Studies of Identification of
Boosted Higgs Decaying Heavy Flavor Quarks
in the LHC ATLAS Experiment（LHC-ATLAS 実験における重いフレーバークォークに崩壊する
ブーストされたヒッグス粒子の識別に関する研究）

Thesis submitted to
The University of Tokyo
for the degree ofMaster of Sciencein
Department of Physics

byJian Wu
January, 2024

Acknowledgements

Acknowledgements
First of all, I would like to extend my deepest gratitude to my supervisor, Prof. Junichi
Tanaka, for his continuous guidance and support throughout my research. His expertisein the field of particle physics and his patience in explaining complex concepts has been
invaluable to my academic journey.
Special thanks also go to Sanmay Ganguly for his expertise in physics analysis andvaluable advice about machine learning techniques. I would like to express my gratitude tosome members of the ATLAS Flavor-Tagging Xbb sub-group, particularly to Arely Cortes
Gonzelez, Jinchao Zheng, Adam Campbell Anderson and Samuel Van Stroud. Their experiences on the tagger development gave me a lot of inspiration and constructive suggestions on the detailed implementation of my research. I also express my profound gratitude
for the contributions of other ICEPP members, particularly Masahiko Saito, Takuya Nobeand Masahiro Morinaga. They have provided me with a lot of valuable advice in my research to help me overcome many technical difficulties.
Additionally, I would like to thank the senior students and my friends in the Tanaka
Lab: Tingyu Zhang, Jiaqi Zang, Marin Furukawa. Their willingness to share technicalexpertise extended beyond the confines of formal research discussions, encompassing aspects of daily life in Japan, offering a holistic support system that significantly contributed
to my overall experience.
Furthermore, my gratitude extends to other friends outside the academic realm inJapan, for their support and encouragement during my studies, and for making my academic journey not only enriching but also enjoyable. Finally, my heartfelt thanks to myfamily for their unconditional love and unwavering support, sustained me through thechallenges of academic rigor and also provided the emotional foundation necessary formy life.

I

Abstract

Abstract
The Higgs boson is a crucial part of the Standard Model (SM) of particle physics,
to explain the origin of the mass of elementary particles. The Large Hadron Collider(LHC) at CERN discovered the Higgs boson in 2012, and since then, detailed studiesof the Higgs boson are being performed. Thus, for precise measurement of the Yukawa
coupling of the Higgs boson to bottom and charm quarks, the identification of the Higgs
boson, especially those generated with high transverse momentum, is a crucial part of thē 𝑐 ̄ tagger is developed to tagging large-𝑅 jets
physics program. Recently, a novel 𝑋 → 𝑏𝑏/𝑐
containing boosted 𝑏-hadrons or 𝑐-hadrons, which may be of great importance for future
Higgs studies.
This thesis covers the introduction, calibration, and improvement attempts of thisnovel 𝑋 → 𝑏𝑏̄ tagger, called GN2X. The GN2X tagger efficiency is determined using
only MC, thus data-to-simulation efficiency correction factors (scale factors) need to be
extracted. The in-situ calibration of the 𝑋 → 𝑏𝑏̄ tagger is performed to determine thescale factors using 𝑍(→ 𝑏𝑏)̄ + jets and 𝑍(→ ℓℓ) + jets events for 𝑝𝑇 > 450 GeV withdata collected by the ATLAS experiment in Run 2 (140 fb−1 ). The dominant background,
dijet events, is modeled by fitting the data directly using an exponentiated polynomial or
polynomial function. The scale factors at 60% working point are measured to be 1.30 ±0.50 for 450 < 𝑝𝑇 < 500 GeV, 0.83 ± 0.27 for 500 < 𝑝𝑇 < 600 GeV, and 0.87 ± 0.27 for
600 < 𝑝𝑇 < 1000 GeV.

III

Table of Contents

Table of Contents
Acknowledgements ................................................................................ I
Abstract............................................................................................ III
Table of Contents .................................................................................V
List of Figures ....................................................................................IX
List of Tables......................................................................................XI
Chapter 1 Introduction .......................................................................... 1
1.1 The Standard Model ....................................................................... 1
1.1.1 Elementary Particles .................................................................. 1
1.1.2 Gauge Theory.......................................................................... 1
1.2 The Higgs Boson ........................................................................... 2
1.2.1 Higgs Boson Measurement .......................................................... 2
1.2.2 Higgs Production and Decay ........................................................ 2
1.2.3 VH Channel ............................................................................ 4
1.3 Boosted Higgs .............................................................................. 5
1.4 Thesis Structure ............................................................................ 7
Chapter 2 LHC-ATLAS Experiment ........................................................ 9
2.1 Large Hadron Collider .................................................................... 9
2.1.1 HL-LHC and Run 3 .................................................................. 11
2.2 ATLAS Detector .......................................................................... 11
2.2.1 Inner Detector ........................................................................132.2.2 Calorimeters ..........................................................................15
2.2.3 Muon Spectrometer .................................................................20
2.2.4 Trigger and Data Acquisition System .............................................21
Chapter 3 Data and Monte Carlo Samples ................................................23
3.1 Collision Data ..............................................................................23
3.2 Monte Carlo Samples ....................................................................23

V

Table of Contents

Chapter 4 Object Reconstruction and Jet Labeling .....................................25
4.1 Jets...........................................................................................25
4.1.1 Large-𝑅 Jets...........................................................................25
4.1.2 Track Jets ..............................................................................25
4.2 Tracks .......................................................................................25
4.3 Primary Vertex .............................................................................27
4.4 Muons .......................................................................................27
4.5 Electrons ....................................................................................28
4.6 Overlap Removal .........................................................................28
4.7 Large-𝑅 Jets Labeling ....................................................................29
Chapter 5 Calibration Strategy ..............................................................31
5.1 Methodology ..............................................................................31
5.2 Event Selection for the 𝜇post−tag Measurement .......................................32
5.2.1 Trigger Strategy ......................................................................32
5.2.2 Pre-selection ..........................................................................32
5.2.3 𝑝𝑇 Symmetry and Rapidity Cut ....................................................33
5.2.4 Large-𝑅 Jet Candidates..............................................................34
5.2.5 𝑋 → 𝑏𝑏̄ Tagger GN2X ..............................................................36
5.3 Event Selection for the 𝜇pre−tag Measurement ........................................39
Chapter 6 Signal and Background Modeling .............................................41
6.1 Modeling for the 𝜇post-tag Measurement ................................................41
6.1.1 Comparison of Data and Simulation...............................................41
6.1.2 Signal and Background Modeling .................................................44
6.2 Modeling for the 𝜇pre-tag Measurement .................................................48
6.2.1 Comparison of Data and Simulation...............................................48
6.2.2 Signal and Background Modeling .................................................48
Chapter 7 Results ...............................................................................51
7.1 Systematic Uncertainties .................................................................51
7.2 Results ......................................................................................52
Chapter 8 Conclusion and Outlook .........................................................57
References .........................................................................................59
Appendix A Additional Plots ..................................................................65
VI

Table of Contents

Appendix B Identifying Boosted Higgs Bosons Decaying using Graph Neural Network ...............................................................................73
Appendix C Studies of training GN2X tagger using Equivariant Subgraph Aggregation Networks ....................................................................77VII

List of Figures

List of Figures
Figure 1.1 Elementary particles in the SM [1]. .............................................. 2𝑚

Figure 1.2 Reduced coupling strength modifiers 𝜅F vF for fermions (F = 𝑡, 𝑏, 𝜏, 𝜇) and𝑚V√𝜅V v for weak gauge bosons (V = 𝑊 , 𝑍) as a function of their masses
𝑚F and 𝑚V [18]. .................................................................... 3

Figure 1.3 Feynman diagrams of the main Higgs boson production modes at the LHC[19]. .................................................................................. 4
Figure 1.4 Higgs boson production cross-sections (left) and branching ratios (right) asa function of the Higgs boson mass [20]. ....................................... 5
Figure 1.5 Boosted and resolved topologies. ................................................ 5
Figure 1.6 Normalized Higgs 𝑝𝑇 distribution in a 𝑍𝐻 MC sample at √𝑠 = 13 TeV and𝑚(𝐻) = 125 GeV. .................................................................. 7
Figure 2.1 Cern’s accelerator complex [25]. ................................................. 9
Figure 2.2 LHC/HL-LHC upgrade plan [31]................................................ 11
Figure 2.3 Schematic view of the ATLAS detector and its main components [24]. ...12
Figure 2.4 Schematic view of the interaction of different particles with the ATLAS detector [33]. ..........................................................................13
Figure 2.5 Schematic overview of the Inner Detector [34]................................14
Figure 2.6 3D vision of the barrel of the Inner Detector [35]. ............................14
Figure 2.7 Longitudinal view of the ATLAS calorimeter system [36]...................16
Figure 2.8 Accordion structure and the granularity of the different layers of thecalorimeter [37]. ...................................................................17
Figure 2.9 Geometry of the tile calorimeter module [24]..................................18
Figure 2.10 Geometry of the HEC module [24]. ...........................................19
Figure 2.11 Geometry of the FCal modules located in the end-cap cryostat [24]. .....19
Figure 2.12 Cut-away view of the ATLAS muon spectrometer [24].....................20
Figure 3.1 Cumulative luminosity versus time delivered to ATLAS (green) and recorded
by ATLAS (yellow) during stable beams for pp collisions at 13 TeV centreof-mass energy in LHC Run 2 [29]. ............................................23
Figure 4.1 The perigee representation [68]. .................................................26

IX

List of Figures

Figure 5.1 The 𝑝𝑇 symmetry distribution of the 𝑍 → 𝑏𝑏,̄ 𝑍 → 𝑞 𝑞 ̄ (𝑞 = 𝑢, 𝑑, 𝑠, 𝑐), 𝑊 →𝑞 𝑞,̄ dijets and 𝑡𝑡 ̄ samples. ..........................................................34
Figure 5.2 The rapidity difference distribution of the 𝑍 → 𝑏𝑏,̄ 𝑍 → 𝑞 𝑞 ̄ (𝑞 =𝑢, 𝑑, 𝑠, 𝑐), 𝑊 → 𝑞 𝑞,̄ dijets and 𝑡𝑡 ̄ samples. ......................................35
Figure 5.3 Truth labels of the leading large-𝑅 jet and the sub-leading large-𝑅 jet in 𝑍 →𝑏𝑏,̄ 𝑍 → 𝑞 𝑞 ̄ (𝑞 = 𝑢, 𝑑, 𝑠, 𝑐), 𝑊 → 𝑞 𝑞,̄ dijets and 𝑡𝑡 ̄ samples. .................35
Figure 5.4 The discriminant score of 𝐻(𝑏𝑏)̄ jets in 𝑍 → 𝑏𝑏,̄ 𝑍 → 𝑞 𝑞 ̄ (𝑞 =𝑢, 𝑑, 𝑠, 𝑐), 𝑊 → 𝑞 𝑞,̄ dijets and 𝑡𝑡 ̄ templates. The red line shows the cut value
for 60% WP. .......................................................................37
Figure 5.5 Schematic diagram of the 𝑍 → 𝑏𝑏̄ event selection............................38
Figure 5.6 Schematic diagram of the 𝑍 → ℓℓ event selection. ..........................40
Figure 6.1 The comparison of data and MC samples prediction before 𝑋 → 𝑏𝑏̄ tagger
for different 𝑝𝑇 bins. Different MC samples are stacked together. The MC
error is shown as the shaded band, but it’s too small to be seen. ............42
Figure 6.2 The comparison of data and MC samples prediction after 60% WP of 𝑋 → 𝑏𝑏̄
tagger for different 𝑝𝑇 bins. Different MC samples are stacked together. The
MC error is shown as the shaded band..........................................43
Figure 6.3 The mass distribution of 𝑍 → 𝑏𝑏,̄ 𝑍 → 𝑞 𝑞,̄ 𝑊 → 𝑞 𝑞,̄ 𝑡𝑡 ̄ templates after
50%, 60%, 70% and 80% working point of GN2X tagger. ..................44
Figure 6.4 The 𝜒 2 fits to the 𝑍 candidate mass distribution (𝑍 → 𝑏𝑏̄ template) via a
DSCB function, passing the 𝑋 → 𝑏𝑏̄ 60% WP for 450 ≤ 𝑝𝑇 < 1000 GeV.
.......................................................................................46
Figure 6.5 The 𝜒 2 fits to the 𝑍 candidate mass distribution based on only 𝑍 → 𝑏𝑏̄ anddijet MC templates (left) and all MC templates (right), passing the 𝑋 → 𝑏𝑏̄
60% WP for 450 ≤ 𝑝𝑇 < 500 GeV. .............................................47
Figure 6.6 The comparison of data and MC prediction for 𝑍 → ℓ+ ℓ− in three 𝑍-boson𝑝𝑇 bins...............................................................................49
Figure 7.1 The 𝑍 → 𝑏𝑏̄ candidate invariant mass distribution and applying the 𝑍(→̄𝑏𝑏)+jetsselection and the 𝑋 → 𝑏𝑏̄ 60% WP for events with the large-𝑅 jet 𝑝𝑇
in the 450 < 𝑝𝑇 < 500 GeV(a); 500 < 𝑝𝑇 < 600 GeV(b); 600 < 𝑝𝑇 < 1000
GeV(c) range. The fit result is shown by a red solid curve. Signal (green)
and background (blue) components are shown. ...............................53

X

List of Tables

List of Tables
Table 1.1 Production cross-sections of the 𝑚𝐻 = 125 GeV Higgs boson at the LHC[20]. .................................................................................... 3
Table 2.1 Design and performance of the LHC up to 2022 [26][27].....................10
Table 4.1 Track selection requirements, where 𝑑0 is the transverse impact parameter (IP)of the track, 𝑧0 is the longitudinal IP with respect to the primary vertex and𝜃 is the track polar angle. Shared hits are hits used in the reconstruction ofmultiple tracks. A hole is a missing hit, where one is expected, on a layer
between two other hits on a track. ...............................................27
Table 4.2 Truth label used in the analysis and its requirements. .........................29
Table 4.3 The fraction of each truth label of the leading large-𝑅 jet in 𝑍 → 𝑏𝑏,̄ 𝑍 →𝑞 𝑞 ̄ (𝑞 = 𝑢, 𝑑, 𝑠, 𝑐), 𝑊 → 𝑞 𝑞,̄ dijets and 𝑡𝑡 ̄ samples. .............................30
Table 5.1 Overview of the triggers used for the 𝜇post−tag Measurement. They are applied
as an OR and all are required to be active. The offline threshold corresponds
to the offline jet cut above which the triggers are 99% efficient [70]. ......33
Table 5.2 GN2X threshold values for all WPs with 𝑓Hcc = 0.02 and 𝑓top = 0.25 .....37
Table 5.3 The number of events for 𝑍 → 𝑏𝑏,̄ 𝑍 → 𝑞 𝑞 ̄ (𝑞 = 𝑢, 𝑑, 𝑠, 𝑐), 𝑊 →𝑞 𝑞,̄ dijets and 𝑡𝑡 ̄ templates with mass range 50 ≤ 𝑚 < 150 GeV from Run
2 MC simulation (normalized to 140 fb−1 ) after each selection. ............38
Table 5.4 Overview of single muon triggers used for the 𝜇pre−tag Measurement. They
are applied as an OR and all are required to be active. .......................39
Table 5.5 Overview of single electron triggers used for the 𝜇pre−tag Measurement. They
are applied as an OR and all are required to be active. .......................40
Table 6.1 Event yields for different Run 2 MC samples (normalized to 140 fb−1 ) before
𝑋 → 𝑏𝑏̄ tagger in different 𝑝𝑇 bins in large-𝑅 jet mass range 50 ≤ 𝑚 < 150
GeV. Statistical uncertainties of MC samples are shown. .....................41
Table 6.2 Event yields for different Run 2 MC samples (normalized to 140 fb−1 ) after
60% WP of 𝑋 → 𝑏𝑏̄ tagger in different 𝑝𝑇 bins in large-𝑅 jet mass range
50 ≤ 𝑚 < 150 GeV. Statistical uncertainties of MC samples are shown. ...41

XIList of Tables

Table 6.3 The parameters of the DSCB function from a fit to the 𝑍 → 𝑏𝑏̄ template for
the 𝑍 → 𝑏𝑏̄ MC templates after the 𝑋 → 𝑏𝑏̄ tagging requirement at 60%
working point for 450 ≤ 𝑝𝑇 < 1000 GeV. .......................................45
Table 6.4 The parameters of fitting signal and background models for different background treatments (only dijet or dijet+𝑊 + 𝑡𝑡)̄ after the 𝑋 → 𝑏𝑏̄ tagging
requirement at 60% working point for 450 ≤ 𝑝𝑇 < 500 GeV. ................47
Table 6.5 Optimal functions to describe the multijet background in the 𝜇post-tag measurement. ..................................................................................48
Table 7.1 The parameters of fitting the real data after the 𝑋 → 𝑏𝑏̄ tagging requirement
at 60% working point for different 𝑝𝑇 bins. .....................................54
Table 7.2 The parameters of fitting the MC samples after the 𝑋 → 𝑏𝑏̄ tagging requirement at 60% working point for different 𝑝𝑇 bins. ..............................55
Table 7.3 Post-tag (𝜇post-tag ) signal strength for the 𝑋 → 𝑏𝑏̄ tagger at 60 % efficiency
WP measured using 𝑍(→ 𝑏𝑏)̄ + jets calibration methods. ....................55
Table 7.4 Pre-tag (𝜇pre-tag ) signal strength measured using 𝑍(→ ℓ+ ℓ− )+jets calibration
methods...............................................................................55
Table 7.5 Pre-tag (𝜇pre-tag ) and post-tag (𝜇post-tag ) signal strength and the resulting signal
efficiency scale factors (SF) for the 𝑋 → 𝑏𝑏̄ tagger at 60 % efficiency WPmeasured using 𝑍(→ 𝑏𝑏)̄ + jets calibration methods. Systematic uncertainties
are also shown. ......................................................................56

XII

Chapter 1 Introduction

Chapter 1 Introduction
In this chapter, the SM is introduced in Section 1.1, and the Higgs measurement at
LHC is summarized and the role of the VH channel is briefly described in Section 1.2. In̄ 𝑐.̄ Then, the purpose
Section 1.3, the boosted Higgs is discussed, in particular, 𝐻 → 𝑏𝑏/𝑐of this thesis is given. Section 1.4 explains the structure of this thesis.

1.1 The Standard Model
1.1.1 Elementary Particles
The Standard Model (SM) of particle physics describes elementary particles and interactions between them. In SM, there are two types of elementary particles, fermionsand bosons, which are shown in Figure 1.1.
Quarks and leptons are fermions, which have 1/2 spin and build matter. There are
3 generations of quarks and leptons, and each particle has an antiparticle. The first generation of quarks and leptons are the lightest and most stable of three generations. The
second and third generations are heavier and except neutrinos, they can decay into the first
generation, which means that they can only be produced in high-energy environments.
Gauge bosons are bosons, which have 1 spin and mediate interactions. There are 3
forces in the SM: the electromagnetic force, the weak force and the strong force, which
are mediated by photon (𝛾), weak bosons (W± , Z) and gluons (g) respectively. Graviton(G) is the hypothetical gauge boson of gravity, which is not included in the SM.
The Higgs boson (H) is the only scalar boson in the SM. It has 0 spin is responsible
for the mass of elementary particles.

1.1.2 Gauge Theory
The SM is a gauge theory with the symmetry group SU(3)𝐶 × SU(2)𝐿 × U(1)𝑌 . The
SU(3)𝐶 group describes the strong interaction, which is mediated by gluons and acts onparticles with color charge. The SU(2)𝐿 × U(1)𝑌 group describes the electroweak interaction, which is mediated by the weak bosons and photons and acts on particles with weakisospin and weak hypercharge.

1Chapter 1 Introduction

Figure 1.1

Elementary particles in the SM [1].

1.2 The Higgs Boson
1.2.1 Higgs Boson Measurement
The Higgs boson was the last missing piece of the SM, which was discovered by
ATLAS and CMS experiments in 2012 [2-3]. The mass of the Higgs boson is measured
to be 125.11 ± 0.11 GeV [4]. The total width is measured to be 4.5+3.3
MeV [5].
−2.5
For the discovery of Higgs, evidence for Higgs was present in three decay modes
𝐻 → 𝛾𝛾, 𝐻 → 𝑊 𝑊 (∗) → ℓ𝜈ℓ𝜈 and 𝐻 → 𝑍𝑍 (∗) → 4ℓ in both experiments waspresent [6-11]. Then, the 𝐻 → 𝜏𝜏 was observed in 2016 [12] by CMS and in 2018 by
ATLAS [13]. After that, Higgs production in association with a top quark-antiquark pair(ttH) [14-15] and the 𝐻 → 𝑏𝑏̄ was confirmed in 2018 [16-17]. The summary of themeasured couplings to gauge bosons and fermions is shown in Figure 1.2. 𝐻 → 𝜇𝜇 and𝐻 → 𝑐 𝑐 ̄ are not confirmed yet and the observation of such decays is one of the mostimportant topics in Run 3 (2022-2025) and High-Luminosity LHC (HL-LHC, 2029-).

1.2.2 Higgs Production and Decay
The main Higgs production mechanisms at the LHC are as follows:• gluon-gluon fusion (ggF)2mm
κ F vF or κ V vV

Chapter 1 Introduction

1

ATLAS

s = 13 TeV, 24.5 - 79.8 fb−1
m H = 125.09 GeV, |y H | < 2.5, p SM = 78%

10−2

10

τ b

t

W

SM Higgs boson

10−1

−3

Z

68% CL
95% CLµm q (m H ) used for quarks−4κF or κV

10

1.4

10−1

1

102

10

Particle mass [GeV]

1.2
1
0.8

10−1

1

102

10

Particle mass [GeV]𝑚𝑚

Figure 1.2 Reduced coupling strength modifiers 𝜅F vF for fermions (F = 𝑡, 𝑏, 𝜏, 𝜇) and √𝜅V vV
for weak gauge bosons (V = 𝑊 , 𝑍) as a function of their masses 𝑚F and 𝑚V [18].

• vector boson fusion (VBF)• associated production with a vector boson (VH)̄• associated production with a top quark pair (ttH)
The detailed Feynman diagrams of these processes are shown in Figure 1.3. The
cross-sections for the production of an SM Higgs boson as a function of its mass areshown in Figure 1.4(a). Table 1.1 shows the Higgs boson production cross-sections andrelative uncertainties for a Higgs boson mass of 125 GeV at √𝑠 = 7, 8, 13 and 13.6 TeV.
Table 1.1

√𝑠 (TeV)

Production cross-sections of the 𝑚𝐻 = 125 GeV Higgs boson at the LHC [20].

Production cross-section (pb) for 𝑚𝐻 = 125 GeV
ggF

VBF

WH

ZH

̄
ttH

Total

7

16.9+5.5%−7.6%

1.24+2.2%−2.2%

0.58+2.2%−2.3%

0.34+3.1%−3.0%

0.09+5.6%−10.2%

19.1

8

21.4+5.4%−7.6%

1.60+2.1%−2.1%

0.70+2.1%−2.2%

0.42+3.4%−2.9%

0.13+5.9%−10.1%

24.2

13

48.6+5.6%−7.4%

3.78+2.1%−2.1%

1.37+2.0%−2.0%

0.88+4.1%−3.5%

0.50+6.8%
−9.9%

55.1

13.6

54.7+5.6%−7.4%

4.28+2.1%−2.1%

1.51+1.8%−1.9%

0.99+4.1%−3.7%

0.61+6.9%
−9.8%

62.1

The Higgs boson branching ratios and production cross-sections are shown in Figure
3Chapter 1 Introduction

q

q

g

H
H

q

g

(a) ggFqq(b) VBF
g

H

t, b

H

q

g

W, Z

̄
(d) ttH(c) VH
Figure 1.3

t, bFeynman diagrams of the main Higgs boson production modes at the LHC [19].

1.4(b). 𝐻 → 𝑏𝑏̄ is the dominant decay mode of the Higgs boson, which is 58.2% for
𝑚𝐻 = 125 GeV. ggF and VBF are the 1st and 2nd largest cross-sections. However, they
can not be used for 𝐻 → 𝑏𝑏̄ search, because of the large amount of multijet background.
Therefore, the VH channel, the 3rd largest cross-section, is the most promising channel
to observe the 𝐻 → 𝑏𝑏̄ decay. It has about 1 pb cross-section in the SM. In this channel,
signal events can be selected efficiently using final state leptons from the vector boson
decay.

1.2.3 VH Channel
In the VH channel, the Higgs boson is produced in association with a vector boson.
There are three channels depending on number of reconstructed leptons:• VH → 𝜈𝜈qq (V=Z, 0-lepton channel)• VH → ℓ𝜈qq (V=W, 1-lepton channel)• VH → ℓℓqq (V=Z, 2-lepton channel)
Using the decay products of the gauge boson (V), we can trigger the events and also
reduce the background. VH channel is the most sensitive Higgs production channel,
and thus, it is one of the promising channels to observe charm Yukawa coupling using
4

1
bb

10-1

10

-2

1

10

pp → ZH (NNLO QCD + NLO EW)

120

10-3

4FS)

pp → tH (NLO QCD)

122

cc
ZZ
γγ

pp → ttH (NLO QCD + NLO EW)
pp → bbH (NNLO QCD in 5FS, NLO QCD in

10−1

WW
gg
ττ

pp → qqH (NNLO QCD + NLO EW)
pp → WH (NNLO QCD + NLO EW)

LHC HIGGS XS WG 2016

s= 13 TeV

pp → H (N3LO QCD + NLO EW)

LHC HIGGS XS WG 2016

σ(pp → H+X) [pb]102

Branching Ratio

Chapter 1 Introduction

Zγ
µµ

124

126

10-4
120 121 122 123 124 125 126 127 128 129 130128130MH [GeV]MH [GeV](a)(b)

Figure 1.4 Higgs boson production cross-sections (left) and branching ratios (right) as a functionof the Higgs boson mass [20].

a boosted event topology, which is explained in the next section.

1.3 Boosted Higgs
The LHC’s high collision energies can lead to the generation of Higgs bosons withtransverse momenta (𝑝𝑇 ) significantly higher than their mass. There are two kinds ofevent topologies possible for the 𝑉 𝐻 channel, the boosted and resolved topologies, as
Figure 1.5 shows. The boosted Higgs bosons exhibit highly collimated decay products,
and in cases of fully hadronic decays, they can be reconstructed as a single hadronic jet.
̄ 𝑐 ̄ decays, it’s reconstructed as a large-𝑅 jet and the 𝑏/𝑐-quarks are
For boosted 𝐻 → 𝑏𝑏/𝑐
reconstructed as subjets. On the contrary, with the resolved topology, the Higgs boson
candidate was reconstructed from two 𝑏-tagged small-𝑅 jets in the event. Due to thehighly collimated 𝑏-jets at large transverse momentum, with the resolved topology, theHiggs boson candidate reconstruction efficiency was highly degraded.

Figure 1.5

Boosted and resolved topologies.

In addition, during years of runs and upgrades, the LHC has been operated from √𝑠 =5

Chapter 1 Introduction

7 to 13.6 TeV and the production of the Higgs boson at 𝑚𝐻 = 125 GeV from pp collisions
increased from 19.1 fb to 55.1 fb. A 400 fb−1 total integrated luminosity is expected tobe collected by the end of Run 3 1 . In the future, as the LHC gears up (HL-LHC), theinstantaneous luminosity will increase, and more data of 3,000 fb−1 will be collected,
enabling further observation and study of bottom or charm quark Yukawa couplings.
The expected number of events from WH/ZH can be evaluated using MC samples. By
using 𝑍𝐻 MC sample shown in Fig 1.6, the efficiency of the boosted Higgs (𝑝𝑇 > 450
GeV) is estimated as about 0.33 %., Because 𝑍 and 𝑊 mass are similar, this value isassumed to be also applicable to 𝑊 𝐻. By using this value, the number of events can becalculated as follows:
𝑁0-lepton = ℒ × 𝜎 × BR(𝐻 → 𝑏𝑏/𝑐𝑐) × BR(𝑍 → 𝜈𝜈) × 𝜖
𝑁1-lepton = ℒ × 𝜎 × BR(𝐻 → 𝑏𝑏/𝑐𝑐) × BR(𝑊 → ℓ𝜈) × 𝜖
𝑁2-lepton = ℒ × 𝜎 × BR(𝐻 → 𝑏𝑏/𝑐𝑐) × BR(𝑍 → ℓℓ) × 𝜖
where ℓ means 𝑒 or 𝜇, ℒ is the luminosity, 𝜎 is the cross-section and 𝜖 is the efficiency.
Thus, a total of about 411 𝑉 𝐻, 𝐻 → 𝑏𝑏̄ events and 20 𝑉 𝐻, 𝐻 → 𝑐 𝑐 ̄ events are expected
to be collected in Run 3. In the HL-LHC, a total of about 3,078 𝑉 𝐻, 𝐻 → 𝑏𝑏̄ events and
160 𝑉 𝐻, 𝐻 → 𝑐 𝑐 ̄ events are expected to be collected. However, to get these values, any
selection except Higgs 𝑝𝑇 is not taken into account, so they are just for the ideal case.
The identification of the boosted Higgs bosons (Xbb tagger) is performed with deeplearning, which is explained in Section 5.2.5. Such a development is done based on
the simulated data but it will be applied to data. So, one of the important tasks to use
the boosted object identification tool is the calibration, that is, the tool is tuned to data
properly. This thesis focuses on the calibration of a new Xbb tagger, GN2X, usinḡ
𝑍(→ 𝑏𝑏)+jet
events. boosted 𝑍(→ 𝑏𝑏)̄ + jets and 𝑍(→ 𝑒𝑒/𝜇𝜇) + jets events. The GN2X
[21] Xbb tagger has been developed for the coming Run 3 analysis including Run 2 data.
The method used is based on the previous study [22] but uses a new Xbb tagger and MC
simulated data for Run 3 analysis with a new ATLAS software release.

1

In Fig 2.2, the expected integrated luminosity is 450 fb−1 at the end of Run 3 but due to an issue with the LHC
accelerator in 2023, data of 70 fb−1 was taken in 2022-2023. So, here we assume 400 fb−1 instead of 450 fb−1 .

6Normalized number of events

Chapter 1 Introduction

10−1

10−2

10−3

10−4

0

100 200 300 400 500 600 700 800 900 1000
Higgs p [GeV]T

Figure 1.6
125 GeV.

Normalized Higgs 𝑝𝑇 distribution in a 𝑍𝐻 MC sample at √𝑠 = 13 TeV and 𝑚(𝐻) =1.4 Thesis StructureThis thesis introduces the LHC and ATLAS experiment in Chapter 2. Chapter 3
presents the data and MC samples used in this thesis. The objection reconstruction andthe jet labeling used are introduced in Chapter 4. Chapter 5 shows the methodology of thecalibration for the Xbb tagger. Then, the signal and background modeling are discussed
in Chapter 6. The results are presented in Chapter 7. Finally, Chapter 8 concludes thisthesis and gives an outlook for future work.

7

Chapter 2 LHC-ATLAS Experiment

Chapter 2 LHC-ATLAS Experiment
The Large Hadron Collider (LHC) [23] is the world’s largest and most powerful particle accelerator, which is located at the European Organization for Nuclear Research(CERN) in Geneva, Switzerland. The ATLAS (A Toroidal LHC ApparatuS) detector [24]is a general-purpose detector at the LHC. In this chapter, the LHC is briefly introduced in
Section 2.1, and the ATLAS detector is described in Section 2.2.

2.1 Large Hadron Collider
The LHC is a circular proton-proton (pp) collider with a ring with a circumference of
27 km buried 100 m underground. It is designed to accelerate two counter-rotating beams
of protons to a center-of-mass energy of 13.6 TeV. The two proton beams are accelerated
in opposite directions in two separate beam pipes, which are kept at ultrahigh vacuum andare brought into collision at four interaction points (IP), where the detectors are located.
The accelerator complex of the LHC is shown in Figure 2.1.

Figure 2.1

Cern’s accelerator complex [25].

9Chapter 2 LHC-ATLAS Experiment

The luminosity of the LHC is defined by the following equation:ℒ=

𝑁𝑏2 𝑛𝑏 𝑓rev 𝛾𝑟

𝐹,
(2.1)
4𝜋𝜖𝑛 𝛽 ∗where 𝑁𝑏 is the number of particles per bunch, 𝑛𝑏 is the number of bunches per beam,𝑓rev is the revolution frequency, 𝛾𝑟 is the relativistic gamma factor, 𝜖𝑛 is the normalized
transverse beam emittance, 𝛽 ∗ is the beta function at the collision point, and 𝐹 is thegeometric luminosity reduction factor due to the crossing angle at the interaction point.
The design and performance of the LHC up to 2022 are summarized in Table 2.1.
Table 2.1

Design and performance of the LHC up to 2022 [26][27].

Parameter

Design

2015

2016

2017

2018

2022

Energy (TeV)

7.0

6.5

6.5

6.5

6.5

6.8

Number of bunches

2808

2244

2220

2556-1868

2556

2748

Max. stored energy (MJ)

362

280

280

315

312

400

55

80

40

40→30

30→27→25

60

Bunch population, 𝑁𝑏 (10 p)

1.15

1.2

1.25

1.25

1.1

1.4

Normalized Emittance Stable Beams (𝜇m)3.752.6-3.5

1.8-2

1.8-2.2

1.8-2.2

1.8

34

1.0

<0.6

1.5

2.0

2.1

1.9

𝛽 ∗ (cm)
11−2 −1

Peak Luminosity (10 cm s )The primary goal of the LHC is to search for the Higgs boson and new physics beyond
the Standard Model (SM). The Higgs boson was discovered by the ATLAS and CMS
experiments in 2012 [2-3].
The energy collision at 7 TeV started in 2010 (Run 1). After two years of operation,
the collision energy was increased to 8 TeV in 2012 (Run 1). The LHC was shut down
for two years for maintenance and upgrade. Run 2 started in 2015 and the beam energyof the LHC was increased to 6.5 TeV, which corresponds to a center-of-mass energy of
13 TeV. After Run 2, the LHC was shut down again for a three-year upgrade and started
Run 3 in 2022 with 13.6 TeV.
In Run 1, the LHC delivered the collision data with a total integrated luminosity of
5.46 fb−1 at 7 TeV and 22.8 fb−1 at 8 TeV [28]. In Run 2, the LHC delivered a total
integrated luminosity of 156 fb−1 at 13 TeV [29]. In Run 3 till 2023, the LHC delivered
70 fb−1 at 13.6 TeV [30].
To achieve such high luminosity, the LHC delivers as high as possible collision rates.
As a direct consequence, an effect called pile-up which means multiple proton-protoninteractions occur in the same or nearby bunch crossings, pollutes the final state of thecollision events.
10Chapter 2 LHC-ATLAS Experiment2.1.1 HL-LHC and Run 3
The LHC has been continuously upgraded to increase the collision’s energy and luminosity. Figure 2.2 shows the operation and upgrade plan of the LHC. After Run 3,
the LHC will enter into three years of the long shutdown 3 (LS3) for the installation of
new upgrades for the High Luminosity phase of LHC (HL-LHC). The HL-LHC runs areplanned to start from 2029 with a luminosity of 5 to 7.5 times the design one.

LHC
Run 1
LS1

7 TeV

8 TeV

HL-LHC

Run 2

13 TeV

Run 3
LS2

EYETS

splice consolidation
button collimators
R2E project

cryolimit
interaction
regions

13.6 TeV

Diodes Consolidation
LIU Installation
pilot beam

Civil Eng. P1-P5

Run 4 - 5...
EYETS
inner triplet
radiation limit

LS3

2027

experimentbeam pipes
75% nominal Lumi

upgrade phase 1

30 fb-1

2 x nominal Lumi

2028

2040

ATLAS - CMS
HL upgrade

2 x nominal Lumi

ALICE - LHCb
upgrade-1
integrated 3000 fb
luminosity 4000 fb-1

450 fb-1

190 fb-1

HL-LHC TECHNICAL EQUIPMENT:
DESIGN STUDY

2029

5 to 7.5 x nominal Lumi

ATLAS - CMS
nominal Lumi

13.6 - 14 TeV

HL-LHC
installation

PROTOTYPESCONSTRUCTIONINSTALLATION & COMM.

PHYSICS

HL-LHC CIVIL ENGINEERING:
DEFINITION

Figure 2.2

EXCAVATIONBUILDINGS

LHC/HL-LHC upgrade plan [31].

2.2 ATLAS Detector
The ATLAS experiment at the LHC features a multi-purpose particle detector characterized by a forward-backward symmetric cylindrical design with comprehensive coverage nearing 4𝜋 in solid angle. The detector comprises an inner tracking detector(ID) enveloped by a slender superconducting solenoid, alongside electromagnetic andhadronic calorimeters, a muon spectrometer (MS), and a trigger and data acquisition system (TDAQ). Notably, the ATLAS detector spans a length of 44 meters, boasts a diameterof 25 meters, and impressively weighs 7000 tons. The schematic view of the ATLAS detector is shown in Figure 2.3.
The nominal interaction point (IP) is located at the center of the detector, defining theorigin of the ATLAS coordinate system right-handed. The 𝑥-axis points from the IP tothe center of the LHC ring. The 𝑦-axis points upward. The 𝑧-axis is defined by the beam
direction. Therefore the 𝑥-𝑦 plane is the transverse plane. Additionally, on this plane, the11Chapter 2 LHC-ATLAS Experiment

Figure 2.3

Schematic view of the ATLAS detector and its main components [24].

coordinates 𝜙 and 𝑟 are defined as the azimuthal angle and the radial distance from thebeam axis, respectively.
The pseudorapidity 𝜂 for particles coming from the primary vertex [32] is defined as:𝜂 = − ln tan(𝜃/2),
where 𝜃 is the polar angle with respect to the 𝑧-axis. Therefore the 𝜂 is zero for particles
traveling along the 𝑥-𝑦 plane, and infinity for particles traveling along the 𝑧-axis.
The rapidity 𝑦 is defined as:
1 𝐸 + 𝑝𝑧ln,
2 𝐸 − 𝑝𝑧
where 𝐸 is the energy and 𝑝𝑧 is the momentum along the 𝑧-axis. Differences in rapidity𝑦=are invariant under Lorentz boosts along the 𝑧-axis and the density of emitted particles
as a function of rapidity 𝑑𝑁
is invariant under longitudinal boosts. For highly relativistic𝑑𝑦particles (𝐸, 𝑝 ≫ 𝑚), the rapidity 𝑦 is approximately equal to the pseudorapidity 𝜂.
To help the reconstruction of the collision events, quantities such as transverse momentum 𝑝𝑇 = 𝑝 sin 𝜃 and transverse energy 𝐸𝑇 = 𝐸 sin 𝜃 are used. Also, to measure theangular distance of two objects, a quantity Δ𝑅 is used:
Δ𝑅 = √(Δ𝜂)2 + (Δ𝜙)2 ,where Δ𝜂 and Δ𝜙 are the differences in pseudorapidity and azimuthal angle, respectively.
As particles pass through, they interact with sub-systems that capture details like their

12Chapter 2 LHC-ATLAS Experiment

trajectory, momentum, and energy as hits and energy deposits (cells). The way particles
interact with these sub-systems differs for each particle, as illustrated in Figure 2.4. This
interaction influences the materials employed in the sub-detectors and guides the methods
for particle reconstruction and identification in ATLAS.

Figure 2.4

Schematic view of the interaction of different particles with the ATLAS detector [33].

In this section, the ID, calorimeters, MS and TDAQ are briefly introduced in Section
2.2.1, 2.2.2, 2.2.3 and 2.2.4, respectively.

2.2.1 Inner Detector
The inner tracking detector covers the pseudorapidity range |𝜂| < 2.5 and provides
high-precision measurements of the trajectories of charged particles in the magnetic field.
The ID is immersed in a 2 T axial magnetic field provided by a thin superconducting
solenoid and contained in the cylindrical envelope of length 3.5 m and diameter 1.15 m.
It consists of three sub-detectors: the pixel detector, the semiconductor tracker (SCT),
and the transition radiation tracker (TRT). The overview of the ID is shown in Figure 2.5.
As shown in Figure 2.6, the innermost component is the pixel detector, followed by the
SCT and the TRT. The pixel detector and the SCT cover the range |𝜂| < 2.5, while theTRT covers the range |𝜂| < 2.0.

13Chapter 2 LHC-ATLAS Experiment

Figure 2.5

Schematic overview of the Inner Detector [34].

Figure 2.6

3D vision of the barrel of the Inner Detector [35].

14Chapter 2 LHC-ATLAS Experiment

Pixel Detector The innermost detector in ATLAS is the pixel detector, tasked with precisely measuring the trajectories of charged particles. Its role extends beyond track reconstruction, encompassing the measurement of track impact parameters relative to theprimary vertex. The barrel region features 4 layers, and each end-cap region has 3 disks,
resulting in a total of 80.4 million channels. The pixel’s innermost layer, known as theb-layer, plays a crucial role in secondary vertex measurement.
Semiconductor Tracker The SCT is positioned following the pixel detector and consists of 4 concentric cylindrical layers of silicon microstrip detectors in the barrel region
surrounding the beam axis. The end-cap region is equipped with 9 disks, each containing
up to 3 rings of modules. Each SCT layer is constructed with 2 microstrips to capture hit
space points, with one strip aligned parallel to the beam axis and the other rotated at astereo angle of 40 mrad.
Transition Radiation Tracker The TRT is a tool designed for electron identification
through the measurement of transition radiation. It consists of straws, each having a 4
mm diameter tube filled with a gas mixture (70% Ar, 27% CO2 , and 3% O2 in Run 2). As
charged particles pass through, they ionize the gas within the straw, causing free electrons
to drift towards a centrally located gold-tungsten wire with a diameter of 31 𝜇m. The wireis maintained at a potential of −1500 V.

2.2.2 Calorimeters
The ATLAS detector utilizes sampling calorimeters with complete 𝜙 coverage. The
overall structure of the ATLAS calorimeter system is depicted in Figure 2.7. Electromagnetic (EM) energy measurements, characterized by high granularity, are obtained throughlead/liquid-argon (LAr) sampling calorimeters. Hadronic energy measurements in thecentral pseudorapidity range (|𝜂| < 1.7) are provided by a steel/scintillator-tile hadronic
calorimeter known as TileCal. LAr calorimeters are employed in the endcap and forward
regions to measure both electromagnetic and hadronic energies up to |𝜂| = 4.9.
LAr Electromagnetic Calorimeter The EM calorimeter can measure electron and photon energy and a part of jet energy. It uses liquid argon (LAr) as the active material andlead as the absorber. The liquid argon is chosen because of its radiation hardness andlinearity of the response. The lead absorber induces electromagnetic showers when an
15

Chapter 2 LHC-ATLAS Experiment

Figure 2.7

Longitudinal view of the ATLAS calorimeter system [36].

electron or a photon passes through it. The shower and the ionized particles are detectedby the LAr cells and then used for the energy measurement.
The calorimeter is divided into three parts: the barrel (EMB), the end-cap (EMEC)
and the forward (EMFCAL) regions. EMFCAL is described in the next paragraph of thehadronic calorimeter. The barrel region cover the pseudorapidity range 0 < |𝜂| < 1.475,
while the end-cap region covers the range 1.375 < |𝜂| < 3.2. The LAr calorimeter has afour-layer structure (layers 0, 1, 2, 3), and an accordion geometry is used for the absorbers
and the electrodes. Figure 2.8 shows the three-layer structure (layers 1, 2, 3) of the LAr
calorimeter and the accordion geometry.
The front layer (layer 1) is highly granular of 𝜂 to measure the start of the showers
and to distinguish between single isolated photons and 2 photons from 𝜋 0 decays. The
middle layer (layer 2) collects the majority of the shower energy. The back layer (layer 3)
is used to contain the showers and measure the energy leakage beyond the middle layer.
Additionally, the resampler (layer 0) is used to provide a measurement of the energy lostin front of the EM calorimeter in the range of 0 < |𝜂| < 1.8. The resolution of the EM
calorimeter is parameterized as:
𝜎(𝐸)
𝑎
𝑏
=
⊕
⊕ 𝑐,
𝐸
√𝐸[GeV] 𝐸[GeV](2.2)

where 𝑎 is for the stochastic behavior of the shower development, 𝑏 accounts for the electronic noise and pile-up, and 𝑐 quantifies the non-uniformity of the calorimeter response,
16Chapter 2 LHC-ATLAS Experiment

Figure 2.8

Accordion structure and the granularity of the different layers of the calorimeter [37].

aging and the radiation damage. The pile-up noise means energy deposits from otherproton-proton collisions in the same or nearby bunch crossings. The intrinsic sampling
term 𝑎 is typically about 10% √GeV [38], the noise term 𝑏 is 10 MeV to 600 MeV without pile-up contribution [39] and is expected to be 30 MeV to 3 GeV in Run 3 pile-up
conditions [40], and the constant term 𝑐 is 1% to 2% [41].
Hadronic Calorimeter The hadronic calorimeter is designed to measure the energyof hadrons, which consists of the tile calorimeter (TileCal), the LAr hadronic end-cap
calorimeter (HEC) and the LAr forward calorimeter (FCal).
Tile Calorimeter The tile calorimeter plays a crucial role in reconstructing the energy of hadrons and jets, as well as measuring the missing transverse energy 𝐸𝑇miss . It spansthe pseudorapidity range |𝜂| < 1.7. Specifically, the central barrel covers 0 < |𝜂| < 1.0,
while the two extended barrels span 1 < |𝜂| < 1.7. To address the transition region,
special modules composed of steel scintillator sandwiches are employed. The structureof the tile calorimeter is illustrated in Figure 2.9, where each barrel is subdivided into 64
modules. The steel grid establishes a 1.5 mm modular gap at the inner radius, serving
17

Chapter 2 LHC-ATLAS Experimentboth as the volume for readout electronics and as the flux return for the solenoid field.

Figure 2.9

Geometry of the tile calorimeter module [24].

Hadronic End-cap Calorimeter The HEC, which is a sampling calorimeter, employs LAr as the active material and flat-plate-designed copper as the absorber integrated
with the end-cap cryostat, it spans the pseudorapidity range of 1.5 < |𝜂| < 3.2. Comprising two wheels per end-cap, each wheel is made up of 32 identical wedge-shaped
modules. Figure 2.10 illustrates the HEC’s structure, with the front wheel containing 24
copper plates and the back wheel featuring 16 copper plates.
Forward Calorimeter The end-cap cryostat incorporates the Forward Calorimeter(FCal), covering the pseudorapidity range of 3.2 < |𝜂| < 4.9. This positioning exposes
the FCal to high fluxes, necessitating a design with LAr gaps to prevent ion build-up
issues and ensure maximum density. The FCal consists of three modules, illustrated in
Figure 2.11. One module employs copper as the absorber to enhance resolution and heat
18

Chapter 2 LHC-ATLAS Experiment

Figure 2.10

Geometry of the HEC module [24].

removal for electromagnetic measurements. The remaining two modules use tungsten as
the absorber, focusing on containing hadronic showers and minimizing their spread. Thisconfiguration allows the FCal to deliver accurate measurements of forward jets while
concurrently reducing background interference in the muon spectrometer.

Figure 2.11 Geometry of the FCal modules located in the end-cap cryostat [24].

19Chapter 2 LHC-ATLAS Experiment2.2.3 Muon Spectrometer
The muon spectrometer aims to deliver accurate standalone measurements of muons
up to 3 TeV within the |𝜂| < 2.7 range. Positioned as the outermost component of the
ATLAS detector, it encases the calorimeters. The capacity to reconstruct high-momentum
muons, even in the absence of ID information, facilitates rapid muon triggering in the|𝜂| < 2.4 region.
Figure 2.12 shows the arrangement of the muon spectrometer, consisting of threelarge superconducting air-core toroidal magnets, each with eight coils. The field integralof the toroids ranges from 2.0 to 6.0 Tm across the muon detectors. For precise tracking,the muon spectrometer incorporates Monitored Drift Tube Chambers (MDT) and Cathode
Strip Chambers (CSC). The system also includes fast detectors for triggering purposes:
Resistive Plate Chambers (RPC) and Thin Gap Chambers (TGC) within the |𝜂| < 2.4
range. This system ensures a Bunch-Crossing Identification (BCID) efficiency exceeding 99%, well-defined 𝑝𝑇 thresholds, and the measurement of the unbending direction ofmuon tracks.

Figure 2.12

Cut-away view of the ATLAS muon spectrometer [24].

20Chapter 2 LHC-ATLAS Experiment

Monitored Drift Tubes The barrel MDTs cover the range |𝜂| < 1.05, as well as theend-cap MDTs cover the range 1.05 < |𝜂| < 2.7. Their size increases with the distancefrom the interaction point. They are arranged in three to eight layers of drift tubes, filledwith a gas mixture of 93% Ar and 7% CO2 . The average resolution for a single tube is 80
𝜇m and for a chamber is 35 𝜇m.
Cathode Strip Chambers

The CSC is used in the forward region of the muon spec-

trometer, covering the range 2.0 < |𝜂| < 2.7, to improve the resolution under the highhit rate near the beam pipe. Similar to end-cap MDTs, the CSCs are arranged in 8 large
sectors and 8 small sectors. Trigger time for the CSC is less than 30 ns and the average
resolution is 60 𝜇m.
Resistive Plate Chambers

In the muon spectrometer’s barrel region, RPCs are em-

ployed to cover the range |𝜂| < 1.05. These RPCs consist of parallel resistive plates anda 2 𝜇m gas-filled gap. The RPC’s time resolution is approximately 1.5 nm, while theposition resolution is around 1 cm.
Thin Gap Chambers

The TGCs are used in the end-cap region of the muon spectrom-

eter, covering the range 1.05 < |𝜂| < 2.4. The time resolution of the TGC is about 4 ns
and the position resolution is around 2 to 6 mm.

2.2.4 Trigger and Data Acquisition System
The LHC is designed to produce a staggering 1.6 billion proton-proton collisions
every second in the case of the averaged pile-up value of about 40, generating a combined
data volume of approximately 60 TB/s for the ATLAS system. With protons bunchingup and intersecting every 25 ns, around 40 million collisions occur per second, and eachbunch carries about 1011 protons. Operating at the designed luminosity of 1034 cm−2 s−1 ,an average of 20 interactions take place per bunch crossing. Due to this high rate, asophisticated trigger system selectively captures only a small fraction of the collisions.
The ATLAS trigger system carries out the selection process in two stages. The firststage is the hardware-based Level-1 (L1) trigger, which reduces the event rate from thenominal 40 MHz bunch crossing rate to a maximum recording rate of 100 kHz. The
second stage is the software-based High-Level Trigger (HLT), which further reduces theevent rate to a few hundred Hz for permanent storage and offline analysis.
21

Chapter 2 LHC-ATLAS Experiment

Level-1 Trigger The L1 trigger functions as a hardware-based system, utilizing information from the calorimeters and muon spectrometer at reduced granularity. Capable ofprocessing a maximum input rate of 40 MHz, it efficiently identifies noteworthy events
within a time frame of less than 2.5 𝜇s from the collision. Subsequently, the triggered
objects’ geometric locations are transmitted to the next tier of the trigger system in theform of Regions of Interest (RoI) at an event rate of 100 kHz.
High-Level Trigger The HLT is a software-based system. Its operation relies primarilyon commercially available computing resources and networking infrastructure. With theutilization of the complete detector granularity of the RoI supplied by the L1 trigger, the
HLT is capable of managing input rates ranging from 75 to 100 kHz.

22

Chapter 3 Data and Monte Carlo Samples

Chapter 3 Data and Monte Carlo Samples
3.1 Collision Data
The analysis targets the dataset gathered in ATLAS during Run 2 (2015-2018), whichcorresponds to luminosities of 36.4 fb−1 , 44.6 fb−1 , 58.8 fb−1 for triggers used in the2015+2016, 2017 and 2018 data-taking periods, respectively [42]. The total luminosity
is 140 fb−1 , which is obtained by applying detector operation quality requirements etc. tothe recorded data as shown in Figure 3.1.

Figure 3.1 Cumulative luminosity versus time delivered to ATLAS (green) and recorded by
ATLAS (yellow) during stable beams for pp collisions at 13 TeV centre-of-mass energy in LHC
Run 2 [29].

3.2 Monte Carlo Samples
All simulated events were run through the full detector simulation [43] using Geant4[44]. The effects of pile-up from multiple proton-proton interactions in the same andnearby bunch crossings are modeled by overlaying minimum bias events, simulated using
the soft QCD processed of Pythia 8.186 [45] with the A3 tune [46] and the NNPDF2.3LO[47] parton distribution function (PDF) set. The average number of interactions per crossing obtained from data is used for the pile-up effect simulation. For all simulated event
23

Chapter 3 Data and Monte Carlo Samples

samples, except for those generated using Sherpa [48], the EvtGen 1.6.0 program [49]is used to describe the decays of bottom and charm hadrons. The simulated events areprocessed through the same reconstruction algorithms as the data.
𝑍(→ 𝑏𝑏)̄ + jets, 𝑍(→ 𝑞 𝑞)̄ + jets (𝑞 = 𝑢, 𝑑, 𝑠, 𝑐) and 𝑊 (→ 𝑞 𝑞)̄ + jets processes are
simulated with the Sherpa 2.2.8 [50] generator using matrix elements with next-to-leading
order (NLO) accuracy for one additional parton, and matrix elements accurate to leading
order (LO) for up to four partons calculated with the Comix and OpenLoops libraries.
They are matched with Sherpa PS [51] using the MEPS@NLO prescription and the set of
tuned parameters developed by Sherpa authors. The NNPDF3.0NNLO set of PDFs [52]is used and the samples are normalized to an NNLO prediction.
The process of the multijet events, which is called multijets or dijets, is generatedusing Pythia 8.235 generator, using the A14 PS and hadronization tune and NNPDF2.3LO
PDF set.
The process of 𝑡𝑡 ̄ is simulated with the Powheg Box v2 [53-54] generator together with the NNPDF3.0NLO [52] PDF set. The simulated events were interfaced to
Pythia8.230 [46] for parton shower (PS) and hadronization using the A14 tune [55-56]
together with the NNPDF2.3LO PDF set. The top-quark mass was set to 172.5 GeV andthe ℎ𝑑𝑎𝑚𝑝 parameter, which controls the transverse momentum (𝑝𝑇 ) of the first additionalemission beyond the Born configuration, was set to 1.5 times the top-quark mass. The 𝑡𝑡 ̄
production cross-section is corrected to the theory prediction calculated at next-to-nextto-leading (NNLO) order and next-to-next-to-leading log approximation. The production of 𝑡𝑡 ̄ + 𝑊 /𝑍 is simulated with the aMC@NLO 2.3.3 [57] and Pythia8.210 using
NNPDF2.3NLO PDF set.
Diboson (𝑊 𝑊 , 𝑊 𝑍 and 𝑍𝑍) processes were simulated with Sherpa 2.2.1, interfaced with the NNPDF3.0NNLO PDF sets for both the matrix element calculation and
the PS. Sherpa provides a combination of different matrix elements with different parton
multiplicities: processes with zero or one additional partons are calculated at NLO in thematrix element, while two or three additional partons are included at LO in QCD.
The 𝑍 → ℓℓ (ℓ = 𝑒, 𝜇) events are generated using Sherpa 2.2.8 and with exactly
the same setup as for the hadronically decaying 𝑍 events. 𝑍 → ℓℓ events have been
generated with MadGraph using multileg leading order approach up to 4 additional parton
in the matrix element with the ckkw merging approach. Pythia 8.230 has been used in theparton shower.

24

Chapter 4 Object Reconstruction and Jet Labeling

Chapter 4 Object Reconstruction and Jet Labeling
4.1 Jets
4.1.1 Large-𝑅 Jets̄ 𝑐,̄ 𝑍 → 𝑏𝑏/𝑐
̄ 𝑐,̄ 𝑊 → 𝑞 𝑞,̄ etc. are reA boosted object originating from 𝐻 → 𝑏𝑏/𝑐
constructed as a single object, which is called large-𝑅 jet. In this analysis, the inputs tothe large-𝑅 jet reconstruction algorithm are Unified Flow Objects (UFOs) [58]. UFOs
are obtained from merging Particle-Flow Objects (PFOs) [59] and Track-Calo Clusters(TCCs) [60]. They have neutral and charged components. The PFO and TCC are constructed from both calorimeter clusters and tracks but their algorithms are different. The
former is a typical method of so-called particle-flow, that is, cells or clusters matched tocharged tracks are considered as charged components and the remaining as neutral. On
the other hand, the latter is an algorithm specialized for high 𝑝𝑇 objects, that is, the direction is obtained from a charged track and the energy from a cluster. The large-𝑅 jets
are built using the anti-𝑘𝑇 algorithm [61] with radius parameter 𝑅 = 1.0 implemented in
FastJet [62]. Pile-up and underlying event contributions are removed via grooming with
the Soft-Drop algorithm [58] along with Constituent Subtraction [63] and SoftKiller [64].

4.1.2 Track Jets
Smaller radius jets (subjets) are used to investigate the constitute of the large-𝑅 jets forthe identification of heavy flavor hadrons. In this study, the variable-radius (VR) track jets
are used as subjets. Charged tracks reconstructed from the inner detector are used to form
subjets using the anti-𝑘𝑇 algorithm. For VR subjets, the radius parameter 𝑅 is defined
as a function of the jet 𝑝𝑇 and a constant parameter 𝜌 = 30 GeV, scaling as 𝑅 = 𝜌/𝑝𝑇 .
Minimum and maximum values for the radius parameter are kept as 𝑅𝑚𝑖𝑛 = 0.02 and𝑅𝑚𝑎𝑥 = 0.4. The VR subjets are ghost-associated [65] to the large-𝑅 jet and are required
to have 𝑝𝑇 > 7 GeV.

4.2 Tracks
The reconstructed trajectories of charged particles, known as tracks, are reconstructedby utilizing hits that these particles create while passing through the inner detector. The
25

Chapter 4 Object Reconstruction and Jet Labelingprecise reconstruction of tracks is a critical task because they play a crucial role in reconstructing various other objects such as vertices and jets. The process of track reconstruction in the Inner Detector involves employing a series of algorithms, as detailed in Ref.
[66-67].
Tracks are described using a perigee representation, employing five parameters anda reference point, as shown by Figure 4.1. The reference point utilized corresponds to theaverage position of the proton-proton interactions (beamspot position). The five parameters are outlined below:• The transverse impact parameter 𝑑0 , representing the projection of the point of closest approach in the transverse direction.
• The longitudinal impact parameter 𝑧0 sin 𝜃, denoting the projection of the point ofclosest approach along the 𝑧-axis direction.
• The inverse transverse momentum 𝑝/𝑝𝑇 , providing information about the curvatureof the particle track.
• The track azimuthal angle 𝜙, indicating the direction of the track in the 𝑟-𝜙 planeat the point of closest approach; 𝜙 ranges between [−𝜋, 𝜋].
• The track polar angle 𝜃, varying within the range [0, 𝜋].
𝑑0 , 𝑧0 sin 𝜃, 𝑝/𝑝𝑇 are primary parameters to evaluate the tracking performance.

Figure 4.1

The perigee representation [68].

Tracks are ghost-associated to the large-𝑅 jet and are required to satisfy the track
selection summarised in Table 4.1.
26

Chapter 4 Object Reconstruction and Jet Labeling

Table 4.1 Track selection requirements, where 𝑑0 is the transverse impact parameter (IP) of the
track, 𝑧0 is the longitudinal IP with respect to the primary vertex and 𝜃 is the track polar angle.
Shared hits are hits used in the reconstruction of multiple tracks. A hole is a missing hit, where
one is expected, on a layer between two other hits on a track.
Parameter

Selection

𝑝𝑇> 500 MeV

|𝑑0 |< 3.5 mm|𝑧0 sin 𝜃|< 5.0 mm

Silicon hits

≥8

Shared silicon hits

<2

Silicon holes<3

Pixel holes<2

4.3 Primary Vertex
The process of reconstructing interaction vertices involves utilizing a set of reconstructed tracks. Tracks may originate either from a primary vertex (PV), which is theinteraction point between two partons, or from a secondary vertex (SV) resulting fromparticle decays, photon conversions, or hadronic interactions.
Generally, the reconstruction of the PV occurs through three sequential steps. Initially, a seed position is determined based on the beam spot in the transverse plane. Subsequently, the selected tracks and seeds are fitted to establish the best-estimated vertex
position. Once the vertex position is defined, tracks incompatible with the vertex are
eliminated. The discarded tracks are then employed to initiate a new PV, and this process
is reiterated until there are no unassociated tracks remaining or no additional vertices canbe identified. It is a requirement for PVs to be associated with a minimum of two tracks.
Additionally, a single track may be linked to multiple vertices. The PV exhibiting thehighest sum of squared transverse momenta for its associated tracks is designated as thehard-scatter PV, and the remaining PVs are categorized as interaction vertexes from thepile-up.

4.4 MuonsMuon tracks are reconstructed independently in the inner detector and the muon spectrometer. They are required to have a minimum number of hits in each system, and must
be compatible in terms of geometrical and momentum matching. Finally, the informationfrom both the inner detector and muon spectrometer systems is used in a combined fit to27

Chapter 4 Object Reconstruction and Jet Labelingrefine the muon momentum measurement. In this analysis, muons are required to pass”medium” identification and ”tight” track-based isolation criteria. Muons are required tohave a transverse momentum above 20 GeV and |𝜂| < 2.5. The muon reconstruction
efficiency and the muon momentum scale and resolution corrections are measured in data
and applied to the simulated events.

4.5 Electrons
Electrons are reconstructed from energy deposits in the calorimeter matched to innerdetector tracks. In order to select and identify electrons, requirements are imposed on the
track properties and quality, the shape of the clusters of calorimeter energy deposits and thetrack-to-cluster match. In this analysis, the identification is performed using a likelihood
technique and is required to pass a ”medium” working point. Electrons are further required
to be isolated by imposing the ”tight” isolation working point requirement. This isolation
requires the absence of nearby tracks within a 𝑝𝑇 -dependent variable-size cone aroundthe electron. The electron energy scale is calibrated in data, and the energy resolution iscalibrated in MC, using 𝑍 → 𝑒+ 𝑒− events. Electrons are required to have a transverse
momentum above 20 GeV and |𝜂| < 2.5, excluding the crack region (1.37 < |𝜂| < 1.52).
The significance of the transverse impact parameter, |𝑑0 |/𝜎(𝑑0 ), is required to be less than
5.0. The quantity |𝑧0 sin 𝜃| is required to be less than 0.5 mm, where 𝑧0 is the longitudinal
impact parameter, to ensure that electrons are consistent with having been produced at the
primary vertex.

4.6 Overlap Removal
The following overlap removal procedure is applied to resolve ambiguities in which
multiple electrons, muons or jets are reconstructed from the same detector signature.
First, any electrons that share a track are removed. Second, if an electron and a muonshare a track, the electron is rejected if the muon is associated with a signature in themuon spectrometer, otherwise, the muon is rejected. Third, any jet within Δ𝑅 < 0.2
of an electron is rejected. Fourth, any jets within Δ𝑅 < 0.2 of a muon are rejected
if they have fewer than three associated tracks. Fifth, any electrons or muons within𝑙𝑒𝑝

Δ𝑅 < min(0.4, 0.04 + 10 GeV/𝑝𝑇 ) of a jet passing the previous requirements are rejected. Finally, any large-𝑅 jet found within Δ𝑅 < 1.0 of an electron is rejected.

28

Chapter 4 Object Reconstruction and Jet Labeling

4.7 Large-𝑅 Jets Labeling
The large-𝑅 jet truth labeling defines the acceptance of the analysis. Truth matchingis done in two steps: [69]• First, match a truth particle to truth jets such that Δ𝑅(truth particle, truth jet) < 0.75,
and get the truth label of the truth jets
• Further match a reconstructed VR jet to a truth jet such that Δ𝑅(truth jet, reco jet)
< 0.75, and copy the truth label of the matched truth jet to the reco jet
Table 4.2 shows the truth label used in the analysis and its requirements.
Table 4.2

Truth label used in the analysis and its requirements.

Num.

Label

Requirements
There are a matched top quark and 𝑊 boson;
there is at least one 𝐵-hadron;
the truth jet mass is larger than 140 GeV.
There is at least one 𝑐 or 𝑢-quark in the first 2 leading partons;
and their invariant mass is in the 60-140 GeV range;
the truth jet mass is in the 50-100 GeV range.
There’re at least 2 ghosted associated 𝑏-hadrons;
and their invariant mass is in the 50-140 GeV range;
the truth jet mass is in the 50-110 GeV range.
There’re at least 2 ghosted associated 𝑐-hadrons;
and their invariant mass is in the 50-140 GeV range;
the truth jet mass is in the 50-110 GeV range.
The first 2 leading partons are with opposite charge;
and their invariant mass is in the 50-140 GeV range;
the truth jet mass is in the 50-110 GeV range.
There are a matched top quark and 𝑊 -boson;
there is no 𝑏-hadron;
the truth jet mass is in the 50-100 GeV range.

1

tqqb

2

Wqq

3

Zbb

4

Zcc

5

Zqq

6

Wqq from top

7other from top

8other from V

9no truth

There is no matched truth jet.

10

QCD

The truth jets are not matched to any heavy particles.

There is only a matched top quark.
There is at least one 𝑐 or 𝑢-quark in the first 2 leading partons
OR the first 2 leading partons have opposite charge;
their invariant mass is required in the 60-140 GeV range.

As explained in Section 3.2, There are MC samples of 𝑍(→ 𝑏𝑏)̄ + jets, 𝑍(→ 𝑞 𝑞)̄ +jets (𝑞 = 𝑢, 𝑑, 𝑠, 𝑐), 𝑊 + jets and 𝑡𝑡 ̄ etc. in this analysis. In the MC events, there arēdifferent types of large-R jets in one specific process, for example, even in 𝑍(→ 𝑏𝑏)+jets,
there are large-𝑅 jets of Zbb, Zqq or even QCD. So, the following templates (a set of large𝑅 jets) are prepared using the following truth-matching requirement. The details fractionof each truth label in each sample is shown in Table 4.3.
29

Chapter 4 Object Reconstruction and Jet Labeling• 𝑍 → 𝑏𝑏̄ template: It is created from the 𝑍(→ 𝑏𝑏)̄ + jets sample. The large-𝑅 jets
are required to be labeled as Zbb.
• 𝑍(→ 𝑞 𝑞)̄ + jets (𝑞 = 𝑢, 𝑑, 𝑠, 𝑐) template: It is created from the 𝑍(→ 𝑞 𝑞)̄ + jets
sample. The large-𝑅 jets are required to be labeled as Zqq or Zcc.
• 𝑊 → 𝑞 𝑞 ̄ template: It is created from the 𝑊 (→ 𝑞 𝑞)̄ + jets sample. The large-𝑅 jets
are required to be labeled as Wqq or Other from V.
• 𝑡𝑡 ̄ template: It is created from the 𝑡𝑡 ̄ sample. The large-𝑅 jets are required to belabeled as tqqb, Wqq from top or other from top.
• dijet template: It is created from the dijet sample. The large-𝑅 jets are required tobe labeled as QCD.
Table 4.3 The fraction of each truth label of the leading large-𝑅 jet in 𝑍 → 𝑏𝑏,̄ 𝑍 → 𝑞 𝑞 ̄ (𝑞 =𝑢, 𝑑, 𝑠, 𝑐), 𝑊 → 𝑞 𝑞,̄ dijets and 𝑡𝑡 ̄ samples.
Leading large-𝑅 jets fraction
𝑍 → 𝑏𝑏̄

𝑍 → 𝑞𝑞 ̄

tqqb

0

0

Wqq

0

Zbb

Sub-leading large-𝑅 jets fraction
𝑍 → 𝑏 𝑏̄ 𝑍 → 𝑞 𝑞 ̄ 𝑊 → 𝑞 𝑞 ̄
𝑡𝑡 ̄
dijet

𝑊 → 𝑞𝑞 ̄

𝑡𝑡 ̄

dijet

0

0.62

0

0

0

0

0.53

0

0

0.56

<0.01

0

0

0

0.34

<0.01

0

0.48

<0.01

0

0

0

0.39

<0.01

0

0

0

Zcc

<0.01

0.12

0

0

0

<0.01

0.08

0

0

0

Zqq

0.03

0.45

0

0

0

0.02

0.26

0

0

0

Wqq from top

0

0

0

0.07

0

0

0

0

0.08

0

other from top

0

0

0

0.11

0

0

0

0

0.15

0

other from V

Truth labels

<0.01

<0.01

0.01

<0.01

0

<0.01

0.02

0.03

<0.01

0

no truth

0

<0.01

<0.01

<0.01

<0.01

<0.01

<0.01

<0.01

<0.01

<0.01

QCD

0.49

0.42

0.43

0.2

1

0.58

0.64

0.63

0.23

1

30

Chapter 5 Calibration Strategy

Chapter 5 Calibration Strategy
This section introduces methods to calibrate GN2X tagger signal efficiency usinḡ
𝑍(→ 𝑏𝑏)+jets
events at high 𝑍-boson transverse momenta, discusses relevant systematic
uncertainties and presents the results of the calibration. This calibration method has beendeveloped based on Ref. [22], but the analysis in this thesis is based on a new Xbb tagger
and uses a new version of ATLAS software release (version 22), which will be used for
Run 3 and reprocessed Run 2 data.

5.1 Methodology
The efficiency of the GN2X tagger to select 𝑍 → 𝑏𝑏̄ signal events in data (𝜖 data ) isdata)
defined as the number of data events 1 which pass the GN2X tagger requirement (𝑁passed
data
divided by the total number of signal events in data (𝑁total). Due to imperfect modeling of

the MC simulation process, this can be different from the efficiency in simulation (𝜖 MC ):

MC
MC
data
data
𝜖 data = 𝑁passed/𝑁total, 𝜖 MC = 𝑁passed/𝑁total.

(5.1)

Thus a data-to-simulation scale factor (SF) needs to be measured (SF = 𝜖 data /𝜖 MC )and applied to the MC simulation to correct the difference between data and simulation.
The equation can be rewritten as:
MC
data
data
data
𝜖 data 𝑁passed /𝑁total 𝑁passed /𝑁passed 𝜇post−tag.
SF = MC = MC==𝜇pre−tag𝜖𝑁/𝑁 MC
𝑁 data /𝑁 MC
passed

total

total

(5.2)

total

The values 𝜇post−tag and 𝜇pre−tag are the number of signal events in data divided by the
number of signal events in MC simulation before and after the GN2X tagger requirement,
respectively.
̄
Huge backgrounds make the 𝜇pre−tag measurement using 𝑍(→ 𝑏𝑏)+jets
events in data
before the GN2X tagger impossible. Thus, the 𝜇pre−tag is measured using 𝑍(→ ℓ+ ℓ− ) +jets , ℓ = 𝑒, 𝜇 process, which exhibits a smaller relative background contribution. The

1

Strictly speaking, the GN2X tagger is applied to each boosted object in an event. So, the number of data eventsmeans ”the number of objects”. However, in this study, there is exactly one object (”the leading large-R jet”) per
event. So, the term ”event” is used.

31

Chapter 5 Calibration Strategy

number of signal events in data before tagging can be estimated by:
MC
data
𝑁𝑍→𝑏
= 𝑁𝑍→𝑏
⋅
𝑏̄
𝑏̄

data
𝑁𝑍→ℓℓ
MC
𝑁𝑍→ℓℓ

MC
= 𝑁𝑍→𝑏
⋅
𝑏̄

MC
data
𝑁ℓℓ
− 𝑁bkg,ℓℓ
MC
𝑁𝑍→ℓℓ

,

(5.3)

MC
where 𝑁𝑍→𝑏is the number of 𝑍 → 𝑏𝑏̄ signal events in MC simulation before tagging,
𝑏̄
MC
data
is the number of background events𝑁ℓℓis the number of selected events in data, 𝑁bkg,ℓℓMC+ −in MC simulation and 𝑁𝑍→ℓ+ ℓ− is the number of 𝑍 → ℓ ℓ signal events in MC simu-

lation. Thus, the 𝜇pre−tag can be calculated as:𝜇pre−tag =

MC
data
𝑁ℓℓ
− 𝑁bkg,ℓℓ
MC
𝑁𝑍→ℓℓ

,

(5.4)

and depends only on the yields of 𝑍 → ℓ+ ℓ− channel. The event selections for 𝑍 → 𝑏𝑏̄
and 𝑍 → ℓ+ ℓ− events are described in Section 5.2 and 5.3, respectively.
The SFs are measured as a function of the 𝑍-boson candidate 𝑝𝑇 . As the large-𝑅
jet 𝑝𝑇 > 450 GeV, in order to have a uniform division of the 𝑝𝑇 range with respect toavailable statistics, three leading large-𝑅 jet 𝑝𝑇 bins are defined based on the numberof events observed in the data: 450 < 𝑝𝑇 < 500 GeV, 500 < 𝑝𝑇 < 600 GeV and
600 < 𝑝𝑇 < 1000 GeV.

5.2 Event Selection for the 𝜇post−tag Measurement
5.2.1 Trigger Strategy
Unprescaled single large-𝑅 jet triggers are employed for the trigger strategy. These
triggers are adapted throughout the 4 data-taking periods to accommodate machine conditions, involving to increase in the 𝑝𝑇 threshold and to introduce a jet mass requirement.
This additional requirement on the jet mass allows for a reduction in the cut for the reconstructed large-𝑅 jet 𝑝𝑇 . The relaxation of the 𝑝𝑇 cut significantly influences the analysis
sensitivity due to the sharply declining 𝑝𝑇 spectrum.
A summary of the triggers utilized, including 99% efficiency points determinedthrough fitting the Fermi function, is shown in Table 5.1.

5.2.2 Pre-selection
Pre-selection requirements are applied as follows:• Passing the detector quality criteria (for data only)– Passing calorimeter operation goodness criteria
32

Chapter 5 Calibration Strategy

Table 5.1 Overview of the triggers used for the 𝜇post−tag Measurement. They are applied as an
OR and all are required to be active. The offline threshold corresponds to the offline jet cut above
which the triggers are 99% efficient [70].
Year

Trigger

Offline Threshold [GeV]

Luminosity [fb−1 ]2015

HLT_j360_a10_lcw_sub_L1J100

𝑝𝑇 ,𝐽 > 410 GeV

3.2

2016
2017

HLT_j420_a10_lcw_L1J100

𝑝𝑇 ,𝐽 > 450 GeV

33.0

HLT_j440_a10t_lcw_jes_L1J100

𝑝𝑇 ,𝐽 > 450 GeV

41.2

HLT_j390_a10t_lcw_jes_30smcINF_L1J100

𝑝𝑇 ,𝐽 > 420 GeV, 𝑚𝐽 > 50 GeV

41.0

HLT_j460_a10t_lcw_jes_L1J100

𝑝𝑇 ,𝐽 > 490 GeV

58.5

HLT_j420_a10t_lcw_jes_30smcINF_L1J100

𝑝𝑇 ,𝐽 > 450 GeV, 𝑚𝐽 > 60 GeV

58.5

HLT_j420_a10t_lcw_jes_30smcINF_L1J100_a10_sub_L1SC111

𝑝𝑇 ,𝐽 > 450 GeV, 𝑚𝐽 > 60 GeV

55.4

2018

– Passing calorimeter noise cleaning criteria• Passing the triggers as shown in Table 5.1• Presence of a primary vertex• At least two large-𝑅 calorimeter jets with 𝑝𝑇 > 200 GeV to ensure the dijet topology• Applied overlap removal on the selected events as shown in Section 4.6• No isolated electron or muon with 𝑝𝑇 > 25 GeV

5.2.3 𝑝𝑇 Symmetry and Rapidity Cut
In addition to pre-selections, the following event selections are applied to increase
the signal significance and get rid of mismodeling phase space. Two additional cuts areapplied:𝑝−𝑝• 𝑝𝑇 symmetry cut: 𝑝𝑇 ,1 +𝑝𝑇 ,2 < 0.15
𝑇 ,1

𝑇 ,2

• Rapidity difference cut: |Δ𝑦1,2 | < 1.2
where 𝑝𝑇 ,1 is the transverse momentum of the leading large-𝑅 jet (the jet with the highest𝑝𝑇 ) and 𝑝𝑇 ,2 is the transverse momentum of the sub-leading large-𝑅 jet (the jet with 2nd
highest 𝑝𝑇 ). Δ𝑦1,2 is the rapidity difference between the leading and sub-leading large-𝑅
jets.
These two selections help to get rid of the mismodeling of multijet. The distribution ofthese two is shown in Figure 5.1 and 5.2. After the pre-selection as shown in Section 5.2.2,
most of the remaining events come from dijets (multijet process). So, data is comparedwith the dijet MC samples. For the 𝑝𝑇 symmetry cut, the ratio starts to decrease from
0.15. For the rapidity difference, it is tightened to 1.2 to reject more multijet events.

33

Normalised number of events

Chapter 5 Calibration Strategy

0.1

data
Z→ bb
Z→ qq
W→ qq
tt
dijet

After pre-selection

0.08

0.06

0.04

Data/dijet

0.02

1.50 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
p symmetry1
T
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
p symmetry
T

Figure 5.1 The 𝑝𝑇 symmetry distribution of the 𝑍 → 𝑏𝑏,̄ 𝑍 → 𝑞 𝑞 ̄ (𝑞 = 𝑢, 𝑑, 𝑠, 𝑐), 𝑊 →𝑞 𝑞,̄ dijets and 𝑡𝑡 ̄ samples.

5.2.4 Large-𝑅 Jet Candidates
The candidates for the calibration are selected from leading large-𝑅 jets with mass
range 50 ≤ 𝑚 < 150 GeV and transverse momentum larger than 450 GeV which cansatisfy the trigger condition for all the data-taking periods. The candidates must have atleast two ghost-associated VR track jets with 𝑝𝑇 > 7 GeV.
The fraction of the leading large-𝑅 jets originate from different MC templates is asshown in Figure 5.3. In the 𝑍(→ 𝑏𝑏)̄ + jets process, the 𝑍 → 𝑏𝑏̄ could be either theleading large-𝑅 jet or the sub-leading large-𝑅 jet. Since only the leading large-𝑅 jet isconsidered as the 𝑍 → 𝑏𝑏̄ candidate, about 40% of the signal events which are the subleading large-𝑅 jets are lost. A similar situation happens in other processes, statistics arelost by only using leading large-𝑅 jets. However, it’s not trivial to add the contributionof subleading large-𝑅 jets because of the large fraction of the wrong-labeled large-R jets.
This will be one of the improvements in the future.

34

Normalised number of events

Chapter 5 Calibration Strategy

0.09

data
Z→ bb
Z→ qq
W→ qq
tt
dijet

After pre-selection

0.08
0.07
0.06
0.05
0.04
0.03
0.02

Data/dijet

0.01
1.50
1

0.5

0

0.5

1

1.5

2

2.5

3

3.5
4
∆y
1,2

1

1.5

2

2.5

3

3.5
4
∆y
1,2

0.8

10

9

8

6

0

10

9

8

7

6

5

3

0.2

4

0.2

2

0.4

1

tt
dijet

0.6

0.4

Leading large-R jet truth label

W→ qq

7

0.6

1

Z→ qq

1: tqqb
2: Wqq3: Zbb
4: Zcc5: Zqq
6: Wqq_From_t
7: other_From_t
8: other_From_V
9: notruth
10: qcd

5

tt
dijet

Z→ bb

Before tagging

4

W→ qq

1.2

3

Z→ qq

1: tqqb
2: Wqq3: Zbb
4: Zcc5: Zqq
6: Wqq_From_t
7: other_From_t
8: other_From_V
9: notruth
10: qcd

2

0.8

Z→ bb

Before tagging

1

1

Normalised number of events

1.2

0Normalised number of events

Figure 5.2 The rapidity difference distribution of the 𝑍 → 𝑏𝑏,̄ 𝑍 → 𝑞 𝑞 ̄ (𝑞 = 𝑢, 𝑑, 𝑠, 𝑐), 𝑊 →𝑞 𝑞,̄ dijets and 𝑡𝑡 ̄ samples.

Subleading large-R jet truth label

Figure 5.3 Truth labels of the leading large-𝑅 jet and the sub-leading large-𝑅 jet in 𝑍 → 𝑏𝑏,̄ 𝑍 →𝑞 𝑞 ̄ (𝑞 = 𝑢, 𝑑, 𝑠, 𝑐), 𝑊 → 𝑞 𝑞,̄ dijets and 𝑡𝑡 ̄ samples.

35

Chapter 5 Calibration Strategy

5.2.5 𝑋 → 𝑏𝑏̄ Tagger GN2X
The 𝑋 → 𝑏𝑏̄ double 𝑏-tagger aims to identify the large-𝑅 jets that contain two 𝑏-jetsfrom the decay of massive particles. GN2X, a new algorithm based on Graph Neural
Networks (GNNs) and transformers, is trained to classify large-𝑅 jets based on their origin, discriminating jets from boosted Higgs boson decaying into pairs of bottom quarks,
̄𝐻(𝑏𝑏)-jets,and charm quarks, 𝐻(𝑐 𝑐)-jets,̄
from those originating from background processes.
GN2X benefits from the study of novel advances in flavor tagging of small-radius
jets using GNNs and transformers. A more detailed description of the GN2X algorithm
can be found in Appendix B. Also, we have implemented an alternative Xbb tagger basedon GN2X, incorporating a method called subgraphs, as detailed in Appendix B.2, withthe aim of enhancing the performance of the base GN2X.
GN2X provides four outputs for each large-𝑅 jet, corresponding to the probabilities
̄
of the jet being a 𝐻(𝑏𝑏)-jet(𝑝Hbb ), a 𝐻(𝑐 𝑐)-jet̄(𝑝Hcc ), multijet (𝑝QCD ), or a top-quark(𝑝top ) jet. A discriminant, roughly corresponding to a log-likelihood ratio, is constructedfrom these four outputs:
𝐷Hbb = ln

𝑝Hbb,
𝑓Hcc ⋅ 𝑝Hcc + 𝑓top ⋅ 𝑝top + (1 − 𝑓Hcc − 𝑓top ) ⋅ 𝑝QCD

(5.5)

where 𝑓Hcc and 𝑓top are two free parameters that determine the relative weights of 𝑝Hcc
and 𝑝top respectively to 𝑝QCD , controlling the trade-off among 𝐻(𝑐 𝑐),̄ top and multijet
rejections. For the following studies, the values of 𝑓Hcc and 𝑓top are set to 0.02 and 0.25[21], respectively, which were obtained after optimization procedure to maximize the rejection for a given signal efficiency. The tagging of a large-𝑅 jet as originating from an
𝐻 → 𝑏𝑏̄ decay is performed by applying a cut on the discriminant 𝐷Hbb .
̄
Figure 5.4 shows the normalized distribution of the discriminant score for 𝐻(𝑏𝑏),𝐻(𝑐 𝑐),
̄ top and multijet jets.
The performance of GN2X is evaluated in terms of the signal efficiency and the rejection of the background processes. The signal efficiency (𝜖) is defined as the tagging
̄efficiency of 𝐻(𝑏𝑏)-jets.
The background rejection factors are defined as the inverse of abackground mis-tagging efficiency (1/𝜖) for 𝑡𝑡 ̄ and multijet events.
There are different working points (WPs) for GN2X, which are shown in Table 5.2.
In summary, events used to extract the 𝜇post-tag are selected as follows:• Pre-selection as described in Section 5.2.2

36

Normalised number of events

Chapter 5 Calibration Strategy

Z→ bb

Before tagging

Z→ qq

0.05

W→ qq
tt
dijet

0.04

0.03

0.02
60 WP

0.01

−10 −8

−6

−4

−2

0
2
4
6
8 10
Leading large-R jet D
Xbb

Figure 5.4 The discriminant score of 𝐻(𝑏𝑏)̄ jets in 𝑍 → 𝑏𝑏,̄ 𝑍 → 𝑞 𝑞 ̄ (𝑞 = 𝑢, 𝑑, 𝑠, 𝑐), 𝑊 →𝑞 𝑞,̄ dijets and 𝑡𝑡 ̄ templates. The red line shows the cut value for 60% WP.

Table 5.2

GN2X threshold values for all WPs with 𝑓Hcc = 0.02 and 𝑓top = 0.25.

Working point

50%

60%

70%

80%

Threshold value

4.335

3.818

3.166

2.211

37

Chapter 5 Calibration Strategy• The leading large-𝑅 jet is required to have 𝑝𝑇 > 450 GeV• At least two ghost-associated VR track jets with 𝑝𝑇 > 7 GeV• The jet mass of leading-𝑝𝑇 large-𝑅 jet is required to be above 50 GeV• Additional requirements are applied to the large-𝑅 jets to suppress the mis-modelingof multijets and to reject backgrounds as shown in Section 5.2.3• The leading large-𝑅 jet is required to pass the 𝑋 → 𝑏𝑏̄ tagger
A schematic diagram of the 𝑍 → 𝑏𝑏̄ event selection is also shown in Figure 5.5. After eachselection and the GN2X tagging mentioned above, the number of events for 𝑍 → 𝑏𝑏,̄ 𝑍 →𝑞 𝑞 ̄ (𝑞 = 𝑢, 𝑑, 𝑠, 𝑐), 𝑊 → 𝑞 𝑞,̄ dijets and 𝑡𝑡 ̄ templates with mass range 50 ≤ 𝑚 < 150 GeV
is shown in Table 5.3.

Figure 5.5

Schematic diagram of the 𝑍 → 𝑏𝑏̄ event selection.

Table 5.3 The number of events for 𝑍 → 𝑏𝑏,̄ 𝑍 → 𝑞 𝑞 ̄ (𝑞 = 𝑢, 𝑑, 𝑠, 𝑐), 𝑊 → 𝑞 𝑞,̄ dijets and 𝑡𝑡 ̄
templates with mass range 50 ≤ 𝑚 < 150 GeV from Run 2 MC simulation (normalized to 140
fb−1 ) after each selection.

Selection

Number of events
𝑍 → 𝑏𝑏̄

𝑍 → 𝑞𝑞 ̄

𝑊 → 𝑞𝑞 ̄𝑡𝑡 ̄

dijets

Pre-selections

52445

258324803963422781254586038

𝑝𝑇 symmetry < 0.1541918

205807642392322625

188926756|Δ𝑦1,2 | < 1.2

31790

155751480084230729119146981

Large-𝑅 jet candidates

7534

37534

11514340312

26357350

GN2X tagger 80% WP

5957

345.8

514.3

1661

262739

GN2X tagger 70% WP

5194

141.2

76.46

715.7

145703

GN2X tagger 60% WP

4416

53.52

71.16

356.0

89019

GN2X tagger 50% WP

3712

16.40

35.37

195.1

56380

38

Chapter 5 Calibration Strategy

5.3 Event Selection for the 𝜇pre−tag Measurement
As discussed in Section 5.1, we use 𝑍(→ ℓ+ ℓ− ) + jets instead of 𝑍(→ 𝑏𝑏)̄ + jets tocalculate 𝜇pre-tag . At least one additional high 𝑝𝑇 jet is required in order to ensure a similar
event topology as the 𝑍(→ 𝑏𝑏)̄ + jets case. For the other selections, the 𝑝𝑇 symmetry andrapidity difference cuts are similar to the simuation of 𝑍(→ 𝑏𝑏)̄ + jets. The selection issummarized as follows:• Passing the detector quality criteria (for data only)– Passing calorimeter operation goodness criteria– Passing calorimeter noise cleaning criteria• Passing the triggers as shown in Table 5.4 and 5.5• Presence of a primary vertex• Applied overlap removal on the selected events as shown in Section 4.6• At least two leptons of the same flavor• At least one large-𝑅 jet with 𝑝𝑇 > 200 GeV and |𝜂| < 2.0• For 𝑍 → 𝜇𝜇, at least one of the selected muons has 𝑝𝑇 > 27 GeV and opposite
charge• For 𝑍 → 𝑒𝑒, at least one of the selected electrons has 𝑝𝑇 > 25 GeVℓℓ• The lepton 𝑝𝑇 balance is required: (𝑝𝑇1 − 𝑝𝑇2 ) /𝑝ℓℓ
𝑇 < 0.8• In analogy to the 𝜇post−tag measurement, additional requirements are applied as follows:– 𝑝ℓℓ
𝑇 is required to be above 450 GeV and larger than the leading large-𝑅 jet
lead.jet𝑝𝑇 : 𝑝ℓℓ
𝑇 > 𝑝𝑇

lead.jet– 𝑝𝑇 symmetry requirement:

𝑝ℓℓ
𝑇 −𝑝𝑇

lead.jet

𝑝ℓℓ
𝑇 +𝑝𝑇

< 0.15– rapidity difference: |Δ𝑦ℓℓ−lead.jet | < 1.2• The signal region is defined by a mass window requirement of 66 < 𝑚𝑍→ℓ+ ℓ− <116 GeVA schematic diagram of the 𝑍 → 𝑏𝑏̄ event selection is also shown in Figure 5.6.
Table 5.4 Overview of single muon triggers used for the 𝜇pre−tag Measurement. They are applied
as an OR and all are required to be active.
Year

Trigger

Offline Threshold [GeV]2015

HLT_mu20_iloose_L1MU15

𝑝𝑇 ,ℓ > 20 GeV

2015-2018

HLT_mu50

𝑝𝑇 ,ℓ > 50 GeV

2016-2018

HLT_mu26_ivarmedium

𝑝𝑇 ,ℓ > 26 GeV

39

Chapter 5 Calibration Strategy

Figure 5.6

Schematic diagram of the 𝑍 → ℓℓ event selection.

Table 5.5 Overview of single electron triggers used for the 𝜇pre−tag Measurement. They areapplied as an OR and all are required to be active.
Year

2015

2016-2018

Trigger

Offline Threshold [GeV]

HLT_e24_lhmedium_L1EM20VH

𝑝𝑇 ,ℓ > 24 GeV

HLT_e60_lhmedium

𝑝𝑇 ,ℓ > 60 GeV

HLT_e120_lhloose

𝑝𝑇 ,ℓ > 120 GeV

HLT_e26_lhtight_nod0_ivarloose

𝑝𝑇 ,ℓ > 26 GeV

HLT_e60_lhmedium_nod0

𝑝𝑇 ,ℓ > 40 GeV

HLT_e120_lhloose_nod0

𝑝𝑇 ,ℓ > 140 GeV

40

Chapter 6 Signal and Background Modeling

Chapter 6 Signal and Background Modeling
6.1 Modeling for the 𝜇post-tag Measurement
6.1.1 Comparison of Data and Simulation
The yields before and after the tagger are shown in Table 6.1 and 6.2. For 450 ≤𝑝𝑇 < 500GeV, 500 ≤ 𝑝𝑇 < 600GeV and 600 ≤ 𝑝𝑇 < 1000GeV 𝑝𝑇 bins, the comparisonplots for the large-𝑅 jet kinematics before the 𝑋 → 𝑏𝑏̄ tagging are shown in Figure 6.1,
and after the 𝑋 → 𝑏𝑏̄ tagging, for 60% working point, are shown in Figure 6.2. Similarly,
the comparison plots for other working points are shown in Appendix A.1. Before the𝑋 → 𝑏𝑏̄ tagging, for all the 𝑝𝑇 bins, the data/MC ratio is seen to be smaller than 1 because
the cross-section of dijets is overestimated. After the 𝑋 → 𝑏𝑏̄ tagging, the data/MC ratio
is slightly larger than 1 and almost flat with a small positive slope.
Table 6.1 Event yields for different Run 2 MC samples (normalized to 140 fb−1 ) before 𝑋 → 𝑏𝑏̄
tagger in different 𝑝𝑇 bins in large-𝑅 jet mass range 50 ≤ 𝑚 < 150 GeV. Statistical uncertainties
of MC samples are shown.

MC Sample

450 ≤ 𝑝𝑇 < 500 GeV

500 ≤ 𝑝𝑇 < 600 GeV

600 ≤ 𝑝𝑇 < 1000 GeV

𝑍 → 𝑏𝑏̄

9770 ± 51

4660 ± 33

2860 ± 23

𝑍 → 𝑞𝑞 ̄

42260 ± 370

20030 ± 24012430 ± 160

𝑊 → 𝑞𝑞 ̄

129100 ± 480

61700 ± 320

38600 ± 220

𝑡𝑡 ̄45800 ± 140

21100 ± 100

11900 ± 75

dijet20675500 ± 4700

9421600 ± 2800

5046300 ± 1100

Table 6.2 Event yields for different Run 2 MC samples (normalized to 140 fb−1 ) after 60% WP
of 𝑋 → 𝑏𝑏̄ tagger in different 𝑝𝑇 bins in large-𝑅 jet mass range 50 ≤ 𝑚 < 150 GeV. Statisticaluncertainties of MC samples are shown.

MC Sample

450 ≤ 𝑝𝑇 < 500 GeV

500 ≤ 𝑝𝑇 < 600 GeV

600 ≤ 𝑝𝑇 < 1000 GeV

𝑍 → 𝑏𝑏̄1880 ± 21

1620 ± 17

900 ± 11

𝑍 → 𝑞𝑞 ̄

30.8 ± 9.2

55.4 ± 8.6

36 ± 13

𝑊 → 𝑞𝑞 ̄

74 ± 1274.5 ± 9.7

75 ± 11𝑡𝑡 ̄

177.9 ± 9.2

160.2 ± 9.0

88.5 ± 6.8

dijet

40000 ± 210

31800 ± 140

16300 ± 59

41

×103
800

data
Z→ bb
Z→ qq
W→ qq
tt
dijet
MC errorRun 2 (140 fb-1)
Before tagging, p 450-500 GeV
T

700

Number of events

Number of events

Chapter 6 Signal and Background Modeling

600
500

350

Run 2 (140 fb-1)
Before tagging, p 500-600 GeV
T

300

data
Z→ bb
Z→ qq
W→ qq
tt
dijet
MC error

250

150

300

100

100

50
60 70

80

90 100 110 120 130 140 150
Leading large-R jet mass [GeV]80

90 100 110 120 130 140 150
Leading large-R jet mass [GeV]
Number of events

60 70

220

Data/MC

200

1.550
1
0.5
50

×103

200

400

Data/MC

400

1.550
1
0.5
50

60 70

80

90 100 110 120 130 140 150
Leading large-R jet mass [GeV]

60 70

80

90 100 110 120 130 140 150
Leading large-R jet mass [GeV]

×103

200
180

Run 2 (140 fb-1)
Before tagging, p 600-1000 GeV
T

160

data
Z→ bb
Z→ qq
W→ qq
tt
dijet
MC error

140
120
100
80
60
40

Data/MC

20
1.550
1
0.5
50

60 70

80

90 100 110 120 130 140 150
Leading large-R jet mass [GeV]

60 70

80

90 100 110 120 130 140 150
Leading large-R jet mass [GeV]

Figure 6.1 The comparison of data and MC samples prediction before 𝑋 → 𝑏𝑏̄ tagger for different 𝑝𝑇 bins. Different MC samples are stacked together. The MC error is shown as the shaded
band, but it’s too small to be seen.

42

1400

Number of events

Number of events

Chapter 6 Signal and Background Modeling

1200

data
Z→ bb
Z→ qq
W→ qq
tt
dijet
MC errorRun 2 (140 fb-1)
Xbb 60%, p 450-500 GeV
T

1200

Run 2 (140 fb-1)
Xbb 60%, p 500-600 GeV
T

1000

1000
800

data
Z→ bb
Z→ qq
W→ qq
tt
dijet
MC error

800
600

600
400
400
200
60 70

80

90 100 110 120 130 140 150
Leading large-R jet mass [GeV]

60 70

80

Data/MC

1.550
1
0.5
50

90 100 110 120 130 140 150
Leading large-R jet mass [GeV]
Number of events

Data/MC200600

Run 2 (140 fb-1)
Xbb 60%, p 600-1000 GeV
T

500

1.550
1
0.5
50

60 70

80

90 100 110 120 130 140 150
Leading large-R jet mass [GeV]

60 70

80

90 100 110 120 130 140 150
Leading large-R jet mass [GeV]

data
Z→ bb
Z→ qq
W→ qq
tt
dijet
MC error

400
300
200

Data/MC

100
1.550
1
0.5
50

60 70

80

90 100 110 120 130 140 150
Leading large-R jet mass [GeV]

60 70

80

90 100 110 120 130 140 150
Leading large-R jet mass [GeV]

Figure 6.2 The comparison of data and MC samples prediction after 60% WP of 𝑋 → 𝑏𝑏̄ tagger
for different 𝑝𝑇 bins. Different MC samples are stacked together. The MC error is shown as theshaded band.

43

Chapter 6 Signal and Background Modeling6.1.2 Signal and Background Modeling
The multijet background is determined using data-driven techniques. Other backgrounds and the signal events are modeled using MC simulations. The signal and background modeling are given in the following sections. Techniques differ for the 𝜇pre-tag and𝜇post-tag measurements. For the 𝜇post-tag measurement a fit to the 𝑍 → 𝑏𝑏̄ mass distribution is performed, while for the 𝜇pre-tag measurement only signal and background yields

220
200

Run 2 (140 fb-1)
Xbb 50%

Number of events

Number of eventsneed to be extracted after selections described in Section 5.3. The mass distribution of
𝑍 → 𝑏𝑏,̄ 𝑍 → 𝑞 𝑞,̄ 𝑊 → 𝑞 𝑞,̄ 𝑡𝑡 ̄ templates after tagging are shown in Figure 6.3.
Z→ bb
5x Z→ qq180

5x W→ qq

160

5x tt

140

250

Run 2 (140 fb-1)
Xbb 60%Z→ bb
5x Z→ qq
5x W→ qq

200

5x tt

150

120
100

100

80
60

50

40
20
60 70

80

90 100 110 120 130 140 150
Leading large-R jet mass [GeV]

300

250

Run 2 (140 fb-1)
Xbb 70%50

Number of events

Number of events

50

Z→ bb
5x Z→ qq
5x W→ qq
5x tt

200

300

60 70

80

Run 2 (140 fb-1)
Xbb 80%90 100 110 120 130 140 150
Leading large-R jet mass [GeV]Z→ bb
5x Z→ qq
5x W→ qq

250

5x tt

200
150
150
100

100

50

50

50

60 70

80

90 100 110 120 130 140 150
Leading large-R jet mass [GeV]

50

60 70

80

90 100 110 120 130 140 150
Leading large-R jet mass [GeV]

Figure 6.3 The mass distribution of 𝑍 → 𝑏𝑏,̄ 𝑍 → 𝑞 𝑞,̄ 𝑊 → 𝑞 𝑞,̄ 𝑡𝑡 ̄ templates after 50%, 60%,
70% and 80% working point of GN2X tagger.

44

Chapter 6 Signal and Background Modeling6.1.2.1 Signal Modeling
To model the 𝑍 → 𝑏𝑏̄ signal invariant mass distribution for the 𝜇post-tag measurement,a double sided crystal ball (DSCB) function [71] is used:
−𝑛

2

𝐿
𝛼𝐿 𝑛𝐿
⎧exp − 𝛼𝐿− 𝛼𝐿 − 𝑡)],𝑡 < −𝛼𝐿( 2 ) [ 𝑛𝐿 ( 𝛼𝐿⎪⎪
𝑓 (𝑚|𝑚𝑍 , 𝜎𝑍 , 𝛼𝐿 , 𝛼𝐻 , 𝑛𝐿 , 𝑛𝐻 ) = 𝑁 ⋅ ⎨exp − 1 𝑡2 ,−𝛼𝐿 ≤ 𝑡 ≤ 𝛼𝐻
( 2 )
⎪
2
−𝑛
𝐻
𝛼𝐻 𝑛𝐻
⎪exp − 𝛼𝐻− 𝛼𝐻 + 𝑡)], 𝑡 > 𝛼𝐻
[
(
2
𝑛
𝛼
)
(
𝐻
𝐻
⎩

(6.1)

where 𝑡 = (𝑚 − 𝑚𝑍 )/𝜎𝑍 , the first and the third case of the equation describes the tail andthe second case describes the core of the distribution. 𝑁 is a normalization parameter,𝑚𝑍 and 𝜎𝑍 denote the mean and standard deviation of the Gaussian core. 𝛼𝐿 , 𝑛𝐿 and 𝛼𝐻 ,𝑛𝐻 are the decay constants and normalization on the low and the high side tails.
The parameters of the DSCB function are derived fitting the 𝑍 → 𝑏𝑏̄ MC templates
after applying the requirements listed in Section 5.2.
Figure 6.4 and Table 6.3 shows the 𝜒 2 fits to the signal MC samples for the 𝑋 → 𝑏𝑏̄
tagging requirement at 60% working point for 450 ≤ 𝑝𝑇 < 1000 GeV. Other results fordifferent working points are shown in Appendix A.2.
Table 6.3 The parameters of the DSCB function from a fit to the 𝑍 → 𝑏𝑏̄ template for the𝑍 → 𝑏𝑏̄ MC templates after the 𝑋 → 𝑏𝑏̄ tagging requirement at 60% working point for 450 ≤𝑝𝑇 < 1000 GeV.
𝑁

199.1 ± 1.95

𝑚𝑍 [GeV]87.2 ± 0.08

𝜎𝑍 [GeV]

7.71 ± 0.09

𝛼𝐿

1.08 ± 0.05

𝑛𝐿

16.0 ± 7.95

𝛼𝐻

2.11 ± 0.04

𝑛𝐻

0.46 ± 0.06

𝜒2

135.8

𝜒 /NDF

1.46

2

6.1.2.2 Background Modeling
The dominant source of background in the 𝑍 → 𝑏𝑏̄ 𝜇post-tag measurement is multijet
events. The contribution from 𝑊 (→ 𝑞 𝑞)̄ + jets and 𝑡𝑡 ̄ process is found to be negligible. To
confirm that ignoring them will not bias the yield estimated, a test to model the signal bycomparing between using all MC samples and using only 𝑍 → 𝑏𝑏̄ and dijet MC samples
45

Number of events

Chapter 6 Signal and Background Modeling250

Xbb 60%χ^2/NDF: 1.460

Zbb

200

fit

150
100

Pull

50

550
0
−5
50

60 70

80

90 100 110 120 130 140 150
Leading large-R jet mass [GeV]

60 70

80

90 100 110 120 130 140 150
Leading large-R jet mass [GeV]

Figure 6.4 The 𝜒 2 fits to the 𝑍 candidate mass distribution (𝑍 → 𝑏𝑏̄ template) via a DSCB
function, passing the 𝑋 → 𝑏𝑏̄ 60% WP for 450 ≤ 𝑝𝑇 < 1000 GeV.

is performed. The results are shown in Figure 6.5 and 6.4. After the test, the number ofsignal and background events by fitting is nearly the same. Thus, in this study, only dijet
background is considered.
The modeling of multijet events is performed using classes of exponential and polynomial functions of 2nd to 5th order in bins of the transverse momentum of the 𝑍 → 𝑏𝑏̄
candidate. The choice of the functional form is made using binned maximum likelihood fit to the sidebands of the invariant 𝑍 → 𝑏𝑏̄ mass distribution in data, defined as
50 < 𝑚𝑍→𝑏𝑏̄ < 70 GeV and 110 < 𝑚𝑍→𝑏𝑏̄ < 150 GeV. To decide on the suitable numberof free parameters (the order) of the two classes of functions: a 𝐹 -test is performed [72].
The test statistic 𝐹𝑝,𝑞 is calculated as:
𝐹𝑝,𝑞 =

𝜒𝑝2 − 𝜒𝑞2

𝜒𝑞2/,
𝑛𝑞 − 𝑛𝑝 𝑛 − 𝑛𝑞

(6.2)

where 𝜒𝑝2 and 𝜒𝑞2 describe quantitatively the goodness of the fit, computed in 𝑛 bins of
two fits with 𝑛𝑝 and 𝑛𝑞 degrees of freedom. The optimal functions to describe the multijet
background are summarised in Table 6.5 [73]. These functions are used in the final fit
46

600

Xbb 60%, p 450-500 GeVTχ^2/NDF: 1.388

Number of events

700

sig
bkg
sig+bkg

500

700
600

300

300

200

200

100

100

−5
50

60 70

80

90 100 110 120 130 140 150
Leading large-R jet mass [GeV]

60 70

80

90 100 110 120 130 140 150
Leading large-R jet mass [GeV]sigbkg
sig+bkg

400

550
0

Xbb 60%, p 450-500 GeVTχ^2/NDF: 1.382

500

400

Pull

Pull

Number of events

Chapter 6 Signal and Background Modeling

550
0
−5
50

60 70

80

90 100 110 120 130 140 150
Leading large-R jet mass [GeV]

60 70

80

90 100 110 120 130 140 150
Leading large-R jet mass [GeV]

Figure 6.5 The 𝜒 2 fits to the 𝑍 candidate mass distribution based on only 𝑍 → 𝑏𝑏̄ and dijet MC
templates (left) and all MC templates (right), passing the 𝑋 → 𝑏𝑏̄ 60% WP for 450 ≤ 𝑝𝑇 < 500
GeV.

Table 6.4 The parameters of fitting signal and background models for different background treatments (only dijet or dijet+𝑊 + 𝑡𝑡)̄ after the 𝑋 → 𝑏𝑏̄ tagging requirement at 60% working point
for 450 ≤ 𝑝𝑇 < 500 GeV.
Parameter

𝑍 → 𝑏𝑏̄ and dijet

𝑍 → 𝑏𝑏,̄ dijet, 𝑊 → 𝑞 𝑞,̄ 𝑡𝑡 ̄

𝑚𝑍 [GeV]

84 ± 1.1

84 ± 1.2

𝜎𝑍 [GeV]

7.71 (fixed)

7.71 (fixed)

𝛼𝐿

1.08 (fixed)

1.08 (fixed)𝑛𝐿

16.0 (fixed)

16.0 (fixed)

𝛼𝐻

2.11 (fixed)

2.11 (fixed)𝑛𝐻

0.46 (fixed)

0.46 (fixed)𝑎0−34 ± 58

−29 ± 55𝑎11110 ± 40

1100 ± 60

𝑎2−1344.1 ± 5.3−1350 ± 65

𝑎3459.7 ± 4.6

460 ± 24

2

129.9

130.5

𝜒 2 /NDF

1.38

1.39

Signal1550 ± 254

1530 ± 244

Background40350 ± 325

40170 ± 318

𝜒47

Chapter 6 Signal and Background Modelingdescribed in Section 7.2.
Table 6.5

Optimal functions to describe the multijet background in the 𝜇post-tag measurement.
𝑍 → 𝑏𝑏̄ 𝑝𝑇 bin

Optimal function

450 ≤ 𝑝𝑇 < 500 GeV𝑚∑𝑖=0 𝑎𝑖 ( 100[GeV])500 ≤ 𝑝𝑇 < 500 GeV𝑚∑𝑖=0 𝑎𝑖 ( 100[GeV])600 ≤ 𝑝𝑇 < 1000 GeV𝑚𝑎0 exp ∑3𝑖=1 𝑎𝑖 ( 100[GeV]
))
(

𝑖

3
3

𝑖
𝑖

6.2 Modeling for the 𝜇pre-tag Measurement
6.2.1 Comparison of Data and Simulation
Figure 6.6 shows one of the most representative distributions for the 𝑍 → ℓ+ ℓ− +jets
process, the 𝑍-boson invariant mass distribution in various 𝑍-boson candidate 𝑝𝑇 bins.
A good shape agreement between data and MC simulation is found.

6.2.2 Signal and Background ModelingTo extract signal events of 𝑍(→ ℓℓ) + jets, MC simulated events are used. thebackground events are subtracted from the number of observed events. The background
events are obtained from the MC simulation of 𝑍𝑍, 𝑊 𝑍, 𝑊 𝑊 , 𝑍𝜏𝜏 and 𝑊 ℓ𝜈. The
main backgrounds are 𝑊 𝑍 and 𝑍𝑍 diboson processes but they are small. Only total
yields are needed to calculate 𝜇pre-tag .

48

350
300
250

Events / 1 GeVEvents / 1 GeV

Chapter 6 Signal and Background Modeling

Data
Z(→ ll)+jets
ZZ
WZ
WW
Z(→ττ)+jets
Wlν
Stat. unc.
Stat.+Syst. unc.

s = 13 TeV, 140 fb-1
Z(→ bb)+jets calibration
Z(→ l+l )+jets selectionp (ll): 450-500 GeV
T

200

300
250

Data
Z(→ ll)+jets
ZZ
WZ
WW
Z(→ττ)+jets
Wlν
Stat. unc.
Stat.+Syst. unc.

s = 13 TeV, 140 fb-1
Z(→ bb)+jets calibration
Z(→ l+l )+jets selectionp (ll): 500-600 GeV
T

200
150

150
100

100

50

50

0
2
1.5
1
0.5
0

0
2
1.5
1
0.5
0

70

75

80

85

90

95

(Data-Bkg)/Z+jets(Data-Bkg)/Z+jets

350

100 105 110 115
mll [GeV](a) 450 ≤ 𝑝𝑇 < 500 GeVm [GeV]
Events / 1 GeV

140

80

85

90

95

100 105 110 115
mll [GeV]

ll

200

160

75

(b) 500 ≤ 𝑝𝑇 < 600 GeVm [GeV]

ll

180

70

Data
Z(→ ll)+jets
ZZ
WZ
WW
Z(→ττ)+jets
Wlν
Stat. unc.
Stat.+Syst. unc.

s = 13 TeV, 140 fb-1
Z(→ bb)+jets calibration
Z(→ l+l )+jets selectionp (ll): 600-1000 GeV
T

120
100
80
60
40

(Data-Bkg)/Z+jets

20
0
2
1.5
1
0.5
0

70

75

80

85

90

95

100 105 110 115
mll [GeV](c) 600 ≤ 𝑝𝑇 < 1000 GeV m [GeV]llFigure 6.6

The comparison of data and MC prediction for 𝑍 → ℓ+ ℓ− in three 𝑍-boson 𝑝𝑇 bins.

49Chapter 7 Results

Chapter 7 Results
In Section 7.1, the systematic uncertainties for this calibration are explained. Some
values are based on previous studies. Then, the results are shown in Section 7.2.

7.1 Systematic Uncertainties
In the previous study [22], several different systematic uncertainties were studied:• 𝑍 + jets modeling• Fit model• Spurious signal• Other background modeling• Lepton related (momentum scale and resolution, identification and trigger)• Jet related (mass scale, mass resolution and energy scale, trigger)
The uncertainties evaluated in this thesis are as follows. But for others, the numbers
are reused due to a delay in the MC preparation and so on.
Statistical Uncertainties The statistical uncertainties of the Monte Carlo simulations
are considered for all analyses.
𝑍 + jets modeling

The uncertainty considered for 𝑍 → 𝑏𝑏̄ shall be estimated using thealternative generator, but in this thesis, this uncertainty is not considered due to the MC
sample preparation problem. The uncertainty considered for 𝑍 → ℓℓ are estimated bythree aspects: generator uncertainty (Sherpa 2.2.8 VS MadGraph+Pythia8), scale uncertainties and PDF+𝛼𝑠 uncertainties. The details are as shown in Appendix A.5. However,in this thesis, the values of 𝑍 + jets modeling uncertainties are reused from the previous
study [22], because those results cover both 𝑍 → 𝑏𝑏̄ and 𝑍 → ℓℓ modeling uncertainties.
Fit Model for 𝜇post-tag

An additional systematic uncertainty on the fit model due tothe choice of the fit mass range is added. The signal strength 𝜇post-tag is evaluated for one
alternative mass range (50-140 GeV). The uncertainty is estimated by taking the difference
between the nominal and alternative fit results. The fit parameters are shown in Appendix
A.3.
51

Chapter 7 Results

Spurious Signal for 𝜇post-tag

The spurious signal is evaluated by fitting the mass distri-bution of the background-only MC samples with the signal plus background model. The
spurious signal is defined as the fitted signal strength. The spurious signal test results areshown in Appendix A.4.
Other Background Modeling for 𝜇pre-tag

A 20% normalization uncertainty is assigned

to the 𝑉 𝑉 (𝑊 𝑊 , 𝑍𝑍, 𝑊 𝑍) background. The uncertainty is estimated by recalculating
the 𝜇pre-tag and extracting the SFs again.

7.2 Results
The 𝜇post-tag parameter is measured using the 𝑍 → 𝑏𝑏̄ invariant mass distribution for
the three large-𝑅 jet 𝑝𝑇 bins mentioned above. To extract the signal strength, a binned
maximum likelihood fit is performed. The functional form that describes the smoothbackground is chosen using the method in Section 6.1.2.2.
Figure 7.1 shows the 𝑍 → 𝑏𝑏̄ candidate invariant mass distribution after the fit andapplying the GN2X tagger at 60% working point. The pulls, defined as data minus fitted
model prediction divided by the data statistical uncertainty, are mostly within 3 standard
deviations. The fitting parameters are shown in Table 7.1. We perform the same fitting
using MC samples, and the results are shown in Table 7.2. The 𝜇post-tag can be calculated
as shown in Table 7.3. The data statistical uncertainty is calculated by setting the MCstatistical uncertainty to zero, while the MC statistical uncertainty is the opposite.
The 𝜇pre-tag parameter is calculated as a ratio of observed yields in data minus the
expected background yields divided by the expected 𝑍 → ℓ+ ℓ− signal yields as shownin Equation 5.3. All yields are determined after the 𝑍 → ℓ+ ℓ− selection requirements foreach 𝑍-boson candidate 𝑝𝑇 bins. The 𝜇pre-tag are shown in Table 7.4 with the observed
yields and expected signal and background. Similar to the 𝜇post-tag , the data statisticaluncertainty is calculated by setting the MC statistical uncertainty to zero, while the MCstatistical uncertainty is the opposite.
From the 𝜇post-tag and 𝜇pre-tag shown before, a SF for each 𝑝𝑇 region can be obtained
as shown in Table 7.5. Some other systematic uncertainties are not estimated in this thesis,
the values from the previous study [22] are reused, including 𝑍 + jets modeling, spurious
signal, lepton related, jet mass scale, jet mass resolution and jet energy scale.

52

Number of events

Number of events

Chapter 7 Results

800
700

Run 2 (140 fb-1)
Xbb 60%, p 450-500 GeVTχ^2/NDF: 1.213

sig
bkg

600

sig+bkg

500
400

600
500

Run 2 (140 fb-1)
Xbb 60%, p 500-600 GeVTχ^2/NDF: 1.234

sigbkg
sig+bkg

400
300

300
200
200
100

550
0
−5
50

60 70

80

90 100 110 120 130 140 150
Leading large-R jet mass [GeV]

60 70

80

90 100 110 120 130 140 150
Leading large-R jet mass [GeV]

Pull

Pull

100

−5
50

(a) 450 < 𝑝𝑇 < 500 GeV
Number of events

550
0

60 70

80

90 100 110 120 130 140 150
Leading large-R jet mass [GeV]

60 70

80

90 100 110 120 130 140 150
Leading large-R jet mass [GeV](b) 500 < 𝑝𝑇 < 600 GeV

350
300

Run 2 (140 fb-1)
Xbb 60%, p 600-1000 GeVTχ^2/NDF: 1.105

sigbkg
sig+bkg

250
200
150
100

Pull

50
550
0
−5
50

60 70

80

90 100 110 120 130 140 150
Leading large-R jet mass [GeV]

60 70

80

90 100 110 120 130 140 150
Leading large-R jet mass [GeV](c) 600 < 𝑝𝑇 < 1000 GeV
Figure 7.1 The 𝑍 → 𝑏𝑏̄ candidate invariant mass distribution and applying the 𝑍(→ 𝑏𝑏)̄ + jets
selection and the 𝑋 → 𝑏𝑏̄ 60% WP for events with the large-𝑅 jet 𝑝𝑇 in the 450 < 𝑝𝑇 < 500
GeV(a); 500 < 𝑝𝑇 < 600 GeV(b); 600 < 𝑝𝑇 < 1000 GeV(c) range. The fit result is shown by ared solid curve. Signal (green) and background (blue) components are shown.

53

Chapter 7 Results

Table 7.1 The parameters of fitting the real data after the 𝑋 → 𝑏𝑏̄ tagging requirement at 60%
working point for different 𝑝𝑇 bins.
Large-𝑅 jet 𝑝𝑇

Parameter450-500 GeV

500-600 GeV

600-1000 GeV

𝑚𝑍

82.4 ± 0.8

84.1 ± 0.8

85.3 ± 1.1

𝜎𝑍7.71 (fixed)

7.71 (fixed)

7.71 (fixed)

𝛼𝐿

1.08 (fixed)

1.08 (fixed)

1.08 (fixed)𝑛𝐿

16.0 (fixed)

16.0 (fixed)

16.0 (fixed)

𝛼𝐻

2.11 (fixed)

2.11 (fixed)

2.11 (fixed)𝑛𝐻

0.46 (fixed)

0.46 (fixed)

0.46 (fixed)𝑎0

347 ± 25

175 ± 2135.9 ± 1.7

𝑎1

935 ± 591134 ± 47

6.8 ± 0.1𝑎2−1310 ± 54−1470 ± 41−7.9 ± 0.1

𝑎3

470 ± 21510 ± 172.70 ± 0.04

2

114.1

116.1

103.9

𝜒 /NDF

1.21

1.23

1.11

Signal2343 ± 252

1729 ± 230

904 ± 135

Background45440 ± 327

35930 ± 295

17750 ± 186

𝜒
2

54

Chapter 7 Results

Table 7.2 The parameters of fitting the MC samples after the 𝑋 → 𝑏𝑏̄ tagging requirement at
60% working point for different 𝑝𝑇 bins.
Large-𝑅 jet 𝑝𝑇

Parameter450-500 GeV

500-600 GeV

600-1000 GeV

𝑚𝑍

83.9 ± 1.1

84.9 ± 0.6

86.9 ± 0.5

𝜎𝑍7.71 (fixed)

7.71 (fixed)

7.71 (fixed)

𝛼𝐿

1.08 (fixed)

1.08 (fixed)

1.08 (fixed)𝑛𝐿

16.0 (fixed)

16.0 (fixed)

16.0 (fixed)

𝛼𝐻

2.11 (fixed)

2.11 (fixed)

2.11 (fixed)𝑛𝐻

0.46 (fixed)

0.46 (fixed)

0.46 (fixed)𝑎0−34 ± 58

88 ± 7347 ± 84𝑎11110 ± 40

990 ± 738.1 ± 0.6

𝑎2−1344.1 ± 5.3−1328 ± 81

−9.6 ± 0.6

𝑎3459.7 ± 4.6

477 ± 313.3 ± 0.2

𝜒2

130.1

89.3

94.2

𝜒 /NDF

1.40

0.96

1.01

Signal1550 ± 254

1840 ± 163

844 ± 72

Background40400 ± 330

31680 ± 210

16460 ± 93

2

Table 7.3 Post-tag (𝜇post-tag ) signal strength for the 𝑋 → 𝑏𝑏̄ tagger at 60 % efficiency WP measured using 𝑍(→ 𝑏𝑏)̄ + jets calibration methods.

Table 7.4

𝑝𝑇 [GeV]450 < 𝑝𝑇 < 500

500 < 𝑝𝑇 < 600

600 < 𝑝𝑇 < 1000

data
𝑁𝑍𝑏𝑏,GN2X
60%
MC
𝑁𝑍𝑏𝑏,GN2X
60%

2343 ± 252

1729 ± 230

904 ± 135

1547 ± 254

1841 ± 163

844 ± 72

𝜇post-tag

1.515 ± 0.297

0.939 ± 0.150

1.071 ± 0.184

Data stat. error

0.163

0.125

0.160

MC stat. error

0.249

0.083

0.091

Pre-tag (𝜇pre-tag ) signal strength measured using 𝑍(→ ℓ+ ℓ− )+jets calibration methods.
𝑝𝑇 [GeV]450 < 𝑝𝑇 < 500

500 < 𝑝𝑇 < 600

600 < 𝑝𝑇 < 1000

data
𝑁ℓℓ

1967

1827

1137

MC
𝑁bkg,ℓℓ

97.3 ± 2.4

49.7 ± 1.5

34.3 ± 1.2

MC
𝑁𝑍→ℓℓ

1607.5 ± 6.9

1559.9 ± 6.1

891.2 ± 3.9

𝜇pre-tag

1.163 ±0.028

1.139 ±0.028

1.237 ±0.038

Data stat. error

0.028

0.027

0.038

MC stat. error

0.005

0.005

0.006

55

Chapter 7 Results

Table 7.5 Pre-tag (𝜇pre-tag ) and post-tag (𝜇post-tag ) signal strength and the resulting signal efficiency scale factors (SF) for the 𝑋 → 𝑏𝑏̄ tagger at 60 % efficiency WP measured using
𝑍(→ 𝑏𝑏)̄ + jets calibration methods. Systematic uncertainties are also shown.
𝑝𝑇 [GeV]450 < 𝑝𝑇 < 500

500 < 𝑝𝑇 < 600

600 < 𝑝𝑇 < 1000

𝜇post-tag

1.52

0.94

1.07

𝜇pre-tag

1.16

1.14

1.24

SF

1.30

0.83

0.87

Uncertainty (±𝜎) of SFs
Data stat.

0.14

0.11

0.13

Others from previous study [22]

0.34

0.21

0.21

MC stat.

0.21

0.07

0.07

Fit model

0.16

0.10

0.02

Spurious signal

0.21

0.03

0.08

MC stat.

<0.01

<0.01

<0.01

Other background modeling

0.01

<0.01

<0.01

0.50

0.27

0.27

Syst. (𝜇post-tag )Syst. (𝜇pre-tag )Total uncertainty

56

Chapter 8 Conclusion and Outlook

Chapter 8 Conclusion and Outlook
The Higgs boson generated with high transverse momentum presents an opportunity
for measuring the charm Yukawa coupling, and also exhibits sensitivity to novel physics.
To explore the Higgs boson under these conditions, advanced techniques for object reconstruction and identification, and innovative strategies for physics analysis are essential.
Throughout this thesis, the in-situ calibration of a novel 𝑋 → 𝑏𝑏̄ tagger using 𝑍(→𝑏𝑏)̄ + jets events is presented, and an attempt to improve the performance of the 𝑋 → 𝑏𝑏̄
tagger is made.
Calibrating the 𝑋 → 𝑏𝑏̄ tagger is a crucial endeavor to enable its utilization in physics
analyses focused on boosted 𝑏𝑏̄ and even 𝑐 𝑐 ̄ topologies. 𝑍 + jets events are employed todetermine signal scale factors for 𝑝𝑇 > 450 GeV using data collected by the ATLAS
experiment in Run 2. Dijet, 𝑡𝑡,̄ and 𝑊 + jets are considered as background. The dijet
background is modeled by fitting the data directly using an exponentiated polynomial or
polynomial function, depending on 𝑝𝑇 . While other backgrounds are negligible small andneglected. The scale factors measured for the 𝑋 → 𝑏𝑏̄ tagger at 60% working point (WP)
are 1.30 ± 0.50 for 450 < 𝑝𝑇 < 500 GeV, 0.83 ± 0.27 for 500 < 𝑝𝑇 < 600 GeV, and0.87 ± 0.27 for 600 < 𝑝𝑇 < 1000 GeV. This calibration is achieved by the methodology
documented in Ref. [22].
Concerning the calibration work, some improvements can be made in the future as
follows.
Systematic Uncertainties

All the systematic uncertainties described in Section 7.1 shallbe evaluated. Due to the MC samples preparation problem etc., only part of the systematic
uncertainties is considered in this thesis. For example, the uncertainties on the modelingof the 𝑍 + jets events can be evaluated using the alternative Herwig++ generator [74]samples. Also, a spurious signal uncertainty can be evaluated by applying signal + background fit to the mass distribution of the background-only MC samples.
Unbinned Fit

The binned fit is used for 𝜇post-tag in this thesis, which differs from theunbinned fit used in the calibration work before [22]. Though the unbinned fit will takemore time to perform, it is more accurate than the binned fit, and thus should reduce thesystematic uncertainties of the scale factors.
57

Chapter 8 Conclusion and Outlook

Tagger Efficiency-Mass Dependence From the comparison plots of data and MC samples, the tagger efficiency is seen to be dependent on the large-𝑅 jet mass, causing the
curve of the dijet background to be not a smooth falling curve but wiggled and thus it
increases the difficulty of the background modeling. In this thesis, some parameters ofthe modeling functions are fixed, which may cause the systematic uncertainties to be underestimated.
The investigations into boosted Higgs boson physics presented in this thesis, including the 𝑋 → 𝑏𝑏̄ tagger introduction, calibration and improvement, has the potential forsignificant value in future searches. The methodology used to calibrate the 𝑋 → 𝑏𝑏̄
tagger using 𝑍 → 𝑏𝑏̄ events, can be also applied to calibrate the 𝑋 → 𝑐 𝑐 ̄ tagger, andpotentially enables the observation of 𝐻 → 𝑐 𝑐 ̄ (charm Yukawa), which is a goal of myfurther research. Also, these investigations carry relevance for the LHC Run 3 and upcoming HL-LHC plans, and we look forward to obtaining further insights in the future
regarding boosted Higgs boson studies and new physics searches.

58

References

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ATLAS Collaboration. Observation of a new particle in the search for the Standard Model
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Chatrchyan S, et al. Observation of a New Boson at a Mass of 125 GeV with the CMS Experiment at the LHC. Phys. Lett. B, 2012, 716: 30-61. DOI: 10.1016/j.physletb.2012.08.021.

[4]

ATLAS Collaboration. Combined measurement of the Higgs boson mass from the 𝐻 → 𝛾𝛾and 𝐻 → 𝑍𝑍 ∗ → 4ℓ decay channels with the ATLAS detector using √𝑠 = 7, 8 and 13 TeV 𝑝𝑝
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[5]

ATLAS Collaboration. Evidence of off-shell Higgs boson production from ZZ leptonic decay
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[6]

ATLAS Collaboration. Measurement of Higgs boson production in the diphoton decay channel
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Khachatryan V, et al. Observation of the Diphoton Decay of the Higgs Boson and Measurementof Its Properties. Eur. Phys. J. C, 2014, 74(10): 3076. DOI: 10.1140/epjc/s10052-014-3076-z.

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ATLAS Collaboration. Measurements of Higgs boson production and couplings in the fourlepton channel in pp collisions at center-of-mass energies of 7 and 8 TeV with the ATLAS
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Chatrchyan S, et al. Measurement of the Properties of a Higgs Boson in the Four-Lepton Final
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Appendix A Additional Plots

Appendix A Additional Plots

1000

Number of events

Number of events

A.1 Additional Plots for Comparison of Data and Simulation

data
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Data/MC

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Figure A.1 The comparison of data and MC samples prediction after 50% WP of 𝑋 → 𝑏𝑏̄ tagger
for different 𝑝𝑇 bins. Different MC samples are stacked together. The MC error is shown as theshaded band.

65

Data/MC

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2400
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data
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tt
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600

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60 70

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Leading large-R jet mass [GeV]

Figure A.2 The comparison of data and MC samples prediction after 70% WP of 𝑋 → 𝑏𝑏̄ tagger
for different 𝑝𝑇 bins. Different MC samples are stacked together. The MC error is shown as theshaded band.

66Appendix A Additional Plots

3000

Number of events

Number of events

4000

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Figure A.3 The comparison of data and MC samples prediction after 80% WP of 𝑋 → 𝑏𝑏̄ tagger
for different 𝑝𝑇 bins. Different MC samples are stacked together. The MC error is shown as theshaded band.

67

Appendix A Additional Plots

Number of events

A.2 Additional Plots and Tables for Signal Modeling

300
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Zbb
fit

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Figure A.4 The 𝜒 2 fits to the 𝑍 candidate mass distribution via a DSCB function, passing the𝑋 → 𝑏𝑏̄ 50% WP for 450 ≤ 𝑝𝑇 < 1000 GeV.
Table A.1 The parameters of the DSCB function for the 𝑍 → 𝑏𝑏̄ MC templates after the 𝑋 → 𝑏𝑏̄
tagging requirement at 50% working point for 450 ≤ 𝑝𝑇 < 1000 GeV.
𝑁

172.4 ± 4.37

𝑚𝑍

87.2 ± 0.20

𝜎𝑍

7.56 ± 0.22

𝛼𝐿

1.08 ± 0.10

𝑛𝐿

13.1 ± 11.7

𝛼𝐻

2.08 ± 0.13

𝑛𝐻

0.62 ± 0.18

2

135.4

𝜒 /NDF

1.46

Yield

3709.8𝜒
2

68

Number of events

Appendix A Additional Plots

300
250

Xbb 70%χ^2/NDF: 1.637

Zbb
fit

200
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60 70

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Figure A.5 The 𝜒 2 fits to the 𝑍 candidate mass distribution via a DSCB function, passing the𝑋 → 𝑏𝑏̄ 70% WP for 450 ≤ 𝑝𝑇 < 1000 GeV.
Table A.2 The parameters of the DSCB function for the 𝑍 → 𝑏𝑏̄ MC templates after the 𝑋 → 𝑏𝑏̄
tagging requirement at 70% working point for 450 ≤ 𝑝𝑇 < 1000 GeV.
𝑁

227.5 ± 4.74

𝑚𝑍

87.3 ± 0.18

𝜎𝑍

7.86 ± 0.18

𝛼𝐿

1.11 ± 0.10

𝑛𝐿

13.6 ± 11.8

𝛼𝐻

2.12 ± 0.08

𝑛𝐻

0.31 ± 0.08

2

152.1

NDF

93

𝜒 2 /NDF

1.64

Yield

5189.3

𝜒

69

Number of events

Appendix A Additional Plots300

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250

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Figure A.6 The 𝜒 2 fits to the 𝑍 candidate mass distribution via a DSCB function, passing the𝑋 → 𝑏𝑏̄ 80% WP for 450 ≤ 𝑝𝑇 < 1000 GeV.
Table A.3 The parameters of the DSCB function for the 𝑍 → 𝑏𝑏̄ MC templates after the 𝑋 → 𝑏𝑏̄
tagging requirement at 80% working point for 450 ≤ 𝑝𝑇 < 1000 GeV.
𝑁

252.5 ± 5.01

𝑚𝑍

87.4 ± 0.17

𝜎𝑍

8.00 ± 0.18

𝛼𝐿

1.14 ± 0.10

𝑛𝐿

9.24 ± 5.80

𝛼𝐻

2.11 ± 0.07

𝑛𝐻

0.23 ± 0.07

2

164.2

NDF

93

𝜒 2 /NDF

1.77

Yield

5943.0𝜒

70Appendix A Additional Plots

A.3 Additional Results for Fit Model Uncertainties
Table A.4 The parameters of fitting the real data after the 𝑋 → 𝑏𝑏̄ tagging requirement at 60%
working point for different 𝑝𝑇 bins for alternative mass range.
Large-𝑅 jet 𝑝𝑇 [GeV]Parameter450-500 GeV

500-600 GeV

600-1000 GeV

𝑚𝑍

82.9 ± 0.78

84.7 ± 0.89

85.4 ± 1.13

𝜎𝑍

7.73 (fixed)

7.73 (fixed)

7.73 (fixed)

𝛼𝐿

1.08 (fixed)

1.08 (fixed)

1.08 (fixed)𝑛𝐿

16.4 (fixed)

16.4 (fixed)

16.4 (fixed)

𝛼𝐻

2.12 (fixed)

2.12 (fixed)

2.12 (fixed)𝑛𝐻

0.44 (fixed)

0.44 (fixed)

0.44 (fixed)

𝑎08.60 ± 9.37

−111.7 ± 7.85

30.63 ± 1.59

𝑎1

2139.8 ± 12.66

2153.0 ± 10.42

7.34 ± 0.10

𝑎2−2645.0 ± 8.35

−2602.8 ± 11.96−8.56 ± 0.10

𝑎3

942.5 ± 6.46

914.5 ± 7.21

2.93 ± 0.06

2

97.1

101.0

100.6

𝜒 2 /NDF

1.16

1.20

1.20

Signal2055.51520.3889.0

Background46114.4

36478.4

17696.8𝜒

A.4 Additional Results for Spurious Signal Test
Table A.5 The parameters of fitting the mass distribution of the dijet MC samples using signal
plus background model after the 𝑋 → 𝑏𝑏̄ tagging requirement at 60% working point for different
𝑝𝑇 bins.
Large-𝑅 jet 𝑝𝑇 [GeV]Parameter
Spurious Signal

450-500 GeV

500-600 GeV

600-1000 GeV−502.386 ± 240.502−23.9656 ± 155.688−111.684 ± 62.2142

71

Appendix A Additional Plots

A.5 Additional Results for 𝜇pre-tag Measurement
Table A.6 Systematics on 𝜇pre−tag ,450 < 𝑝𝑇 < 500

Modeling 𝑍(ℓℓ) + jets

+0.18
−0.14

Modeling 𝑍𝑍±0.002Modeling 𝑊 𝑍±0.004Modeling 𝑊 𝑊±0.000Modeling 𝑍(𝜏𝜏) + jets

±0.006

Modeling 𝑊 (ℓ𝜈) + jets

±0.000Luminosity
Total

Table A.7 Yields, 450 < 𝑝𝑇 < 500

+0.02
−0.02
+0.18
−0.14

±0.002Modeling 𝑊 𝑍±0.004Modeling 𝑊 𝑊±0.000Modeling 𝑍(𝜏𝜏) + jets

±0.000Modeling 𝑊 (ℓ𝜈) + jets

±0.000Luminosity
Total

+0.02
−0.02
+0.11
−0.10

±0.002Modeling 𝑊 𝑍±0.006

Modeling 𝑊 𝑊±0.000Modeling 𝑍(𝜏𝜏) + jets

±0.000Modeling 𝑊 (ℓ𝜈) + jets

±0.000Luminosity
Total

𝑊𝑍

31.6 ± 1.2

𝑊𝑊0.0 ± 0.0𝑍(𝜏𝜏) + jets

50.4 ± 1.9

𝑊 (ℓ𝜈) + jets

0.08 ± 0.05

Background97.3 ± 2.4

signal + background

1704.8 ± 7.3
1967

𝑍(ℓℓ) + jets

1559.9 ± 6.1

𝑍𝑍15.4 ± 0.9

𝑊𝑍34.1 ± 1.3

𝑊𝑊0.0 ± 0.0𝑍(𝜏𝜏) + jets

0.14 ± 0.07

𝑊 (ℓ𝜈) + jets

0.10 ± 0.06

Background49.7 ± 1.5

signal + background1609.6 ± 6.3
1827

Table A.11 Yields, 600 < 𝑝𝑇 < 1000

+0.41
−0.25

Modeling 𝑍𝑍

15.3 ± 0.8

dataTable A.10 Systematics on 𝜇pre−tag ,600 < 𝑝𝑇 < 1000

Modeling 𝑍(ℓℓ) + jets

𝑍𝑍

Table A.9 Yields, 500 < 𝑝𝑇 < 600

+0.11
−0.09

Modeling 𝑍𝑍

1607.5 ± 6.9

data

Table A.8 Systematics on 𝜇pre−tag ,500 < 𝑝𝑇 < 600

Modeling 𝑍(ℓℓ) + jets

𝑍(ℓℓ) + jets

+0.02
−0.02
+0.42
−0.25

𝑍(ℓℓ) + jets

891.2 ± 3.9𝑍𝑍6.8 ± 0.6

𝑊𝑍

27.4 ± 1.1

𝑊𝑊0.0 ± 0.0𝑍(𝜏𝜏) + jets

−0.03 ± 0.10

𝑊 (ℓ𝜈) + jets

0.12 ± 0.05

Background34.3 ± 1.2

signal + background925.5 ± 4.1

data

72

1137

Appendix B Identifying Boosted Higgs Bosons Decaying using Graph Neural Network

Appendix B Identifying Boosted Higgs Bosons
Decaying using Graph Neural Network
B.1 Introduction
GN2X, a new algorithm has been developed to identify the decays of high-𝑝𝑇 Higgs
̄ 𝑐 ̄ pairs. This algorithm is trained to classify large-𝑅 jets based on theirbosons to 𝑏𝑏/𝑐
origin, discriminating jets. The background processes are considered to be multijet processes and fully hadronic top-quark decays. GN2X utilizes the recent advances in graphneural networks (GNNs) and transformer architectures to learn the jet substructure.
In GN2X, the charged particle trajectories within the large-𝑅 jet are employed to discern the characteristic indicators of 𝑏- and 𝑐-hadron decays: displaced secondary (andperhaps tertiary, in the case of 𝑏-hadrons) vertices and tracks with substantial impact parameters. Other GN2X versions are also investigated, where trajectories are amalgamatedwith large-𝑅 jet calorimeter constituents and subjets.

B.2 Neural Network Architecture and Training
The base GN2X model takes three large-𝑅 jet variables and 20 variables associatedwith each track as input to the network. The large-𝑅 jet inputs include the jet transverse
momentum, signed pseudorapidity, and mass. The complete set of inputs is presented inTable B.1. Up to 100 tracks associated with the jet are provided to the network, sorted bydecreasing transverse impact parameter significance denoted as 𝑠(𝑑0 ).
The GN2X architecture is an advancement of the GN1 architecture [B.1], as shownin Figure B.2. GN1 employs a Graph Neural network, while GN2X (and GN2) adopts
a Transformer network architecture [B.2]. The model receives the sequence of tracks ina jet as input, with jet- and track-level inputs. Concatenating the jet and track inputs, as
shown in Figure B.1, the resulting combined jet-track sequence vectors are input into a
per-track initializer network. The initializer network for each input type comprises twodense layers projecting the input representations to an embedding dimension of 192.
The track representations feed into a Transformer Encoder, where the transformer
architecture utilized aligns with that introduced in Ref. [B.3]. Multiple Layer Normalization layers [B.4] are incorporated to enhance stability during training, along with residual73Appendix B Identifying Boosted Higgs Bosons Decaying using Graph Neural Network

Table B.1

Input features to the GN2X model.

Jet Input

Description

𝑝𝑇

Large-𝑅 jet transverse momentum𝜂

Signed large-𝑅 jet pseudorapidity

mass

Large-𝑅 jet mass

Track Input

Description

𝑞/𝑝Track charge divided by momentum (a measure of curvature)𝑑𝜂

Pseudorapidity of track relative to the large-𝑅 jet 𝜂𝑑𝜙Azimuthal angle of the track, relative to the large-𝑅 jet 𝜙𝑑0

Closest distance from track to primary vertex (PV) in the transverse plane𝑧0 sin 𝜃

Closest distance from track to PV in the longitudinal plane𝜎(𝑞/𝑝)

Uncertainty on 𝑞/𝑝labels for training, truth production vertices
within 0.1 on
mmtrackare merged.
𝜎(𝜃)Uncertainty
polarTrack-pairs
angle 𝜃 where one or bothof the tracks in the pair have an origin label of either Pileup or Fake are given a label of 0. Using the𝜎(𝜙)Uncertainty
track azimuthal
anglecan𝜙 be grouped into
pairwise predictions from the model,collections ofoncommonlycompatible tracks
vertices. The addition of this auxiliary training objective removes the need for inputs from a dedicated𝑠(𝑑0)secondaryvertexing algorithm. Lifetime signed transverse IP significance𝑠(𝑧0Bothsin 𝜃)
signedaslongitudinal
IP onsignificanceauxiliary training objectivesLifetime
can be considered“stepping stones”
the way to classifying theflavour of the jet. By requiring the model to predict the truth origin of each track and the vertex compatibility

nPixHitsof pixelof each track-pair, the model is guided to learnNumber
representationsof thehits
jet which are connected to theunderlying physics and therefore relevant for classifying the jet flavour.

nSCTHits

Number of SCT hitsnIBLHits
3.3 Architecture

Number of IBL hits

nBLHits

Number of B-layer hits

As discussed above, the GN1 model combines a graph neural network architecture [38] with auxiliary
training objectives in order to determine the Number
jet flavour. of
Coarseoptimisationof the network architecturenIBLSharedsharedIBL hits
hyperparameters, for example number of layers and number of neurons per layer, has been carried out tomaximise the tagging efficiency.
nIBLSplit
Number of split IBL hits
The model architecture is based on a previous
implementationof a pixel
graph neuralnPixShared
Numberof shared
hits network jet tagger [9].
As compared to the previous approach, GN1 uses a only a single graph neural network and makes use ofa more sophisticated graph neural network layer[39], described
nPixSplit
Numberof splitbelow.
pixelThesehits changes yield improved
tagging performance and a significant reduction in training time with respect to the previous approach.

nSCTShared

Number of shared SCT hits

The model takes jet- and track-level information as inputs, as detailed in Section 3.1. The jet inputs areconcatenated with each track’s inputs, as shown in Fig. 2. The combined jet-track vectors are then fed into
a per-track initialisation network with three hidden layers, each containing 64 neurons, and an output layer
with a size of 64, as shown in Fig. 3. The track initialisation network is similar to a Deep Sets model [40],but does not include a reduction operation (mean or summation) over the output track representations.

Figure The
2: Theinputs
inputs to GN1
are thetwo jet features
andtwoan array𝑛tracks , wheretrack
described
byjf = 2),
Figure B.1
to theGN2X
model(𝑛arethejetoffeatures(𝑛each3), isandan arrayof 𝑛t ,
jf = jet-track
21 track features (𝑛tf = 21). The jet features are copied for each of the tracks, and the combined
vectors of
where eachtrack
is thedescribed
by 20 track features (𝑛tf = 20). The jet features are copied for eachlength23 form
inputs of GN1.
of the tracks, and the combined jet-track vectors of length 23 form the inputs of GN2X [B.1].

A fully connected graph is built from the outputs of the track initialisation network, such that each node in
the graph neighbours every other node. Each node ℎ𝑖 in the graph corresponds to a single track in the jet,and is characterised by a feature vector, or representation. The per-track output representations from theinitialisation networks are used to populate the initial feature vectors of each node in the graph. In each74
layer of the graph network, output node representations ℎ𝑖′ are computed by aggregating the features of ℎ𝑖and neighbouring nodes N𝑖 as described in Ref. [39]. First, the feature vectors of each node are fed into afully connected layer W, to produce an updated representation of each node Wℎ𝑖 . These updated feature
vectors are used to compute edge scores 𝑒(ℎ𝑖 , ℎ 𝑗 ) for each node pair,Appendix B Identifying Boosted Higgs Bosons Decaying using Graph Neural Network
Pooled graphrepresentation

GNN

Graph
Network

Jet flavour
prediction

Intial track
representation

Node
Network

Combined
Inputs

Track
Initialiser

Track origin
predictions

Conditional track
representation

Edge
Network

Vertexpredictions

Figure B.2 The network architecture of GN1. Inputs are fed into a per-track initialization network, which outputs an initial latent representation of each track. These representations are thenused to populate the node features of a fully connected graph network. After the graph network,
the resulting node representations are used to predict the jet flavor, the track origins, and the trackpair vertex compatibility [B.1].
𝑒(ℎ𝑖 , ℎ 𝑗 ) = a⊥ 𝜃 Wℎ𝑖 ⊕ Wℎ 𝑗 ,(1)connections. GN2X employs 6 encoder blocks with 4 attention heads. The heteroge-

where ⊕ denotes vector concatenation, 𝜃 is a non-linear activation function, and a is a second fully
neousmodels refrain from using separate transformer encoders for each input type, given
connected layer. These edge scores are then used to calculate attention weights 𝑎 𝑖 𝑗 for each pair of nodes

the softmax
functioninover
the edge scores
theusing
substantial
increaseparametercount.

The resulting representation of each track is then combined to create a global rep𝑎 𝑖 𝑗 = softmax 𝑗 𝑒(ℎ𝑖 , ℎ 𝑗 ) .

(2)

resentation of the jet for classification. This global representation is crafted through a′

Finally, the updated node representation ℎ𝑖 is computed by taking the weighted sum over each updated
weightedsum over the track representations, where the attention weights for the sum arenode representation Wℎ𝑖 , with weights 𝑎 𝑖 𝑗learned during training.
ℎ𝑖 = 𝜎 𝑎 𝑖 𝑗 · Wℎ 𝑗  .

 a∑︁ to GN1 [B.1]. The training sesGN2X undergoes training employing′ method akin(3) 4 NVIDIA A100 GPUs, requir∈ N𝑖sions for GN2X are conducted on a cluster 𝑗equippedwith

ingTheapproximately
1 hour tocompletean epochmillionabove set of operations
constitutea singlegraph comprising
network layer.62Threesuchjets.
layersTheare model
stacked istoconstruct the graph network, representing a balance between achieving optimal performance and preventing
overtraining. The final output node feature vectors from the network are representations of each track thatconditional
the otherthe
tracksin the andjet. The
output representationfor eacharetrack
is combinedusing
outarethetraining on
process,
primary
auxiliarytasks of the model
assignedweights
a weighted sum to construct a global representation of the jet, where the attention weights for the sum
to areensurethat
theirtraining.
lossesThree
are ofcomparable
magnitude,
mirroring
the approachlearnedduringseparatefully connected
feedforward
neural networks
are thenusedused into
independently
perform
thedifferent
classification
objectives
of
GN1.
Each
of
the
objectives
makes
use
of
Ref. [B.1]. Additionally, the model is subjected to training with a one-cycle learning rate
the global representation of the jet. A summary of the different classification networks used for the various
policy,whereintheislearning
rate initiates
at a minimal value of 10−7 and steadily increases
training
objectives
shown in Table
4.

fine-tuned utilizing the Adam optimizer with a batch size of 1,000 for 40 epochs. Through-A nodenetwork,
which takes
as inputs thefeaturesa single
output node fromthe graphover
the classification
initial 4 epochs,
reachinga maximumvalue
of from
0.005.
Subsequently,
the learning
network and the global jet representation, predicts the track truth origin, as defined in Table 3. This

−7
rate
undergoesa gradual
decrease,concluding
at 10.
network
has threehidden layers
containing
128, 64 and32 neurons
respectively, and an output size ofseven, corresponding to the seven different truth origins.

References
9 Jet Flavour Tagging with the ATLAS Detector.
[B.1] ATLAS Collaboration. Graph Neural Network

2022.

75

Appendix B Identifying Boosted Higgs Bosons Decaying using Graph Neural Network[B.2] Vaswani A, Shazeer N, Parmar N, et al. Attention is all you need. Advances in neural information processing systems, 2017, 30.
[B.3] Shleifer S, Weston J, Ott M. Normformer: Improved transformer pretraining with extra normalization. 2021.
[B.4] Ba J L, Kiros J R, Hinton G E. Layer normalization. 2016.

76

Appendix C Studies of training GN2X tagger using Equivariant Subgraph Aggregation Networks

Appendix C Studies of training GN2X tagger using
Equivariant Subgraph Aggregation Networks
This appendix presents a study of training the GN2X tagger using a new method
called subgraphs. It’s based on an architecture called Equivariant Subgraph Aggregation
Networks (ESANs) [C.1].

C.1 Motivation
The architectures of Message-Passing Neural Networks (MPNNs) are at most as expressive as the Weisfeiler-Lehman Graph Isomorphism Test (WL test) [C.2]. However,the WL test sometimes cannot distinguish between very simple graphs, as shown in Figure
C.1. To overcome this limitation, an observation is that these graphs may not be distinguishable by an MPNN, but they often contain distinguishable subgraphs. Thus, ESANs
represent each graph as a set of subgraphs derived by some predefined policy.

Figure C.1 Left: A pair of graphs not distinguishable by the WL test. Right: The corresponding
bags (multisets) of edge-deleted subgraphs, which can be distinguished by ESAN [C.1].

Considering the subjets structure of large-𝑅 jets for the boosted Higgs boson tagging,an idea to improve the current performance of the GN2X tagger is to use the subjets as
inputs of the GN2X tagger.

77

Appendix C Studies of training GN2X tagger using Equivariant Subgraph Aggregation Networks

C.2 Architecture and Training
ESAN uses bags of subgraphs as inputs, as shown in Figure C.2. To generate subgraphs, a policy called node-deleted policy is used. In this policy, a graph is mapped tothe set containing all subgraphs that can be obtained from the original graph by removing a single node. Notably, only 3 nodes to remove are considered in this study. The
inputs, which are bags of subgraphs, are fed into an architecture called DSS-GNN, whichis shown in Figure C.3.

Figure C.2 The symmetry structure of a bag of subgraphs, in this case, the set of all 𝑚 = 3
edge-deleted subgraphs. This set of subgraphs is represented as an 𝑚 × 𝑛 × 𝑛 tensor [C.1].

Figure C.3 DSS-GNN layers and architecture. Left panel: the DSS-GNN architecture is composed of three blocks: a Feature Encoder, a Readout Layer and a Set Encoder. Right panel:a DSS-GNN layer is constructed from a Siamese part (orange) and an information-sharing part(yellow) [C.1].

In this study, the DSS-GNN architecture will replace the GNN part of the GN2X tagger. Inside the DSS-GNN, a so-called H-equivariant Layer is used, which is a transformer
encoder originally used by GN2X, for both the Siamese part and the information-sharing
78

Appendix C Studies of training GN2X tagger using Equivariant Subgraph Aggregation Networks

part. The large-𝑅 jets will be represented as fully connected graphs in the transformer,
where each node represents a track. The training process is similar to GN2X, except thatthe inputs are bags of subgraphs. The training sessions for this study are conducted on acluster equipped with 2 NVIDIA A100 GPUs, requiring approximately 9 hours to complete 50 epochs comprising 1 million jets.
In addition, instead of representing the large-𝑅 jets as fully connected graphs, knearest neighbor graphs are also investigated. In this case, each node still represents a
track, but only the k nearest neighbors of each track are connected to it, where the distanceis defined as the Euclidean distance in the (𝜂, 𝜙) plane. In this study, 𝑘 = 9 is used, whichis the average number of tracks in each subjet.

C.3 Results and Conclusion
The results of this study are shown in Figure C.4 and C.5. The performance of thebase GN2X tagger is also shown for comparison. The results show that the subgraphmethod is not so effective for fully-connected graphs. For k-nearest neighbor graphs, thesubgraph methods can improve the performance, compared to the fully-connected graphs.
However, graphs with attention, or so-called transformer encoder architecture, have better
performance than the k-nearest neighbor graphs method. In conclusion, the transformer
is a highly advanced architecture for dealing with the large-𝑅 jets, which contain lots ofsubjet or tracks. The transformer itself can learn the complex substructure, even better
than the subgraph methods.

References[C.1] Bevilacqua B, Frasca F, Lim D, et al. Equivariant subgraph aggregation networks. 2021.
[C.2] Leman A. The reduction of a graph to canonical form and the algebra which appears therein//2018. https://api.semanticscholar.org/CorpusID:49579538.

79Appendix C Studies of training GN2X tagger using Equivariant Subgraph Aggregation Networks

Figure C.4

The background rejection versus signal efficiency for 𝐻 → 𝑏𝑏̄ tagging.

80Appendix C Studies of training GN2X tagger using Equivariant Subgraph Aggregation Networks

Figure C.5

The background rejection versus signal efficiency for 𝐻 → 𝑐 𝑐 ̄ tagging.

81