Doctoral Dissertation
博士論文

Search for the neutral heavy Higgs bosons decaying to hadronic
ditau in proton-proton collisions at √𝑠 = 13 TeV(重心系エネルギー13 TeV の陽子衝突におけるタウ粒子のハドロニック崩壊を用いた重い中性ヒッグス粒子の探索)

A Dissertation Submitted for the Degree of Doctor of Philosophy
July 2019
令和元年 7 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

I-Huan Chiu邱 奕寰

Abstract
After the discovery of the scalar Higgs boson that is predicted in the Standard Model of the particle
physics (SM) with a mass of 125 GeV, the remaining issues in particle physics, such as dark matter in theuniverse and hierarchy problem of the Higgs boson, are to be solved by an extension of the SM. A bosonfermion symmetry, which is known as a “supersymmetry”, is one of the most motivated extensions of the
SM as it might address the missing of dark matter candidates, the hierarchy problem of Higgs boson mass,
and realization of the grand unification, simultaneously. The supersymmetry requires the Higgs sector of
the SM to be extended with at least one additional Higgs doublets, resulting in five physical Higgs states;
two neutral CP-even Higgs states (h, H), one CP-odd Higgs state (A), and two charged Higgs states(H ± ). One of the two neutral CP-even Higgs states is considered to be the discovered 125 GeV boson(h), and the other will be an additional heavy Higgs boson (H). An observation of the new heavy Higgs
boson (H and A) can provide important insight into the nature of the supersymmetry. The coupling
constants of the new heavy Higgs bosons are expected to depend on the ratio of the vacuum expectation
values of the two Higgs doublets (tan β), and the coupling constants to τ leptons are enhanced for a large
tan β scenario. This thesis presents a search for the neutral heavy Higgs boson (H or A) decaying into
a pair of tau leptons (H/A → τ + τ − ), which can provide the best sensitivity for a large tan β scenarioof the Higgs sector extension. Hadronic decay mode of τ leptons (τ → hadrons + ν) is considered in
the identification of the tau leptons. This analysis uses 139 fb−1 of proton-proton collisions recordedby the energy frontier ATLAS experiment at the Large Hadron Collider with a center-of-mass energy of√s = 13 TeV. This analysis applies an optimal set of event selection criteria to enhance H/A → τ + τ −signals. Possible backgrounds remaining after the selection are estimated with data-driven techniques,
exploiting control regions, and with the assistance of the simulation of the background processes. New
analysis techniques have been developed to maximize the search sensitivity. An improved τ selection
and categorization in the signal extraction are used in the H/A → τ τ search for the first time in thisanalysis. The result confirms no significant excess from SM prediction in the search for H/A → τ + τ − . An
exclusion limit in the context of the hMSSM scenario is presented, and the analysis excludes tan β > 23
at MH/A = 1500 GeV at 95% confidence level. This analysis allows setting the most stringent limit forthe production of the heavy neutral Higgs boson.

2

Acknowledgment
I thank Prof. Shoji Asai at the University of Tokyo for supervising me during the four years of my
Ph.D. course. I would like to express Prof. Junichi Tanaka and Associate Prof. Yasuyuki Okumura. They
support throughout my thesis, provide lots of advice for the research, and give me the good opportunity
to join many conferences in the ATLAS. I cannot accomplish this goal without their support.
I appreciate the staffs of the International Center for Elementary Particle Physics (ICEPP). Thanks to
Associate Prof. Ryu Sawada, Dr. Koji Terashi, Dr. Yuji Enari, Dr. Tatsuya Masubuchi, Dr. Tomoyuki
Saito, Dr. Takuya Nobe. They provide me lots of knowledge and advice for the detectors, analysis
techniques, and way to presentation in the weekly meetings. A special thanks to Dr. Masahiro Morinaga,
who is a reliable and knowledgeable collaborator in this analysis.
I would like to thank my colleagues at CERN, who make an enjoyable work environment for me. Thanks
to Dr. Syunsuke Adachi, Mr. Yuji Minegishi, Dr. Masahiko Saito, Dr. Yuya Kano, Mr. Tomohiro
Yamazaki, Mr. Masahiro Yamatani, Mr. Kenta Uno, Mr. Ryunosuke Iguchi, Mr. Kenta Uchidai, andMr. Nobuo Matsuzawa, especially Mr. Yi-Lin Yang, who always accompany me to eat kebabs and gossip
every Friday.
I am very grateful to work in a wonderful environment with my collaborators in the MSSM group in
ATLAS. Thanks to Prof. Luca Fiorini, Dr. Lei Zhang, Dr. Adam Bailey, Dr. Max Maerker, Dr. Dirk
Duschinger, and Mr. Lino Gerlach. They help me a lot to slove the difficult issues of this analysis.
A huge thanks to Ms. Wong Wing Lam for her kind support, that helps me to complete my Ph.D.
course. Last but not the least, I would like to thank my family for being there for me.

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Contents

1 Introduction

1

2 Theoretical Foundations
2.1 Standard Model of Particle Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.1 Problems in the Standard Model . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Supersymmetry and The Minimal Supersymmetric Standard Model . . . . . . . . . . . . .
2.2.1 The MSSM Higgs Sector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3 Phenomenology of MSSM Higgs Bosons in the Proton-Proton Collisions . . . . . . . . . .
2.3.1 MSSM Benchmark Scenarios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.2 Search Channels for the Neutral Heavy Higgs Boson . . . . . . . . . . . . . . . . .
2.4 Simulation of Physics Process at the Proton-Proton Collisions . . . . . . . . . . . . . . . .
2.4.1 Parton Distribution Function (PDF) . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4.2 Hadronization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4.3 Underlying events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4.4 Pileup simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5 Experimental Constraints of Heavy Higgs Bosons Searches . . . . . . . . . . . . . . . . . .

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3 The ATLAS Experiment at the LHC
3.1 The Large Hadron Collider . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 The ATLAS experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.1 The Inner Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.2 The Calorimeter System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.3 The Muon Spectrometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.4 Forward Detectors for Luminosity Measurement . . . . . . . . . . . . . . . . . . .
3.2.5 The Trigger System and Dada Acquisition System . . . . . . . . . . . . . . . . . .
3.3 Data Recorded of LHC Full Run 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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4 Physics Object Reconstruction
4.1 Low-Level Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.1 Track Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.2 Primary Vertices Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.3 Calorimeter Clusters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Jets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.1 Jet Reconstruction and Clustering Definition . . . . . . . . . . . . . . . . . . . . .
4.2.2 Jet Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.3 Heavy Flavour Jet Tagging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.4 Pile-up Jet Tagging and Rejection . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3 Electrons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.1 Electron Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.2 Electron Energy Scale and Resolution . . . . . . . . . . . . . . . . . . . . . . . . .

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30
31
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33
35
38
39
41
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Contentsii

4.3.3 Electron Identification and Isolation . . . . . . . . . . . . . . . . . . . . . . . . . .
Muons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4.1 Muon Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4.2 Muon Identification and Isolation . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4.3 Muon Momentum Scale and Resolution . . . . . . . . . . . . . . . . . . . . . . . .
Hadronic τ Decays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.5.1 Tau Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.5.2 Tau Energy Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.5.3 Tau Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.5.4 Tau Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Hadronic τ Decays with Two Charged Particles . . . . . . . . . . . . . . . . . . . . . . . .
4.6.1 Identification Investigation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.6.2 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Missing Transverse Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
miss Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.7.1 ETmiss Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.7.2 ET

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59
63
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5 Search for Neutral Heavy Higgs Bosons to τhad τhad Decay
5.1 Collision Data and Simulation Data Samples . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.1 Collision Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.2 Simulated Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2 Event selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2.1 Triggering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2.2 Event Reconstruction and Basic Selection . . . . . . . . . . . . . . . . . . . . . . .
5.2.3 Event Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2.4 Di-tau mass reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3 Categorization Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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6 Background Events Estimation
6.1 Estimation of the Irreducible Backgrounds . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2 Estimation of the reducible backgrounds . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2.1 Fake Factor Method (FF) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2.2 Fake Rate Method (FR) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.3 Expected Event Yields in the Signal Regions . . . . . . . . . . . . . . . . . . . . . . . . .

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7 Systematic Uncertainties
7.1 Experimental uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.2 Theoretical Uncertainties on Monte Carlo Simulation . . . . . . . . . . . . . . . . . . . . .
7.3 Uncertainties on the Data-Driven Background Estimation . . . . . . . . . . . . . . . . . .

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4.4

4.5

4.6

4.7

8 Result
100
8.1 Statistical Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
8.1.1 The Profile Likelihood Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
8.1.2 Hypothesis Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
8.2 Observed Data in the Signal Regions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
8.3 Constraints on the Cross Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
8.3.1 Independent Cross-Section limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
9 Discussion
110
9.1 MSSM interpretations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

Contents
9.2
9.3

iii

Major achievements in the thesis work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
Future Prospect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

10 Conclusions

113

Auxiliary Material

115

A Cutflow for Event Selection

115

B Fake Factor

118

C Fake Rate

123

D Distribution in SS Validation Region and OS Signal Region

134

E QCD Background Estimation in the Di-jet Control Region

141

F Investigation of BDT input variables for 2-prong tau

144

1 Introduction

The Standard Model of the particle physics (SM) is turned out to be well-consistent with most of theexperimental results. After the discovery of the scalar Higgs boson with the mass of 125 GeV at theLarge Hadron Collider (LHC) at CERN, there are still a lot of questions remaining to be answered, suchas unknown nature of the astrophysical dark matter, the hierarchy problem of the Higgs mass, unificationof the fundamental interactions, and quantization of the gravitational interaction. Extensions of theStandard Model of the particle physics are expected to address the problems. Extensive studies to provethe beyond-the-SM (BSM) physics have been actively conducted in both theoretical and experimental
methodologies.
√
The LHC is the energy frontier proton-proton collider running at the center-of-mass energy s =13 TeV. Many questions of the incomplete SM may be addressed by an observation of a new symmetry
between bosons and fermions, which is known as a “supersymmetry” or SUSY. The supersymmetry is
one of the most motivated extensions of the SM as it may address the missing of dark matter candidates,
the hierarchy problem of Higgs boson mass, and realization of the grand unification simultaneously. The
supersymmetry requires the Higgs sector of the SM to be extended with at least one additional Higgs
doublet, resulting in five physical Higgs states; two neutral CP-even Higgs states (h, H), one CP-odd
Higgs state (A), and two charged Higgs states (H ± ). One of the two neutral CP-even Higgs states is
considered to be the discovered 125 GeV boson (h), and the other will be an additional heavy Higgs boson(H). An observation of the new neutral heavy Higgs boson (H and A) can provide important insight
into the nature of the supersymmetry. The coupling constants of the new neutral heavy Higgs bosons are
expected to depend on the ratio of the vacuum expectation values of the two Higgs doublets (tan β), andthe coupling constants to down-type fermions are enhanced for a large tan β scenario. Among the decay
channels of the new neutral heavy Higgs boson, τ τ̄ and bb̄ channels are dominant modes with the typicalbranching ratios of ∼ 10% and ∼ 90%, respectively, for the high tan β region.
This thesis presents a search for the neutral heavy Higgs boson (H or A) decaying into a pair of tau
leptons (H/A → τ + τ − ), which can provide the best search sensitivity for a large tan β scenario of the
Higgs sector extension. This thesis work uses 139 fb−1 of proton-proton collisions recorded by the energy√
frontier ATLAS experiment at the Large Hadron Collider at a center-of-mass energy of s = 13 TeV
during the 2015 and 2018 data-taking period, which is denoted as the LHC “Run2”. The tau leptons
will further decay in either of a hadronic decay mode (τ → hadrons + ν) and a leptonic decay mode(τ → ντ `ν` ). As τ leptons decay hadronically approximately 65% of the time, the hadronic decay modeof τ leptons is considered in the identification of the tau leptons in this analysis. The channel where theboth tau leptons decay hadronically (H/A → τhad τhad ) is found to provide the best sensitivity in thehigh-mass region (mH/A > 600 GeV) of all the search channels. The hadronically decaying tau leptons
can be reconstructed with experimental data by the combination of the information of the calorimeterclusters and charged particle tracks (τhad reconstruction and identification).
This analysis exploits an optimal set of event selection criteria, including the τhad reconstruction and+−identification, to enhance H/A → τhad
τhad
signals. Considering the largest contribution of multi-jets

1

2background process with hadronic jets wrongly identified as tau leptons, the tau identification is tuned
to suppress such a “fake” backgrounds effectively. Possible backgrounds remaining after the selection
are estimated with a data-driven technique, exploiting control regions, and with the assistance of thesimulation of the background processes. The signal extraction will be performed on the categorized data
samples by mtot
T variable (defined as Equation 6.1), and the signal hypothesis will be tested in the context
of hMSSM scenario [1].
+−Further, this thesis work has introduced the following two major improvements in the H/A → τhad
τhad
search in order to pursue the search sensitivity in a wide-range;• Improvement of the tau reconstruction with use of “2-prong” signature: A new “2-prong
tau reconstruction” has been developed to maximize the search sensitivities in the high mass regions(MH/A > 1.5 TeV). This thesis describes that the traditional way of tau reconstruction based on
signatures characterized with one charged track (1-prong) and three charged tracks (3-prong) is not
fully efficient for a high pT τ objects due to possible hit sharing among tracks and the contaminationof additional tracks from e+ e− pair-creation associated with π 0 → γγ. It is found that often the tau
lepton can be associated with two charged tracks (2-prong). A new tau reconstruction techniquewith the 2-prong signature have been developed to maximize the signal selection efficiency in thissearch. The details are discussed in Section 4.6.
• Categorization: A new event categorization with respect to the number of tracks and the output
of tau identification algorithm, which corresponds to “tau-likelihood”, is newly introduced in thisanalysis to maximize the search sensitivities. This new technique efficiently improve the sensitivity
in particular in the low mass regions (MH/A < 600 GeV). Given the different fraction between
signals and backgrounds for the different tau identification requirements, the categorization in the
final signal extraction improve statistical sensitivities. The details of categorization are discussed
in Section 5.3.
With the development of two new techniques, 2% ∼ 10% better results have been achieved for the
hypothesis of MH/A > 1500 GeV (high mass), and 25% ∼ 50% better results for MH/A < 600 GeV (lowmass).
This thesis is structured as follows. The theoretical foundations of this analysis is discussed in Chapter 2.
The LHC experiment and ATLAS detectors are illustrated in Chapter 3. Chapter 4 provides an overview
for the reconstruction of the collision events, including reconstruction and identification of final-state
objects. The dataset used in this analysis and the event selection for signal extraction optimal to selectH/A → τhad τhad and background events are described in Chapter 5. The estimation of backgrounds areachieved via the several methods. They are discussed in Chapter 6, in particular for the data-driven
estimation technique for the backgrounds with fake τhad . The study of the systematic uncertainties fromthe sources of each analysis step and detectors are summarized in Chapter 7. Chapter 8 presents the results
including the statistical methods applied to test signal hypothesis. The interpretation in the context ofhMSSM, major achievements of this thesis work, and future prospect are discussed in Chapter 9. The
conclusion is given in Chapter 10.

2 Theoretical Foundations

This chapter presents an overview of theoretical foundations of this search. An introduction of theStandard Model (SM) is given in Section 2.1. The remaining issues in particle physics, such as dark matterand hierarchy problem provide a strong motivation for this analysis. To solve the remaining problems in
the Standard Model, one of the extensions of the Standard Model [2], Minimal Supersymmetry Standard
Model (MSSM), is discussed in Section 2.2. Section 2.3 presents the phenomenology of the proton-proton
collisions at the LHC. A large phase space of initial and final states in the high energy collisions aremodeled by the Monte Carlo simulation, which is given in the Section 2.4.

2.1

Standard Model of Particle Physics

The SM is an established theoretical framework which describes properties of the particles and theirinteractions using quantum field theory with the gauge symmetry in SU (3)C ⊗SU (2)L ⊗U (1)Y group [3–5].
The SM explains three of the four known fundamental forces. It also provides a mechanism for elementary
particles to obtain masses as a result of spontaneous garge symmetry breaking, which is known as the
Higgs mechanism.
A unification of electromagnetic and weak interactions is described with SU (2)L ⊗ U (1)Y group. The
four gauge bosons, W ± , Z and γ are associated to SU (2)L ⊗ U (1)Y group. The gauge theory wasdeveloped based on the invariance of field theory for the strong interaction and electroweak theory. The
gravitational interaction is not described by SM.
The SM contains twelve fermions (quark and lepton) and five bosons with their electromagnetic charges,
colors, and isospin as shown in Table 2.1. Six flavors of quarks are grouped into three generations; (up,down), (charm, strange) and (top, bottom). The lepton sector consists of three charged leptons (electron,
muon and tau) with their corresponding neutrinos which are electron neutrino (νe ), muon neutrino (νµ )and tau neutrino (ντ ). Electron, muon and tau lepton are the fermions carrying electric charge -1 andcolorless.

2.1.1

Problems in the Standard Model

Although the SM successfully describes experimental data of particle physics, unsolved problems, suchas dark matter, still adjudicate a revise of the SM or an extension models. Theories that include anextention of the SM is called “physics beyond the Standard Model” (BSM). This section presents a brief
overview of major problems of the SM that remain after Higgs discovery such as dark matter and hierarchy
problem.
Dark Matter and Dark Energy
The cosmic microwave background (CMB) analysis with Wilkinson Microwave Anisotropy Probe (WMAP) [7]and the Planck Collaboration [8] have provided for a lot of information of the early Universe. The Λ-CDM

3

2.1. Standard Model of Particle Physics
Nameelectronmuon
tauelectron neutrino
muon neutrino
tau neutrino
up
down
charm
strangetopbottom
gloun
γ
Z
W
Higgs

4
ChargeLeptons
-1
-1
-1
0
0
0
Quarks
2/3
-1/3
2/3
-1/3
2/3
-1/3
Bosons
0
0
0
±1
0

Spin

Mass

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

0.5 MeV105.6 MeV
1.7 GeV< 2.2 eV< 1.7 eV< 15.5 eV

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

2.2 MeV
4.7 MeV
1.3 GeV
96 MeV
173.1 GeV
4.2 GeV

1
1
1
1
0

0
0
91.2 GeV
80.4 GeV
125 GeV

Table 2.1.: Table of the SM particles with the corresponding charge, spin and mass [6].

(Cold Dark Matter) model may explain phenomena of the CMB and the accelerating expansion. Basedon the experimental result of the combined data from WMAP and the Planck, the dark energy density
parameter is defined as ΩΛ for cosmological constant [9, 10]. It predicts dark energy and dark matter(DM) contribute 68% and 27% of the total energy of Universe, respectively [11]. The SM does not provide
a candidate particle for dark matter and an explanation for dark energy.
Hierarchy Problem in Higgs Section
Loop corrections for the particle coupling to the Higgs field includes contributions of virtual particles
with the energy upto the Plank scale Λ = (8πGN )−1/2 ∼ 1019 GeV where GN is Newton’s constant [12,13]. An example is shown in Fig 2.1a which present the 1-loop process containing a Dirac fermion f withits mass mf . The correction for the Higgs mass due to the virtual fermion loop is given as the following:∆m2H = −|λf |2 2
Λ + O(logΛ),
8π 2

(2.1)

where the Λ is in the order of the Plank scale. This quantum correction, which is used for the calculationof physical mass, to bare mass of Higgs is derived to be O(1038 )(GeV)2 . Thus, it leads to the fine-tuningof the bare Higgs mass with the unnaturally large and precise quantum corrections to be consistent withthe observed Higgs boson mass of 125 GeV. The problem is called “Hierarchy Problem” or “fine-tuning
problem”. It shows that the SM have to be extended to describe physics at higher energies.
Suppose that a new heavy complex scalar particle, referred to as S, is introduced with its mass mS . Its
coupling to the Higgs boson is given by a Lagrangian term −λS |H|2 |S|2 . The corresponding correction
for the Higgs mass is given byλS 2
Λ + O(logΛ),(2.2)∆m2H =
16π 2

2.2. Supersymmetry and The Minimal Supersymmetric Standard Model

5

where the Feynman diagram is shown in Fig 2.1b.
The additional heavy particle predicted demonstrates that the quadratic terms Λ2 can be eliminated
via the regularization on the loop integral [14]. If the restrictions on the theory is accompanied with
λS = |λf |2 , the Λ2 term will be cancelled. The λS = |λf |2 can be satisfied by a hypothetical symmetry
relating the fermions and bosons. It is called “Supersymmetry” or “SUSY” [15]. This new symmetry
theory includes additional Higgs bosons, which encourage the motivation of this thesis as discussed below.

(a) Top loop.

(b) Scalar-top loop.

Figure 2.1.: (a) and (b) are the illustration for 1-loop processes corrections to the Higgs mass by Dirac fermion fand a scalar S, respectively.

2.2

Supersymmetry and The Minimal Supersymmetric Standard Model

The major problems discussed in Sec. 2.1.1 of the SM can be addrssed by the new symmetry, called aSupersymmetry (SUSY). It predicts a new symmetry between bosons and fermions [16, 17]. The SUSY
has to introduce new particles (sparticles), which are partners of the SM particles [18, 19]. The spin of asparticle is 1/2 different from its SM partner [20, 21]. The supersymmetry transformation is given as:
Q |fermioni = |bosoni , Q |bosoni = |fermioni .

(2.3)

These operators are constructed according to Haag-Lopuszanski-Sohnius extension of the Coleman-Mandula
theorem in the quantum field theory [22, 23].
R-parity
A new quantum number, which is referred to as “R-parity”, is defined with the baryon number(B ) andthe lepton number (L) number as follows [24]:R = (−1)3(B−L)+2s ,(2.4)

where s stands for the spin of the particles. The R is equal to 1 (even parity) for all particles, while all
sparticles have R = −1 (odd parity). As a consequence, R-parity conservation results in the following
phenomenological features:• The lightest supersymmetric particle (LSP) with R = −1 must be stable, which is a candidate of adark matter.
• Other sparticles must eventually decay into stable particles that contains SM particles and odd
number of LSPs.
• Each interaction vertex has even number of sparticle [15].

2.2. Supersymmetry and The Minimal Supersymmetric Standard Model

6

The sparticle search has been conducted with various experimental approach with respect to the phenomenological features.

2.2.1

The MSSM Higgs Sector

The Minimal Supersymmetric Standard Model (MSSM) is built based on several hypotheses to minimize
the matter contents and freedom on the SUSY [25–29]. The MSSM requires an additional Higgs doublet,which corresponds to two-Higgs-doublet models (2HDM) [30]. The 2HDM introduces the complex Higgs
doublets, Hu and Hd , for the up-type and down-type fermions. It results in the five Higgs bosons; twocharged Higgs bosons (H ± ), a CP-odd pseudoscalar Higgs (A) and two CP-even scalar Higgs (h and H).
In the unconstrained MSSM, a huge number (105) of unknown parameters with 19 parameters of the
SM are introduced [25, 31]. After the assumptions for the SUSY–breaking parameters, the MSSM is constrained with only 22 input parameters [32]. It contains 13 mass parameters for sparticles, six trilinear
couplings terms (so called A-parameters) and the ratio of the vacuum expectation values (VEVs) corresponding to the two–Higgs doublet superfields (tan β) with two Higgs mass parameters. The two–Higgs
doublet superfields Ĥup and Ĥdown corresponding to the two Higgs doublets Hu and Hd have the Yukawa
couplings to give masses to up-type quarks and down-type fermions,
respectively (type II 2HDM [30]).
q

The VEVs of Ĥup and Ĥdown are defined as υu and υd . The υu2 + υd2 is suited with 246 GeV to realize
the mass of W boson. The ratio of VEVs is a parameter of MSSM, called tan β,tan β =

υu
.
υd

(2.5)

In the MSSM, the superpotential W is introduced with the supersymmetric Lagrangian LW and thesuperfields. The superpotential represents the Yukawa interaction and the supersymmetric version of the
Higgs boson mass in the SM [15].
In the MSSM, there are three different sources with the superfields in the scalar Higgs potential VH ;Higgs interactions, superpotential and soft SUSY–breaking. [33].
g2

2= g8u [4|Hd† · Hu |2 − 2|Hd |2 |Hu |2 + (|Hd |2 )2 + (|Hu |2 )2 ] + 8d (|Hu |2 − |Hd |2 )2 Higgs interactions,+µ2 (|Hd |2 + |Hu |2 )Superpotential,††
2
2
Soft SUSY–breaking,+mHd Hd Hd + mHu Hu Hu + Bµ(Hu · Hd + h.c.)(2.6)
where gu and gd show gauge couplings of up- and down-type fermions, respectively. The µ is a parameterfor the Higgs mass terms, µHu Hd . When the potential VH (∂VH /∂Hu,d = 0) is minimized, one can obtain
the relation between υu and υd :VH

υu2 + υd2 =

4MZ2= (246 GeV)2 .
(gu2 + gd2 )(2.7)

In order to obtain the Higgs physical fields and their masses, representation of the two doublet complex
scalar fields around the vacuum in introduced as follows,
 + 


1
Hu
Hu+
Hu =
=√
.
(2.8)
0
0
Hu0
2 υu + Hu + iPu

Hd =

Hd0
Hd−



1
=√
2



υd + Hd0 + iPd0
Hd−


,

(2.9)

where real(imaginary) parts indicates the CP–even(CP-odd) Higgs bosons. The vacuum mass matrices

2.3. Phenomenology of MSSM Higgs Bosons in the Proton-Proton Collisions

A
H
h

gV V
0
cos(β − α)sin(β − α)

guu
cos β
sin α/ sin β
cos α/ sin β

gdd,lltan β
cos α/ cos β− sin α/ cos β

7gΦAZ /gΦH + W −∝0/1∝ sin(β − α)
∝ cos(β − α)

Table 2.2.: The effective coupling of the MSSM Higgs to the massive vector boson or SM ferminons. The couplings,
g, with SM ferminons and bosons are depends on the β and α.

with their mixing angles for CP–even and CP–odd neutral Higgs bosons are given by:−m̄23 tan β + MZ2 cos2 βm̄23 − MZ2 sin β cos β2MR =m̄23 − MZ2 sin β cos β−m̄23 cos β + MZ2 sin2 β
M2I =



−m̄23 tan β
m̄23
2
m̄3
−m̄23 cot β(2.10)

.

(2.11)

Since Det(M2I ) = 0, the pseudoscalar Higgs mass is given as MA2 = −2m̄23 / sin 2β. The mass of CP-even
Higgs bosons, the mass of the charged Higgs boson, and the rotation angle α are expressed as following:222MH± = MA + MW

1
2
= [MA2 + MZ2 ±
Mh,H
2
α=

q
(MA2 + MZ2 )2 − 4MA2 MZ2 cos2 2β].

M 2 + MZ21π), − ≤ α ≤ 0.
arctan(tan 2β A2222MA − MZ(2.12)(2.13)(2.14)The role of the SM Higgs boson h in the MSSM is shared by Ĥup and Ĥdown .The neutral scalar MSSM
Higgs has interactions with bosons and SM fermions. Table. 2.2 summarizes the effection coupling constracts for the MSSM Higgs.

2.3

Phenomenology of MSSM Higgs Bosons in the Proton-Proton Collisions

2.3.1

MSSM Benchmark Scenarios

A benchmark model was built, reducing the number of MSSM Higgs parameters down to two; themass of A (MA ) and tan β [34–36]. In this “hMSSM” approximation, the range for the tan β is around1 < tan β < 60 [37]. In the large tan β region, the neutral heavy Higgs bosons dominantly couple withbottom quarks and τ lepton. A high seach sensitivity for the neutral heavy Higgs bosons H/A (denotedas Φ) is expected with the final state with a pair of τ in the high tan β region. Since a mass of 125 GeV
for SM Higgs boson cannot be obtained for the region in tan β < 3, the low tan β region was excluded in
the context of the hMSSM.
The mass matrix of neutral components CP–even (h and H) can be formed in the following formula,related to the MA , MZ and β [38]:∆M211 ∆M212
2
2
M = MR +(2.15)∆M212 ∆M222 ,where M2R is the same tree-level matrix described in Eq. 2.10. The ∆M2ij corresponds to the radiative

2.3. Phenomenology of MSSM Higgs Bosons in the Proton-Proton Collisions

8

corrections [39]. It is used to calculate the Higgs masses and couplings. In the context of SUSY, thethe average of the two stop (t˜1 and t˜2 ) masses, MS , also plays an improtant role for the radiative
corrections [34]. 1
Three assumptions for the hMSSM approach are discussed in the items below.
• the observed Higgs boson is the light scalar h.
• only the element ∆M222 has non zero value and ∆M211 , ∆M212 , and ∆M221 can ne considered to be
zero.
• all SUSY particles are heavy enough to escape detection at the LHC, so that search for the modelis possible with experimental data.
In general, the SUSY radiative corrections are known to be very small. A basic assumption for hMSSM
shows that ∆M222 is to be much larger than ∆M211 and ∆M212 [25]. The ∆M222 is derived as follows withthe known mass value of Mh = 125 GeV:
∆M222 =

Mh2 (MA2 + MZ2 − Mh2 ) − MA2 MZ2 cos2 2β.
MZ2 cos2 β − Mh2(2.16)

The assumption is valid for the current experimental constraints in most of cases, such as large MS or
large tan β value. For instance, the maximal value of the h mass is computed as Mhmax ∼ 130 GeV in the
MS at the TeV scale.
The mass of the heavier neutral CP even Higgs particle, H, and the mixing angle α are then given as:2
MH=(MA2 + MZ2 − Mh2 )(MZ2 cos2 β + MA2 sin2 β) − MA2 MZ2 cos2 2β.
MZ2 cos2 β + MA2 sin2 β − Mh2
α = − arctan((MZ2 + MA2 ) cos β sin β).
MZ2 cos2 β + MA2 sin2 β − Mh2(2.17)(2.18)

2 = M 2 + M 2 by tree–level
In the hMSSM approach, the mass of the charged Higgs boson is given as MHA
W±
relation.

Production of the Neutral Heavy Higgs Bosons
The production of H/A bosons (denoted as Φ) is dominated by two main production processes; gluongluon fusion (gg → Φ) and bottom-annihilation (gg or q q̄ → bb̄Φ), is known as four-flavour scheme 2 .
The bottom-annihilation process also contains five-flavour scheme (bb̄ → Φ) in this analysis. The otherproduction processes, such as top-quark associated production (pp → Φtt̄), has much smaller corss-section
than them due to the small couplings with VV or tt̄, and therefore not considered in this study. In thehigh tan β region, the production rates of H and A states are approximately same.
In this analysis, the σ(gg → Φ) and σ(bb → Φ) are computed by the code SusHi 1.5.0 [40] using the Next-to-Next-to-Leading order (NNLO) in Quantum Chromodynamics (QCD) [41] perturbation
theory [42] and Next-to-Leading order (NLO) in the MΦ > 2mQ [43]. 3 The top- and bottom-loop contributions at NNLO in QCD, NNLO-QCD top contributions and the Leading order (LO) electroweak
contributions by light quarks are exploited for gluon-gluon fusion in the code. The b-associated production in the four-flavour scheme are calculated using Ref. [44]. In the five-flavor scheme case, the√MS is mt˜1 mt˜2 , which can be few TeV or 100 TeV scale.
b-quarks are not considered as partons.
3
mQ is defined as the quark mass as the pole of the propagator. For instance, mt of 175 GeV and mb of 5 GeV areconsidered for the t and b pole mass.
12

2.3. Phenomenology of MSSM Higgs Bosons in the Proton-Proton Collisions

9

amplitude for the production of SM Higgs boson is re-weighted with the effective coupling gdd given in
Table. 2.2. Finally, the cross section of bottom-annihilation production is obtained with the combination of the five-flavor and four-flavor schemes by the “Santander matching” and overlap is removed [45].
The computed cross sections of gluon-gluon fusion and bottom-annihilation production are of the sameorder of magnitude. The production cross sections of the A in (tan β,MA ) plane for gluon-fusion andbottom-annihilation mechanism are shown in Fig.2.2.

(a) bottom-annihilation production(b) gluon-fusion

Figure 2.2.: The production cross sections of the neutral Higgs bosons A (shown as the color column in right partof the figure) in (tan β,MA ) plane at the hMSSM benchmark scenarios for gluon-fusion (a) and bottom-annihilation
mechanism (b) [34].

Decay of the Neutral Heavy Higgs Bosons
H/A bosons strongly couple to down-type quarks and charged leptons in high tan β region (tan β >10). Among entire decay channels of Φ, the branching fraction (referred to as BF) of τ τ pair is computed
to be BF(Φ → τ τ ) ≈ m2τ /(m2τ + 3m2b ). 4 The τ lepton mass mtau = 1.78 GeV and bottom quark mass atthe scale of the Higgs mass mb ≈ 3 GeV result that the branching fractions of τ τ and bb̄ decay channelsof 10% and 90%, respectively [34]. The other decay channels of Φ states, especially to up–type quarks,
are strongly suppressed at high tan β since the coupling to up–type fermions is inversely proportional totan β. In the MA  MZ condition, the α shown in Eq. 2.18 is drived as:α

MA MZ−→− arctan(1/ tan β) = −(

π
− β).
2

(2.19)The relation of the coupling in the approximation [46] for up–type quarks (gu,u shown in Table 2.2) canbe written as:
sin α MA MZ sin(−( π2 − β))
1
guu =
−→
=−
.
(2.20)
sin β
sin β
tan β
In the Φ → V V , where V stands for W or Z boson, and Φ → hh cases, the couplings gets to be closeM M
to zero for large MA value (gV V = cos(β − α) A−→ Z 0) [25]. Figure 2.3 shows branching ratios of Φ in(tan β,MA ) parameter space based on the hMSSM benchmark scenario for each decay channels.

2.3.2

Search Channels for the Neutral Heavy Higgs Boson

As a consequence of hMSSM benchmark scenarios, gluon-fusion and bottom-annihilation production
are main processes for high tan β. The other processes are negligible as they are highly suppressed at
the target parameter space. Since that BF(Φ → τ + τ − ) is 10% and BF(Φ → bb̄) is 90% for high tan β
4The branching fraction of bb̄ is computed by BF(Φ → bb̄) ≈ m2b /(m2τ + 3m2b ).

2.3. Phenomenology of MSSM Higgs Bosons in the Proton-Proton Collisions(a) A → τ τ(b) H → τ τ(c) A → tt̄(d) H → tt̄

10

Figure 2.3.: The branching fractions of the neutral heavy Higgs bosons Φ in (tan β,MA ) plane (shown as the color
column in right part of the figure). (a) and (b) show the dominated decay channel for τ τ . The BF plots for the
suppressed decay channels with up-type quark, top quark for instance, are shown in (c) and (d) [34].

2.4. Simulation of Physics Process at the Proton-Proton Collisions

11

condition, they are sensitivity in the neutral heavy Higgs search. Requiring tau lepton significance in the
final state suppresses background effectively, and therefore a better sensitivity is expected in τ + τ − searchchannels than bb̄ channel. Three sub-channels for τ + τ − decay channel are classified for A/H search basedon the final state of τ lepton decay products. The H/A decay channels with leptonic decaying tau (τ` )and hadronic decaying tau (τhad ) are grouped as the τ` τ` , τ` τhad and τhad τhad final states. The branching
fractions of each sub-channel are around 12% (τ` τ` ), 45% (τ` τhad ) and 40% (τhad τhad ) as discussed inSec. 4.5. The τ` τhad channel is significant in low mass region because requirement of final state lepton
suppresses large fraction of background, while the τhad τhad provides the best sensitivity in high mass
region due to lower contribution for QCD background. This analysis focuses on the search for the neutral
heavy Higgs boson H/A in gluon-fusion and bottom-annihilation production. The τhad τhad final state ischosen as best sensitivie channel in high mass region. The current experimental constraints of H/A are
described in Sec. 2.5.

2.4

Simulation of Physics Process at the Proton-Proton Collisions

Monte Carlo (MC) simulation used to assist the definition for the complex signal extraction, backgroundsuppression as well as the analysis techniques [47]. Hard scattering processes is a dominant process ofproton-proton collision. It is described using the parton distribution functions (PDF). A very flexible
tree-level matrix-element generator (ME) is used to simulate hard scattering processes. The phenomenon
occurring in the final state of proton scattering where color-charged quarks and gluon transformed into thecolor-neutral hadrons is called “hadronization”. The low energy interactions which are QCD factorization
theorems is referred to as underlying event. There is still no complete theory for this phenomenon. The
additional interactions normally happen as a nuisance. The lowest order partons emit hard particles,
which carry the colour and electric charges as the initial state radiation (ISR) and final state radiation(FSR) in parton-shower model due to the effects of QCD Bremsstrahlung [48].

2.4.1

Parton Distribution Function (PDF)

High energy proton-proton collisions in LHC are known as deep-inelastic scattering (DIS) processes.
The universal Parton Distribution Function (PDF) was investigated carefully from the rates of the various
proton scattering process of LHC data-taking based on the theoretical factorization scheme. In the past
decades, heavy flavors with the different gluon distributions and different values of the strong coupling
are imported into the PDF analysis [49–51]. A parton carries the fraction x of hadron’s momentum. µF is
the factorization scale in the parton model. The PDF f (x, µF ) is evaluated to calculate the cross section
for the processes in hadron-hadron collisions. The PDFs, which is related hard scattering processes, arestudied based on all possibles DIS at the different order in QCD perturbation theory. 5 However, ahigher-order correction to reduce µF dependence is essential. It leads to the choice of the µF to play
an important role. In the hard-scattering cross-section calculation, the µF is usually chosen to be oforder Q which denotes an energy scale of the hard interaction. The factorization scale is separated toshort-distance physics and long-distance hadronic physics for the different phenomenon of the evolution.
Figure 2.4 presents an example of MSTW 2008 PDFs at NLO with 1-σ confidence level uncertainty bands.
The corresponding uncertainties of the PDF are computed by the global fits to the experimental data.
The other PDF set used in the LHC are extracted from the global data analysis such as PDF4LHC [52], NNPDF [50] , CT14 [53] and MSTW [54].

5

Leading-order (LO), next-to-leading order (NLO) and next-to-next-to-leading order (NNLO)

2.4. Simulation of Physics Process at the Proton-Proton Collisions

12

1.2

xf(x,Q2)

xf(x,Q2)MSTW 2008 NLO PDFs (68% C.L.)
Q2 = 10 GeV21

1.2

Q2 = 104 GeV2

1

g/10

g/10

0.8

0.8

u

0.6

0.4

0.2

0
10-4

0.6

d
c,c

10

-3

s,s

10-2

u

b,b

0.4

10-1

d

c,c
s,s

0.2

d

u

u

1

x

0
10-4

10

-3

10-2

d

10-1

1

x

Figure 2.4.: MSTW Parton distribution functions at the interaction scale of Q2 = 10 GeV2 and Q2 =104 GeV2 [55].

2.4.2

Hadronization

Hadronization is the transition process where the color quarks and gluons in a generated parton event
into the hadrons [56–58]. A complex and well-known string fragmentation model are introduced based on
the Lund-String Model [59]. The Lund string framework is implemented in the Pythia event generator [60].
The space-time of a Lund string is illustrated as shown in the left plot of Fig. 2.5. In a simple conditionof q q̄ two parton event, the potential energy increases when q q̄ move away from the creation vertex z-axis.
The string, which indicates strong color field, is known to break and create new q 0 q¯0 . The set of qi q¯0 i pairs
as the i-primary hadrons are created. The q 0 has no mass and transverse momentum and the primary
hadrons of the different breaks are separated independently in space (z-axis). A constant string tension,
which corresponds to the energy–momentum, is defined as κ = |dE/dz|. Furthermore, two adjacent breaks
are constrained by the mass shell of the produced hadron as shown in the right plots of Fig. 2.5. The
transverse mass is computed to be m2⊥ = E 2 − p2z . Based on the Quantum mechanics, the field energy canbe transformed into the transverse mass m2⊥ . In addition, the quark production must be limited in one
point and tunnel out to an allowed region. The production probability for this tunnelling process is written
by exp(−πm2⊥ )/κ. The computed result with the experimental data presents a high suppression value forheavy quark. It shows the fractions to generate a pair of q q̄ with uū : dd¯ : ss̄ : cc̄ ≈ 1 : 1 : 0.3 : 10−11 .

2.4.3

Underlying events

The hard interactions irrelevant with the primary hard process are called “underlying events”. The
number of those soft collisions with low transverse momenta is expected to be huge in the proton-proton
collision at the LHC. The models based on multiple parton interactions (MPI) is used to describe thecharacteristic of soft QCD. It provides a rigorous and reasonable explanation for the phenomenon ofseveral parton-parton interactions happened within a single hadron-hadron collision. The MPI for theunderlying events is implemented in all Pythia, Sherpa and Herwig++ models. However, the simulationof the additional jets is still difficult even those jets affect the total amount of scattered energy. The
poorly understood part on the color reconnection related to color-space correlations also cause significant
uncertainties in the MPI models. In the analysis step, these soft particles from underlying events present

2.5. Experimental Constraints of Heavy Higgs Bosons Searches

!=&

!=&−#

!=&−$

!=%

(a) Lund string system

!=$

13

!=#

(b) Mass shell

Figure 2.5.: (a) shows the motion of a Lund string system with n hadrons. z-axis and t respond to space-time
plane. (b) indicates the mass shell conditions on nearby string breaks [56–58].

the impacts for jet energy calibrations and performance of missing transverse momentum.

2.4.4

Pileup simulation

Multiple collisions in a single bunch crossing, which is called as “pile-up”, is known as another source ofthe soft QCD interactions. During the high-energy run of the LHC, the average number of collisions per
bunch crossing reaches up to 50 with a peak value 80. Additional collisions are generated by Pythia8 fortwo dominant components of pile-up background, named as “In-time pile-up” and “Out-of-time pile-up”
which are discussed in the chapter 3. Moreover, the pileup simulation is implemented in the MC step
to model the mixture of both hard and soft interactions. The minimum-bias event generation for single
proton-proton interactions is done with Pythia8, A3 tune [61] and NNPDF23LO PDFs [62] set.

2.5

Experimental Constraints of Heavy Higgs Bosons Searches

The search for heavy neutral Higgs bosons predicted by MSSM has been conducted by the experiments
including the LEP, the Tevatron, and the CMS and the ATLAS at the LHC.
LEP experiments
The search for the neutral Higgs bosons was studied with the data recorded in the LEP by the four
collaborations, which are the ALEPH, DELPHI, L3, and OPAL. [63] The interpretation on (mA , tan β)plane is carried out based on the accepted lower bound of SM Higgs mass of 114.4 GeV at 95% confidence level in a number of benchmark models. The exclusion limit in the mmax
benchmark scenario [36]his shown in Fig. 2.6. 6 The LEP experiments recorded e+ e− collision with center-of-mass energies of
91 GeV to 209 GeV. The two main signal processes, Higgsstrahlung e+ e− → HZ(orhZ) and pair production e+ e− → AH(orAh), are considered. The final states of H are bb̄ and τ + τ − with Z decaying
to q q̄, e+ e− , µ+ µ− , ν + ν − or τ + τ − . Finally, the combined statistical result with the several topologicalsearches is computed based on the CLs method.

6

mmax
benchmark scenario is originally made to obtain the exclusion bounds on tan β in LEP experiments [].
h2.5. Experimental Constraints of Heavy Higgs Bosons Searches

14

Tevatron experiments
Results of the MSSM neutral Higgs (h, H and A are marked as φ) searches were provided with 2.6
fb−1 and 5.2 fb−1 of data collected by the CDF and the DØ collaborations, respectively [64]. The main
decay mode φ → bb̄ with 90% branching fractions and the second decay mode φ → τ − τ + were dominated
due to the factor of tan β. As the interpretation in the mmax
benchmark scenario shown in Fig. 2.6,hthe Tevatron experiments provided a limits on neutral heavy Higgs boson. Since the coupling of neutral
heavy Higgs boson is dominant to bottom quark, a useful b-jet tagging technique was developed at theTevatron experiments. This method is also applied in the analyses at the LHC experiments.
ATLAS and CMS collaboration at the LHC experiments
The ATLAS (CMS) collaboration provided search results for H/A in τ + τ − final states with protonproton collision data at a center-of-mass energy of 13 TeV corresponding to an integrated luminosity of
36.1 (35.9) fb−1 at the LHC [65, 66]. Due to the higher center-of-mass energy and the huge integrated
luminosity, the sensitivity was significantly improved in the high tan β and high mA region compared to
the Tevatron results. The τ + τ − channel has a much better sensitivity, in spite of its small branching
fraction, than the bb̄ channel because of the lower background rate. Figure 2.7 shows the interpretations
benchmark scenarios at 95% confidence level. Two dominated signal processes, gluon fusionin the mmaxhand bottom annihilation production, are exploited with the three (four) most sensitive final states ofτ + τ − pair. A pair of τ + τ − are considered to be eτhad , µτhad and τhad τhad (eµ, eτhad , µτhad and τhad τhad )for the ATLAS (CMS) experiments. The other Higgs decay mode beside φ → τ + τ − are also presented at
LHC Run1 and Run2 analyses as shown in Fig. 2.8.

(a) LEP result(b) Tevatron result

Figure 2.6.: Exclusion limits for MSSM Higgs searches at LEP (a) and Tevatron (b) in the mmax
benchmarkhscenario at 95% confident level [67]. The light (dark) green area shows the limit at 95% (99.7%) confident level.

2.5. Experimental Constraints of Heavy Higgs Bosons Searches

15

ATLAS

40

GeV

mh = 126.2 GeV

mH = 1000 GeV

mh

.3
= 126
mH = 300 GeV

60mH = 500 GeV

s = 13 TeV, 36.1 fb-1
mod+
MSSM mhscenario, MSUSY = 1 TeV
H / A → ττ 95% CL limits

95% CL excluded:
Observed
68% expected
Expected
95% expected

CMS
tanβ

tanβ

35.9 fb-1 (13 TeV)
Observed
Expected
± 1σ
± 2σ

60

mmod+
scenarioh5040
mh = 126 GeV

20

30
20

mh = 125 GeV
mh = 124 GeV
mh = 123.5 GeV

500

1000

10

mMSSM
≠ 125 ± 3 GeV
h

1500

500

1000

1500

m A [GeV]

2000

mA (GeV)(a) ATLAS result(b) CMS result

Figure 2.7.: The newest exclusion limits at 95% confident level by MSSM Higgs searches with τ + τ − final state
at ATLAS (a) [65] and CMS (b) [66] in the mmod+
benchmark scenario. The total integral luminosities of protonh
proton collision data are around 36 fb−1 recorded during 2015 to 2016 at a center-of-mass energy of 13 TeV. In the
ATLAS limit, dashed lines of constant mh and mH are shown in red and blue, respectively.

tan βOctober 2018
H/A→ττ
s = 13 TeV, 36.1 fb-1

40
30

JHEP 01 (2018) 055+

H → τν

s = 13 TeV, 36.1 fb-1

JHEP 09 (2018) 139+

H → tbs = 13 TeV, 36.1 fb-1

20

arXiv:1808.03599 [hep-ex]

H→ ZZ→ 4l/llν ν

s = 13 TeV, 36.1 fb-1Eur. Phys. J. C (2018) 78: 293

gg→ A→ Zh

10s = 13 TeV, 36.1 fb-1

JHEP 03 (2018) 174

ATLAS Preliminary
hMSSM, 95% CL limits

4
3

Observed
Expected

H→ WW→ lν lν
s = 13 TeV, 36.1 fb-1
Eur. Phys. J. C 78 (2018) 24

H→ hh→ 4b,→ bb γ γ / ττ,→ WWγ γs = 8 TeV, 20.3 fb-1

Phys. Rev. D92, 092004 (2015)

H→ hh → bb γ γ2

s = 13 TeV, 3.2 fb-1
ATLAS-CONF-2016-004

h couplings [κ V, κ u, κ d]1
200

s = 13 TeV, 36.1 - 79.8 fb
ATLAS-CONF-2018-031

300 400

1000

-1

2000
mA [GeV]Figure 2.8.: Exclusion limits on the (mA , tan β) plane for MSSM Higgs searches with the different decay modesin the hMSSM benchmark scenario at 95% confident level by the ATLAS collaboration [68].

3 The ATLAS Experiment at the LHC

3.1

The Large Hadron Collider

The LHC is a synchrotron accelerator with four interaction points for four large experiments 1 withthe circumference of 27 km [70, 71]. It is re-utilizing the Large Electron Positron collider (LEP) tunneland crosses the France-Swiss border. The LHC provides the high-energy collisions with the existing
injector chain which consists of linear accelerator (LINAC2), Proton Synchrotron Booster (PSB), Proton
Synchrotron (PS) and Super Proton Synchrotron (SPS). The LINAC2 is the beginning for accelerating
the protons to reach the energy up to 50 MeV. The proton is accelerated up to 1.4 GeV by PSB, which
receives protons from the LINAC2. The proton’s energy is further increased to 26 GeV by the PS.
The last pre-accelerator of LHC is the SPS. The SPS is the second largest accelerator at the European
Organisation for Nuclear Research (CERN) with the circumference of 7 km. It brings the proton’s energy
up to 450 GeV. The proton is accelerated up to 7 TeV in LHC by oscillating radio-frequency (RF) electricfields2 . The LHC accelerator consists of the 1232 superconducting dipole magnets, cooled by liquid helium
to 1.9 K. The magnetic fields up to 8.33 T to bend the counter-rotating proton beams. Figure 3.1 shows aschematic overview of the LHC accelerator complex. Typically, a beam in LHC has 2808 bunch collisions
at Point-1, where ATLAS detector is located with a crossing angle of 285 mrad. One bunch consists of
1.15 × 1011 protons. The obtained luminosity is given as the function of:L=

nb Nb2 f γF,
4πβ ∗(3.1)

where nb is the number of bunches per beam, Nb is the number of protons per bunch, f is the revolution
frequency, and γ is the relativistic gamma factor. The denominator is a production of the normalized
transverse beam emitting  and the beta function at the collision point β ∗ . The geometric luminosity
reduction factor F due to the crossing angle at the interaction point is given as:
F = (1 + (θσz −1/2
))
,
2σ ∗

(3.2)

which is computed based on the crossing angle at interaction point θ with σz , and σ ∗ is RMS bunch
length and RMS of beam size in transverse plane, respectively. The achievement of the peak luminosity
in both main experiments, ATLAS and CMS, amounts up to L = 0.7 - 1.4 × 1034 cm−2 s−1 in 2015 and2016 runs, and L ∼ 2 × 1034 cm−2 s−1 for 2017 and 2018 runs for proton operation. Another collision
data with the heavy ions (Pb) with an energy of 2.8 TeV with a peak luminosity L = 1027 cm−2 s−1 is1There are ATLAS (A Toroidal LHC ApparatuS), CMS (Compact Muon Solenoid), LHCb (The Large Hadron Collider
beauty), and ALICE (A Large Ion Collider Experiment) are located on the accelerator ring of the LHC for the different
purposes [69].
2
The RF is delivered to all the system not only to the accelerator apparatus but also to the detector system, so that theoperation coherent to the LHC operation is achieved.

16

3.2. The ATLAS experiment17

not described in this thesis.

Figure 3.1.: Schematic overview of the current CERN accelerator complex, with year of first operation andcircumference in parentheses [72].

3.2

The ATLAS experiment

ATLAS and CMS are two general purpose detectors to proceed with energy fronier physics programs
at the LHC. Several important missions of these main detectors are like the search for SM Higgs boson,and test the SUSY model or other BSM theories.
The requirement to the ATLAS detectors are summarized in the following items:• The ATLAS provides a capability to handle the particle fluxes, which is produced in high luminosity
conditions at the LHC with overlapping events.
• The acceptance of the detectors is maximized in pseudo-rapidity. ATLAS provides a high geometrical coverage up to 4 π .
• For tagging of τ lepton and b hadron jets, the high-resolution information of vertices are essential.
The inner tracker of the ATLAS presents a good resolution for the charged-particle momentum andreconstruction efficiency as discussed in Sec. 4.5.
• The measurement of particle’s energy and momentum is one of the most important purposes of thedetector. The electromagnetic (EM) calorimetry and the hadronic calorimetry in ATLAS accurately
provide the basis of the particles studies for the identification and measurement of the electron,
photon, jet, and missing transverse energy.
• The muon spectrometers of the ATLAS provides the information for the muon identification andmomentum measurement.

3.2. The ATLAS experiment18• The trigger system of ATLAS successfully collects collision data from the design bunch-crossing rateof 40 MHz. ATLAS trigger system provides an average recording rate of a few hundred Hz in highluminosity collision at the LHC [73].
An overview of the detector is shown in Fig. 3.2, which consists of inner detectors, calorimeter systems
and the muon spectrometers. The origin of the coordinate system is defined as the center of the detector
corresponding to the nominal interaction point of p-p collisions [74]. The beam pipe is located along
the z-axis, and the x-axis points the center of the LHC ring. The y-axis is vertical to the ground. The
coordinate (x, y, z) corresponds to a right-handed coordinate system, also, the polar coordinate (φ, θ, z)
is used to describe the coordinate system of ATLAS detector. The pseudo-rapidity η defined as,η = − ln tan(θ/2),

(3.3)

q
is used instead of the polar angle θ as shown in Fig. 3.3. The transverse momentum pT = p2x + p2y andq
the transverse energy ET = Ex2 + Ey2 are the parameters used for describing the particles. The ∆R isq2.
used to represent for the distance between two particles i and j as ∆Rij = ∆φ2ij + ∆ηij

Figure 3.2.: A schematic diagram of the ATLAS detector with its subsystems. The ATLAS consists of tracking
detectors, calorimeter and the muon spectrometers. [75]3.2.1

The Inner Detector

The Inner Detector (ID) is the detector closest to the collision point with a length of about 7 m and adiameter up to 2.3 m. It was designed to measure the charged particles trajectories and vertices in around1000 particle’s emerging every 25 ns. ID is illustrated in Fig. 3.4, which is installed in a magnetic field of
2 T along the z-axis generated by the central solenoid magnet [77]. There are three subdetectors of ID;
Pixel, silicon microstrip tracker (SCT), and Transition Radiation Tracker (TRT). The tracks of chraged
particles are recontructed within the coverage of the ID. The coverage of Pixel deterctor and SCT is theregion of |η| < 2.5, while the TRT covers |η| < 2.0.

3.2. The ATLAS experiment

19

Figure 3.3.: Visualization of pseudo-rapidity η and polar angle θ [76]

(a)

(b)

Figure 3.4.: Schematic diagram of the Inner Detector [78].

3.2. The ATLAS experiment

20

The Pixel Detector
The silicon Pixel Detector is the innermost detector of the ATLAS located between 3.4 cm - 12.0 cm
from the beam pipe. It consists of four pixel layers with a coverage of |η| < 2.5 [79]. The Insertable bLayer (IBL), the innermost layer of Pixel Detector, was introduced during the first Long Shutdown of the
LHC 3 and installed at 3.4 cm from the beam line. It directly improves the resolution of b-hardon tagging
and also takes an important role for the pileup issues [80, 81]. 4 The three outer layers placed in theradii range larger 5 cm are referred B-Layer, Layer-1 and Layer-2 for a important role involved with thereconstruction of jets and τ . 1744 pixel modules with 47232 pixels on each module are building around 80
million readout channels. The operating voltages can be up to 600 V to cover detector efficiency in caseof radiation damage. In addition, since the noise is very sensitive with the temperature, the operation
temperature is requested to be as low as −5 ◦C to .0 ◦C in order to reduce the dark current [82].
The Silicon Microstrip Tracker (SCT)The Silicon Microstrip Tracker is the second component of ID located in the central ID region withthe radii range between 29.9 cm to 51.4 cm and a length of 14.9 cm. It is built of 4 088 modules with
6.3 million readout channels for a position measurment in two dimensions by 2 pairs of silicon p-in-n
microstrip sensors and provide a coverage up to |η| < 2.5. The SCT and Pixel are often called the“Silicon Detectors”, and the two detectors cover a same pseudorapidity range |η| < 2.5. They are used for
precision measurement from the initial interaction point. The SCT is operated in a temperature range of−10 ◦C to −5 ◦C to reduce the noise from leeakage current [83].
Transition Radiation Tracker (TRT)
Transition Radiation Tracker is the outermost tracking system. It is a straw-tube tracker, that consistsof 73 tubes in the barrel and 160 tubes in the end-cap, while the diameter of each tube is around 4 mm.
The tube is filled by a gas mixture of 70 % xenon, 27 % carbon dioxide and 3 % oxygen [84]. TRT
precisely measures each particle trajectory with the creation of the transition radiation, which depends
on the Lorentz factor γ:1γ=p,(1 − υ 2 /c2 )(3.4)

where υ is the velocity of the particle and c is the speed of light in vacuum. Lorentz factor provides
a parameter to distinguish electrons and the pions decaying to protons with the energy range 1 GeV- 200 GeV in the ATLAS detector. Electron candidates from photon conversions and Z boson decays
are separated with the corresponding Lorentz factor of 103 - 104 and 105 respectively. While the pion
candidates are selected with the criteria of a minimum of 20 TRT and four silicon hits to reject electronsand protons candidates. Additionally, the track selection for pion reduces the contamination from protons
in low momentum region. Two different sets on thresholds for the TRT, low- and high-threshold. The
low-threshold is used to identify electrons from the particles, while the high-threshold is used to identify
a large energy transition radiation [85] [86].

3.2.2

The Calorimeter System

The Calorimeter measures energy of the particles. The Calorimeter System of ATLAS is installedaround the inner track to absorb all incoming electrons, photons, and hadrons these from collision forparicle identication and energy measurment. It must prevent most of the particles from passing through3
4

A period of almost two years since February 2013.
The quality of track recontruction and b tagging performance in high luminosity pileup environment provide a strong
motivation for the IBL.

3.2. The ATLAS experiment21

into muon detector. The calorimeter system covers a large pseudorapidity range η of 4.9. Two sub-detetor
components with different technologies are employed as shown in the Fig. 3.5 which presents a composition of each calormeter sub-system. The electromagnetic calorimeter (ECAL) is designed to measureelectrons and photons. The ECAL provide the precise three-dimentional position of the “electromagnetic(EM) showers” based on the e+ e− pair creaion and Bremsstrahlung processes. The hadronic calorimeter(HCAL) is suited for hadrons reconstruction. The energy of the high energy hadrons is estimated bymeasuring the hadron showers. The HCAL is designed as a absorber for the hadron particles. Furthermore, thanks to the large η converage, the calorimeter system ensures a good missing transfer energy
measurement for weakly interacting particles like neutrinos escaping detection.
Tile barrel

Tile extended barrel

LAr hadronic
endcap(HEC)
LAr EM
endcap(EMEC)

LAr EM barrel
LAr forward(FCal)

1
Figure 3.5.: Cut-away view of the ATLAS calorimeter system [87].

LAr Electromagnetic Calorimeter
Liquid Argon calorimeter (LAr) was chosen for the barrel and the two end-caps of the electromagnetic
calorimeter (ECAL). The LAr is benefit in its intrinsic radiation-hardness, and high level resolution for
the reconstruction of electron and photon objects [87, 88]. The LAr sampling calorimeter was built andinterleaved with lead absorber plates and electrode. The size of gap of the electrode is 2.1 mm with abias voltage of typically 2000 V, which correspond to the total drift time of 450 ns. The pseudorapidity
converage of ECAL is divided into |η| < 1.475 for the Electromagnetic Barrel (EMB) and 1.375 < |η| < 3.2
for the two Electromagnetic End-Caps (EMECs). The EMEC is further splited into two sub-calorimeterswith a spacing of about 3 mm, the outer ring located in pseudorapidity range of 1.375 < |η| < 2.5 andthe inner ring of 2.5 to 3.2 in absolute η. The total thickness is overall 22 radiation length X0 , increasingfrom 22X0 to 33X0 and 24X0 to 38X0 for the EMB and the EMEC respectively. EMB and EMEC
components described above are further divided in three layers based on the segmentation of cells inη − φ plane to present a good angular resolution. The innermost layer, is also referred to as strip layer,with a granularity of ∆η × ∆φ = 0.0031 × 0.098 is suitable for the identification of π 0 → γγ decays in
the 6X0 . The second layer with the cells of ∆η × ∆φ = 0.025 × 0.0245 is the largest volume (16 X0 )used for providing a best resolution of enery measurment. The last layer is desiged to measure the tailof EM showers with a granularity of ∆η × ∆φ = 0.05 × 0.0245. Futhurmore, the ECAL consist of anadditional thin layer, so called presampler, located in front of three layers with coverage up to |η| = 1.8.
The presampler is used to recover mainly the jet energy measuremen and The segmentationof the EMB
pis illustrated in Fig. 3.6. Energy resolution of ECAL is computed as σE /E = 10%/ E/ GeV ⊕ 0.7%,
which is an excellent performance on the energy resolution for the electrons and photons reconstruction.

3.2. The ATLAS experiment

22

Figure 3.6.: An overview of the EM LAr calorimeter barrel module and The components of 4-layers in EMB, which
are the Presampler, the fornt Layer, the middle Layer and the back Layer [87]. The front layer with a granularityof ∆η × ∆φ = 0.0031 × 0.098 is suitable for the identification of π 0 → γγ decays in the 6X0 . The middle layer withthe cells of ∆η × ∆φ = 0.025 × 0.0245 is the largest volume (16 radiation lengths X0 ) used for povideing a best
resolution of enery measurment. The back layer is desiged to measure the tail of EM showers with a granularity of∆η × ∆φ = 0.05 × 0.0245.

Hadronic Calorimeter
The Hadronic Calorimeter (HCAL) is behind the LAr ECAL with three main components, Tile calorimeter (TileCal), LAr Hadronic End-Cap (HEC), and LAr forward calorimeter (FCAL). TileCal covers
the region from η < 1.7 as a absorber and active material in the barrel parts of HCAL. The coverage for
the HEC is 1.5 < η < 3.2, while FCAL coverage is upto 3.1 < η < 4.9. The significant overlaps between
TileCal, HEC and FCAL are designed for a smooth transition with suppressing energy losses.
TileCal is a sampling calorimeter with steel layers and scintillators. It is positioned behind the EM
calorimeter. It has a cylindrical structure with inner (outer) radius of 2280(4230) mm and 5 640 mm inlength along the z-axis. The missing-energy, which plays a important role in many particle searches,
depends on the acceptance of TileCal and its thickness. A approximately 30% of jets are captured by
the TileCal. TileCal provides a good jet- and missing-energy measurement. The photo-multiplier tubes(PMTs) are used as the photon detectors.
HEC is a LAr ionization detector for the calibration accuracy on the jet energy resolution. HEC1 and
HEC2 are the two wheel components of HEC. Thay are made of 32 identical wedge-shaped modeules witha small size read-out cell (∆η × ∆φ = 0.1 × π/32). It was designed with a good performance in a highradiation, high rate and low temperature environment.
Since the pseudorapidity range of FCAL is a very high, it is close to the beams axis. The three modules
with electrode structures made with copper tubes and electrode rods are referred FCal1, FCal2 and FCal3.
FCal1 is used for avoiding local heating to protect the liquid argon, while the roles for FCal2 and FCal3
are to have an precision measurement. It improves the resolution accuration of missing transverse energy,
which is a key parameter for the much searches [89].
In term of resolution of HCAL, the overall energy resolutions,
within a segmentationpof ∆η × ∆φ =p
0.1×0.1, of the HCAL
p for hadronic jets are σE /E = 53%/ E/ GeV ⊕6%, σE /E = 50%/ E/ GeV ⊕3%,and σE /E = 100%/ E/ GeV ⊕ 10% for the TileCal, HEC and FCAL respectivily [90].

3.2.3

The Muon Spectrometer

The muon particle has very small interactions characteristic. It usually passes through the Electromagnetic Calorimeter or the Hadronic Calorimeter with small enregy deposit around 3 GeV. Therefore, the3.2. The ATLAS experiment

23

Muon Spectrometer (MS) was located at the outermost part of the ATLAS detector to identify muonsand measure the momentum. A large barrel magnet constructed around hadron calorimeter provide a
pseudorapidity coverage range of |η| < 1.4. In the pseudorapidity range of 1.6 < |η| < 2.7, the two end-cap
magnet is inserted into both ends of barrel toroid. The transition interval region with pseudorapidity
range of 1.4 < |η| < 1.6 is covered to measure the momentum of the muons by magnetic deflection. The
MS provides a overall pseudorapidity range up to |η| < 2.7 with three large toroids which generate theR→− −magnetic field. The field strength for MS is estimated from the muon trajectory given by B d˙→
s , where
the B is the normalized field to the muon direction s. The field range are 1.5 Tm to 5.5 Tm and 1.0 Tm
to 7.5 Tm in barrel and endcap magnetic toroids respectively.
The global view of the Muon Spectrometer are presented in Fig. 3.7. Monitored Drift Tubes (MDT)
provides a precision measurement of the muon trajectory and the muon momentum, while Cathode Strip
Chambers (CSC) occupies the forward region designed to replace MDT for the regions of high particle
densities. Resistive Plate Chambers (RPC), and Thin Gap Chambers (TGC) are the trigger system of the
MS used in the barrel and end-cap regions respectively [91]. The futher detail are presented in following
subsection.
Monitored Drift Tubes (MDT)MDT performes the precision measurement of muon momentum in the coverage |η| < 2.7. It consists of
the aluminum tubes with 3 cm diameter and length in the range 0.9 to 6.2 m. The chambers are filled withthe gas maxture of Ar-CO2 (93% and 7%) in 3 bar absolute pressure. In high luminosity environment,
the resolution range with multi-layers reaches approximately 40 µm. An MDT chamber is constituted bysix layers of drift tubes which are arranged on the both sides of a support structure to against backgroundand ensures a good discovery potential of signal at the TeV scale [92].
Cadcade Strip Chamners (CSC))
The four-layered CSCs are multi-wire proportional chambers with a coverage of 2.0 < |η| < 2.7.
Overall 16 CSCs located on each end-cap offer high rate capability and excellent spatial resolution. A gas
mixture of Ar-CO2 (80% and 20%) is used to fill chambers with a high voltage of 1900 V. Both cathodes
are segmented; one with the strips perpendicular to the wires and the other parallel to the wires. The
resolution for the muon trajectory is better than 50 µm on bending plane.
Resistive Plate Chambers (RPC)
The RPCs with 596 RPC chambers and 355000 read-out channels are used for triggering signals inthe barrel region with the coverage |η| < 1.05. The low-(pT > 6 GeV) and high-momentum (pT >20 GeV) thresholds are built by three stations located near the magnetic field region and outer radius of
the magnet. It provides the trigger with the good discrimination on the muon transverse momentum pT .
The typical spatial and timing resolution achieved by a RPC chamber are 1 cm and 2 ns, respectively.
Thin Gap Chambers (TGC)
TGC provides the Level-1 muon trigger in the end-cap with the coverage of 1.05 < |η| < 2.7. The
chamber uses the highly quenching gas maxture of CO2 (55%) and n-pentane (45%). The anode-cathodegaps of TGSs (around 1.4 mm) is smaller than the wire spacing (1.8 mm) for the goal to obtain the best
time resolution with the lowest operating voltage of 3.1 kV. Typical time resolution is around 4 ns rms
for the efficiency of 98% [93].

3.2. The ATLAS experiment

(a)

24

(b)

Figure 3.7.: Schematic diagram of the barrel part of the muon Spectrometer (left) and the overview in y-z plane(right) [94].

3.2.4

Forward Detectors for Luminosity Measurement

The Forward Detectors consist of three small sub-detectors, LUCID5 , ZDC6 and ALFA7 . They cover
the forward region of the ATLAS [95]. The LUCID is located at the distance of 17m from the IP for ahigh acceptance and time resolution for the events. It is the dedicated detector for luminosity monitoring
and requested to have the good resistance to the extreme radiation of 60 − 70 kGray per year 8 . The main
purpose of LUCID is designed to detect proton-proton inelastic scattering in the IP. ALFA is designed todetermine the elastic proton-proton scattering at very small angles. 9
An overview of the Forward Detectors is shown in Fig. 3.8.

3.2.5

The Trigger System and Dada Acquisition System

In the LHC Run2 data taking period, the bunch spacing of protons is 25 ns. It results the collision rate
at the ATLAS detector is around 40 MHz. Considering the average size for the raw data is approximate 1.6
megabytes (MByte) per event, the bandwidth of more than 50 terabytes (TByte) per second for storingthem [98]. This is far away from the limitation on the bandwidth of the data storage and achievable
computing resources at CERN. Furthermore, there are huge amount of inelastic scattering processes,
therefore, a fast and efficient trigger system is extremely essential. The trigger and data acquisition
system (TDAQ) consists of a hardware-based first-level trigger (Level-1 trigger) and a software-based
high-level trigger (HLT) to select major interest events from the hard scattered collision. The data flowof the system ATLAS TDAQ in Run2 is shown in Fig. 3.9.
The Level-1 trigger is deployed to fastly reduce the collision rate from 40 MHz to 100 kHz in the firststage by the muon detectors and the calorimeter with a latency of less than 2.5 µs [99]. Regions of Interest(RoI), which is used to determine the acception of events for the adjudgment of further processing, isthen collected from the 100 kHz dataset by the ATLAS Region of Interest Builder. Level-1 trigger
5

LUminosity measurement using Cerenkov Integrating Detector
Zero-Degree Calorimeter
7
Absolute Luminosity For ATLAS
8“Gray” is a derived unit of ionizing radiation. The design for PMTs is 3 − 5 kGray per year
9
ALFA is located at the distance of approximately 240 m at both sides of the ATLAS IP. It is also related with a total
proton-proton cross section based on the optical theorem given in the following function [96]. For the LHC beam, theprotons at very small angles corresponds to a very small t-values (t = 0).
6

3.3. Data Recorded of LHC Full Run 2

25

Figure 3.8.: Overview of the ATLAS Forward Detectors with the position description of four sub-detectors fromIP [97].

system consists of the three main sub-trigger systems, L1 calorimeter system (L1Calo), L1 muon trigger
system (L1Muon) and L1 topological trigger modules (L1Topo). L1Calo uses calorimeter information
to search for high transverse-momentum electrons, photons, jets, and hadronic τ leptons, as well aslarge missing transverse energy. The reconstruction of the input for L1Calo is based on a segmented
blocks of combined calorimeter cells called “Trigger Towers” (TT). The 7200 trigger towers are builtwith a granularity of 0.1 ×0.1 in the η-φ range of the electromagnetic and hadronic calorimeters. The
sliding window algorithms based on TT and programmable thresholds are used to identify the electronand γ with the EM calorimeter, while the τ candidate is defined based on same TT window size withthe hadronic calorimeter. L1 jets are determined with both hadronic calorimeter and EM calorimeter.
“L1Muon” makes fast decisions on a muon candidate based on the signals exceeds a piece of predefined
threshold information on the RPC and TGC. (see Section 3.2.3) Finally, L1 missing transverse energy
trigger (L1XE) provides a missing transverse energy based on the vectorial sum of the TT energy of thefull L1 candidates. L1Topo combines output from L1Calo and L1Muon objects to apply topological event
selections at Level-1 [100].
The further process of TDAQ is a software-based trigger, High-Level Trigger (HLT), with a average
recording rate of ∼ 1 kHz. The HLT applys offline reconstruction algorithms with the RoI defined at
Level-1 and makes the final decision to store into data cernter 10 [101]. The trigged event is transferred to
the Tier-0 computing center for the final event reconstruction. The HLT runs on a conventional computercluster with up to approximately 40000 CPU cores and take about 200 ms on average of the processing
time per an event [102].

3.3

Data Recorded of LHC Full Run 2

After the first Long Shutdown for the maintenance and the detector upgrade, LHC attempted to restart√with the increasing center-of-mass energy up to a maximum collision energy s = 14 TeV 11 . LHC is
10
11

Tier-0 is the CERN Data Centre for the raw data from the online DAQ system.
√
ATLAS records data corresponding total integrated luminosity of 25 fb−1 at the centre-of-mass energy s = 7 TeV and
8 TeV during 2011 and 2012, so called as Run1, respectively.

3.3. Data Recorded of LHC Full Run 2

26

Figure 3.9.: The overview for the ATLAS trigger system in Run2, while the L1Topo (topological trigger) andFTK (Fast Tracker) in the illustration were being commissioned since 2015 and not used anymore [103].

designed initially and expected to get a better sensitivity on the discovery of the Higgs particles and the√study of rare events at a high collision energy s = 14 TeV. However, the super higher the magnetic fieldand electric current in the magnet’s superconducting coils cause a issue that retraining to 14 TeV would
take much longer time away from physics research compare with retraining to 13 TeV. Finally, taking the
expected integrated luminosity reduction12 for operation to 14 TeV into consideration, CERN decides tochoose 13 TeV for getting to new results quickly [104, 105].
The LHC is designed with the specifications on the bunch spacing of 25 ns, which corresponds to an
achieved peak luminosity of 1 × 1034 cm−2 s−1 . The recored data on the operation with the bunch spacingof 50 ns was employed in early 2015. They are used for the previous studies of the gradual effect reduction,such as the source from pressure rise and beam instability. An achieved peak luminosity in the study is
7.7 × 1033 cm−2 s−1 for the bunch spacing of 50 ns results the separation technology has to be considered
due to the different calibration.These data corresponding to a small integrated luminosity (about 0.1 fb−1 )are not considered in this analysis. Furthermore, the data recording with small luminosity (0.2 fb−1 ) in
two runs of 2015 is also not used in this analysis due to the technical problem the IBL 13 during the√data taking. The bunch spacing of 25 ns is selected for 2017 and 2018 runs at s =13 TeV. In 2017, theLHC was operated with “8b4e” bunch train operation 14 to investigate the effect from peak luminosityand pileup [106]. This analysis only uses the dataset after good quality checking of the ATLAS. 15 An
integrated luminosity of 139 fb−1 is measured by the LUCID-2 detector described in Sec. 3.2.4 [105] with
1.7% error given. An overview for the total integrated luminosity recorded by ATLAS from 2015 to 2018
and the one certified to be good quality data for physics is shown in Fig. 3.10(a). Table 3.1 shows an
overview of the luminosities for each year, together with the LHC parameters.
The number of proton-proton interactions occurring per bunch crossing (µ), which is calculated using
the following function, highly relates with the instantaneous luminosity and referred as in-time pile-up
12

Approximately 21% to 37% compared to 13 TeV case. The study is based on the performance for 1 year before Long
Shutdown 2
13
The reason for the low data quality efficiency of 2015 data taking
14
A pattern of eight bunches separated by 25 ns followed by a four bunch-slot gap.
15
The good quality checking of the ATLAS is called as Good Runs Lists (GRL).

3.3. Data Recorded of LHC Full Run 2

27

Parameter
Bunch spacing (ns)Peak luminosity (1033 cm−2 s−1 )Peak number of inelastic interactions (hµi)
Integrated luminosity (fb−1 )

2015
25
5
∼ 16
3.2

2016
25
13
∼ 41
33.9

2017
25
16
∼ 45
43.8

2018
25
19
∼ 55
60.1

√
Table 3.1.: LHC parameters for pp collisions at s =13 TeV in 2015–2018 The physics data delivered during 2015
with 50 ns and the 2015 data with technical problem are not listed [104].

(PU) 16 .
µ=

L × σinel
,
Nb fr

(3.5)

where L is the luminosity, σinel is the total inelastic cross-section, Nb is the number of colliding bunches
and fr is the frequency. The average µ is summarized in Table 3.1. The measured mean number ofinteraction per bunch-crossing for the recorded data 2015-2018 by ATLAS is shown in Fig. 3.10(b).
On the other hand, out-of-time PU is occurring before or after the interesting collision. It might affectthe signal in the collision of interest if the detectors are sensitive. Two independent sources of PU are
the significant background to the events, which impact the event reconstruction or trigger performancein the ATLAS. The corrections for the PU effect are considered in the ATLAS simulation step based on
the superimposing and overlap techniques for In-time PU and Out-of-time PU, respectively [107, 108].
The uncertainty of the calibration is discussed in Sec. 7.1.
After the trigger application at the “Point 1” of CERN discussed in Sec. 3.2.5, the recorded data isstored in the ”Tier-0” center as the ATLAS Raw data [109]. The prompt reconstruction for each physics
object is applied to the ATLAS Raw data and stored as Analysis object data (AOD). The derivation
frameworks are built by Athena software to reduce the AOD datasets of petabyte size to the derivatedAOD, which is called as DAOD. The AOD datasets sized to DAOD datasets of terabyte size in thederivation steps by skimming, slimming and thinning [110]. The dedicated DAOD samples for Higgs
search are used in this analysis by the ROOT -based analysis frameworks with calibrations and common
object selections.

16

In-time PU is several additional proton-proton collisions occurring in the same bunch crossing.

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

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

(a)

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

40

28

Recorded Luminosity [pb-1/0.1]

160

2/19 calibration

Total Integrated Luminosity fb-1

3.3. Data Recorded of LHC Full Run 2

100
0
0

10

20

30

40

50

60

70

80

Mean Number of Interactions per Crossing(b)

Figure 3.10.: (a) is the cumulative luminosity versus time. The delivered data by the LHC (Green), recorded
data by the ATLAS (yellow), and certified data (blue) by the ATLAS are present for pp collisions at 13 TeV during
2015-2018. (b) shows the luminosity-weighted distribution of mean number of interaction per bunch crossing forfor 2015-2018 recorded data. The hµi for 2017-2018 data are both larger than 40, that shows the PU is obviously
higher than the one for 2015 data [111].

4 Physics Object Reconstruction

The raw data information recorded by the ATLAS detector is translated into physics quantities throughthe sequence of reconstruction, identification and calibration. Though it is partially performed at thetrigger level, the recorded events are further elaborated by the sophisticated off-line algorithms. The
particles reconstructed by the off-line algorithms are referred to as “object”. Following the “online requirements” of the detectors, such as TDAQ (See Sec. 3.2.5), three important processes of reconstruction,
identification and calibration (so called as “online algorithms”) define the physics objects. The off-line
algorithm is built by the ATLAS dedicated software framework, so-called Athena framework. The main
purpose of the identification algorithm is made to maximize the performance with the reduction power for
mis-reconstructed objects and the identification efficiency. The calibration process is applied to correct
the differences of the reconstruction and identification efficiencies.
In the H/A → τhad τhad search, the jets and hadronic τ objects play the major roles. This section
overviews the procedures regarding to the object definitions. They are discussed in Sec. 4.2 and Sec. 4.5.
The lower-level object like tracks or vertex are also described in Sec. 4.1. In order to suppress backgrounds,
other objects, such as electrons and muons, are used in this analysis. The algorithms for electrons andmuons are discussed in Sec. 4.3 and Sec. 4.4. In Sec. 4.7, the missing transverse energy (MET) is also
described.

4.1

Low-Level Objects

Analysis-level objects are built in the reconstruction and identification with low-level objects, such as
tracks, vertices and calorimeter clusters. The performance of the low-level object reconstruction highly
depends on the resolution of the detectors. The Sec. 4.1.1 provides a description about the definition of
the track reconstruction [112].The vertex candidates are defined based on the reconstruction of chargedparticle tracks in the Inner Detector and presented in Sec. 4.1.2 [113]. Furthermore, the Sec. 4.1.3 shows
the clustering algorithm based on the the information of electromagnetic and hadronic showers detectedby ECAL and HCAL for jet and MET reconstructions.

4.1.1

Track Reconstruction

The charged track is a fundamental unit various off-line particle reconstructions. Standard tracks usedin ATLAS, which are reconstructed by hits created in the inner detector (ID), are referred to as ID tracks.
In the ATLAS, the inside-out track is the main sequence used for the track reconstruction of the primarycharged particles to the interaction point. The inside-out algorithm is built using the hit informationin the innermost layers of the Pixel detector and the outer layers of the SCT for the track candidates.
The hits in a space of Pixel detector and the SCT are detected as a cluster, and the TRT provides theinformation at the higher radii. Hits from a particle are identified and merged using a combination of apattern recognition technique called connected component analysis (CCA) [114, 115] and a neural network29

4.1. Low-Level Objects

30

1.1
ATLAS Preliminary
Simulation, τ→ντ3π±≤ 2 Shared SCT Clusters
No Secondaries

1

0.9

Baseline
TIDE

Track Reconstruction Efficiency

τ Algorithmic Efficiency

classifier (NN) [116]. More neighboring pixel hits are considered as a CCA cluster in eight cells of Pixel
Detector and also provide the position information by CCA. The strategy for the optimization of track
quality is based on the basic criteria of the number of associated track measured by the pixel and SCT
detectors. The track quality of the χ2 fitter also need to be satisfied to remove track duplicates and thefake tracks [117]. The clusters are assembled from the measurement of the ID and the SCT by the CCA,
and then the loss of identification efficiency for the merged clusters is minimized by the NN. Based on
the three-dimensional position information and the readout charge associated to each hit in the silicondetectors, spatial charge profile is constructed. The CCA and NN tools, have been introduced since Run1
studies, make a precise three-dimensional measurement of the position of charged particles possible.
For a further separations of high pT jets and τ -leptons in the search for new heavy particles decaying
to highly boosted objects, a dedicated environments (TIDE) [112] is used from Run2 to cope with thedense particle environment. The TIDE is a dedicated algorithm of track reconstruction for the denser
particle environment and provides a significant improvement for high pT track reconstruction. Figure 4.1
shows the reconstruction efficiency of tracks for τ lepton which are the important objects in this search.

0.96

ATLAS Preliminary

TIDE
Baseline

Simulation, s=13 TeV, Z’(3 TeV)

0.94
0.92
0.9
0.88
0.86
0.84
0.82
0.8
0.78

0.8
0

200

400

600

800

1000

100

200

300

400

500

τ p [GeV]

700

800

900 1000

Truth Jet p [GeV]

T

(a)

600

T

(b)

Figure 4.1.: (a) is the efficiency to reconstruct all decay products of τ with three charged tracks. (b) shows theresult of the average efficiency of track reconstruction and observed the significant increasing in efficiency for highpT jet momenta [112].

4.1.2

Primary Vertices Reconstruction

A precise reconstruction of positions on primary vertices (PVs), which are locations of inelastic protonproton collisions, is important. Accurate assignment of charged-particle trajectories to the correct primaryvertex is essential to reconstruct a full kinematics property of an event. The reconstruction of PV is basedon the reconstruction of charged tracks described in Sec. 4.1.1. There are the quality requirements in PV
reconstruction for the track such as the cuts in pT and the number of hits of the sub-detectors. There
two steps for the PV reconstruction; vertex finding algorithm [118] and vertex fitting algorithm [119],for associating reconstructed tracks to the vertex candidates and reconstructing the vertex position withthe fitting quality respectively. The best vertex position of PV is determined with selected tracks in thethree-dimensional information and required to have at least two associated tracks. The PV position is also
often used as the initial point of the objects in the analysis. The overall efficiency of PV reconstruction
is sufficiently high as shown in Fig. 4.2.

Vertex Reconstruction Efficiency

4.1. Low-Level Objects

311< nVertices >

0.995

0.99

0.985

Simulation
Simulation Fit

70

Crab Kissing beamspot

60

Crab Kissing lost vertices (masking)

Simulation

50

tt
Z→µµ

40

Z→ee

20

0.98

0

80

Lost vertices (masking)Statistical extrapolation
Fake vertices are neglected

30

ATLAS Preliminary

ATLAS Preliminary
Simulation

105

10 15 20 25 30 35 40 45

0
0

µ

50

100

150

200

Average number of interactions

(a)

(b)

Figure 4.2.: (a) is the efficiency to reconstruct the hard-scatter interaction vertex as a function of the number ofinteractions per bunch crossing per bunch crossing. (b) is the expected average number of reconstructed vertices
with high-µ data taking runs in the future [120].

4.1.3

Calorimeter Clusters

In order to reconstruct the hadronically decaying τ and jet objects, a three-dimensional topologicalclustering (Top-Cluster or TC for short) of cell signals with a signal-significance pattern based on theshower information of ECAL and HCAL system is used. Topo-cluster is a basic unit of energy measurement in the calorimeters and used as the input for jet clustering. It is formed by three-dimensionallygrouping cells with significant energy deposit. The clusters of the TC are used to connect the informationof the calorimeter cells to reconstruct a final state with isolated hadrons, jets and hadronically decaying
τ leptons. Therefore, the signal of the calorimeter cell can largely improve the performance for jet andmissing transverse momentum reconstruction. The signal significance algorithm is made by highly granular calorimeter system (See Sec. 3.2.2) for removing the background like the electronic noise, the noisefrom pile-up sources and other insignificant signals which are not close enough with the significant signal
cells. Figure. 4.3 shows the expected noise in the different sub-detectors with two different µ settings.
The signal significance for a cell is given by the following formula:
EM
ςcell
=

EM
Ecell
EM
σnoise,cell

,

(4.1)

EM
EM are measured onwhere the average expected noise in this cell σnoise,cell, and the signal of the cell Ecellthe electromagnetic (EM) energy scale. Three parameters {S,N,P} with a set of default values {4,2,0}
are defined as the boundary features of topo-clusters as shown below.
EM > S : The first and primary threshold for all the cells to select seed cells passing this threshold.
• ςcell
The corresponding cluster is called “proto-cluster”. The proto-cluster is defined to include only a
EM > S.
core of cells with highly ςcell
EM > N : The neighbouring cells of the seed are subsequently merged to the seed if they passed• ςcellthis threshold.

4.2. Jets

32

EM > P : If a seed cell, satisfying with this threshold, is a neighbour of two proto-cluster, the two• ςcell
proto-clusters are merged.

104

103

PS
EM1
EM2
EM3
Tile1
Tile2
Tile3
Gap

ATLAS
Simulations = 7 TeV, µ = 0

Total Noise [MeV]Total Noise [MeV]The spatial signal structures of the large proto-cluster are ignored when the more than an injecting
energy into the cell is identified as a single signal maximum. The proto-clusters with multi-local maximal
seed cell are split to another cluster in the three dimensions. The threshold definition of local signal
EM > 500 MeV. In addition, the cell with at least four neighbors andmaximum for the splitting is Ecellno larger signal in the neighbors are required. The proto-cluster after the splitting step corresponds to
TC. The direction of TC is reconstructed as (ηclus , φclus ) and used for the shower axis measurement of
the incoming particles. It plays an important role to build the cluster signal used to the calibrations andcorrections. The precise measurement is sensitive to the calibrations of missing transverse momentum
and improves the cluster energy resolution. The calibrations are related to cell signal weighting, which iscalled “Local Hadronic Cell Weighting” (LCW). It is built for the energy scale based on the comparisonof energy distribution between data and MC. The TC with a good performance and well-modeled bysimulation after all the calibrations have been introduced in [121]. In this search, TC with energy scaleand LCW are used in the jets and τ lepton reconstruction described in the following section.

FCal1
FCal2
FCal3
HEC1
HEC2
HEC3
HEC4

Simulation
50 ns bunch spacings = 8 Te V, µ = 30

10 3

PS
EM1
EM2
EM3
Tile1
Tile2
Tile3
Gap

10 2

102

10

10
0

ATLAS

10 4

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0

0.5

1

1.5

2

2.5

3.5

4

FCal2
FCal3
HEC1
HEC2
HEC3
HEC4

4.5

5
|η|

|η|

(a)

3

FCal1

(b)

Figure 4.3.: The expected energy noise as a function of |η| for the cell on the electromagnetic (EM) scale for eachsub-detector. The one with µ = 0 configuration is shown in 4.3(a), while 4.3(b) is with the configuration of µ =30 [121].

4.2

Jets

Jets are reconstructed using the topo-clusters calibrated with EM scale and LCW as described inSec. 4.1.3. Several main components of the jets reconstruction are introduced in this section. The
algorithm for the reconstruction is defined in Sec. 4.2.1. The identification of jets so-called flavor tagging
is shown in Sec. 4.2.3. And, a detail of the jets calibration is described in Sec. 4.2.2.

4.2.1

Jet Reconstruction and Clustering Definition

The topo-clusters after the calibration in the previous section are used for jet reconstruction. The jetreconstruction is implemented in the FastJet software package with the anti-kt clustering algorithm [122–124]. The anti-kt algorithms are used for consisting the group’s pairs of proto-jets to form a new proto-jet.
It labels the combined proto-jet as a “jet” object. There is no other additional manipulation applied.

4.2. Jets

33

The nearby proto-jets in (pT , η, φ) space are defined as a group pair of proto-jets shown in Eq. 4.2.
−2
dij = min(pT −2
i , pT j )

2
∆Ri,j
,
r2

(4.2)

p
2 is an angular distinace between two proto-jets in η-φ plane calculated bywhere ∆Ri,j(∆η)2 + (∆φ)2 .
A radius parameter of the algorithm is defined as r with a default value of 0.4. If the angular distance
2 is smaller than the distance between the proto-jet i and the beam (d ), the pair of proto-jets i, j
∆Ri,jiB
is grouped into a new proto-jet. This process continues until clusters are associated with one jet.

4.2.2

Jet Calibration

As the energy of TC is calibrated in the EM scale, the clustered jet needs an additional calibration
based on the hadronic interaction activity. Particle-level jet in simulated events (referred as “truth jet”)
are used for the reference of the truth energy. They are clustered by the same algorithm (anti-kt withr of 0.4) using only stable and final-state particles as input. The input particles are required to havea life-time of cτ > 10 mm. The muon neutrinos and particles from pile-up activity are excluded [125].
A series of dedicated calibration procedures is employed to restore the energy to that of the truth jets
reconstructed at the particle-level energy scale. It proceeds as following stages.
Origin Correction
The origin correction forces the four-momentum of the jet to point to the hard-scatter primary vertex
rather than to the center of the detector, while keeping the jet energy constant. Despite the default
angular coordinate of TC for the energy of particles is to point at the IP position or the center of thedetector, the jet direction is recalculated based on the primary vertex position that the jet is associatedwith. This correction significantly improves the η resolution.
Pile-up Correction
Effects of pile-up events provide an unexpected background from the low-energy particles. The contribution of the particles from pile-up jets is removed using the method of area-based density subtraction.
The jet-area is a way of measuring its susceptibility to contamination from soft radiation. The “ghost”
particles in jet area is defined as the infinitesimally soft particles (pT = O(10−100 GeV)) with fourmomenta gi and transverse momentum density νg within jet j. The four-momentum of jet area Aj can be
written as Aj = Numberofghosts
and provides the effect from pile-up. Pile-up contributions to the measured
νgjet energies are accounted for by using a two step procedure. First, the effect of pile-up is corrected forin the reconstructed jet energy using the average energy density in the event and the area of the jet.
Second, a residual correction is applied to remove the remaining dependence of the jet energy on thenumber of reconstructed primary vertexes, NPV , and the expected average number of interactions per
bunch crossing, µ. The pT density subtraction discussed below is applied to reduce pile-up jets:
pcorr.
= preco− ρ · A,
T
T

(4.3)

where transverse momentum before and after correction of jet are pcorr.
and precoTT , while ρ is average pTdensity measured in the event.
The pile-up correction on pT is defined as the following function after the pile-up suppression:
pcorr.
= preco− ρ × A − α(pT , η) × (NPV − 1) − β(pT , η) × µ.
T
T

(4.4)

The pile-up correction is determined using the simulation as function of pT and η and linear coefficients
α and β. Figure. 4.4 shows the simulation distribution before and after corrections.

4.2. Jets

34

(a)

(b)

Figure 4.4.: The pT distributions before and after subtraction and correction. (a) shows the effect on in-time
pile-up, and (b) is for the one on out-of-time pile-up as a function of jet η [125].

Jet energy scale and and η calibration
The reconstructed jet energy is corrected to the particle-level jet energy using MC simulation. In
addition, a correction is applied to the reconstructed jet pseudo-rapidity to account for the biases causedby the transition between different calorimeter regions and the differences in calorimeter granularity. The
calibration factor is a response with the Gaussian fitting result on ETreco /ETtrue distribution of jets, where
ETreco and ETtrue are the transverse energies of reconstructed jet and truth jet, respectively. The output isbinned in various pT and η for correcting the reconstructed jet energy to the truth jet energy. These jetenergy scale (JES) and calibration in η are employed in simulation step and the very small uncertainty 1
is considered in this search. Figure 4.5 shows the average energy response.
Global Sequential Calibration
The Global Sequential Calibration (GSC) corrects the jet four-momenta to reduce the response dependence on the flavour of the initiated-jet parton. The GCS is determined using the following information:
The significant improvement of resolution of energy is expected with further information from muon spectrometer as well as the inner detector. GSC consists of the five stages for the jet response on each itemin following table:• The energy of HCAL.
• The energy of ECAL.
• The number of tracks with pT > 1GeV .
• Average distance of all tracks in the η − φ plane from the jet.
• The number of muon track.

1

Around 1% for the jet with pT of 20GeV and much smaller than 1% with increasing pT

35

Energy Response

4.2. Jets

1.1
1
0.9
0.8

truth

ATLAS SimulationE= 30 GeV
truth
E= 60 GeV
truth
E= 110 GeV
truth
E
= 400 GeV
truth
E
= 1200 GeV

s = 13 TeV, Pythia Dijet
anti-k t R = 0.4, EM scale

0.7
0.6
0.5
0.4
0.3
0.2

−4

−3

−2

−1

0

1

2

3

4
η

det

Figure 4.5.: The average energy response as a function of η for jets after applying origin correction and pile-up
correction discussed in the previous items [125].

GSC is an extension of main jet calibrations like EM scale, LCW, and JES. It improves the jet performancewith more information about the energy in the calorimeter and track information from the other detectors.
After the full stages of GSC applied, the deviations between data and Monte Carlo 2 is within 2-4%.
In-Situ Calibration
The In-Situ calibration applied to data for the combined measurement of data-to-MC ratio in the jet
pT distribution is the final calibration discussed in this section. The γ/Z+jet and multijet processes
corresponding with the physics objects (photons, Z bosons or jets) in the transverse plane are used forfinding the correction which is applied to jets reconstructed in data [126, 127]. (See Fig. 4.6) The formula
data
for the ratio ( R
RM C ) is obtained to compare with data and MC. Finally, the in-situ calibration makes thejet response the same in data and MC simulation as a function of detector pseudo-rapidity using dijet
events, and as a function of jet transverse momentum using well calibrated reference objects in Z/γ andmulti-jet events.

4.2.3

Heavy Flavour Jet Tagging

Heavy flavor jet tagging relies on the unique properties of the b-hadrons with the largest mass and long
decay length. The long lifetime (cτ ∼ 450µm) of b-hadron leads to a measurable decay length to makean identification of b-jet possible. For identifying b-jets, the three dedicated sub-algorithms are built.
Impact Parameter based Algorithm (IP2D and IP3D), Secondary Vertex Finding Algorithm (SV), andDecay Chain Multi-Vertex Algorithm (JetFitter) are a set of algorithms to exploit the different properties
between b-hadrons and light jet [128]. The ID system with the components of the pixel detector, SCT and
TRT provides the important trajectories information for flavor tagging algorithms to reconstruct particle
tracks as well as their parameter determination [129]. Furthermore, the outputs of the sub-algorithms are
combined by the BDT classifier. In this heavy Higgs search, the b-tagging is used not only for extracting
bottom-annihilation production signal but also to make a control region enriched tt̄ events for backgroundestimation.
2

Both full and fast simulations

36

1.1

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

1.05

R

Data

/R

MC

4.2. 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 4.6.: Data to nominal MC event generator ratio as a function of jet pT for γ/Z+jet and multijet processes.
The black line presents the final calibration for the In-Situ combination with the corresponding statistical (darkblue) and total (light green) uncertainty bands.

Impact Parameter based Algorithm : IP2D and IP3D
Two track-based impact parameter taggers, IP2D and IP3D, are used for separating tracks associated tojets by a log-likelihood ratio (LLR) discriminant with the consideration of track-to-track correlations. The
IP2D tagger is determined for the transverse impact parameter significance (d0 /σd0 ), whereas the IP3D
includes both transverse and longitudinal impact parameter significance (Z0 sin θ/σZ0 sin θ ). Probability
density functions are obtained from two impact parameter taggers. The transverse impact parameter (d0 )and longitudinal impact parameter (Z0 sin θ) present the closest distance between the track and IP in r-φplane. The LLR distributions of IP2D and IP3D, which are the input variables for MV2, are shown in
Fig. 4.7 for b-, c- and light flavor-jets.
Secondary Vertex finding algorithm : SV
Secondary Vertex Finding Algorithm is used to reconstruct a secondary vertex, which carries a large
fraction of jet energy due to the harder b-jet fragmentation, from high pT IP tracks associated with thejet [130]. All combination of track pairs within a jet is tested with the two-track vertex hypotheses.
The vertexes originating from the decay of photon conversions, a long-lived particle such as Ks and Λor hadronic interactions with the detector material are discarded. Two track vertex candidates with theinvariant mass > 6 GeV are removed. The distance between each track of two-track vertex candidates
and the primary vertex is requested larger than 2, and IP2+IP3 of the track should also be higher than
2. Futhermore, χ2 < 4.5 [131] requirement is applied for the fitted tracks. Figure 4.8 shows several
properties of the reconstructed SV for b-, c- and light-flavor jets, which are also one of the inputs for the
final MV2 discriminator. An efficiency of the SV reconstruction is 80% for b-jets, while the efficiency on
c-jets is only a few %.
Decay Chain Multi-Vertex Algorithm : JetFitter
JetFitter based on the Kalman Filter [133, 134] is a kinematic fitting algorithm, exploiting the topological structure of b- and c-hadron decays inside the jet and attempts to reconstruct the full b-hadron

37

Arbitrary units

10

ATLAS Simulation Preliminary1

s = 13 TeV, tt

b jets10−1

c jetsLight-flavour jets

Arbitrary units

4.2. Jets10

s = 13 TeV, tt
10−2

10−3

10−3

10−4

10−4

10−5

10−5

10−6

10−6
−10

0

10

20

b jets

10−1

10−2

−20

ATLAS Simulation Preliminary

1c jetsLight-flavour jets

−20

30
40
50
IP2D log(Pb/Pu)

−10

0

10

(a)

20

30
40
50
IP3D log(Pb/Pu)(b)s = 13 TeV, tt

b jets1c jetsLight-flavour jets

10

ATLAS Simulation Preliminary1

s = 13 TeV, tt

b jetsc jetsLight-flavour jets

10

ATLAS Simulation Preliminary1

s = 13 TeV, tt

b jetsc jetsLight-flavour jets

10−1

10−1

10−2

10−2

Arbitrary units

ATLAS Simulation Preliminary

Arbitrary units

10

Arbitrary units

Arbitrary units

Figure 4.7.: The LLR distributions for IP2D (a) and IP3D (b) sub-algorithm. The MC sample of tt̄ events is used
for b- (solid blue), c- (dashed green) and light-flavour (dotted red) jets [128].

10

ATLAS Simulation Preliminarys = 13 TeV, tt

b jets1c jetsLight-flavour jets

10−1

10−1

10−2

10−2

−3

10

10−3
10−4

10−3

10−5
0

10

20

30

40

50

60

70

80

90 100

Lxyz/ σL (SV)
xyz

(a)

0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1fE(SV)

(b)

0

1

2

3

(c)

4

5
6
m(SV) [GeV]

2

4

6

8

10

12
14
NTrkAtVtx(SV)(d)

Figure 4.8.: The properties of secondary vertexes reconstructed by the SV algorithm for b-, c- and light jets in tt̄
events. (a) number of two-track vertexes, (b)the transverse decay length, (c) 3D decay length significance and (d)the energy fraction [132].

4.2. Jets

38

-1

t t
Data 2016
MC16
b jetsc jetslight−flavour jets

10

Preliminary
0.14 sATLAS
t t= 13 TeV, 2.5 fb-1

Data 2016
MC16
b jetsc jetslight−flavour jets

0.12
0.1
0.08

10−2

0.3

0.2

3

4

5

6

7

8

9

10

Data/MC

Data/MC

Data/MC

2

1.2
1
0.8
0.6

1

Number of Tracks at JetFitter vertex

(a)

2

3

4

5

6

t t
Data 2016
MC16
b jetsc jetslight−flavour jets

0.15
0.1

0

1.4
1.2
1
0.8
0.6

0

0.2

0.4

0.6

0.8

1

0

1.4
1.2
1
0.8
0.6

0

10

20

30

40

(c)

50

60

70

(d)

Figure 4.9.: The distribution with MC-data comparison for the variables of JetFitter: the number of tracks
associated with a JetFitter secondary vertex 4.9(a), the secondary vertex mass 4.9(b), the secondary vertex energy
fraction 4.9(c) the 3D significance of the decay length 4.9(d) [132].

Multivariate Algorithm : MV2
A boosted decision tree (BDT) is used to achieve a single discriminant with the best performance withthree sub-algorithm described above. The training procedure for Multivariate Algorithm (MV2) [135] iscompleted with the algorithmic strategies of IP2D, IP3D, SV and JetFitter to combine in a single very
powerful discriminant.Three types of MV2 are provided as the MV2c00, MV2c20, and MV2c10. The
MV2c10 is recommended for the a standard b-tagging discriminant in 2016 and also used in this analysis.
The number in the tagger name expresses the component of background samples in the training. For
instance, the mixture background with 10% c-jets and 90% light-flavor jets is used for the MV2c10
training. Fig 4.10 shows the MV2c10 BDT output for signal and background with the highly suppressing
power for c- and light-flavor jet. In 77% b-jet efficiency working point chosen in this thesis, the rejection 3
for c-jets (light-flavor jets) is up to 6 (134) for the overall jet with pT above 20 GeV.

4.2.4

Pile-up Jet Tagging and Rejection

A further pile-up subtraction is applied, in addition to the jet area-based method as described in theprevious section. In order to suppress the contamination, a pile-up jet rejection is applied using the Jet
Vertex Tagger (JVT) discriminant exploiting the vertex information. An original track-based method,
Jet Vertex Fraction (JVF), has been used for the pile-up suppression since 2012 [136]. It is developed by
the DØ collaborations and applied to identify the jets originating in the hard-scatter interaction. The
corresponding tracks are combined with their primary vertexes based on the JVF discriminant. Thisway reduces the effect from pile-up and the uncorrelated soft collisions. JVF updated with two newvariables to improve the separated power between hard-scatter (HS) and pileup (PU) jets is referred toas ”corrJVF”. Furthermore, a new algorithm Jet Vertex Tagger (JVT) which consists of corrJVF and

3

The rejection is typically defined as 1/ε.

80

JetFitter Lxyz / σ Lxyz

JetFitter Evtx/Ejet

JetFitter Vertex Mass [GeV]

(b)

-1

0.05

0.05

0
1.4

ATLAS Preliminarys = 13 TeV, 2.5 fb

0.2

0.1

0.02

1.4
1.2
1
0.8
0.6

0.25

0.15

0.04

10

t t
Data 2016
MC16
b jetsc jetslight−flavour jets

0.25

0.06
−3

ATLAS Preliminarys = 13 TeV, 2.5 fb-1

1/N dN/d(L/σ)

s = 13 TeV, 2.5 fb

Data/MCATLAS Preliminary−1

1/N dN/d(Evtx/Ejet)

1/N dN/dM

1/N dN/dNTrk

decay chain. JetFitter searches for three vertexes on the common axis based on the property of c-hadron
decay vertex which is often close to b-hadron flight axis. Figure 4.9 shows the distributions for the JetFitter algorithm with a good agreement between data and simulation in tt̄ events. The variables are
exploited to maximize discriminating power for charm-tagging from b-hadron in the MV2 algorithm with
the number, mass, and energy information of the particles associated with the secondary vertex.

39

Background rejection

Arbitrary units

4.3. Electrons

10

ATLAS Simulation Preliminary1

s = 13 TeV, tt

b jetsc jetsLight-flavour jets

10−1

104

ATLAS Simulation
Light-flavour jet rejection

103

c-jet rejection

102

10−2
10

10−3

jet p >20 GeV, |η|<2.5
T

0.55
−1

− 0.8 − 0.6 − 0.4 − 0.2

0

0.2

0.4

0.6

0.8

0.6

0.65

0.7

0.75

0.8

1

0.85

0.9

0.95

1

b-jet efficiency

MV2c10 BDT Output

(a)

(b)

Figure 4.10.: The MV2c10 output shows in (a) for b-jets (solid line), c-jets (dashed line) and light-flavour jets
(dotted line) in tt̄ events. (b) presents the curve for the background rejection of light-flavour jet (dashed line) andc-jet (solid line) versus signal b-jet tagging efficiency [132].

RpT is used during the Run2. The corrJVF and RpT defined as:
corrJV F =trkkΣk p T(P V0 )l
Σl ptrk
T (P V0 ) +trkΣn≥l Σl pT k (P Vn )(κ·nPUtrk ), RpT =k
Σk ptrk
T (P V0 )

pjet
T

(4.5)

where the hard-scatter vertex is written as P V0 and P Vj with j ≥ l for the primary vertexes of pileup
trkkkinteractions in same bunch crossing. The Σk ptrk
T (P V0 ) and Σn≥l Σl pT (P Vn ) show the pT sum of all
tracks of the jet in the hard-scatter vertex and any of pile-up interaction respectively. The scale factor
κ = 0.01 is applied for the number of pileup tracks nPU
trk in corrJVF to correct for the linear increase injetΣpT (P U ). The pT of RpT is the transverse momentum of calibrated jet after the pile-up subtraction.
Finally, the new discriminant JVT is built with RpT and corrJVF with two dimensional likelihood
ratio based on a k-nearest neighbor (kNN) algorithm [137]. It has been trained with HS signal and PU
background in 20 < pT < 50 GeV in |η| < 2.4 region by using a sample of Z → µµ events. Figure 4.11
shows the distribution for corrJVF, RpT , and the fake rate from pileup jets versus hard-scatter jet efficiency
curves for JVT. The JVT (aqua dot line) shows the efficiency of 95% on the signal HS jet with the fakerate of less than 3%.

4.3

Electrons

Information from ID tracking and EM calorimeter detectors make precise measurements of trajectory,
position and energy reconstruction possible. Since the full hadronic decaying τ is considered in this analysis, the electron object is important to remove backgrounds with leptons. Section 4.3.1 and Sec. 4.3.3
provide an introduction of reconstruction and identification for electrons. A brief overview of calibration for energy and resolution is described in Sec. 4.3.2. The more detail for the electron is shown inReference [138].

4.3. Electrons

40

(a)

(b)

(c)

Figure 4.11.: The comparison plots for pileup (PU) and hard-scatter (HS) jets with 20 < pT < 30 GeV. (a) shows
the one for corrJVF and RpT is illustrated in (b). Fake rate from pileup jets versus hard-scatter jet efficiency curves
shown in (c), JVT composed of corrJVF and RpT provides the good performance that signal jet efficiencies of 95%
is achieved for the rejection of pileup fake rate 3% [137].

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 4.12.: The overview for electron trajectory in the ATLAS detector. The illustration presents an electron pass through ID detector and is absorbed by EM calorimeter. The full information of tracking system andcalorimeter provide is useful for the electron reconstruction.(taken from Ref. [139].)

4.3. Electrons

4.3.1

41

Electron Reconstruction

Several steps are applied for the reconstruction in the region of EM calorimeter (|η| < 2.46).
• Seed-cluster reconstruction : Electron cluster ”seeds” are formed using a clustering algorithm basedon information from 0.025 × 0.025 granularity of the EM calorimeter with the window size of3 × 5 towers. The transverse energy threshold to the cluster is above 2.5 GeV, and the removalof the duplicates is applied also. The efficiency of cluster search ranges provide more than 95% at
ET = 7 GeV which is also the pT threshold for the electron-veto selection in this analysis.
• Track reconstruction : The 30% energy loss in the detector due to the possible Bremsstrahlung [140]is expected based on the pion hypothesis for the pattern recognition study. In the pion hypothesis,
the track with a transverse momentum larger than 1 GeV might not be successfully reconstructedwithin the EM cluster region of interest.The new pattern recognition using an electron hypothesis
to allow energy loss is used for this issue. The final fit for track candidates by ATLAS Global χ2
Track Fitter [141] with the pion or the electron hypothesis provides a minimal interference in trackreconstruction. The hypothesis application depends on which one presents a success fit.
p
• Track matching : The angular distance, (∆η)2 + (∆φ)2 , of the track is considered as a parameterof matching criteria between ID tracks to EM cluster. The matched track to EM cluster with
precision hits (≥ 4) are refitted by Gaussian Sum Fitter (GSF) [142].
• Electron reconstruction : Using the seed-cluster and matched track as described above, electronreconstruction procedure can be completed. The further energy calibration of the clusters to theoriginal electron energy based on simulation samples is done by multivariate algorithm [143].
The four-momentum of the electrons is calculated with the information of both the final calibrated
energy cluster and matched track in the ID track. Since Run2, the primary interaction vertex of the
HS has been also considered to the Track matching step of electron reconstruction, in order to reduce
conversion particles. Study for the reconstruction efficiency and corresponding correction factors are
based on the tag-and-probe method with Z → ee events. Figure 4.13 shows the comparison distribution
used for the correction faction measurement as a function of ET and η.

4.3.2

Electron Energy Scale and Resolution

This section provides the calibration for the reconstructed electron. The relative energy resolution forreconstructed EM objects (electron and γ) can be written as:σEab= √ ⊕ ⊕ c,
E
E
E

(4.6)

where the stochastic term a, the noise term b and the constantterm c are the parameters with a dependencepon η. The stochastic term is assumed to be around 10%/ E[GeV]. 4 . It shows the stochastic term depends
on the energy of incoming particle measured in calorimeter [144, 145]. The noise term is composed of thesource of electronic noise of the EM calorimeter and the pile-up. The pile-up noise is dominant at high η
region. The constant term is dominant in the energy resolution in the higher energy. In the most of thecentral region, The energy resolution is better than 2% for ET > 25GeV . However, in the region close
to transition of the barrel and end-cap calorimeters, it exceeds 3% due to the large amount of passive
material [146]. The resolution curve of electron is shown in Fig. 4.14. The invariant mass distributions
are also shown.
4

The stochastic term is computed as 3%/p

E[GeV] for CMS electromagnetic calorimeter.

42

1

Efficiency

Efficiency

4.3. Electrons

0.99

Reconstruction efficiency εreco

1.02

ATLAS

1.01

s = 13 TeV, 37.1 fb-1
80 GeV < ET < 150 GeV

Data
MC

1
0.99

0.98

0.98

0.97

0.97

ATLAS

0.96

Data / MCs = 13 TeV, 37.1 fb-1
Reconstruction efficiency εreco

0.96

Data
MC

0.95
20

40

60

80

100

120

140

1.04
1.02
1
0.98
0.96
−2.5 −2 −1.5 −1 −0.5

0

0.5

1

1.5

2

ET [GeV]

2.5
η

(a)

(b)

0.04

ATLAS

0.035

∫

s=8 TeV, Ldt = 20.3 fb-1
Electrons, |η|=0.2

0.03
0.025

Arbitrary units

σ/E

Figure 4.13.: The reconstruction efficiency for the real data (closed points) and Z → ee simulation events (openpoints). (a) is the plot as a function of electron transverse energy, while the one for high ET region (80 − 150GeV )for pseudo-rapidity is presented in (b) [143].

0.14
0.12
0.1

s=8 TeV;∫ L dt = 20.3 fb-1

Cluster
Combined

0.08

0.02
0.015

0.06

0.01

0.04

0.005

0.02

0

ATLAS

20

40

60

80

100 120 140 160 180 200

0
50

60

70

80

90

(a)

100

110

120

130

mee [GeV]ET [GeV](b)

Figure 4.14.: (a) is the resolution curve as a function for ET of electrons with |η| = 2 requirement. (b) shows theelectron pair invariant mass distribution for Z → ee events with one electron candidate in 1.37 < |η| < 1.52. (takenfrom Ref. [143].)

4.3. Electrons

43

The calibration steps illustrated in Fig. 4.15 are applied for the reconstructed electrons [143]. Though
the energy of cell deposit in EM calorimeter and electron cluster are already calibrated in EM scale, it
still suffers from the residuals due to the energy loss in the material upstream of the calorimeter, energy
leakage out of the envelope of the cluster or the EM calorimeter. In order to equalize the response overcell’s energy of the longitudinally segmented structure of EM calorimeter, the overall energy scales foreach layer are computed with simulation. MC-based e/γ response calibration was employed for this issue
by using a multivariate algorithm (MVA). The first-layer energy of the EM calorimeter are comparedwith the second-layer energy, the higher ratio value indicates the EM showers development is helpful tounderstand an energy excess in the simulation comparison. It performs the optimization in the separation
power between electrons and γ.
The other correction for data is called ”Inter-calibration of the calorimeter layers”. Due to the shower
development of the longitudinal layers in the calorimeter, the effects in the full pT range need to beconsidered. The inter-calibration is used for first, second layers and PS in calorimeter for energy scale. 5
It effectively corrected possible mis-modeling of each layer from other material.
A set of corrections are applied to data to account for the non-uniformity of φ due to various instrumental effects that are not included in simulation, such as non-optimal high-voltage setting, geometricaleffects or biases in the LAr calorimeter electronics calibration.
The other corrections to data and simulation are used for improving the electron energy resolution.
The residual mis-calibration is defined as the difference between data and simulation as a function of φ.
The residual mis-calibration is corrected by shifting the energy scale using a sample of Z → ee decays.
Furthermore, since data provide a slightly worse performance with the pre-event selection in step 5 ofFig. 4.15 used in the simulation, the additional resolution smearing is used in the simulation. The energy
dependent resolution smearing is performed by comparing the peak width of data and simulation in the
Z invariant mass distribution.
simulation!

1! training of !

5! Zàee #3!

resolution
smearing !

MC-based !
e/γ calibration!

EM !
cluster!
energy!

calibrated !
e/γ !
energy!

MC-based !
e/γ energy!
calibration!
data!

2!

4!

longitudinallayer intercalibration!

uniformity
corrections!

5!

Zàee #
scale
calibration!

6!

J/ψàee Zàllγ#
data-driven scale validation!

Figure 4.15.: The overview for the calibration of electron candidates in ATLAS [143].

4.3.3

Electron Identification and Isolation

Since the reconstructed electron still has huge background from heavy-flavour decay or photon conversion additional fake reductions are necessary. The background for the prompt electrons can be suppressedby a powerful identification (ID) based on the likelihood-based method. The ID for an electron is based on
the tracking and calorimeter system information by the probability density functions defined as following
formula:nY
LS
LS(B) (~x) =PS(B),i (xi ), dL =(4.7)
LS + LB
i=1

5

No dedicated inter-calibration is applied for the third layer since the energy contribution is negligible.

4.4. Muons

44

Fraction of events

where ~x is the variable value vector and PS(B),i (xi ) is signal (background) probability density function
at variable xi of the discriminant LS(B) . Significant discrimination power variables are selected as the
inputs of ID training. EM calorimeter information detected in each layer and the information from TRT
significantly improve the separated power for light-flavor jets (referred to as LF, all quarks beside theb- or c-quarks) and γ. ∆η, ∆φ, and a ratio of the cluster energy to the track momentum from trackcluster matching also provide powerful discrimination for LF and γ. Heavy-flavor jets (b- or c-quarks,
so call HF) background is rejected from prompt electrons with track condition such as shower width
and the ratio of cell energy to the electron cluster position. The more detail of the input variables isshown in Reference [147]. Figure 4.16 shows the likelihood-based (LH) discriminant dL used for ID of thereconstructed electron candidates.

0.09
0.08
0.07

SignalBackground

ATLAS Simulations = 13 TeV
30 GeV<ET<35 GeV, |η|<0.6

0.06
0.05
0.04
0.03
0.02
0.01
0
−4

−3

−2

−1

0

1

2

Log-transformed likelihood discriminantFigure 4.16.: The LH-based discriminant dL for Z → ee signal simulation sample (black histogram) and the redhistogram is for background from jets and γ conversion. The good quality tracks of the reconstructed electron
candidates are requested with 30 GeV < ET < 35 GeV and |η| <0.6 [147].

Three different working points (WPs) are available, Loose, M edium, and T ight. The corresponding
efficiencies are 93%, 88% and 80% for identifying a prompt electron with ET = 40GeV . Figure 4.17
includes the electron-ID efficiencies with all measurement uncertainties in Z → ee simulation samples asa function of ET and η. The range for scale factors, calculated with the data-to-simulation comparison, isfrom 0.5% to 10% with the largest uncertainties found at low ET . In this analysis, Loose WP is applied
for electron-veto selection to remove lepton background as much as possible.

4.4

Muons

Muons play a key role in many particles physics. However, comparing to other particles like electrons, it
is very difficult to be detected due to its weak Bremsstrahlung behavior. Combined information from the
ID and calorimeters supplements the information used for reconstruction. Muons escape from most of thedetectors without leaving the signature and only the hadronic calorimeter provides a very small energy
deposit beside the Muon spectrometers. The muon spectrometers are built with a strong magnetic field45

1

Efficiency

Efficiency

4.4. Muons

0.95
0.9

0.9

0.85

0.85

0.8

0.8

0.75

ATLAS

0.75

0.7

s = 13 TeV, 37.1 fb-1

0.7

Data identification efficiency εid

0.65

0.65

Loose
Medium
Tight

0.6

0.6

Data identification efficiency εid

ATLAS

Loose
MediumTights = 13 TeV, 37.1 fb-1
ET>4.5 GeV

0.55

Data / MC

0.55

Data / MC

1
0.95

1.1
1
0.9
20

40

60

80

100

120

140

1.1
1
0.9
−2.5 −2 −1.5 −1 −0.5

(a)

0

0.5

1

1.5

2

2.5
η

ET [GeV](b)

Figure 4.17.: The electron-ID efficiencies in Z → ee simulation corresponding to Loose (blue), Medium (red), andTight (black). The data-to-simulation ratio also presents the scale factor for three WPs used in the analysis. (a) isformed as function of ET and (b) is the one in η function. The range for scale factor is from 0.5% to 10% with thelargest uncertainties found at low ET .

integral in ranging between 2 and 6 Tm for very high precision measurement of muon trajectory 6 [148].
Like the electron object, the muons are used in the veto requirement for the lepton background in thissearch. The muon reconstruction is described in Sec. 4.4.1 and the muon momentum calibration in
Sec. 4.4.3. The identification algorithms and isolation efficiency study of muon candidates are describedin Sec. 4.4.2. This Section widely refers to [149].

4.4.1

Muon Reconstruction

Each sub-detector in ATLAS, such as ID and MS, provides individual information for the propertiesof the muon track. ID track reconstruction was already explained in electron Section, so this section is
focused on the Muon reconstruction in the MS.
The muon reconstruction is based on the hits patterns in the ID and MS. The four different muon
objects for physics analysis are defined based on the muon trajectory recorded by the sub-detectors:• Combined muons (CB): The primary muon object with a global χ2 fit on ID track and MS track.
A combination reconstruction for muon with an inside-out information was completed.
• Calorimeter tagged muons (CT): Only a track in the ID and a minimum-ionizing particle signaturein the calorimeter are used for CT muon.
• Segment-tagged muons (ST): The ST muons are used to recover acceptance at low pT , where muons
can reach only the first layers of the MS.
• Extrapolated muons (ME): MS track with no associated ID track, so-called Standalone muons, isused for reconstructing muons traveling outside the ID region.
6

The position resolution for the chamber of MS is 35 µm.

4.4. Muons

46

Variableq/psignif icanceρ0χ2Description
Sum of the difference between the ratio of the charge and momentum in the ID and MS.
The difference between transverse momentum measurements divide track pT in ID and MS.
χ2 value of the combined track fit using for muon reconstruction.

Table 4.1.: The variables used in muon identification. They offer good discrimination for prompt muons andbackground muon candidates [150].

The additional overlap study between different muon types is completed by comparing the ID track andanalyzing the track hit content. Not only CB muons and ME muon are used in this search, but also the
ST muons and CT muons are also considered with the restriction.

4.4.2

Muon Identification and Isolation

Efficiency

Efficiency

Different requirements are imposed on the track information obtained from the ID and MS to identify
good quality muons. The variables information used in the requirements are listed in the Tab. 4.1: Fourdifferent identification criteria (Medium, Loose, Tight, and High-pT ) are provided in the ATLAS. The
Loose requirement is used in this high mass Higgs search. It is designed to maximize the reconstruction
efficiency of the good-quality muon tracks and optimized for Higgs boson candidate reconstruction in
four-lepton final state [151]. All muon types are used in Loose ID, while CT and ST muons are usedwithin the restricted η region. The contribution of CB , CT and ST muons within |η| < 2.5 are 97.5%,
1.5% and 1%, respectively. The corresponding efficiency for signal muons in overall momentum is larger
than 96% with the 0.5% fake rate of hadrons background. The efficiency study of muon ID is measured
based on J/ψ → µµ and Z → µµ tag-and-probe analysis, and calculate the scale factor from the efficiency
difference between the simulated and experimental data. Figure 4.18 shows the reconstruction efficiency
for Loose working point and the corresponding SF.

1

1

0.98

0.98
J/ ψ →µµ Data
J/ ψ →µµ MC
Z→µµ Data
Z→µµ MC0.96-1

s = 13 TeV, 3.2 fb

Data / MC

Loose muons, |η|>0.1

1.02

6 7 8 910

20

0.96
ATLAS

0.94

30
40 50 60
100
Stat only
Sys ⊕ Stat1
0.98
6 7 8 910

20

30

2

10
40 50 60
p [GeV]T(a)

Data / MC

ATLAS

Z→µµ

s = 13 TeV, 3.2 fb-1

Data

Loose muons

MC

1415
1819
2021
Stat
only1617
Sys⊕ Stat1.01 1 2 3 4 5 6 7 8 910111213

1
0.99
2

4

6

8

10 12 14 16 18 20

No. of Primary Vertices(b)

Figure 4.18.: The reconstruction efficiency for Loose working point and the corresponding SF as a function of(a) pT and (b) the number of PVs. They are measured in J/ψ → µµ and Z → µµ tag-and-probe analysis withpT >10 GeV for the muon candidates and several event selections. The panel at the bottom shows the ratio of thesimulated and experimental data, which is used as the SF [151].

The other powerful method for rejecting background originating from semi-leptonic heavy flavor had-

4.5. Hadronic τ Decays

47

Efficiency

ron decays is referred to as muon isolation, built based on the information from the detector property
around a muon candidate. It consists of two based variables, track-based pvarcone30
and calorimeter-basedT
ETvarcone20 . pTvarcone30 presents the sum of the tracks (pT larger than 1GeV) around the muon within a cone
size ∆R = min(10GeV /pµT , 0.3), where pµT is the transverse momentum of the muon. While ETvarcone20 ,defined as the one based on transverse energy of topological clusters with cone size ∆R = 0.2, improves the
suppression power for the pile-up background. The gradient isolation working point provides ≥ 90(99)%efficiency for the muons with pT > 25(60) GeV, is used in this analysis. The systematic uncertainties
are estimated smaller than 0.5% for overall region with pT > 20 GeV. Figure 4.19 shows the efficiency
included full systematic and statistical uncertainties in the overall pT range of muons.

1

ATLAS
s = 13 TeV, 3.2 fb-1

Gradient isolation

0.95
Z µµ

0.9

Data
MC

Data / MC

0.85

1Stat only

0.98
20

30 40 50

100

Sys ⊕ Stat

200 300
p [GeV]T

Figure 4.19.: The efficiency for isolation with gradient working point as a function of muon pT . The error bandof the bottom panel shows the statistical only, as well as the bottom panel presents the ratio between data andsimulation with statistical uncertainties and combination with full systematic uncertainties. The measurement wasstudied in Z → µµ events [151].

4.4.3

Muon Momentum Scale and Resolution

A set of corrections studied using J/ψ → µµ and Z → µµ samples is applied to the simulation.
It is necessary to apply such corrections to account for the discrepancy between data and simulation.
That muon transverse momenta constructed in the ID and MS must be calibrated with the identified
Det (η, φ) and sDet (η, φ) stand for the momentum resolution and the scale corrections forcorrections. ∆rmn(η, φ) region. The significant improvement comparing to uncorrected simulation samples can be observedin the invariant mass distribution of both J/ψ → µµ and Z → µµ candidate events with CB muons.

4.5

Hadronic τ Decays

The tau lepton plays the most important role in this analysis for background rejection, backgroundestimation, and final discriminant calculation. Due to a high mass of mτ = 1776.86 ± 0.12M eV [152], thetau lepton known as the heaviest lepton is only lepton that can decay both hadronically and leptonically,4.5. Hadronic τ Decays

1-prong (35.2%)µ− ν¯µ ντ (17.4%)e− ν¯e ντ (17.8%)

Decay Mode (Faction)
Leptonic (35.2%)
3-prong (6.4×10−3 %)1-prong (48.9%)µ− e− e+ ν¯µ ντ (3.6×10−3 %)π − ντ (10.8%)− − +−3e e e ν¯e ντ (2.8×10 %)π − π 0 ντ (25.5%)
π − 2π 0 ντ (9.5%)

48

Hadronic (64.0%)
3-prong (15.1%)
π − π − π + ντ (9.3%)
π − π − π + π 0 ντ (4.8%)π − π − π + 2π 0 ντ (0.5%)

Table 4.2.: The table for the main decay mode of tau lepton. The leptonic or hadronic decay modes with one(three)charge particle are referred to as 1-prong(3-prong). The fraction of each main decay modes corresponding to total
branching fractions was also described. The other modes with such as 5prong with a small fraction are not listed
in this table. It widely reference from [152].

so called τlep and τhad . 7 The summary table for the decay mode is described in Table. 4.4. Most of
the hadronic decay modes are dominated with one or three charged particle, referred to as 1-prong and3-prong decays, respectively, including charged pions, π ± , and kaons, K ± . The 3-prong leptonic decays
with very small branching fractions are also considered in this analysis The main target of τ identification
is to distinguish the τhad decays from hadronic jets.
Section 4.5.1 shows the reconstruction for τ objects with the LCW topo-clusters with a smaller cone andthe reconstructed tracks. A dedicated energy momentum calibration procedure is presented in Sec. 4.5.2
for τhad candidates. To separate τhad from hadronic jets from quark and gluon, the number of hits of ID
detector is one of the most important variables and highly depends on the charged track’s number from
tau and their momenta. The two identification techniques are defined for 1-prong τhad and 3-prong τhadseparately as shown in Sec. 4.5.3. The Tau Trigger (STT) is used in this analysis and shown in Sec. 4.5.4.
The contribution of 2-prong τhad is expected to be sizable in this analysis with high-pT tau, hence the
2-prong tau reconstruction and identification are considered in this analysis for the first time in ATLAS.
The further detail of 2-prong τhad is shown in Sec. 4.6.

4.5.1

Tau Reconstruction

Discovery with H → τ τ decay relies not only on high-purity selection on τhad candidates but the fourmomenta reconstruction for the charged and neutral pion. The tau reconstruction is performed basedon the method of ATLAS Run1, so-called ”Baseline”. Over 90% of hadronic taus decay into charged
hadrons (h± ), neutral pions (π 0 ) and a tau neutrino as discussed above. π 0 decays exclusively to apair of photons and photons convert into e− e+ . h± stands for for π ± and K ± with small contribution.
However, only the difference of charged hadrons between tau decay modes is taken into account. The
fake track backgrounds like hadrons produced from pile-up interactions have affected the efficiency ofτhad reconstruction. A new method called ”Tau Particle Flow” (TPF) is applied for reconstructing
the individual charged and neutral hadrons in tau decay modes. The goals of TPF is to reduce thosebackground by classifying the main five decay modes. 8 Charge and momentum of h± are determinedusing the ID track, however, the overestimation of h± is also expected due to the source coming fromconversion electrons. The behavior of the five decay modes has been well-understood by the correlationof following three parameters of TPF: the branching fractions, tau selection efficiency of simulated tau
without jet/electron, and fake rate of simulated tau passing electron or jet selection. The TPF algorithm
is built by Toolkit for Multivariate Data Analysis (TMVA) in the reconstruction step and suppress thosebackgrounds effectively 9 . Boosted decision trees (BDT) of TMVA tool is employed with several input
7

Since the neutrino in tau decays goes undetected by ATLAS detector, those particles are ”invisible” and omitted in further
reconstruction. Therefore, the reconstructed taus are also referred as τlep−vis and τhad−vis .
8 ±h , h± π 0 , h± ≥ 2π 0 , 3h± , 3h± ≥ 1π 0
9
TPF also often be referred to as TMVA tracking since it used TMVA to optimize the track resolution.

4.5. Hadronic τ Decays

49

400
350
300

Data (8 TeV, 5.0 fb-1)
Z / γ *→τ τ
BackgroundStat. Uncertainty

ATLAS

250

Events / 0.1

Data (8 TeV, 5.0 fb-1)
Z / γ *→τ τ
BackgroundStat. Uncertainty

ATLAS

Events / 0.1

2400
2200
2000
1800
1600
1400
1200
1000
800
600
400
200
0
1.5

200

600
500

Data (8 TeV, 5.0 fb-1)
Z / γ *→τ τ
BackgroundStat. Uncertainty

ATLAS

400
300

150

200

100
100

1
0.5
−1

−0.5

0
0.5
1
h± {0,1}π 0 BDT Score

0
1.5

1
0.5
−1

−0.5

(a)

0
0.5
1
h± {1,≥2}π 0 BDT Score

Obs. / exp.

50

Obs. / exp.

Obs. / exp.

Events / 0.1

variables from π0 candidates, such as energy fraction in the different layers of the EM calorimeters, η anddepth of cluster used for reconstruction, and the number of cells. The final output of BDT score is shownin Fig .4.20 for the different tau-hadronic decay modes of h± and π 0 . The BDT is trained using with
Z/γ ∗ → τ τ signal sample and multijet and W → τ ν+jets backgrounds. The number of τhad candidates
distribution and mode classification efficiency matrix compared to truth decay modes in simulation withseparating of classified decay modes are presented in Fig. 4.21. The TPF reconstruction significantly
improves the η and φ resolutions of the reconstructed τhad candidates (Shown in Fig. 4.22).

0
1.5

1
0.5
−1

−0.5

(b)

0
0.5
1
3h± {0,≥1}π 0 BDT Score(c)

ATLAS Simulation
Diagonal fraction: 70.9%
Tau Particle Flow (π 0 reconstruction) Z / γ *→τ τ

3h ± ≥1π 0

0.2

2.5

3.5

11.0

55.3

3h ±

0.2

0.6

0.4

86.8

41.5

h ± ≥2π 0

1.2

12.4

39.6

0.2

0.7

h± π 0

9.7

67.5

50.9

0.7

2.1

h±

88.6

16.9

5.6

1.4

0.5

h±

h± π 0h ± ≥2π 03h ±3h ± ≥1π 0

ATLAS

Data (8 TeV, 5.0 fb-1)
Z / γ *→τ τ (3h ± ≥1π 0)
Z / γ *→τ τ (3h ± )Z / γ *→τ τ (h ± ≥2π 0)Z / γ *→τ τ (h ± π 0)
Z / γ *→τ τ (h ± )BackgroundStat. Uncertainty

6000

4000

2000

Generated decay mode(a)

Events / Decay mode

Reconstructed decay mode

Figure 4.20.: Distribution of BDT score for separating the different decay modes of h± and π 0 . The signal sample
responds Z/γ ∗ → τ τ . The background are dominated by multijet and W → τ µ+jets production [153].

0h±h± π 0h ± ≥2π 03h ±3h ± ≥1π 0

Reconstructed decay mode(b)

Figure 4.21.: The number of τhad candidates distribution (b) and decay mode classification efficiency matrix(a) [153].

The shower information of h± measured in calorimeters is used for the reconstruction of tau energy
and direction. The energy of π 0 is deposited in the EM calorimeter. The energy reconstruction of τhadstarts with jet reconstruction from TC using anti-kT algorithm with a distance parameter of 0.4 andis calibrated with a local hadronic calibration (LC) [154]. However, only the TCs within the new core

103

50

ATLAS Simulation
Z / γ *→τ τ

Tau Particle Flow
Baseline

102

10Probability density

Probability density

4.5. Hadronic τ Decays

103

10−1

10−1
0

0.02

0.04

η-η

Baseline

10

1

−0.02

Tau Particle Flow

102

1

−0.04

ATLAS Simulation
Z / γ *→τ τ

−0.04

−0.02

0

(a)

0.02

φ-φ

gen

0.04
gen

[rad]

(b)

Figure 4.22.: The comparison plots for the distribution of (a) τhad η and (b) φ between Tau Particle Flow andBaseline reconstruction [153].

definition, around the tau candidate, referred to as core region (∆R(τhad ,jetinitial ) < 0.2), is used to thecalculation of the τhad four-momentum. The outer core region (0.2 < ∆R(τhad ,jetinitial ) < 0.4) is used tosuppress background as isolation region.
The primary vertex or pile-up vertex is not always the same with tau vertex. In order to reduce theeffect from others vertices, the tau vertex (TV) association algorithm to separate decay vertex of τhadis defined with all tau tracks information in the ∆R(τhad ,jetinitial ) < 0.2 described above [155] [156]. By
finding the jet with the highest TV value, it contributes to the improvement for track selection efficiency
as shown in Fig. 4.23. Compared with the track reconstruction efficiency with default primary vertex,
TV algorithm shows a better performance, especially for high pile-up region.
By summing up the reconstructed h± and π 0 candidates, the four-momentum reconstruction and hadronic decay mode defination of τhad , jetinitial are finished. Figure 4.24 shows the reconstruction efficiency as
a function of pT in overall transverse momentum region and the decay mode classification of τhad , jetinitial
candidates. The overall efficiency for τhad , jetinitial is around 70% for 1-prong and 3-prong τhad , jetinitial .
The figure displays the efficiency slightly drop in high pT region for 3-prong τhad , jetinitial due to themerged phenomenon for the ID tracks. For a instance, two high pT tracks with the same charge from a
3-prong τhad might be reconstructed to the similar trajectory in the ID due to the boosting property.

4.5.2

Tau Energy Calibration

The energy of τhad is reconstructed with TC clusters and calibrated with LC scale [157]. In order tofurther correct the energy measurement in the detector to true visible energy obtained at the generated
level, the tau energy scale (TES) is applied in simulation. The calibrated energy of τhad is calculated as:
Ecalib =ELC − Epileup,
R(ELC − Epileup , |η|, nprong )(4.8)

where ELC and Epileup is a random pileup contribution at the LC-calibrated energy within the cone of∆R < 0.2 of tau candidate and the one from the pileup. Since Epileup linearly increases with number

51

1.05

Efficiency

Efficiency

4.5. Hadronic τ Decays

1

1.05
1

0.95

0.95

0.9

0.9

0.85

0.85
ATLAS Preliminary
Simulation mc15
1-prongs = 13 TeV

0.8
0.75
0.7
0

10

20

30

40

50

ATLAS Preliminary
Simulation mc15
1-prongs = 13 TeV

0.8

Default primary vertex
Tau Vertex

0.75
60

70

80

0.7
0

90 100

5

10

Default primary vertex
Tau Vertex

15

20

25

30

pτ [GeV]
T

NVtx

(a)

(b)

1.4
1.2

ATLAS Preliminary

normalized

efficiency

Figure 4.23.: Due to the difference of decay mode for 1-prong and 3-prong, the TV algorithm is employed for the
1-prong and 3-prong separately. (a) presents the efficiency of track selection for 1-prong τhad , jetinitial with default
PV (black) and TV(red) as a function of τhad , jetinitial pT . (b) shows the one for the average number of pile up
interactions. Obviously, TV improves the association efficiency of 1-prong for high pile-up region [155, 156].

truth 1p
truth 3p

Simulations = 13 TeV

1ATLAS Preliminary

truth 1p
truth 3p

Simulations = 13 TeV

0.8

1
0.6

0.8
0.6

0.4

0.4
0.2

0.2
0

50

100 150 200 250 300 350 400 450 500
τ had-vis

truth p

T

(a)

[GeV]

0

0

1

2

3

4

5

reconstructed number of tracks(b)

Figure 4.24.: The combined efficiency of reconstruction and classification as a function of pT in overall transverse
momentum region and the decay mode classification of τhad , jetinitial candidates. As shown in (b), there are the misreconstruction tau to 2-prong from truth 1-prong. In the case that the not clear pile-up jets or photon conversion
tracks in the inner detector passed the track selection, the overestimation of the number of prongs is happened.
The one from truth 3-prong is because the similar trajectory reconstructed by the ID track of multiple tracks withthe same charge and high pT are merged and cannot be well-reconstructed.

4.5. Hadronic τ Decays

52

0.6

ATLAS Preliminary

1-prong τ

s = 13 TeV Simulation

multi-prong τ

1.3
1.25

ATLAS Preliminarys = 13 TeV Simulation

Response

0.7

Response

A [GeV]of PV, the Epileup is derived as Epileup = A × (NPV − hNPV i) with average number of primary vertex
hNPV i ∼ 14. The linear coefficient A is from the fitting result of ELC of the simulation samples and R
vis . The contribution of pileup correction factor
extracted as the Gaussian mean of the (ELC − Epileup )/Etrue
A and the calibration function of the detector response R are shown in Fig. 4.25 and applied as the TES
to the tau candidate. The corresponding systematic uncertainty is discussed in Sec 7.1.

|η| < 0.3
0.3 < |η| < 0.8
0.8 < |η| < 1.3
1.3 < |η| < 1.6
1.6 < |η| < 2.4

1.15
1.1

0.5

1.2

0.4

1.15

0.3

1.1

0.2

1.05

0.9

0.1

1

0.85

0

|η| < 0.3

0.3 < |η| < 0.8

0.8 < |η| < 1.3

1.3 < |η| < 1.6

1.6 < |η| < 2.4

ATLAS Preliminarys = 13 TeV Simulation|η| < 0.3
0.3 < |η| < 0.8
0.8 < |η| < 1.3
1.3 < |η| < 1.6
1.6 < |η| < 2.4

1.05
1

1-prong τ

0.95
20

102

30 40

|η|

(a)

0.95

2×102
pileup-corr
[GeV]
ELC

multi-prong τ

0.8
20

(b)

102

30 40

2×102
pileup-corr
[GeV]
ELC

(c)

Figure 4.25.: The pileup correction factor A in bins of |η| for 1-prong τhad , jetinitial and multi-prong τhad , jetinitial
pileup−corr, whichshown in (a). The detector response R for 1-prong and multi-prong tau decays as the function of ELC
indicates the average pileup-corrected energy, are present in (b) and (c) respectively [153].

35
30
25

ATLAS Preliminarys = 13 TeV Simulation|η|<0.3
0.3 < |η| < 0.8
0.8 < |η| < 1.3
1.3 < |η| < 1.6
1.6 < |η| < 2.4

1-prong τResolution [%]Resolution [%]vis with fit. The final
The resolution of τhad is computed based on Gaussian width of the Ecalib /Etrue
resolution curve is illustrated in Fig. 4.26 in separate bins of |η| and nprong bins.

35
30
25

20

20

15

15

10

10

5

5

0
0

100

200

300

400

500

600

0
0

ATLAS Preliminarys = 13 TeV Simulation
multi-prong τ

100

200

300

Ecalib [GeV](a)|η|<0.3
0.3 < |η| < 0.8
0.8 < |η| < 1.3
1.3 < |η| < 1.6
1.6 < |η| < 2.4

400

500

600
Ecalib [GeV](b)

Figure 4.26.: The curve for the resolution of reconstructed 1-prong (a) and multi-prong (b) tau decays in thecalibrated energy bins [153].

4.5.3

Tau Identification

The leptonic decay tau (electron or muon decaying modes) cannot be identified due to the limit of
ATLAS detector and the tau decay length. Identification for tau on charged and neutral pions modes isonly considered in this analysis. Since quark- and gluon-initiated jets are the dominated background forτhad after the reconstruction, the combined information of shower shape in the calorimeter and tracks inID [137] provides a powerful discrimination ability from jets. A multivariate tau identification algorithm
applied separately for 1-prong and 3-prong τhad , so-called Tau ID, is trained by boosted decision trees(BDTs) of MVA tools. Furthermore, only the τhad candidates that have pT > 15 GeV and |η| < 2.5

4.5. Hadronic τ Decays

53

and have one or three associated tracks are used for the Tau ID training. 10 The useful discriminating
variables are described as the following items, and the difference between 1-prong and 3-prong inputs issummarized in Table. 4.3. Each variable is corrected by applying an additional correction, which linearly
depends on the average number of pileup interactions per bunch crossing (hµi). This correction reduces
the pileup dependence on the efficiency of Tau ID.
• Central energy fraction (fcent ): Transverse energy deposit of the topo-clusters of the calorimeterwithin a small cone region (∆R < 0.1 around τhad candidate) divided by the one within larger cone
region (∆R < 0.2 around τhad candidate). The energy deposit is also calibrated in the EM-scale.
−1• Leading track momentum fraction (fleadtrack): Transverse energy of the EM scale topo-clusterin the τhad core region divided by the charged track with leading transverse momentum pT in thesame core region.
0.2 ): ∆R weighted by the track transverse momentum of the τ• Track radius (Rtrack
had and theassociated tracks in core region.

• Leading track IP significance (|Sleadtrack |): The impact parameter of the highest pT tracks incore region by calculating with the TV and its estimated uncertainty.
track ): Ratio of the transverse momentum p• Fraction of tracks pT in the isolation region (fisoTscalar sum of the associated tracks of τhad candidate in isolation core region (0.2 < ∆R < 0.4) withrespect to the one of all associated tracks.

• Maximum ∆R (∆RMax ): The maximum distance in between the associated track and the τhadcandidate based on ∆R. Only the associated tracks in core region are considered.
• Transverse flight path significance (STflight ): Define the flight path based on the decay lengthfrom the secondary vertex of the associated tracks in core region. It is calculated with respect to
the TV divided by its uncertainty• Track mass (mtrack ): Invariant mass of all tracks in both core and isolation regions with theassumption of each track being pion.
track−HAD• Fraction of EM energy from charged pions (fEM): Ratio of two values related withthe energy deposit associated with the τhad candidate in the EM calorimeter and TC energy depositin the hadronic calorimeter. The numerator is the difference between the momentum sum of all
tracks in core region and TC energy deposited in the hadronic calorimeter including Back layer of
EM calorimeter information. The denominator is sum of TC energy in EM calorimeter with only
pre-sampler, Front-layer and Middle-layer information.
EM ): Ratio of the sum of EM cluster energy and• Ratio of EM energy to track momentum (ftracksum of the momentum of tracks in core region. The TC and tracks are associated with the τhadcandidate and calibrated with the LC energy scale.

• Track-plus-EM-system mass (mEM+track ): Invariant mass of the system composed of all tracks
and two highest energetic EM cluster in the core region. Only the cluster from leading three layersof the EM calorimeter is considered. 11 In addition, the hypothesis of zero mass with TC seed
direction is applied to the four-momentum calculation of an EM cluster.
10

ATLAS suggests using only 1-prong and 3-prong only for any physics analysis. However, this thesis provides the first try
with the τhad candidate with two associated tracks.
11
presampler, Front-layer and Middle-layer only. Back layer designed specially to measure the tail of EM showers is notconsidered in this variable.

4.5. Hadronic τ Decays
Variable Namefcent
−1
fleadtrack
0.2
Rtrack|Sleadtrack |
track
fiso
∆RM axSTf light
mtracktrack−HAD
fEM
EM
ftrackmEM +track+track
pEM
/pT
T

54
1-prong
◦
◦
◦
◦
◦

◦
◦
◦
◦

3-prong
◦
◦
◦

◦
◦
◦
◦
◦
◦
◦

Table 4.3.: The discriminating input varaibles to Tau ID BDT training for 1-prong and 3-prong τhad respectively [153].

/pT ): The variable related with the meas• Ratio of track-plus-EM-system to pT (pEM+trackTurement τhad pT . Ratio is the vector sum of track momenta combined EM cluster and ID track
information divide to the one for two highest energetic EM cluster of the calorimeter only in coreregion.
The background rejection versus signal efficiency, which is also referred to as “ROC curve”, with each
optimized working points are displayed in Fig. 4.27. The multi-jet dominated simulation background
events and signal Z/γ ∗ → τ τ events are used in BDT discriminant training. The three working points forphysics analysis, loose, medium and tight, are optimized based on the signal efficiencies (0.6, 0.55, 0.45)
for truth 1-prong τhad and (0.5, 0.4, 0.3) for truth 3-prong τhad . For this high mass Higgs analysis, thecorresponding efficiency after each tau ID working points requirements of truth 1-prong (3-prong) τhad arepresented in Fig 4.28. The black point in the histogram also presents the rate of the generated level τhad
object being reconstructed as a corresponding τhad candidates. To deal with the discrepancy of data andMC simulation after tau ID application, the corresponding scale factor are applied as the corrections for
MC simulation. A special uncertainty is predicted for high-pT τhad region to cope with the low statisticalproblem in data. The larger combined uncertainties up to around 55%(40%) are applied for 1-(multi)prong modes to cover both uncertainties associated with reconstruction and identification efficiency. Dueto the high-pT τ in this analysis, the tau ID uncertainty is the main systematic uncertainties.

4.5.4

Tau Trigger

The Region of Interest (RoI) has been defined in level 1 trigger built with the electromagnetic (EM) andhadronic (HAD) calorimeter trigger tower of typical granularity in ∆φ × ∆η = 0.1 × 0.1. The precision
tracking consists of calorimeter clustering and tracking information from the Level-1 Tau RoI. Eventsfor τhad τhad channel are recorded using the single tau trigger (STT). The STT is with the requirements
on tau pT , Tau ID threshold and the number of tau tracks for having high efficiency as well as goodresolution. The two levels of the number of tracking requirement, so-called as tracktwo, is applied on the
pre-selection step of the τhad objects for identifying candidates and against hadronic backgrounds. Tau
trigger identification working point medium1 is built with a slightly higher signal efficiency compared to
Tau ID medium working point for reconstructed τhad . The L1 Tau seed objects are also requested with 60
GeV and 100 GeV pT cuts, therefore the pT thresholds at HLT are adjusted accordingly. The lowest pT
threshold of STT in this analysis is 80 GeV. In the further high luminosity environment, the pT thresholdhas been harder and raised to 125 GeV and 160 GeV. The tau trigger efficiencies at the L1 and HLT are

55

Inverse Background Efficiency

4.5. Hadronic τ Decays

105
ATLAS Preliminary Simulation
104
103
102

p > 20 GeV, |η| < 2.5T

1-track τhad-vis

10
1
0

3-track τhad-vis

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

1

Signal Efficiency

Reco

Loose

Reco

Loose

MediumTight

MediumTight

1
1-prong

0.9
0.8

Efficiency

Efficiency

Figure 4.27.: The inverse background efficiency versus signal efficiency of Tau ID for 1-prong τhad (red line) and3-prong τhad (blue line). (tight, medium, loose) working points are also represents as the dots on the curve from left
to right, while the fourth (rightmost) point corresponds to the signal efficiency of 95 % is called very loose working
point, which never used in this analysis [158] [159].

1

0.8

0.7

0.7

0.6

0.6

0.5

0.5

0.4

0.4

0.3

0.3

0.2

0.2

0.1

0.1

0

103

102

3-prong

0.9

0

103

102

True Tau p [GeV]

True Tau p [GeV]

T

(a)

T

(b)

Figure 4.28.: (a) and (b) show the pT distribution of τhad objects matched with the generated level objects for
1-prong and 3-prong. The black point shows the reconstructed rate of the generated level τhad . While the efficiencyof each working point includes the reconstruction rate are shown in green (for loose), blue (for medium) and red(for tight) points.

4.6. Hadronic τ Decays with Two Charged Particles
Trigger name
HLT tau80 medium1 tracktwo L1T AU 60
HLT tau125 medium1 tracktwo
HLT tau160 medium1 tracktwo
HLT tau160 medium1 tracktwo L1T AU 100

56
For Years
2015-20162015-20162016-20182017-2018

Luminosity (f b−1 )
5.3
9.3
103.4
22.3

Table 4.4.: Table of STT used in this analysis. Each STT used for different data taking year corresponding to
its luminosity.

Efficiency

Efficiency

shown in Fig. 4.29 as a function of pT of τhad or the number of pp interaction vertices. The STT used inthis search are listed in Table 4.4:
The efficiency of STT is studied in the Z → τ τ events. It is calculated using the probe τhad candidates
that passing the STT. The difference between the data subtracted backgrounds and the simulated Z → τ τevents is computed as a scale factor for simulation in the analysis. Figure 4.30 shows the result of single
tau trigger with isolated requirement for the objects at L1, and the offline pT cut are also applied for τhadcandidates. Tau trigger shows very good performance especially for high-pT region. For 1-prong τhad , theefficiency is almost full above pT > 40 GeV .

1

1

ATLAS Preliminary

ATLAS Preliminary-1

s = 13 TeV, 3.2 fb

0.5

s = 13 TeV, 3.2 fb-1

0.5

Z→τµ τhad

Z→τµ τhad, p (τhad-vis)>30 GeVT

HLT tau25 medium trigger

0100

HLT tau25 medium trigger

L1

L1

HLT

HLT

200

300

0
0

5

10

p (τhad-vis) [GeV]20

Number of vertices

T

(a)

15

(b)

Figure 4.29.: The tau trigger efficiency estimated by data subtracted backgrounds as the functions of τhad pT(a) and number of vertices (b). Red and blue dots show the efficiency for Level 1 and High Level Trigger respectively [160].

4.6

Hadronic τ Decays with Two Charged Particles

The track reconstruction and identification are important for reliable reconstruction of τhad object. It
highly depends on the geometrical information from ATLAS detector and the technology of fake background suppression. In the search for heavy Higgs to di-τhad channel, the final state with high pT τhad is
expected. As discussed in Sec 4.5, τhad is generally dominated in the final state with one or three charged
tracks. However, the τhad with mis-reconstructed charged tracks, such as 2-prong τhad , appears due toATLAS Preliminary

1.4

s = 13 TeV, 33 fb-1
Z→τµτhad , 1-prong
HLT tau25 medium trigger

Data/exp.

1.2

MC Z→ττMC stat. error
Data 2016
Data syst. error
Data stat. + sys. error

Efficiency

1.6

ATLAS Preliminary

1.4

s = 13 TeV, 33 fb-1
Z→τµτhad, 3-prong
HLT tau25 medium trigger

1

1

0.8

0.8

0.6

0.6

0.4

0.4

0.2

0.2

0
1.5

0
1.5

1
0.5

30

40

50 60 70200100

MC Z→ττMC stat. error
Data 2016
Data syst. error
Data stat. + sys. error

1
0.5

300

57

1.6

1.2

Data/exp.

Efficiency

4.6. Hadronic τ Decays with Two Charged Particles

30

40

50 60 70

T

Data/exp.

1.2

ATLAS Preliminarys = 13 TeV, 33 fb-1
t t , 1-prong
HLT tau160 medium trigger

MC tt
MC stat. error
Data 2016
Data sys. error
Data stat. + sys. error

Efficiency

(b)

1.6

ATLAS Preliminary

1.4

s = 13 TeV, 33 fb-1
t t , 3-prong
HLT tau160 medium trigger

1.2

1

1

0.8

0.8

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Data/exp.

Efficiency

(a)

1.4

1
0.5

160

180

200

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240

260

280

300

MC tt
MC stat. error
Data 2016
Data syst. error
Data stat. + sys. error

1
0.5

160

180

200

220

Offline tau p [GeV]

240

260

280

300

Offline tau p [GeV]

T

(c)

300

Offline tau p [GeV]

T

1.6

200

100

Offline tau p [GeV]T(d)Figure 4.30.: The trigger efficiency with the corresponding scale factors for (a) 1-prong and (b) 3-prong. The
efficiency is measured by tag-and-probe method in Z → τ τ control region with data and simulation. The bottom
two plots show the efficiency measured by tag-and-probe method in tt̄ events for high-pT (c) 1-prong and (d) 3-prong
τhad [161].

4.6. Hadronic τ Decays with Two Charged Particles

58

the possible reasons illustrated in Fig 4.31.

1-prong !"#$
tau trackcore

fake track

3-prong !"#$
tau tracks(merged)core
tau track(a) 1-prong → 2-prong case(b) 3-prong → 2-prong case

Figure 4.31.: The reasons for hadronic τ reconstructed with two charged tracks. In 1-prong τhad → to 2-prong
τhad case, an additional fake track passed the tau track core selections is expected from π 0 decay and taken into
the hadronic τ reconstruction. For the 3-prong → 2-prong case, the high pT τhad produces two geometrically close
tracks are merged due to the boosting phenomenon.

When the τhad is produced with high pT , the tau decay products are highly collocated and the twosame charged tracks from 3-prong tau are merged into a single track. In this case, many 3-prong τ are
mis-reconstructed as 2-prong τ . On the other hand, around 30% contribution of 2-prong τ of this analysis
comes from 1-prong τ due to an additional fake track from e+ e− pair-creation associated with π 0 → γγ.
Since an additional fake track is taken into τhad reconstruction, it causes the 1-prong → 2-prong case. In
most of ATLAS analysis, 2-prong tau is not exploited due to the negligible contribution in low pT region.
There is no the support staff from the ATLAS for 2-prong τ application.
In this analysis with high pT τhad , there are many 2-prong τhad in the high mass signal. Ah shownin Fig. 4.32, the pT distribution of τhad shows that the τhad object from heavy Higgs is with high pT .
Moreover, the 2-prong τhad contribution of 1500 GeV signal is larger than the one of 300 GeV signal. The
signal efficiency is significantly improved by adding the 2-prong τhad . In the gluon-gluon fusion signal with
Higgs mass of 1500 GeV, the contribution of 2-prong τhad with pT > 50 GeV is around 15%. After event
selection and trigger application in this analysis, 2-prong τhad application saves the ggH signal efficiency
of about 20%. Approximately 65% of reconstructed 2-prong τhad s originate from the 3-prong taus in thisanalysis. The corresponding identification, calibration and systematic uncertainties are discussed in thesection.
Tau Track
Normalized

Normalized

Tau pT0.12

0.1

ggH 300 GeV

0.7

ggH 300 GeV

0.6
0.5

0.08

ggH 1500 GeV

0.06

ggH 1500 GeV

0.4
0.3

0.04
0.2
0.02
0.1
0

100

200

300

400

500

600

700

(a) τhad pT

800
900
1000
Reco. tau pT [GeV]

1

1.5

2

2.5

3

3.5
4
Number of Charged Tracks(b) number of charged track of τhad

Figure 4.32.: The pT distribution of gen-matching τhad in (a) shows the importance of high-pT τhad in the heavy
Higgs search. (b) shows the number of charged tracks associated to τhad in signal with different mass region.

4.6. Hadronic τ Decays with Two Charged Particles

4.6.1

59

Identification Investigation

An identification of 2-prong tau requires a algorithm. It is developed based on boosted decision
trees, similarly to the 1- and 3-prong tau identification. The Toolkit for Multivariate Data Analysis(TMVA) [137] is applied for the 1-prong and 3-prong τhad identification algorithms. The same schemes
are also used for the investigation of identification algorithms of 2-prong τhad . The training programfor 1-prong τhad is not considered since most of the 2-prong τhad comes from 3-prong τhad . Each input
variables of TMVA training for 3-prong τhad algorithms are surveyed for 2-prong τhad candidates. The
comparison of input variables and training output scores are summarized in Appendix F. Due to thesimilar distributions between 3-prong τhad and 2-prong τhad , it supports to use 3-prong identification
algorithm for 2-prong τhad . Figure 4.33 presents the fake rate of hadron jets in three working points ofidentification (loose, medium and tight) together with signal efficiency and background rejection, so called
as “ROC” curve 12 . Based on the background rejection curve shown in Fig 4.33(b), the strong rejection
power of identification is expected to suppress fake 2-prong τhad background. Fig 4.33(c) shows the signal
efficiency. The slightly low signal efficiency for truth 2-prong τhad due to the 1-prong→2-prong τhad case(yellow line).
The current 3-prong identification algorithms is used for 2-prong τhad in this analysis. It is acceptable
due to the strong rejection power. The performance improvement for the detectors is necessary to improve
the signal efficiency.

Loose

Medium1-prong

1-prong
2-prong
2p from truth1p3-prong

2-prong

2-prong

0.014
0.012

10

Truth Tau Efficiency

0.016

Fake Rate

Fake Rate

Tight

1
10−1

0.01
0.008

10−2

3-prong
2p from truth3p

10

1

0.006
10−3

0.004

0

10−1

10−4

0.002
103

102

Reco Tau p [GeV]
T

(a)

0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

10

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

1

BDTSigTrain cutting point

BDTSigTrain cutting point

(b)

(c)

Figure 4.33.: Performance of 2-prong τhad to a training 3-prong identification. (a) shows fake rate of multi-jet
background with the loose, medium and tight working point applications. The fake rate comparison with 1-prong
and 3-prong τhad in the function of training output score is presented in (b). The corresponding signal efficiency isillustrated in (c).

4.6.2

Calibration

Introduction
The correction for 2-prong τhad identification is computed based on the tag-and-probe analysis. Considering 2-prong τhad is dominated in high-pT region, a tt̄ control region is chosen for scale factor measurement
for the wide pT region. The higher mass of top quark compared to the Z boson provides a higher pT
spectrum for decaying tau lepton as shown in Fig 4.34 [162]. It provides enough statistics for the scale
factor measurement of 2-prong τhad .
12

Receiver Operating Characteristic of TMVA is called as ROC for short.

4.6. Hadronic τ Decays with Two Charged Particles

60

Figure 4.34.: The pT normalized distribution of gen-matched tau candidates from tt̄ and Z → τ τ events [162].

Compared with the electron object, the muon is much harder to deposit enough energy in the calorimeters. In order to choose a suited tag object, the muon object with high resolution is used in the tt̄
tag-and-probe analysis with probe τhad . The tt̄ → bµνµ + bτ ντ process is exploited to measure the fractionof efficiency between analyzed data and MC simulation.
Event Selection
A single-muon trigger with the threshold of 50 GeV is selected to choose tt̄ control region. Muon
candidates are requested to satisfy the pT > 55GeV threshold within the |η| < 2.5 region and the medium
quality as well as the isolation [163]. The events are required to include exactly one selected muoncandidate. The events with the one electron passing loose identification, pT > 15 GeV and cone region
selection are rejected. In order to maximize the purityq
of tt̄ events in the control region, the transverse mass

miss (m =miss (1 − cos ∆φ(µ, E miss ))) is applied. The
requirement of the muon candidate and ET
2pµT · ET
T
Tb-tagged algorithm is used with MV2c10 algorithm in 70% efficiency working point. The events with atleast two btagged jets with pT > 20 GeV is required. The probe object is defined as the leading pT τhadcandidate selected with pT larger than 40 GeV and with two charged tracks. In order to obtain highpurity τhad and reduce the effect from fake jets, a lower identification with BDT score > 0.04 is applied
for the probe object.

Signal and background processes
The tt̄ events with at least one truth τhad accounts as the signal process (so called truth tt̄). The tt̄
events without truth τhad are the fake background process (so called fake tt̄). The signal and backgroundare shown in Fig 4.35. The opposite sign charge requirement (OS) of tag and probe objects is applied toreduce fake tt̄ events. The number of non-b jets is different between the signal and background processes
considered here (see Fig. 4.35). The distributions of number of non-b-tagged jet is used to extract the
tau ID efficiency. Figure 4.36 shows the signal region number of non-btagged jets distribution before tau
ID application and the corresponding shape comparison between signal and background. The correction
factor is obtained as the ratio of the tau ID efficiency derived from data to that from simulation The
numerator is the tau ID efficiency of estimated data by fitting. The denominator is the tau ID efficiencyof truth tt̄ MC simulation.

4.6. Hadronic τ Decays with Two Charged Particles

!

#

%̅

()*+
-∓
-

!

±

∓

61

!

"

%̅

"
&±
"

%

(
(
&±

)∓
)±
!

#

%

#

"

(a)

(b)

Normalized

Figure 4.35.: Feynman diagrams for tt̄ event. (a) shows the signal process with one τhad , and (b) present thebackground process includes W boson decay to quark production.

0.4

0.35
0.3

truth tt NoID

0.25
fake tt NoID

0.2
0.15
0.1
0.05
0
0

1

2

3

4

5

6

7

8

9 10

Number of non b-jets(a) data vs. MC(b) MC templates

Figure 4.36.: Number of non-btagged jets distribution before tau ID application. (b) The histograms of signal
and background used in fitting are normalized to unit.

4.6. Hadronic τ Decays with Two Charged Particles

62

ResultThe scale factor for 2-prong τhad is measured with respect to the efficiency of tau ID and single tau
trigger. Since the medium ID selection with single tau trigger and only loose ID selection are applied to
the leading and sub-leading τhad in heavy Higgs search, the corresponding scale factors are considered.
Comparison of the simulation events and data are shown in the upper part of Fig 4.37. The bottom threeplots show the fitting result (post-fit plots) from data. The scale factor for 2-prong τhad is computed in
one bin due to the statistical issue. Table 4.5 shows the number of simulation signal and estimated eventin data.

Events

(a)

240
220
200
180
160
140
120
100
80
60
40
20
0

(b)

(c)

(e)

(f )

ATLAS Work in progresss = 13 TeV;ò L =79.79206 fb-1 DataTotal
tt fakett truth0 1 2 3 4 5 6 7 8 9 10
Number of non b-jets(d)Figure 4.37.: Number of non-btagged jets distribution used for 2-prong τhad scale factor measurement. Upper
three pre-fit plots show the comparison with the simulation samples and analyzed data. The bottom post-fit plotspresent the estimated event from data by fitting with signal and background templates. From left to right plots, itshows the distribution given for the probe τhad without any ID requirement (shown in (a) and (d)), with loose ID(shown in (b) and (e)) and with medium ID plus single tau trigger (shown in (c) and (f)).

The dominated systematic uncertainty of scale factor measurement comes from data statistics. The
uncertainty and scale factor are written as:
SF =

data
.
mc

r
σ
σ
σSF = SF × ( mc )2 + ( data )2 ,
mc
data

(4.9)

(4.10)

4.7. Missing Transverse Energy
Sample Namett̄ fakett̄ truth
Total MCData
tt̄ fakett̄ fake
Total MC
Data

63

No-ID

Loose
Pre-fit result
508.8 ± 12.4
71.0 ± 4.8
133.3 ± 6.8
71.0 ± 4.6
642.1 ± 14.1
142.0 ± 6.6
691.00 ± 26.3
169.00 ± 13.0
Post-fit result494.6 ± 46.5
61.9 ± 21.5
196.4 ± 43.2
107.2 ± 22.5
691.0 ± 63.5
169.1 ± 31.1
691.00 ± 26.3
169.00 ± 13.0

Med. + trigger
20.2 ± 2.6
40.9 ± 3.8
61.1 ± 4.6
74 ± 8.6
24.9 ± 13.2
49.1 ± 14.0
74.0 ± 19.2
74 ± 8.6

Table 4.5.: The yield of each simulation events and data before and after ID and trigger selections. The error
part of pre-fit result are only presented the standard statistical uncertainties, while the error part of post-fit result
includes the fitting uncertainties. The uncertainty of total MC is computed based on the propagation principle forerror calculation.

data
mc
Scale Factor

Loose
0.546 ± 0.140
0.533 ± 0.044
1.024 ± 0.276

Medium + trigger
0.250 ± 0.084
0.307 ± 0.033
0.814 ± 0.287

Table 4.6.: The numerator of the data efficiency and the denominator is the tau ID efficiency of truth tt̄ MC
simulation are taken into account for the scale factor measurement. The systematic uncertainties of SF are computed
following the propagation error principles.

where the statistical uncertainty of data efficiency σdata is investigated by the propagation method.
Propagation of uncertainty is written as a common formula with neglecting correlations:s∂f 2 2
σf = Σi ()σXi ,(4.11)∂Xi
where f is a function with the neglecting correlation variables Xi . The function shows that the uncertainties is relative with the event number of the passing and failing regions. The systematic uncertainties
are computed with scale factor and summarized in Table 4.6.

4.7

Missing Transverse Energy

ATLAS detector provides the precision measurement for most of the particles, however, neutrinos are
not detected. For any process with neutrino like tau lepton decay or weakly-interacting, the reconstructionof the neutrino is indispensable and crucial. In ATLAS physics analysis, the intrinsic momentum in thetransverse plane is negligible that helps to measure the transverse momentum of the undetectable neutrino
with all other detectable particles. Based on the fact that the momentum in the transverse plane to thebeam axis should be summed as zero, any disproportion is called as Missing Transverse Energy (MET)
miss as shown in Fig. 4.38 13 . To understand the missing energy from the particles
or referred to as ET
miss is calculated from all calibrated physics objects. Selected physics objects
originated from neutrino, ET
13

missIllustration to explain the structure of ET
calculation. It is also used to measure the relative systematic uncertainty as
shown in Reference [164].

4.7. Missing Transverse Energy

64like electrons, photons, τhad−vis , muons and jets coming from the primary vertex are known as hard term.
On the other hand, the reconstructed tracks from the objects, which are associated with the hard-scatter
vertex and not associated to the hard term, are taken into account as a soft term, which is expected tobe perfectly balanced against hard term if there is no missing energy. Pile-up event is hard to predict
as described in the previous section, while it affects the calculation both of the hard term and the soft
term. Therefore, the fully calibrated and corrected methods are considered for hard term and soft term.
miss is highly dependent on the calibration and accuracy of the measurement for all hard
In addition, ET
miss in events. Due to extremely complex condition for E miss reconstruction, theterms if there is no real ET
T
resolution is always the key point for analysis. Sec. 4.7.1 present the detailed reconstruction procedure
miss , and the corresponding performance is shown in Sec. 4.7.2. This section is widely referenced inof ET[165].

psoft
k

hard
p~T

soft
p~T
soft
~ T
∆p
psoft
?
~ soft~ miss = ∆p
E
TT

soft,true
p~T

Figure 4.38.: Sketch shows that the an imbalance in the event would be computed as Missing Transverse Energy(ETmiss ) [165].

4.7.1

ETmiss Reconstruction

Calorimeter signal of the hard term and the not associated soft term are taken into account for the
The soft term can be reconstructed in two ways: the track-based soft term fromID track and calorimeter-based soft term from calorimeter signals. In order to avoid the track which is
unassociated with primary vertex, the calorimeter-based soft term is not considered for the reconstruction.
miss is computed with E miss components defined as:
The ETx(y)ETmiss reconstruction.

miss,τ

miss,emiss,γ
miss,jets
miss,µmiss,soft
miss
Ex(y)
= Ex(y)+ Ex(y)+ Ex(y) had−vis + Ex(y)+ Ex(y)+ Ex(y)
miss
ET
=

q
(Exmiss )2 + (Eymiss )2 , φmiss = arctan(Eymiss /Exmiss )
τ

µ
soft
ΣET = ΣpeT + ΣpγT + ΣpThad−vis + Σpjets
T + ΣpT + ΣpTmiss,(objects)(4.12)(4.13)(4.14)

miss and, where the Ex(y)is the sum of x(y)-components of the momenta of individual objects. ET
miss , respectively. ΣE is another related observable
φmiss are the magnitude and azimuthal angle of ET
T
defined as the scalar sum of transverse momenta of all hard and soft terms.
miss soft term. The main purpose is
Unlike hard term, a dedicated algorithm is necessary to develop ET
to maximize the reduction power for pile-up interactions. Track Soft Term (TST) is build with ID tracks
information and the association of the primary vertex. Only tracks not matched to any hard term withpT > 0.4 GeV within |η| < 2.5 and several minor reconstruction quality requirements are used in TST.
Cuts on transverse and longitudinal impact parameter of d0 < 1.5 cm and z0 < 1.5 cm are also applied
to the vertices reconstructed by track with the hit requirements in the ID. In additional requirement in4.7. Missing Transverse Energy

65

TST, the overlap removal between track and calorimeter clusters is defined as the following items. Basedon the rigorous requirement, the TST provides a highly precise measurement for the soft term used inmiss reconstruction.
ET• Removing tracks around other tracks , electron or photon cluster (Default value : ∆R < 0.05)• Removing tracks around other tracks , τ lepton (Default value : ∆R < 0.2)
• Removing tracks associated with jets based on the ghost-association technique• Removing tracks in ID associated with muons based on combined ID+MS fit.
• Removing tracks with large momentum uncertainties (> 40%)

4.7.2

ETmiss Performance

30
28
26
24

ATLAS Preliminarys = 13 TeV 36 fb-1
Loose EmissT
Z → eeEmiss,EmissRMS Resolution [GeV]
x
y

Emiss
,EmissRMS Resolution [GeV]xymiss performance depends strongly on the selection of jets, two different working points are
Since the ET
defined based on selection criteria of jets [164]. Loose working point includes all jets with criteria of pT >20 GeV within |η| < 2.4 or pT > 60 GeV for ETmiss reconstruction. While the forward jets with |η| > 2.4
and 20 < pT < 30 GeV are excluded in Tight working point. On this thesis, the Loose working point
is used for avoiding degradation of reconstruction since the hard-scatter might be removed with T ight
working point. The performance study of ETmiss is based on Z → ll events thanks to good modeling in thecurrent ATLAS simulation and the final state for ETmiss rebuilding. The resolution of ETmiss performed
for Z → ee event topologies are shown in Fig 4.39 as function of the number of primary vertices and hµi
in the event. The resolution increases linearly to approximately 24 GeV as a function of a number ofprimary vertices.

EMTopo MC
EMTopo MC Syst Err
EMTopo Data
PFlow Data

22
20
18
16
14

30
25

ATLAS Preliminarys = 13 TeV 36 fb-1
Loose EmissT
Z → ee20
15
EMTopo MC
EMTopo MC Syst Err

10

EMTopo Data

120

PFlow Data

5

10

15

20

25

30

35

40

Average number of interactions 〈µ〉

(a)

0

5

10

15

20

25

30

35

40

Number of primary vertices N

PV

(b)

Figure 4.39.: The RMS resolution distributions of Exmiss and Eymiss for data and simulation using Loose working
point in a Z → ee events. (a) shows the distribution as a function of average number of interactions, and (b) shows
the one as a function of number of primary vertices [164, 165].

The corresponding uncertainty is computed by all systematics associated with hard term and soft term
employed in the reconstruction step. Figure 4.40 shows the agreement between data and simulation withthe dominated systematic uncertainties coming from soft term evaluated by the specific method and pileup modeling. It is clear the resolution in simulation is slightly smaller than the observed data while thediscrepancy can be covered with the uncertainties.

b

Pred
Data

2
0
1.40
1.2
1
0.8
0.6

0

10

20

30

40

10

20

30

40

100

50

100

60

70

80

90

80

) [GeV2]

100

ATLAS Preliminarys = 13 TeV 36 fb-1
Z → eeEMTopo jets
Jet inclusive

60

miss,SoftTerm) [GeV2]

Data
Powheg+Pythia8
Madgraph+Pythia8
Powheg+Pythia8 AFII
SherpaTST Syst. Error
50
60
70
80
90

120

1.20
1
0.8

10

20

30

40

Data
Powheg+Pythia8
Madgraph+Pythia8
Powheg+Pythia8 AFII
SherpaTST Syst. Error
50
60
70
80
90

0

10

20

30

40

50

40
20

phard [GeV]

70

80

90

70
60

ATLAS Preliminarys = 13 TeV 36 fb-1
Z → eeEMTopo jets
Jet inclusive

50

1.20
1
0.8

10

20

30

40

Data
Powheg+Pythia8
Madgraph+Pythia8
Powheg+Pythia8 AFII
SherpaTST Syst. Error
50
60
70
80
90

0

10

20

30

40

50

40
30

100

100

phard [GeV]

T

(a)

60

σ2(E

4

66

Pred
Data

6

ATLAS Preliminarys = 13 TeV 36 fb-1
Z → eeEMTopo jets
Jet inclusive

miss,SoftTerm

8

σ2(E

10

Pred
Data

〈E

miss,SoftTerm〉 [GeV]4.7. Missing Transverse Energy

70

80

90

100

phard [GeV]

T

(b)

60

100

T

(c)

Figure 4.40.: The parallel scale (a), parallel resolution squared (b) and transverse resolution squared (c) discomparing with the different Monte Carlo simulation generations and observed
tribution as a function of phardTdata in Z → ee events. The pink band shows the final systematic uncertainties applied to the simulation in theanalysis [164, 165].

5 Search for Neutral Heavy Higgs Bosons
to τhadτhad Decay

This chapter describes an overview of the analysis. Details of the collision data and the backgroundsimulation samples are described in Sec. 5.1. The event selection, including the triggering strategy andthe offline event selection, is discussed in Sec. 5.2. The categorization is applied to maximize the searchsensitivities, the details of which are presented in Sec. 5.3.

5.1

Collision Data and Simulation Data Samples

5.1.1

Collision Data√
This analysis uses the 139 fb−1 of proton-proton collision data at a center-of-mass energy of s = 13 TeV
recorded by the ATLAS detector in 2015, 2016, 2017, and 2018, which is referred to as the “Run2” datataking period. As discussed in Sec. 5.2.1, the single-tau trigger algorithm is used to collect data. To be
selected in the analysis, events are required to satisfy a set of basic data-quality selection criteria withrespect to the system operation status, which guarantees all the relevant sub-detectors of the ATLAS
systems are functional in a good condition.

5.1.2

Simulated Samples

The simulation is used to model the signal and background processes. The simulated samples are used
to estimate yields of signals and some of the backgrounds remaining after the event selection.
Signal Process
The major production process of neutral heavy Higgs bosons are the bottom-annihilation and gluongluon fusion processes as shown in Fig. 5.1. The details of the simulation setup, used in the signal
sample simulations in total 8 mass points between 200 and 2500 GeV, for such as the Matrix element
calculation, Parton Distribution Function (PDF), Parton-Shower simulation, are summarized in Tab. 5.1
The simulated events are interfaced to Geant 4 [166, 167], the full ATLAS detector simulator for thegluon-gluon fusion process, and AtlasfastII [168] fast simulation framework for the bottom-annihilation
process. The production cross sections and decay branching fractions of the heavy Higgs bosons are
estimated in the MSSM frameworks [29], and the details are summarized in Tab. 5.2 for various MA andtan β scenarios.
Backgrounds Processes
Some of backgrounds processes are estimated with assistance of the Monte Carlo simulation as discussed in Chapter 6, for those associated with top-quark production (denoted as tt̄, single top), W boson

675.2. Event selection

68

_

(a)

(b)

(c)

Figure 5.1.: Lowest-order Feynman diagrams of three main production proceese of the neutral MSSM Higgs
boson; (a) gluon-fusion processes, (b) four-flavour schemes bottom-annihilation process, and (c) five-flavour schemes
bottom-annihilation process.
Process
gluon-gluon fusion
bottom-annihilation

Generator (PDF)
Powheg-v2 (CT10)MadGraph5 aMC@NLO 2.1.2 (CT10nlo nf4)

ShowerPythia8
Pythia8

Tune
AZNLO
A14

Hadronisation
CTEQ6L1
NNPDF2.3LO

Table 5.1.: The generator and shower model used for the simulation of the signal processse in this analysis [169–174].

production (denoted as W +jets), the Drell-Yan process (denoted Z/γ ∗ +jets). The diagrams are shownin Fig. 5.2 and Fig. 5.3. These background processes are simulated with the setup as shown in Tab. 5.2.
The simulated events are interfaced to the full detector simulation with Geant 4 [166].
"

!

!

(

(a)

+±

!
#$%& ±&'() ∓+∓#$%& ∓""%̅&'() ±

#

#

%

"
(b)

Figure 5.2.: Feynman diagrams of irreducible background in this analysis with the final state charactorized witha pair of τhad ; (a) Z/γ ∗ +jets (b) tt̄ in the final state with at least truth two τhad .

5.2

Event selection

To extract the H/A → τhad τhad signals from backgrounds, an optimal set of event selection criteria areused in this analysis.

5.2. Event selection
ProcessZ/γ ∗ + jetstt̄ + jets
single-top, s-channel
single-top, t-channel
single-top, W t-channel
W → `ν
Diboson69
Generator (PDF)
Powheg-v2 (CT10)
Powheg-v2 (CT10)
Powheg-v2 (CT10)
Powheg-v2 (CT10)
Powheg-v2 (CT10)
Sherpa 2.2 (NNPDF30NNLO)
Sherpa 2.2 (NNPDF30NNLO)

ShowerPythia8
Pythia8
Pythia8
Pythia8
Pythia8
Sherpa 2.2
Sherpa 2.2

Tune
AZNLO
A14
A14
A14
A14
-

σ (pb)
1901
730
10
216
75
20080
45

Order
NLO
NNLO
NLO
NLO
NNLO
NLO
NLO

Table 5.2.: The generator and shower model used for the simulation of the background processse in this analysis. [175–177]

"

!

!

,∓

#$%& ∓
)

∓

,±

!

"

#

&̅

'()* ±

$

&
(
(a)

"
"

#
(b)

Figure 5.3.: Feynman diagrams of reducible background in this analysis with fake τhad ; (a) W+jet process, (b) tt̄
process with at least W decays to non-τhad channel.

5.2.1

Triggering

The single-tau trigger (STT) is used to collect the data for this analysis. The details of the tau trigger
algorithm and performance can be seen in Sec. 4.5.4. The STT with pT thresholds of 80 GeV, 125 GeV,
and 160 GeV are used in the data taking. The pT thresholds depend on the instantaneous luminosity as
shown in Table. 4.4. The trigger efficiency is measured with the collision data, and the efficiency of thesimulation samples is corrected accordingly.

5.2.2

Event Reconstruction and Basic Selection

This analysis uses reconstructed muon, electron, hadron jets, and hadronically decaying tau objects,
which are introduced in Chapter 4. The selection criteria for each object in this analysis are summarizedin Table. 5.3. The leading tau leptons are required to satisfy the requirement of triggering with STT
algorithm in terms of pT threshold and the ID requirement. The corresponding offline pT cuts are 5 GeV
above the pT thresholds of triggering selection, namely 85 GeV, 130 GeV, and 165 GeV for different trigger
thresholds. The Tau identification cuts for sub-leading τhad is used in the categorization which is discussed
in Sec. 5.3. Electrons and muons are used for a veto selection to reduce the weak-interaction backgrounds,
which often are associated with additional electrons or muons. As summarized in the Table. 5.3, a loose
threshold is used, which is found to be optimal for the veto selection. Jet reconstruction and b-tagging
are used to distinguish the gluon-gluon fusion and the bottom-annihilation processes.
The geometrical overlap between selected objects is solved in preference of precision measurementof muons, electrons, taus, and jets. The overlap removal procedure consists of four steps as shown in
Table. 5.4 with respect to the distance defined as ∆R between objects.
Further, the background jets from beam-induced backgrounds, cosmic particles, and detector noise
miss calculation. It is known that such background jets
signals can affect the features of the event and ET

5.2. Event selection
1st τhadMedium-id
pT > 85, 130, 165 GeV|η| < 2.5
no crack region
1,2 or 3 tracks|charge| == 0,1 or 270
2nd τhad
Loose-idpT > 65 GeV|η| < 2.5
no crack region
1,2 or 3 tracks|charge| == 0,1 or 2

muon
Loose quality
pT > 7 GeV|η| < 2.5

electron
Loose-idpT > 15 GeV|η| < 2.47
no crack region

jet
JVT
pT > 20 GeV|η| < 2.5
70% efficiency with b-tagging

Table 5.3.: The table to list the selections used for the physics objects. Electron and tau are excluded the “crack
region” corresponding to the transition region between the barrel and end-cap calorimeters at 1.37 < |η| < 1.52.
Gradation
step1
step2
step3
step4

Benchmarkmuon
electron or muon
electron or muon
τhadDiscarded object
electron
τhad
jet
jet

Matching condition∆R <0.2∆R <0.2∆R <0.4∆R <0.2

Table 5.4.: Four steps for overlap removal based on ∆R between objects in preference of precision measurementof muons, electrons, taus and jets. The selections shown in Table. 5.3 beside the one for τhad are applied for eachobjects.

have typically low pT < 60 GeV. A basic selection, which is referred to as “event cleaning” selection, is
designed and used in the analysis to reject events that are possibly affected by such components. If a
selected jet object with pT < 60 GeV) does not pass the quality cut in an event, the event will be discarded
miss reconstruction. This event cleaning helps to reduce the negative effects
to avoid the effects on the ET
misson ET from the non-collision components.

5.2.3

Event Selection

Following the basic selection discussed in the previous section, a series of event selection criteria is
applied in this analysis to suppress background contributions while keeping signal acceptance as high as
possible. To be selected, the candidate events are required to have at least two identified τhad to selectthe H/A → τhad τhad signals, following the object selection criteria which are summarized in Table. 5.3.
Backgrounds with additional electrons and muons in the final state can be suppressed by zero electron andzero muon selection, so-called the lepton veto selection. An opposite charge requirement of two pT leadingτhad is used as long as both of the τhad s are associated with an odd number of charged tracks. It is known
to suppress fake τhad contributions effectively. If “2-prong” τhad candidate is included in the selected
events, the sum of the charge of two tracks of the τhad candidate should be 0 or opposite to the other τhad .
This cut is referred to as an opposite sign or OS requirement. A geometrical selection of ∆φ, which is an
opening angle of two pT leading τhad in the transverse plane, is requested to be ∆φ > 2.7 to more purity
signals, considering the signal event topology of heavy Higgs decaying two τhad is expected with high pTand the approximately opposite direction in the transverse plane. Figure 5.4 presents the distributions∆φ for signals and backgrounds after the OS requirement is applied. In order to avoid bias due to thestatistical fluctuation of the data sample in the optimization, the data can not be directly surveyed in thesignal region before confirming background estimation. In this analysis, the validation regions, referred toas ”VR”s, are defined to verify the multijet background from the data-driven method, which is discussed
in Sec. 6.2.1. the events are required to pass the all selection criteria as the signal selection but required to
fail the opposite charge requirement. It allows selecting the validation samples with multijet backgrounds
enhanced and suppress the potential signal contribution in the validation sample.

Events

5.2. Event selection

71

7

10
106
105
104
103
102
10

s = 13 TeV, 139.0 fb-1
H/A → τhadτhadt t , single top Fakeloose incprongtan β =15
hMSSM A1000 → τ τb-veto OS

Data

MultijetZ/γ * → τ τ + jets

W → τ ν + jetst t , single top Truth
Others
Uncertainty

Data/Bkg

1

stat.

1.5
1
0

0.5

1

1.5

2

2.5

3
∆φ

Figure 5.4.: ∆φ distribution in OS before the ∆φ > 2.7 cut. The mis-modeling in low ∆φ region is expected since
only the ∆φ region larger than 2.7 are considered in fake factor estimation for multi-jet background. The cut valueon ∆φ is computed to extract best signal significant.

5.3. Categorization Definition

5.2.4

72

Di-tau mass reconstruction

The final discriminant is defined to provide the best separation power between signals and backgroundafter all the event selection criteria are applied. A “total transverse mass” (mtot
T ) is chosen as the final
discriminant in this analysis, which is defined as a sum of the visible decay product of the two τhadmiss .
(denoted as τhad,1 and τhad,2 ) and ETqmiss )2 + m (τmiss 2mT (τhad,1 , τhad,2 )2 + mT (τhad,1 , ET
(5.1)
mtot
=
T had,2 , ET ) .
TmT (i, j) =q

2piT pjT (1 − cos ∆φi,j ).

(5.2)

Data

4

10

Z/ γ * → ττ + jets
tt, single top

310

tan β=15
hMSSM A 1000 → ττs = 13 TeV, 139.0 fb-1
H/A → τhadτhad
W → τν + jets
loose incprong
Othersb-tag OSMultijet

EventsEventsFor the high mass resonance of τhad τhad events, the mtot
T will be the very different distribution for each
SM background and therefore can be a good final discriminant. As shown in Figure 5.5, the QCD multijet
miss and with low p of jets
background is expected to be dominant in lower mtot
T
T region with the low ET
totwhich are typical for the multijet process. The high mT region is dominated by tt̄ and Z → τ τ SM
background which contain at least two true τhad in the final state. The tt̄ and Z → τ τ events containmiss will be larger than the multijet backgrounds. It results in theneutrinos in the final state and the ET
fact that tt̄ and Z → τ τ background are dominant processes in the large mtot
T region.
107
6

10

5

10

Uncertaintys = 13 TeV, 139.0 fb-1
H/A → τhadτhadloose incprong
b-veto OS

Data

MultijetZ/ γ * → ττ + jets

W → τν + jets

tt, single top

Otherstan β=15
hMSSM A 1000 → ττUncertainty

4

10
102

103

10

102
10
1

1.4
stat.
1.2
1
0.8
0.6
150 200 250 300 350 400 450 500 550 600

Data/Bkg

Data/Bkg

1

1.4
1.2
1
0.8
0.6

stat.

200 300 400 500 600 700 800 900 1000

mtot
T [GeV](a) BTAG

mtot
T [GeV](b) BVETO

Figure 5.5.: mtot
T distribution in the BTAG (at least one b-tagged jet) and BVETO (without b-tagged jet) signal
regions after event selection.

5.3

Categorization Definition

In order to maximize the search sensitivity, a categorization technique is used. The categorization isbuilt with respect to the tightness of tau identification of the sub-leading τhad , the number of tracks
associated with the sub-leading τhad and number of b-tagged jets of the events as illustrated in Fig 5.6.
The 2-prong τhad discussed in the previous section is also used in the categorization. To cover both ofgluon-gluon fusion and bottom annihilation processes with the best signal sensitivities, the candidate
events are categorized with respect to the number of b-tagged jets in the events. Events with at least one

5.3. Categorization Definition73

selected b-tagged jet is accommodated into the “BTAG” category, and the inverse events (0 b-jets events)
are brought into “BVETO” category. The main background process in BVETO categories is multijet.
The tt̄ is dominant in the BTAG region. Given the multijet process is the major background in the low
mtot
T region, a tighter tau identification can help the analysis improve the signal sensitivity for low mass
scenarios. The currently available working point of tau ID, loose, medium and tight, which are discussed in
Sec.4.5.3, are exploited in the BVETO categorization. The following categorization is introduced based on
the identification information; loose-not-medium (lnm for short), medium-not-tight (mnt for short), andtight. The BVETO region takes advantage of the categorization based on the number of tracks associatedwith the sub-leading τhad . The BTAG region does not use the categorization based on the number oftracks associated with the sub-leading τhad due to the limited statsitcs mainly in the validation region of
3-prongs if b-tagging requirement is applied. A particular category, which is denoted to be “2P category”,
is built to accommodate events with at least one high pT 2-prong τhad . The additional separation basedon tau ID is not applied for 2P category due to the statistical problem occurred in the validation region.

Event Selection
Event Categorization : based on track number and ID of 2nd !"#$%&'(BVETO ()* = ,)2nd !"#$%&'( is 1prong0
×0

2nd !"#$%&'( is 3prong

tight

tight

med. not tightmed. not tightloose not med.

loose not med.

fail loose

fail loose

BTAG ()* > ,)2P Category ()* ≥ ,)2nd !"#$%&'( is1or 3prong

1st or 2nd !"#$%&'(
includes 2prong

loose

loose

fail loose

fail loose

1

2nd !"#$%&'( fail loose ID region. Used for data-driven background estimation.

Figure 5.6.: Illustration of the event categorization used in this analysis. The number of b-tagged jets, the numberof tracks of sub-leading pT τhad and the tightness of tau identification are exploited for the BVETO categorization.
BVETO and BTAG regions correspond to event without b-jets and with at least one b-tagged jet, respectively. The
additional categorization is only used for BVETO region based on tau ID tightness of sub-leading and the numberof the track associated to the sub-leading τhad . The additional 2P categorization presents the performance for the
events with at least one 2-prong τhad (leading τhad or sub-leading τhad ). 2P categorization and BTAG region don’t
have the further categorization.

6 Background Events Estimation

This section describes the estimation of the background components of the analysis. Background processes
are separately discussed for the “irreducible” backgrounds, which are characterized by two hadronicallydecaying tau leptons in the final state, and for “reducible” backgrounds, which contain at least one
reconstructed τhad originated from a hadron jet but not a tau lepton. Such misidentified τhad is referred
to as “fake” τhad . The major contributions in the class of the irreducible backgrounds are Z/γ ∗ → τ τin “BVETO” categories while tt̄ in the “BTAG” categories. Multijet background is the most major
component of the reducible backgrounds, which can pass the signal selection due to two fake τhad originatedfrom hadron jets. Although the tau identification can reject fake backgrounds effectively as discussed inSec. 4, the very large cross-section of the multijet production process still results in a non-negligible
contribution in the analysis. A full data-driven technique, which is called fake factor (FF) method in thisanalysis, is employed for the multijet estimation to obtain an accurate estimation of the backgrounds,
avoiding uncertainties for the possible wrong model of the fake τhad leptons in the multijet backgrounds.
Top production and W (→ τ ν) + jets processes can be a part of the reducible backgrounds with one
genuine τhad and one fake τhad . The backgrounds are estimated based on simulations with the assistanceof measurements of the τhad fake rate (FR). Top production and W (→ τ ν) + jets events with one fake
τhad , events in the simulation which contain hadron jets that can be potentially wrongly selected in theanalysis are weighted by fake rate measured in W + jets and top-quark control regions. Other reducible
production processes due to leptons mimicking the τhad , such as di-boson, (Z → ee) or µµ and (W → eνor µν)+jets, are turned to have a negligible impact in the analysis owing to the lepton veto selection.
The irreducible background estimation is discussed in Sec. 6.1. For the reducible background, the fakefactor method is presented in the Sec. 6.2.1, and Sec. 6.2.2 describes the background estimation with thefake rate. The expected results with the background events estimation are shown in Sec 6.3.

6.1

Estimation of the Irreducible Backgrounds

MC simulation is used to estimate the irreducible backgrounds. As discussed in Sec. 4, corrections areapplied to the simulation with respect to the performance measurements of the trigger, reconstruction,
isolation, and isolation selection efficiencies to account the mis-modeling of the detector performance inthe simulation samples. The main systematic uncertainties are also introduced in the Chapter. 7.

6.2

Estimation of the reducible backgrounds

6.2.1

Fake Factor Method (FF)The multijet background is the most major component of the reducible backgrounds due to its large
production cross section. A data-driven FF method has been applied to obtain an accurate estimation of74

6.2. Estimation of the reducible backgrounds

75

10

105

Events6

s = 13 TeV, 139.0 fb-1
H/A → τhadτhad
W → τν + jets
loose incprong
Othersb-veto Same-Sign
MultijetDataZ/ γ * → ττ + jets
tt, single top
tan β=15

hMSSM A 1000

→ ττ

Uncertainty

107
106
105

104

104

103

103

102

102

10

10

1

1

1.4
1.2
1
0.8
0.6
0

Data/Bkg

Data/Bkg

Eventsthis background. A “di-jet control region” is used to estimate the fake-factor, which is defined as the ratioof the number of τhad candidates that pass to those that fail the tau identification criteria. The selectionof the di-jet control region is designed to be as similar to the signal selection as possible while enhancing
the fake τhad candidate and suppress the contribution of the genuine τhad candidates. The di-jet control
region samples are collected by the single-jet triggers with the jet pT thresholds of 420, 400, 380, 360,
260, 175, 110, 85, 60, 45, 35, 25 and 15 GeV. The event is required to have at least two τhad candidates.
The leading τhad is required to fail the “medium” tau identification condition to enhance the multijet
backgrounds and guarantee the statistical independence from the data samples selected by the analysis
selection for the signal extraction. The leading τhad candidate has to have the pT > 85 GeV and also
exceed the trigger threshold by 10%. The sub-leading τhad is required to fulfill the pT > 65 GeV condition.
The two τhad candidates have to satisfy the opposite sign charge requirement and have a back-to-back
topology in the transverse plane with respect to ∆φ > 2.7. The pT of the sub-leading τhad candidate mustbe at least 30% of the pT of the leading τhad candidate. As shown in Fig. 6.1, the pT -balance selection
discard a tiny fraction of multi-jets in order to reduce the impact of tail events.

stat.

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

1

1.4
1.2
1
0.8
0.6
0

Data

MultijetZ/ γ * → ττ + jets

W → τν + jets
Otherstt, single top
tan β=15

hMSSM A 1000→ ττs = 13 TeV, 139.0 fb-1
H/A → τhadτhadloose incprong
b-veto OS

Uncertainty

stat.

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

p (τ2) / p (τ1)
T

p (τ2) / p (τ1)T(a) SS BINC.

1

T

T

(b) OS BINC.

Figure 6.1.: Fake factor is expected to be depending on the ratio of leading and sub-leading tau in the di-jet control
region. A selection of pT -balance larger than 30% is considered to reduce the impact of any residual dependency:(a) same-side plot and (b) opposite-side plot as a function of pT -balance also show the low value region with low
distribution of multi-jet process is unimportant in the signal region.

The sub-leading τhad is used to measure the fake factors to avoid trigger bias. A loose selection on thetau identification score (BDT score > 0.03) is applied to control the quark and gluon composition in the
FF calculation. As defined above, the FF is computed as follows:FF =NpassID (pT , Ntrack )|di−jet .
NfailID (pT , Ntrack )(6.1)

The fake factors are measured for the different tau ID tightness used in the category definition (seeFig. 5.6), and fake factors are estimated with the various types of numerator for the different tau ID
tightness, corresponding to the target signal region categories. The FF is measured as a function of
the number of tracks (i.e. 1-, 2-, or 3-prong) and pT of the sub-leading τhad candidate. The multi-jets6.2. Estimation of the reducible backgrounds

76

background in the signal region is estimated with the fake factors as shown in Eq. 6.2.
SR
SR
Npass
= F F × Nfail
,

(6.2)

SR is the number of events that pass the same selection as the signal region except for thewhere Nfail
SR , the sub-leading τ
tau identification conditions for sub-leading τhad . In counting Nfail
had candidates are
required to fail the tau identification selection. The concept of the Eq. 6.2 is illustrated in Fig. 6.2. ThisSR .
way the evaluated fake factor keep the consistency with their application to the Nfail

2nd ! pass ID

Leading ! fail ID (Dijet CR)
)) =

01
,-.//

+

Control Region

01
,2.34
5$6$789:

Leading ! pass ID (SR)MJ ='())×"#$%&&
<

9(
">$::

Signal Region
5$6$789:

2nd ! fail ID

MJ-FF

'(
"#$%&&
9(
"#$%&

MCs
Data

Lower ID cut (disuse)

MJ
MCs (ie: ;; )Lower ID cut (disuse)

Figure 6.2.: Sketch for the FF measurement and application in the signal region. The left pattern shows the di-jet
control region with single jet trigger, and the right pattern presents the signal region with single tau trigger. The
di-jet control region is requested leading τhad candidate fail medium ID to orthogonality with signal region. The
lower Tau ID cut (BDT score > 0.03) is applied in di-jet control region to avoid the different property to signal
region. The FFs are computed with respect to sub-leading τhad and trained to as a function of pT . The MCs(purple part) are used for the subtraction on data to obtain high purity of multi-jet process. The FFs are applied
to signal region to estimate the multi-jet process (blue part) passing ID.

Accounting the categorization applied in the signal region, the fake factors are computed with respect
to 1-prong, 2-prong and 3-prong of sub-leading tau separately in di-jet control region. The difference
between BTAG and BVETO categories are not accounted but a fake factor is estimated in an inclusive
manner for the b-tagging conditions (referred to as “B-inc.”). It is mainly due to the limited statistics
in control regions. Although there is no significant difference found in the fake factor between BTAG
and BVETO categories, minor differences of the fake factors between BTAG and BVETO regions areaccounted as the systematic uncertainties (see Sec 7.3).
The fake factors for BVETO category are also measured in dijet samples as summarized in Fig. 6.3.
The fake factors for BVETO and 2P categories are summarized in Fig. 6.4. The same-sign (SS) fakefactors are used to validate the data-driven method in SS region as described below. The opposite-sign
SR to measure multi-jets process background in signal region. The(OS) fake factors are applied to Nfailstatistical uncertainty from data and MC used for the subtraction are shown on the plots.

6.2. Estimation of the reducible backgrounds

data stat.

0.3
0.25
0.2
0.15

data stat.

s = 13 TeV, 139.0 fb-1
same sign, 1p, b-inc

0.05

0.14

0.12

0.12

0.1

0.1

0.08

0.08

s = 13 TeV, 139.0 fb-1
same sign, 1p, b-inc

0.020(a) SS 1p loose-not-med.

(b) SS 1p med.-not-tightdata stat.

(c) SS 1p tightNominal fake factor

0.035

0.03

0.03

0.025

0.025

0.06

0.02

0.02

0.04

0.015

0.015

0

s = 13 TeV, 139.0 fb-1
same sign, 3p, b-inc

subleading τ pT(d) SS 3p loose-not-med.

(e) SS 3p med.-not-tightdata stat.

Nominal fake factor

data stat.

0.3
0.25
0.2
0.15
-1

s = 13 TeV, 139.0 fb
opposite sign, 1p, b-inc

0.05

0.14
0.12

0.1

0.1

0.08

0.08

-1

s = 13 TeV, 139.0 fb
opposite sign, 1p, b-inc0.020(h) OS 1p med.-not-tight0.05

data stat.

0.12

data stat.

subleading τ pT(i) OS 1p tightNominal fake factor

0.03

0.025

0.025

0.02

0.02

0.04

0.015

0.015

0

s = 13 TeV, 139.0 fb-1
opposite sign, 3p, b-inc

100 150 200 250 300 350 400

0.01
0.005
0

data stat.

mc stat.

0.035

0.03

0.06

0.02

100 150 200 250 300 350 400

0.04

0.035

0.08

0

0.045

mc stat.

0.04

0.1

s = 13 TeV, 139.0 fb-1
opposite sign, 1p, b-inc

0.02

0.05

Nominal fake factor

0.045

0.04

100 150 200 250 300 350 400(g) OS 1p loose-not-med.

mc stat.

data stat.

mc stat.

0.06

0.04

subleading τ pT

Nominal fake factor

Nominal fake factor

0.16

subleading τ pT

0.14

0.2

0.12

100 150 200 250 300 350 400

100 150 200 250 300 350 400(f ) SS 3p tight

0.14

0.06

0.1

s = 13 TeV, 139.0 fb-1
same sign, 3p, b-inc

subleading τ pT

0.18

mc stat.

0.16

0.35

0

0.2

0.18

mc stat.

0fake factor

fake factor

Nominal fake factor

0.4

0.01
0.005

100 150 200 250 300 350 400

subleading τ pT

fake factor

fake factor

0

100 150 200 250 300 350 400

0.45

fake factor

0.01
0.005

fake factors = 13 TeV, 139.0 fb-1
same sign, 3p, b-inc

0.02

data stat.

mc stat.

0.04

0.035

0.08

100 150 200 250 300 350 400
subleading τ pT

0.045

mc stat.

0.04

0.1

0

0.05

Nominal fake factor

0.045

s = 13 TeV, 139.0 fb-1
same sign, 1p, b-inc

0.02

fake factor

fake factor

0.05

data stat.

mc stat.

0.04

100 150 200 250 300 350 400
subleading τ pT

Nominal fake factor

data stat.

mc stat.

0.06

0.04

subleading τ pT

0.12

Nominal fake factor

0.16

0.14

100 150 200 250 300 350 400

0.14

0.2

0.18

mc stat.

0.06

0.1

fake factor

Nominal fake factor

0.16

0.35

0

0.2

0.18

mc stat.

fake factor

Nominal fake factor

0.4

fake factor

fake factor

0.45

77

s = 13 TeV, 139.0 fb-1
opposite sign, 3p, b-inc

100 150 200 250 300 350 400

subleading τ pT

subleading τ pT(j) OS 3p loose-not-med.

(k) OS 3p med.-not-tight

0.01
0.005
0

s = 13 TeV, 139.0 fb-1
opposite sign, 3p, b-inc

100 150 200 250 300 350 400
subleading τ pT(l) OS 3p tight

Figure 6.3.: Tau fake factors for the BVETO category in same-sign validation region and opposite-sign signal
region. The same-sign FFs for 1-prong tau candidates are shown in the plots on the first row, for 3-prong tau
candidates are shown in the plots on second row. The bottom two rows are shown for opposite-sign FFs for 1-prong
and 3-prong tau candidates. From left to right plots, the FF is corresponding to loose-not-med, med-not-tight andtight tau ID.

data stat.

0.2
Nominal fake factor

0.18

mc stat.

0.6

0.4

s = 13 TeV, 139.0 fb-1
same sign, 1p, b-inc

0.2
0.1

0.14

0.14

0.12

0.12

0.1

0.1

0.08

0.08

s = 13 TeV, 139.0 fb-1
same sign, 2p, b-inc

0.02
0data stat.

0.7

0.2
Nominal fake factor

data stat.

0.5
0.4

0.2
0.1

s = 13 TeV, 139.0 fb-1
opposite sign, 1p, b-inc

100 150 200 250 300 350 400
subleading τ pT(d) OS 1p loose(c) SS 3p loose
0.2
Nominal fake factor

0.14

0.12

0.12

0.1

0.1

0.08

0.08

0.04
0.02
0

data stat.

mc stat.

0.16

0.14

0.06

0.3

100 150 200 250 300 350 400
subleading τ pT

0.18

mc stat.

0.16

0.6

0

(b) SS 2p loose

0.18

mc stat.

s = 13 TeV, 139.0 fb-1
same sign, 3p, b-inc

0.02

subleading τ pT

fake factor

Nominal fake factor

0.04

100 150 200 250 300 350 400

subleading τ pT(a) SS 1p loose

data stat.

mc stat.

0.06

0.04

100 150 200 250 300 350 400

0.8Nominal fake factor

0.16

0.06

0.3

0.2

0.18

mc stat.

0.16

0.5

fake factor

data stat.

fake factor

Nominal fake factor

0.7

78

fake factor

0.8

fake factor

fake factor

6.2. Estimation of the reducible backgrounds

0.06
s = 13 TeV, 139.0 fb-1
opposite sign, 2p, b-inc

100 150 200 250 300 350 400
subleading τ pT(e) OS 2p loose

0.04
0.02
0

s = 13 TeV, 139.0 fb-1
opposite sign, 3p, b-inc

100 150 200 250 300 350 400
subleading τ pT(f ) OS 3p loose

Figure 6.4.: Tau fake factors for the BTAG and 2P categories in same-sign validation region and opposite-sign
signal region. Only loose is available to BTAG and 2P categories. The same-sign FFs are shown in the top plots,
and opposite-sign FFs are shown in the bottom plots. From left to right plots, the FF is corresponding to 1-prongtau, 2-prong tau, and 3-prong tau candidates.

6.2. Estimation of the reducible backgrounds

79

Validation Region for QCD Multi-jets Background

5

10

ATLAS Work in progresss = 13 TeV, 140.4 fb-1
H/A → τhadτhadloosenotmed 1prong
b-veto Same-Sign

Data

MultijetW → τ ν + jets

Z/γ * → τ τ + jetst t , single top Trutht t , single top Fake

Otherstan β =15
hMSSM A1000 → τ τ

Uncertainty

4

10

ATLAS Work in progress105

s = 13 TeV, 140.4 fb-1
H/A → τhadτhad
mednottight 1prong
b-veto Same-Sign

410Z/γ * → τ τ + jetst t , single top Trutht t , single top Fake

Otherstan β =15
hMSSM A1000 → τ τ

Uncertainty

106
105
4

10

102

10

10

10

1

1

1

1.4
1.2
1
0.8
0.6

stat.

syst.

mtot
T [GeV](a) SS BVETO 1p loose-not-med(b) SS BVETO 1p med-not-tight

105
4

10

ATLAS Work in progresss = 13 TeV, 140.4 fb-1
H/A → τhadτhadloosenotmed 3prong
b-veto Same-Sign

Data

MultijetW → τ ν + jets

Z/γ * → τ τ + jetst t , single top Trutht t , single top Fake

Otherstan β =15
hMSSM A1000 → τ τ

Uncertainty

3

10

102
10

stat.

Data/Bkg

1

syst.

1.5
1

1.4
1.2
1
0.8
0.6

200 300 400 500 600 700 800 900 1000

mtot
T [GeV]

200 300 400 500 600 700 800 900 1000
mtot
T [GeV](d) SS BVETO 3p loose-not-med

ATLAS Work in progress

104
103

s = 13 TeV, 140.4 fb-1
H/A → τhadτhad
mednottight 3prong
b-veto Same-Sign

Data

MultijetW → τ ν + jets

Z/γ * → τ τ + jetst t , single top Trutht t , single top Fake

Otherstan β =15
hMSSM A1000 → τ τ

Uncertainty

104
3

10

10

10

1

1

syst.

200 300 400 500 600 700 800 900 1000
mtot
T [GeV](e) SS BVETO 3p med-not-tightMultijetW → τ ν + jets

Z/γ * → τ τ + jetst t , single top Trutht t , single top Fake

OthershMSSM A1000

tan β =15

→ ττ

Uncertainty

stat.

syst.

(c) SS BVETO 1p tight

102

stat.

Data

mtot
T [GeV]

102

1.4
1.2
1
0.8
0.6

s = 13 TeV, 140.4 fb-1
H/A → τhadτhadtight 1prong
b-veto Same-Sign

200 300 400 500 600 700 800 900 1000

Events / GeV

syst.

Data/Bkg

stat.

Data/Bkg

10

1.4
1.2
1
0.8
0.6

ATLAS Work in progress

103

102

Events / GeV

Events / GeV

MultijetW → τ ν + jets

103

200 300 400 500 600 700 800 900 1000

Data/Bkg

Data

2

Data/Bkg

Data/Bkg

103

106

Events / GeV

106

Events / GeV

Events / GeV

A fake factor measurement is validated with the use of samples selected by a requirement of the same
sign of charge of di-τ pairs. The same selection criteria with the signal region are applied except for the
charge condition. A validation region with the same sign (SS) of charge of di-τ is designed to enhance
the fake τhad candidate from the multijet process while suppressing the other background process. FF
method for multi-jet background in the SS validation region is found to provide a good model of the mtot
T
distribution of fake background, as shown in Fig. 6.5 and Fig. 6.6. The validation region corresponding
to the total eight signal regions based on the categorization method are presented. The FF method isinvestigated carefully in the validation region with mtot
T as well as other variables. All the plots for thevaluation study are shown in Appendix D.

ATLAS Work in progresss = 13 TeV, 140.4 fb-1
H/A → τhadτhadtight 3prong
b-veto Same-Sign

stat.

Data

MultijetW → τ ν + jets

Z/γ * → τ τ + jetst t , single top Trutht t , single top Fake

OthershMSSM A1000

tan β =15

→ ττ

Uncertainty

syst.

1.5
1
200 300 400 500 600 700 800 900 1000
mtot
T [GeV](f ) SS BVETO 3p tight

Figure 6.5.: The six validation regions as a function of mtot
T are investigated for BVETO category. The plots for
1-prong (3-prong) sub-leading τ are shown in upper (bottom) plots. From left to right, the plots present the region
with sub-leading τ passing loose-not-med, med-not-tight and tight tau ID selection. The FF method presents goodmodeling for multi-jet background in validation region.

6.2.2

Fake Rate Method (FR)

Reducible backgrounds other than multijet production are estimated with Monte Carlo simulation andmeasured “fake-rates”. Instead of applying the actual tau identification selection to the hadron jets inthe simulation, they are weighted according to the probability for the hadron jets to pass the signal tau

1.5

s = 13 TeV, 139.0 fb-1
H/A → τhadτhadloose incprongb-tag Same-Sign

Data

MultijetZ/ γ * → ττ + jets

W → τν + jets
Otherstt, single top
tan β=15

hMSSM A 1000

→ ττ

Uncertainty

Events / GeV

90
80
70
60
50
40
30
20
10

80

104
3

10

ATLAS Work in progresss = 13 TeV, 140.4 fb-1
H/A → τhadτhadloose 2prong
b-veto Same-Sign

Data

MultijetW → τ ν + jets

Z/γ * → τ τ + jetst t , single top Trutht t , single top Fake

OthershMSSM A1000

tan β =15

→ ττ

Uncertainty

102
10
1

stat.

Data/Bkg

Data/Bkg

Events

6.2. Estimation of the reducible backgrounds

syst.

1
150 200 250 300 350 400 450 500 550 600

1.4
1.2
1
0.8
0.6

stat.

syst.

200 300 400 500 600 700 800 900 1000

mtot
T [GeV](a) SS BTAG 1p+3p loose

mtot
T [GeV](b) SS BINC 2p loose

Figure 6.6.: The two validation regions as a function of mtot
T are investigated for BTAG (a) and 2P (b) categories.
The plot (a) presents the region with sub-leading τ , which can be 1-prong or 3-prong, passing loose tau ID selection
for BTAG category. The plot (b) shows the validation region for 2P category which is built for the events withat least one 2-prong τhad . They show good modeling for multi-jet background for BTAG and 2P categories invalidation region.

trigger as well as the tau identification criteria, which is referred to as a “fake-rate” in this analysis. The
fake-rate is measured in the control regions as discussed below. The fake rate are used to hadron jets of thesimulations instead of trigger or identification application for leading or sub-leading τhad candidates. Thismethod allows not only an accurate estimation based on the measured fake-rates but also an efficient useof the simulated samples without discarding a large fraction of events with the tau identification selection.
The fake-rate method is used for the following dominant processes; single top, tt̄ and W (→ τ ν) + jets.
It is known that the fake-rate for quark-initiated jets is higher than gluon-initiated jets. Given thatthe composition of the hadron jet flavor is different between top-quark production (single top and tt̄)and W (→ τ ν) + jets, two control regions are built for the top-quark production and the W production
backgrounds, separately. Control regions characterized by the final state of µν + jets are exploited. Theµν final state is used to enhance the purity of the target processes, and the associated jets are used forthe measurement of fake-rates in the processes. The number of b-tagged jets is used to separate the data
samples into the following two control regions; a control region to measure fake-rates for W (→ τ ν) + jets
processes and the other region to measure fake-rates for top-quark production processes.
The single muon trigger with the 50 GeV threshold is used to collect data for the µν+jets control
regions. The medium quality requirement with pT > 70 GeV threshold is used for muon candidate. The
candidate events are required to have at least one τhad candidates with pT > 50 GeV, which are supposed
to be originated from hadron jets in the W + jets and top-quark processes. If an event has an additionalmuon which passes loose quality cut with pT > 7 GeV, the event will be discarded. Similarly, if an
event has an additional electron which passes loose identification with pT > 15 GeV, the event will bediscarded. For the leading τhad candidates and the selected muons, a requirement for the opposite charge
configuration and a requirement on the opening angle (∆φ(µ, jet) > 2.4) are applied to guarantee themiss ) > 40 GeV is required to reduce thesimilar quark/gluon composition as the signal region. mT (µ, ET
multijet contributions. Finally, samples with at least one b-tagged jet is categorized into “top control

6.3. Expected Event Yields in the Signal Regions
Process
Top control region
W control region
High pT W control region

W (→ µν)+jets
4.7%
83.2%
14.0%

81
Top
88.5%
15.5%
79.8%

Other
6.7%
1.3%
6.1%

Table 6.1.: The purity of SM processes in W , top and high pT W control regions. The purity of W (→ µν)+jets
is expected around 90% in the W control region and the purity of top-quark process in the top control region isaround 80%.

region”, and the other samples (i.e. a sample with no b-tagged jet) are categorized into “W control
region”. As a part of the W control region, a dedicated control region is defined for W production
simulation to measure fake-rates for events with highly boosted W . The “high pT W control region” isdefined with an increased muon pT requirement (pT > 110 GeV). The data and simulation comparison ineach control regions is shown in Fig. 6.7. The purity of each control region is summarized in Table. 6.1.
The leading τhad candidates in control regions are used for the fake-rate measurements, which aresupposed to be originated from hadron jets in the W + jets and top-quark processes. The fake rate to agiven single tau trigger as well as tau identification criteria are computed based on following formula:
FR(pT ) = Npass ID /Nall .

(6.3)

Minor contributions of true τhad candidates are subtracted based on the simulation as backgrounds in the
fake-rate measurements. The fake rate is computed for 1-prong, 2-prong, and 3-prong of sub-leading tau,separately. The fake-rates are measured also as a function of pT of the τhad candidates. The measured
fake-rates are shown in Fig. 6.8, Fig. 6.9 and Fig. 6.10 for 1-prong τhad , 3-prong τhad and 2-prong τhad .
For bins in which the data statistics are limited in the control regions for fake-rate measurements, theτhad identification criteria are exceptionally applied for these backgrounds instead of weighting with themeasured fake-rates. All the results of the fake rate measurements are summarized in Appendix C.
Given that the µν +jets control regions have an event topology compatible with the signal of H/A → τ τ
if one of the tau leptons decays into µνν and the other decays hadronically, it is shown that the possible
impact of the signal contributions in the control region is small enough for signals with 1000 GeV and
300 GeV of the neutral heavy Higgs boson mass. The expected impact on the fake-rate measurements
due to possible signals is shown in Fig. 6.11 as a function of the pT of τhad and the cross-section times
branching-fraction of H/A → τ τ signals. Since the potential effect on the fake rate is smaller than 1%,
the signal contribution in the control region is found to be significantly smaller than the uncertainty on
the measurement.

6.3

Expected Event Yields in the Signal Regions

After background modeling for ,the expected yield and mtot
T distribution are investigated before thestatistical analysis with likelihood method. The “pre-fit” (before the likelihood fit discussed in Sec. 8.1)
of signal and background are summarized in the Table 6.2 and Table 6.3. Figure 6.12 and Fig. 6.13 show
the mtot
T distribution in BVETO, BTAG and 2P categories. Appendix D presents the pre-fit distributionof other variables. The background expectation estimated by simulation and data-driven method presents
a good agreement with observed data in the pre-fit distribution. The systematic uncertainties illustrated
in the figures will be discussed in the chapter 7.

1.4
1.2
1
0.8
0.6
0

s = 13 TeV, 139.0 fb-1
H/A → τlep τhad
µ + jet t t CR

1.4
1.2
1
0.8
0.6
0

µ + jet t t CR

stat.

50

Events / GeV

1012
1011
1010
109
108
107
106
105
104
103
102
10
1

1.4
stat.
1.2
1
0.8
0.6
50 100 150 200 250 300 350 400 450 500µ p [GeV]
T(g) High pT W CR muon pT

100

150

200

s = 13 TeV, 139.0 fb-1
H/A → τlep τhad
W → µν + jets CR

Data

W → µν + jetst t , single top Fake τ

t t , single top Truth τ

W → τ ν + jets

Z/γ * → µµ + jets

Others

Uncertainty

1011
1010
109
108
107
106
105
104
103
102
10
1

1.4
1.2
1
0.8
0.6
0

50 100 150 200 250 300 350 400 450 500

1.4
1.2
1
0.8
0.6
0

s = 13 TeV, 139.0 fb-1
H/A → τlep τhad
W → µν + jets CR 2300(c) top CR mT

stat.

ATLAS Internal

250

mT [GeV]Data
W → µ ν + jets
tt, single top Fake τtt, single top Truth τ
W → τν + jets
Z/ γ * → µ µ + jets
Others
Uncertainty

ATLAS Internals = 13 TeV, 139.0 fb-1
H/A → τlep τhad
W → µν + jets CR

stat.

50

100

150

200

250

300

mT [GeV]T

Data/Bkg

Events / GeV

Data/Bkg

s = 13 TeV, 139.0 fb-1
H/A → τlep τhad(e) W CR tau pT

Data
W → µ ν + jets
tt, single top Fake τtt, single top Truth τ
W → τν + jets
Z/ γ * → µ µ + jets
Others
Uncertainty

Data
W → µ ν + jets
tt, single top Fake τtt, single top Truth τ
W → τν + jets
Z/ γ * → µ µ + jets
Others
Uncertainty

ATLAS Internal

leading τ p [GeV](d) W CR muon pT

W → µν + jets CR 2

1.4
1.2
1
0.8
0.6
0

Events / GeVATLAS InternalTs = 13 TeV, 139.0 fb-1
H/A → τlep τhad

Uncertainty

Data/Bkg

Events / GeV

1013
1012
1011
10109
108
10
1076
105
10
1043
10
102
10
1

Data
W → µ ν + jets
tt, single top Fake τtt, single top Truth τ
W → τν + jets
Z/ γ * → µ µ + jets
Others
Uncertaintyµ p [GeV]ATLAS Internal

Others(b) top CR tau pT

1.4
stat.
1.2
1
0.8
0.6
50 100 150 200 250 300 350 400 450 500

1011
1010
109
108
107
106
105
104
103
102
10
1

Z/γ * → µµ + jets

TData/Bkg

Events / GeV

Data/Bkg

W → µν + jets CR

W → τ ν + jets

109
108
107
106
105
104
103
102
10
1

leading τ p [GeV](a) top CR muon pT

s = 13 TeV, 139.0 fb-1
H/A → τlep τhadt t , single top Truth τ

50 100 150 200 250 300 350 400 450 500

T

ATLAS Internal

W → µν + jetst t , single top Fake τstat.

µ p [GeV]

1011
1010
109
108
107
106
105
104
103
102
10
1

Data

Events / GeV

1.4
stat.
1.2
1
0.8
0.6
50 100 150 200 250 300 350 400 450 500

ATLAS Internal(f ) W CR mT

Data

W → µν + jetst t , single top Fake τ

t t , single top Truth τ

W → τ ν + jets

Z/γ * → µµ + jets

Others

Uncertainty

1010
109
108
107
106
105
104
103
102
10
1

Events / GeVµ + jet t t CR

1011
1010
109
108
107
106
105
104
103
102
10
1

Data
W → µ ν + jets
tt, single top Fake τtt, single top Truth τ
W → τν + jets
Z/ γ * → µ µ + jets
Others
Uncertainty

Data/Bkg

s = 13 TeV, 139.0 fb-1
H/A → τlep τhad

Events / GeVATLAS Internal

Data/Bkg

Data/Bkg

Events / GeV

1010
109
108
107
106
105
104
103
102
10
1

82

Data/Bkg

6.3. Expected Event Yields in the Signal Regions

stat.

50 100 150 200 250 300 350 400 450 500
leading τ p [GeV]T(h) High pT W CR tau pT

1.4
1.2
1
0.8
0.6
0

Data
W → µ ν + jets
tt, single top Fake τtt, single top Truth τ
W → τν + jets
Z/ γ * → µ µ + jets
Others
Uncertainty

ATLAS Internals = 13 TeV, 139.0 fb-1
H/A → τlep τhad
W → µν + jets CR 2

stat.

50

100

150

200

250

300

mT [GeV](i) High pT W CR mT

Figure 6.7.: The event distribution in tt̄ (upper plots) and W(→ µν) (middle plots) control regions. For left toright: µ pT , τ pT and mT (µ, ETmiss . The W(→ µν) control region with higher pT selection for µ object is shown inthe bottom.

6.3. Expected Event Yields in the Signal Regions

83

0.16

SS topOS top
SS W+jets
OS W+jets-1

s = 13 TeV, 139.0 fb
Loose not Medium-ID

70
60

0.14

fake rate

0.18

80 ×10fake rate

fake rate−3

0.2

SS topOS top
SS W+jets
OS W+jets-1

s = 13 TeV, 139.0 fb
Medium not Tight-ID

0.1
0.09
0.08
0.07

0.12

50

0.06

0.1

40

0.05

0.08

30

0.04

0.06

0.03

20

0.04
0.02

10

0

0

100

150

200

250

300

0.02
0.01
100

150

200

250

pT(τ1) [GeV]-1

s = 13 TeV, 139.0 fb
Loose-ID

SS topOS top
SS W+jets
OS W+jets

fake rate

fake rate

0.3

150

200

250

300

pT(τ1) [GeV](c) tight 1-prong

0.1
0.09

s = 13 TeV, 139.0 fb-1

0.08 Trigger+Medium-ID

SS topOS top
SS W+jets
OS W+jets

0.07

0.25

0.06

0.2

0.05

0.15

0.04
0.03

0.1

0.02

0.05
0

100

(b) med-not-tight 1-prong

0.4
0.35

0

300

pT(τ1) [GeV](a) loose-not-med 1-prong

SS topOS top
SS W+jets
OS W+jetss = 13 TeV, 139.0 fb-1
Tight-ID

0.01
100

150

200

250

300

pT(τ1) [GeV](d) loose 1-prong

0

100

150

200

250

300

pT(τ1) [GeV](e) med+trig. 1-prong

Figure 6.8.: The overall fake rate measured from data in tt̄ and W(→ µν). FRs corresponding to the different
working points for 1-prong are shown in the plots.

6.3. Expected Event Yields in the Signal Regions−3

25

SS topOS top
SS W+jets
OS W+jetss = 13 TeV, 139.0 fb-1
Loose not Medium-ID

9

SS topOS top
SS W+jets
OS W+jetss = 13 TeV, 139.0 fb-1

8 Medium not Tight-ID

15
10
5

100

150

200

250

3
2.5

4

2

3

1.5

2

1

1

0.5
100

150

200

250

150

200

250

300

pT(τ1) [GeV](c) tight 3-prong−3

SS topOS top
SS W+jets
OS W+jetss = 13 TeV, 139.0 fb-1
Loose-IDfake rate−3

fake rate

100(b) med-not-tight 3-prong

50 ×1040

0300

pT(τ1) [GeV](a) loose-not-med 3-prong

SS topOS top
SS W+jets
OS W+jetss = 13 TeV, 139.0 fb-1

4 Tight-ID

5pT(τ1) [GeV]

45

4.5

6

0

300

5 ×10

3.5

7

20

0

−3

10 ×10fake rate

30 ×10fake rate

fake rate−384

10 ×10
9
8

35

7

30

6

25

5

20

4

15

3

10

2

5

1

0

0

100

150

200

250

300

SS topOS top
SS W+jets
OS W+jetss = 13 TeV, 139.0 fb-1
Trigger+Medium-ID

100

150

200

pT(τ1) [GeV]

250

300

pT(τ1) [GeV](d) loose 3-prong(e) med+trig. 3-prong

Figure 6.9.: The overall fake rate measured from data in tt̄ and W(→ µν). FRs corresponding to the different
working points for 3-prong are shown in the plots.

0.09

SS topOS top
SS W+jets
OS W+jetss = 13 TeV, 139.0 fb-1
Loose-ID

0.08

fake rate

fake rate−3

0.1

10 ×10
9
8

0.07

7

0.06

6

0.05

5

0.04

4

0.03

3

0.02

2

0.01

1

0

0

100

150

200

250

300

pT(τ1) [GeV](a) loose 2-prong

SS topOS top
SS W+jets
OS W+jetss = 13 TeV, 139.0 fb-1
Trigger+Medium-ID

100

150

200

250

300

pT(τ1) [GeV](b) med+trig. 2-prong

Figure 6.10.: The overall fake rate measured from data in tt̄ and W(→ µν). 2-prong FRs given to the loose andmed.+trigger working points are used for sub-leading and leading τhad .

1.0025
1.002
−1

10

1.07
1.06
1.05
1.04

−1

10

1.00151.03
1.001
s = 13 TeV, 139.0 fb-1
Sig. impact, top CR, Loose, 1-prong

10−2

100

150

200

250

s = 13 TeV, 139.0 fb-1
Sig. impact, top CR, Loose, 1-prong

1.0005
10−2

300

100

150

200

τ pT [GeV]

0.1
0.08
0.06

10−1

σ × BR(φ→ττ) [pb]0.121

s = 13 TeV, 139.0 fb
Significance, top CR, Loose, 1-prong

150

200

250

1.03
1.025

10−2

300

τ pT [GeV]

1.4
1.2
1
10−1

0.8
0.6

1.015
s = 13 TeV, 139.0 fb-1
Sig. impact, top CR, Loose, 1-prong

100

150

(e) Significance ggH300

s = 13 TeV, 139.0 fb
Significance, top CR, Loose, 1-prong

200

250

1.4
10−2

1.3
1.2

200

250

s = 13 TeV, 139.0 fb-1
Sig. impact, top CR, Loose, 1-prong

1.005
10−3

300

100

300

150

200

τ pT [GeV](f ) Significance bbH300

300

10−1

50
40
30

10−2
s = 13 TeV, 139.0 fb
Significance, top CR, Loose, 1-prong

100

150

200

250

1

×10−3
1.2
1

10−1

0.8
0.6

10−2

0.4

20
-1

10−3

1.1

(d) bbH1000

60

0.2
0

250

τ pT [GeV]

×10−6
70

0.4

-1

150

1.5

τ pT [GeV]

1.6

100

1.6

1.01
10−3

1.8
1

10−2

1.7
10−1

1.02

1.01

×10−3
2

0.02

1.8

(c) ggH1000

0.04
-1

100

10−1

1.02

300

1.035

(b) bbH300
×10−3
0.14

10−2

1.04

τ pT [GeV](a) ggH300

σ × BR(φ→ττ) [pb]

250

1.045

σ × BR(φ→ττ) [pb]

1.003

1.08

1

85

σ × BR(φ→ττ) [pb]

1

1.09

σ × BR(φ→ττ) [pb]1.0035σ × BR(φ→ττ) [pb]σ × BR(φ→ττ) [pb]1.004

σ × BR(φ→ττ) [pb]6.3. Expected Event Yields in the Signal Regions

-1

10

300

τ pT [GeV](g) Significance ggH1000

s = 13 TeV, 139.0 fb
Significance, top CR, Loose, 1-prong

10−3

100

150

200

250

0.2

300

τ pT [GeV](h) Significance bbH1000

Figure 6.11.: Impact of a potential H/A → τhad τlep signal with 1000 GeV mass on the measured 1-prong fakerates of loose ID in tt̄ control region as a function of the pT of τhad and the cross-section times branching-fractionof H/A → τ τ signals. The exclusion limit results of publish result with 36 fb−1 are illustrated in white line [65].
The “probe” tau leptons of signal passes the loose ID criterion and are taken into account. Upper plots show thechange in the fake rates with the different signal events in tt̄ control regions. Bottom plots show the corresponding
significances of the shifts in the fake rate.

6.3. Expected Event Yields in the Signal Regions

86

Processes
Multijet
WtaunuZtautauTop
OthersBkg
data
data/Bkg
ggH1500
bbH1500
ggH300bbH300

1P BVETO loose-not-med
2501 ± 92
32 ± 1
183 ± 77±04±02728 ± 0.81%
2780
1.02
1030 ± 38
466 ± 1742 ± 228 ± 1

1P BVETO med-not-tight1370 ± 80
43 ± 3278 ± 1610 ± 17±01708 ± 0.77%
1769
1.04
1594 ± 93
816 ± 48
60 ± 448 ± 3

1P BVETO tight959 ± 38178 ± 71289 ± 52
37 ± 131 ± 12494 ± 0.46%
2356
0.94
8501 ± 341
5425 ± 218
243 ± 10232 ± 9Processes
Multijet
WtaunuZtautauTop
OthersBkg
data
data/Bkg
ggH1500
bbH1500
ggH300bbH3003P BVETO loose-not-med
644 ± 87
17 ± 273 ± 104±02±0740 ± 0.86%779
1.05
264 ± 36144 ± 19
21 ± 320 ± 3

3P BVETO med-not-tight
232 ± 69
18 ± 584 ± 253±12±1
338 ± 0.94%347
1.03
291 ± 85
190 ± 56
24 ± 715 ± 4

3P BVETO tight
115 ± 2459 ± 12292 ± 60
11 ± 28±2
485 ± 0.88%464
0.961182 ± 244
733 ± 151
67 ± 1469 ± 14

Table 6.2.: The events yields before the fit. Only statistical uncertainties are considered and listed in the table.
The expected contributions from signal events with masses of 300 and 1500 GeV and cross sections of 1 pb are
shown.

Processes
Multijet
WtaunuZtautauTop
OthersBkg
data
data/Bkg
ggH1500
bbH1500
ggH300bbH300BTAG loose
168 ± 458±2
29 ± 8159 ± 442±0
365 ± 2.62%389
1.07376 ± 103
5302 ± 14528±2
184 ± 50

2P loose
3551 ± 92
87 ± 2
189 ± 532 ± 16±03864 ± 0.74%
4012
1.04
1965 ± 51
2031 ± 53
19 ± 023 ± 1

Table 6.3.: The events yields before the fit. Only statistical uncertainties are considered and listed in the table.
The expected contributions from signal events with masses of 300 and 1500 GeV and cross sections of 1 pb are
shown.

106
5

10

s = 13 TeV, 139.0 fb-1
H/A → τhadτhadloosenotmed 1prong
b-veto OS

104

Data

MultijetZ/ γ * → ττ + jets

W → τν + jets

tt, single top

Otherstan β=15
hMSSM A 1000 → ττUncertainty

EventsEvents6.3. Expected Event Yields in the Signal Regions

Data

MultijetZ/ γ * → ττ + jets

W → τν + jets

tt, single top

Otherstan β=15
hMSSM A 1000 → ττUncertainty

10

102

102

10

10

1

stat.

Data/Bkg

1

Data/Bkg

104

s = 13 TeV, 139.0 fb-1
H/A → τhadτhadloosenotmed 3prong
b-veto OS

3

103

1.5

105

87

syst.

1

1.5

stat.

syst.

1

200 300 400 500 600 700 800 900 1000

200 300 400 500 600 700 800 900 1000

mtot
T [GeV]mtot
T [GeV]

106
105
104

s = 13 TeV, 139.0 fb-1
H/A → τhadτhad
mednottight 1prong
b-veto OS

Data

MultijetZ/ γ * → ττ + jets

W → τν + jets

tt, single top

Otherstan β=15
hMSSM A 1000 → ττ(b) 3p BVETO loose-not-med
EventsEvents(a) 1p BVETO loose-not-med

Uncertainty

104

s = 13 TeV, 139.0 fb-1
H/A → τhadτhad
mednottight 3prong
b-veto OS

103

Data

MultijetZ/ γ * → ττ + jets

W → τν + jets

tt, single top

Otherstan β=15
hMSSM A 1000 → ττUncertainty

3

10

102

2

10

10

10

1

1.4
1.2
1
0.8
0.6

stat.

Data/Bkg

Data/Bkg

1

syst.

stat.

1.5

syst.

1

200 300 400 500 600 700 800 900 1000

200 300 400 500 600 700 800 900 1000

mtot
T [GeV]mtot
T [GeV]106510

s = 13 TeV, 139.0 fb-1
H/A → τhadτhadtight 1prong
b-veto OS

104

Data

MultijetZ/ γ * → ττ + jets

W → τν + jets

tt, single top

Otherstan β=15
hMSSM A 1000 → ττ(d) 3p BVETO med-not-tight
EventsEvents(c) 1p BVETO med-not-tight10

s = 13 TeV, 139.0 fb-1
H/A → τhadτhadtight 3prong
b-veto OS

3

Data

MultijetZ/ γ * → ττ + jets

W → τν + jets

tt, single top

Otherstan β=15
hMSSM A 1000 → ττUncertainty

10

102

102

10

10

1

stat.

Data/Bkg

1

Data/Bkg

4

Uncertainty

103

1.4
1.2
1
0.8
0.6

105

syst.

200 300 400 500 600 700 800 900 1000

1.4
1.2
1
0.8
0.6

stat.

syst.

200 300 400 500 600 700 800 900 1000

mtot
T [GeV](e) 1p BVETO tightmtot
T [GeV](f ) 3p BVETO tight

Figure 6.12.: Distributions of total transverse mass for BVETO category. The plots show the expected distribution
before the likelihood fit. Events containing 1-prong sub-leading τhad are illustrated in left plots and the events
containing 3-prong sub-leading τhad are shown in right plots. From top to bottom, the plots is made with respect totau identification for sub-leading τhad (loost-not-med., med-not-tight and tight). The underflow events and overflow
evnets are included in the first and last bins, respectively. In the label, “Others” background refers to contributions
from diboson, Z/γ ∗ (→ ``)+jets and W (→ `ν)+jets production. The “Top” containing the tt̄ and single top
production. The data is shown as the black point in the histogram. The red line shows signal contribution ofgluon-fusion and bottom-annihilation productions which are normalized to tan β = 15 based on the ATLAS publish
result [65]. In the lower panels, the fraction of data and overall background is illustrated.

1.5

s = 13 TeV, 139.0 fb-1
H/A → τhadτhadloose incprongb-tag OS

Data

MultijetZ/ γ * → ττ + jets

W → τν + jets

tt, single top

Otherstan β=15

hMSSM A 1000

→ ττ

Events

240
220
200
180
160
140
120
100
80
60
40
20

88

107
106
5

10

Uncertaintys = 13 TeV, 139.0 fb-1
H/A → τhadτhadloose 2prong
b-veto OS

Data

MultijetZ/ γ * → ττ + jets

W → τν + jets
Otherstt, single top
tan β=15

hMSSM A 1000

→ ττ

Uncertainty

4

10

103
102
10
1

stat.

Data/Bkg

Data/Bkg

Events6.3. Expected Event Yields in the Signal Regions

syst.

1
150 200 250 300 350 400 450 500 550 600

1.4
1.2
1
0.8
0.6

stat.

syst.

200 300 400 500 600 700 800 900 1000

mtot
T [GeV](a) 1p+3p BTAG loose

mtot
T [GeV](b) 2p B-inc. loose

Figure 6.13.: Distributions of total transverse mass for BTAG (left) and 2P (right) categories. The plots show the
expected distribution before the likelihood fit. The underflow events and overflow evnets are included in the first andlast bins, respectively. In the label, “Others” background refers to contributions from diboson, Z/γ ∗ (→ ``)+jets
and W (→ `ν)+jets production. The “Top” containing the tt̄ and single top production. The data is shown as
the black point in the histogram. The red line shows signal contribution of gluon-fusion and bottom-annihilation
productions which are normalized to tan β = 15 based on the ATLAS publish result [65]. In the lower panels, thefraction of data and overall background is illustrated.

7 Systematic Uncertainties

The systematic uncertainties are taken into account in the statistical analysis. They significantly affectto the yield result of signal and background. In this section, the systematic uncertainties are classified
into several sources. Instrumental uncertainties are relate to the physics object reconstruction with thecalibration shown in Sec. 7.1. This section also provides the exposition for other uncertainties fromluminosity, pile-up, muon and electron object. The uncertainties for Monte Carlo modeling are presented
in Sec. 7.2. They explain the theoretical modeling for SM backgrounds. The evaluation of uncertainties onbackground which derived from the mis-identified tau using data-driven method is described in Sec. 7.3.
Uncertainties described above are treated for the result of analysis in the two types to investigate theeffect on signal and background yield and kinematic shape of the final discriminant variable mtot
T .

7.1

Experimental uncertainties

Due to imperfect detector simulation, uncertainties on reconstructed physics objects are estimated in
the calibration step. This section focuses reconstruction, calibration and identification uncertainties forthe main physics objects, which are τhad , jets and ET miss, in this analysis. The experimental systematics
for this analysis are summarized in Table 7.1.
Hadronic tau
The τhad object plays a primary role in this analysis. It is widely used in the trigger step, signal
extraction and final discriminant calculation. The detectors related uncertainties, such as τhad trigger,
identification, reconstruction, as well as energy calibration, are essential and should be carefully investigated. The reconstruction efficiency of τhad have been described in Sec 4.5.1, and the corresponding
systematic uncertainties are illustrated in Fig. 7.1. Pileup and the inner detector material are the main
sources of reconstruction uncertainties since they strongly affect the correctness performance of tau vertex (TV) which provides the identification for vertex reconstruction efficiency in the events [178]. Total
uncertainty of the τhad reconstruction is around 2% to 4.5%.
Uncertainty of τhad identification is different in the central region |η| < 1.37 and forward region 1.52 <|η| < 2.47. It has been estimated for each region with different working point separately. Z/γ ∗ → τ τevents are used to tune the τhad identification efficiency and estimate corresponding uncertainties. This
uncertainty highly depends on the input variables of tau ID BDT training, for example, the calorimeterbased and tracking-based input variables show huge variation in shapes. In pT > 100 GeV region, it
provides around 10% uncertainty for 3-prong in barrel region. The pileup effect and material uncertainties
also play the major roles in 1-prong decays. They provide large impact on the leading track IP significance(|Sleadtrack |) which is a variable only used in 1-prong BDT training. The systematic uncertainty with
Medium ID working point for 1-prong and 3-prong in the central and forward region are shown in Fig 7.2.
They are approximately 10% uncertainties in wide pT range of the forward region for both 1-prong

897.1. Experimental uncertainties

90

Uncertainty

Description

Lumi
T AU
T ES
M U ON

Integrated luminosity measurement
τhad reconstruction and identification
τhad energy scalemuon systematics, including trigger, reconstruction,
isolation, identification and energy scale
electron systematics, including trigger, reconstruction, isolation, identification and energy scale
missET
soft terms
jet energy scale and resolution
flavor-tagging
pile-upEGM ET Sof t
JER, JES, Jvt
btag
P RW

Scheme (number of NPs)
1
6
3
13
6
2
7
14
1

0.14
0.12

ATLAS Simulation
Preliminary|η | < 2.50
1-prong

Material

Physics list

PileupThreshold

Underlying event

Total

0.1
0.08

Fractional Uncertainty

Fractional Uncertainty

Table 7.1.: Summary table for the experimental systematics with number of nuisance parameterss, which isreferred to as NPs, for likelihood fit and brief description.

0.14
0.12

0.04

0.04

0.02

0.02
40 50

102

0

2×102

Physics list

PileupThreshold

Underlying event

Total

0.08
0.06

30

Material

0.1

0.06

0

ATLAS Simulation
Preliminary|η | < 2.50
3-prong

30

40 50

102

p [GeV]p [GeV]

T

(a)

2×102
T

(b)

Figure 7.1.: Uncertainties for reconstruction efficiency for 1-prong in (a) and 3-prong in (b). Each source ofsystematic uncertainties is also shown in the figure as a function of τhad pT . The sources of uncertainties, such as
calorimeter noise thresholds, are discussed in Ref. [178].

and 3-prong. Therefore, the maximum values for 1-prong and 3-prong in central reach 15% and 20%,
respectively.
The uncertainty of τhad energy scale calibration (TES) is the one of dominant uncertainties in thisanalysis. It is computed using Monte Carlo simulation with a reconstructed τhad passing Loose ID basedvison the Gaussian mean of the ET,calib /ET,true
which is also used in resolution calculation. A small effect of
uncertainty from pileup is computed to be lower than 1%. Alternative Geant 4 hadronic shower model,
which is significant to the uncertainty in central regions, provides an important source of uncertainties.
It also affects the energy deposited in TC. Moreover, the material modeling and the variation of thecalorimeter noise in MC simulation are also considered as the uncertainty sources. They affect thematerial correction weights and the modeling of the calorimeter calibration. The total uncertainty iscomputed and orthogonality with each systematic uncertainty as a function of the calibrated transverse
energy as displayed in Fig 7.3 and Fig 7.4 for 1-prong and 3-prong, respectively. Overall uncertainties
vary within the range of 2% to 6% depending on pT and |η|.
The trigger efficiency with the relative uncertainty is computed with Z → τµ τhad events using the
tag-and-probe method. The tau trigger uncertainties consist of three components, which are statisticaluncertainties associated with data and simulation, and the systematic uncertainty. Jet fake background,muon performance, pileup and soft component of MET are the main sources of systematic uncertainties

91

0.35
0.3
0.25

ATLAS Simulation
Preliminary|η | < 1.37
1-prongMedium ID

Material

Physics list

PileupThreshold

Underlying event

Total

0.2
0.15

Fractional Uncertainty

Fractional Uncertainty

7.1. Experimental uncertainties

0.35
0.3
0.25

0.05

0.05
40 50

102

0

2×102

Physics list

PileupThreshold

Underlying event

Total

0.15
0.1

30

Material

0.2

0.1

0

ATLAS Simulation
Preliminary
1.52 ≤ |η | < 2.47
1-prongMedium ID

30

40 50

102

2×102

p [GeV]p [GeV]

T

T

(b)

0.35
0.3
0.25

ATLAS Simulation
Preliminary|η | < 1.37
3-prongMedium ID

Material

Physics list

PileupThreshold

Underlying event

Total

0.2
0.15

Fractional Uncertainty

Fractional Uncertainty

(a)
0.35
0.3
0.25

0.05

0.05
40 50

102

0

2×102

Physics list

PileupThreshold

Underlying event

Total

0.15
0.1

30

Material

0.2

0.1

0

ATLAS Simulation
Preliminary
1.52 ≤ |η | < 2.47
3-prongMedium ID

30

40 50

102

p [GeV](c)

2×102p [GeV]T

T(d)Figure 7.2.: Systematic uncertainty for τhad efficiency with Medium ID working point as a function of τhad pT for
1-prong is shown in the upper two plots (a) (b), and for 3-prong is shown in the bottom two plots (c) (d). The
systematic uncertainties are measured in the central |η| < 1.37 and 1.52 < |η| < 2.47 forward region separately [178].

0.14
0.12

ATLAS Simulation
Preliminary|η | < 0.30
1-prong

0.1

92

ClosureMaterial

Physics list

PileupSingle particle resp.

Threshold

Underlying event

Total

Fractional Uncertainty

Fractional Uncertainty

7.1. Experimental uncertainties

0.08

0.14
0.12
0.1

0.06

0.04

0.04

0.02

0.02
30

40 50

0

2×102

102

ClosureMaterial

Physics list

PileupSingle particle resp.

Threshold

Underlying event

Total

0.08

0.06

0

ATLAS Simulation
Preliminary
0.30 ≤ |η | < 0.80
1-prong

30

40 50

102

2×102

p [GeV]p [GeV]

T

T

0.14
0.12

ATLAS Simulation
Preliminary
0.80 ≤ |η | < 1.30
1-prong

0.1(b)ClosureMaterial

Physics list

PileupSingle particle resp.

Threshold

Underlying event

Total

Fractional Uncertainty

Fractional Uncertainty

(a)

0.08

0.14
0.12
0.1

0.06

0.04

0.04

0.02

0.02
30

40 50

0

2×102

102

ClosureMaterial

Physics list

PileupSingle particle resp.

Threshold

Underlying event

Total

0.08

0.06

0

ATLAS Simulation
Preliminary
1.30 ≤ |η | < 1.60
1-prong

30

40 50

102

p [GeV]

2×102
p [GeV]T

T(d)Fractional Uncertainty

(c)

0.14
0.12

ATLAS Simulation
Preliminary
1.60 ≤ |η | < 2.40
1-prong

0.1

ClosureMaterial

Physics list

PileupSingle particle resp.

Threshold

Underlying event

Total

0.08
0.06
0.04
0.02
0
30

40 50

102

2×102
p [GeV]T(e)

Figure 7.3.: Uncertainties of TES calibration for 1-prong τhad as a function of pT . They are separated to five regions
depend on |η|. Each corresponding source of systematic uncertainties is also displayed in the histograms [178].

0.14
0.12

ATLAS Simulation
Preliminary|η | < 0.30
3-prong

0.1

93

ClosureMaterial

Physics list

PileupSingle particle resp.

Threshold

Underlying event

Total

Fractional Uncertainty

Fractional Uncertainty

7.1. Experimental uncertainties

0.08

0.14
0.12
0.1

0.06

0.04

0.04

0.02

0.02
30

40 50

0

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102

ClosureMaterial

Physics list

PileupSingle particle resp.

Threshold

Underlying event

Total

0.08

0.06

0

ATLAS Simulation
Preliminary
0.30 ≤ |η | < 0.80
3-prong

30

40 50

102

2×102

p [GeV]p [GeV]

T

T

0.14
0.12

ATLAS Simulation
Preliminary
0.80 ≤ |η | < 1.30
3-prong

0.1(b)ClosureMaterial

Physics list

PileupSingle particle resp.

Threshold

Underlying event

Total

Fractional Uncertainty

Fractional Uncertainty

(a)

0.08

0.14
0.12
0.1

0.06

0.04

0.04

0.02

0.02
30

40 50

0

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102

ClosureMaterial

Physics list

PileupSingle particle resp.

Threshold

Underlying event

Total

0.08

0.06

0

ATLAS Simulation
Preliminary
1.30 ≤ |η | < 1.60
3-prong

30

40 50

102

p [GeV]

2×102
p [GeV]T

T(d)Fractional Uncertainty

(c)

0.14
0.12

ATLAS Simulation
Preliminary
1.60 ≤ |η | < 2.40
3-prong

0.1

ClosureMaterial

Physics list

PileupSingle particle resp.

Threshold

Underlying event

Total

0.08
0.06
0.04
0.02
0
30

40 50

102

2×102
p [GeV]T(e)

Figure 7.4.: Uncertainties of TES calibration for 3-prong τhad as a function of pT . They are separated to five regions
depend on |η|. Each corresponding source of systematic uncertainties are also displayed in the histograms [178].

7.1. Experimental uncertainties

94

of the background subtraction for the efficiency measurement. As shown in the Fig. 4.30, the tau trigger
systematic uncertainties provide a larger uncertainty in low-pT region than the one in high-pT region due
to higher background contribution [161, 162].
Jets

0.1

0.08

Data 2015-2017, s = 13 TeV
anti-k t R = 0.4, EM+JES
η = 0.0

ATLAS Preliminary

Total uncertainty
Absolute in situ JES
Relative in situ JES
Flav. composition, inclusive jets
Flav. response, inclusive jets
Pile-up, average 2015-2017 conditions
Punch-through, average 2015-2017 conditions

0.06

0.04

0.02

Fractional JES uncertainty

Fractional JES uncertainty

Main systematic uncertainties of jet object come from energy and tagging. Jet energy scale (JES)
provides 80 propagated sources from electron, photon, and muon energy scale calibrations [179]. Fourpile-up sources for uncertainties are considered due to MC mis-modeling of the dependence for the different
variables. Moreover, six other independent uncertainties are considered for the jet object. They are intercalibration, statistic, method non-closure and the response of the difference from a jet composition oflight-quark, b-quark, and gluon-initiated jets.
The JES uncertainties are shown in Fig. 7.5 as the function of η and pT . The uncertainties are expected
at a level 5% for the low-pT region and 2% at the most for the high-pT region.
0.1

0.08

ATLAS Preliminary

Data 2015-2017, s = 13 TeV
anti-k t R = 0.4, EM+JES
jet
p = 60 GeV

Total uncertainty
Absolute in situ JES
Relative in situ JES
Flav. composition, inclusive jets
Flav. response, inclusive jets
Pile-up, average 2015-2017 conditions
Punch-through, average 2015-2017 conditions

T

0.06

0.04

0.02

0
20 30 40

102

2×102

103

2×103
p [GeV]

0

−4

−3

−2

−1

0

T

(a)

1

2

3

4
η

jet

(b)

Figure 7.5.: The combined uncertainty in the JES with over 90 components include instrumental, pile-up andjet composition effect. (b) shows the one as a function of pjet
T at η = 0. (a) is as a function of η with pT = 60
selection [127].

Jet vertex tagging (JVT) calibration measured in Z → µµ events provides a small contribution to
the systematic uncertainty based on the jet efficiency of MC and data. The systematic uncertainty of
JVT consists of two components; the discrepancy between MC and data in ∆φ(Z,jet) distribution andthe non-negligible difference in hard-scatter efficiency of Sherpa and Powheg MC generators. The overall
uncertainties are found in the 2% to 1% range in 20 GeV < pT < 60 GeV
The systematic uncertainties for flavor tagging are measured based on the b-tagging efficiency andthe corresponding scale factor which is defined as data/sim.
bb . Since the flavor tagging and scale factor
are measured in tt̄ control region, the tt̄ modeling is considered as a main source of uncertainties. The
difference between Powheg+Pythia 8 and MC@NLO+Pythia 8 is taken into account for tt̄ modeling.
Illustration of scale factor shows in Fig. 7.6 with the related statistical and systematic uncertainties. The
combined uncertainty of the statistical and systematic uncertainties with the 77% operating working point
for this analysis is below 7% in low pT range (60 GeV < pT < 300 GeV), and the uncertainty increases
up to approximately 10% due to the dominated statistical uncertainty [180].
Missing Transverse Energy, ETmiss
Uncertainty of missing transverse energy is highly related with each physics objects.Due to the precision
measurement of hard term, the main uncertainty of MET comes from soft term. Figure 4.38 shows asketch for two projection component of the soft term which are used to define three input parameters of7.1. Experimental uncertainties

(a)

95

(b)

Figure 7.6.: The scale factor for b-tagging efficiencies for the MV2c10 algorithm at the 77% working point as afunction of jet transverse momentum (a) and the absolute pseudo-rapidity (b). The mean value of scale factors andcorresponding total uncertainties are shown black dots and green band respectively. (taken from Reference [180])

the systematic uncertainty calculation. The parallel scale Ekmiss,soft−term and parallel resolution squared
σ 2 (Ekmiss,soft−term ) show the mean value and root-mean-square (RMS) of the parallel projection of psoft
Tmiss,soft−term2), presents
to phard
T , respectively. The final parameter, transverse resolution squared σ (E⊥soft
the RMS information for perpendicular projection of pT . Figure 4.40 shows the agreement of threeparameters between data and the simulation with the different generators in the Z → ee final states
events. The systematic uncertainty, which is illustrated as the pink band in the figure, is computed as
the function of three parameters based on the maximal differences between data and simulations. The
systematic uncertainties (at most 20% depending on phard
value) are employed to the simulations in thisT
analysis. It provides a small impact (< 0.5%) on the distribution of the final discriminant variable.

Other Uncertainties
Other insignificant sources of systematic uncertainties come from luminosity, pile-up, electron and muon
objects. ATLAS luminosity is determined by the LUCID detector as described in Sec 3.2.4 with thecorresponding uncertainties for each data-taking year independently. There dominated uncertainties are
considered as the bunch charge production, beam condition, and instrumental effects. The uncertainties
of the integrated luminosity measurement for the 2015 to 2018 data-taking year are estimated separately
as 2.1%, 2.2%, 2.4%, and 2.0%, and total uncertainty for the combined run-2 dataset is around 1.7%.
Considering the integrated luminosity as 139 fb−1 is used in this analysis, the absolute uncertainty isquoted as around ±2.4 fb−1 .
The Pileup re-weighting uncertainty is measured. MC is compared with data as a function of theinstantaneous luminosity. Since the re-weighting is applied into the simulation to correct the µ, theuncertainties are defined as the propagation value for MC by recalculating the re-weighting with ±1σ [181].
These uncertainties are considered in the analysis with respect to data period.
The muon identification and reconstruction uncertainty are computed with efficiency measurement
based on both J/ψ → µµ and Z → µµ tag-and-probe method [149, 182]. Additional uncertainties aremeasured from the correlation of ID-MS efficiencies and different kinematic distributions between theselected muon and probe muon up to 1-2% in the small |η| region. The total uncertainties for muonreconstruction and identification of around 3% are taken into account in this analysis. For the muon
objects, there are around 1% and 5% uncertainties in wide pT range.
The uncertainties of electron object are considered. Since only ID, pT and η selection are applied
for electron objects in this analysis, the electron isolation uncertainty is not taken into account. The7.2. Theoretical Uncertainties on Monte Carlo Simulation
Sourcehadronization model
hard scatter

Generator
Herwig
MG5 aMC@NLO

PDF
CTEQ6L1
CT10

96
Tune
UE-EE-5-CTEQ6L1
A14

Table 7.2.: The generator and shower model used for tt̄ systematic samples.

combined uncertainties of reconstruction and identification efficiencies are measured using J/ψ → ee andZ → ee tag-and-probe methods. These uncertainties of 2% and 5% are given in the barrel and end-cap
region, respectively. Considering the effect from calorimeter with Z → ee analysis, the energy resolution
uncertainty for electron are obtained by the simulation. The minimal relative uncertainty for electrons
at ET = 40GeV is around 5%, while it increases at a higher transverse energy region due to the detectormaterial.
The uncertainties from muon and electron objects are expected to provide small impact (< 0.1%) in
this analysis.

7.2

Theoretical Uncertainties on Monte Carlo Simulation

Uncertainties for the theory of Monte Carlo simulation must be taken into account.
cross section
The overall theoretical cross section of backgrounds provides general 5 to 6% uncertainties for threemain backgrounds in the signal region, Z/γ ∗ + jets, W +jets, and Top sample [183]. The uncertainties ofthe minor background, di-boson, is 6% for the theoretical cross section of MC modeling [184].
Z/γ ∗ +jets
The theoretical systematic uncertainties of Z/γ ∗ + jets modeling due to the chosen PDF, beam energy,
parton shower model and αs are produced as the weights by a factor calculation tool [185]. The total
uncertainties of Z/γ ∗ + jets modeling in the acceptance are in the amount of 5%.
W +jets
Based on the W +jets control region discussed in Sec 6.2.2, no big discrepancy from data indicates that
the W→ µν background modeling is good and no further uncertainty is needed. Since the W boson decay
production is independent of the W +jets process modeling, it is fair to determine the same situation
for W→ eν and W→ τ ν. The sources of W +jets process modeling come from the CKKW parameter,
renormalization scale, factorization scale and the PDF in the SHERPA Monte Carlo generator [186]. The
parameters are modified in sample generation and computed in the expected limit checking. Since theresult shows the small impact on the limit (around <0.5%), additional systematic uncertainty of W→ τ νmodeling is not considered [65].
Top
The nominal pair and single production of top quark processes are applied for background modelingin this analysis. Therefore, the different setting for the generating parameters 1 are considered for the tt̄
and single top modeling. The generators with different matrix-element and parton-shower are used [177].
The samples for systematic uncertainties are listed in Table. 7.2.
1

For instance, there are PDF, scale and top-quark mass variations

7.3. Uncertainties on the Data-Driven Background Estimation
Uncertainty

Description

LP X(Mainly on Z+jets) systematics on PDF
choose, QCD scale, stronge interaction
coefficient
Cross section prediction uncertainty
Top modeling sys (mainly shape sys)
Fake rate uncertainties for the backgrounds such as top and W +jets with fake
τhadFake QCD sys, which is related withpT binning and number of tracks of sub-leadingτhadxsec for Diboson or top
T T BAR
Fakes Rate

Fake Factor

97

Scheme (number of NPs)
10

2
4
2

30

Table 7.3.: Summary table for the background modeling systematics with number of NPs for likelihood fit andbrief description.

Moreover, the impact from the variations are studied by modifying
q the factorization and renormalization
scale by factor two up and down for the transverse mass setting m2t + (p2T,t + p2T,t̄ )/2. The systematic
variations of multi-parton interaction and ISR/FSR parameters are included in Var1-Var3c parametervariations of A14 tune [187].
Total uncertainties of top quark modeling present the large systematic uncertainties (∼ 80% in thenormalization) for the BTAG category in the high mass region (larger than 400 GeV). The impact in theb-veto category is very limited since the tt̄ is not a main background in this signal region.
Signal Acceptance
Like systematic uncertainty study of SM background modeling, the several sources affect the simulation
signal sample and must to be taken into account as the signal acceptance. To compare the different sample
generation with varying generator parameters, the systematic variations for all configurations of simulation
can be obtained. The normalization uncertainties are based on the truth particle information. The
different PDF setting, such as NNPDF30 nlo as 0118 nf 4, CT14nlo NF4 and MSTW2008nlo68cl nf4
are exploited to estimate the uncertainty. To measure the uncertainties of the generator tune in ISR,
FSR, and MPI, the different scale factor are applied in the parameter of these shower model. For instance,systematic uncertainties of modeling ISR, FSR and MPI are discussed in AZNLO tune [188]. Based on thefitting result for systematic variations of the tuning, it only covers the ISR uncertainty. The uncertainty
is computed utilizing a factor of 2 up and down to scale FSR shower parameter and variations of the MPI
cut-off between 1.91 to 2.05 to cover the full range of PS and MPI uncertainties. For the QCD scale usedin cross sections measurement, the factorization and renormalization scale up and down by a factor oftwo.
The systematic uncertainty of signal acceptance provides small impact on the cross section limit (smaller
than 0.1%).

7.3

Uncertainties on the Data-Driven Background Estimation

As discussed in Sec. 7.2, all the background modeling systematics containing data-driven techniques
and theoretical Uncertainties are summarized in Table 7.3.
fake factor
For the fake factor method for the multi-jet background in this analysis, three main sources of uncertainties are considered. The biggest uncertainty comes from the statistical uncertainty of the measured

7.3. Uncertainties on the Data-Driven Background Estimation

98

events of data, as well as the MC simulation background. 2 The statistical uncertainties are treateduncorrelated with respect to number of tracks as well as the pT bins of sub-leading τhad .
The fake factors are measured in an inclusive manner for the b-tagging conditions. The difference
between BTAG and BVETO fake factors must be taken into account for the corresponding category.
Figure 7.7 presents the shape difference between BTAG and BVETO categories for 1-prong and 3-prong
fake factor in OS di-jet control region.
Figure 7.8 shows the total systematic uncertainties (data stat., mc stat. and systematic uncertainty
from the b-tagging conditions) in the pT dependence of the fake factors for 1-prong and 3-prong tau
candidates in BVETO category of this analysis.
Overall fake factor uncertainties for BVETO, BTAG and 2P categories are summarized in Appendix B.

0.4

0.14

b-tag

b-inc

b-vetofake factor

fake factor

0.45

b-tag

b-inc

b-veto

0.12

0.35
0.3

0.1

0.25

0.08

0.2

0.06

0.15

0.04

0.1
ATLAS Work in progress

0.05
0s = 13 TeV, 140.4 fb-1
opposite sign, 1 prong

100 150 200 250 300 350 400

0.02
0ATLAS Work in progresss = 13 TeV, 140.4 fb-1
opposite sign, 3 prong

100 150 200 250 300 350 400

subleading τ pT(a) 1-prong

subleading τ pT(b) 3-prong

Figure 7.7.: Shape difference comparing with BTAG and BVETO in OS di-jet control region with loose-not-med.
tau identification applied on sub-leading τhad . The difference is taken into account as an additional source of fakefactor uncertainties.

fake rate
In the uncertainties of the fake rate measurement for the other backgrounds with fake τhad , the main
uncertainties come from the data statistical uncertainty. The effect of true τhad MC simulation used for
subtraction of fake rate method is negligible due to the low contribution of MC in each control regions. The
uncertainties are treated to affect the shape of fake τhad in pT dependence and the expected backgroundyields. Overall fake rates with the uncertainties in this analysis are summarized in Appendix C.

2As described in Sec. 6.2.1, those background with truth τhad is used for subtraction in the di-jet control region.

7.3. Uncertainties on the Data-Driven Background Estimation

0.4

0.14

Nominal fake factor
b-tag vs. b-incl. syst.

data stat.

fake factor

fake factor

0.45
mc stat.

Nominal fake factor
b-tag vs. b-incl. syst.

0.3

mc stat.

0.1

0.25

0.08

0.2

0.06

0.15

0.04

0.1

0

data stat.

0.12

0.35

0.05

99

-1

s = 13 TeV, 139.0 fb
opposite sign, 1 prong

100 150 200 250 300 350 400
subleading τ pT(a) 1-prong BVETO

0.020s = 13 TeV, 139.0 fb-1
opposite sign, 3 prong

100 150 200 250 300 350 400
subleading τ pT(b) 3-prong BVETO

Figure 7.8.: Fake factors for 1-prong (left) and 3-prong (right) tau candidates in the BVETO category with loosenot-med. tau ID application. The sum of all sources of uncertainties is shown as the orange uncertainty bands
which include the statistical uncertainties and difference with the fake factor of BTAG or BVETO.

8 Result

The number of observed events in H/A → τhad τhad search is investigated based on the statistical analysis.
A general binned likelihood function is exploited to construct the product of probability terms withbackground-only or signal-plus-background hypothesis. The combined likelihood function is discussed in
Sec 8.1. Section 8.2 presents the statistical result for each signal region in this analysis. The limit for the
cross section times branching fraction are computed for both gluon-gluon fusion and bottom-annihilation
production at the 95% confidence level (CL) as shown in Sec. 8.3. The interpretation with respect to
MSSM mA -tan β space is discussed in the chapter 9 based on the context of hMSSM benchmark scenario.

8.1

Statistical Analysis

To inspect the signature of neutral heavy Higgs H/A → τ τ signal, the construction of the likelihood
ratio and the hypothesis test are introduced in this section. The continuous parameter of interest (PoI) in
the statistical analysis is defined as the “signal strength” µ. It is obtained by the maximum-likelihood fit
from the observed data to estimate the discovery significance or the exclusion limits. In the investigation
for the observed events, the “likelihood ratio” is known as the most efficient test for the statistical
hypotheses based on the Neyman-Pearson lemma [189].
The hypothesis test provides the likelihood-based method to quantify the exclusion or observed significance of new physics search. The hypothesis with µ = 0, which is corresponds to background-only one,is referred to a null hypothesis, so-called H0 . The hypothesis with µ = 1 corresponding to signal plus
background is defined as alternative hypothesis, so-called H1 . A quantified parameter, “p-value (pµ )”,corresponding to µ is obtained via maximum-likelihood fit for the H0 or H1 investigation (reject H0 or
accept H0 ).
The CLs technique is appropriate to derive the upper limit for the constraint and discovery significanceof search results [190, 191]. The upper limit on cross section times branching fraction with respect tohypothesis test are investigated based on the confidence level of 95% which is also corresponding to pµ of
0.05. This value is defined as a common enactment for new physics search in LHC.
The full reconstruction and fitting tools for the statistical analysis are contained in the software packages
HistFactory [192] , RooStats [193] and RooFit [194] in the RooStats framework. The detail of the profile
likelihood function, the hypothesis test and Asymptotic formula with Asimov dataset are discussed in thefollowing sections.

8.1.1

The Profile Likelihood Function

The binned likelihood function is implemented based on the Poisson probability term for the final
discriminant x, which is a total transverse mass in this analysis, of signal and SM backgrounds. The
expected number of total signal and background events are symbolized as S and B in this analysis. The
si and bi correspond to the expected events of signal and background in each bin i of the discriminant100

8.1. Statistical Analysis

101

x. The expected number in the bin i is given by the model µsi + bi . The binned likelihood function istypically built as:nY
bins
L(µ; xi ) =P ois(ni |µsi + bi ),(8.1)
iwhere the Poisson probability term is defined as P ois(n|λ) = λn e−λ /n!. It provides probability to observeni events while expecting the number of signal plus background of λ. The systematic uncertainties aretreated as nuisance parameters θ in the fit, which are constrained by Gaussian probability density function
G(θ). A default sigma of ±1σ deviation is used for each NP. The Gaussian PDF for the systematic
uncertainties is written as:1θ2
G(θ) = √exp(− 2 ).
(8.2)
2σ
2πσ
The full representation of the likelihood is given as :L(µ, θ; xi ) =NY(µsi + bi )ni
i=1

ni !

e−(µsi +bi )

Y

G(θ),

(8.3)

k∈sys.

The MINUIT framework [195] is used in this analysis to handle the statistical study with the given
likelihood. It provides a simple method for the complex statistical problem such as the optimized valueof a multi-parameter likelihood functions (so called FCN) [196]. A solution of the combined likelihood
function is obtained by minimizing the negative logarithm of the likelihood function (NLL). The best-fit
parameter values of NLL contains the uncertainties and correlations between each parameters. The µ̂ (θ̂) is
defined as the best-fit value µ (θ) of the likelihood fit in this analysis. The maximum-likelihood estimators(MLEs) (µ̂,θ̂) are obtained following the formula: −lnL(µ̂, θ̂)) = min(−lnL(µ, θ)). The conditional MLEˆˆ
is formed as θ̂(µ) (θ̂(0)) with the given µ (µ = 0).

8.1.2

Hypothesis Test

The hypothesis test is a likelihood-based method to quantify the upper limit on on signal strength of
new physics search. In a hypothesis test, a profile likelihood ratio (PLR), which is a choice of the LHC,
is built for the search. The PLR is determined as the optimal discriminator as described in the following
formula:ˆL(µ, θ̂(µ))λ(µ) =.
(8.4)
L(µ̂, θ̂)For the agreement of H1 in a physical theory, the µ ≥ 0 is used for the positive signal process. In thecase of µ̂ with a value smaller than 0, it leads to use the boundary value µ = 0 to instead of µ < 0. Since
non-negative values is expected for signal, µ = 0 is used to inspect the agreement between the data andebackground (H0 hypothesis) [197]. The alternative PLR λ(µ)
is then modified as:ˆ L(µ,θ̂(µ)) for µ̂ ≥ 0
L(µ̂,
θ̂)
e
λ(µ)
=
(8.5)
ˆ
L(µ,
θ̂(µ))


for
µ̂
<
0
ˆ
L(0,θ̂(0))

The test statistic qµ is defined based on the PLR as the following formula. It is a quantified value for8.1. Statistical Analysis

102

upper limits at signal strength µ.


qµ =


ˆ


−2ln L(µ,ˆθ̂(µ))
L(0,θ̂(0))

e−2lnλ(µ)
for µ̂ ≤ µˆ
=L(µ,θ̂(µ))−2ln0for µ̂ > µ
L(µ̂,θ̂)
0for µ̂ < 0
for 0 ≤ µ̂ ≤ µ(8.6)

for µ̂ > µ

A higher value of test statistic qµ indicates the disagreement with the assumption. The p-value provides a
judgment for the discovery significance as well as the exclusion limits. The p-value and the correspondingesignificance are given as following using on the test statistic qµ = −2lnλ(µ):
Z ∞ˆf (qµ |µ, θ̂(µ, obs))dqµ .
(8.7)
pµ =
qµ ,obs.

Zµ = Φ−1 (1 − pµ ),

(8.8)

ˆ
where the f (qµ |µ, θ̂(µ, obs)) shows the distribution of test statistic. The Φ−1 is the inverse of the cumulative distribution for a Gaussian with unit parameters.
Moreover, the CLs technique provides a estimation method for the exclusion or discovery limit basedon the p-value. The formula is constructed based on the ratio of pµ and 1 − pb as: CLs = pµ /(1 − pb ).
The 1 − pb , which is the p-value of H0 hypothesis, is given as:
Z ∞ˆf (qµ |0, θ̂(0, obs))dqµ(8.9)
1 − pb =qµ ,obs.

At 95% confident level, the upper limit for µ is computed based on the pµ value of 0.05.
In general, the discovery limit is discussed based on q0 for µ = 0 background-only hypothesis. It
effectively leads to discovery of signal with rejecting H0 hypothesis. The equations of q0 and p0 are
written as:e−2lnλ(0)for µ̂ ≥ 0(8.10)q0 =0for µ̂ < 0
Z ∞
bb
p0 =
f (q0 |0, θ(0,obs))dq0 .
(8.11)
q0 ,obs.

The q0 clearly against background-only hypothesis (µ = 0) to show the discovery of a new signal. The p0
is defined to quantify this disagreement between data and hypothesis of µ = 0. Based on the equivalentsignificance of p-value, 5-σ Gaussian standard deviation is sorted as the standard discovery significanceas the LHC. It corresponds to p-value (p0 ) of 2.87 × 10−7 .
For the p0 and pµ of hypothesis test, they are usually investigated via Monte Carlo calculations, socalled “toy Monte Carlos” method. The Monte Carlo is used to simulate the distribution of the quantified
number, f (qµ |µ). However, this method is computationally expensive. 1 Based on the Wilks [198] andWald [199] theorem, a approximate method is introduced as Asymptotic formulae [197] for the large
sample case. The Asymptotic formulae is assumed to follow Gaussian distribution with mean of µ̂ andthe standard deviation σ of µ̂. A data set, which is related to σ measurement, is discussed as “Asimov”
dataset [200]. 2 The test statistic of Asymptotic formulae is given as:− 2λ(µ) =12(µ − µ̂)2
1+ O( √ ),2σN

One LHC collision might take around 10 mins to generate.
Name of Asimov data set is enlightened from a short story Franchise written by American writer, Isaac Asimov.

(8.12)

8.2. Observed Data in the Signal Regions

103

where N responds the data sample size.
The profile likelihood ratio λA are evaluated as following with “Asimov likelihood” LA :λA =ˆLA (µ, θ̂)LA (µ̂, θ̂)=ˆLA (µ, θ̂),LA (µ0 , θ)

(8.13)

where a strength parameter µ0 (zero or nonzero) is defined as the mean of Gaussian distribution witha standard deviation σA . The Gaussian distribution is used to suppose the distribution of data. Equation 8.12 and test statistic qµ,A are obtained with Asimov dataset as following:− 2lnλA (µ) ≈(µ − µ0 )2
= Λ.
2
σA

(8.14)

qµ,A = −2lnλA (µ).

(8.15)(µ − µ0 )2.
qµ,A(8.16)

2
σA=

Considering the exclusion limit (assuming µ0 = 0 for no signal found) based on the signal-plus-background2 is equivalent to µ2 /q
hypothesis (µ), the σAµ,A . For the case of discovery with background-only hypothesis2(µ = 0), the σA is written as µ02 /q0,A . Eventually, Wald approximation shows that the test statistics isonly related to µ̂.
The cumulative distribution of Λ and corresponding the p-value of the µ hypothesis as following function:µ − µ0√F (qµ |µ0 ) = Φ( qµ −).
(8.17)
σpµ = 1 − F (qµ |µ0 ).

(8.18)The upper limit is then computed based on pµ ≤ 0.05 at 95% CL as discussed above. The upper limit µup
is defined as µ̂ + σΦ−1 (1 − 0.05). On the other hand, the discovery significance is obtained by a simple√
formula : Z0 = Φ−1 (1 − p0 ) = q0 . The ±1 or ±2σ variation of Gaussian distributed µ̂ corresponding
to the 68% and 95% bands are used to calculate error bands of the median significance. The µup PDF
distribution is used to derive the error bands (frequently uses green and yellow to illustrate) around the
median µup .

8.2

Observed Data in the Signal Regions

The events yield of analyzed data is investigated for each signal region based on the null hypothesis, H0 .
The result of the background-only hypothesis is obtained based on the conditional MLEs with the givenµ = 0 (“post-fit”). 3 The post-fit yields of likelihood fit are summarized in the Table 8.1 and Table 8.2.
Figure 8.1 and Fig. 8.2 show the corresponding mtot
T distribution for each signal region. The observed
local p-values in this analysis for the gluon-fusion and bottom-annihilation production with respect tomass hypothesis are shown in Fig 8.3. The local p-value based on H0 or H1 investigation from the MLEs
exhibits no significant excess of data events.

3

The “pre-fit” results are discussed in Sec. 6.3. They show the results before the likelihood fit.

105
104
103

∫ L =139 fb

data
Multijet
WtaunuPost-fit BVETO_loosenotmed_1p Ztautau
Top
OthersPre-fits = 13 TeV;

104

EventsEvents

8.2. Observed Data in the Signal Regions

-1

103

102

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mtot
T [GeV]

200 300 400 500 600 700 800 900 1000

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4

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3

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Eventss = 13 TeV;

data
Multijet
WtaunuZtautauTop
OthersPre-fit

10

1

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mtot
T [GeV]

200 300 400 500 600 700 800 900 1000

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mtot
T [GeV]data
Multijet
WtaunuZtautauTop
OthersPre-fit-1

4

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3

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Ratio

Events∫ L =139 fb

10

1

10−1

10−1
600

700

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mtot
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200 300 400 500 600 700 800 900 1000

mtot
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400

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Multijet
WtaunuZtautauTop
OthersPre-fit

700

800

900

1000

mtot
T [GeV]

200 300 400 500 600 700 800 900 1000

∫ L =139 fb

data
Multijet
WtaunuZtautauTop
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10

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500

300

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200

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10

300

-1

4

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Post-fit BVETO_mednottight_3p

105

102

2
1.5
1
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1000

(d) 3p BVETO med-not-tight

Ratio

Eventss = 13 TeV;

900

mtot
T [GeV](c) 1p BVETO med-not-tight

105

800

200 300 400 500 600 700 800 900 1000

10

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mtot
T [GeV]s = 13 TeV;

10

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(b) 3p BVETO loose-not-med

Ratio

Events

105

200

mtot
T [GeV](a) 1p BVETO loose-not-med

10

-1

10−1
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2
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∫ L =139 fb

data
Multijet
WtaunuPost-fit BVETO_loosenotmed_3p Ztautau
Top
OthersPre-fits = 13 TeV;

104

10−1

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105

2
1.5
1
0.5

200

300

400

500

600

700

800

900

1000

mtot
T [GeV]

200 300 400 500 600 700 800 900 1000

mtot
T [GeV](f ) 3p BVETO tight

Figure 8.1.: Distributions of total transverse mass for BVETO category. The plots correspond to post-fit resultwith µ = 0 hypothesis. Events containing 1-prong sub-leading τhad are illustrated in left plots and the events
containing 3-prong sub-leading τhad are shown in right plots. From top to bottom, the plots is made with respect totau identification (loost-not-med., med-not-tight and tight). The underflow events and overflow evnets are includedin the first and last bins, respectively. In the label, “Others” background refers to contributions from diboson,
Z/γ ∗ (→ ``)+jets and W (→ `ν)+jets production. The “Top” containing the tt̄ and single top production. The datais shown as the black point in the histogram. The blue lines show the total expected background from pre-fit. In
the lower panels, the fraction of data and overall background is illustrated.

200
180

s = 13 TeV;∫-1

L =139 fb

160 Post-fit BTAG_loose
140

data
Multijet
WtaunuZtautauTop
OthersPre-fit105

EventsEvents

8.2. Observed Data in the Signal Regions105
s = 13 TeV;
104

∫ L =139 fb

data
Multijet
WtaunuZtautauTop
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120
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100
80

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2150 200 250 300 350 400 450 500 550 600
1.5
mtot
1
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0.5
150 200 250 300 350 400 450 500 550 600

mtot
T [GeV](a) 1p+3p BTAG loose

Ratio

Ratio

20

2
1.5
1
0.5

200

300

400

500

600

700

800

900

1000

mtot
T [GeV]

200 300 400 500 600 700 800 900 1000

mtot
T [GeV](b) 2p BINC. loose

Figure 8.2.: Distributions of total transverse mass for BTAG (left) and 2P (right) categories. The plots correspondto post-fit result with µ = 0 hypothesis. The underflow events and overflow evnets are included in the first andlast bins, respectively. In the label, “Others” background refers to contributions from diboson, Z/γ ∗ (→ ``)+jets
and W () → `ν+jets production. The “Top” containing the tt̄ and single top production. The data is shown as theblack point in the histogram. The blue lines show the total expected background from pre-fit. In the lower panels,
the fraction of data and overall background is illustrated.

8.3. Constraints on the Cross Section

106

Processes
Multijet
WtaunuZtautauTop
OthersBkg
data

1P BVETO loose-not-med
2510 ± 19
33 ± 2168 ± 67±1
4±02723 ± 212780

1P BVETO med-not-tight1386 ± 16
45 ± 3254 ± 98±37±11700 ± 181769

1P BVETO tight968 ± 12184 ± 131171 ± 41
38 ± 530 ± 32390 ± 39
2356

Processes
Multijet
WtaunuZtautauTop
OthersBkg
data

3P BVETO loose-not-med
665 ± 1617 ± 167 ± 34±12±0755 ± 16779

3P BVETO med-not-tight
243 ± 818 ± 276 ± 33±1
2±0343 ± 8347

3P BVETO tight
125 ± 860 ± 5265 ± 108±28±1
466 ± 13464

Table 8.1.: The events yields after the global fit with µ = 0. Overall systematic and statistical uncertainties are
considered and listed in the table.
Processes
Multijet
WtaunuZtautauTop
OthersBkg
data

BTAG loose
168 ± 58±1
26 ± 2186 ± 202±0
390 ± 19389

2P loose
3575 ± 24
94 ± 11185 ± 935 ± 96±03894 ± 31
4012

Table 8.2.: The events yields after the global fit with µ = 0. Overall systematic and statistical uncertainties are
considered and listed in the table.

8.3

Constraints on the Cross Section

No indication of an excess over the SM background is found in this analysis. The upper limits of thecross section for the gluon-fusion and the bottom-annihilation processes are obtained via MLE with theasymptotic method. The model-independent upper limits with the impact for each NP are introduced inSec. 8.3.1.

8.3.1

Independent Cross-Section limits

The independent upper limits of H/A → τ τ with 95% and 68% confidence interval for the gluon-fusion
and the bottom-annihilation models in the different mass hypotheses are shown in Fig. 8.4. The figures
also show the upper limits of σ × BF(H/A → τ τ ) for two signal production modes in each categorycontaining BVETO, BTAG and 2P categories. The BTAG category presents a better sensitivity for thebottom-annihilation signal as shown in the left plot. In the right plot, the result shows that the best
sensitivity of gluon-fusion production signal is from BVETO category. The orange broken line, so called
as “paper method” in this analysis, shows a investigation with the previous method used in the ATLAS
36 fb−1 paper [65]. In this method, the 2-prong τhad and new categorization are not applied.
The new categorization strategy presents the significant improvement in the low mass region. Comparedwith orange broken line, the gluon-gluon fusion production limit improves around 54% at MA = 300 GeV.

107

Local p-value

Local p-value

8.3. Constraints on the Cross Sections = 13 TeV, 139 fb-1, 95% CLs
10gluon-fusion

Observed1

s = 13 TeV, 139 fb-1, 95% CLs
10bottom-annihilation

Observed

1

1σ

10−1

1σ

10−1

2σ
10−2

2σ
10−2

400 600 800 1000 1200 1400 1600 1800 2000
mA [GeV]

400 600 800 1000 1200 1400 1600 1800 2000
mA [GeV](a) gluon-fusion(b) bottom-annihilation

Figure 8.3.: (a) and (b) show the observed local p-values in this analysis for the gluon-fusion and bottomannihilation. The figures show that there is no significant excess in this analysis.

The bottom-annihilation production limit improves around 24% at MA = 300 GeV. Moreover, around
20% events of signal is saved by an additional 2P category in the analysis as discussed in Sec 4.6. It resultsin the 2% to 10% improvement in the upper limit of the high mass hypotheses (larger than 1.5 TeV) as
shown in the upper limit plots.
The exclusion limits from the observed data are drawn as the solid line. In the single production
hypothesis of the gluon-gluon fusion the exclusion limit is 236(2) fb at mA = 300(1500) GeV. The
exclusion limit is 145(1) fb at mA = 300(1500) GeV in the bottom-annihilation only hypothesis.
The impact of each systematic uncertainty on µ is investigated. Figure 8.5 presents the 15 mostimportant nuisance parameters for µ of the combined likelihood fit with mA = 300 GeV (low mass)and mA = 1500 GeV (high mass) signal mass hypotheses. The corresponding tan β hypotheses for
mA = 300 GeV and mA = 1500 GeV Higgs are assumed as 2 and 23 based on the result discussed in
Chapter 9. The impacts on pre-fit and post-fit result are investigated via shifting the nuisance parameterto the 1σ boundaries. Each nuisance parameter is fixed to its ±1σ and found the best-fit µ̂ via the
combined likelihood fit. Obviously, the major systematic uncertainty comes from tau energy scale as well
as tau-ID, and other sources are considered as minor uncertainties. Overall, the systematic uncertainties
are much smaller than statistical uncertainties in both low mass and high mass hypotheses as shown in
top part of Fig. 8.5.

10Observed

H/A → ττ, 95 % CL limits

Expected-1

s = 13 TeV, 139 fb± 1σ

gluon-gluon fusion± 2σ

1b-vetob-tag
2-prong10−1paper method 139 fb-1

108

σ× BR(H/A→ττ)[pb]σ× BR(H/A→ττ)[pb]8.3. Constraints on the Cross Section10

s = 13 TeV, 139 fb

b-vetob-tag
2-prong10−1

10−31200 1500 1800 2100 2400
mA [GeV](a) gluon-fusion

± 2σ

1

10−3
900

± 1σ

b-associated production

10−2

600

Expected

-1

10−2

300

Observed

H/A → ττ, 95 % CL limits

300

paper method 139 fb-1

600

900

1200 1500 1800 2100 2400
mA [GeV](b) bottom-annihilation

Figure 8.4.: The upper limits on the cross section times branching fraction to τ τ for bottom-annihilation production(a) and gluon-fusion (b) at the different mass hypotheses. The limits of σ × BF(H/A → τ τ ) are set as a functionof the boson mass. The dashed lines and solid lines are shown for the expected limit and observed limit at
95% confidence level, along with ±1σ (green) and ±2σ (yellow) uncertainty bands for the expected limit. The
independent upper limits for BVETO, BTAG, and 2P categories are illustrated as blue, red, and green dot lines,
respectively.

8.3. Constraints on the Cross Section

statistics
systematics
total

−0.6

−0.4

109

∆µ
−0.2

0

0.2

0.4

0.6

statistics
systematics
total

Tau energy scale

K-factor of EV4 PDF

Tau ID sys.

K-factor of PDF 30

QCDFF stat data 1p bin1

Tau ID sys.

K-factor of PDF20

LPXKFACTORPDF

QCDFF stat data 3p bin1

LPX KFACTOR CHOICE epWZ16 Corr2017 Trigger (data stat.)

HHFAKERATELPX KFACTOR CHOICE epWZ16 Corr

Tau energy scale

LPXKFACTORPDF

K-factor of PDF EV3

K-factor of PDF EV1

K-factor of PDF20

TTBar METAUIDHighPt

TTBar PS

K-factor of PDF EV2

QCDFF stat data 3p bin3

K-factor of EW PDF

2017 Trigger (MC stat.)

TTBar MELUMILPXKFACTORPI

−0.4

−0.2

∆µ
0

0.2

0.4

0.6

QCDFF stat data 3p bin1

K-factor of EV4 PDF

s = 13 TeV, 139 fb-1
mA=300 GeV

Pull
1 standard deviation+1σ Postfit Impact on µ
-1σ Postfit Impact on µ
Prefit Impact on µ

−3 −2 −1.5
2 −1−1−0.5 0 0.5 1 1 1.5
2 2 3
−2.5
(θ - θ0)/∆θ(a) mA = 300 GeV

Pull
1 standard deviation+1σ Postfit Impact on µ
-1σ Postfit Impact on µ
Prefit Impact on µs = 13 TeV, 139 fb-1
mA=1500 GeV

−6
3

−4
2

−21

0

21

2
4

3
6

(θ - θ0)/∆θ(b) mA = 1500 GeV

Figure 8.5.: Impact from each nuisance parameter on the fitted signal strength for mA = 300 GeV and mA =1500 GeV. The corresponding tan β hypotheses for mA = 300 GeV and mA = 1500 GeV Higgs are assumed as 2
and 23. The red lines in the ranking plots are shown as “1 standard deviation”. The black points with the blacklines in the plots are the fitted value and corresponding ±1 − σ values after the shifting, so called as “pull value”.
The pull value is quantified to as pull(θ) = (θ̂ − θ0 )/σθ [201]. It shows the difference between the expected value
and the fitting result of MLE. The nuisance parameters are ordered by their impact on the signal strength µ̂. The
blue opened box presents the impact on post-fit result and the impact on the pre-fit result is shown as the yellow
box. The impact on µ̂ from overall systematic uncertainties is illustrated as pink line in the top of ranking plots.
The statistical uncertainty is also presented as green line. The combined uncertainty of statistic and systematic isshown as blue line.

9 Discussion

9.1

MSSM interpretations

The observed mtot
T distributions show good agreement with the background predictions. With respect
to the results, upper limits on the signal production rate of σ × BF (H/A → τ + τ − ) are set for gluongluon fusion production and bottom-annihilation production scenarios, as discussed in Chapter 8. The
limits are combined and interpreted in the context of the MSSM scenarios, in particular, in the hMSSM
scenario as the benchmark of this analysis. 1 A set of hypotheses with a various tan β values is tested
by a comparison between the observed upper limit and the prediction of the signal production rates per
MH/A point. The exclusion on tan β has been evaluated in the mass range up to 1800 GeV. Figure 9.1
shows the exclusion limit on mA − tan β plane in terms of the hMSSM benchmark scenario. The observed
upper limit of signal production rate excludes tan β > 2 hypothesis for mA = 300 GeV and tan β > 23
region for mA = 1500 GeV. As the discussion of the current experimental constraints of heavy neutral
Higgs bosons searches in Sec 2.5, this is the most stringent observed constraints for the hMSSM scenarioswith addition high mass heavy neutral Higgs bosons and high tan β.

9.2

Major achievements in the thesis work

The search for additional heavy neutral Higgs bosons have been performed with an improved searchsensitivities, compared to the previous result with 36 fb−1 .
The reducible backgrounds are estimated by data-driven techniques. Taking advantage of the improved statistics of the control region data, the precision for multi-jet backgrounds has been significantly
improved. Reducible backgrounds associated with W and top-quark productions are carefully studied
with measurements of fake-rates and assistance of Monte Carlo Simulation. A difference of the fake-rates
between quark-initiated jets and gluon-initiated jets have been studied to achieve accurate estimate forthese backgrounds, accounting possible topology dependence.
In addition to the improvement of the data statistics, this thesis work has improved the search sensitivities by introducing the following new techniques with data-driven techniques.
• Categorization of signal regions: A new categorization with respect to the tightness of tau
identification criteria has been introduced. It allows effective use of a tight tau identification cut
to suppress fake τhad backgrounds while a good signal selection efficiency will be maintained bykeeping a looser condition. This technique introduces a major improvement in a low MH/A region(MH/A < 1 TeV). In the MH/A = 300 GeV scenario, the categorization techniques improve thesensitivity of gluon-fusion production over 54% and bottom-annihilation production limit about
24%.
1

The constraint presented here is applicable more generally to type II 2HDM, which has been discussed for the phenomenology of SUSY [30].

110

tanβ

9.2. Major achievements in the thesis work

11180
H/A → ττ, 95 % CL limits

Observed
Expected70s = 13 TeV, 139 fb

-1

± 1σ
± 2σ

hMSSM scenario

ATLAS 36.1 fb-1 (Obs.)60
ATLAS Run1, SM Higgs

50

boson couplings (Obs.)

40
30
20
10
300

600

900

1200

1500
1800
mA [GeV]Figure 9.1.: The exclusion limits (black solid line) in the two dimension mA - tan β parameter space at 95%
confidence level, along with ±1σ (green) and ±2σ (yellow) uncertainty bands for the expected limit (black dotline). The previous result with 36 fb−1 (light purple block) [65] and the MSSM interpretation for the SM 125 GeV
Higgs (red line) [202, 203] are shown.

9.3. Future Prospect112• 2-prong τhad reconstruction: To maximize the signal efficiency, reconstructed τhad candidates
which are associated with two reconstructed charged tracks are considered in this analysis in addition
to the 1-prong and 3-prong τhad signatures. The additional 2-prong signature introduces a major
improvement of the sensitivities for high mass heavy neutral Higgs scenarios (MH/A > 1.5 TeV). In
the MH/A = 1.5(2.4) TeV scenario, it provides around 12% (8%) and 2% (10%) improvement forgluon-fusion production and bottom-annihilation production, respectively.

9.3

Future Prospect

The LHC is going to collect more proton-proton collision data with an integrated luminosity of 150 fb−1
at a center-of-mass energy of 14 TeV in Run3, which will start 2021 and run util 2025. In the HighLuminosity LHC (HL-LHC) physics runs, the integrated luminosity will reach up to 3000 to 4000 fb−1 [204,205]. It is ten times more than the combined luminosity of the LHC Run1 to Run3. Furthermore, aFuture Circular Collider facility (FCC) is designed as a 100 TeV proton–proton Collider [206]. Although
no evidence is shown with the current data, the new data allow heavy Higgs in few TeV scale for large
MA , tan β in the contest of hMSSM. The limit of the 2σ sensitivity for the heavy neutral Higgs search isillustrated in Fig. 9.2.

(a)√s = 14 TeV, 3000 fb−1(b)√s = 100 TeV, 3000 fb−1

Figure 9.2.: Projections for the limit of the 2σ sensitivity in the hMSSM (tan √β, mA ) plane corresponding to3000 fb−1 data. (a) shows the one for the HL-LHC
atacenter-of-massenergyofs = 14 TeV and the expected√
limit for FCC at a center-of-mass energy of s = 100 TeV is presented in (b) [34, 204].

10 Conclusions

The supersymmetry is one of the most motivated extensions of the SM as it may address the remained
problems after the discovery of the scalar Higgs boson with the mass of 125 GeV at the Large Hadron
Collider. It requires the Higgs sector of the SM to be extended at least five physical Higgs bosons; the SM
125 GeV Higgs (h), two heavy neutral Higgs bosons (H/A) and a charged Higgs bosons (H ± ). Two heavy
neutral Higgs bosons H/A provide important insight into the nature of the SUSY. The coupling of H/A
constants to down-type fermions are enhanced for a large tan β hMSSM scenario. This analysis is focusedon the neutral heavy Higgs boson hadronic decaying into a pair of tau leptons (H/A → τ + τ − ), which
provides best sensitivity at the LHC. This thesis uses an integrated luminosity of 139 fb−1 of protonproton collision data recorded by the energy frontier ATLAS experiment at a center-of-mass energy of√s = 13 TeV during Run2 data.
Possible backgrounds remaining after the selection are estimated with the data-driven methods, which
provide significant improvement for the precision of reducible backgrounds associated with W , top-quark
productions and multi-jet backgrounds taking advantage of large data statistics in the control region.
In order to improves search sensitivity, 2-prong τhad reconstruction and the categorization have beendeveloped in this analysis. The 2-prong τhad reconstruction improves sensitivity in high mass region
while the categorization improves sensitivity in low mass region. The sensitivities of gluon-gluon fusion
production (bottom-annihilation production) improve 12% (2%) and 54% (24%) at a high mass hypothesis
mA = 1500 GeV and a low mass hypothesis mA = 300 GeV with the two new techniques.
Since no indication of an excess over the expected SM background is found, this thesis sets the upper
limits on the cross section times branching fraction to τ τ 1 for the production of heavy neutral Higgs
bosons H/A at 95% confidence level for bottom-annihilation and gluon-gluon fusion processes.
In the single production hypothesis of the gluon-gluon fusion and bottom-annihilation, the exclusion
limits are around 236(2) fb and 145(1) fb at mA = 300(1500) GeV, respectively. In the context of thehMSSM scenario, the observed upper limit of signal production rate excludes tan β > 2 hypothesis for
mA = 300 GeV and tan β > 23 region for mA = 1500 GeV.

1

The cross section times branching fraction to τ τ is labeled as σ × BF(H/A → τ τ )113

Appendix

114

A Cutflow for Event Selection

The number of expected events for SM background and signal after each event selection are shown in
the table. The one for the observed data is also shown. The tables are separated to BTAG and BVETO
categories. The opposite sign is the signal region and same sign is for validation region. Only statisticaluncertainties are shown in the table and multijet background is estimated by data-driven method.

115

9669.09669.06546.05266.0SS
K-factor for EW
deltaPhi
leading tau pT

27675.027675.012367.011783.0368845.0368845.0
329577.0
323494.0

hMSSM Atanβ=1510002184492.0
2184492.0
1915168.0
1588419.0
1313021.0
474141.0396520.0

Table A.1.: Cutflow for SM background and mH/A signal in BVETO region

27836.027836.017167.014343.0

Data515967425.0
515967425.0
110184781.0
103185115.0
101805104.0
3006433.0
37505.0

OS
K-factor for EW
delta Phi
leading tau pT

Names:ALL
MC WEIGHTMIN TWO TAUSMUON VETO
ELE VETO
OLR + Event Cleaning + 1PV
Loose 2nd tau + Trigger

BVETO
OthersW → τν
Z/γ∗ → τ τ49154955.0 30394663.0 10077689.0
49154955.0 30394663.0 10077689.0
26055781.0 18113578.0 8280969.0
16718428.0 16336027.0 7483878.0
9207611.0 15671624.0 5701622.0
2884518.0
5215876.0
2809880.0
2809120.0
4678123.0
2337690.0
Opposite Sign
1950917.0
3325877.0
2080581.0
1950917.0
3325877.0
2080581.0
960984.0
1845786.0
1945037.0873733.0
1631293.0
1912883.0
Same Sign
858203.0
1352246.0
257109.0858203.0
1352246.0
257109.0410425.0706381.0211224.0
364077.0
617779.0206759.0766442.0766442.0335125.0
288219.0

1645263.0
1645263.0
727730.0642011.0tt̄, single top
82871406.0
82871406.0
46369457.0
28980295.0
25281098.0
2498261.0
2411705.0——
30301.024615.0——79426.066228.0

Multijet
—
—
—
—
—
—
—

116

493.0
493.0
222.0
165.0

SS
K-factor for EW
deltaPhi
leading tau pT

15557.015557.06537.06232.0213718.0
213718.0
177645.0
174734.0

hMSSM Atanβ=1510002184492.0
2184492.0
1915168.0
1588419.0
1313021.0275955.0
229275.0

Table A.2.: Cutflow for SM background and mH/A signal in BTAG region

1697.01697.0
783.0
619.0

Data
515967425.0
515967425.0
110184781.0
103185115.0
101805104.0
148642.0
2190.0OS
K-factor for EW
deltaPhi
leading tau pT

Names:ALL
MC WEIGHTMIN TWO TAUSMUON VETO
ELE VETO
OLR + Event Cleaning + 1PV
Loose 2nd tau + Trigger

BTAG
OthersW → τν
Z/γ∗ → τ τ49154955.0 30394663.0 10077689.0
49154955.0 30394663.0 10077689.0
26055781.0 18113578.0 8280969.0
16718428.0 16336027.0 7483878.0
9207611.0 15671624.0 5701622.0
207702.0359162.062457.0
201962.0
326748.0
51837.0
Opposite Sign
139401.0229392.044004.0139401.0229392.044004.057018.0100419.0
36041.051135.089009.035447.0
Same Sign
62561.097356.07833.062561.097356.07833.025425.041020.04980.022270.035682.0
4820.01077656.0
1077656.0
395414.0331703.02451562.0
2451562.0931538.0801205.0tt̄, single top
82871406.0
82871406.0
46369457.0
28980295.0
25281098.0
3652972.0
3529218.0——
1159.0905.0——3159.02473.0Multijet
—
—
—
—
—
—
—

117

B Fake Factor

Since multijet background is estimated by data-driven method, so called fake factor (FF) method. The
overall fake factors for all tau ID working points (loose, loose-not-medium, medium, medium-not-tight,
tight) are investigated as following plots. The fake factors are computed for 1-prong, 2-prong and 3prong, respectively. The fake factors are also separated to OS and SS for signal and validation regions,
respectively.

118

0.8
b-tag

b-inc

fake factor

fake factor

119b-veto

0.7
0.6

0.8
b-tag

0.5

0.4

0.4
0.3
-1

s = 13 TeV, 139.0 fb
opposite sign, 1 prong

0.2
0.1

s = 13 TeV, 139.0 fb-1
same sign, 1 prong

0.2
0.1

100 150 200 250 300 350 400

100 150 200 250 300 350 400

subleading τ pT

subleading τ pT(b) Loose 1-prong SS

0.2
b-tag

b-inc

fake factor

fake factor(a) Loose 1-prong OS

0.18

b-veto

0.2

0.18

0.16

b-tag

b-inc

0.14

0.12

0.12

0.1

0.1

0.08

0.08

0.06

0.06

0.04

s = 13 TeV, 139.0 fb-1
opposite sign, 2 prong

0.02

0.04

s = 13 TeV, 139.0 fb-1
same sign, 2 prong

0.02
0

100 150 200 250 300 350 400

100 150 200 250 300 350 400

subleading τ pT

subleading τ pT(d) Loose 2-prong SS

0.2
b-tag

b-inc

fake factor

fake factor(c) Loose 2-prong OS

0.18

b-veto

0.2

0.18

0.16

0.14

0.12

0.12

0.1

0.1

0.08

0.08

0.06
0.02
0

b-tag

b-inc

b-veto

0.16

0.14

0.04

b-veto

0.16

0.14

0

b-veto

0.6

0.5

0.3

b-inc

0.7

0.06
-1

s = 13 TeV, 139.0 fb
opposite sign, 3 prong

100 150 200 250 300 350 400
subleading τ pT(e) Loose 3-prong OS

0.04
0.02
0

s = 13 TeV, 139.0 fb-1
same sign, 3 prong

100 150 200 250 300 350 400
subleading τ pT(f ) Loose 3-prong SS

Figure B.1.: Comparison of BINC FF to BTAG and BVETO FFs. The loose-not-med. FFs of 1-prong (top),
2-prong (middle) and 3-prong (bottom) for signal region (left) and validation region (right) are shown. The loose
FFs of 1-prong and 3-prong are not used in this analysis.

120

0.4

0.45

b-tag

b-inc

fake factor

fake factor

0.45
b-veto

0.35

0.4

b-inc

0.3

0.3
0.25

0.2

0.2

0.15

0.15

0.1

s = 13 TeV, 139.0 fb-1
opposite sign, 1 prong

0.05

0.1

s = 13 TeV, 139.0 fb-1
same sign, 1 prong

0.05
0100 150 200 250 300 350 400

100 150 200 250 300 350 400

subleading τ pT

subleading τ pT(a) Loose-not-med 1-prong OS(b) Loose-not-med 1-prong SS
0.14

b-tag

b-inc

fake factor

fake factor

0.14
b-veto

0.12

b-tag

b-veto

0.1

0.08

0.08

0.06

0.06

0.04

0

b-inc

0.12

0.1

0.02

b-veto

0.35

0.25

0

b-tag

0.04
-1

s = 13 TeV, 139.0 fb
opposite sign, 3 prong

100 150 200 250 300 350 400
subleading τ pT(c) Loose-not-med 3-prong OS

0.02
0s = 13 TeV, 139.0 fb-1
same sign, 3 prong

100 150 200 250 300 350 400
subleading τ pT(d) Loose-not-med 3-prong SS

Figure B.2.: Comparison of BINC FF to BTAG and BVETO FFs. The loose-not-med. FFs of 1-prong (top)and 3-prong (bottom) for signal region (left) and validation region (right) are shown. The loose-not-med. FFs of
2-prong are not used in this analysis.

0.2

0.18

b-tag

b-inc

b-veto0.16

fake factor

fake factor

121

0.2

0.18

b-inc

0.14

0.12

0.12

0.1

0.1

0.08

0.08

0.06

0.06

0.04

s = 13 TeV, 139.0 fb-1
opposite sign, 1 prong

0.02

0.04

s = 13 TeV, 139.0 fb-1
same sign, 1 prong

0.02
0

100 150 200 250 300 350 400

100 150 200 250 300 350 400

subleading τ pT

subleading τ pT(a) Med-not-tight 1-prong OS(b) Med-not-tight 1-prong SS
0.05

b-tag

b-inc

b-veto0.04

fake factor

fake factor

0.05

0.045

0.045

0.03

0.03
0.025

0.02

0.02

0.015

0.015

0

b-inc

b-veto

0.035

0.025

0.01

b-tag

0.04

0.035

0.005

b-veto

0.16

0.14

0

b-tag

s = 13 TeV, 139.0 fb-1
opposite sign, 3 prong

100 150 200 250 300 350 400
subleading τ pT(c) Med-not-tight 3-prong OS

0.01
0.005
0

s = 13 TeV, 139.0 fb-1
same sign, 3 prong

100 150 200 250 300 350 400
subleading τ pT(d) Med-not-tight 3-prong SS

Figure B.3.: Comparison of BINC FF to BTAG and BVETO FFs. The med-not-tight FFs of 1-prong (top) and3-prong (bottom) for signal region (left) and validation region (right) are shown. The med.-not-tight FFs of 2-prong
are not used in this analysis.

0.2

0.18

b-tag

b-inc

b-veto0.16

fake factor

fake factor

122

0.2

0.18

b-inc

0.14

0.12

0.12

0.1

0.1

0.08

0.08

0.06

0.06

0.04

s = 13 TeV, 139.0 fb-1
opposite sign, 1 prong

0.02

0.04

s = 13 TeV, 139.0 fb-1
same sign, 1 prong

0.02
0

100 150 200 250 300 350 400

100 150 200 250 300 350 400

subleading τ pT

subleading τ pT(a) Tight 1-prong OS(b) Tight 1-prong SS
0.05

b-tag

b-inc

b-veto0.04

fake factor

fake factor

0.05

0.045

0.045

0.03

0.03
0.025

0.02

0.02

0.015

0.015

0

b-inc

b-veto

0.035

0.025

0.01

b-tag

0.04

0.035

0.005

b-veto

0.16

0.14

0

b-tag

s = 13 TeV, 139.0 fb-1
opposite sign, 3 prong

100 150 200 250 300 350 400
subleading τ pT(c) Tight 3-prong OS

0.01
0.005
0

s = 13 TeV, 139.0 fb-1
same sign, 3 prong

100 150 200 250 300 350 400
subleading τ pT(d) Tight 3-prong SS

Figure B.4.: Comparison of BINC FF to BTAG and BVETO FFs. The tight FFs of 1-prong (top) and 3-prong(bottom) for signal region (left) and validation region (right) are shown. The tight FFs of 2-prong are not used inthis analysis.

C Fake Rate

The other data-driven method applied in this analysis is called as fake rate method. They are used tomeasure the misidentified rate of jet based on tau ID. Considering the different fake rates for quark- andgluon-initiated jets, the fake rates are measured in top and W control regions, respectively. Like the fakefactor measurement, the fake rate is separated to 1-prong, 2-prong and 3-prong, as well as OS and SS
region. An additional tau ID working points (medium + trigger) is also investigated for fake rate of theleading tau candidate which is used to match to STT in this analysis Due to the statistical limitations ofdata for the tighter ID criteria, some bins for fake rate calculation emerge zero event which is considered
to present the incorrect fake rate. In that case, the Monte Carlo fake rates validated in µν+jets control
region is exploited.

0.08

s = 13 TeV, 139.0 fb-1
Trigger+Medium-ID

SS topOS top
SS W+jets
OS W+jets−3

10 ×109

SS topOS top
SS W+jets
OS W+jetss = 13 TeV, 139.0 fb-1
Trigger+Medium-ID

8

fake rate

0.09

fake rate

fake rate−3

0.1

10 ×10
9
8

0.07

7

7

0.06

6

6

0.05

5

5

0.04

4

4

0.03

3

3

0.02

2

2

0.01

1

1

0

0

0

100

150

200

250

300

pT(τ1) [GeV](a) Med+trigger 1-prong

100

150

200

250

300

pT(τ1) [GeV](b) Med+trigger 2-prongs = 13 TeV, 139.0 fb-1
Trigger+Medium-ID

100

150

200

SS topOS top
SS W+jets
OS W+jets

250

300

pT(τ1) [GeV](c) Med+trigger 3-prong

Figure C.1.: The fake rates for leading τhad passing trigger + medium tau ID working point in this analysis.

123

124

0.3

SS topOS top
SS W+jets
OS W+jetss = 13 TeV, 139.0 fb-1
Loose-ID

0.1
0.09

SS topOS top
SS W+jets
OS W+jetss = 13 TeV, 139.0 fb-1

0.08 Loose-ID

fake rate

0.35

fake rate

fake rate−3

0.4

50 ×10
45

0.07

35

0.25

0.06

30

0.2

0.05

25

0.15

0.04

20

0.03

15

0.02

10

0.05

0.01

5

0

0

0.1

100

150

200

250

300

pT(τ1) [GeV](a) Loose 1-prong

100

150

200

250

300

pT(τ1) [GeV](b) Loose 2-prong

SS topOS top
SS W+jets
OS W+jetss = 13 TeV, 139.0 fb-1

40 Loose-ID

0

100

150

200

250

300

pT(τ1) [GeV](c) Loose 3-prong

Figure C.2.: The fake rates for sub-leading τhad passing loose tau ID working point in BTAG and P2 categories.

125

0.18
0.16

s = 13 TeV, 139.0 fb-1
Loose not Medium-ID

SS topOS top
SS W+jets
OS W+jets

fake rate

fake rate

−3

0.2

0.14

30 ×1025

s = 13 TeV, 139.0 fb-1
Loose not Medium-ID

SS topOS top
SS W+jets
OS W+jets

20

0.12
0.1

15

0.08
10

0.06
0.04

5

0.02
0

100

150

200

250

0

300

100

150

200

pT(τ1) [GeV](b) Med+trigger 3-prong−3

s = 13 TeV, 139.0 fb-1
Medium not Tight-ID

SS topOS top
SS W+jets
OS W+jets

fake rate

fake rate−3

80 ×1060300pT(τ1) [GeV](a) Med+trigger 1-prong

70

250

10 ×1098

s = 13 TeV, 139.0 fb-1
Medium not Tight-ID

SS topOS top
SS W+jets
OS W+jets

7

50

6

40

5

30

4
3

20

2

10

1

0

0

100

150

200

250

300

100

150

200

pT(τ1) [GeV]

250

300

pT(τ1) [GeV](c) Med+trigger 1-prong(d) Med+trigger 3-prong

0.09
0.08

s = 13 TeV, 139.0 fb-1
Tight-ID

SS topOS top
SS W+jets
OS W+jets

0.07

fake rate

fake rate

−3

0.1

5 ×10
4.5
4

SS topOS top
SS W+jets
OS W+jets

3.5

0.06

3

0.05

2.5

0.04

2

0.03

1.5

0.02

1

0.01

0.5

0

s = 13 TeV, 139.0 fb-1
Tight-ID

100

150

200

250

300

pT(τ1) [GeV](e) Med+trigger 1-prong

0

100

150

200

250

300

pT(τ1) [GeV](f ) Med+trigger 3-prong

Figure C.3.: The fake rates for sub-leading τhad passing loose-not-med.(top), med-not-tight(middle) andtight(bottom) tau ID working point in BVETO category.

0.2
0.18

Data

s = 13 TeV, 139.0 fb-1

0.16 top CR, OS

tt, single top
Simulation

fake rate

fake rate

126

0.14

0.12

0.12

0.1

0.1

0.08

0.08

0.06

0.06

0.04

0.04

0.02

0.02
100

150

200

250

0

300

W → µν
Simulation

100

150

200

250

300

pT(τ1) [GeV]

pT(τ1) [GeV](a) Loose-not-med TCR OS 1-prong(b) Loose-not-med WCR OS 1-prong−3

30 ×1025

Data

s = 13 TeV, 139.0 fb-1
top CR, OS

tt, single top
Simulation

fake rate−3

fake rate

Data

s = 13 TeV, 139.0 fb-1

0.16 W CR, OS

0.14

0

30 ×10
25

20

20

15

15

10

10

5

5

0

100

150

200

250

0

300

Data

s = 13 TeV, 139.0 fb-1
W CR, OS

100

150

200

W → µν
Simulation

250

300

pT(τ1) [GeV]

pT(τ1) [GeV](c) Loose-not-med TCR OS 2-prong(d) Loose-not-med WCR OS 2-prong−3

30 ×1025

s = 13 TeV, 139.0 fb-1
top CR, OS

Data
tt, single top
Simulation

fake rate−3

fake rate

0.2
0.18

30 ×10
25

20

20

15

15

10

10

5

5

0

100

150

200

250

300

0

s = 13 TeV, 139.0 fb-1
W CR, OS

100

150

200

Data
W → µν
Simulation

250

300

pT(τ1) [GeV]

pT(τ1) [GeV](e) Loose-not-med TCR OS 3-prong(f ) Loose-not-med WCR OS 3-prong

Figure C.4.: Comparison of data FR to MC FRs. The loose-not-med. FRs of 1-prong (top), 2-prong (middle)
and 3-prong (bottom) in top control region (left) and W control region (right) are shown. The loose-not-med. FRsof 2-prong are not used in this analysis.

127

−3

70

Data

s = 13 TeV, 139.0 fb-1
top CR, OS

60

tt, single top
Simulation

fake rate

fake rate−3

80 ×10

50

40

40

30

30

20

20

10

10
100

150

200

250

0

300

Data

s = 13 TeV, 139.0 fb-1
W CR, OS

60

100

150

200

W → µν
Simulation

250

300

pT(τ1) [GeV]

pT(τ1) [GeV](a) Med-not-tight TCR OS 1-prong(b) Med-not-tight WCR OS 1-prong−3

10 ×109Data

s = 13 TeV, 139.0 fb-1
top CR, OS

8

tt, single top
Simulation

fake rate−3

fake rate

70

50

0

10 ×10
9
7

6

6

5

5

4

4

3

3

2

2

1

1

0

0

100

150

200

250

300

Data

s = 13 TeV, 139.0 fb-1

W → µν
Simulation

8 W CR, OS

7

100

150

200

250

300

pT(τ1) [GeV]

pT(τ1) [GeV](c) Med-not-tight TCR OS 2-prong(d) Med-not-tight WCR OS 2-prong−3

10 ×109s = 13 TeV, 139.0 fb-1

8 top CR, OS

Data
tt, single top
Simulation

fake rate−3

fake rate

80 ×10

10 ×10
9

7

7

6

6

5

5

4

4

3

3

2

2

1

1

0

0

100

150

200

250

300

s = 13 TeV, 139.0 fb-1

8 W CR, OS

100

150

200

Data
W → µν
Simulation

250

300

pT(τ1) [GeV]

pT(τ1) [GeV](e) Med-not-tight TCR OS 3-prong(f ) Med-not-tight WCR OS 3-prong

Figure C.5.: Comparison of data FR to MC FRs. The med-not-tight FRs of 1-prong (top), 2-prong (middle) and3-prong (bottom) in top control region (left) and W control region (right) are shown. The med-not-tight FRs of
2-prong are not used in this analysis.

0.1
0.09

Data

s = 13 TeV, 139.0 fb-1

0.08 top CR, OS

tt, single top
Simulation

fake rate

fake rate

128

0.1
0.09

0.07

0.07

0.06

0.06

0.05

0.05

0.04

0.04

0.03

0.03

0.02

0.02

0.01

0.01

0

100

150

200

250

0

300

100

150

200

pT(τ1) [GeV]

tt, single top
Simulation

fake rate

fake rate

Data

s = 13 TeV, 139.0 fb-1
top CR, OS

5 ×10
4.5

W → µν
Simulation

3.5
3

2.5

2.5

2

2

1.5

1.5

1

1

0.5

0.5
100

150

200

250

0

300

100

150

200

pT(τ1) [GeV]300(d) Tight WCR OS 2-prong−3

s = 13 TeV, 139.0 fb-1

Datatt, single top
Simulation

4 top CR, OS
3.5

fake rate

−3

5 ×10
4.5

250

pT(τ1) [GeV](c) Tight TCR OS 2-prong
fake rate

Data

s = 13 TeV, 139.0 fb-1

4 W CR, OS

3

5 ×10
4.5

s = 13 TeV, 139.0 fb-1

4 W CR, OS

Data
W → µν
Simulation

3.5

3

3

2.5

2.5

2

2

1.5

1.5

1

1

0.5

0.5

0

300

−3

3.5

0

250

(b) Tight WCR OS 1-prong

−3

5 ×10
4

W → µν
SimulationpT(τ1) [GeV](a) Tight TCR OS 1-prong

4.5

Data

s = 13 TeV, 139.0 fb-1

0.08 W CR, OS

100

150

200

250

300

pT(τ1) [GeV](e) Tight TCR OS 3-prong

0

100

150

200

250

300

pT(τ1) [GeV](f ) Tight WCR OS 3-prong

Figure C.6.: Comparison of data FR to MC FRs. The tight FRs of 1-prong (top), 2-prong (middle) and 3-prong(bottom) in top control region (left) and W control region (right) are shown. The tight FRs of 2-prong are notused in this analysis.

0.1
0.09

Data

s = 13 TeV, 139.0 fb-1

0.08 top CR, OS

tt, single top
Simulation

fake rate

fake rate

129

0.07

0.06

0.06

0.05

0.05

0.04

0.04

0.03

0.03

0.02

0.02

0.01

0.01
100

150

200

250

0

300

W → µν
Simulation

100

150

200

250

300

pT(τ1) [GeV]

pT(τ1) [GeV](a) Med+trigger TCR OS 1-prong(b) Med+trigger WCR OS 1-prong−3

10 ×109Data

s = 13 TeV, 139.0 fb-1
top CR, OS

8

tt, single top
Simulation

fake rate−3

fake rate

Data

s = 13 TeV, 139.0 fb-1

0.08 W CR, OS

0.07

0

10 ×10
9
7

6

6

5

5

4

4

3

3

2

2

1

1

0

0

100

150

200

250

300

Data

s = 13 TeV, 139.0 fb-1

W → µν
Simulation

8 W CR, OS

7

100

150

200

250

300

pT(τ1) [GeV]

pT(τ1) [GeV](c) Med+trigger TCR OS 2-prong(d) Med+trigger WCR OS 2-prong−3

10 ×109s = 13 TeV, 139.0 fb-1

8 top CR, OS

Data
tt, single top
Simulation

fake rate−3

fake rate

0.1
0.09

10 ×10
9

7

7

6

6

5

5

4

4

3

3

2

2

1

1

0

0

100

150

200

250

300

s = 13 TeV, 139.0 fb-1

8 W CR, OS

100

150

200

Data
W → µν
Simulation

250

300

pT(τ1) [GeV]

pT(τ1) [GeV](e) Med+trigger TCR OS 3-prong(f ) Med+trigger WCR OS 3-prong

Figure C.7.: Comparison of data FR to MC FRs. The medium + tau trigger FRs of 1-prong (top), 2-prong(middle) and 3-prong (bottom) in top control region (left) and W control region (right) are shown. The medium +tau trigger FRs of 2-prong are not used in this analysis.

0.2
0.18

Data

s = 13 TeV, 139.0 fb-1

0.16 top CR, SS

tt, single top
Simulation

fake rate

fake rate

130

0.14

0.12

0.12

0.1

0.1

0.08

0.08

0.06

0.06

0.04

0.04

0.02

0.02
100

150

200

250

0

300

W → µν
Simulation

100

150

200

250

300

pT(τ1) [GeV]

pT(τ1) [GeV](a) Loose-not-med TCR SS 1-prong(b) Loose-not-med WCR SS 1-prong−3

30 ×1025

Data

s = 13 TeV, 139.0 fb-1
top CR, SS

tt, single top
Simulation

fake rate−3

fake rate

Data

s = 13 TeV, 139.0 fb-1

0.16 W CR, SS

0.14

0

30 ×10
25

20

20

15

15

10

10

5

5

0

100

150

200

250

0

300

Data

s = 13 TeV, 139.0 fb-1
W CR, SS

100

150

200

W → µν
Simulation

250

300

pT(τ1) [GeV]

pT(τ1) [GeV](c) Loose-not-med TCR SS 2-prong(d) Loose-not-med WCR SS 2-prong−3

30 ×1025

s = 13 TeV, 139.0 fb-1
top CR, SS

Data
tt, single top
Simulation

fake rate−3

fake rate

0.2
0.18

30 ×10
25

20

20

15

15

10

10

5

5

0

100

150

200

250

300

0

s = 13 TeV, 139.0 fb-1
W CR, SS

100

150

200

Data
W → µν
Simulation

250

300

pT(τ1) [GeV]

pT(τ1) [GeV](e) Loose-not-med TCR SS 3-prong(f ) Loose-not-med WCR SS 3-prong

Figure C.8.: Comparison of data FR to MC FRs. The loose-not-med. FRs of 1-prong (top), 2-prong (middle)
and 3-prong (bottom) in top control region (left) and W control region (right) are shown. The loose-not-med. FRsof 2-prong are not used in this analysis.

131

−3

70

Data

s = 13 TeV, 139.0 fb-1
top CR, SS

60

tt, single top
Simulation

fake rate

fake rate−3

80 ×10

50

40

40

30

30

20

20

10

10
100

150

200

250

0

300

Data

s = 13 TeV, 139.0 fb-1
W CR, SS

60

100

150

200

W → µν
Simulation

250

300

pT(τ1) [GeV]

pT(τ1) [GeV](a) Med-not-tight TCR SS 1-prong(b) Med-not-tight WCR SS 1-prong−3

10 ×109Data

s = 13 TeV, 139.0 fb-1
top CR, SS

8

tt, single top
Simulation

fake rate−3

fake rate

70

50

0

10 ×10
9
7

6

6

5

5

4

4

3

3

2

2

1

1

0

0

100

150

200

250

300

Data

s = 13 TeV, 139.0 fb-1

W → µν
Simulation

8 W CR, SS

7

100

150

200

250

300

pT(τ1) [GeV]

pT(τ1) [GeV](c) Med-not-tight TCR SS 2-prong(d) Med-not-tight WCR SS 2-prong−3

10 ×109s = 13 TeV, 139.0 fb-1

8 top CR, SS

Data
tt, single top
Simulation

fake rate−3

fake rate

80 ×10

10 ×10
9

7

7

6

6

5

5

4

4

3

3

2

2

1

1

0

0

100

150

200

250

300

s = 13 TeV, 139.0 fb-1

8 W CR, SS

100

150

200

Data
W → µν
Simulation

250

300

pT(τ1) [GeV]

pT(τ1) [GeV](e) Med-not-tight TCR SS 3-prong(f ) Med-not-tight WCR SS 3-prong

Figure C.9.: Comparison of data FR to MC FRs. The med-not-tight FRs of 1-prong (top), 2-prong (middle) and3-prong (bottom) in top control region (left) and W control region (right) are shown. The med-not-tight FRs of
2-prong are not used in this analysis.

0.1
0.09

Data

s = 13 TeV, 139.0 fb-1

0.08 top CR, SS

tt, single top
Simulation

fake rate

fake rate

132

0.1
0.09

0.07

0.07

0.06

0.06

0.05

0.05

0.04

0.04

0.03

0.03

0.02

0.02

0.01

0.01

0

100

150

200

250

0

300

100

150

200

pT(τ1) [GeV]

tt, single top
Simulation

fake rate

fake rate

Data

s = 13 TeV, 139.0 fb-1
top CR, SS

5 ×10
4.5

W → µν
Simulation

3.5
3

2.5

2.5

2

2

1.5

1.5

1

1

0.5

0.5
100

150

200

250

0

300

100

150

200

pT(τ1) [GeV]300(d) Tight WCR SS 2-prong−3

s = 13 TeV, 139.0 fb-1

Datatt, single top
Simulation

4 top CR, SS
3.5

fake rate

−3

5 ×10
4.5

250

pT(τ1) [GeV](c) Tight TCR SS 2-prong
fake rate

Data

s = 13 TeV, 139.0 fb-1

4 W CR, SS

3

5 ×10
4.5

s = 13 TeV, 139.0 fb-1

4 W CR, SS

Data
W → µν
Simulation

3.5

3

3

2.5

2.5

2

2

1.5

1.5

1

1

0.5

0.5

0

300

−3

3.5

0

250

(b) Tight WCR SS 1-prong

−3

5 ×10
4

W → µν
SimulationpT(τ1) [GeV](a) Tight TCR SS 1-prong

4.5

Data

s = 13 TeV, 139.0 fb-1

0.08 W CR, SS

100

150

200

250

300

pT(τ1) [GeV](e) Tight TCR SS 3-prong

0

100

150

200

250

300

pT(τ1) [GeV](f ) Tight WCR SS 3-prong

Figure C.10.: Comparison of data FR to MC FRs. The tight FRs of 1-prong (top), 2-prong (middle) and 3-prong(bottom) in top control region (left) and W control region (right) are shown. The tight FRs of 2-prong are notused in this analysis.

0.1
0.09

Data

s = 13 TeV, 139.0 fb-1

0.08 top CR, SS

tt, single top
Simulation

fake rate

fake rate

133

0.07

0.06

0.06

0.05

0.05

0.04

0.04

0.03

0.03

0.02

0.02

0.01

0.01
100

150

200

250

0

300

W → µν
Simulation

100

150

200

250

300

pT(τ1) [GeV]

pT(τ1) [GeV](a) Med+trigger TCR SS 1-prong(b) Med+trigger WCR SS 1-prong−3

10 ×109Data

s = 13 TeV, 139.0 fb-1
top CR, SS

8

tt, single top
Simulation

fake rate−3

fake rate

Data

s = 13 TeV, 139.0 fb-1

0.08 W CR, SS

0.07

0

10 ×10
9
7

6

6

5

5

4

4

3

3

2

2

1

1

0

0

100

150

200

250

300

Data

s = 13 TeV, 139.0 fb-1

W → µν
Simulation

8 W CR, SS

7

100

150

200

250

300

pT(τ1) [GeV]

pT(τ1) [GeV](c) Med+trigger TCR SS 2-prong(d) Med+trigger WCR SS 2-prong−3

10 ×109s = 13 TeV, 139.0 fb-1

8 top CR, SS

Data
tt, single top
Simulation

fake rate−3

fake rate

0.1
0.09

10 ×10
9

7

7

6

6

5

5

4

4

3

3

2

2

1

1

0

0

100

150

200

250

300

s = 13 TeV, 139.0 fb-1

8 W CR, SS

100

150

200

Data
W → µν
Simulation

250

300

pT(τ1) [GeV]

pT(τ1) [GeV](e) Med+trigger TCR SS 3-prong(f ) Med+trigger WCR SS 3-prong

Figure C.11.: Comparison of data FR to MC FRs. The medium + tau trigger FRs of 1-prong (top), 2-prong(middle) and 3-prong (bottom) in top control region (left) and W control region (right) are shown. The medium +tau trigger FRs of 2-prong are not used in this analysis.

D Distribution in SS Validation Region and
OS Signal Region

The distributions of the different varaibles are shown in following plots in the signal region (OS) andvalidation region (SS). The agreement between MC and data is investigated with these variable comparison
in each validation region of the categorization.

134

500

Data

MultijetZ/ γ * → ττ + jets

W → τν + jets

tt, single top

Otherstan β=15

hMSSM A 1000→ ττs = 13 TeV, 139.0 fb-1
H/A → τhadτhadloosenotmed 1prong
b-veto Same-Sign

1.4
1.2

Uncertainty

400

Data

MultijetZ/ γ * → ττ + jets

W → τν + jets

tt, single top

Otherstan β=15

hMSSM A 1000

200

0.6

0.6

0.4

0.4

0.2

0.2

Data/Bkg

Data/Bkg

0.8

stat.

1.5
1

50 100 150 200 250 300 350 400 450 500

020 40 60 80 100 120 140 160 180 200

s = 13 TeV, 139.0 fb-1
H/A → τhadτhad
mednottight 1prong
b-veto Same-Sign

250

Data

MultijetZ/ γ * → ττ + jets

W → τν + jets

tt, single top

Otherstan β=15

hMSSM A 1000→ ττ(b) loosenotmed 1-prong met
Events

Uncertainty

200

900

s = 13 TeV, 139.0 fb-1
H/A → τhadτhad
mednottight 1prong
b-veto Same-Sign

800
700

Data

MultijetZ/ γ * → ττ + jets

W → τν + jets

tt, single top

Otherstan β=15

hMSSM A 1000

→ ττ

Uncertainty

700

600

600
400

100

300

300

200

200

100

100

Data/Bkg

0

50 100 150 200 250 300 350 400 450 500

stat.

20 40 60 80 100 120 140 160 180 200

leading τ p [GeV]

Data

MultijetZ/ γ * → ττ + jets

W → τν + jets

tt, single top

Otherstan β=15
hMSSM A 1000 → ττ

stat.

1.5
1
0

600
s = 13 TeV, 139.0 fb-1
H/A → τhadτhadtight 1prong
b-veto Same-Sign

500

Uncertainty

Data/Bkg

s = 13 TeV, 139.0 fb-1
H/A → τhadτhadtight 1prong
b-veto Same-Sign

220
200
180
160
140
120
100
80
60
40
20

50 100 150 200 250 300 350 400 450 500
leading τ p [GeV]T(g) tight 1-prong 1st tau pT

Data

MultijetZ/ γ * → ττ + jets

W → τν + jets

tt, single top

Otherstan β=15
hMSSM A 1000 → ττ

600

300
200

100

100

Emiss
[GeV]
T

(h) tight 1-prong met

Uncertainty

50 100 150 200 250 300 350 400 450 500

s = 13 TeV, 139.0 fb-1
H/A → τhadτhadtight 1prong
b-veto Same-Sign

500

200

20 40 60 80 100 120 140 160 180 200

Others→ ττ(f ) mednottight 1prong 2nd tau pT

3000tan β=15

T

400

stat.

W → τν + jets

tt, single top

stat.

Uncertainty

1

Z/ γ * → ττ + jets

hMSSM A 1000

1.4
1.2
1
0.8
0.6
0

400

1.5

MultijetDatasubleading τ p [GeV](e) mednottight 1-prong met
Events(d) mednottight 1-prong 1st tau pT

Uncertainty

50 100 150 200 250 300 350 400 450 500

Emiss
[GeV]
T

T

Events1

Data/Bkg

500

1.4
1.2
1
0.8
0.6
0

Others→ ττstat.

s = 13 TeV, 139.0 fb-1
H/A → τhadτhad
mednottight 1prong
b-veto Same-Sign

800

400

stat.

tan β=15(c) loosenotmed 1-prong 2nd tau pT

500

1.5

W → τν + jets

tt, single top

T

150

50

Z/ γ * → ττ + jets

subleading τ p [GeV]

Data/Bkg

Events(a) loosenotmed 1-prong 1st tau pT

300

1.4
1.2
1
0.8
0.6
0

Emiss
[GeV]
T

Eventsstat.

Multijet

Data

hMSSM A 1000

0.8

T

Data/Bkg

1.2

300

1.4
1.2
1
0.8
0.6
0

Events

Uncertaintys = 13 TeV, 139.0 fb-1
H/A → τhadτhadloosenotmed 1prong
b-veto Same-Sign

1.4

1

leading τ p [GeV]

Data/Bkg

→ ττ

×103

1

100

Data/Bkg

×103

1.6

Eventss = 13 TeV, 139.0 fb-1
H/A → τhadτhadloosenotmed 1prong
b-veto Same-Sign

EventsEvents

135

1.5

Data

MultijetZ/ γ * → ττ + jets

W → τν + jets

tt, single top

Otherstan β=15
hMSSM A 1000 → ττUncertainty

stat.

1
0

50 100 150 200 250 300 350 400 450 500
subleading τ p [GeV]T(i) tight 1-prong 2nd tau pT

Figure D.1.: The distribution of 1st tau pT , met and 2nd tau pT for BVETO SS validation region.

140

Data

MultijetZ/ γ * → ττ + jets

W → τν + jets

tt, single top

Otherstan β=15

hMSSM A 1000

120

→ ττ

s = 13 TeV, 139.0 fb-1
H/A → τhadτhadloosenotmed 3prong
b-veto Same-Sign

350
300

Uncertainty

Data

MultijetZ/ γ * → ττ + jets

W → τν + jets

tt, single top

Otherstan β=15

hMSSM A 1000

150

40

100

100

20

50

0

stat.

20 40 60 80 100 120 140 160 180 200

leading τ p [GeV]

Data

MultijetZ/ γ * → ττ + jets

W → τν + jets

tt, single top

Otherstan β=15

hMSSM A 1000

50

→ ττ

(b) loosenotmed 3-prong met
Events

Uncertainty

40

s = 13 TeV, 139.0 fb-1
H/A → τhadτhad
mednottight 3prong
b-veto Same-Sign

140
120

Data

MultijetZ/ γ * → ττ + jets

W → τν + jets

tt, single top

Otherstan β=15

hMSSM A 1000

→ ττ

140

100

100

40

40

10

20

20

Data/Bkg

60

Data/Bkg

60

2
1.5

stat.

1

50 100 150 200 250 300 350 400 450 500

0s = 13 TeV, 139.0 fb-1
H/A → τhadτhadtight 3prong
b-veto Same-Sign

40

Data

MultijetZ/ γ * → ττ + jets

W → τν + jets

tt, single top

Otherstan β=15
hMSSM A 1000 → ττ(e) mednottight 3-prong met
Events(d) mednottight 3-prong 1st tau pT
120

s = 13 TeV, 139.0 fb-1
H/A → τhadτhadtight 3prong
b-veto Same-Sign

100

Uncertainty

Data

MultijetZ/ γ * → ττ + jets

W → τν + jets

tt, single top

Otherstan β=15
hMSSM A 1000 → ττZ/ γ * → ττ + jets

W → τν + jets
Otherstt, single top
tan β=15→ ττ

Uncertainty

stat.

0

50 100 150 200 250 300 350 400 450 500
subleading τ p [GeV]

Emiss
[GeV]
T

T

50

2.5
2
1.5
1

20 40 60 80 100 120 140 160 180 200

leading τ p [GeV]Multijet

Data

hMSSM A 1000

20

0

50 100 150 200 250 300 350 400 450 500

Uncertainty

80

1

stat.

s = 13 TeV, 139.0 fb-1
H/A → τhadτhad
mednottight 3prong
b-veto Same-Sign

120

80

stat.

Uncertainty(c) loosenotmed 3-prong 2nd tau pT

30

2

Others→ ττTT(f ) mednottight 3-prong 2nd tau pT
EventsEventss = 13 TeV, 139.0 fb-1
H/A → τhadτhad
mednottight 3prong
b-veto Same-Sign

60tan β=15

subleading τ p [GeV]

Events

T

70

1.4
1.2
1
0.8
0.6
0

Emiss
[GeV]
T

(a) loosenotmed 3-prong 1st tau pT

W → τν + jets

tt, single top

50

2.5
2
1.5
1

Data/Bkg

Data/Bkg

200

50 100 150 200 250 300 350 400 450 500

Z/ γ * → ττ + jets

250

150

1

Multijet

Data

hMSSM A 1000

300

60

0

s = 13 TeV, 139.0 fb-1
H/A → τhadτhadtight 3prong
b-veto Same-Sign

100
80

Uncertainty

Data

MultijetZ/ γ * → ττ + jets

W → τν + jets

tt, single top

Otherstan β=15
hMSSM A 1000 → ττUncertainty

80

30

60

60
20

40

40
10

20

stat.

2
1.5
1
0

50 100 150 200 250 300 350 400 450 500
leading τ p [GeV]T(g) tight 3-prong 1st tau pT

Data/Bkg

20

Data/Bkg

Data/Bkg

350

200

stat.

Data/Bkg

Uncertaintys = 13 TeV, 139.0 fb-1
H/A → τhadτhadloosenotmed 3prong
b-veto Same-Sign

400

80

1.5

Events

→ ττ

250

100

Data/Bkg

400

Eventss = 13 TeV, 139.0 fb-1
H/A → τhadτhadloosenotmed 3prong
b-veto Same-Sign

160

EventsEvents

136

stat.

1.5
1
0

20 40 60 80 100 120 140 160 180 200
Emiss
[GeV]
T

(h) tight 3-prong met

2.5
2
1.5
1

stat.

0

50 100 150 200 250 300 350 400 450 500
subleading τ p [GeV]T(i) tight 3-prong 2nd tau pT

Figure D.2.: The distribution of 1st tau pT , met and 2nd tau pT for BVETO SS validation region.

s = 13 TeV, 139.0 fb-1
H/A → τhadτhadloose incprongb-tag Same-Sign

140

Data

MultijetZ/ γ * → ττ + jets

W → τν + jets

tt, single top

Otherstan β=15

hMSSM A 1000

120

→ ττ

s = 13 TeV, 139.0 fb-1
H/A → τhadτhadloose incprongb-tag Same-Sign

120

Uncertainty

Data

MultijetZ/ γ * → ττ + jets

W → τν + jets

tt, single top

Otherstan β=15

hMSSM A 1000

100

100

→ ττ

Uncertainty

80

80

60

60

40

40

Data/Bkg

1.5

stat.

1
0

1.5

Data/Bkg

20

20

Data/Bkg

140

Events160

EventsEvents

137

stat.

1

50 100 150 200 250 300 350 400 450 5000(a) loose 1st tau pT

Z/ γ * → ττ + jets

W → τν + jets
Otherstt, single top
tan β=15→ ττ

Uncertainty

stat.

1
0

50 100 150 200 250 300 350 400 450 500
subleading τ p [GeV]

Emiss
[GeV]
T

T

Multijet

Data

hMSSM A 1000

1.5

20 40 60 80 100 120 140 160 180 200

leading τ p [GeV]s = 13 TeV, 139.0 fb-1
H/A → τhadτhadloose incprongb-tag Same-Sign

200
180
160
140
120
100
80
60
40
20

T

(b) loose met(c) loose 2nd tau pT

Data

MultijetZ/ γ * → ττ + jets

W → τν + jets

tt, single top

Otherstan β=15

hMSSM A 1000

→ ττ

90
80

s = 13 TeV, 139.0 fb-1
H/A → τhadτhadloose 2prong
b-veto Same-Sign

70
60
50

Uncertainty

Data

MultijetZ/ γ * → ττ + jets

W → τν + jets

tt, single top

Otherstan β=15

hMSSM A 1000

→ ττ

Eventss = 13 TeV, 139.0 fb-1
H/A → τhadτhadloose 2prong
b-veto Same-Sign

Events

45
40
35
30
25
20
15
10
5

1
0

50 100 150 200 250 300 350 400 450 500

Z/ γ * → ττ + jets

W → τν + jets
Otherstt, single top
tan β=15

hMSSM A 1000

→ ττ

Uncertainty

30
20
10

2
1.5

stat.

1
0

20 40 60 80 100 120 140 160 180 200

leading τ p [GeV]

Emiss
[GeV]
T

T

(a) loose 1st tau pT

Multijet

Data

40

Data/Bkg

stat.

s = 13 TeV, 139.0 fb-1
H/A → τhadτhadloose 2prong
b-veto Same-Sign

70
50

10

2

80
60

Uncertainty

40
30
20

Data/Bkg

Data/Bkg

EventsFigure D.3.: The distribution of 1st tau pT , met and 2nd tau pT for BTAG SS validation region.

(b) loose met

1.5

stat.

1
0

50 100 150 200 250 300 350 400 450 500
subleading τ p [GeV]T(c) loose 2nd tau pT

Figure D.4.: The distribution of 1st tau pT , met and 2nd tau pT for 2P validation region.

W → τν + jets

tt, single top

Otherstan β=15

hMSSM A 1000

→ ττ

Uncertainty

500
400
300
200

1.5

Data/Bkg

Data/Bkg

100
stat.

1
0

50 100 150 200 250 300 350 400 450 500

2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2

1.4
1.2
1
0.8
0.6
0

s = 13 TeV, 139.0 fb-1
H/A → τhadτhadloosenotmed 1prong
b-veto OS

Data

MultijetZ/ γ * → ττ + jets

W → τν + jets

tt, single top

Otherstan β=15

hMSSM A 1000

20 40 60 80 100 120 140 160 180 200

W → τν + jets

tt, single top

Otherstan β=15

hMSSM A 1000

1.5

→ ττ

1
0

×103

1.2

1

s = 13 TeV, 139.0 fb-1
H/A → τhadτhad
mednottight 1prong
b-veto OS

Uncertainty

stat.

Data

MultijetZ/ γ * → ττ + jets

W → τν + jets

tt, single top

Otherstan β=15

hMSSM A 1000

50 100 150 200 250 300 350 400 450 500

W → τν + jets

0.2

tt, single top

Otherstan β=15
hMSSM A 1000 → ττ1

Uncertainty

0.8

W → τν + jets

tt, single top

Otherstan β=15
hMSSM A 1000 → ττ

200

0.4

100

0.2

tan β=15

Others→ ττUncertainty

stat.

50 100 150 200 250 300 350 400 450 500
T(f ) mednottight 1prong 2nd tau pT
×103
s = 13 TeV, 139.0 fb-1
H/A → τhadτhadtight 1prong
b-veto OS

1.4
1.2

Uncertainty

Data

MultijetZ/ γ * → ττ + jets

W → τν + jets

tt, single top

Otherstan β=15
hMSSM A 1000 → ττUncertainty

1

0.6

300

W → τν + jets

tt, single top

subleading τ p [GeV](e) mednottight 1-prong met

MultijetZ/ γ * → ττ + jets

1
0

400

0.8
0.6
0.4

stat.

50 100 150 200 250 300 350 400 450 500
leading τ p [GeV]T(g) tight 1-prong 1st tau pT

1.4
1.2
1
0.8
0.6
0

0.2

Data/Bkg

1.4
1.2
1
0.8
0.6
0

Data/Bkg

Data/Bkg

1.5

20 40 60 80 100 120 140 160 180 200

Z/ γ * → ττ + jets

Multijet

Data

hMSSM A 1000

0.2

Data

Uncertainty

50 100 150 200 250 300 350 400 450 500

s = 13 TeV, 139.0 fb-1
H/A → τhadτhad
mednottight 1prong
b-veto OS1

0.4

s = 13 TeV, 139.0 fb-1
H/A → τhadτhadtight 1prong
b-veto OS

Others
→ ττ

×103

0.6

×103

tan β=15

stat.

Emiss
[GeV]
T

EventsEvents500

MultijetZ/ γ * → ττ + jets

Uncertaintystat.

W → τν + jets

tt, single top
hMSSM A 1000

1.2

0.4

1.4
1.2
1
0.8
0.6
0

Z/ γ * → ττ + jets(c) loosenotmed 1-prong 2nd tau pT0.6(d) mednottight 1-prong 1st tau pT
Data

→ ττ

Multijet

Data

T

0.8

T

s = 13 TeV, 139.0 fb-1
H/A → τhadτhadtight 1prong
b-veto OS

s = 13 TeV, 139.0 fb-1
H/A → τhadτhadloosenotmed 1prong
b-veto OS

1.4
1.2
1
0.8
0.6
0

0.8

leading τ p [GeV]

600

2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2

subleading τ p [GeV]

Data/Bkg

Z/ γ * → ττ + jets

EventsMultijet(b) loosenotmed 1-prong met

Data/Bkg

Data/Bkg

Events(a) loosenotmed 1-prong 1st tau pT
Data

×103

Emiss
[GeV]
T

T

s = 13 TeV, 139.0 fb-1
H/A → τhadτhad
mednottight 1prong
b-veto OS

Uncertainty

stat.

leading τ p [GeV]

450
400
350
300
250
200
150
100
50

→ ττ

EventsZ/ γ * → ττ + jets

×103

Data/Bkg

Multijet

Events600

Data

Eventss = 13 TeV, 139.0 fb-1
H/A → τhadτhadloosenotmed 1prong
b-veto OS

700

EventsEvents138

stat.

20 40 60 80 100 120 140 160 180 200
Emiss
[GeV]
T

(h) tight 1-prong met

1.4
1.2
1
0.8
0.6
0

stat.

50 100 150 200 250 300 350 400 450 500
subleading τ p [GeV]T(i) tight 1-prong 2nd tau pT

Figure D.5.: The distribution of 1st tau pT , met and 2nd tau pT for BVETO OS signal region.

Multijet

Z/ γ * → ττ + jets

W → τν + jets

tt, single top

Otherstan β=15

hMSSM A 1000

→ ττ

600

s = 13 TeV, 139.0 fb-1
H/A → τhadτhadloosenotmed 3prong
b-veto OS

500

Uncertainty

Data

MultijetZ/ γ * → ττ + jets

W → τν + jets

tt, single top

Otherstan β=15

hMSSM A 1000

50 100 150 200 250 300 350 400 450 500

200

200

100

100

Data/Bkg

300

stat.

MultijetZ/ γ * → ττ + jets

W → τν + jets

tt, single top

Otherstan β=15

hMSSM A 1000

80

→ ττ

Uncertainty

60
40

2
1.5

Data/Bkg

Data/Bkg

20

stat.

1
0

220
200
180
160
140
120
100
80
60
40
20

s = 13 TeV, 139.0 fb-1
H/A → τhadτhad
mednottight 3prong
b-veto OS

Data

MultijetZ/ γ * → ττ + jets

W → τν + jets

tt, single top

Otherstan β=15

hMSSM A 1000

10MultijetZ/ γ * → ττ + jets

W → τν + jets

tt, single top

Otherstan β=15
hMSSM A 1000 → ττ

20 40 60 80 100 120 140 160 180 200(e) mednottight 3-prong met

Uncertainty

80
60
40

Data/Bkg

20

stat.

2
1.5
1
0

50 100 150 200 250 300 350 400 450 500
leading τ p [GeV]T(g) tight 3-prong 1st tau pT

250

s = 13 TeV, 139.0 fb-1
H/A → τhadτhad
mednottight 3prong
b-veto OS

200

MultijetDataZ/ γ * → ττ + jets

W → τν + jets
Otherstt, single top
tan β=15

hMSSM A 1000

1.4
1.2
1
0.8
0.6
0

→ ττ

Uncertainty

stat.

50 100 150 200 250 300 350 400 450 500
subleading τ p [GeV]

Emiss
[GeV]
T

Events100Data(c) loosenotmed 3-prong 2nd tau pT50T

s = 13 TeV, 139.0 fb-1
H/A → τhadτhadtight 3prong
b-veto OS

50 100 150 200 250 300 350 400 450 500

100

stat.

(d) mednottight 3-prong 1st tau pT

Uncertainty

T

Uncertainty

1.5

50 100 150 200 250 300 350 400 450 500

Others→ ττ

150

leading τ p [GeV]

120

→ ττ

tan β=15

subleading τ p [GeV]

EventsData

W → τν + jets

tt, single top

10Data/Bkg

s = 13 TeV, 139.0 fb-1
H/A → τhadτhad
mednottight 3prong
b-veto OS

100(b) loosenotmed 3-prong met
EventsEvents(a) loosenotmed 3-prong 1st tau pT

Z/ γ * → ττ + jets

stat.

Emiss
[GeV]
T

T

Multijet

Data

hMSSM A 1000

1.5

20 40 60 80 100 120 140 160 180 200

leading τ p [GeV]

220
200
180
160
140
120
100
80
60
40
20

s = 13 TeV, 139.0 fb-1
H/A → τhadτhadtight 3prong
b-veto OS

Data

MultijetZ/ γ * → ττ + jets

W → τν + jets

tt, single top

Otherstan β=15
hMSSM A 1000 → ττT(f ) mednottight 3-prong 2nd tau pT
Events

1

300

1.4
1.2
1
0.8
0.6
0

s = 13 TeV, 139.0 fb-1
H/A → τhadτhadloosenotmed 3prong
b-veto OS

500
400

Uncertaintys = 13 TeV, 139.0 fb-1
H/A → τhadτhadtight 3prong
b-veto OS

250
200

Data

MultijetZ/ γ * → ττ + jets

W → τν + jets

tt, single top

Otherstan β=15
hMSSM A 1000 → ττUncertainty

150
100
50

1.5

Data/Bkg

stat.

1.5

Events

Uncertainty

4000Data/Bkg→ ττ

EventsData

Eventss = 13 TeV, 139.0 fb-1
H/A → τhadτhadloosenotmed 3prong
b-veto OS

200
180
160
140
120
100
80
60
40
20

Data/Bkg

Data/Bkg

Events

139

stat.

1
0

20 40 60 80 100 120 140 160 180 200
Emiss
[GeV]
T

(h) tight 3-prong met

1.4
1.2
1
0.8
0.6
0

stat.

50 100 150 200 250 300 350 400 450 500
subleading τ p [GeV]T(i) tight 3-prong 2nd tau pT

Figure D.6.: The distribution of 1st tau pT , met and 2nd tau pT for BVETO OS signal region.

300

s = 13 TeV, 139.0 fb-1
H/A → τhadτhadloose incprongb-tag OS

Data

MultijetZ/ γ * → ττ + jets

W → τν + jets

tt, single top

Otherstan β=15

hMSSM A 1000

→ ττ

Uncertainty

250
200
150
100

1.4
1.2
1
0.8
0.6
0

Data/Bkg

Data/Bkg

50
stat.

240
220
200
180
160
140
120
100
80
60
40
20

s = 13 TeV, 139.0 fb-1
H/A → τhadτhadloose incprongb-tag OS

Data

MultijetZ/ γ * → ττ + jets

W → τν + jets

tt, single top

Otherstan β=15

hMSSM A 1000

→ ττ

Uncertaintys = 13 TeV, 139.0 fb-1
H/A → τhadτhadloose incprongb-tag OS

400
350

MultijetDataZ/ γ * → ττ + jetstan β=15

hMSSM A 1000

300

W → τν + jets
Otherstt, single top→ ττ

Uncertainty

250
200
150
100
50

1.5

stat.

1

50 100 150 200 250 300 350 400 450 500

Events350

Data/Bkg

400

EventsEvents140

020 40 60 80 100 120 140 160 180 200

leading τ p [GeV]

1.5

stat.

1
0

50 100 150 200 250 300 350 400 450 500
subleading τ p [GeV]

Emiss
[GeV]
T

T

(a) loose 1st tau pTT(b) loose met(c) loose 2nd tau pT

1.21

s = 13 TeV, 139.0 fb-1
H/A → τhadτhadloose 2prong
b-veto OS

Data

MultijetZ/ γ * → ττ + jets

W → τν + jets

tt, single top

Otherstan β=15

hMSSM A 1000

→ ττ

Uncertainty

0.8

×103

2.5

2

s = 13 TeV, 139.0 fb-1
H/A → τhadτhadloose 2prong
b-veto OS

Data

MultijetZ/ γ * → ττ + jets

W → τν + jets

tt, single top

Otherstan β=15

hMSSM A 1000

→ ττ

Events×103

EventsEventsFigure D.7.: The distribution of 1st tau pT , met and 2nd tau pT for BTAG OS signal region.

Uncertainty

1.5

0.6

1

0.4

Data/Bkg

Data/Bkg

1.4
1.2
1
0.8
0.6
0

stat.

50 100 150 200 250 300 350 400 450 500

1.4
1.2
1
0.8
0.6
0

Data/Bkg

0.5

0.2

stat.

20 40 60 80 100 120 140 160 180 200

leading τ p [GeV]

Emiss
[GeV]
T

T

(a) loose 1st tau pT(b) loose met

×103

1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2

1.4
1.2
1
0.8
0.6
0

s = 13 TeV, 139.0 fb-1
H/A → τhadτhadloose 2prong
b-veto OS

MultijetDataZ/ γ * → ττ + jets

W → τν + jets
Otherstt, single top
tan β=15

hMSSM A 1000

→ ττ

Uncertainty

stat.

50 100 150 200 250 300 350 400 450 500
subleading τ p [GeV]T(c) loose 2nd tau pT

Figure D.8.: The distribution of 1st tau pT , met and 2nd tau pT for 2P signal region.

E QCD Background Estimation in the Dijet Control Region

The di-jet control region is very pure in QCD with negligible amount of background as shown in thefollowing plots. The pT distributions of sub-leading 1-prong tau in each category are presented. The
W+jets and top-backgrounds are main background. Although MC background is less important in di-jet
control regions, these backgrounds are subtracted for the fake factor measurement.

141

108
7

10

6

10

s = 13 TeV, 139.0 fb-1
H/A → τhadτhad
Same-Sign
1prong loose

105

Data

Z/ γ * → ττ + jets

W → τν + jetst t , single top

Others

Uncertainty

EventsEvents

142

108
107
6

10

s = 13 TeV, 139.0 fb-1
H/A → τhadτhad
OS1prong loose

105

10

10

103

103

2

10

102

10

10

1

1

10−1
50

10−1
50

100

150

200

250

300

350

400

100

150

200

subleading τ p [GeV]

EventsEventss = 13 TeV, 139.0 fb-1
H/A → τhadτhad
Same-Sign
1prong loosenotmed

Z/ γ * → ττ + jets

Data

107
6

W → τν + jetst t , single top

10

Others

Uncertainty

105
104

103

103

102

102

10

10

1

1

10−1
50

10−1
50

100

150

200

250

300

350

400

s = 13 TeV, 139.0 fb-1
H/A → τhadτhad
OS1prong loosenotmed

100

150

200

subleading τ p [GeV]10W → τν + jetst t , single top

105

Others

Uncertaintys = 13 TeV, 139.0 fb-1
H/A → τhadτhad
Same-Sign
1prong med

107
106
105

104

104

103

103

102

102

10

10

1

1

10−1
50

10−1
50

100

150

200

250

400

300

350

400

subleading τ p [GeV]T(e) medium SS

Data

Z/ γ * → ττ + jets

W → τν + jetst t , single top

Others

Uncertainty

250

300

350

400

(d) loose-not-med OS
EventsEventsZ/ γ * → ττ + jets

350T(c) loose-not-med SS

Data

300

subleading τ p [GeV]

T

6

250

(b) loose OS

104

107

Uncertainty

T(a) loose SS

105

t t , single top

Otherssubleading τ p [GeV]T

106

Z/ γ * → ττ + jets

W → τν + jets

4

4

107

Data

s = 13 TeV, 139.0 fb-1
H/A → τhadτhad
OS1prong med

100

150

200

Data

Z/ γ * → ττ + jets

W → τν + jetst t , single top

Others

Uncertainty

250

300

350

400

subleading τ p [GeV]T(f ) medium OS

Figure E.1.: The pT distributions of 1-prong sub-leading tau passing “loose” (top), “loose-not-med.” (middle)
and “medium” (bottom) tau identification working points for opposite sign (right) and same sign regions (left).

107
106
5

10

s = 13 TeV, 139.0 fb-1
H/A → τhadτhad
Same-Sign
1prong mednottightData

Z/ γ * → ττ + jets

W → τν + jetst t , single top

Others

Uncertainty

EventsEvents

143

107
106
5

10

104

104

103

3

10

102

102

10

10

1

1

10−1
50

10−1
50

100

150

200

250

300

350

400

s = 13 TeV, 139.0 fb-1
H/A → τhadτhad
OS1prong mednottight

100

150

200

subleading τ p [GeV]t t , single top

Others

Uncertaintys = 13 TeV, 139.0 fb-1
H/A → τhadτhad
Same-Sign
1prong tight

106
5

10
10

3

10

3

10

102

102

10

10

1

1

10−1
50

10−1
50

150

200

s = 13 TeV, 139.0 fb-1
H/A → τhadτhad
OS1prong tight

4

104

100

250

300

350

400

100

150

200

subleading τ p [GeV]

106
105

350

400

Data

Z/ γ * → ττ + jets

W → τν + jetst t , single top

Others

Uncertainty

250

300

350

400

(d) tight OS
EventsEvents107

s = 13 TeV, 139.0 fb-1
H/A → τhadτhad
Same-Sign
1prong fail300

T(c) tight SS

108

250

subleading τ p [GeV]T

109

Uncertainty(b) med-not-tight OS
EventsEvents105

Z/ γ * → ττ + jets

W → τν + jetst t , single top

OthersT(a) med-not-tight SS

Data

Z/ γ * → ττ + jets

W → τν + jets

subleading τ p [GeV]

T

106

Data

109

Data

Z/ γ * → ττ + jets

W → τν + jetst t , single top

10

Others

Uncertainty

106

108
7

s = 13 TeV, 139.0 fb-1
H/A → τhadτhad
OS1prong failData

Z/ γ * → ττ + jets

W → τν + jetst t , single top

Others

Uncertainty

105

104

104

103
102
10

103
102
10

1

1

10−1
50

10−1
50

100

150

200

250

300

350

400

subleading τ p [GeV]T(e) fail loose SS

100

150

200

250

300

350

400

subleading τ p [GeV]T(f ) fail loose OS

Figure E.2.: The pT distributions of 1-prong sub-leading tau passing “med-not-tight” (top) and “tight” (middle)
tau identification working points for opposite sign (right) and same sign regions (left). The bottom plots show the
1-prong sub-leading tau failing “loose” tau identification.

F Investigation of BDT input variables for
2-prong tau

The distribution comparison between Z/γ ∗ → τ τ signal and multi-jets background candidates in 3-prong
τhad (upper plots) and 2-prong τhad (bottom plots) cases are shown in Fig. F.1, Fig. F.2 and Fig. F.3.
(Detail of each variables are also described in Sec 4.5.3)

0.45

Events / 0.01

3-prong

0.2

Z/ γ *→τ τ

Multijet

3-prong

0.4
0.35
0.3

0.15

0.25

3-prong

0.2

0.2

0.05

0.6

0.8

1

1.2

0

0.02
1

2

3

TauJets centFrac(a)2-prong

0.25

5

6

10

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

TauJets etOverPtLeadTrk

TauJets innerTrkAvgDist

TauJets dRmax

(b)

(c)

Z/ γ *→τ τ

Multijet

Events / 0.5

Events / 0.06

Z/ γ *→τ τ

4

0.2

7

8

9

Z/ γ *→τ τ

Multijet

2-prong

0.3
0.25
0.2

(d)
Z/ γ *→τ τ

Multijet

2-prong

0.18
0.16
0.14

Multijet

2-prong

0.1

0.08

0.12

0.15

0.1

0.15

0.06

0.08

0.1
0.1
0.05

0.06

0.04

0.04

0.05

0.02
0
0

Events / 0.01

0.4

Events / 0.01

0.2

0.1

0.04

0.1
0.05

0
0

3-prong

0.12

0.06

0.1

0.15
0.05

Multijet

0.08

0.15

0.25
0.1

Z/ γ *→τ τ

Multijet

Events / 0.01

Z/ γ *→τ τ

Multijet

Events / 0.5

Events / 0.06

Z/ γ *→τ τ

0.25

0.2

0.4

0.6

0.8

1

1.2

TauJets centFrac

(e)

0

1

2

3

4

5

6

7

8

9

0.02

10

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

TauJets etOverPtLeadTrk

TauJets innerTrkAvgDist

(f )

(g)

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

TauJets dRmax(h)Figure F.1.: The Z/γ ∗ → τ τ signal versus multi-jets background candidates distribution of the BDT training
input variables for 3-prong τhad (2-prong τhad ) are shown in upper (bottom) plots. From left to right, it responds”central energy fraction”, ”leading track momentum fraction”, ”track radius” and ”maximum ∆R”.

144

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0.16
0.14
0.12
0.1
0.08

3-prong

0.35
0.3
0.25

1

2

3

4

5

6

7

8

9

0.1

0.05

0.05

TauJets trFlightPathSig

Events / 250 MeV

Events / 0.5

Z/ γ *→τ τ

Multijet

2-prong

0.2
0.18
0.16
0.14
0.12

−3

0.1

−2

−1

0

1

2

3

0

1

2

3

Z/ γ *→τ τ

Multijet

2-prong

0.25
0.2

4

5

6

7

8

9

10

TauJets EMPOverTrkSysP

TauJets ChPiEMEOverCaloEME

(c)

(d)
Z/ γ *→τ τ

Multijet

2-prong

0.4
0.35
0.3

Multijet

2-prong

0.25
0.2

0.25
0.15

0.15

0.2

0.1
0.08

0.4

0.2

(b)

Z/ γ *→τ τ

3-prong

0.3

TauJets massTrkSys [MeV]

(a)

0.15

0.1

0.06

0.1

0.1

0.04

0.05

0.05

0.05

0.02
0

0.3

Multijet

0.5

0.15

0
0 500 100015002000250030003500400045005000

10

0.35

0.1

Events / 0.3

0

0.4

0.2

0.15

0.02

3-prong

0.25
0.2

0.06
0.04

Z/ γ *→τ τ

Multijet

0.45

Events / 0.5

0.18

Z/ γ *→τ τ

Multijet

0.4

Events / 0.3

3-prong

Events / 0.5

Z/ γ *→τ τ

Multijet

Events / 250 MeV

Events / 0.5

Z/ γ *→τ τ

1

2

3

4

5

6

7

8

9

10

TauJets trFlightPathSig(e)00 500 100015002000250030003500400045005000

TauJets massTrkSys [MeV]

(f )

−3

−2

−1

0

1

2

3

TauJets ChPiEMEOverCaloEME

(g)

0

1

2

3

4

5

6

7

8

9

10

TauJets EMPOverTrkSysP(h)Figure F.2.: From left plot to right plot, it presents the distribution for ”transverse flight path significance”,”track mass”, ”fraction of EM energy from charged pions” and ”ratio of EM energy to track momentum”. The
distribution for 3-prong τhad and 2-prong τhad are shown in upper and bottom part, respectively.

146

Z/ γ *→τ τ

3-prong0.25
0.2

Z/ γ *→τ τ

Multijet

0.45

Events / 0.02

Multijet

Events / 0.2

Events / 250 MeV

Z/ γ *→τ τ

3-prong

0.4
0.35
0.3
0.25

0.15

Multijet

3-prong

1
10−1
10−2

0.2
0.1

10−3

0.15
0.1

0.05

10−4

0.05
0
0 500 100015002000250030003500400045005000

0

0.5

1

1.5

TauJets mEflowApprox [MeV]

3

3.5

4

4.5

10−5
0

5

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9(c)Z/ γ *→τ τ

2-prong

0.2
0.18
0.16
0.14

Z/ γ *→τ τ

Multijet

Events / 0.02

Multijet1

Reco Tau Flattened BDT Jet Score(b)

Events / 0.2

Events / 250 MeV

Z/ γ *→τ τ

2.5

TauJets ptRatioEflowApprox

(a)

0.22

2

2-prong

0.4
0.35
0.3

Multijet

2-prong

1
10−1

0.25

0.12
0.1

0.2

0.08

0.15

0.06

10−2
10−3

0.1
10−4

0.04
0.05

0.02
0
0 500 100015002000250030003500400045005000

TauJets mEflowApprox [MeV]

(d)

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

TauJets ptRatioEflowApprox(e)0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

1

Reco Tau Flattened BDT Jet Score(f )Figure F.3.: The Z/γ ∗ → τ τ signal versus multi-jets background candidates distribution of the BDT training
input variables for 3-prong τhad (2-prong τhad ) are shown in upper (bottom) plots. Left plot and middle plot
responds ”track-plus-EM-system mass” and ”ratio of track-plus-EM-system to pT ” respectively. Two rightest plots
F.3(c) and F.3(f) show the training BDT score for 3-prong τhad (upper) and 2-prong τhad (bottom).

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