Master Thesis
Signiﬁcant improvement of Quark/Gluon separation
with the ATLAS detector at the LHC（LHC-ATLAS 実験におけるクォーク．グルーオンの識別の向上）

CHENG-YU LU

The University of Tokyo
Graduate School of Science
January 2022

1

Abstract
Higgs boson was discovered at the Large Hadron Collider (LHC) in 2012 andmany measurements were performed for understanding its properties. The
Higgs mechanism predicts the mass of elementary particles and provides thesource of the electroweak symmetry breaking. The vector boson scatteringwith the same leading order term as Feynman diagrams gives an essential way
to test the relation between the Higgs mechanism and electroweak symmetry
breaking. In addition, beyond the standard model physics predicts other
Higgs sectors, denoting another contribution to the vector boson scattering
process.
The semileptonic vector boson scattering process provides more statistics
than the full-leptonic process and fewer QCD backgrounds than the fullhadronic process. Hence, this thesis aims to improve the sensitivity of thesemileptonic process. There are four quarks in the event, two from the vectorboson decay, the other two from the spectator quarks, which originate frompartonic quarks. The considerable gluons produced due to the QCD eﬀect
are the major backgrounds in this channel.
Machine-learning models to separate quark-induced hadron jets from gluoninduced ones (q/g tagging) are developed in this thesis. Several kinds ofneural network q/g tagging models are studied and found to have signiﬁcant
improvement compared to the conventional boosted decision tree machinelearning model. The best neural network q/g tagging model has improved thebackground rejection rate by approximately 10% than the boosted decision
tree model. Developed q/g tagging is applied to the semileptonic vectorboson scattering analysis, and the sensitivity is improved by around 8.2%.
There is still room to improve the sensitivity more in the future analysis,
which is discussed in the last part of this thesis. As a result, the eﬃciency ofsearching signal became better but still have space to develop.

2

Acknowledgments
I would like to express my sincere thanks to everyone who helped me complete this thesis, especially the following people.
To begin with, I am deeply indebted to my supervisor, Prof. Shoji Asai forsupporting me not only in the research but also in getting used to my student
life abroad. He gave plenty of novel ideas and his expansive view of particle
physics always provides another insight.
I would also like to extend my incredible gratitude to Dr. Takuya Nobe.
His knowledge of theoretical and experimental particles physics was aweinspiring. His precious advices have improved my study and analysis signiﬁcantly during the discussions. I have learned a lot about experimental
particle physics from his fantastic foresight.
Without the support and nurturing of Dr. Masahiko Saito, it is impossible
to ﬁnish this study. He has a deep understanding of particle physics andmachine learning, which fascinates me immensely. He has warmly helped mystudies from the experimental particle physics knowledge to the technicaldetails of the analysis.
I very much appreciate Prof. Junichi Tanaka, who invited me to participate
in the seminar. I am grateful to have his support that gave me a stage topresent my research and have a deeper discussion.
I would like to give special thanks to Prof. Koji Terashi, Prof. Yasuyuki
Okumura and Dr. Tatsuya Masubuchi. The discussions in the seminar arealways impressed me and have vastly improved the quality of my studies.
Finally, I must thank my parents for their support throughout my life. Despite the pandemic, they still encourage me to chase my dreams and always
stay positive, giving me many strengths. Also, thanks to my little sister, whoalways brings joy to me.

Contents
1 Introduction

5

2 Background Knowledge
2.1 The Standard Model of particle physics . . . . . . . . . . . . .
2.1.1 Gauge Interaction . . . . . . . . . . . . . . . . . . . . .
2.1.2 Elementary Particle . . . . . . . . . . . . . . . . . . . .
2.1.3 Higgs Potential and Electronweak Symmetry . . . . . .
2.2 Weak Vector Boson Scattering . . . . . . . . . . . . . . . . . .
2.2.1 VBS Processes . . . . . . . . . . . . . . . . . . . . . .
2.3 Jet Struture . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.1 Reconstruction for Jet . . . . . . . . . . . . . . . . . .
2.3.2 Quark Jet and Gluon Jet . . . . . . . . . . . . . . . . .
2.3.3 Jet Discriminant . . . . . . . . . . . . . . . . . . . . .

7
7
7
8
9
10
10
13
13
15
15

3 The ATLAS Experiment at the LHC
3.1 Overview of the ATLAS Detector . . . . . . . . . . . . . . . .
3.2 Inner Dector . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.1 Pixel Detector . . . . . . . . . . . . . . . . . . . . . . .
3.2.2 Semiconductor Tracker . . . . . . . . . . . . . . . . . .
3.2.3 Transition Radiation Tracker . . . . . . . . . . . . . .
3.3 Calorimeters . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.1 Electromagnetic Calorimeter . . . . . . . . . . . . . . .
3.3.2 Hadronic Calorimeter . . . . . . . . . . . . . . . . . . .
3.4 Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.1 Tracks and Vertices . . . . . . . . . . . . . . . . . . . .
3.4.2 Topological-Clusters . . . . . . . . . . . . . . . . . . .

19
19
21
21
21
23
24
26
26
27
27
28

4 Quark/Gluon Tagging
4.1 MC sample . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Quark/Gluon Tagging Models . . . . . . . . . . . . . . . . . .
4.2.1 BDT Model . . . . . . . . . . . . . . . . . . . . . . . .

30
30
31
32

3

CONTENTS

4

4.2.2 MLP Model . . . . . . . . . . . . . . . . . . . . . . . .
4.2.3 CNN Model . . . . . . . . . . . . . . . . . . . . . . . .
4.2.4 MLP-CNN Model . . . . . . . . . . . . . . . . . . . . .
4.2.5 Pointwise Model . . . . . . . . . . . . . . . . . . . . .
Performance of q/g Tagging Models . . . . . . . . . . . . . . .
4.3.1 Receiver Operating Characteristic Curve Result . . . .
4.3.2 Diﬀerence Between Pythia and Herwig MC sample . .

34
35
38
39
43
43
49

5 1-lepton Semileptonic VBS Application
5.1 Introduction of MC samples . . . . . . . . . . . . . . . . . . .
5.1.1 Signal Sample and Background Samples . . . . . . . .
5.1.2 Physics Object . . . . . . . . . . . . . . . . . . . . . .
5.2 1-lepton Event Selection . . . . . . . . . . . . . . . . . . . . .
5.2.1 Preselection . . . . . . . . . . . . . . . . . . . . . . . .
5.2.2 BDT Discriminant . . . . . . . . . . . . . . . . . . . .
5.2.3 Quark/Gluon Tagging Enhance . . . . . . . . . . . . .
5.3 Application Results . . . . . . . . . . . . . . . . . . . . . . . .
5.3.1 Discovery signiﬁcance and Uncertainty . . . . . . . . .
5.3.2 Sensitivity of the Baseline Analysis . . . . . . . . . . .
5.3.3 q/g tagging Improving Limit . . . . . . . . . . . . . . .
5.3.4 q/g tagging Improvement . . . . . . . . . . . . . . . . .

52
53
53
54
58
58
61
63
65
66
67
67
68

6 Conclusions

72

A Input and output of Quark/Gluon Tagging Models

74

B The distributions for 1-lepton semileptonic preselection

77

4.3

C Input Variable of BDT Discriminant80
C.1 2leading input variables . . . . . . . . . . . . . . . . . . . . . 80
C.2 minmass input variables . . . . . . . . . . . . . . . . . . . . . 83
D Tuning BDT discriminant and q/g tagger
D.1 Neural 2leading . . . . . . . . . . . . . . . . . . . . . . . . . .
D.2 BDT 2leading . . . . . . . . . . . . . . . . . . . . . . . . . . .
D.3 Neural minmass . . . . . . . . . . . . . . . . . . . . . . . . . .
D.4 BDT minmass . . . . . . . . . . . . . . . . . . . . . . . . . . .

85
85
88
90
92

E Order Stragety

94

Chapter 1
Introduction
The ultimate purpose of particle physics is to discover the equation of motion
which is able to describe elementary particles in our universe. Although thestandard model (SM) of elementary particle physics predicts numerous particle phenomena, there are still several unexplained issues. For instance, darkenergy [1], dark matter [2], Higgs boson mass [3] and strong CP problem [4]are the mysteries needed to uncover. These new physics beyond SM (BSM)
are believed to exist at the TeV-scale or higher energy region.
√
The Large Hadron Collider (LHC), which the center-of-mass energy s = 13
TeV, is the largest and highest energy collider in the world. TeV-scale energy experiment gives us a chance to examine the properties of elementary
particle physics. The ATLAS detector at the LHC is built to investigate
the latest high-energy physics research. The ATLAS [5] and CMS [6] experiments at the LHC made a milestone for the discovery of the Higgs bosonin 2012, which means the SM is ﬁnally completed. In order to understandthe beyond SM (BSM) physics, LHC will be upgraded√to High Luminosity
LHC (HL-LHC), providing a center-of-mass energy of s = 14 TeV with an
integrated luminosity up to 3000 fb−1 .
Vector Boson Scattering (VBS) is a sensitive probe to examine the electroweak symmetry breaking (EWSM) in SM and BSM physics. If the coupling between the vector bosons and Higgs deviate from the SM prediction,
the VBS cross-section increase when the center-of-mass energy rises to thehigher energy scale. Moreover, the cross-section of the VBS process is expected to increase from new resonances, originating from an extended Higgs
sector predicted from the BSM model [7]. SM examination and BSM investigation imply the VBS process’s importance, motivating this thesis toimprove the VBS signal searching.
5CHAPTER 1. INTRODUCTION

6The VBS process decays to two vector bosons (W or Z boson). Both W
and Z bosons have hadronic and leptonic decay channels. W boson decays
into qq and ℓν, hadronically and leptonically, respectively. Z boson decays
hadronically and leptonically to qq and ℓℓ or νν. (νν is not considered infull-leptonic decay since the analysis strategy is diﬀerent from ℓℓ.) The fullleptonic decay has the most signiﬁcant signal-to-background ratio comparedto other processes. The full-leptonic channel was observed during Run I
at the LHC and conﬁrmed by Run II. Besides the full-leptonic VBS process, full-hadronic and semileptonic are also measured by the ATLAS [8] andCMS collaborations [9]. The full-leptonic VBS process has a severe statistical problem because of the low branch ratio of leptonic decays in vectorbosons. The full-hadronic VBS process research is highly aﬀected by quantum chromodynamics (QCD), causing a large amount of background. Hence,
this thesis focuses on the semileptonic decay process.
Since the gluons generated from the QCD are the primary background particles in the semileptonic VBS process, it is essential to develop a tool toseparate the quarks and gluons, which is known as quark/gluon tagging (q/gtagging). The q/g tagging has been developed for a while since gluons usually represent an annoying background source. Furthermore, neural networkmodels have played a pivotal role in machine learning in the last decades.
Compared to conventional machine learning such as BDT, neural networkmodels are able to make use of more low-level information, providing a way
to avoid information loss. This thesis discusses several neural networks q/g
tagging models and examines the improvement. The validation of q/g tagging models considered in this thesis is taken by the 1-lepton semileptonic
VBS process for convenience.
This thesis consists of ﬁve chapters: Chapter 2 introduces some brief particle physics theory and the background knowledge for this study. The innerdetector, calorimeters and some functions in the ATLAS are demonstrated
in Chapter 3. The discussion of quark/gluon tagging models and their performance is shown in Chapter 4. Chapter 5 describes the deﬁnitions of thephysics objects of the 1-lepton semileptonic VBS process. Then, the application and improvement of q/g tagging are examined by applying the q/g
tagging models to the 1-lepton semileptonic VBS process. Chapter 6 gives abreif conclusion of entire thesis.

Chapter 2
Background Knowledge
Chapter 2 gives a brief introduction to the semileptonic VBS analysis. Section 2.1 describes the SM of elementary particle physics. Section 2.2 shows
the importance of weak vector boson scattering and the mechanism of theprocess. Since jet phenomenology takes a vital role in the VBS scatteringand the q/g tagging study in this thesis is also making use of jets, the introductions to the jet structure are explained in Section 2.3.

2.1

The Standard Model of particle physics

The success of the Standard Model in explaining the matter interactions
governed by three fundamental forces is astounding. There are mainly threeparts: the gauge interaction, the fermion ﬁelds, and the Higgs mechanism.
In Section 2.1.1, the introduction of the gauge interaction is given to explain
the interaction between fermion and gauge particles. The fermion ﬁelds dueto the matters themselves are described in Section 2.1.2. Section 2.1.3 introduces the Higgs mechanism used to demonstrate the masses of the elementary
particle due to the EWSB.

2.1.1

Gauge Interaction

One of the most remarkable insights in particle physics is that interactions
are governed by the symmetry principle. The gauge interaction is one ofsymmetry mechanism and the gauge transformation is shown in Equation
2.1.
ψ(x) → ψ ′ (x) = Û (x)ψ(x) = eiqχ(x) ψ(x),(2.1)
where ψ is a complex ﬁeld and qχ(x) here can be seen as a gauge parameter. The phase qχ(x) varies at all points in space-time. Other than U (1)7CHAPTER 2. BACKGROUND KNOWLEDGE

8transformation, there are also SU (2) transformation dictating electroweak
interaction and SU (3) transformation which describes strong force in thegauge transformation.
Using U (1), SU (2) and SU (3) symmetry, the SM Lagrangian density isderivated as following equation,1
L = − (Faµν )2 + ψ̄(iγ µ Dµ ψ) + yij ψ̄i ψj ϕ + h.c. + |Dµ ϕ|2 + µ2 ϕ† ϕ − λ(ϕ† ϕ)2 ,
4
(2.2)
a
a
a
abc b ca awhere Fµν = ∂µ Aν − ∂ν Aµ + gf Aµ Aν and Dµ = ∂µ − igAµ tr for gauge ﬁeld
A, fermion ﬁeld ψ, scalar ﬁeld ϕ, Yukawa coupling yij , Higgs self-coupling λ,representation matrices tar , gauge coupling g, structure constant fabc , matrix
representation of the Cliﬀord algebra γ µ and h.c. stands for Hermitian conjugate.
Investigating SM Lagrangian closer, fermions do not suppose to have masses
in nature in Equation 2.2. However, physicists have measured the massterm for fermion particles, which is considered from fundamental symmetry
broken. The Higgs mechanism explains the origin of masses for elementary
particles by the EWSB.

2.1.2

Elementary Particle

The electron, the electron neutrino, the up quark and the down quark are
known as the ﬁrst generation particles. As higher energy goes in the highenergy collider, further complexity of elementary particles other than the ﬁrst
generation is discovered. Second generation and third generation particles
have the same properties as ﬁrst generation particles except for their masses.
Besides, the gauge boson particles are also found at high-energy collision experiments. The gauge boson is regarded as the origin of three fundamental
forces. With the discovery of the Higgs boson at LHC, all of the elementary
particles predicted by the SM have now been observed.
The properties of all elementary particles are summarized in Table 2.1. The
fermion particles such as leptons, neutrinos and quarks are dictated by the
Fermi-Dirac statistics, indicating the proportional relation between theirmasses and Yukawa couplings. There are four kinds of gauge boson particles which are spin-1 particles and are described by Bose-Einstein statistics.
The couplings of electroweak force are demonstrated by photon γ and W± /Zboson whose masses are approximately 80/91 GeV. On the other hand, thegauge boson for strong force is massless gluon g and it has eight color multiplets. The Higgs particle is also a boson particle but with spin-0.

CHAPTER 2. BACKGROUND KNOWLEDGE

9

Table 2.1: The essential quantum number of the elementary particles in the
SM. J and Q stand for the spin and the electric charge.
ParticleJQe,µ, τ
1/2 -1νe , νµ , ντ 1/2
0u,c,t
1/2 2/3d,s,b
1/2 -1/3
γ
1
0
±
1
±1
W
Z
1
0
g
1
0
0
0
h

2.1.3

Higgs Potential and Electronweak Symmetry

The Higgs mechanism represents an integral sector of the SM. Without the
Higgs boson, the W+ W− → W+ W− scattering will violate unitarity at a
center-of-mass energy of TeV scale. The unitarity violation comes fromWL WL → WL WL scattering, where WL indicates W boson is polarized longitudinally. As a result, the violation can be associated with the massive
W bosons originating from the Higgs mechanism. The unitarity violationin WW scattering cancels out if the exchange of a scalar boson is included.
This scalar boson is the Higgs boson which can solve the violation issue, as
shown in Figure 2.1.
Consider a complex scalar ﬁeld Equation as 2.3,
1
ϕ = √ (ϕ1 + iϕ2 ),
2

(2.3)

which the Lagrangian can be written as following,
L = (∂µ ϕ)∗ (∂ µ ϕ) − V(ϕ) with V(ϕ) = µ2 (ϕ∗ ϕ) + λ(ϕ∗ ϕ)2 ,(2.4)

then substituting the Equation 2.3 into the Equation 2.4,
11
1
1
L = (∂µ ϕ1 )(∂ µ ϕ1 ) + (∂µ ϕ2 )(∂ µ ϕ2 ) − µ2 (ϕ21 + ϕ22 ) − λ(ϕ21 + ϕ22 )2 . (2.5)
22
2
4For the convex shape potential to have a ﬁnite minimum, λ must be a positive
number. Because of global U (1) symmetry, Equation 2.4 is invariant after′
ϕ → ϕ = eiα ϕ transformation. The ground state occurs when µ2 <0 isknown as EWSB. Then, the potential can be deﬁned by
ϕ21 + ϕ22 =−µ2= v2 ,
λ(2.6)

CHAPTER 2. BACKGROUND KNOWLEDGE

10

where the v in Equation 2.6 is called vacuum expectation value. Consequently, W± /Z stands for three of degrees of freedom (The mixture of theSU (2)×U (1)). The remaining one degree for Higgs potential is Higgs boson.

Figure 2.1: The mass of W boson originating from Higgs boson makes the
local gauge invariance conserved in SM model.

2.2

Weak Vector Boson Scattering

The EWSB and Higgs boson properties are often examined by the VBS
processes since the leading order Feynman diagrams are only related to electroweak bosons or Higgs bosons. VBS processes are also considered as awindow to discover the portent of the BSM. For instance, BSM predicts that
there are heavy particles that may modify the dynamics of electroweak interactions, which results in the increment of cross sections [10]. It can bemeasured in the VBS process. The Feynman diagram of VBS is shown in
Figure 2.2. The details of the VBS decaying process will be discussed in
Section 2.2.1.

2.2.1

VBS Processes

VBS processes consist of the Z bosons or W bosons scattering. The totalchannels there are W± W± , W± W∓ , W± Z and ZZ. The W± W∓ scattering
has a dominant contribution compared to the W ± W± scattering process and
VZ process, where V represents the vector boson.
W boson decays into mainly lν and qq. On the other hand, Z boson also has
dominant qq decay which is approximately 70% and less chance decay to ννand ℓℓ. The branching fractions for the W and Z bosons are given in Table

CHAPTER 2. BACKGROUND KNOWLEDGE

11

Figure 2.2: Two vector bosons are produced due to the proton-proton collision and then scattering each other.
2.2. Both Z and W bosons have leptonic and hadronic processes, implying
full-leptonic, semileptonic and full-hadronic decay in the VBS ﬁnal channel.
ZZ → 4ν ﬁnal state is counted as full-invisible because neutrinos are invisible
in the ATLAS detector. The decay branching ratio is shown at Table 2.3.
Table 2.2: The branching fractions of the W boson and Z boson are on theleft hand and right hand sides. Values are obtained from Reference [11].
Particle
Decay Branching Ratio
Particle
Decay Branching Ratioqq69.91±0.056%
qq67.41±0.27%
ee3.363±0.004%eν
10.71±0.16%
W
−→
Z
−→
µµ
3.366±0.007%µν
10.63±0.15%
ττ
3.370±0.008%
τν
11.38±0.21%
νν
20±0.055%
Table 2.3 indicates that full-hadronic channel has a dominant ratio overall ﬁnal states. However, since there is an extensive QCD background in
full-hadronic ﬁnal states, estimating the cross sections in this background isharsh. Although the full-leptonic ﬁnal states have the cleanest backgroundto analyze, the limited branching ratio is fatal for the statistics. The sec-

CHAPTER 2. BACKGROUND KNOWLEDGE

12

Table 2.3: The branching ratio of ﬁnal state for each VBS process. The fullhadronic represents WW/WZ/ZZ → 4q. The full-leptonic stands for WW →ℓνℓν, WZ → ℓνℓℓ and ZZ → ℓℓℓℓ/ℓℓνν, where ℓ is leptons e and µ, and ν
represents three kinds of neutrino (νe , νµ and ντ ). The including τ s means
there is one or more τ s in ﬁnal states. The semileptonic represents WW →ℓνqq, WZ → ℓνqq/ℓℓqq, and ZZ → ℓℓqq/ννqq. This is because the analysis
strategies of τ s are diﬀerent from the electrons and muons. The full-invisible
consists of ZZ → 4ν.
VBS Process
Final States
Branching Ratio
full-hadronic
45.7%
full-leptonic
4.7%
WW
including τ s
20.4%
semileptonic
29.2%
full-hadronic
47.3%
full-leptonic
5.8%
WZ
including τ s
13.8%
semileptonic
33.2%
full-hadronic
48.9%
full-leptonic
3.1%
ZZ
including τ s
6.6%
semileptonic
37.4%
full-invisible
4.0%CHAPTER 2. BACKGROUND KNOWLEDGE

13

ond largest branching ratio goes to the semileptonic ﬁnal state. Hence, thesemileptonic VBS ﬁnal state is a suitable process to investigate and worthwhile to improve.
In the semileptonic VBS ﬁnal state, there are four quarks in the event, detected as four jets in the ATLAS. The background mainly comes from V+jets
events, and approximately half of the selected jets are gluons. The VBS processes are studied with the luminosity of 36fb−1 in Reference [12] in the
ATLAS. The VBS processes is measured to have observed (expected) significance of 2.7 (2.5) standard deviations.

2.3

Jet Struture

Semileptonic ﬁnal states has 0-lepton, 1-lepton and 2-lepton types of ﬁnal
states, which are qqVZ → qqqqνν, qqVW → qqqqℓν and qqVZ → qqqqℓℓ.
There are four quarks in each type of ﬁnal state. The quarks and gluons
are observed as jets in the ATLAS detector, reconstructed as two kinds ofjets, respectively. One is Small-R Jet, another is Large-R Jet, where SmallR Jet primarily for quarks/gluons and Large-R Jet mostly for larger mass
particles such as W/Z/top. The neural network tagger for q/g tagging usedin this study takes Small-R Jet as the target. This section will give somebrief introductions to the jet structure. The reconstruction of the jet will
be described in Section 2.3.1. Since this study focuses on q/g tagging, thequark and gluon jets are demonstrated in Section 2.3.2. The jet discriminant
is introduced in Section 2.3.3.

2.3.1

Reconstruction for Jet

There are several stages to reconstruct a jet: ﬁrst deﬁning the four-vectors ofjet, and then deﬁning jet algorithm and parameters, and ﬁnally either smallR jets or large-R jets will be reconstructed. First of all, the four-vectors is
deﬁned as the summation of all particles in the jet, shown in the Equation
2.7.
√∑
∑
∑
∑
∑
→
−
→
−
pJ =
pi = (Ei ,Ei ) 2 − (p i ), mJ = (p i )2 ,
(2.7)
i

i

i

i

→
where Ei and −p i represent the energy and momentum of i-th particle injet. ATLAS primarily uses inner detector and topo-cluster to reconstruct
the four-vectors of each jet, which the details will be given in Section 3.2 and
3.3.

CHAPTER 2. BACKGROUND KNOWLEDGE

14

The anti-kt algorithm [13] with topo-cluster inputs is utilized for jet reconstruction at the ATLAS. Depending on the approaches of physics research,
there are two types of jets often used, one is small-R (R=0.4) EM jets, theother one is large-R (R=1.0) LCM jets [14], where EM and LCW represent
calibrated at either the electromagnetic (EM) scale or local cell weighting(LCW) scale. The jet consists of a group of particles forming a narrow coneof hadrons produced by the hadronization of quarks or gluons. Using the

Figure 2.3: The simple illustration of the anti-kt algorithm. Using the Equation 2.8 to accumulate the close particles to form the jet until the distance
between the selected jet and other particles is far enough.
anti-kt algorithm is the ﬁrst step to diﬀerentiate a small-R jet from a large-R
jet. Deﬁning a distance named dij and calculating the distance of every twoparticles to ﬁnd the minimum of d, seen in Equation 2.8.
−1
d = min(p−1T,i , pT,j )

∆2i,j
,
R2

(2.8)

where ∆2i,j = (yi − yj )2 + (ϕi − ϕj )2 , and pT,i stands for the transverse momentum of i-th particle, and yi and ϕi are the rapidity and azimuth of particle
i. Radius parameter R is a parameter of choosing small-R jet (R=0.4). Figure 2.3 gives a brief image for the anti-kt algorithm. The jets reconstructedby the anti-kt algorithm are needed to be calibrated due to some eﬀects, suchas pile-up, data/MC diﬀs and non-compensation calorimeter response [15].
The steps of anti-kt are shown as follows. In the ﬁrst step, all reconstructedparticles list is deﬁned. Then, calculate the minimum of the d ij combination
over the list. Third, if dij < dj B, then the i and j particles will be removed
and the new particle pnew = pi + pj will be added. In this step, if dij > dj B,
then the i particle will be considered as a jet. Repeat the step 1 to 3 until
no particles are left. Finally, the jets can be deﬁned from the reconstructedparticles.

CHAPTER 2. BACKGROUND KNOWLEDGE

2.3.2

15

Quark Jet and Gluon Jet

Both quarks and gluons will be hadronized to a group of hadronic particles
because of the QCD conﬁnement, which only allows the colorless states. This
group of particles is observed as a narrow cone and deﬁned as a jet in the
ATLAS. The key diﬀerence between a quark and gluon jets originates fromtheir carrying color. Quark contains only one QCD color while gluon carries
both color and anti-color. According to Altarelli-Parisi splitting functions[16], gluon radiation from a gluon has a factor of CA = NC = 3, and gluon
N2C −1
radiation from a quark has a factor of CF = 2N
= 34 , where the ratio equatesC
CA /CF = 9/4 = 2.25. Hence, gluon jets tend to have more constituents thanquark jets, causing gluon jets to have a broader radiation pattern than quark
jets. ATLAS has developed a tagger based on ntrack , trackwidth, trackC1
and also other variables to separate quark jets and gluon jets with theseproperties. Since there are more particles in gluon jets on average, n track ,trackwidth and trackC1 are also larger than quark jets, shown in Figure 2.4
and 2.5. The quark and gluon jets are deﬁned by the labels generated in
the Monte-Carlo Sample (MC sample). The d, u, s and g labels are used in
Figure 2.4 and 2.5.

2.3.3

Jet Discriminant

There are several types of jet discriminant variables. Some of them are useful
to have a jets identiﬁcation. Some are usually utilized to remove pile-up jets.
A representative variables are the number of tracks (ntrack ), trackwidth andtrackC1 widely used for q/g tagging at the LHC analysis. This thesis also uses
these three variables to identify quark and gluon. The ATLAS experimentmeasures the tracks with an inner detector (ID), including silicon microstrips, and a transition radiation tracking detector in a 2 T axial ﬁeld whichis generated by a solenoid magnet [5]. More details will be introduced in
Section 3.2. For the limitation of the inner detector, tracks are reconstructed
at pseudorapidity of |η| < 2.5 and the transverse momentum pT > 500
MeV. Both the distance from the primary vertex and the longitudinal length
are required to be smaller than 1.5 mm. And at least 6 SCT hits are alsoneeded. After the criterion above, the anti-kT algorithm will select the tracks
associated with the jet. ntrack means the number of tracks associated withthe jet observed by the inner detector. The distribution of n track varies withpT and diﬀerent particles, and ntrack also increases at higher pT , shown in
Figure 2.4.
Trackwidth is also found to be a useful variable for identifying the origin of

CHAPTER 2. BACKGROUND KNOWLEDGE

16

a jet, and the deﬁnition is seen as Equation 2.9.
∑ trk
(pT,i × ∆R(trki , Jet))∑ trk
trackwidth = i,
i pT,i(2.9)√
where ∆R(x, y) = (ηx − ηy )2 + (ϕx − ϕy )2 , and ptrk
T,i is the transverse momentum of i-th tracks in the selected jet.
TrackC1, is called ”track-based-energy-correlation angularity”, and showsthe energy correlation among the tracks that are associated with the jet,shown in Equation 2.10.
∑ ∑ trk trk
βij (pT,i pT,j × ∆R (trki , trkj ))∑trackC1 =.
(2.10)
2( i ptrk
T,i )Normalized Entries

The indexes run over all the tracks in the jet with j > i, and the parameterβ is tunable. β = 0.2 is utilized in this thesis.
0.25

0.2

ATLAS Simulation Work in progresss = 13 TeV
QGTagger_NTracks|η|<2.1

Quark Jet
Gluon Jet
50<p <100 GeVT
400<p <500 GeV
T
1200<p <1500 GeV

0.15

T

0.1

0.05

0
0

10

20

30

40

50

60

70
ntrackFigure 2.4: The distribution of ntrack . The solid line stands for quark jets
and the dotted line stands for gluon jets. Diﬀerent colors indicate diﬀerent
pT regions. As transverse momentum pT goes to higher, ntrack also becomeslarger. Jets are required within the tracking acceptance which |η| < 2.1 andpT > 500 MeV.
Figure 2.5 shows the distribution of trackwidth and trackC1. Trackwidth
and trackC1 are also important discriminating variables. These three variables are also utilized in Boosted Decision Trees (BDT), a machine learning
tool usually implemented in the LHC analysis for q/g tagging. This study
makes use of ntrack , trackC1, trackwidth for q/g tagging in Chapter 4.

1
0.9
0.8

Normalized Entries/0.02mm

Normalized Entries/0.01mm

CHAPTER 2. BACKGROUND KNOWLEDGE

ATLAS Simulation Work in Progresss = 13 TeV
QGTagger_NTracks|η|<2.1

0.7
Quark Jet

0.6

Gluon Jet
0.5

17

1
0.9
0.8

ATLAS Simulation Work in Progresss = 13 TeV
QGTagger_NTracks|η|<2.1

0.7
Quark Jet

0.6

Gluon Jet
0.5

1200<p <1500 GeV
T

0.4

1200<p <1500 GeV

0.3

0.3

0.2

0.2

0.1

0.1

0
0

0.05

0.1

0.15

T

0.4

0.2

0.25
Widthtrack

0
0

0.05

0.1

0.15

0.2

0.25

Figure 2.5: The distribution of trackwidth (left) and trackC1 (right) for gluonand quark at 1200 < pT < 1500 GeV. The distribution for gluon is slightly
larger than the distribution for quark in general because of the diﬀerence ofcolor factor, and more details are described in Section 2.3.3. Jets are required
within the tracking acceptance which |η| < 2.1 and pT > 500 MeV.
Apart from jet identiﬁcation for diﬀerent particles, pile-up jets from additional proton-proton interactions at the LHC gives a crucial issue for numerous physics analysis. To identify the jets colliding correctly against pile-up
jets, jet-vertex-tagger (JVT) is a type of discriminaxnt to clean the pile-up
jet constructed from RpT and corrJVF (correlated jet-vertex-fraction [17]).
The JVT discriminant is based on a k-nearest neighbor (kNN) algorithm [18]by the MC simulations. The deﬁnition of RpT and corrJVF used in the JVT
is described as follows.
∑ track
pT,k (PV0 )R pT = k,(2.11)
pjetT∑ trackm pT,m (PV0 )∑∑ track
corrJVF = ∑,(2.12)n≥1
l pT,l (PVn )track
l pT,l (PV0 ) +
k·nPU
track

where PV0 here means the hard-scatter vertex and PVn stands for primaryvertices originating from pile-up interactions and PV n is pileup vertices. k isa constant parameter and nPU
track represents the pileup tracks number in theevent.
It is shown that using track and vertex information with JVT variables canremove pile-up jets eﬀectively. According to reference [19], jets with pT < 50
GeV and |η| < 2.4 required at the medium JVT working point accepts 92%

0.3

0.35
0.4
trackC1

CHAPTER 2. BACKGROUND KNOWLEDGE

18

of hard-scatter jets and rejects 98% of pile-up jets.
In summary, this thesis uses the ntrack , trackwidth and trackC1 as the inputs
for the q/g tagger in both BDT and neural network models. On the other
hand, in order to reduce the pile-up jets, all jets generated by the Monte
Carlo method passed the medium JVT working point in this study.

Chapter 3
The ATLAS Experiment at theLHC
The Large Hadron Collider, the highest energy and most powerful particle
accelerator, was built 100 m underground of CERN in Geneva. LHC collides
proton to proton at center-of-mass equating to 13 TeV.
There are several purpose detectors in the LHC, which are ATLAS (A Toroidal
LHC Apparatus), Compact Muon Solenoid (CMS), ALICE (A Large Ion
Collider Experiment) and The Large Hadron Collider beauty (LHCb) experiments. ALICE specializes in heavy-ion physics and is designed to investigate
strong interaction matter physics. LHCb is dedicated to studying the diﬀerence between matter and antimatter by investigating the b quark. ATLAS
and CMS have similar scientiﬁc goals to study a wide range of physics but
have diﬀerent magnet-system designs and calorimeter material. The ATLAS
detector [5] is the largest detector and is now used to ﬁnd new physics beyond
the SM.
This thesis focuses on the ATLAS and a brief introduction of the ATLAS
detector is introduced in Section 3.1. The inner detector (ID) and Calorimeters used to detect the particles are described in Section 3.2 and 3.3. The
track and topological cluster used for physics object reconstruction will be
introduced in Section 3.4.

3.1

Overview of the ATLAS Detector

The ATLAS detector consists of several sub-detectors (inner tracker, calorimeter, muon spectrometer) built for various physics analysis at the TeV scale.
The overall layout is shown in Figure 3.1. The inner detector’s 2 T solenoidal
ﬁeld originates from four large superconducting magnets. The diameter and
19CHAPTER 3. THE ATLAS EXPERIMENT AT THE LHC

20

Figure 3.1: The schematic illustration for the ATLAS detector is taken from[5]. The detector is constructed in toroidal shape with 25 m in height andlength in 44 m. The detector consists of an inner detector, solenoid magnet,
calorimeters and muon spectrometer.
length of each magnet are approximately 2.56 m and 5.6 m, respectively. The
magnet system provides a 2 T magnetic ﬁeld in the detector.
The coordinate of the ATLAS detector is described as follows. The x-y plane
is perpendicular to the beam direction while the z-axis goes to the collision
direction.
There are several variables usually used in the LHC.
√
• Transverse particle momentum : pT = p2x + p2y .
• Azimuthal angle : ϕ = arctan py /px , where is usually used for x-y plane.
• Polar angle : θ = arctan pz /px .
• Pseudorapidity : η = − ln tan θ/2, which describes the angle between
the particle momentum and the beam axis.

CHAPTER 3. THE ATLAS EXPERIMENT AT THE LHC

3.2

21

Inner Dector

Inner Detector consists of three subsystems, designed to have signiﬁcant momentum resolution and measure primary and secondary vertex for charged
tracks above around 0.5 GeV with |η| < 2.5. A schematic overview of theinner detector is shown in Figure 3.2. For against the high radiation environment, enormous strategies are designed such as the material of the sensor
and the temperature in the system. The inner detector provides the momentum of charged particles by calculating the curvature of the trajectory. It
also identiﬁes particle charge since opposite charged particles have opposite
curves in the magnetic ﬁeld. High resolution silicon pixel detector will bedemonstrated in Section 3.2.1. Semiconductor Tracker (SCT) used a classic
single-sided p-in-n technology as described in Section 3.2.2. Transition Radiation Tracker (TRT) consisting of polyimide straw tubes is introduced in
Section 3.2.3.

3.2.1

Pixel Detector

Pixel detector is built at the most inside part of the inner detector. Therefore, pixels are designed with two dimension sensors with high resolution.
There are nearly 400 thermistors installed within the pixel detector, utilized
to make sure the cooling loops system works appropriately. The sensors are
made of radiation-tolerant humidity sensors to reduce the eﬀect of high radiation environment and moisture. Four barrel layers and three double-sided
end-caps layers cover |η| < 2.5 by 1736 and 288 pixel sensors, respectively.
The most inside one barrel layer named insertable b-layer (IBL) was installed
in 2014. Preventing the leakage current, the entire system is operated at thetemperature ∼ −10◦ C. The sizes of each pixel are 50 × 250 µm2 and 50 ×
400 µm2 . The readout ﬁbers have been improved recently to handle the datafrom high luminosity in the future upgrade. The pixel sensor uses oxygenatedn-type wafers with readout on the n+ -implanted side of the detector. The n+
implanted side allows the detector has the powerful charge-collection ability.
The oxygenated materials provide good radiation tolerance while detecting
the tracks of hadrons. These properties make the pixel detector have significant resolution and high granularity and good tolerance for the beginningarea of detecting the charged particles.

3.2.2

Semiconductor Tracker

Semiconductor Tracker (SCT) detector is located at 30-50 cm from the beam.
SCT is made of one dimension sensors named silicon microstrips. Two types

CHAPTER 3. THE ATLAS EXPERIMENT AT THE LHC

22

Figure 3.2: The illustration of inner detector taken from [20]. The radiusof the detector is approximately 1 m. Pixel layer is placed at R = 33.5 122.5 mm, SCT is built at R = 299 - 514 mm, and TRT is located at R
= 554 - 1082 mm. All of them consist of barrel layers and end-cap layers.
The barrel layers cover at lower pseudorapidity while the end-cap extends tohigher pseudorapidity.

CHAPTER 3. THE ATLAS EXPERIMENT AT THE LHC

23of sensors are made for the SCT detector. The barrel sensor has 80 µm
strips with two 6 cm long sensors. The end-cap sensors are designed withradial strips with a mean pitch of around 80 µm. Thermal pyrolytic graphite
technology [21] is applied to give a high thermal conductivity between thesensors and cooling system. There are four sensors in each barrel layer, twoon the top and two on the bottom sides. There are only two sensors in each
end-cap layer, each sensor on the top and bottom sides. The top and bottom
sides of the SCT sensors are rotated with a ±20 mrad angle, allowing thestrip-type sensors to measure the two-dimensional space observation. The
heat is cooled down by evaporating C3 F8 at around -25 ◦ C, where coolingpipes are attached to each module.

3.2.3

Transition Radiation Tracker

The Transition Radiation Tracker is placed at the most outer part of the inner detector at 56.3 – 106.6 cm from the beamline. TRT detector uses tubes
ﬁlled with a gas mixture of 70% Xe, 27% CO2 and 3% O2 with roughly 10
mbar pressure. Diﬀerent from the pixel and SCT detector, the TRT can measure the 1-dimensional space points for each tube. In order to avoid pollution
from permeation, the tubes are enveloped with CO2 gas. TRT tube has aconcentric circle shape, where the gold wire is surrounded by the tubes. The
gold wire inside and tube layer outside are anode and cathode, respectively.
The voltage is operated at -1530 V toward the inside gold wire, giving the
maximum electron collection time can be down to 48 ns. Due to the emission
electron drift-time, TRT space resolution is around 130 µm.
When the charged particle passes the TRT tubes, it ionizes the gas companying with the radiated photons. The radiated photons interact with thegas molecules, producing more electrons moving toward the gold wire andgenerating the electronic signal.
All charged particles with pT > 0.5 GeV and |η| < 2.0 will go through at least
36 straws, which can be used to reconstruct the trajectory of their tracks andtransverse momentum.
The TRT detector can also distinguish diﬀerent sorts of charged particles at
an early stage. When a pion (electron) transverse the tubes, it radiates fewer(more) photons that bring fewer (more) electrons. These properties allow thedevice to separate charged particles by the magnitude of the electronic signal.
The TRT contains 73 layers of straws for a barrel module and 160 straws
planes for an end-cap module. The barrel TRT is separated into three rings,
each consisting of 32 modules. The TRT end-caps are made of two sets ofstraw wheels. One contains 12 wheels while the other one contains eightCHAPTER 3. THE ATLAS EXPERIMENT AT THE LHC

24

Figure 3.3: The schematic ﬁgure for the ATLAS calorimeter is taken from [5].
The calorimeter consists of LAr forward (FCal), LAr electromagnetic barrels,
LAr electromagnetic end-cap (EMEC), LAr hadronic end-cap (HEC), Tile
barrel and Tile extended barrel. Each system contains several layers which
can determine the energy for particles.
wheels.

3.3

Calorimeters

Calorimeter systems stop the particles with electromagnetic and hadronicinteraction to measure the energy. Therefore, it is located outside the innerdetector. ATLAS calorimeter contains several regions, shown in Figure 3.3,
and contains mainly electromagnetic and hadronic systems. Electromagnetic
calorimeter samples the energy of photons and electrons with electromagnetic
interaction. On the other hand, hadronic calorimeters measure the energy ofhadronic particles such as protons and mesons by hadronic interaction. Combined with the Inner Detector and Muon Chamber [5], ATLAS detector canidentify considerable diﬀerent particles, as seen in Figure 3.4. Section 3.3.1
describes an Electromagnetic Calorimeter that mainly interacts with electrons and photons. Section 3.3.2 shows Hadronic Calorimeter which allows
ATLAS detector to discriminate the hadrons from other particles.

CHAPTER 3. THE ATLAS EXPERIMENT AT THE LHC

25

Figure 3.4: The particle identiﬁcation schematic illustration is taken from[22]. Photons only interact with the matters at electromagnetic calorimeter.
Electrons leave the tracks at the inner detector and stop at the electromagnetic calorimeter. Muons go through the tracking system and both calorimeters to the muon system. Charged hadrons are stopped at the hadronic
calorimeter. Neural hadrons don’t have tracks but also stop at the hadronic
calorimeter. These properties allow the ATLAS detector to distinguish different sorts of particles.

CHAPTER 3. THE ATLAS EXPERIMENT AT THE LHC

3.3.1

26

Electromagnetic Calorimeter

Lead and Liquid Argon (LAr) are the main materials for the electromagnetic
calorimeter. It is used to detect the particles having electromagnetic interaction such as electrons and photons. The electromagnetic calorimeter consistsof barrel and end-caps ones which cover |η| < 1.4 and 1.4 < |η| < 3.2, respectively.
Two half-barrels constitute the barrel electromagnetic calorimeter and surround the beamline to cover the entire azimuthal angle ϕ. The thickness ofa module varies from 22 to 30 radiation lengths (X0 ) between |η| = 0 and|η| = 0.8, and increases from 24 X0 to 33 X0 between |η| = 0.8 and |η| = 1.3[5]. The end-cap calorimeters are made of two wheels used to measure theenergy of particles in the area 1.375 < |η| < 3.2. The end-cap calorimeterhas thickness of 24 to 38 X0 between 1.457 < |η| < 2.5, and 26 to 36 X0
between 2.5 < |η| < 3.2. Therefore, the electromagnetic calorimeters cover alarger area than the inner detector at |η| > 2.5 region. The LAr calorimetersurrounding the inner detector stops the particles and converts them into anelectromagnetic shower which contains a set of lower energy particles. The
shower particles ionize lead and liquid argon layers and produce an electronic
signal. It is designed as an accordion geometry in order to cover all ϕ regions without time dependence. LAr calorimeter is set at -184 ◦ C to keep theargon in liquid form. The electronmagnetic calorimeter energy resolution isσ(E[GeV])10∼17%≈√⊕ 0.7%.
E[GeV]
E[GeV]

3.3.2

Hadronic Calorimeter

The hadronic calorimeter is built outside the electromagnetic calorimeter. It
is subdivided into three types of calorimeters: one is Tile calorimeter, another one is LAr hadronic end-cap calorimeter (HEC) and the other is LAr
Forward Calorimeter (FCal).
Since hadrons are predicted to go further at the calorimeter layers, hadronic
calorimeters are located outside of electromagnetic ones. The hadrons passthrough the electromagnetic calorimeters lose some energy and completely
stop at the hadronic calorimeter.
When particles hit the steel layers, they are also converted to lower energy
shower particles. The plastic scintillators generate photons and the photomultiplier tubes (PMT) amplify the electronic signal which will be sent to
the readout system.
• Tile Calorimeter

CHAPTER 3. THE ATLAS EXPERIMENT AT THE LHC

27

The tile calorimeter is placed at |η| < 1.0 region, with two 0.8 < |η| <1.7 extended barrels. It uses scintillating tiles as an active material andsteel as an absorber. The three-layer barrel has approximately 1.5, 4.1
and 1.8 interaction lengths. On the other hand, the extended barrelhas 1.5, 2.6 and 3.3 interaction lengths, respectively.
• LAr Hadronic End-Cap calorimeter
There are two wheels in the HEC, placed behind the end-cap electromagnetic calorimeter out to |η| = 3.2. The wheels of the HEC are
made of copper plates to absorb the hadronic particles. The HEC has
approximately 11 interaction lengths for overall thickness.
• LAr Forward Calorimeter
The FCal is located at around 4.7 m from the interaction point. The
tungsten is an absorber material while LAr is an active medium forhadronic interaction. And copper and LAr are used as absorbers andactive materials for electromagnetic interaction. The FCal has roughly
10 interaction lengths.
≈ √ 50%The haronic jets energy resolution in the HEC and tile calorimeter is σ(E[GeV])
E[GeV]

E[GeV]The FCal energy resolution is estimated as σ(E[GeV])≈ √100%
E[GeV]

E[GeV]

3.4⊕ 10%.

Reconstruction

Track and topo-cluster play a vital role for the physics objects (such as electrons, muons and jets) reconstructions in the early step at the ATLAS. Thissection shows how the ATLAS reconstructs the track and cluster. Section
3.4.1 gives a brief introduction of tracks and vertices in the ATLAS. Section
3.4.2 describes the topological-clusters system.

3.4.1

Tracks and Vertices

The track and vertex reconstruction algorithms in the ALTAS have provensigniﬁcant in considerable studies. The Inner Detectors (ID) introduced in
Section 3.2 gives the data of hits from particles in a three-dimensional position. These multi-hits in the ID can be reconstructed into tracks for charged
particles. First, the seed track starts from the inside layers of the pixel detector to the SCT detector and extends to the TRT detector. Then Kalman
Filter [23] provides an excellent estimate for early measurements. The algorithm calculates the energy loss in the ID for an ionization particle and⊕ 3%.

CHAPTER 3. THE ATLAS EXPERIMENT AT THE LHC

28

bremsstrahlung by the track parameter. Secondly, a track search is takenfrom segments in TRT and reconstructs the trajectory with the pixel and
SCT hits. On the other hand, the tracks with TRT segments but without silicon detectors are counted as TRT-standalone tracks. According to[12], track reconstruction eﬃciencies are shown as follow, 82% ∼ 94% at
0.006 < ∆R(jet, track) < 0.01 for light ﬂavor jets.
For the reasons such as pile-up and proton-proton collisions, the ALTAS experiment is in the harch environment to distinguish the signal from a large
amount of background. A vertex reconstructed from tracks with p T > 400
MeV is utilized for ﬁnding the signal. Vertex Finding algorithm [24] is used
to identify the
position for tracks. After all, vertices are reconstructed,∑ vertex2
the highest pT vertex is deﬁned as a primary vertex. The details of ﬁnding
primary vertex are written in [25]. The hard-scatter jets satisfy that an MC
sample truth-particle jet with pT > 10 GeV and is found within ∆R < 0.3.
Tracks are necessary for jets reconstruction. Jet consists of several hadrons
which leave numerous tracks. The tracks in the associated jet are utilized
to reconstruct its four-vector. The variables for discriminating described in
Section 2.3.2 (ntrack , trackwidth and trackC1) are also calculated from thefour-vector of tracks.
The tracks of jets in the ATLAS are reconstructed from the hits in the innerdetectors. The azimuthal range and pseudorapidity of jet tracks are selectedin the range of 0 < ϕ < 2π and |η| < 2.5. Tight quality criteria [26] isapplied to reduce the eﬀect from pile-up background and reject fake tracks
from the noise or charged particles. The following describes several additional cuts for the jets in this thesis. Each track in the associated jet satisﬁes
pT > 0.5 GeV and comes from the hard-scatter primary vertex. Track-tovertex matching is implemented to deﬁne the primary vertices by the vertex
reconstruction. Track excluded in vertex reconstruction are implanted thenearest vertex strategy with the distance |∆z × sin θ| < 3 mm, where ∆z represents the longitude distance between the object and deﬁned vertex. This
study requires |η| < 2.1 for jets in order to obtain full tracker acceptancein the ID. Jet pT > 25 GeV is also required for reducing the soft emission.
The working point of JVT is set at Medium working point [19] and energy
calibration [27] is applied.

3.4.2

Topological-Clusters

A topological-cluster (topo-cluster) is to assemble a group of particles into
clusters from the electromagnetic and hadron calorimeter measurement. The
topo-cluster is usually exploited for reconstructing jets from calorimeter cells.
The reconstruction of the topo-cluster is shown as follows. The seed ﬁnding

CHAPTER 3. THE ATLAS EXPERIMENT AT THE LHC

29

EM
in the ﬁrst step is searching the calorimeter cells with E EM
cell /σnoise,cell > 4.
Here EEM
cell represents energy corrected by EM-scale (The scales for e γ in the
ATLAS electromagnetic calorimeters). The reconstructed seeds are collected
as a proto-cluster from the primary vertex. Secondly, the adjacent cells in theEMgiven region overlapping in the (η, ϕ) with EEM
cell /σnoise,cell > 2 are added to theEMEMproto-cluster. Finally, the Ecell /σnoise,cell > 0 cells nearby each proto-cluster
will be merged to one cluster.

Chapter 4
Quark/Gluon Tagging
Quark/Gluon tagging is necessary for many physics analysis in high-energy
physics. Especially, the LHC experiment with proton and proton collisioncauses the immense QCD eﬀect. The QCD interaction generates many background gluons, which are seen as jets in the ATLAS detector. Therefore, theseparation of quark and gluon helps physicists discriminate the signal fromthe background. This chapter introduces several kinds of q/g tagging models
and compares their performances. Section 4.1 shows the MC sample used
when the q/g tagging models are trained. Section 4.2 gives the details of eachq/g tagging model, including conventional BDT model and neural networkmodels. Section 4.3 describes the performance of the models and compares
their pT and η dependence, respectively, and introduces the training andtesting results by the diﬀerent MC generators.

4.1

MC sample

The dijet process@leading order (multijet) MC samples have been used totrain the q/g tagging models. The jets are evolved with Pythia 8. The
pileup and noise are also considered in order to approach the real data. The
generator Pythia 8 [28] utilizes the NNPDF2.3 PDF set [29], the A14 tune[30], and run all simulation in the ATLAS detector. For generating heavy
ﬂavor decays, Pythia 8 is interfaced with EvtGent v1.2.0.
The quark and gluon jets are deﬁned by the labels generated in the MC
sample. There are three kinds of labels (d, u, s) and one label (g) for quarkand gluon jets, respectively.
To have better learning for the q/g tagging model, other steps are taken.
The pT of quark jet and gluon jets is ﬂatted to the same distribution and30

Event/50GeV

CHAPTER 4. QUARK/GLUON TAGGING103

ATLAS Simulation Work in progress

Small-R Jet (Anti-k R=0.4)
s=13 TeV, |η|<2.1 t

31

Quark
Gluon

2

10

10

1

10− 1

10− 2
1000

2000

3000

4000

5000
p [GeV]T

Figure 4.1: The pT of quark and gluon jet in multijet MC sample is ﬂatted
to one in order not to aﬀect by pT bias.
normalized to one to make sure models are not aﬀected by p T bias, shown in
Figure 4.1. The quark and gluon inputs are collected in the same numbers
since the training performs better with the same amount of quark and gluon
inputs in neural network models.
Training is performed using a single NVIDIA Tesla T4 GPU with 500000
quark jet and 500000 gluon jet while 250000 quark jet and 250000 gluon
jet for testing. The testing here means that the trained q/g tagging models
are applied to other samples to check that the overtraining does not occur.
Diﬀerent models require diﬀerent times to train. The BDT model is thefastest one with around half an hour while Deep Sets and Energy Flow models
need the most time with approximately 6 hours.

4.2

Quark/Gluon Tagging Models

This study uses several q/g tagging models to predict whether it is quarkor gluon. This section has documented the details of q/g tagging models.

CHAPTER 4. QUARK/GLUON TAGGING32

The conventional q/g tagging model usually used is the BDT model whileneural network models are usually used in recent decades. This is because
compared to the BDT model which can only use high-level input such as
ntrack , trackwidth and trackC1, the neural network models are able to utilize
more low-level inputs such as the pT of each track in the associated jet andthe energy from each calorimeter layer. The performance of q/g separation
usually increases in the neural network since low-level input represents more
information used for inference.
The BDT model and its conventional inputs (ntrack , trackwidth, trackC1)
are described in Section 4.2.1. BDT model is used as a baseline to makethe comparison with other neural network models. The neural models are
introduced from Section 4.2.2 to 4.2.5. MultiLayer Perceptron (MLP) model,
the simplest neural network model (Since the MLP only uses the dense layers,
the most straightforward unit in the neural network models, it can only input
the high-level information.), is shown in Section 4.2.2. Convolutional Neural
Network (CNN) model is demonstrated in Section 4.2.3. CNN model is aneural network model using image input. Hence, CNN can use the positionand pT of each track information that represents low-level input. MLP and
CNN models are combined into the MLP-CNN model demonstrated in 4.2.4.
Pointwise models are introduced in Section 4.2.5 which there are two typesof models, the Deep Sets model and the Energy Flow model. These twomodels have a similar structure while energy ﬂow multiplies track p T withother terms such as ϕ, η in the model.

4.2.1

BDT Model

The BDT machine algorithms are implemented by the Toolkit called Multivariate Data Analysis (TMVA [18]) on ROOT [31] based analysis tool. The
principle of the BDT model is having a diﬀerent cut on diﬀerent variables toobtain the best classiﬁcation. First of all, give a cut on one of the variables
and calculate the remaining signal and background percentage. Secondly,choose the better one and give another cut on another variable. This second
cut also provides the remaining signal and background sample percentage.
The step above keeps performing until it is stopped which usually depends
on the MaxDepth of the BDT. The schematic illustration is shown in Figure
4.2. The signal background ratios are calculated with the diﬀerent decision
trees until the best selection is determined. Boosting here means that thetrees depend on the prior trees. This ensures that the ﬁnal trained model
is more stable and has better accuracy. Quark jets are input as the signal
sample while gluon jets are input as background in the BDT model. The
setup of BDT model is listed in Table 4.1.

CHAPTER 4. QUARK/GLUON TAGGING
Pure Signal Nodes

33
Decision Tree no.: 0S/(S+B)=0.512
ntrack> 24

Pure Backgr. Nodes

S/(S+B)=0.756

S/(S+B)=0.252

trackC1>0.183

S/(S+B)=0.880

S/(S+B)=0.573
trackC1>0.211

S/(S+B)=0.711

S/(S+B)=0.440

Figure 4.2: The illustrating ﬁgure for the decision tree. In this example,
the ﬁrst threshold cut is the number of tracks larger than 24. The sample
satisfying the threshold goes left, otherwise right. The additional selection
thresholds are performed depending on the MaxDepth setup in the BDT.
The BDT model learns the MC samples with ntrack , trackwidth and trackC1
variables, shown in Figure 4.3. The brief descriptions of the BDT setup
option are explained as follows.
• AnalysisType : The learning samples have binary labels, so classiﬁcation analysis is used.
• NTrees : Number of trees in the BDT model.
• MinNodeSize : Minimum fraction of training events• MaxDepth : Max depth of the decision tree.
• AdaBoostBeta : The parameter in the AdaBoost boosting technique.
• AdaBoost : An algorithm that can learn the past error sequentiallyfrom the previous training.
• BaggedSampleFraction : Relative size of bagged event sample used in
the MC sample.

CHAPTER 4. QUARK/GLUON TAGGING

34

Table 4.1: The setup of BDT model.
AnalysisType=Classiﬁcation
NTrees=850
MinNodeSize=2.5%
MaxDepth=3
AdaBoostBeta=0.5
BaggedSampleFraction=0.5
SeperationType=GiniIndex
nCuts=20• Bagged event sample : The sample selected from the bagging method is
an algorithm to reduce the variance of the sample to avoid overﬁtting.
• SeparationType : The separation criterion for node splitting.
• node splitting : A decision tree makes the decision and divides a node
into multiple sub-nodes to determine the better decision.
• nCuts : Number of grid points in the variable region used in determining the optimal cut in the node splitting.

4.2.2

MLP Model

MLP model is the simplest neural network model that connects several dense
layers. The structure is displayed in Figure 4.4. The dense layer consists ofseveral neurons with diﬀerent kernel functions and weights. The weight (Thearrow mark in Figure 4.4.) is upgraded by the gradient descent method,
shown as follows.
∂ε(n)∆ωji (n) = −λyi (n),(4.1)∂νj (n)where λ is the learning rate, yi is the output of the previous neuron. ε is thesquare sum of error (truth value − prediction). ν is the variable in the kernel
function. Each neuron is connected to all neurons in the previous dense layer
or all inputs. The input values with weights will be calculated in the kernel
function and output a value to the following dense layer.
There are 31 inputs for each small-R jet. The inputs are connected to two
iterations of the dense layer with 64 neurons and ﬁnally output the quarkand gluon jet classiﬁcation. The 31 inputs are described as follows, n track ,trackwidth, trackC1, electromagnetic energy fraction and the energy of thecalorimeter layers. The calorimeter layers used in the MLP model are shownin Table 4.2. Rectiﬁed Linear Unit (ReLU) [32] activation is utilized for allNormalized Event

CHAPTER 4. QUARK/GLUON TAGGING

0.1

35

ATLAS Simulation Work in progresss = 13 TeV
Small-R Jet (Anti-k R=0.4)t|η|<2.1, p >25 GeV
T
Training on Pythia with BDT Tagger

0.09
0.08

Quark Jet on Pythia

0.07

Gluon Jet on Pythia

0.06
0.05
0.04
0.03
0.02
0.01
0

−0.15

− 0.1

−0.05

0

0.05

0.1

0.15

0.2

0.25
BDT

Figure 4.3: The BDT response of quark jet and gluon jet with the pythia
multijet MC test sample.
dense layers. Dropout=0.3 [33] is also applied to all dense layers in order toprevent overtraining. Additionally, an L2 regularization [33] with strength10−8 is used in all layers. Also, earlystopping is applied to patience=15
to prevent overﬁtting and epochs = 100. The optimizer is Adam and its
learning rate equates to 10−5 . The loss function is set as SparseCategoricalCrossentropy1 [33]. The MLP output is a softmax function [33] of size two
which provides the probability of quark and gluon relatively. The option issummarized in Table 4.3.

4.2.3

CNN Model

The MLP and BDT can only utilize the high-level inputs, causing information loss during the calculations. The image inputs are considered as a new
input that includes low-level information. 2D Convolutional Neural Network(CNN) is a deep learning model used to learn visual images. Therefore,
1

A format of true label inputs when training the models.

CHAPTER 4. QUARK/GLUON TAGGING

36

Figure 4.4: The structure of the MLP model used in this study. There are
31 inputs with one input jet, passing through two 64-neurons dense layers.
Finally, the input jet is classiﬁed as a quark or gluon jet.
Table 4.2: The energy inputs of calorimeter layers used in the MLP model.
LAr barrel
LAr EM endcap
Hadronic endcap
Tile barrel
PreSamplerB PreSamplerE
HEC0
TileBar0
EMB1
EME1
HEC1
TileBar1
EMB2
EME2
HEC2
TileBar2
EMB3
EME3
HEC3
Tile gap
TileGap1
TileGap2
TileGap3

Tile extended barrel
TileExt0
TileExt1
TileExt2

Forward EM endcap
FCAL0
FCAL1
FCAL2

Mini FCALMINIFCAL0
MINIFCAL1MINIFCAL2MINIFCAL3

converting the track and topo-cluster information into a visual image is necessary.
The CNN model and its inputs in this study follow the previous study [34].
All constituents in a jet are rotated to ϕjet = ηjet = 0 based on the center of
the associated jet to form a jet image. And then, the pT of each track andcluster in the associated jet is used to ﬁll into a ﬁxed grid of size 16 × 16 at|η| < 0.4 and |ϕ| < 0.4 region. After the transformation, the center of thejet is at the center of the image and∑ the pixel size is η × ϕ = 0.05 × 0.05.
Next, the image is normalized to i pT,i = 1. The normalization must dropsome information, but according to [34], the impact is small enough to ignore. Another advantage of normalization is that it will work better in neuralnetwork training. The topo-cluster and track constituents of a quark jet image are displayed in Figure 4.5. The average of millions of quark and gluon

CHAPTER 4. QUARK/GLUON TAGGING

37

Table 4.3: The setup of neural network models in this thesis.
Activation Function=ReLU
Dropout=0.3
Regularization=L2
Optimizer=Adam
Learning Rate=10−5
Output=Softmax function
Loss function=SparseCategoricalCrossentropy
topo-cluster images and their image diﬀerence are displayed in Figure 4.6.
Reminding that the trackwidth distribution of gluon jet is more signiﬁcantthan quark jet. This property can also be seen in Figure 4.6. The middle
image in Figure 4.6 shows that the average of quark jets concentrates morethan gluon jets which is a good discriminant in the CNN model to separate
quark and gluon particles.
The jet images reconstructed above are implemented as inputs into the CNN
model. The CNN model is a feed-forward artiﬁcial neural network that calculates the weights linearly on a m × n size input image. The input image isdivided into several pixels and sent to the Convolutional ﬁlter. In the convolutional ﬁlters, the output of each ﬁlter is calculated by dot-product with
diﬀerent weights, shown in the following equation.
O = MI + B,

(4.2)

where, O and I represent the output and input of the convolutional ﬁlter. M
is the weighting matrix and B is a constant matrix. Tuning the weighting
matrix can change the image size of output and input.
After the operation, a new output image is reconstructed for the next ﬁlter. Max-pooling is another procedure for down-sampling the image. The
output of Max-pooling is the maximum value in the deﬁned image. The
non-overlapping sets of pixels are taken from convolutional ﬁlter input andﬁnd the maximum value in the sets of pixels as output. The process in the
Max-pooling is implemented to obtain the characteristic feature in the image. After the convolutional ﬁlter or Max-pooling, the 2-dimension image is
ﬂat into a 1-dimension dense layer. Then, the same thing done in the MLP
model performs again to obtain the probability of quark jet and gluon jet.
The illustration of the CNN model is shown in Figure 4.7. Track and topocluster normalized pT images are used as one input in which the input shapeis (16,16,2) in the CNN model. The CNN model consists of three iterationsof a convolutional layer and is then connected with one Max-pooling layer.
The Max-pooling layer is ﬂatted and connected to two 1-dimension denseCHAPTER 4. QUARK/GLUON TAGGING

0.4

ATLAS Simulation Work in progress

Quark Small-R Jets, Cluster Constituentss =13TeV, | η |<2.1

ηη

ATLAS Simulation Work in progress

38

10−1

0.3
0.2

0.4

Quark Small-R Jets, Track Constituentss =13TeV, | η |<2.1

10−1

0.3
0.2

0.1

0.1
10−2

10−2

0

0

−0.1

−0.1

−0.2

10−3

−0.3

−0.2

10−3

−0.3

−0.4
−0.4 −0.3 −0.2 −0.1

0

0.1

0.2

0.3

0.4
φ

−0.4
−0.4 −0.3 −0.2 −0.1

0

0.1

0.2

0.3

0.4
φ

Figure 4.5: The CNN input image of quark jet. The topo-cluster constituents
image is on the left hand side while the track constituents image is on theleft hand side. Both of them have 16×16 pixels at |η & ϕ| < 0.4 region. The
constituents in the∑associated jets are rotated to ηjet = ϕjet = 0 and their pT
are normalized topT = 1.
layers followed by a softmax function of size two, giving the probability forquark and gluon jet. Three convolutional ﬁlters have respectively 256, 128,64 ﬁlters, which the sizes of ﬁlters are 7 × 7, 5 × 5, 3 × 3. The Max-poolinglayers are operated with 2 × 2 downsampling. Two dense layers have 64 neurons, followed by softmax function. The setup of the CNN neural networkmodel is the same as the MLP model, shown in Table 4.3.

4.2.4

MLP-CNN Model

MLP-CNN model consists of MLP model and CNN model described in Section 4.2.2 and 4.2.3. For the MLP part, there are 31 inputs including ntrack ,trackwidth, trackC1, EM energy fraction and energy of the calorimeter layers shown as Table 4.2. For the CNN part, topo-cluster and track images,
same with the CNN model in Section 4.2.3. Combining MLP and CNN models means both high-level and low-level inputs are able to be used for more
information of jets. There are two dense layers with 64 neurons for DNN
parts. Same as CNN model in Section 4.2.3, three convolutional ﬁlters of
256, 128, 64 ﬁlters with size of 7 × 7, 5 × 5 and 3 × 3 respectively. Thenthe convolutional ﬁlters are followed by a Max-pooling layer with a size of(2,2). Finally, the output images are ﬂatted to a 128-neuron dense layer. In
order to combine MLP and CNN models, concatenate function is operated

CHAPTER 4. QUARK/GLUON TAGGINGATLAS Simulation Work in progress

ATLAS Simulation Work in progress

T

10−1

0.3

0.1

0.4

0.08

0.3

η

(Quark - Gluon) Small-R Jets, Cluster Constituents

Quark Small-R Jets, Cluster Constituentss =13TeV, | η |<2.1, 25 <p <100 GeVηη

ATLAS Simulation Work in progress
0.4

39

0.4

Gluon Small-R Jets, Cluster Constituentss =13TeV, | η |<2.1, 25 <p <100 GeV
T

10−1

0.3

0.06
0.2

0.2

0.2
0.04

0.1

0.1

0.02

10−2
0

0

0

−0.1

−0.02

−0.1

−0.2

−3

10

−0.3

−0.04

−0.2

−0.06

−0.3

−0.4
−0.4 −0.3 −0.2 −0.1

0

0.1

0.2

0.3

0.4
φ

−0.4
−0.4 −0.3 −0.2 −0.1

−0.08
0

0.1

0.2

0.3

0.4
φ

−0.1

0.1
10−2
0
−0.1
−0.2

10−3

−0.3
−0.4
−0.4 −0.3 −0.2 −0.1

0

0.1

0.2

0.3

0.4
φ

Figure 4.6: The average intensity of topo-cluster quark and gluon jets. The
left image shows the average of topo-cluster quark jets while the right image
shows the topo-cluster gluon jets. The middle image is drawn with thediﬀerence between the average of quark jets and gluon jets.

Figure 4.7: The schematic illustration of CNN architecture is taken from[34]. Track and topo-cluster normalized pT images are used as input in thisthesis.
to connect the 64-neuron dense layer in the MLP model with the 128-neuron
dense layer in the CNN model. After combining two dense layers from MLP
and CNN, respectively, it is followed by a 192-neuron dense layer and thenoutput the softmax function with the size of two neurons which predict thequark-like and gluon-like probability. The setup of the MLP-CNN neuralnetwork model is listed in Table 4.3.

4.2.5

Pointwise Model

The CNN model is needed to have an image input, making the learning inconvenient. The Pointwise model is introduced as a model that can directly
use input variables. This section has two Pointwise models: The Deep Sets

CHAPTER 4. QUARK/GLUON TAGGING

40

Figure 4.8: The schematic image of the Deep Sets and Energy Flow. For
the Deep Set, the pT , η, ϕ of topo-cluster or track is sent to input andthe summation is operated to output the result followed by several dense
layers. On the other hand, for Energy Flow, only η and ϕ are input and they
are weighted by the associated pT before the summation. Then after thesummation, they are also sent to several dense layers. The dense layers above
are connected to the MLP input dense layers to perform the quark/gluon
separating.
model and the Energy Flow model. The Deep Sets and Energy Flow models
have been recently developed well. For example, in ref [35], the Deep Sets
model is used to generalize the permutation-invariant functions of variablelength in point clouds. Using the Deep Sets model, it is possible to solve
the problems such as red-shift estimation of galaxy clusters. The criticaloperation in Deep Sets is the summation since symmetry usually exists inmany physics ﬁelds. The summation operation can encapsulate the symmetric eﬀect in the latent space. Consider a physics observable O is a symmetricfunction. Then the Deep Sets model can be written as follow.
O(x1 , ..., xM ) = F (M∑Ψ (xi ))

(4.3)

i=1

Here xi is (pT , η, ϕ) of i-track or i-topo-cluster for Deep Sets model. And Ψ
represents the operation before summation.
Next, let’s consider a homogenous physics observable O again. With a modiﬁcation of Equation 4.3, infrared-safe and collinear-safe (IRC-safe) observables
can be added, shown as the following equation.
O(x1 , ..., xM ) = F (M∑zi Ψ (xi ))

(4.4)

i=1

Here xi represents (η, ϕ) of i-track or i-topo-cluster and zi is the pT of eachtrack in the Energy Flow model. Ψ is the operation before summation. The

CHAPTER 4. QUARK/GLUON TAGGING

41summation operation implies that the infrared safety is still satisﬁed. The p T
weighting indicates that although the particles split into two particles, they
can be reconstructed as if a vector with pT weight. Hence, the Energy Flowmodel satisﬁes infrared safety and collinear safety which is named IRC-safe.
The deﬁnition of IRC-safe is shown as follows.
1. Infrared safety : The observable is not aﬀected by the low-energy andlong distance physics, such as soft emission.
2. Collinear safety : Collinear splittings of particles don’t aﬀect the result.
The Pointwise model consists of several 1×1 kernel convolution layers. The
calculations of the Pointwise model and the CNN model are similar. They
are both operated by matrices to obtain the outputs. The output of the
CNN model is an image. However, the output of the Pointwise model is one
dimension layer. There are 140 sets of inputs for the tracks in the Deep Setscase. Each set of inputs will be operated with a matrix and output into a(64,1) one dimension layer. Therefore, there are 140 sets of one dimension
layers after the operation.
Unlike the CNN model that only tackles the image inputs, Pointwise models
are more ﬂexible to have other kinds of inputs. Another advantage of the
Pointwise model over the CNN model is that it is more convenient to input
all pT , η, ϕ information of associated tracks and topo-clusters. In the CNN
model, the pixel size of the image is always a troublesome issue. If the pixel
size is too large, the resolution and accuracy decrease. On the other hand,
computer memory and training time become a fatal problem if the pixel size
is made too tiny. This leads to a fundamental defect for the CNN model. In
the Pointwise model, it can take pT , η and ϕ as a set of input. Hence, as
there are, says ﬁfteen tracks, only ﬁfteen inputs are needed in the associatedjet. This saves the computer memory and time, and can use the jet information directly (the CNN model needs to transform the jet information into an
image, so some information is lost actually.).
Since the Deep Sets and Energy Flow models are similar, the entire architecture will be introduced ﬁrst, followed by the precise structure. The inputs
are separated into two parts, MLP inputs and CNN inputs. For the MLP
inputs part, it is the same as the MLP model, ntrack , trackwidth, trackC1
and calorimeter layer energy; a total of 31 inputs are taken. For CNN parts,
the input shape is diﬀerent for track and topo-cluster. The shape of track
and topo-cluster is (140, Φ) and (70, Φ), respectively. Here Φ is (p T , η,ϕ)for the Deep Sets model and (η,ϕ) for the Energy Flow model. The number of 140 and 70 is set because the maximum of ntrack and ncluster is foundfewer than these two numbers. This ensures that all track and topo-cluster

CHAPTER 4. QUARK/GLUON TAGGING

42

information is taken as inputs. If the inputs don’t approach the upper limit,
say 140 or 70 for track and topo-cluster inputs, respectively, then the inputs
are set to zero in order not to aﬀect the training result. Then all inputs
above are connected with several 1×1 convolutional layers followed by some
operations and several dense layers. (1×1 kernel convolutional layer is calledby Conv1D function in TensorFlow [36].) The following describes three input parts, track input, topo-cluster input and MLP input for Deep Sets andEnergy Flow models.
• Track and topo-cluster inputs(140/70, [pT , η, ϕ]) and (140/70, [η, ϕ]) are inputs in Deep Sets
and Energy Flow for track/topo-cluster, respectively. Then there arethree iterations of 1×1 kernel convolutional layers with the size of (64,1)/(32,1). After passing three 1×1 convolutional layers, there is a small
diﬀerence between Deep sets and Energy Flow models. For Deep Sets
one, the output of the last 1×1 convolutional layer is multiplied with
the initial input (pT , η, ϕ). The reason for multiplying them is that
there are some zero terms in the 140/70 inputs initially because thetrack number varies in diﬀerent jets. The multiplying operation initializes the 1×1 convolutional layers by multiplying with the initial
inputs. For example, there are ﬁve tracks in a jet. Therefore, the 140
1×1 convolutional layers multiplying with the initial inputs make only
the ﬁrst ﬁve 1×1 convolutional layers have value and the others are
initialized to zero. Next, the summation is implemented to satisfy theInfrared Safety. For the Energy Flow model, the output of the 1×1
convolutional layer is multiplied with (pT ) in the initial input. Thenthe summation is performed again. Multiplying p T and summing operation satisfy the IRC-safe for the Energy Flow model. Finally, twodense layers with 128/64 neurons follow the summing operation output
in both cases.
• MLP input
In the MLP input section, Deep Sets and Energy Flow models have thesame structures. There are 31 inputs connected to three iterations of a
1×1 convolutional layer with a size of (16, 1) followed by two 64-neuron
dense layers.
Then the outputs from MLP, track and topo-cluster are connected and sent
to a 192-neuron dense layer followed by a softmax function of size two to
perform the q/g discriminant.
Same as the models mentioned before, the setup of Pointwise models is described in Table 4.3.

CHAPTER 4. QUARK/GLUON TAGGING

43

Table 4.4: A summary of the input variables in each model.
Model
Input variables
ntrack
BDT
trackwidth
trackC1
ntrackMLP
trackwidth
calorimeter layer energy
trackC1pT (ϕ,η)CNNη, ϕ= pT,norm
all pT
ntrackη, ϕ, pT,norm
Pointwise calorimeter layer energy
trackwidth
trackC1

4.3

Performance of q/g Tagging Models

This section demonstrates the performance of the BDT, MLP, CNN, MLPCNN, Deep Sets and Energy Flow model and the performance between thediﬀerent testing samples. The input variables are summarized in the Table 4.4. Section 4.3.1 shows the Receiver Operating Characteristic Curve(ROC) curve of each model. Also, it describes the dependence of both p Tand η of associated jets and explains the diﬀerence among all models. Section
4.3.2 compares two kinds of MC samples generated Pythia and Herwig. The
Pythia MC sample is a leading-order generator, and the Herwig MC sample
is a next-leading-order generator. The diﬀerence between the Pythia andHerwig generators is the hadronization model. The hadrons are generated
based on the string generating and cluster model in the Pythia and Herwig,
respectively. Comparing these two MC samples gives brief research of studying MC sample generators for future works.
Since the earlystopping is applied to all neural models to avoid overtraining, the loss function convergence is examined and the overtraining didn’t
happen.

4.3.1

Receiver Operating Characteristic Curve Result

The receiver operating characteristic curve (ROC curve) shows the discrimination ability of a binary classiﬁer system. Since the q/g tagger in this model
is a binary tagger, it is convenient to compare the performance among diﬀerent tagging models. There are many diﬀerent types of ROC curves. In thissection, the x axis represents the quark eﬃciency rate which means the per-

Gluon Jet Rejection Rate

CHAPTER 4. QUARK/GLUON TAGGING

44

1
0.9
0.8
0.7
0.6

ATLAS Simulation Work in progresss = 13 TeV
Small-R Jet (Anti-k R=0.4)t|η|<2.1

0.5
0.4
0.3
0.2
0.1

CNN Tagger
MLP Tagger
MLP_CNN Tagger
Energy Flow Tagger
Deep Sets Tagger
BDT Tagger

0
0

0.2

0.4

0.6

0.8
1
Quark Jet Efficiency Rate

Figure 4.9: The ROC curves of all q/g taggers are described in Section 4.2.
Quark Eﬃciency/Gluon Rejection (x and y axis) represents the percentageof remaining quark/rejected gluon after the threshold cut on quark/gluon
discrimination output.
centage of remaining quark after the discrimination threshold. On the other
hand, the y axis represents the gluon rejection rate which means the percentage of rejected gluon after the discrimination threshold. The deﬁnitionis shown in the following equations.
Quark Eﬃciency =Ntrue postive
Ntrue negative, Gluon Rejection = 1 −, (4.5)
Npositive
Nnegative

where Npositive and Nnegative are the numbers of particles with a quark anda gluon labels generated by the MC generator (it is the numbers of quarks
and gluons, respectively.). True positive means it is a quark and predicted
as a quark by the q/g tagging models. True negative means it is a gluon andrecognized as a gluon by the q/g tagging models. Using this deﬁnition, theROC curve of q/g taggers in this study are shown as concave curves and the
ROC curve with up and right curvature has better performance.
Figure 4.9 shows the ROC curve of all q/g tagger introduced in Section 4.2.

CHAPTER 4. QUARK/GLUON TAGGING

0.4

ATLAS Simulation Work in progress

Quark Small-R Jets, Cluster Constituentss =13TeV, | η |<2.1, 1000 <p <1500 GeVTηη

ATLAS Simulation Work in progress

45

0.3

Quark Small-R Jets, Cluster Constituentss =13TeV, | η |<2.1, 1000 <p <1500 GeV
T

10−1

0.3

10−1
0.2

0.2
0.1
0.1
10−2

−0.1

−0.1

−0.2

10−3

10−3
−0.2

−0.3
−0.4
−0.4 −0.3 −0.2 −0.1

10−2
0

0

0

0.1

0.2

0.3

0.4
φ

−0.3
−0.3

−0.2

−0.1

0

0.1

0.2

0.3
φ

Figure 4.10: The topological cluster image in 1000 < pT < 1500 GeV region.
Left image has the pixel size of 0.05 at |ϕ, η| < 0.4 while right image has the
pixel size of 0.0375 at |ϕ, η| < 0.3.
Deep Sets (red curve) and Energy Flow (yellow curve) models have almost
the same performance and achieve the best performance among all models.
The inputs of the Pointwise model (Deep Sets and Energy Flow) are thesame as MLP-CNN (green curve) model but better than it. This implies
that compared to the MLP-CNN model, the Pointwise model utilizes theinformation of inputs more eﬃciently. The pointwise model utilizes the track
and topo-cluster information better than the MLP-CNN model since CNN
input is needed to consider pixel size limitations.
Ideally, the CNN (blue curve) model should have performed better than MLP(black curve) and BDT (dotted brown curve) tagger because the CNN model
uses more low-level inputs with more information than the MLP and BDT
with only high-level inputs. However, the ROC curve shows that the CNN
model is worse. This is because pixel size optimization is needed to maximize
the performance of the CNN model. To check how pixel size optimization
problems aﬀect the performance, the pixel is tuned to a smaller size, shown in
Figure 4.10. The η and ϕ range are changed from smaller than 0.4 to smaller
than 0.3, and the pixel size becomes from 0.05 to 0.0375. This smaller pixel
size allows one to see the track and topo-cluster image more precisely. The
result is shown in Figure 4.11. The pixel size is related to the amount of input
information. Therefore, the performance of smaller pixel sizes better thanlarger pixel size emphasizes how signiﬁcant the input variables are. As the
pixel size becomes smaller, the performance of the CNN model gets better as

Gluon Jet Rejection Rate

CHAPTER 4. QUARK/GLUON TAGGING

46

1
0.9
0.8
0.7
0.6

ATLAS Simulation Work in progresss = 13 TeV
Small-R Jet (Anti-k R=0.4)t|η|<2.1, p > 25 GeVT
CNN Tagger

0.5
0.4

pixel size = 0.05
pixel size = 0.0375

0.3
0.2
0.1
0
0

0.2

0.4

0.6

0.8
1
Quark Jet Efficiency Rate

Figure 4.11: The comparison between diﬀerent pixel size CNN tagger. A
smaller pixel size CNN model (brown curve) is apparently having a better
larger pixel one (black curve). This indicates that ideally reducing the pixel
size gives the same performance as the Pointwise model.
expected. Nevertheless, the smaller pixel size in the same η, ϕ range implies
more pixel numbers. This requires more computer memory and takes moretime to train the models, which is impractical.
Although the performance of the MLP-CNN model is worse than the Pointwise model, it is better than any others. The MLP-CNN inputs usage gives
a better result than MLP, BDT, and CNN models that use partially or lessinformation.
The MLP model is better than the BDT model because MLP utilized thecalorimeter layer energy as additional inputs. Again, these things imply theimportance of the input. For comparing the diﬀerence between diﬀerent architecture, the MLP using only ntrack , trackwidth, trackC1 variables are also
input. The result is shown in Figure 4.12 and the diﬀerence between themis tiny. From this, it is known that the tagger performance depends more on
the input variables and the way to tackle the inputs, and not so much on themodel architecture.
Finally, compared to the conventional tagger (BDT model), considered as
the baseline of machine learning, the gluon rejection rate of the PointwiseGluon Jet Rejection Rate

CHAPTER 4. QUARK/GLUON TAGGING

47

1
0.9
0.8
0.7
0.6
0.5
0.4

ATLAS Simulation Work in progresss = 13 TeV
Small-R Jet (Anti-k R=0.4)t|η|<2.1
ntrack , trackwidth, trackC1 input

MLP Tagger
BDT Tagger

0.3
0.2
0.1
0
0

0.2

0.4

0.6

0.8
1
Quark Jet Efficiency Rate

Figure 4.12: Compare MLP and BDT tagger with same inputs (ntrack , trackwidth, trackC1). With the same inputs, the performance of the two models issimilar, indicating that input information is more important than the modelarchitecture.
models improved approximately 10% better at the 80% quark eﬃciency rate,
where the gluon rejection rates of Pointwise and BDT models are around
75% and 68%, respectively. This shows that neural network models using
low-level inputs can improve the q/g tagging signiﬁcantly.
Besides the performance at all ranges, the dependence on p T and η is also essential. Diﬀerent transverse momentum and pseudorapidity range indicatesthe diﬀerent ﬁelds of physics analysis. Hence, diﬀerent strategies are needed
to consider in the associated region. Figure 4.13 displays the pT and η dependance for all models. They are plotted at 80% quark eﬃciency whichmeans 80% quark remains as gluon jet rejection rate is obtained.
In the pT dependance plot (top), the bin is set to 100 GeV below 1000 GeV
such as 0-100 GeV, 100-200 GeV, etc. Above 1000 GeV, 1000-1500, 15002000, 2000-3000, 3000-4000, 4000-5000 GeV bins are selected. It comes tobe better performance as pT increases in the plot. Worse performance at low
pT region results from the similar track and topo-cluster distribution of lowenergy quark/gluon. The high-energy gluon jet turns into generating moreparticles, making it easier to implement the q/g tagging. At pT < 100 GeV

Gluon Jet Rejection Rate

CHAPTER 4. QUARK/GLUON TAGGING

0.9
0.8

48

ATLAS Simulation Work in progress
Gluon Rejection Rate @80% Quark Efficiency Rates = 13 TeV
Small-R Jet (Anti-k R=0.4)|η|<2.1, p >25 GeVt
T

0.7
0.6
0.5
0.4
0.3

Deep Sets Tagger
Energy Flow Tagger
MLP_CNN Tagger
CNN Tagger
MLP Tagger
BDT Tagger

0.2
0.1
0
0

500

1000

1500

2000

2500

3000

3500

4000

4500
p [GeV]

Gluon Jet Rejection RateT

0.9

ATLAS Simulation Work in progress
Gluon Rejection Rate @80% Quark Efficiency Rates = 13 TeV
Small-R Jet (Anti-k R=0.4)
tp >25 GeV

0.8

T

0.7

0.6

0.5

Deep Sets Tagger
Energy Flow Tagger
MLP_CNN Tagger
CNN Tagger
MLP Tagger
BDT Tagger

0.4

0.3

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

|η|

Figure 4.13: The transverse momentum (top) and pseudorapidity (bottom)
dependence of all models introduced in Section 4.2. The y axis in both plots
is gluon jet rejection rate at 80% quark eﬃciency rate.

CHAPTER 4. QUARK/GLUON TAGGING

49

region, all model has similar performance. At 100 < pT < 200 GeV region,
the Deep Sets, Energy Flow and MLP-CNN tagger have better performance.
In the η dependance plot (bottom), the |η| bin is selected as 0-0.5, 0.5-1, 1-1.5,
1.5-2.1. It performs better at the low η region because of the inner detector
in the ATLAS. At lower η, the number of associated jet tracks increases andgives more information. More information brings better accuracy and better
performance. Same as the pT dependence plot, Deep Sets and Energy Flowtaggers have the best performance among all models in all regions. It can beconcluded that neural network models can use more information and better
performance at all pT and η regions.
In conclusion, it is worthwhile to use diﬀerent types of ﬂexible neural network models to include more jets information to operate the q/g tagging. For
example, besides the pT intensity of track and topo-cluster used in Pointwisemodels, the charge of particles inside the jets can be added to the Deep Sets
model as another input information.

4.3.2

Diﬀerence Between Pythia and Herwig MC sample

The MC sample used in Section 4.3.1 is generated by Pythia 8 generator.
To compare the diﬀerence between other MC generators, this Section introduces another MC sample based on Herwig 7 generator [37]. The multijet
MC sample generated by Herwig 7 matches to next-to-leading order (NLO)
calculations developed by Matchbox module [38]. Predictions of the NLO
calculations in the perturbative eﬀects of QCD in the strong coupling givesigniﬁcant accuracy in the LHC experiments. Moreover, the MC sample generated by Herwig 7 in this section exploits the angular-ordered and dipole
showers for the multijet merging algorithm [37, 38].
The multijet MC samples generated by Pythia 8 and Herwig 7 are learnedin Deep Sets and Energy Flow models, respectively. And then the models
trained on diﬀerent MC samples are used to test Pythia 8 and Herwig 7
generated Samples. There are four diﬀerent categories. Trained on Pythia
and tested on Pythia, trained on Pythia and tested on Herwig, trained on
Herwig and tested on Herwig, trained on Herwig and tested on Pythia. Comparing these four categories with Deep Sets and Energy Flow to investigate
the properties of diﬀerent models and MC samples. The ROC curves for
Deep Sets and Energy Flow models are plotted in Figure 4.14. From the
ROC curves, it is clear that no matter what samples are used to train, theperformance of testing on Pythia Sample is always better than testing on
Herwig Sample.

CHAPTER 4. QUARK/GLUON TAGGING

50

Another thing is that the Energy Flow satisﬁes IRC-safety, and it is expected to have several advantages. First, the IRC-safe satisfying models lessaﬀected by the soft emission indicate they can perform better at the lower
energy scale, which is extremely important for the quark/gluon discriminant.
Second, IRC-safe models correspond to the robustness of the collinear splitting, implying the consistency of distinguishing quarks and gluons’ ability.
Third, the models have more generality on both Pythia and Herwig Samples,even when based on diﬀerent hadronization generating methods.
From diﬀerence panels in Figure 4.14, the diﬀerence between Pythia andHerwig testing on Energy Flow is smaller than on the Deep Sets model. The
results above give several brief conclusions. Either trained on Pythia MC
sample or Herwig Sample, testing on the same MC sample has similar results. This can be seen by comparing the dotted lines or solid lines. Then,the MC sample generated by the Pythia seems more accessible to separate
quarks and gluons by q/g tagging than the MC sample generated by the
Herwig generator. Finally, the Energy Flow model has more similar performance between the diﬀerent MC samples, but further research is still needed
to investigate whether this is from IRC-safe ability. These might result fromthe fundamental diﬀerence of the generating strategy between Pythia andHerwig generators.
The diﬀerence of ntrack , trackwidth and trackC1 between Pythia and Herwig
MC samples are described in Appendix A. This section gave a brief work forstudying these two MC samples with Deep Sets and Energy Flow models.
It is also attractive to analyze the Pythia and Herwig MC samples with not
only Deep Sets and Energy Flow but also other neural network models thatcan utilize more low-level information for future works.

Gluon Jet Rejection Rate

CHAPTER 4. QUARK/GLUON TAGGING

51

1
0.9
0.8
0.7
0.6
0.5

ATLAS Simulation Work in progresss = 13 TeV
Small-R Jet (Anti-k R=0.4)|η|<2.1, 25GeV< p t < 2TeVDeep Sets

T

Trained on Herwig, Tested on Herwig
Trained on Pythia, Tested on Pythia
Trained on Pythia, Tested on Herwig
Trained on Herwig, Tested on Pythia

0.4
0.3
0.2

Difference (Testing on Pythia)

Difference (Trained on Herwig)

0.1
0
0.08
0.06
0.04
0.02
0

0.08
0.06
0.04
0.02
0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Gluon Jet Rejection Rate

Quark Jet Efficiency Rate

1
0.9
0.8
0.7
0.6
0.5

ATLAS Simulation Work in progresss = 13 TeV
Small-R Jet (Anti-k R=0.4)|η|<2.1, 25GeV< p t < 2TeV

Energy FlowT

Trained on Herwig, Tested on Herwig
Trained on Pythia, Tested on Pythia
Trained on Pythia, Tested on Herwig
Trained on Herwig, Tested on Pythia

0.4
0.3
0.2

Difference (Testing on Pythia)

Difference (Trained on Herwig)

0.1
0
0.08
0.06
0.04
0.02
0

0.08
0.06
0.04
0.02
0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Quark Jet Efficiency Rate

Figure 4.14: The ROC curves trained on Herwig or Pythia and tested on
Herwig or Pythia with Deep Sets/Energy Flow models are shown in the
top/bottom ﬁgure. Solid/Dotted curves represent testing on Pythia/Herwig
Sample. Blue/Red curves represent training on Pythia/Herwig Sample. The
black solid/dotted line stands for the diﬀerence between the models training
on the diﬀerent samples and testing on the same samples.

Chapter 5
Quark/Gluon tagging
Application in 1-lepton
Semileptonic VBS
The q/g tagger should improve the sensitivity to searches and measurementsof electroweak processes in the hadronic ﬁnal state, characterized by quarkinduced jets in the events. Usually, analyses using hadronic ﬁnal states arecomplex at the LHC due to the huge amount of multijet background. However, if the q/g tagger can select quark-induced jets while suppressing thegluon-induced jets, it can strongly suppress the multijet background. As abenchmark electroweak process at the LHC, VBS has been studied in thischapter. Since the Energy Flow model has the best performance among allmodels, it is used to separate the VBS signal and background samples forvalidation.
The measurement of the semileptonic VBS processes was performed by ATLAS using a 36fb−1 dataset [12]. This thesis only focuses on the 1-lepton
resolved channel for convenience. In the 1-lepton resolved channel, aiming
for WW and WZ scatterings at the lower eﬀective center-of-mass energy, thesignal candidate events were selected by four hadron jets, in addition to exactly one lepton in the event. For signal events, all four jets are originatedfrom quarks. The main sources of the background process are W+jets and t t̄.
About 32%, 12%, and 1% of W+4jets events have 2, 3 and 4 gluon-induced
jets in the selected jets. In this thesis, the analysis in Reference [12] is tried
to be reproduced, and the impact of the q/g tagger is studied.
The MC samples used for Application and the setup for their generators aredemonstrated in Section 5.1. The Event Selection for 1-lepton semileptonic
VBS and background Samples are shown in Section 5.2. There are mainly
three q/g tagging strategies for selecting purer VBS signal, also introduced
52

CHAPTER 5. 1-LEPTON SEMILEPTONIC VBS APPLICATION

53

Figure 5.1: An illustrating diagram of a VBS topology taken from [12].
in Section 5.2. The performance and comparison of diﬀerent strategies aredescribed in Section 5.3.

5.1

Introduction of MC samples

The signal sample used for q/g tagging application is the semileptonic VBS
MC sample. For the brief application, only two kinds of background samples
are used in this Chapter. One is W+jet and the other one is t t̄ MC sample.
In the VBS process, two forward jets originate from spectator quarks. This
forward jet pair is required with the highest invariant mass (referred to m tag
jj )of all small-R jet pairs in each event. There are also two Vector bosons (Z or
W bosons). In this thesis, one decays into two quarks and the other decays
through the leptonic process, which is the so-called semileptonic process.
The schematic diagram is shown in Figure 5.1. Section 5.1.1 gives a brief
introduction for Semileptonic VBS Sample and Background Samples in the
study. Section 5.1.2 explains the Object Deﬁnition such as lepton, jets, etc.

5.1.1

Signal Sample and Background Samples

The√ATLAS experiment collects the luminosity 139 fb−1 of pp collision data
at s = 13 TeV from 2015 to 2018 during Run II of the LHC. Therefore,
the signal and background samples used in this Chapter are scaled to theluminosity of 139 fb−1 .
This Chapter focuses on the 1-lepton channel of the Semileptonic Vector Boson Scattering MC sample. There are two channels considered, which are
WW → ℓνqq and WZ → ℓνqq. The semileptonic VBS samples are generatedby MadGraph (v.2.6.6)[39]+Pythia8[28]+EvtGen(v.1.7.0)[40]. The genera-

CHAPTER 5. 1-LEPTON SEMILEPTONIC VBS APPLICATION

54

Table 5.1: The MC samples used in Chapter 5.
Process
Generator
Cross section[pb]VWjj→ ℓνqq+jj
MadGraph + Pythia8 +EvtGen
2.25
W+jet → ℓν + jet SHERPA 2.2.1
6.16×104tt̄ → ℓνqqbb
POWHEG + Pythia8 + EveGen
396.89tor uses the A14[30] and NNPDF23LO PDF[41] as a set of tuned parameters.
The VBS MC samples are generated with two on-shell vector bosons (WWor ZW), which one decays leptonically (W → ℓν, where ℓ = e, µ, τ ) and theother one decays hadronically (V → qq). The details of the MC sample areshown in Table 5.1.
There are two background MC samples used in this application. One is
W+jet and the other one is tt̄ sample. The W+jet Sample is generated by
the SHERPA 2.2.1 event generator[42]. The W+jet event generator uses theparameter set of NNPDF30LO PDF [41]. The W boson is enforced to decay
to a lepton and a neutrino in the W+jet MC samples.
tt̄ → WbWb → ℓνbqqb/ℓνbℓνb process is considered in the tt̄ MC sample. It is generated by the event generator POWHEG[43] + Pythia 8[28]+ EvtGen (v1.6.0). The POWHEG event generator is the abbreviation of
POsitive Weight Harrest Emission Generator. As its name, only the positive
event weight is generated. The POWHEG event generator is developed totackle the negative event weight problem and is usually utilized in a hadronic
process.
This thesis aims to simulate the jjjjℓν ﬁnal states. Electromagnetic particles and hadrons are simulated at the inner detector and calorimeters in the
ATLAS detector. Muons are simulated from the inner detector to the muon
spectrometer.
The backgrounds from the additional proton-proton collisions are referred toas pile-up, presenting a serious issue to the analyses in the ATLAS. Thus,
pile-up background events are considered to study more data-like samples.
The Monte Carlo simulation method[44] is applied to generate the pile-up
events and add them with other events. Figure 5.2 shows the distribution ofinteractions mean number utilized to run the simulation events.

5.1.2

Physics Object

Physics Object is deﬁned from the particles representing the observed characteristics and used to reconstruct the events. In this section, the lepton(e, µ),Jet and Emiss
will be described for the later analysis.
TCHAPTER 5. 1-LEPTON SEMILEPTONIC VBS APPLICATION

55

Figure 5.2: Mean number of interactions per crossing from 2015 to 2018.
• Electron
In this analysis, the electron pT threshold is set at 30 GeV and |η| <2.47 is required for the reason of inner detector cover range.
There are three working points (Loose/Medium/Tight) for Electron
ID[45], using the Likelihood-based (LH) algorithm. The electron object in this chapter uses the TightLH working points. The details is
described in Table 5.2.
d0 is the minimum distance between the primary vertex and the track.
When d0 is calculated, the minimum distance point will be found on
the track. z0 represents the projecting distance between the primaryvertex and this minimum distance point on the z axis. The BL meansthat the parameters are relative to the beamline and σ is its uncertainty.
The electron object energy is calibrated by the BDT to reduce the effect from the calorimeters and their neighboring materials. The BDT
is trained by the MC simulations and tested by the MC samples andreal data detected in the ATLAS[46].
• MuonMuons are minimum ionizing particles having long decay life. They
are expected to go through all devices in the ATLAS detector, fromCHAPTER 5. 1-LEPTON SEMILEPTONIC VBS APPLICATION

56

Table 5.2: The electron object deﬁnition used in this study.
Cut
Selection
pT
pT > 30 GeVη|η| < 2.47
BL
Track to Vertex Association |d0 (σ)| < 5, |∆zBL
0 sin θ| < 0.5 mm
ElectronID = TightLH
Identiﬁcation
Inner Detector, calorimeter, to Muon Spectrometer[5]. Therefore, thisanalysis requires that muons leave the tracks in these three regions.
The deﬁnition of the signal muon is shown in Table 5.3.
Z → µµ and J/ψ → µµ events are exploited to calibrate muon energy
scale and resolution. The calibration is imposed by ﬁtting the invariant
mass of muon pairs of these two processes on the MC simulation to theobserved data.
Table 5.3: The Muon object deﬁnition used for the MC sample in this chapter.
Cut
Selection
pT
pT > 30 GeVη|η| < 2.5
(σ)|
<
|∆zBL
Track to Vertex Association |dBL
3,0 sin θ| < 0.5 mm
0Identiﬁcation
MuonQuality = Medium• Small-R Jet
Jet is one of the essential physics objects in LHC experiments. The JVT
cut is utilized to suppress the object from the pile-up jet. The introductions of jet reconstruction are already shown in Section 2.3.1. This application study focuses on the small-R jet investigating the quark/gluon
tagging. Table 5.4 shows the details of the deﬁnition for Small-R Jet
Object.
Small-R jet calibration consists of several serial steps: the origin correction, the jet are a based pile-up correction, the MC-based calibration,and the global sequential calibration.
The origin correction performed in the ﬁrst step is reorienting a small-R
jet to the primary vertex. Secondly, the jet area-based pile-up correction is imposed to reduce the impact of the pile-up contamination. In
the third step, the MC-calibration uses the MC simulation sample todetermine the energy response function of |η|. In the global sequential calibration step, the residual dependence on the jet substructure

CHAPTER 5. 1-LEPTON SEMILEPTONIC VBS APPLICATION

57

is corrected by the fraction of the jet energy measured in the hadronic
calorimeter.
Table 5.4: The Small-R Jet object deﬁnition used for the MC sample inthis chapter. EMPFlow represents the particle ﬂows (small-R jets here) arereconstructed with electromagnetic scale topo-cluster.
Cut
Selection
Algorithm
anti-kT (R=0.4)
Input Constituent
EMPFlow
pT >20 GeV
pTη
|η| < 4.5
> 0.95 for pT < 120 GeV and |η| < 2.4
JVT> 0.11 for pT < 120 GeV and 2.4 < |η| < 2.5(Medium Working Point)• Missing ET
Since neutrinos don’t interact with anything in the ATLAS detector,
observable physics objects’ energy and momentum vector are not conserved. The missing transverse momentum vector in the detector isdeﬁned as Emiss
T . The calculation can be written as Equation 5.1 easily.
∑
∑
∑
∑
ET =
EeT +
ET γ +ET τ∑ jet ∑ µ
+
ET +
ET
(5.1)
∑ soft object
miss
+
ET
+ ET

Ee,γ,τ,jet
represents the transverse energy ET of electron photon, τ lepT
objectton and jet. EµT represents the transverse energy of muon. Esoft
T
represents the object is observable but cannot be deﬁned as an object with the selection, such as the soft particles not reconstructed intojets.
The missing ET calibration is performed with Z → ee and Z → µµ
events. Since these events do not have neutrinos, the transverse momentum is used to calibrate the missing ET by measuring the deviations
from the ee, µµ events.

CHAPTER 5. 1-LEPTON SEMILEPTONIC VBS APPLICATION

5.2

58

1-lepton Event Selection

The selections are performed to enhance the signal purity. For an easy discussion, this section only describes the 1-lepton event. Section 5.2.1 demonstrates the preselection ﬁrst. Section 5.2.2 will introduce the BDT discriminant and its variables. Section 5.2.3 shows that diﬀerent strategies by q/g
tagging.

5.2.1

Preselection

According to the jet selection criteria, there are mainly two categories in thesemileptonic VBS process. One or more large-R jet in events is categorized
as merged events. Otherwise, events without large-R jets are categorized as
resolved events. For validating q/g tagging, this paper only discusses 1-lepton
resolved events.
For 1-lepton resolved events, the candidates include one lepton and one neutrino, a pair of tagging jets1 . And a pair of signal jets originating from thesignal vector boson. Therefore, the preselection is imposed to obtain the pure
1-lepton resolved events.
The preselection cut is shown as follows.
The lepton trigger is applied to the MC samples in this Chapter. Common
small-R jet selection is applied to both tagging and signal jets, p T > 20 GeV
for |η| < 2.1 and pT > 30 for 2.1 < |η| < 4.5. The cut of |η| < 2.1 is because
the q/g tagging models uses the input variables at |η| < 2.1 region only.
For W → ℓν samples, only one tight lepton, and no loose lepton are required.
The tight lepton and loose lepton stand for the lepton passing through theElectronID and MuonQuality cut with a tight or loose working point. The
lepton (e and µ) transverse momentum threshold is pT > 30 GeV. The missing ET cut is also imposed with Emiss> 80 GeV because of the existence ofTthe neutrino.
For tagging jets selections, tagging jets are selected by choosing the largest
invariant mass(mtag
jj ) of a small-R jets pair each event. Both leading andsubleading tag jet transverse momentum is required as p T > 30 GeV. The
taginvariant mass of tagging jets pair satisﬁes with mtag
jj > 400 GeV. The mjj
distribution is displayed in Figure 5.3.
For signal jets selection, other than tagging jets, the number of small-R jetsneeds to be greater than or equal to two jets. To acquire more signal-likeevents, leading signal jets transverse momentums are required as p T > 40
GeV.
1

A jets pair directly coming from partonic quarks inside the collision protons.

Event/100GeV

CHAPTER 5. 1-LEPTON SEMILEPTONIC VBS APPLICATION

107

59

ATLAS Simulation
Work in progress-1
s = 13 TeV, 139 fb

VBS Sample x 300
W+jet Sample

610

t t Sample

5

10

104

3

10

significance

102

20
18
16
14
12
10
8
6
4
2
0

1000

2000

3000

4000

5000 tag6000

mjj [GeV]

Figure 5.3: The mtag
jj distribution of 1-lepton resolved process. The events
are selected with the 1-lepton trigger and have exactly one lepton. Missing
ET cut and jet pT cut are also required as shown in Section 5.2.1.
Additional two preselection cuts are applied to enhance the purity. The number of b-tagged jets equal to zero is needed. The invariant mass of two signal
jets and a speciﬁc jet is required as mjjj > 220 GeV. The speciﬁc jet is selectedby calculating the closest invariant mass mjjj from the top quark mass2 . This
selection is also imposed to reduce the background from the t t̄ → ℓνqqbb
process since top quark mainly decays through the process t → Wb → qqb.
After the selections above, two diﬀerent signal jets pair section strategies are
considered in this analysis. One is 2leading and the other one is minmass,
shown as follows.
• 2leading : The signal jets pair is selected by choosing the two highest
2

mt = 172.76 is used in this study.

CHAPTER 5. 1-LEPTON SEMILEPTONIC VBS APPLICATION
3

× 10
350

Event/15GeV

Event/15GeV

3

60

ATLAS Simulation
Work in progress-1
s = 13 TeV, 139 fb

300

VBS Sample x 100
W+jet Sample

250

t t Sample
2leading

× 10
400

ATLAS Simulation Work in progresss = 13 TeV, 139 fb-1

350

VBS Sample x 100
W+jet Sample

300

t t Sample
minmass

250
200
200

150

100

100

50

50

0

0
2.2
2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2

significancesignificance

150

2.5
2
1.5
1
0.5
0

100

200

300

400

500

mjj [GeV]

100

200

300

400

500

mjj [GeV]

Figure 5.4: The distribution of signal jets pairs invariant mass. All preselection cuts except signal region cut are applied to both plots. The 2leading andminmass strategies plots are shown on left and right, respectively. The 2leading has better signiﬁcance because the background is less than the minmass
strategy. However, the minmass strategy has more signal and background
events, implying it might have more space to improve by q/g tagging.
pT small-R jets other than tagging jets.
• minmass : The signal jets pair is selected by choosing the two small-R
jets other than tagging jets that have the closest invariant mass from
W/Z boson mass3 .
The 2leading strategy is a new selection strategy introduced in this thesis.
On the other hand, the minmass strategy was applied in the Reference [12].
Both 2leading and minmass strategies have diﬀerent advantages and disadvantages. 2leading strategy has a larger probability of selecting the jets fromtt̄ samples, but the signiﬁcance is better than the minmass strategy. The
invariant mass selection makes sure that the minmass strategy obtains morejets decaying from W/Z vector bosons. However, the mjj distribution tends
to concentrate at 80-90 GeV region leading to the decrement of signiﬁcance.
The mjj distributions of 2leading and minmass strategies are shown in Figure
5.4.
The signal region (SR) selection is deﬁned as the invariant mass of signal jets
pair is within the range of W/Z boson mass. 64 < mjj < 106 GeV is imposed
to obtain a pure VBS signal. The summary of preselection is listed in Table
3

This analysis utilizes mW = 80.385 GeV and mZ = 91.187 GeV.

CHAPTER 5. 1-LEPTON SEMILEPTONIC VBS APPLICATION

61

Table 5.5: A list of preselection for 1-lepton semileptonic VBS signal searchin this analysis. The jet mtag
jj and pT are shown in Figure 5.3 and 5.6,
respectively. Other distributions are described in Figure Appendix B
Objects
Cuts
threshold
Number of Tight leptons
1
Number of Loose leptons
0
W → ℓν
missET> 80 GeVpT (ℓ)> 30 GeV
tagging jets pT> 30 GeV
tagging jets pairmtag>
400 GeVjj
Number of signal jets
≥2
> 20 GeV for |η| < 2.1
Signal jets pairpT (signal jet)> 30 GeV for 2.1 < |η| < 4.5
Leading jet pT> 40 GeV
Signal Region
64 < mjj < 106 GeV
OthersNumber of additional b-tagged jets0mjjj
> 220 GeV
5.5.
The BDT discriminant in Section 5.2.2 and q/g tagging model in Section
5.2.3 will be applied to both two strategies. And then the performance ofthem will be discussed in Section 5.3.

5.2.2

BDT Discriminant

The SR (64 < mjj < 106 GeV) deﬁned in the previous section is not enoughto observe the VBS signal process with the required signiﬁcance. Hence,
the BDT machine learning tool is performed to enhance the SR purity. The
BDT is used to learn the signal sample (VBS sample) and background samples (W+jet and tt̄ samples), respectively. The W+jet and tt̄ MC samples
are applied the preselection individually. The input variable set and hyperparameters of the BDT in this analysis follow the example in Reference [12].
The chosen hyperparameters are shown in Table 5.6. The hyperparameters
are considered to be against overtraining eﬀect.
Input variables are selected to have higher discriminant between signal andbackground samples. Most variables are related to kinematics such as transverse momentum. Furthermore, the quark/gluon separating variables suchas the number of tracks and trackwidth is also considered since the backgrounds most come from QCD interactions which generate numerous gluons.

CHAPTER 5. 1-LEPTON SEMILEPTONIC VBS APPLICATION

62

Table 5.6: A summary of hyperparameters in BDT Discriminant model.
BDT hyperparameters
1-lepton
NTrees800
MaxDepth
4
Shrinkage
0.3
MinNodeSize
5%
nCuts
20
UseBaggedBoost
True
0.5
BaggedSampleFraction
SeparationType
GiniIndex
There are totally 23 input variables for the BDT discriminant training. The
deﬁnition of each variable is described as follows.
• mjetjet : Invariant mass of jets pair.
• ∆ηjjjetjet : η diﬀerence between two jets.
• pjet1: Transverse momentum of leading jet.
T• pjet2: Transverse momentum of subleading jet.
T• wjet : Trackwidth of jet.
• njettracks : Number of tracks within jet.
• nj : The number of jets having track constituents.
• nj,extr : The number of additional jets other than the jets from thevector boson.
• ∆R(ℓ, ν) : Angular separation between lepton and neutrino.
• ςV : Boson centrality, a topological variable.
• mVV : Invariant mass of two vector bosons from signal jets pair and
lepton-neutrino pair.
• mVVjj : Invariant mass of vector bosons pair and tagging jets pair.
Boson centrality is deﬁned as ςV = min(∆η− , ∆η+ ),where ∆η+ = max[ηtag,j1 , ηtag,j2 ] − max[η(Vhad ), η(Vlep )]and ∆η− = min[η(Vhad ), η(Vlep )] − min[ηtag,j1 , ηtag,j2 ]. This variable is sensitive when the tagging jet has a signiﬁcant separation in η.

CHAPTER 5. 1-LEPTON SEMILEPTONIC VBS APPLICATION

63

The W boson mass constraint determines the momentum of the neutrino on
the lepton because of W → ℓν decay. The entire calculation is shown as
following equations.
√→→mW 2 = (Eℓ + p2T,ν + p2z,ν )2 − ((−p T,ν + −p T,ℓ ) + (pz,ν + pz,ℓ )),
√
(5.2)
→
−
→
−
2
2
= mℓ + 2Eℓ pT,ν + pT,ℓ − 2 p T,ν · p T,ℓ − 2pz,ν pz,ℓ ,where the mass of neutrino is set to zero. The pT,ν is assumed to be missing
ET and px,ν and py,ν are obtain from known ϕEmiss. Therefore the remainTing unknown variable is pz,ν only and it can be calculated by a quadratic
equation.
→→→→
0 = 4p2T,ℓ ·p2z,ν −4(m2W +2−
p T,ν · −p T,ℓ )]pz,ℓ ·pz,ν −(m2W +2−
p T,ν · −p T,ℓ )2 +4E2ℓ p2T,ν ,(5.3)
where pz,ν is acquired by solving the root of the quadratic formula. The
smaller real component of the solutions is selected since it is close to the real
physics in this analysis. Eventually, four-momentum of neutrino is obtain, pz,ℓν and massless property.
able by collecting Emiss
T , ϕEmiss
T
To avoid overtraining and use all samples, cross-validation is used in BDT.
Cross-validation is a method that uses diﬀerent portions of samples to train
and test on diﬀerent steps. For example, the samples are divided into two
portions A and B in this analysis. In the ﬁrst step, A sample is trained andtested on B sample. And then the model trained with B sample is utilized
to test on A sample. Cross-validation is powerful to use better the training
and testing samples, which exploits much more information. The input variables and their linear correlation coeﬃcients are evaluated and described inAppendix C. Smaller linear correlation coeﬃcients represent the weak correlation worth inputting them to train. Generally, all input variables are foundto be good training inputs into BDT.
After training and testing in the BDT, the BDT score is output as a discriminant between signal and background samples. A suitable BDT scorethreshold is required to separate signal and background, which will be introduced in Chapter 5.3. As a result, the BDT score threshold cuts down theratio of signal and background signiﬁcantly. The BDT score distributions of
VBS signal sample, W+jet and tt̄ background sample are shown, respectively
in Figure 5.5.

5.2.3

Quark/Gluon Tagging Enhance

Quark/Gluon tagging models are studied in the previous Chapter. This section will introduce the strategies of exploiting the Energy Flow tagger trained

0.07

ATLAS Simulation Work in progress

Small-R Jet (Anti-k R=0.4)ts=13 TeV, 139 fb-1
BDT Discriminant

0.06

0.05

VBS Sample
W+jet Sample
tt Sample
2leading

Normalized Event

Normalized Event

CHAPTER 5. 1-LEPTON SEMILEPTONIC VBS APPLICATION

0.07

0.03

0.03

0.02

0.02

0.01

0.01

− 0.2

− 0.1

0

0.1

0.2

0.3
BDT

W+jet Sample
tt Sample
minmass

0.05

0.04

− 0.3

ATLAS Simulation Work in progress

Small-R Jet (Anti-k R=0.4)ts=13 TeV, 139 fb-1
VBS Sample
BDT Discriminant

0.06

0.04

− 0.3

64

− 0.2

− 0.1

0

0.1

0.2

0.3
BDT

Figure 5.5: The BDT discriminant output of the 2leading (left) and theminmass (right) strategies. From the comparison, the 2leading strategy has
a better separation between signal and background samples. Note that thesignal and background events are normalized to 1 in both ﬁgures.
Table 5.7: A summary of diﬀerent selection strategies applied in this thesis.
Energy Flow q/g tagging
BDT q/g tagging

2leading with BDT Discriminant
Neural 2leading
BDT 2leadingminmass with BDT Discriminant
Neural minmass
BDT minmass

in Chapter 4 to improve the signal signiﬁcance. Moreover, the BDT q/g tagger is also discussed to implement a quick comparison between the neuralnetwork model and the BDT model. Including Energy Flow and BDT models, there are four types of strategies, described in Table 5.7. Basically, thesignal purity improved outstandingly after preselection and BDT discriminant enhance. Hence, the q/g tagging is based on the selection above as well.
Energy Flow and BDT q/g tagger output is utilized as a threshold cut after
2leading and minmass strategies mentioned in the previous section. Because
both Energy Flow and BDT q/g taggers are trained at |η| < 2.1, the output threshold cut is only imposed for the jets that |η| <2.1. The ratios of|η| < 2.1 quarks in the 2leading and minmass strategies are 60165/2137700≈ 28.1% and 926571/3462640 ≈ 26.8%, respectively. The 2leading and minmass strategies followed by the Energy Flow model are referred to as neural
2leading and neural minmass strategies. In addition, 2leading and minmass
followed by BDT q/g tagger are referred to as BDT 2leading and BDT minmass strategies. Selecting signal jets pair with the order of Energy Flow or
BDT q/g tagger output is considered as another strategy. However, the performance declined a lot compared to 2leading and minmass strategies. Thisorder strategy is shown in Appendix E.

CHAPTER 5. 1-LEPTON SEMILEPTONIC VBS APPLICATION

65

Figure 5.6: The transverse momentum distribution of the 2leading (left) andminmass (right) jets at 139 fb−1 . Both signal and tagging jets that |η| < 2.1
are chosen because they are the targets for implementing q/g taggers.
Although the Energy Flow tagger is shown much better than BDT tagger
in previous, their performance is comparable in this analysis since the jetsof the MC samples range at lower transverse momentum (approximately
smaller than 200 GeV, shown in Figure 5.6). This indicates that it is worthwhile comparing these two diﬀerent q/g taggers. The outputs of Energy Flowand BDT q/g taggers are shown in Figure 5.7 and Figure 5.8, respectively.

5.3

Application Results

Both the 2eading and minmass strategies with BDT discriminant are wellstudied in the previous research and improved a lot. Unlike the BDT discriminant that uses high-level input variables, Energy Flow q/g tagging with
low-level inputs is expected to improve much more than the previous methods. Therefore, the diﬀerent strategies introduced above will be compared inthis section. Section 5.3.1 introduces a criterion, signiﬁcance, for the performance judgment. Section 5.3.2 describes the signal-backgrounds separation
performance of the BDT discriminant as a baseline analysis of the following
q/g tagging models. Section 5.3.3 will show the q/g tagging ability and its
improving limit. Section 5.3.4 demonstrates the signiﬁcance of all strategies
and shows the improvement after applying Energy Flow q/g tagging.

Normalized Event

Normalized Event

CHAPTER 5. 1-LEPTON SEMILEPTONIC VBS APPLICATIONATLAS Simulation Work in progress

0.07

Small-R Jet (Anti-k R=0.4)ts=13 TeV, 139 fb-1
qg tagger

0.06
0.05

VBS Sample
W+jet Sample
tt Sample
2leading

ATLAS Simulation Work in progress

0.07
0.06
0.05

0.04

0.04

0.03

0.03

0.02

0.02

0.01

0.01

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9
1
Energy Flow

66

0

Small-R Jet (Anti-k R=0.4)ts=13 TeV, 139 fb-1
qg tagger

VBS Sample
W+jet Sample
tt Sample
minmass

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9
1
Energy Flow

Figure 5.7: The Energy Flow q/g output distribution of 2leading (left) andminmass (right) jets. Both signal and tagging jets that |η| < 2.1 are chosenbecause they are the targets for implementing q/g taggers. The energy ﬂow
output is the likelihood probability of quark. Therefore, it ranges between 0
to 1.

5.3.1

Discovery signiﬁcance and Uncertainty

Discovery signiﬁcance is an estimating value to describe the opportunity thatthe observation is not from the background ﬂuctuation and is believable.
Signiﬁcance can also be related to the p-value which provides the probabilityof diﬀerent observations occurring. The smaller p-value implies that thetest hypothesis is false. The relation of signiﬁcance Z and p-value can be
described as Equation 5.4.
√
Z(Ns , Nb , δb ) = 2erf −1 (1 − 2p),(5.4)
where Ns , Nb and δb represents the number of signal events, the number ofbackground events and the uncertainty of background events. erf represents
the error function. And the deﬁnition of p-value is shown in the equation
below.
∫ ∞∞∑p=
db N(b; Nb , δb Nb )P(i; b),(5.5)
0i=Ns +Nb

where N and P are Gaussian and Poisson distribution, respectively.
The signiﬁcance in this study was calculated by BinomialExpZ in RooStats.
To compare diﬀerent situations, the background systematic uncertainty is set
to 10%, 20% and 30%, respectively.

Normalized Event

Normalized Event

CHAPTER 5. 1-LEPTON SEMILEPTONIC VBS APPLICATIONATLAS Simulation Work in progress

0.12

Small-R Jet (Anti-k R=0.4)ts=13 TeV, 139 fb-1
qg tagger

0.1

VBS Sample
W+jet Sample
tt Sample
2leading

0.08

Small-R Jet (Anti-k R=0.4)ts=13 TeV, 139 fb-1
qg tagger

0.12

VBS Sample
W+jet Sample
tt Sample
minmass

0.08

0.06

0.06

0.04

0.04

0.02

0.02

− 0.3

ATLAS Simulation Work in progress

0.14

0.1

67

− 0.2

− 0.1

0

0.1

0.2

0.3
BDT

− 0.3

− 0.2

− 0.1

0

0.1

0.2

0.3
BDT

Figure 5.8: The BDT q/g output distribution of 2leading (left) and minmass(right) jets. Both signal and tagging jets that |η| < 2.1 are chosen because
they are the targets for implementing q/g taggers.

5.3.2

Sensitivity of the Baseline Analysis

The 2leading and minmass with BDT discriminant strategies are usuallyused for the VBS signal searching studies. For example, Reference [12] exploits the minmass with BDT discriminant selection to ﬁnd the VBS signals.
Therefore, it is helpful to calculate the signiﬁcance of the 2leading and minmass with BDT discriminant strategies as the performance baseline of VBS
searching compared to the additional q/g tagging selection discussed in thelater sections.
There are 1059 VBS signal events, 297845 W+jet events, and 235519 t t̄events, respectively for 2leading strategy selections.
For minmass strategy, there are 1419 VBS signal events, 454939 W+jet
events, and 409285 tt̄ events.
The results are shown in the ﬁrst column in Table 5.8, where the best significances at 10% background systematic uncertainty are 0.78 and 0.73 for the
2leading and minmass strategies, respectively. The signiﬁcance drops when
the systematic uncertainty increases as expected. Comparing the 2leading
and minmass with BDT discriminant, it is found that the 2leading strategy isalways better than the minmass no matter what the systematic uncertainty
is.

5.3.3

q/g tagging Improving Limit

The BDT discriminant is a powerful tool for separating VBS signal eventsfrom background events. However, the high-level input variables limit its
improvement to another level. Using the q/g tagging model, especially neu-

CHAPTER 5. 1-LEPTON SEMILEPTONIC VBS APPLICATION

68

ral network q/g tagging, provides another way to enhance the signals by
inputting the lower-level information in the ATLAS.
To deﬁne the improving limit of q/g tagging, it is necessary to investigate how
many gluons and quarks are in each event when the 2leading and minmass
selections are imposed. Figure 5.9 shows the number of |η| < 2.1 gluons for2leading and minmass selections. |η| < 2.1 gluons are counted since the q/g
tagging models in this thesis can only be utilized at |η| < 2.1 region. There
are four gluons at most from two signal small-R jets and two tagging small-R
jets.
In order to estimate the limit of the q/g tagging in this study, suppose thatquarks and gluons can be separated perfectly. In other words, only zero|η| < 2.1 gluon events are selected in this situation. Then, applying the
BDT discriminant to only none gluon events to estimate the q/g tagging improving limit. The signiﬁcance estimation of perfect q/g tagger is shown in
Table 5.8 when the q/g tagging diﬀerentiates quarks and gluons with 100%
eﬃciency.
Applying perfect q/g tagging to the 2leading and minmass with BDT discriminant, the signiﬁcance improved obviously no matter how large the systematic
uncertainty is. This indeed demonstrates the potential of q/g tagging. On
average, the 2leading and minmass with BDT discriminant have 56.9% and76.4% improvement by perfect q/g tagging, respectively.
On the other hand, q/g tagging seems to work better on the minmass strategy than the 2leading strategy. Although the 2leading is better than theminmass with only BDT discriminant, the minmass strategy has more remarkable improvement and larger signiﬁcance after the perfect q/g tagging
is imposed.

5.3.4

q/g tagging Improvement

This section will show the improvement of 1-lepton VBS searching after applying the Energy Flow and BDT q/g models trained in Chapter 4.
The threshold cuts of q/g tagger output and BDT discriminant are calculated
separably. In the ﬁrst step, the BDT discriminant is applied to the 2leading
and minmass strategies to obtain the outputs. Secondly, Energy Flow and
BDT q/g taggers are applied to the 2leading and minmass strategies to get
the output distribution. The output distribution of the BDT discriminant
is displayed in Figure 5.5. And the output distribution of Energy Flow and
BDT q/g tagging models are shown in Figure 5.7 and Figure 5.8, respectively.
Finally, drawing a two dimensional signiﬁcance plot, which x axis is BDT
discriminant output and y axis is q/g tagger output. The two dimensionalsigniﬁcance plots of Energy Flow and BDT taggers with 10%, 20% and 30%

CHAPTER 5. 1-LEPTON SEMILEPTONIC VBS APPLICATION

69

Event

Event

3

900

ATLAS Simulation Work in progress

800

s = 13 TeV, 139 fb-1
Small-R jet, |η|<2.1
2leading

700

×10
220

ATLAS Simulation Work in progresss = 13 TeV, 139 fb-1
Small-R jet, |η|<2.1
2leading

200
180

tt
160

VBS

600

140

500

120

W+jet

100

400

80

300

60
200

40

100
0

20
0

1

2

0

3
4
Number of Gluons each event

0

1

2

3
4
Number of Gluons each event

1200

ATLAS Simulation
Work in progress-1
s = 13 TeV, 139 fb
Small-R jet, |η|<2.1
minmass

1000

Event

Event

3

×10
350

ATLAS Simulation Work in progresss = 13 TeV, 139 fb-1
Small-R jet, |η|<2.1
minmass

300

tt
VBS

W+jet

250

800
200
600
150
400

100

200

0

50

0

1

2

3
4
Number of Gluons each event

0

0

1

2

3
4
Number of Gluons each event

Figure 5.9: The number of gluons each event for the VBS (left) and thebackground (right) MC samples for 2leading (top) and minmass (bottom)
strategies. The VBS signal sample has the most number for non-gluon events,
while the W+jet and tt̄ samples dominate at 1-gluon event. Therefore, it isuseful to separate signals and backgrounds by applying the q/g tagging.
systematic uncertainty are shown in Appendix D. The tremendous signiﬁcance is obtained by these two dimensional signiﬁcance plots, summarized inTable 5.8.
Compared to the baseline signiﬁcance calculated in Section 5.3.2, it is foundthat all strategies improved after the q/g tagging models were applied. The
signiﬁcances of the neural 2leading and neural minmass strategies are improving by approximately 3.9% and 8.2%, respectively on the average of all
systematic uncertainty assumptions. On the other hand, the BDT 2leading
and BDT minmass strategies improve by about 0.6% and 5.1%.
Taking 10% background systematic uncertainty for example, the signiﬁcancesof the neural 2leading and neural minmass are 0.81 and 0.77, respectively,
which are better than the baseline signiﬁcance discussed in the previous section. The signiﬁcances of the BDT 2leading and BDT minmass are 0.78 and
0.73. From the comparison between the signiﬁcance of Energy Flow and BDTCHAPTER 5. 1-LEPTON SEMILEPTONIC VBS APPLICATION70

q/g tagger, the Energy Flow model performs better than BDT q/g tagging
model. The ability to input low-level variables gives the neural network q/g
tagging models having more space for improvement.
The improvement rate shows that the improving amplitude of the minmass
strategy is more signiﬁcant than the 2leading strategy, which is consistent
with the perfect q/g tagging discussion. This indicates that the minmass
strategy using q/g tagging has a larger potential for better VBS signal searching.

CHAPTER 5. 1-LEPTON SEMILEPTONIC VBS APPLICATION

71

Table 5.8: A summary of all strategies performance discussed in Section
5.3.2 (baseline), 5.3.3 (perfect q/g tagger) and 5.3.4 (Energy Flow and BDT
models). The uncertainty of W+jet and tt̄ includes both systematic and statistical uncertainties. All strategies are applied with the BDT discriminant.
The signiﬁcance is calculated with both the statistical and systematic error.
Selection stratgy
Bkg systematic Signal W+jettt̄
Signiﬁcanceuncertainty
10%
44
42±14 128±380.782leading
20%4442±14 128±38
0.58
30%
37
30±14 99±43
0.40
10%
45
57±18 103±39
0.73
minmass30%
45
57±20 103±43
0.57
30%
45
57±24 103±49
0.39
10%
65
14±6 134±421.112leading
20%
65
14±7
134±480.91
with perfect q/g tagger
30%
60
13±7 114±51
0.70
10%
71
13±7
168±42
1.19
minmass
20%
53
3±4
99±37
0.97
with perfect q/g tagger
30%
53
3±4
99±43
0.76
10%
48
46±13 148±410.81
neural 2leading
20%
48
46±15 148±48
0.60
30%
34
18±10 89±40
0.42
10%
65
83±22 242±580.77
neural minmass20%3533±15 79±34
0.59
30%
22
1±1
40±23
0.44
10%
75
88±18 366±70
0.79
BDT 2leading20%
4442±15 128±44
0.58
30%
37
30±14 99±43
0.40
10%
44
51±17 83±360.73
BDT minmass20%31
32±15 59±27
0.58
30%
28
26±14 50±270.44

Chapter 6
Conclusions
The Vector Boson Scattering (VBS) is the highly critical process to probe
the properties of the electroweak interaction in the Standard Model. The
cross-section of the VBS process is highly sensitive to electroweak symmetry
breaking[47] which is still one of the mysteries in physics. Additionally, theVBS process has the same leading order term of Feynman diagrams with
Higgs bosons, indicating that studying the VBS process is an indirect way
to investigate the Higgs boson properties. With
√ LHC which can operate theparticle collisions at center-of-mass energy s = 13 TeV, the physicists can
examine the vector boson scattering and electroweak symmetry breaking issues. 1-lepton semileptonic VBS process is studied to validate q/g tagging
trained in this thesis. The MC samples are scaled to the integrated luminosity of 139 fb−1 corresponding to the Run II data from 2015 to 2018 at theLHC.
1-lepton semileptonic VBS process decays through WZ and WW channels.
The W boson decays into lepton and neutrino in the ﬁrst and second channels, while the other vector boson decays into two quarks. Combing with thetagging quark originating from the colliding protons, there are totally fourquarks. Hence, it is essential to utilize the q/g tagging to discriminate thequarks and gluons which are the main backgrounds.
The diﬀerent properties between quarks and gluons are helpful to separate
them. For example, ntrack , trackwidth and trackC1 are the usually used variables in the Boosted Tree Decision (BDT) q/g tagging in the past. However,the BDT q/g tagger limitation implies that the input variables will lose some
information during the calculation from the low-level variables such as η, pT ,etc. Neural network q/g tagging models are considered to solve this kind ofissue in this study. Three types of neural network models are compared in
72

CHAPTER 6. CONCLUSIONS

73

Chapter 4, which are MLP, CNN and Pointwise q/g tagging models. As aresult, the Energy Flow and Deep Sets models belonging to Pointwise models
have the best performance among all q/g tagging models. The gluon rejection
rate of the Energy Flow and Deep Sets models improved approximately 10%than the conventional BDT q/g tagging model at the 80% quark eﬃciency
rate. Moreover, both Energy Flow and Deeps Sets models are applied to
diﬀerent multijet MC to examine the IRC-safe. The result is that the gluon
rejection rate diﬀerences between trained on the diﬀerent MC samples with
Energy Flow are smaller than Deep Sets. Also, it is found that no matterthe models are trained in the Pythia or Herwig MC samples, the separationof quarks and gluons always works better in the Pythia MC samples. Thismight indicate that the diﬀerence between these two MC samples is more
prominent, which is a vital issue for future works.
The Energy Flow and BDT q/g tagging models are examined in the 1-lepton
semileptonic VBS process. There are two selection strategies for the signal
quarks considered for the 1-lepton semileptonic VBS process, the 2leading
and minmass selections. The BDT discriminant discussed in Section 5.2.2
enhances both strategies and creates a baseline for the previous research.
The improving limit of q/g tagging is investigated. The 2leading and minmass strategies with BDT discriminant with perfect q/g tagging can havethe maximum improvement of 56.9% and 76.4% compared to the baseline
signiﬁcance calculated from the non-q/g tagging cases. This is exciting since
the q/g tagging still has the space to develop. The improving amplitude of
the neural 2leading and neural minmass is approximately 3.9% and 8.2%,
respectively, indicating that the q/g tagger seems to perform more potent in
the neural minmass strategy. The best performance obtained in this thesis
is neural 2leading, which its signiﬁcance is 0.81. Another thing found is thatthe backgrounds seriously aﬀect the signiﬁcance and fewer backgrounds givea better performance. This results in better performance occurring at thestrict BDT discriminant and q/g tagger threshold cuts that lower the numberof background events.
Signiﬁcant improvement of quark/gluon separation with the q/g tagging
models is examined by the 1-lepton VBS process at the ATLAS in this paper. Since the improvement of q/g tagging models in this study still has
space from the improving limit, it is worth researching diﬀerent q/g tagging
models, especially the neural network models. Furthermore, improving theq/g tagging models with additional low-level input variables and tuning thehyperparameter is perspective research for future works.

Appendix A
Input and output of
Quark/Gluon Tagging Models
Figure A.1, A.2 and A.3 shows the input variables in the BDT q/g tagging
model.

Normalized Event

Figure A.4 compares the diﬀerence between the testing on Pythia and Herwig
MC samples.

0.08

ATLAS Simulation Work in progress
0.07

Small-R Jet (Anti-k R=0.4)ts=13 TeV

0.06

Quark Jet
Gluon Jet

0.05
0.04
0.03
0.02
0.01
0
0

10

20

30

Figure A.1:

74

40

50

ntrackNormalized Event

APPENDIX A. INPUT AND OUTPUT OF QUARK/GLUON TAGGING MODELS75

0.25

ATLAS Simulation Work in progress
Small-R Jet (Anti-k R=0.4)ts=13 TeV

0.2
Quark Jet
Gluon Jet
0.15

0.1

0.05

0
0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45
0.5
trackwidth

0.35

0.4

0.45
0.5
trackC1

Normalized Event

Figure A.2:

0.1

ATLAS Simulation Work in progress

Small-R Jet (Anti-k R=0.4)ts=13 TeV

Quark Jet
0.08
Gluon Jet

0.06

0.04

0.02

0
0

0.05

0.1

0.15

0.2

0.25

0.3

Figure A.3:

Normalized Event

APPENDIX A. INPUT AND OUTPUT OF QUARK/GLUON TAGGING MODELS76

0.1

ATLAS Simulation Work in progress

0.09

s = 13 TeV
Small-R Jet (Anti-k R=0.4)

0.08|η|<2.1, 25< p <2000 GeVT
Training on Pythia with Deep Set Taggert

0.07
Quark Jet on Pythia
Gluon Jet on Pythia
Quark Jet on Herwig
Gluon Jet on Herwig

0.06
0.05
0.04
0.03
0.02
0.01
0
0

0.1

0.2

0.3

0.4

0.5

Figure A.4:

0.6

0.7

0.8
0.9
1
Deep Sets Output

Appendix B
The distributions for 1-lepton
semileptonic preselection

Event/15GeV

and the lepton pT .
Figure B.1 and B.2 show the distributions of the Emiss
T
Figure B.3 and B.4 show the distributions of the mjjj of 2leading and minmass
strategies.

ATLAS Simulation
Work in progress-1
s = 13 TeV, 139 fb

107

VBS Sample x 100
W+jet Sample
t t Sample

6

10

5

significance

10

2
1.5
1
0.5
100

200

300

400

miss

500

ET [GeV]Figure B.1:

77

Event/10GeV

APPENDIX B. THE DISTRIBUTIONS FOR 1-LEPTON SEMILEPTONIC PRESELECTION78

90

× 10

ATLAS Simulation Work in progress80

s = 13 TeV, 139 fb-1

VBS Sample x 100

70

W+jet Sample
60

t t Sample

50
40
30
20
10

significance

0

0.6
0.4
0.2
0

50

100

150

200

250

pT

300

[GeV]

leptonFigure B.2:

Event/15GeV

3

× 10

ATLAS Simulation Work in progress

1200

s = 13 TeV, 139 fb-1

VBS Sample x 100
W+jet Sample

1000

t t Sample
2leading
800

600

400

200

significance

0

1.2
1
0.8
0.6
0.4
200

300

400

500

Figure B.3:

600

700

800

mjjj[GeV]APPENDIX B. THE DISTRIBUTIONS FOR 1-LEPTON SEMILEPTONIC PRESELECTION79

Event/15GeV

3

× 10
800

ATLAS Simulation Work in progresss = 13 TeV, 139 fb-1

VBS Sample x 100

700

W+jet Sample
t t Sample
minmass

600

500

400
300

200

100

significance

0

0.7
0.6
0.5
200

300

400

500

Figure B.4:

600

700

800

mjjj[GeV]Appendix C
Input Variable of BDT
DiscriminantFigure C.1, C.2, C.3 and C.4 displays the BDT discriminant inputs with the2leading strategy selection.
Figure C.5, C.6, C.7 and C.8 shows the BDT discriminant inputs with theminmass strategy selection.

2leading input variables

0.00060.00040.0002
0

1000

2000

3000

4000

5000

0.3
0.25
0.2
0.15
0.1
0.05

6000

1

tag

2

3

4

5

6

7

mjj

0.02
0.01
0

50

100

150

200

250

300

350

p

tag,j2

0.004
0.002
0

9

tag

∆η

100

200

300

400

500

600

Input variable: ptj1
(1/N) dN/ 9.06

1
0.8
0.6
0.4
0.2
0
0

0.5

1

1.5

2

2.5

∆η

jj

T

Figure C.1:

80

700

p

Input variable: detajj

U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%

0.03

0.006

(1/N) dN/ 0.0689

U/O-flow (S,B): (0.0, 0.0)% / (0.1, 0.0)%(1/N) dN/ 8.42

0.04

0.008

jj

Input variable: pttagj2

0.05

8

0.01

U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%

0.001
0.00080.35

tag,j1
T

0.014
0.012

U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%

0.0012ATLAS Simulation Work in Progress
U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%

0.0014

Input variable: pttagj1

0.4(1/N) dN/ 19.2

Input variable: detatagjj

SignalBackground0.0016

U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%(1/N) dN/ 151

Input variable: mtagjj}(1/N) dN/ 0.23

C.1

0.01
0.008
0.006
0.004
0.002
0

50

100

150

200

250

300

350

400

p

j1

T

0.02
0.015
0.01
0.005
40

60

80

100 120 140 160 180

8
6
4
2
0
−1

j2

−0.8 −0.6 −0.4 −0.2(1/N) dN/ 0.743

0.14
U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%

0.12
0.1
0.08
0.06
0.04
0.02
10

15

20

25

30

35

j1

0.4

40

0.22
0.2
0.18
0.16
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
0

j

5

10

7
6
5
4
3
2
1
0
−1

−0.8 −0.6 −0.4 −0.2

0

0.2

0.4

w

1

j

2

Input variable: widthtagj1

U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%

Input variable: ntrackj2

5

0.2

w

Input variable: ntrackj1

0
0

0

T

(1/N) dN/ 1.03

p

ATLAS Simulation Work in Progress

U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%

0.03
0.025

10

81

15

20

25

ntrack10
U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%

0.035

Input variable: widthj2(1/N) dN/ 0.0396

0.04

Input variable: widthj1

U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%

0.045

SignalBackground(1/N) dN/ 0.0402

0.05

U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%(1/N) dN/ 4.28

Input variable: ptj2

(1/N) dN/ 0.0391

APPENDIX C. INPUT VARIABLE OF BDT DISCRIMINANT

8
6
4
2
0
−1

j2

−0.8 −0.6 −0.4 −0.2

00.2

ntrack

0.4

0.6

w

tag,j

1

10
8
6
4
2
0
−1

−0.8 −0.6 −0.4 −0.2

0

0.2

0.4

ATLAS Simulation Work in Progress

0.25
0.2
0.15
0.1
0.05
0
0

0.6

tag,j

10

20

30

40

50

0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0

tag,j15

10

ntrackInput variable: num_extraj

Input variable: met(1/N) dN/ 11.4

1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0

2

4

6

8

10

9
8

U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%

U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%

1.8

7
6
5
4
3
2
1
0
0

0.5

1

1.5

2

2.5

3

nj

3.5

4

nj,extr

Figure C.3:

20

25

30

35

tag,j2

0.022
0.02
0.018
0.016
0.014
0.012
0.01
0.008
0.006
0.004
0.002
0

U/O-flow (S,B): (0.0, 0.0)% / (0.1, 0.1)%

Input variable: num_trkj
215

ntrack(1/N) dN/ 0.103

2(1/N) dN/ 0.254w

Input variable: ntracktagj2

0.3

U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%

12Input variable: ntracktagj1(1/N) dN/ 0.961

14

SignalBackgroundU/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%

16

U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%(1/N) dN/ 0.0406

Input variable: widthtagj2(1/N) dN/ 1.44

Figure C.2:

100 150 200 250 300 350 400 450 500

miss

ET

0.25
0.2
0.15
0.1
0.05
−2

−1

0

1

2

ATLAS Simulation Work in Progress

1
0.8
0.6
0.4
0.2
0

η

1

2

3

4

l

0.002
0.00150.001
0.0005
0

−2000

−1000

0

1000

2000

0.001
U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%

0.0025(1/N) dN/ 282

Input variable: mVVjj

U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%(1/N) dN/ 132

Input variable: mVV

5∆ R(l,ν )0.00080.00060.00040.0002
0

−2000

0

2000

4000

mVV

Figure C.4:

6000

mVVjj

82

0.45
0.4

U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%

0.3

Input variable: centrality(1/N) dN/ 0.239

0.4
0.35

Input variable: deltaRlnu

U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%

SignalBackgroundU/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%(1/N) dN/ 0.128

Input variable: etal

(1/N) dN/ 0.141

APPENDIX C. INPUT VARIABLE OF BDT DISCRIMINANT

0.35
0.3
0.25
0.2
0.15
0.1
0.05
0

−5

−4

−3

−2

−1

0

1

2

3

4

ς

V

APPENDIX C. INPUT VARIABLE OF BDT DISCRIMINANT

minmass input variables

0.00080.00060.00040.0002
1000

2000

3000

4000

5000

0.2
0.15
0.1
0.05

6000

1

tag

2

3

4

5

6

7

8

mjj

0.02
0.01

200

250

300

100

200

300

400

500

600

700

p

Input variable: detajj

Input variable: ptj1

1
0.8
0.6
0.4
0.2
0
0

350

p

0

∆η

(1/N) dN/ 9.77

0.03

150

0.002

9
tag

U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%

0.04

100

0.004

(1/N) dN/ 0.0846

U/O-flow (S,B): (0.0, 0.0)% / (0.1, 0.0)%(1/N) dN/ 8.25

0.05

50

0.006

jj

Input variable: pttagj2

0

0.01
0.008

tag,j2

0.5

1

1.5

2

2.5

3

T

0.014
0.012
0.01
0.008
0.006
0.004
0.002
0

∆η

50

100

150 200250

300 350

400

p

jj

T

tag,j1

U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%

0

0.3
0.25

U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%

0.001

U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%

0.0012

Input variable: pttagj1

ATLAS Simulation Work in Progress

0.35(1/N) dN/ 19.2

Input variable: detatagjj

SignalBackgroundU/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%(1/N) dN/ 155

Input variable: mtagjj(1/N) dN/ 0.23

C.2

83

j1

T

Figure C.5:

60

80

100

120 140160p−0.8 −0.6 −0.4 −0.2

0

0.2

0.4

j

0.08
0.06
0.04
0.02
20

25

30

35

40

j1

0.24
0.22
0.2
0.18
0.16
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
0

5

10

(1/N) dN/ 0.0396

6
5
4
3
2
1
0
−1

0.6

w

U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%(1/N) dN/ 1.05

0.1

15

0
−1

−0.8 −0.6 −0.4 −0.2

0

0.2

0.4

w

1

Input variable: ntrackj2

0.12

10

2

T

0.14

5

4

j2

Input variable: ntrackj1

0
0

6

j

2

Input variable: widthtagj1

U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%

40

8

7
U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%

0.01

10

15

20

ntrack25

j2

ntrackFigure C.6:

10
U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%

0.02

ATLAS Simulation Work in Progress
U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%

0.03

Input variable: widthj2

12(1/N) dN/ 0.0402

0.04(1/N) dN/ 0.0409

0.05

Input variable: widthj1

SignalBackgroundU/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%

0.06(1/N) dN/ 0.732(1/N) dN/ 3.93

Input variable: ptj2

8
6
4
2
0
−1

−0.8 −0.6 −0.4 −0.2

0

0.2

0.4

w

0.6

tag,j

1

10
8
6
4
2
−1 −0.8 −0.6 −0.4 −0.2

0

0.2

0.4

w

0.05
0
0

10

20

30

40

50

U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%

1
0.8
0.6
0.4
0.2
4

6

8

10

0.3
0.2
0.1
0
0

5

10

15

20

25

30

4
3.5
3
2.5
2

1
0.5
0
0

1

2

tag,j2

Input variable: met

4.5

1.5

nj

35

ntrackInput variable: num_extraj

1.2

0.5

ntrack

2

1.4

0.6

0.4

tag,j1

U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%(1/N) dN/ 0.282

0.1

0.6

1.6

2

0.15

tag,j

Input variable: num_trkj

0
0

0.2

0.7
U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%

12

0.25

84

3

4

5

6

0.022
0.02
0.018

U/O-flow (S,B): (0.0, 0.0)% / (0.1, 0.1)%

14

Input variable: ntracktagj2

ATLAS Simulation Work in Progress

0.3(1/N) dN/ 11.3

16

Input variable: ntracktagj1(1/N) dN/ 0.951

U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%

SignalBackground18(1/N) dN/ 0.174(1/N) dN/ 0.0412

20

U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%

Input variable: widthtagj2(1/N) dN/ 1.45

APPENDIX C. INPUT VARIABLE OF BDT DISCRIMINANT

0.016
0.014
0.012
0.01
0.008
0.006
0.004
0.002
0

nj,extr

100 150 200 250 300 350 400 450 500

miss

ET

Input variable: deltaRlnu

Input variable: centrality(1/N) dN/ 0.142(1/N) dN/ 0.27

0.35

Background

0.3
0.25
0.2
0.15
0.1
0.05
−2

−1

0

1

2

ATLAS Simulation Work in Progress

1
0.8
0.6
0.4
0.2
0

1

η

2

3

4

l

0.002

0.00150.001
0.00050−2000 −1000

01000 2000

mVV

0.9

×10

0.8
U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%

U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%

0.0025(1/N) dN/ 286

Input variable:−3 mVVjj(1/N) dN/ 131

Input variable: mVV

5∆ R(l,ν )

0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

−2000

0

2000 4000 6000 8000

Figure C.8:

mVVjj

0.45
U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%

SignalU/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%

0.4

U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%

Input variable: etal

(1/N) dN/ 0.128

Figure C.7:

0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0

−6

−4

−2

0

2

4

ςV

Appendix D
Tuning BDT discriminant andq/g tagger
The z axis represents the signiﬁcance after the thresholds are applied. D.1
and D.2 shows the neural 2leading and BDT 2leading two dimensional significance plots. D.3 and D.4 shows the neural minmass and BDT minmass twodimensional signiﬁcance plots, respectively. There are some gaps in the 2D
plots, such as the place of BDT = 0.13 and EnergyFlow = 0 − 0.8 in Figure
D.1. The reason for these gaps is considered from the deﬁciency of statistics.

D.1

Neural 2leading

85

APPENDIX D. TUNING BDT DISCRIMINANT AND Q/G TAGGER 86

Energy Flow Tagger

ATLAS Simulation Work in progresss = 13 TeV, 139 fb-1, bkg Systematic Uncertainties = 10%
2leading

0.8
0.9
0.7

0.8
0.7

0.6

0.6

0.5

0.5

0.4

0.4
0.3
0.3
0.2

0.2

0.1

0.1
0
− 0.1

−0.05

0

0.05

0.1

0.15
BDT Discriminant0

Figure D.1:

Energy Flow Tagger

ATLAS Simulation Work in progresss = 13 TeV, 139 fb-1, bkg Systematic Uncertainties = 20%
2leading

0.6

0.9
0.5

0.8
0.7

0.4
0.6
0.5

0.3

0.4
0.2

0.3
0.2

0.1

0.1
0
− 0.1

−0.05

0

0.05

Figure D.2:

0.1

0.15
BDT Discriminant

0APPENDIX D. TUNING BDT DISCRIMINANT AND Q/G TAGGER 87

Energy Flow Tagger

ATLAS Simulation Work in progresss = 13 TeV, 139 fb-1, bkg Systematic Uncertainties = 30%
2leading

0.9

0.4

0.8

0.35

0.7

0.3

0.6

0.25

0.5
0.2
0.4
0.15

0.3

0.1

0.2

0.05

0.1
0
− 0.1

−0.05

0

0.05

Figure D.3:

0.1

0.15
BDT Discriminant

0APPENDIX D. TUNING BDT DISCRIMINANT AND Q/G TAGGER 88

D.2

BDT 2leading
ATLAS Simulation
Work in progress-1

BDT Taggers = 13 TeV, 139 fb , bkg Systematic Uncertainties = 10%
2leading

0.7
0.15
0.6
0.1
0.5
0.05

0.4
0.3

0
0.2
− 0.05
0.1
− 0.1
− 0.1

−0.05

0

0.05

Figure D.4:

0.1

0.15
BDT Discriminant

0APPENDIX D. TUNING BDT DISCRIMINANT AND Q/G TAGGER 89

ATLAS Simulation
Work in progress-1
BDT Taggers = 13 TeV, 139 fb , bkg Systematic Uncertainties = 20%
2leading

0.15

0.5

0.1

0.4

0.05

0.3

0

0.2

− 0.05

0.1

− 0.1
− 0.1

−0.05

0

0.05

0.1

0.15
BDT Discriminant0

Figure D.5:
ATLAS Simulation
Work in progress-1
BDT Taggers = 13 TeV, 139 fb , bkg Systematic Uncertainties = 30%
2leading

0.4
0.35

0.15

0.3
0.1
0.25
0.05

0.2
0.15

0

0.1
− 0.05
0.05
− 0.1
− 0.1

−0.05

0

0.05

Figure D.6:

0.1

0.15
BDT Discriminant

0APPENDIX D. TUNING BDT DISCRIMINANT AND Q/G TAGGER 90

D.3

Neural minmass

Energy Flow Tagger

ATLAS Simulation Work in progresss = 13 TeV, 139 fb-1, bkg Systematic Uncertainties = 10%minmass

0.7

0.9
0.8

0.6

0.7
0.5
0.6
0.5

0.4

0.4

0.3

0.3
0.2
0.2
0.1

0.1
0
− 0.1

−0.05

0

0.05

Figure D.7:

0.1

0.15
BDT Discriminant

0APPENDIX D. TUNING BDT DISCRIMINANT AND Q/G TAGGER 91

Energy Flow Tagger

ATLAS Simulation Work in progresss = 13 TeV, 139 fb-1, bkg Systematic Uncertainties = 20%
minmass

0.6

0.9
0.5

0.8
0.7

0.4
0.6
0.5

0.3

0.4
0.2

0.3
0.2

0.1

0.1
0
− 0.1

−0.05

0

0.05

0.1

0.15
BDT Discriminant0

Figure D.8:

Energy Flow Tagger

ATLAS Simulation Work in progresss = 13 TeV, 139 fb-1, bkg Systematic Uncertainties = 30%
minmass

0.45
0.9

0.4

0.8

0.35

0.7
0.3
0.6
0.25
0.5
0.2

0.4

0.15

0.3
0.2

0.1

0.1

0.05

0
− 0.1

−0.05

0

0.05

Figure D.9:

0.1

0.15
BDT Discriminant

0APPENDIX D. TUNING BDT DISCRIMINANT AND Q/G TAGGER 92

D.4

BDT minmass
ATLAS Simulation
Work in progress-1

BDT Taggers = 13 TeV, 139 fb , bkg Systematic Uncertainties = 10%minmass

0.7
0.15
0.6
0.1

0.5
0.4

0.05

0.3
0
0.2
− 0.05

− 0.1
− 0.1

0.1
−0.05

0

0.05

Figure D.10:

0.1

0.15
BDT Discriminant

0APPENDIX D. TUNING BDT DISCRIMINANT AND Q/G TAGGER 93

ATLAS Simulation
Work in progress-1
BDT Taggers = 13 TeV, 139 fb , bkg Systematic Uncertainties = 20%
minmass

0.6

0.15

0.5

0.1

0.4

0.05

0.3

0

0.2

− 0.05

0.1

− 0.1
− 0.1

−0.05

0

0.05

0.1

0.15
BDT Discriminant0

Figure D.11:
ATLAS Simulation
Work in progress-1
BDT Taggers = 13 TeV, 139 fb , bkg Systematic Uncertainties = 30%
minmass

0.4
0.15

0.35
0.3

0.1

0.25
0.05

0.2
0.15

0

0.1
− 0.05
0.05
− 0.1
− 0.1

−0.05

0

0.05

Figure D.12:

0.1

0.15
BDT Discriminant0Appendix E
Order Stragety
Unlike 2leading and minmass selection strategies, order strategy selects tagging jet and signal jet pairs by the magnitude of Energy Flow tagger output.
In the ﬁrst step, choose the largest four Energy Flow output jets. And then,select the largest invariant mass jet pair as a tagging jet pair, and the remaining two jets are chosen as a signal pair. After picking up the tagging
and signal jet pairs, the preselection is performed as Table 5.5.
To obtain the best signiﬁcance, A threshold of the Energy Flow and BDT
discriminant outputs is investigated, same as neural 2leading and neural minmass strategies. The systematic uncertainty is determined with 10%, 20%
and 30% to study the diﬀerent situations.
The signiﬁcance is shown in Table E.1 and the two dimensional plot of Energy Flow and BDT discriminant output is displayed in Figure E.1, E.2 andE.3 with 10%, 20% and 30% systematic uncertainty. Compared to the signiﬁcance baseline in Section 5.3.2, it is found that the neural order selection
strategy discussed in this Appendix performs worse than the 2leading with
only the BDT discriminant strategy. This indicates that using q/g tagger
output to select tagging and signal jet pairs is still not a suitable method
and shows the worse eﬃciency compared to 2leading and minmass selection
strategies.

94

APPENDIX E. ORDER STRAGETY

95

Table E.1: A summary of the order strategy signiﬁcance.
Selection Stratgy Bkg Systematic Signal W+jettt̄
SigniﬁcanceUncertainty
10%59
68±16 208±51
0.754
order
20%
59
68±16 208±51
0.529
30%
24
8±6
59±24
0.363

Energy Flow Tagger

ATLAS Simulation Work in progresss = 13 TeV, 139 fb-1, bkg Systematic Uncertainties = 10%
order

0.7

0.9
0.8

0.6

0.7
0.5
0.6
0.5

0.4

0.4

0.3

0.3
0.2
0.2
0.1

0.1
0
− 0.1

−0.05

0

0.05

Figure E.1:

0.1

0.15
BDT Discriminant

0APPENDIX E. ORDER STRAGETY

96

Energy Flow Tagger

ATLAS Simulation Work in progresss = 13 TeV, 139 fb-1, bkg Systematic Uncertainties = 20%
order

0.5

0.9
0.8

0.4

0.7
0.6

0.3
0.5
0.4

0.2

0.3
0.2

0.1

0.1
0
− 0.1

−0.05

0

0.05

0.1

0.15
BDT Discriminant0

Figure E.2:

Energy Flow Tagger

ATLAS Simulation Work in progresss = 13 TeV, 139 fb-1, bkg Systematic Uncertainties = 30%
order

0.35

0.9

0.3

0.8
0.7

0.25

0.6
0.2

0.5

0.15

0.4
0.3

0.1

0.2
0.05

0.1
0
− 0.1

−0.05

0

0.05

Figure E.3:

0.1

0.15
BDT Discriminant0Bibliography[1] J. Zuntz et al. Dark Energy Survey Year 1 Results: Weak Lensing ShapeCatalogues. In:Mon.Not.Roy Astron.Soc.481.1, pages 1149–1182, 2018.
DOI : 10.1093/mnras/sty2219. arXiv: 1708.01533[astro − ph.CO].
[2] F. Zwicky. Die Rotverschiebung von extragalaktischen Nebeln.
In:Helvetica Physica Acta 6, pages 110–127, 1933.
arXiv: 1711.01693[astro − ph.IM].
[3] M. Aaboud et al. Measurement of the Higgs
boson mass in the√∗
H→ZZ →4l and H→ γγ channels with s=13 Tev pp collisions
using the ATLAS detector. Physics Letters B, 784:345–366, 2018.
DOI : 10.1016/j.physletb.2018.07.050. arXiv: 1806.00242[hep − ex].
[4] R. D. Peccei and Helen R. Quinn. CP Conservation in the Presenceof Pseudoparticles. In: Phys. Rev. Lett. 38, pages 1440–1443, 1977.
DOI : 10.1103/PhysRevLett.38.1440.
[5] ATLAS Collaboration. The ATLAS Experiment at the CERN Large
Hadron Collider. Jinst, 3:S08003, 2008.
DOI : 10.1088/1748 − 0221/3/08/S08003.
[6] CMS Collaboration. The CMS experiment at the CERN LHC. Jinst,
803:S08004, 2008. DOI : 10.1088/1748 − 0221/3/08/S08004.
[7] Michele Gallinaro et al. Beyond the Standard Model in vector boson
scattering signatures. 2020. arXiv: 2005.09889[hep − ph].
[8] Shu Li. Latest VBS measurements in ATLAS. 2020.
URL : https : //cds.cern.ch/record/2710588/.
[9] Nadezda Chernyavskaya. Latest results on VBF and VBS processes from
CMS experiment. LHCP2018, 321, 2018. DOI : 10.22323/1.321.0291.

97

BIBLIOGRAPHY

98[10] A Dedes et al. SM EFT eﬀects in Vector-Boson Scattering at the LHC.
Phys. Rev. D, 104(1):013003, 2021.
DOI : 10.1103/PhysRevD.104.013003. arXiv: 2011.07367[hep − ph].
[11] M. Tanabashi et al. Review of Particle Physics, volume 98. 2018.
DOI : 10.1103/PhysRevD.98.030001.
[12] Tatsumi Nitta. Search for the weak vector√ boson scattering in semileptonic ﬁnal states in pp collisions at s = 13 Tev with the ATLAS
detector. 2020. URL : https : //cds.cern.ch/record/2754187/.
[13] Matteo Cacciari and Gavin P. Salam. The anti-kt jet clustering algorithm. JHEP 08, 2008(04):063, 2008.
DOI : 10.1088/1126 − 6708/2008/04/063. arXiv: 0802.1189[hep − ph].
[14] Steven Schramm. ATLAS Jet Reconstruction, Calibration, and Tagging of Lorentz-boosted Objects. Physical Review D, 182:02113, 2018.
URL : https : //cds.cern.ch/record/2291608.
[15] ATLAS Collaboration. Pile-up subtraction and suppressio for jet in
ATLAS. 2013. URL : http : //cds.cern.ch/record/1570994.
[16] G.Parisi G.Altarelli. Asymptotic freedom in parton language. Nuclear
Physics B, 126(2):298–318, 1977.
DOI : 10.1016/0550 − 3213(77)90384 − 4.
[17] KG Tomiwa. Performance of Jet Vertex Tagger in suppression of pileup
in ATLAS detector. J. Phys.: Conf. Ser., 802(1):012012,
jets and EmissT
2017. DOI : 10.1088/1742 − 6596/802/1/012012.
[18] A. Hoecker et al. TMVA - Toolkit for Multivariate Data Analysis. 2007.
DOI : 10.1063/1.4771869. arXiv: physics/0703039[physics.data − an].
[19] M. Aaboud et al. Jet energy scale measurements √and their systematic uncertainties in proton-proton collisions at s = 13 TeV
with the ATLAS detector.
Phys. Rev. D, 96(7):072002, 2017.
DOI : 10.1103/PhysRevD.96.072002. arXiv: 1703.09665[hep − ex].
[20] B. Abbott et al. Production and integration of the ATLAS Insertable
B-Layer. Journal of Instrumentation, 13(05):T05008, 2018.
DOI : 10.1088/1748 − 0221/13/05/t05008.
arXiv: 1803.00844[physics.ins − det].

BIBLIOGRAPHY

99[21] R.J. Apsimon et al. Application of advanced thermal management technologies to the ATLAS SCT barrel module baseboards. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 565(2):561–571, 2006.
DOI : 10.1016/j.nima.2006.06.058.
[22] Christian Lippmann. Particle identiﬁcation. Nucl. Instrum. Methods
Phys. Res., A, 666:148–172, 2012. DOI : 10.1016/j.nima.2011.03.009.
arXiv: 1101.3276[hep − ex].
[23] NA Thacker and A Lacey. Tutorial: The Kalman Filter. Imaging Science and Biomedical Engineering Division, Medical School, Universityof Manchester, page 61, 1998.
URL : http : //citeseerx.ist.psu.edu/viewdoc/download?doi = 10.1.1.408.5594&rep = rep1&type = pdf.
[24] Atlas Collaboration. Performance of the ATLAS Inner Detector Trackand Vertex Reconstruction in the High Pile-Up LHC Environment. 2012.
URL : https : //cds.cern.ch/record/1435196.
[25] G Piacquadio, K Prokoﬁev, and A Wildauer. Primary vertex reconstruction in the ATLAS experiment at LHC. J. Phys.: Conf. Ser.,
119(3):032033, 2008. DOI : 10.1088/1742 − 6596/119/3/032033.
[26] ATLAS collaboration.
Early Inner Detector Tracking Performance in√the 2015 data at s = 13 TeV. 2015.
URL : https : //cds.cern.ch/record/2110140.
[27] Atlas Collaboration. Jet energy√measurement with the ATLAS detector
in proton-proton collisions at s = 7 TeV. Eur. Phys. J. C, 73(2304),
2013. DOI : 10.1140/epjc/s10052 − 013 − 2304 − 2
arXiv: 1112.6426[hep − ex].
[28] Peter Skands Torbjorn Sjostrand, Stephen Mrenna. PYTHIA 6.4
Physics and Manual. JHEP, 2006(05):026, 2006.
DOI : 10.1088/1126 − 6708/2006/05/026. arXiv: hep − ph/0603175.
[29] Richard D. Ball et al. Parton distributions for the LHC Run II. JHEP,
2015(4):1–148, 2015. DOI : 10.1007/JHEP04(2015)040.
arXiv: 1410.8849[hep − ph].
[30] Atlas Collaboration. ATLAS Pythia 8 tunes to 7 TeV data. 2014.
URL : https : //cds.cern.ch/record/1966419?ln = ja.

BIBLIOGRAPHY

100[31] Rene Brun and Fons Rademakers. ROOT - An Object Oriented Data
Analysis Framework. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and AssociatedEquipment, 389(1-2):81–86, 1997.
DOI : 10.1016/S0168 − 9002(97)00048 − X.
[32] Xavier Glorot, Antoine Bordes, and Yoshua Bengio. Deep Sparse Rectiﬁer Neural Networks. Proceedings of the fourteenth international
conference on artiﬁcial intelligence and statistics, 15:315–323, 2011.
URL : https : //proceedings.mlr.press/v15/glorot11a.html.
[33] Y. Bengio I. Goodfellow and A. Courville.
URL : https : //www.deeplearningbook.org.

DeepLearning.

2016.

[34] ATLAS Collaboration. Quark versus Gluon Jet Tagging Using Jet Images with the ATLAS Detector. 2017.
URL : https : //cds.cern.ch/record/2275641.
[35] Manzil Zaheer et al. Deep Sets. 2017. arXiv: 1703.06114[cs.LG].
[36] Martı́n Abadi et al. Tensorﬂow: Large-scale machine learning on heterogeneous distributed systems. 2016. arXiv: 1603.04467[cs.DC].
[37] J. Bellm et al. Herwig 7.0/Herwig++ 3.0 release note. Eur. Phys. J. C,
76(4):1–8, 2016. DOI : 10.1140/epjc/s10052 − 016 − 4018 − 8.
arXiv: 1512.01178[hep − ph].
[38] Stefan Gieseke Simon Platzer. Dipole Showers and Automated NLO
Matching in Herwig++. Eur. Phys. J. C, 72(11):1–19, 2012.
DOI : 10.1140/epjc/s10052 − 012 − 2187 − 7.
arXiv: 1109.6256[hep − ph].
[39] Tim Stelzer Fabio Maltoni. MadEvent: Automatic event generation
with MadGraph. JHEP, 2003(02):027, 2003.
DOI : 10.1088/1126 − 6708/2003/02/027. arXiv hep − ph/0208156.
[40] David J. Lange. The EvtGen particle decay simulation package. Nuclear
Instruments and Methods in Physics Research Section A: Accelerators,
Spectrometers, Detectors and Associated Equipment, 462(1-2):152–155,
2001. DOI : 10.1016/S0168 − 9002(01)00089 − 4.
[41] Richard D. Ball et al. Parton distributions with LHC data. Nuclear
Physics B, 867(2):244–289, 2013.
DOI : 10.1016/j.nuclphysb.2012.10.003. arXiv: 1207.1303[hep − ph].

BIBLIOGRAPHY

101[42] T Gleisberg et al. Event generation with SHERPA 1.1. JHEP,
2009(02):007, 2009.
DOI : 10.1088/1126 − 6708/2009/02/007. arXiv: 0811.4622[hep − ph].
[43] Stefano Frixione, Giovanni Ridolﬁ, and Paolo Nason. A Positive-Weight
Next-to-Leading-Order Monte Carlo for Heavy Flavour Hadroproduction. JHEP, 2007(09):126, 2007.
DOI : 10.1088/1126 − 6708/2007/09/126. arXiv: 0707.3088[hep − ph].
[44] Zachary Marshall et al. Simulation of Pile-up in the ATLAS Experiment.
J. Phys.: Conf. Ser., 513(2):022024, 2014.
DOI : 10.1088/1742 − 6596/513/2/022024.
[45] Atlas Collaboration. Electron reconstruction and identiﬁcation in the
ATLAS experimentusing the 2015 and 2016 LHC proton–proton colli√sion data at s = 13 tev. Eur. Phys. J. C, 79(639), 2019.
DOI : 10.1140/epjc/s10052 − 019 − 7140 − 6
arXiv: 1902.04655[physics.ins − det].
[46] Atlas Collaboration. Electron and photon energy calibration with the
ATLAS detector using the 2015-2016 LHC proton-proton collision data.
JINST, 14(P03017), 2019.
DOI : 10.1088/1748 − 0221/14/03/P03017
arXiv: 1812.03848[hep − ex].
[47] Kaustubh Agashe and Roberto Contino. The minimal composite
Higgs model and electroweak precision tests. Nuclear physics B,
742(1-3):59–85, 2006. DOI : 10.1016/j.nuclphysb.2006.02.011. arXiv:
hep − ph/0510164.