 18.6

Diboson113 ± 2483.3 ± 18.7
1074 ± 232

45 ± 9844 ± 151
42.7 ± 8.5
596 ± 10723.9 ± 5.3
21.1 ± 5.2

Single-t0.34 ± 0.06
0.58 ± 0.13
0.3 ± 0.06
2.03 ± 0.39
4.72 ± 1
13.4 ± 2.6

00.43 ± 0.09
0.49 ± 0.38

2831 ± 501
1972 ± 351
21186 ± 3691

Background estimates
VBF category

tt̄

-

-

27124 ± 2321

958 ± 144--

Multijet

107 ± 73667 ± 56
152 ± 86216 ± 59
1602 ± 33
44651 ± 219

96.5 ± 6.3
181 ± 81656 ± 34

46914 ± 703
78335 ± 587
647100 ± 5655

1112 ± 64
1871 ± 77
18586 ± 539

982 ± 82
31116 ± 1134
1269 ± 83
52358 ± 2030

575 ± 38906 ± 46

Total

94
3671
141
6095
1583
44604

101
162
1685

47330
78380
645610

1096
1846
18530

978
31074
1277
52396

589
936

Data

Table 10.1: The expected background events with breakdowns from individual sources in 6 W W and 15 ZZ SRs compared with the data. The backgrounds are estimatedfrom a background-only simultaneous fit to all W W and ZZ SRs and their corresponding CRs.

10.1. Search for X → W W/ZZ signal
109

110

Chapter 10. Results

10.2 Test of background-only hypothesis
Since no significant deviation is observed in the background only post-fit distributions, p0 -value is calculated
for each signal model with all three lepton channels combined, as shown in Figure 10.5. p0 -value is calculated
for ggF and VBF Radion with all three lepton channels combined in X → W W/ZZ, as shown in Figure 10.5a–
10.5b. Results for HVT W 0 in X → W Z analysis are shown in Figure 10.5c and 10.5d. No significant excesses
with respect to the background only hypothesis have been observed. The largest excess is found to be lessthan 3σ of local significance around 1.5 TeV in VBF signal produced. This corresponds to the slight excess
observed in Figure A.3 (g) and Figure A.4 (c). Similar plots for Graviton are also shown in Figure 10.5e–10.5f.
No significant excesses with respect to the background only hypothesis have been observed.

(a)

(b)

(c)

(d)

(e)

(f)

Figure 10.5: Scan of p0 as a function of the resonance mass of (a) ggF Radion, (b) VBF Radion, (c) DY HVT W’,(d) VBF HVT W’, (e) ggF Graviton and (f) VBF Graviton with three lepton channels combined.

111

10.3. Interpretations

10.3 Interpretations
Since there are no significant deviations from background-only hypothesis, 95% CL upper limits on the crosssection times branching ratio are set on several signal models: Spin-0 Radion, Spin-1 HVT and Spin-2 Bulk
RS Graviton.

10.3.1 Results for spin-0 Radion models

σggF(pp→R→VV) [pb]

95% CL upper limits on σ(pp → X) × BR(X → V V ) are set for spin-0 Radions. Both ggF and VBF
production modes are considered. Figure 10.6 shows exclusion limits on σ(pp → X) × BR(X → V V ) for
ggF and VBF Radion with all three lepton channels combined. Comparison of exclusion limits from the
combined fit and each lepton channel is also shown. At the highest-mass region of greater than 3 TeV thesensitivity equally comes from `νqq and ννqq channels, while ``qq channel contributes to it at lower-mass
region. m < 3.45 TeV for spin-0 Radion via ggF production is excluded at 95% CL.

103
102
10

Observed 95% CL
Expected 95% CL
Expected ± 1σ
Expected ± 2σ
Radion2lep Expected 95% CL
1lep Expected 95% CL
0lep Expected 95% CL

s=13 TeV, 139 fb-1
ggF R → WW+ZZ

1
10−1
10−2
10−3
10−4
0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

m(R) [TeV]

σVBF(pp→R→VV) [pb]

(a)

103
102
10

Observed 95% CL
Expected 95% CL
Expected ± 1σ
Expected ± 2σ
Radion2lep Expected 95% CL
1lep Expected 95% CL
0lep Expected 95% CL

s=13 TeV, 139 fb-1
VBF R → WW+ZZ

1
10−1
10−2
10−3
10−4
0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

m(R) [TeV](b)

Figure 10.6: 95% CL upper limit on cross section times branching ratio of Radions produced via (a) ggF and (b)VBF decaying to W W/ZZ pair, with all three lepton channels combined.

112

Chapter 10. Results

10.3.2 Results for spin-1 HVT models

σDY(pp→W'→WZ) [pb]

95% CL upper limits on σ(pp → X) × BR(X → W Z) are set for spin-1 HVT W 0 . Both Drell-Yan and VBF
production modes are considered.
Figure 10.7 shows exclusion limits on σ(pp → X) × BR(X → W Z) for DY and VBF HVT W 0 withall three lepton channels combined. Comparison of exclusion limits from the combined fit and each lepton
channel is also shown. At the highest-mass region of greater than 3 TeV the sensitivity equally comes from`νqq and ννqq channels, while ``qq channel contributes to it at lower-mass region. For the phenomenologicalheavy-vector-triplet benchmark Model A (B) with coupling constant gV = 1 (3) , m(W 0 ) < 4.08 (4.36) TeV
for spin-1 vector triplet produced via DY mode is excluded at 95% CL.

103
2

10

10

Observed 95% CL
Expected 95% CL
Expected ± 1σ
Expected ± 2σ
HVT Model A, g = 1
V
HVT Model B, g = 3
V2lep Expected 95% CL
1lep Expected 95% CL
0lep Expected 95% CL-1

s=13 TeV, 139 fb
DY W' → WZ

1
10−1
10−2
10−3
10−4
0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

m(W') [TeV]

σVBF(pp→W'→WZ) [pb]

(a)

103
102
10

Observed 95% CL
Expected 95% CL
Expected ± 1σ
Expected ± 2σ
HVT Model C, g = 1
V
2lep Expected 95% CL
1lep Expected 95% CL
0lep Expected 95% CL

s=13 TeV, 139 fb-1
VBF W' → WZ

1
10−1
10−2
10−3
10−4
0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

m(W') [TeV](b)

Figure 10.7: 95% CL upper limit on cross section times branching ratio of HVT W 0 produced via (a) DY and (b)VBF decaying to W Z pair, with all three lepton channels combined.

Constraints on the coupling strengths to both quarks and bosons (gq , gH ) have been studied in the context
of HVT models, as shown in Figure 10.8. As with Figure 1.10, the limits are not valid in the shaded region
since resonance would have a width greater than 5% of their mass and the area outside each curve is excluded
for each mass point. The constraints become weak when the couplings for both gH and gf decrease since113

10.3. Interpretations

the resonance couplings to V V and V H decreases as the gH coupling approaches zero, and production of theresonance tends to zero as the gf couplings approach zero.

Fermion coupling gf

1

Observed

0.8

s = 13 TeV
139 fb-1
V' → VV

0.6
0.4

5 TeV
4 TeV

0.2

B
2 TeV

0
−0.2
−0.4
A

−0.6

Γ
m > 5%

−0.8
−1
−3

−2

−1

0

1

2

3

Higgs and vector boson coupling gH(a)Fermion coupling g

f

ATLAS 2 TeV
EW fits 2 TeVATLAS 4 TeV
EW fits 4 TeV

ATLAS 5 TeV
EW fits 5 TeV

1

0.8
0.6
0.4
0.2

Observeds = 13 TeV
139 fb-1
V' → VV
B

0
−0.2
−0.4
A

−0.6
−0.8
−1
−3

−2

−1

0

1

2

3

Higgs and vector boson coupling gH(b)

Figure 10.8: Observed 95% CL exclusion contours in the HVT parameter space {gH , gf } for resonances of mass2, 4 and 5 TeV for the combination of (a) V V channel, and (b) V V channel with the filled regions which show
the constraints from precision EW measurements. The dot A, B in the plots indicate Model A and Model B,
respectively.

114

Chapter 10. Results

10.3.3 Results for spin-2 Graviton models

σggF(pp→GKK→VV) [pb]

95% CL upper limits on σ(pp → X) × BR(X → V V ) are set for spin-2 Graviton. Both ggF and VBF
production modes are considered.
Figure 10.9 shows exclusion limits on σ(pp → X) × BR(X → V V ) for ggF and VBF Graviton withall three lepton channels combined. Comparison of exclusion limits from the combined fit and each lepton
channel is also shown. At the highest-mass region of greater than 3 TeV the sensitivity equally comes from`νqq and ννqq channels, while ``qq channel contributes to it at lower-mass region. For the bulk RandallSundrum model with k/M¯Pl = 1, m(GKK) < 2.0(0.84) TeV for a spin-2 Kaluza-Klein graviton produced via
ggF (VBF) is excluded at 95% CL.

103
102

s=13 TeV, 139 fb-1

10

ggF G

KK

Observed 95% CL
Expected 95% CL
Expected ± 1σ
Expected ± 2σ
GKK , k/ MPl = 1
2lep Expected 95% CL
1lep Expected 95% CL
0lep Expected 95% CL→ WW+ZZ

1
10−1
10−2
10−3
10−4
0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

m(G ) [TeV]KK

σVBF(pp→GKK→VV) [pb]

(a)

103
102

s=13 TeV, 139 fb-1

10

VBF GKK → WW+ZZ

Observed 95% CL
Expected 95% CL
Expected ± 1σ
Expected ± 2σ
GKK , k/ MPl = 1
2lep Expected 95% CL
1lep Expected 95% CL
0lep Expected 95% CL

1
10−1
10−2
10−3
10−4
0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

m(G ) [TeV]KK(b)Figure 10.9: 95% CL upper limit on cross section times branching ratio of Graviton produced via (a) ggF and (b)VBF decaying to W W/ZZ pair, with all three lepton channels combined.

115

10.4. Impact of systematic uncertainties

10.4 Impact of systematic uncertainties
The effects of systematic uncertainties are studied for hypothesized signals using the signal-strength parameterµ. The relative uncertainties in the best-fit µ value from the leading sources of systematic uncertainty are
shown in Table 10.2 for ggF and VBF Radion signal with m(X) = 600 GeV and 2 TeV, respectively. The tables
for spin-1/2 signals can be found in Appendix C. The uncertainties with the largest impact on the sensitivityof the searches are from the size of the MC samples, floating background normalizations, measurements ofsmall-R and large-R jets, and background modeling. The effects of systematic uncertainties for the othersearches are similar to those shown for the ggF Graviton search.
Table 10.2: Ranking of the nuisance parameter impact on the best-fit µ value on ggF Radion with m(X) = 600 GeV
and σ(pp → X) × BR(X → V V ) = 0.01 pb, ggF Radion with m(X) = 2000 GeV and σ(pp → X) × BR(X →V V ) = 0.002 pb, VBF Radion with m(X) = 600 GeV and σ(pp → X) × BR(X → V V ) = 0.01 pb and VBF
Radion with m(X) = 2 TeV and σ(pp → X) × BR(X → V V ) = 0.002 pb, corresponding to approximately the
expected median upper limits at these two mass values.

600 GeV

SourceV +jets Generator difference
MC statistical uncertainty
Z+jets cross-section normalization
Small-R jet JER
VV RF Scale
Small-R jet b-tag efficiency SF
Large-R jet JER
Boson tag SF ttbar ModelingVV cross-section normalization
ttbar cross-section

600 GeV

SourceMC statistical uncertainty
Small-R jet JER
Large-R jet pT scale
V +jets Generator difference
Z+jets cross-section normalization
VV EW contribution
W +jets cross-section
Boson tag SF ttbar Modeling
Boson tag SF b-tag efficiency SF
MET

ggF Radion∆µ0.02940.02190.01470.00950.00900.00860.00720.00610.00570.0044 normalization
VBF Radion∆µ0.01670.00590.00510.00470.00410.00350.00250.00220.00210.0013

2000 GeV
SourceV +jets Generator difference
MC statistical uncertainty
Boson tag SF b-tag effieicny
Large-R jet pT scale
Boson tag SF ttbar Modeling
Boson tag SF Gamma+jet
VV RF Scale
VR track jet b-tag efficiency SF
Boson tag SF Dijet
Boson tag SF other∆µ × 10−3
1.001
0.340
0.180
0.158
0.141
0.138
0.104
0.085
0.082
0.071

2000 GeV

SourceLarge-R jet pT scale
V +jets Generator difference
Boson tag SF b-tag efficiency SF
MC statistical uncertainty
Boson tag SF ttbar Modeling
Boson tag SF other
Small-R jet JER
ttbar PH7
Boson tag SF Gamma+jet
VR track jet b-tag efficiency SF∆µ × 10−3
0.253
0.123
0.113
0.108
0.076
0.051
0.031
0.021
0.020
0.019

116

Chapter 11

Conclusion
Although the discovery of the Higgs boson represents a major milestone in the understanding of electroweak
symmetry breaking, it is also known that the SM is not the ultimate theory due to underlying problems suchas Dark Matter and Hierarchy problem. Several kinds of BSMs are proposed in order to solve them. The
BSMs predict a TeV-scale new particle which can decay into a pair of vector bosons. We have several decay
modes for the diboson resonance: V V → ````, ```ν, `ν`ν, ``νν, ννqq, `νqq, ``qq, and qqqq. Since these final
states can be reconstructed and explored by the ATLAS experiments, it is one of the biggest motivations tosearch for the new heavy diboson resonances at the LHC.
The full-leptonic channels like lllν have better sensitivity in low mV V region, while the full-hadronic
channel (qqqq) shows the compatible sensitivity with `νqq and ννqq channels in high mV V region. However,both full-leptonic and full-hadronic channels can only probe the lower or higher mV V region. On the other
hand, the semi-leptonic channels can probe the broader range of mV V by combining each channel: ννqq,`νqq and ``qq, and therefore it could be the good probe for exploring new physics. In addition, most of theresonance mass produced via VBF is not excluded, and VBF production can be searched by only the semileptonic analysis. In ggF production mode, the higher mass region is still not excluded for most of benchmark
signal models. Therefore sensitivity improvements for higher mass region are significantly important. Since
the semi-leptonic analysis could be a significant indicator of new physics, the analysis improvement for higher
mass region and VBF signal is surely helpful.
To achieve the analysis improvement, the author introduce several new ideas such as TCC (Section 5),variable-radius (VR) track-jet b-tagging for the boosted Z → bb reconstruction (Section 6.5.1), machinelearning (ML) based ggF(DY)/VBF categorization (Section 6.4). The author contributed in the ATLAS
collaboration to all of the developments, in particular the optimization of boson tagging criteria and thecalibration of TCC jets. By introducing the TCC jets, the signal sensitivity is improved by ∼ 30% in highmass region (3–5 TeV).
This thesis presents searches for new heavy √diboson resonances, using pp collision data collected with the
ATLAS detector at a center-of-mass energy of s = 13 TeV in years 2015-18 corresponding to an integrated
luminosity of 139 fb−1 . The semi-leptonic final states of the heavy diboson resonances are used, where oneof the boson pair decays leptonically and the other decays hadronically. The invariant-mass (for 1-leptonand 2-lepton channels) and transverse mass (for the 0-lepton channel) reconstructed by the final-state boson
candidates are used as a final discriminant, and an excess against the estimated SM background is explored.
The observed data is consistent with the SM background expectation and no significant excess is found in
all regions. 95% CL upper limits on the production cross-section times branching ratio, σ × BR (X → V V ),as a function of the new resonance mass are set for various new physics models. For spin-0 Radion via
ggF production, mV V < 3.45 TeV is excluded at 95% CL. For the phenomenological heavy-vector-triplet
benchmark Model A (B) with coupling constant gV = 1 (3) , mV V < 4.08 (4.36) TeV for spin-1 vector
triplet produced via DY mode is excluded at 95% CL. For the bulk Randall-Sundrum model with k/M¯Pl = 1,
mV V < 2.0 (0.84) TeV for a spin-2 Kaluza-Klein graviton produced via ggF (VBF) is excluded at 95% CL.
The mild excess is observed around 1.5 TeV for signals produced via VBF with p0 -value less than 3σ, asshown in Figure 10.6b, 10.7b and 10.9b. This excess is already reported in 36.1 fb−1 results corresponding to
Figure 1.5d, 1.7b and 1.7d and still observed in 139 fb−1 results. Since 1.5 TeV signal via VBF production
mode can be explored by only the semi-leptonic analysis, further improvement is not expected by combining
other channels with full Run 2 dataset. To confirm if the excess is real or not, more data in the LHC Run 3
and further improvement of analysis is needed.

117

Appendix A

Search for X → W Z signal

1010

s = 13 TeV, 139 fb-1

108
107
10

ZCR

WCR

107
106

TCR

105

105

104

104

3

10

103

102

102

10

10

2-lepton

Data
Z+jetsDibosonTop PairW+jetsSingle-t
MultijetUncertainty

1-lepton

0-lepton

1

VBF HP
VBF LP
VBF Resolved
GGF HP Tag
GGF LP Tag
GGF Resolved Tag
GGF HP Untag
GGF LP Untag
GGF Resolved Untag

VBF HP
VBF LP
VBF Resolved
GGF HP Tag
GGF LP Tag
GGF Resolved Tag
GGF HP Untag
GGF LP Untag
GGF Resolved Untag

VBF HP
VBF LP
VBF Resolved
GGF HPGGF LPGGF Resolved

0.9

Prefit/Postfit Data/Postfit

1

1.1

1.4
1.2
1
0.8
0.6

s = 13 TeV, 139 fb-1

1081
Prefit/Postfit Data/Postfit

109

1.1
1
0.9
1.4
1.2
1
0.8
0.6

VBF HP
VBF LPGGF HPGGF LP

61010

VBF HP
VBF LP
VBF Resolved
GGF HP Tag
GGF LP Tag
GGF Resolved Tag
GGF HP Untag
GGF LP Untag
GGF Resolved Untag

10

Data
Z+jetsDibosonTop PairW+jetsSingle-t
MultijetUncertainty

VBF HP
VBF LP
VBF Resolved
GGF HPGGF LPGGF Resolved

9

EventsEventsW Z background-only fit results are summarized in this section. All regions of the W Z analysis of three
lepton channles are included in the fit. Fit values of the nuisance parameters are derived from a fit in bothsignal and control regions. All experimental and statistical uncertainties are included.
Since single-bin control regions are used in the fit, event yields in signal/control region are summarized
in Figure A.1. Good agreement between observed data and post-fit predictions is observed in both control
regions and signal regions. The final discriminant variable in the signal regions are shown in Figures A.2-A.4.
No significant deviations from the post-fit predictions are indicated. Table A.1 shows the post-fit estimatedbackground event yields from different sources in all W Z SRs compared with the number of the observed
events in data.

Figure A.1: Postfit distributions in all (left) control regions and (right) signal regions of the W Z analysis

118

Data
Z+jetsDibosonttbar
Single-t
W+jets
Uncertainty

104

s=13 TeV, 139 fb-1
ZW 2-lepton
ggF/DY merged HP

103

Events / 30 GeV

Events / 30 GeVAppendix A. Search for X → W Z signal

Data
Z+jetsDibosonttbar
W+jetsSingle-t
Uncertainty

s=13 TeV, 139 fb-1
ZW 2-lepton
ggF/DY merged LP

103

102

102

10

10

1

1

10−1

10−1

Data/Postfit

Data/Postfit

104

1.4
1.2
1
0.8
0.6
500

1000

1500

2000

2500

3000

3500

1.4
1.2
1
0.8
0.6
500

1000

1500

2000

2500

m(llJ) [GeV]

(b)

105

s=13 TeV, 139 fb-1
ZW 2-lepton
ggF/DY resolved

103

Data
Z+jetsDibosonttbar
Single-t
W+jets
Uncertainty

Events / 20 GeV

Events / 20 GeV

(a)

104

3000
m(llJ) [GeV]

104

Data
Z+jetsDibosonttbar
Single-t
W+jets
Uncertainty

s=13 TeV, 139 fb-1
103

ZW 2-lepton
VBF resolved

102

102
10
10
1
1

10−1

Data/Postfit

Data/Postfit

10−1

1.4
1.2
1
0.8
0.6
500

1000

1500

1.4
1.2
1
0.8
0.6

2000

400

600

800

1000

m(lljj) [GeV]ZW 2-lepton
VBF merged HP

1600

(d)

Data
Z+jetsDibosonttbar
Single-t
W+jets
Uncertainty

Events / 30 GeV

Events / 30 GeV

102

1400

m(lljj) [GeV](c)s=13 TeV, 139 fb-1

1200

103

s=13 TeV, 139 fb-1
ZW 2-lepton
VBF merged LP

102

Data
Z+jetsDibosonttbar
W+jetsSingle-t
Uncertainty

10
10

1

1

10−1

Data/Postfit

Data/Postfit

10−1

1.4
1.2
1
0.8
0.6
600

800 1000 1200 1400 1600 1800 2000 2200

1.4
1.2
1
0.8
0.6
600

800 1000 1200 1400 1600 1800 2000 2200m(llJ) [GeV](e)m(llJ) [GeV](f)

Figure A.2: Postfit distributions in the llqq (a) GGF merged HP WZ SR (b) GGF merged LP WZ SR (c) GGF
resolved WZ SR (d) VBF merged HP WZ SR (e) VBF merged LP WZ SR (f) VBF resolved WZ SR.

119

-1

s=13 TeV, 139 fb

WZ 1-lepton
ggF/DY merged HP b-tagged

103

Data
ttbar
W+jetsSingle-t
DibosonZ+jets
Uncertainty

104

s=13 TeV, 139 fb-1
103

102

102

10

10

1

1

WZ 1-lepton
ggF/DY merged LP b-tagged

Data
ttbar
W+jetsSingle-t
DibosonZ+jets
Uncertainty

Events / 40 GeV

104

Events / 60 GeV

Events / 60 GeVAppendix A. Search for X → W Z signal

105

s=13 TeV, 139 fb-1
WZ 1-lepton
ggF/DY resolved b-tagged

104

Data
ttbar
W+jetsSingle-t
DibosonMultijet
Z+jets
Uncertainty

103

102

10

1
10−1

1000

1500

2000

2500

3000

3500

4000

Data/Postfit

1.4
1.2
1
0.8
0.6
500

10−1

1000

1500

2000

2500

3000

m(lvJ) [GeV]

Data
W+jetsttbar
DibosonSingle-t
Z+jets
Uncertainty

s=13 TeV, 139 fb-1
WZ 1-lepton
ggF/DY merged HP

104

4000

400

600

800

1000

1200

1400

105

103

103

102

102

10

10

1

1

−1

−1

1800

(c)

Data
W+jetsttbar
DibosonSingle-t
Z+jets
Uncertainty

s=13 TeV, 139 fb-1
WZ 1-lepton
ggF/DY merged LP

104

1600

m(lvjj) [GeV](b)
Events / 60 GeV

Events / 60 GeV

(a)

105

3500

1.4
1.2
1
0.8
0.6

m(lvJ) [GeV]

Events / 40 GeV

1.4
1.2
1
0.8
0.6
500

Data/Postfit

Data/Postfit

10−1

106

s=13 TeV, 139 fb-1

105

WZ 1-lepton
ggF/DY resolved

4

10

Data
W+jetsttbar
MultijetSingle-t
DibosonZ+jets
Uncertainty

103
102

10

1000

1500

2000

2500

3000

3500

4000

Data/Postfit

10

1.4
1.2
1
0.8
0.6

4500

1000

2000

3000

4000

m(lvJ) [GeV]

800 1000 1200 1400 1600 1800 2000 2200
m(lvjj) [GeV]

(e)

Data
W+jetsttbar
DibosonSingle-t
Z+jets
Uncertainty-1s=13 TeV, 139 fb
WZ 1-lepton
VBF merged HP

102

Events / 70 GeV

Events / 70 GeV

400 600m(lvJ) [GeV]

(d)

103

1.4
1.2
1
0.8
0.6

5000

(f)

Data
W+jetsttbar
DibosonSingle-t
Z+jets
Uncertainty-1s=13 TeV, 139 fb
103

WZ 1-lepton
VBF merged LP

102

Events / 40 GeV

1.4
1.2
1
0.8
0.6
500

10
Data/Postfit

Data/Postfit

10

1
−1

105

104

s=13 TeV, 139 fb-1
WZ 1-lepton
VBF resolved

103

Data
W+jetsttbar
Single-t
Multijet
Z+jetsDibosonUncertainty

102
10

10
10

1

1
1

1000

1500

2000

2500

3000

1.4
1.2
1
0.8
0.6
500

10−1

Data/Postfit

1.4
1.2
1
0.8
0.6
500

10−1

Data/Postfit

Data/Postfit

10−1

1000

1500

2000

m(lvJ) [GeV]

(g)

2500

3000

1.4
1.2
1
0.8
0.6
400

600

800

1000

m(lvJ) [GeV](h)1200 1400

1600 1800m(lvjj) [GeV](i)Figure A.3: Postfit distributions in the `νqq (a) merged HP W Z VBF SR and (b) Merged LP W Z VBF SR (c)Resolved W Z VBF SR. Fit is performed using data from all W Z regions.

120

105

Data
Z+jetsttbar
W+jetsDibosonSingle-t
Uncertainty-1s=13 TeV, 139 fb

ZW 0-lepton
ggF/DY merged HP

104

105

s=13 TeV, 139 fb

ZW 0-lepton
ggF/DY merged LP

104

102

102

10

10

1

1

10−1

10−1

1.4
1.2
1
0.8
0.6
500

1000

1500

2000

2500

3000
mT(vvJ) [GeV]

1.4
1.2
1
0.8
0.6
500

1000

1500

10

-1

s=13 TeV, 139 fb
ZW 0-lepton
VBF merged HP

Data
Z+jetsW+jetsttbar
DibosonSingle-t
Uncertainty

103

1

1

10−1

10−1

1.4
1.2
1
0.8
0.6
1000 1200 1400 1600 1800 2000 2200
mT(vvJ) [GeV](c)s=13 TeV, 139 fb
ZW 0-lepton
VBF merged LP

10

800

3000
3500
mT(vvJ) [GeV]

Data
Z+jetsW+jetsttbar
DibosonSingle-t
Uncertainty

-1

10

600

2500

102

Data/Postfit

Data/Postfit

102

2000

(b)

Events / 30 GeV

Events / 30 GeV

(a)

3

Data
Z+jetsW+jetsttbar
DibosonSingle-t
Uncertainty

-1

103

Data/Postfit

Data/Postfit

103

Events / 40 GeV

Events / 40 GeVAppendix A. Search for X → W Z signal

1.4
1.2
1
0.8
0.6
600

800

1000

1200

1400

1600

1800 2000
mT(vvJ) [GeV](d)Figure A.4: Postfit distributions in the ννqq(a) merged HP W Z VBF SR, (b) merged LP W Z VBF SR. Fit isperformed using data from all W Z regions.

2-lepton

1-lepton

0-lepton

ChannelHP
LPrecon.

MergedResolved

MergedResolved

MergedResolved

MergedLP00.31 ± 0.02
0.19 ± 0.01

0.73 ± 0.01
2.98 ± 0.02
8.57 ± 0.06

HP
LP

HP
LP

Tag
Untag

331 ± 4022788 ± 186
577 ± 4341819 ± 222
6217 ± 440
341725 ± 2068

Merged

Tag
Untag
Tag
Untag

482 ± 34988 ± 4410196 ± 247

HP
LPResolved

8103 ± 681
21933 ± 1832HP
LP

175 ± 19475 ± 42

W + jets

MergedHP

Signalregions

V → qq3788 ± 49
8751 ± 71
50005 ± 184

101 ± 7247 ± 111714 ± 32

7.8 ± 0.8428 ± 5
11.6 ± 1.2
765 ± 6183 ± 199961 ± 33

7.7 ± 0.5
20.8 ± 0.9
529 ± 1 115323 ± 814
39265 ± 1956

255 ± 19598 ± 33

Z + jets
40 ± 1040.2 ± 8.7

5.16 ± 0.1
13.6 ± 0.2
116 ± 2445 ± 43388 ± 37
1705 ± 133

ggF/DY category

0.22 ± 0.02
0.76 ± 0.07
12.7 ± 0.6

8.92 ± 1.92
10.6 ± 2
56.8 ± 9.6

100 ± 112998 ± 264
63.8 ± 7.6
2238 ± 202
616 ± 57
14378 ± 1187

VBF category1020 ± 32
11721 ± 194
709 ± 268919 ± 128
38206 ± 391
112923 ± 1974

114 ± 38
112 ± 38383 ± 151

2768 ± 333
2562 ± 300

ggF/DY category

339 ± 25186 ± 184973 ± 206

VBF category

8111 ± 521
7336 ± 473

ggF/DY category

123 ± 2678.2 ± 18.1

Diboson23.3 ± 5.1
18.7 ± 4.5

Single-t

1.38 ± 0.23
2.89 ± 0.51
13.7 ± 2.2

00.27 ± 0.06
0.84 ± 0.3

172 ± 292066 ± 317
152 ± 25
1353 ± 207
3403 ± 540
18202 ± 2716

78.3 ± 16.9
58.6 ± 12.8
1076 ± 235

1041 ± 160
862 ± 131

Background estimates
VBF category

tt̄

-

-

600 ± 128
25513 ± 2078

773 ± 126--

Multijet

4240 ± 66
9159 ± 80
51848 ± 227

110 ± 7259 ± 111784 ± 33

1630 ± 60
40020 ± 492
1514 ± 56
55095 ± 386
49226 ± 811
522702 ± 4613

1020 ± 59
1365 ± 62
17929.3 ± 444

35345 ± 1239
71959 ± 2743

616 ± 39
1210 ± 57

Total

4197
9088
51655

118
243
1831

1699
40193
1559
54735
48919
521813

1018
1313
17826

35426
71892

629
1252

Data

Table A.1: The numbers of observed data events in the 19 W Z SRs are compared with the expected background events with breakdowns from individual sources. The
backgrounds are estimated from a background-only simultaneous fit to all W Z SRs and their corresponding CRs. The uncertainties on the estimated backgrounds combine
statistical and systematic contributions.

Appendix A. Search for X → W Z signal
121

122

Appendix B

Yields Table, Pulls and Correlation
B.1 Background only Fit results for the X → W Z search
Fit values of the nuisance parameters are derived from a fit in both signal and control regions. All experimental
and statistical uncertainties are included.

Yields in Signal and Control Region
A table of all the final value of all floating normalization factors can be found in Tables B.1.
RegionW +jets GGF Merg HP Tag
W +jets GGF Merg HP Untag
W +jets GGF Merg LP Tag
W +jets GGF Merg LP Untag
W +jets GGF Res Tag
W +jets GGF Res Untag
Z+jets GGF Merg HP
Z+jets GGF Merg LP
Z+jets GGF Res
tt̄ GGF Merg HP Tag
tt̄ GGF Merg HP Untag
tt̄ GGF Merg LP Tag
tt̄ GGF Merg LP Untag
tt̄ GGF Res Tag
tt̄ GGF Res Untag
W +jets VBF Merg HP
W +jets VBF Merg LP
W +jets VBF Res
Z+jets VBF Merg HP
Z+jets VBF Merg LP
Z+jets VBF Res
tt̄ VBF Merg HP
tt̄ VBF Merg LP
tt̄ VBF Res

Normalization
0.92 ± 0.114
0.95 ± 0.00753
0.915 ± 0.0694
0.879 ± 0.00462
1.21 ± 0.0859
1.01 ± 0.0061
0.962 ± 0.0118
0.893 ± 0.00698
1.06 ± 0.0035
0.955 ± 0.0272
0.896 ± 0.0147
0.976 ± 0.0329
0.896 ± 0.0128
1.0 ± 0.0102
0.968 ± 0.0169
0.911 ± 0.0618
0.915 ± 0.0398
0.945 ± 0.0211
0.942 ± 0.0593
0.879 ± 0.0366
0.936 ± 0.0166
0.931 ± 0.0665
0.693 ± 0.0643
0.991 ± 0.0404

Table B.1: Fitted values of background normalization factors in the W Z region.

Postfit event yields are summarized in Tab B.2-B.4 for each lepton channel after the combined W Z fit.

Nuisance parameter pulls and constraints
The pull distribution from the fits in all W Z regions using data are shown in Figures B.1.

B.1. Background only Fit results for the X → W Z search123

W Z GGF Untagged WCR
Merged HP
Merged LP
Resolved
Electron Multi-jet
15105.22 ± 2292.09
Muon Multi-jet
28493.93 ± 2747.40
Diboson1499.85 ± 145.64
2737.54 ± 267.69
8959.86 ± 695.06
Single-top
1740.58 ± 267.21
2878.57 ± 446.35
20290.50 ± 3073.01
tt̄
13177.71 ± 216.77
21848.33 ± 311.89
140473.53 ± 2452.46
W +jets
40723.97 ± 322.79
87872.35 ± 462.38
663555.44 ± 4011.61
Z+jets
744.42 ± 9.15
1585.50 ± 12.40
17739.60 ± 58.48
Total
57886.54 ± 493.84 116922.29 ± 762.96 894618.12 ± 6696.22
Data57699.00
117306.00
895362.00
W Z GGF Tagged WCR
Merged HP
Merged LP
Resolved
Electron Multi-jet
384.46 ± 57.11
Muon Multi-jet
614.17 ± 190.78
Diboson30.16 ± 4.51
47.54 ± 6.60
259.72 ± 26.65
Single-top
303.33 ± 49.13
364.84 ± 60.45
5625.30 ± 897.67
tt̄
1685.72 ± 47.98
2048.23 ± 68.96
58454.48 ± 597.34
W +jets
592.30 ± 73.26
1113.22 ± 84.40
11997.53 ± 850.07
Z+jets13.19 ± 1.34
23.05 ± 2.33
324.69 ± 32.84
Total
2624.69 ± 100.53 3596.87 ± 124.83 77660.34 ± 1388.05
Data
2565.00
3546.00
77973.00
W Z VBF WCR
Merged HP
Merged LP
Resolved
Electron Multi-jet
866.19 ± 132.61
Muon Multi-jet
522.95 ± 167.75
Diboson76.75 ± 26.52
133.06 ± 45.66
305.03 ± 116.92
Single-top
85.02 ± 18.46
143.61 ± 31.79
1463.68 ± 320.99
tt̄
415.10 ± 30.54
497.00 ± 46.62
6661.92 ± 271.84
W +jets
897.58 ± 57.07
2047.84 ± 84.41
19084.95 ± 425.96
Z+jets
18.42 ± 1.20
41.62 ± 1.82
761.86 ± 13.55
Total
1492.86 ± 72.35 2863.12 ± 111.35 29666.56 ± 646.49
Data1495.00
2898.00
29755.00
Table B.2: Postfit yield in the `νqq W Z WCR in the (top) GGF Untag, (middle) GGF Tag, and (bottom) VBF
regions from a simultaneous fit in all W Z regions
W Z GGF Untagged TCR
Merged HP
Merged LP
Resolved
Diboson285.05 ± 26.82
342.87 ± 33.14
639.95 ± 62.83
Single-top
3033.37 ± 462.34
2216.99 ± 336.29
9432.03 ± 1507.44
tt̄
31095.54 ± 511.51 26994.93 ± 385.36
92100.61 ± 1607.94
W +jets2240.10 ± 17.76
4885.96 ± 25.71
16065.98 ± 97.13
Z+jets69.27 ± 0.85
140.09 ± 1.10
620.64 ± 2.05
Total36723.33 ± 690.24 34580.84 ± 513.18 118859.20 ± 2207.09
Data36677.00
34573.00
118928.00
W Z GGF Tagged TCR
Merged HP
Merged LP
Resolved
Diboson9.62 ± 1.07
8.73 ± 1.07
34.24 ± 4.82
Single-top
102.51 ± 17.98
115.15 ± 19.73
643.72 ± 118.29
tt̄
1907.09 ± 49.78 1488.68 ± 46.25 17972.40 ± 183.66
W +jets
32.85 ± 4.16
86.02 ± 6.86
493.37 ± 34.96
Z+jets1.27 ± 0.13
1.93 ± 0.20
19.14 ± 1.94
Total
2053.34 ± 53.10 1700.51 ± 50.76 19162.86 ± 221.29
Data
2047.00
1708.00
19143.00
W Z VBF TCR
Merged HP
Merged LP
Resolved
Diboson12.26 ± 4.44
10.48 ± 3.83
15.80 ± 6.44
Single-top
64.76 ± 14.27
41.71 ± 9.21
236.26 ± 56.86
tt̄
456.43 ± 30.06 292.72 ± 25.47
2345.71 ± 82.77
W +jets
51.16 ± 3.84
111.50 ± 5.75
378.31 ± 11.82
Z+jets1.21 ± 0.08
4.24 ± 0.20
16.78 ± 0.40
Total
585.81 ± 33.79 460.65 ± 27.95 2992.86 ± 101.31
Data
584.00459.003001.00
Table B.3: Postfit yield in the `νqq W Z TCR in the (top) GGF Untag, (middle) GGF Tag and (bottom) VBF
regions from a simultaneous fit in all W Z regions

ConstraintPdf_SigAcc_ISRFSR_llqq(c)

MJ_ttbar_lvqq_ResVBF

MJ_ttbar_lvqq_ResGGF= 0.002(θfit - θ0) / ∆θ(θfit - θ0) / ∆θ

2

(a)
(b)

FATJET_JER
FATJET_Medium_JET_Rtrk_Baseline_pT
FATJET_Medium_JET_Rtrk_Closure_pT
FATJET_Medium_JET_Rtrk_Modelling_pT
FATJET_Medium_JET_Rtrk_TotalStat_pT
FATJET_Medium_JET_Rtrk_Tracking_pT
FT_EFF_Eigen_B_0_AntiKt4EMTopoJets
FT_EFF_Eigen_B_0_AntiKtVR30Rmax4Rmin02TrackJets
FT_EFF_Eigen_B_1_AntiKt4EMTopoJets
FT_EFF_Eigen_B_1_AntiKtVR30Rmax4Rmin02TrackJets
FT_EFF_Eigen_B_2_AntiKt4EMTopoJets
FT_EFF_Eigen_C_0_AntiKt4EMTopoJets
FT_EFF_Eigen_C_0_AntiKtVR30Rmax4Rmin02TrackJets
FT_EFF_Eigen_C_1_AntiKt4EMTopoJets
FT_EFF_Eigen_C_1_AntiKtVR30Rmax4Rmin02TrackJets
FT_EFF_Eigen_C_2_AntiKtVR30Rmax4Rmin02TrackJets
FT_EFF_Eigen_Light_0_AntiKt4EMTopoJets
FT_EFF_Eigen_Light_0_AntiKtVR30Rmax4Rmin02TrackJets
FT_EFF_Eigen_Light_1_AntiKt4EMTopoJets
FT_EFF_Eigen_Light_1_AntiKtVR30Rmax4Rmin02TrackJets
FT_EFF_Eigen_Light_2_AntiKt4EMTopoJets
FT_EFF_extrapolation_from_charm_AntiKt4EMTopoJets
JET_BGSF_Dijet_Modelling
JET_BGSF_Dijet_Stat
JET_BGSF_Gammajet_Modelling
JET_BGSF_Gammajet_Stat
JET_CR_JET_BJES_Response
JET_CR_JET_EffectiveNP_Detector1
JET_CR_JET_EffectiveNP_Detector2
JET_CR_JET_EffectiveNP_Mixed1
JET_CR_JET_EffectiveNP_Mixed2
JET_CR_JET_EffectiveNP_Mixed3
JET_CR_JET_EffectiveNP_Modelling1
JET_CR_JET_EffectiveNP_Modelling2
JET_CR_JET_EffectiveNP_Modelling3
JET_CR_JET_EffectiveNP_Modelling4
JET_CR_JET_EffectiveNP_Statistical1
JET_CR_JET_EffectiveNP_Statistical2
JET_CR_JET_EffectiveNP_Statistical3
JET_CR_JET_EffectiveNP_Statistical4
JET_CR_JET_EffectiveNP_Statistical5
JET_CR_JET_EffectiveNP_Statistical6
JET_CR_JET_EtaIntercalibration_Modelling
JET_CR_JET_EtaIntercalibration_TotalStat
JET_CR_JET_Flavor_Composition
JET_CR_JET_Flavor_Response
JET_CR_JET_JER_DataVsMC
JET_CR_JET_JER_EffectiveNP_1
JET_CR_JET_JER_EffectiveNP_2
JET_CR_JET_JER_EffectiveNP_3
JET_CR_JET_JER_EffectiveNP_4
JET_CR_JET_JER_EffectiveNP_5
JET_CR_JET_JER_EffectiveNP_6
JET_CR_JET_JER_EffectiveNP_7restTerm
JET_CR_JET_Pileup_OffsetMu
JET_CR_JET_Pileup_OffsetNPV
JET_CR_JET_Pileup_PtTerm
JET_CR_JET_Pileup_RhoTopology
JET_SigSF_V_qq_Modelling_highPt
JET_SigSF_ttbar_Modelling_bTagB_0
JET_SigSF_ttbar_Modelling_bTagB_1
JET_SigSF_ttbar_Modelling_bTagLight_0
JET_SigSF_ttbar_Modelling_hadronisation
JET_SigSF_ttbar_Modelling_matrixElement
JET_SigSF_ttbar_Modelling_radiation
JET_SigSF_ttbar_Stat
Nonclosure_GGF_SR_wjets_vvqq_MergGGF
Nonclosure_GGF_SR_zjets_vvqq_MergGGF
Nonclosure_VBF_SR_wjets_vvqq_MergVBF
Nonclosure_VBF_SR_zjets_vvqq_MergVBF

XS_Zjets_Tag_lvqq_ResGGF

XS_Zjets_Tag_lvqq_MergGGF

XS_MJ_mu_lvqq_ResVBF

XS_MJ_mu_lvqq_ResGGF

XS_MJ_mu_Tag_lvqq_ResGGF

XS_MJ_el_lvqq_ResVBF

XS_MJ_el_lvqq_ResGGF

XS_MJ_el_Tag_lvqq_ResGGF

XS_Zjets_Res_VBF

XS_Zjets_Res_GGF

XS_Zjets_Merg_VBF= 0.00
4

0
0

−2
−2

−4
−4

4

0
0

−2
−2

−4
−4

VV_AlphaS_llqq_MergGGF
VV_AlphaS_llqq_MergVBF
VV_AlphaS_llqq_ResGGF
VV_AlphaS_llqq_ResVBF
VV_AlphaS_lvqq_MergGGF
VV_AlphaS_lvqq_MergVBF
VV_AlphaS_lvqq_ResGGF
VV_AlphaS_lvqq_ResVBF
VV_AlphaS_vvqq_MergGGF
VV_AlphaS_vvqq_MergVBF
VV_CT14_llqq_MergVBF
VV_CT14_lvqq_MergVBF
VV_MMHT_llqq_MergVBF
VV_MMHT_lvqq_MergVBF
VV_PDFVar_llqq_MergVBF
VV_PDFVar_llqq_ResGGF
VV_PDFVar_lvqq_MergGGF
VV_PDFVar_lvqq_MergVBF
VV_PDFVar_lvqq_ResGGF
VV_PDFVar_lvqq_ResVBF
VV_PDFVar_vvqq_MergGGF
VV_PDFVar_vvqq_MergVBF
VV_RFScale_llqq_MergGGF
VV_RFScale_llqq_MergVBF
VV_RFScale_llqq_ResGGF
VV_RFScale_llqq_ResVBF
VV_RFScale_lvqq_MergGGF
VV_RFScale_lvqq_MergVBF
VV_RFScale_lvqq_ResGGF
VV_RFScale_lvqq_ResVBF
VV_RFScale_vvqq_MergGGF
VV_RFScale_vvqq_MergVBF
Vjets_AlphaS_lvqq_MergVBF
Vjets_AlphaS_lvqq_ResVBF
Vjets_CT14_llqq_MergGGF
Vjets_CT14_lvqq_MergGGF
Vjets_CT14_vvqq_MergGGF
Vjets_GenMG_llqq_MergGGF
Vjets_GenMG_llqq_MergVBF
Vjets_GenMG_llqq_ResGGF
Vjets_GenMG_llqq_ResVBF
Vjets_GenMG_lvqq_MergGGF
Vjets_GenMG_lvqq_MergVBF
Vjets_GenMG_lvqq_ResGGF
Vjets_GenMG_lvqq_ResVBF
Vjets_GenMG_vvqq_MergGGF
Vjets_GenMG_vvqq_MergVBF
Vjets_MMHT_llqq_MergGGF
Vjets_MMHT_lvqq_MergGGF
Vjets_MMHT_vvqq_MergGGF
Vjets_PDFVar_llqq_MergGGF
Vjets_PDFVar_lvqq_MergGGF
Vjets_PDFVar_lvqq_MergVBF
Vjets_PDFVar_vvqq_MergGGF
Vjets_RFScale_llqq_MergGGF
Vjets_RFScale_llqq_MergVBF
Vjets_RFScale_llqq_ResVBF
Vjets_RFScale_lvqq_MergGGF
Vjets_RFScale_lvqq_MergVBF
Vjets_RFScale_lvqq_ResVBF
Vjets_RFScale_vvqq_MergGGF
Vjets_RFScale_vvqq_MergVBF
ttbar_FSR_lvqq_MergGGF
ttbar_FSR_lvqq_MergVBF
ttbar_FSR_lvqq_ResVBF
ttbar_FSR_vvqq_MergGGF
ttbar_ISR_lvqq_MergGGF
ttbar_ISR_lvqq_MergVBF
ttbar_ISR_lvqq_ResGGF
ttbar_ISR_lvqq_ResVBF
ttbar_ISR_vvqq_MergGGF
ttbar_PH7_llqq_ResGGF
ttbar_PH7_lvqq_MergGGF
ttbar_PH7_lvqq_MergVBF
ttbar_PH7_lvqq_ResGGF
ttbar_PH7_lvqq_ResVBF
ttbar_PH7_vvqq_MergGGF
ttbar_aMC_llqq_ResGGF
ttbar_aMC_lvqq_MergGGF
ttbar_aMC_lvqq_MergVBF
ttbar_aMC_lvqq_ResGGF
ttbar_aMC_lvqq_ResVBF
ttbar_aMC_vvqq_MergGGF

lumiNP

Nonclosure_VBF_SR_ttbar_vvqq_MergVBF

Nonclosure_GGF_SR_ttbar_vvqq_MergGGF

fixed

MJ_W_lvqq_ResVBF

µ
fixed

MJ_W_lvqq_ResGGF

s=13 TeV, 139 fb-1
XS_Zjets_Merg_GGF

XS_Zjets_LP_Merg_VBF

XS_Zjets_LP_Merg_GGF

XS_Wjets_Tag_lvqq_ResGGF

XS_Wjets_Tag_lvqq_MergGGF

XS_Wjets_Res_VBF

XS_Wjets_Res_GGF

XS_Wjets_Merg_VBF

XS_Wjets_Merg_GGF

XS_Wjets_LP_Tag_lvqq_MergGGF

XS_Wjets_LP_Merg_VBF

XS_Wjets_LP_Merg_GGF

XS_Top_Tag_lvqq_ResGGF

XS_Top_Tag_lvqq_MergGGF

XS_Top_Res_VBF

XS_Top_Res_GGF

XS_Top_Merg_VBF

XS_Top_Merg_GGF

XS_Top_LP_Tag_lvqq_MergGGF

XS_Top_LP_Merg_VBF

XS_Top_LP_Merg_GGF

XS_SingleTop_VBFµ

Diboson_EWcontribution_lvqq_ResVBF

XS_Dibosons_VBF

XS_Dibosons_GGF

s=13 TeV, 139 fb-1

Diboson_EWcontribution_lvqq_MergVBF

PRW_DATASFMUON_SAGITTA_RESBIASMUON_MSMUON_ID

MET_SoftTrk_Scale

MET_SoftTrk_ResoPerp

MET_SoftTrk_ResoPara

EL_EFF_Trigger_TOTAL_1NPCOR_PLUS_UNCOR

EL_EFF_Iso_TOTAL_1NPCOR_PLUS_UNCOR

EL_EFF_ID_TOTAL_1NPCOR_PLUS_UNCOR

EG_SCALE_ALL

EG_RESOLUTION_ALL

ConstraintPdf_SigAcc_PDF_vvqq

ConstraintPdf_SigAcc_PDF_lvqq

ConstraintPdf_SigAcc_PDF_llqq

ConstraintPdf_SigAcc_ISRFSR_vvqq

4
XS_SingleTop_GGF(θfit - θ0) / ∆θ4ConstraintPdf_SigAcc_ISRFSR_lvqq(θfit - θ0) / ∆θ124
Appendix B. Yields Table, Pulls and CorrelationW Z GGF ZCRMerged HP
Merged LP
Resolved
Diboson212.73 ± 21.22
383.79 ± 37.93
1095.52 ± 84.04
Single-top
1.20 ± 0.25
2.58 ± 0.48
20.25 ± 3.36
tt̄
7.67 ± 0.13
20.41 ± 0.29
181.37 ± 3.17
W +jets
1.53 ± 0.01
7.79 ± 0.04
10.43 ± 0.06
Z+jets5982.12 ± 73.54 13013.78 ± 101.77 82819.46 ± 273.03
Total
6205.25 ± 76.54 13428.35 ± 108.61 84127.03 ± 285.71
Data6210.00
13531.00
84316.00
W Z VBF ZCRMerged HP
Merged LP
Resolved
Diboson5.08 ± 1.05
10.41 ± 2.08
61.41 ± 10.05
Single-top
0.00 ± 0.00
0.59 ± 0.12
2.75 ± 0.80
tt̄
0.57 ± 0.04
1.09 ± 0.10
28.92 ± 1.23
W +jets
0.02 ± 0.00
0.20 ± 0.01
0.32 ± 0.01
Z+jets
171.13 ± 10.56 368.89 ± 15.12 3635.61 ± 55.51
Total
176.80 ± 10.62 381.18 ± 15.27 3729.02 ± 56.44
Data
163.00374.003685.00

Table B.4: Postfit yield in the ``qq W Z CR in the (top) GGF and (bottom) VBF regions from a simultaneous fit
in all W Z regionss=13 TeV, 139 fb-1

2µ

s=13 TeV, 139 fb-1

µ

fixed

fixed

= 0.002= 0.00(d)

Figure B.1: Pull distributions for the nuisance parameters (a) Jet relevant NPs (b) Other experimantal NPs (c)Theory NPs (d) XS NPs.

Correlation matrices

The correlation matrix from the fits in all regions using data is shown in Figures B.2. Only nuisance paramterswith more than a cross-correlation 0.25 positive or negative correlation are shown. Visible off-diagonally correlations come from normalization, which are expected to be anti-correlated, and the large-R jet experimental
systematics, which are expect to be constrained.

125

B.1. Background only Fit results for the X → W Z search
s=13 TeV, 139 fb-1
1

EL_EFF_Iso_TOTAL_1NPCOR_PLUS_UNCOR
FATJET_Medium_JET_Rtrk_Baseline_pT
FATJET_Medium_JET_Rtrk_Closure_pT
FATJET_Medium_JET_Rtrk_Modelling_pT
FATJET_Medium_JET_Rtrk_Tracking_pT
FT_EFF_Eigen_B_0_AntiKt4EMTopoJets
FT_EFF_Eigen_C_0_AntiKt4EMTopoJets
FT_EFF_Eigen_Light_0_AntiKt4EMTopoJets
JET_CR_JET_EffectiveNP_Modelling1
JET_CR_JET_Flavor_Composition
JET_CR_JET_Flavor_Response
JET_CR_JET_JER_EffectiveNP_1
JET_CR_JET_JER_EffectiveNP_2
JET_CR_JET_JER_EffectiveNP_3
JET_CR_JET_JER_EffectiveNP_5
JET_CR_JET_JER_EffectiveNP_7restTerm
JET_SigSF_ttbar_Modelling_hadronisation
JET_SigSF_ttbar_Modelling_matrixElement
XS_Dibosons_GGF
XS_SingleTop_GGF
XS_SingleTop_VBF
XS_Top_LP_Merg_GGF
XS_Top_LP_Merg_VBF
XS_Top_LP_Tag_lvqq_MergGGF
XS_Top_Merg_GGF
XS_Top_Merg_VBF
XS_Top_Res_GGF
XS_Top_Res_VBF
XS_Top_Tag_lvqq_MergGGF
XS_Top_Tag_lvqq_ResGGF
XS_Wjets_LP_Merg_GGF
XS_Wjets_LP_Merg_VBF
XS_Wjets_LP_Tag_lvqq_MergGGF
XS_Wjets_Merg_GGF
XS_Wjets_Merg_VBF
XS_Wjets_Res_GGF
XS_Wjets_Res_VBF
XS_Wjets_Tag_lvqq_MergGGF
XS_Wjets_Tag_lvqq_ResGGF
XS_Zjets_LP_Merg_GGF
XS_Zjets_LP_Merg_VBF
XS_Zjets_Merg_GGF
XS_Zjets_Res_GGF
XS_Zjets_Res_VBF
Diboson_EWcontribution_lvqq_MergVBF
Nonclosure_GGF_SR_ttbar_vvqq_MergGGF
Nonclosure_GGF_SR_wjets_vvqq_MergGGF
Nonclosure_GGF_SR_zjets_vvqq_MergGGF
Nonclosure_VBF_SR_ttbar_vvqq_MergVBF
Nonclosure_VBF_SR_wjets_vvqq_MergVBF
Nonclosure_VBF_SR_zjets_vvqq_MergVBF
XS_MJ_el_lvqq_ResGGF
XS_MJ_el_lvqq_ResVBF
XS_MJ_mu_lvqq_ResGGF
XS_MJ_mu_lvqq_ResVBF
VV_RFScale_llqq_MergGGF
VV_RFScale_llqq_ResGGF
VV_RFScale_lvqq_MergGGF
VV_RFScale_lvqq_MergVBF
VV_RFScale_vvqq_MergGGF
Vjets_GenMG_llqq_ResGGF
Vjets_GenMG_lvqq_MergGGF
Vjets_GenMG_lvqq_ResGGF
Vjets_GenMG_vvqq_MergGGF
Vjets_RFScale_vvqq_MergGGF
ttbar_ISR_lvqq_ResGGF
ttbar_PH7_lvqq_ResGGF
ttbar_aMC_lvqq_ResGGF

0.8
0.6
0.4
0.2
0
−0.2
−0.4
−0.6

EL_EFF_Iso_TOTAL_1NPCOR_PLUS_UNCOR
FATJET_Medium_JET_Rtrk_Baseline_pT
FATJET_Medium_JET_Rtrk_Closure_pT
FATJET_Medium_JET_Rtrk_Modelling_pT
FATJET_Medium_JET_Rtrk_Tracking_pT
FT_EFF_Eigen_B_0_AntiKt4EMTopoJets
FT_EFF_Eigen_C_0_AntiKt4EMTopoJets
FT_EFF_Eigen_Light_0_AntiKt4EMTopoJets
JET_CR_JET_EffectiveNP_Modelling1
JET_CR_JET_Flavor_Composition
JET_CR_JET_Flavor_Response
JET_CR_JET_JER_EffectiveNP_1
JET_CR_JET_JER_EffectiveNP_2
JET_CR_JET_JER_EffectiveNP_3
JET_CR_JET_JER_EffectiveNP_5
JET_CR_JET_JER_EffectiveNP_7restTerm
JET_SigSF_ttbar_Modelling_hadronisation
JET_SigSF_ttbar_Modelling_matrixElement
XS_Dibosons_GGF
XS_SingleTop_GGF
XS_SingleTop_VBF
XS_Top_LP_Merg_GGF
XS_Top_LP_Merg_VBF
XS_Top_LP_Tag_lvqq_MergGGF
XS_Top_Merg_GGF
XS_Top_Merg_VBF
XS_Top_Res_GGF
XS_Top_Res_VBF
XS_Top_Tag_lvqq_MergGGF
XS_Top_Tag_lvqq_ResGGF
XS_Wjets_LP_Merg_GGF
XS_Wjets_LP_Merg_VBF
XS_Wjets_LP_Tag_lvqq_MergGGF
XS_Wjets_Merg_GGF
XS_Wjets_Merg_VBF
XS_Wjets_Res_GGF
XS_Wjets_Res_VBF
XS_Wjets_Tag_lvqq_MergGGF
XS_Wjets_Tag_lvqq_ResGGF
XS_Zjets_LP_Merg_GGF
XS_Zjets_LP_Merg_VBF
XS_Zjets_Merg_GGF
XS_Zjets_Res_GGF
XS_Zjets_Res_VBF
Diboson_EWcontribution_lvqq_MergVBF
Nonclosure_GGF_SR_ttbar_vvqq_MergGGF
Nonclosure_GGF_SR_wjets_vvqq_MergGGF
Nonclosure_GGF_SR_zjets_vvqq_MergGGF
Nonclosure_VBF_SR_ttbar_vvqq_MergVBF
Nonclosure_VBF_SR_wjets_vvqq_MergVBF
Nonclosure_VBF_SR_zjets_vvqq_MergVBF
XS_MJ_el_lvqq_ResGGF
XS_MJ_el_lvqq_ResVBF
XS_MJ_mu_lvqq_ResGGF
XS_MJ_mu_lvqq_ResVBF
VV_RFScale_llqq_MergGGF
VV_RFScale_llqq_ResGGF
VV_RFScale_lvqq_MergGGF
VV_RFScale_lvqq_MergVBF
VV_RFScale_vvqq_MergGGF
Vjets_GenMG_llqq_ResGGF
Vjets_GenMG_lvqq_MergGGF
Vjets_GenMG_lvqq_ResGGF
Vjets_GenMG_vvqq_MergGGF
Vjets_RFScale_vvqq_MergGGF
ttbar_ISR_lvqq_ResGGF
ttbar_PH7_lvqq_ResGGF
ttbar_aMC_lvqq_ResGGF−0.8

Figure B.2:
Correlation matrix for the nuisance
HP+LP+Res,Tag+Untag, 0+1+2-lepton fit using data.

parameters

for

the

final

A summary of exclusion limits for HVT W 0 can be found in Tables ??-??.
Table B.5: A summary of exclusion limits for HVT W 0 from W Z fit.
M [GeV]
400
500
600
700
800
1000
1200
1400
1500
1600
1800
2000
2400
2600
3000
3500
4000
4500
5000

Observed [pb]2.17E-01
1.37E-01
1.21E-01
7.44E-02
2.03E-02
2.68E-02
1.05E-02
3.94E-03
3.12E-03
3.24E-03
2.97E-03
2.94E-03
1.17E-03
7.48E-04
4.75E-04
2.19E-04
1.69E-04
1.49E-04
1.24E-04

Expected [pb]3.93E-01
2.14E-01
9.88E-02
5.55E-02
3.39E-02
1.69E-02
8.34E-03
5.00E-03
3.96E-03
3.19E-03
2.46E-03
1.60E-03
9.40E-04
6.97E-04
5.22E-04
3.61E-04
2.60E-04
2.24E-04
1.63E-04±1σ [pb]
1.54E−01
1.10E−01
8.40E−02
5.99E−02
3.87E−02
2.76E−02
2.17E−02
1.55E−02
1.33E−02
9.46E−03
6.60E−03
4.71E−03
3.27E−03
2.33E−03
1.96E−03
1.40E−03
1.55E−03
1.11E−03
1.25E−03
8.92E−04
9.65E−04
6.89E−04
6.26E−04
4.47E−04
3.68E−04
2.63E−04
2.73E−04
1.95E−04
2.04E−04
1.46E−04
1.41E−04
1.01E−04
1.02E−04
7.27E−05
8.76E−05
6.25E−05
6.40E−05
4.57E−05±2σ [pb]
3.40E−01
1.82E−01
1.86E−01
9.94E−02
8.55E−02
4.58E−02
4.80E−02
2.57E−02
2.93E−02
1.57E−02
1.46E−02
7.81E−03
7.22E−03
3.86E−03
4.33E−03
2.31E−03
3.43E−03
1.84E−03
2.76E−03
1.48E−03
2.13E−03
1.14E−03
1.38E−03
7.40E−04
8.14E−04
4.35E−04
6.03E−04
3.23E−04
4.52E−04
2.42E−04
3.13E−04
1.67E−04
2.25E−04
1.21E−04
1.94E−04
1.04E−04
1.41E−04
7.57E−05−1

WZ

GGF+VBF,

126

Appendix B. Yields Table, Pulls and Correlation

Table B.6: A summary of exclusion limits for HVT VBF W 0 from W Z fit.
M [GeV]
300
400
600
700
800
1000
1200
1500
1800
2000
2400
2600
3000
3500
4000

Observed [pb]1.29E+00
2.43E-01
6.71E-02
6.11E-02
2.26E-02
2.22E-02
8.43E-03
9.18E-03
4.71E-03
2.19E-03
1.14E-03
9.47E-04
6.42E-04
3.61E-04
3.04E-04

Expected [pb]1.80E+00
3.98E-01
7.06E-02
4.08E-02
2.40E-02
1.12E-02
6.09E-03
3.53E-03
2.16E-03
1.61E-03
1.15E-03
9.11E-04
7.10E-04
5.34E-04
4.59E-04±1σ [pb]
7.04E−01
5.03E−01
1.56E−01
1.11E−01
2.76E−02
1.97E−02
1.60E−02
1.14E−02
9.40E−03
6.70E−03
4.40E−03
3.14E−03
2.39E−03
1.70E−03
1.38E−03
9.86E−04
8.46E−04
6.04E−04
6.32E−04
4.51E−04
4.49E−04
3.20E−04
3.57E−04
2.55E−04
2.78E−04
1.99E−04
2.09E−04
1.49E−04
1.80E−04
1.28E−04±2σ [pb]
1.56E+00
8.33E−01
3.45E−01
1.85E−01
6.11E−02
3.27E−02
3.53E−02
1.89E−02
2.08E−02
1.11E−02
9.72E−03
5.20E−03
5.27E−03
2.82E−03
3.05E−03
1.63E−03
1.87E−03
1.00E−03
1.40E−03
7.48E−04
9.92E−04
5.31E−04
7.89E−04
4.22E−04
6.15E−04
3.29E−04
4.63E−04
2.48E−04
3.98E−04
2.13E−04

B.2. Background only Fit results for the X → W W/ZZ search

127

B.2 Background only Fit results for the X → W W/ZZ search
Fit values of the nuisance parameters are derived from a fit in both signal and control regions. All experimental
and statistical uncertainties are included. S

Yields in Signal and Control Region
A table of all the final value of all floating normalization factors can be found in Tables B.7.
RegionW +jets GGF Merg HP
W +jets GGF Merg LP
W +jets GGF Res
Z+jets GGF Merg HP
Z+jets GGF Merg LP
Z+jets GGF Res
tt̄ GGF Merg HP
tt̄ GGF Merg LP
tt̄ GGF Res
W +jets VBF Merg HP
W +jets VBF Merg LP
W +jets VBF Res
Z+jets VBF Merg HP
Z+jets VBF Merg LP
Z+jets VBF Res
tt̄ VBF Merg HP
tt̄ VBF Merg LP
tt̄ VBF Res

Normalization
0.934 ± 0.00788
0.886 ± 0.00455
1.02 ± 0.00562
0.963 ± 0.0118
0.889 ± 0.00714
1.06 ± 0.00361
0.942 ± 0.019
0.908 ± 0.00162
0.949 ± 0.0146
0.934 ± 0.0599
0.905 ± 0.0369
0.929 ± 0.0195
0.909 ± 0.0605
0.85 ± 0.0378
0.928 ± 0.017
0.847 ± 0.0644
0.767 ± 0.0675
0.973 ± 0.0361

Table B.7: Fitted values of background normalization factors in the W W ZZ region.

fit.

Postfit event yields are summarized in Tab ??-B.10 for each lepton channel after the combined W W ZZ

Nuisance parameter pulls and constraints
The pull distribution from the fits in all W W/ZZ regions using data are shown in Figures B.3.

Correlation matrices
The correlation matrix from the fits in all regions using data is shown in Figures B.4. Only nuisance paramterswith more than a cross-correlation 0.25 positive or negative correlation are shown. Visible off-diagonally correlations come from normalization, which are expected to be anti-correlated, and the large-R jet experimental
systematics, which are expect to be constrained.
A summary of exclusion limits for spin-0/2 signals can be found in Tables B.11-B.14.

128

Appendix B. Yields Table, Pulls and Correlation

W W GGF WCR
Merged HP
Merged LP
Resolved
Electron Multi-jet
16462.82 ± 2306.77
Muon Multi-jet
20745.21 ± 2618.33
Diboson1849.20 ± 166.53
3433.12 ± 307.53
8587.28 ± 718.49
Single-top
2048.82 ± 368.16
3382.40 ± 605.16
20442.62 ± 3712.72
tt̄
15627.72 ± 315.41
24159.79 ± 430.27
137818.89 ± 2115.56
W +jets
40300.21 ± 338.28
88368.52 ± 451.96
672246.81 ± 3706.95
Z+jets753.24 ± 9.24
1576.65 ± 12.67
17694.56 ± 60.25
Total
60579.19 ± 614.23 120920.48 ± 922.15 893998.19 ± 6685.66
Data60264.00
120852.00
895362.00
W W VBF WCR
Merged HP
Merged LP
Resolved
SignalElectron Multi-jet
886.59 ± 136.47
Muon Multi-jet
474.05 ± 144.25
Diboson73.37 ± 23.62
129.05 ± 41.54
426.21 ± 250.72
Single-top
103.42 ± 22.29
183.64 ± 40.16
1215.74 ± 268.92
tt̄
378.80 ± 29.86
547.21 ± 49.06
4843.50 ± 182.68
W +jets
912.11 ± 54.35
1986.92 ± 77.44
18499.61 ± 382.88
Z+jets
17.53 ± 1.21
39.61 ± 1.84
741.49 ± 13.57
Total
1485.23 ± 70.01 2886.44 ± 108.38 27087.18 ± 595.62
Data
1495.00
2898.00
27120.00
Table B.8: Postfit yield in the `νqq W W ZZ WCR in the (top) GGF and (bottom) VBF regions from a simultaneous
fit in all W W ZZ regions

W W GGF TCR
Merged HP
Merged LP
Resolved
Diboson422.35 ± 35.88
529.79 ± 47.47
964.98 ± 106.50
Single-top
4434.82 ± 783.34
3353.14 ± 593.35
18516.60 ± 3469.99
tt̄
39218.39 ± 791.54
33963.82 ± 604.88 222535.00 ± 3415.98
W +jets
2267.26 ± 19.03
6583.81 ± 33.67
23433.17 ± 129.22
Z+jets64.17 ± 0.79
190.45 ± 1.53
904.09 ± 3.08
Total
46407.01 ± 1114.37 44621.01 ± 849.32 266353.84 ± 4872.14
Data46354.00
44629.00
266443.00
W W VBF TCR
Merged HP
Merged LP
Resolved
Diboson13.64 ± 4.72
19.83 ± 7.36
35.48 ± 22.03
Single-top
95.84 ± 20.22
76.64 ± 16.41
439.20 ± 102.19
tt̄
470.27 ± 34.04 386.81 ± 32.43 3665.64 ± 127.45
W +jets
53.57 ± 3.76
147.99 ± 7.11
448.53 ± 11.37
Z+jets1.19 ± 0.08
4.56 ± 0.22
27.94 ± 0.61
Total
634.50 ± 40.05 635.84 ± 37.76 4616.79 ± 165.23
Data
636.00634.004615.00
Table B.9: Postfit yield in the `νqq W W ZZ TCR in the (top) GGF and (bottom) VBF regions from a simultaneous
fit in all W W ZZ regions

129

B.2. Background only Fit results for the X → W W/ZZ search

ZZ GGF Untagged ZCR
Merged HP
Merged LP
Resolved
Diboson206.58 ± 21.18
392.37 ± 39.55
1119.49 ± 83.85
Single-top
1.21 ± 0.28
2.25 ± 0.48
21.11 ± 4.04
tt̄
7.43 ± 0.15
19.29 ± 0.34
181.46 ± 2.79
W +jets
1.51 ± 0.01
8.25 ± 0.04
10.86 ± 0.06
Z+jets5647.09 ± 69.24 13715.71 ± 110.25 82747.66 ± 281.74
Total
5863.83 ± 72.41 14137.85 ± 117.13 84080.58 ± 294.00
Data
5876.00
14236.00
84128.00
ZZ GGF Tagged ZCR
Merged HP
Merged LP
Resolved
Diboson5.17 ± 0.69
9.94 ± 1.24
55.55 ± 6.54
Single-top
0.12 ± 0.02
0.19 ± 0.03
10.18 ± 2.71
tt̄
0.37 ± 0.04
1.48 ± 0.15
203.02 ± 20.08
W +jets
0.04 ± 0.00
0.32 ± 0.03
0.14 ± 0.01
Z+jets
154.35 ± 10.74 257.94 ± 13.74 2495.09 ± 50.08
Total
160.05 ± 10.77 269.87 ± 13.80 2763.98 ± 54.42
Data
171.00280.002788.00ZZ VBF ZCRMerged HP
Merged LP
Resolved
Diboson
6.03 ± 1.25
13.60 ± 2.65
74.72 ± 13.10
Single-top
0.00 ± 0.00
0.63 ± 0.12
5.34 ± 1.47
tt̄
0.48 ± 0.04
1.23 ± 0.11
47.00 ± 1.85
W +jets
0.03 ± 0.00
0.19 ± 0.01
0.26 ± 0.01
Z+jets157.60 ± 10.34 383.59 ± 16.59 3677.06 ± 57.53
Total
164.13 ± 10.41 399.23 ± 16.80 3804.38 ± 59.05
Data
154.00404.003777.00
Table B.10: Postfit yield in the ``qq W W ZZ ZCR in the (top) GGF Untagged, (middle) GGF Tagged and(bottom) VBF regions from a simultaneous fit in all W W ZZ regions

M [GeV]
300
400
500
600
700
800
1000
1200
1400
1500
1600
1800
2000
2400
2600
3000
3500
4000
4500
5000

Observed [pb]2.48E+00
2.90E-01
1.67E-01
7.55E-02
5.58E-02
3.17E-02
2.02E-02
8.81E-03
5.33E-03
4.54E-03
3.68E-03
2.94E-03
1.79E-03
1.23E-03
9.06E-04
5.91E-04
4.63E-04
3.23E-04
3.38E-04
2.90E-04

Expected [pb]2.07E+00
1.30E-01
2.09E-01
8.60E-02
4.83E-02
1.97E-02
3.11E-02
4.58E-03
4.45E-03
3.78E-03
3.31E-03
2.44E-03
3.01E-03
1.60E-03
7.99E-04
3.77E-04
3.68E-04
2.31E-04
2.71E-04
2.47E-04±1σ [pb]
9.73E−01
6.94E−01
1.14E−01
8.11E−02
6.55E−02
4.67E−02
2.96E−02
2.11E−02
2.18E−02
1.56E−02
1.24E−02
8.85E−03
7.89E−03
5.63E−03
3.45E−03
2.46E−03
2.09E−03
1.49E−03
1.78E−03
1.27E−03
1.44E−03
1.03E−03
1.15E−03
8.21E−04
7.02E−04
5.01E−04
4.82E−04
3.44E−04
3.55E−04
2.53E−04
2.31E−04
1.65E−04
1.81E−04
1.29E−04
1.26E−04
9.01E−05
1.32E−04
9.43E−05
1.13E−04
8.09E−05±2σ [pb]
2.15E+00
1.15E+00
2.51E−01
1.34E−01
1.45E−01
7.74E−02
6.54E−02
3.50E−02
4.83E−02
2.58E−02
2.74E−02
1.47E−02
1.74E−02
9.34E−03
7.62E−03
4.08E−03
4.61E−03
2.47E−03
3.93E−03
2.10E−03
3.18E−03
1.70E−03
2.54E−03
1.36E−03
1.55E−03
8.30E−04
1.06E−03
5.70E−04
7.84E−04
4.20E−04
5.11E−04
2.74E−04
4.01E−04
2.15E−04
2.79E−04
1.49E−04
2.92E−04
1.56E−04
2.51E−04
1.34E−04

Table B.11: A summary of exclusion limits for Radion from W W/ZZ fit.

2

= 0.00(θfit - θ0) / ∆θ

XS_MJ_el_lvqq_ResVBF

XS_MJ_el_lvqq_ResGGF(θfit - θ0) / ∆θ

= 0.00(a)(b)

FATJET_JER
FATJET_Medium_JET_Rtrk_Baseline_pT
FATJET_Medium_JET_Rtrk_Closure_pT
FATJET_Medium_JET_Rtrk_Modelling_pT
FATJET_Medium_JET_Rtrk_TotalStat_pT
FATJET_Medium_JET_Rtrk_Tracking_pT
FT_EFF_Eigen_B_0_AntiKt4EMTopoJets
FT_EFF_Eigen_B_0_AntiKtVR30Rmax4Rmin02TrackJets
FT_EFF_Eigen_B_1_AntiKt4EMTopoJets
FT_EFF_Eigen_B_1_AntiKtVR30Rmax4Rmin02TrackJets
FT_EFF_Eigen_B_2_AntiKt4EMTopoJets
FT_EFF_Eigen_C_0_AntiKt4EMTopoJets
FT_EFF_Eigen_C_0_AntiKtVR30Rmax4Rmin02TrackJets
FT_EFF_Eigen_C_1_AntiKtVR30Rmax4Rmin02TrackJets
FT_EFF_Eigen_C_3_AntiKtVR30Rmax4Rmin02TrackJets
FT_EFF_Eigen_Light_0_AntiKt4EMTopoJets
FT_EFF_Eigen_Light_0_AntiKtVR30Rmax4Rmin02TrackJets
FT_EFF_Eigen_Light_1_AntiKt4EMTopoJets
FT_EFF_Eigen_Light_1_AntiKtVR30Rmax4Rmin02TrackJets
FT_EFF_Eigen_Light_2_AntiKt4EMTopoJets
FT_EFF_extrapolation_AntiKtVR30Rmax4Rmin02TrackJets
JET_BGSF_Dijet_Modelling
JET_BGSF_Dijet_Stat
JET_BGSF_Gammajet_Modelling
JET_BGSF_Gammajet_Stat
JET_CR_JET_BJES_Response
JET_CR_JET_EffectiveNP_Detector1
JET_CR_JET_EffectiveNP_Detector2
JET_CR_JET_EffectiveNP_Mixed1
JET_CR_JET_EffectiveNP_Mixed2
JET_CR_JET_EffectiveNP_Mixed3
JET_CR_JET_EffectiveNP_Modelling1
JET_CR_JET_EffectiveNP_Modelling2
JET_CR_JET_EffectiveNP_Modelling3
JET_CR_JET_EffectiveNP_Modelling4
JET_CR_JET_EffectiveNP_Statistical1
JET_CR_JET_EffectiveNP_Statistical2
JET_CR_JET_EffectiveNP_Statistical3
JET_CR_JET_EffectiveNP_Statistical4
JET_CR_JET_EffectiveNP_Statistical5
JET_CR_JET_EffectiveNP_Statistical6
JET_CR_JET_EtaIntercalibration_Modelling
JET_CR_JET_EtaIntercalibration_TotalStat
JET_CR_JET_Flavor_Composition
JET_CR_JET_Flavor_Response
JET_CR_JET_JER_DataVsMC
JET_CR_JET_JER_EffectiveNP_1
JET_CR_JET_JER_EffectiveNP_2
JET_CR_JET_JER_EffectiveNP_3
JET_CR_JET_JER_EffectiveNP_4
JET_CR_JET_JER_EffectiveNP_5
JET_CR_JET_JER_EffectiveNP_6
JET_CR_JET_JER_EffectiveNP_7restTerm
JET_CR_JET_Pileup_OffsetMu
JET_CR_JET_Pileup_OffsetNPV
JET_CR_JET_Pileup_PtTerm
JET_CR_JET_Pileup_RhoTopology
JET_SigSF_V_qq_Modelling_highPt
JET_SigSF_ttbar_Modelling_bTagB_0
JET_SigSF_ttbar_Modelling_bTagB_1
JET_SigSF_ttbar_Modelling_bTagLight_0
JET_SigSF_ttbar_Modelling_hadronisation
JET_SigSF_ttbar_Modelling_matrixElement
JET_SigSF_ttbar_Modelling_radiation
JET_SigSF_ttbar_Stat
Nonclosure_GGF_SR_wjets_vvqq_MergGGF
Nonclosure_GGF_SR_zjets_vvqq_MergGGF
Nonclosure_VBF_SR_wjets_vvqq_MergVBF
Nonclosure_VBF_SR_zjets_vvqq_MergVBF

XS_Wjets_Tag_vvqq_MergGGF

XS_Wjets_Tag_llqq_ResGGF

XS_Wjets_Tag_llqq_MergGGF

XS_Top_Tag_vvqq_MergGGF

XS_Top_Tag_llqq_ResGGF

XS_Top_Tag_llqq_MergGGF

XS_MJ_mu_lvqq_ResVBF

XS_MJ_mu_lvqq_ResGGF

2

(c)

4

0
0

−2
−2

−4
−4

4

0
0

−2
−2

−4
−4
VV_AlphaS_llqq_MergGGF
VV_AlphaS_llqq_MergVBF
VV_AlphaS_llqq_ResGGF
VV_AlphaS_llqq_ResVBF
VV_AlphaS_lvqq_MergGGF
VV_AlphaS_lvqq_MergVBF
VV_AlphaS_lvqq_ResGGF
VV_AlphaS_lvqq_ResVBF
VV_AlphaS_vvqq_MergGGF
VV_AlphaS_vvqq_MergVBF
VV_CT14_llqq_MergVBF
VV_CT14_lvqq_MergVBF
VV_MMHT_llqq_MergVBF
VV_MMHT_lvqq_MergVBF
VV_PDFVar_llqq_MergGGF
VV_PDFVar_llqq_MergVBF
VV_PDFVar_llqq_ResGGF
VV_PDFVar_lvqq_MergGGF
VV_PDFVar_lvqq_MergVBF
VV_PDFVar_lvqq_ResGGF
VV_PDFVar_lvqq_ResVBF
VV_PDFVar_vvqq_MergGGF
VV_PDFVar_vvqq_MergVBF
VV_RFScale_llqq_MergGGF
VV_RFScale_llqq_MergVBF
VV_RFScale_llqq_ResGGF
VV_RFScale_llqq_ResVBF
VV_RFScale_lvqq_MergGGF
VV_RFScale_lvqq_MergVBF
VV_RFScale_lvqq_ResGGF
VV_RFScale_lvqq_ResVBF
VV_RFScale_vvqq_MergGGF
VV_RFScale_vvqq_MergVBF
Vjets_AlphaS_llqq_ResVBF
Vjets_AlphaS_lvqq_ResVBF
Vjets_CT14_llqq_MergGGF
Vjets_CT14_lvqq_MergGGF
Vjets_CT14_vvqq_MergGGF
Vjets_GenMG_llqq_MergGGF
Vjets_GenMG_llqq_MergVBF
Vjets_GenMG_llqq_ResGGF
Vjets_GenMG_llqq_ResVBF
Vjets_GenMG_lvqq_MergGGF
Vjets_GenMG_lvqq_MergVBF
Vjets_GenMG_lvqq_ResGGF
Vjets_GenMG_lvqq_ResVBF
Vjets_GenMG_vvqq_MergGGF
Vjets_GenMG_vvqq_MergVBF
Vjets_MMHT_llqq_MergGGF
Vjets_MMHT_lvqq_MergGGF
Vjets_MMHT_vvqq_MergGGF
Vjets_PDFVar_llqq_MergGGF
Vjets_PDFVar_lvqq_MergGGF
Vjets_PDFVar_lvqq_MergVBF
Vjets_PDFVar_vvqq_MergGGF
Vjets_RFScale_llqq_MergGGF
Vjets_RFScale_llqq_MergVBF
Vjets_RFScale_llqq_ResVBF
Vjets_RFScale_lvqq_MergGGF
Vjets_RFScale_lvqq_MergVBF
Vjets_RFScale_lvqq_ResVBF
Vjets_RFScale_vvqq_MergGGF
Vjets_RFScale_vvqq_MergVBF
ttbar_FSR_lvqq_MergVBF
ttbar_FSR_lvqq_ResVBF
ttbar_FSR_vvqq_MergGGF
ttbar_ISR_lvqq_MergGGF
ttbar_ISR_lvqq_MergVBF
ttbar_ISR_lvqq_ResGGF
ttbar_ISR_lvqq_ResVBF
ttbar_ISR_vvqq_MergGGF
ttbar_PH7_llqq_ResGGF
ttbar_PH7_lvqq_MergGGF
ttbar_PH7_lvqq_MergVBF
ttbar_PH7_lvqq_ResGGF
ttbar_PH7_lvqq_ResVBF
ttbar_PH7_vvqq_MergGGF
ttbar_aMC_llqq_ResGGF
ttbar_aMC_lvqq_MergGGF
ttbar_aMC_lvqq_MergVBF
ttbar_aMC_lvqq_ResGGF
ttbar_aMC_lvqq_ResVBF
ttbar_aMC_vvqq_MergGGF

lumiNP

Nonclosure_VBF_SR_ttbar_vvqq_MergVBF

Nonclosure_GGF_SR_ttbar_vvqq_MergGGF

MJ_ttbar_lvqq_ResVBF

MJ_ttbar_lvqq_ResGGF

fixed

MJ_W_lvqq_ResVBF

XS_Zjets_Tag_vvqq_MergGGF

XS_Zjets_Tag_llqq_ResGGF

XS_Zjets_Tag_llqq_MergGGF

XS_Zjets_Res_VBF

XS_Zjets_Res_GGF

XS_Zjets_Merg_VBF

XS_Zjets_Merg_GGF

XS_Zjets_LP_Tag_vvqq_MergGGF

XS_Zjets_LP_Tag_llqq_MergGGF

XS_Zjets_LP_Merg_VBF

XS_Zjets_LP_Merg_GGF

XS_Wjets_Res_VBF

XS_Wjets_Res_GGF

XS_Wjets_Merg_VBF

XS_Wjets_Merg_GGF

XS_Wjets_LP_Merg_VBF

XS_Wjets_LP_Merg_GGF

XS_Top_Res_VBF

XS_Top_Res_GGF

XS_Top_Merg_VBF

XS_Top_Merg_GGF

XS_Top_LP_Merg_VBF

XS_Top_LP_Merg_GGF

XS_SingleTop_VBF

fixed

MJ_W_lvqq_ResGGFµ

Diboson_EWcontribution_lvqq_ResVBF

XS_Dibosons_VBF

XS_Dibosons_GGFµ

Diboson_EWcontribution_lvqq_MergVBF

s=13 TeV, 139 fb-1

PRW_DATASFMUON_SCALEMUON_SAGITTA_RESBIASMUON_MSMUON_ID

MET_SoftTrk_Scale

MET_SoftTrk_ResoPerp

MET_SoftTrk_ResoPara

EL_EFF_Trigger_TOTAL_1NPCOR_PLUS_UNCOR

EL_EFF_Iso_TOTAL_1NPCOR_PLUS_UNCOR

EL_EFF_ID_TOTAL_1NPCOR_PLUS_UNCOR

EG_SCALE_ALL

EG_RESOLUTION_ALL

ConstraintPdf_SigAcc_PDF_vvqq

ConstraintPdf_SigAcc_PDF_lvqq

ConstraintPdf_SigAcc_PDF_llqq

ConstraintPdf_SigAcc_ISRFSR_vvqq

4
XS_SingleTop_GGF

s=13 TeV, 139 fb-1

Figure B.4:
Correlation matrix for the nuisance parameters for the final W W/ZZ
HP+LP+Res,Tag+Untag, 0+1+2-lepton fit using data.

EL_EFF_ID_TOTAL_1NPCOR_PLUS_UNCOR
EL_EFF_Iso_TOTAL_1NPCOR_PLUS_UNCOR
FATJET_Medium_JET_Rtrk_Baseline_pT
FATJET_Medium_JET_Rtrk_Closure_pT
FATJET_Medium_JET_Rtrk_Modelling_pT
FATJET_Medium_JET_Rtrk_Tracking_pT
FT_EFF_Eigen_B_0_AntiKt4EMTopoJets
JET_CR_JET_Flavor_Composition
JET_CR_JET_JER_EffectiveNP_1
JET_CR_JET_JER_EffectiveNP_3
JET_CR_JET_JER_EffectiveNP_4
JET_CR_JET_JER_EffectiveNP_7restTerm
XS_Dibosons_GGF
XS_SingleTop_GGF
XS_SingleTop_VBF
XS_Top_LP_Merg_GGF
XS_Top_LP_Merg_VBF
XS_Top_Merg_GGF
XS_Top_Merg_VBF
XS_Top_Res_GGF
XS_Top_Res_VBF
XS_Wjets_LP_Merg_GGF
XS_Wjets_LP_Merg_VBF
XS_Wjets_Merg_GGF
XS_Wjets_Merg_VBF
XS_Wjets_Res_GGF
XS_Wjets_Res_VBF
XS_Zjets_LP_Merg_GGF
XS_Zjets_LP_Merg_VBF
XS_Zjets_LP_Tag_llqq_MergGGF
XS_Zjets_LP_Tag_vvqq_MergGGF
XS_Zjets_Merg_GGF
XS_Zjets_Res_GGF
XS_Zjets_Res_VBF
XS_Zjets_Tag_llqq_ResGGF
XS_Zjets_Tag_vvqq_MergGGF
Diboson_EWcontribution_lvqq_MergVBF
Diboson_EWcontribution_lvqq_ResVBF
Nonclosure_GGF_SR_ttbar_vvqq_MergGGF
Nonclosure_GGF_SR_wjets_vvqq_MergGGF
Nonclosure_GGF_SR_zjets_vvqq_MergGGF
Nonclosure_VBF_SR_ttbar_vvqq_MergVBF
Nonclosure_VBF_SR_wjets_vvqq_MergVBF
Nonclosure_VBF_SR_zjets_vvqq_MergVBF
XS_MJ_el_lvqq_ResGGF
XS_MJ_el_lvqq_ResVBF
XS_MJ_mu_lvqq_ResGGF
XS_MJ_mu_lvqq_ResVBF
XS_Top_Tag_llqq_ResGGF
XS_Top_Tag_vvqq_MergGGF
XS_Wjets_Tag_vvqq_MergGGF
VV_RFScale_llqq_MergGGF
VV_RFScale_llqq_ResGGF
VV_RFScale_lvqq_MergGGF
VV_RFScale_lvqq_MergVBF
VV_RFScale_lvqq_ResGGF
VV_RFScale_vvqq_MergGGF
Vjets_GenMG_llqq_ResGGF
Vjets_GenMG_lvqq_MergGGF
Vjets_GenMG_lvqq_ResGGF
Vjets_GenMG_lvqq_ResVBF
Vjets_RFScale_lvqq_ResVBF
ttbar_FSR_lvqq_ResVBF
ttbar_PH7_lvqq_ResGGF
ttbar_aMC_lvqq_ResGGF

ConstraintPdf_SigAcc_ISRFSR_llqq(θfit - θ0) / ∆θ4ConstraintPdf_SigAcc_ISRFSR_lvqq(θfit - θ0) / ∆θ130
Appendix B. Yields Table, Pulls and Correlation2

s=13 TeV, 139 fb-1µ

s=13 TeV, 139 fb-1µ

EL_EFF_ID_TOTAL_1NPCOR_PLUS_UNCOR
EL_EFF_Iso_TOTAL_1NPCOR_PLUS_UNCOR
FATJET_Medium_JET_Rtrk_Baseline_pT
FATJET_Medium_JET_Rtrk_Closure_pT
FATJET_Medium_JET_Rtrk_Modelling_pT
FATJET_Medium_JET_Rtrk_Tracking_pT
FT_EFF_Eigen_B_0_AntiKt4EMTopoJets
JET_CR_JET_Flavor_Composition
JET_CR_JET_JER_EffectiveNP_1
JET_CR_JET_JER_EffectiveNP_3
JET_CR_JET_JER_EffectiveNP_4
JET_CR_JET_JER_EffectiveNP_7restTerm
XS_Dibosons_GGF
XS_SingleTop_GGF
XS_SingleTop_VBF
XS_Top_LP_Merg_GGF
XS_Top_LP_Merg_VBF
XS_Top_Merg_GGF
XS_Top_Merg_VBF
XS_Top_Res_GGF
XS_Top_Res_VBF
XS_Wjets_LP_Merg_GGF
XS_Wjets_LP_Merg_VBF
XS_Wjets_Merg_GGF
XS_Wjets_Merg_VBF
XS_Wjets_Res_GGF
XS_Wjets_Res_VBF
XS_Zjets_LP_Merg_GGF
XS_Zjets_LP_Merg_VBF
XS_Zjets_LP_Tag_llqq_MergGGF
XS_Zjets_LP_Tag_vvqq_MergGGF
XS_Zjets_Merg_GGF
XS_Zjets_Res_GGF
XS_Zjets_Res_VBF
XS_Zjets_Tag_llqq_ResGGF
XS_Zjets_Tag_vvqq_MergGGF
Diboson_EWcontribution_lvqq_MergVBF
Diboson_EWcontribution_lvqq_ResVBF
Nonclosure_GGF_SR_ttbar_vvqq_MergGGF
Nonclosure_GGF_SR_wjets_vvqq_MergGGF
Nonclosure_GGF_SR_zjets_vvqq_MergGGF
Nonclosure_VBF_SR_ttbar_vvqq_MergVBF
Nonclosure_VBF_SR_wjets_vvqq_MergVBF
Nonclosure_VBF_SR_zjets_vvqq_MergVBF
XS_MJ_el_lvqq_ResGGF
XS_MJ_el_lvqq_ResVBF
XS_MJ_mu_lvqq_ResGGF
XS_MJ_mu_lvqq_ResVBF
XS_Top_Tag_llqq_ResGGF
XS_Top_Tag_vvqq_MergGGF
XS_Wjets_Tag_vvqq_MergGGF
VV_RFScale_llqq_MergGGF
VV_RFScale_llqq_ResGGF
VV_RFScale_lvqq_MergGGF
VV_RFScale_lvqq_MergVBF
VV_RFScale_lvqq_ResGGF
VV_RFScale_vvqq_MergGGF
Vjets_GenMG_llqq_ResGGF
Vjets_GenMG_lvqq_MergGGF
Vjets_GenMG_lvqq_ResGGF
Vjets_GenMG_lvqq_ResVBF
Vjets_RFScale_lvqq_ResVBF
ttbar_FSR_lvqq_ResVBF
ttbar_PH7_lvqq_ResGGF

ttbar_aMC_lvqq_ResGGF

fixed

fixed

= 0.002= 0.00(d)

Figure B.3: Pull distributions for the nuisance parameters (a) Jet relevant NPs (b) Other experimantal NPs (c)Theory NPs (d) XS NPs.

s=13 TeV, 139 fb-1
1

0.8

0.6

0.4

0.2

0

−0.2

−0.4

−0.6

−0.8

−1

GGF+VBF,

131

B.2. Background only Fit results for the X → W W/ZZ search

M [GeV]
300
400
500
600
700
800
1000
1200
1400
1500
1600
1800
2000
2400
2600
3000
3500
4000
4500
5000

Observed [pb]8.37E-01
1.35E-01
5.22E-02
2.15E-02
1.34E-02
8.97E-03
4.16E-03
2.25E-03
1.59E-03
1.34E-03
1.06E-03
6.27E-04
5.45E-04
4.61E-04
3.80E-04
2.41E-04
1.81E-04
1.60E-04
1.71E-04
1.65E-04

Expected [pb]4.59E-01
9.21E-02
4.92E-02
1.97E-02
1.26E-02
8.42E-03
8.78E-03
2.01E-03
2.60E-03
2.82E-03
2.24E-03
5.97E-04
6.11E-04
5.54E-04
3.96E-04
1.84E-04
1.47E-04
1.20E-04
1.39E-04
1.41E-04±1σ [pb]
3.28E−01
2.34E−01
5.27E−02
3.76E−02
2.04E−02
1.46E−02
8.42E−03
6.01E−03
5.24E−03
3.74E−03
3.51E−03
2.51E−03
1.63E−03
1.16E−03
8.80E−04
6.28E−04
6.22E−04
4.44E−04
5.27E−04
3.76E−04
4.13E−04
2.95E−04
2.46E−04
1.75E−04
2.13E−04
1.52E−04
1.81E−04
1.29E−04
1.49E−04
1.06E−04
9.42E−05
6.72E−05
7.09E−05
5.06E−05
6.27E−05
4.48E−05
6.71E−05
4.79E−05
6.47E−05
4.61E−05±2σ [pb]
7.25E−01
3.88E−01
1.17E−01
6.23E−02
4.52E−02
2.42E−02
1.86E−02
9.96E−03
1.16E−02
6.20E−03
7.77E−03
4.16E−03
3.60E−03
1.93E−03
1.94E−03
1.04E−03
1.38E−03
7.36E−04
1.16E−03
6.23E−04
9.13E−04
4.89E−04
5.43E−04
2.91E−04
4.72E−04
2.52E−04
3.99E−04
2.14E−04
3.29E−04
1.76E−04
2.08E−04
1.11E−04
1.57E−04
8.39E−05
1.39E−04
7.42E−05
1.48E−04
7.94E−05
1.43E−04
7.65E−05

Table B.12: A summary of exclusion limits for Radion VBF from W W/ZZ fit.

M [GeV]
300
400
600
700
800
1000
1200
1500
1800
2000
2400
2600
3000
3500
4000
4500
5000

Observed [pb]3.60E+00
5.16E-01
9.67E-02
6.29E-02
4.17E-02
2.05E-02
1.03E-02
5.02E-03
3.20E-03
2.01E-03
1.19E-03
8.96E-04
6.15E-04
4.08E-04
3.05E-04
2.69E-04
2.60E-04

Expected [pb]1.30E+00
2.08E-01
1.28E-01
8.14E-02
3.38E-02
2.82E-02
4.92E-03
4.16E-03
2.77E-03
3.14E-03
1.52E-03
8.17E-04
3.96E-04
3.33E-04
2.19E-04
2.18E-04
2.20E-04±1σ [pb]
1.41E+00
1.01E+00
2.02E−01
1.44E−01
3.79E−02
2.70E−02
2.46E−02
1.76E−02
1.63E−02
1.16E−02
8.02E−03
5.72E−03
4.04E−03
2.89E−03
1.97E−03
1.40E−03
1.25E−03
8.94E−04
7.86E−04
5.61E−04
4.65E−04
3.31E−04
3.51E−04
2.50E−04
2.41E−04
1.72E−04
1.60E−04
1.14E−04
1.19E−04
8.52E−05
1.05E−04
7.52E−05
1.02E−04
7.27E−05±2σ [pb]
3.11E+00
1.67E+00
4.47E−01
2.39E−01
8.37E−02
4.48E−02
5.45E−02
2.91E−02
3.61E−02
1.93E−02
1.77E−02
9.49E−03
8.94E−03
4.78E−03
4.35E−03
2.33E−03
2.77E−03
1.48E−03
1.74E−03
9.30E−04
1.03E−03
5.49E−04
7.75E−04
4.15E−04
5.33E−04
2.85E−04
3.53E−04
1.89E−04
2.64E−04
1.41E−04
2.33E−04
1.25E−04
2.25E−04
1.20E−04

Table B.13: A summary of exclusion limits for RSG from W W/ZZ fit.

132

Appendix B. Yields Table, Pulls and Correlation

M [GeV]
300
400
500
600
700
800
1000
1200
1500
1600
1800
2000
2400
2600
3000
3500
4000
4500
5000

Observed [pb]4.29E-01
2.97E-01
1.06E-01
4.78E-02
2.70E-02
1.78E-02
7.72E-03
4.11E-03
2.27E-03
1.79E-03
1.02E-03
8.57E-04
7.32E-04
6.14E-04
3.67E-04
2.82E-04
2.44E-04
2.40E-04
2.22E-04

Expected [pb]2.79E-01
1.83E-01
9.17E-02
4.27E-02
2.44E-02
1.72E-02
1.59E-02
4.01E-03
4.80E-03
3.52E-03
8.70E-04
9.71E-04
9.15E-04
6.22E-04
2.79E-04
2.35E-04
1.79E-04
2.02E-04
1.94E-04±1σ [pb]
1.68E−01
1.20E−01
1.16E−01
8.30E−02
4.13E−02
2.95E−02
1.87E−02
1.34E−02
1.06E−02
7.56E−03
6.96E−03
4.96E−03
3.02E−03
2.16E−03
1.61E−03
1.15E−03
8.90E−04
6.35E−04
7.00E−04
4.99E−04
4.01E−04
2.86E−04
3.36E−04
2.39E−04
2.87E−04
2.05E−04
2.41E−04
1.72E−04
1.44E−04
1.03E−04
1.10E−04
7.87E−05
9.55E−05
6.81E−05
9.40E−05
6.71E−05
8.70E−05
6.21E−05±2σ [pb]
3.72E−01
1.99E−01
2.57E−01
1.38E−01
9.14E−02
4.89E−02
4.14E−02
2.22E−02
2.34E−02
1.25E−02
1.54E−02
8.23E−03
6.68E−03
3.58E−03
3.56E−03
1.90E−03
1.97E−03
1.05E−03
1.55E−03
8.28E−04
8.85E−04
4.74E−04
7.42E−04
3.97E−04
6.34E−04
3.39E−04
5.32E−04
2.84E−04
3.18E−04
1.70E−04
2.44E−04
1.30E−04
2.11E−04
1.13E−04
2.08E−04
1.11E−04
1.92E−04
1.03E−04

Table B.14: A summary of exclusion limits for RSG VBF from W W/ZZ fit.

133

Appendix C

Impact of systematic uncertainties
The relative uncertainties in the best-fit µ value from the leading sources of systematic uncertainty are shownin Table C.1 for ggF and VBF HVT W’ signal with m(X) = 600 GeV and 2 TeV, respectively.
Table C.1: Ranking of the nuisance parameter impact on the expected exclusion limits on ggF HVT W’ withm(X) = 600 GeV and σ(pp → X) × BR(X → W Z) = 0.01 pb, ggF HVT W’ with m(X) = 2000 GeV and σ(pp →X) × BR(X → W Z) = 0.002 pb, VBF HVT W’ with m(X) = 600 GeV and σ(pp → X) × BR(X → W Z) = 0.01
pb and VBF HVT W’ with m(X) = 2 TeV and σ(pp → X) × BR(X → W Z) = 0.002 pb.

600 GeV

SourceLarge-R jet pT scale
MC statistical uncertainty
NonClosure ttbar
V +jets Generator difference
Small-R jet JER
VV RFScale
Large-R jet JER
Z+jets cross-section
VV cross-section
Boson tag SF Gamma+jets

600 GeV

SourceZ+jets cross-section
MC statistical uncertainty 0.0247
Large-R jet pT scale
VV EWcontribution
Small-R jet JER
W +jets cross-section
Boson tag SF ttbar Modeling
Large-R jet JER
METVV RFScale

ggF HVT W’
∆µ
0.058
0.056
0.028
0.026
0.025
0.021
0.019
0.018
0.011
0.010
VBF HVT W’∆µ
0.0288MC statistical uncertainty
0.00930.00770.00720.00470.00430.00380.00370.0036

2000 GeV
SourceV +jets Generator difference
Boson tag SF b-tag efficiency SF
Large-R jet pT scale
MC statistical uncertainty
Boson tag SF ttbar Modeling
Boson tag SF Gamma+jets
Boson tag SF other
VV RFScale
NonClosure ttbar
Boson tag SF dijet

2000 GeV
SourceLarge-R jet pT scale
0.65
Boson tag SF b-tag efficiency SF
Boson tag SF other
V +jets Generator difference
Small-R jet JER
ttbar PH7
ttbar ISR/FSR
ttbar cross-section
NonClosure ttbar∆µ × 10−3
1.08
0.65
0.61
0.42
0.42
0.20
0.19
0.14
0.12
0.10

∆µ × 10−3
0.68

The relative uncertainties in the best-fit µ value from the leading sources of systematic uncertainty are
shown in Table C.2 for ggF and VBF Graviton signal with m(X) = 600 GeV and 2 TeV, respectively.

0.54
0.19
0.16
0.12
0.09
0.08
0.07
0.06

134

Appendix C. Impact of systematic uncertainties

Table C.2: Ranking of the nuisance parameter impact on the expected exclusion limits on ggF Graviton withm(X) = 600 GeV and σ(pp → X) × BR(X → V V ) = 0.01 pb, ggF Graviton with m(X) = 2000 GeV and σ(pp →X) × BR(X → V V ) = 0.002 pb, VBF Graviton with m(X) = 600 GeV and σ(pp → X) × BR(X → V V ) = 0.01
pb and VBF Graviton with m(X) = 2 TeV and σ(pp → X) × BR(X → V V ) = 0.002 pb.

600 GeV

SourceV +jets Generator difference
Z+jets
Large-R jet pT scale
MC statistical uncertainty
VV RFScale
Small-R jet JER
Small-R jet b-tag efficiency SF
Large-R jet JER
VV cross-section
ttbar cross-section

600 GeV

SourceSmall-R jet JER
V +jets Generator difference
Z+jets cross-section
Large-R jet pT scale
VV EWcontribution
W +jets cross-section
MC statistical uncertainty
Boson tag SF b-tag efficiency SF
MET
Small-R jet Pileup

ggF Graviton∆µ
0.04090.02230.02040.01530.01410.01390.01290.00880.00830.00742000 GeV
SourceV +jets Generator difference
Boson tag SF b-tag efficiency SF
MC statistical uncertainty
Large-R jet pT scale
Boson tag SF ttbar Modeling
Boson tag SF other
VR track jet b-tag efficiency SF
Boson tag SF Gamma+jets
VV RFScale
Boson tag SF dijets∆µ × 10−3
1.465
0.635
0.523
0.469
0.463
0.184
0.167
0.157
0.112
0.109

VBF Graviton∆µ
0.01540.01280.01160.01120.00740.00730.00390.00280.00270.00252000 GeV
SourceLarge-R jet pT scale
Boson tag SF b-tag efficiency SF
Boson tag SF ttbar Modeling
V +jets Generator difference
Boson tag SF other
Small-R jet JER
MC statistical uncertainty
VR track jet b-tag efficiency SF
ttbar PH7
ttbar ISR/FSR∆µ × 10−3
0.517
0.474
0.306
0.169
0.168
0.113
0.113
0.083
0.068
0.051

135

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CMS Collaboration. “Observation of a new boson at a mass of 125 GeV with the CMS experimentat the LHC”. In: Phys. Lett. B 716 (2012), p. 30. doi: 10.1016/j.physletb.2012.08.021. arXiv:
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