学位論文

Search for Heavy Higgs Bosons Decaying toa Pair of τ Leptons in Proton-Proton Collisions√
at s = 13 TeV
(重心系
13TeV
粒子対 崩壊重陽子陽子衝突粒子 探索)

平成 28 年 12 月博士 (理学) 申請

東京大学理学系研究科
物理学専攻

森永 真央

Ph.D Thesis

Search for Heavy Higgs Bosons Decaying toa Pair of τ Leptons in Proton-Proton Collisions√
at s = 13 TeV

December 2016

Depertment of Physics, Faculty of Sience
The University of Tokyo

Masahiro Morinaga

Abstract
This thesis presents the search for the heavy Higgs bosons decaying into a pair of τ ’s at proton√
proton collisions with a center-of-mass energy s = 13 TeV at the Large Hadron Collider (LHC).
After the discovery of the new scalar boson with a mass of 125 GeV, several problems of the Standard Model still remain. An extended Higgs boson which expected from several physics beyond theStandard Model provides solutions for such given problems. The Minimal Supersymmetric Standard
Model (MSSM) is one of simplest extension of the Standard Model based on supersymmetry. The
Higgs bosons are extended into five physical particles h, H, A and H ± . The hMSSM scenario is recently developed and the new 125 GeV boson is treated as the neutral Higgs boson h, other neutral
H and A are heavier than 125 GeV. A decay mode of final state with a pair of τ -leptons has a largepart of branching fraction in possible decay modes. A search for such decay mode is most promisingexperimental content and one of the first priorities of experimental particle physics programs.
An integrated luminosities of 28 fb−1 is used in this thesis. This analysis is focused on the di-τ
events in final states characterised by one isolated high pT light lepton, one hadronically decaying
miss ) corresponding to three neutrinos from τ -lepton
τ -lepton and a large missing transverse energy (ETdecays.
The search covers following achievements: establishment of a data-driven way to model a background with mis-identified hadronic-τ objects, and an improvement of search sensitivity for wider
miss information. The background estimation method which developed inmass range by using the ET
this thesis improves understanding of the mis-identified hadronic-τ background. The analysis sensitmiss based analysis categorisation by 25-50% at heavy signal hypotheses.
ivity is imporved using the ET
Using the obtained samples, no obvious excess is observed and the exclusion limits for on the hMSSM
is set to tan β > 36.8 at mA = 1 TeV.

Acknowledgements
This thesis has been written with the help of my supervisor Prof. Shoji Asai at the University ofTokyo. During the four years of Ph.D I received great support fromDr. Junichi Tanaka, Dr. Yuji Enari, Dr. Takashi Yamanaka and Dr. Takuya Nobe.
I benefited from working in close collaboration with Dr. Nikolaos Rompotis and Dr. Lei Zhang.

Contents

1 Introduction

1

2 Theoretical Overview
2.1 The Standard Model of Particle Physics . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.1 The Higgs Mechanism in the Standard Model . . . . . . . . . . . . . . . . . . .
2.1.2 Unsolved Problem on Particle Physics . . . . . . . . . . . . . . . . . . . . . . .
2.2 Supersymmetry and The Minimal Supersymmetric Standard Model . . . . . . . . . . .
2.2.1 The Higgs Sector of the MSSM . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.2 MSSM Benchmark Scenarios . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3 Experimental Status of Heavy Higgs Bosons Searches . . . . . . . . . . . . . . . . . . .
2.3.1 Direct Searches for the Neutral MSSM Higgs Bosons . . . . . . . . . . . . . . .

3
3
4
4
5
6
7
9
9

3 Phenomenology of Proton-Proton Collisions
11
3.1 Simulation of Hadron Collisions and Calculation of Cross-Section . . . . . . . . . . . . 11
3.1.1 The Factorisation Theorem, Parton Distribution and Fragmentation Functions 12
3.1.2 Partonic Cross-Section and Event Generation . . . . . . . . . . . . . . . . . . . 13
3.1.3 The Partonic Process Simulation and Parton Shower Matching . . . . . . . . . 14
3.1.4 Hadronisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.1.5 Underlying Event and Multiple Parton Interaction . . . . . . . . . . . . . . . . 16
3.1.6 Pile-up Events Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.1.7 Detector Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.2 Phenomenology of Heavy Higgs Bosons . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.2.1 Production of Heavy Higgs bosons in Benchmark Scenario . . . . . . . . . . . . 17
3.2.2 Decay of Heavy Higgs bosons in Benchmark Scenario . . . . . . . . . . . . . . . 19
3.2.3 Experimental Search Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
4 The ATLAS Experiment at the LHC
22
4.1 The Large Hadron Collider . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
4.2 The ATLAS Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4.2.1 Coordinate System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
4.2.2 The Inner Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
4.2.3 The Calorimeter System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
4.2.4 The Muon Spectrometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
4.2.5 The Luminosity and Forward Detectors . . . . . . . . . . . . . . . . . . . . . . 29
4.2.6 The Trigger System and Data Acquisition System . . . . . . . . . . . . . . . . 29
4.3 Data Taking During LHC Run2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
5 Physics Object Reconstruction andParticle Identification
32
5.1 Tracks and Vertices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

iii

Contents

iv

5.2
5.3

34
35
35
36
38
38
39
40
40
40
41
43
44
44
45
46
47
47
49
49
50
51
52
53
56
61
61
63
64

5.4

5.5

5.6

5.7

Topological Clustering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Jets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3.1 Jet Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3.2 Jet Energy Calibration and Resolution . . . . . . . . . . . . . . . . . . . . . . .
5.3.3 Jet Flavour Identification and Pile-up Suppression . . . . . . . . . . . . . . . .
5.3.4 IP2D and IP3D: The Impact Parameter based Algorithm . . . . . . . . . . . .
5.3.5 Secondary Vertex Finding Algorithm : SV . . . . . . . . . . . . . . . . . . . . .
5.3.6 Decay Chain Multi-Vertex Algorithm : JetFitter . . . . . . . . . . . . . . . . .
5.3.7 Multivariate Algorithm : MV2 . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3.8 Tagging and Suppression of Pile-up Jets . . . . . . . . . . . . . . . . . . . . . .
Electrons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4.1 Electron Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4.2 Electron Energy Calibration and Resolution . . . . . . . . . . . . . . . . . . . .
5.4.3 Electron Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4.4 Electron Isolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4.5 Electron Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Muons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.5.1 Muon Reconstruction and Identification . . . . . . . . . . . . . . . . . . . . . .
5.5.2 Muon Momentum Calibration and Resolution . . . . . . . . . . . . . . . . . .
5.5.3 Muon Isolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.5.4 Muon Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Hadronic Tau Decays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.6.1 Hadronic-τ Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.6.2 Hadronic-τ Energy Calibration and Resolution . . . . . . . . . . . . . . . . . .
5.6.3 Hadronic-τ Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
miss ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Missing Transverse Energy (ETmiss
5.7.1 ET Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
miss Performance and Uncertainty . . . . . . . . . . . . . . . . . . . . . . . .
5.7.2 ETmiss Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.7.3 ET

6 Search for the MSSM Higgs Bosons in the τ` τhad Final State66
6.1 Experimental Signature of H/A → τ` τhad Decays . . . . . . . . . . . . . . . . . . . . . 66
6.1.1 Signal Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
6.1.2 Dominant Background Processes . . . . . . . . . . . . . . . . . . . . . . . . . . 67
6.1.3 mτ τ Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
6.2 Simulated Event Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
6.2.1 Signal Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
6.2.2 Backgrounds Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
6.3 Data Samples and Trigger Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
6.3.1 Trigger Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
miss Trigger Efficiency . . . . . . . . . . . . . . . . . . . . 71
6.3.2 Measurement of the ET
6.4 Event Selection and Categorisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
6.4.1 Object Definitions and Event Preselection . . . . . . . . . . . . . . . . . . . . . 72
6.4.2 Categorisation and Event Selection . . . . . . . . . . . . . . . . . . . . . . . . . 73
6.5 Backgrounds Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
6.5.1 Estimation of Background Events with Misidentified τhad Objects . . . . . . . . 75
6.5.2 Modelling Additional Background Processes . . . . . . . . . . . . . . . . . . . . 83
6.6 Systematic Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
6.6.1 Experimental Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

Contents

6.7

6.6.2 Theoretical Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

v
88
89

7 Statistical Analysis of the Searchfor H/A → τ` τhad Decays
95
7.1 The Profile Likelihood Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
7.2 Treatment of Systematic Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
7.2.1 Symmetrization and Smoothing . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
7.2.2 Pruning and Systematic Uncertainties Type . . . . . . . . . . . . . . . . . . . . 97
7.3 Hypothesis Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
7.3.1 The Test Statistic Distribution and p-values . . . . . . . . . . . . . . . . . . . . 99
7.3.2 Asymptotic Formulas and Asimov Data . . . . . . . . . . . . . . . . . . . . . . 100
7.4 Statistical Results and Interpretation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
7.4.1 Results on Null Hypothesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
7.4.2 Result on Model Independent Cross Section . . . . . . . . . . . . . . . . . . . 102
7.4.3 Result on Benchmark Scenario . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
7.4.4 Disscusion of Obtained Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
8 Conclusions

108

Auxiliary Material

111

Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
miss Trigger Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
AET
B
Validation of Event Selection Variables . . . . . . . . . . . . . . . . . . . . . . . 112
C
Plots of Control Regions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
D
Definition of Experimental Systematic Uncertainties . . . . . . . . . . . . . . . 124
E
Variation of Systematic Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . 124
F
Theoretical Systematic Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . 130
G
Validation of Maximum Likelihood Fit . . . . . . . . . . . . . . . . . . . . . . . 131
H
Plots for the Post-Fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

1 Introduction

To get and understand insight into the constitutions of matter and their interactions are one of theoldest questions in fundamental science. There are three forces in the elementary particle physics,
the weak, electromagnetic and strong force. A unified theoretical explanation of the electromagnetic
and weak interactions was established by Glashow, Salam and Weinberg. They introduced the gauge
symmetry which forms the core of the theoretical foundation for the description of the structure of theStandard Model. The Standard Model (SM) is the modern description of elementary particles andinteractions together with a model of the strong interaction. A consistent quantum theory with thegravity has not yet established. The Standard Model describes particle interactions very accurately
for the last 40 years. The missing part in the Standard Model was the Higgs boson, which have been
discovered in July 2012.
In spite of the success of the Standard Model in describing many experimental results, the Higgs
boson mass is subject to large radiative corrections. It means a huge difference between the Higgs
mass parameter and the measured Higgs boson mass mH ' 125 GeV. Without further explanationof this, we have to accept unnatural difference. Furthermore the Standard Model does not provide aparticle that could make up dark matter which was established by the WMAP and Planck satellite
missions.
In order to address these problems, the Standard Model need to be extended. Supersymmetry is asymmetry between bosons and fermions. A superpartner is introduced for every SM particle with half
integer different spin. Two-Higgs-doublets which produce five physical Higgs bosons are introducedin the Minimal Supersymmetric Standard Model (MSSM). The five physical state consists of threeelectrically neutral Higgs bosons and two electrically charged Higgs bosons. Three neutral Higgs
bosons have different state of CP-even h and H, CP-odd A, while the two charged Higgs are same
quantum state with electrically different charge H ± . The decays of H/A into down-type fermions isenhanced and the τ τ decay mode provides a particular sensitivity to the MSSM models.
Energy of colliding particles is crucial to prove a new physics beyond the Standard Model (BSM).
√
Large Hadron Collider (LHC) was operated with a center-mass-energy s = 7 TeV in first physics run√
2011. A center-mass-energy was increased up to s = 8 TeV after the first year run and discovered
the Higgs boson in 2012. The Standard Model was tested with recorded data and also several searches
for BSM physics were performed. From 2013 to 2014, the LHC have been upgraded its proton beam√energy up to 6.5 TeV. The LHC has started again with a center-mass-energy of s = 13 TeV from√2015 spring. New particles expected from the BSM are produced at higher rates in s = 13 TeV.
There are four large detectors within the LHC proton ling. Two general purpose experiments
ATLAS1 and CMS2 perform searches for new physics and measurements of the SM particle properties.
The LHC provided the integrated luminosities of up to 3.3 fb−1 in 2015 data-taking and 24.7 fb−1
until August 2016 data-taking periods at the ATLAS detector.
1
2

A Toroidal LHC ApparatuS
Compact Muon Solenoid1

2
In this thesis a search for the neutral Higgs bosons A and H in the decay mode of H/A →τ τ → τ` τhad is performed, where τhad and τ` denotes a tau lepton hadronically and laconically decay
respectively. The search is based on recorded data with the ATLAS detector during 2015 to 2016
summer technical shutdown. The τ` τhad decay channel includes approximately 45% of all events in
the H/A → τ τ mode. The search with τ` τhad chanel is clean and simple compared to other two decay
channels. As a trigger is important component of the experiments at the LHC, the τ` τhad channel
has one electron and muon which gives clear signature in terms of triggering. Electron and muon can
suppress background events from the QCD multijets process which is largest part of interactions in
miss )
proton-proton collisions. The τ` τhad channel tends to have larger transverse missing energy (ETwhich is made up from three neutrinos produced in di-τ decays. A new analysis strategy focused on
events with a large transverse missing energy are introduced and it significantly improves experimental
sensitivity. In addition, a method to estimate background events containing mimicking τhad is newly
developed and performed.
A brief review of the Standard Model is given together with an introduction to the concepts ofsupersymmetry focused on the MSSM in Chapter 2. An overview of the method used to calculate event
rates and differential distributions for several physics production processes including backgrounds andsignal processes is described in this chapter. In addition, a short review of a benchmark signal model isalso given. The LHC and the ATLAS experiment are described in Chapter 4. The reconstruction andidentification procedures of particle objects and event kinematics based on output from the ATLAS
detector is given in Chapter 5. Details of the search for heavy Higgs bosons decaying into a pair of τ
leptons is given in Chapter 6. An experimental signatures of heavy Higgs bosons production and decay
is described. Event selection criteria and event categorisations to separate signal from background
events is also given. Estimating background process of a mis-identified τhad play an important role inthe search, detailed description is also given in Chapter 6 including other background processes. The
statistical methods used to interpret results of the analysis and its results is presented in Chapter 7.

2 Theoretical Overview

The theoretical concepts relevant for this search are introduced in this chapter. A brief overview of theStandard Model is given in Section 2.1 based on reference [1]. Among the extension of the Standard
Model, the Minimal Supersymmetric Standard Model (MSSM) is most promising. The MSSM is
introduced in Section 2.2 with emphasis on the Higgs boson sector based on reference [2, 3]. A briefsummary of the search for the neutral MSSM Higgs boson is given in Section 2.3. Phenomenology ofthe heavy Higgs bosons are described in Chapter 3.

2.1

The Standard Model of Particle Physics

The Standard Model (SM) is the established theoretical framework that describes properties of
elementary particles and their interactions. The Standard Model was developed in 20th century,
and was confirmed by the discovery of W ± and Z bosons in 1983. In addition, the SM predicts theexistence of a Higgs boson. In 2012 a new boson was found by the ATLAS1 and CMS2 experiments [4,5]. A new boson seems to be consistent with the SM Higgs boson A general description of the SM isbased on reference [6]. A brief overview is given below.
Interactions between particles can be associated with three forces, the electromagnetic, weak andstrong force. The gravitational interaction is not described by the Standard Model. The effects of thegravitational force can usually be neglected in particle physics. The model is based on the gauge symmetry assumption in SU(2)L × SU(3)C × U(1)Y group which has 12 generators and gauge field. The
electromagnetic and weak interactions [7–9] are described by the SU(2)L × U(1)Y symmetry group,
while SU(3)C is the group of the strong colour forces of Quantum Chromodynamics (QCD) [10].
Eight gluons are associated to the SU(3)C colour group, while four gauge bosons, W ± , Z and γ, areassociated to the electroweak symmetry SU(2)L × U(1)Y . Gluons and photons are massless while theremaining weak gauge bosons have mass. The spontaneous symmetry breaking [11–14] give a mass tothese gauge bosons without spoiling the electroweak gauge symmetry. An additional complex scalar
field is required and lead up to a new scalar particle, the Higgs boson, which interacts with particles
with a strength proportional to their masses.
Quarks are subject to all three SM interactions. Each quark flavour is a colour triplet and carries
electroweak charge including electric charges of +2/3 and -1/3 for up-type and down-type quarks
respectively. Leptons are colourless but have electroweak charges. Electrons, muons and τ leptons
carry unit electric charge -1, while the associated neutrinos νe , νµ and ντ are electrically neutral.
The respective anti-leptons carry opposite sign electric charge. Quarks and leptons group in three
generations with equal charge quantum numbers but different masses. If the type of the charge is not
1
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A Toroidal LHC ApparatuS
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4

explicitly specified, charge refers to the electric charge.

2.1.1

The Higgs Mechanism in the Standard ModelAll fermions have masses, and the W ± and Z are massive and masses of
mW ± = 80.385 ± 0.015 GeV

mZ = 91.1876 ± 0.0021 GeV

(2.1)
(2.2)

have been measured [15], while photon is massless. The neutrino flavour oscillations strongly predicts
neutrinos are massive.
Masses can be generated with the spontaneous symmetry breaking of a gauge symmetry. The Higgs
mechanism introduces a SU(2) doublet. The Higgs potential
V (φ) = µ2 φ† φ + λ(φ† φ)2(2.3)

where φ = (φ1 , φ2 )T , and φ1 and φ2 is a complex scalar field, µ is a mass parameter. A self coupling
parameter λ is invariant under SU(2)L × U(1)Y symmetry transformations. A SU(2) doublet is
assigned weak hypercharge Y = +1.
For µ2 < 0 and λ > 0 the potential of the Higgs field V , has minimum at
r
−µ2
µ4
v4
, with values V (φ0 ) = −
= −λ
(2.4)
v = |φ0 | =2λ4λ
4When the neutral complex scalar field φ has non-zero for vaccum expectation, the SU(2)L × U(1)Ysymmetry is spontaneously broken with the electromagnetic gauge symmetry U(1)EM remaining
as a symmetry of the ground state. Three degrees of freedom of the scalar field are absorbed as
longtitudinal polarisation states of the W ± and Z bosons, which in this way acquire their masses,
while photon remains massless. The remaining degree of freedom corresponds to a physical scalarparticle, i.e. the Higgs boson. The masses of the fermions can be generated via so-called, the Yukawa
interaction term [16].

2.1.2

Unsolved Problem on Particle Physics

In the last decades the SM has been proven by amount of experiments and has widely accepted.
However, there are some experimetal aspects that cannot be explained by the SM which is usuallyreferred to as physics beyond the Standard Model (BSM). A overview of unsolved problems are briefly
reviewed in following.
Dark Matter and Dark Energy
The WMAP [17] and Plank [18] satellite have measured the spectrum of the cosmic microwave
background (CMB). The CMB is the radiation from the period of recombination when temperture
dropped to below the hydrogen ionisation temperture. The multipole spectrum is fitted by a sixparameter cosmological model, ΛCDM [19]. The results of a fit with the model predicts that thefraction of baryonic matter contributes only 4.9% to the total matter and energy distribution. Dark
matter and dark energy contributes 68.3% and 26.8% respectively. The Standard Model cannot
provide an explanation for dark energy or a candidate particle for dark matter.
Baryon Asymmetry and CP violation
Universe seems to be completely dominated by matter, Sakharov’s three conditions [20] need to be
filled. One of three conditions requires baryon number violation, which is absent from perturbative

2.2. Supersymmetry and The Minimal Supersymmetric Standard Model5

descriptions of the Standard Model. The baryon number is conserved in the Standard Model. CP
violation which is induced from the CKM matrix is too small to explain the baryon number asymmetry
within the Standard Model framework. In order to explain this a further source of CP violation form
the physics beyond the Standard Model is necessary.
Neutrino Masses
When neutrinos have mass, it can oscillate between three flavour eignestates. Th first hint of
neutrino flavour oscillation was the solar neutrino problem(νe ) [21, 22]. The anti-neutrinos fromreactors ν̄e [23] and atmospheric (anti-) neutrinos νµ , ν̄µ [24] were observed disapperance effects as thesame as ν3 . Experiments of appearance of ντ [25] observed the oscillations as well, which uses beams ofneutrinos created in their muonic interaction state. The neutrino oscillation predicted by extensions of
the Standard Model in which neutrinos are massive particles. The oscillation probabilities P (ν` → ν`0 )depends on the mass difference between two neutrnis states ∆m2`,`0 and the ratio between the distanceand energy L/2E of the system. The fit of the experimental data imply|∆m221 | ' 7.5 × 10−5 eV2 ,|∆m231 | ' 2.5 × 10−3 eV2 ,|∆m221 |/|∆m231 | ' 0.03.

(2.5)
(2.6)
(2.7)

Hierarchy and Fine-tuning Problem
The bare mass parameter for the Higgs boson is corrected by loop contributions to obtain theobserved mass due to the renormalisation procedure. The loop contributoions are proportional toΛ2UV , where ΛUV is the ultraviolet momentum cut-off scale. As the contributions to the source ofHiggs boson mass after the renormalisation from fermion - anti-fermion loops are O(30) of magnitudelarger than the observed Higgs boson mass. Therefore, the bare mass has to be fine-tuned to cancelout between the fundamental and quantum corrections. Hierarchy problem problems are connected
to fine-tuning and problem of naturalness.
Above many extensions of the Standard Model, supersymmetry is theoretically favoured as itprovides natural solutions to problems on the Standard Model. Supersymmetry can solve the hierarchy problem, provide a stable dark matter candidate and predict unification of the three SM gauge
couplings at the GUT scale.

2.2

Supersymmetry and The Minimal Supersymmetric Standard Model

Supersymmetry (SUSY) [26–28] is a symmetry that relates bosons and fermions. An overview ofthe Minimal Supersymmetric Standard Model (MSSM) is given based on References [2, 29].
One superpartner has to be introduced for every Standard Model particle. The superpartner of theboson states are the Winos, Bino, gluinos and the Higgsinos. The superpartner of fermions are calledsquarks and sleptons for quarks and leptons respectively. All supersymmetric particles are referred toas sparticles, the superpartners of the gauge bosons are referred to as gauginos. The SUSY generators
Q transform fermions into bosons and vice versa :Q |Fermioni = |Bosoni , Q |Bosoni = |Fermioni ,(2.8)

2.2. Supersymmetry and The Minimal Supersymmetric Standard Model

2.2.1

6

The Higgs Sector of the MSSM

An overview of the MSSM Higgs sector is given based on Reference [30] in this section. The
MSSM requires the complex Higgs doublets Hu and Hd to provide masses for up-type and down-type
fermions via the spontaneous breaking of the SU(2)L × U(1)Y gauge symmetry. Two complex Higgs
doublets implies the existence of five Higgs bosons, i.e. two charged Higgs bosons, H ± , and threeneutral Higgs bosons: a CP-odd (pseudoscalar) state A, and two CP-even (scalar) states, h and H,
with mh < mH . The masses of these five Higgs bosons and their mixing can be written by the gaugeboson masses mW and mZ with two additional parameters, the pseudoscalar mass mA and the ratioof the vacuum expectation values of the neutral components of the two Higgs doublets tan β,tan β =

hHu0 i
vu
= ,
0
vd
hHd i

(2.9)

where vu and vd need to be satisfied (vu2 + vd2 )1/2 ∼ 246 GeV. The tree-level mass of charged Higgs
states is given by m2H ± = m2A + m2W , the mass matrix for the neutral CP-even states is given by
M2tree =

m2A sin2 β + m2Z cos2 β −(m2A + m2Z ) sin β cos β−(m2A + m2Z ) sin β cos β m2A cos2 β + m2Z sin2 β(2.10)

This matrix is diagonalized by an angle α, and the mass eigenvalues are given by :−(m2A + m2Z ) sin 2βq.
(m2Z − m2A ) cos 2β + (m2A + m2Z )2 − 4m2A m2Z cos2 2β


q
1
2
2
2
2
2
2
2
2
2
mh,H =
mA + mZ ∓ (mA + mZ ) − 4mA mZ cos 2β .
2tan α =

(2.11)(2.12)The role of the SM Higgs boson is shared between the scalars h and H in the MSSM. The relative
coupling to the corresponding SM of the neutral scalars to pairs of massive vector bosons and fermions
are summarised in Table 2.1

H
h
A

gV V

guu

gdd,``cos(β − α)sin(β − α)0sin α/ sin β
cos α/ sin β
cot β tan β

cos α/ cos β− sin α/ cos β

Table 2.1: The relative coupling to massive boson pairs and the SM fermions to the SM couplings. In
addition to these couplings, there are non-SM couplings of the neutral scalars to ZA and to W ± H ∓ . Theseare proportional to cos(β − α) for h and to sin(β − α) for H. The ZAA coupling vanishes and the W ± H ∓ A
coupling does not depends on α or β.

The decoupling limit
Figure 2.1 shows the tree-level mass of mH , mh and mH ± as a function of mA . The mixing angle
in the CP-even sector can be simplified as α ∼ β − π/2 in the decoupling limit (mA > mZ ). As
a consequence of the decoupling limit, the masses of the neutral scalar h becomes approximately
constant value, mh ∼ mZ | cos β|, and its coupling become similar to the SM Higgs boson. The massesof H and H ± are approximately degenerated with mA , the coupling of H to the massive gauge bosons
vanish and to up-type (down-type) SM fermions are also suppressed (enhanced) for higher tan β. A

Higgs mass [GeV]

2.2. Supersymmetry and The Minimal Supersymmetric Standard Model

400
300
200

H (tanβ =3)H (tanβ =5)H (tanβ =10)
H±

7

Figure 2.1: Tree-level values masses of
the charged scalar, mH ± and of the neutral scalars mH and mh as a function of
the pseudoscalar mass mA . Orange (blue)
curves are for the H and h respectively.

h (tanβ =3)h (tanβ =5)h (tanβ =10)

125
90

40
50

90

125

200

mA [GeV]

300 400

heavy and mass-degenerate multiplet (H, A, H ± ) with vanishing couplings to massive gauge bosons
is shown in this limit.
The Radiative Corrections
Tree-level masses of the MSSM Higgs bosons are affected by the radiative corrections. Loops of
top quark and top squarks (stops) are dominant contributions to the lightest-scalar mass. In thedecoupling limit it takes the approximated form

m2SUSY
Xt2
Xt4
3m4t
2
+ 2
−
,
(2.13)∆mh ∼ 2 2 log
2π v
m2t
mSUSY
12m4SUSY
where mSUSY = (mt̃1 mt̃2 )1/2 is an average scale for the stop mass, and Xt = At − µ cot β is the stop
mixing term, where At is the soft SUSY-breaking Higgs-stop coupling and µ is the higgsino mass
parameter. The one-loop top/stop√ contributions can be maximised if mSUSY is large and for the
maximal mixing condition |Xt | = 6mSUSY . A smaller negative contribution from sbottom loops canbe relevant for only large tan β. Full one-loop calculation of the MSSM Higgs mass is available withpartial two-loop corrections and the leading three-loop corrections.

2.2.2

MSSM Benchmark Scenarios

Several constraints on the parameter space of the MSSM can be taken into account after the LHC
Run1 :• The discovery of a scalar particle with a mass of 125.09 ± 0.24 GeV [31–33].
• Measured values of couplings are consistent with the predictions for the SM Higgs boson withaccuracy of ± ∼ 20% [34, 35].
• No observation of additional neutral or charged Higgs bosons n direct searches [36–39].
• No observation of SUSY particles.
The Higgs boson that have been discovered in the LHC is interpreted a the lightest neutral scalar h in
the MSSM. The lightest scalar mass is usually treated as a constraint on unknown SUSY parameters,with mh = 125 ± 3 GeV. ±3 GeV variation corresponds to theoretical uncertainty of the MSSM
prediction for mh due to unknown effects of higher-order corrections [40, 41].

2.2. Supersymmetry and The Minimal Supersymmetric Standard Model

8

Tree-level mass of h is constrained the bound mh < mZ , so that the mSUSY which is around∼ 1 TeV need to reproduce the observed mh in the case of tan β & 10 and the decoupling region ofmA . A few TeV stop masses are necessary for smaller Xt . A strong constraint has been obtained bydirect searches by ATLAS and CMS in the (mA , tan β) plane.
The heavy Higgs bosons are not yet excluded by direct searches at the LHC where mA are less than
200 GeV in the case of low tan β. The heavy Higgs bosons whose mass is lighter than 200 GeV has
not been excluded for low tan β case. Decay modes of H → W W, H → ZZ, H → hh and A → Zh
still have significant branching fraction in the lower-tan β region, especially below the threshold for
decaying to a top-quark pair.
The hMSSM Approach
Lower tan β case implies a lower tree-level mass of h, and require larger mSUSY with the radiative
corrections to satisfy the mass constraint (mh = 125 ± 3 GeV). The hMSSM approach [42–44] isthe phenomenological approach under assumptions with treating mh as input for the calculation of
the radiative corrections and used to predict masses and couplings of the remaining MSSM Higgs
bosons. The Higgs sector of the MSSM is described in terms of the parameters entering the treelevel expressions for masses and mixing with the experimental mh value. The hMSSM approach canbe considered as model independent, because the predictions for the MSSM Higgs bosons does notdepend on details of the un-observed SUSY sector. The mass matrix for the neutral CP-even states
can be expanded by∆M211 ∆M212,(2.14)
M2 = M2tree +∆M212 ∆M222
where the tree-level matrix M2tree is given by Eq. 2.10 and ∆M2ij (i, j = 1 or 2) are the radiative
corrections. The hMSSM approach is based on the following assumptions• The observed Higgs boson is the light-scalar h.
• Only the element ∆M222 , which contains the leading logarithmic terms from top-stop loops,
needs to be taken into account.
• All SUSY particles are heavy enough to escape detection at the LHC, and it can be neglected
for the Higgs sector.
With these assumptions ∆M222 can be calculated by inverting the relation in Eq. 2.14 as∆M222 =

m2h (m2A + m2Z − m2h ) − m2A m2Z cos2 2β.
m2Z cos2 β + m2A sin2 β − m2h(2.15)The heavy-scalar mass and the mixing angle can also be written asm2H =tan α =

(m2A + m2Z − m2h )(m2Z cos2 β + m2A sin2 β) − m2A m2Z cos2 2β,
m2Z cos2 β + m2A sin2 β − m2h(m2A + m2Z ) cos β sin β.
m2Z cos2 β + m2A sin2 β − m2h(2.16)(2.17)The mass of the charged Higgs scalar coincides with the tree-level value, i.e. mH ± = m2A + m2W inthis approach.
The production cross sections and the decay branching fractions of all the MSSM Higgs bosons
depend on only mA and tan β for a fixed mh , under the assumptions that characterise the hMSSM.

2.3. Experimental Status of Heavy Higgs Bosons Searches

9

There is a minimum value of mA (mminA ) which it is not possible to reproduce the desired mh with2
only a correction to M22 for any given value of tan β. For large tan β case, it has mmin
∼ mh ,
A
2 − m2 )1/2 . It is
while for the low tan β case the minimum value of mA increases up to mmin
=
(m
A
Z
h
discussed about the validity of the assumption of neglecting M211 and M212 on References [43, 44].
The dominant contributions from top-stop loops shows that the M211 and M212 are proportional topowers of the ratio term µXt /m2SUSY . mSUSY is a few TeVin the hMSSM scenarios, the full one-loop
and the known two-loop contributions does not changed this assumption. A numerical comparison
between the predictions for mH and α obtained from the codes SuSpect [45] and FeynHiggs [40,
46–49] and the hMSSM approximations in References [43, 44]. A comparison with the EFT havebeen also studied in Reference [30].

2.3

Experimental Status of Heavy Higgs Bosons Searches

Searches for the heavy Higgs bosons with 2HDMs and MSSM are reviewed. Direct searches using
collider have been tested by several experiments. A brief review of direct searches at LEP, Tevatronand LHC are described.

2.3.1

Direct Searches for the Neutral MSSM Higgs Bosons

Direct searches have been performed at LEP, Tevatron and LHC. Figure 2.2 shows a summary

tanβ

100
70
50
30
20
mhmax (µ >0) scenario

10

Figure 2.2: Observed exclusion limits at the
95% confidence level for the mmax
benchmarkhscenarios on (mA, tan β) plane with four independent search results from LEP, DØ, ATLAS and CMS (taken from Reference [37, 50,
51] and [36] respectively).

ATLAS(φ→ττ)
CMS(φ→ττ)
LEP(φ→ττ,bb̄)

45

DØ(φ→ττ)

2
1
90

125

200

300 400 500 700 1000

mA [GeV]

for the searches. Several exclusion limits has been set by φ → τ τ and φ → bb̄ decay modes. TheDØ result was performed by φ → τ τ, bb̄ with integrated luminosities of 5.2-7.3 fb−1 . The results of√
the ATLAS and CMS collaboration have obtained by Run1 with s = 7, 8 TeV using integrated
luminosities of 19.5-20.3 fb−1 and 24.6 fb−1 respectively. Before the discovery of SM Higgs boson at
mh ∼ 125 GeV, the mmax
scenario was used for a benchmark to search for the MSSM Higgs bosons.
hSearches for the Neutral MSSM Higgs Bosons at LEP
Direct searches for the neutral heavy Higgs bosons were performed by the LEP experiments,
ALEPH, DELPHI, L3 and OPAL [50]. LEP was electron-positron collider, so that the experimental
signature was e− e+ → hZ mode. There are two Higgs boson decay modes of bb̄ and τ − τ + with
Z boson decaying to q q̄, ν ν̄, e− e+ , µ− µ+ , τ − τ + and q q̄, ν ν̄, τ − τ + respectively. The region filled withgreen in Figure 2.2 shows the 95% confidence level exclusion limits on the (mA , tan β) plane.

2.3. Experimental Status of Heavy Higgs Bosons Searches

10

Searches for the Neutral MSSM Higgs Bosons at the Tevatron
The neutral MSSM Higgs bosons have been searched by the CDF and DØ collaborations withs = 1.96 TeV. A combined result by the CDF and DØ were reported in Reference [52], but the DØcollaboration has updated results in Reference [51] as shown in Figure 2.2. They searched φ → τ τ andφ → bb̄ decay modes for the mmax
with µ > 0 scenario using integrated luminosities of 5.2-7.3 fb−1 .
hThey considered only τµ τhad decay channel as a final state. In addition to an algorithm of tagging
hadronic τ -lepton decay products, b-quarks are also identified using the b-jet tagging technique. This
leads analysis sensitivity even better at high-tan β region which enhance b-quark couplings. This
technique have been also used in experiments in LHC.
√

Searches for the Neutral MSSM Higgs Bosons at the LHC
Since a center-of-mass energy of LHC is highest among above collider , the production cross sectionof the heavy Higgs bosons are highest. The analysis sensitivity for the heavy Higgs bosons have beensignificantly improved at high-tan β region even wider mA range. In Figure 2.2, gray (ATLAS [37])and blue (CMS [36]) region presents the observed exclusion limits at the 95% confidence level for√mmax(µ > 0) scenario using φ → τ τ decay mode with s = 7, 8 TeV. Reconstruction techniquehof an invariant mass of di-τ system have been developed at searches for the SM Higgs boson at theTevatron [53]. This technique improved a mτ τ resolution typically 20-30% at mh ∼ 125 GeV. Results
at both experiments used three decay channels (τ` τ` , τ` τhad , τhad τhad ) and the b-jet tagging to identify
the bottom annihilation production process. Besides φ → τ τ decay mode, several other decay mode
like H → V V have been also developed [54] can be seen in Figure 3.11. As discussed in Section 3.2.3
φ → τ τ decay mode is most important experimental searches.

3 Phenomenology of Proton-Proton Collisions

The Lagrangian of the Standard Model or MSSM are not directly observable. The process of deriving
physical observable, like the interaction rate for given physical process, and the simulation of hadroncollisions are evaluated by the Monte Carlo simulation. A review of the simulation of such physics
process is given in Section 3.1 based on References [55–57] Phenomenology of heavy Higgs bosons
production and decay are briefly described in Section 3.2 based on reference [58].

3.1

Simulation of Hadron Collisions and Calculation of Cross-Section

Number of
R some physics processes, Nint , is determined by the cross-section σ, and the integrated
luminosity Ldt. An instantaneous luminosity L is given approximately by :Z
f N1 N2
Nint = σ Ldt, L =,(3.1)
2πΣx Σywhere f is the frequency of collision, N1 and N2 are the number of protons per bunch for both beam,
Σx and Σy are the horizontal and vertical convoluted beam width [59] under the assumption of a
Gaussian density profile of beam. The integrated luminosity depends on the machine parameters andthe length of the data-taking only, but the cross-section for hard scattering events are independent
on the machine parameters.
Figure 3.1 shows a schematic overview of a proton-proton collision.

underlying event

protonx1

Fragmentation→2

f (x1 , Q )proton

FSR→

ISR→

x2

jet

Hard Scatterjet2

f (x2 , Q )jetFigure 3.1: Illustration of the perturbative and non-perturbative subprocesses for the simulation of hadroncollisions. The momentum of two initial state partons are described by the
PDFs, the hard scatter event is described by a matrix element calculated
perturbation theory followed by phenomenological models for soft QCD effects as parton showering and hadronisation (fragmentation).

jetPhenomenological models of non-perturbative effects must interplay with theoretical predictions for11

3.1. Simulation of Hadron Collisions and Calculation of Cross-Section

12

the hard scattering process. The remnants of proton-proton collision undergo a series of low-energy
interactions, denoted as underlying event. The initial and final state particles at the hard scattercarry colour and electric charge. Additional interactions, denoted as the initial (ISR) state radiationand final state radiation (FSR) can happen. A jet consists of a narrow cone of the colour neutral
hadrons which is hadronised from the colour charged final-state partons The instrumental detector
effects should be accounted to compare experimental data with theoretical predictions. A detailed
detector simulation including accurately models the particle matter interaction in the sub-detectorsof ATLAS. A brief review of the chain of various methods to simulate of proton-proton collisions is
described in following sub-sections.

3.1.1

The Factorisation Theorem, Parton Distribution and Fragmentation Functions

It is impossible to calculate the cross-section of hard-process directly from proton-proton collision,
since low-energy QCD effects govern the parton structure. While it is possible to factorise the effects
that can be described by perturbation theory from non-perturbative low-energy effects.
The factorisation theorem make it possible to approximately calculate from the convolution of alow-energy, long-range function and a high-energy, short-range function. This scale is called as thefactorisation scale µF that is used to distinguish low- and high-energy effects. Details of factorisation theorem can be found in Reference [60]. The factorisation scale is not a physical parameter,
so that it is not expected that the physical value of an observable depends on the factorisation
scale. It is conventionally checked a variation of varying it with a certain range and its variation istreated as a systematic uncertainty. The factorisation scale is employed for the parton distributionfunctions (PDF) and the process of hadronisation described in Section 3.1.4.
Quarks and gluons, i.e. partons, can be treated as the point-like constituents of hadrons. According
to the factorisation theorem the differential cross-section for a physical observable O in a collision of
hadrons h1,2 can be written as
X
dσ
=
dO
a,b

Z 1

Z 1
dxa

0

dxb
0

X
F

dΦF fah1 (xa , µF )fbh2 (xa , µF )dσ̂ab→FdÔDF Ô → O, µF ,(3.2)

where a and b in the outer sum runs over all partonic constituents of a hadrons h1 and h2 . The
inner sum includes all possible final states of F in the processes ab → F with phase space ΦF . The
functions fah1 (xa , µF ) and fah2 (xb , µF ) are the non-perturbative parton distribution functions. σ̂ isthe perturbative partonic cross-section and DF (Ô → O, µF ) is a non-perturbative fragmentation
function, which describes the transition from the quantity Ô based on the partons from final state
F to the observable O. The parton distribution function fah1 (xa , µF ) implies the probability to finda parton of type a with a fraction of momentum to original hadron h1 momentum, xa . The valueof the parton distribution and the fragmentation function at a scale Q02 can be achieved from thevalue at Q2 , where Q denotes an energy scale of the hard interaction. This evolution is describedby the Dokshitzer–Gribov–Lipatov–Altarelli–Parisi (DGLAP) evolution equations [62–64]. Since theparton distribution functions cannot be calculated in the perturbative QCD, so that it needs to be
extracted from an experimental data, mainly from deep inelastic scattering experiments. Several
collaborations have performed combined fits to dataset, with small differences in the exact choiceof input data and the chosen parameterization of the parton-density functions. The following sets
recently provide results: PDF4LHC [65], NNPDF [66], CT14 [67], MSTW [61] and AZNLO [68]. The
major uncertainties on the PDF fits are experimental uncertainties of the input data, uncertainties
on the strong coupling αS and the functional form used as parameterization. Figure 3.2 shows theparton density as a function of x as provided by the MSTW2008 PDF set and its uncertainty at two
different momentum transfer scales.

xf(x,Q2 )3.1. Simulation of Hadron Collisions and Calculation of Cross-Section

1.6
c,c̄
u
1.4
ū
s,s̄
1.2
d
b,b̄
d̄
g
1.0
0.8
0.6
0.4
0.2
0.0 -4 -3 -2 -1 -4 -3 -2 -1
10 10 10 10 10 10 10 10 100

x

3.1.2

13

Figure 3.2: MSTW 2008 parton distribution functions at Q2 = 10 GeV2 (left) andQ2 = 104 GeV2 (right) with 68% confidence level uncertainty bands. The productsof the proton momentum fraction of quarks
or gluon, x, and the parton distributionfunction f (x, Q2 ) are shown. The parton
distribution function for gluons are scaled
down by a factor of 10 (made from References [61]).

x

Partonic Cross-Section and Event Generation

When the energy scale of the hard scatter is large enough to allow for a perturbative treatment
of QCD, the partonic differential cross-section for an inclusive production of a final state F can be
expanded in powers of the strong coupling constants:
dσab→F
dÔ

Z
=

2 
∞ Z
∞
 X

X
l
dΦF |MF | δ Ô − Ô(ΦF ) =dΦF +kMF +k δ Ô − Ô(ΦF ) ,
2



k=0

(3.3)

l=0

where MF is the matrix element for the production of the final state F with phase space ΦF . The
matrix element is perturbatively expanded in αS . The sum over k runs over additional partons in
the final state, which are real emissions from QCD interactions. The sum over l runs over virtual
corrections, which are loops from QCD interactions.
MlF +k is the matrix element for the final state F with real emissions k, loops l and phase spaceΦF +k . If the sum includes only the term for k = 0, l = 0, the result is the leading order of αS
approximation (conventionally called as LO), for k = n, l = 0 the result is the leading order of αS
approximation for F + n jets if all real emissions are quarks or gluons (LO). Finally in the case of
k + l ≤ n, the result is Nn−1 LO approximation. The processes used for the matrix element can becalculated by the Feynman rules. Practical calculations can be also additionally included the Feynman
diagrams with the leading logarithmic divergences (LL) of a higher order. A detailed explanation of
the Feynman rules can be found in References [6, 55].
If observable O is calculated at fixed order in αS with perturbation theory, it is still possible thatthe result is divergent due to loop effects. It is not possible to calculate all orders in the perturbation
theory, the divergences are removed by normalising the theory.
In the renormalization, the charges, masses and fields in the Lagrangian ( bare quantities) are
replaced by observable quantities that formally include divergences. This divergences would cancelout with loop-induced divergences of the bare quantities, so that the observable quantities are finite.
An unnatural scale µR is introduced, which is similar to the factorisation scale in the renormalization
theorem. It is also conventionally varied and a variation of results is used to be as a systematic
uncertainty. A detailed overview of the renormalization can be found in Reference [6].
It is important to understand effects of detector’s acceptance and experimental efficiency. A measurement of differential distributions is necessary to compare a multi-dimensional phase space of experimental data and theoretical estimation. Monte Carlo Event Generators perform the numericalintegrations and generate sets of four-momentum of the final state particles.

3.1. Simulation of Hadron Collisions and Calculation of Cross-Section

3.1.3

14

The Partonic Process Simulation and Parton Shower Matching

The initial state partons for the hard process (F ) are chosen by the parton distribution functions.
The final state partons and the corresponding four-momenta are produced with probability density
functions that are proportional to the differential cross-sections based on fixed-order calculations. For
the final state F +n jets, the additional partons are required to have a minimum transverse momentum
pT and minimum angular separation ∆R, so that soft and collinear divergences are avoided in the
NLO generators calculation. Other partons are generated by the parton shower algorithm. The
parton shower algorithms are complementary to the simulation of partonic process. All orders of
perturbative calculation are included in the parton shower algorithm to avoid the divergences, which
is based on the resummation of the leading collinear and soft logarithms. A relation of the differential
cross-section for ax final state with n partons and the differential cross-section of a final state withn + 1 partons are also built by the parton shower algorithm :dσn+1 = σnX αS dθ2
i→jk

2π θ2

dzPi→jk (z, φ)dφ,(3.4)

where z is the energy fraction between a parton k and its parent parton i, θ is an opening angle
between the partons k and i, φ is an azimuthal angle of a parton j around an axis defined by theparton i and the sum accordingly i → jk runs over possible splitting pars to j, k. Pi→jk (z, φ) are thespin averaged splitting functions [57] defined by :1 + z2
1 + (1 − z)2, Pq→gq = CF,1−zzz 4 + a + (1 − z)4, Pg→qq̄ = TR (z 2 + (1 − z)2 ,Pg→gg = CAz(1 − z)Pq→qg = CF

(3.5)
(3.6)

with
CF =

NC2 − c
dk 2
dθ2
dq 2
, CA = NC and 2 = 2 = 2T ,
2NC
θ
q
kT

2
q 2 = z(1 − z)θ2 E 2 , kT
= z 2 (1 − z)2 θ2 E 2 ,

(3.7)
(3.8)

where NC is the number of colours, q is the virtuality of the propagator and kT is the transverse
momentum of the parton k with respect to the parton i, TR is a colour factor that is fixed only convention, TR = 1/2. Pq→qg , Pq→gq , Pg→gg and Pg→qq̄ correspond to the splittings q → qg, q → gq, g → gg
and g → q q̄ respectively1 . The parton shower algorithm are implemented as successive parton splittings with a probability (so called Sudakov form factor) proportional to the differential cross-section
as a function of kT or θ. The parton splitting is stopped at q which is below a cut-off that corresponds to the hadronisation scale for virtuality-ordered parton showers. For other implementation,e.g. Sherpa [69] and Pythia8 [70], is built on the Catani-Seymour dipole factorisation 2 .
If the parton showers are used together with generators for NLO or LO F + n jets production, aphase space overlap between jets created by the partons shower and the fixed-order generator. The
overlap are removed with following matching algorithms.

1
2

A fifth splittings function Pq→q̄q corresponding to g → q̄q is equal to Pg→qq̄
see References [71]15

3.1. Simulation of Hadron Collisions and Calculation of Cross-Section
CKKW algorithm

CKKW [72, 73] algorithm is based on a resolution of the kT jet algorithm [74]. Two jets i and j
are resolved when the distance parameter yij is greater than the resolution parameter ycut ,yij = 2 min(Ei2 , Ej2 )(1 − cos θij )/Q2 > ycut ,(3.9)

where Ei is the energy of jet i, θij is an angular difference between jet i and j. ycut is the pre-definedresolution and Q2 is the scale of the interaction [75]. The fixed-order calculation is used for the parton
splittings with yij > ycut and the parton showers for yij < ycut . An event with F + n jets production
is generated and the resolution parameters ycut to obtain 2, 3, · · · , n jets are determined. A backward
parton shower is performed in a clustering process. Only particle combinations that can result froma parton splitting are clustered.
The Sudakov form factor [76] introduces a cut-off scale for the parton shower evolution. It depends
on a variable whcih describes the parton shower evolution. It ensures that partons are only generated
with values of the evolution higher than the marging scale by the fixed-order generators. The parton
shower emissions are only produced below the cut-off scale for the parton shower evolution variable.
The CKKW algorithm is used in the SHERPA.
MLM algorithm
MLM algorithm [77] is an alternative algorithm. A hard scattering event based on a fixed-order
calculation is generated with partons with a minimum transverse momentum , pT,min and a minimum
angular distance ∆Rmin . Dividing event samples into two categories with events ≥ n partons, arecalled as inclusive sample, and with all other events are called as exclusive samples. A parton shower
is evaluated and a jet clustering algorithm (kT algorithm) with a distance parameter ∆Rcluster isapplied to obtain jets with pT > pT,cluster which are matched to the partons from the fixed-order
generator within ∆R < 1.5∆Rcluster . If two partons are matched to the same jet, the jet is selected.
Otherwise a jet is rejected.

3.1.4

Hadronisation

Hadronisation is a transition of a parton event with colour-charged quarks and gluons into an eventwith colour-neutral hadrons. The most common model is the Lund-String-Model [75] which are usedin Pythia. An overview is given in the following, a more detail can be found in Reference [57].
n
m2⊥

t

q̄

j
m2⊥

1

2
3

q

j−1

t

q̄

q

A
z

(a) High-energy string break-up

A

Figure 3.5: (a):The break-up
in space-time of a Lund string
into n hadrons. The fragmentation area is denoted by A. (b):A
sketch of the fragmentation of aone-dimensional q q̄-string.

z(b) Fragmentation

The model is based on a few general assumptions :• Final state particles originate from a break-up of a string-like force field spanned between thecoloured constituents.
• There is causality and Lorentz invariant.
• The production of the particles can be described in terms of a stochastic process which obeys
a saturation assumption.
• The force field is considered as a massless relativistic string with a pair of quark at the endpoints.

3.1. Simulation of Hadron Collisions and Calculation of Cross-Section

16• Gluons are treated as internal excitations on the string field which behaves a constant force
field with κ ∼ 1 GeV/fm corresponding to a linear potential spanned between an original pair
The string is split into two pieces after a new pair is created. The production probability of a pair isgiven by following :πm2⊥
P (m⊥ ) = exp −,(3.10)
κq
2 with transverse momentum k . The final state mesons in the Lund-Stringwhere m⊥ = µ2 + kT
T
Model correspond to isolated string pieces containing a q from one break-up vertex and a q̄ from theadjacent vertex together with the produced transverse momentum and the field energy. Figure 3.5(a)shows the break-up of the string. The procedure of string breaking are summarised following:• Generate q q̄ with uū : dd¯: ss̄ : cc̄ = 1 : 1 : 0.3 : 10−11 corresponding to be probability Equation 3.10.
• Set transverse momentum with Gaussian momentum (Fermi motion).
• Select the hadron state (L = 0, S = 0 or 1 for mesons), which has dynamical effect should betaken account by experimental data.

3.1.5

Underlying Event and Multiple Parton Interaction

The underlying event is a hadronic activity from a collision between partons of colliding hadrons
not contribute to a hard process. The underlying event includes effects from the hadronisation ofbeam remnants and multiple 2 → 2 parton interactions. An accurate model of the underlying event
is of the highest interest, since soft particles from the underlying have impacts on the performance of
momentum measurements significantly, like for instance jet-energy calibrations and the determination
miss (see Section 5.7). There are several models and implemented in common multi-purpose Monteof ET
Carlo event generators. Usually these models include various parameters, which can be tuned withexperimentally accessible observable like the charged particle multiplicity [78, 79].

3.1.6

Pile-up Events Simulation

In addition to the underlying event, another origin of soft QCD interactions exist, so-called pile-up.
The pile-up is caused by multiple proton-proton interactions per bunch crossing and a major issue inthe high luminosity environment of the LHC. From 2015 LHC proton-proton collisions, bunch trains
rise up to 1011 protons with a transverse size of roughly 16 µm. During the 2016 data taking period,
the number of interactions per bunch crossing is expected to 20 ∼ 40. In order to save a lot of timeand simulation resources for a full simulation with pile-up activity, the interactions is modelled bygenerating an inclusive proton-proton collision event samples and by overlaying them to the hard
scatter event samples. To model conditions in real data as precise as possible, the number of overlaid
event is varied and reweighted to match actual distributions of the number of interactions per bunch
crossing.

3.1.7

Detector Simulation

The ATLAS detector is an extremely complex detector, consisting of multiple sub-detectors andmore than 100 millions of read-out channels. The detector description is given in Chapter 4. A
detailed description can be found in References [80, 81]. Generated events including non-perturbative
corrections like the parton shower, hadronisation and pile-up activity are passed through a detailed
detector simulation. The simulation is based on Geant4 [82] which performs all interaction between

17

3.2. Phenomenology of Heavy Higgs Bosons

particles and materials. After Geant4 simulation event samples need to pass a digitisation, which
simulates electrical response in sub-detectors. It is ensured that the simulated event samples can beused same output format as the actual experimental data.

3.2

Phenomenology of Heavy Higgs Bosons

The production and decay of Higgs bosons are described for the MSSM benchmark scenario in thissection. The cross-sections and decay branching fraction are shown for the MSSM Higgs boson in√
proton-proton collisions at s = 13 TeV.

3.2.1

Production of Heavy Higgs bosons in Benchmark Scenario

The cross-section for a production of the neutral Higgs bosons φ ≡ (h, H, A) via gluon-fusion (gg →φ) and bottom-annihilation (bb̄ → φ) have been computed with the code SusHi 1.5.0 [83]. The SM
input parameters for SusHi have been chosen to the values listed in Table 3.1 in calculation of the
production cross-section. The renormalization scale µR and the factorisation scale µF have been
Parameter
PDF(NLO)
PDF(NNLO)
αS (mZ )¯
mc (mc )MS¯
mb (mb )MS
mpole
c
mpole
b
mpole
t
GF
mZ
mW
ΓZ
ΓW
−1
αEW
(mZ )

SusHi 1.5.0

HDECAY 6.42

MSTW2008nlo68cl
MSTW2008nnlo68cl
0.119
0.119
1.28 GeV
1.28 GeV
4.16 GeV
4.16 GeV
1.42 GeV (1-loop value)
4.75 GeV
4.49 GeV (1-loop value)
172.5 GeV
172.5 GeV
1.16637 × 10−5 GeV−2 1.16637 × 10−5 GeV−2
91.1876 GeV
91.15349 GeV (Complex mass scheme)
80.36951 GeV (Complex mass scheme)
2.49581 GeV (Derived NLO)
2.08856 GeV (Derived NLO)
127.67 (value to obtain mW =80.398 GeV)

Table 3.1: SM parameters used for the calculation of the Higgs production cross-section and branching ratiowith the code SusHi 1.5.0 and HDECAY 6.40. The listed value of αS (mZ ) is used for RG evolution and passed
to FeynHiggs for the calculation of the Higgs boson masses and mixing, whereas the corss section calculation
use the values of αS associated to the PDFs.

fixed as µR = µF = mφ /2 in the case of the gluon-fusion and as µR = 4µF = mφ , in the caseof the bottom-annihilation(see in Reference [30]). Uncertainties on these scales have been obtained
from the envelope of seven independent variation of µR and µF by factor 2 within the constraint
1/2 ≤ µR /µF ≤ 2 in the case of the gluon-fusion, and 2 ≤ µR /µF ≤ 8 in the case of the bottomannihilation. The MSTW2008 parton distribution function set has been used, and residual uncertainties
on the parton distribution functions and on the strong coupling constant αS have been obtained byproposed method in Reference [65].

18

400

600

800 1000 1200pbb

10 −1pb

10 −3p

200mA [GeV]

1pb

pb
10 1

10 −2

tanβ

pb

10 −
3

200

60
50
40
30
20
10

10 2 pbpbb

10 −1p

1pb

10 1 pb

60
50
40
30
20
10

10 −2

tanβ

3.2. Phenomenology of Heavy Higgs Bosons(a) CP-even Higgs, H

400

600

800 1000 1200

mA [GeV](b) CP-odd Higgs, A

Figure 3.6: The production cross-section for the Higgs bosons with the gluon-fusion process in (mA , tan β)plane. Left(right) shows the cross-section of the CP-even(odd) Higgs, gg → H(A).

Gluon-Fusion Production Cross-Section
The code implements top- and bottom-loop contributions at NLO [84, 85], NNLO top contributionsin the heavy-top limit from [86–90] and electroweak contributions by light quarks [91, 92]. There areno contributions from squark loops since consistency with the assumption. Figure 3.6 shows the
production cross-section for gg → φ in (mA , tan β) plane.
Bottom-Annihilation Production Cross-Section

200

−2

10

400

600

pb

10−3 pb

800 1000 1200

mA [GeV](a) CP-even Higgs, H

200

1

pb

1pb

10 1pb10 2 pb

60
50
40
30
20
10

10 −

10 −

1

pb

tanβ

10 1pb10 2 pb

60
50
40
30
20
10

1pb

tanβ

SusHi implements the NNLO results in the five-flavour scheme from Reference [93]. The amplitude
for the production of the SM Higgs boson mass mφ is re-weighted with the effective coupling gdd
given in equation in Table. 2.1. In addition to the five-flavour scheme, the four-flavour scheme cross-

−2

10

400

600

pb

10−3 pb

800 1000 1200

mA [GeV](b) CP-odd Higgs, A

Figure 3.7: The production cross-section for the Higgs bosons with the Bottom-Annihilation process in (mA ,tan β) plane. Left(right) shows the cross-section of the CP-even(odd) Higgs, bb → H(A).

section (gg → bb̄φ) [94, 95] is combined by the “Santander matching method” [96]. The production
cross-section with the Santander matching for the CP-even and CP-odd Higgs bosons are presented

19

3.2. Phenomenology of Heavy Higgs Bosons
in Figure 3.7.
Comparison of Two Production Cross-Section

600

20.0 10.0
0.1

800 1000 1200

mA [GeV](a) CP-even Higgs, H

200

15.0

10.0

tanβ

60.0

50.0

70

.0

40.0

30.0

400

0.5

5.0

0

200

1.0

60
50
40
30
20
10

35.

60
50
40
30
20
10

40.0

tanβ

Since down-type fermions are strongly enhanced at higher-tan β it is important to compare two
production cross-sections. Figure 3.8 shows ratios for the bottom-annihilation and the gluon-fusion

400

600

0.1

1.0

5.0

25.0 30.0
20.0
10.0

0.5

800 1000 1200

mA [GeV](b) CP-odd Higgs, A

Figure 3.8: Ratio of the production cross-section the bottom-annihilation process and the gluonfusion (bbA/ggF) in (mA , tan β) plane. Left(right) shows the cross-section of the CP-even(odd) Higgs.

production process in (mA , tan β) plane for the CP-even Higgs (a) and the CP-odd Higgs (b). As expected from the down-type fermion enhancement, tan β & 15 the bottom-annihilation cross-section islarger than the gluon-fustion by a factor of ' 10(80) for CP-even Higgs (CP-odd Higgs). Identificationof b-quarks is important which is described in Section 5.3.3.

3.2.2

Decay of Heavy Higgs bosons in Benchmark Scenario

The branching fraction have been calculated with the code HDECAY [97, 98] which can take mh as
input and obtain mH and mixing angle α from the hMSSM prescriptions in Eq. (2.11) and (2.13).
The value of the SM input parameters are summarised in Table 3.1. The hMSSM mode of HDECAY
implements: N4 LO-QCD corrections to the decays to a pair of quarks [99–111]; LO results are used
for the decays to lepton pairs and for the decays involving massive gauge bosons. Figure 3.9 shows
the branching fraction of several decay modes which can be searched at the LHC for both CP-evenand CP-odd Higgs bosons. For the CP-odd Higgs the W W and ZZ couplings are vanished. The
φ → τ τ decay mode shows relatively larger branching fraction for tan β = 3 and 30 compared withother decay modes in the CP-even and CP-odd Higgs bosons. The bb̄ mode has larger branching
fraction than the φ → τ τ mode, however φ → bb̄ mode is experimentally difficult at the LHC due
to difficulty of triggering only b-quarks (or including other light-flavour). The CP-even Higgs boson
have φ → W W/zZ decay modes. Leptonic decay of Z/W ± are useful for triggering and suppressionof backgrounds, but branching fraction is suppressed. Figure 3.10 shows the branching fraction ofA
the φ → τ τ decay mode in (mA , tan β) plane (BrHτ τ , Brτ τ ). Figure 3.10 (b) shows “edge” aroundmA ∼ 350 GeV and tan β < 10 due to decay mode opens to A → tt̄ channel. For tan β ≥ 10 bothABrH
τ τ and Brτ τ has greater than 10% branch and less dependency against tan β.

203.2. Phenomenology of Heavy Higgs Bosons

100

10-1

tt̄
bb̄
ττ

hh
WW
ZZ

10-2
10-3200

400

Branching ratio

Branching ratio

100

10-1

800 1000 1200
mA [GeV]

ττ
Zh

10-2
10-3200

600

tt̄
bb̄

(a) CP-even Higgs, H

400

600

800 1000 1200

mA [GeV](b) CP-odd Higgs, A

200

400

13.0%
10.0%

5.0%

600

1.0%

800 1000 1200
mA [GeV](a) CP-even Higgs, H

tanβ

12.0%
%
.0
1
1

60
50
40
30
20
10

12.0%
%
.0
1
1

200

400

14.0%

60
50
40
30
20
10

14.0%

tanβ

Figure 3.9: Branching ratios for CP-even and CP-odd Higgs bosons as a function of the pseudoscalar mass
mA with two different tan β values in log-scale. All solid(dashed) lines correspond to tan β = 3(30). Only
decay modes which has > 10−3 are presented in both tan β values.

13.0%
10.0%

5.0%

600

1.0%

800 1000 1200
mA [GeV](b) CP-odd Higgs, A

Figure 3.10: The branching ratios of φ → τ τ for CP-even and CP-odd Higgs bosons in (mA , tan β) plane.

3.2.3

Experimental Search Channels

Searches for heavy Higgs bosons is one of important BSM physics search in experiments at the
LHC. Only several combinations of production and decay mode are accessible due to experimental
considerations because of triggering or signal-background separation. Because of tan β enhancement
and suppression, any experimental signature cannot cover whole region on (mA , tan β) plane, sothat several experimental signatures are need to search entire region of (mA , tan β). Experimentally searching the neutral Higgs bosons (H/A) are well established and tested so far. Searches forthe neutral Higgs bosons can be separated in two groups, which is sensitive at high- or low-tan β.
Figure 3.11 shows direct and indirect exclusion limit for the hMSSM scenario in (mA , tan β) plane.
At low tan β, H → ZZ, H → W ± W ∓ , H → hh, A → Zh and H/A → tt̄ dominate sensitivities due
to tan β suppression. Diboson modes are suppressed above mA & 350 GeV due to the branching
fraction open to H → tt̄ mode, and the branching fraction at higher tan β are strongly decreased.
Diboson decay modes are sensitive only region of (mA , tan β) . (350 GeV, 5). The indirect exclusion

21

3.2. Phenomenology of Heavy Higgs Bosons///////////// Obs., h couplings [κV, κu, κd]

tan β

Exp.
Obs., A/H→ττExp.
Obs., A→ Zh→ ll/νν bb
Exp.
Obs., H+→ τνExp.

Figure 3.11: Regions of the (mA , tan β)plane excluded in the hMSSM scenario via
direct searches for heavy Higgs bosons andfits of the measured rate of observed Higgs
boson production and decays. The observed (expected) exclusion region is indicated by the hashed (dashed) line. (takenfrom Reference [112], detailed description
can be found in Reference [54] )Obs., H→ ZZ→ 4l, ll qq/bb/ννExp.
Obs., H→ WW→ lν qq/lν
Exp.
Obs., H→ hh→ 4b, bb γ γ /ττ, WWγ γ
Exp.

40
30
20
10

ATLAS
s=7 TeV, 4.5-4.7 fb-1
s=8 TeV, 19.5-20.3 fb-1

5
4
3

hMSSM, 95% CL limits

2
1
200

250

300

350

400

450

500
mA [GeV]limit from the SM Higgs boson measurements is expected even higher than ∼ 375 GeV for most oftan β region (blue hashed and line as shown in Figure 3.11). While H → tt̄ mode has large branching
fraction at mA > 350 GeV and low-tan β, but difficulty of separation against the SM tt̄ processes
are crucial to search them. There is also an interference effect between H → tt̄ and the SM tt̄,
estimation of the effect recently developed [113] and its sensitivity is not yet fully optimised. On theother hand, at high-tan β two decay mode are promising, H/A → bb̄ and H/A → τ τ . Since the LHC
is proton-proton collider, the QCD multijet (dijet) process is dominated its event rate (cross-sectionis O(mb)). H/A → bb̄ has only b-quarks (or gluons) in the final state, this leads hard situation to
trigger its event, the ATLAS single jet (or b-jet) trigger tends to have large jet pT threshold of about
pT & 400 (150) GeV. In addition to trigger, background-to-signal ratio is poor due to large contributions from the QCD multijets and SM tt̄ processes. H/A → τ τ have relatively large branching ratio
at wider range of mA and tan β > 10. In terms of triggering H/A → τ τ has an unique final statewith leptons (` = e, µ) and hadronic τ -lepton decay products. Accordingly the branching fraction
channelfinal stateBR (%)

triggerbackgroundsearch rangeτ` τ`τ` τhadτhad τhad` + ` + 4ν
` + τhad + 3ν
τhad + τhad + 2ν

12.4
45.1
40.1

leptons,
miss
lepton, had. τ ,EThadronic-τvery clean
clean
relatively highlow mass
low/ high mass
high mass

Table 3.2: Summary of decay channels of H/A → τ τ mode with final states particles, branching ratio,
accessible triggers, background cleanness and search range on mA .

of τ -lepton, H/A → τ τ are grouped three decay channels, τhad τhad , τ` τhad and τ` τ` has two hadronic τ -lepton products, one leptonic τ -lepton decay products and one hadronic τ -lepton products
and two leptonic τ -lepton decay products respectively. Three decay channels are summarised inTable 3.2. In the sense of trigger, τ` τhad channel has several choices and their total trigger efficiency
is nearly 100%. While τhad τhad channel has only hadronic-τ triggers and its trigger threshold is alreadypτThad & 100 GeV at the beginning of the Run23 commissioning phase. The single-lepton-trigger4 aremissstill kept its threshold about p`T & 25 GeV. The τ` τhad channel are also characterised as large ET
compared to other two channels. Neutrinos emitted from di-τ are relatively balanced in the τhad τhadand `+ `− .
√The Run2 started from 2015 and will continue 2018 with s = 13 TeV. The instantaneous luminosities will go up-to
2.0 × 1034 cm−2 s−1 .
4
Trigger decision with only one lepton signature, details are given in Chapter 5.
3

4 The ATLAS Experiment at the LHC

The ATLAS experiment [114] is one of the four large experiments at the Large Hadron Collider (LHC) [115].
The detector is located at the European Organisation for Nuclear Reserch (CERN) in Geneva, Swizerland. The accelerator complex is used to accelerate and collide particles in the LHC is introduced in
Section 4.1, As well as an overview of the ATLAS experiment and its detector concept is describedin Section 4.2.1. A run condition during data-taking periods in 2015 and 2016 is summarised in
Section 4.3.

4.1

The Large Hadron Collider

The Large Hadron Collider(LHC) is the most powerful particle accelerator ever built. It was first
conceived in the 1980s a facility to find the Higgs boson and physics beyond our current understanding.
√
The LHC accelerator is designed as a proton-proton collider at a center-of-mass energy of s = 14 TeV
with a high instantaneous luminosity of 1034 cm−2 s−1 . This performance can be achieved with aninjector complex and the following 27 km LHC main ring as summarised in Figure 4.1.
Figure 4.1: Schematic view of the
CERN accelerator complex including
the LHC injection chain consisting of
the accelerators, LINAC2, PS and SPS.

The injector system consists of a series of accelerators, the LINAC2, Proton Synchrotron Booster (PSB),
Proton Synchrotron (PS) and Super Proton Synchrotoron (SPS), which boost protons from 50 MeV (after
LINAC2) to 450 GeV. The LHC is designed to accelerate protons from injected energy up to 7 TeV
by oscillating radio-frequency (RF) electric fields1 . Superconducting coils are operated in a superfluid
1

The RF is delivered to all the system, not only to the accelerator apparatus but also to the detector system, so that

22

23

4.2. The ATLAS Detector

helium at 1.9 K in order to generate 8.33 Tesla to bend the 7 TeV proton beams in the LHC main
ring. The LHC is composed of octant 2.45 km arcs and 1232 bending magnets are aligned along beamlines.
In total, 39 bunch trains2 are filled into the LHC in a design conditions, so that 2808 bunches per
beam are brought to collision in the LHC. Each bunch contains about 1011 protons. A peak luminosityof L = 1034 cm−2 s−1 is achieved at a beam crossing angle of 285 mrad. The two general purpose
detectors ATLAS and CMS [116] reside at these points. LHC beam parameters are summarised inTable 4.1. Besides ATLAS and CMS the LHC has two other large detectors, the ALICE3 and LHCb4
DesignLength of the rings
Magnetic field of dipoles
Current
Beam energy
Luminosity
Number of bunches
Number of protons per bunch
Time between collisions
Beam radius at IP (σx,y )Beam length at IP (σz )Full crossing angle

26.7 km8.33 Tesla
11.85 kA
14 TeV1034 cm−2 s−1
2808
1.15 × 1011
25 ns
16.6 µm7.55 mm≈ 0.3 µrad

Table 4.1: LHC beam parameters.
In addition to the four large experiments, several experiments dedicated to important physics arelocated at the LHC. LHCf5 and TOTEM6 and MODEL7 .

4.2

The ATLAS Detector

ATLAS is a general-purpose detector covering a solid angle of nearly 4π. It provides an excellent
resolution of physical objects and reconstructs hard scatter events and detects a physical phenomenon
beyond the Standard Model without failing if it exists. To satisfy that, the following performances
are provided :• Good spatial resolution in vertex reconstruction for efficient identification of secondary vertices
from b hadron and τ lepton decays, an identification of the primary interaction vertex.
• Fine transverse segmentation of the electromagnetic calorimeter for distinction of π 0 → γγ
decays from primary photons and good angular resolution in photon and electron reconstruction.
the operation coherent to the LHC operation is achieved.
Protons are bunched together with 115 billion protons and 72 bunches are grouped into a bunch train
3
A Large Ion Collider Experiment detector [117] which have been built for the heavy ion experiment of the LHC
4
Large Hadron Collider beauty detector [118] which are an asymmetric detector with extremely good vertex detector
for studying rare b-hadron decays.
5
Large Hadron Collider forward experiment [119] is a far forward detector intended to study physics of cosmic ray andto deepen the understanding of forward scattering
6
Total Cross-Section, Elastic Scattering and Diffraction Dissociation [120] measure the total elastic and diffractive
cross-section of proton-proton collisions which cannot be calculated by perturbative approaches.
7
Monopole and Exotics Detector at the LHC [121] is an experiment searching for exotic particle like magnetic monopoles224

4.2. The ATLAS Detector

Figure 4.2: The ATLAS detector consists of tracking detectors, calorimeters, and the muon
spectrometers.
It is 25 m inheight and 45 m in length. The
overall weight of the detector isapproximately 7000 tons.

• High geometrical coverage to maximise a total detector acceptance.
• High energy resolution for the electromagnetic and the hadronic calorimeter for electron, photon
and hadronic jet energy measurements and a precise reconstruction of missing transverse energy.
• High muon momentum resolution over a wide range of momenta.
• Efficient and extremely fast triggering algorithm to cope with high luminosities delivered by
the LHC.
Figure 4.2 shows a schematic view of the ATLAS detector consisting of the inner detectors, calorimeter systems, and the muon spectrometers. The detector is constructed as a symmetric detector
system in terms of forward-backward direction. The detector contains a solenoid as well as three
toroidal magnets to measure charged particle momentum. The superconducting solenoid provides a
2 T magnetic field to measure charged particle momentum by the inner detectors. It is hosted in thesame cryostat as the barrel electromagnetic calorimeter. The electromagnetic calorimeter is sampling
calorimeter fulfilled with liquid Ar. The hadronic calorimeter is placed after the electromagnetic
calorimeter. Three toroidal magnets provide a magnetic field for additional bending of muon trajectories for a precision measurement in the muon spectrometers. The sub-detector and triggeringsystems are briefly introduced based on References [122, 123] in the following subsections.

4.2.1

Coordinate System

The ATLAS coordinate system is a right-handed Cartesian system. Its z-axis points along thebeam pipe, the x-axis to center of the LHC ring and y-axis as well upward direction. Sphericalcoordinates are better to describe rotational invariant
p properties and it is suited to collider experiments. The (r, φ, θ) coordinate is defined by r = x2 + y 2 , φ = arctan(y/x) and θ = − ln tan(r/z).
The pseudorapidity, η is used instead of the polar angle θ where η = − ln tan(θ/2). The pseudorapidity coincide with the rapidity y for the massless limit of particles. Since rapidity differences ∆y are
Lorentz-invariant, so η provides a physically better measurement than the polar angle. Table 4.2
summarise kinematical quantities based on the ATLAS coordinate system.

4.2.2

The Inner Detector

In the ATLAS detector, the tracking system usually means the inner detectors (ID) without outermost muon spectrometers (MS). The inner detectors consist of three different detectors as shownin Figure 4.3. It reconstructs tracks of charged particles with a coverage of |η| < 2.5.

25

4.2. The ATLAS Detector
Variable

Description

Definitionp~

MomentumpT

Transverse momentumpµ = (E, q
px , py , pz )φθAzimuthal angle
Polar angleyRapidityη

Pseudorapidity∆φ∆η

Opening angle in φ
Difference angle in η

∆R

Opening in (η, φ) spacepT =p2x + p2yφ = arctan(py /py )θ = arctan(pT /pz )1 E + pz
y = ln2 E − pzθ
η = − ln(tan )2∆φij = min(|φi − φj |, π − |φi − φj |)∆η
qij = |ηi − ηj |∆Rij =

2∆φ2ij + ∆ηij

Table 4.2: Definitions of commonly used variables in the description of particle and event properties in the
ATLAS coordinate system.

Figure 4.3: Schematic view of the tracking system. In the barrel pseudorapidity region, from inner layer
it consists of the pixel, semiconductor detectors and transition radiation tracker. In the End-cap region,
semiconductor detectors and transition radiation trackers stands in.

The Pixel Detector
The silicon Pixel detector is the closet detector component to the interaction vertex and made up
of four cylindrical layers located between 31 mm–120 mm in radial distance from the beam pipe. The
innermost layer is often referred to as Insertable B-Layer (IBL), as it is a crucial detector component
for secondary vertexing for b-hadron decay reconstruction. The IBL is one of a new detector installed
during a 2 years shutdown after the LHC Run1. The three outer layers are referred to as B-Layer,
Layer-1 and 2. Three disks provide a coverage up to |η| < 2.5 in the forward region. In total, thepixel detector consists of 6.2 and 80.4 million pixels for the IBL and three outer layers with a nominal
size of 50 × 250 and 50 × 400 µm2 respectively. A charged particle produces four hits on an average,
with an intrinsic resolution of 4 µm in the R − φ plane and 115 µm along the z-axis. The pixel areoperated at a temperature of 0 ◦C in order to suppress an electronic noise.

4.2. The ATLAS Detector

26

The Silicon Microstrip Tracker
The Silicon Microstrip Tracker (SCT) is a silicon strip detector made up of four cylindrical layers
in the barrel region and two endcaps with nine disks. In total, the SCT provides an active are 63 m2
to measure four space-points over the full inner detector coverage. Two sensors are mounted back-toback on the modules titled against each other by a small stereo angle of 40 mrad. A sensor contains
768 active strips with 285 µm thick and a strip pitch of 80 µm. This angle breaks a degeneracy along
the z-direction. It allows to measure three-dimensional space-points with an accuracy of 17 µm in the
R − φ plane, 580 µm along the z-axis for the barrel region. The endcap disks are built from inner,middle and outer wheel modules with slightly different geometry. The sensors are single sided p-in-nsilicon detectors with an applied bias voltage of about 150 V. The SCT is operated at a temperatureof −10 ◦C to −5 ◦C to suppress electronic noise.
Transition Radiation Tracker
The concept of the TRT is based on a transition radiation, which is emitted by charged particles
passing a boundary of two di-electric materials. It is make of polymide drift tubes with a diameter of
4 mm and a length of 144 cm and interleaved with polyproyplen/polyethylen fibres. Each tube is filled
by a xenon-based gas mixture and contains a gold plated tungsten wire to collect the charge fromthe gas ionisation. Two type of hits of high- and low-threshold are considered. The low-threshold
is optimised to detect an ionisation from primary traversing particles, while the high-threshold hits
indicate a transition radiation. The intensity of a transition radiation is proportional to the Lorentz
factor γ of particles. So the TRT can provide a particle identification, especially e± /π ± separation
over a wide momentum range 0.5 GeV to 150 GeV by counting the number of high-threshold hits
along the path of flight. Although the accuracy per hit is quite poor, the TRT can provide valuable
information for a track reconstruction given that each particle provides about 36 hits in the TRT
easing pattern recognition. The TRT covers pseudorapidity of |η| < 2.

4.2.3

The Calorimeter System

The calorimeter system is intended to provide an accurate measurement of particle energies by absorbing them and measuring shower properties, which also helps particle identification. The electromagnetic calorimeter is designed to fully absorb and precisely measure the energies of electromagnetic
cascades of subsequent e+ e− pair production and Bremsstrahlung processes initiated from electronsand photons from a hard scatter. The hadronic calorimeter fully absorbs hadronic showers whichcannot be detected at the electromagnetic calorimeter. The calorimeter system covers a region of|η| < 4.9. The detector is build as a sampling calorimeter with alternating samples of passive andactive material to detect secondary particles. An accurate spatial resolution is required for a precise
reconstruction of photon and electron, so that the calorimeter system is finely segmented to both
longitudinal and azimuthal direction. It is also important for a reconstruction of the missing transverse energy. The three-dimensional shower position can be reconstructed using topological clustering
algorithm as described in Section 5.2. Figure 4.4 (a) shows the different calorimeter sub-system in a
cut-away view.
The Electromagnetic Calorimeter
The electromagnetic (EM) calorimeter is a finely segmented sampling calorimeter. It consists of
two components, the central barrel and endcap calorimeter covering pseudorapidity up to |η| < 1.4
with a small gap of 4 mm at |z| = 0 and |η| < 3.2 respectively. The cylindrical barrel has innerand outer diameters of r =2.8 m and 4 m, respectively and covers full azimuthal angle. The endcaps
calorimeter covers from r =0.33 m to 2.1 m with respect to the beam pipe.
The EM calorimeter is constructed as a liquid argon (LAr) sampling calorimeter with a lead27

4.2. The ATLAS Detector

Tile barrel

Tile extended barrel

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

LAr EM barrel
LAr forward(FCal)

(a)

1

(b)

Figure 4.4: Cut away view of the ATLAS calorimeter system. From innermost, the LAr calorimeter stands andthe hadronic calorimeter is placed after the EM calorimeter. (b) shows an overview of the EM LAr calorimeterbarrel module. The first layer is referred to as strip layer with a granularity of ∆η × ∆φ = 0.0031 × 0.098 toallow an excellent identification of π 0 → γγ decays as one important background to primary photons. The
second layer has a granularity of ∆η × ∆φ = 0.025 × 0.0245 and is the thickest layer with 16 radiation length
X0 . The third layer measures the tails of electromagnetic showers and can therefore be used to distinguishfrom hadronic deposits.

absorber plate. It is built with an accordion shaped in Figure 4.4 (b) in order to reduce insensible region.
The LAr calorimeter provides a good energy resolution of approximately σE /E =p10%/ E/ GeV ⊕ 0.7%. A thickness of the lead plate is 1.13 mm to 1.53 mm depending on modules. Three copper layers are used as readout electrodes in the gaps. A high voltage is applied to thegaps between each absorber materials. The inner plate is a readout using capacitive coupling. The
charge drift time is approximately 450 ns. Fine angular resolution and full shower containment are
obtained by three different layers.
The layered structure provides additional information about the shower development referred toas shower shapes like the longitudinal depth of the shower. The first layer of the barrel module isreferred to as strip layer with a granularity of ∆η × ∆φ = 0.0031 × 0.098. It allows an excellent
identification of the primary photon from π 0 → γγ decays. The second layer is the thickest layer with
16 radiation length X0 with a granularity of ∆η × ∆φ = 0.025 × 0.0245. The third layer measures
the tails of electromagnetic showers and can be used to distinguish e/γ from hadrons.
Each endcap calorimeter consists the inner and outer wheel with a spacing of about 3 mm in
between. The layout of the endcaps follows the barrel geometry. Three layers are used between
1.5 < |η| < 2.5 including a strip layer, while only two layers of a coarser granularity are used in theoutermost part of the outer and inner wheel.
Since the electromagnetic calorimeter is a sampling calorimeter, a deposit energy is measured by abipolar pulse shape transfer. When the pile-up activity overlaps over signal, it should be subtracted.
The subtraction is performed for all signals in the calorimeter, so that there is a negative energy
signal after plus shaping. This is corrected by dedicated algorithm and event cleaning criteria asshown in Chapter 5.

4.2. The ATLAS Detector

28

The Hadronic CalorimeterAs the hadronic calorimeter, there are the hadronic tile, the hadronic endcap and the liquid argon
forward calorimeter for different pseudorapidity regions. All hadronic calorimeters are sampling
calorimeters. The
barrel and endcap calorimeter isp typical jet energy resolution of the hadronic p
σE /E = 50%/ E/ GeV ⊕ 3%, while it is about σE /E = 100%/ E/ GeV ⊕ 10% for the forward
calorimeter. Steel and a scintillating tile is used as the absorber and active material of the tile barrel
calorimeter. A photo-multiplier tube is used as a readout of the scintillating tile at the tile edges by
wavelength shifting fibers.
The tile calorimeter is cylindrically build around the EM calorimeter with an inner radius ofr = 2.3 m and an outer radius of 4.3 m. It is divided into the central barrel with length of 5.8 m andtwo extended barrel parts with length of 2.6 m covering pseudorapidity of up to |η| < 1.7 as shown in
Figure 4.4. There are service cables between the central and extended barrel for the inner detectorand LAr pipes are mounted, so that a gap of 60 cm exists.
All barrel parts consist of three layer. The granularity of the hadronic calorimeter is coarser thanthe EM calorimeter due to hadronic showers tend to become wider than EM showers. The cell
granularity of the tile barrel is ∆η × ∆φ = 0.1 × 0.1 in the first two layers, while ∆η × ∆φ = 0.1 × 0.2
in the third layer.
The hadronic endcap is built by copper and liquid-argon sampling calorimeter and consists of two
disks for the forward and backward region covering 1.5 < |η| < 3.2. The size of disk cell is 0.1 × 0.1
and 0.2 × 0.2 for 1.5|η| < 2.5 and 2.5|η| < 3.2 respectively.
The LAr forward calorimeter is a combined electromagnetic and hadronic calorimeter and consistsof three layers. A copper is used as the absorber material in the first layer to absorb electromagnetic
interactions. While a tungsten is used in the second and third layer to absorb hadronic showers. The
far forward region of 3.1 < |η| < 4.9 is covered by the LAr forward calorimeter. There are significant
overlaps with the hadronic endcap calorimeters, this is because of a smooth transition between theendcap and LAr forward calorimeter. Liquid argon is used as an active material and is filled in small
gaps which are drilled inside the absorber material. It is hosted in the same cryostat structure as theelectromagnetic endcap and the hadronic endcap calorimeters.

4.2.4

The Muon Spectrometer

The outermost part of the ATLAS detector is the muon spectrometer (MS) consisting of carious
sub-detectors to detect muons efficiently and measure their momentum over a broad range. The
MS consists of different types of subdetectors, the Monitored Drift Tubes (MDT), the Cascade Strip
Chambers (CSC), the Resistive Plate Chambers (RPC) and the Thin Gap Chambers (TGC). Schematic view of the ATLAS Muon Spectrometer and its components are shown in Figure 4.5. It provides
an overall acceptance up to |η| < 2.7 and measures momenta ranging from 3 GeV to a few TeV.
At design specifications, it offers a relative momentum resolution of 10% for muons at pT = 1 TeV.
Three air-core toroidal magnets provide the magnetic field to bend the muon trajectories; covering
the barrel (|η| < 1.7) and the two Rendcap region (1.6 < |η| < 2.7). Each toroidal consists of eightcoils. The integrated field strength B⊥ d⊥ ranges from 1.5 Tm to 5.5 Tm in the barrel and between
1.0 Tm to 7.5 Tm in the endcaps.
MDT provides precision measurements for muons with |η| < 2.7. 1150 chambers with 354,000
channels are installed which consist of two batches of three or four layers of drift tubes. The individual
drift tubes are built from aluminium tubes with a diameter of 3 cm and length of 0.9 m to 6.2 m. The
drift tubes are strained a tungsten-rhenium wire at a potential of 3 080 V and pressurised with amixture gas of Ar and CO2 (93%/7%). This leads to a gas gain of 2 × 104 and a maximum drift timefrom the wall of the tubes to the wire take about 700 ns.
MDT cannot be operated a hit rates above 150 cm−1 s−1 . This rate are expected in the first endcap

29

4.2. The ATLAS Detector

Figure 4.5: Schematic cross section viewof the ATLAS Muon Spectrometer system.
Precision muon track measurements areprovided by the MDT in the barrel (BIL,
BML, BOL) and the endcap (EIL, EEL,
EML, EL) and the CSC. Triggering areprovided the RPC in the barrel and the
TGC in the endcap (taken from Reference [114]).

wheel at |z| = 7.4 m for |η| > 2, where CSC are installed with 32 modules with 31,000 channels
up-to |η| < 2.7. CSC is multi-wire proportional chambers which are placed in radial direction andtwo cathodes, so that one cathode is segmented parallel and one cathode perpendicular to the wires
applied a potential of 1 900 V. chambers are filled with a mixture gas of Ar and CO2 (80%/20%) thatprovides an average gain of 6 × 104 and a drift time is about 30 ns.
RPC is used for triggering in the barrel, which consists of 606 modules with 373,00 channels. RPC
is a gaseous resistive parallel plate detectors which are segmented at a distance of 2 mm from eachother with the electric field of 4.9 kV mm−1 , so that one plate can measure the φ direction and theother plate η. Time resolution of RPC is less than 2 ns.
In the forward region with 1.05 < |η| < 2.4, a total 3588 of the TGC are mounted with 318,000
channels for the trigger detectors. TGC are a multi-wire proportional chamber with a gain of ×105
for a wire potential of 2 900 V. One coordinate is measured by the wire and a second coordinate canbe inferred from pickup strips that are perpendicular to the wires. TGC provides triggers within 5 ns.
3

4.2.5

The Luminosity and Forward Detectors

The integrated luminosity is determined by the LUCID8 and ALFA9 detectors. LUCID is placed
at 17 m away from the interaction point in the the beam axis direction for both side of the ATLAS
detector. It consists of an array of 20 Cerenkov tubes and provides an online determination of
luminosity values by counting the number of charged particles in the far forward area from inelastic
proton-proton interactions. The ALFA detector is located 240 m from the interaction point to measure
the elastic scattering amplitude at extremely small scattering angles, which can be related to the total
cross-section using the optical theorem. The luminosity detectors have been calibrated using van derMeer scans [124, 125], which measure the beam spread in the vertical and horizontal planes.

4.2.6

The Trigger System and Data Acquisition System

The extremely high collision rate of 40 MHz does not allow to readout of the full signal of all
detectors due to the limitation of bandwidth in data storage infrastructures and computing resources.
A dedicated trigger system picks up events of interesting, predefined physical topologies to reduce
the event rate. The trigger and data acquisition system (TDAQ) consists of a hardware-based level 1
trigger (L1) and a single software-based high-level trigger (HLT). This two-stage system can reduce
the event rate to 100 kHz at L1 and to an average recording rate of 1 kHz at the HLT. A detailed
8
9

LUminosity measurement using Cerenkov Integrating Detector
Absolute Luminosity for ATLAS

4.3. Data Taking During LHC Run230

description of the ATLAS trigger system can be found in Reference [126].
Fast electronics are employed to find region of interest (RoI) using the calorimeter and muon Spectrometer with coarse information within a latency of 2.5 µs at L1. L1 trigger consists of L1 calorimetersystem (L1Calo), L1 muon trigger system (L1Muon), L1 topological trigger modules (L1Top) [127]and Central Trigger Processors (CTP) [128]. L1 trigger selects muons, electromagnetic clusters (usedmiss and sum of the transverse energy inas electrons and photons), jets, hadronic τ -lepton decays, ET
all calorimeter cells. L1Calo reads out 7000 projective trigger towers10 which are coarse granularityof ∆η × Φ = 0.1 × 0.1 to allow for a fast readout. The energy which is readout from the trigger
tower is calibrated to the full expected energy by a special procedure. L1 electrons and photons are
2 × 2 trigger tower clusters in the EM calorimeter with an isolation-window which consists of thesurrounding twelve trigger towers for vetoing a fake signal. L1 hadronic τ -leptons are made up withsame trigger tower size as L1 electrons and photons with only the hadronic calorimeter. L1 jet are
identified using sums of ET within windows consisting of 2 × 2, 3 × 3 and 4 × 4 trigger towers in
the EM and hadronic calorimeters. L1 muon trigger is based on coincidence requirements between
different trigger chambers using predefined look-up-table. In addition, L1 calculates the scalar andvectorial sum of the energy deposits to provide the L1 missing transverse energy trigger (L1XE).
At HLT, fast algorithm accessing signals around a RoI defined at L1, or offline-like algorithm using
the full event information performs on a unique PC farmware within a processing time of 0.2 s on anaverage. The event that is triggered by the HLT is subsequently sent to event storage infrastructures.
Event reconstruction is applied by data Acquisition system (DAQ).
Efficiencies of each triggers are measured by data as well as simulated samples and corrections areapplied to the simulated sample. Details of trigger efficiencies are described in Chapter 5 including
its systematic uncertainty.

4.3

Data Taking During LHC Run2√
The first run period of the LHC at s = 13 TeV was successfully completed in 2015. Since
November 2009, proton-proton collisions with energy of protons have been risen to 450 GeV to√
6.5 TeV. During the Run1, the beam energy was s = 7 TeV in 2011 and 8 TeV in 2012 respectively.
The bunch spacing was 50 ns which is doubled compared to the design specifications of the LHC.
The achieved peak luminosity was 7.73 × 1033 cm−2 s−1 which is close to the design value of 1 × 1034
cm−2 s−1 . Figure 4.6 (a) shows the integrated and peak luminosity as a function of data-taking
date. An integrated Luminosity of 3.38 fb−1 was delivered by the LHC, of which ATLAS recorded
3.21 fb−1 in 2015 run. Part of 2016 data-taking period is used in this thesis, which have the integrated
luminosity of 26.07 (24.8) fb−1 delivered from LHC (recorded by ATLAS). The peak luminosity was
1.2 × 1034 cm−2 s−1 The number of interactions per bunch-crossing was increased due to the larger
luminosity. The presence multiple proton-proton collisions in a single bunch-crossing will be denotedas pile-up (PU). Besides the direct impact of pile-up on the event reconstruction or trigger decision, asecondary effect impacts the object reconstruction performance and the trigger performance. In-time
pile-up is proton-proton collisions occurring in the same bunch crossing as the collision of interest.
Out-of-time pile-up is additional collisions occurring in bunch crossings before and after the collisionof interest. The measured mean number of interaction per bunch-crossing is shown in Figure 4.6 (b)for 2015 and 2016 data-taking periods analysed in this thesis.
All detector subsystems permanently monitor their performance during data-taking with automatically and dedicated shifts check data quality in order to ensure that no faulty detector affecting theperformance. If there are large defects like offline subsystem, such information are recorded in a data
10

Energy deposits in the calorimeter are gathered into one output as input to trigger decision, which is called as trigger
tower.

31(a) Luminosity

1.5
1.0
0.5
0.0

Recorded luminosity [fb−1 ]35
Delivered(2015) Delivered(2016)
Good(2015)
Good(2016)
30
25
20
15
10
5
0
Jul Aug Sep Oct Nov
May JunPeak luminosity [1034 cm−2 s−1 ]Integrated luminosity [fb−1 ]4.3. Data Taking During LHC Run2

1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.00

2016(24.8fb−1 )2015(3.2fb−1 )

10
20
30
40
50
Mean Number of Interaction per Crossing(b) Pile-up

Figure 4.6: (a): The integrated luminosity and the maximum instantaneous luminosity per run delivered to
ATLAS as a function of the date for both 2015 and 2016. (b) : Luminosity-weighted distribution of the mean
number of interactions per bunch-crossing for 2015(blue) and 2016(red) data. The mean number of interactions
per cross is the mean of the Poisson distribution of the number of interactions per crossing calculated for eachbunch.

quality database. This database is so-called Good Runs Lists (GRL) which can define later the run
available for physics analyses.

5 Physics Object Reconstruction andParticle Identification

The object reconstruction and identification processes are important steps to convert experimental
detector-level information into physical information like particle four-momentum. For data events
passing the online trigger requirements and simulated events, the raw detector data signals are recorded for further processing and event reconstruction. The object reconstruction and identification are
based on higher-level detector information such as reconstructed tracks instead of hits in the tracking detectors. Besides the reconstructed four-momentum of the particle candidate, additional usefulvariables for physics analyses are computed. Dedicated reconstruction and identification algorithms
are implemented in the Athena software framework [129], which can be used for data and simulated
events. The purpose of the reconstruction algorithm is an accurate reconstruction of the object fourmomentum vector with higher efficiency. The identification algorithm reduces the mis-reconstructedobjects while keeps a high identification efficiency.
An overview and performance of the reconstruction and Identification method used in the searchfor H/A → τ τ decay are given used in the data-taking in 2015 and 2016. A brief overview of tracks
and cluster of energy deposit which are the most common higher-level detector object are given in
Section 5.1 and 5.2. The Reconstruction of the jets, electrons, muons and hadronic τ -lepton decays
are introduced in the Section 5.3–5.6. As neutrinos cannot be detected with ATLAS due to small
miss ) plays a important role in constraining
interaction rate with matter, transverse missing energy (ETmiss reconstruction is described in Section 5.7.
the momentum of escaped neutrinos. The ET

5.1

Tracks and Vertices

Reconstructed tracks originating from charged particles passing the inner detector are one of themost important basic objects for further physics object reconstruction and identification. In thisanalysis, extremely high momentum τ -lepton’s decays introduce strongly collinear set of the charged
pions. It makes difficult to reconstruct each track because of sharing hits with each other charged
pions. A brief overview is given based on Reference [130] in this section.
In the Pixel detector each hit equates to one space-point while the SCT detector hits from bothsides of a strip layer must be combined to obtain a three-dimensional measurement. The measured
charge in a pixel sensor is often collected by multiple pixels. The total charge is determined by theincident angle of the particle with respect to the sensor. A connected component analysis [131] makes
clusters. The cluster is a set of hits in the detector, which is expected from one charged particle. The
charged particle’s intersection point to the sensor is determined from the cluster pixel content using
a linear approximation with a charge interpolation technique. To identify the cluster is merged ornot, An artificial neural network (NN) [132] is used to determine the cluster is originated from one

32

33

5.1. Tracks and Vertices

ρ Algorithmic Efficiency

1.05
ATLAS Preliminary
Simulation, ρ→π+π-≤ 2 Shared SCT Clusters
No Secondaries

1

0.95

Baseline
TIDE

0.9
0

200

400

600

800

1000

τ Algorithmic Efficiency

charged particle or more than two particles. The cluster is splitted into two or three clusters if theNN judges that it is merged cluster1 .
The primary track reconstruction algorithm (track seed finding) works iteratively after cluster
making. A staged pattern recognition approach is used. Seeds consists of sets of three space-points.
The perigee parameters of a track seed are estimated by assuming a perfect trajectory in a uniform
magnetic field. Four possible pattern of combinations can be made from the pixel detector and
SCT detector space-points. To reduce mis-reconstructed seeds it is considered starting with SCTonly then Pixel-only seeds. Purity can be improved by requiring one additional space-point to becompatible with the seed. After iterative seed-finding a combinatorial Klakman filter [133] is used
to build track candidate from the seed. The filter creates multiple track candidates per seed if morethan one compatible space-point extension exist on the same layer. New reconstruction algorithm
is recently developed to improve the track reconstruction efficiency in the dense environment withmultiple collinear tracks. New algorithm is called as Tracking In Dense Environment (TIDE) [130].
Figure 5.1 shows the track reconstruction efficiency in ρ → π ± π ∓ (a) and τ → 3π ± + ντ (b) events
1.1
ATLAS Preliminary
Simulation, τ→ντ3π±≤ 2 Shared SCT Clusters
No Secondaries

1

0.9

Baseline
TIDE

0.8
0

200

400

600

1000

τ p [GeV]ρ p [GeV]T

T(a) Luminosity

800(b) Pile-up

Figure 5.1: Efficiency to reconstruct all decay products from a ρ meson or τ -lepton decay in events (takenfrom Reference [130]). Green (red) points present baseline(TIDE) algorithm efficiency.

as a function of the transverse momentum. The reconstruction efficiency of complex charged particle
groups is improved at high pT . After the reconstruction a set of track quality selection is applied,which is summarised in the following:• pT > 400 MeV and |η| < 2.5• number of silicon hits ≥ 9 and 11 for |η| ≤ 1.65 and > 1.65 respectively.
• number of shared2 modules ≤ 1• number of silicon holes3 ≤ 1 and no holes in pixel, one IBL or next innermost pixel layer hit.
1

Merged cluster is referred as a cluster which overlaps with other particle detections, and it is reconstructed as one
cluster.
2
A pixel detector with a hit used by more than one tracks and SCT with two hits in the same SCT layer used by morethan none tracks are referred to as shared modules
3
Holes are defined as intersection of the track trajectory with no hits in detector which is caused by inactive modules
or region such as edge ares.

34

5.2. Topological Clustering

Vertices are reconstructed using the distribution of z coordinates of reconstructed tracks along thebeamline. A vertex candidate is reconstructed by Iterative Vertex Finding procedure [134, 135]. The
tracks are extrapolated to the point of closest approach to the beam spot center. The algorithm finds
the maximum of the distribution of extrapolated z-coordinates. Vertex position is determined using
the adaptive vertex fitting algorithm [136] which is based on a robust χ2 fitting. Tracks are refitted
under the assumption that they produced from this vertex candidate. The procedure is repeated until
all tracks are associated to some vertices. Vertices with less than two associated tracks are discard.
Event have more than one vertices, so that the primary vertex is P
chosen as the vertex with the largest
sum of squared transverse momentum of the associated tracks ( p2T ).

5.2

Topological Clustering

The topological cluster (TopCluster or just TC) is used as seeds of jet and hadronic τ -lepton decay
reconstruction. The topological cluster algorithm aims at grouping deposits at the calorimeter into
each particle shower and suppressing the calorimeter noise. The energy collection of the calorimeter
cell signals into one topo-cluster follows signal-significance patterns generated by particle showers.
EM which is defined
The basic observable for making the topp-cluster is the cell signal significance ςcell
by
EM
=
ςcell

EM
Ecell
EM
σnoise,cell

,

(5.1)

104

3

10

PS
EM1
EM2
EM3
Tile1
Tile2
Tile3
Gap

ATLAS
Simulations = 7 TeV, µ = 0

Total Noise [MeV]Total Noise [MeV]EM
EM and σ EM
where the cell signal Ecellnoise,cell are measured in the electromagnetic (EM) energy scale. EcellEM
is a noise level of the cell. The EM scaleis energy measured in the cell at the EM scale, σnoise,cellis defined by calibration constants derived in test-beam measurements using ATLAS calorimeter
prototype [137]. Topo-cluster are formed by a highly significant seed. The seeding, growth and

FCal1
FCal2
FCal3
HEC1
HEC2
HEC3
HEC4

10

50 ns bunch spacings = 8 Te V, µ = 30

3

PS
EM1
EM2
EM3
Tile1
Tile2
Tile3
Gap

10 2

102

10

10
0

ATLAS
Simulation

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

4

FCal2
FCal3
HEC1
HEC2
HEC3
HEC4

4.5

5
|η|

|η|

(a) hµi = 0

3.5

FCal1

(b) hµi = 30

Figure 5.2: Expected noise level per cell in the different calorimeter subdetectors for two different luminosity
conditions. (a) plot shows the only the electric noise, while (b) plot includes energy deposits from multiple
proton-proton collisions at instantaneous luminosity of 1034 cm−2 s−1 (taken from Reference [138]).

boundary feature of topo-cluster are controlled by the three parameters S,N,P, which defines signal
EM
EM . The default values of (S,N,P) isthresholds in terms of σnoise,cell. Selection is applied based on ςcell(4,2,0) which are derived from optimizations of the response of cluster energy and the relative energy

35

5.3. Jets

resolution for charged pions with the test-beam [137]. Figure 5.2 shows the expected noise in the
different calorimeter sub-systems for two different pile-up profiles.
After constructing seeds, the collect step starts. These seed and collect steps are repeated until all
EM > S, N and their neighbours
clusters topologically connected cells passing the criteria given in ςcell
EM > P . The algorithm starts by selecting cells with ς EM > S and ordering insatisfying the ςcellcell
EM
EM > N .
decreasing ςcell . Neighbouring cells are subsequently merged into the seed if they satisfy ςcell
In the case of a cell is a neighbour to two potential clusters, the clusters are merged. This procedure
EM > P .
is iteratively applied until the last set of neighbouring cells with passing ςcell
Finally the cluster splitting step identifies and isolates local energy maxima in the clusters. The
clusters with two or more local maxima are splitted into corresponding signal peaks in all three
EM > 500 MeV. In addition to the topologicaldimensions. A local signal maxima is defined by Ecellrequirements, it is required to have at least four neighbours and none of the neighbours with larger
signal. This step can find cells which are neighbours to two or more signal maxima. The cell is
assigned to the two highest-energy clusters after splitting of the original topo-cluster in this case.
EM > 0 has a full set of geometrical moments.
Each topo-cluster with at least three cells with Ecell
Simple (η, φ) direction and a center of weighted moment points are calculated as a geometricalmoment. They has the EM scale and Local Cluster Weighting (LCW or just LC) calibration [139,140] for energy scale. This calibration is based on comparison between the reconstructed and theirtrue energy of simulated charged and neutral pions energy. The corrections are applied using theshower classification observable pEM4 . Jets built from local calibrated topo-cluster can be improved
energy resolution with respect to the EM scale. Both jets and hadronic τ -lepton are reconstructedusing calibrated topo-clusters with the EM scale and the LCW scale respectively in this analysis.

5.3

Jets

Jets are narrow clustering of particles (quarks or gluons) reconstructed from topo-clusters andtracks by jet reconstructing algorithm. Jets are used for selecting the bottom-annihilation production
process. A brief overview of the reconstruction algorithm is given in Section 5.3.1. Energy calibration
and resolution are shown in Section 5.3.2. The flavour tagging, so-called b-tagging, and the pile-up
suppression are described in Section 5.3.3 and 5.3.8. Reconstruction of the hadronic τ -lepton decays
is an important role of this analysis. Hadronic-τ objects is reconstructed based on jet seeds. Detailsof the hadronic-τ reconstruction is given in Section 5.6.

5.3.1

Jet Reconstruction
Observable
Theory and Modelling

EM

HAD

Trackerscatter
Parton jet

Hadronization
Fragmentation

ProtonFigure 5.3: Illustration of simple
example of an event showing thepoint of collision, the fragmentationand hadronisation of the quarks andgluons and the resulting jet foundthrough the detection of the stableparticle.

ProtonParticle jet
Calo jet4

A probability to be of hadronic or electromagnetic origin based on the cluster shower shape.

36

5.3. Jets

Coloured particles in the final state of a hard scatter are hadronised at typical scales of the strong
interactions. Secondary particles are collimated due to highly boosted partons with colour neutral
particles like pions or kaons. Jet properties like the particle multiplicity, energy profile and otherspatial distributions cannot be predicted from first principle because the hadronisation is a nonperturbative effect. Special care needs to take into account in terms of the definition of jets. It allows
a fair comparison between parton jets in parton-level calculation (perturbative QCD, pQCD) and calo
jets reconstructed from topo-clusters in the calorimeter. Figure 5.3 shows a sketch of these different
level jets. The jet reconstruction algorithm should satisfy stability criteria, i.e. should be stableagainst additional collinear and infrared radiation of additional partons and invariant under boost
transformation along the z-axis. Collinear and infrared safety are important properties to ensure theapplicability of the algorithm at parton-level due to soft and collinear radiations dominate in theparton shower. The anti-kT algorithm [141] is mostly used for jet reconstruction is implemented in
the FastJet package [142]. The following measures are defined with object i and j :

 ∆R2
i,j
−2
di,j = min p−2,p,T,i T,jr2
di,B = p−2
T,i ,

(5.2)
(5.3)

2 is the distance between topo-clusters i and j in the η − φ plane r is a size parameter ofwhere ∆Ri,jthe algorithm. r = 0.4 is used in this analysis. The algorithm calculates the di,j and di,B for all input
topo-clusters and finds the minimum among these quantities. The topo-cluster i and j are merged
into a single one until the minimum one becomes di,B , This cluster is considered as a jet removed
from the list of input topo-clusters. The algorithm repeats this steps until no more input clusters
are left over the list. The algorithm reduces circular jets in the η − φ plane with the radius of r. A
detailed description of this algorithm can be found in Reference [143]. Truth jets are reconstructedby the anti-kT algorithm as well, using truth particles in the simulated events. Truth jets are used
as references of the jet energy calibration, as shown in Section 5.3.2.

Jet Energy Calibration and Resolution
Energy Response

5.3.2

1.1
1
0.9
0.8

Etrue = 30 GeV
Etrue = 60 GeV
Etrue = 110 GeV
Etrue = 400 GeV
Etrue = 1200 GeV

Figure 5.4: Energy response as afunction of η before calibration for
EM scale anti-kT , r = 0.4.All pile-up
correction have been applied (takenfrom Reference [144]).

ATLAS Simulation Preliminary
Pythia Dijet s = 13 TeV
anti-k t EM jets R=0.4
true
ET >20 GeV

0.7
0.6
0.5
0.4
0.3
0.2

-4

-3

-2

-1

0

1

2

3

4
η

det

As mentioned above, an additional jet calibration is applied to correct for effects not accounted
for in the local cluster calibration. The pile-up correction is also applied using the jet are dependent
correction [145]. The average jet pT response( jet energy response) is defined by:
D
E
truth
R = pjet
/p
,
(5.4)
T
T
truth is the transverse momentum of calo-jet and truth jet respectively. The average
where pjet
T and pT

37

5.3. Jets∂p / ∂µ [GeV]T

1.2 ATLAS Simulation Preliminary
1 Pythia Dijet s = 13 TeV
0.8 anti-kt EM R=0.4

0.6

ATLAS Simulation Preliminary
0.4 Pythia Dijet s = 13 TeV

anti-kt EM R=0.4

T∂p / ∂NPV [GeV]truth distribution within a range of 1.6 σ from its mean value.
is taken from a Gaussian fit to the pjet
T /pT
Before applying the response correction, the effects of pile-up on jet calibration are subtracted using
an area-based subtraction method [146].

0.2

0.6
0

0.4
0.2

-0.2

0

-0.4
0

-0.4

Before any correction
After ρ×A subtraction
After residual correction

-0.2

0.5

1 1.5

2

2.5

3

3.5

Before any correction
After ρ×A subtraction
After residual correction

-0.6
4

4.5

0

0.5

1 1.5

2

2.5

3

3.5

4

|η|

(a) in-time pile-up correction

4.5
|η|

(b) out-of-time pile-up correction

Figure 5.5: Dependence of the reconstructed jet pT on in-time pile-up(a) and out-of-time (b) pile-up as afunction of jet η with three correction stages (taken from Reference [144]).

The jet are [147] is based on “ghost” particle5 association technique implemented in FaseJet
package. It assumes that the pile-up activities provide an uniform density distribution n the detector
and they are included in the jet clustering. The jet ares of the jet j which is belonged by the ghost
g is given by Aj = Ngj /νg , where Ngj is the number of ghosts contained in jet j, νg is the numberof ghosts per unit are. The jet are provides an estimate of a jet’s sensitivity to pile-up effects. The
jet
median pT density ρ is defined by ρ = median {pjet,jT /Aj } which the index j enumerates the jets
found with the kT algorithm [148, 149]. Effects of hard scatters can be reduced by taking the medianto estimate the pile-up effects. The use of the kT algorithm for the ρ calculation is motivated by its
sensitivity to soft radiation [145]. The pile-up subtracted pT based on residual correction is given by:
pcorr
= pEM
T
T − ρ × A − α × (NPV − 1) − β × hµi ,(5.5)

where α and β are parameters for residual correction for additional pile-up effects which are denotedby in-time and out-of-time pile-up, NPV is the number of primary vertex in events and hµi is anaverage of the number of interaction per bunch crossing. Figure 5.5 shows the correction factor ofin-time and out-of-time pile-up as a function of jet pseudorapidity. A set of data-driven corrections
is applied to correct the jet response differences between the simulated and real calorimeter [144].
These corrections are derived by comparing the jet energy to that reference object like a Z boson or
jet system. The direct balance with respect to well calibrated objects (electrons, muons and photons)
is used for absolute scale, di-jet balance allows to reduce systematic uncertainties. In addition tothese uncertainties, various systematical source of uncertainties need to be taken account like flavour
compositions. Full systematic uncertainty variations are shown in Figure 5.6 (a).
The resolution of the reconstructed jet is measured by the dijet balance technique. The dijet
balance technique measures the asymmetry A between the transverse momenta pjT1 , pjT2 of the dijet
system. The asymmetry A is defined by A = (pjT1 − pjT2 )/(pjT1 + pjT2 ). Its standard deviation σA gives
5

Neutral and infinitesimally soft (pT ∼ 10−100 GeV) particle

38

0.08

T

0.1
ATLAS Preliminary

Total uncertainty
Total uncertainty, 2012
Absolute in situ JES (2012)
Relative in situ JES (scaled 2012)
Flav. composition
Flav. response
Pileup, predicted 2015 conditions
Punch-through, predicted 2015 conditions
2012 to 2015 extrapolation uncertainty

0.06

0.04

0.02

0.1

T

s = 13 TeV, 25 ns
anti-kt EM+JES + in situ , R = 0.4
η = 0.0

Uncertainty on σ(p )/pFractional JES uncertainty

5.3. Jets

0.08

s = 13 TeV
anti-kt EM+JES + in situ , R = 0.4
η = 0.0

ATLAS Preliminary

Total uncertainty
Total uncertainty, 2012
Noise term
Dijet in situ measurement
γ +jet in situ measurement
Z+jet in situ measurement
2012 to 2015 extrapolation

0.06

0.04

0.02

0
20

30 40

102

2×102

(a) Energy scale uncertainty

103
2×103
jet
p T [GeV]

0
20

30 40

102

2×102

103
2×103
jet
p T [GeV](b) Energy resolution uncertainty

Figure 5.6: Jet energy resolution and scale uncertainties as a function of jet (η = 0) pT (taken from Reference [144]).

the resolution by taking approximation ofq(pjT1 )2 + (pjT2 )21 σ
E ' √ pT .
σ= D
j1
j2
2 pT
pT + pT(5.6)

The jet energy resolution is also measured by Z+jets and γ+jets events using same technique. It is
about 20% at pT = 30 GeV, 10% at pT = 100 GeV. The systematic uncertainties on the jet energy
resolution is shown in Figure 5.6 (b).

5.3.3

Jet Flavour Identification and Pile-up Suppression

An overview of the b-tagging or flavour-tagging [150, 151] is given in this section. The flavour
tagging is a key part in many physics analyses, for example in the b-jet multiplicity in tt̄ decays.
The identification of b-quark induced jets in ATLAS is based on unique strategies with three basic
b-tagging algorithms. The results of three algorithm are combined using a multivariate discriminant.
A brief overview are given in the following.

5.3.4

IP2D and IP3D: The Impact Parameter based Algorithm

The long lifetime of hadrons containing a b-quark (cτ ∼ 450 µm) can be used to build lifetimebased algorithms. The transverse (longitudinal) impact parameter (IP) d0 (z0 sin θ) is defined as the
distance of closet approach in the r-φ plane of the track to the primary vertex. Tracks from b-hadrons
tend to generate large impact parameters. The IP2D and IP3D tagger are based on a log-likelihood
ratio (LLR) between three jet-flavour hypothesis (b, c, light). Probability density function (PDF)
obtained from Monte Carlo simulation based on impact parameters with certain categorisation. The
IP2D tagger uses of the transverse Impact parameter significance d0 /σd0 as discriminating variablewhile the IP3D tagger uses both the longitudinal and transversePimpact parameters. The LLR
discriminant is computed as the sum of the per-track combination,log pb /pu , the sum run over all
track candidates. pb and pu are probability for the b- and light-flavour jet hypotheses respectively.
No correlation is assumed among the tracks contributions to the sum. Figure 5.7 shows the LLR
distributions for three jet-flavour using tt̄ Monte Carlo simulation.

39

10

10

Arbitrary units

Arbitrary units

5.3. Jets

ATLAS Simulation Preliminary1s=13 TeV, tt
b jets-1c jets10

10

ATLAS Simulation Preliminary1s=13 TeV, tt
b jets-1c jetsLight-flavour jets
10
10
10
10
10

Light-flavour jets

-2

10

-3

10

-4

10

-5

10

-6

-20

-10

0

10

20

30
40
50
IP2D log(P /P )
b

10

-2

-3

-4

-5

-6

-20

-10

0

10

20

u

(a) IP2D distribution

30
40
50
IP3D log(P /P )bu(b) IP3D distribution

Figure 5.7: The log-likelihood ratio for the IP2D (a) and IP3D (b) b-tagging algorithm for b- (solid green),c- (dashed blue) and light-flavour (dotted red) jets in tt̄ events (taken from Reference [150]). If no tracks inthe jet, a large negative value is assigned as output.

5.3.5

Secondary Vertex Finding Algorithm : SV

s=13 TeV, tt

10-1b jetsc jetsLight-flavour jets

ATLAS Simulation Preliminarys=13 TeV, tt

1010

Arbitrary units

ATLAS Simulation Preliminary

Arbitrary units

Arbitrary units

The secondary vertex finding algorithm [152] reconstructs an inclusive displaced secondary vertex
within the jet from all tracks in the jet. All track pairs are tested for a two-track vertex hypotheses
and rejected if they were to originate from the decay of a long-lived particle decay (Ks or Λ), photon
conversions or hadronic interaction with a material. The track candidate is selected by certain
criteria [150]. Each track pair should have a significant distance between the track and the primaryvertex, ∆R(PV, trk) > 2. The sum of the two impact parameter significance of the tracks in the
track pair vertex should be higher than 2. In addition the χ2 of the fitted track pair should be lessthan 4.5 and an invariant mass of the track pair should be less than 6 GeV to remove tracks fromb- or c-hadron decays. Figure 5.8 shows properties of the secondary vertex reconstructed by the SV
ATLAS Simulation Preliminary
10

10

-2

s=13 TeV, tt

-1

-2

-2

b jetsc jetsLight-flavour jets0

10 20 30 40 50 60 70 80 90 100
S (SV)xyz(a) The 3D decay length significance010

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
f (SV)b jetsc jetsLight-flavour jets

-3

0

1

E

(b) The energy fraction

2

3

4

5
6
m(SV) [GeV](c) The invariant mass

Figure 5.8: Properties of secondary vertices reconstructed by the SV algorithm for b- (solid green), c- (dashedblue) and light-flavour (dotted red) jets in tt̄ events (taken from Reference [150]). Note that: the energy
fraction (b) is defined as a fraction of the tracks in the displaced vertex and all tracks reconstructed within thejet.

algorithm. These properties are inputs for the final multivariate discriminator.

40

5.3. Jets

5.3.6

Decay Chain Multi-Vertex Algorithm : JetFitter

s=13 TeV, tt

10

10

-1

10

ATLAS Simulation Preliminarys=13 TeV, tt

10

-2

-1

b jetsc jetsLight-flavour jets

10

20

30

40

50

60

70 80 90
S (JF) (JF)xyz(a) The 3D decay length significance

0

10

10

-3

0

ATLAS Simulation Preliminary

10-2b jetsc jetsLight-flavour jets
10

Arbitrary units

ATLAS Simulation Preliminary

Arbitrary units

Arbitrary units

The JetFitter algorithm [153] can reconstruct multiple vertices in the jet. The full b-hadron decay
chain can be reconstructed. Kalman filter is used to find a common decay line from the primaryvertex into bottom and charm vertices with b-hadron decay in flight constraint. The JetFitter uses

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
f (JF)
E(b) The energy fraction

s=13 TeV, tt-1-2

b jetsc jetsLight-flavour jets

-3

0

1

2

3

4

5

6

7
8
9
m(JF) [GeV](c) The invariant mass

Figure 5.9: Properties of secondary vertices reconstructed by the JetFitter algorithm for b- (solid green),c- (dashed blue) and light-flavour (dotted red) jets in tt̄ events (taken from Reference [150]). Note that: theenergy fraction (b) is defined as a fraction of the tracks in the displaced vertex and all tracks reconstructedwithin the jet.

kinematical constraints in the fit. Figure 5.9 shows properties of the secondary vertex reconstructedby the JetFitter algorithm. These properties are inputs for the final multivariate discriminator.

5.3.7

Multivariate Algorithm : MV2

The input variables obtained from the three basic algorithms are combined using a boosted decision tree (BDT) to discriminate the b-quark from c-quark and light-flavour quark jets. The training
is performed on a few million tt̄ Monte Carlo simulation events. The MV2c20(MV2c10,MV2c00) algorithm is defined as the output of BDT with the training performed b-jets as signal and mixture of
80% (93%,100%) light-flavour jets and 20% (7%,0%) c-jets as a background. A detailed description of
the MV2 algorithm can be found in Reference [151]. Figure 5.10 shows the output score distributionof the MV2c20 and its rejection power to the c- and light-flavour jets with two different backgroundmixture hypotheses. In this thesis, The MV2c10 tagger is used with a working point is chosen toachieve 77% efficiency to the b-jet tagging while the c-jet rejection rate is 6 and light-flavour jet is134. To evaluate systematic uncertainties, several validations are performed by different training
configuration and alternative background samples with observed data(tt̄ → eµ + bb sample). It isassigned of roughly 5 ∼ 10% for inclusive |η| region over pbT = 20 GeV ∼ 300 GeV [151].

5.3.8

Tagging and Suppression of Pile-up Jets

Further subtraction of the pile-up activity in addition to the jet area method is important toimprove accuracy of missing transverse energy reconstruction. The Jet Vertex Tagger algorithm isused [154] which consist of the JVF and RpT variable. The Jet Vertex Fraction (JVF) and EpT is

41

10

10

-1

c jetsLight-flavour jets
-2

10

10

4

ATLAS Simulation Preliminary3

MV2c2010

ATLAS Simulation Preliminary2MV2c20MV2c00MV2c00
10

2

10

-3

10

s=13 TeV, tt
10c-jet rejection

10

ATLAS Simulation Preliminary
b jetsLight-flavour jet rejection

Arbitrary units

5.4. Electrons

jet

jet

p >20 GeV, | η |<2.5

jet

jet

-4

s =13 TeV, t t

s =13 TeV, t t
p >20 GeV, | η |<2.5

T

1

T

1

-1

-0.5

0

0.5
1
MV2c20 output

0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1
b-jet efficiency(a) The MV2c20 output distribution(b) The light-flavour rejection efficiency

0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1
b-jet efficiency(c) The c-jet rejection efficiency

Figure 5.10: The MV2 algorithm output distribution (a) and its rejection efficiency comparison between
MV2c20 and MVc00 for light-flavour (b) and c-jet (c) (taken from Reference [150]).

defined as following:trkk
k pT (PV0 )

JVF =

trkl
l pT (PV0 ) +

P

P

n≥l

trkk
l pT (PVn )(κ · nPU
trk )

P

trkk
k pT (PV0 )
.
pjet
T

P

P

, RpT =

(5.7)

where PV0 is the hard-scatter vertex (HS) and PVj , j ≥ 1 corresponds to primary vertices due to theof pile-up tracks
per event with the scaling factor
in-time pile-up interaction. nPU
trk is the total
DPnumberE
P trkkPU
κ = 0.01 determined by correlation withn≥ll pT (PVn ) and ntrk . It measures the fractionalpT from tracks associated with the hard-scatter vertex. The RpT is defined as the scalar pT sum of the
tracks associated with the jet from the HS vertex divided by the fully calibrated jet pT : The JVT isconstructed using JVF and RpT as a two dimensional likelihood based on a k-nearest neighbour (kNN)
algorithm. The JVT is defined by only jets with 20 < pT < 60 GeV and |η| < 2.4 since the PU jets
tend to have low pT . The likelihood is a ratio of the number of signal local neighbourhood and thenumber of signal + background local neighbourhood. The local neighbourhood is defined as the 100
nearest neighbours around the (JVF, RpT ) point using a Euclidean metric. Figure 5.11 shows the
JVF, RpT and JVT distribution for the HS and PU jets with certain jet pT range. Both JVF and
JVT = -1 events imply no-track candidate within the jet. a cut of JVT > 0.59 is used for suppressing
the pile-up jets. Figure 5.12 shows the selection efficiency for the simulated events and data. The
efficiency is measured using Z → µµ+jets events. If the jet is balanced to Z → µµ system then it
comes from the HS, while not balanced to Z → µµ, then it is likely from the PU. The systematic
uncertainties are evaluated by changing selection criteria, muon momentum variations and jet energy
scale uncertainty. The systematic uncertainty is a few percent level.

5.4

Electrons

Electron is an important experimental signature for many physics analyses, because it can bereconstructed and measured with high precision and purity. This is obtained by combined measurements and reconstructions with the tracking detectors and electromagnetic calorimeters. Electron
also provides a clean signature at the trigger level, so single electron trigger items are used in thisendlinger

42

ATLAS Simulation Preliminary

101

PU jets
HS jets

Pythia8 dijets
Anti-k t LCW+JES R=0.4|η| < 2.4, 20 < pT < 30 GeV
0 ≤ NVtx ≤ 30

10-1

102
ATLAS Simulation Preliminary

10
1

10-2

10-3

10-3

-0.5

0

0.5

Pythia8 dijets
Anti-k t LCW+JES R=0.4|η| < 2.4, 20 < pT < 30 GeV
0 ≤ NVtx ≤ 30

102
ATLAS Simulation Preliminary
Pythia8 dijets
t LCW+JES R=0.4
10 Anti-k|η| < 2.4, 20 < p < 30 GeV

0 ≤ NVtx ≤ 30

PU jets
HS jets

T

1
10-1
10-2

10-40

1
corrJVFPU jets
HS jets

10-1

10-2

10-4-1

Normalized Entries

102

Normalized Entries

Normalized Entries

5.4. Electrons

0.5

1

1.5

10-3

0

0.5

RpT

(a) JVF distribution(b) RpT distribution

1
JVT(c) JVT distribution

JVT selection efficiency

Figure 5.11: Distribution of the JVF, RpT and JVT for HS and PU jets with 20 < pT < 30 GeV (taken from
Reference [155]).
ATLAS Preliminarys = 13 TeV, 13.3 fb-1 (2015 + 2016 data)

1.3
Z→µ µ selection

1.2

MC Powheg+Pythia8

1.1

data

1
0.9
0.8
0.7
20

Data / MC

Figure 5.12: The hard-scatter jet
selection efficiency for Monte Carloand observed data (2015+2016) of
JVT > 0.59 cut with Z → µµ
events. Overall systematic uncertainties are obtained from datadriven way and it shows less than
5% in lowest jet pT bin, at highest
jet pT bin it is roughly 1% level.

1.5
1.4

Default working point (JVT > 0.59)
25

30

35

40

25

30

35

40

45

50

45

50

55

60

55

60

1.05
1
0.95
20

Leading jet p [GeV]T

hadronic calorimeter

third layerelectromagnetic
calorimetersecond layer∆η×∆φ = 0.025×0.0245

first layer (strips)

η∆η×∆φ = 0.0031×0.098

presamplerφ

TRT (72 layers)
Rφ
SCTbeam axis

pixelsbeam spot

eProbabilityHT

Rη

Figure 5.13: Schematic view ofthe electron reconstruction andidentification (taken from Reference [156]). Electron is reconstructed by full information using theinner detector including the TRT
hit probability likelihood information and the EM calorimeter cluster
shower shapes.

d0
insertable b-layer

hadronic calorimeter
third
layer
TRT
pe/(pe+pπ)
TRT pe/(pe+pπ)

analysis. Figure 5.13 shows a schematicview
ofelectromagnetic
the electron reconstruction and identification, which
PID
secondlayerTRT
calorimeterF
described in Section 5.4.1 and 5.4.3 respectively.
An overview of the energy calibration, resolution
ηfirst layer (strips)
and its uncertainty measurements
are given in Section 5.4.2. In addition, an electron isolation ispresampler
φa key item to reduce mis-identification
objects originatedfrom hadronic jets. An brief overview of
TRT (72 layers)
an isolation selection is given in Section 5.4.4. A description
R φ of the electron trigger is also given in
SCTSection
5.4.5
pixelsWZ#Overlap#Removal#Studies
beam axis
4HTbeam spot

FHT

d0
insertable b-layer

Rη

43

5.4. Electrons

5.4.1

Electron Reconstruction

The electron reconstruction in the central region of the ATLAS detector (|η| < 2.46) is given byfollowing procedure. A detailed description can be found in Reference [156].
• Seed-cluster reconstruction : Electron seed clusters are reconstructed by a sliding window witha size of 3 × 5 (unit is 0.025 × 0.025) in η × φ by the EM calorimeter. A seed clustering efficiency
ranges from 95% at ET = 7 GeV to more than 99% above ET = 15 GeV.
• Track reconstruction : A pattern recognition and track fit are performed for electron track seeds.
In order to take into account the Bremsstrahlung the pattern recognition algorithm allows
up to 30% energy loss at each intersection of the track assuming the pion hypothesis. Afterthat a second pattern recognition is performed by an electron hypothesis. The ATLAS Global
χ2 Track Fitter [157] is used to fit track candidates with firstly the pion hypothesis and if it
fails then refitted with the electron hypothesis.
• Gaussian Sum Filter : The obtained tracks are required to natch with the EM clusters using a
distance in η − φ considering energy loss due to the Bremsstrahlung. Tracks are refitted using
Gaussian Sum Filter (GSF) [158] which can take into account non-linear Bremsstrahlung effects.
• Electron reconstruction : A matching of the track candidate and the cluster seed is performed
finally. If several tracks satisfy matching criteria, one “primary” track is chosen based on analgorithm using the cluster-track distance R calculated with a different momentum hypothesis.
The number of pixel hits and the presence of hits in the first layer of the silicon detectors areused [159].

ATLAS Preliminarys=13 TeV, 3.2 fb-1

0.98
-2.47<η<2.47
0.96

Data
Z → ee MC

0.94
1.02
1
0.98

20

40

60

80

100 120 140
Cluster ET [GeV](a) Efficiency (ET )Reconstruction efficiency

1

Data/MC

Data/MC

Reconstruction efficiency

The four-momentum of electron is calculated using information from both the calibrated energy
cluster6 and the best track matched to the original seed cluster. The energy is given by the calibrated
cluster, while the η and φ direction are from the corresponding track parameter with respect to theprimary vertex of a hard scatter. Figure 5.14 reconstruction efficiencies using Z → ee events for

1

ATLAS Preliminarys=13 TeV, 3.2 fb-1

0.98
15 GeV < ET < 150 GeV

0.96

Data
Z → ee MC

0.94
1.02

E

1
0.98

−2

−1

0

1

2
Cluster η(b) Efficiency (η)

Figure 5.14: Efficiencies and scale factors fro the electron reconstruction as a function of electron transverse
momentum (left) and pseudorapidity (left) using Z → ee events(taken from Reference [156]). Markers withclosed (open) circle shows real (simulated) data in upper panels, while the scale factors in represented in thebottom panels.

simulated and experimental data. Differences between simulated and experimental data should be
6

Based on multivariate technique, details can be found in Reference [160]44

5.4. Electrons

taken account by correction factors ( scale factors, SF ). The scale factor have been evaluated using
Z → ee tag-&-probe method [156] in this analysis.

5.4.2

Electron Energy Calibration and Resolution

0.04

ATLAS

0.035

∫

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

0.03∆σ / σσ/EA detailed description about the electron calibration is found in Reference [161]. There are several different steps in the procedure to calibrate the energy response of electrons for simulated andexperimental data. The procedure can be split up to 5 ∼ 4 steps. Starting from the EM cluster
energy, a MC-based e/γ energy calibration is applied for the simulated and real data. The longitudinal calorimeter layer inter-calibration is applied for only real data. The MC-based e/γ energy
calibration is based on a multivariate technique. Uniformity corrections are applied for only real datato correct the energy response difference of φ-angle plane. Then the Z → ee resolution smearing andscale calibration is applied for the simulated and real data. The calibrated electron energy scale isvalidated with electron candidates from J/ψ → ee and Z → e+ e− events in real data. The electron
0.5
0.45
0.4
0.3

0.02

0.25

Electrons, |η|=0.2

0.2

0.015

0.15

0.01

0.1

0.005
0

Total
Cst. term (Z→ ee)
Sampling term
Material
Pileup

0.35

0.025

∫

s=8 TeV, Ldt = 20.3 fb-1

ATLAS

0.05
20

40

60

80

100 120 140 160 180 200

0

20

40

60

80

100 120 140 160 180 200
ET [GeV]ET [GeV](a) Energy resolution(b) Resolution uncertainty

Figure 5.15: Resolution curve and its uncertainty as a function of electron ET (left) and its enveloped withdifferent systematical uncertainties source (right) (taken from Reference [161]).

energy resolution is defined by the following:σE1b= √ ⊕ ⊕ c,
E
E E

(5.8)

where a, b and c are η-dependent parameter: a is the sampling term, b is the noise term and cis constant term. The sampling term is derived from the calorimeter intrinsic resolution. It is
obtained from detector simulation and its systematic uncertainties is assumed as 10% from test-beamstudies [162]. The pile-up and electric noise of the EM calorimeter are a source of he noise term. The
constant term is measured by Z → ee events assuming hET e i ' 40 GeV in Z → ee event. Figure 5.15
shows the electron energy resolution and its systematics uncertinties as a function of the electron ET .
In addition to three terms above, systematic uncertainties of a material in calorimeter is obtained byalternative simulations. The relative energy resolution at ET = 40 GeV is about 2% with relatively
7% uncertainty.

5.4.3

Electron Identification

In order to reduce mis-identified hadronic jets and converted photons, an algorithm for electron
identification (ID) is constructed by using properties of reconstructed electrons. The electron ID
algorithm is based on a likelihood (LH) technique with the signal and background probability density

45

5.4. Electrons
function (PDF) given by :
n

dL =

Y
LS
, LX (~x) =PX,i (xi ),LS + LB

(5.9)

i=1

1
0.95

Reco + ID efficiency

Reco + ID efficiency

where ~x is the vector of discriminating variables and PX,i (xi ) is the value of the signal or background
PDF of the variable xi . The input variable list is summarised in Reference [156]. For example theshower shape of the topo-cluster and information of hit in TRT are used in the electron ID algorithm.
The PDFs for the signal and background are obtained from simulated samples of Z → ee and dijet
respectively. The electron ID has three different working point, Loose, Medium and Tight. The
ATLAS Preliminary

0.9
0.85
0.8
0.75

1

0.9
0.85
0.8
0.75

s = 13 TeV, 3.2 fb-1

0.7

s = 13 TeV, 3.2 fb-1

0.7

-2.47<η<2.47
Loose
Medium
Tight

0.65
0.6

0.6

Data: full, MC: open

1
0.9
0.8
10

20

30

40

50

60

ET>15 GeV
Loose
MediumTight

0.65

Data / MC

Data / MCATLAS Preliminary

0.95

70

80

Data: full, MC: open

1
0.9
0.8
−2.5 −2 −1.5 −1 −0.50(a) ET

0.5

1

1.5

2

2.5
η

ET [GeV](b) ηFigure 5.16: The efficiency and scale factor of the electron LH ID including reconstruction efficiency as afunction of electron transverse momentum (left) and pseudorapidity (left) using Z → ee events with threedifferent ID working points (Loose, Medium and Tight) (taken from Reference [156]).

working points are constructed for different identification efficiencies. At ET = 40% efficiencies of
Loose, Medium and Tight correspond to about 78%, 87% and 97% for signal electrons in real data.
The Medium working point is used for default electron ID and its scale factors is derived by Z → eetag-&-probe method. Figure 5.16 shows the efficiency of the electron ID for the signal electrons using
Z → ee events in simulated and real data. The systematic uncertainties are derived in data-driven
ways and also alternative detector simulations using different condition of the Genat4 simulation.
Besides identification of electron, the LH ID is used for the hadronic τ -lepton identification which
described in Section 5.6.3.

5.4.4

Electron Isolation

In addition to the identification, an isolation requirement is useful to further distinguish the signal
and background. The isolation variable quantify the energy of the particles produced around theelectron candidate. Two discriminating variables are used for this purpose.
cone0.2 : defined as the sum of transverse energies of topo-clusters calib• Calorimeter isolation ET
rated at the EM scale within a cone of ∆R = 0.2 around the electron candidate. An (ET , η)dependent correction is applied to take into account the electron energy leakage outside cluster
and pile-up. Underlying effects is also corrected on event-by-event [145]• Track isolation pvarcone0.2: defined as the sum of transverse momenta of all tracks which satisfyTcertain track selection criteria within cone of ∆R = min(0.2, 10 GeV/ET ) around the candidate

46

5.4. Electrons
electron track [156].

1
0.95

ATLAS Preliminary-1

s = 13 TeV, 3.2 fb
0.1 < η < 0.6

0.9

FixedCutLoose
Data
Z → ee MC

0.85
0.8

Electron isolation efficiency

Electron isolation efficiency

Several working points are constructed for the isolation selection, in this thesis analysis Gradientworking point has been chosen as a default isolation selection. In addition to Gradient working point,
the Tight and FixedCutLoose are used in the electron trigger (Section 5.4.5) and background estimcone0.2 and pvarcone0.2
ations (description is in Section 6.5.1). It is two-dimensional selection using ET
T. Selection cut values depend on the transverse momentum correspondingly satisfying efficiencyof min ((0.1143 × ET + 92.14)%, 99%). The total efficiencies are 90 (99)% at 25 (60) GeV of electron ET . Figure 5.17 shows the efficiency and scale factors of the electron isolation selection with
1

0.995

0.99

ATLAS Preliminarys = 13 TeV, 3.2 fb-1
35 GeV < ET < 40 GeV

FixedCutLoose
Data
Z → ee MC

0.985

1.02

40

60

Stat ⊕ Syst

80

100

120

Stat only140
ET [MeV]

1
0.98
20

40

60

80

100

120

140

ET [GeV]

Data / MC

Data / MC

0.98
20

1.005

−2

− 1.5

−1

− 0.5

Stat ⊕ Syst

0

0.5

1

Stat only

1.5

2
η

1
0.995

−2 −1.5(a) ET−1 −0.5

0

0.5

1

1.5

2

η

(b) η

Figure 5.17: The efficiency and scale factor of the electron isolation selection (FixedCutLoose) as a functionof electron transverse momentum (left) and pseudorapidity (left) using Z → ee events (taken from Refervarcone0.2
cone0.2/ET < 0.15.
/ET < 0.2 and pTence [156]). The FixedCutLoose requires ET

FixedCutLoose working point. The total uncertainties are within 2 ∼ 3% level at low ET region. In
this analysis the electron is required ET > 30 GeV so its uncertainties are about less than 1% level.

5.4.5

Electron Trigger

As discussed in Section 4.2.6, at each stage of the ATLAS trigger system the identification andisolation algorithm are used. At the L1 RoIs, the identification and isolation using a sliding window
algorithm on calorimeter trigger towers with a granularity of ∆η × ∆φ = 0.1 × 0.1 are required
using a dedicated electronics. HLT uses the full granularity from the RoIs (L1EM items) withcombining the calorimeter clusters and tracks, which is close to the offline-like algorithm. The trigger
items used in the analysis are called as single-electron-trigger, requiring the presence of one electron
candidate above a certain pT threshold, identification and isolation criteria. In this analysis, six singleYearpT

identification

2015
2016

24, 60, 120(20) GeV for HLT (L1)26, 60, 140(22) GeV for HLT (L1)medium, medium, loose
tight, medium, loose

Table 5.1: The single-electron-trigger items used in this analysis for 2015 and 2016 data-taking.

electron-trigger items are used corresponding to data-taking periods and its pT thresholds based on
Reference [163]. Table 5.1 summarise the single-electron-trigger which used in this analysis. Threedifferent pT threshold menus are taking OR-ing to reduce uncertainties and suppress online isolation

47

5.5. Muons

1
0.8
0.6

ATLAS Preliminarys=13 TeV, 3.2 fb-1

Trigger Efficiency

Trigger Efficiency

inefficiency. Figure 5.18 shows the trigger efficiency of the 2015 lowest-pT single-electron-trigger for
1
0.8
0.6

ATLAS Preliminarys=13 TeV, 3.2 fb-1

0.4

0.4

single electron trigger
Data
Z → ee MC

0.2

0.2

single electron trigger
Data
Z → ee MC

Data / MCET [GeV]

1
0.95
20

40

60

80

100

Data / MC

0
1.05

0
1.05

η

1
0.95

120 140
ET [GeV](a) ET−2 −1.5 −1 −0.5

0

0.5

1

1.5

2

η

(b) η

Figure 5.18: The efficiency and scale factor of the single-electron-trigger of 2015 pT threshold of 24 GeV as
a function of electron transverse momentum (a) and pseudorapidity (b) using Z → ee events (taken from
Reference [156]).

simulated and experimental data using Z → ee tag-&-probe method. (a) shows the trigger efficiency
as a function of the offline electron pT . Small drop in low pT region can be seen. In this analysis
pT > 30 GeV is required, so the efficiency in all range of pT has greater than 80%. (b) shows thetrigger efficiency as a function of the offline electron η. There are non-negligible efficiency drop in|η| ∼ 1.5, this region is so-called crack-region due to a large amount of dead-material (service cableof the inner detectors). In this analysis electrons which pointed in 1.37 < |η| < 1.52 are vetoed.

5.5

Muons

Muon is a minimal ionised particle (MIP), so energy deposit in the calorimeter is extremely small.
The ATLAS detector has dedicated muon spectrometers outside of the hadronic calorimeter, which
can measure its momentum. The muon spectrometers are located inside a magnetic field of a average
field strength of 0.5 T providing a bending power to ensure a high momentum resolution for muon
up to 1 TeV. Thanks to low mis-identification rate of backgrounds and the precise momentum measurement, muons provide an excellent trigger signature. Explanation of the muon reconstruction andits identification are given in Section 5.5.1 A brief overview of the muon momentum calibration andisolation is described in Section 5.5.2. and 5.5.3. The muon signature trigger used in the analysis isshown in Section 5.5.4.

5.5.1

Muon Reconstruction and Identification

Muon reconstruction is performed independently in the inner detector (ID) and muon spectrometer (MS). Muons are reconstructed as described in Section 5.1 in the inner detector. The muonreconstruction in the MS and its combination are focused in this section.
In each MDT chamber and other trigger chamber, a Hough transform [164] is used to find hitsaligned on the bending plane of the detector. For example, MDT segments are reconstructed by
performing a straight-line fit to the hits found in each layer. Muon track candidates are built by
fitting together the segments from in the different layers. At least two matching segments are required
to build a muon track, except in the barrel-endcap transition region. The different track candidates

5.5. Muons48

can initially share the same segment. The hits associated with each track candidates are fitted tominimise a global χ2 . A track candidate is selected by certain criteria using the χ2 of the fit. The fit
is repeated until no additional hits are found around the track candidates.
The combined ID-MS muon reconstruction is performed according to various algorithm based on
the information provided by the ID, MS and calorimeter. Following four-types are defined dependingon which subdetectors are used in reconstruction:• Combined muon (CB) : The muon are first reconstructed in MS, then the outside-in patternrecognition extrapolates the MS track into the inner detector to find corresponding a ID track.
The inside-out pattern recognition is used to find a MS track matched with the ID track.
• Segment-tagged muons (ST) : In order to recover the efficiency to low pT muons, a track in
the inner detector is classified as a muon if it can be extrapolated to MS. Because the low pT
track has only one segment hit in muon chambers, the ID track is required at least one track
segment.
• Calorimeter-tagged muons (CT) : Tracks in the inner detector is identified as a muon if it
can be matched to an energy deposit in the calorimeter is compatible with a MIP. CT muonhas the lowest purity of all the muon types. CT muon can recover acceptance in the region
where the ATLAS MS is only partially installed for cabling and services to the calorimeterand inner detector. The identification criteria is optimised for region of |η| < 0.1 where otherreconstruction algorithm efficiency drops.
• Extrapolated muons (ME) : This type consists of a muon track based on only a MS track. Loosematching with originating the interaction point is required. ME muons are mainly used torecover an acceptance for a muon in the region of 2.5 < |η| < 2.7 where there are no innerdetectors.
Chain 3rd algorithm is used in this analysis as described in Reference [165]. The chain 3rd algorithm
takes OR of existing tracks and removes overlapped tracks.
In addition to muon reconstruction, identification selection is applied using three variables listed
in below:• q/p significance : defined as the absolute value of the difference of the ratio of the charge to its
momentum. It is divided by the quadrature sum of its uncertainties.
• ρ0 :

defined as the absolute value of the difference between the transverse momentum in the ID
and MS. It is also divided by the pT of the combined track.

• χ2 : defined as normalised χ2 of the combined track fit.
Four muon identification working points are defined. The Medium working point is used as a default
in this analysis. The Medium working point requires the muon tracks reconstructed by only the CB
tracks. It has greater than three hits in at least two MDT layers, except for tracks in the |η| < 0.1
region, where there is only one MDT layer. No more than one MDT hole are allowed. The q/p
significance should be less than seven and ρ0 is required by a loose compatibility selection. Figure 5.19
shows the reconstruction and identification efficiency for the medium working point using Z → µµ
and J/ψ → µµ tag-&-probe method. The efficiency is ≥ 98% for a muon with 20 < pT < 100 GeV.
While the efficiency of fake muons from hadrons is less than 0.2%. The total uncertainties are lessthan 3% level at hole range of the muon pT and also muon η.

49

Efficiency

Efficiency

5.5. Muons1

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

Medium muons, |η|>0.1

1.02

Stat only

Sys ⊕ Stat1
0.98
6 7 8 910

20

30

40 50 60
102
p [GeV]

0.98
0.96

0.65

ATLAS

Z→µµ

s = 13 TeV, 3.2 fb-1

0.6

Data

Medium muons

MC

Loose muons (|η| < 0.1)

Data / MC

ATLAS

1

1.02

Stat only

Sys ⊕ Stat1
0.98
−2.5 −2 −1.5 −1 −0.5 0 0.5 1 1.5 2 2.5
ηT(a) pT(b) η

Figure 5.19: Reconstruction efficiency for the medium working point as a function of pT (a) and η (b) measured by Z → µµ and J/ψ → µµ tag-&-probe method for simulated and experimental data (taken from
Reference [166]). The error band on top (bottom) panel indicate the statistical (statistical plus systematical)
error.

5.5.2

Muon Momentum Calibration and Resolution

The muon momentum calibration is defined as corrections to the simulated muon transverse momenta reconstructed in the ID and MS to reproduce the experimental data. It corrects the ID and
MS components of the CB track. The corrected transverse momentum pcorr,det(det = ID,MC) isT
defined by following :pcorr,det=
TP
MC,det n)+ n=0 1sdet
pMC,detn (η, φ)(pTT,
P2MC,det m−1
det)
gm
1 + m=0 ∆rm (η, φ)(pT(5.10)

is the un-corrected pT in the simulated samples, gm is random Gaussian distribution
where pMC,detT
det (η, φ) and sdet (η, φ) represents the momentum reswith zero mean and unit width. The term of ∆rmnolution smearing and scale correction factors respectively. Detailed values of the resolution smearing
and scale correction can be found in Reference [165]. The correction factors are obtained from theobserved Z → µµ and J/ψ → µµ line shape with fitting the momentum scale and smearing, which
are shown in Figure 5.20 On mZ shapes, total uncertainties are estimated to about 2 ∼ 5% in rangeof 20 < pT < 100 GeV.

5.5.3

Muon Isolation

The muon isolation selection is also applied to reduce the fake background coming from semileptonic decay of B-meson or other hadrons. The track and calorimeter based isolation are defined
as well as the electron isolation. The definition of the muon isolation requirement is similar to theelectron. The correction against pile-up effects are slightly different but it is not relevant to explainin this thesis [165]. The Gradient isolation selection working point of the muon is also used which issame definition as the electron. Figure 5.21 shows the efficiency of the isolation selection as a functionof the transverse momentum. The efficiency is measured to about 92% for low pT muons, while ¿ 99%
is achieved for high pT muons. The systematic uncertainty is derived by uncertainty of backgroundsubtractions, muon momentum and Identification. It is estimated as less than 1% in wider pT range.

50

5.5. Muons

3

35
30

ATLAS

Data

s = 13 TeV, 2.7 fb-1

MC

Entries / 0.01 GeV

Entries / 0.60 GeV

3×10

MC (uncor.)Z→µ µSyst. uncert.

25
20

ATLAS

120

s = 13 TeV, 2.7 fb-1

DataMC
MC (uncor.)
BackgroundSyst. uncert.

J/ ψ →µ µ
100
80
60

15
10

40

5

20

0
1.2

1.2

0

Data/MC

Data/MC

×10
140

1.1
1
0.9
0.8

1.1
1
0.9
0.8

75

80

85

90

95

100

105

m µ µ [GeV](a) Z → µ+ µ−

2.9

2.95

3

3.05

3.1

3.15

3.2

3.25

m µ µ [GeV](b) J/ψ → µµ

Efficiency

Figure 5.20: Dimuon invariant mass distribution of Z → µµ (a) and J/ψ → µµ candidate events (taken from
Reference [166]). Solid (dashed) histograms present before (after) applying momentum corrections. The lower
panels shows the ratio between the MC simulation and experimental data. Good agreements can be seen after
the corrections.

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

Figure 5.21: Isolation efficiency for theGradient working point (taken from Reference [166]). The efficiency is shown as
a function of the muon pT by Z → µµ
events. The closed (open) markers indicate the efficiency measured in data (simulation) samples. The error bands shownon the efficiency are statistical only. The
bottom panel shows the ratio between efficiency measured in data and simulation,
as well as the statistical and systematic uncertainties.

p [GeV]T

5.5.4

Muon Trigger

The ATLAS muon trigger follows the two-level design of the ATLAS trigger system. The L1
trigger takes a decision based on coincident signals in the muon trigger chambers. RPC work inbarrel-region (|η| < 10.5) and TGC work in the endcap region (1.05 < |η| < 2.4). The L1 send
the RoIs information to the central trigger processor to make the HLT decision. The HLT used byoffline-like muons using full detector information from RoIs also has option of HLT level full scan ofmuons. Three single-muon-triggers are used in this analysis. An OR of single-muon-triggers with pT
threshold of 20 GeV (with loose isolation selection) and 50 GeV is used for the 2015 data. While pT
threshold of 26 GeV (with medium isolation selection) and 50 GeV are used for the 2016 data.
The single-muon-trigger has extremely good resolution on both the L1 and HLT items. Figure 5.22
shows the muon trigger efficiency as a function of offline muon pT and φ for the barrel and endcap
region. An inefficiency can be seen at the L1 trigger (mu15) due to inefficiencies of RPC chambers inthe barrel region. There are also efficiency drop around φ ∼= −1.2 ∼ −2.0, due to huge materials of
the toroidal magnet arms. While in the endcap region, the L1 has > 90% efficiency at the plateau
region. The HLT efficiency with regard to the L1 is greater than 90% for both the barrel and endcap
region. The total efficiency of the single-muon-trigger is 70 (85)% in the barrel (endcap) region.

51

5.6. Hadronic Tau Decays

ATLAS Preliminarys=13 TeVµ

Z → µµ, |η | < 1.05

Efficiency

Efficiency

miss trigger is introduced in this
The inefficiency in the barrel region is not negligible. So the ET∫ Ldt = 522 pb

-1

1

0.5

ATLAS Preliminary
µ

T

20

40

60

L1 MU15
HLT mu20_iloose or mu50
HLT mu20_iloose or mu50
with respect to L1

80

0

100

−2

0

2

offline muon φ

T

ATLAS Preliminarys=13 TeVµ

Z → µµ, 1.05 < |η | < 2.4(b) φ, barrel

Efficiency(a) pT , barrel

Efficiency

-1

0.5

offline muon p [GeV]∫ Ldt = 522 pb

-1

1

0.5

ATLAS Preliminarys=13 TeVµ∫ Ldt = 522 pb-1

Z → µµ, p > 21 GeV, 1.05 < |ηµ| < 2.4
T

1

0.5
L1 MU15
HLT mu20_iloose or mu50
HLT mu20_iloose or mu50
with respect to L100∫ Ldt = 522 pb

Z → µµ, p > 21 GeV, |ηµ| < 1.05

1

L1 MU15
HLT mu20_iloose or mu50
HLT mu20_iloose or mu50
with respect to L100s=13 TeV

20

40

60

L1 MU15
HLT mu20_iloose or mu50
HLT mu20_iloose or mu50
with respect to L1

80

100

offline muon p [GeV]

0

−2

0

T

(c) pT , endcap

2

offline muon φ(d) φ, endcap

Figure 5.22: Efficiency of the single-muon-trigger (mu20 iloose L1MU15 or mu50) for the barrel and endcap
region as a function of offline muon pT (a,c) and φ (b,d) (taken from Reference [167]). The efficiency is measured
by using a Z → µµ tag & probe method.

analysis to recover them. Detailed description is given in Section 5.7.3. The scale factor are obtainedby experimental data using Z → µµ and J/ψ → µµ tag-&-probe method. The uncertainties ofthe single-muon-trigger are obtained from the Z → µµ tag-&-probe method. Variation of Geant4
simulation parameterization is taken into account as an additional systematic uncertainty. It is ranges
1 ∼ 5% on inclusive muon pT range.

5.6

Hadronic Tau Decays

The τ -lepton is the heaviest lepton with a mass of mτ = 1776.86 ± 0.12 MeV [168]. The τ -leptons
decay with a mean lifetime of τ = (290.4 ± 0.5) × 10−15 s via weak charged current interactions into
hadrons or light leptons (electron or muon). Table 5.2 summarises decay modes for leptonic (τ` ) andhadronic (τhad ) decay7 . The main leptonic modes decays into one charged lepton and two neutrinos.
In addition to these modes very rare decay with multiple charged leptons exist below the branching
fraction of < 2.8 × 10−5 . Since in the ATLAS detector lepton from the τ -leptonic decay cannot be
identified, our target of an identification of the τ -lepton decay is to distinguish hadronically decaying
τ from the τ -lepton hadronic decay.
In the decay products of the hadronic decay mode should contain an odd number of charged
7

The symbol τ` and τhad is used to denote both a leptonically and hadronically decay. In addition to this τvis is used
to its reconstructed visible decay products without neutrinos.

52

5.6. Hadronic Tau Decays

hadrons for the charge conservation. The 1- or 3-prong decay modes dominate its branching fractionsof hadronic τ -lepton decays. The main process for the 1- or 3-prong modes can be seen in Table 5.28 .
The difference of the number of neutral hadrons are not taken into account in this analysis9 . In the
future this technique will be important in precision measurement of the SM Higgs boson.
decay mode

final state

main decay mode

BR (%)

Total (%)

leptoniceµe− + ν̄e + ντµ− + ν̄µ + ντ

17.82
17.39

35.21

1prong1π ∓ + 0π 0
1π ∓ + 1π 0
1π ∓ + 2π 0

π − + ντ−
ρ → π− + π0

10.82
25.93
12.15

48.90

3π ∓ + 0π 00−a−
1 →ρ +πω + ρ0

9.8
5.29

15.09

3prong3π ∓ + 1π 0a1→ ρ− + π 0

Table 5.2: Main decay modes, the corresponding branching ratio, its main decay process. The branching
fractions are the result of a combined fit to several experimental data, taken from Reference [168].

The hadronic-τ decay products are highly collimated, because typical momenta of the τ -leptons
produced in electroweak interactions are larger than its mass. This collimated hadrons can be reconstructed as a narrower jet compared with jets from quark or gluon hadronisation. The reconstruction
procedures are described in Section 5.6.1. The number of reconstructed tracks and cluster shower
shape profiles are used to distinguish hadronic-τ from hadronic jets. Besides hadronic jets, electrons
provide similar signature to the 1-prong decay when an electron track is accidentally combined withhadronic calorimeter activity. A dedicated set of identification criterion is used to suppress electrons
mis-identified as hadronic-τ objects. The identification algorithm including separation of electrons
are described in Section 5.6.3. A specific energy momentum calibration is performed to the visible
τhad objects. This calibration procedure is described in Section 5.6.2.

5.6.1

Hadronic-τ Reconstruction

The visible hadronic-τ 10 reconstruction algorithm have been developed and tested during the Run1
data-taking [170, 171]. Several improvements have been implemented as in Reference [169] from theRun2. As an input for seeds of the hadronic-τ reconstruction, hadronic jets reconstructed by the antikT with a distance ∆R = 0.4. Seed jets are calibrated by the local hadronic topo-cluster scale (LC).
The seed jets are required to selection criteria of pT > 10 GeV and |η| < 2.5. Topo-clusters in thecore region (∆R < 0.2) are used to reconstruct kinematic of hadronic-τ , while those in the isolation
region (0.2 < ∆R < 0.4) are used to suppress the background. The topo-cluster is reconstructed withthe hadronic calorimeter and the last layer of the EM calorimeter. Other layers of the EM calorimeterare used for referring the energy deposit in the EM calorimeter.
Vertex Association and Track Selection
The seed jet is required to have ID tracks within the core region, which satisfy:• pT > 1 GeV
8

in addition to the pion mode, there are non-negligible Kaon decay process, but the ATLAS detector cannot separate
them, so only the pion decay mode are summarised.
9
The ATLAS collaboration have already developed an algorithm to distinguish this “substructure of hadronic decay”
in Reference [169] by using a particle flow algorithm.
10”visible” means only hadronic components without neutrino, same argument visible-τ is also used in this thesis.

53

5.6. Hadronic Tau Decays• Number of pixel + IBL hits ≥ 2 and number of pixel + SCT hits ≥ 7• |d0 | < 1.0mm and |z0 sin θ| < 1.5mm

where d0 (z0 ) is the distance of closest approach of the track to the vertex in the transverse (longitudinal) plane. These two impact parameter selections should be robust against high pile-up environment. The 1-prong decay consists of only one charged tracks (or, and neutral π 0 activity). So thetrack-to-vertex association is important to reconstruct the 1-prong hadronic-τ . Usually the trackto-vertex association is performed using d0 and |z0 sin θ|. This association becomes difficult under
the high pile-up
environment. The primary vertex (PV) is chosen as the highest sum of transverse
P∈vtx
2
momentum ( trk (ptrk
T ) ) vertex. The Tau Vertex association (TV) algorithm [155] chooses thevertex using the fraction of the sum pT between all tracks in the jet and tracks associated to thevertex defined by following :P∈vtx trk
pT
vtx
fTV = Ptrk,
(5.11)∈jet trk
trk pT

1

1.05
1

0.95

0.95

0.9

0.9

0.85

0.85

0.8
0.75
0.7
0

ATLAS Preliminary
Simulation mc15
1-prongs = 13 TeV
10

20

30

40

50

Default primary vertex

0.8

Tau Vertex

0.75
60

70

80

90 100normalized

1.05

Efficiency

Efficiency

where the vertex association selection is optimised for the 1-prong and 3-prong separately. Fig-

0.7
0

ATLAS Preliminary

truth 1p
truth 3p

Simulations = 13 TeV

0.8
0.6

ATLAS Preliminary
Simulation mc15
1-prongs = 13 TeV
5

10

15

0.4
Default primary vertex
Tau Vertex

20

0.2

25

pτ [GeV]

30
NVtx

T

(a) Efficiency (pT )1(b) Efficiency (NPV )

0

0

1

2

3

4

5

reconstructed number of tracks(c) The number of tracks

Figure 5.23: Efficiency for correct production vertex association in 1-prong hadronic-τ with default (black
circle) PV and TV (red circle) as a function of visible-τ pT (a) and the number of reconstructed vertices (b)using MC simulation. Plot (c) shows the number of track associated with the selected TV for the 1- and3-prong visible-τ objects (taken from Reference [171]).

ure 5.23 shows the efficiency of the TV and the default PV selection. The TV algorithm improves
its association efficiency for the 1-prong τ . The number of tracks associated with the TV is shownin Figure 5.23 (c). Most of the 1- and 3-prong are reconstructed as correct decay mode. Figure 5.24
shows the efficiency of the reconstruction of visible-τ objects and its systematic uncertainties. The
reconstruction efficiency is about 70% on an average. The efficiency to the 3-prong visible-τ objects
slightly drop at higher-pT , because multiple charged tracks cover each other and one of them cannot
be reconstructed at the track reconstruction. Leading systematic uncertainty is the pile-up effect using MC-based estimation for both decay mode. At lower-pT region (20-30 GeV) the total uncertainty
is about 4.5%.

5.6.2

Hadronic-τ Energy Calibration and Resolution

The energy of the visible-τ candidate is calibrated at the LC scale using only calorimeter information
after the reconstruction. The visible-τ energy scale (so-called TES) is corrected from measured
energy into the true visible energy (Etrue ). The four-momentum of the visible-τ is determined in thecalorimeter assuming that it is massless. The energy contributed from pile-up interaction is subtracted
by the similar way to the jet energy calibration. A response correction is applied to account for decay

54

1.2

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truth 1p
truth 3p

Simulations = 13 TeV

1
0.8
0.6

0.14

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Preliminary|η | < 2.50
1-prong

0.12

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Physics list

PileupThreshold

Underlying event

Total

0.1
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1.4

Fractional Uncertainty

efficiency

5.6. Hadronic Tau Decays

0.14
0.12

0.06

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0.04

0.2

0.02

0.02

0

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30

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truth pτ had-vis [GeV]

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0.4

100 150 200 250 300 350 400 450 500

Material

0.1

0.06

50

ATLAS Simulation
Preliminary|η | < 2.50
3-prong

30

40 50

102

2×102

p [GeV]Tp [GeV]T(a) Efficiency

T(b) Uncertainty,1-prong(c) Uncertainty,3-prong

Figure 5.24: Efficiency for reconstructing the same number of tracks as decay products as a function ofvisible-τ pT (a). Relative systematic uncertainties on the efficiency for the reconstruction of visible-τ objects
with same number of tracks as the number of charged decay products of the τ -lepton as a function of thevisible-τ pT for the 1-prong (b) and 3-prong (c). The individual sources of systematic uncertainties are in plots
and total systematic are shown in blue filled histograms (taken from Reference [171]).

products not detected the calorimeter. The corrected energy of the visible-τ is described as:
Ecorr = ELC − A × (NPV − hNPV i), Ecalib =Ecorr,
R(Ecorr , |η|, nprong )(5.12)

0.6

ATLAS Preliminary

1-prong τ

s = 13 TeV Simulation

multi-prong τ

1.3
1.25

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

Response

0.7

Response

A [GeV]

where A is a correction factor with regard to pile-up effects which is shown in Figure 5.25 (a), R isa response function, ELC is the visible-τ energy with the LC scale. The pile-up correction factor A
1.15
1.1

1.2

0.4

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0.3

1.1

0.2

1.05

0.9

0.1

1

0.85

|η| < 0.3

0.3 < |η| < 0.8

0.8 < |η| < 1.3

1.3 < |η| < 1.6

1.6 < |η| < 2.4|η|(a) Pile-up correction factor

0.95|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

0.5

0

ATLAS Preliminarys = 13 TeV Simulation1
1-prong τ

20

30 40

102

2×102
pileup-corr
ELC
[GeV]

(b) Response, 1-prong

0.95

0.8

multi-prong τ

20

30 40

102

2×102
pileup-corr
ELC
[GeV]

(c) Response, 3-prong

Figure 5.25: Pile-up correction factor (a) as a function of visible-τ pseudorapidity and number of reconstructed
tracks and detector response R as a function of the visible-τ energy with the pile-up correction for 1-prong (b)and multi-prong (c) decay mode (taken from Reference [171]).

corresponds to the average contribution per vertex to the visible-τ energy. The average number ofprimary vertex is calculated as hNPV i ∼ 14 in MC simulation. The response R is obtained from theGaussian mean of the Ecorr /Etrue distribution depending |η| and n-prong.
The resolution of the visible-τ objects is derived as the Gaussian width of the Ecalib /Etrue distribution. The resolution is estimated in several |η| and n-prong as shown in Figure 5.26 which follows
a usual parameterization :σEab= √ ⊕ ⊕ c,
E
E E

(5.13)

where a, b and c are the sampling, noise and constant term respectively. The systematic uncertaintyof the tau energy scale (TES) are evaluated from the simulation using the alternative MC samples.

55

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 [%]5.6. Hadronic Tau Decays

35
30
25

20

20

15

15

10

10

5

5

0
0

100

200

300

400

500

600

0
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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

multi-prong τ

100

200

300

400

500

Ecalib [GeV](a) Resolution, 1-prong

600
Ecalib [GeV](b) Resolution, 3-prong

Figure 5.26: Resolution on the visible-τ energy after calibration for reconstructed 1-prong (a) and 3-prong (b)modes. Each curve are fitted by parameterization from Equation (5.13) (taken from Reference [171]).

Individual sources of systematic uncertainties are shown in Figure 5.27, which are summarised in
below:• Pile-up : defined as difference between default simulated samples and alternative samples withdifferent pile-up parameterization. Several checks of the out-of-time pile-up effects are performed
and obtained its effects less than 1%. In addition to the out-of-time pile-up, the residual
dependence with respect to the in-time pile-up is also taken into account to this uncertainty.
• Underlying : different tuning of the underlying event is checked, and its impact is negligible.
• Material : the amount of materials in front of the calorimeter is varied, and its difference is taken
into account.
• Physics list : alternative Geant4 hadronic shower model is used to estimate uncertainty on the
response function. Different shower model can affect the clustering of the energetic cells into
topo-clusters. The topo-cluster calibration is affected in this variation.
• Threshold : The noise suppression threshold variations estimates a modelling of response in thecalorimeter calibration.
• Closure : The shift in the Gaussian mean of Ecorr /Etrue distribution using the alternative samples
from the nominal samples. Corresponding to deviations from unity of that same Gaussian mean.
this is taken into account for the closure uncertainty.
• Single-particle response : This is the largest uncertainty, In the Run1, the particle deconvolution
method [172] was used to estimate single-pion response measurement in low-µ data-taking andtest beam data. This method is not yet used for this analysis. The other MC-based response
uncertainties covers the components entering the single-particle response uncertainty, As thedetector has not dramatically changed since the Run1, so that this uncertainty has been included
as an additional systematic uncertainty inflated by a safety factor of 2.
The total uncertainty is obtained by symmetrizing each systematic uncertainty and summing up
them in quadrature. Uncertainties vary in the 2-6% range depending on visible-τ pT and |η|. The
single-particle response is always important component, Additional contribution from the calorimeter
calibration becomes relevant at low-pT . The Geant4 shower model contribution is also significant in
the central region.

56

0.12

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Preliminary|η | < 0.30
1-prong

0.1

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PileupSingle particle resp.

Threshold

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Fractional Uncertainty

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5.6. Hadronic Tau Decays

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30

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1.60 ≤ |η | < 2.40
1-prong

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0.30 ≤ |η | < 0.80
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Fractional Uncertainty(d) 1-prong, 1.3 < |η| < 1.6

0.1

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p [GeV]T(i) 3-prong, 1.3 < |η| < 1.6

40 50

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2×102
p [GeV]T(j) 3-prong, 1.6 < |η| < 2.4

Figure 5.27: Systematic uncertainties on the visible-τ energy after calibration for 1- and 3-prong tau decays.
The individual uncertainties as well as their quadratic sum are shown as a function of the visible-τ pT for fivedifferent η binning (taken from Reference [171]).

5.6.3

Hadronic-τ Identification

An additional τ identification algorithm is introduced to suppress mis-identified jet (or electron)
objects. Rejection against jets is provided by a multivariate technique using the track and topocluster information found in the core and isolation region around the visible-τ candidate. Rejection
against electrons is constructed using the electron LH discriminant as shown in Section 5.4.3.

57

5.6. Hadronic Tau Decays
Identification for jets separation

The identification to discriminate hadronic jets from the visible-τ candidates is performed by the
Boosted Decision Trees (BDT) [173]. The BDT is trained separately for the 1-prong and 3-prong
visible-τ objects using Z/γ ∗ → τ τ as a signal and di-jet events as a background. The BDT input
variables are different for the 1-prong and 3-prong as shown in Table 5.3. Definitions of each variablevariable

fcent

−1
flead
trk

trk
fiso

trk−HAD
fEM

EM
ftrk

pEM+trk/pT
T

1-prong
3-prong

3
3

3
3

3
7

3
3

3
3

3
3

variable

0.2
Rtrk

∆Rmax

|Slead trk |flightST

mtrk

mEM+trk

1-prong
3-prong

3
3

7
3

3
7

7
3

7
3

3
3

Table 5.3: Discriminating variables used as input in the tau BDT identification for 1-prong and 3-prong
respectively.

is listed below and detailed distributions can be found in Reference [174]:• Central energy fraction (fcent ) : Fraction of the calorimeter transverse energy deposit in the regionof ∆R < 0.1 with respect to all energy in the region of ∆R < 0.2 around the visible-τ candidate.
Energy deposit is calculated by summing up the energies of topo-clusters calibrated in the EMscale.
−1• Leading track momentum fraction (fleadtrk ) : Fraction between the transverse energy of the EMscale topo-cluster in the core region and the transverse momentum of the highest-pT charged
particle in the core region.
trk ) : Scalar sum of the track p associated with
• Fraction of tracks pT in the isolation region (fisoT
the visible-τ candidate in the isolation region divided by scalar sum of all tracks pT associatedwith the visible-τ candidate.
trk−HAD• Fraction of EM energy from charged pions (fEM
) : Fraction of energy deposit in the EM
calorimeter to charged tracks in the core region. The denominator is the sum of the topo-cluster
energy in the EM calorimeter associated to the visible-τ candidate. The numerator is difference
between the sum of the track momentum in the core region, and the sum of topo-cluster energies
in the hadronic calorimeter. All topo-clusters are calibrated in the LC-scale.
EM ) : Fraction of the sum of energy in the EM calor• Ratio of EM energy to track momentum (ftrk
imeter part of topo-cluster associated with the candidate and the sum of the track momentum
in the core region. All topo-cluster are calibrated at the LC-scale.

• Ratio of track+EM-system to pT (pEM+trk/pT ) : Ratio of the visible-τ pT estimated by theTvector sum of track momentum and two highest energetic EM clusters in the core region to thecalorimeter measured visible-τ pT .
0.2 ) : p
• Track radius (Rtrk
T weighted track ∆R associated in the core region to the τ direction.

• Maximum ∆R (∆Rmax ) : The maximum ∆R between the track associated with the visible-τ
candidate in the core region and the visible-τ object direction.

58

5.6. Hadronic Tau Decays• Leading track IP significance (|Slead trk |) : Absolute value of the transverse impact parameterof the highest-pT track in the core region with respect to the TV divided by its uncertainty.
flight• Transverse flight path significance (ST) : The transverse decay length of the secondary vertex reconstructed from the tracks associated with the core region with respect to the TV divided
by its uncertainty• Track mass (mtrk ) :Invariant mass calculated from the vectorial sum of the all track fourmomentum in the core and isolation regions, assuming each track is pion (mass of tracks are
assumed mπ± ).
• Track+EM-system mass (mEM+trk ) : Invariant mass of the tracks and two highest energetic EM
clusters in the core region, The mass of topo-cluster is set to zero and topo-cluster seed direction
is used as the four-momentum.

SignalBackground

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Event fraction / 0.02

Event fraction / 0.02

To ensure the pile-up robustness, a correction is applied to each input variable, which depends
linearly on the average number of interaction per bunch crossing (hµi) calculating from the instantaneous luminosity. The usage of hµi instead of the number of reconstructed primary vertices gives
compatibility with the HLT-tau trigger, which cannot use the primary vertex. The BDT score distri103

0.4

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Tau identification score(a) 1-prong

00

1-prong
3-prong

T

102

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0.4

0.6

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1

Tau identification score(b) 3-prong

1

0.4

0.6

0.8

1

Signal efficiency(c) Rejection power

Figure 5.28: BDT score distribution for visible-τ candidate for 1-prong (a) and 3-prong (b) with signal (redcircles) and background (black squares). Inverse of the efficiency for mis-identified hadronic jets as a functionof thee identification efficiency for true visible-τ candidates (c). Two lines refer to 1-prong and 3-prong
respectively. Each point(circles and triangles) present three working point (Loose, Medium, Tight) (takenfrom Reference [174]).

bution of the signal and background is shown in Figure 5.28 for 1-prong (a) and 3-prong (b) modes.
Three working points, Loose, Medium and Tight are defined. The threshold of each working point depends on the visible-τ pT to achieve a constant efficiency. Simplified cut values are about 0.675, 0.725
and 0.75 for the 1-prong loose, medium and tight working points, corresponding the 3-prong loose,medium and tight are about 0.75, 0.8 and 0.85. The dependence of the combined reconstruction andidentification efficiency as a function of pT and hµi is significantly reduced as shown in Figure 5.29
after the tuning of the pT -dependent cut values and the pile-up corrections. The identification scale
factor is set to equal 1 with MC-based systematic uncertainty [171]. Due to a lack of data statistics,
the scale factor for the τ -ID is not evaluated. The scale factor obtained in the Run1 is applied withadditional systematic uncertainties in this analysis. The medium working point is used. Its combined
reconstruction and identification efficiency is about 55% for 1-prong and 39% for 3-prong modes.

59

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truth 3-prong

100 150 200 250 300 350 400 450 500

truth pτ had-vis [GeV]Ttruth pτ had-vis [GeV]
T

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efficiency

efficiency(a) 1-prong, pT
ATLAS

Reco+Loose

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Preliminary
Simulations = 13 TeV
truth 1-prong

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(c) 1-prong, hµi

Preliminary
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truth 3-prong

30

35

40

45
<µ>

(d) 3-prong, hµi

Figure 5.29: Efficiency for the visible-τ identification (open symbols) and combined reconstruction and identification efficiency (filled symbols) as a function of the visible-τ and the average number of interaction per
bunch crossing for 1-prong (a,c) and 3-prong (b,d) (taken from Reference [174]).

Difference between the 1-prong and 3-prong arise from track reconstruction. Systematic uncertainties on the identification efficiency are evaluated using alternative simulated samples with different
configurations as discussed in Section 5.6.1. The result for the medium working point are shownin Figure 5.30 for the 1-prong and 3-prong with different |η| bins. The calorimeter calibration andperformance uncertainty is the highest contribution at pT < 100 GeV, which is variation in shapesof calorimeter-based and tracking-based input variables. It has up to 16% for the 3-prong decay
in central region. At higher-pT , the pile-up uncertainty is dominant due to the impact parameter
resolution can change the |Sleaddaggerrk | distribution. This uncertainty is one of dominant source of
uncertainties on signal strength in this analysis as discussed in Chapter 7.
Identification for electrons separation (e-veto)
To suppress electron background, it is useful to use same discriminant as used in the electron
identification discussed in Section 5.4.3. The electron likelihood (electron LH) is constructed byshower shape information from the calorimeter and track information from the inner detectors. In
terms of separation between electrons and charged pions, TRT plays an important role, which canmeasure two operating points for optimising electron and charged pion detection using ionisationthreshold information. The electron-veto procedure is simple compared to the jet-discriminant. First
it finds the electron objects around the visible-τ objects with ∆R < 0.4, here electron objects should

60

0.35
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1-prongMedium ID

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T(b) 3-prong, |η| < 1.52

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102

2×102

p [GeV]p [GeV]T(c) 1-prong, |η| > 1.52

T(d) 3-prong, |η| > 1.52

Figure 5.30: Relative uncertainties on the identification efficiency for the medium working point as a functionof the visible-τ pT for 1-prong (a,c) and 3-prong (b,d) in the central |η| < 1.52 region and forward region|η| > 1.52 (taken from Reference [174]).

satisfy loose identification criteria and pT > 5 GeV. If it is found, the visible-τ objects are vetoed. If
there are no such electrons, it finds the electron candidate is required by pT > 5 GeV and failing theloose identification. If electron candidate is found, the electron LH score is examined. This electron
faking the visible-τ objects, called “e → τ fake”, rises from Z/γ ∗ → ee process in the di-τ final state
analysis. Figure 5.31 (a) shows the electron LH score distribution for the signal and background.
The default working point for the e-veto is set to achieve the signal efficiency is 95%, the backgroundrejection capability are shown in Figure 5.31 (b) for several different pseudorapidity regions. The scale
factor of the e-veto identification for electrons is measured as shown in Figure 5.31 (c). The scale
factors are measured using Z/γ ∗ → ee tag-&-probe method with 3.2 fb−1 2015 data. The systematic
uncertinty is obtained by evaluating the τ -ID and electron ID systematic uncertinties. In addition tothem, additional systematic uncertinty corresponding the electron and tau energy scale. In the mostforward bin (|η| ∼ 2.45), there are no TRT detector, so the electron LH consists of different shower
shape information. This leads significant mis-modelling as shown in Figure 5.31 (c). Therefore in thisthesis, the visible-τ objects are selected by |η| < 2.3. The scale factors of the e-veto identification fortrue hadronic-τ objects is not yet measured due to a lack of data statistics.

0.25

ATLAS Simulation
Preliminarys = 13 TeV

e Backgroundτhad-vis Signal|ηtrk| < 2.47

0.2

p > 15 GeV
T

0.15
0.1

103

ATLAS Simulation
Preliminarys = 13 TeV

102

10

0.05
0
-4

-3

-2

-1

0

1

2

3

4

61

1
0.7

|ηtrk | < 0.6
0.6 < |ηtrk | < 0.8
0.8 < |ηtrk | < 1.15
1.15 < |ηtrk | < 1.37
1.37 < |ηtrk | < 1.52
1.52 < |ηtrk | < 1.81
1.81 < |ηtrk | < 2.01
2.01 < |ηtrk | < 2.37
2.37 < |ηtrk | < 2.47

0.8

0.9

1

Signal efficiency

Electron LH score(a) Electron LH score

Scale factor

0.3

Inverse background efficiency

fraction of events

miss )
5.7. Missing Transverse Energy (ET(b) Inverse background efficiency

3.5 stat ⊕syst
3.0 statcenter value
2.5
2.0
1.5
1.0
0.50.0 0.5 1.0 1.5 2.0 2.5
visible-τ |η|(c) Scale factor

Figure 5.31: Electron likelihood score distribution for the visible-τ and electron candidate from signal (Z/γ ∗ →τ τ ) and background (Z/γ ∗ → ee). (v) : Inverse background efficiency as a function of the signal efficiency for
different |η| region (taken from Reference [174]). Events with score equal to -4 has no electron candidates within∆R < 0.4. (c) : Scale factors for the e-veto identification selection of true electrons using Z/γ ∗ → ee tag-&probe method. Black circles show center values, green (blue) region shows statistical (systematic) uncertainties
for this measurements.

5.7

Missing Transverse Energy (ETmiss )Tau leptons decaying into leptons (e, µ) or hadrons and at least one neutrino. In order to reconstruct
H/A → τ τ event topology, reconstruction of such neutrinos is essential and crucial. Neutrino cannot
be detected at the ATLAS detector, so that additional assumption is necessary to obtain neutrino
momentum. Since the LHC is proton-proton collider, initial parton momentum always changes andconservation of momentum is validated only transverse plane to the beam axis. The missing transverse
miss ) is be measured as an imbalance in the sum of visible transverse momentum. It
momentum (ETis important to reconstruct efficiently hard objects which come from the primary vertex. Due toextremely high pile-up condition of the LHC, dedicated algorithm is applied to catch up hard objects
only from such interaction point. In addition to hard objects, there are soft particles which cannot bereconstructed as any physics objects, for example underlying activity with lower-pT than the thresholdof the hadronic jet reconstruction. This should be taken into account as a “soft term”. The soft termis one of the difficult objects to correctly obtain, due to mis-identification of the pile-up activity.
miss is given based on Reference [175] in Section 5.7.1.
A detailed reconstruction procedure of the ET
miss
The ET reconstruction performance and its systematic uncertainty is described in Section 5.7.2. A
miss is briefly described in Section 5.7.3.
trigger related to the ET

5.7.1

ETmiss Reconstruction

miss is calculated by the calibrated and reconstructed objects. The input objects consists of
The ETcharged leptons, photons, visible-τ and hadronic jets. In addition to these physics objects, the soft

miss )
5.7. Missing Transverse Energy (ET62term is also calculated by the tracks not associated with any physics objects.
miss
miss,emiss,γ
miss,τ
miss,µmiss,jetmiss,soft+ Ex,y+ Ex,y+ Ex,y+ Ex,y,Ex,y= Ex,y+ Ex,yq2missET= (Exmiss )2 + Eymiss ,φmiss = arctan(Eymiss /Exmiss ),
X
X
X γ X
X µ X jet X
ET =
peT +
pT +
pτT +
pT +
pT +
psoft
T ,

(5.14)(5.15)(5.16)(5.17)The term for jets, electrons (e),P muons (µ), visible-τ s (τ ) and photons (γ) are the negative vectorial
sum of the momentum. The
ET is the scalar sum of transverse momentum of all input objects.
The reconstruction procedure is so-called as Track Soft Term (TST) [175]11 . In addition to thedefault (tight) track selection as shown in Section 5.1, several selections are applied to ensure trackto-vertex association. Tracks must satisfy the transverse and longitudinal impact parameters ofd0 < 2mm and z0 sin θ < 3mm with respect
P to2 the primary vertex. The primary vertex is selected by
the vertex which has the largest value ofpT , where scalar sum run over all tracks associated withthat vertex.
Before summing up all hard objects and the soft term, geometrical overlap between hard objects
should be solved (overlap removal(OLR)). Selection using the geometrical distance of ∆R(i, j) for
object i and j is performed. Starting from muons, all hard objects (obj = e, γ, τ and jets) are removed
if ∆R(µ, obj) < 0.2. Then same OLR are performed with order of e → γ → τ with ∆R = 0.1, 0.2, 0.2.
For jets and tracks special treatment is applied, because partial internal overlaps can happen withclusters and tracks between jets and others. The JVT selection is applied for jets to ensure production
from hard collision. If the calibrated jet pT is greater than 20 GeV and a unique fraction12 is greater
miss,jetthan 0.5, the jet is added to a list of Ex,y. Otherwise, jets are treated as the soft term with track
momentum. Before constructing the soft term, the OLR and a cleaning process is applied to all track
candidates which described following:• Tracks within ∆R < 0.05 are removed between tracks and electron/photon cluster.
• Tracks within ∆R < 0.2 are removed between tracks and visible-τ .
• Tracks associated with jets using the ghost-association technique are removed.
• Tracks associated to combined or segment-tagged muons are replaced with the combined ID+MS
tracks.
0.2 /p >• high-pT ((pT > 200 GeV and |η| < 1.5) or (pT > 120 GeV and |η| > 1.5)) non-isolated (pcone
TT0.1) tracks are removed if satisfy following:cone 0.2
cone 0.2
ET
pT
<
0.6,
and
0.2
cone 0.2 > 0.6.
pT + pcone
pT + pT
T(5.18)• Tracks has its track momentum uncertainties larger than 40% are removed.
Association to the primary vertex is relatively sensitive to pile-up effects.

11

miss
There is another procedure using calorimeter clusters as input of the soft term, Cluster Soft Term (CST). Track ET
missconsist of only tracks without any hard objects The resolution of CST and Track ET is even worse than the TST’s.
12
Fraction of jet energy between calorimeter measured scale and constituents scale.

miss )
5.7. Missing Transverse Energy (ET

5.7.2

63

ETmiss Performance and Uncertainty

Since Z → µµ events have small background and muon can be precisely measured, Z → µµ
miss performance. In Z → µµ events neutrinos are
events provide an ideal final state to evaluate of ET
produced only by heavy-flavour meson decay, so it can be negligible. In addition to Z → µµ events,
miss from one true neutrino. Performance andW → µν events is a good candidate to measure the ET
resolution measurement by Z → µµ and W → µν events is evaluated in and details can be found in
Reference [175, 176]. Only results and its uncertainties are given based on these Reference in thismiss performance, the E miss response, linearity and resolution are usuallythesis. In terms of the ETTmiss response is defined as a projection to the axis of the p of the Z boson. It isconsidered. The ETTmiss response R
sensitive to balance between leptons and the soft hadronic recoil. Definition of the ET
and linearity L are defined by following :
+
*
`+
`−
p
~
+
p
~
T
T
miss
~
,
(5.19)
R= E
· `+
−
T
pT + p`T*+
miss − E miss,trueET
TL=(5.20)
miss,trueET±

all jets
20

40

60

80 100 120 140 160 180 200
pZT [GeV]

miss(a) ET
response

0.6

W → µν 25ns

0.4

all jets

TST ET
miss
Track ET

0.2

miss

0
-0.2
-0.4

40
35
30

Z → µµ 25ns

CST EmissT
TST EmissT

all jets

Track EmissTs = 13 TeV

25
20
15
10

-0.6
-1
0

,EmissResolution [GeV]y

CST ET-0.8

ATLAS Simulation Preliminary
-100
0

miss

s = 13 TeV

miss

Z → µµ 25ns

1
0.8

Ex

miss,True〉-80s = 13 TeV

〈 (ET

-60

miss,recoT-40) / ET

miss

CST ETTST EmissT
missTrack ETmiss,True

-20

- ET

0

Z

〈 Emiss⋅ A 〉 [GeV]

where p~T ` are the transverse momentum of leptons from the Z boson decay. Figure 5.32 shows themiss response, linearity and resolution. For the E miss response, perfect balance of leptons against
ET
T

5

ATLAS Simulation Preliminary
20

40

60

80 100 120 140 160 180 200
miss, True

ET

miss
(b) ET
linearity

[GeV]

0
0

ATLAS Simulation Preliminary
100 200 300 400 500 600 700 800 900 1000ΣET(event) [GeV]miss(c) ET
resolution

missFigure 5.32: Performance of the ET
reconstruction using Z → µµ (a,c) and W → µν (b) simulated samples.
miss
Plots includes results of three ET reconstruction algorithm, in this thesis only TST (green circle) is used.
miss
miss
linearity
response R as a function of the transverse momentum of the Z boson. (b) : the ET(a) : the ET
miss
miss
L as a function of the true ET from W → µνdecay. (c) : the ET resolution as a function of the sum
ET (taken from Reference [176]).

miss
the soft recoil R = 0 would expected. A good response are shown in Figure 5.32 (a) for the ET
miss linearity is almost flat above E miss,true & 60 GeV for the E miss TST as shown in
TST. The ET
TTP
miss resolution as shown in (c) is typically 10 GeV at
Figure 5.32 P(b). The ET
ET ∼ 400 GeV and
15 GeV at
ET ∼ 650 GeV. An comparison between data and MC simulation is also shown inmiss response and resolution.
Figure 5.33. A good agreement is obtained for both the ET
miss
For uncertainties related to the ET reconstruction, only the soft term is taken into account.
Because other hard objects can handle via each reconstruction, identification or energy calibration
procedures. To derive the soft term systematic uncertainties, p~T hard is defined as the vector sum of thetransverse momenta of the hard objects in the event. As the track soft term systematic uncertainty,
difference between different simulated samples are taken into account (details for MC generators is
described in Reference [176]). Systematic uncertainties are calculated by projecting the soft termcomponents onto the transverse and longitudinal of the p~T hard . The soft term scale longitudinal toRMS [GeV]ATLAS Preliminary

Data

Data 2016, s = 13 TeV

Z(→ ee) MC,Ey

Z → ee, 8.5 fb-1

miss

1.5

64

30

ATLAS Preliminary

20

TST Ex1

Data

Data 2016, s = 13 TeV

miss

1 + 〈 ET,

miss

T

/ pZ 〉TST

miss )
5.7. Missing Transverse Energy (ETZ(→ ee) MC

Z → ee, 8.5 fb-1
0 jets, pT > 20 GeV

10

0.5
0

20

40

60

80

100

120

140

160

180 200
pZ [GeV]

0
0

5

10

15

T

miss
(a) ET
response

20
25
30
Number of primary vertices NPVmiss(b) ET
resolution

missFigure 5.33: ET
response and resolution using Z → ee events of simulated and experimental data.
Black (green) circles show data and Z → ee simulation respectively (taken from Reference [177]).

Ratio

Eventsp~T hard is sensitive to the modelling of the hadronic recoil. The one σ of the systematic uncertainty is
obtained from the variation between nominal MC samples and two alternative samples with checking
a Kolmogorov-Smirnov test to avoid statistical fluctuations. An additional uncertainty is assigned if
there is 5% or smaller probability of a KS-test. In addition to this generator difference systematic
uncertainty, an alternative simulation with different detector material budget condition are evaluated.
Total systematic uncertainty is shown in Figure 5.33. As shown in plot, relatively larger uncertainty
1013
1012
1011
1010
109
108
107
106
105

ATLAS Simulation Preliminary

NominalUp
Down
Statistical uncertaintys = 13TeV
Z → µµ

1.15
1.1
1.05
1
0.95
0.9
0.85
0

50

100

150

200

miss
systematic uncertainty
Figure 5.34: Total ET
missmagas a function of the reconstructed ET
nitude (take from Reference [177]). In the ratio,
the hatched band shows the statistical uncertainty,
red (blue) lines shows +1σ (−1σ) variation of thesystematic uncertainty including the statistical uncertainty.

250
300
Emiss
[GeV]
T

miss events, typically ±10% at E miss ∼ 250 GeV.
is expected for higher-ET
T

5.7.3

ETmiss Trigger

miss trigger is good item to include
Since the single-lepton-trigger efficiency is not perfect, the ET
miss compared with other two
in the search for heavy Higgs bosons. The τ` τhad channel has larger ET
misschannels. Events with large ET is interesting because the most of background processes doesn’t
miss . The E miss trigger is introduced for the first time in this analysis.
have such large ET
T
miss
As described in Section 4.2.6, the ATLAS trigger is two steps pipe-line system. At the L1, the ET
is roughly reconstructed by the L1 calorimeter RoIs, so-called L1XE. The level 1 trigger is hardwarebased trigger which cannot precisely measure energy or transverse momentum13 . The level 1 muon
trigger processor is separated from other L1 trigger processors, so that in the L1XE calculation muons
are not taken into account. These feature leads that L1XE trigger resolution become coarse, typically∼ 30 − 40 GeV.
13

The L1EM has only 0.5 GeV step at hardware level, L1Calo is coarser than the L1EM.

miss )
5.7. Missing Transverse Energy (ET65miss trigger (so-called HLT xe) is evaluated using offline-like alAfter L1XE decision, the HLT ET
gorithm. The vertex reconstruction cannot be performed during the HLT processing. So the samemisssoft-term cannot be obtained, this leads that the pile-up effect becomes crucial to the HLT ET
trigger. To suppress the pile-up effects, there are several algorithm related to how to calculate thesoft term components [178]. Three algorithm are used in this analysis described in following:• Cell-based algorithm (xe) : In each LAr and Tile calorimeter cell, contributions are calculatedby the sum of each cell pix,y = Ei cos θi sin φi , Ei cos θi sin φi . To suppress noise, the cells withenergy |Ei | > 2σi and Ei > −5σi are considered, where σi is the noise threshold significance.
miss is calculated by taking the negative vector sum of all active cells.
ETmiss is calculated directly from the negative vector sum of the• Jet-based algorithm (xe tc mht) : ETtransverse momentum from all jets reconstructed by the jet trigger algorithm, which have been
applied correction for the pile-up contribution as shown in Section 5.3, but the JVT selection
is not applied.
miss is calculated from topo-clusters calibrated• Topo-cluster-based algorithm (xe tc lcw) : ETwith the LC-scale of the entire calorimeter. Each topo-cluster is calculated with masslessmiss is reconstructed from the negative vector sum of topo-clusters.
particle assumption. The ET
miss trigger is sensitive to the instantaneous luminosity. The E miss trigger threshold was
The ETT
miss trigger items usedchanged many times during data-taking period. Table 5.4 summarised the ET
in this analysis. During 2015 data-taking threshold and algorithm has not been changed. While

Period2015 All2016 A-C
2016 D1-D3
2016 D4-F1
2016 F2-

peak lumi.

integrated lumi.

trigger items

0.50 × 1034 cm−2 s−1
0.88 × 1034 cm−2 s−1
0.99 × 1034 cm−2 s−1
1.03 × 1034 cm−2 s−1
1.21 × 1034 cm−2 s−1

3193.6 pb−15380.2 pb−1
736.2 pb−16545.3 pb−1
12138.0 pb−1

xe70 or xe70 mht or xe70 tc lcw
xe80 tc lcw or xe90 mht
xe90 mht
xe100 mht or xe110 mht
xe110 mht

missTable 5.4: The ET
trigger items used in this analysis for 2015 and 2016 data-taking.

miss trigger threshold was increased as the peak luminosities induring 2016 data-taking, the ET
creases up. Unexpectedly non-linear trigger rate ascent was observed for the topo-cluster-basedalgorithm (xe tc lcw). So from 2016 period D1 this trigger threshold was rose up to 130 GeV. While,jet-based algorithm (xe tc mht) have kept its trigger threshold. During 2016 period D4-F1, at startof higher luminosity runs xe100 mht was pre-scaled14 , so taking OR with xe110 mht is required.
miss trigger strongly depends on event topology, i.e. the efficiency depends on
The efficiency of the ET
miss source, from real E miss (from neutrinos) and fake E miss originated by the pile-up
the source of ET
T
T
activity. Detailed of measurement are discussed in Section 6.3.

14

pre-scaled means that trigger is vetoed with certain rate. For example, the pre-scaled is 0.5, 50% of events fired thistrigger is recorded.

6 Search for the MSSM Higgs Bosons inthe τ`τhad Final State

The search for H/A → τ τ decays in τ` τhad final state is discussed, which is developed, implemented
and performed in the course of this thesis. It is based on a mass bump hunting to discriminate thesignal from background events. Three event categories are defined, optimised for the gluon-fusion andbottom-annihilation signal production mechanisms. A maximum-likelihood fit to a mass distributions
and to additional control regions is performed to estimate the parameter of the combined signal andbackground model and to extract a measurement of the product of signal cross-section and decaybranching fraction. The experimental signature of the signal processes and comparison of the main
background processes is introduced in Section 6.1. The analysed data samples, as well as simulated
event samples used in this analysis are described in Section 6.2 and 6.3 respectively. The event
selection and categorisation is given in Section 6.4. To establish a potential excess of data over the
expected SM background, a reliable model of the background processes is necessary. The backgroundmodelling is described in Section 6.5 and comparisons between the observed data and background arealso given. The systematic uncertainties and their propagation to the final observable is explainedin Section 6.6. An important role of the analysis is a construction of the profiled likelihood model.
The profiled likelihood fit is used to estimate the number of expected events yields for the signal
and background with nuisance parameters. A concept of the profiled likelihood and other statisticalanalysis is described in Chapter 7.

6.1

Experimental Signature of H/A → τ` τhad Decays

The experimental signature of H/A → τ τ signal depends on the decays of the τ leptons, as well ason the Higgs boson production mechanism. The τ` τhad channel consists of a single electron or muon,
denoted as `, two neutrinos from the leptonic τ decay, and one reconstructed visible-τ object and one
neutrino from the hadronically decaying τ -lepton. The lepton and the visible-τ object carry opposite
electric charge. Neutrinos, which escape from direct detection, lead to a significant amount of themissing transverse energy which can be used to complement the information from the reconstructeddecay products. The event selection criteria discussed in Section 6.4 are constructed based on these
final state objects. The kinematic properties of the signal processes as well as dominant backgroundprocesses are described in the following.

6.1.1

Signal Processes

Figure 6.1 shows the Feynman diagrams of the two main Higgs boson production mechanisms
considered in this analysis. The bottom-annihilation process is dominant in terms of the experimental
sensitivity as shown in Section 3.2.2. The bottom-annihilation process has two leading order diagram

66

6.1. Experimental Signature of H/A → τ` τhad Decays

g

g

67

b
b

h/H/A
g

b

h/H/A
b

g
(a) Gluon fusion

h/H/A

g

(b) Bottom annihilation (4FS)(c) Bottom annihilation (5FS)

Figure 6.1: Feynman diagrams of the three main production diagrams of H/A bosons at the LHC. Only
leading diagram is shown for each process.

as shown in Figures 6.1 (b) and (c). There are at least one b-quark in the final state, but the transverse
momentum of the b-quark tends to be small. It is difficult to model the transverse momentum of
the Higgs bosons, so the analysis does not actively use information related to them. This leads thatan event topology of signal becomes back-to-back in terms of two decay products of the heavy Higgs
bosons.
Since the di-τ system originates from the intermediate resonant state, the combined four-momentumof all the decay products allows to reconstruct information about the Higgs boson four-momentum.
A crucial property of the di-τ system is the invariant di-τ mass mτ τ . Z/γ ∗ → τ τ process has
similar kinematical properties to the signal process. So the mass difference between Z and Higgs
bosons provides a powerful discriminating property these two processes. The event cannot directly
reconstructed due to the multiple neutrinos though away. A brief overview of those observabledefinitions is given in Section 6.1.3.

6.1.2

Dominant Background Processes

Background processes contributing to the final state can be grouped. One is processes with a real
hadronically decaying τ -lepton and lepton, Other processes have either a hadronic jet or a lepton
is mis-identified as a τvis-had object1 and mis-identified as a lepton (e, µ)2 . The estimation of thesecond group are complicated. Because the τhad mis-identification probability is not well modelledin simulation. The major background with real τhad is Z/γ ∗ → τ τ and tt̄ → bb̄τ τ ν ν̄. Z/γ ∗ → τ τ

q̄

t

g

t

g

t

g
t̄

q

t̄

g

t

t̄

g

t̄

g

Figure 6.2: Feynman diagrams of tt̄ production at the LHC. Only leading diagram is shown.

process is irreducible with the gluon-fusion signal processes in terms of di-τ decay products andhadronic jets production. Figure 6.2 shows the tt̄ production diagrams. In the case of tt̄ eventswith di-leptonic decay of two W ± bosons, additional two b-quark can be seen. So tt̄ → bb̄τ τ ν ν̄process has similar final state with the bottom-annihilation signal process in terms of di-τ decay
12referred to as “fake τhad ”
referred as to “fake lepton”.

6.1. Experimental Signature of H/A → τ` τhad Decays

68

products and b-quark production. Besides these two background processes, other processes become
background. The production cross-sections of such processes is small compared to Zzero/γ ∗ → τ τand tt̄ → bb̄τ τ ν ν̄ processes. Such background processes are estimated by the MC simulations with
data-driven corrections.

gq2 /q¯2

q2 /q¯1g

q2 /q¯2W±q¯1 /q1gν` /ν¯`W`±

q1 /q¯1±ν` /ν¯`ν` /ν¯`q1 /q¯1`±

W±`±

Figure 6.3: Feynman diagrams of W +jets production with one jet at the LHC. Only leading diagram isshown.

Background with mis-identified τhad objects mainly consists of four physical processes, W +jets,tt̄ → bb̄`+jets Z → ``, and the QCD multijets. Origin of mis-identified τhad objects should beconsidered. The fake j → τhad and ` → τhad objects originate from hadronic jets and leptons
respectively. The dominant process of j → τhad is W +jets, tt̄ and the QCD multijet processes. In
addition to the fake hadronic-τ , the QCD process has the fake lepton (j → ` ).
W +jets process has additional hadronic jets which become the fake τ . An origin of additional jets
is practically quarks as shown in Figure 6.3. A probability of the j → τhad fake is not large, but
the production cross-section of W +jets is large enough to observe in this analysis. The other fakeτ background comes from the tt̄ process is semi-leptonic channel. It has one real lepton from W ±decay and the fake τ from mainly quarks. The transverse mass mW
T is useful to distinguish eventswith or without W ± → `± ν` process:q
miss (1 − cos ∆φmW
2p`T ET(6.1)
T =`,E miss ),T

where p`T is the transverse momentum of charged lepton, ∆φ`,E miss is an angle difference between theTmiss direction in the transverse plane. The mW has a unique peak at around W ± boson
lepton and ET
T
mass.

Figure 6.4: Feynman diagrams of the QCD multijets process at the LHC. Only leading diagram is shown.

The QCD multijets process has the fake τ and the fake lepton as well. As shown in Figure 6.4 the
QCD multijets process has more gluons in the final state compared to W +jets and tt̄.

6.2. Simulated Event Samples

69

The q/g fraction3 is an important feature in terms of the j → τhad fake probability. In generalgluon jet instantly spreads geometrically wider than quarks. Typically probability of gluon to τhadfake object become smaller than quark one. The QCD multijets has the fake lepton, probability ofj → ` is smaller than j → τhad at a factor of . 1%. A detailed description of the fake τ estimation
including the fake lepton is given in Section 6.5.1.
Z/γ ∗ → `` + jets is also background. It has two kind of the fake τ , one is event with a charged
lepton and the j → τhad fake, i.e. the other lepton fails to identify. Such event rate is not so large
and it is possible to estimate them together with above three fake backgrounds. In addition to its
rate, the q/g fraction is similar to W +jets, so it is estimated by together with W +jets.
Another component is one real lepton and one ` → τhad fake. e → τhad fake is dominant
in practice. Z → ee process is main source of the e → τhad fake background. It is suppressed bydedicated identification criteria as described in Section 5.6.3. It is estimated by data-driven technique
as described in Section 6.5.1. Other processes like diboson and single-top production, its production
cross-section is small. So it is reasonable to use simulated event samples with correction factors.

6.1.3mτ τ Reconstruction

The invariant mass of di-τ system is one of the most important event properties in the search.
Since multiple neutrinos are emitted, some assumptions is necessary. There are several techniqueswith regards to a type of assumption.
Visible Mass, mvis
Most simple definition is ignoring such missing neutrinos, it is called as “visible mass” mvis anddefined as :qmvis = (E` + Eτvis-had )2 − (~p`T + p~τTvis-had )2 .
(6.2)
As the neutrinos carry a large fraction of the τ -lepton momenta, the visible mass distribution isshifted to lower value with respect to true mτ τ value. The visible mass is often used to validate
kinematical modelling of lepton and hadronic-τ .
Total transverse mass, mtot
T
The total transverse mass mtot
T is the sum of transverse mass between two visible-τ objects and themiss defined as following :ETq
2pT,i pT,j (1 − cos ∆φi,j ),qmiss )2 + m (τmiss 2mtot
mT (`, τhad )2 + mT (`, ET
T had , ET ) .
T =mT (i, j) =

(6.3)
(6.4)

The total transverse mass has softer for The QCD multijets has softer distribution compare to otherbackground processes. The total transverse mass is used in this analysis as a final discriminant.

6.2

Simulated Event Samples

Various simulated event samples are used in the analysis to model differential distributions ofsignal and background processes. Even through the background estimation is performed by datadriven ways, simulated event samples are used in the design and validation of such methods, as wellas in the development of background-suppression strategies. An overview of the various simulated
3

The fraction of a jet origin, it is usually defined as the ratio between quark jets and gluon jets.

70

6.2. Simulated Event Samples
event samples of signal and background processes is given In the following subsections.

6.2.1

Signal Processes

Simulated events for heavy neutral MSSM Higgs bosons signal is generated by PowHeg-Box v2 [179–181]4 and MadGraph5 aMC@NLO 2.1.2 [182, 183] programs for the gluon-fusion and the bottomannihilation process respectively. For the gluon-fusion process, the CT10[184] is used as a PDF
set and pythia8 (version is 8.210). The AZNLO [68] tuning is applied for the parton shower, underlying event and hadronisation. For the bottom-annihilation process, the CT10nlo nf4 [67] andthe Pythia8 (version is 8.210) with the A14 [185] tuned parameters us used as well for the parton
shower and underlying event and hadronisation. EvtGen v1.2.0 [186]5 is used to revise the heavy
flavour quark production and decay in the parton shower. This leads that improvements of b-tagging,
provides a common efficiency reference across all generators and extrapolation to non-calibrated regions. I is assumed that the difference between CP-even and CP-odd Higgs bosons is negligible at allreconstructed object level. The reconstructed mτ τ resolution is not compatible to a generated mass
width of Higgs bosons, so an effects of mass width difference is neglected. Each signal is normalised
to the sum of cross-section with the CP-even plus the CP-odd. The signal samples are produced at
the pseudoscalar mass of mA = 200, 300, 350, 400, 500, 600, 700, 800, 1000, 1200 GeV. Pythia 8.186
is used to overlay the minimum-bias6 events on each generated event in order to model the pile-up
for all simulated samples including the background processes,

6.2.2

Backgrounds Processes

Background process except the QCD multijets are generated for major processes summarised inTable 6.1 W +jets and Z+jets samples are generated by PowhegBox v2 interfaced to Pythia 8.186
Process

Generator (PDF set)

Shower (tune,PDF set)

Order

σ[pb]

Z+jetsW ± → `± νtt̄
single-t/t̄, t-channel
single-t/t̄, W t-channel
single-t/t̄, s-channel
DibosonPowheg-v2 (CT10)
Powheg-v2 (CT10)
Powheg-v2 (CT10)
Powheg-v1 (CT10f4)
Powheg-v2 (CT10)
Powheg-v2 (CT10)
Sherpa (CT10)

Pythia8(AZNLO,CTQ6L1)
Pythia8(AZNLO,CTQ6L1)
Pythia6(P2012,CTQ6L1)
Pythia6(P2012,CTQ6L1)
Pythia6(P2012,CTQ6L1)
Pythia6(P2012,CTQ6L1)
-

NNLO
NNLO
NNLO
NNLO
NNLO
NNLO
NLO

1950
20079
993.8
216.95
75.57
10.32
45.42

Table 6.1: Description of Monte Carlo samples used in this analysis for background modelling.

with the AZNLO tune [68]. Photos++ v3.52 [188, 189] is used for photon radiations from electroweak
vertices ad charged leptons. All W/Z+jets samples are normalised to the next-to-next-to-leadingorder (NNLO) cross section calculated by FEWZ [190–192]. tt̄ and single-top production except singletop t-channel are generated by Powheg-Box v2 with CT10 PDF set. Single-top t-channel is generated with Powheg-Box v1 jointing the four-flavour scheme for the NLO matrix element calculations
to ether with the fixed four-flavour scheme PDF set CT10f4. Top-quark decay is simulated with
MadSpin [193]. For all top-quark production, the spin correlations are preserved and the partonsshower, fragmentation and underlying event are simulated Pythia 6.428 [194] with the CTQ6L1 PDF
4The PowHeg is a generator with the matrix element (ME) at NLO in QCD.
EvtGen is an “afterburner” which runs after the Standard MC generation has taken place. EvtGen perform “re-decay”
them with more accurate lifetime and decay table.
6
The minimum-bias samples are generated with Pyhia8 using the A2 tune [187] and the MSTW2008LO PDF set.
5

6.3. Data Samples and Trigger Selection71

set corresponding to Perugia 2012(P2012) tuning [78]. The tt̄ production sample is normalised to
the NNLO cross section including soft-gluon resummation to next-to-next-leading-logarithm accuracy [195]. The single-top samples are also normalised to an approximated NNLO calculation [196–198]. Diboson sample are generated by Sherpa 2.1.1 with the CT10 PDF set, up to one additional
parton at NLO (depending on the process) and up to three additional parton at LO are calculated.
The diboson samples are normalised to their NLO cross sections as computed by Sherpa.

6.3

Data Samples and Trigger Selection

The data sample analysed in this analysis was recorded during the data-taking periods in 2015 and2016. Basic data quality criteria are applied to ensure that the detector worked well condition asshown in Section 4.3. An integrated luminosities of 3.2 fb−1 and 24.8 fb−1 for 2015 and 2016 areused for the search after this data quality selection. The luminosity calibration is obtained from vander-Meer scans with uncertainties of ±2.8% for the 2015 and ±5% for 2016 data-taking period. The
peak instantaneous luminosity increased significantly to 1.2 × 1034 cm−2 s−1 in the 2016 data-taking,while 0.5 × 1034 cm−2 s−1 in the 2015 data-taking.
Events are collected using the single-electron-trigger, single-muon-trigger and the missing transverse energy triggers. As the instantaneous luminosity varied during data-taking periods, the online
threshold of these trigger items were adjusted several times to cope with the limited bandwidth available for data storage. Three different electron trigger items are used for the 2015 data samples with pT
threshold of 24, 60, 120 GeV in the 2015 data, 26, 60, 140 GeV for the 2016 data-taking respectively.
Three different muon trigger items are used with pT threshold of 20, 26, 50 GeV for the 2015 andmiss trigger items in the 2015 data-taking is 70 GeV.
2016 data-taking. The online threshold of the ET
While during the 2016 data-taking period, the threshold were varied between 80 - 110 GeV.

6.3.1

Trigger Selection

Since this analysis has two decay channel, the eτhad and µτhad channels, the trigger selection is
miss trigger are used in the eτ
performed corresponding to the channel. The single-electron and ET
had
misschannel, as well as the single-muon and ET trigger are used in the µτhad channel. To avoid unexpected effects, the matching criteria between online trigger objects and offline7 objects are considered.
For the single-lepton-trigger(SLT), it is required that the transverse momentum of the offline lepton
is greater than the online pT threshold. All leptons are required pT > 30 GeV, which reaches a stableefficiency of offline triggers. In addition to the pT requirement, a geometrical matching is taken into
account between the online and offline leptons. This is performed by using a cone matching criterion,∆R(offline, online) < 0.1 .
miss is poor compared to the lepton triggers. The trigger selection for
A resolution of the online ET
miss trigger is discussed together with its efficiency measurements in next subsection.
the ET

6.3.2

Measurement of the ETmiss Trigger Efficiency

miss trigger is introduced
In order to recover the trigger efficiency of the single-lepton-trigger, the ET
miss trigger
in H/A → τ τ searches for the first time in this analysis. Since a simulation of the ET
is difficult, so that for the simulated samples including the signal samples, simulated results does
miss trigger efficiency is measured in data. The
not used. Instead of using simulated results, the ET
missmiss > 150 GeV is usedefficiency of the ET trigger is measured using the tag-&-prove method. ET
for an offline trigger threshold requirement. As a tag-trigger, the SLT is used and the efficiency is

7

Usually a trigger and analysis level are called “online” and “offline” respectively.

72

6.4. Event Selection and Categorisation
measured by data. The trigger efficiency is evaluated by following fitting curve :
x − p1
f = p0 1 + erf+ p3 ,
p2(6.5)

where p0 , p1 , p2 and p3 are plateau, half, scale and offset parameters. Figure 6.5 shows the fitted
curves for eτhad and µτhad respectively8 . Figures containing five data-taking periods, three different
selection stages are listed in Appendix A Figure A.1. A region filled by several colour represents one

1.2

ptau-id : ⌧µ⌧had channel

Efficiency

Efficiencye⌧had channels = 13 TeV, 3.2fb 1

1

1.2

0.8

0.6

0.6
data

data

0.4

pT (`) > 30 GeV(`, ⌧ ) > 2.4

0.2

s = 13 TeV, 3.2fb 1

1

0.8

0.4

p

tau-id : ⌧pT (`) > 30 GeV(`, ⌧ ) > 2.4

0.2mT (`, ETmiss ) < 40 GeV
0

100

150

200

250

mT (`, ETmiss ) < 40 GeV
300

0ETmiss TST[ GeV ](a) eτhad

100

150

200

250

300

~ miss |[ GeV ]|~pT (⌧` ) + E
T(b) µτhadmisstrigger of eτhad (a) and µτhad (b) channel with 2015 data-taking period as a
Figure 6.5: Efficiency for the ET
miss
miss
~
+
p
~
(µ)|
(b). Each plots have three different curves, after the preselection (pT (`) >function of ET (a) |E
TT
miss
30 GeV), ∆φ(`, τvis ) > 2.4 and mT (`, ET) < 40 GeV.

miss > 150 GeV and thissigma error from the fitting results. The 90% efficiency is achieved at ET
threshold is used as a trigger selection.

6.4

Event Selection and Categorisation

Event selection criteria are used to define phase-space regions of special interest. Basic requirements are applied to select events with the final state objects, called as “preselection”. The trigger
requirements and kinematical selection are applied to enhance the signal processes and suppress the
background events after the preselection. The definition of the preselection is given in Section 6.4.1.
The signal region is described in Section 6.4.2.

6.4.1

Object Definitions and Event Preselection

An overview of definition of the physics objects is summarised in Table 6.2. The physics object isselected independently to each other. The overlap removal solves overlaps between each objects toavoid double-counting. The overlap removal procedure is described in the following :step 1 : Remove electron, hadronic-τ and jet if ∆R(µ, e/τhad /jet) < 0.2/0.2/0.4.
step 2 : Remove hadronic-τ and jet if ∆R(e, τhad /jet) < 0.2/0.4 after the step 1
8

missMuons is not taken into account in the trigger decision, so the vector sum of the ET
and muon pT is used as a
missonline-ET.

73

6.4. Event Selection and Categorisation
physics object

muon

electronhadronic-τ

jetidentificationpT
η rangeisolationothermedium30 GeV|η| < 2.5
gradient WP
ID requirements

medium30 GeV|η| < 2.47*
gradient WP-

medium25 GeV|η| < 2.3*
1 or 3 tracks
charge = ±1`-vetoJVT
20 GeV|η| < 2.5
jet cleaning

Table 6.2: Definitions of physics objects for the event selection. The mark ”*” present |η| require except
1.37 < |η| < 1.52 addition to it.

step 3 : Remove hadronic-τ if ∆R(τhad , loose µ/e) < 0.2 after the step 2
step 4 : Remove jet if ∆R(τhad , jet) < 0.4 after the step 3
where loose e and µ is selected using same selection criteria but with the loose ID requirement, noisolation selection and pT > 20 GeV. After the overlap removal, it requires the number of survived
leptons is exactly one. An opposite sign with regard to electric charge between lepton and visible-τ
objects are required. The trigger requirement is described in Section 6.4.2.

6.4.2

Categorisation and Event Selection

Event selection and categorisation are applied to selected events after the preselection. Figure 6.6

Event Categorisation
missET< 150GeV

Nb = 0missET> 150GeV

Figure 6.6: Flow chart of analysis categorisation, triggering and event selection. Events
failed trigger or event selections are rejectedfrom analysis.

Nb > 0lepton trigger

missET
trigger

Event Selection
b-vetob-tag

misshigh-ET

shows a flow chart of analysis categorisation, trigger and event selection. The event categorisation
separates events into three categories to improve analysis sensitivity. The event selection distinguishes
the signals from background events. The regions passing all event selection are called as “signal
regions (SRs)”. There are several regions dominated by background processes called as “control
regions (CRs)”. Details of the control regions are described in Section 6.5.
Event Categorisation
miss , b-tag and b-veto categories. One of major improvement
There are three categories, the high-ET
miss of signal processes. The heavy Higgs bosonsof this thesis’s work is taking closer notice of the ET
misshave larger ET than background processes. In order to enhance the heavy Higgs bosons signal, an
miss > 150GeV (high-E miss category). Muon is
event categorisation firstly separates events using ET
T

74

6.5. Backgrounds Modelmiss trigger calculation. So instead of E miss , p (µ) + E miss is used
not taken into account in the ET
T
T
T
miss > 150 GeV for the µτ
in the µτhad channel, i.e. pT (µ) + ET
had channel. A comparison of themiss is shown in Figure 6.7 (a). Events with E miss < 150 GeV (low E miss category)reconstructed ET
T
T

Cut : pT (`) > 30 GeV

p

0.25

s = 13 TeV, 28.0fb 1
0.3TeV
0.5TeV
1TeV

0.2

Z/ ⇤ ! ⌧ ⌧Fake ⌧

Cut : mT (`, ETmiss ) < 40 GeV`⌧had channel

Events/1.0[unit]

Events/10.0[ GeV]

lephad channel

0.3

1

p

s = 13 TeV, 28.0fb 1
ggF 0.5TeV
ggF 1TeV
bbA 0.5TeV
bbA 1TeV

0.8

0.6

tt̄, tModel Uncert.

0.15

Model Uncert.
0.4

0.1
0.2

0.05

0

50

100

150

200

250

300

ETmiss [ GeV ]miss(a) ET

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Number of b-jet(pT > 20 GeV)(b) The number of b-jet

missFigure 6.7: Distributions of the ET
and number of b-jet for the signal processes and major backgrounds
processes.

are separated correspondingly the number of b-jets (Nb ). The b-tag category requires at least one b-jet
to enhance sensitivity for the bottom-annihilation production. Events without b-jet are categorised
as the b-veto category to enhance the gluon-fusion process. The number of b-jet distribution is shown
miss trigger is used for the high-E miss category as described in Section 6.3.1.
in Figure 6.7 (b). The ET
T
The single-lepton-trigger is are used for the b-tag and b-veto categories corresponding channel.
Event Selection
Same event selections are applied for three categories. Event selection criteria consists of two commiss ) < 40 GeV.
mon selections corresponding to event kinematics, ∆φ(τ` , τhad ) > 2.4 and mT (τ` , ET
Figure 6.8 shows event kinematic variables used in the event selection. Three different signal mass
hypothesis are included and Z → τ τ and fake τvis processes are shown as a background process. The
signal tends to have ∆φ ∼ π. The signal processes have lower mT values, while the fake τ has a peakaround mT ∼ 80 GeV. In order to suppress e → τhad fake events from Z → ee process, events are
rejected when a visible mass is within 80 < mvis < 100 GeV for only eτhad channel.

6.5

Backgrounds Model

The description of methodology to model the background processes is given in this section. The
fake τvis background contributes significantly on the tail of Z/γ ∗ → τ τ distributions as discussed in
Section 6.1.2. Major contribution of the fake τvis is the W +jets process, but also the multijets, tt̄ andZ+jets processes contributes. These multiple source process are estimated by “combined fake factor
method” as described in Section 6.5.1. Other background like a Z/γ ∗ → τ τ and tt̄ with real lepton
and real τvis process are described in Section 6.5.2. A validation of estimated background processes
is given in Section 6.7.

75

6.5. Backgrounds Model

p

0.25

Cut : pT (`) > 30 GeV

s = 13 TeV, 28.0fb 1
0.3TeV
0.5TeV
1TeV

0.2

Z/ ⇤ ! ⌧ ⌧Fake ⌧

0.15

lephad channel

Events/5.0[ GeV]

Events/0.05[unit]

lephad channel

Model Uncert.

Cut :(`, ⌧ ) > 2.4

0.2

p

0.18
0.16

s = 13 TeV, 28.0fb 1
0.3TeV
0.5TeV
1TeV

0.14

Z/ ⇤ ! ⌧ ⌧Fake ⌧

0.12

Model Uncert.

0.1
0.08

0.1

0.06
0.04

0.05

0.02
0

0.5

1

1.5

2

2.5

3

0

20

40

60

80

100

120

140

160

180

200

mT (⌧` , ETmiss TST)[ GeV ](⌧` , ⌧had )miss(b) mT (τ` , ET)(a) ∆φ(τ` , τhad )Figure 6.8: Event kinematic variables using in event selections, (a) and (b) show a shape of ∆φ(τ` , τhad ) andmiss) respectively. (a) is after the preselection, while (b) is after ∆φ(τ` , τhad ) > 2.4. Both plots threemT (τ` , ETdifferent signal mass samples (300 GeV, 500 GeV, 1 TeV) and two major backgrounds with arbitrary scale.

6.5.1

Estimation of Background Events with Misidentified τhad Objects

Background events with mis-identified τvis objects are hard to simulate by several reason. The
identification algorithms deployed to suppress fake τvis objects relies on various kind of shower shapevariables describing the evolution of the hadronic and electromagnetic showers of the charged andneutral pions. Hadronic shower evolution consists of a large amount of random components, it needs
that a large set of simulated events. Since hadronic jets are hadronised from gluons and quarks, a
crucial aspect in the simulation is the modelling of the q/g fraction within samples of jets. Gluons
have larger effective colour charge than quarks, this leads that gluons tend to hadronise into wider
jets than quarks. The τvis mis-identification probability of gluons differs significantly from quark’s
one. It is focused on an estimation of the j → τhad fake and also the e → τhad fake is given in mostpart of this section.
The Fake Factor Method
The fake factor method was first developed in the Tevatraon analysis and further improvements
was applied at the ATLAS analysis Reference [199]. The fake factor method extrapolates the event
yields from the control region into the signal regions by using the fake factor (FF) defined as following
:
SR
SR
Npass
= Nfail
×

CR
Npass
CR
Nfail
| {z
}

,

(6.6)

FF

where the “pass” and “fail” means that event with passing and failing an identification selection toSRcontrol fake probability, for example the τ identification is used in the fake τvis estimation. The Npass
SR has exactly same event kinematics but only an identification condition is different. The
and Nfailphysics meaning of the fake factor is a probability of transition from the failed into passed events.
The fake τvis background contributing in the signal regions consists of the QCD multijets, tt̄ and
W/Z+jets. As a numerator default τ identification (medium WP) is used. While as a denominator
events with not loose and BDT score>0.35 is defined. This denominator is so-called “anti-id τ (τ̄76

6.5. Backgrounds Model)”. Evens yields of the fake τvis would be expected following :
SR
SR
SR
SR
SR
+ Nfake,t
Nfake= Nfake,q+ Nfake,Wt̄ + Nfake,Z ,(6.7)

where q, W and Z means the QCD multijets, W +jets and Z+jets respectively. Equation (6.7) canbe transformed into Equation (6.8) using Equation (6.6):
SR
W
SR
tt̄
SR
Z
SR
Nfake
= F Fτ̄q→τ × Nτ̄SR,q + F Fτ̄ →τ × Nτ̄ ,W + F Fτ̄ →τ × Nτ̄ ,tt̄ + F Fτ̄ →τ × Nτ̄ ,Z ,

X
Nτ̄SR
,i
SR
i
= Nτ̄ ×F Fτ̄ →τ × SR ,
Nτ̄
i

(6.8)
(6.9)

= Nτ̄SR × F Fτ̄comb
→τ
X
comb
i
F Fτ̄ →τ =F Fτ̄ →τ × ri .

(6.10)(6.11)iwhere the sum runs over the background processes, ri is a ratio of background i and the sum of all
backgrounds, F Fτ̄comb→τ is the combined fake factor. In order to simplify the combined fake factor, thededicated fake factors for each background processes can be merged into two groups. Here again, thequark and gluon fraction is most influential parameter to decide the fake probability. So processes
which has similar q/g fraction can be merged. The Z+jets production diagrams are almost same as
the W +jets, so an origin of their jets is also similar. In terms of the number of quarks in the final
state, the tt̄ with semi-leptonic channel is dominated with quarks, gluons contribute only initial orfinal state radiation. As shown in Figure 6.4 the QCD multijets process has the larger number ofgluons in final state than other three EW processes. As a result of this simplification, the combined
fake factor is simplified as the following :q
EW
F Fτ̄comb→τ ' rq × F Fτ̄ →τ + rEW × F Fτ̄ →τ ,= rq × F Fτ̄q→τ + (1 − rq ) × F Fτ̄EW→τ .

(6.12)(6.13)

where the EW denotes the W/Z+jets and tt̄ processes, and rq + rEW = 1 is assumed. To estimate the fake τvis background, three variables need to be obtained, F Fτ̄q→τ , F Fτ̄EW→τ and rq . The
aremeasuredatdedicated
controlregions.
A
measurementof the rq is synF Fτ̄q→τ and F Fτ̄EW→τ
onymous with an estimation of the QCD multijets process, so that the QCD multijets estimation is
described in next sub-subsection.
Estimation of rq :The Lepton Fake Factor Method
The rq is defined as a ratio of the QCD multijets contribution and the QCD plus EW process.
In order to measure the rq , the QCD multijets contributions in the SR with anti-id τ objects is
estimated. In a past study, there are several way to measure the rq , the simplest way is just using
the simulated samples with assuming there are no additional source of the fake τvis . This leads thatrq = 1 − rEW where rEW = NEW /(Ntotal − Nreal ). A large systematic uncertainties should be taken
into account. The QCD multijets processes have two fake objects, the fake τvis and the fake lepton.
To estimate the fake lepton, a similar method is used called as the lepton fake factor method. The
lepton isolation criteria suppress the fake lepton, so the lepton isolation is used as a control variable.
SR
SR
N`,τ̄
= N`,τ̄
¯ ×

SR
N`,τ̄
SR
N`,τ̄
¯
| {z }F F`→`¯,(6.14)

77

6.5. Backgrounds Modelq
SR the number of events in the signal region with isolated
is the lepton fake factor, N`,τ̄
where F F`→`¯
SR is the number of events in the signal region with anti-isolated
lepton (`) and anti-id τvis . N`,τ̄¯¯ and anti-id τvis . The anti-isolated lepton is a lepton with failing default isolation selection.
lepton (`)
The lepton fake factor is measured in the region where has more jet-like τvis fake. The jet-like τvis isdefined by BDT score<0.35 called as loose-anti-id τvis (τ̄ 0 ). Before proceeding to actual estimations,definition of dedicated control regions is given in Figure 6.9. The signal region is same condition as

Figure 6.9: Description of the region forcontrolling the fake background. There are
six dedicated regions for τ identificationand lepton isolation conditions. Bottom
column is isolated-lepton (`) region, while¯ retop column is non-isolated-lepton (`)
gion. From right side the id-τ (τ ), anti-id
τ (τ̄ ) and loose-anti-id τ (τ̄ 0 ) regions lie.

` isolation
Fail¯ τ̄ 0 )(`,¯ τ̄ )
(`,

¯ τ)
(`,

Pass

(`, τ̄ 0 )(`, τ̄ )(`, τ )

0.35

loose
medium τvis id

the (`, τ ) region, other regions are used for the fake background estimation. The fake factor F Fτ̄EW→τ
is defined as a fraction between the region of (`, τ̄ ) and (`, τ ). F Fτ̄q→τ is derived as a fraction between¯ τ̄ ) and (`,¯ τ ). While the lepton fake factor F F ¯q is defined as a fraction between thethe region (`,`→`¯ τ̄ 0 ) and (`, τ̄ 0 ).
region of (`,As there are several backgrounds in the control region of the lepton fake factors, a numerator
need to subtract such non-QCD multijets background, mainly the W +jets process. A modellingof such simulated visible-τ objects is not well performed as discussed, so some kind of correction
is necessary to use the simulated samples. Figure 6.10 shows the transverse mass distributions for
Cut : pT (`) > 30 GeV

p

200

Data
0.4TeVs = 13 TeV, 28.0fb 1

Z/ ⇤ ! ⌧ ⌧Z/ ⇤ ! ``(` ! ⌧ )Z/ ⇤ ! ``(jet ! ⌧ )W +jetstt̄, t(jet ! ⌧ )tt̄, t(` ! ⌧ )tt̄, t

180
160
140
120

µ⌧had channel

Events/5.0[ GeV]

Events/5.0[ GeV]e⌧had channel⇥103

Dibosons
Model Uncert.

100

Cut : pT (`) > 30 GeV

⇥103
p

250

Data
0.4TeVs = 13 TeV, 28.0fb 1

Z/ ⇤ ! ⌧ ⌧Z/ ⇤ ! ``(` ! ⌧ )Z/ ⇤ ! ``(jet ! ⌧ )W +jetstt̄, t(jet ! ⌧ )tt̄, t(` ! ⌧ )tt̄, t200

Dibosons
Model Uncert.

150

80

100

60
40

50

20
0

20

40

60

80

100

120

140

160

180

200

mT (⌧` , ETmiss TST)[ GeV ](a) eτhad

0

20

40

60

80

100

120

140

160

180

200

mT (⌧` , ETmiss TST)[ GeV ](b) µτhad

Figure 6.10: The transverse mass distribution in the region of (`, τ̄ 0 ) for eτhad (a) and µτhad (b) channels
after the preselection.

eτhad (a) and µτhad (b) channels in the (`, τ̄ 0 ) region after the preselection. As expected there are alarge amount of excess at lower mT region, this would come from the QCD multijets fake process. An
important feature is a difference of a j → ` fake probability between electrons and muons as shown in78

6.5. Backgrounds Model

Figure 6.10, there are a larger fake electrons than muon. To obtain correction for the simulated fakeτvis , a dedicated control region is defined. The W +jets has a unique peak around mW GeV, so it ismiss ) < 120 GeV as a control region for the W +jets (WCR).
natural to use a window of 60 < mT (`, ET
Along the mT window cut, default selection of mT < 40 GeV is replaced. In addition to the mT
miss > 40 GeV is also applied to suppress the QCD multijets contaminations. In the WCR
window, ET
Cut : pT (`) > 30 GeV`⌧had,1pe⌧had,1pµ⌧had,1p`⌧had,3pe⌧had,3pµ⌧had,3p2.5
2ps = 13 TeV, 28.0fb 1

Opposite Sign : anti-id tau

Correction Factor

Correction Factor

Opposite Sign : loose anti-id tau

3

2
1.5

1

1

0.5

0.5

30

40

50

60

70

80

90

102

¯ τ̄ 0 )(a) correction in (`,150

p⌧Thad [ GeV ]`⌧had,1pe⌧had,1pµ⌧had,1p`⌧had,3pe⌧had,3pµ⌧had,3p

2.5

1.5

0

Cut : pT (`) > 30 GeV

3

0

30

40

p

50

60

70

80

90

s = 13 TeV, 28.0fb 1

102

150

p⌧Thad [ GeV ](b) correction in (`, τ̄ )Figure 6.11: Correction factors for the simulated τvis fake objects as a function of the transverse momentumof τvis . Plot show six variations for eτhad and µτhad channel with 1, 3-prong and inclusively. Error bars include
its statistical and systematic uncertainties, systematic uncertainty is obtained from a q/g fraction difference¯ τ̄ 0 ) andbetween the WCR and the SR as described in later. (a) and (b) shows the correction factor in the (`,(`, τ̄ ) respectively.

a correction factor is obtained as a function of the visible-τ pT as shown in Figure 6.11 (a). The
correction factors depends only n-prong. This correction factors does not change event yields but
its shapes. For the overall scale corrections are performed with independently for eτhad , µτhad andn-prong decay channels. As an extrapolation bias check the q/g fraction difference between the WCR
and SR is evaluated by simulated samples. Figure 6.12 shows comparisons of the q/g fraction andshape difference between the WCR and the SR as a function of the τhad pT . Each content is the ratioof fraction and shape between the WCR and SR. Overall uncertainties are less than 5 % at low-pT andabout 10% at higher pT region. The error band is directly used as an extrapolation uncertainty of thiscorrection. As expected from origin of the fake lepton, there are non-negligible dependencies on events
has more quarks or not. The lepton fake factor is splitted to the b-tag and b-veto events. Figure 6.13
shows the lepton fake factors and reweighting factors. The lepton fake factor F F`→`is defined as a¯function of lepton pT . Two reweighting factors for eτhad channels are also given as a function absolute
miss (d)values of lepton pseudorapidity (c) and angle difference between direction of lepton and ET
in the transverse plane. These reweighting factors correct a kind of calculation difference between
the isolated- and non-isolated lepton. The R`¯(|η|)) corrects difference of the electron identification
criteria among pseudorapidity regions9 as discussed in Section 5.4.3. The R`¯(∆φ)) corrects difference
miss reconstruction procedure in terms of the soft term subtraction10 . As a result of the QCDof the ET
multijets, the rq is measured in the (`, τ̄ ) region. Since the rq is a fraction of the QCD multijets
components in the (`, τ̄ ) region, so other components in that region should be understood. To ensure
9

The electron identification likelihood has strong dependency against pseudorapidity due to the TRT detector components are different.
10
The isolated-electron, tracks around electrons are calculated as the soft term, while tracks around the non-isolated
lepton are account as EM cluster or electron itself.

79

6.5. Backgrounds Modelq/g Fraction Comparison : Opposite Sign

Error
quark
gluon

1.8

p

s = 13 TeV, 28.0fb 1

1.6

2
Error
quark
gluon

1.8

p

s = 13 TeV, 28.0fb 1

1.6

1.4

1.4

1.2

1.2

1

1

0.8

0.8

0.6

q/g Fraction Comparison : Opposite Sign`⌧had,3p

ratio SR / CRratio SR / CR`⌧had,1p

2

0.6
25

30

40

50

60

70

80

10

2

150

200

25

30

40

50

60

70

80

p⌧Thad [ GeV ]1p(a) τhad

102

150

200

p⌧Thad [ GeV ]3p(b) τhad

Figure 6.12: Comparison of the q/g fraction and shape difference between the WCR and the SR as a functionof the transverse momentum of τvis objects.

other component, the WCR is used and correction factors is obtained by similar way in the WCR.
Figure 6.11 (b) shows the correction factors for the τ̄ events from the WCR including statisticaland systematic uncertainties obtained from comparison of the q/g fraction difference between the
WCR and the SR as shown in Figure 6.14. Uncertainty are a few % order at lower pT region, whileat higher pT region, it is up to 30% level due to non-negligible difference of the q/g shapes. The
scale correction of each fake component is performed by fitting the transverse momentum of lepton
in the WCR and they are extrapolated into the SR. The fit is performed by floating only the fakeτvis sources, the W +jets, tt̄ and Z+jets, other processes including the QCD multijets are fixed. The
systematic uncertainties with respect to this fit are taken into account from fitting results, typically
it is 3 ∼ 5% level.
The rq is measured in each SR with (`, τ̄ ) regions after the scale and shape corrections, As asystematic uncertainty, several source is considered, statistical and systematic uncertainties related
to the lepton fake factor, the scale and shape correction. Figure 6.15 shows the measured rq as afunction of the transverse momentum of the fake τvis objects. For the value greater than 1.0 are
constrained with rq = 1.0 with additional 5% uncertainty. As shown in plots, the eτhad and µτhad
channel show different trends at higher pT region, the eτhad channel lower than µτhad channel. The
rq is extrapolated by same values as 200 GeV with additional 10% uncertainty for pT > 200 GeV. In
miss category, the high-E miss category is checked. The QCD multijets process
addition to the low-ETTmiss
has no ET source except neutrinos from hadronic jets, so that the met is powerful variable tomiss category is already applied E miss > 150 GeV, so the fake lepton
suppress them. Since the high-ET
Tmiss (`, τ̄ ) region.
is extremely small. Figure 6.16 shows the transverse mass distributions for the high-ET
The background expectation agrees well with observed data within uncertainties. The fake leptons are
extremely small, they are less than 0.1% of total background expectation. The systematic uncertainty
is considered from difference in Figure 6.16 between data and background expectation. The systematic
uncertainty, hence, is estimated ±7% and ±12% for eτhad and µτhad channel respectively.
Measurements of The QCD Fake Factors : F Fτ̄q→τ¯ τ̄ ) amd (`,¯ τ ) which
The QCD fake factor F Fτ̄q→τ is measured in the QCD CR with condition of (`,are inverted the lepton isolation criteria. The QCD multijets processes dominates in that region, so
a subtraction of other EW processes is negligible for the QCD fake factor. It is necessary to consider

80

Opposite Sign : eτhad

3√

Opposite Sign : µτhad

Fake Factor

Fake Factor

6.5. Backgrounds Models = 13 TeV, 28.0fb−1

2.5

b-veto,2015
b-veto,2016
b-tag,2015
b-tag,2016

2

1

√

0.9

s = 13 TeV, 28.0fb−1

0.8

b-veto,2015
b-veto,2016
b-tag,2015
b-tag,2016

0.7
0.6

1.5

0.5
0.4

1

0.3
0.2

0.5

0.1
0

40

50

60

70

80

90

0

150

102

40

50

60

70

80

pT (`)

Opposite Sign : eτhad√3

s = 13 TeV, 28.0fb−1
b-veto,2015
b-veto,2016
b-tag,2015
b-tag,2016

2.5
2

2

1

0.5

0.5

1

1.5

2

2.5

0

s = 13 TeV, 28.0fb−1
b-veto,2015
b-veto,2016
b-tag,2015
b-tag,2016

2.5

1

0.5

√

3

1.5

0

Opposite Sign : eτhad

3.5

1.5

0

102

(b) µτhad ,F F`→`¯

Reweighting Factor

Reweighting Factor(a) eτhad , F F`→`
¯

3.5

90

pT (`)

0

0.5

1

1.5

2

3

∆φ(`, ETmiss )|η(`)|(c) eτhad , R`¯(|η|)2.5(d) eτhad , R`¯(∆φ)

Figure 6.13: The lepton fake factors for electrons (a) and muons (b) as a function of the lepton pT . And
missreweighting factors for eτhad channel as a function of ∆φ(`, ET) (c) and |η(`)| (d). For all plots, it is separated
with b-tagged or b-veto events and 2015 or 2016 data-taking period.

an extrapolation bias as a systematic uncertainty. It is evaluated by checking difference of the fakefactor between default QCD CR and modified QCD CR. The modified QCD CR has slightly closer
condition to the SR in terms of the lepton isolation criteria, which fails the gradient working point
but passes the loose WP. The pile-up effects is also evaluated as the systematic uncertainty. In orderto check the pile-up effects, two fake factors with lower and higher pile-up condition are comparedusing the average number of interactions per bunch crossing hµi. It is estimated by 1 ∼ 4% on the
QCD fake factor. Figure 6.17 shows the QCD fake factor for the 1-prong and 3-prong decay channels
with four different events, data-taking period and the number of b-tagged jets.
Measurements of The EW Fake Factors : F Fτ̄EW→τThe EW fake factor F Fτ̄EW→τ is measured in the WCR with condition of (`, τ ) and (`, τ̄ ). The WCR
is defined as 60 < mT < 110 GeV. The other components from real hadronic-τ is subtracted fromdenominator and numerator of the fake factors. As the real visible-τ subtraction simulated samples

15

81

6.5. Backgrounds Modelq/g Fraction Comparison : Opposite Sign

Error
quark
gluon

1.8

p

s = 13 TeV, 28.0fb 1

1.6

2
Error
quark
gluon

1.8

p

s = 13 TeV, 28.0fb 1

1.6

1.4

1.4

1.2

1.2

1

1

0.8

0.8

0.6

q/g Fraction Comparison : Opposite Sign`⌧had,3p

ratio SR / CRratio SR / CR`⌧had,1p

2

0.6
25

30

40

50

60

70

80

10

2

1p
(a) τhad

150

200

25

30

40

50

60

70

80

p⌧Thad [ GeV ]

102

150

200

p⌧Thad [ GeV ]3p(b) τhad

Figure 6.14: Comparison of the q/g fraction and shape difference between the WCR and the SR as a functionof the transverse momentum of τvis objects.

is used and it is evaluated as less than 5%. As a other systematic uncertainty, an extrapolation bias
is obtained by using the simulated q/g fraction comparison. The pile-up effect is also estimated bysame way as doing for the QCD fake factors, it is less than 1%. Figure 6.18 shows the EW fake factor
for the 1-prong and 3-prong channels with four different events, data-taking period and the number
miss category same fake factors are used due to a lack of data statisticsof b-tagged jets. For the high-ET
miss and high=E miss events
to estimate. Potential differences of the EW fake factor between the low-ETT
are obtained by the simulated samples, it is estimated as 3 ∼ 8%. This differences are taken into
miss category.
account as an additional systematic uncertainty for only the high-ET
missCorrections on ∆φ(τ, ET

Since the fake factor method extrapolates from τ̄ region, a correction is applied correspondingly
miss reconstruction procedure between the id-τ and τ̄ regions. This is similar cordifference of the ET
miss reconstruction. An
rection to the lepton fake factor method, an affected term is the τ term of the ET
miss
miss
angle difference between visible-τ and ET ∆φ(τ, ET ) is used as correction target. The correction
miss ) is defined as a ratio between the id-τ and τ̄ region, as shown in Figure 6.19.
factor on ∆φ(τ, ET
The correction factor is interpolated using the PCHIP algorithm11 to obtain smooth lines. No significant difference between those event categorisation was found, so the correction factors is used
inclusively. Only statistical error on the denominator and numerator is propagated as a systematic
uncertainty.
Background with e → τhad Fake

Other source of fake τhad need to be taken account, in Z/γ ∗ → ee events one electron is identified aselectron, another electron mimicking into τhad objects. They dominates in eτhad 1-prong channel, the3-prong fake e → τhad can be negligible. The electron LH identification criteria is used to estimate

11

The Piecewise Cubic Hermite Interpolating Polynomial technique, which can perform more stable than other algorithm
like the cubic interpolation.

82

6.5. Backgrounds Model

Cut : mT (`, ETmiss ) < 40 GeVeτhad (stat)eτhad (stat ⊕ syst)µτhad (stat)µτhad (stat ⊕ syst)

1√

s = 13 TeV, 3.2fb−1

1.2

0.8

0.6

0.6

0.4

0.4

0.2

0.2

40

60

80

100

eτhad (stat)eτhad (stat ⊕ syst)µτhad (stat)µτhad (stat ⊕ syst)

1

0.8

0

120

140

160

180

Cut : mT (`, ETmiss ) < 40 GeV

Opposite Sign : b-tag

rQCD

rQCD

Opposite Sign : b-veto

1.2

0

200

40

60

80

100

√

120

s = 13 TeV, 3.2fb−1

140pτThad [ GeV ]Cut : mT (`, ETmiss ) < 40 GeV√

s = 13 TeV, 24.8fb−1

1.2

0.8

0.6

0.6

0.4

0.4

0.2

0.2

60

80

100

eτhad (stat)eτhad (stat ⊕ syst)µτhad (stat)µτhad (stat ⊕ syst)

1

0.8

40

120

140

160

180

Cut : mT (`, ETmiss ) < 40 GeV

Opposite Sign : b-tag

rQCD

rQCD

Opposite Sign : b-veto0200(b) b-tag, 2015

1.2
1

180

pτThad [ GeV ](a) b-veto, 2015eτhad (stat)eτhad (stat ⊕ syst)µτhad (stat)µτhad (stat ⊕ syst)

160

200

0

40

60

80

100

√

120

pτThad [ GeV ]s = 13 TeV, 24.8fb−1

140

160

180

200

pτThad [ GeV ](c) b-veto, 2016(d) b-tag, 2016

Figure 6.15: The measured rq for b-tag and b-veto splitting 2015 and 2016 data-taking period as a functionof the τvis pT . All plots show eτhad (red) and µτhad (blue) points with statistical uncertainty and filled regionswith quadratic sum of statistical and systematic uncertainty.

the e → τhad fake events using the fake factor method:
SR
SR
Ne→τ
= Nfail
eLH ×
had

CR
Npass
eLH

,
CR
Nfail
eLH
| {z }(6.15)F Fe→τhad

where the CR is inside a window of 80 < mvis < 110 GeV, the eLH is the electron likelihood
identification selection. Figure 6.20 shows the e → τhad fake factor for eτhad 1-prong channel as a
miss categories, extremely small contributionfunction of the visible-τ pT . For the b-tag and high-ET
from Z → ee process is expected, so that the e → τhad fake process can be neglected.

83

6.5. Backgrounds Model

p

2500

Cut : pT (⌧ ) > 25 GeV

Data
0.4TeVs = 13 TeV, 28.0fb 1

1500

Z/ ⇤ ! ⌧ ⌧Fake `
Z/ ⇤ ! ``(` ! ⌧ )Z/ ⇤ ! ``(jet ! ⌧ )W +jetstt̄, ttt̄, t(` ! ⌧ )tt̄, t(jet ! ⌧ )

8000
6000

Dibosons
Model Uncert.

4000
2000

0

20

40

60

80

100

120

140

160

180

200

Obs/Exp

Obs/Exp

Data
0.4TeVs = 13 TeV, 28.0fb 1

10000

500

1.5
1
0.5

Cut : pT (⌧ ) > 25 GeV

12000

Dibosons
Model Uncert.

1000

p

14000

Z/ ⇤ ! ⌧ ⌧Fake `
Z/ ⇤ ! ``(` ! ⌧ )Z/ ⇤ ! ``(jet ! ⌧ )W +jetstt̄, ttt̄, t(` ! ⌧ )tt̄, t(jet ! ⌧ )2000µ⌧had channel

Events/10.0[ GeV]

Events/10.0[ GeV]e⌧had channel

1.5
1
0.5

0

20

40

60

80

100

mT (⌧` , ETmiss )[ GeV ]

120

140

160

180

200

mT (⌧` , ETmiss )[ GeV ](a) eτhad(b) µτhad

missFigure 6.16: Transverse mass distributions at the high-ET
category for eτhad (a) and µτhad (b) channels inthe (`, τ̄ ) region.

6.5.2

Modelling Additional Background Processes

Additional background processes are validated and corrected using dedicated control regions. The
Z → τ τ CR (ZCR) is defined as applying same selections of the signal region and mvis < 80 GeV,
since this region does not impact on any signal. The tt̄ → `τhad CR (TCR) is defined as applying samemiss andselections of the signal region but applied mT > 120 GeV. The TCR is defined in the high-ETb-tag SR, not for the b-veto SR. The W +jets CR (WCR) is defined as same selections of the signal
miss and b-veto SR. The
region but applied 70 < mT < 110 GeV. The WCR is defined in the high-ET
same sign CR (SSCR) which have large QCD contributions are defined as the all SRs but requiredq` × qτhad > 0. Table 6.3 summarises the result of validation of each background process. In the WCRCR
misshigh-ETb-tag

b-veto

TCR
ZCR
WCR
SSCR
TCR
ZCR
SSCR
WCR
ZCR
SSCR

1p
eτhad

3p
eτhad

1p
µτhad

3p
µτhad

0.920± < 0.01
1.192± < 0.01
0.885 ± 0.07
0.613 ± 0.06
0.830± < 0.01
0.795 ± 0.07
1.010± < 0.01
1.011 < 0.01
1.045 < 0.01
1.249 < 0.01

0.855 ± 0.04
1.024 ± 0.04
0.779 ± 0.04
1.062 ± 0.05
1.019± < 0.01
0.990 ± 0.02
1.089 ± 0.03
0.944 < 0.01
0.961 < 0.01
1.070 < 0.01

0.896 ± 0.03
1.264 ± 0.03
0.938 ± 0.02
0.955± < 0.01
0.984± < 0.01
1.255 ± 0.14
1.028± < 0.01
0.967 < 0.01
0.934 < 0.01
0.987 < 0.01

0.827 ± 0.08
1.112± < 0.01
0.865 ± 0.05
0.921 ± 0.05
0.944± < 0.01
1.591 ± 0.06
1.196 ± 0.03
0.923± < 0.01
0.983± < 0.01
0.987 ± 0.02

Table 6.3: Scale factors measured in several CRs.

and SSCR, a validations of the fake τhad is performed for the EW and QCD components respectively.
miss
A residual is taken into account as an additional non-closure systematic uncertainty. In the low-ET
categories, results of the TCR are propagated into b-veto regions. The result from the WCR in theb-veto is not used for correcting the fake τhad background. It is used for validation of the fake τhad

84

6.6. Systematic UncertaintiespτT` > 30 GeV

1p, F Fτ̄q→τ (stat)
1p, F Fτ̄q→τ (stat ⊕ syst)
3p, F Fτ̄q→τ (stat)
3p, F Fτ̄q→τ (stat ⊕ syst)

0.5
0.4

√

s = 13 TeV, 28.0fb−1

0.6

0.4
0.3

0.2

0.2

0.1

0.1

30

40

50

60

1p, F Fτ̄q→τ (stat)
1p, F Fτ̄q→τ (stat ⊕ syst)
3p, F Fτ̄q→τ (stat)
3p, F Fτ̄q→τ (stat ⊕ syst)

0.5

0.3

0

70

80

90

102

0

200

30

40

pτT` > 30 GeV√

s = 13 TeV, 28.0fb−1

0.4

0.2

0.2

0.1

0.1

40

50

60

70

80

90

102

200

pτThad90102(c) 2016, b-veto200∆φ(`, τhad ) > 2.4

1p, F Fτ̄q→τ (stat)
1p, F Fτ̄q→τ (stat ⊕ syst)
3p, F Fτ̄q→τ (stat)
3p, F Fτ̄q→τ (stat ⊕ syst)

0.5

0.3

30

80

0.6

0.3

0

70

2016 : Opposite Sign, b-veto

Fake Factor

Fake Factor

2016 : Opposite Sign, b-tag

0.4

60

s = 13 TeV, 28.0fb−1(b) 2015, b-tag

0.6
0.5

50

√

pτThad(a) 2015, b-veto

1p, F Fτ̄q→τ (stat)
1p, F Fτ̄q→τ (stat ⊕ syst)
3p, F Fτ̄q→τ (stat)
3p, F Fτ̄q→τ (stat ⊕ syst)pτT` > 30 GeV

2015 : Opposite Sign, b-tag

Fake Factor

Fake Factor

2015 : Opposite Sign, b-veto

0.6

0

30

40

50

60

√

70

80

pτThad90s = 13 TeV, 28.0fb−1

102

200

pτThad(d) 2016, b-tag

Figure 6.17: The fake factors for the QCD components, F Fτ̄q→τ as a function of visible-τ pT for 1-prong (blue)and 3-prong (red). Plots (a,b) and (c,d) shows the fake factors of 2015 and 2016 data-taking period respectively. The fake factors are splitted events with b-veto (a,c) and b-tag (b,d) respectively. In each plots, points
with marker present center values and its statistical uncertainty, while filled regions present total uncertainty
including all systematic uncertainties.

background and assigning an additional uncertainty as a non-closure systematic uncertainty. Diboson
process is too small to validate its accuracy and there are no regions which can measure them.

6.6

Systematic Uncertainties

To extract experimental results, various systematic uncertainties are taken into account together
with the statistical uncertainty. There are various systematic uncertainties on the physics object
reconstruction and calibration. The theoretical modelling of signal and background processes, as wellas on the background modelling are considered.
It affects the number of expected signal and background events in the analysis regions. The systematic uncertainties is splitted into two type of systematic uncertainties, “acceptance” and “shape”

85

6.6. Systematic UncertaintiespτT` > 30 GeV

1p, F Fτ̄EW→τ (stat)
1p, F Fτ̄EW→τ (stat ⊕ syst)
3p, F Fτ̄EW→τ (stat)
3p, F Fτ̄EW→τ (stat ⊕ syst)

0.5
0.4

√

s = 13 TeV, 28.0fb−1

0.6

0.4
0.3

0.2

0.2

0.1

0.1

30

40

50

60

1p, F Fτ̄EW→τ (stat)
1p, F Fτ̄EW→τ (stat ⊕ syst)
3p, F Fτ̄EW→τ (stat)
3p, F Fτ̄EW→τ (stat ⊕ syst)

0.5

0.3

0

70

80

90

102

0

200

30

40

pτT` > 30 GeV√

s = 13 TeV, 28.0fb−1

0.4

0.2

0.2

0.1

0.1

40

50

60

70

80

90

102

200

pτThad

90

102

200

pτT` > 30 GeV

1p, F Fτ̄EW→τ (stat)
1p, F Fτ̄EW→τ (stat ⊕ syst)
3p, F Fτ̄EW→τ (stat)
3p, F Fτ̄EW→τ (stat ⊕ syst)

0.5

0.3

30

80

0.6

0.3

0

70

2016 : Opposite Sign, b-tag

Fake Factor

Fake Factor

2016 : Opposite Sign, b-veto

0.4

60

s = 13 TeV, 28.0fb−1(b) 2015, b-tag

0.6
0.5

50

√

pτThad(a) 2015, b-veto

1p, F Fτ̄EW→τ (stat)
1p, F Fτ̄EW→τ (stat ⊕ syst)
3p, F Fτ̄EW→τ (stat)
3p, F Fτ̄EW→τ (stat ⊕ syst)pτT` > 30 GeV

2015 : Opposite Sign, b-tag

Fake Factor

Fake Factor

2015 : Opposite Sign, b-veto

0.6

0

30

40

50

60

√

70

80

pτThad(c) 2016, b-veto90

s = 13 TeV, 28.0fb−1

102

200

pτThad(d) 2016, b-tag

Figure 6.18: The fake factors for the EW components, F Fτ̄EW→τ as a function of visible-τ pT for 1-prong (blue)and 3-prong (red). Plots (a,b) and (c,d) shows the fake factors of 2015 and 2016 data-taking period respectively.
The fake factors are splitted events with b-veto (a,c) and b-tag (b,d) respectively. In each plot, points withmarker present a center value and its statistical uncertainty, while filled regions present total uncertainty
including all systematic uncertainties.

uncertainties. The acceptance uncertainty does not change a shape of final discriminating variable. Itchanges only event weights12 . While a shape uncertainty changes its kinematic distributions, so it ispropagated to the final discriminating distributions13 . Further grouping is done with respect to sourceof uncertainty, an experimental and theoretical uncertainties. The various systematic uncertainties
are summarised in this section. Their inclusion into the combined likelihood fit and their impact
on the final analysis result is discussed in Section 7.1. Description of the experimental systematic
uncertainties are given in Section 6.6.1. The theoretical systematic uncertainties are briefly describedin Section 6.6.2. Detailed values of each systematic uncertainties for all relevant background andsignal processes are shown in Appendix E.
1213for example a analysis scale factor of the hadronic-τ identification efficiency.
for example a transverse momenta of lepton or hadronic-τ .

86

6.6. Systematic UncertaintiesqpτT` > 30 GeV√

2.2

Reweighting Factor

Reweighting Factorq2015 : Opposite Sign, Rτ̄ →τ

2.4

s = 13 TeV, 28.0fb−12eτhad,1peτhad,3pµτhad,1pµτhad,3p

1.8
1.6
1.4
1.2

√

2.2

eτhad,1peτhad,3pµτhad,1pµτhad,3p

1.8
1.6
1.4
1.2
1

0.8

0.8

0.6

0.6

0.4

0.4

0.2

0.2
0

0.5

1

1.5

2

2.5

0

3

0

0.5

1

1.5

2

∆φ(τhad , ETmiss )√Reweighting Factor

Reweighting FactorpτT` > 30 GeV

2.2

s = 13 TeV, 28.0fb−12eτhad,1peτhad,3pµτhad,1pµτhad,3p

1.8
1.6
1.4

3

(b) 2016, Rτ̄q →τ

2015 : Opposite Sign, Rτ̄EW
→τ

2.4

2.5

∆φ(τhad , ETmiss )(a) 2015, Rτ̄q →τ

1.2

pτT` > 30 GeV

2016 : Opposite Sign, Rτ̄EW
→τ

2.4

√

2.2

s = 13 TeV, 28.0fb−12eτhad,1peτhad,3pµτhad,1pµτhad,3p

1.8
1.6
1.4
1.2

1

1

0.8

0.8

0.6

0.6

0.4

0.4

0.2

0.2

0

s = 13 TeV, 28.0fb−1

2

1

0

pτT` > 30 GeV

2016 : Opposite Sign, Rτ̄ →τ

2.4

0

0.5

1

1.5

2

2.5

3

0

0

0.5

1

1.5

∆φ(τhad , ETmiss )(c) 2015, Rτ̄EW
→τ

2

2.5

3

∆φ(τhad , ETmiss )(d) 2016, Rτ̄EW→τFigure 6.19: The correction factor Rτ̄q →τ , Rτ̄EW→τ for two data-taking period with four decay mode channels.
Filled regions represent uncertainty bands, which applied interpolation with the PCHIP technique to perform
stable smoothing from original points with filled circle.

6.6.1

Experimental Uncertainties

The performance of the particle reconstruction, calibration, identification and the trigger performance is measured in real data. The respective uncertainties are discussed in Chapter 5. All such
uncertainties are propagated and compared to the nominal expectation. Such uncertainties affectonly simulated events. The experimental systematic uncertainties are summarised correspondingly
the physics objects in the following. The systematic uncertainty of data-driven background modellingis also described.
missMissing Transverse Energy, ET
miss is reconstructed from several physics objects, the energy resolution and scale are
Since the ET
taken into account from each physical objects uncertainties. The soft-term is enough for the systematic
uncertainties. Two systematic uncertainties is defined as the soft-term systematic uncertainties. A
measurement of resolution is performed using Z+jets event samples, and it is defined as in direction

87

6.6. Systematic Uncertainties

Fake Factor

Opposite Sign

1.2p

Cut : pT (`) > 30 GeV

s = 13 TeV, 28.0fb 1
1p
F Fe!⌧(stat)
1p
F Fe!⌧(stat syst)

1
0.8

Figure 6.20: The e → τhad fake factor forthe eτhad 1prong channel as a function of thevisible-τ pT . Each points with marker present
center values and statistical uncertainty, while
filled regions present total uncertainty including systematic uncertainty.

0.6
0.4
0.2
0

30

40

50

60

70

80

90

102

200

p⌧Thad [ GeV ]Z
of pZ
T . An absolute and accidental effect of is measured in the parallel direction of pT . While inZ
perpendicular direction it slightly depends on pT accuracy and it is affected by muons or electrons
momentum resolution. The soft-term resolution uncertainty is evaluated using the vector sum of allsoft tracks. It is splitted into the parallel and perpendicular direction. The uncertainty on the softterm scale is calculated using track parameters. In addition to the soft-term systematic uncertainties,
miss trigger efficiency uncertainty is also assigned.
the ET

Electrons
The electron object has four acceptance uncertainties related to efficiency of the reconstruction,
identification, isolation and trigger. In addition to acceptance uncertainties, several shape uncertainties are evaluated, one energy resolution and six energy calibration scale uncertainties. All uncertainties are summarised in Table D.13. The uncertainty of the LAr calorimeter simulation is evaluatedby 2015 and 2016 data-taking conditions separately. The four acceptance uncertainties are measured
using the Z → ee tag-&-probe method as described in Section 5.4.
Muons
The muon object has four acceptance uncertainties related to the efficiency of the reconstruction,
TTVA (Track-to-vertex-association), isolation and trigger. One energy resolution and six energy calibration scale uncertainties are evaluated as the shape uncertainty. All uncertainties are summarisedin Table D.13. The four acceptance uncertainties are measured using the Z → µµ tag-&-probe method
as described in Section 5.5. All acceptance uncertainties have two type of uncertainties correspondto statistical and systematic uncertainties on its efficiency measurements.
Jets
There are one acceptance and several energy scale and resolution shape uncertainties in the jet objects. The jet vertex tagging (JVT), jet energy scale (JES), resolution (JER) and flavour tagging (FT)
is summarised in Table D.13 . The FT Eigen uncertainties are statistically determined by smoothingalgorithm of transverse momentum of b-,c- and light-quark using the Kernel density estimator withthe local polynomial function. This technique performs a smoothing of input distributions using
locally optimised polynomial functions which has the same number of functions as input data points.
The systematic uncertainties which has same or similar shape of the Kernel density are merged into
one combined systematic uncertainty with certain threshold of merging. The JES has similar grouping, but this is performed by some assumptions depending on its measurement procedures. The JER
is measured by several physics processes and its uncertainty is evaluated by taking difference between

6.6. Systematic Uncertainties

88

measurements.
Hadronic-τ
Uncertainties on the hadronic-τ object are one of important systematic uncertainties in this analysis. There are six acceptance uncertainties and three shape uncertainties corresponds to the tau
energy scale (TES). Table D.13 summarises their uncertainties and its type. For the identification
uncertainties, an extrapolation is performed from low pT into higher pT events (pT > 250 GeV) due
to a lack of data with high pT τ . High-pT systematic uncertainties have additional 10 ∼ 20% uncertainties including sample dependence and extrapolation procedure difference. Uncertainty of TES is
one of important systematic uncertainties in this analysis. It directly changes the mτ τ shape, so it isassigned as the shape nuisance parameter as described in Section 7.2.
Background Modelling Uncertainties
As shown in Section 6.5.1, several uncertainties are assigned corresponding background estimations.
Besides the fake τhad background, uncertainties on correction for tt̄ → `τhad and Z → τ τ process, aswell as fake τhad non-closer should be taken into account.
Luminosity and Pile-up
The luminosity uncertainty is determined by the forward detector and with the var-der-Meer scan
as described in Section 4.2.5. The Luminosity uncertainty depends on the data-taking period, forthe 2015 and 2016 data-taking it is estimated as 2.8% and 5% respectively. The pile-up reweighting
as described in Section 3.1.6, the uncertainty on this technique is derived by an error of fitting toobserved correlation between (hµi , nPV).

6.6.2

Theoretical Uncertainties

As uncertainties on theoretical calculation, modelling and assumption are estimated by changing its
tuning parameters or different calculation model. The parton distribution function, the factorisation
and renormalization scale and the MC tuning is considered in this analysis. In addition to these
uncertainties, the difference between alternative MC generator is also taken into account for the
background processes.
PDF Uncertainties
The PDF fit contains inherent uncertainties due to the fitting procedure. These uncertainties arepropagated to the final observable. As sundry PDF sets are provided from different collaborations,
there are The difference of center values among alternative PDF sets is taken into account as asystematic uncertainty. CT10(CT14), MMHT2014, NNPDF3.0 are commonly used for this purpose. For
signal processes, the CT10 is used, so two other PDF sets are used to take variations14 . This variationis performed by reweighting scheme, this makes the assumption that to change the PDF used in thematrix element is negligible in the parton shower evolution. Secondary effect is dependency of theinitial state radiation and underlying event, it is also treated by following approach.
w=

pdfnew (x1 , f1 , Q) × pdfnew (x2 , f2 , Q),
pdfold (x1 , f1 , Q) × pdfold (x2 , f2 , Q)

(6.16)

where x1 , x2 is parton density, pdfold and pdfnew is the original and compared value of the PDF.
Totally 101 variations exist in each PDF set, so the maximum variation is symmetries and taken as
14

These PDF sets agree well on the gluon-gluon initiated process, while disagrees on the valence PDF and also thequark-gluon process.

89

6.7. Results
the total PDF uncertainty.
Factorisation and Renormalization Scale Uncertainties

Since the factorisation and renormalization scale are not physical parameters, but parameters
for calculating physical observable and its cross sections. In principle, it is not expected that theobservable depends on the factorisation and renormalization scale, to ensure this dedicated test is
performed. The factorisation and renormalization µF,R is varied by factor 0.5 to 2.0, and its deviation
is taken into account as a systematic uncertainty.
MC Tuning Uncertainties
The final to consider are the uncertainties corresponding the Monte Carlo tuning. For this purpose,
there are established methodology. Since two signal processes are made by different MC generatorswith different PDF set and tuning. Table F.13 and F.13 summarise internal parameter variations
for the MC tuning variation based on Reference [185]. For both signal processes, there are different
variation sets, the gluon-fusion samples has three variations, while the bottom-annihilation samples
has five variations.
Uncertainties on Signal Modelling
The uncertainties on the signal acceptance which are considered as normalisation uncertainties
It is evaluated by alternative samples with truth particle information. In addition to use truth
samples, it is not realistic to generate truth event samples for all signal process including different
mass hypothesis. It is compromised to use three different mass hypothesis, the 200, 500, 1000 GeV
are choices. The results are shown in below Eq. (6.17).
fggH = 18.4654 − 0.0027954 × mA (%)

fbbA = 17.6896 + 0.0059865 × mA (%)(6.17)(6.18)In order to use for all mass samples, a linear fit is performed for total uncertainties by resultssummarised in Table D.13.
Uncertainties on Background Modelling
Theoretical cross-section uncertainties for Z+jets and diboson process is assigned as 5% and 6%
respectively based on Reference [Butterworth:1287902]. For the tt̄ process, five variation is evaluated. Table F.13 summerizes various systematic uncertainties for tt̄ processes. Figure 6.21 shows
variations for three dedicated uncertainties on tt̄ sample using alternative simulated samples. For
Z → τ τ background process, an addtional uncertainty is evaluated using the ZCR events as shownin Figure 6.21 (b).

6.7

Results

The results as described in the preceding sections is given in this section.
Several important variables are shown in Figure 6.22 - Figure 6.24. For di-τ mass distributions,the total transverse mass is chosen as a final discriminant.
Table 6.4 shows event yields for three signal regions with statistical uncertainty only, the systematic
uncertinties are described in Section 6.6.

90

6.7. Results

Processeτhad
1-prongµτhad
3-prong

1-prong

3-prongmisshigh-ET

Diboson

5.1 ± 1.0

1.3 ± 0.534 ± 3.1

10 ± 2.1

j → τhad

126 ± 4.529 ± 0.9901 ± 11208 ± 2.3

tt̄ → `τhad

49 ± 3.5

19 ± 2.2323 ± 9117 ± 5.6

Z → ττ

25 ± 6.2

18 ± 7.2

171 ± 1962 ± 10Total

205 ± 8.5

67 ± 7.6

1 429 ± 24

397 ± 12Signal10 ± 3.1

3.5 ± 1.1

40 ± 1014 ± 3.4

Data

194

1451

387

57
b-tag

Diboson

8.0 ± 1.7

2.8 ± 1.0

6.2 ± 1.6

0.6 ± 0.8

` → τhad

126 ± 6.6

1.7 ± 0.877 ± 17< 0.1

j → τhad

1 344 ± 15309 ± 3.3

1 277 ± 13

335 ± 3.4

tt̄ → `τhad

708 ± 14261 ± 8.5676 ± 14232 ± 8.0

Z → ττ

301 ± 29135 ± 22381 ± 34

138 ± 18

Total

2 487 ± 36

710 ± 24

2 417 ± 43

706 ± 20Signal9.3 ± 2.5

3.6 ± 1.0

3.8 ± 1.1

1.3 ± 0.4

Data

2286

709

2668

818

b-vetoDiboson338 ± 11113 ± 6.4

467 ± 12134 ± 6.4

` → τhad

5 612 ± 39

36 ± 2.99 292 ± 182

60 ± 16j → τhad

30 692 ± 70

9 669 ± 20

29 227 ± 70

8 365 ± 19tt̄ → `τhad

177 ± 6.9

60 ± 4.1

161 ± 6.4

61 ± 3.9

Z → ττ

22 725 ± 224

8 411 ± 136

32 061 ± 264

12 312 ± 162

Total

59 545 ± 239

18 290 ± 138

71 208 ± 328

20 932 ± 164

Signal18 ± 4.2

5.8 ± 1.4

8.0 ± 2.0

2.0 ± 0.5

Data

59729

17434

68182

20272

Table 6.4: Events yields for three signal regions with four decay channels. As a signal mA = 600 GeV andtan β = 15 is assumed.

91

160
140
120
100
80
60
100

+ Radiation+ Hard process+ Showering + UE

150 200- Radiation- Hard process- Showering + UE

300 400 500

mTtot [GeV](a) tt̄

700 900

Relative value [\%]

Relative value [\%]

6.7. Results

160
140
120
100
80
60
50

1p
+ eτhad1p- eτhad3p+ eτhad3p- eτhad1p+ µτhad1p- µτhad3p+ µτhad3p- µτhad60 70 80 90 100

mTtot [GeV]

150

200

(b) Z → τ τFigure 6.21: Systematic uncertainties for tt̄ process (a) with variation of radiation (red lines), hard process (blue line) and showering + underlying uncertainties as a function of final discriminant variable (mtot
T ).
From 500 GeV, it is not relevant to estimated them due to a lack of event statistics, so an extrapolation is
performed. And hard process uncertainty for Z → τ τ process (b) with + and - variation from comparison
between nominal and alternative simulated sample.

92

6.7. Results

high-ETmiss : `τhad

10√high-ETmiss : `τhad

Pre-FitData
0.6TeVs = 13 TeV, 28.0fb−1∗

Z/γ → τ τtt̄, tFake τ

102

Dibosons
stat ⊕ syst

10

104

Events / 1 GeVEvents / 1 GeV

3√Z/γ ∗ → τ τtt̄, tFake τ

102

Dibosons
stat ⊕ syst

10
1

10−2

10−2

1.2
1
0.8
30

1.2
1
0.8
25
1000

50

70

100

200

500

Obs/Bkg

10−1

Obs/Bkg

10−1

pT (`)[GeV]50(a) pT (τ` )Events / 1 GeV√

Data
0.6TeVs = 13 TeV, 28.0fb−1

Z/γ ∗ → τ τtt̄, tFake τ

Dibosons
stat ⊕ syst

10

102

√

10−1

10−2

10−2

1.2
1
0.8
10

1.2
1
0.8
100 120

250

400

1000

ETmiss [GeV]

Obs/Bkg

10−1

miss(c) ET

500

pT (τhad )[GeV]

Pre-FitData
0.6TeVZ/γ ∗ → τ τtt̄, tFake τ

Dibosons
stat ⊕ syst

10

1

100

200

s = 13 TeV, 28.0fb−1

1

20

100

high-ETmiss : `τhad

Pre-Fit10270(b) pT (τhad )high-ETmiss : `τhad

Events / 1 GeV

Data
0.6TeVs = 13 TeV, 28.0fb−1

103

1

Obs/Bkg

Pre-Fit

150

200

300

400

1000

mtot
T [GeV](d) mτ τ

miss
Figure 6.22: Distributions for several variables in the high-ET
category. In the bottom panels a ratio of dataand expected background model and the uncertainties correspond to the statistical uncertainties are shown.
The signal process is assumed mA = 600 GeV and tan β = 15 with the gluon-fusion and bottom-annihilation
production processes.

93

6.7. Results

Events / 1 GeV

10√Pre-FitData
0.6TeVs = 13 TeV, 28.0fb−1

Z/γ ∗ → τ τ
Fake ` → τ
tt̄, tFake τ

104
103

Dibosons
stat ⊕ syst

102
10b-tag : `τhad

Events / 1 GeV

b-tag : `τhad
5

105

103

Dibosons
stat ⊕ syst

102
10
1
−1

10

−2

10

10−2

1.2
1
0.8
30

1.2
1
0.8
25

50

70

100

200

500

Obs/Bkg

10

pT (`)[GeV]50(a) pT (τ` )Pre-FitData
0.6TeVs = 13 TeV, 28.0fb−1

Z/γ ∗ → τ τ
Fake ` → τ
tt̄, tFake τ

103
102

Dibosons
stat ⊕ syst

10

104

√

1.2
1
0.8
50 60

miss
(c) ET

Obs/Bkg

10−2

1.2
1
0.8
10

ETmiss [GeV]

Dibosons
stat ⊕ syst

10

10−2

80 100 120 150

Z/γ ∗ → τ τ
Fake ` → τ
tt̄, tFake τ

102

10−1

50 60

Pre-FitData
0.6TeV

10

10−1

40

500

pT (τhad )[GeV]s = 13 TeV, 28.0fb−1

1

30

200

3

1

20

100

b-tag : `τhad

Events / 1 GeVEvents / 1 GeV√70(b) pT (τhad )b-tag : `τhad

Obs/Bkg

Z/γ ∗ → τ τ
Fake ` → τ
tt̄, tFake τ

10

1

104

Data
0.6TeVs = 13 TeV, 28.0fb−1

4−1

Obs/Bkg√

Pre-Fit80 100120 150

200

300

400 500

1000

mtot
T [GeV](d) mτ τ

Figure 6.23: Distributions for several variables in the b-tag category. In the bottom panels a ratio of dataand expected background model and the uncertainties correspond to the statistical uncertainties are shown.
The signal process is assumed mA = 600 GeV and tan β = 15 with the gluon-fusion and bottom-annihilation
production processes.

94

6.7. Results

108
107

√

Pre-FitData
0.6TeVs = 13 TeV, 28.0fb−1

Z/γ ∗ → τ τ
Fake ` → τ
tt̄, tFake τ

106
105

Dibosons
stat ⊕ syst

4

10

3

10

b-veto : `τhad

Events / 1 GeVEvents / 1 GeV

b-veto : `τhad

8

10

107

103
10

10−1

10−2

10−2

1.2
1
0.8
30

1.2
1
0.8
25

500

Obs/Bkg1

10−1

Obs/Bkg

1

200

Dibosons
stat ⊕ syst

104

10

100

pT (`)[GeV]50(a) pT (τ` )Pre-FitData
0.6TeVs = 13 TeV, 28.0fb−1

Z/γ ∗ → τ τ
Fake ` → τ
tt̄, tFake τ

6

10

105
104

Dibosons
stat ⊕ syst

3

10

7

10

√

s = 13 TeV, 28.0fb−1

10−2

10−2

1.2
1
0.8
10

1.2
1
0.8
50 60

miss
(c) ET

Obs/Bkg

10−1

Obs/Bkg1

10−1

ETmiss [GeV]

Dibosons
stat ⊕ syst

103
10

80 100 120 150

Z/γ ∗ → τ τ
Fake ` → τ
tt̄, tFake τ

104

1

50 60

Pre-FitData
0.6TeV

10

10

40

500

pT (τhad )[GeV]

5

102

30

200

106

102

20

100

b-veto : `τhad

Events / 1 GeVEvents / 1 GeV

107

√

70

(b) pT (τhad )b-veto : `τhad

108

Z/γ ∗ → τ τ
Fake ` → τ
tt̄, tFake τ

105

102

70

Data
0.6TeVs = 13 TeV, 28.0fb−1

106

102

50

√

Pre-Fit80 100120 150

200

300

400 500

1000

mtot
T [GeV](d) mτ τ

Figure 6.24: Distributions for several variables in the b-veto category. In the bottom panels a ratio of dataand expected background model and the uncertainties correspond to the statistical uncertainties are shown.
The signal process is assumed mA = 600 GeV and tan β = 15 with the gluon-fusion and bottom-annihilation
production processes.

7 Statistical Analysis of the Searchfor H/A → τ`τhad Decays
The combined likelihood fit is described in this chapter. The general concept of the maximum
likelihood fit and likelihood function is introduced in Section 7.1. The likelihood function needs toreflect the various statistical and systematic uncertinties of the background and signal expectation.
The parameterization of the signal event rate and the compatibility of the data with the backgroundonly-hypothesis is quantified using a hypothesis test described in Section 7.3. The statistical result
and an interpretation of signal hypothesis is presented in Section 7.4

7.1

The Profile Likelihood Function

An extended maximum-likelihood fit to the observed data is used to estimate the parameters of the
combined signal and background model, including the signal strength parameter µ. The probabilitydensity-function (PDFs) of the background and signal model are denoted as fB (x; θ) and fS (x; θ)respectively. It is a function of an observable x and normalised to unity. A set of parameter θ,
nuisance parameters (NP), reflects PDFs. The NPs reflects several systematic uncertainties, but it
is not the primary goal of the analysis. The PDFs will consists of several contributions from various
physics processes as discussed above chapters. The probability to observed N events in data with the
expected number of signal and background events S and B can be written as"N#e−(µS+B) (µS + B)N Y µSfS (xe ; θ) + BfB (xe ; θ)P(x; µ, θ) =
.
(7.1)
N!
µS
+
B
e
The first term describes the Poisson probability to observed N events while expecting and the numberof signal plus background events of (µS + B). The second term describes the probability to observed
the N events at values xe of the observable x. When the data can be considered as a constantvalue, this probability is regarded as a function of only the parameters. The likelihood function isusually denoted as L(µ, θ|x). A maximum-likelihood fit is used to estimate the parameters. Thisis performed by maximising the likelihood function given the observed data. As it is shown several
analysis categories is used to enhance the analys sensitivity. This property can be incorporated bymultiplying the likelihood functions defined in each categories. Eq.( 7.1) is transformed as following
if the input data is binned distribution, as in this analysis performs :#"Y (µsi (θ) + bi (θ))ni−(µsi (θ )+bi (θ ))
0
e
,
(7.2)
P (ni ; µ, θ) = C
ni !
i

95

96

7.2. Treatment of Systematic Uncertainties

where ni denotes the number of data events in i-th bin, si (θ) and bi (θ) are the expected number ofsignal and background events in the bin and C is combinatorial constant which can be neglected in
the maximisation procedure as it is constant. The various bins in the combined likelihood function
may describes different categories, including those which consider the shape of an observable andother which just consider the event count.
To simplify the maximisation procedure, it is useful to consider to take logarithm of the likelihood
function, since the product then decouples into a sum. It is also considered as the negative logarithmof the likelihood function (NLL) instead. MINUIT [200] is to solve minimisation problems, which isvery common and fast. The estimators (µ̂, θ̂) or best-fit values are defined as values minimising the
NLL, it follows min(− ln L(µ, θ)) = − ln L(µ̂, θ̂). The variance of the estimators (µ̂, θ̂) is defined byconsidering the change in the “profile” of the likelihood function. The likelihood profile is definedˆby ∆(− ln L(θ0 , θ̂0 )). This equation describes the absolute change of the likelihood as a function of avariable θ0 , while the likelihood is minimised with respect to all other dependencies θ0 pointwise. Theˆ
notation of L(θ0 , θ̂0 ) refers to the conditional minimum of the likelihood with respect to θ0 and fixedparameter θ0 . So one NP is fixed at the profiling process and other NPs are profiled to minimise theNLL. A simple likelihood depending on only one parameter θ0 are described as :!
(θ0 − θˆ0 )L(θ0 ) = Lmax exp −
,
(7.3)
2σ 2
(θ0 − θˆ0 ),2σ 2∆NLL = ln Lmax + − ln L(θˆ0 + σ).

− ln L(θ0 ) = − ln Lmax +

(7.4)
(7.5)

This leads that the uncertainty of a parameter θ0 can be obtained from value which the NLL differ
by 1/2 from the its minimum. This procedure can be generalised for multidimensional likelihood
functions.

7.2

Treatment of Systematic Uncertainties

The systematic uncertinties are propagated into the analysis by taking same analysis after changing
the corresponding parameter of uncertinties by one standard deviation. To take into account such
effects, the systematic uncertinties is treated as additional measurements into the likelihood function.
The likelihood function is modified by terms, assuming a Gaussian form of Pi (θi ) = G(θi |0, 1) where
normalised sigma by its ±1σ deviation.
Y
Y
L(µ, θ) =P 0 (ni ; µ, θ) ×G (θj |0, 1) ,(7.6)
i∈binsj

To incorporate into the likelihood function, a smooth parameterization is considered. The ±1σ valuesof events yields corresponding systematic uncertainty is measured in this analysis. The systematic
uncertinties can have an impact on both the absolute normalisation and its differential distribution
so different interpolation procedures are necessary. The number of expected events can be written as
following:
np,c,i (θ) = ηp,c (θ) × σ p,c,i (θ) × νp,c,i ,(7.7)

where νp,c,i is the number of events of process p in channel c at i-th bin of parametric histogram,and η and σ denote acceptance and shape effects corresponding to nuisance parameters reflecting the7.2. Treatment of Systematic Uncertainties

97

systematic uncertainties. The negative number of event is considered by an interpolation of suchη and σ. A piecewise exponential and linear technique is used for acceptance and shape nuisanceparameter respectively. The η and σ can be written byX+−ηp,c (θ) = 1 +Iexp. (θj ; 1, ηp,c,j, ηp,c,j),(7.8)
j=syst0σp,c,i (θ) = σp,c,i

Y

+
−
0
Ilin. (θj ; σp,c,i, σp,c,i,j, ηp,c,i,j
),

(7.9)

j=systwhere, Ilin. and Iexp. describe a piecewise linear and exponential interpolation defined as following:(θ × (I + − I 0 ) for θ ≥ 0
0 + −Ilin. (θ; I , I , I ) =,(7.10)
θ × (I 0 − I − ) for θ ≤ 0((I + /I 0 )+θ for θ ≥ 0
Iexp. (θ; I 0 , I + , I − ) =.
(7.11)(I − /I 0 )−θ for θ ≤ 0
The piecewise exponential interpolation does not reach at η ≤ 0, this is the reason why an acceptance nuisance parameter is made up by this interpolation. While a shape nuisance parameter isconstructs by i-th bin of a histogram. The likelihood function is built using the HistFactory [201]and RooFit/RooStats [202, 203] software package within ROOT [204] framework. HistFactory constructs the likelihood function based on histograms of expected event yields for all background andsignal processes with all systematic uncertainties. An acceptance and shape Uncertainties is taken as
OverAllSys and HistoSys, and it can be separated with different systematic uncertainties, analysis
categories and physical processes.

7.2.1

Symmetrization and Smoothing

A smoothing procedure is exploited to flatten statistical fluctuations in the systematically varied histograms to avoid a statistical fluctuation. The smoothing algorithm denoted as 353QH algorithm [205]is based on a computation of subsequent medians of the bin contents1 To keep a track of an exact
identifier of events present in each individual bin, a fraction of a nominal to varied histogram issmoothed instead of varied histogram directly. It is often happened that an upward and downward
variation deviates from the nominal expectation in the same direction. Such case of one-sided systematic variation might lead multiple minima in the likelihood minimisation procedure and disturb
to find true minima. The most of such one-sided variations are caused by statistical fluctuation, toavoid this situation it is set to lower variation to nominal expectation.

7.2.2

Pruning and Systematic Uncertainties TypeA lot of systematic variation is introduced in the likelihood function, but there might be variations
which does not have any impact on the result. As the complexity of the likelihood function takes
longer processing time with the number of shape degrees of freedom, it is desirable to reduce their
number. For this purpose, a number of tests is applied to each systematic variation in order to reducethem. All tests are performed before the smoothing and symmetrization, and it is not done fortheoretical uncertinties. The test is denoted as “pruning” in the following. Figure 7.1 shows relative
differences on the expected significance as a function of a pruning threshold for shape (red) andoverall (blue) variations. The pruning criteria is described in following. Applying the Symmetrization1

It computes two medians which constructed by three bins and five bins around the bin and checks its difference.The
algorithm is implemented in the ROOT framework.

98

3.0 no pruning, with symm. and smooth.
uncertainties
2.5 original
ShapeSys pruning
2.0 OverAllSys pruning(shape=0.98)
1.5
1.0
0.5
0.0
0.5
1.0 0.90 0.92 0.94 0.96 0.98 1.00
pruning threshold

Figure 7.1: Relative difference in the expecteddiscovery significance at mA = 600 GeV masspoint. Points with red circle represent a pruning
criteria on shape variations, while blue triangles
show on overall variations. Solid line is uncertinties with symmetrization and smoothing, but notapplied pruning criteria. Broken line is uncertinties from original variations.

relative difference(%)

7.2. Treatment of Systematic Uncertainties

and smoothing procedure effectively increases the systematic uncertinties and lowers the significanceby about 0.9%. It is relevant to compare with this 0.9% for a shape and overall systematic pruning.
About the shape pruning, relative differences increase significantly, the pruning threshold of 0.98 is
obtained. While the overall pruning rapidly increases after threshold of 0.995, so that the pruningthreshold of 0.995 (0.5%) is obtained.
χ2 TestThe compatibility between the nominal and varied histograms is tested using following χ2 definition:
χ2u,d =

Xi∈bins2
tot i
tot N i(Nnomnom − Nu,d Nu,d )tot i
tot σ i22
(Nnomnom ) + (Nu,d σu,d )(7.12)

i,tot
i,tot
where Nnom
and Nu,drefer to the bin content and total of the nominal and up/down varied histogram,and σnom and σu,d is the statistical uncertainties of the bin content among nominal and varied
histogram. The p-values under a χ2 distribution with the degrees of freedom given by the number ofhistogram bins are obtained for up/down variation respectively and its minimum among up and down
variation: p = min{Pχ2 (χ2u ), Pχ2 (χ2d )}. If the p-values are greater than 0.98, then corresponding
variations are taken into account only an acceptance uncertainty (OverAllSys). Besides a shape ofvariation, its acceptance variation is tested by checking same χ2 but with only event yields. If it isgreater than 0.5%, then it is assigned as an acceptance variation. These two tests are independently
checked.

Kolmogorov-Smirov Test
The pruning using a “Kolmogorov-Smirov” test is considered as well as the χ2 based test describedabove. A normalisation is not considered, only a difference of shape is considered.
Maximum Deviation Test
If the maximum relative deviation of the varied histogram to the nominal histogram among all bins
is smaller than 0.5%, it is considered as only an acceptance uncertainty.

99

7.3. Hypothesis Testing

7.3

Hypothesis Testing

Definitions of several quantity are given based on Reference [206, 207]. The maximum likelihood (ML) estimates µ̂ and θ̂, the values of the parameters that maximise the likelihood function
L(µθ) and equivalently, minimise − ln L(µ, θ). The first to consider is the test statistic and the profile
likelihood ratio as given in following:
λ(µ) =ˆL (µ, θ̂(µ))
L (µ̂, θ̂),(7.13)

ˆ
where θ̂ is the conditional maximum likelihood estimate, which maximises the likelihood function
with fixed µ, it is often called “the profiled value of θ”. The profile likelihood ratio λ(µ) depends
on the parameter of interest µ, but not on the nuisance parameters θ which have been eliminatedvia “’profiling’. In any physical theory the rate of signal events would have non-negative values, thisleads a constraint of µ > 0. It is convenient to allow µ < 0 in minimisation step, so a trick is used to
avoid complication at the boundary of µ = 0 in Reference [206]. The profile likelihood ratio follows
this modification as :ˆˆ
 L (µ,θ (µ)) for µ̂ ≥ 0ˆL (µ̂,θ )λ̃(µ) =.
(7.14)ˆˆ L (µ,θˆ (µ)) for µ̂ < 0
L (0,θ (0))
This is not necessary if ensembles of pseudo-experiments are performed with “toy-Monte Carlo” techniques, But the toy-MC always takes extremely long computation time and power, so the asymptotic
formulas [206] is used for all calculation as described later section. For the test statistic of discoveryq̃0 is used to distinguish the background-only-hypothesis, i.e. µ = 0 from the alternative hypothesisµ > 0:(−2 ln λ̃(µ) for µ̂ > 0q̃0 =.
(7.15)
0for µ̂ ≤ 0
For the test statistic of limiting setting q̃µ is used to distinguish the signal produced at signal strengthµ from the alternative hypothesis of signal events product at less- or more signal strength µ0 ≤ µ:ˆL (µ, θ̂(µ))


−2 ln
for µ̂ ≤ 0


(
ˆ


θ̂(0))
L(0,−2 ln λ̃(µ) for µ̂ ≤ µ
ˆ
q̃µ =
=
(7.16)L (µ, θ̂(µ))

0for µ̂ > µ
−2 ln
for 0 ≤ µ̂ ≤ µL (µ̂, θ̂)0for µ̂ > µ
The test statistic t̃µ is used to similar definition as q̃µ but with µ0 6= µ of t̃µ = −2 ln λ̃ (µ).

7.3.1

The Test Statistic Distribution and p-values

The observed test statistic has a given value of q̃µobs and when the experiment repeat many times,
the test statistic would take on different values. Thus, the test statistic achieves a distribution and
it is denoted as f (q̃µ |µ, θ). The p-value for a given observation under a hypothesis (µ, θ) is the

100

7.3. Hypothesis Testing
probability defined as :Z ∞pµ,θ =obsq̃µf (q̃µ |µ, θ)dq̃µ .

(7.17)The important reason for using the test statistic on the profile likelihood ratio is the distribution of
the profile likelihood ratio is asymptotically independent of the values of the nuisance parameters.
Above definition of the p-value depends on the nuisance parameters, so the p-value are modified asfollowing :Z ∞ˆpµ,θ =f (q̃µ |µ, θ̂(µ, obs))dq̃µ .
(7.18)
obsq̃µThis is based on assumption on Wilk’s theorem and Hybrid Resampling method as discussed in
Reference [207, 208] (as also known in “profile construction”). To construct two-sided confidence
interval, the modified frequentest method called “CLS ” [209, 210] is introduced. A ratio of p-values,pµwhere pb is the p-value under the background-only-hypothesis.
p0µ is defined as p0µ = 1−pbpb = 1 −

Z ∞
obs
q̃µ

ˆ
f (q̃µ |0, θ̂(µ = 0, obs))dq̃µ .

(7.19)The upper-limit on µ CLS is obtained by solving for p0µ = 5% for 95% confidence-level, which isdenoted by µ95 Statistically, a discovery means that to reject the background-only hypothesis, this iscalculated by p0 as defined following:Z ∞ˆf (q̃0 |0, θ̂(µ = 0, obs))dq̃0 .
p0 =(7.20)
q̃0obsBased on the p0 the significance of the result can be written as Z = Φ−1 (1 − p0 ), where Φ−1 isthe inverse of the cumulative distribution for a Gaussian with unit parameters. Conventionally thestandard discovery significance is 5σ corresponding to p0 = 2.87 · 10−7 in the particle physics.
Other important quantities are introduced, the expected sensitivity for limits and discovery and its
uncertainty bands are calculated by similar way. The expected limit is the upper limit which would
expect to obtain if the background-only hypothesis is true. In order to find the expected limit andsignificance, a distribution of f (µup |µ = 0, θ) and f (p0 |µ = 1, θ) are necessary respectively. These
distributions depend on the nuisance parameters which are unknown without measuring observed
data. So that the nuisance parameters need is profiled based on observed data, this leads that twoˆˆ
distributions are re-written as f (µup |0, θ̂(µ = 0, obs)) and f (p0 |1, θ̂(µ = 1, obs)) respectively. Using
above definition, ±1, 2σ bands around the median upper limit is defined as following :Z µ±1,2ˆf (µup |0, θ̂(µ = 0, obs))dµup = Φ−1 (±1, 2),(7.21)
0where µ±1,2 present µ̂ ± 1∆µ, 2∆µ.

7.3.2

Asymptotic Formulas and Asimov Data

Integration of the test statistic is performed using the asymptotic formulas introduced on Reference [206] instead of performing the toy-MC. As a result of Wald’s theorem [211], the test statistic is

101

7.3. Hypothesis Testing
approximated as :−2 ln λ(µ) =√(µ − µ̂)2
+
O(1/
N ),
σ2

(7.22)

where N represents the data sample size. Here, µ̂ follows a Gaussian distribution with a standard
deviation σ and mean µ0 . If V denotes the covariance matrix of the estimation for all the parameter
including the parameter of interests µ, the standard deviation σ of µ̂ is obtained by Vij = cov[θ̂i ], θ̂jand take θ0 = µ, σ 2 = V00 . In the limit of large data sample, the bias term of the maximum likelihood
estimators can be neglected, so the inverse of the covariance matrix is written as :
 2 
∂ L
−1
Vij = −E,
(7.23)∂θi ∂θjwhere the expectation value assumes a signal strength parameter µ0 . The asymptotic formulae needs
this σ, for this purpose the “Asimov” dataset is constructed by sum of the number of expected events.
By using the Asimov dataset, a mean value of µ0 gives µ̂ = µ0 and the test statistic is approximatedas:−2 ln λA (µ) ≈(µ − µ0 )2µ − µ0
,
with
σ
=
√
σ2
qµ,A

(7.24)

where the test statistic under the Asimov dataset satisfies qµ,A = λA (µ). For the hypothesis assuming√µ, it becomes µ0 = 0, a mean value is obtained as σ ∼ µ/ qµ,A .
By using the asymptotic formulae the probability density function f (q̃0 |µ0 ) is approximated by 0 



µ
1 1
1
1 √
µ0
0
f (q̃0 |µ ) = 1 − Φδ(q0 ) + √ √ exp −q0 −,(7.25)
σ2 2π q0
2
σ
 q 
1
1
1 1
0
f (q̃0 |0) = δ(q0 ) + √ √ exp −(7.26)
22 2π q02
where the PDF consists of a mixture of a delta function at zero and a χ2 distribution for one degreeof freedom which has a weight of 1/2. The corresponding cumulative distribution is obtained as :


µ0
√
0
,
(7.27)F (q̃0 |µ ) = Φ
q0 −σ√F (q̃0 |0) = Φ ( q0 ) .
(7.28)As a result of this approach, the p-value of the null hypothesis µ = 0 and the significance is
p0 = 1 − F (q0 |0)
−1

Z=Φ

√
(1 − p0 ) = q0 .

(7.29)(7.30)For the f (q̃µ |µ) as well, same approximation can be applied and one obtains pµ = 1 − F (q̃µ |µ). The
upper limit on µ at confidence level 1 − α is found as µup = µ̂ + σΦ−1 (1 − α) by solving pµ = α.
where this should be solved numerically. The expected limit and its bands is calculated by the CLS
method. It needs distributions of q̃µ at the hypothesis at µ and µ = 0, The p-value is found as :p0µ =√1 − Φ( qµ )√ ,√Φ( qµ,A − qµ )(7.31)

102

7.4. Statistical Results and Interpretation
So the median and expected bands become :µup+n = σ(Φ−1 (1 − αΦ(n)) + n),with σ = √

µ
,
qµ,A

(7.32)

where n represents values at nσ. Usually it takes α = 0.05 ( 95% confidence level), µ can be taken in
the calculation of σ. For the case of the median limit, i.e. n = 0, is written as:


1
med
−1
1− α .
µup = σΦ(7.33)
2

7.4

Statistical Results and Interpretation

Exclusion at the 95% confidence level are obtained with the frequentest method described in Section 7.3. Results assuming background-only hypothesis are shown in Section 7.4.1. Model independent results are given in Section 7.4.2. Results based on the hMSSM benchmark scenario are given in
Section 7.4.3. A validation of the likelihood fit is described in Appendix G.

7.4.1

Results on Null Hypothesis

Firstly results assuming the null hypothesis is obtained by the combined likelihood fit with µ = 0.
The events yields and the mτ τ distributions are shown in Table 7.1 and Figure 7.2 after the fit(“postfit”). As shown in table and figures, the background expectation agrees well with observed data
within the uncertinties. Other important variable with the post-fit are shown in Appendix H.

Process

b-tag

miss
high-ETb-veto

eτhad

µτhad

eτhad

µτhad

eτhad

µτhad

Diboson

9.7 ± 2.2

6.1 ± 1.9453 ± 41605 ± 57

6.6 ± 1.1

45 ± 7` → τhad

135 ± 2983 ± 18

2 709 ± 600

9 034 ± 850

< 0.1

< 0.1

tt̄, single-t

859 ± 100

1 223 ± 480

209 ± 30

227 ± 3253 ± 11354 ± 58

Z → ττ

333 ± 65610 ± 115

31 702 ± 6 207

38 767 ± 6 256

44 ± 12286 ± 53

j → τhad

1 634 ± 221

1 575 ± 161

42 144 ± 2 705

39 742 ± 2 420

158 ± 15

1 149 ± 107

Total

2 970 ± 257

3 497 ± 548

77 216 ± 6 807

88 375 ± 7 033

262 ± 23

1 834 ± 140

data

2 986

3 486

77 16288 454250

1 834

Table 7.1: Events yields after the µ = 0 fit. The uncertinties on the total background yields reflect the fullstatistical and systematic uncertainty, while the uncertinties on the individual background components reflect
the statistical uncertainty only.

7.4.2

Result on Model Independent Cross Section

The search are interpreted in the more generic case of a single scalar boson φ that is produced ineither the gluon-fusion or the bottom-annihilation production mode. A model independent results
considering only single signal production process is important . The combined likelihood fit is performed and its results based on only the bottom-annihilation and gluon-fusion signal hypothesis areshown in Figure 7.3 (a) and (b) as a function of signal mass mA respectively. The expected sensitivity

103

7.4. Statistical Results and Interpretation

102√

b-tag : `τhad

Post-Fit

Events / 1 GeVEvents / 1 GeV

high-ETmiss : `τhad

Datas = 13 TeV, 28.0fb−1

Z/γ ∗ → τ τtt̄, tFake τ

Dibosons
stat ⊕ syst
Pre-Fit

10

4

10

√

Post-Fit

Datas = 13 TeV, 28.0fb−1

Z/γ ∗ → τ τ
Fake ` → τ
tt̄, tFake τ

103

Dibosons
stat ⊕ syst
Pre-Fit

102
10

1
1

10−1

10−1

1.2
1
0.8
100 120

1.2
1
0.8
50 60

150

200

300

400

1000

Obs/Bkg

10−2

Obs/Bkg

10−2

80 100120 150

miss(a) high-ET

Events / 1 GeV

10

300

400 500

1000

mtot
T [GeV](b) b-tagb-veto : `τhad

7

200

mtot
T [GeV]√

Post-Fit

Datas = 13 TeV, 28.0fb−1

Z/γ ∗ → τ τ
Fake ` → τ
tt̄, tFake τ

106
105

Dibosons
stat ⊕ syst
Pre-Fit

104
3

10

102
10
1

10−1

Obs/Bkg

10−2
1.2
1
0.8
50 60

80 100120 150

200

300

400 500

1000

mtot
T [GeV](c) b-vetoFigure 7.2: Post-fit mτ τ distributions for three signal regions assuming µ = 0 hypothesis. In the ratio plots,
gray filled regions represent the full statistical systematic uncertainty, the red lines show the total expectedbackground before the combined likelihood fit (so-called, “pre-fit”).

for each analysis category is shown in Figure 7.3 (c) and (d). An important comparison between thisanalysis and past strategy is shown. The pas strategy consists of only events fired the single-leptonmiss , but with b-tag or b-veto event categorisation. The
trigger and it is inclusive in terms of the ET
gluon-fusion production limit improves about 25% of its sensitivity at mA = 1 TeVby including themiss category While the bottom-annihilation production limit improves about 50% at m =high-ETA
1 TeV. Figure 7.4 shows the observed local p-value with the gluon-fusion and bottom-annihilation
production hypothesis.
miss signal region significantly contributes in both
In addition to this improvement, the high-ET
production processes. This is important feature in terms of analysis robustness for “other” processes,
like a non-Higgs resonance signal. Besides one-dimensional limits, the fit on the gluon-fusion andbottom-annihilation process corss section times the branching ratios of H/A → τ τ is obtained using
two-dimensional fit. Figure 7.5 shows the bset fit point on the cross-section times the branching
fraction plane of the gluon-fusion and bottom-annihilation production process with several mass

104

10

13 TeV, 28.0 fb 1

Observed
Expected

95 % C.L. limits±1±2

gluon-fusion

ATLAS, 13.3fb⇥ BR(H/A ! ⌧ ⌧ )[pb]⇥ BR(H/A ! ⌧ ⌧ )[pb]7.4. Statistical Results and Interpretation

10

1

1

10 2

10 2
600

800

1000

1200

200

mA [ GeV]

10

combinationhigh ETmissb-tag
b-vetolepton trigger only

95 % C.L. limits
gluon-fusion

1

10

10−2

10−2
600

800

(c) gluon-fusion

ATLAS, 13.3fb 1

600

800

1000

1200

mA [ GeV]

1000

1200

mA [ GeV]

13 TeV, 28.0 fb−1
95 % C.L. limits

combinationhigh ETmissb-tag
b-vetolepton trigger only

1

10−1

400

400

bottom-annihilation.

10−1

200

±1
±2

(b) bottom-annihilation

σ × BR(H/A → τ τ )[pb]

σ × BR(H/A → τ τ )[pb](a) gluon-fusion
13 TeV, 28.0 fb−1

95 % C.L. limits

1

10 1

400

Observed
Expectedbottom-annihilation.

10 1

200

13 TeV, 28.0 fb 1

200

400

600

800

1000

1200

mA [ GeV](d) bottom-annihilation

Figure 7.3: Expected (dashed line) and observed (solid line), 95% confidence level limits on the cross-sectionfor Higgs boson production in gluon-fusion (a) and bottom-annihilation (b) times the branching ratio into apair of τ leptons, along with ±1σ (green) and ±2σ (yellow) uncertainty bands for the expected limit in uppercolumn. The region filled with blue represents the exclusion limit of search for heavy Higgs boson decaying intoτ leptons with 13.3 fb−1 (from Reference [212]) In bottom column, expected limit for the combination (solid
missblack line), high-ET(red broken line), b-tag (blue broken line), b,-veto (green broken line) and the leptontrigger-only results (orange broken line) are shown. limits on the cross section for Higgs boson production ingluon-fusion (a) and bottom-annihilation (b) times the branching ratio into a pair of τ leptons.

hypotheses. Each plots has the best fit point and 68(95)% confidence interval contours. The limits
represents the best sensitivity up until now with corresponding decay mode search.

105

local p-value

local p-value

7.4. Statistical Results and Interpretation

13 TeV, 28.0 fb−1
95 % C.L. limits

1

Observed

gluon-fusion

13 TeV, 28.0 fb−1

1

95 % C.L. limits

Observedbottom-annihilation.

1σ
−1

1σ
−1

10

10

2σ
10−2200

400

600

800

1000

1200

mA [ GeV](a) gluon-fusion

2σ10−2200

400

600

800

1000

1200

mA [ GeV](b) bottom-annihilation

Figure 7.4: Observed local p-value with hypotheses of the gluon-fusion (a) and bottom-annihilation (b)production process.

7.4.3

Result on Benchmark Scenario

The limits on the parameter space of the MSSM is obtained by using the hMSSM benchmark
scenario. For given mA and various tan β hypotheses the excluded signal strength µ95% is calculated.
Figure 7.6 shows the exclusion limit for the hMSSM scenario in the (mA , tan β) parameter space.
The value of tan β excluded at the 95% confidence level is obtained by interpolating between thevalues of mA . The limits represents the best sensitivity up until now with corresponding decay mode
search.

7.4.4

Disscusion of Obtained Results

In collision data 165616 events are observed in the b-veto event category, where 165000±460 (stat.)±
9800 (syst.) background events are expected. For the b-tag event category 6472 events are observed,
misswhile for background process 6700 ± 64 (stat.) ± 610 (syst.) events are expected. In the high-ET
category 2084 events are observed, where 2095 ± 30 (stat.) ± 140 (syst.) background events are
expected. The distribution of the di-τ mass of three categories exhibit no significant excess of data
events compared with the background expectation.
Several interpretations are shown in this section using above results. There is approximately 2σmiss category excess,excess in the gluon-fusion only hypothesis. The excess comes from the high-ET
especially last three bins in Figure 7.2 (a). These three bins surplus looks consistent with signal shape,
but such excess does not appear in the b-tag and b-veto categories. The Z → τ τ background process
dominates in such region, if Z → τ τ has a mis-modelling on its shape, it follows this excess. The
reason why the Z → τ τ has a shape mis-modelling would be expected from the TES mis-modelling.
The TES is currently estimated by the simulated samples, because the integrated luminosity of data
is not enough to precisely measure the TES. The in-situ TES measurement is also important in termsof reducing its uncertainty, because the TES is the highest ranked systematic uncertainty in terms ofan impact on the likelihood fit. The largest source of the TES systematic uncertainty is the signlepartile-responce, it is a responce of a charged pion energy scale. This uncertainty is estimated by
Run1 data and asigned with two times higer safe factor, so that it will be approximately half size of

106

1.2

0.4

Best fit

0.4

68%C.L.

13 TeV, 28.0 fb−1
mA = 350GeV

0.35

95%C.L.

Best fit

95%C.L.

0.2
0

0.3

0.6

0.9

1.2

0.15

0.1

0.1

0.05

0.05

0

1.5

σ(ggF) × BR(H/A → τ τ )[pb](a) mA = 200 GeV

0

0.08

0.16

0.24

0.32

(b) mA = 350 GeV

0.16

Best fit

13 TeV, 28.0 fb−1
mA = 600GeV

0.18

68%C.L.

0.16

95%C.L.

0.14

Best fit

68%C.L.

0.16

95%C.L.

0.06

0.06

0.04

0.04

0.04

0.02

0.02

0.02

0

0

0.08

0.12

0.16

0.2

σ(ggF) × BR(H/A → τ τ )[pb]0(d) mA = 500 GeV

0.04

0.08

0.12

0.16

13 TeV, 28.0 fb−1
mA = 1000GeV

0.09

68%C.L.

0.08

0.07

Best fit

68%C.L.

0.08

95%C.L.

0.03

0.03

0.02

0.02

0.02

0.01

0.01

0.01

0

0

0.04

0.06

0.08

0.1

(g) mA = 0.8 TeVBest fit

68%C.L.
95%C.L.

0.04

0.03

σ(ggF) × BR(H/A → τ τ )[pb]

0.2

0.05

0.04

0.02

0.16

0.06

0.05

0.04

0.12

0.07

0.06

0.05

0.08

σ(ggF) × BR(H/A → τ τ )[pb]

13 TeV, 28.0 fb−1
mA = 1200GeV

0.09

0.07

0.06

0.04

(f ) mA = 0.7 TeV
σ(bbA) × BR(H/A → τ τ )pb

Best fit

95%C.L.

00

0.1

σ(bbA) × BR(H/A → τ τ )pb

σ(bbA) × BR(H/A → τ τ )pb

0.08

0

0.2

σ(ggF) × BR(H/A → τ τ )[pb]

0.1

13 TeV, 28.0 fb−1
mA = 800GeV

68%C.L.
95%C.L.

(e) mA = 0.6 TeV

0.1

0.09

Best fit

0.08

0.06

0.04

0.4

0.1

0.08

0

0.32

0.12

0.1

0.08

0.24

0.14

0.12

0.1

0.16

σ(ggF) × BR(H/A → τ τ )[pb]

13 TeV, 28.0 fb−1
mA = 700GeV

0.18

0.14

0.12

0.08

0.2

σ(bbA) × BR(H/A → τ τ )pb

13 TeV, 28.0 fb−1
mA = 500GeV0(c) mA = 400 GeV

0.2

σ(bbA) × BR(H/A → τ τ )pb

0.2

0.18

0

0.4

σ(ggF) × BR(H/A → τ τ )[pb]σ(bbA) × BR(H/A → τ τ )pb

095%C.L.

0.2

0.15

0.4

68%C.L.

0.25

0.2

0.6

Best fit

0.3

0.25

0.8

13 TeV, 28.0 fb−1
mA = 400GeV

0.35

68%C.L.

0.3

1

σ(bbA) × BR(H/A → τ τ )pb

13 TeV, 28.0 fb−1
mA = 200GeV

1.4

σ(bbA) × BR(H/A → τ τ )pb

σ(bbA) × BR(H/A → τ τ )pb

7.4. Statistical Results and Interpretation

0

0.02

0.04

0.06

0.08

0.1

σ(ggF) × BR(H/A → τ τ )[pb](h) mA = 1 TeV

0

0

0.02

0.04

0.06

0.08

0.1

σ(ggF) × BR(H/A → τ τ )[pb](i) mA = 1.2 TeVFigure 7.5: Observed limit on the gluon-fusion production and bottom-annihilation production processes ineach mA hypotheses. The 68% (95%) confidence level contour is presented as solid (broken) line in each plot.
A red star shows the best fit value on the two dimensional plane.

current uncertainty if more data is available to estimate by the tag-&-probe method.

107

7.4. Statistical Results and Interpretationtan

95 % C.L. limits

60

±1
±2

hMSSM scenario

ATLAS, 13.3fb

tan

Observed
Expected

13 TeV, 28.0 fb 1

1

60

boson couplings (Obs.)

95 % C.L. limits±1±2

hMSSM scenario

ATLAS, 13.3fb 1

20

40

10
7
5
4
3

30
20

Run1, SM Higgs
boson couplings (Obs.)

2

10
1
200

Observed
Expected

4030Run1, SM Higgs

50

13 TeV, 28.0 fb 1

400

600

800

(a) linear scale

1000

1200

mA [ GeV]

1
200

300

400 500

700

900

1200

mA [ GeV](b) log scale

Figure 7.6: Expected (dashed line) and observed (solid line), 95% confidence level limits on the cross sectionfor Higgs boson production in gluon-fusion (a) and bottom-annihilation (b) times the branching ratio into apair of τ leptons, along with ±1σ (green) and ±2σ (yellow) uncertainty bands for the expected limit. The
region filled with blue represents the exclusion limit of search for heavy Higgs boson decaying into τ leptons
with 13.3 fb−1 (from Reference [212]). The region filled with green shows the indirect exclusion limit using the
SM Higgs boson coupling measurements of the ATLAS Run1 results.

8 Conclusions√
The LHC proton-proton collisions leads the high-energy frontier at a center-of-mass energy s =13 TeV. A new boson was found by ATLAS [31] and CMS [32] collaboration in July 2012. The measurements of the cross-section for the different production processes and the spin are consistent with
the Standard Model Higgs boson hypothesis. It is still possible that the observed boson stems froman extended Higgs sector, such as the two-Higgs-doublets of the Minimal Supersymmetric Standard
Model (MSSM). The MSSM leads to five physical Higgs bosons, the electrically neutral Higgs bosonh, A and H and the electrically charged Higgs bosons H ± .
A search for the neutral heavy Higgs boson H and A in the decay channel with a electron ormuon and hadronically decaying τ lepton is documented in this thesis. The search exploits eventswith a large missing transverse energy produced from an imbalance decay of a pair of τ leptons.
An enhancement of down-type fermions is important property of the two-Higgs-doublets model toenhance analysis sensitivity. The hMSSM scenario is considered as a benchmark model of the MSSM
Higgs boson mechanism. The hMSSM scenario considers the new boson with mh = 125 GeV as
the neutral Higgs boson h. Invariant mass of remaining two neutral Higgs boson H and A are
degenerated at the pseudoscalar Higgs boson mass mA due to the decoupling limit. Two production
mechanisms are considered as the signal process in the MSSM Higgs sector. The bottom-annihilation
process produces at least one b-quark and their cross-section is enhanced from the down-type fermionsenhancement in higher-tan β parameter space. The gluon-fusion process produces only the Higgs
bosons at leading order of strong coupling constant and their corss-section dominates in lower-tan β√parameter space. The search is based on proton-proton collisions at a center-of-mass energy s =13 TeV. The collisions have been recorded with the ATLAS detector at the LHC in 2015 and 2016
correspond to the integrated luminosity of 3.2 fb−1 and 24.8 fb−1 respectively.
Three analysis categories are defined to distinguish signals and backgrounds expected from theStandard Model particle productions. A region with large missing transverse energy is developed
miss category). Events with the large missing
and optimised in this analysis for the first time (high-ETtransverse energy are collected by triggers based on a signature of the missing transverse energy.
While events with the small missing transverse energy are collected by trigger based on electron ormuon and events are categorised by requiring at least one identified b-jet for the b-tag signal region
and for no b-jet for the b-veto signal region. The heavy Higgs boson cannot be highly boosted anda topology where two decay products kinetically lie back-to-back is selected. In order to suppress
background processes, event selection criteria based on final states particle topology are performed
to three analysis categories.
A variety of background processes contributes to the selected final state. Besides events with true τ leptons, events with mis-identified hadronic-τ objects is an important source of background. The misidentified hadronic-τ background consists of several physics processes. It is divided two components
with the QCD multijets and the W +jets/tt̄ processes. It is necessary to model both components
and a dedicated method to estimate the mis-identified hadronic-τ background is established. The

108

109
QCD multijets component is estimated by the data-driven technique as well and its estimates arepropagated in the combined mis-identified background estimation. Z → τ τ background is irreducible,
because it has exactly same final states as signals. The simulated event samples are used and it isvalidated in the dedicated control regions. tt̄ → `τhad process is an important background in theb-tagged signal topology. It is modelled by simulated event samples and it is cross-checked together
with the mis-identified hadronic-τ background. A smaller contribution to the background events is
expected from the diboson and Z+jets production process and it is estimated by the simulated event
samples.
The statistical interpretation of the search based on two classes of signal hypotheses and moremodel-independent case of a single scalar boson produced in eigher the gluon-fusion or bottomannihilation process is presented. Based on the reconstructed invariant mass distributions, 95%
confidence level exclusion limits are derived with the frequentest CLS procedure using the profile
likelihood ratio as a test statistic. In the single production hypothesis of the gluon-fusion the exclusion limit is 0.043 pb at mA = 1 TeV. The exclusion limit is 0.029 pb at mA = 1 TeV in thebottom-annihilation only hypothesis. A two dimensional likelihood scan of the cross-section times
the branching fraction for the gluon-fusion and bottom-annihilation process is provided. The best fit
point of mA = 1 TeV hypothesis is (0.02, < 0.001) for the gluon-fusion and bottom-annihilation, it
is still consistent to null hypothesis within ±1σ uncertainty. The exclusion limit is given in mA andtan β parameter space assuming the hMSSM scenario. tan β > 36.8 are excluded at mA = 1 TeV,
while the expected exclusion is tan β > 34.1.
The search presented in this thesis is published together with the other decay channel. Recently
the new result by the CMS [213] with all decay channels including eµ final state is published with
13.3 fb−1 . The sensitivity of eµ decay channel shows non-negligible contribution at extremely highmass hypotheses in the CMS result. This channel would help improving the search sensitivity as wellas in the feature result of the ATLAS. It might be useful to split a large missing transverse energy
event category into two categories correspondingly the number of b-tagged jets when more dataset isrecorded. The dataset incoming next two years and recorded in 2016 helps getting further sensitivity
and understanding important systematic uncertainties.
After the discovery of a boson with a mass near 125 GeV, the search for the MSSM Higgs bosons
provides important insight into whether the discovered boson can be a Higgs boson that is describedby the two-Higgs-double model also the MSSM. Even though a large region of the parameter spaceof the hMSSM scenario is excluded and no obvious excess of data is observed, a significant part ofthe parameter space is still compatible with the results of the performed searches for Higgs bosons
from extended Higgs sectors. Additional information could be obtained from the two-Higgs-doublet
benchmark models like a parameterization mixing angle of the h and H bosons, α. Such information
will provide the possibility to determine the nature of the electroweak symmetry breaking.

Appendix

110

111

Auxiliary Material
ETmiss Trigger Efficiencye⌧had channel

1
0.8

1.2

p

tau-id : ⌧

1
0.8

0.6

(`, ⌧ ) > 2.4

0.2

150

200

(`, ⌧ ) > 2.4

0.2

250

0

300

100

150

200

p

tau-id : ⌧(`, ⌧ ) > 2.4

1

0

100

150

200

150

200

1.2

p

(`, ⌧ ) > 2.4

0

100

150

(`, ⌧ ) > 2.4

ptau-id : ⌧s = 13 TeV, 6.5fb 1

1
0.8

1

data

pT (`) > 30 GeV(`, ⌧ ) > 2.4

100

150

200

mT (`, ETmiss ) < 40 GeV

250

300

µ⌧had channel

1.2

p

0

100

150

200

250

(h) µτhad , 2016,D1-D3
tau-id : ⌧s = 13 TeV, 12.1fb 1

1

0.6
data

0.4

(`, ⌧ ) > 2.4

0.2

data

0.4

pT (`) > 30 GeV

pT (`) > 30 GeV(`, ⌧ ) > 2.4

0.2mT (`, ETmiss ) < 40 GeV
100

150

200

250

mT (`, ETmiss ) < 40 GeV
300~ miss |[ GeV ]|~pT (⌧` ) + E
T(i) µτhad , 2016,D4-F1

0

100

150

200

250

300

~ miss |[ GeV ]|~pT (⌧` ) + E
T

0.8

0.6

0

tau-id : ⌧s = 13 TeV, 736.3pb 10.2(g) µτhad , 2016,A-C
Efficiency

Efficiencyµ⌧had channel

1.2

p

0.4

pT (`) > 30 GeV~ miss |[ GeV ]|~pT (⌧` ) + E
T(f ) µτhad , 2015

300

0.6
data

0

300

250

µ⌧had channel

1.2

mT (`, ETmiss ) < 40 GeV

250

200

0.8

~ miss |[ GeV ]|~pT (⌧` ) + ET(e) eτhad , 2016,F2-

150(d) eτhad , 2016,D4-F1

1

0.2

200

100

ETmiss TST[ GeV ]tau-id : ⌧mT (`, ETmiss ) < 40 GeV
300

0

300

s = 13 TeV, 5.4fb 1

0.4

pT (`) > 30 GeV

ETmiss TST[ GeV ](`, ⌧ ) > 2.4
mT (`, ETmiss ) < 40 GeV

250

0.6
data

0.2

250

100

0.8

mT (`, ETmiss ) < 40 GeV

pT (`) > 30 GeV

0.2µ⌧had channels = 13 TeV, 3.2fb 1

0.4

pT (`) > 30 GeV

0.2(`, ⌧ ) > 2.4(c) eτhad , 2016,D1-D3

0.6
data

0.4

data

ETmiss TST[ GeV ]

0.8

0.6

1

0.4

pT (`) > 30 GeV

0300

Efficiency

1
0.8

1.2

tau-id : ⌧s = 13 TeV, 6.5fb 1

mT (`, ETmiss ) < 40 GeV

250µ⌧had channel

Efficiency

Efficiency

tau-id : ⌧s = 13 TeV, 12.1fb 1

p

0.6
data

0.2

(b) eτhad , 2016,A-C

e⌧had channele⌧had channel

1.2

0.8

ETmiss TST[ GeV ](a) eτhad , 2015p

1

mT (`, ETmiss ) < 40 GeV

ETmiss TST[ GeV ]1.2

tau-id : ⌧s = 13 TeV, 736.3pb 1

0.4

pT (`) > 30 GeV

mT (`, ETmiss ) < 40 GeV
100

p

0.6
data

0.4

pT (`) > 30 GeV

1.2

0.8

0.6
data

0.4

0

e⌧had channels = 13 TeV, 5.4fb 1

Efficiency

tau-id : ⌧s = 13 TeV, 3.2fb 1

Efficiencyp

Efficiency

Efficiencye⌧had channel

1.2

EfficiencyA300~ miss |[ GeV ]|~pT (⌧` ) + E
T(j) µτhad , 2016,F2-

misstrigger of eτhad (a-e) and µτhad (f-j) channel with dedicated dataFigure A.1: Efficiency for the ETmiss~ miss + p~T (µ)| . Each plots have three different curves, after thetaking periods as a function ET
and |ET
misspreselection (pT (`) > 30 GeV), ∆φ(`, τvis ) > 2.4 and mT (`, ET) < 40 GeV.

112

B

Validation of Event Selection Variables

Figure B.2 shows the angle difference between lepton and hadronic-τ in the transverse plane forthree signal regions.
Cut : pT (`) > 30 GeV

Data
0.4TeV25000

p

Z/ ⇤ ! ⌧ ⌧Fake ` ! ⌧Fake ⌧tt̄, t20000

s = 13 TeV, 28.0fb 1

35000

Cut : pT (`) > 30 GeV

Data
0.4TeVZ/ ⇤ ! ⌧ ⌧Fake ` ! ⌧Fake ⌧tt̄, t

30000
25000

Dibosons
Model Uncert.

15000µ⌧had channel

Events/0.05[unit]

Events/0.05[unit]e⌧had channelps = 13 TeV, 28.0fb 1

2

2.5

Dibosons
Model Uncert.

20000
15000

10000

10000

1.5
1
0.5

5000

0

0.5

1

1.5

2

2.5

3

Obs/Exp

Obs/Exp

5000

1.5
1
0.5

0

0.5

1

1.5

(⌧` , ⌧had )(a) b-veto, eτhad(b) b-tagµτhad

Events/0.1[unit]

Cut : pT (`) > 30 GeV

Data
0.4TeVp

Z/ ⇤ ! ⌧ ⌧Fake ` ! ⌧Fake ⌧tt̄, t2000

s = 13 TeV, 28.0fb 1

Cut : pT (`) > 30 GeV

Data
0.4TeV3000

Z/ ⇤ ! ⌧ ⌧Fake ` ! ⌧Fake ⌧tt̄, t2500

Dibosons
Model Uncert.

1500µ⌧had channel

Events/0.1[unit]e⌧had channel

2500

3

(⌧` , ⌧had )ps = 13 TeV, 28.0fb 1

2

2.5

Dibosons
Model Uncert.

2000
1500

1000
1000

1.5
1
0.5

500

0

0.5

1

1.5

2

2.5

3

Obs/Exp

Obs/Exp

500

1.5
1
0.5

0

0.5

1

1.5

(⌧` , ⌧had )(c) b-tageτhad(d) b-tagµτhadpZ/ ⇤ ! ⌧ ⌧Fake ⌧tt̄, t300
250

s = 13 TeV, 28.0fb 1

Cut : pT (⌧ ) > 25 GeV

Data
0.4TeV1200

Z/ ⇤ ! ⌧ ⌧Fake ⌧tt̄, t1000

Dibosons
Model Uncert.

200ps = 13 TeV, 28.0fb 1

2

2.5

Dibosons
Model Uncert.

800
600

150

400

100

Obs/Expµ⌧had channel

Events/0.1[unit]

Cut : pT (⌧ ) > 25 GeV

Data
0.4TeV

50

200

1.5
1
0.5

1.5
1
0.5

0

0.5

1

1.5

2

2.5

3

Obs/Exp

Events/0.1[unit]e⌧had channel

350

3(⌧` , ⌧had )

0

0.5

1

1.5

(⌧` , ⌧had )miss(e) high-ET, eτhad3(⌧` , ⌧had )miss(f ) high-ET, µτhadFigure B.2: ∆φ(`, τhad ) distributions for all signal regions and channels.

113
Figure B.3 shows the transverse mass between lepton and the missing transverse energy for threesignal regions.

Events/4.0[ GeV]

p

14000

Cut : pT (`) > 30 GeV

Data
0.4TeVs = 13 TeV, 28.0fb 1

Z/ ⇤ ! ⌧ ⌧Fake ` ! ⌧Fake ⌧tt̄, t16000

Dibosons
Model Uncert.

14000
12000
10000

6000

8000

4000

6000
4000

2000

2000

0

20

40

60

80

100

120

140

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Obs/Exp

Obs/Exps = 13 TeV, 28.0fb 1

18000

8000

1.5
1
0.5

Cut : pT (`) > 30 GeV

Data
0.4TeV

20000

Dibosons
Model Uncert.

10000

p

22000

Z/ ⇤ ! ⌧ ⌧Fake ` ! ⌧Fake ⌧tt̄, t12000µ⌧had channel

24000

Events/4.0[ GeV]e⌧had channel

16000

1.5
1
0.5

0

20

40

60

80

100

mT (⌧` , ETmiss )[ GeV ](a) b-veto, eτhad

1800

Cut : pT (`) > 30 GeV

2500

Data
0.4TeVs = 13 TeV, 28.0fb 1

Z/ ⇤ ! ⌧ ⌧Fake ` ! ⌧Fake ⌧tt̄, t

1600
1400

p

160

180

200

Cut : pT (`) > 30 GeV

Data
0.4TeVs = 13 TeV, 28.0fb 1

Z/ ⇤ ! ⌧ ⌧Fake ` ! ⌧Fake ⌧tt̄, t2000

Dibosons
Model Uncert.

1200µ⌧had channel

Events/5.0[ GeV]

Events/5.0[ GeV]p140(b) b-tagµτhad

e⌧had channel

2000

120

mT (⌧` , ETmiss )[ GeV ]Dibosons
Model Uncert.

1500

1000
800

1000

600
400

500

1.5
1
0.5

0

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Obs/Exp

Obs/Exp

200
1.5
1
0.5

0

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mT (⌧` , ETmiss )[ GeV ](c) b-tageτhads = 13 TeV, 28.0fb 1

250

150

200

Cut : pT (⌧ ) > 25 GeV

s = 13 TeV, 28.0fb 1

Z/ ⇤ ! ⌧ ⌧Fake ⌧tt̄, tDibosons
Model Uncert.

800

400

100

200

50
Obs/Exp

180

600

200

1.5
1
0.5

160

Data
0.4TeV

1000

Dibosons
Model Uncert.

300

p

1200

Z/ ⇤ ! ⌧ ⌧Fake ⌧tt̄, t350µ⌧had channel

Events/5.0[ GeV]

Cut : pT (⌧ ) > 25 GeV

Data
0.4TeV

0

20

40

60

80

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120

140

160

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200

mT (⌧` , ETmiss )[ GeV ]miss(e) high-ET, eτhadObs/Exp

Events/10.0[ GeV]

p

400

140

(d) b-tagµτhad

e⌧had channel

450

120

mT (⌧` , ETmiss )[ GeV ]

1.5
1
0.5

0

20

40

60

80

100

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mT (⌧` , ETmiss )[ GeV ]miss(f ) high-ET, µτhadmiss
Figure B.3: mT (`, ET) distributions for all signal regions and channels.

114

C

Plots of Control Regions

miss
Figure C.4 – C.7 shows validation plots in the WCR, TCR, ZCR and SSCR for the high-ET
category respectively.

Events/20.0[ GeV]p104

Cut : OS Event

Data
0.4TeVs = 13 TeV, 28.0fb 1

Z/ ⇤ ! ⌧ ⌧Fake ⌧tt̄, t103µ⌧had channel

Events/20.0[ GeV]e⌧had channel

105

Dibosons
Model Uncert.

102

Dibosons
Model Uncert.

102
10

10 1

10 2

10 2

1.5
1
0.5

1.5
1
0.5

50

100

150

200

250

300

350

400

p⌧T` [ GeV ]Obs/Exp

1

10 1

50

100

(a) eτhad , pT (`)
Cut : OS Event

Data
0.4TeVs = 13 TeV, 28.0fb 1

Z/ ⇤ ! ⌧ ⌧Fake ⌧tt̄, t104

Dibosons
Model Uncert.

3

102

p

106

250

300

350

400

p⌧T` [ GeV ]Cut : OS Event

Data
0.4TeVs = 13 TeV, 28.0fb 1

Z/ ⇤ ! ⌧ ⌧Fake ⌧tt̄, t105
104

Dibosons
Model Uncert.

103
102

10

10

1

1

10 1

10 2

10 2

1.5
1
0.5

1.5
1
0.5

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p⌧Thad [ GeV ]Obs/Exp

10 1

Obs/Exp200µ⌧had channel

Events/20.0[ GeV]

Events/20.0[ GeV]

p

105

150

(b) µτhad , pT (`)

e⌧had channel

50

100

(c) eτhad , pT (τhad )p

Cut : OS Event

Data
0.4TeVs = 13 TeV, 28.0fb 1

Z/ ⇤ ! ⌧ ⌧Fake ⌧tt̄, t140
120

Dibosons
Model Uncert.

100

200

250

300

350

400

p⌧Thad [ GeV ]µ⌧had channel

Events/4.0[ GeV]

160

150

(d) µτhad , pT (τhad )e⌧had channel

Events/5.0[ GeV]

Z/ ⇤ ! ⌧ ⌧Fake ⌧tt̄, t103

1

10

Cut : OS Event

Data
0.4TeVs = 13 TeV, 28.0fb 1

104

10

Obs/Exp

p

105

p

500

Cut : OS Event

Data
0.4TeVs = 13 TeV, 28.0fb 1

Z/ ⇤ ! ⌧ ⌧Fake ⌧tt̄, tDibosons
Model Uncert.

400
300

80
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100

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1
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0

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Obs/Exp

20

1.5
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mT (⌧` , ETmiss )[ GeV ]miss(e) eτhad , mT (`, ET
)
80

Data
0.4TeV70p

Z/ ⇤ ! ⌧ ⌧Fake ⌧tt̄, t60

s = 13 TeV, 28.0fb

1

Dibosons
Model Uncert.

50

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miss
(f ) µτhad , mT (`, ET)
Cut : OS Eventµ⌧had channel

Events/0.1[unit]

Events/0.2[unit]e⌧had channel

120mT (⌧` , ETmiss )[ GeV ]Cut : OS Event

Data
0.4TeV250

Z/ ⇤ ! ⌧ ⌧Fake ⌧tt̄, t200p

s = 13 TeV, 28.0fb 1

2

2.5

Dibosons
Model Uncert.

150

40
30

100

20
50

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1
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0

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3

Obs/Exp

Obs/Exp

10

1.5
1
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0.5

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(⌧` , ⌧had )(g) eτhad , ∆φ(`, τhad )3(⌧` , ⌧had )(h) µτhad , ∆φ(`, τhad )missFigure C.4: Comparisons of data and background in the high-ET
WCR for eτhad and µτhad channel withfour important variables.

115

p

Cut : OS Event

Data
0.4TeVs = 13 TeV, 28.0fb 1

Z/ ⇤ ! ⌧ ⌧Fake ⌧tt̄, t104

Dibosons
Model Uncert.

103
10µ⌧had channel

Events/40.0[ GeV]

Events/40.0[ GeV]e⌧had channel

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Model Uncert.

102
10

10 1

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p⌧T` [ GeV ]Obs/Exp

1

10 1

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(a) eτhad , pT (`)
p

Cut : OS Events = 13 TeV, 28.0fb

Data
0.4TeV1

Z/ ⇤ ! ⌧ ⌧Fake ⌧tt̄, t105
4

Dibosons
Model Uncert.

103
102

106

p

105

500

600

700

800

p⌧T` [ GeV ]Cut : OS Events = 13 TeV, 28.0fb

Data
0.4TeV1

Z/ ⇤ ! ⌧ ⌧Fake ⌧tt̄, t104

Dibosons
Model Uncert.

103
102
10

10

1

10 1

10 1

10 2

10 2

1.5
1
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1.5
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800

p⌧Thad [ GeV ]Obs/Exp

1

Obs/Exp400µ⌧had channel

Events/25.0[ GeV]

Events/40.0[ GeV]

106

300

(b) µτhad , pT (`)

e⌧had channel

50

100

(c) eτhad , pT (τhad )Cut : OS Events = 13 TeV, 28.0fb

Data
0.4TeV1

Z/ ⇤ ! ⌧ ⌧Fake ⌧tt̄, t

200

200

250

300

350

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500

p⌧Thad [ GeV ]µ⌧had channel

Events/20.0[ GeV]

p

250

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(d) µτhad , pT (τhad )e⌧had channel

Events/20.0[ GeV]

Z/ ⇤ ! ⌧ ⌧Fake ⌧tt̄, t3

1

10

Cut : OS Event

Data
0.4TeVs = 13 TeV, 28.0fb 1

104

10

Obs/Expp

105

Dibosons
Model Uncert.

150

600

p

Cut : OS Events = 13 TeV, 28.0fb

Data
0.4TeV1

Z/ ⇤ ! ⌧ ⌧Fake ⌧tt̄, t500

Dibosons
Model Uncert.

400
300
200

50

100

1.5
1
0.5

1.5
1
0.5

0

50

100

150

200

250

300

350

400

450

500

Obs/Exp

Obs/Exp

100

0

50

100

150

200

250

mT (⌧` , ETmiss )[ GeV ]miss)(e) eτhad , mT (`, ETp

Z/ ⇤ ! ⌧ ⌧Fake ⌧tt̄, t300

s = 13 TeV, 28.0fb

1

Dibosons
Model Uncert.

250
200

450

500

350

Cut : OS Event

Data
0.4TeVZ/ ⇤ ! ⌧ ⌧Fake ⌧tt̄, t300p

s = 13 TeV, 28.0fb 1

2

2.5

Dibosons
Model Uncert.

250
200
150

150
100

100

50

50

1.5
1
0.5

1.5
1
0.5

Obs/Exp400µ⌧had channel

Events/0.2[unit]

Cut : OS Event

Data
0.4TeV350

miss)(f ) µτhad , mT (`, ET

0

0.5

1

1.5

2

2.5

3

Obs/Exp

Events/0.2[unit]e⌧had channel

350

300

mT (⌧` , ETmiss )[ GeV ]

0

0.5

1

1.5

(⌧` , ⌧had )(g) eτhad , ∆φ(`, τhad )3(⌧` , ⌧had )(h) µτhad , ∆φ(`, τhad )missFigure C.5: Comparisons of data and background in the high-ET
TCR for eτhad and µτhad channel withfour important variables.

Figure C.8 – C.10 shows validation plots in the TCR, ZCR and SSCR for the b-tag category
respectively.
Figure C.11 – C.13 shows validation plots in the WCR, ZCR and SSCR for the b-veto category

116

Events/20.0[ GeV]p104

Cut : OS Event

Data
0.4TeVs = 13 TeV, 28.0fb 1

Z/ ⇤ ! ⌧ ⌧Fake ⌧tt̄, t103µ⌧had channel

106

Events/20.0[ GeV]e⌧had channel

105

Dibosons
Model Uncert.

102

10

Dibosons
Model Uncert.

102
10
1

10 1

10 2

10 2

1.5
1
0.5

50

100

150

200

250

300

350

400

p⌧T` [ GeV ]Obs/Exp

10 1

1.5
1
0.5

50

100

(a) eτhad , pT (`)
p

Cut : OS Events = 13 TeV, 28.0fb

Data
0.4TeV1

Z/ ⇤ ! ⌧ ⌧Fake ⌧tt̄, t104

Dibosons
Model Uncert.

103
102

10

250

300

p

6

350

400

p⌧T` [ GeV ]Cut : OS Events = 13 TeV, 28.0fb

Data
0.4TeV1

Z/ ⇤ ! ⌧ ⌧Fake ⌧tt̄, t105
104

Dibosons
Model Uncert.

103
102

10

10

1

1

10 1

10 2

10 2

1.5
1
0.5

1.5
1
0.5

50

100

150

200

250

300

350

400

p⌧Thad [ GeV ]Obs/Exp

1

Obs/Exp200µ⌧had channel

Events/20.0[ GeV]

Events/20.0[ GeV]

105

150

(b) µτhad , pT (`)

e⌧had channel

50

100

(c) eτhad , pT (τhad )160

Cut : OS Events = 13 TeV, 28.0fb

Data
0.4TeV1

Z/ ⇤ ! ⌧ ⌧Fake ⌧tt̄, t140

Dibosons
Model Uncert.

120

200

250

300

350

400

p⌧Thad [ GeV ]µ⌧had channel

Events/5.0[ GeV]p150(d) µτhad , pT (τhad )e⌧had channel

Events/5.0[ GeV]

Z/ ⇤ ! ⌧ ⌧Fake ⌧tt̄, t103

1

10

Cut : OS Event

Data
0.4TeVs = 13 TeV, 28.0fb 1

104

10

Obs/Exp

p

5

100

p

600

Cut : OS Events = 13 TeV, 28.0fb

Data
0.4TeV1

Z/ ⇤ ! ⌧ ⌧Fake ⌧tt̄, t500

Dibosons
Model Uncert.

400
300

80
60

200

40
100

1.5
1
0.5

0

20

40

60

80

100

120

140

160

180

200

Obs/Exp

Obs/Exp

20

1.5
1
0.5

0

20

40

60

80

100

mT (⌧` , ETmiss )[ GeV ]miss)(e) eτhad , mT (`, ET

p

Cut : OS Events = 13 TeV, 28.0fb

Data
0.4TeV1

Z/ ⇤ ! ⌧ ⌧Fake ⌧tt̄, t180
160

Dibosons
Model Uncert.

140

140

160

180

200

miss
)
(f ) µτhad , mT (`, ETµ⌧had channel

Events/0.2[unit]

Events/0.2[unit]e⌧had channel

200

120

mT (⌧` , ETmiss )[ GeV ]

120

p

600

Cut : OS Events = 13 TeV, 28.0fb

Data
0.4TeV1

Z/ ⇤ ! ⌧ ⌧Fake ⌧tt̄, t500

Dibosons
Model Uncert.

400
300

100
80

200

60
40

100

1.5
1
0.5

0

0.5

1

1.5

2

2.5

3

Obs/Exp

Obs/Exp

20
1.5
1
0.5

0

0.5

1

1.5

2

2.5

(⌧` , ⌧had )(g) eτhad , ∆φ(`, τhad )3(⌧` , ⌧had )(h) µτhad , ∆φ(`, τhad )missFigure C.6: Comparisons of data and background in the high-ET
ZCR for eτhad and µτhad channel withfour important variables.

respectively.

117

Events/25.0[ GeV]p

Cut : pT (⌧ ) > 25 GeV

s = 13 TeV, 28.0fb

Data
0.4TeV1

Z/ ⇤ ! ⌧ ⌧Fake ⌧tt̄, t104
103µ⌧had channel

Events/40.0[ GeV]e⌧had channel

105

Dibosons
Model Uncert.

102

106
105

s = 13 TeV, 28.0fb

Dibosons
Model Uncert.

102
10
1

10 1

10 2

10 2

1.5
1
0.5

1.5
1
0.5

50

100

150

200

250

300

350

400

450

500

p⌧T` [ GeV ]Obs/Exp

10 1100(a) eτhad , pT (`)
Cut : pT (⌧ ) > 25 GeV

s = 13 TeV, 28.0fb

Data
0.4TeV1

Z/ ⇤ ! ⌧ ⌧Fake ⌧tt̄, t104

Dibosons
Model Uncert.

103

107

102

400

500

600

700

800

p⌧T` [ GeV ]Cut : pT (⌧ ) > 25 GeV

s = 13 TeV, 28.0fb

Data
0.4TeV1

Z/ ⇤ ! ⌧ ⌧Fake ⌧tt̄, t105

Dibosons
Model Uncert.

104
103
102
10

1

1

10 1

10 2

10 2

1.5
1
0.5

1.5
1
0.5

50

100

150

200

250

300

350

400

450

500

p⌧Thad [ GeV ]Obs/Exp

1

Obs/Exp

p

106

10

100

(c) eτhad , pT (τhad )
p

100

Data
0.4TeVs = 13 TeV, 28.0fb 1

Z/ ⇤ ! ⌧ ⌧Fake ⌧tt̄, tDibosons
Model Uncert.

80

200

300

400

500

600

700

800

p⌧Thad [ GeV ](d) µτhad , pT (τhad )Cut : pT (⌧ ) > 25 GeVµ⌧had channel

Events/4.0[ GeV]e⌧had channel

Events/10.0[ GeV]300µ⌧had channel

Events/40.0[ GeV]

Events/25.0[ GeV]

p

5

200

(b) µτhad , pT (`)

e⌧had channel

10Z/ ⇤ ! ⌧ ⌧Fake ⌧tt̄, t103

1

10

Cut : pT (⌧ ) > 25 GeV

Data
0.4TeV

1

104

10

Obs/Exp

p

60

p

220
200

Cut : pT (⌧ ) > 25 GeV

Data
0.4TeVs = 13 TeV, 28.0fb 1

Z/ ⇤ ! ⌧ ⌧Fake ⌧tt̄, t180

Dibosons
Model Uncert.

160
140
120
100

40

80
60

20

40

1.5
1
0.5

1.5
1
0.5

0

20

40

60

80

100

120

140

160

180

200

Obs/Exp

Obs/Exp

20

0

20

40

60

80

100

mT (⌧` , ETmiss )[ GeV ]miss)(e) eτhad , mT (`, ET
Cut : pT (⌧ ) > 25 GeV

Data
0.4TeVp

Z/ ⇤ ! ⌧ ⌧Fake ⌧tt̄, t

80

140

160

180

200

miss
)
(f ) µτhad , mT (`, ET

s = 13 TeV, 28.0fb 1

Dibosons
Model Uncert.

µ⌧had channel

Events/0.1[unit]

Events/0.2[unit]e⌧had channel

100

120

mT (⌧` , ETmiss )[ GeV ]Cut : pT (⌧ ) > 25 GeV

Data
0.4TeV300

Z/ ⇤ ! ⌧ ⌧Fake ⌧tt̄, t250p

s = 13 TeV, 28.0fb 1

2

2.5

Dibosons
Model Uncert.

200

60
150
100

20

50

1.5
1
0.5

1.5
1
0.5

0

0.5

1

1.5

2

2.5

3

Obs/Exp

Obs/Exp

40

0

0.5

1

1.5

(⌧` , ⌧had )(g) eτhad , ∆φ(`, τhad )3(⌧` , ⌧had )(h) µτhad , ∆φ(`, τhad )missFigure C.7: Comparisons of data and background in the high-ET
SSCR for eτhad and µτhad channel withfour important variables.

118e⌧had channelp

Cut : OS Event

Data
0.4TeV1

s = 13 TeV, 28.0fb

1000

s = 13 TeV, 28.0fb

Z/ ⇤ ! ⌧ ⌧Fake ` ! ⌧Fake ⌧tt̄, t1600

Dibosons
Model Uncert.

1400
1200
1000

600

800

400

600
400

200

200

1.5
1
0.5

50

100

150

200

250

300

350

400

p⌧T` [ GeV ]Obs/Exp

Obs/Exp

Cut : OS Event

Data
0.4TeV

1

1800

Dibosons
Model Uncert.

800

p

2000

Z/ ⇤ ! ⌧ ⌧Fake ` ! ⌧Fake ⌧tt̄, t1200µ⌧had channel

2200

Events/20.0[ GeV]

Events/20.0[ GeV]

1400

1.5
1
0.5

50

100

(a) eτhad , pT (`)
1600

Cut : OS Events = 13 TeV, 28.0fb

Z/ ⇤ ! ⌧ ⌧Fake ` ! ⌧Fake ⌧tt̄, t

1400
1200

p

350

400

p⌧T` [ GeV ]Cut : OS Event

Data
0.4TeV1

s = 13 TeV, 28.0fb

Z/ ⇤ ! ⌧ ⌧Fake ` ! ⌧Fake ⌧tt̄, t2500
2000

Dibosons
Model Uncert.

1000

300

3000

Data
0.4TeV1250µ⌧had channel

Events/10.0[ GeV]

Events/10.0[ GeV]p200(b) µτhad , pT (`)

e⌧had channel

1800

150

Dibosons
Model Uncert.

1500

800
1000

600
400

500

1.5
1
0.5

40

60

80

100

120

140

160

180

200

220

p⌧Thad [ GeV ]Obs/Exp

Obs/Exp

200

1.5
1
0.5

40

60

(c) eτhad , pT (τhad )Cut : OS Event

Data
0.4TeVs = 13 TeV, 28.0fb 1

140

160

180

200

220

p⌧Thad [ GeV ]Cut : OS Event

Data
0.4TeVs = 13 TeV, 28.0fb 1

Z/ ⇤ ! ⌧ ⌧Fake ` ! ⌧Fake ⌧tt̄, t2500

Dibosons
Model Uncert.

1500

p

3000

Z/ ⇤ ! ⌧ ⌧Fake ` ! ⌧Fake ⌧tt̄, t2000

120µ⌧had channel

Events/20.0[ GeV]

Events/20.0[ GeV]p100(d) µτhad , pT (τhad )e⌧had channel

2500

80

Dibosons
Model Uncert.

2000
1500

1000

1000

1.5
1
0.5

500

0

50

100

150

200

250

300

350

400

450

500

Obs/Exp

Obs/Exp

500

1.5
1
0.5

0

50

100

150

200

250

mT (⌧` , ETmiss )[ GeV ]miss)(e) eτhad , mT (`, ET
Cut : OS Event

Data
0.4TeVp

Z/ ⇤ ! ⌧ ⌧Fake ` ! ⌧Fake ⌧tt̄, t500

s = 13 TeV, 28.0fb 1

Dibosons
Model Uncert.

400

350

400

450

500

miss
)
(f ) µτhad , mT (`, ETµ⌧had channel

Events/0.1[unit]

Events/0.1[unit]e⌧had channel

600

300

mT (⌧` , ETmiss )[ GeV ]Cut : OS Event

Data
0.4TeV700

Z/ ⇤ ! ⌧ ⌧Fake ` ! ⌧Fake ⌧tt̄, t600p

s = 13 TeV, 28.0fb 1

2

2.5

Dibosons
Model Uncert.

500
400

300

300
200

200

1.5
1
0.5

100

0

0.5

1

1.5

2

2.5

3

Obs/Exp

Obs/Exp

100

1.5
1
0.5

0

0.5

1

1.5

(⌧` , ⌧had )(g) eτhad , ∆φ(`, τhad )3(⌧` , ⌧had )(h) µτhad , ∆φ(`, τhad )Figure C.8: Comparisons of data and background in the b-tag TCR for eτhad and µτhad channel with four
important variables.

119

p

400

Cut : OS Events = 13 TeV, 28.0fb

Data
0.4TeV1

Z/ ⇤ ! ⌧ ⌧Fake ` ! ⌧Fake ⌧tt̄, t350

Dibosons
Model Uncert.

300µ⌧had channel

Events/1.0[ GeV]

Events/1.0[ GeV]e⌧had channel

450

250

p

500

Cut : OS Events = 13 TeV, 28.0fb

Data
0.4TeV1

Z/ ⇤ ! ⌧ ⌧Fake ` ! ⌧Fake ⌧tt̄, t400

Dibosons
Model Uncert.

300

200
200

150
100

100

1.5
1
0.5
25

30

35

40

45

50

55

60

65

70

75

p⌧T` [ GeV ]Obs/Exp

Obs/Exp

50
1.5
1
0.5
25

30

(a) eτhad , pT (`)

Z/ ⇤ ! ⌧ ⌧Fake ` ! ⌧Fake ⌧tt̄, tDibosons
Model Uncert.

300

p

500

1.5
1
0.5
25

1.5
1
0.5
25

50

55

60

65

70

75

p⌧Thad [ GeV ]Obs/Exp100

45

Z/ ⇤ ! ⌧ ⌧Fake ` ! ⌧Fake ⌧tt̄, tDibosons
Model Uncert.

400

30

100

1.5
1
0.5

1.5
1
0.5

80

100

120

140

160

180

200

Obs/Exp

200

100

60

35

40

45

50

0

Cut : OS Event

Z/ ⇤ ! ⌧ ⌧Fake ` ! ⌧Fake ⌧tt̄, t120

Dibosons
Model Uncert.

100

75

Cut : OS Event

Z/ ⇤ ! ⌧ ⌧Fake ` ! ⌧Fake ⌧tt̄, t

20

40

60

80

100

120

140

160

180

200

miss
)
(f ) µτhad , mT (`, ET

Data
0.4TeV

14070mT (⌧` , ETmiss )[ GeV ]µ⌧had channel

Events/0.05[unit]

Events/0.05[unit]e⌧had channels = 13 TeV, 28.0fb 1

65p⌧Thad [ GeV ]Dibosons
Model Uncert.

miss)(e) eτhad , mT (`, ET

p

60

Data
0.4TeVs = 13 TeV, 28.0fb 1

mT (⌧` , ETmiss )[ GeV ]

160

55

400
300

40

Z/ ⇤ ! ⌧ ⌧Fake ` ! ⌧Fake ⌧tt̄, t

500

200

20

p

600

300

0

75

Data
0.4TeV1µ⌧had channel

Events/4.0[ GeV]

Data
0.4TeV500

Obs/Exp

Events/4.0[ GeV]

600

70

p⌧T` [ GeV ](d) µτhad , pT (τhad )Cut : OS Events = 13 TeV, 28.0fb 1

65

Cut : OS Events = 13 TeV, 28.0fb(c) eτhad , pT (τhad )e⌧had channelp60

Dibosons
Model Uncert.

100

40

55

300
200

35

50

400

200

30

45

µ⌧had channel

Events/1.0[ GeV]

s = 13 TeV, 28.0fb

Data
0.4TeV

400

Obs/Exp

Events/1.0[ GeV]

500

Cut : OS Event140(b) µτhad , pT (`)

e⌧had channel

p

35

140

p

Cut : OS Event

Data
0.4TeVs = 13 TeV, 28.0fb 1

Z/ ⇤ ! ⌧ ⌧Fake ` ! ⌧Fake ⌧tt̄, t

120
100

80

Dibosons
Model Uncert.

80
60

60
40

20

20

1.5
1
0.5

1.5
1
0.5

0

0.5

1

1.5

2

2.5

3

Obs/Exp

Obs/Exp

40

0

0.5

1

1.5

2

2.5

(⌧` , ⌧had )(g) eτhad , ∆φ(`, τhad )3(⌧` , ⌧had )(h) µτhad , ∆φ(`, τhad )Figure C.9: Comparisons of data and background in the b-tag ZCR for eτhad and µτhad channel with four
important variables.

120

p

106

Cut : pT (`) > 30 GeV

s = 13 TeV, 28.0fb

Data
0.4TeV1

Z/ ⇤ ! ⌧ ⌧Fake ` ! ⌧Fake ⌧tt̄, t105
104

Dibosons
Model Uncert.

103µ⌧had channel

Events/20.0[ GeV]

Events/20.0[ GeV]e⌧had channel

107

10

10 2

10 2

1.5
1
0.5

1.5
1
0.5

300

350

400

p⌧T` [ GeV ]Obs/Exp

10 1

Obs/Exp

1

10 1

250

Dibosons
Model Uncert.

103

1

200

50

100

(a) eτhad , pT (`)
Events/20.0[ GeV]

108
10

p

7

s = 13 TeV, 28.0fb

Data
0.4TeV1

Z/ ⇤ ! ⌧ ⌧Fake ` ! ⌧Fake ⌧tt̄, t106
105

Dibosons
Model Uncert.

104
103

108
10
10

10 2

1.5
1
0.5

1.5
1
0.5

350

400

p⌧Thad [ GeV ]Obs/Exp

10 2
Obs/Exp

1

10 1

50

100

200

250

Dibosons
Model Uncert.

p

500

400

Cut : pT (`) > 30 GeV

Z/ ⇤ ! ⌧ ⌧Fake ` ! ⌧Fake ⌧tt̄, tDibosons
Model Uncert.

300

100

1.5
1
0.5

1.5
1
0.5

0

20

40

60

80

100

120

140

160

180

200

Obs/Exp

200

100

0

20

40

60

80

100

mT (⌧` , ETmiss )[ GeV ]Cut : pT (`) > 30 GeV

Data
0.4TeVp

Z/ ⇤ ! ⌧ ⌧Fake ` ! ⌧Fake ⌧tt̄, t250

s = 13 TeV, 28.0fb 1

Dibosons
Model Uncert.

200

140

160

180

200

miss
)
(f ) µτhad , mT (`, ET150µ⌧had channel

Events/0.05[unit]e⌧had channel

300

120

mT (⌧` , ETmiss )[ GeV ]miss)(e) eτhad , mT (`, ET
350

Cut : pT (`) > 30 GeV

Data
0.4TeVZ/ ⇤ ! ⌧ ⌧Fake ` ! ⌧Fake ⌧tt̄, t300
250p

s = 13 TeV, 28.0fb 1

2

2.5

Dibosons
Model Uncert.

200
150

100

100

50

50

1.5
1
0.5

1.5
1
0.5

0

0.5

1

1.5

2

2.5

3

Obs/Exp

Events/0.05[unit]

350

p⌧Thad [ GeV ]Data
0.4TeVs = 13 TeV, 28.0fb 1

400

200

Obs/Exp300µ⌧had channel

Events/4.0[ GeV]

Z/ ⇤ ! ⌧ ⌧Fake ` ! ⌧Fake ⌧tt̄, t300150(d) µτhad , pT (τhad )Data
0.4TeVs = 13 TeV, 28.0fb 1

Z/ ⇤ ! ⌧ ⌧Fake ` ! ⌧Fake ⌧tt̄, tDibosons
Model Uncert.

Cut : pT (`) > 30 GeV

400

Obs/Exp

Events/4.0[ GeV]p

500

Cut : pT (`) > 30 GeV

s = 13 TeV, 28.0fb(c) eτhad , pT (τhad )e⌧had channel

400p⌧T` [ GeV ]

103

10 1

300

350

Data
0.4TeV

1

104

10

250

300

5

1

200

250

106

102

150

p

7

10

100

200

µ⌧had channel

102

50

150

(b) µτhad , pT (`)
Cut : pT (`) > 30 GeV

Events/20.0[ GeV]e⌧had channel

Z/ ⇤ ! ⌧ ⌧Fake ` ! ⌧Fake ⌧tt̄, t

104
102

150

s = 13 TeV, 28.0fb

105

10

100

Cut : pT (`) > 30 GeV

Data
0.4TeV

1

106

102

50

p

107

0

0.5

1

1.5

(⌧` , ⌧had )(g) eτhad , ∆φ(`, τhad )3(⌧` , ⌧had )(h) µτhad , ∆φ(`, τhad )Figure C.10: Comparisons of data and background in the b-tag SSCR for eτhad and µτhad channel with four
important variables.

121e⌧had channel

Cut : pT (`) > 30 GeVµ⌧had channel

102

109
108
107
106
105
104
103
102

10

10

10

p

8

Data
0.4TeV1

s = 13 TeV, 28.0fb

Z/ ⇤ ! ⌧ ⌧Fake ` ! ⌧Fake ⌧tt̄, t

107
106
105

Dibosons
Model Uncert.

104
10Events/10.0[ GeV]

Events/10.0[ GeV]

109

3

1

1

10 2

10 1
10 2

1.5
1
0.5

1.5
1
0.5

Obs/Exp

10

40

60

80

100

120

140

160

180

200

220

p⌧T` [ GeV ]Obs/Exp1

ps = 13 TeV, 28.0fb

40

60

p

s = 13 TeV, 28.0fb

Data
0.4TeV

1

100

120

140

160

µ⌧had channel

Z/ ⇤ ! ⌧ ⌧Fake ` ! ⌧Fake ⌧tt̄, tDibosons
Model Uncert.

1010
109
108
107
106
105
104
103
102

10

180

200

220

p⌧T` [ GeV ]p

Cut : pT (`) > 30 GeV

s = 13 TeV, 28.0fb

Data
0.4TeV1

Z/ ⇤ ! ⌧ ⌧Fake ` ! ⌧Fake ⌧tt̄, tDibosons
Model Uncert.

10
1

1

10
10 2

10 1
10 2

1.5
1
0.5

1.5
1
0.5

50

100

150

200

250

300

350

400

p⌧Thad [ GeV ]Obs/Exp

1

Obs/Exp80(b) µτhad , pT (`)
Cut : pT (`) > 30 GeV

Events/20.0[ GeV]

Events/20.0[ GeV]

109
108
107
106
105
104
103
102

Z/ ⇤ ! ⌧ ⌧Fake ` ! ⌧Fake ⌧tt̄, tDibosons
Model Uncert.

(a) eτhad , pT (`)
e⌧had channel

Cut : pT (`) > 30 GeV

Data
0.4TeV150100(c) eτhad , pT (τhad )Events/4.0[ GeV]

9000

p

8000

Data
0.4TeVs = 13 TeV, 28.0fb 1

6000

300

p

350

400

p⌧Thad [ GeV ]Cut : pT (`) > 30 GeV

Data
0.4TeVs = 13 TeV, 28.0fb 1

Z/ ⇤ ! ⌧ ⌧Fake ` ! ⌧Fake ⌧tt̄, t

10000

Dibosons
Model Uncert.

5000

250

µ⌧had channel

12000

Z/ ⇤ ! ⌧ ⌧Fake ` ! ⌧Fake ⌧tt̄, t7000

200(d) µτhad , pT (τhad )Cut : pT (`) > 30 GeV

Events/4.0[ GeV]e⌧had channel

150

Dibosons
Model Uncert.

8000
6000

4000
3000

4000

2000

Obs/Exp

1.5
1
0.5

0

20

40

60

80

100

120

140

160

180

200

Obs/Exp

2000

1000

1.5
1
0.5

0

20

40

60

80

100

mT (⌧` , ETmiss )[ GeV ]miss)(e) eτhad , mT (`, ET
Cut : pT (`) > 30 GeV

Data
0.4TeVp

Z/ ⇤ ! ⌧ ⌧Fake ` ! ⌧Fake ⌧tt̄, t1400
1200

s = 13 TeV, 28.0fb 1µ⌧had channel

2500

160

180

200

Cut : pT (`) > 30 GeV

Data
0.4TeVZ/ ⇤ ! ⌧ ⌧Fake ` ! ⌧Fake ⌧tt̄, t2000

Dibosons
Model Uncert.

1000

140

miss
)
(f ) µτhad , mT (`, ET
Events/0.05[unit]

Events/0.05[unit]e⌧had channel

1600

120

mT (⌧` , ETmiss )[ GeV ]p

s = 13 TeV, 28.0fb 1

2

2.5

Dibosons
Model Uncert.

1500

800
1000

600
400

500

1.5
1
0.5

0

0.5

1

1.5

2

2.5

3

Obs/Exp

Obs/Exp

200
1.5
1
0.5

0

0.5

1

1.5

(⌧` , ⌧had )(g) eτhad , ∆φ(`, τhad )3(⌧` , ⌧had )(h) µτhad , ∆φ(`, τhad )Figure C.11: Comparisons of data and background in the b-veto WCR for eτhad and µτhad channel with four
important variables.

122

p

Cut : OS Events = 13 TeV, 28.0fb

Data
0.4TeV

1

2000

35

40

45

50

55

60

65

70

75

p⌧T` [ GeV ]Obs/Exp

4000

2000

Obs/Exp

6000

4000

30

s = 13 TeV, 28.0fb

Dibosons
Model Uncert.

1.5
1
0.5
25

30

(a) eτhad , pT (`)
Cut : OS Events = 13 TeV, 28.0fb

7000

Data
0.4TeV1

Z/ ⇤ ! ⌧ ⌧Fake ` ! ⌧Fake ⌧tt̄, t

8000
7000

45

50

55

p

60

65

70

75

p⌧T` [ GeV ]Cut : OS Events = 13 TeV, 28.0fb

Data
0.4TeV1

Z/ ⇤ ! ⌧ ⌧Fake ` ! ⌧Fake ⌧tt̄, t6000
5000

Dibosons
Model Uncert.

6000

40

µ⌧had channel

Events/1.0[ GeV]

Events/1.0[ GeV]p35(b) µτhad , pT (`)

e⌧had channel

9000

Z/ ⇤ ! ⌧ ⌧Fake ` ! ⌧Fake ⌧tt̄, t

8000

6000

1.5
1
0.5
25

Cut : OS Event

Data
0.4TeV1

10000

Dibosons
Model Uncert.

8000

p

12000

Z/ ⇤ ! ⌧ ⌧Fake ` ! ⌧Fake ⌧tt̄, t10000µ⌧had channel

Events/1.0[ GeV]

Events/1.0[ GeV]e⌧had channel

12000

Dibosons
Model Uncert.

4000

5000
4000

3000

3000

2000

2000

Obs/Exp

1.5
1
0.5
25

30

35

40

45

50

55

60

65

70

75

p⌧Thad [ GeV ]Obs/Exp

1000

1000

1.5
1
0.5
25

30

(c) eτhad , pT (τhad )Data
0.4TeV9000

Z/ ⇤ ! ⌧ ⌧Fake ` ! ⌧Fake ⌧tt̄, t

8000

45

50

55

60

65

70

75

p⌧Thad [ GeV ]µ⌧had channel

Events/4.0[ GeV]

Events/4.0[ GeV]

10000

Cut : OS Events = 13 TeV, 28.0fb 1

40(d) µτhad , pT (τhad )e⌧had channel

p

35

p

8000

Cut : OS Event

Data
0.4TeVs = 13 TeV, 28.0fb 1

Z/ ⇤ ! ⌧ ⌧Fake ` ! ⌧Fake ⌧tt̄, t7000

Dibosons
Model Uncert.

Dibosons
Model Uncert.

6000
5000

6000

4000
4000

3000
2000

2000

0

20

40

60

80

100

120

140

160

180

200

Obs/Exp

Obs/Exp

1000
1.5
1
0.5

1.5
1
0.5

0

20

40

60

80

100

mT (⌧` , ETmiss )[ GeV ]miss)(e) eτhad , mT (`, ET
Events/0.05[unit]

Cut : OS Event

Data
0.4TeVp

Z/ ⇤ ! ⌧ ⌧Fake ` ! ⌧Fake ⌧tt̄, t10000
8000

s = 13 TeV, 28.0fb 1

160µ⌧had channel

180

200

Dibosons
Model Uncert.

Cut : OS Event

Data
0.4TeV

10000

Z/ ⇤ ! ⌧ ⌧Fake ` ! ⌧Fake ⌧tt̄, t8000p

s = 13 TeV, 28.0fb 1

2

2.5

Dibosons
Model Uncert.

6000

6000

4000

4000

2000

1.5
1
0.5

1.5
1
0.5

0

0.5

1

1.5

2

2.5

3

Obs/Exp

2000

Obs/Exp

140

miss
)
(f ) µτhad , mT (`, ET
Events/0.05[unit]e⌧had channel

12000

120

mT (⌧` , ETmiss )[ GeV ]

0

0.5

1

1.5

(⌧` , ⌧had )(g) eτhad , ∆φ(`, τhad )3(⌧` , ⌧had )(h) µτhad , ∆φ(`, τhad )Figure C.12: Comparisons of data and background in the b-veto ZCR for eτhad and µτhad channel with four
important variables.

123

p

Cut : pT (`) > 30 GeV

s = 13 TeV, 28.0fb

Data
0.4TeV1µ⌧had channel

Events/10.0[ GeV]

Events/20.0[ GeV]e⌧had channel

1010
109
108
107
106
105
104
103
102

Z/ ⇤ ! ⌧ ⌧Fake ` ! ⌧Fake ⌧tt̄, tDibosons
Model Uncert.

109
108
107
106
105
104
103
102
1

1

10
10 2

10 1
10 2

1.5
1
0.5

1.5
1
0.5

50

100

150

200

250

300

350

400

p⌧T` [ GeV ]Obs/Exp1

s = 13 TeV, 28.0fb

40

60

p

s = 13 TeV, 28.0fb

Data
0.4TeV

1

80

100

120

160

µ⌧had channel

Z/ ⇤ ! ⌧ ⌧Fake ` ! ⌧Fake ⌧tt̄, tDibosons
Model Uncert.

1010
109
108
107
106
105
104
103
102

180

200

220

p⌧T` [ GeV ]p

Cut : pT (`) > 30 GeV

s = 13 TeV, 28.0fb

Data
0.4TeV1

Z/ ⇤ ! ⌧ ⌧Fake ` ! ⌧Fake ⌧tt̄, tDibosons
Model Uncert.

10

10

1

1

10
10 2

10 1
10 2

1.5
1
0.5

1.5
1
0.5

50

100

150

200

250

300

350

400

p⌧Thad [ GeV ]Obs/Exp

1

50

100

(c) eτhad , pT (τhad )
8000

p

Data
0.4TeVs = 13 TeV, 28.0fb 1

6000

3000

2000

2000

1000

1000

1.5
1
0.5

1.5
1
0.5

60

80

100

120

140

160

180

200

Obs/Exp

3000

40

p

Z/ ⇤ ! ⌧ ⌧Fake ` ! ⌧Fake ⌧tt̄, tDibosons
Model Uncert.

0

20

40

60

80

100

Z/ ⇤ ! ⌧ ⌧Fake ` ! ⌧Fake ⌧tt̄, t5000

s = 13 TeV, 28.0fb 1

6000

2000

1000

1000

1.5
1
0.5

1.5
1
0.5

1

1.5

2

2.5

3

Obs/Exp

3000

2000

0.5

Z/ ⇤ ! ⌧ ⌧Fake ` ! ⌧Fake ⌧tt̄, tps = 13 TeV, 28.0fb 1

0

0.5

1

1.5

2

2.5

(⌧` , ⌧had )(g) eτhad , ∆φ(`, τhad )

180

200

Dibosons
Model Uncert.

4000

3000

0

160

Cut : pT (`) > 30 GeV

Data
0.4TeV

5000

Dibosons
Model Uncert.

4000µ⌧had channel

Events/0.05[unit]

Events/0.05[unit]

6000

140

miss
)
(f ) µτhad , mT (`, ET

Cut : pT (`) > 30 GeVp

120

mT (⌧` , ETmiss )[ GeV ]miss)(e) eτhad , mT (`, ET
Data
0.4TeV400

Cut : pT (`) > 30 GeV

mT (⌧` , ETmiss )[ GeV ]µ⌧had channel

350p⌧Thad [ GeV ]Data
0.4TeVs = 13 TeV, 28.0fb 1

5000
4000

20

300

6000

4000

0

250

7000

Dibosons
Model Uncert.

5000

200

µ⌧had channel

8000

Z/ ⇤ ! ⌧ ⌧Fake ` ! ⌧Fake ⌧tt̄, t7000

150(d) µτhad , pT (τhad )Cut : pT (`) > 30 GeV

Events/4.0[ GeV]

Events/4.0[ GeV]µ⌧had channel

Obs/Exp140(b) µτhad , pT (`)
Cut : pT (`) > 30 GeV

Events/20.0[ GeV]

Events/20.0[ GeV]

1010
109
108
107
106
105
104
103
102

Obs/Exp

Z/ ⇤ ! ⌧ ⌧Fake ` ! ⌧Fake ⌧tt̄, tDibosons
Model Uncert.

(a) eτhad , pT (`)
e⌧had channel

Obs/Exp

Cut : pT (`) > 30 GeV

Data
0.4TeV1

10

10

Obs/Expp3(⌧` , ⌧had )(h) µτhad , ∆φ(`, τhad )Figure C.13: Comparisons of data and background in the b-veto SSCR for eτhad and µτhad channel with four
important variables.

124

D

Definition of Experimental Systematic Uncertainties
Uncertainty

Alias

Type

Description

Resolution

MET SoftTrk ResoPara
MET SoftTrk ResoPerp
MET SoftTrk Scale
MET TrigEff elhad
MET TrigEff muhad

shape
shape
shape
accep.
accep.

soft term resol. in parallel direction
soft term resol. in perpendicular direction
soft term scale
trig. eff. for eτhad channel
trig. eff. for µτhad channel

Scale
TriggermissTable D.13: Systematic uncertainties for ET
with alias in the final fit and its type.

Uncertainty

Alias

Type

Description

Reconstruction
Identification
Isolation
Trigger
Energy resolution

EL Reco
EL Id
EL IsoEL Trig
EG RESOLUTION ALL
EG SCALE ALLCORREG SCALE E4SCINTILLATOREG SCALE LARCALIB EXTRA2015PRE
EG SCALE LARCALIB EXTRA2016PRE
EG SCALE LARTEMP EXTRA2015PRE
EG SCALE LARTEMP EXTRA2016PRE

accep.
accep.
accep.
accep.
shape
shape
shape
shape
shape
shape
shape

reco. eff. measurement
id eff. measurement
iso. eff. measurement
trig. eff. measurement
MC energy resolutionenergy calib. correction
LAr calo. 4th layer simulation
LAr calo. calib. for 2015
LAr calo. calib. for 2016
LAr calo. temperture for 2015
LAr calo. temperture for 2016

Energy scale

Table D.13: Systematic uncertainties for electron objects with alias in the final fit and its type.

Uncertainty

Alias

Type

Description

Reconstruction
TTVA
Isolation
TriggerMomentum scale

MU Reco Stat/Syst
MU TTVA Stat/Syst
MU Iso Stat/Syst
MU Trig Stat/Syst
MU Scale
MU ID
MU MS

accep.
accep.
accep.
accep.
shape.
shape
shapereco. eff. stat/syst term
TTVA eff. stat/syst term
iso. eff. stat/syst term
trig. eff. stat/syst term
MC momentum scale
MC momentum resol. at ID
MC momentum resol. at MS

Momentum resolution

Table D.13: Systematic uncertainties for muon objects with alias in the final fit and its type.

E

Variation of Systematic Uncertainty

As the results of evaluation of systematic uncertinties, Table E.13 and E.13 show variations for themiss category with each decay channels. Each systematic uncertinties are taken as quadrature
high-ETsum. For signal processes, both production processes are assumed mA = 600 GeV mass hypothesis.
Table E.13 and E.13 show variations for the b-veto category with each decay channels.

125

Uncertainty

Alias

Type

Description

JVT

JET JVTJET GroupedNP 1,2,3
JET EtaIntercalib NonClosure
JET JER SINGLE NP
FT Eigen B 00∼01
FT Eigen C 00∼02
FT Eigen L 00∼03
FT ExtraFT ExtraC

accep.
shape
shape
shape
accep.
accep.
accep.
accep.
accep.

JVT eff.
JES groped as 1,2,3
non closer for inter calib. η binningenergy resolution
eigne vector for real b-quark
eigne vector for real c-quark
eigne vector for other light-quark
extrapolation
extrapolation for c-quark

Energy scale
Energy resolution

b-tagging

Table D.13: Systematic uncertainties for jet objects with alias in the final fit and its type.

Uncertainty
Reconstruction
Identification
Energy Scale

Alias

Type

Description

TAU Reco LowPt/HighPt
TAU Reco TrueEleEleOLRTAU Reco TrueTauEleOLRTAU Id LowPt/HighPt
TAUS SME TES DETECTOR
TAUS SME TES MODEL
TAUS SME TES INSITU

accep.
accep.
accep.
accep.
shape
shape
shape

reco. eff. for low-pT /high-pT
eVeto eff. for real electron
eVeto eff. for real hadronic-τ
id.. eff. for low-pT /high-pT
TES on detector simulation
TES on simulation modelTES on in-situ measurement

Table D.13: Systematic uncertainties for hadronic-τ objects with alias in the final fit and its type.

Uncertainty

Alias

Type

Description

F Fτ̄q→τ
F Fτ̄EW→τFFQ Btag/Bveto
FFW Btag/Bveto
Fake HM el/muhad
Fake Btag el/muhad
Fake Bveto el/muhad
rQ HM el/muhadrQ Btag el/muhadrQ Bveto el/muhad
SFZ HM el/muhad
SFZ Btag el/muhad
SFZ Bveto el/muhad
SFT HM el/muhad
SFT Btag el/muhad
SFT Bveto el/muhad

shape
shape
accep.
accep.
accep.
shape
shape
shape
accep.
accep.
accep.
accep.
accep.
accep.

QCD Fake factor for b-tagged/-veto event
EW Fake factor for b-tagged/-veto event
miss e/µτ
fake non-closer for the high-ET
had SR
fake non-closer for the b-tag e/µτhad SR
fake non-closer for the b-veto e/µτhad SR
miss e/µτ
rq for the high-ET
had SRrq for the b-tag e/µτhad SR
rq for the b-veto e/µτhad SR
miss e/µτ
SF for Z → τ τ in the high-ET
had SRSF for Z → τ τ in the b-tag e/µτhad SR
SF for Z → τ τ in the b-veto e/µτhad SR
miss e/µτ
SF for tt̄ → `τhad in the high-ET
had SRSF for tt̄ → `τhad in the b-tag e/µτhad SR
SF for tt̄ → `τhad in the b-veto e/µτhad SR

W +jets non-closerrq

Z → τ τ SF
tt̄ → `τhad SF

Table D.13: Systematic uncertainties for background modelling.

Table E.13 and E.13 show variations for the b-tag category with each decay channels.

126

Uncertainty
PDFµF,R
MC tuning
total

200 GeVggF
500 GeV

1 TeV

4.100
17.4003.835
18.2834.800
15.5002.795
16.4654.300
15.1002.488
15.896200 GeVbbA
500 GeV

1 TeV

5.978
17.5694.744
19.1556.529
18.7553.983
20.25412.35620.0433.718
23.837

Table D.13: Systematic uncertainties for signal samples. MC tuning values are quadratic sum of each MC
tuning variations. All values are denoted by %.

Uncertainty

ggF

bbA

Diboson
1peτhadElectron
Jet
MET
TES
Tau
TheoryTotal
Electron
Jet
MET
TES
Tau
Theory
Total

±1.5%
±3.5%
±0.6%
±16.6%±6.0%±15.1%±23.5%

±1.2%
±2.4%
±1.2%
±16.8%±6.0%±24.9%±30.7%

±1.1%
±1.3%
±0.5%
±23.3%±6.4%±15.1%±28.5%

±1.8%
±3.2%
±1.9%
±24.6%±6.4%±24.9%±35.8%

±1.9%
±9.5%
±4.8%
±8.6%
±5.3%
±6.0%
±15.9%

3p
eτhad
±1.0%
±16.8%±17.5%±14.6%±5.7%±6.0%±29.5%

j → τhadtt̄, tZ → ττ

±13.5%

±1.7%
±9.4%
±1.8%
±6.2%
±6.1%
±17.0%±23.6%±1.3%±18.7%±1.1%±32.7%±5.5%±16.5%±41.5%±10.6%

±1.2%
±8.5%
±2.7%
±8.3%
±6.0%
±16.5%±23.6%±23.2%
±0.4%
±0.3%
±2.4%
±6.5%
±31.9%±40.0%

miss
Table E.13: Values of systematic uncertainty variation to nominal expectation for the high-ET
categoryeτhad channel.

127

Uncertainty

ggF

bbA

Diboson
1p
µτhad

Muon
Jet
MET
TES
Tau
Theory
Total
Muon
Jet
MET
TES
Tau
Theory
Total

±0.7%
±2.0%
±1.3%
±8.9%
±5.9%
±15.1%±18.7%

±0.7%
±2.9%
±0.7%
±7.9%
±5.9%
±24.9%±26.9%

±1.0%
±3.3%
±1.0%
±9.8%
±6.3%
±15.1%±19.4%

±0.7%
±4.1%
±0.8%
±10.8%±6.3%±24.9%±28.2%±1.1%±11.0%±2.0%±10.3%±4.9%±6.0%±17.1%
3p
µτhad
±1.3%
±15.8%±5.3%±10.8%±5.6%±6.0%±21.5%

j → τhadtt̄, tZ → ττ

±11.5%

±0.9%
±4.1%
±1.7%
±7.5%
±6.1%
±12.0%±18.9%

±4.3%
±1.7%
±0.3%
±8.7%
±5.8%
±23.5%±26.2%±10.4%

±0.7%
±4.8%
±2.0%
±12.5%±6.0%±12.3%±21.8%±2.0%±10.3%±8.7%±26.8%±6.1%±24.1%±39.0%

misscategory
Table E.13: Values of systematic uncertainty variation to nominal expectation for the high-ETµτhad channel.

Uncertainty

ggF

bbA

Diboson
1peτhadElectron
Jet
FT
MET
TES
Tau
TheoryTotal
Electron
Jet
FT
MET
TES
Tau
TheoryTotal
Table E.13:
channel.

±1.6%±20.4%±25.0%±3.6%±11.3%±6.6%±15.1%±38.2%

±1.6%
±4.3%
±4.3%
±2.5%
±1.2%
±6.3%
±24.9%±26.6%±1.3%±21.3%±37.1%< 0.01%±18.2%±6.0%±15.1%±49.2%

±1.9%
±4.9%
±4.6%
±2.7%
±3.1%
±6.2%
±24.9%±26.9%±5.3%±14.6%±18.0%
±5.3%
±7.2%
±6.0%
±6.0%
±26.8%
3p
eτhad
±1.1%
±14.5%±10.3%±3.9%±19.2%±6.1%±6.0%±27.8%

j → τhad` → τhadtt̄, tZ → ττ

±15.9%±21.0%

±1.3%
±4.0%
±2.7%
±0.7%
±6.0%
±6.4%
±6.9%
±15.8%±3.5%±19.4%±10.9%
±5.4%
±6.4%
±6.9%
±5.4%
±25.6%±20.5%±21.0%

±1.7%
±4.4%
±2.8%
±0.9%
±7.6%
±6.0%
±7.2%
±16.6%±2.1%±11.6%±16.3%±25.9%±8.3%±6.4%±10.7%±36.0%

Values of systematic uncertainty variation to nominal expectation for the b-tag category eτhad

128

Uncertainty

ggF

bbA

j → τhadZ → ``(→ τ )tt̄, t(` → τ )tt̄, tDibosonZ → ττ

1p
µτhad

Muon
Jet
FT
MET
TES
Tau
Theory
Total
Muon
Jet
FT
MET
TES
Tau
TheoryTotal
Table E.13:
channel.

±7.0%±23.9%±18.8%±7.0%±16.3%±5.9%±15.1%±39.4%±2.0%±13.0%
±5.1%
±2.0%
±3.0%
±5.8%
±24.9%±29.4%±12.2%±1.6%±20.7%±8.7%±7.7%< 0.01%< 0.01%±5.0%±24.4%

±2.8%
±9.9%
±4.1%
±5.1%
< 0.01%< 0.01%±6.7%±14.0%±1.7%±21.0%±2.6%±17.3%
±5.3%
±6.3%
±7.1%
±29.5%±2.8%±24.0%±15.0%±8.2%±12.3%±5.0%±6.0%±33.0%±1.8%±15.6%±13.5%±20.9%
±8.5%
±6.8%
±9.6%
±32.8%±28.2%±25.6%±16.7%±24.4%±25.4%±6.0%±15.1%±56.9%±1.9%±10.2%±4.4%±3.9%±21.3%±6.0%±24.9%±35.4%±16.9%< 0.01%< 0.01%< 0.01%< 0.01%< 0.01%< 0.01%
±5.0%
±5.0%

±1.6%
±30.9%±5.5%±11.8%< 0.01%< 0.01%±10.0%±35.0%±1.7%±19.5%±2.8%±16.6%
±8.6%
±6.0%
±6.8%
±28.9%±1.1%±18.4%±13.4%±10.2%±10.6%±5.2%±6.0%±27.8%±3.8%±23.3%±9.7%±17.7%±9.4%±6.3%±10.6%±34.7%

3pµτhadValues of systematic uncertainty variation to nominal expectation for the b-tag category µτhad

Uncertainty
Electron
Jet
FT
MET
TES
Tau
TheoryTotal
Electron
Jet
FT
MET
TES
Tau
Theory
Total

ggF

bbA

Diboson

±1.5%
±4.1%
±0.4%
±1.4%
±0.3%
±6.3%
±15.1%±17.0%

±1.5%
±5.9%
±3.3%
±1.7%
±2.0%
±6.3%
±24.9%±26.7%

1p
eτhad
±1.5%
±2.3%
±0.3%
±1.1%
±5.1%
±6.5%
±6.0%
±10.7%

±1.6%
±2.5%
±0.5%
±1.8%
±3.1%
±6.1%
±15.1%±16.9%

±1.7%
±7.1%
±2.6%
±2.9%
±3.6%
±6.0%
±24.9%±27.1%

3p
eτhad
±2.0%
±1.9%
±0.4%
±2.1%
±7.2%
±5.7%
±6.0%
±11.5%

j → τhad` → τhadtt̄, tZ → ττ

±8.6%±21.0%±1.3%±6.3%±11.3%
±1.1%
±3.4%
±6.4%
±6.8%
±19.2%±1.4%±13.1%±0.2%±15.0%
±2.6%
±6.9%
±6.6%
±22.3%±8.6%±21.0%±1.5%±5.9%±10.7%
±2.0%
±6.4%
±6.0%
±7.2%
±19.6%

±1.5%
±5.2%
±0.2%
±11.0%
±1.1%
±6.4%
±7.7%
±15.8%

Table E.13: Values of systematic uncertainty variation to nominal expectation for the b-veto category eτhadchannel.

129

Uncertainty

ggF

bbA

j → τhadZ → ``(→ τ )tt̄, t(` → τ )tt̄, tDibosonZ → ττ

1p
µτhad

Muon
Jet
FT
MET
TES
Tau
Theory
Total
Muon
Jet
FT
MET
TES
Tau
Theory
Total

±1.9%
±6.3%
±0.4%
±2.8%
±6.6%
±5.9%
±15.1%±18.9%

±1.9%
±9.7%
±2.4%
±0.8%
±8.1%
±5.8%
±24.9%±28.7%

±8.1%

±1.0%
±2.9%
±0.1%
±5.1%
< 0.01%< 0.01%
±5.0%
±7.8%

±1.3%
±13.1%±5.0%±3.8%< 0.01%< 0.01%±8.3%±16.8%±1.6%±7.0%±10.3%
±1.2%
±4.4%
±6.2%
±7.1%
±19.2%

±1.4%
±2.5%
±0.3%
±0.7%
±5.6%
±5.3%
±6.0%
±10.2%

±1.1%
±8.5%
±0.2%
±14.8%
±5.6%
±6.7%
±8.1%
±20.9%

±1.8%
±7.2%
±0.4%
±1.8%
±10.0%±6.0%±15.1%±20.6%

±2.2%
±8.8%
±4.7%
±0.9%
±10.8%±5.9%±24.9%±29.6%

±8.2%

±5.7%
±4.4%
±0.4%
±7.0%
< 0.01%< 0.01%±5.0%±11.3%±4.7%±11.4%±1.3%±6.4%< 0.01%< 0.01%±9.3%±16.8%

±1.8%
±7.6%
±9.6%
±1.5%
±6.4%
±6.0%
±6.8%
±19.5%

±1.9%
±8.2%
±0.3%
±2.5%
±11.3%±5.9%±6.0%±16.6%

±1.1%
±7.1%
±0.1%
±11.9%
±6.3%
±6.3%
±7.4%
±18.1%

3pµτhad

Table E.13: Values of systematic uncertainty variation to nominal expectation for the b-veto category µτhad
channel.

130

F

Theoretical Systematic Uncertainties
Parameter

default

vari, 1vari. 2MPI

Hard interaction primordial k⊥
ISR αS
ISR pT cutoff
MPI pT cutoff

1.749480.118
1.923589
2.002887

1.719/1.780
1.919/1.928-

1.762/1.737
1.844/2.004-

2.05/1.97

Table F.13: Parameters of MC tuning variation for ggH signal samples.

Parameter

default

vari. 1vari. 2vari. 3avari. 3bvari. 3c

ISR pT cutoff
f max ISR evol. scaleµF,R dampling
ISR αSFSR αSMPI αS
Colour reconn. strengh

1.56
0.91
1.05
0.127
0.127
0.126
1.71

0.131/0.121
1.73/1.69

1.60/1.50
1.05/0.91
1.04/1.08
0.139/0.111-

1.67/1.51
0.98/0.88
1.36/0.93
0.136/0.124
0.125/0.127-

1.00/0.83
1.04/1.07
0.129/0.126
0.114/0.138-

0.140/0.115-

Table F.13: Parameters of MC tuning variation for ggH signal samples.

Sourcedescription

variation (%)

Scale

it is considered varying µF,R by factor of 0.5 and 2.0.
PDF uncertinties are evaluated by above way,
αS uncertinty is evaluated by takning 68% C.L. on its uncertinty.
mtop variation of ±1.0 GeV.
By taking enriched or reduced initial state radiation conditions.
Diff. between nom. and samples generated by aMC@NLO+Herwig.
Diff. between nom. and samples generated by Powheg+HerwigUE.

+2.37/ − 3.51

PDF + αS
mtop
Radiation
Hard process
Showering and UE±4.21+2.77/ − 2.70
shape plus ±0.92
shape plus ±0.51
shape plus ±1.98

Table F.13: Systematic uncertainties for tt̄ process. For radiation, hadronisation and parton showering
uncertinty, it is changed event rates and its shape on the final discriminant. It is shown in Figure 6.21 as aratio to nominal sample.

131

G

Validation of Maximum Likelihood Fit

For the validation of the values of the nuisance parameters obtained in the minimisation procedure
have been performed. Figure G.14 shows the fitted values of the nuisance parameters in the combined
likelihood fit using the benchmark scenario of mA = 600 GeV, tan β = 20. The impact of individual

Post Fit Impact
Pre Fit Impact
Pull

13 TeV, 28 fb−1
mA = 600 GeV
-0.02

-0.01

±1σ
0

∆µ̂

0.01

0.02

TAU SME TES DETECTORJET JER SINGLE NP
bbH Theory
FakeTau FFW HM 1p
FakeTau FFW bveto 1p
TAU SME TES INSITU
FakeTau FFQ bveto 1p
JET GroupedNP 1
Top Norm
TAU Id LowPt
LUMI 1516
FakeTau rQCD bveto muhad
FakeTau rQCD bveto ehad
ZJets Theory
FF e2tau
TAU SME TES MODEL
Top Theory
FakeTau FFQ bveto 3p
FakeTau FFW bveto 3p
ggH Theory
TopHardProcess
TAU Reco LowPt
FakeTau FFQ btag 1p
FakeTau FFW HM 3p
TopRadiation
MUONS ID
FT Eigen L 00
FT Eigen B 00
VV Theory
FakeTau rQCD btag muhad
EL Id
JET JVTFakeTau FFW btag 3p
FakeTau FFW btag 1p
TAU Reco TrueTauEleOLR
FT Eigen C 00
TopShowerUE
MET SoftTrk Scale
FakeTau FFQ btag 3p
FakeTau rQCD hMET muhad
Ztt Theory
FakeTau rQCD hMET ehad
JET GroupedNP 2
FakeTau FFQ HM 1p
FakeTau FFQ HM 3p
FakeTau rQCD btag ehad
MU Trig Stat
EG SCALE ALLCORRTAU Id HighPt
TAU Reco TrueEleEleOLR
FT Eigen B 01
TAU Reco HighPt
MET SoftTrk ResoPara
FT Eigen C 01
MET SoftTrk ResoPerp

-1.5

-1

-0.5

0

0.5

1

1.5

(θ̂ − θ0 )/∆θ
Figure G.14: Fitted values of the nuisance parameters obtained in the combined likelihood fit with mA= 600 GeV and tan β = 20 hypothesis. Each nuisance parameters show fitted value (opend circle) and its±1σ (black line), original ±1σ is given as gray line. The nuisance parameters are listed by ordering its post-fit
impact on the signal strength, it is shown in red filled region, while a pre-fit impact is shown in blue regions.

uncertainties on the results is defined as following. Each nuisance parameter is is fixed to its ±1σ
estimates and the impact on µ̂ is evaluated after re-minimising the combined likelihood with respect

132
to all other nuisance paramters of the fit model. The absolute change in the fitted signal strength ∆µ̂with respect to the default estimate is used as the impact on the model for the pre-fit and post-fit.
The highest ranked nuisance parameter is the uncertinty of the hadronic-τ energy scale on a detector
sumulation. This systematic uncertinty dramatically changes the mτ τ shape. The second highest
ranked nuisance paramter is the energy resolution of jet objects, in this analysis jet is not directly
miss , however, strongly depends on inputs from jet objects, so that this systematicused. The ET
uncertinty has strong impact on the mτ τ shape. In general, the uncertinties on the fake backgroundare constrained by the combined likelihood fit. Because the fake backgrund is leading background inall signal region and its property can be measured. This feature is confirmed using the Asimov data
result, the uncertinties related to the fake backgrund can potentially be constrained.
0

10

2

1

-3

-1

2 100 -0 -0 0
1 -0 100 2 -0
-0 2 100 0-1 0 -0 0 100

-3

-1

-1

2

-2

0

0

-0

0

0

0

-0

-2

-0

1

1

0

0

-0

-1

0

-2

-7

6

2

-13 -2

0

-0

-8

0

-0

-1

1

-0

-1

-0

2

-6

2

0

1

-0

-1

-11 10

0

0

-9

1

-0

-0

-2

0

-1

0

0

3

1

-1

4

-3

4

-1

19

1

0

-5

0

1

-0

-0

-0

3

-1
0

-1

-2

-0

2

7

5

-2

1

-0

-1

1

3

-6

-0

1

-1

-0

-3

-2

-7

-0

0

1

-1

-1

-2

4

9

-0

1

0

1

1

0

1

1

3

1

-0

-0

-0

1

2

0

-0

-3

-0

-0

-0

-0

1
-1

1

0

1
-1

1

-0

-20 -9

-1

-0

-6

-0

0

-1
-6

1

1

-0

-1

-0

-0

1

2

0

3

0

-3

0

-2

-21 -1

-0

-3

5
1

3

-0

4

-2

-1

2

-1

-1

5

4

-4

-5

-2

-2

0

0

-2

-2

4

1

-1

-1

2

0

1

1

2

1

0

-0

0

1

-0

-1

-0

0

1

1

0

0

1

-2

1

-0

-0

6

1

0

2

1

0

0

1

-0

0

1

1

1

0

1

-2

-1

1

1

0

0

-2

0

-2 100 -7 0
-7 -7 100 0

2

-1

11

4

-1

1

2

2

1

7

2

0

-4

-6

1

0

-0

8

-0

-5

7

1

-1

-1

0

-3

0

1

6

-0

-1

2

-8

-3

1

3

-0

0

2

0

-0

-0

-0

0 100 0 -0
11 0 100 2

0

0

-11

0

1

1

-0

0

-0

-0

0

-0

-0

-0

1

-0

0

-0

1

-0

-0

-0

0

-0

0

-0

0

0

-1

-0

0

1

-0

-0

1

-2

-2

-1 -21

5

-0

0

-0

5

-1

-0

-3

-5

-0

-4

-3

-1

-1

-1

-0

-1

-1

-1

0

-2

0

0

-0

0

0

-1

4

-0

2

-3

-1

-0

4

1

1

-0

1

0

-2

1

4

-0

1

-1

0

0

-7

-1

0

-0

-1

-1

-0

0

1

-0

-1

-1

0

-0

2

-0

-1

0

0

0

-1

23

-0

-0

1

-0

8

1

2

3

-2

2

-1

-2

-6

-2

1

0

0

2

1

2

-3

-2

-0

-6

-11 -110 2-2 -24 -0 -0
2 -1 -41 2

0

0
-0

-1

1

0

-2

0

-2

-9 -31 -2

1

19

-2

0

-6

1

-11 -1

-2

-1

-3

0

3

-1

5

10

-2

-2

-1

-2

-1

-2

-1

-1

-0

0

-2

0 100 9

11

2

-9

-0

-0

2

2

-0

-1

1

5

-2

2

-2

2

1

-1

-2

6

-3

-2

1

3

0

2

1

-0

0

-0

12

-4

-3

0

3

-0

-0

-3

0

1

-2

-2

-2

3

4

5

-5

-2

-0

1

0

-0

-1

18

0

-5

2

-1

-1

0

1

-6

-1

-1

-1

-5

-2

1

1

2

8

-3

11

-9

-4

-1

4

-0

2

8

-1

1

-0

-1

-4

0

-5

-7

0

0

-5

1

-1

2

-2

2

2

-1

5

-10 -4

-0

2

-0

0

11

-0

2

-0

-9

-1

-5

-4

2

-6

1

4

0

1

-1

-1

-0

-2

-1

-4

5

2

-0

-5

1 100 5 -1 1 -12
5 100 -1 1
52
8 -1 -1 100 61
6 100 0
1
-1 1
0 100
1 -12 5
1

2

0

-1

0

2

0

-1

0

0

1

-9

5

1

1

1

-0

1

4

1

7

1

-21 -2 2
5 -24 -1

-2

-1

-8

-0

-1

-0

-4

0

2

-0

-0

-2

-1

3

-3

-5

0

0

-0

-0 -41 -9-0 2 -31

2

-1

0

0

1

4

-0

1

-4

-0

2

0

0

-2

2

1

18

1

0

-1

-1

-2

-2

-6

-0

4

1

-1

1

-0

-0

0

FakeTau rQCD bveto ehad
FakeTau rQCD bveto muhad
FakeTau rQCD hMET muhad
JET GroupedNP 1
JET GroupedNP 2
JET JER SINGLE NP
JET JVT

-3

0

4

19

-2

1

1

0

-1

-1

23 19

-1

0

-3

-0

0

LUMI 1516
MET SoftTrk ScaleTAU Id LowPt
TAU Reco LowPt
TAU Reco TrueTauEleOLRTAU SME TES DETECTORTAU SME TES INSITUTAU SME TES MODEL
TopHardProcess
TopRadiation
TopShowerUE
Top Norm
Top Theory
ZJets Theory
Ztt Theory
bbH Theory
ggH Theory

1
-6

9

11
3
2

0

1

-1

-4

5

-1

7

-1

-5

-1

3

9

-10 130

4-18 -5

-1

-0

-0

-0

-0

5

-5

1

-0

-0

-0

-1

9

0

-0

-1

-0

2

3

-1

1

-7

3

-4

3

-0

-0

-1

0

-0

0

0

2

1

-7

2

1

1

1

-0

-3

-2

-1

5

1

2

1

2

1

1

-1

-0

0

7

-0

6

-1 -10 -1

1

3

-2

6

0

2

-7

-6

-1

-0

-1

-1

-0

1

-1

1

0

-1

-0

0

1

1

0

-0

-0

-0

-1

-6

0

-0

0

-0

0

-0

-2

1

-0

2

-0

11

5

-0

-0

7 100 0

-3

1

4

-0

1

-0

1

-1

0

-0

-0

0

-0

-0

-0

0

0

-0

0

-2

12

-1

-1

-0

-1

-0

0

-0

0 100 0

1

-0

-1

0

-0

1

-0

1

-3

-0

-2

6

8

-0

0

-7

1

-6 -11 -4

-1

-4

2

7

-0

2

6

-3

0

1

-0

-1

1

-0

1

-0

-1

-0

1

2

-3

0

0

-0

-1

-1

1

-1

1

3

-0

9

-7

-2

0

-5

-0

5

0

8

-11 -1

0

1

-5

-9

-5

9

-7 -10

4

-1

-0

1

-1

7

0

-3

-0

1

-1

5

3

-6

-7

-1

-1

0

2

-0

-6

0

-0

3

1

1

1

-0

-1

-1

2

-2

-2

-0

-1

0

-5

3

-0

1

1

1

0 100 -8 -1 -1 4
55
1 -8 100 1
1 -1 -1 -1-0 -1 1 100 3 -3 -14 -30
3 10
0 -0 -2-1 -1 10
4 -1 -3 0 100 -10 2

0

1

4

0

0

-1

1

-0

-1

3

-1

2

-0

-1

0

-4

9

-1

1

3

-0

-0

5

1

-2

-2

1

0

-1

-0

-1

-1

-2

-3

-2

-3

-1

-5

1

-2

1

1

5

2

-1

-3

5

-1

1

0

-0

-0

-0

2

0

-4

0

-5

1

-10 -0-6 13 2

-0

6

-1

-0

7

0

-0

-2

-2

-1

-0

-3

-0

2

0

-1

3

2

1

-2

-1

1

0

3

-3

0

-1

-0

-21 -1

-0

1

2

0

0

0

4

1

-2

-1

1

-2

1

2

4

4

-1

-2

2

0

1

0

-18

1

-1

-7

8

1

-5

-1

0

2

-0

0

2

1

1

-0

1

-0

-6

5

-1

-2

1

-2

2

-1

-1

0

2

0

0

1

-0

1

0

-1

-1

-1

1

7

-1

2

1

9

2

4

1

-0

-0

5

4

1

0

-1

1

1

-0

8

-1

1

1

1

-0

-0

-1

-1

0

-0

13

12

-3

9

-17

6

6

4

6

3

-4

-5

-1

-0

-0

1

-2

-1

-2

-2

-3

-1 -10 -4

0

3

-0

-1

1

2

-7

0

0

0

0

-2

-2

-1

-1

-1

0

-0 -18-0 -11

1
2

-0

-3

-1

-0

1

-12 -4

1

-3

-0

2

1

-1

0
-1 -14 -0 -10 100 5 -10 2
5 100 -18 -0 -2-1 -3 -2 2
-1 13 -0 -1 -10 -18 100 -4 1
1 12 11
2 -0 -4 100 0

-2

4

2

2

1

2

2

1

-3

-2

2

0

-2

1

-6

0

1

-0

9

-1

-7

-2

-0

1

0 100 -6 0
4 -1 50
1-2 -6 100 -3 0
0 -3 100 -2 -2 -1
4
0 -2 100 -4 -21
2
4
2 -1 1 -2 -4 100 -4
5
0 -1 -21 -4 100
1

-2

-1

0

-0

7

-1

3

1

6

0

-3

-0

-2

10

-2

-2

-7

5

-6

2

0

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-1 -17 -2

0

-2

-3

-3

1

-0

1

-1

1

1

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-5

-1

1

-2

6

3

8

2

-1

-1

3

1

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0

-1

2

1

6

-2

0

-1

-1

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-1

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1

1

1

0

-1

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-2

6

4

-3

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-1

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-4

2

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0

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1

6

-3

0

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-1

1

1

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-1

8

5

11

5

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3

1

-1

1

-1

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1

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2

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-5

-9 -10 -2

-0

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1

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6

-10 -00-12 -4

2

-6

-2

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1

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-4

0

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1
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-7

2

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2

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2

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5

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-18 -11

1

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1

1

-7

1

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3

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4

2

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3

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-27 -24 -2

1

2

-2

2

1

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-0

1

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FF e2tau

FT Eigen B 00

FT Eigen L 00

FakeTau FFQ HM 1p

FakeTau FFQ btag 1p

FakeTau FFQ btag 3p

FakeTau FFQ bveto 1p

FakeTau FFQ bveto 3p

FakeTau FFW HM 1p

FakeTau FFW HM 3p

FakeTau FFW btag 1p

FakeTau FFW btag 3p

FakeTau FFW bveto 3p

FakeTau rQCD btag ehad

FakeTau rQCD btag muhad

FakeTau rQCD bveto ehad

FakeTau rQCD bveto muhad

FakeTau rQCD hMET muhad

JET GroupedNP 1

JET GroupedNP 2

JET JER SINGLE NP

JET JVTLUMI 1516

MET SoftTrk ScaleTAU Id LowPt

TAU Reco LowPt

TAU Reco TrueTauEleOLRTAU SME TES DETECTORTAU SME TES INSITUTAU SME TES MODEL

TopHardProcess

TopRadiation

TopShowerUE

Top Norm

Top Theory

ZJets Theory

0

3

-0 -0
-0 100 2-0 2 100

Ztt Theory

FT Eigen C 00

0-0

6 100 -20 1 15
6
2 -20 100 00 100 0-0 1
0 100
-1 15 6

EL Id

0

-27 1
-1 -24 -0
1

SigXsecOverSM

2-0

EG RESOLUTION ALL

2

0

-0

-0

2

8

-0

-5

4

6

bbH Theory

-0

0

-0

0

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3

-1

1

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9 100 650
6 100 16 1
9
5 16 100 1

0

-2
-0

2

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-2 -11-11 -2

2

2

2

0

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0
2 100 -0 1
1 -0 100 11 -2
1 11 100 0

41

ggH Theory

2

0

6

-13 -1

1

0

-1

5

2

-1

FakeTau FFW bveto 1p

SigXsecOverSM
EG RESOLUTION ALL
EL Id
FF e2tau
FT Eigen B 00
FT Eigen C 00
FT Eigen L 00
FakeTau FFQ HM 1p
FakeTau FFQ btag 1p
FakeTau FFQ btag 3p
FakeTau FFQ bveto 1p
FakeTau FFQ bveto 3p
FakeTau FFW HM 1p
FakeTau FFW HM 3p
FakeTau FFW btag 1p
FakeTau FFW btag 3p
FakeTau FFW bveto 1p
FakeTau FFW bveto 3p
FakeTau rQCD btag ehad
FakeTau rQCD btag muhad

100
80
60
40
20
0
-20
-40
-60
-80
-100

Figure G.15: Mutual correlation coffieents of the nuisance paramters in percentage, only with the highly
correlated nuisance parameter pairs.

Figure G.15 shows the mutual correlation coffieents of the nuisance parameters with only highly
correlated nuisance parameter pairs. Large correlation cofficients would indicate potential degeneracies between parameters. The largest correlations are of the order of -40% and are found between
the fake factor systematic uncertinties. These uncertinties, in principle, should be separated in the
1- or 3-prong hadronic-τ decay channels, but the combined likelihood fit is perfromed together with
only eτhad or µτhad , so this behaviour is expected. The second largest correlations are of the orderof −20 ∼ −30% between the Z → τ τ theory and the hadronic-τ reconstruction and identification
uncertinties for the low-pT candidates. Since this signal hypotesis has higher-pT compared with one
from Z → τ τ background, so these systematic uncertinties dominate from Z → τ τ background, it isexpected behaviour.

133

Plots for the Post-Fit

high-ETmiss : `τhad

Events / 1 GeV

3

10

√

high-ETmiss : `τhad

Post-Fit

Datas = 13 TeV, 28.0fb−1

Z/γ ∗ → τ τtt̄, tFake τ

102

Dibosons
stat ⊕ syst
Pre-Fit10

104

Events / 1 GeV

H

√

103

Post-Fit

Datas = 13 TeV, 28.0fb−1

Z/γ ∗ → τ τtt̄, tFake τ

Dibosons
stat ⊕ syst
Pre-Fit

102
10

1

1

−1

10−2

10−2

1.2
1
0.8
30

1.2
1
0.8
25
1000

50

70

100

200

500

Obs/Bkg

10−1

Obs/Bkg

10

pT (`)[GeV]50(a) pT (τ` )Datas = 13 TeV, 28.0fb−1

Z/γ ∗ → τ τtt̄, tFake τ

Dibosons
stat ⊕ syst
Pre-Fit

10

102

√

10−2

10−2

1.2
1
0.8
10

1.2
1
0.8
100 120

miss(c) ET

400

1000

ETmiss [GeV]

Obs/Bkg

10−1

Obs/Bkg

10−1

250

Post-Fit

Z/γ ∗ → τ τtt̄, tFake τ

Dibosons
stat ⊕ syst
Pre-Fit

10

1

100

500

pT (τhad )[GeV]Datas = 13 TeV, 28.0fb−1

1

20

200

high-ETmiss : `τhad

Post-Fit

Events / 1 GeVEvents / 1 GeV√

100(b) pT (τhad )high-ETmiss : `τhad

102

70

150

200

300

400

1000

mtot
T [GeV](d) mτ τ

miss
Figure H.16: Distributions for several variables in the high-ET
category after the combined likelihood fit.
In the bottom panels a ratio of data and expected background model and the uncertainties correspond to thesystematic and statistical uncertainties are shown. All plots are in logarithmic scale in x- and y-axis. Red linein the ratio shows the ratio of pre-fit expectation.

134

Events / 1 GeV

10√

Post-Fit

Datas = 13 TeV, 28.0fb−1

Z/γ ∗ → τ τ
Fake ` → τ
tt̄, tFake τ

104
103

Dibosons
stat ⊕ syst
Pre-Fit102b-tag : `τhad

Events / 1 GeV

b-tag : `τhad
5

105

103

Dibosons
stat ⊕ syst
Pre-Fit

102
10

1

1
−1

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−2

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10−2

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0.8
30

1.2
1
0.8
25

50

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100

200

500

Obs/Bkg

10

pT (`)[GeV]50(a) pT (τ` )Post-Fit

Datas = 13 TeV, 28.0fb−1

Z/γ ∗ → τ τ
Fake ` → τ
tt̄, tFake τ

103

Dibosons
stat ⊕ syst
Pre-Fit

102

104

√

10−2

10−2

1.2
1
0.8
10

1.2
1
0.8
50 60

miss
(c) ET

ETmiss [GeV]

Obs/Bkg

10−1

80 100 120 150

Z/γ ∗ → τ τ
Fake ` → τ
tt̄, tFake τ

Dibosons
stat ⊕ syst
Pre-Fit

10

10−1

50 60

Post-Fit

Data

102

1

40

500

pT (τhad )[GeV]s = 13 TeV, 28.0fb−1

1

30

200

103

10

20

100

b-tag : `τhad

Events / 1 GeVEvents / 1 GeV√70(b) pT (τhad )b-tag : `τhad

Obs/Bkg

Z/γ ∗ → τ τ
Fake ` → τ
tt̄, tFake τ

10

−1

104

Data

s = 13 TeV, 28.0fb−1

4

10

Obs/Bkg√

Post-Fit

80 100120 150

200

300

400 500

1000

mtot
T [GeV](d) mτ τ

Figure H.17: Distributions for several variables in the b-tag category after the combined likelihood fit. In
the bottom panels a ratio of data and expected background model and the uncertainties correspond to thesystematic and statistical uncertainties are shown. All plots are in logarithmic scale in x- and y-axis. Red linein the ratio shows the ratio of pre-fit expectation.

135

108
107

√

Post-Fit

Datas = 13 TeV, 28.0fb−1

Z/γ ∗ → τ τ
Fake ` → τ
tt̄, tFake τ

106
105

Dibosons
stat ⊕ syst
Pre-Fit

4

10

103

b-veto : `τhad

Events / 1 GeVEvents / 1 GeV

b-veto : `τhad

8

10

107
105
103
10

10−1

10−2

10−2

1.2
1
0.8
30

1.2
1
0.8
25

500

Obs/Bkg1

10−1

Obs/Bkg

1

200

Dibosons
stat ⊕ syst
Pre-Fit

104

10

100

pT (`)[GeV]50(a) pT (τ` )Post-Fit

Datas = 13 TeV, 28.0fb−1

Z/γ ∗ → τ τ
Fake ` → τ
tt̄, tFake τ

6

10

105

Dibosons
stat ⊕ syst
Pre-Fit

104
3

10

7

10

√

s = 13 TeV, 28.0fb−1

10−2

10−2

1.2
1
0.8
10

1.2
1
0.8
50 60

miss
(c) ET

Obs/Bkg

10−1

Obs/Bkg1

10−1

ETmiss [GeV]

Dibosons
stat ⊕ syst
Pre-Fit10

10

80 100 120 150

Z/γ ∗ → τ τ
Fake ` → τ
tt̄, tFake τ

3

1

50 60

Post-Fit

Data

104

10

40

500

pT (τhad )[GeV]

105

102

30

200

106

102

20

100

b-veto : `τhad

Events / 1 GeVEvents / 1 GeV

107

√

70

(b) pT (τhad )b-veto : `τhad

108

Z/γ ∗ → τ τ
Fake ` → τ
tt̄, tFake τ

10

102

70

Data

s = 13 TeV, 28.0fb−1

6

102

50

√

Post-Fit

80 100120 150

200

300

400 500

1000

mtot
T [GeV](d) mτ τ

Figure H.18: Distributions for several variables in the b-veto category after the combined likelihood fit. In
the bottom panels a ratio of data and expected background model and the uncertainties correspond to thesystematic and statistical uncertainties are shown. All plots are in logarithmic scale in x- and y-axis. Red linein the ratio shows the ratio of pre-fit expectation.

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