Search for dark sector promptly
decaying neutral particles in 140 fb−1√
proton-proton collisions at s = 13 TeV
with the ATLAS detector

Tingyu Zhang//2024

CERN-THESIS-2024-131

Department of Physics
The University of Tokyo

This dissertation is submitted for the degree ofDoctor of Philosophy

August 2024

Acknowledgements

I would like to express my deepest gratitude to my supervisor, Prof. Junichi Tanaka, for his
unwavering support and insightful guidance throughout my doctoral studies. His profoundexpertise, thoughtful advice, and rigorous approach to research have been invaluable to thesuccessful completion of this thesis.
I am also deeply grateful to the members of the thesis defense committee, Prof. Yutaka
Ushiroda, Prof. Masashi Yokoyama, Prof. Masahiro Ibe, Prof. Taku Gunji, and Prof. Kentaro
Yako, for their constructive feedback and diverse perspectives, which greatly enhanced thequality of this work.
Special thanks go to the faculties, colleagues, and friends at ICEPP, the University ofTokyo, for their collaboration and discussions that enriched my research experience. I
am particularly thankful to Prof. Yuji Enari for his guidance on my work with the LAr
calorimeter and physics analysis, as well as for introducing me to CERN and the delightful
local restaurants. I am also grateful to Prof. Shion Chen, Prof. Yasuyuki Okumura, Prof.
Masaya Ishino, Prof. Tatsuya Masubuchi, Prof. Takuya Nobe, and all the staff members fortheir constructive suggestions during meetings that helped me overcome many challenges
in my work. My heartfelt thanks also go to Dr. Yi-Lin Yang, Dr. Reiyo Oishi, and Dr. Gen
Tateno from Tanaka-lab for their assistance with my qualification work in LAr. Additionally,
I am grateful to my friends and colleagues in Building 188 for their support in work and life,and for the good times we shared. In particular, I would like to thank Jiaqi Zang and Marin
Furukawa for their companionship and the memorable moments we shared at CERN.
I am thankful to my analysis contacts in ATLAS, Dr. Cristiano Sebastiani, Dr. Iacopo
Longarini, and Prof. Joseph Izen, for their expertise, coordination, and support in my physics
analysis work. I also appreciate Dr. Elena Pompa Pacchi for showing me around Romeduring conferences and my team members, Dr. Luis Pascual Dominguez and Bernardo Ricci,
for their excellent collaboration in preparing our analysis for publication.
I extend my heartfelt thanks to all the friends I made during my time at CERN. The
group of Dr. Zhelun Li, Dr. Miaoran Lu, Dr. Tianyu Yang, and Dr. Yousen Zhang mademy two years at CERN among the most memorable experiences of my life. I cherish our
discussions on work, life, love, and other abstract topics. Additionally, I would like to thankiv
Mengyang Li, Wenhao Ma, and Yanxi Gu for kindly driving us around Geneva, and Luxin
Zhang, Pingxin Zhang, and Danning Liu for the wonderful gatherings. A special appreciation
goes to Zihan Zhao for the enjoyable badminton matches and intellectual challenges and forshowing me around the USTC campus.
Finally, I am profoundly grateful to my parents for their love, patience, and understanding.

Abstract

Several new physics models predict the existence of dark neutral particles, or dark photons,
which decay promptly to collimated pairs of leptons, referred to as lepton jets. In thedark sector model, both couplings between Higgs and dark Higgs via the Higgs portal andcouplings between photon and dark photons via the vector portal are favored to be probed in
the LHC-ATLAS experiment.
In this thesis, we present a search for low-mass dark neutral particles, γd , in the range
between 17 MeV and 0.24 GeV using 140 fb−1 of data collected from 2015 to 2018 during√
the LHC Run-2 pp collisions at s = 13 TeV. By exploring the electron final states using
channels of H → (γd → e+ e− )(γd → e+ e− ) + X in the Falkowski-Ruderman-VolanskyZupan (FRVZ) model and H → (γd → e+ e− )(γd → e+ e− ) in the Hidden Abelian Higgs
Model (HAHM), we extend the search limits for γd mass from the previous 0.25 GeV to 17
MeV.
No excess is observed, and we set an exclusion limit of 0.7% BR(H → 2γd + X) for the
FRVZ model and 0.07% BR(H → 2γd ) for the HAHM model at mγd = 17 MeV. Comparedto other experiments, this analysis extends the search limits for both the Higgs and vector
portals.

Table of contents
1

Introduction

1

2 The Standard Model and Beyond
2.1 Particles in the Standard Model . . . . . . . . . . . . . . . . . . . . . . .
2.2 Quantum Electrodynamics . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3 Quantum Chromodynamics . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4 Quantum Electroweak Theory . . . . . . . . . . . . . . . . . . . . . . . .
2.5 Higgs Mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.6 Physics Beyond the Standard Model . . . . . . . . . . . . . . . . . . . . .

3
3
4
6
7
9
11

3

Dark Matter Search at the LHC
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Dark Sector Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.1 Vector Portal . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.2 Higgs Portal . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.3 Benchmark Models . . . . . . . . . . . . . . . . . . . . . . . . . .

15
15
19
19
21
23

4 The ATLAS experiment at LHC
4.1 Accelerator and the LHC . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.1 pp collisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.2 Data-taking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.3 Luminosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.4 Bunch-crossing and Pile-up . . . . . . . . . . . . . . . . . . . . .
4.2 The ATLAS detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.2 Coordinate system . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.3 The magnet system . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.4 Inner Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . .

27
27
28
29
29
31
32
32
32
33
34

viii

Table of contents
4.2.5 Calorimeter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.6 Muon Spectrometer . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.7 Trigger and Data Acquisition . . . . . . . . . . . . . . . . . . . . .
4.2.8 Event Simulations . . . . . . . . . . . . . . . . . . . . . . . . . .
Reconstruction of Physics Objects . . . . . . . . . . . . . . . . . . . . . .
4.3.1 Tracks and Primary Vertex . . . . . . . . . . . . . . . . . . . . . .
4.3.2 Electrons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.3 Muons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.4 Jets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.5 Overlap Removal . . . . . . . . . . . . . . . . . . . . . . . . . . .

35
36
38
40
42
42
43
48
50
53

5

Prompt Dark Photon Signatures
5.1 Data and Simulated Events . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2 Dark Photon Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3 Physics Objects in Prompt Lepton Jets . . . . . . . . . . . . . . . . . . . .
5.3.1 Close-by Isolation Corrections . . . . . . . . . . . . . . . . . . . .
5.3.2 Merged EM clusters . . . . . . . . . . . . . . . . . . . . . . . . .
5.4 Prompt Lepton Jets Reconstruction . . . . . . . . . . . . . . . . . . . . . .
5.4.1 eLJ Reconstruction Efficiency . . . . . . . . . . . . . . . . . . . .
5.5 Triggers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.5.1 Trigger Choice . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.5.2 Trigger Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . .
5.5.3 Trigger-matching . . . . . . . . . . . . . . . . . . . . . . . . . . .

55
55
58
61
61
63
65
67
67
68
68
73

6

Event Selection
6.1 Signal Region Definition . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2 Expected Signal yields and Background processes . . . . . . . . . . . . . .
6.3 Checks of Selection Variables . . . . . . . . . . . . . . . . . . . . . . . .

75
75
79
81

7

Background estimation
7.1 ABCD Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.2 Selection of Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.3 Validation of the Background Estimation Method . . . . . . . . . . . . . .

85
85
86
91

8

Systematic Uncertainties
8.1 Experimental Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . .
8.1.1 Standard Objects . . . . . . . . . . . . . . . . . . . . . . . . . . .

99
99
99

4.3

Table of contents
8.1.2 Triggers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.1.3 Luminosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.1.4 Pile-up Reweighting . . . . . . . . . . . . . . . . . . . . . . . . .
8.1.5 eγ energy scale and resolution . . . . . . . . . . . . . . . . . . . .
8.1.6 Jet Energy Scale and Jet Energy Resolution . . . . . . . . . . . . .
8.1.7 MC Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Theoretical Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . .
Non-closure Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . .

100
100
100
100
100
100
101
102

Results and Discussions
9.1 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.2 Likelihood fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.3 Exclusion Limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.3.1 Impact of signal contamination . . . . . . . . . . . . . . . . . . . .
9.3.2 Limits from Muon and Mixed Channel . . . . . . . . . . . . . . .
9.3.3 Higgs portal interpretation . . . . . . . . . . . . . . . . . . . . . .
9.3.4 Vector portal interpretation . . . . . . . . . . . . . . . . . . . . . .
9.4 Future developments . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

109
109
109
112
112
112
112
117
118

8.2
8.3
9

ix

10 Conclusion

121

References

123Chapter 1
Introduction
The Standard Model (SM) forms the basis of modern particle physics, having achieved
remarkable success in experimental verifications and predictions. However, the limitations
within the SM necessitate the exploration of theories beyond the Standard Model (BSM).
One promising path for BSM research is the study of dark matter.
Traditional approaches to dark matter research have focused on searches for dark mattercandidates in models such as Weakly Interacting Massive Particles (WIMPs). Alternatively,
dark matter can be explored model-independently through dark sector portals, representing
groups of theoretical interactions and mixings with SM particles, leading to rich phenomenology.
Among these portals, the vector portal has been extensively explored by numerous
experiments [1]. On the other hand, the ATLAS experiment at the Large Hadron Collider(LHC) offers the potential to provide unique insights into the Higgs portal since only LHC
can produce Higgs bosons. This is possible thanks to the invisible decays of Higgs bosons,with an upper limit on the branching ratio of 11% [2]. One of the striking signatures is the
scenario where dark photons (γd )s promptly decay into collimated pairs of leptons (ℓ = e, µ),often referred to as lepton jets (LJs).
Previous Higgs portal searches at the LHC have set exclusion limits for dark photons
with masses greater than 250 MeV [3] [4] [5], focusing primarily on the muon final states.
To expand to the lower undiscovered mass region, which is physics-motivated, we hereby
present an analysis that explores the electron final states, referred to as electron lepton jets
(eLJs). Through studies of the subdetector responses, we have introduced an innovative
definition of eLJs: merged clusters with separately reconstructed tracks, thereby reducing
the overwhelming background. In this thesis, we will search for eLJ signatures in thechannel H → (γd → e+ e− )(γd → e+ e− ) or H → (γd → e+ e− )(γd → e+ e− ) + X, where Xs

2Introduction

are undetectable particles, using the 140 fb−1 full Run-2 pp collision data taken between
2015-2018 in the ATLAS experiment at the LHC.
The flow of the thesis is as follows. Chapter 2 overviews the SM and motivations for
BSM theories, which drive our search for low-mass dark photons using eLJs. Chapter 3
reviews previous dark matter searches and the theoretical basis of dark sector models,
focusing on the portals used in the benchmark models exploited in this thesis, and discusses
the event signatures and topologies for the H → (γd → e+ e− )(γd → e+ e− )(+X) searchchannel. Chapter 4 describes the experimental setup for LHC and the ATLAS experiment,
and discusses the standard reconstruction and identification of standard physics objects
in ATLAS. Chapter 5 introduces the unique signatures and customizations to detect dark
photons, including the simulation of events, kinematic distributions, eLJ object definitions,and trigger strategies. Chapter 6 presents the event selections for dark photons with suchsignatures. Chapter 7 details the data-driven background estimation method. Chapter 8
evaluates the systematic uncertainties arising in this analysis. Chapter 9 shows the results
and discusses the interpretations. Then, Chapter 10 gives a conclusion.

Chapter 2
The Standard Model and Beyond
As the single theory that certainly represents one of the significant achievements of physicalscience, the Standard Model provides a comprehensive framework for understanding thefundamental interactions of elementary particles. Proposed by Glashow [6], Salam [7], andWeinberg [8] in the 1960s, the theory has made successful predictions and been extensively
tested during the last 50 years. The experimental discovery of the scalar field Higgs Boson
by ATLAS [9] and [10] CMS experiments at the Large Hadron Collider (LHC) in 2012
completed the last missing piece to the full empirical confirmation of the theory. This chapter
introduces the theoretical basis of the Standard Model and the motivations for studies of
Beyond Standard Model (BSM) theories.

2.1

Particles in the Standard Model

The SM describes three of the four fundamental forces: the electromagnetic interaction,
the weak interaction, and the strong interaction, except for the gravitational interaction.
Formulated in the relativistic Quantum Field Theory (QFT) framework, each particle isrepresented by a field, and the Lagrangian defines its dynamic. The fundamental natureof particles and interactions comes from symmetry principles, where the gauge invariant
governs the SM [11] under the SU(3)C × SU(2)L × U(1)Y gauge symmetry. The SU(3)C
non-abelian group is related with strong interaction, and the SU(2)L × SU(1)Y is associatedwith the electroweak interaction.
Based on their spin nature, particles can be categorized into two basic types: fermions
with an integer spin, which follow Bose-Einstein statistics, and bosons with a half-integer
spin, which follow Fermi-Dirac statistics.

4

The Standard Model and Beyond

Fermions, including leptons and quarks, have a spin value of 1/2 and are the building
blocks of matter. Up until now, 12 flavors of elementary fermions have been found. They are
sub-categorized into three generations:• first generation: electron (e− ), electron neutrino (νe ), up (u), and down (d) quarks,• second generation: muon (µ − ), muon neutrino (νµ ), charm (c) and strange (s) quarks,
and• third generation: tau (τ − ), tau neutrino (ντ ), top (t), and bottom (b) quarks.
Each generation is a heavier copy of the previous one, with similar charge and spin
properties. Fermions that do not undergo strong interactions are known as leptons, which
are e− , νe , µ − , νµ , τ − and ντ . On the other hand, fermions that undergo both strong andelectroweak interactions are known as quarks, which are u, d, c, s, t, and b. With the strong
interaction color charge, quarks can only be detected in the color-free composite form called
hadrons.
Gauge bosons, with spin value 1, including γ, W , Z bosons, and gluons, are the forcecarrying particles that mediate interactions between fermions. Gluons mediate the strong
interaction, and there are eight in total, corresponding to the number of generators in theSU(3)C gauge symmetry. The electroweak bosons W + , W − and Z 0 mediate the weakinteraction. W + and W − bosons couple only the left-handed (doublets under SU(2)L ) partsof fermions via the weak isospin, while Z 0 boson couples to both left-handed and righthanded (singlet under SU(2)L ) part of fermions via both isospin and hypercharge. The photon
γ is massless and mediates the electromagnetic field.
The Higgs boson is a scalar particle (spin value 0) associated with the Higgs field, which
gives mass to all particles. Through the process of spontaneous symmetry breaking [12]of the SU(2)L ×U(1)Y to U(1)EM gauge symmetry, W and Z bosons acquire mass while γ
remain massless, leading to weak interaction mediated to be short-range, and electromagnetic
interaction to be long-range.
A summary of elementary particles in the SM is shown in Fig. 2.1.

2.2

Quantum Electrodynamics

Quantum electrodynamics (QED) [14] is the relativistic quantum field theory that describes
the phenomena of charged particles interacting in exchange of photons. We can derive thegeneral Lagrangian form of QED by the gauge invariance: we start from the Lagrangian of

5

2.2 Quantum Electrodynamics

Fig. 2.1 A summary of elementary particles in the SM [13].

free Dirac fermion field ψ(x):L0 = iψ̄(x)γ µ ∂µ ψ(x) − mψ̄(x)ψ(x).

(2.1)

Under the local gauge transformation
U(1)ψ(x) −−−→ ψ ′ (x) ≡ exp {iQθ (x)} ψ(x)U(1)∂µ ψ(x) −−−→ exp{iQθ (x)}(∂µ + iQ∂µ θ (x))ψ(x).

(2.2)
(2.3)

Here, Q is an arbitrary real charge constant, and θ (x) is the gauge phase transformation that
depends on space-time coordinates. For gauge invariance to hold to cancel the extra term in

6

The Standard Model and Beyond

Eq. 2.1, we introduce a new gauge field Aµ (x) and the covariant derivative1
U(1)Aµ (x) −−−→ A′µ (x) ≡ Aµ (x) − ∂µ θ (x),eDµ ψ(x) ≡ ∂µ + ieQAµ (x) ψ(x),

(2.4)
(2.5)

which satisfies the local gauge invariance we need. The Lagrangian then becomes:
L = iψ̄(x)γ µ Dµ ψ(x) − mψ̄(x)ψ(x) = L0 − eQAµ (x)ψ̄(x)γ µ ψ(x).

(2.6)

The vertex of QED is the interaction between Dirac fermion ψ and gauge field Aµ (x).
Consider Aµ (x) to be propagating, and we add the kinetic terms of the electromagnetic field:
1
LKin = − Fµν (x)F µν (x),
4

(2.7)

where Fµν ≡ ∂µ Aν − ∂ν Aµ is the electromagnetic field strength tensor, which is invariant
under gauge transformation of Aµ (x) in Eq. 2.4. It is important to note that a photon ismassless so that a mass term like Lm = 12 m2 Aµ Aµ , which violates the gauge invariant
requirement is not necessary. The complete Lagrangian form of propagating the QED field is
as follows:
1
LQED = ψ̄(x)(iγ µ ∂µ − m)ψ(x) − Fµν (x)F µν (x) − eQAµ (x)ψ̄(x)γ µ ψ(x),
4

(2.8)

from which the Maxwell equations can be derived:∂µ F µν = eQψ̄γ ν ψ.

2.3

(2.9)

Quantum Chromodynamics

Quantum Chromodynamics (QCD) is the theory that describes the strong interaction ofquarks, which is based on SU(3)C color symmetry.
In QCD, the color states of quark fields ψC are SU(3)C triplets, where C corresponds tored, green, and blue spinor elements. The free and classical QCD Lagrangian is constructed
as follows:
L0 = iψ̄(x)γ µ ∂µ ψ(x) − mψ̄(x)ψ(x),(2.10)

2.4 Quantum Electroweak Theory

7

which is gauge symmetric globally. If we extend the gauge symmetry to local symmetry
again:
SU(3)ψ(x) −−−→ ψ ′ (x) ≡ exp {iθa (x)ta } ψ(x),Dµ ψ(x) ≡ ∂µ − ig0ta Aµ (x) ψ(x).

(2.11)(2.12)

Here the quark field ψ(x) couples to the gluon field Aµ (x) with a coupling strength g0 . ta is
the infinitesimal SU(3) generator given by Ta = λa /2 where λa are the Gell-Mann matrices
where [ta ,tb ] = i fabctc . We can define the QCD field tensor:
Gaµν ≡ ∂µ Aaν − ∂ν Aaµ + g0 fabc Abµ Acν .

(2.13)

Unlike the QED tensor, the last term in Gµ νa implies that gluons are color-charged andinteract with each other. Including also the kinetic energy term, we reach the complete QCD
Lagrangian:
1
LQCD = ψ̄(x)(iγ µ ∂µ − m)ψ(x) − Gµν (x)Gµν (x) + g0ta Aµ (x)ψ̄(x)γ µ ψ(x).
4(2.14)

One of the phenomena of QCD theory is color confinement, where detecting an isolated
quark from a composite state is impossible. This is due to the coupling strength g0 becoming
very strong at high distances (low energy scales), and at some point, it is more energeticallyfavorable to create a quark-antiquark pair. As a result, when individual quarks are producedin particle accelerators, we always observe clustered "jets" of many color-neutral particles.
Conversely, at high energy scales, the coupling strength g0 becomes asymptoticallyweaker, leading to a phenomenon known as asymptotic freedom. Such free particle statesallow perturbative calculations in the QCD theory.

2.4

Quantum Electroweak Theory

The unification of QED and weak interaction was developed in the 1960s by Sheldon
Glashow [6], Abdus Salam [7], and Steven Weinberg [8] in the electroweak theory. We
choose the SU(2)L ×U(1)Y gauge group for such unification. The gauge fields corresponding
to each generator are
SU(2)L → Wµ1 , Wµ2 , Wµ3 ,U(1)Y → Bµ .

8The Standard Model and Beyond

We can define the strength tensors for the abelian U(1)Y and non-abelian SU(2)L gauge
fields asjiWµν= ∂µ Wνi − ∂ν Wµi + gε i jkWµ Wνk ,Bµν = ∂µ Bν − ∂ν Bµ .
Let us also group the leptons to left-handed weak isospin doublet L (T = 1/2) and righthanded weak isospin singlet R (T = 0) as follows:
L=

!
νL
,
lL

R = lR ,where T3 = +1/2 and T3 = −1/2 are the left-handed part of neutrino and charged lepton of
any flavor (l = e, µ, τ). Since there is no observed right-handed neutrino component, theright-handed part is a weak isospin singlet.
We start from the free Lagrangian
L0 = L̄iγ µ ∂µ L + R̄iγ µ ∂µ R,(2.15)and introduce the covariant derivatives:g′g
L : Dµ ≡ ∂µ + i τ iWµi + i Y Bµ ,22(2.16)

g′
R : Dµ ≡ ∂µ + i Y Bµ ,2(2.17)

where g and g′ are the coupling constants associated with SU(2)L and U(1)Y , respectively, Y
is the hypercharge associated with U(1)Y , and τ i are Pauli matrices.
Therefore, the Lagrangian becomes
LQEW = L0 + LCC + LNC ,(2.18)

where the charged current part LCC and the neutral current part LNC are
 1

τ
τ2 2
1
LCC = −gLγ
W + Wµ L,
2 µ2µ

LNC = −gLγ µτ3 3
g′Wµ L − (Lγ µ Y L + Rγ µ Y R)Bµ .
22(2.19)(2.20)

9

2.5 Higgs Mechanism
First, LCC can be rewritten asg
LCC = − √ [νγ µ (1 − γ 5 )lWµ+ + lγ µ (1 − γ 5 )νWµ− ],2 2(2.21)

where Wµ± are the charged gauge bosons defined as
1Wµ± = √ (Wµ1 ±Wµ2 ).
2(2.22)

This LCC shows the weakly charged current’s (V − A) structure [15].
Next, we look at LNC and observe the structure of the Gell-Mann-Nishijima relation [16][17]. To couple it with the electromagnetic current, we introduce rotation using the Weinberg
angle [15]:
Aµ
Zµ

!
=

cos θW sin θW− sin θW cos θW

!

Bµ
Wµ3

!
(2.23)

wheresin θW = pg′g, cos θW = p,
g2 + g′2
g2 + g′2(2.24)and the Lagrangian becomes
LNC = −g sin θW (lγ µ l)Aµ −gψγ µ (gVi − giA γ 5 )ψZµ ,∑2 cos θW ψ=ν,l(2.25)

where gV and gA are vector and axial-vector coupling constants. We can find the electromagnetic current coupled to photon field Aµ and the electromagnetic chargee = g sin θW = g′ cos θW .

(2.26)

So far, we have introduced four massless gauge fields Wµ± , Zµ , Aµ , and two massless
fermions ν and l. How the gauge bosons acquire mass will be explained in Sec. 2.5.

2.5

Higgs Mechanism

In this section, we will add scalar fields to spontaneously break the symmetry [18] [19] andexplain how mass of Wµ± and Zµ is given through the Higgs mechanism. Firstly, we introduce
the scalar doublet

10

The Standard Model and Beyond

!
φ+
.
φ0

Φ≡

(2.27)The scalar Lagrangian is given by coupling as
LScalar = ∂µ Φ† ∂ µ Φ −V (Φ† Φ),(2.28)

where the potential is given by
V (Φ† Φ) = µ 2 Φ† Φ + λ (Φ† Φ)2 .

(2.29)

Then we choose a constant vacuum expectation value (VEV) at the bottom of Higgs fieldpotential as1⟨Φ⟩0 = √
2

!
0
,
v

(2.30)

pwhere v = −µ 2 /λ . In this way, when SU(2)L ×U(1)Y → U(1)EM symmetry is spontaneously broken, VEV is conserved.
We parameterize the SU(2)L transformation by fluctuations of the Higgs boson H1⟨Φ⟩0 = √
2

!
0
.
v+H

(2.31)

By introducing again the SU(2)L ×U(1)Y covariant derivative as in Eqs. (2.16) and (2.17),
the scalar Lagrangian in Eq. (2.28) can be written as



g i i
g′
LScalar = ∂µ + i τ Wµ + i Y Bµ
2
2

0
v+H
√
2

!2
− µ2

(v + H)2(v + H)4−λ.
2
4(2.32)

Since only the mass contribution at the tree level is considered here, we ignore the Hinteraction terms. With Eqs. (2.22) and (2.23) the Lagrangian becomes v2 
2
1
v2 g2  1 2
LScalar = ∂µ H∂ µ H +(Wµ ) + (Wµ2 )2 +gWµ3 − g′ Bµ + other terms,
2
4
8
2
2
2
2
g v + −µ 1 g v
1= ∂µ H∂ µ H +W W +Zµ Z µ + 0 · Aµ Aµ + other terms.
24 µ
2 4 cos2 θW

11

2.6 Physics Beyond the Standard ModelWe can identify the mass of W ± and Z
mW =

gv
gv
, mZ =.
2
2 cos θW

(2.33)

It is also evident that the photon remains massless.
Using the approximation VEV of Higgs field of 246 GeV [20], the SM predicts theW mass to be ∼ 80 GeV and Z mass to be ∼ 90 GeV, which is consistent with precise
experimental measurements [21].

2.6

Physics Beyond the Standard Model

The Standard Model is a remarkably successful theoretical framework in particle physics. It
offers extensive predictive power and explains a wide range of phenomena. However, it also
has limitations. Growing evidence suggests the need for new physics Beyond the Standard
Model (BSM). Here we list a few phenomena that are not explained well by the SM:• Hierarchy Problem: as one of the most argued problems with the SM, the hierarchy
problem is an essential question of scale. We saw how the Higgs field gives rise to
the W and Z boson’s mass. To reproduce the observed values of mass, one demandsµ ∼ O(100 GeV), which has a large difference to the Planck scale (about 1019 GeV)
corresponding to gravity. Unlike chiral symmetry to fermions that prohibits fermions
from having a direct mass term and gauge symmetry to gauge bosons protecting themass, the µ value for Higgs should be much larger like the Planck scale due to nosymmetry to protect it. Even on the first-order correction
δ µ2 ∼

Λ2
16π 2(2.34)

is divergent in Λ. One has to impose a cancellation between the O(MPlanck ) andO(100 GeV), which is clearly a fine-tuning and comes unnatural.
• Neutrino oscillations: neutrino oscillation is the fact that a neutrino changes lepton
flavor when propagating through space. For neutrino oscillation, the mass eigenstatemust differ from a flavor eigenstate. While in the SM, no right-handed neutrinos cancouple to the Higgs field to obtain mass. From the results of the Super-Kamiokande
experiment in 1998 [22], it is evident that neutrino mass is not zero, thus requiring amodification of the SM.

12

The Standard Model and Beyond• Dark matter and dark energy: in modern cosmology, numerous observations suggest
the presence of an undetected mass and an unknown form of energy. For instance,
gravitational lensing [23], where gravity bends the path of light, reveals the effects ofsubstantial dark matter halos. Additionally, the study of galactic rotation curves andthe dynamics of galaxy clusters points to a significant quantity of invisible mass. It isnecessary to align the observed cosmic microwave background spectrum with the total
matter content and the universe’s critical density, including dark energy. The universe
is estimated to comprise 72.8% dark energy, 22.7% dark matter, and 4.5% ordinary
matter [24].
• Gravity: as two fundamental theories in physics, SM is widely considered incompatible with gravity, as described by General Relativity (GR) [25]. One difficulty informulating a quantum theory of gravity is the emergence of infinite probabilities
that cannot be neutralized through renormalization. Unlike the SM based on local
gauge symmetries, GR is founded on symmetry under arbitrary smooth coordinatetransformations. Additionally, any theory that seeks to unify GR and the SM must be
valid from the electroweak scale (around 100 GeV) to the Planck scale (approximately
1019 GeV). Several efforts have been made to unify GR and the SM, often called a
Theory of Everything (TOE). However, as of now, there is no consensus on any single
candidate.

Although no experimental result has been accepted to contradict the Standard Model atthe 5 σ level definitively, several experiments have yielded results suggesting the presence of
new physics beyond the SM, which would motivate further detailed investigation. Below, we
provide some notable results:• Anomalous magnetic dipole moment: the anomalous magnetic moment, which rises
from the deviation between tree-level Feynman loops to the Dirac prediction of themagnetic moment of the particle, is an intrinsic property that provides a good test of
the SM framework:g−2
α=.
(2.35)
2
The most recent combined results from the BNL and FNAL muon g-2 experiment at
Fermilab show that αµ = 116592059(22) × 10−11 [26]. This value shows a discrepancy when compared to the SM prediction αµ = 116591810(43) × 10−11 [27]. Thissuggests potential evidence for new physics. Theoretical work is ongoing to refine
the SM predictions with calculations based on lattice QCD to further understand thisdiscrepancy.

13

2.6 Physics Beyond the Standard Model• Mass of W boson: as one of the most critical parameters of the SM, the CDF
collaboration reported a precise measurement of the W boson mass in 2022, finding mW = 80433.5 ± 9.4 MeV/c2 [28]. This exceeds the SM prediction of mW =80357 ± 6 MeV/c2 [29] with a significance of 7 σ . However, the most recent result
from the ATLAS experiment shows mW = 80366.5 ± 15.9 MeV/c2 [30], which aligns
with the Standard Model.
• X17 anomaly: the X17 anomaly refers to an unexpected peak observed in data collectedby the ATOMKI team [31] when protons were injected into thin lithium-7 targets,
producing e+ and e− pairs. As shown in Fig. 2.2, the excess was observed at an
opening angle of 140 degrees. This excess can be explained by a new vector gaugeboson with a mass around 17 MeV, inspiring the name "X17" [32]. However, the X17
anomaly has not yet been confirmed by independent experiments and requires further
investigation.
• RD and RD∗ anomalies: a number of experiments involving B meson decays haveshown deviations in the ratio of the branching fraction RD and RD∗ defined as:RD(∗) =

BR(B̄ → D(∗) τ ν̄τ ),BR(B̄ → D(∗) l ν̄l )(2.36)

where l = e or µ. An estimate of the world average by Heavy Flavour Averaging Group(HFAG) [33] shows that RD = 0.356 ± 0.029 and RD∗ = 0.284 ± 0.013, which deviate
from the SM prediction that RD = 0.300 ± 0.008 [34] and RD∗ = 0.252 ± 0.003 [35].
So far, we have discussed various experimental evidence for BSM theories. One ofthe possible explanations is the existence of dark photons associated with Higgs bosons.
Motivated by the X17 anomaly, and with the current dark photon searches at the LHC limited
to mγd > 250 MeV, the work in this thesis aims to extend the dark photons search range to
17 MeV using the H → (γd → e+ e− )(γd → e+ e− )(+X) channel in the ATLAS experiment.
The next chapter will introduce the theoretical framework for dark photons and theirevent topology in the dark sector models.

14

The Standard Model and Beyond

(a)

(b)

Fig. 2.2 (a) Internal pair conversion correlation (IPCC) measured in the 7 Li(p, e+ e− ) reaction
at E p = 1.10 MeV with −0.5 < y < 0.5 (closed circles) and |y| ≥ 0.5 (open circles). Simulation results assuming boson masses of 15.6 MeV (dotted line), 16.6 MeV (full curve), 17.6
MeV (dashed-dotted line), and without boson (dashed line) are overlayed. (b) Determinationof boson mass using χ 2 / f method [31].

Chapter 3
Dark Matter Search at the LHC
With rapid advancements in theoretical frameworks and improvements in experimental
accuracy, we are pushed to the boundary of our current understanding of the universe.
Irrefutable experimental evidence from astrophysics points to the existence of unknown dark
matter and energy as explained in Section 2.6. Along with the pressing need for alternative
BSM theories, it drives us to seek new solutions. One promising pathway is the study of dark
matter to uncover new physics and find connections between particle physics and cosmology.
In this chapter, we explore the mechanisms of dark matter and introduce a unique method
for investigating it using the ATLAS experiment at the LHC. This approach allows us toprobe dark matter in previously unexplored regimes, potentially unlocking insights into new
physics.

3.1

Introduction

Dark matter, as its name suggests, does not interact with ordinary matter and is detectable
only through its gravitational effects. The first question we must address is how dark matter
evolved to reach its current abundance of 22.7% of the universe’s mass-energy content.
Various scenarios explain its formation mechanism.
• Freeze-out: under the assumption that dark matter (χ) was in thermal equilibrium withparticle bath ( f ) in the early universe, χ χ ⇔ f f , the production rate and annihilation
rate were equal. The annihilation rate decreased as the universe cooled down. This
continued until a critical point when the annihilation rate fell below the universe’s
expansion rate. At this point, the number of particles froze out, and their abundance
became fixed. Assuming that annihilations are s-wave dominant, the process can be16

Dark Matter Search at the LHC

(a)

(b)

Fig. 3.1 Dark matter abundance in the (a) freeze-out, and (b) freeze-in processes [36].
described using the approximated Boltzmann transport equation:dYχA2= − 2 (Yχ2 −Yχ,eq
),
dx
x
r
π
g∗ mχ MPl σ0 ,
A=
45

(3.1)

(3.2)

where Yχ is the dark matter yield evolution, and Yχ,eq is the yield at equilibrium state.
mx ≡ Tχ where T is the temperature of universe. g∗ is the effective relativistic degrees
of freedom contributing to the energy density, MPl = 1.22 × 1019 GeV is the Planck
mass and σ0 is the cross-section. A plot of yield Y as a function of x to visualize thefreeze-out process is shown in Fig. 3.1 (a).
• Freeze-in: the alternative mechanism assumes the existence of a weak interaction
between dark matter particles and SM bath particles. Through rare processes, theyield of dark matter accumulated. As the universe expanded, the rate reached a halt
(freeze-in). The plot to visualize the freeze-in process is shown in Fig. 3.1 (b).
The second question is the properties and candidates for dark matter particles. Based on
the information collected on dark matter, from the observational evidence of abundance inthe universe, the dark matter candidate is expected to be stable with a lifetime comparablewith the universe. Additionally, in the freeze-out scenario, the relic density at the initial
thermal equilibrium is given by
m2χ
1
Ωχ ∝
∼ 4,
< σv >gχ

(3.3)

3.1 Introduction

17

where < σ v > is the time-averaged annihilation cross section. It is observed that, by
coincidence, the electroweak scale (around 100 GeV) and coupling give rise to the canonicalvalue of the cross-section < σ v >= 3.0 × 10−26 cm3 s−1 . The fact that electroweak scaleparticles could make good dark matter candidates is the well-known Weakly Interacting
Massive Particle (WIMP) miracle. Thus far, extensive efforts to search for WIMPs havebeen conducted through direct detection, indirect detection, and particle colliders. Fig. 3.2
schematically shows the different detection approaches.

Fig. 3.2 Schematic overview of different dark matter detection approaches [37].
Direct detection methods aim to observe the effects of dark matter directly interacting withordinary matter. Typically, detectors are shielded deep underground for minimal interference
from cosmic rays and other background radiation. When dark matter wind travels fromsources like a halo in the Milky Way and collides with a nucleus in the detector, it might
impart energy to cause detectable recoils: vibrations detected as rising temperature, excitation,or ionization of recoiled atoms. Fig. 3.3 summarizes the spin-independent WIMP scattering
limits and the signals of various models. We also see a neutrino floor where neutrinos produce
an irreducible background, limiting the discovery potential of detectors.
Indirect detection focuses on the byproducts of WIMP annihilation or decay rather thanthe WIMPs themselves. Experiments like the IceCube [39] and the SuperKamiokande [40]collaborations look for excess neutrino fluxes. Fig. 3.4 shows the WIMP spin-dependent
cross-section upper limit from different experiments.

18

Dark Matter Search at the LHC

Fig. 3.3 WIMP nucleon spin-independent cross-section experimental bounds [38].
A final strategy to search for dark matter is in the products of high-energy particle
colliders like the LHC, providing a completely different approach with much suppressedcosmic backgrounds. The dark matter particles would be undetectable in detectors unlessthey are produced in association with SM particles. Traditionally, ATLAS [42] and CMS[43] experiments in the LHC exploit the so-called mono-X signature where only one jet or
vector boson is detected accompanied by sizeable missing energy in the detector. Fig. 3.5
shows the constraints set by the latest ATLAS mono-X search compared to direct detection
experiments.
Extensive efforts were made to look for WIMP. Unfortunately, no evidence of new physics
has been found yet. The increasingly stringent limits and trickier models motivate us tolook for dark matter models outside the WIMP paradigm. LHC has been pushing the limitof high energy physics on the energy frontier, making TeV scale new physics more andmore accessible. On the luminosity frontier, increasingly more data has also been collected.
However, we are still left with another possibility: searching for dark matter at the currently
reachable scale but from a different approach. One of the most promising methods is using
dark sector models. Instead of model-specific dark matter particles, we are shifted to searchfor signatures of hidden portals linking dark matter and SM.

3.2 Dark Sector Models

19

Fig. 3.4 90% upper limits (solid lines) and expected sensitivity (dotted lines) in the spindependent cross section as a function of WIMP mass. Figure from [41].

3.2

Dark Sector Models

Unlike the WIMP paradigm, dark sector models assume interactions between the dark andvisible sectors through the so-called portals, making dark matter particles experimentally
detectable. Several well-motivated portals with specific couplings exist, including thevector (spin-1) portal, the neutrino (spin-1/2) portal, the Higgs (scalar) portal, and the axion(pseudo-scalar) portal. Dark sector models shift the focus from the specifics of dark mattercomposition to the mediator itself, leading to a new model-independent manner and providing
rich phenomenology as channels to probe new physics with improved sensitivity.
In the simplest form of such models, a dark vector boson, which we can denote as γdand call a dark photon, is required to mediate by describing with the U(1)d gauge group.
In addition, the latest results [2] show that the SM Higgs branching fraction to unknown
final states is constrained to be less than 11%, offering unique insights into the Higgs portal
through the exotic decay mode of Higgs bosons. As a result, the ATLAS experiment at LHC
is motivated and favored to probe both the vector portal and the Higgs portal.

3.2.1

Vector Portal

In the presence of Abelian gauge symmetry U(1)d , the mixing with SM hypercharge U(1)Y
is described by [44]
1
1 ε
1
1
L = − Bµν Bµν − A′µν A′µν +A′µν Bµν + m2A′ ,0 A′µ A′µ ,442 cos θw
2

(3.4)

20

Dark Matter Search at the LHC

(a)

(b)

Fig. 3.5 A comparison of the limit inferred from the ATLAS mono-X result (black line) withthe constraints from direct-detection experiments on the spin-dependent (a) WIMP–proton
scattering and (b) WIMP–neutron scattering cross sections as a function of the WIMP
mass [42].
where Bµν and A′µν are the field strength tensors for SM photon γ and dark photon γd ,respectively. θw is the Weinberg mixing angle. The mixing term associated with the kinetic
mixing parameter ε allows coupling between γd and γ, which can be arbitrarily small. To
avoid interactions at the infinite range, we assume γd to acquire mass through spontaneouselectroweak symmetry breaking (see Sec. 2.5), which originates a lifetime for γd . In suchcase, the decay width of γd decaying into pair of charged leptons is given by [45]4m24Γγd →ll¯ = ε 2 αmγd 1 − 2l
3
mγd

!1/2

2m2
1 + 2l
mγd

!
.

(3.5)

When mγd > 2mπ , hadronic decay is also possible, with a resulting decay width of4
Γγd →hadrons = ε 2 αmγd
3

s

4m2µ
1− 2
mγd

2m2µ
1+ 2
mγd

!
R(s = m2γd ),

(3.6)

where
σe+ e− →hadrons.
(3.7)
σe+ e− →µ + µ −√Here R is evaluated at the center-of-mass energy s = mγd . The branching ratios of γd aresummarized in Fig. 3.6 for different masses. The resulting mean proper decay length of γdR=

21

3.2 Dark Sector Models

Fig. 3.6 Branching ratio of γd at different mass. For mγd < 2mµ ∼ 210 MeV, γd decays toelectrons only. For mγd > 2mµ ∼ 210 MeV, as a consequence of lepton universality, electrons
and muons have the same branching ratio. For mγd > 2mπ ∼ 279 MeV, hadronic decays
start to enter. The mass resonances correspond to mρ ∼ 776 MeV, mω ∼ 782 MeV andmφ ∼ 1019 MeV [46].
can be expressed as functions of ε and mγd by the approximation relation [45]cτγd [mm] ≈ 0.1(

100
10−4 2) ().
ε
mγd [MeV](3.8)

A summary of latest bounds on the ε and mγd is shown in Fig. 3.7. We can see an
undiscovered region around ε ≲ 10−3 and mγd between the 10 ∼ 100 MeV range where
the electron decay is dominated. The target of the search in this thesis is to explore thisuncovered region.

3.2.2

Higgs Portal

In analogy with the mechanism of the SM Higgs, γd could acquire mass from Higgs-likeboson Hd with non-zero vacuum expectation value. Consider a dark Higgs field S and SM
Higgs field φ , the coupling of such a dark Higgs boson to the visible sector can be described
by
LH,Hd (φ , S) = −µ 2 |φ |2 + λ |φ |2 − µs |S|2 + λs |S|4 + κ|φ |2 |S|2 ,
(3.9)

22

Dark Matter Search at the LHC

Fig. 3.7 Excluded regions in the ε, mγd plane by bump hunt experiments (red), muon magnetic
momentum measurements (green), e+ e− colliders (blue), meson decays (yellow) and LHC(magenta) [47].
where κ is the mixing parameter between the Higgs Boson of the Standard Model and the
Higgs Boson in the dark sector. The mixing between φ and S allows the decay of SM Higgs
bosons to a pair of γd s via the so-called Higgs portal. The decay width of Higgs boson
decaying into a pair of γd is given by [45]:α ′ m3H
ΓH→γd γd = θH2 ×
8m2γd

s
1−

4m2γd
m2H

1−

4m2γd
m2H

+

12m4γd!

m4H.

(3.10)The mixing angle θH ≈ m2κvw, where v and w are the VEVs of SM Higgs and dark Higgs,
−m2
H

Hd

and α ′ is the U(1)d structure constant. Through the κ term, the Higgs can also decay intoa dark Higgs pair if mH > 2mHd , while the opposite is possible if mHd > 2mH . The decay
width is given by [48]:ΓH→Hd Hd =(m2H + 2m2Hd )2 sin2 2θH
128πmH

s
1−

4m2Hd
m2H



1
1
cos θH + sin θHwv

The decay of Higgs into a dark Higgs and a dark photon is also possible.

2.

(3.11)

3.2 Dark Sector Models

23

In the dark photons production mode through Eq. 3.10, γd mixes with γ and decays into
fermions via the vector portal, as mentioned in Sec. 3.2.1. This way, the Higgs portal dark
sectors can be searched at the LHC together with the vector portal. The Higgs portal isparticularly interesting for experiments at the LHC since Higgs bosons can be produced.
In addition, since an upper limit of BR for the invisible decays of Higgs boson is set to
BR = 11% [2], there is enough possibility to produce dark photons from Higgs bosons. In
this analysis, we take the branching fraction as a free parameter to probe the Higgs portal
instead of the mixing parameter κ.

3.2.3

Benchmark Models

The search strategy for dark sectors focuses on utilizing the γd signature, which represents awide range of scenarios, rather than relying on any specific model. We use simplified andwidely recognized dark sector models as benchmarks to investigate vector and Higgs portals,
aiming to optimize object selection and sensitivity throughout the analysis. In this thesis, weselect the Hidden Abelian Higgs Model (HAHM) [49] and Falkowsky-Ruderman-VolanskyZupan (FRVZ) model [50][51] as benchmarks.
FRVZ benchmark Model
The FRVZ benchmark model is a simplified dark sector model with a richer phenomenology
due to the production of multiple BSM particles. As depicted in Fig. 3.8 (a), Higgs bosons
decay to a pair of dark fermions fd . Each fd further decays until the production of the Hidden
Lightest Stable Particle (HLSP) and a dark photon γd . Here, fermions fd correspond to theLightest Supersymmetric Particle (LSP) in the Minimal Supersymmetric Standard Model(MSSM) sector, Ñ1 , and the HLSP corresponds to the “true LSP” in the original paper [50].
Dark photons are mixed with SM photons via the vector portal and finally decay into pairs ofcharged fermions. Various topologies are possible due to the BSM intermediate and hidden
particles in the final state. In addition, depending on the strength of U(1)d coupling, morethan one γd can be radiated, resulting in the multi γd production like a shower. In this study,
we assume αd ≲ 0.01 to avoid additional radiations of γd in the final state.
HAHM benchmark Model
The HAHM model is another simplified dark sector model. As depicted in Fig. 3.8 (b), in thismodel, the Higgs boson mixes with the dark Higgs to produce two γd via the Higgs portal. γdthen decays into two charged fermions via the vector portal. The smaller number of particles
involved makes simpler topology, allowing, e.g., the reconstruction of Higgs boson mass.

24

Dark Matter Search at the LHC

(a)

(b)

Fig. 3.8 Feynman diagram of (a) FRVZ benchmark model and (b) HAHM benchmark model.
Here HLSP stands for the hidden lightest stable particle, and fd for dark fermion [52].
Search Signature
In addition to providing unique insights into the Higgs portal, the ATLAS experiment at the
LHC is also motivated to explore the uncovered vector portal exclusion area, as shown in
Fig. 3.7, particularly around ε ≲ 10−4 and mγd in the 10 ∼ 100 MeV range. To maximize the
ATLAS detector’s potential to access this phase space, a dedicated γd signature is exploitedby choosing the free parameters m fd and mHLSP to be a few GeV, ensuring they are small
relative to the Higgs boson, with mHLSP + mγd < m fd (more details will be provided inSec. 5.1). Similar assumptions are made in other experiments [4] [53]. As a result, the two
γd s are boosted and well separated, and the charged fermions from γd are highly collimated,
often falling into the same region of interest. In this thesis, since we focus on the search
signature of low-mass dark photons, only pairs of electrons and muons are considered in
the final states. Such a collimated lepton pair decaying from γd forms a lepton jet, or LJ.
Fig. 3.9 and Fig. 3.10 show the event topology where two γd s from Higgs boson are produced
back-to-back, and lepton pairs decaying from each γd form a lepton jet in the FRVZ and
HAHM benchmark model, respectively.
Previous results at the LHC to explore Higgs and vector portals using the FRVZ model
are shown in Fig. 3.11. This thesis is devoted to extending the search to cover the gap by
exploiting the lepton jet signature in the ATLAS experiment. As mentioned, we focus on two
dominant decay modes of γd , γd → e+ e− and γd → µ + µ − for the low mass region (by 2 ×
charged pion mass). Since there are two γd s in an event, there are three possible channels:eLJ-eLJ, µLJ-µLJ and eLJ-µLJ. The author has worked on eLJ-eLJ, but the results fromother channels will be shown in Chapter 9. We will explain the object building of both muLJ
and eLJ until Sec. 5.4.1, but after that, we will focus on eLJ-eLJ.

3.2 Dark Sector Models

25

Fig. 3.9 Event topology of lepton jet signature of our interest in the FRVZ benchmark model.
Two γd from Higgs boson are produced back-to-back, and the lepton pair decaying from γdare collimated.

Fig. 3.10 Event topology of lepton jet signature of our interest in the HAHM benchmark
model. Two γd from Higgs boson are produced back-to-back, and the lepton pair decaying
from γd are collimated.

26

Dark Matter Search at the LHC

Vector portal coupling εATLAS

s=8-13 TeV, 20.3-139 fb-1

10−4

FRVZ Model
H→2γ +XdmH = 125 GeV
90% CL observed limits

10−5
10−6

ggF/WH/VBF (139 fb-1)
BR=10%
BR=5%
BR=1%
BR=0.5%BR=0.1%10−7

Prompt (20.3 fb-1)
JHEP 02 (2016) 062

BR=10%

10−8
10−1

1
10
Dark Photon mass [GeV]

Fig. 3.11 Excluded areas in the ε, mγd plane the FRVZ model with different BR(H → 2γd +X)
assumptions [54].

Chapter 4
The ATLAS experiment at LHC
As one of the world’s largest experiments in high-energy physics, the ATLAS experiment
provides a unique chance to experimentally validate our current theoretical framework andsearch for new physics. This chapter briefly introduces the ATLAS detector at the LHC andthe definition of standard physics objects.

4.1

Accelerator and the LHC

CERN, the European Organization for Nuclear Research, is one of the leading particle
physics research organizations established in 1954. Located on the French-Swiss bordernear Geneva, CERN’s accelerator complex consists of a series of machines designed toboost particle energies. During LHC Run-2 operations, the acceleration process begins at
the Linear Accelerator 2 (LINAC2) [55], where protons from hydrogen gas are accelerated
to 50 MeV. The proton bunches then pass through a series of pre-acceleration stages: theProton Synchrotron Booster (PSB) [56], the Proton Synchrotron (PS) [57], and the Super
Proton Synchrotron (SPS) [58], increasing their energies to 1.4 GeV, 25 GeV, and 450 GeV,
respectively, before being injected into the final stage, the LHC ring, achieving the world’s
highest recorded collision energy of 13.6 TeV [59]. In the LHC ring, there are four locations
where proton bunches collide:• A Toroidal LHC Apparatus (ATLAS) [60] and Compact Muon Solenoid (CMS) [61]are general-purposed detectors designed to observe the phenomenon of Higgs bosonand search for new physics beyond the SM.
• A Large Ion Collider Experiment (ALICE) [62] is designed to study the heavy ion
collisions. By creating a state of quark-gluon plasma, properties of strong interaction
can be explored.

28

The ATLAS experiment at LHC

The CERN accelerator complex
Complexe des accélérateurs du CERNCMSNorth Area

LHC

GIF++

2008 (27 km)

CENF

ALICE

2015

LHCb

2016

TT20

TT40

TT41

SPS
1976 (7 km)

TI2

TT10

TI8

AWAKE

ATLAS

HiRadMat
2011

2016

TT66

TT2

AD

ELENA

1999 (182 m)

2016 (31 m)

ISOLDEBOOSTER

1992

1972 (157 m)
RIBs
p

p

2001

East Area

IRRAD/CHARM

PSn1959 (628 m)

p

ions

CLEAR

LINAC 2

LINAC 3Ionsp (protons)

REX/HIE
2001/2015

n-ToF

RIBs (Radioactive Ion Beams)

e-

LEIR

2017

2005 (78 m)n (neutrons)– (antiprotons)pe- (electrons)

LHC - Large Hadron Collider // SPS - Super Proton Synchrotron // PS - Proton Synchrotron // AD - Antiproton Decelerator // CLEAR - CERN Linear
Electron Accelerator for Research // AWAKE - Advanced WAKefield Experiment // ISOLDE - Isotope Separator OnLine // REX/HIE - Radioactive
EXperiment/High Intensity and Energy ISOLDE // LEIR - Low Energy Ion Ring // LINAC - LINear ACcelerator // n-ToF - Neutrons Time Of Flight //HiRadMat - High-Radiation to Materials // CHARM - Cern High energy AcceleRator Mixed field facility // IRRAD - proton IRRADiation facility //GIF++ - Gamma Irradiation Facility // CENF - CErn Neutrino platForm

Fig. 4.1 Schematic overview of CERN accelerator complex [64].
• Large Hadron Collider beauty (LHCb) [63] is dedicated to the study of beauty quarks,
as well as exotic hadrons, charm physics, electroweak physics, QCD physics, and othernew physics searches.

4.1.1

pp collisions

In designing the LHC, proton-proton (pp) collisions were chosen to explore the high-energy
frontier in considerations related to synchrotron radiation given by the relativistic Larmor
formula
Pγ =

q2 c
a2
q2 c
1
E4
=
,
6πε0 c3 (m0 c2 )2 6πε0 c3 (m0 c2 )4 ρ 2

(4.1)

29

4.1 Accelerator and the LHC

which describes the energy loss by accelerated charged particles. Here, a is the acceleration,and ρ is the radius of curvature in circular motion. The mass term shows that electrons in an
accelerator lose energy approximately 1013 times that of protons, making proton collisions
good candidates for machines operating at very high energy. In the typical pp collisions, twopartons interact primarily in hard scattering process where large momentum is transferred.
Fig. 4.2 illustrates a pp collision. Here, the incoming protons are represented by the large
green ellipse from the horizontal direction, and the hard scattering process is in the red circle.
In addition, gluons and quarks can be emitted by the QCD radiation processes both before thecollision as initial state radiation (ISR) and after the collision as final state radiation (FSR).
ISR and FSR are later important in reconstructing and analyzing the collision events. The
products further emit radiation, causing parton showers until hadronization shown as thegreen circles, resulting in bundles of hadrons detected as jets.

4.1.2

Data-taking

The operation of the LHC can be divided into data-taking periods of Run-1 (2011-2012),
Run-2 (2015-2018), and the ongoing Run-3 (2023-), where stable beams are collided andrecorded, and long-shutdown (LS) periods for repairs and upgrades as summarized in Fig. 4.3.
√
The collider is operated at s = 7 and 8 TeV during Run-1, 13 TeV during Run-2, and 13.6
TeV during the ongoing Run-3.

4.1.3

Luminosity

To measure the number of collisions produced in the detector, we define instantaneous
luminosity L as the number of events per time per cross-section:
1 dN
.
σ dt

(4.2)

k f N1 N2,
4πσx σy(4.3)

L=
A simple estimation is given byL=

where N1 and N1 are the number of protons in the two bunches. k and f are the number
and frequency of bunches circulating the LHC ring, and σx (σy ) are the x(y) components ofthe cross-section. The instantaneous luminosity value is 1 × 1034 cm−2 s−1 with the design
condition of LHC [66]. The integrated luminosity at a certain time is given byZ

Lint =

Ldt.

(4.4)

30

The ATLAS experiment at LHC

Fig. 4.2 Illustration of pp collision at LHC [65]. Two partons (large green ellipses) interact
primarily in hard scattering (large red circle) and are accompanied by a secondary interaction(large purple ellipse). Green circles represent the hadron showering and hadronization.
Electromagnetic radiation by charged particles is in yellow.

Fig. 4.3 Timeline of LHC operations.

31

ATLAS
140 Preliminary120

LHC Delivered
ATLAS Recorded100

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

Good for Physics

80
60

20

ATLAS Online, 13 TeV
500'15 ul '15 an '16 ul '16 an '17 ul '17 an '18 ul '18
J
J
J
J
J
J
J

∫Ldt=146.9 fb-1

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

400
300
200
100
0
0

0

Jan

600

2/19 calibration

40

Recorded Luminosity [pb-1/0.1]

160

2/19 calibration

Total Integrated Luminosity fb-1

4.1 Accelerator and the LHC

10

20

30

40

50

60

70

80

Mean Number of Interactions per Crossing

Month in Year

(a)

(b)

Fig. 4.4 (a) Total Integrated Luminosity for pp collisions, and (b) mean number of interactions
per crossing ⟨µ⟩ for the 2015-2018 LHC Run-2 pp collision data at 13 TeV center-of-massenergy [69].
Fig. 4.4 (a) shows the integrated luminosity during LHC Run-2. By combining theluminosity blocks of data collected where all ATLAS sub-detectors operated in good condition (good run list, or GRL), a total of Lint = 139 fb−1 is primarily measured with anuncertainty of 1.7% [67]. The latest study on luminosity determination recovers 1 fb−1 tohave Lint = 140 fb−1 with an uncertainty of 0.83% [68]. In this thesis, we will use the latest
total of Lint = 140 fb−1 pp collision data taken from 2015 to 2018 for physics analysis.

4.1.4

Bunch-crossing and Pile-up

At the LHC, protons are injected in consecutive bunches with approximately 7.5 m between
each other. As a result, each revolution in the 27 km ring has 3564 bunch-crossings. For eachbunch-crossing (BC), multiple protons could collide with each other at the interaction point,
including both hard-scatter events we are interested in, as well as inelastic pp interactions.
To quantitatively describe such a phenomenon, pile-up is used to describe the mean numberof interactions per bunch-crossing:⟨µ⟩ =Lint σ
,
RBC

(4.5)

where RBC is the bunch-crossing rate. Fig. 4.4 (b) shows the mean number of interactions per
crossing during the 2015-2018 LHC Run-2 data-taking periods. Table. 4.1 summarizes therun parameters.

32

The ATLAS experiment at LHC
Table 4.1 Parameter values from 2015 to 2018.
Parameter√s [TeV]
Bunch spacing [n]Peak luminosity [1033 cm−2 s−1 ]Integrated luminosity [fb−1 ]Pile-up (⟨µ⟩)

4.2

The ATLAS detector

4.2.1

Overview

2015

2016

2017

2018

13
25
5
4.0
∼ 13

13
25
13
38.5
∼ 25

13
25
16
50.2
∼ 38

13
25
19
63.4
∼ 36

The ATLAS detector is located at the Point-1 interaction point on the LHC ring. Cylindricalin shape, the detector is measured 46 m long, 25 m in diameter, 7000 t in weight, and sits ina cavern 100 m below ground. As shown in Fig. 4.5, it consists of a series of sub-detector
layers:• Inner Detector: closest to the beam pipe, it consists of pixel detectors, a silicon tracker,
and a transition radiation tracker to provide precise measurement of charged particle
trajectories.
• Calorimeter: the electromagnetic calorimeter captures electrons and photons in EM
showers, while the hadronic calorimeter absorbs hadrons to measure jet energy depositions. Missing transverse energy (missing ET ) is also reconstructed in the calorimeter.
• Muon Spectrometer: identification and measurement of muon tracks.
• Magnet system: a central solenoid for the inner detector and superconducting toroids
magnet for the muon spectrometer.
The details of each subsystem are explained in the following sections.

4.2.2

Coordinate system

The interaction point is the origin of the default coordinate system used in the ATLAS
experiment. The z-axis runs along the beam direction, while the transverse x-y plane isdefined such that the positive x-axis points towards the center of the LHC ring, and the y-axis
points upwards to the surface. The part of the detector with positive z values is called the
A-side, while the part with negative z values is called the C-side. The φ and θ are the azimuthand polar angles as defined in Fig. 4.6.

33

4.2 The ATLAS detector

Fig. 4.5 Schematic view of the ATLAS detector [70].
y
⃗p

⃗pT
φ

θ

ATLAS

z
LHCb

ALICE

x

LHC
CMS

N

Fig. 4.6 Illustration of the coordinate system of the ATLAS detector [71].
Additionally, we introduce the spatial coordinate of pseudorapidity η to describe theangle of a particle relative to the beam axis, defined as  θη ≡ − ln tan.
2
The angular distance between objects in the detector can be described with ∆R =

4.2.3

(4.6)
p
∆η 2 + ∆φ 2 .

The magnet system

The magnet system is essential to the measurements of charged particle tracks. An intense
magnetic field means more precise measurements of high-pT object. The ATLAS experimentfeatures a powerful magnet system with four large superconducting magnets. Fig. 4.7 shows
the geometry of the magnet system.

34

The ATLAS experiment at LHC• The central solenoid is 5.8 m long, 2.56 m in diameter, located inside the calorimeterin parallel with beamline, and provides a magnetic field of 2 T in z direction for the
inner detector. The solenoid is structured with just 4.5 cm thickness to minimize theradiation length before the calorimeter.
• The barrel toroid consists of 8 separate coils to create a magnetic field in the φ direction
up to 3.5 T for the track measurements in the barrel region of the muon spectrometer.
• Two end-cap toroids provide a magnetic field in the end-cap region of the muon
spectrometer. The eight end-cap coils on each side are positioned interleaving with thebarrel toroids.

Fig. 4.7 Schematic view of magnet system in ATLAS [72]. The solenoid winds inside thecalorimeter are purple. At the barrel region, eight toroid coils interleave with end-cap coils.

4.2.4

Inner Detector

The ATLAS inner detector (ID) [73] is designed to provide high-precision measurementsof track transverse momentum and primary and secondary vertexes. The coverage of ID is|η| < 2.5 and full range of φ with a required pT resolution of σ pT /pT = 0.05%pT [GeV] ⊕ 1%[72]. An overview of ID is shown in Fig. 4.8 (a), and increasing in radius, different layers
are shown in Fig. 4.8 (b).
• Pixel Detector: Using silicon microstrip and pixel technology, a total of 1744 pixel
sensors are arranged in three barrel layers and two end-caps to cover the innermost
three layers at 50.5 mm, 88.5 mm, and 122.5 mm in radius. Pixel detectors provide a 12µm resolution in the r −φ plane and 66 µm in the z direction. After the Long Shutdown
after Run-1 during 2013-2015, an additional layer, the insertable B-layer (IBL), wasinstalled at a radius of 33.3 mm, significantly improving the ID performance.

35

4.2 The ATLAS detector

(a)

(b)

Fig. 4.8 Schematic view of different layers of Inner Detector [72] [74].
• Semiconductor Tracker (SCT): In the intermediate layers, SCT works with a Pixel
detector to further provide a measurement of momentum, impact parameters, andvertex position. SCT consists of 4088 modules, each with 768 readout strips arranged
in 4 barrels at 299 mm, 371 mm, 443 mm, and 514 mm, and two endcaps of 9 disks
each. Slightly worse than pixel detector, SCT provides a resolution of 16 µm in r − φplane and 580 µm in z.
• Transition Radiation Tracker (TRT): The outermost layer consists of straw detectors
filled with Xenon gas. As the Xenon gas absorbs transition radiated photons, it
produces distinct readout signals. These signals provide significant discrimination
power between electrons and charged pions within the energy range of 1 GeV to
100 GeV. There are 52544 straw tubes arranged in 1.5 m length in the barrel region
to cover |η| < 1, and 122880 straw tubes in the endcaps to cover 0.8 m < |z| < 2.7 m
and 1 < |η| < 2, each with a diameter of 4 mm. By adding around 36 hits per track,
TRT improves momentum measurement, and overall, TRT has a resolution of 130 µm.

4.2.5

Calorimeter

The calorimeter [75] is the critical component of the detector to provide precision measurement of energy deposition, where the fine granularity of the EM calorimeter is designed forelectrons and photons. In contrast, the hadronic calorimeter absorbs the hadronic showers,
preventing leakage to the muon spectrometer for jets. As shown in Fig. 4.9, the calorimeter

36

The ATLAS experiment at LHC

system includes EM calorimeter, hadronic end-cap (HEC), forward calorimeter (FCal) built
from liquid Argon (LAr) cryostats, and scintillator tile calorimeter:• LAr EM Calorimeter: the EM calorimeter can be divided into two parts: EM barrel(EMB) with |η| < 1.475 and two EM end-caps (EMEC) with 1.375 < |η| < 3.2. The
EM part is a lead-LAr detector with accordion shaped electrodes and lead absorbers, as
shown in Fig. 4.10. The accordion geometry naturally allows full coverage of φ without
cracking. The wave amplitude and folding angle vary with radius to provide linearity
in φ . The EM calorimeter consists of a presampler and several active layers: threelayers in the precise measurement region, |η| < 1.35 for EMB and 1.5 < |η| < 2.5 for
EMEC; two layers in the overlap 1.35 < |η| < 1.5 region and high |η| > 2.5 region.
Usually, the middle layer collects the largest fraction of energy from electrons andphotons. The finest granularity is 0.025 × 0.025 in ∆η × ∆φ , in the middle layer ofprecision measurement regions.
• Scintillator Tile Calorimeter: located right outside the EM calorimeter to measure
hadronic showers in the barrel region, the tile has a barrel part in |η| < 1.0 and two
extended barrels in 0.8 < |η| < 1.7. It uses scintillating tiles as active materials andsteel as an absorber. There are three layers, and the granularity is 0.1 × 0.1 in the firsttwo layers and 0.2 × 0.2 in the last layer in ∆η × ∆φ .
• LAr Hadronic End-cap: the HEC is located right behind EMEC to cover 1.5 < |η| <3.2. Parallel copper plates are interleaved with the LAr gaps to provide an active
medium for the sampling. HEC consists of 4 layers with a coarse granularity of
0.1 × 0.1 and 0.2 × 0.2 in ∆η × ∆φ in the low and high η regions. There are 5632
readout channels in total.
• LAr forward Calorimeter: forward calorimeter covers 3.1 < |η| < 4.9 as the extensionof end-cap calorimeters, and to reduce background entering the muon spectrometer.
FCal consists of 3 layers with 3524 readout channels on both sides.

4.2.6

Muon Spectrometer

The Muon Spectrometer (MS) [77] in ATLAS detects muon tracks in the presence of large
superconducting toroid magnets and consists of separate high-precision tracking chambers
and triggering chambers. The main components are shown in Fig. 4.11. At the barrel region,
MS is structured with three cylindrical layers around the beam axis with the magnetic fieldprovided by the large barrel toroid at |η| < 1.4. At the endcap region for 1.6 < |η| < 2.7,

4.2 The ATLAS detector

37

Fig. 4.9 Illustration of the calorimeter in ATLAS, which consists of LAr EM Calorimeter,
Scintillator Tile Calorimeter, LAr Hadronic End-cap, and LAr forward Calorimeter [76].
the chambers are installed in three layers perpendicular to the beam with a magnetic fieldprovided by the endcap toroids. Finally, in the transition area (1.4 < |η| < 1.6), barrel andendcap toroids contribute to the magnetic field. The precision tracking chambers include
Monitored drift tubes (MDT) and Cathode strip chambers (CSC) while triggering chambers
include Resistive plate chambers (RPC) and thin gap chambers (TGC). Precision tracking
chambers function to precisely track the muon track coordinates from the magnetic fieldbending direction. In contrast, triggering chambers provide bunch-crossing identification(BCID) for synchronizing muon detection, fast trigger information for the later high-level
triggers, and secondary coordinate information to complement MDT precision measurements.
• MDT covers the range of |η| < 2.7 except for the innermost layer where CSC replaces
them for 2 < |η| < 2.7. MDT is built from an aluminum drift tube with a diameter of
29.970 mm and 0.4 mm thickness, operating with a mixture of Argon and CO2 gas at
3 bar to track muons passing the volume.
• CSC is designed to ensure safe operation at high particle fluxes, with higher counting
rates of 1000 Hz/cm2 compared with MDT’s 150 Hz/cm2 , CSC covers 2.0 < |η| < 2.7,
and works in complementary with MDT to provide high spatial, time and double
track resolution. CSC consists of a large and small chamber in φ is a multi-wire
proportional chamber built with wires in the radial direction segmenting cathodes
strips readouts both in parallel and perpendicular to the wire, allowing measurement ofboth coordinates of r and φ . CSC has a good timing resolution of 7 ns, a coordinate
resolution of 60 µm in r, and 5 mm in φ .

38

The ATLAS experiment at LHC

Fig. 4.10 Sketch of LAr EM barrel module with accordion shape. The granularity in η and φis also shown [75].
• RPC is a gaseous detector consisting of resistive Bakelite plates in parallel kept at a
distance of 2 mm, filled with a gas mixture of C2 H2 F4 , C4 H1 0 and SF6 on the barrel
region |η| < 1.05. Three trigger stations are layered around the beam axis, where theinner two stations select low pT tracks with 6 GeV < pT < 9 GeV and the outer station
selects high pT tracks with 9 GeV < pT < 35 GeV.
• TGC is a multi-wire proportional chamber with a narrow 2.8 mm gap between wires
and cathode plates that covers the triggering in the endcap region 1.05 < |η| < 2.4.
The three layers of TGC, one in front of the second MDT layer (TGC1) and two behind(TGC2 and TGC3) work together on the fast coincidence of muon tracks to provide
triggering information.
The overall MS system provides a resolution of σ pT /pT = 10% at 1 TeV.

4.2.7

Trigger and Data Acquisition

During the Run-2 operation of LHC, proton bunches collide at a frequency of 40 MHz,
while most events are soft inelastic pp collisions that are not of physics interest. Recording
such a vast amount of data flow is inefficient and impractical. ATLAS’s trigger and dataacquisition (TDAQ) system are crucial components. It is designed to filter the vast amount4.2 The ATLAS detector

39

Fig. 4.11 Longitudinal projection of the Muon Spectrometer in ATLAS, which consists ofMonitored drift tubes (MDT) and Cathode strip chambers (CSC) for precision tracking, andResistive plate chambers (RPC) and Thin gap chambers (TGC) for triggering [77].
of data produced in pp collisions and select only the potentially interesting physics events.
The system consists of a Level-1 (L1) Trigger, which processes based on fast sub-detector
information, and a High-Level Trigger (HLT), which employs software to perform a finer
selection. The data flow is reduced from 40 MHz to 100 kHz with the L1 trigger, and further
down to 1000 Hz with the HLT trigger.
L1 Trigger
The L1 triggers [78] to perform initial selections through Field Programming Gate Arrays(FPGAs) using limited data from the detector to search for physics objects. It consists of two
subsystems: the calorimeter system (L1Calo) and the muon system (L1Muon).
• L1Calo identifies electrons, photons, jets and τ leptons with high ET , as well as missing
ET with a reduced granularity of 0.1 × 0.1 in ∆η × ∆φ in the calorimeter, where muon
activities found in the muon trigger system are not taken into account in the calculationof L1 missing ET . The signal goes through the path in a sequence of pre-processorsthat digitizes the analog input and assigns bunch crossing: jet/energy processor to
identify jets and cluster processor (CP) to identify electrons/photons and τ leptons
above ET threshold in parallel; L1 central trigger processor (CTP) to make the final
decision.

40

The ATLAS experiment at LHC• L1Muon identifies high ET muons independently within each dedicated sub-detector
segment: RPC for barrel region and TGC for end-cap region triggering. The trigger
decision is based on coincidence across three trigger stations that track the path of amuon through the detector.

The L1 trigger also defines a region of interest (RoI). This RoI includes the geometric locationand sub-detector information for the physically interesting objects that activate the trigger.
This information is then passed to the High-Level Trigger (HLT) system for further analysis.
HLT Trigger
HLT trigger applies more complicated event selections in the processing computer farm tofurther reduce trigger rates. Seeded with detector information from L1 Trigger, HLT uses
full granularity and precision of detector information within the RoI to perform, for example,
a scan of the calorimeter for missing ET building. Data flow with a reduced trigger rate of1000 Hz after HLT selections is stored for physics analysis.
In the ATLAS experiment, a trigger menu [79] stores the chain that fires the trigger torecord an event, specifying thresholds and selection criteria combining information fromboth L1 and HLT. For example, suppose two electrons fire the event with ET larger than
17 GeV passing multivariate-based electron ID at "very loose" working point without including impact parameter d0 information in the HLT algorithm, seeded by two isolated
L1 EM clusters with ET larger than 15 GeV. In that case, the trigger menu is named"HLT_2e17_lhvloose_nod0_L12EM15VHI". A prescaling is sometimes applied during
the actual data taking, where a factor intentionally reduces the firing rate to manage thesystem frequency. In this thesis, we use un-prescaled triggers with objects of interest at thelowest ET threshold to maximize the signal acceptance for the analysis as will be detailed inSec. 5.5.

4.2.8

Event Simulations

Simulation of Monte Carlo (MC) events plays a crucial role in various aspects of physics
analysis at the ATLAS experiment, from feasibility studies of the expected number of signals
and backgrounds to evaluating systematical uncertainties. MC samples used in this thesis are
explained in Section 5.1. Here we explain the MC simulation production steps in ATLAS:
Matrix element calculation
The simulation of proton-proton collision events starts from the Parton Distribution Functions(PDFs), which are the momentum distribution functions of partons within a proton. The

4.2 The ATLAS detector

41

asymptotic freedom [80] allows perturbative computation via matrix elements, and the outcome is a list of partons with high momentum. For example, in this thesis, the M AD G RAPH
event generator [81] has been used, which matches the matrix element to Next-to-LeadingOrder (NLO) accuracy for the signal FRVZ and HAHM samples hard scattering simulation.
POWHEG (Positive Weight Hardest Emission Generator) [82] is used for the generation oftt and single top processes.
Parton showering/hadronization
In this step, QCD processes at a lower energy scale, including the perturbative parton showering and non-perturbative hadronization processes, are simulated, leading to the generationof final state particles stable enough to enter the ATLAS detector, including ISR, FSR, etc.
Interfaced with M AD G RAPH, the PYTHIA8 generator [83] is used to simulate final decays
in the signal samples. HERWIG (Hadron Emission Reactions With Interfering Gluons)(++) [84] is used for the EW-produced processes of W and Z bosons with additional jets. In
addition, standalone generators like S HERPA (High-Energy Reactions of Particles) [85] areused for other SM processes in this analysis, providing both matrix element calculation andparton showering/hadronization.
Detector simulation
So far, the simulation has generated a list of truth particles. Factors such as interaction with
detector material, sub-detector acceptance, and resolution must be considered to comparewith actual experimental measurements. The detector simulation uses GEANT4 (Geometry
And Tracking) [86], which integrates well with the ATLAS detector. GEANT4 simulates
the process from making detector hits, considering any misalignment and distortions of thedetector setup and background noise, such as beam gas and cavern background, to the HLT
and reconstruction in the same treatment with experimental data.
Event weight
Each simulated event is assigned different sources of event weight:• MC weight wmc is calcurated to represent the probability of the simulated process inthe event based on theoretical prediction and PDF. It can also include factors fromcomputational order in the perturbation theory. For example, events generated beyond
LO are assigned with weight to correct the cross-section distribution.

42

The ATLAS experiment at LHC• Pile-up weight wpu is the normalization associated with the reweighting that matches
the simulated average number of interactions per bunch crossing with an observed
number at each actual data-taking period.
The expected number of observed events from the simulation is given by
N=σ2015−2016,2017,2018

nj

∑

Lj ∑

j

i, j

i, j

wmc × w pu
,
w
tot
i

(4.7)

where L j corresponds to the luminosity, n j corresponds to the number of observed events after
i, j
i, j
event selections in each data-taking year, and wtot is the total simulated sum of wmc × w pu .

4.3

Reconstruction of Physics Objects

The customization of a dark photon object with LJ signatures in ATLAS is based on standard
physics objects of tracks, electrons, and muons. To suppress SM background processes, suchas t t¯, jets are also used. This section will discuss the standard reconstructing criteria forphysics objects in the ATLAS experiment, focusing on these components.

4.3.1

Tracks and Primary Vertex

In the presence of a magnetic field from the solenoid in the ID, the trajectory of a track can
be described by a perigee representation with five parameters with respect to a reference
point, which is the average position of pp collisions (beam spot) as shown in Fig. 4.12. d0
and z0 are the impact parameters corresponding to the transverse and longitudinal distance tothe beam spot. φ is the azimuthal angle and θ is the polar angle. The last parameter is the
charge-to-momentum ratio q/p.
The track reconstruction algorithm [88] can be summarized as below:• Track seeding and finding: raw detector hits in the pixel and SCT detectors are firstclustered and then grouped into sets of three to form various "space points" used for
track seeds. A fourth space point from a different layer, with compatible curvature,
confirms the track seed. A combinational Kalman filter is then applied to the extended
path of each seed within the pixel and SCT detectors. This filter searches for adjacentclusters while smoothing the trajectory. Additionally, calorimeter information within
the track seed’s Regions of Interest (ROIs) is checked, and feedback is provided to
track findings. This feedback helps recover efficiency lost due to the Bremsstrahlung
process.

4.3 Reconstruction of Physics Objects

43

Fig. 4.12 Schematic view of perigee representation of track parameters [87].
• Ambiguity solving: overlap between track hits is solved by assigning scores basedon factors like quality for fit χ 2 , number of hits missing from an ID layer (holes),transverse momentum pT .
• TRT extension: track finding algorithms are extended to TRT, and additional TRT hits
are added to track if the refit has good quality. The additional measurements improvethe momentum resolution and particle identification.
Basic working points are defined in Table. 4.2. In the analysis detailed in Chapter 5, tracks
used to build LJ are required to satisfy the Loose working point.
As mentioned in Section 3.1, in each collision of pp bunches at LHC, we are mostlyinterested in the hard-scattering event, which is associated with one hard-scattering primaryvertex (PV). To find PV, an adaptive multi-vertex fitter is used to find the vertex seeds
iteratively, where the same track candidates can be used in multiple vertex candidates withdifferent weights. PV is determined by the vertex with the largest sum of track pT square [90].

4.3.2Electrons

Electrons play an important role in building electronic lepton jets (eLJs), detailed in Section 5.4. This section will explain standard electron reconstruction, identification, andisolation.

44

The ATLAS experiment at LHC

Table 4.2 The ATLAS standard Loose and Tight Primary track working points for physics
analysis [89].
Loose Working Point

Tight Primary Working Point

pT > 0.5 GeV|η| < 2.5
≥ 7 clusters in Pixel/SCT≤ 2 holes in the Pixel/SCT≤ 1 hole in Pixel|d0 | < 2 mm
|z0 sin θ | < 3 mm

All the Loose requirements≥ 9 hits in Pixel/SCT for |η| ≤ 1.65
≥ 11 hits in Pixel/SCT for |η| > 1.65
1 hit in IBL or in the innermost Pixel layer
No Pixel holes-

Reconstruction
The electron object is reconstructed as a cluster in EM calorimeter with associated charged
track(s) from ID. It is performed in the following steps [91]:• Topo-cluster reconstruction: at the first step, topologically connected EM and hadronicEM
EM = Ecell . The
clusters are connected using a ’4-2-0’ threshold of significance ScellEMσnoise, cellEM ≥ 4 and builds a protoclustering initializes from cells of the EM calorimeter with Scellcluster. The presampler and first layer are excluded to avoid forming noise clusters.
EM ≥ 2 and their
Each proto-cluster gets iterated to include neighboring cells with Scell
nearest neighbors without significance requirement. Local maxima in proto-clusters
are split into separate clusters. The EM fraction of total energy deposits fEM > 0.5 and
EM energy EEM > 400 MeV is required.

• Track refitting: reconstructed tracks, as described in the previous section, are considered for electron reconstruction. They are refitted using the Gaussian Sum Filter(GSF) algorithm [92] that describes the radiative energy losses of electrons with nonlinear functions, allowing better estimations of the track parameters in the presence ofbremsstrahlung.
• Track-cluster association: tracks refitted by GSF are extrapolated to the middle layerof the EM calorimeter and matched to topo-clusters. The matching criteria include
an angular separation with |∆η| < 0.05 and −0.10 < q × (φtrack − φtopo-clus ) < 0.05,
where q is the charge of the particle. The requirement on φ is asymmetric to accountfor potential energy loss due to photon radiation, which leads to a smaller value of
measured track φ . When multiple tracks are matched to the same cluster, they areprioritized as follows: first, tracks with pixel hits; second, tracks with SCT hits; and45

4.3 Reconstruction of Physics Objects

third, by the smallest ∆R between the track and the middle layer of the EM calorimeter.
The properties of electrons are then derived from the highest-ranked track.
• Supercluster reconstruction: the supercluster is performed independently for electronsand photons and consists of two parts. Electron seed cluster is required to have
ET > 1 GeV and matched ID track with at least four silicon detector hits, while photon
seed cluster is required to have ET > 1.5 GeV with no requirement on tracks. Satellite
cluster is then searched within a window of ∆η × ∆φ = 0.075 × 0.125 around the seedcluster. For electrons, an additional wider window ∆η × ∆φ = 0.125 × 0.300 also
qualifies the satellite cluster if the best-matched track of the satellite cluster is the sameas the seed cluster. Satellite clusters are added to the seed clusters to form the final
superclusters.
• Object building: in the last step, energy and position calibrations are applied, alongwith matching of tracks and conversion vertex (massless from two opposite-signed
charged tracks) to superclusters, the final object building for physics analysis is asfollowed: for supercluster with associated tracks and no conversion vertex, it is built as
an electron. For a supercluster with conversion vertex and no associated tracks, it isbuilt as a photon. In other cases where a supercluster produces both an electron and aphoton, the object is known as ambiguous.
Identification
To further improve the purity of electron selections and suppress fake electrons from hadronic
jets, photon conversions, and heavy flavor quarks, a likelihood (LH) based electron identification is introduced [91]. The likelihood function is built asnLS(B) (x) = ∏ PS(B),i (xi ),

(4.8)

i=1

where x = xi is the vector of inputs. n is the number of variables, including showering
shapes in the EM calorimeter, ID track qualities, and track-cluster matching information. Pi
corresponds to a pdf in quantity i. The discriminant dL is given by
dL = −τ−1LS + LB
ln
−1 ,
LS

(4.9)

where τ is fixed to 15 [93]. In this way, the efficiency is smoothed, and three standard
working points loose, medium and tight can be defined, which correspond to 93%, 88%,
and 80%, respectively (as shown in Fig. 4.13). All the working points require tracks to have

46

The ATLAS experiment at LHC

(a)

(b)

Fig. 4.13 Electron identification efficiency as a function of (a) transverse energy ET , and (b)η in Z → ee events for different working points [91].
≥ 2 pixel hits and ≥ 7 pixel/silicon hits, where medium and tight require pixel hits in the
innermost layer. In this thesis, we will apply the medium identification working point forelectrons used to build LJs.
Isolation
Prompt production of electrons from the decay of W , Z, and Higgs bosons typically exhibit
minimal detector activity in their vicinity. To quantify this, the term isolation is introduced.
The isolation is defined as the sum of the transverse energy (ET ) or transverse momentump(pT ) within a narrow cone ∆R = ∆η 2 + ∆φ 2 around the electron. Generally, electrons thatare promptly produced have low isolation values. In the ATLAS experiment, two types ofisolation are considered:iso• Calorimeter isolation: the raw isolation energy ET,raw
is computed as the energy
deposit in a fixed-size isolation cone (e.g., ∆R = 0.2). The energy from prompt electron
isoET,coreis subtracted in a central ∆η × ∆φ = 0.125 × 0.175 as shown in Fig. 4.14 (a).
isoThe leakage of prompt electron energy deposits outside the subtraction core ET,leakisalso evaluated by fitting to Crystal Ball function as a function of ET . Lastly, the pileiso
contribution to isolation is estimated by ET,pile-up(η) = ρmedian (η) × (π∆R2 − Acore ),where ρmedian (η) is the median jet energy density in a unit area. The overall calorimeter
isolation is given by
iso
iso
iso
iso
ETiso = ET,
raw − ET,core − ET,leak − ET,pile-up .

(4.10)

47

4.3 Reconstruction of Physics Objects

(a)

(b)

Fig. 4.14 (a) Criteria of central cone subtraction (∆η × ∆φ = 0.125 × 0.175 in yellow) fromisolation cone (in purple). (b) Calorimeter isolation ETiso in ∆R = 0.2 cone as function of ET
for each component [91].
Contribution from each component of ETiso is shown in Fig. 4.14 (b).
• Track isolation: track isolation piso
T is computed as the sum of tracks pT in isolationcone after removing tracks coming from the electron candidate. The finer granularity
in ID allows a variable definition of isolation cone as∆R = min(10 GeV, Rmax ).
pT [GeV](4.11)

Here, Rmax is a fixed maximum isolation cone (e.g., ∆R = 0.2), and tracks in the central∆η × ∆φ = 0.05 × 0.1 are considered as a part of the electron object, thus not includedin the computation. The variable definition of track isolation in Eq. 4.11, which
depends on electron pT allows narrower cone sizes in the boosted decay signatures.
In ATLAS, standard working points for electrons include both calorimeter isolationand track isolation selections. They are summarized in Table. 4.3, where "cone20" and"varcone30" correspond to fixed cone size of ∆R = 0.2 for calorimeter isolation, and Rmax =0.3 for the variable cone size track isolation. In the analysis of this thesis, we select the
Loose_VarRad isolation working point.

48

The ATLAS experiment at LHC

Table 4.3 Summary of Loose_VarRad and Tight_VarRad working point requirements forelectrons. peT is the pT of electrons. "cone20" and "varcone30" corresponds to fixed cone
size of ∆R = 0.2 for calorimeter isolation, and Rmax = 0.3 for the variable cone size track
isolation.
Isolation WP
Loose_VarRad
Tight_VarRad

4.3.3

Calorimeter

Track

ETiso,cone20
< 0.2
peT
ETiso,cone20< 0.06peT

piso,varcone30
T< 0.15peT
piso,varcone30
T< 0.06peT

Muons

Muons are used to build muonic lepton jets (µLJs), which are not the focus of this thesis. To
ensure orthogonality between channels when combining results, muons are discussed here
for the purposes of muon vetoing and overlap removal in the reconstruction of eLJs, as will
be detailed in Sec. 5.4.
Reconstruction
In the ATLAS experiment, the reconstruction of muons involves identifying muons fromtracks in the ID and MS detectors, with additional information from the calorimeter. There
are four types of reconstructed muons [94]:• Combined (CB) muons: reconstructed by performing a combined fit to tracks fromboth MS and ID, taking into account energy loss in the calorimeter. CB muons arereconstructed up in |η| < 2.5.
• Segment-tagged (ST) muons: reconstructed based on tracks from ID that match atleast one MS segment during extrapolation. Muon parameters are assigned directlyfrom ID. ST muons are reconstructed up in |η| < 2.7.
• Calorimeter-tagged (CT) muons: reconstructed based on tracks from ID that matchenergy deposits in the calorimeter matching a minimum ionizing particle. CT muons
are optimized to recover acceptance in the gap region |η| ≤ 0.1.
• MS Extrapolated (ME) muons: reconstructed based on tracks from MS only, in casetracks from MS cannot be matched to ID. ME muons are reconstructed up in |η| < 2.7.
In the analysis in this thesis, CB muons are used.

49

4.3 Reconstruction of Physics Objects

(a)

(b)

Fig. 4.15 Muon identification efficiency as a function of (a)transverse momentum pT , and (b) η in t t¯ events for different working points [95].
Identification
Like electrons, a muon identification algorithm is applied to select muons with high purity
against hadrons. The q/p significance is a powerful variable that checks compatibility
between ID and MS.
|q/pID − q/pMS |q/psignificance = p,
σ 2 (q/pID ) + σ 2 (q/pMS )(4.12)

where q and p are the charge and momentum of muons measured in the corresponding
sub-detector, and σ is their uncertainties. Three selection working points are defined: loose,medium and tight. The loose WP accepts CB and ME muons in |η| < 2.5 with at least
two precision stations and in the gap region |η| < 0.1 with one precision station. In addition,
ST and CT muons in |η| < 0.1 are accepted. The medium WP selects CB and ME muons,
including gap with one precision station, while the tight WP only accepts CB and ME muons
with at least two precision stations. The efficiency of different WPs is shown in Fig. 4.15. In
this thesis, loose identification WP is selected.
Isolation
Like the approach described for prompt electrons in Section 3.2, muon isolation involves
measuring the surrounding activity to distinguish prompt muons from non-prompt ones

50

The ATLAS experiment at LHC
Table 4.4 Summary of different working point requirements for muons [96].
Isolation WP

Calorimeter and Track

Track pT requirement

PFlow_Loose
PFlow_Tight
Loose_VarRad
Tight_VarRad(pvarcone30+ 0.4ETneflow20 ) < 0.16pTTµ(pvarcone30+ 0.4ETneflow20 ) < 0.045pTTµµ
topocone20
pvarcone30< 0.15pT , ET
) < 0.3pTTµµtopocone20
pvarcone30< 0.04pT , ET
) < 0.15pTTµpT > 500 MeV
pT > 500 MeV
pT > 1 GeV
pT > 1 GeV

originating from heavy-flavor hadronic decays. In addition to the track isolation pvarcone30
andT
topoetcone20
calorimeter isolation ET
used in electrons, we introduce an additional calorimeterneflowiso20
based isolation variable, ET. This variable is defined by excluding all energy deposits
in the calorimeter that match ID tracks in the ∆R = 0.2 muon isolation cone, thereby reducing
the correlation with track-based isolation measures. Table 4.4 summarizes the different
working points for muon isolation. In this thesis, the PFlow_Loose isolation working point
is used.

4.3.4

Jets

In this analysis, jets are used to suppress SM background processes like t t¯ and overlap
removal as will be described in Sec. 4.3.5. We will discuss the reconstruction of jets, a jetvertex tagger to suppress pile-ups, and jet energy scale and resolution.
Reconstruction
Jets reconstruction [97] is performed on topo-clusters (see Sec. 4.3.2) using an anti-kT
clustering algorithm [98]. By defining the following metrics:
2p 2p
di, j = min(kT,i, kT, j )2p
di,B = kT,i.

∆2 Ri, j,R2(4.13)(4.14)

Here kT represents the transverse momentum, di,B is the distance between topo-cluster i andbeam, and di, j is the distance between topo-cluster i and j. ∆2 Ri, j corresponds to solid angle
between topo-cluster i and j and R is fixed clustering size. The parameter p = −1 refers
to anti-kT algorithm, p = 1 refers to the sequential recombination kT [99] and p = 0 refers
to the Cambridge-Achen [100] algorithm. The algorithm iteratively tries to find the closest
distance di, j and combines the two clusters if di, j < di,B , namely the cluster-cluster distance

51

4.3 Reconstruction of Physics Objects

is smaller than their cluster-beam distance. Otherwise, a jet is formed, and clusters in the jet
are removed from the pool. We use a clustering size of R = 0.4 to reconstruct jets in ATLAS.
Jet Vertex Tagger
A jet vertex tagger (JVT) based on k-nearest neighbor (KNN) is applied to suppress jets
reconstructed from pile-up. JVT is constructed by 2-D likelihood using the following two
variables:• the corrected jet vertex fraction (corrJVF):
trk-jetcorrJVF =∑l pT,l(PV0 )
trk-jet,∑n ∑l pT,l (PVn )trk-jet∑l pT,l (PV0 ) +(knpu−trk )(4.15)

trk-jetwhere ∑k pT,k (PV0 ) is the sum of pT for tracks associated with jet originated fromhard-scattering PV0 , PVn is the pile-up interaction and k scales the contribution ofpile-up.
• R pT defined as the ratio of scalar sum of track pT associated with jet from hardscattering PV0 to jet pT :trk-jet∑l pT,l (PV0 )R pT =.
(4.16)
jetpT
The contribution from the jets originating from the pile-up interaction is not negligible forlow pT jets. In this analysis, we require a JVT score > 0.11 for 20 GeV < pT < 60 GeV toreduce the pile-up jets.
Jet Energy Scale and Resolution
To account for effects like detector response and energy loss in passive material, corrections
are applied to the jet energy scale (JES) in the following steps [101]:• pile-up contributions: jet pT due to pile-up contributions is corrected bypcorr
T = pT − ρAjet − α(NPV − 1) − β µ,(4.17)

where the size of jet Ajet is determined by the relative number of ghost particles
associated with a jet after clustering and ρ is the median pT density in the y-φ plane. α

52

The ATLAS experiment at LHC

(a)

(b)

Fig. 4.16 Average truth energy response (Ereco /Etrue ) as function of (a) reconstructed η and(b) reconstructed transverse energy ET [102].
and β are the residual correction factors derived in bins of true pT and η for NPV , thenumber of reconstructed vertices, and µ is the average number of interactions per BC.
• absolute MC based calibration: anti-kT jets reconstructed from simulated dijet eventsare matched to truth jets after the pile-up corrections. The jet energy truth response(Ereco /Etrue ) is then fitted by a Gaussian function in fine bins of η and ET (seeFig. 4.16).
• global sequential calibration: a series of corrections based on calorimeter responses
are applied. The corrections are derived from 5 different variables distinguishingquark-initiated and gluon-initiated jets: fraction of jet energy deposits in the firstlayer of tile calorimeter (|η| < 1.7), fraction of jet energy deposits in the third layerof LAr calorimeter (|η| < 3.5), number of ghost-associated tracks with pT > 1 GeV(|η| < 2.5), average pT -weighted transverse distance between the jet axis and ghostassociated tracks with pT > 1 GeV (|η| < 2.5), and the number of ghost-associatedmuon track segments (|η| < 2.7).
• in situ jet calibrations: jet response is corrected by the ratio of average jet pT between
data and MC simulation in the reference processes like Z/γ+jets by balancing thehadronic recoil in an event against the pT of a calibrated Z boson or photon.
The jet energy resolution (JER) is parameterized in the functional form:
σ (pT )NS=
⊕ √ ⊕C.
pT
pT
pT(4.18)

4.3 Reconstruction of Physics Objects

53

The noise (N) contribution corresponds to electronic noise and pile-ups. The stochastic (S)contribution corresponds to the statistical fluctuations in the energy deposits. The constant(C) corresponds to a constant correction from jet energy deposits in passive materials likecryostats and solenoid coils.
Systematic uncertainty arising from JES and JER are evaluated in Chapter 8.

4.3.5

Overlap Removal

Physics objects are reconstructed independently among sub-detectors, which could lead tothe reuse of the same information. For instance, energy deposits detected in the calorimeter
may be simultaneously reconstructed as electrons, muons, and hadronic jets. To prevent
such ambiguity, ATLAS utilizes a technique called overlap removal (OR) to prioritize theassignment of physics objects when they are detected close to each other. Regarding electrons,muons, and hadronic jets, which are used in the search for prompt LJs, the standard OR
criteria are applied in the following sequence:• electron-electron OR: when two electrons share the same track, an electron with lower
pT is rejected.
• muon-electron OR: when muon and electron share the same track, the muon is rejected.
• electron-jet OR: when electron and jet are close-by with angular separation ∆R < 0.2,
jet is rejected. Otherwise, the electron is rejected if ∆R < 0.4.
• muon-jet OR: when muon and jet are close by, jet with less than three associatedtracks and with muon within ∆R < 0.2 or with ghost associated track [103] is rejected.
Otherwise, muon is rejected if ∆R < 0.4.
In this thesis, we optimize OR criteria by removing electron-electron OR to adapt to thecollimated signature of LJs decaying from γd .

Chapter 5
Prompt Dark Photon Signatures
This chapter explores the unique signatures of prompt dark photons that decay into LJs.
These LJs are highly specialized objects derived from standard reconstructed physics objects
described in Section 4.3.
Section 5.1 provides an overview of the data and simulated MC events used in thisanalysis. The kinematic properties of the LJs are presented in Section 5.2. Section 5.3
discusses the customization of physics objects, and Section 5.4 details the reconstruction ofprompt LJs for both electron and muon channels. Later in the thesis, we will focus on theelectron channel only. Section 5.5 describes the trigger strategy.

5.1

Data and Simulated Events

We have simulated two signal benchmark model MC samples and SM background MC
samples to fully exploit the search limits of the complete Run-2 data in ATLAS. They areused to optimize selection cuts, help understand the contributions from different backgroundprocesses, and interpret the search results.
Full Run-2 data√
The full dataset from Run-2 pp collisions at a center-of-mass energy of s = 13 TeV listed
in ATLAS centrally distributed GRLs (see Section. 4.1.3) is used. The data corresponds
to 140 fb−1 integrated luminosity with a 0.8% uncertainty [104], which is summarized inTable 5.1.

56

Prompt Dark Photon Signatures

Table 5.1 Full dataset in run-2 pp collisions at center-of-mass energy ofphysics analysis. The data corresponds to 140 fb−1 integrated luminosity.
Year

Data Period

Luminosity (fb−1 )

2018
2017
2016
2015

period B-Q
period B-K
periods A-Lperiods D-J

58.79
44.31
33.40
32.44

√
s = 13 TeV for

Signal MC samples
Benchmark models FRVZ and HAHM (see Sec. 3.2.3) involving both the Higgs portal andvector portal are simulated. Higgs bosons generated through gluon-gluon fusion production
mode [105] with cross-section of σ = 48.52 pb [106] for mH = 125.09 GeV. Higgs boson
production through vector boson fusion processes with a cross-section of σ = 3.78 pb is notincluded in this analysis, and we suppress it by applying jet-veto. The MG5_aMC@NLO
v2.2.3 generator [81], interfaced with the PYTHIA8 generator [83], is used for simulation of the Higgs boson to subsequent dark-sector particles, along with parton showering/hadronization processes to final products. The detector response is simulated through
GEANT4 [86] and then reconstructed and processed similarly with data.
Signal MC samples are generated with dark photon γd masses ranging from 17 MeV to
40 GeV, aiming to extend the boundaries in previous searches [4]. The decay length is set tocτ < 0.01 mm to optimize for the search for promptly decaying γd s. For the FRVZ signal
samples, the masses of fd and HLSP are selected to be small compared with the Higgs boson
but well below the threshold where γd is kinematically allowed (mHLSP + mγd = m fd ). This
allows the production of dark photons that are well-boosted and separated in the transverse
plane, creating a unique signature for our target, as will be discussed in Section 5.2. Dark
photons decay to fermions according to the branching ratios in Fig. 3.6. Table 5.2 andTable 5.3 summarize the parameters used in generating the FRVZ and HAHM samples,
respectively.
SM background MC samples
The main SM background processes of W+jets, Z+jets, t t¯, single top, multijets, γ+jets andWW , W Z, ZZ dibosons have been generated to help analyze the composition of backgrounds
entering the signal region and to refine the strategy for selection cuts. Simulation of theW+jets, Z+jets, WW, WZ, and ZZ events have been generated using S HERPA 2.2.1 [85] with
the NNPDF 3.0 NNLO [107] PDF set. Single top and t t¯ MC samples are generated using

57

5.1 Data and Simulated Events

Table 5.2 Parameters used for the MC simulation of H → 2γd + X, according to the FRVZ
benchmark model. The cross-section corresponds to BR(H → 2γd + X)= 100%. Each dataset
consists of 390000 events.
mH [GeV]
125
125
125
125
125
125
125
125
125
125
125
125
125

mγd [GeV] mHLSP [GeV]
0.017
0.03
0.06
0.1
0.24
0.4
0.9
2
6
10
15
25
40

2
2
2
2
2
2
2
2
4
6
10
10
7

mfd [GeV] σ [pb]
5
5
5
5
5
5
5
10
25
35
45
45
55

48.52
48.52
48.52
48.52
48.52
48.52
48.52
48.52
48.52
48.52
48.52
48.52
48.52

Table 5.3 Parameters used for the MC simulation of H → 2γd , according to the HAHM
benchmark model. The cross-section corresponds to BR(H → 2γd )= 100%. Each dataset
consists of 390000 events.
mH [GeV]
125
125
125
125
125
125
125
125

mγd [GeV ] σ [pb]
0.017
0.1
0.4
2
10
15
25
40

48.52
48.52
48.52
48.52
48.52
48.52
48.52
48.52

58

Prompt Dark Photon Signatures

Table 5.4 Summary of generator information for SM background processes. The generator
cross-sections are used to generate samples.
Physics process

Generator

PDF setσ Normalization

Parton shower

Tune

W (→ ℓν)+ jets
Z(→ ℓℓ)+ jetst t¯single-top
di-boson
multijetγ+ jets

S HERPA 2.2.11
S HERPA 2.2.11
P OWHEG - BOX V 2
P OWHEG - BOX V 2
S HERPA 2.2.1
P YTHIA 8
P YTHIA 8

NNPDF3.0NNLO
NNPDF3.0NNLO
CT10/CTEQ6L1
CT10/CTEQ6L1
NNPDF3.0NNLO
NNPDF2.3LO
NNPDF2.3LO

NNLO
NNLO
NNLO
NNLO
NNLO
LO
LO

S HERPAS HERPAP YTHIA 8
P YTHIA 8
S HERPAP YTHIA 8
P YTHIA 8

S HERPAS HERPAP ERUGIA 2012
P ERUGIA 2012S HERPAA14
A14P OWHEG -BOX V 2 [82] and P YTHIA 8 [108] with the P ERUGIA 2012 [109] tune for parton
showering and hadronization, and CT10/CTEQ6L1 [110] [111] PDF sets. Multijet andγ+jets samples are generated with P YTHIA 8 in different pT slices of leading parton andphotons, respectively. Like signal MC simulation, a full detector simulation is performed
using the GEANT4 [86] toolkit. The generator information is summarized in Table 5.4.

5.2

Dark Photon Kinematics

From the event topologies shown in Fig. 3.8 (b) and Fig. 3.8 (a) for the HAHM and FRVZ
models, we expect dark photons to be produced back-to-back and decay to collimated pairsof leptons, namely, the LJ signature. In this section, signal MC samples are used to study thekinematic properties of dark photons and their decay to electrons without any cuts.
Angular separation ∆φ between two γd s in both FRVZ and HAHM benchmark MC
samples is shown in Fig. 5.1. It is observed that two γd are well separated in the transverse
plane. As γd mass gets larger, around 6 GeV for the FRVZ model, ∆φ starts to get flattened.
Due to the absence of hidden particle final states in the HAHM model, two γd are more
separated in the transverse plane.
Angular separation ∆R between electron pairs decaying from γd is shown in Fig. 5.2. It isobserved that electron pairs are highly collimated, especially at low γd mass region, resulting
in the unique signature of LJs we target. Electrons separate as the γd mass increases, and weare less sensitive (more details will be given in Sec. 5.4).
Transverse momentum pT of γd , and the decay product electrons are shown in Fig. 5.3
and Fig. 5.4, respectively. It is observed that both γd and electron pT are similar among
different γd mass points, while for HAHM γd and electrons are more boosted due to theabsence of HLSP, resulting in a better acceptance and efficiency.

59

5.2 Dark Photon Kinematics

(a)

(b)

Fig. 5.1 Normalized distribution of angular separation ∆φ between two γd in the benchmark(a) FRVZ and (b) HAHM signal MC simulations.

(a)

(b)

Fig. 5.2 Normalized distribution of angular separation ∆R between two electrons decaying
from γd in the benchmark (a) FRVZ and (b) HAHM signal MC simulations.

60

Prompt Dark Photon Signatures

(a)

(b)

Fig. 5.3 Normalized distribution of transverse momentum pT of γd in the benchmark (a)FRVZ and (b) HAHM signal MC simulations.

(a)

(b)

Fig. 5.4 Normalized distribution of transverse momentum pT of electrons decaying from γdin the benchmark (a) FRVZ and (b) HAHM signal MC simulations.

61

5.3 Physics Objects in Prompt Lepton Jets

5.3

Physics Objects in Prompt Lepton Jets

The construction of LJs begins with physics objects in the standard ATLAS reconstruction.
Table 5.5 summarizes the requirements for electrons and muons to build LJs. The pT
requirements for electrons and muons are set to the lowest thresholds in the phase space
where calibrations are valid to maximize signal acceptance. Due to the hadronic fakes, events
involving electrons present a less clean signature than those involving muons. Therefore,
we use the Medium identification WP for electrons and the CB Loose identification WP formuons. The collimated signatures of LJs motivate the study of modification to the isolation
requirements. As will be discussed in Sec. 5.3.1, we apply the standard Loose_VarRad
isolation WP for electrons, while for muons, we use a modified PFlowLoose_VarRad
isolation WP.
Table 5.6 summarizes the requirements for tracks associated with electrons and muons.
We require the Loose quality (as detailed in Table 4.2), with additional criteria on track
quality d0 and z0 to further suppress non-prompt lepton fakes.
Table 5.5 Summary of requirements for muons and electrons. Electrons reconstructedin the transition region between the barrel and the endcap of the calorimeter system at
1.37 < |η| < 1.52 are excluded due to poor performance. PFlowLoose_VarRad isolation
WP is modified, as will be explained in Sec. 5.3.1.
ObjectpT [GeV]|η|

Identification

Isolation

Electron
Muon

> 4.5
>3

|η| < 1.37 or 1.52 < |η| < 2.5|η| < 2.5

MediumCB Loose

Loose_VarRad
modified PFlowLoose_VarRad

Table 5.6 Summary of requirements for muon and electron associated tracks.

5.3.1

Associated Track

pT [GeV]|η|

Quality |d0 |/σd0

Electron-track
Muon-track

> 0.5
> 0.5

< 2.5
< 2.5

Loose
Loose

<5
<3

|z0 | sin θ [mm]
< 0.5
< 0.5

Close-by Isolation Corrections

As mentioned in Sec. 4.3, the isolation is defined as the surrounding energy of a muon orelectron used to suppress non-prompt particles, typically accompanied by nearby additional
particles. While the standard isolation identifies prompt objects well in many other analyses,
the nature of LJs to build from highly collimated leptons presents a challenge. This section
introduces a correction method for isolation when dealing with prompt LJs.

62

90
12000

80
70

14000

16000

12000

14000

10000

12000

8000

10000

6000

8000

4000

6000

4000

2000

4000

2000

0

2000

10000

60
8000
50
6000

40
30

Events

14000

Eventsptvarcone30 [MeV]3

100 ×10

neflowisol20 [MeV]

Prompt Dark Photon Signatures

20
10
0
0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

∆R (µ, µ)

0

−2000
0

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50∆R (µ, µ)Fig. 5.5 The (a) ptvarcone30 and the (b) neflowisol20 distributions for muons as a functionof their truth opening angle ∆R. Muons are required to be matched to truth muons from γd ,which has a mass of mγd = 2 GeV.
For muons, the particle-flow based (PFlow) isolation WP, PFlowLoose_VarRad, iscomposed of two elements: a charged component, ptvarcone30 using raw track data, anda neutral component, neflowisol20, which relies on energy deposits in the calorimeter.
Fig. 5.5 shows the isolation distributions as a function of the truth ∆R between muons. It
is noted that while neflowisol20 has a standard isolation energy scale, ptvarcone30 has
much higher values in the tens of GeV range, which leads to failures in the isolation WP
criteria. Such large isolation is primarily due to the other muon from γd being counted as
ptvarcone30. On the other hand, in the case of calorimeter isolation, there are no EM
objects for muons. To correct the contribution from the other muon from γd , PFlow objects
associated with any other muon located near the original muon candidate from the isolation
calculation are excluded. Fig. 5.6 illustrates the ptvarcone30 distributions for both thestandard and corrected variables. As expected, the contributions in the standard variable areconsistent with the pT of the nearby muon. Fig. 5.8 (a) shows the WP efficiency before andafter applying corrections.
A similar study was also performed for the case of electrons. Fig. 5.7 shows isolation as afunction of truth ∆R between electrons decaying from γd at 0.9 GeV. It is noted that in regions
sensitive for the electron channel (mγd < 1 GeV), most electrons decaying from γd fall within
the central subtraction region (∆η × ∆φ = 0.125 × 0.175 for calorimeter based isolationand ∆η × ∆φ = 0.05 × 0.1 for track based isolation, (see Fig. 4.14) where they will not
contribute to the isolation computation. This allows the electron to pass standalone isolation
WP selections without correction. In addition, as we will see in Sec. 5.3.2, collimatedelectrons tend to merge to only one cluster, in which case no additional tracks can be
subtracted by correction. Fig. 5.8 (b) shows the isolation WP efficiency before and after

63

Sum of weights / 0.20 GeV

5.3 Physics Objects in Prompt Lepton Jets

103

Standard variable
Corrected variable
p of the other muon

mγ = 400 MeV

102

d

T

10
1
10−1
10−2
10−3 0

5

10

15

20

25

30

35

40

ptvarcone30 [GeV]

Fig. 5.6 Comparison of the standard and corrected piso,varcone30
isolation variable. pT of theTother muon in the dashed line aligns well with a nominal variable in red.
applying corrections. Since we focus on mγd < 240 MeV where there is no improvement
after corrections. As a result, we apply corrected PFlowLoose_VarRad WP to muon objects
and the standalone Loose_VarRad to electron objects to build LJs.

5.3.2

Merged EM clusters

The collimated nature of LJs presents challenges to the standard method of defining objects in
the ATLAS detector. This is especially problematic when an electron enters the reconstruction
region of another electron from the same decay. This section will discuss the responses of ID
and EM calorimeters and the unique signature of objects used to build LJs.
In the EM calorimeter, superclusters are formed from topo-clusters to build electrons(see Sec. 4.3.2). Suppose the separation angle between electron pairs from γd decay is large
enough (i.e., ∆R ≳ 0.1). In that case, they are recognized as distinct EM clusters close toeach other (expected for a high-mass γd ). However, if the electrons are very collimated, theirenergy deposits merge into one single EM cluster (low-mass γd ). From Fig. 5.9 (a), whichshows the number of reconstructed clusters from electron pairs inside LJ, the cluster merging
occurs in ∼ 90% of γd → ee decays when γd mass is lower than 6 GeV. Fig. 5.10 (a) shows
the number of EM clusters as a function of truth ∆R between electrons for FRVZ signal MC
samples for γd mass at 0.1 GeV for the merged cluster scenario, while Fig. 5.10 (b) for FRVZ
signal MC samples for γd mass at 6 GeV is an example of separate close-by clusters scenario.

64

Prompt Dark Photon Signatures

100 ×10

100 ×10

FRVZ model, H → 2 γ + X
d2500

m γ = 0.9 GeV

80

d

70
2000
60
50

1500

40
1000

30

2400

90

Events90

topoetcone20 [MeV]

3

3000

Eventsptvarcone30 [MeV]3

FRVZ model, H → 2 γ + X

2200

m γ = 0.9 GeV

2000

d

80

d

1800

70

1600
60

1400

50

1200

40

1000
800

30

600
20

500

10
0
0

20
400
10

0.05

0.1

0.15

0.2

0.25

(a)

0.3

0.35

0.4

0.45

0.5

∆R (e, e)

0

0
0

200
0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0

∆R (e, e)(b)Fig. 5.7 The (a) ptvarcone30 and the (b) topoetcone20 distributions for electrons as a functionof their truth opening angle ∆R. Electrons are required to be matched to truth electrons from
γd , which has a mass of mγd = 0.9 GeV.

(a)

(b)

Fig. 5.8 Isolation WP efficiency for (a) muon and (b) electron before and after corrections.
The corrected isolation WP is used for muons, while the standard isolation WP is used forelectrons in this thesis.

65

5.4 Prompt Lepton Jets Reconstruction

(a)

(b)

Fig. 5.9 Number of (a) EM clusters and (b) associated tracks inside LJ at different γd mass in
the FRVZ benchmark model.
Tracks, on the other hand, have a better resolution due to the high granularity of ID, andeven in the merged cluster scenario, collimated electron tracks from γd can be reconstructed
separately. In addition, GSF-refitted tracks are associated with clusters (see Sec. 4.3.1). As
shown in Fig. 5.9 (b), electrons from LJs tend to have two associated tracks. The signature of
LJ with merged cluster and two associated tracks provides a window of sensitivity to explore
low mass γd s.

5.4

Prompt Lepton Jets Reconstruction

This section will explore the reconstruction method for γd s that promptly decay into collimated pairs of leptons, referred to as prompt LJs. The LJs are constructed based on themerged EM cluster signature discussed in Section 5.3.2, using standard physics objects suchas electrons, muons, and tracks in the following procedures.
Electrons and muons are first clustered using the Cambridge-Aachen clustering algorithm[112] by selecting the highest PT seed from the pool of reconstructed electrons and muonsthat meet the requirements outlined in Table 5.5. It then searches for additional leptons withina ∆R = 0.4 radius around this seed. Each lepton contributes to updating the four-momentum
vector of the LJ candidate and is subsequently removed from the pool while the updated LJ
stays in. This iterative process continues until no leptons remain in the pool. There is no
upper limit on the number of leptons in LJ, allowing the object to be sensitive to scenarioswith more γd s radiated. Additionally, for each LJ candidate, tracks that meet the requirementssummarized in Table 5.6 are also added. LJs are classified into two exclusive categories, as
illustrated in Fig. 5.11, the following:

66

4frvz model, H → 2 γ + X
dm γ = 0.1 GeV
d

2000
3.5
3

5
22
4.5
4

frvz model, H → 2 γ + X
dm γ = 6 GeV

20

d

18

3.5

16

3

14

1500
2.5

Events2500

Number of EM clusters5
4.5

EventsNumber of EM clusters

Prompt Dark Photon Signatures

12

2.5

10
2

1000

1.5

8
1.5

1

500

0.5
0
0

2
6

1

4

0.5
0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

(a)

0.45
0.5
∆R (e, e)

0

0
0

2
0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45
0.5
∆R (e, e)0(b)Fig. 5.10 Number of EM clusters as a function of truth ∆R between electrons decaying from
FRVZ γd with the mass assumption of (a) 0.1 GeV and (b) 6 GeV. The peak at 1 cluster for
0.1 GeV corresponds to the merged cluster scenario, while the peak at 2 clusters for 6 GeV
corresponds to the separated close-by clusters scenario.
• Electronic Lepton-Jet (eLJ): If at least one electron, at least two associated tracks andno muons are found inside the cone.
• Muonic Lepton-Jet (µLJ): If at least two muons and no electrons are found inside thecone.

(a) electronic LJ(b) muonic LJ

Fig. 5.11 Illustration of reconstructed (a) eLJ, and (b) µLJ.
From the event topology of the FRVZ and HAHM benchmark models, two LJs areproduced back-to-back in the transverse plane. In this analysis, we select two objects ofinterest: leading eLJ for the eLJ with largest pT , and furthest eLJ for the eLJ with largest

5.5 Triggers

67

angular separation ∆φ with leading eLJ in the transverse plane. Based on this configuration,
we define three distinct search channels:• eLJ-eLJ Electron Channel: If both the leading and the furthest LJs are both eLJs.
• µLJ-µLJ Muon Channel: If both the leading and the furthest LJs are both µLJs.
• eLJ-µLJ Mixed Channel: If the leading and the furthest LJs are eLJs and µLJs each.
In this thesis, we will focus on the search for dark photons decaying into electron final
states using the electron channel. Results from the muon and mixed channel are shown in
Chapter 9.

5.4.1

eLJ Reconstruction Efficiency

Reconstruction efficiency of eLJ is also shown as function of truth η, pT , and ∆R between
electrons decaying from γd for the FRVZ and HAHM benchmark model in Fig. 5.12 (b)and Fig. 5.13 (b). The drop in efficiency at |η| = 1.5 in Fig. 5.12 (a) and Fig. 5.13 (a)corresponds to transition regions from calorimeter barrel to end-cap. The eLJ reconstruction
efficiencies as functions of ∆R between electrons from γd decays is shown in Fig. 5.12 (c)and Fig. 5.13 (c). In general, eLJ reconstruction efficiency increases with larger pT and drops
with larger ∆R between electrons for mγd < 2 GeV. This results in higher efficiency for the
HAHM model compared with the FRVZ model.
The eLJ compositions introduce an additional complication. We investigate the reconstruction efficiency of eLJs composed of either a single reconstructed electron (forming amerged cluster) or two separate reconstructed electrons (forming distinct clusters). As shownin Fig. 5.14, the efficiency distribution is relatively flat in η for eLJs composed of a single
electron. In contrast, eLJ consisting of two electrons has higher efficiency for |η| < 1.5. Thisis due to the better calorimeter resolution in the barrel region, which allows close-by clusters
to be reconstructed separately. Fig. 5.15 and Fig. 5.16 show the reconstruction efficiency asfunctions of γd pT and ∆R between electrons from γd decays at different mass points.

5.5

Triggers

A combination of single and multi-electron triggers are used to trigger eLJs. This section
will discuss the details of trigger strategies and efficiencies.

68

Prompt Dark Photon Signatures

(a)

(b)

(c)

Fig. 5.12 eLJ reconstruction efficiency as function of (a) truth η of γd , (b) truth pT of γd , and(c) truth ∆R between electrons decaying from γd at different γd mass in the FRVZ benchmark
model.

5.5.1

Trigger Choice

To maximize signal efficiency, we select a combination of the lowest un-prescaled singleelectron and di-electron triggers for different data-taking periods, as listed in Table 5.7. The
trigger names follow the conventions explained in Sec. 4.2.7.

5.5.2

Trigger Efficiency

Fig. 5.17 shows the trigger efficiency of single-electron, multi-electron, and combination of
any triggers as functions of pT of 17 MeV γd in the FRVZ benchmark model. It is noticed
that even with the tighter isolation requirement and higher pT threshold, single electron
triggers exhibit better trigger efficiency. With the complementary di-electron triggers, overall
efficiency is maximized. Trigger efficiencies of single-electron and di-electron triggers fordifferent mass points are shown in Fig. 5.18 and Fig. 5.19, respectively. Here, events are
pre-selected, requiring both γd to decay into a pair of electrons.

69

5.5 Triggers

(a)

(b)

(c)

Fig. 5.13 eLJ reconstruction efficiency as function of (a) truth η of γd , (b) truth pT of γd ,and (c) truth ∆R between electrons decaying from γd at different γd mass in the HAHM
benchmark model.

(a)

(b)

Fig. 5.14 Reconstruction efficiency in the category of (a) 1 electron and (b) 2 electrons insideeLJ as a function of truth η of γd at different γd mass in the FRVZ benchmark model.
The overall trigger efficiency for the FRVZ benchmark model is summarized in Table 5.10.
The drop in electron trigger efficiency around 2 GeV is due to the transition from mergedclusters to separate clusters scenario, where the standard object reconstruction becomesineffective, as indicated in Fig. 5.9 (a).

70

Prompt Dark Photon Signatures

(a)

(b)

Fig. 5.15 Reconstruction efficiency in the category of (a) 1 electron and (b) 2 electrons insideeLJ as a function of truth pT of γd at different γd mass in the FRVZ benchmark model.

(a)

(b)

Fig. 5.16 Reconstruction efficiency in the category of (a) 1 electron and (b) 2 electrons insideeLJ as a function of truth ∆R between electrons decaying from γd at different γd mass in the
FRVZ benchmark model.
Similarly, the trigger efficiency for the HAHM benchmark model is summarized inTable 5.11. As expected, the HAHM model generally shows higher efficiency due to themore significant boost of γd from the event topology. Note that the drop in electron trigger
efficiency at the transition mass point of mγd = 2 GeV also appears in the HAHM benchmark
model.
The trigger efficiency in each data-taking year is shown in Table 5.8 and Table 5.9. Thesetables show the impact of varying pT thresholds across different years. For each event in theMC simulations, we apply a scale factor, calibrated from data using Z → ee events, based on
the combination of triggers outlined in Table. 5.7.

71

5.5 Triggers

Table 5.7 List electron triggers used in the eLJ-eLJ channel for the corresponding data-taking
periods.
Type

Data-taking periods
2015Single-electron2016 - 2018

Di-electron

Trigger
HLT_e24_lhmedium_L1EM20VH
HLT_e60_lhmedium
HLT_e120_lhloose
HLT_e26_lhtight_nod0_ivarloose
HLT_e60_lhmedium_nod0
HLT_e140_lhloose_nod0

2015
HLT_2e12_lhvloose_L12EM10VH
2016
HLT_2e17_lhvloose_nod0
2017 (only B5-B8)
HLT_2e24_lhvloose_nod0
2017 (except B5-B8) HLT_2e17_lhvloose_nod0_L12EM15VHI
2018
HLT_2e17_lhvloose_nod0_L12EM15VHI

Fig. 5.17 Trigger efficiencies for γd at 17 MeV in the FRVZ signal model, shown for singleelectron, multi-electron, and logical OR of any triggers, shown as a function of truth γd pT.
Table 5.8 Table of electron trigger efficiency for FRVZ benchmark model in different datataking years.
FRVZ γd mass 17 MeV

30 MeV 60 MeV 0.1 GeV

0.24 GeV

0.4 GeV 0.9 GeV 2.0 GeV

6.0 GeV

2015

41%

41%

39%

36%

24%

18%

17%

31%

53%

2016

26%

25%

25%

22%

14%

10%

8.4%

13%

33%

2017

23%

22%

22%

19%

14%

10%

7.4%

8.1%

26%

2018

24%

23%

23%

20%

14%

10%

7.3%

8.4%

26%

72

Prompt Dark Photon Signatures

(a)

(b)

Fig. 5.18 Single-electron trigger efficiencies for the FRVZ signal model, shown for different
mass points and as a function of the γd (a) pT and (b) η.

(a)

(b)

Fig. 5.19 Multi-electron trigger efficiencies for the FRVZ signal model, shown for different
mass points and as a function of the γd (a) pT and (b) η.
Table 5.9 Table of electron trigger efficiency for HAHM benchmark model in different
data-taking years.
HAHM γd mass 17 MeV 0.1 GeV 0.4 GeV 2 GeV 10 GeV 15 GeV

25 GeV40 GeV

2015

80%

75%

46%

36%

84%

85%

85%

91%

2016

72%

68%

37%

20%

78%

80%

81%

84%

2017

69%

66%

41%

13%

72%

76%

78%

81%

2018

69%

66%

40%

13%

73%

77%

80%

83%

Table 5.10 Table of electron trigger efficiency for FRVZ benchmark model at different γdmass points.
FRVZ γd mass

17 MeV

30 MeV

60 MeV

0.1 GeV

0.24 GeV

0.4 GeV 0.9 GeV

2.0 GeV

6.0 GeVSingle-electron

18%

18%

16%

16%

12%

9.3%

6.4%

7.7%

22%

Di-electron

12%

11%

11%

8.4%

4.1%

2.5%

1.7%

3.0%

11%

Combined

25%

24%

24%

21%

15%

11%

7.5%

9.5%

26%

73

5.5 Triggers

Table 5.11 Table of electron trigger efficiency for HAHM benchmark model at different γdmass points.
HAHM γd mass 17 MeV 0.1 GeV

0.4 GeV 2 GeV 10 GeV 15 GeV

25 GeV 40 GeV

Single-electron

58%

56%

34%

12%

67%

72%

73%

75%

Di-electron

52%

46%

18%

5%

56%

63%

66%

69%

Combined

70%

67%

39%

15%

74%

78%

80%

83%

5.5.3

Trigger-matching

To ensure that the electrons firing the triggers are the same ones building the eLJs, we
implement additional trigger-matching criteria as follows:
1. Offline reconstructed electron has pT above HLT threshold of ≥ 1 GeV.
2. ∆R < 0.2 between offline reconstructed electron and HLT trigger objects.
In addition, HLT objects are required to be matched to offline electrons within eLJ. In
the event fired by di-electron triggers, two HLT objects are needed to match electrons fromdifferent eLJs, while single-electron triggers require an HLT object to match electrons fromN
matchedany eLJ. Fig. 5.20 shows the trigger matching efficiency defined as ε = trigger
for theNtriggered
FRVZ and HAHM models, where we see > 85% efficiency at different γd mass points.

Fig. 5.20 Trigger matching efficiencies for the FRVZ signal model, shown for different masspoints.

Chapter 6
Event Selection
This chapter will discuss the event selections in the search for promptly decaying dark
photons conducted through the eLJ-eLJ channel. MC simulations of the signal and SM
background are used to optimize the selections and understand the background compositions.
Sec. 6.1 defines the event selections for the signal region. Sec. 6.2 describes the background processes and presents the yields for both signal and background events. Sec. 6.3
defines the control region in data and compares it with MC simulation for the variables usedin event selections.

6.1

Signal Region Definition

Based on the eLJ signatures of back-to-back γd s, and collimated pairs of electrons from γddecays as described in Sec. 3.2.3, we apply the following pre-selections to each processed
event:• the event must be listed in the good run list where all sub-detectors were in gooddata-taking conditions (see Sec. 4.1.3).
• the presence of a good primary vertex is required (see Sec. 4.3.1).
• at least two eLJs must be reconstructed (see Sec. 5.4).
• the event must be triggered by logical OR of single-electron and di-electron triggers
and matched (see Sec. 5.5).
In each event, as mentioned in Sec. 5.4, the analysis selects two objects of interest: leadingeLJ for the eLJ with the largest pT , and furthest eLJ for the eLJ with most significant angularseparation ∆φ in the transverse plane with respect to leading eLJ.

76

Event Selection

To suppress the dominant SM background events due to the random overlap of electrons
with additional tracks and reduce subdominant SM background events to a negligible level,
the following sets of requirements are applied:• eLJ selections applied for both eLJs:– reconstructed with exactly one EM cluster;– the leading track has pT > 5 GeV;
– |η| < 1.37;– sum of charge for leading two tracks qeLJ = 0.
• event selections applied for each event:lead − φ furthest | > 2.5;
– |φeLJ
eLJ– combined invariant mass meLJ-eLJ must satisfy the Z-mass veto, hence meLJ-eLJ ∈/[80, 100] GeV;
|mlead −mfurthest|eLJ– mass imbalance mimb = meLJ
lead +mfurthest < 0.8, where meLJ is built from leading
eLJ
eLJ
two tracks in eLJ with electron mass hypothesis.
• other selection:– no jet with pT > 40 GeV.
The reason why these cuts are required is explained below. The definition of eLJ includes
both scenarios where merged and separate clusters are found within the cone. Since theeLJ-eLJ channel is particularly relevant for low-mass γd below 2mµ ∼ 0.21 GeV, whichlies within the merged cluster regime as shown in Figs. 5.2 and 5.9, we require exactly one
electron to help simplify the event compositions in the SM background while retaining morethan 90% of the signal yield (see Sec. 5.3.2).
The two eLJs are expected to be back-to-back from the signal event topology, while thisis not the case for generic SM background processes. As we can see from Fig. 6.1 (a), signal
eLJs are more separated in ∆φ .
Two electron tracks from neutral particle decays are expected to possess opposite
signed charges, while random tracks overlapping electrons can have random signed charges.
Fig. 6.1 (b) shows the qeLJ for signal and background processes.
Fig 6.2 (a) shows the leading track pT distributions for signal and background. pT > 5GeV
is selected to optimize the signal-to-background ratio.

77

tt
top

10

w
0.1 GeV γ FRVZdNormalized Events

Normalized Events

6.1 Signal Region Definition

0.1 GeV γ HAHM

102

tt
top
w

10

z
qcd
0.1 GeV γ FRVZ

1d

0.1 GeV γ HAHM

d

d

1

10−1
10−2

10−1

10−3
10−2

10−4
0

0.5

1

1.5

2

2.5

−4

3
|∆Φ| (eLJ, eLJ)

−3

−2

−1

0

1

2

3

4

q

eLJ

(a)

(b)

10

tt
top
w

1

z
qcd
0.1 GeV γ FRVZ
d

0.1 GeV γ HAHM

10−1

d

Normalized Events

Normalized Events

Fig. 6.1 Distributions at pre-selections level of (a) |∆φ | between two eLJs, and (b) qeLJ for
SM processes, FRVZ and HAHM signal with γd = 0.1 GeV.

10

top
w

1

0.1 GeV γ FRVZ

10−2

10−3

10−3

10−4

10−4
10

20

30

40

50

60
70
80
Leading track p in eLJ [GeV]

z
qcd
d

0.1 GeV γ HAHM

10−1

10−2

0

tt

d

−3

−2

−1

0

T

(a)

1

2

3
eLJ η

(b)

Fig. 6.2 Distributions at pre-selections level of (a) leading track pT , and (b) η for SM
processes, FRVZ and HAHM signal with γd = 0.1 GeV.
From Fig 6.2 (b), it is observed that SM processes are dominant in the high-η region,
whereas signal events are more frequently found in the low-η region. This is due to thehigher level of jet backgrounds in the end-cap region (|η| > 1.5), which increases the chanceof mis-associating a random jet with an electron, thereby faking an eLJ.
The invariant mass of eLJ can be reconstructed from the leading two associated tracks withelectron mass hypothesis. Fig. 6.3 shows the reconstructed mass for eLJ in both signal andSM background processes. Signal eLJ peaks at the corresponding γd mass, while backgroundeLJ exhibits a flatter kinematic distribution. Consequently, invariant mass imbalance provides
discrimination over SM processes, as shown in Fig. 6.4 (a).
In addition, it is observed that prompt electrons from Z boson decays can sometimes
be misidentified as two distinct eLJs in the presence of additional tracks. This process canEvent Selection

0.1
0.017 GeV γ FRVZ
d0.030 GeV γ FRVZ
d
0.060 GeV γ FRVZ
d
0.1 GeV γ FRVZ
d0.24 GeV γ FRVZd
SM backgrounds

0.09
0.08
0.07

Normalized events

Normalized events

78

0.1

0.08
0.07

0.06

0.06

0.05

0.05

0.04

0.04

0.03

0.03

0.02

0.02

0.01

0.01

0

20

40

60

80

100

120

140
160
180
200
eLJ invariant mass [MeV]

0.017 GeV γ FRVZ
d0.030 GeV γ FRVZ
d
0.060 GeV γ FRVZ
d
0.1 GeV γ FRVZ
d0.24 GeV γ FRVZd
SM backgrounds

0.09

0

100

200

300

400

(a)

500

600

700
800
900
1000
eLJ invariant mass [MeV]

(b)

10

tt
top
w

1

z
qcd
0.1 GeV γ FRVZ

Normalized Events

Normalized Events

Fig. 6.3 Distributions at pre-selections level of eLJ invariant mass in (a) [0, 200 MeV], and(b) [0, 1000 MeV] range for SM processes, FRVZ and HAHM signal with different γd masspoints.

102
tt
top

10

w
z
qcd

1

0.1 GeV γ FRVZdd

0.1 GeV γ HAHM

10−1

0.1 GeV γ HAHM

d

d

10−1
10−2

10−2

10−3

10−3

10−4

10−4
×10

3

0

0.1

0.2

0.3

0.4

0.5

(a)

0.6

0.7

0.8

0.9
1
mimb (eLJ, eLJ)

0

20

40

60

80

100

120
140
m (eLJ, eLJ) [MeV](b)

Fig. 6.4 Distributions at pre-selections level of (a) eLJ invariant mass imbalance and (b)eLJ-eLJ invariant mass for SM processes, FRVZ and HAHM signal with γd = 0.1 GeV.

79

Normalized events

6.2 Expected Signal yields and Background processes

0.017 GeV γ FRVZ
d0.030 GeV γ FRVZ
d
0.060 GeV γ FRVZ
d
0.1 GeV γ FRVZ
d0.24 GeV γ FRVZ
dttbar backgrounds

1.4
1.2
1
0.8
0.6
0.4
0.2

0

1

2

3

4

5

6

7

8

9
10
Jets multiplicity

Fig. 6.5 Distributions at pre-selections level of the number of jets with pT > 40 GeV for t t¯processes and FRVZ signal with different γd mass points.
be suppressed by rejecting events where the invariant mass of the two eLJs is around the Zboson mass, as illustrated in Fig. 6.4 (b).
Jet multiplicity is used as a discriminating variable to reduce the impact of t t¯ processes.
According to the number distribution of jets with pT > 40 GeV shown in Fig. 6.5, the jet
multiplicity requirement effectively suppresses t t¯ events by a factor of 10 while the signal
events are accepted with a rate more than 80%.

6.2

Expected Signal yields and Background processes

Table. 6.1 and Table. 6.2 present the number of events remaining after each selection step for
the FRVZ and HAHM benchmark signal models, respectively, as described in the previous
section. The MC events are scaled to 140 fb−1 , with the signal MC events assuming
σ = σggF and BR(H → 2γd + X = 0.5%). The event selections are optimized for collimatedeLJ signatures, resulting in higher efficiency at low γd masses. Based on the signal yields
obtained after event selections, we focus on γd mass less than 0.24 GeV for the FRVZ modeland 0.4 GeV for the HAHM model.
To understand the misidentification of SM processes, as illustrated in Fig. 6.6, we firstcategorize fake eLJs into the following types:• electron-fake eLJ: when a real electron, promptly decaying from a hard-scattering
event (e.g., from W or Z bosons), overlaps with additional tracks that are occasionally80

Event Selection

(a)

(b)

(c)

Fig. 6.6 Illustration of (a) electron-fake eLJ, (b) jet-fake eLJ, and (c) photon conversions eLJ.
mis-associated with the electron, a fake eLJ can be formed from the real electron. Here,the additional tracks could come from EM showering or random jets.
• jet-fake eLJ: clusters and multiple tracks induced from jets get reconstructed as fakeeLJ.
• photon conversions eLJ: photons get converted internally or within materials anddecay to collimated pairs of electrons to form fake eLJ.
SM processes generate fake eLJ-eLJ events using two such fake eLJs. The specifics are
as follows: t t¯, single-top, and W +jets events from one electron-fake eLJ and one jet-fake eLJ;
Z+jets events from two electron-fake eLJs; multijet events from two jet-fake eLJs; γ+jets
events from one photon conversion eLJ and one jet-fake eLJ.
Table 6.3 presents the number of events from SM process simulations for t t¯, single-top,
Z+jets, W +jets. Table 6.4 shows the number of multijet events, where some MC events are
scaled to 106 due to large cross-sections at low pT slices. To ensure the effective suppressionof multijet processes, we perform additional checks on the event selections. This involves
relaxing some selection criteria to increase the statistical sample size. Table 6.5 shows thenumber of events for low pT slices of multijet processes without applying identification
or isolation selections on the electrons used to construct eLJs. This shows an additional
suppression factor of 105 beyond the identification and isolation requirements. Therefore,
multijet processes are effectively suppressed by our event selections. Other dibosons, γ+jets,
and Zγ processes are suppressed to be less than 10% of remaining backgrounds based on
MC simulations, mostly due to medium electron identification and the jet veto requirement.
The remaining background is dominated by Z+jets, where both eLJs are electron-fake eLJs
originating from Z boson decays. The actual number of background events entering the SR isestimated using data only as detailed in Chapter 7. The contribution from other processes isaccounted for by systematic uncertainties obtained from validation regions in the backgroundestimation method.

81

6.3 Checks of Selection Variables

Table 6.1 Signal events remaining after each cut applied in the eLJ-eLJ channel. Eventsare generated according to the FRVZ model and are normalized assuming a branching ratio
B(H → 2γd ) = 0.5%, with L = 140 fb−1 and σ = σggF .
mγd [GeV]

0.017

No cut2 eLJsTrigger Matched
1 electron in eLJ
Leading track pT > 5 GeV
eLJ |η| < 1.37
qeLJ = 0∆Φ(eLJ, eLJ) > 2.5
Z mass veto
meLJ imbalance < 0.8
No jet with pt > 40 GeV

0.03

0.06

33500 ± 70 33500 ± 70 33500 ± 70
962 ± 11774 ± 9.9567 ± 8.4
833 ± 10654 ± 9.0
485 ± 7.8753 ± 9.6583 ± 8.5432 ± 7.3753 ± 9.6583 ± 8.5432 ± 7.3
481 ± 7.7357 ± 6.7
265 ± 5.8480 ± 7.7357 ± 6.7
265 ± 5.8
250 ± 5.5185 ± 4.8140 ± 4.2
208 ± 5.0
156 ± 4.4116 ± 3.8203 ± 5.0
154 ± 4.4
115 ± 3.8176 ± 4.6132 ± 4.1
100 ± 3.6

0.1

0.24

33500 ± 70
416 ± 7.2
366 ± 6.7324 ± 6.3
324 ± 6.3
182 ± 4.7
182 ± 4.7
106 ± 3.6
91 ± 3.3
90 ± 3.3
79 ± 3.1

12500 ± 40
107 ± 3.6
101 ± 3.6
96 ± 3.4
96 ± 3.4
59 ± 2.759 ± 2.7
28 ± 1.8
23 ± 1.7
23 ± 1.7
20 ± 1.5

0.4

0.9

2

6600 ± 30 5400 ± 30
27 ± 1.8
4.3 ± 0.71
27 ± 1.8
4.3 ± 0.71
26 ± 1.8
4.2 ± 0.70
26 ± 1.8
4.2 ± 0.70
17 ± 1.5
2.7 ± 0.57
17 ± 1.5
2.7 ± 0.57
7.2 ± 0.94 1.4 ± 0.41
4.8 ± 0.76 1.1 ± 0.36
4.6 ± 0.75 0.88 ± 0.32
4.4 ± 0.73 0.73 ± 0.28

65400 ± 303200 ± 20
0.60 ± 0.25 6.7 ± 0.86
0.60 ± 0.25 6.5 ± 0.85
0.60 ± 0.25 0.23 ± 0.17
0.60 ± 0.25 0.23 ± 0.17
0.19 ± 0.14 0.11 ± 0.11
0.19 ± 0.14 0.11 ± 0.11
0±0
0±0
0±0
0±0
0±0
0±0
0±0
0±0

Table 6.2 Signal events yield after each selection applied in the eLJ-eLJ channel. Events are
generated according to the HAHM model and are normalized assuming a branching ratio
B(H → 2γd ) = 0.5%, with L = 140 fb−1 and σ = σggF .
mγd [GeV]

0.017

No cut2 eLJsTrigger Matched
1 electron in eLJ
Leading track pT > 5 GeV
eLJ |η| < 1.37
qeLJ = 0∆Φ(eLJ, eLJ) > 2.5
Z mass veto
meLJ imbalance < 0.8
No jet with pt > 40 GeV

0.1

0.4

33500 ± 70 33500 ± 70 6600 ± 304200 ± 23 1600 ± 14 240 ± 5.54200 ± 23 1600 ± 14 230 ± 5.53900 ± 22 1500 ± 14 230 ± 5.43900 ± 22 1500 ± 14 230 ± 5.4
2600 ± 18
770 ± 9.9 130 ± 4.2
2600 ± 18
770 ± 9.9 130 ± 4.2
1600 ± 15
460 ± 7.6
65 ± 2.91600 ± 14
420 ± 7.3
62 ± 2.8
1500 ± 14
420 ± 7.3
62 ± 2.81300 ± 13
360 ± 6.8
52 ± 2.5

2

10

15

5500 ± 30 3500 ± 20
4.3 ± 0.70
115 ± 3.7
4.3 ± 0.70
114 ± 3.7
4.2 ± 0.70 2.3 ± 0.50
4.2 ± 0.70
2.3 ± 0.50
2.9 ± 0.57 0.25 ± 0.18
2.9 ± 0.57 0.12 ± 0.12
0.56 ± 0.26
0±00.56 ± 0.26
0±00.56 ± 0.26
0±00.56 ± 0.26
0±0253400 ± 203300 ± 20
24 ± 1.717 ± 1.4
23 ± 1.7
16 ± 1.4
8.3 ± 1.0
10 ± 1.1
8.3 ± 1.0
10 ± 1.1
1.3 ± 0.38
1.4 ± 0.43
0.88 ± 0.32
1.3 ± 0.41
0.18 ± 0.14
0.42 ± 0.21
0.062 ± 0.062 0.19 ± 0.13
0.062 ± 0.062 0.19 ± 0.13
0.062 ± 0.062 0.17 ± 0.13

Table 6.3 Events yield after each selection applied in the eLJ-eLJ channel, for different MC
background samples and full Run-2 data. Events are normalized to L = 140 fb−1 .

No cut2 eLJsTrigger Matched
1 electron in eLJ
Leading track pT > 5 GeV
eLJ |η| < 1.37
qeLJ = 0∆Φ(eLJ, eLJ) > 2.5
Z mass veto
meLJ imbalance < 0.8
No jet with pt > 40 GeV

6.3

t t¯

single-top

Z+jetsW +jetsData

1.3 × 108 ± 2400
1550 ± 161390 ± 151380 ± 151380 ± 15369 ± 7.6
256 ± 6.3
90 ± 3.7
81 ± 3.564 ± 3.1
6.2 ± 0.96

4.7 × 105 ± 71
241 ± 5.9239 ± 5.8
238 ± 5.8
238 ± 5.852 ± 2.6
36 ± 2.2
13 ± 1.4
12 ± 1.3
11 ± 1.2
2.1 ± 0.53

1.3 × 109 ± 27000
130360 ± 760
129470 ± 750
129140 ± 750
129060 ± 750
12650 ± 240
8370 ± 180
6600 ± 170
1222 ± 73
1038 ± 67
936 ± 66

9.1 × 109 ± 130000
1164 ± 1001110 ± 931111 ± 931110 ± 93
147 ± 36
119 ± 35
29 ± 7.2
29 ± 7.0
26 ± 6.9
19 ± 6.6/
123043121746121298121239
17960
12866
9446
2452
1978
1704

Checks of Selection Variables

To verify and compare the shapes of event selection variables, we define a control region tocompare MC simulations of SM background with data. The dominant background process

82

Event Selection

Table 6.4 Multijet events remaining after each cut are applied in the eLJ-eLJ channel in
different pT slices. Events are normalized to L = 140 fb−1 . Large events scales are due tolarge cross sections at low jet pT slices.
multijet slices
jet pT [GeV ]No cut2 eLJsTrigger Matched
1 electron in eLJ
Leading track pT > 5 GeV
eLJ |η| < 1.37
qeLJ = 0∆Φ(eLJ, eLJ) > 2.5
Z mass veto
meLJ imbalance < 0.8
No jet with pt > 40 GeV

Slice 0[0, 20]

Slice 1
[20, 60]

Slice 2[60, 160]

Slice 3[160, 400]

Slice 4[400, 800]

Slice 5[800, 1300]

Slice 6[1300, 1800]

1016 ± 5 × 1011
0 ± 106
0 ± 106
0 ± 106
0 ± 106
0 ± 106
0 ± 106
0 ± 106
0 ± 106
0 ± 106
0 ± 106

3 × 1014 ± 1010
0 ± 106
0 ± 106
0 ± 106
0 ± 106
0 ± 106
0 ± 106
0 ± 106
0 ± 106
0 ± 106
0 ± 106

3 × 1012 ± 3 × 108
11000 ± 7200
1100 ± 1100
1100 ± 1100
1100 ± 1100
0 ± 11000 ± 11000 ± 11000 ± 11000 ± 11000 ± 1100

4 × 1010 ± 106
560 ± 210
300 ± 150
300 ± 150
300 ± 150
90 ± 6390 ± 63
0 ± 450 ± 450 ± 450 ± 45

4 × 108 ± 105
110 ± 1285 ± 1184 ± 1184 ± 1141 ± 7.3
35 ± 6.8
17 ± 4.5
17 ± 4.5
14 ± 4.3
3.8 ± 2.0

9 × 106 ± 400
17 ± 1.1
12 ± 0.89
12 ± 0.89
12 ± 0.89
8.0 ± 0.75
5.4 ± 0.61
4.0 ± 0.50
4.0 ± 0.50
3.4 ± 0.46
0.84 ± 0.21

3 × 105 ± 40
2.2 ± 0.17
1.5 ± 0.15
1.5 ± 0.15
1.5 ± 0.15
1.4 ± 0.15
0.80 ± 0.11
0.67 ± 0.11
0.67 ± 0.11
0.58 ± 0.10
0.082 ± 0.025

Table 6.5 Multijet events remaining after each cut are applied in the eLJ-eLJ channel without
applying identification or isolation selections on the electrons used to construct eLJs. The
suppression factor of these event selections is estimated to be 105 . Events are normalized to
L = 140 fb−1 .
multijet slices
jet pT [GeV ]No cut2 eLJs (medium ID and loose isolation)
2 eLJs (no ID or isolation)
Trigger Matched
1 electron in eLJ
Leading track pT > 5 GeV
eLJ |η| < 1.37
qeLJ = 0∆Φ(eLJ, eLJ) > 2.5
Z mass veto
meLJ imbalance < 0.8
No jet with pt > 40 GeV

Slice 0[0, 20]

Slice 1
[20, 60]

Slice 2[60, 160]

1016 ± 5 × 1011
0 ± 106

3 × 1014 ± 1010
0 ± 106

3 × 1012 ± 3 × 108
11000 ± 7200

1.97 × 1013 ± 2.22 × 1010
2.58 × 109 ± 2.39 × 108
1.67 × 109 ± 1.95 × 108
1.67 × 109 ± 1.95 × 108
2.32 × 108 ± 6.90 × 107
1.28 × 108 ± 4.78 × 107
1.28 × 108 ± 4.78 × 107
7.10 × 107 ± 3.82 × 107
7.10 × 107 ± 3.82 × 107
7.10 × 107 ± 3.82 × 107

3.63 × 1011 ± 4.32 × 108
5.12 × 107 ± 5.01 × 106
3.09 × 107 ± 4.05 × 106
3.09 × 107 ± 4.05 × 106
1.11 × 107 ± 2.49 × 106
8.45 × 106 ± 2.30 × 106
8.45 × 106 ± 2.30 × 106
4.60 × 106 ± 1.46 × 106
3.01 × 106 ± 1.16 × 106
3.01 × 106 ± 1.16 × 106

3.86 × 1011 ± 1.50 × 108
4.73 × 107 ± 1.45 × 106
2.42 × 107 ± 1.12 × 106
2.41 × 107 ± 1.12 × 106
5.97 × 106 ± 4.38 × 105
4.46 × 106 ± 3.92 × 105
3.63 × 106 ± 3.80 × 105
3.04 × 106 ± 3.58 × 105
2.57 × 106 ± 3.44 × 105
2.38 × 106 ± 3.35 × 105

involves additional tracks overlapping with prompt electrons decaying from Z bosons. Since
the charge of these extra tracks is random relative to the electron, we can define a control
region by requiring |qeLJ | > 0. This CR should, in principle, contain the same backgroundprocesses as the SR but with negligible signal events (see Fig. 6.1 (b)).
Additionally, a scale factor is applied to the background MC simulations in the CR since
our focus is on comparing the shapes of the variables rather than their normalization. The
scale factor, determined to be 0.76, is derived from the ratio of data to MC simulations byapplying the pre-selections defined in Sec. 6.1 and requiring |qeLJ | > 0.
Fig. 6.7 and Fig. 6.8 present the comparisons between data and MC simulations for the
event topology variables of the leading and furthest eLJs. The reasonable agreement between
data and MC simulations validates our understanding of background compositions. Fig. 6.9

83

tt
qcd

105

top
data

w

Events

106

z

106

104

103

103

102

102

10

10

1

1

2

eLJ-eLJ invariant mass [MeV]

1.5
1
0.5

tt
qcd

105

104

Data / MC

Data / MCEvents

6.3 Checks of Selection Variables

top
data

w

2

z

|∆ Φ | (eLJ, eLJ)

1.5
1
0.5

3

0

0

20

40

60

80

100

120

140

×10

0

0

0.5

1

1.5

(a)

2

2.5

3

∆ φ between eLJs

Invariant mass of eLJ-eLJ [MeV](b)

Fig. 6.7 MC simulation to data comparisons for (a) eLJ-eLJ invariant mass, and (b) ∆φ
between eLJs. Here, MC simulations are scaled to the observed number of events in the CR
requiring pre-selections and |qeLJ | > 0.
shows the kinematic variables of leading track pT and γd η. In this case, the MC simulationshows some deviations from the data. These mismodelings motivate us to use data rather
than MC simulations to estimate the number of events entering the SR. In Chapter 7, we will
introduce the fully data-driven background estimation approach used in this analysis.

Event Selection

106

tt
qcd

5

10

top
data

w

EventsEvents

84

z

104

103

103

2

10

102

10

10

top
data

w

z

mimb (eLJ, eLJ)

1.5
1Data / MC

1

2

0.5
0

tt
qcd

105

104

1

Data / MC

1062

Sum of track charge inside eLJ

1.5
1
0.5

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0

1

−4

−3

−2

−1

0

1

2

3

4

q

eLJ mass imbalance

eLJ

(a)

(b)

EventsEventsFig. 6.8 MC simulation to data comparisons for (a) eLJ-eLJ invariant mass, and (b) ∆φ
between eLJs. Here, MC simulations are scaled to the observed number of events in the CR
requiring pre-selections and |qeLJ | > 0.

107

tt
qcd

6

10

top
data

w

z

106

tt
qcd

105

top
data

w

z

5

10

104
104
103
103
102
102
10

10

1

2

η of eLJ

1.5
1
0.5
0

Data / MC

Data / MC12

η of eLJ

1.5
1
0.5

0

10

20

30

40

50

60

70

80

0

−3

−2

−1

0

T

(a)

1

2

3

eLJ η

Leading track p in eLJ [GeV](b)

Fig. 6.9 MC simulation to data comparisons for (a) leading track pT , and (b) η of eLJs.
Here, MC simulations are scaled to the observed number of events in the CR requiring
pre-selections and |qeLJ | > 0.

Chapter 7
Background estimation
Based on what we observed in Sec. 6.3, MC simulation-based methods are unreliable inthe search involving customized prompt dark photons in this thesis. Therefore, we employ
entirely data-driven approaches for background estimation. Sec. 7.1 introduces the datadriven ABCD method [113]. Sec. 7.2 discusses the selection of variables and definitions of
the signal region and control regions in the ABCD plane. Sec. 7.3 validates the backgroundestimation method by defining three additional validation regions and confirming the ABCD
assumptions.

7.1

ABCD Method

A data-driven ABCD method is selected for background estimation. In this method, data
is divided into four regions (A, B, C, and D) based on two uncorrelated variables, x and y.
Region A is the SR enriched by signal events, while regions B, C, and D are the three CRs
dominated by background events. A schematic view of ABCD methods is shown in Fig. 7.1.
These variables are chosen to discriminate the signal and background events effectively.
Under the assumption that the signal is well-contained in region A, we can estimate thenumber of backgrounds in region A using the number of observed events in region B, C, and
D as:
bkg

NA
bkg

=

NB · NC.
ND

Here, NA represents the estimated number of background events in the SR A, and NB , NC ,and ND are the observed numbers of events in the CR B, C, and D. Note that the method
remains robust in the presence of multiple background sources in the plane, provided that theevents from these different backgrounds result in a uniform distribution across the plane.

86

Background estimation

High yyD

Background

BackgroundA

B

Signal + Background

Background

Low x

High x

Low y

C

x

Fig. 7.1 Schematic view of ABCD background estimation method. A is the SR, while B, C,
and D are the CRs.

7.2

Selection of Variables

The choice of variables x and y is critical for the success of the ABCD method. Thesevariables are required to be:
1. sensitive in kinematic features of signal events, to ensure that signal events are wellcontained in region A;
2. background events propagate uniformly in all regions.
As mentioned in Sec. 6.2, the primary source of residual background events comes fromthe prompt production of electron pairs with random crossing of tracks like Z+jets. For thisanalysis, we define the variables as follows:• x: leading eLJ pimb
T represents the pT imbalance of the leading two tracks in the leading
sublead| plead|T −pT
eLJ, where pimb
T = plead +psublead ;TT• y: furthest eLJ shower ratio Rφ represents the ratio of 3 × 3 to 3 × 7 (η × φ ) cell
energy depositions in the middle layer of the EM calorimeter around the furthest eLJ.

87

102

Normalized Events

Normalized Events

7.2 Selection of Variables

tt
top

10

w
z
qcd

1

0.1 GeV γ FRVZ
d

0.1 GeV γ HAHM

10

tt
top
w

1

z
qcd
0.1 GeV γ FRVZ
d

0.1 GeV γ HAHM

10−1

d

d

10−1
10−2

10−2

10−3

10−3

10−4

10−4
0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

pimb

0

0.1

0.2

0.3

0.4

0.5

T

(a)

0.6

0.7

0.8
0.9
1
Shower ratio rΦ

(b)Fig. 7.2 (a) Track pT imbalance pimb
T of leading two tracks of leading eLJ, and (b) electron
shower ratio Rφ of furthest eLJ for simulated SM processes and signals with mγd = 0.1 GeV.
Distributions here are shown by requiring pre-selections.
The choice of ABCD variables, pimb
T and Rφ from different eLJs, ensures their lackof correlation. For eLJ candidates from signal events, both the leading and subleading
tracks originate from an electron pair decaying from a dark photon, which is expected to
be balanced in pT . In contrast, for background events, the leading track originating from a
prompt electron usually has a pT much larger than the subleading track from other sources
due to random overlapping. Additionally, eLJs from dark photons exhibit a broader spreadof energy deposits in the EM calorimeter due to merging two electrons into one cluster. In
contrast, the energy is much more centered in the case of prompt electrons. Fig. 7.2 shows
both the leading eLJ pimb
T and the furthest eLJ Rφ . These variables are further validated bycomparing MC simulations with full Run-2 data in the background dominant CR by requiringthat |qeLJ | > 0, as shown in Fig. 7.3. The shape of data is in reasonable agreement with thatof Z+jets, which indicates the dominant background to be estimated using data is due toevents from two electron-fake eLJs.
Fig. 7.4 shows 2D plots of the ABCD planes for the reference signal sample (FRVZ with
γd mass set to 17 MeV) and background MC simulations. In the ABCD planes, 80% of thesignal events populate in region A, while 80% of the background events populate regions B,
C, and D. Note that background MC simulations are used solely to verify the ABCD method.
Their event counts are not included in the final estimation.
The choices of threshold values of leading eLJ pimb
T and furthest eLJ Rφ are determinedwith the criteria to maximize signal to background sensitivity while keeping signal leakage
defined as the number of signal events over background in regions B/C/D to below 10%.
Fig. 7.5 shows the signal leakage of 17 MeV γd events in the scan over values of ABCD
variables, from which we see the leakage is mainly affecting region B. Fig. 7.6 shows

88

Background estimation

tt
qcd

5

10

top
data

w

EventsEvents

106

z

106

tt
qcd

105

top
data

w

z

104
104
103
103
102
102
10
10

1

10− 1

Data / MC

Track p imbalance in eLJ
T

1.5
1
0.5
0

Data / MC

1

2

2

Rφ

1.5
1
0.5

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0

0

0.1

0.2

0.3

0.4

0.5

pimb

0.6

0.7

0.8

0.9

1

Shower ratio RΦ

T

(a)

(b)

1

B

D

0.9

0.4

0.8

0.35

0.7

0.3

0.6

0.25

0.5
0.4

0.45

A

C

0.2

Furthest eLJ RφFurthest eLJ RφFig. 7.3 MC simulation to data comparisons for (a) track pT imbalance pimb
T of leading two
tracks of leading eLJ, and (b) electron shower ratio Rφ of furthest eLJ in the CR by requiring
pre-selections and |qeLJ | > 0.

1

20

0.8

15

0.7
0.6

10

0.5
0.4

0.15

0.3

0.2

0.1

0.2

0.1

0.05

0.1

0

0

0

(a)

D

0.9

0.3

0 0.10.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Lead eLJ pT imbalance

B

A

C

5
0
−5

0 0.10.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Lead eLJ pT imbalance(b)Fig. 7.4 ABCD plane of leading eLJ pimb
T and furthest eLJ Rφ for (a) a FRVZ benchmark signal sample with mγd = 0.1 GeV, (b) background MC samples. Negative entries corresponds
to events with negative weights in MC.

890.98 12.7 13.3 12.2 11.3 11.7 10.9 10.9 10.6 10.6
12.2

12.8

12.1 11.0

10.7

10.1 10.0

9.9

9.9

9.4

9.4

8.5

7.8

6.8

6.1

5.7

5.1

4.6

4.0

3.8

3.4

3.1

3.0

9.2

8.9

8.3

7.6

7.0

6.3

5.8

5.2

4.6

4.0

3.7

3.3

3.1

2.9

9.8

9.1

8.4

7.7

7.0

6.4

5.9

5.1

4.7

4.2

3.9

3.7

9.5

8.7

8.0

7.2

6.7

5.8

5.2

4.8

4.4

4.1

0.96 13.7 13.6 12.8 11.9 11.9 11.6 11.5 11.6 11.5 10.6 10.2
15.6

15.5

14.8 14.0

13.8 13.4

13.2

13.4 13.2

12.4 11.7

11.0

10.2

9.7

8.9

8.3

7.6

7.0

6.2

5.6

5.1

4.7

4.4

16.7

16.7

16.0 15.4

14.8 14.4

14.2

14.3 14.0

13.1 12.4

11.8

11.0 10.2

9.4

8.8

8.0

7.4

6.5

5.9

5.4

4.9

4.7

9.3

8.6

7.9

7.0

6.3

5.8

5.3

5.0

9.8

8.9

8.2

7.3

6.6

6.0

5.6

5.2

9.3

8.6

7.7

7.0

6.4

5.9

5.5

0.94 15.7 15.7 15.1 14.4 14.1 13.7 13.6 13.7 13.3 12.5 11.9 11.2 10.5

0.92 17.4 17.3 16.7 16.0 15.5 15.2 15.0 15.1 14.6 13.7 13.1 12.5 11.6 10.8 10.0
18.3

18.1 17.5 16.7

16.2 15.9

15.7

15.7

15.1 14.2 13.5

12.9

12.1 11.3

10.4

0.9 19.3 19.1 18.4 17.5 16.9 16.6 16.4 16.3 15.8 14.8 14.1 13.5 12.7 11.8 10.8 10.1
19.5

19.5

18.9 18.0

17.3 17.0

16.8

16.7 16.2

15.1 14.4

13.7

12.9

21.3

21.3

20.8 19.9

19.0 18.6

18.4

18.2 17.5

16.4 15.6

14.8

14.0 13.0

11.9

22.9

23.0

22.5 21.5

20.6

20.1 19.8

19.7 18.8

17.6 16.7

15.9

14.9 13.8

12.7 11.8

12.1

0.9 5.4

7.9

7.1

6.6

6.0

8.2

7.4

6.8

6.3

5.9

0.88 5.8

9.5

8.5

7.7

7.0

6.5

6.2

6.2

9.7

8.7

7.8

7.2

6.6

6.3

10.1

9.0

8.2

7.5

6.9

6.5

9.3

8.4

7.7

7.1

6.7

9.6

10.9

24.0

23.5 22.4

21.4 20.9

20.6

20.4 19.6

18.5 17.6

16.7

15.6 14.5

13.3 12.5

11.5

10.6

8.6

7.9

7.3

6.9

9.7

8.8

8.0

7.4

7.0

25.3

24.7 23.6

22.5 22.0

21.8

21.5 20.5

19.4 18.5

17.6

16.5 15.3

14.1 13.2

12.1

11.1 10.1

9.1

8.3

7.7

7.3

9.3

8.5

7.8

7.4

26.9

26.7

26.2 25.0

23.9 23.3

22.9

22.7 21.6

20.4 19.5

18.5

17.3

16.1 14.8 13.8

12.7

11.7 10.6

9.6

8.7

8.1

7.6

9.7

8.8

8.2

7.7

27.7

27.6

27.0 25.7

24.6

24.1 23.7

23.4 22.4

21.2 20.2

19.1 17.9 16.7

13.2

12.1 10.9

9.8

9.0

8.3

7.8

9.3

8.6

8.1

0.8 25.9 25.8 25.3 24.1 23.1 22.6 22.2 22.0 21.0 19.8 19.0 17.9 16.8 15.6 14.4 13.4 12.4 11.4 10.3
0.78 27.4 27.3 26.7 25.4 24.3 23.7 23.4 23.2 22.1 20.8 19.9 18.8 17.6 16.4 15.1 14.1 13.0 11.9 10.8
15.3 14.3

0.76 28.7 28.6 28.0 26.6 25.5 24.8 24.5 24.1 23.0 21.8 20.8 19.8 18.5 17.3 15.8 14.8 13.6 12.5 11.3 10.2
0.88

5.1

20

9.2

25.4

0.86

4.5

0.92 4.8

8.8

24.0

0.84

0.94 4.2

9.9

0.82 24.5 24.4 23.9 22.8 21.8 21.3 21.0 20.8 19.9 18.7 17.8 17.0 15.9 14.7 13.6 12.7 11.7 10.8

0.82

2.6

3.0

3.9

9.6

0.86 22.0 22.0 21.5 20.5 19.7 19.3 19.0 18.8 18.1 16.9 16.1 15.3 14.3 13.3 12.2 11.4 10.5

0.8

2.7

3.3

0.96 3.6

11.1 10.3

11.1 10.3

0.84 23.5 23.5 23.0 21.9 20.9 20.4 20.2 20.0 19.2 18.0 17.1 16.3 15.2 14.1 13.0 12.2 11.3 10.4

0.78

25

0.98 3.0

5.7

0.88 20.3 20.3 19.8 18.8 18.1 17.7 17.5 17.4 16.9 15.8 15.0 14.3 13.4 12.5 11.6 10.8

0.76

Furthest eLJ RφFurthest eLJ Rφ

7.2 Selection of Variables

0.9

5.6

0.86 6.6

15

6.6

0.84 6.7
7.1

0.82 7.3

10

7.3

0.8 7.6
7.9

0.78 8.05

8.4

0.76 8.2

0.92 0.94 0.96 0.98
Lead eLJ pT imbalance

2.5

2.3

2.1

1.9

1.7

1.5

1.5

1.2

1.1

1.0

0.9

0.8

0.7

0.6

0.4

0.2

2.9

2.8

2.6

2.4

2.2

1.9

1.7

1.7

1.4

1.2

1.1

1.0

0.9

0.8

0.6

0.4

0.2

0.1

3.3

3.1

3.0

2.8

2.6

2.4

2.1

1.9

1.8

1.5

1.4

1.3

1.1

1.0

0.9

0.7

0.5

0.2

0.2

3.6

3.4

3.3

3.1

2.9

2.7

2.4

2.2

2.1

1.8

1.6

1.5

1.3

1.2

1.1

0.8

0.6

0.3

0.2

3.9

3.7

3.6

3.4

3.2

2.9

2.6

2.4

2.2

1.9

1.8

1.6

1.4

1.3

1.2

0.9

0.7

0.3

0.2

4.2

4.0

3.9

3.6

3.4

3.1

2.8

2.6

2.4

2.0

1.9

1.7

1.6

1.4

1.3

1.1

0.7

0.3

0.2

4.4

4.2

4.1

3.8

3.6

3.3

3.0

2.8

2.7

2.2

2.1

1.9

1.7

1.5

1.5

1.2

0.8

0.4

0.3

4.7

4.5

4.3

4.1

3.9

3.5

3.2

3.0

2.9

2.4

2.3

2.1

1.9

1.7

1.6

1.3

0.9

0.4

0.3

5.0

4.7

4.6

4.3

4.0

3.7

3.3

3.1

2.9

2.4

2.3

2.1

1.9

1.7

1.6

1.3

0.9

0.4

0.3

5.3

5.0

4.8

4.5

4.3

3.9

3.5

3.3

3.1

2.5

2.4

2.2

2.0

1.8

1.7

1.3

0.9

0.4

0.4

5.5

5.3

5.1

4.8

4.5

4.2

3.8

3.5

3.3

2.7

2.6

2.4

2.2

1.9

1.8

1.5

1.0

0.5

0.4

5.9

5.6

5.5

5.1

4.9

4.5

4.0

3.7

3.6

2.9

2.8

2.6

2.3

2.0

1.8

1.6

1.0

0.5

0.4

6.3

6.0

5.9

5.6

5.3

4.9

4.4

4.1

4.0

3.2

3.1

2.8

2.5

2.1

2.0

1.7

1.1

0.6

0.5

6.3

6.1

6.1

5.8

5.4

5.0

4.5

4.2

4.0

3.2

3.1

2.8

2.5

2.0

1.9

1.5

0.9

0.5

0.4

6.4

6.1

6.1

5.7

5.4

4.9

4.5

4.2

4.0

3.1

3.0

2.7

2.3

1.8

1.8

1.6

1.0

0.5

0.3

6.7

6.5

6.4

6.1

5.7

5.2

4.7

4.4

4.3

3.4

3.2

2.8

2.4

1.8

1.8

1.6

0.9

0.5

0.3

7.0

6.7

6.7

6.3

6.0

5.5

4.9

4.6

4.5

3.5

3.4

3.0

2.5

1.9

1.8

1.6

0.8

0.6

0.3

6.9

6.6

6.6

6.2

5.9

5.4

4.8

4.5

4.4

3.6

3.4

3.0

2.5

2.0

2.0

1.7

0.9

0.6

0.4

7.2

7.0

7.0

6.6

6.3

5.8

5.2

4.9

4.8

4.0

3.7

3.3

2.8

2.2

2.2

1.9

1.0

0.7

0.4

7.5

7.3

7.3

7.0

6.7

6.0

5.5

5.1

5.0

4.1

3.8

3.4

3.0

2.2

2.2

2.0

1.0

0.7

0.5

7.7

7.4

7.4

7.1

6.9

6.2

5.6

5.2

5.2

4.2

3.9

3.4

2.9

2.3

2.3

2.1

1.0

0.8

0.5

8.0

7.8

7.7

7.4

7.3

6.5

5.9

5.6

5.6

4.6

4.2

3.7

3.2

2.5

2.6

2.4

1.2

0.9

0.5

7.9

7.6

7.5

7.2

7.0

6.2

5.5

5.2

5.4

4.4

4.3

3.8

3.3

2.5

2.6

2.4

1.3

1.0

0.6

0.76

0.78

Furthest eLJ Rφ(a) Percentage leakage in CR B

0.8

0.7

0.7

0.8

0.6

0.6

0.5

0.4

0.4

0.3

0.3

0.3

0.2

0.2

0.2

0.2

0.3

0.3

0.4

1.0

0.8

0.7

0.7

0.6

0.6

0.5

0.5

0.4

0.4

0.3

0.2

0.2

0.2

0.2

0.1

0.2

0.2

0.1

1.0

0.9

1.0

0.8

0.8

0.7

0.6

0.5

0.5

0.3

0.2

0.2

0.2

0.2

0.2

0.2

0.1

0.1

1.0

1.0

1.0

0.8

0.8

0.7

0.5

0.4

0.4

0.3

0.2

0.2

0.2

0.1

0.1

0.1

0.1

0.1

1.2

1.1

1.1

0.9

0.9

0.7

0.6

0.5

0.5

0.4

0.3

0.3

0.2

0.2

0.1

0.2

0.1

0.1

1.2

1.1

1.1

1.0

0.9

0.8

0.6

0.5

0.5

0.4

0.3

0.3

0.3

0.2

0.2

0.1

0.1

0.1

1.3

1.2

1.1

1.0

0.9

0.8

0.6

0.5

0.5

0.4

0.3

0.3

0.2

0.2

0.2

0.1

0.1

0.0

1.3

1.2

1.2

1.1

1.0

0.9

0.7

0.6

0.5

0.4

0.3

0.3

0.2

0.2

0.2

0.1

0.1

0.1

1.3

1.3

1.2

1.2

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.4

0.3

0.3

0.2

0.2

0.1

0.1

1.4

1.3

1.3

1.2

1.1

0.9

0.8

0.7

0.6

0.5

0.4

0.4

0.3

0.3

0.3

0.2

0.1

0.1

1.4

1.4

1.3

1.2

1.1

1.0

0.8

0.7

0.7

0.6

0.5

0.4

0.3

0.3

0.3

0.2

0.1

0.1

1.5

1.4

1.3

1.2

1.1

1.0

0.8

0.7

0.7

0.6

0.5

0.4

0.4

0.4

0.3

0.2

0.2

0.1

1.5

1.4

1.3

1.2

1.1

1.0

0.8

0.7

0.7

0.6

0.5

0.4

0.4

0.3

0.3

0.2

0.2

0.1

1.6

1.5

1.4

1.3

1.2

1.0

0.9

0.8

0.7

0.6

0.5

0.5

0.4

0.4

0.4

0.3

0.2

0.1

0.0

1.7

1.6

1.5

1.4

1.3

1.1

0.9

0.8

0.8

0.7

0.6

0.5

0.5

0.5

0.4

0.3

0.2

0.1

0.1

1.7

1.6

1.5

1.4

1.3

1.2

1.0

0.9

0.8

0.7

0.6

0.6

0.5

0.5

0.5

0.3

0.3

0.1

0.1

1.8

1.7

1.6

1.5

1.3

1.2

1.0

0.9

0.8

0.7

0.6

0.6

0.5

0.5

0.5

0.4

0.3

0.1

0.1

1.8

1.7

1.6

1.5

1.4

1.2

1.1

0.9

0.9

0.7

0.6

0.6

0.6

0.5

0.5

0.4

0.3

0.1

0.1

1.9

1.7

1.7

1.5

1.4

1.2

1.1

0.9

0.9

0.7

0.6

0.6

0.5

0.5

0.5

0.3

0.3

0.1

0.1

1.9

1.8

1.7

1.5

1.4

1.3

1.1

1.0

0.9

0.8

0.7

0.6

0.6

0.5

0.5

0.3

0.3

0.1

0.1

1.9

1.8

1.7

1.6

1.5

1.3

1.1

1.0

0.9

0.8

0.7

0.6

0.6

0.6

0.5

0.4

0.3

0.1

0.1

2.0

1.9

1.8

1.6

1.5

1.3

1.1

1.0

0.9

0.8

0.7

0.6

0.6

0.6

0.5

0.3

0.3

0.1

0.1

2.0

1.9

1.8

1.7

1.5

1.4

1.2

1.1

1.0

0.8

0.7

0.7

0.6

0.6

0.5

0.4

0.3

0.1

0.1

1.2

0.94 1.3
1.4

0.92 1.4
1.4

0.9 1.5
1.6

0.88 1.6
1.7

0.86 1.7
1.8

0.84 1.9
1.90.82 2.0
2.0

0.8 2.1
2.1

0.78 2.2
2.2

0.76 2.2

0.76

0.78

0.8

0.82

0.84

0.86

0.88

0.9

0.92 0.94 0.96 0.98
Lead eLJ pT imbalance

8
7
6
5
4
3
2
1
0

(b) Percentage leakage in CR C

0.98 0.8
0.96 1.1

0.1

0.82

0.84

0.86

0.88

0.9

2.2
2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2

0.92 0.94 0.96 0.98
Lead eLJ pT imbalance0(c) Percentage leakage in CR D

Fig. 7.5 Percentage ratio of the number of 17 MeV FRVZ γd normalized to BR(H → 2γd + X)
of 0.5% over data in CR B/C/D.
p
S/ Bexp in final SR A, where we observe peak at Rφ = 0.96 due to shape in Fig. 7.2 (b).
Considering all factors, we choose the ABCD definition given in Table 7.1.
Yields in the ABCD are reported in Table 7.2 and Table 7.3 for the FRVZ and the HAHM
benchmark models and background MC simulations. Here, the expected NA is computedfrom NB × NC /ND .
Table 7.1 Definition of the signal and control regions used in the background estimation.
Requirement / Region

A (SR)B

C

D

leading eLJ pimbTfurthest eLJ Rφ< 0.82 < 0.82 > 0.82 > 0.82
< 0.96 > 0.96 < 0.96 > 0.96

90Furthest eLJ Rφ

Background estimation

0.98 9.0

9.3

9.0

8.8

8.9

8.7

8.6

8.9

8.2

8.5

8.2

7.8

7.2

6.9

6.7

6.4

6.1

5.6

5.6

5.3

4.6

10.0

10.1

9.8

9.4

9.2

9.2

9.1

9.1

9.3

9.0

8.9

8.7

8.3

8.1

7.7

7.4

7.1

6.8

6.1

6.0

5.8

6.4

9.0

9.1

8.8

8.6

8.6

8.6

8.6

8.7

8.8

8.5

8.4

8.2

8.0

7.7

7.5

7.2

7.0

6.9

6.2

6.2

6.2

6.9

10.2

9.2

9.1

8.9

8.9

8.8

8.8

8.9

9.1

8.9

8.6

8.3

8.1

7.9

7.7

7.4

7.2

7.1

6.4

6.3

6.3

6.7

9.1

9.0

8.8

8.7

8.7

8.7

8.7

8.8

8.7

8.5

8.2

8.0

7.8

7.5

7.3

7.1

7.1

6.6

6.4

6.4

6.8

9.8

0.92 8.8

9.1

9.0

8.8

8.8

8.7

8.7

8.7

8.8

8.6

8.4

8.2

8.0

7.8

7.5

7.3

7.2

7.1

6.6

6.3

6.4

6.5

11.3

8.8

8.7

8.6

8.5

8.5

8.5

8.5

8.5

8.3

8.2

8.0

7.8

7.6

7.4

7.3

7.1

7.0

6.5

6.2

6.5

6.6

11.4

8.8

8.8

8.7

8.5

8.5

8.5

8.4

8.5

8.4

8.2

8.1

7.9

7.8

7.6

7.3

7.2

7.0

7.0

6.5

6.2

6.5

6.7

11.8

8.7

8.6

8.5

8.4

8.4

8.4

8.4

8.4

8.1

8.0

7.9

7.8

7.5

7.2

7.1

6.8

6.8

6.4

6.2

6.5

6.9

10.9

8.6

8.5

8.4

8.3

8.3

8.3

8.3

8.3

8.1

7.9

7.7

7.6

7.4

7.2

7.0

6.8

6.8

6.3

6.0

6.3

6.5

10.1

8.6

8.5

8.4

8.3

8.3

8.3

8.3

8.3

8.1

7.9

7.7

7.6

7.4

7.2

7.1

6.9

6.8

6.4

5.9

6.3

6.4

9.5

8.7

8.6

8.4

8.3

8.3

8.3

8.3

8.3

8.0

7.9

7.7

7.6

7.3

7.1

6.9

6.7

6.7

6.2

5.6

6.0

6.0

8.7

8.8

8.7

8.6

8.5

8.5

8.5

8.5

8.5

8.2

8.0

7.8

7.6

7.4

7.2

7.1

6.9

6.7

6.3

5.8

6.1

6.3

12.2

8.9

8.8

8.6

8.4

8.4

8.4

8.4

8.4

8.1

8.0

7.8

7.6

7.4

7.1

7.0

6.8

6.8

6.2

5.9

6.1

6.7

11.3

8.9

8.8

8.6

8.4

8.4

8.4

8.4

8.4

8.1

8.0

7.8

7.7

7.4

7.1

7.1

6.9

6.8

6.4

6.1

6.4

6.7

10.7

8.8

8.7

8.5

8.3

8.3

8.3

8.4

8.4

8.1

8.0

7.8

7.7

7.4

7.1

7.1

6.9

6.9

6.3

6.0

6.1

6.4

9.9

8.8

8.7

8.5

8.4

8.4

8.3

8.3

8.3

8.0

7.9

7.7

7.6

7.3

7.1

7.0

6.8

6.8

6.3

6.0

6.1

6.3

9.4

8.6

8.5

8.3

8.2

8.2

8.1

8.1

8.1

7.8

7.7

7.5

7.4

7.2

7.0

6.9

6.6

6.5

6.1

5.9

5.9

6.3

8.8

8.5

8.5

8.3

8.1

8.2

8.1

8.1

8.0

7.8

7.7

7.5

7.4

7.2

7.0

6.9

6.6

6.6

6.2

5.9

6.0

6.0

8.3

8.4

8.3

8.1

8.0

7.9

7.9

7.9

7.8

7.6

7.5

7.3

7.2

7.0

6.7

6.6

6.3

6.4

6.1

5.8

5.6

5.6

7.7

8.5

8.4

8.2

8.1

8.0

8.0

8.0

8.0

7.8

7.6

7.4

7.4

7.1

6.8

6.8

6.5

6.6

6.1

5.6

5.3

5.3

7.3

8.4

8.3

8.2

8.1

8.0

8.0

8.0

8.0

7.8

7.6

7.4

7.4

7.2

6.8

6.9

6.6

6.7

6.1

5.7

5.4

5.4

9.9

8.0

8.0

7.8

7.7

7.7

7.6

7.7

7.6

7.4

7.2

7.0

7.0

6.9

6.6

6.7

6.4

6.5

5.8

5.5

5.0

5.0

9.0

0.96 9.1
9.3

0.94 9.1
9.1

0.9 8.7
8.6

0.88 8.6
8.7

0.86 8.8
8.8

0.84 8.8
8.7

0.82 8.8
8.5

0.8 8.5
8.3

0.78 8.4
8.3

0.76 7.9

0.76

0.78

0.8

8.7

0.82

0.84

0.86

0.88

0.9

12

5.9

11

9.9

10
9
8
7
6
5

0.92 0.94 0.96 0.98
Lead eLJ pT imbalancepFig. 7.6 Significance (S/ Nexp ) of the number of events 17 MeV FRVZ γd normalized
to BR(H → 2γd + X) of 0.5% in SR A over the squared root of the expected number ofbackground in data (Nexp = NB × NC /ND ).
Table 7.2 ABCD yields in FRVZ signal and background simulations. Signal yields arenormalized to a BR(H → 2γd + X) of 0.5%. Uncertainties are statistical only, while theuncertainty on the number of expected events in region A is obtained from the propagationof the statistical uncertainty on regions B, C, and D.
RegionFRVZ Signal samples
γd mass [GeV]

NA (expected)
NA (SR)
NB
NC
ND

0.017

0.03

138.65 ± 4.11
14.06 ± 1.31
20.22 ± 1.58
2.58 ± 0.55

Background

0.06

0.1

101.65 ± 3.56 76.21 ± 3.12 58.60 ± 2.65
11.17 ± 1.23 7.84 ± 0.97 6.03 ± 0.92
16.73 ± 1.46 13.81 ± 1.30 12.72 ± 1.23
1.79 ± 0.54
1.66 ± 0.52 1.20 ± 0.35

0.24
15.29 ± 1.35
2.47 ± 0.55
1.60 ± 0.430±0

190
139 ± 50
39 ± 12564 ± 50158 ± 25

Table 7.3 ABCD yields in HAHM signal and background simulations The signal assumes aBR(H → 2γd ) of 0.5%. Uncertainties are statistical only, while the uncertainty on the numberof expected events in region A is obtained from the propagation of the statistical uncertainty
in regions B, C, and D.
RegionHAHM Signal samples
γd mass [GeV]

NA (expected)
NA (SR)
NB
NC
ND

0.017

0.1

1150.23 ± 12.15 278.19 ± 5.94
71.83 ± 3.04
24.87 ± 1.76
90.38 ± 3.33
48.35 ± 2.59
5.29 ± 0.79
4.22 ± 0.70

Background0.4
36.94 ± 2.12
5.05 ± 0.76
8.72 ± 1.08
1.76 ± 0.48

190
139 ± 50
39 ± 12564 ± 50158 ± 25

91

Sublead eLJ Rφ

7.3 Validation of the Background Estimation Method

1

B

D

0.9

18

0.8

16

0.7

14

0.6

12

0.5
0.4

20

A

C

10
8

0.3

6

0.2

4

0.1

2

0
0
0 0.10.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Lead eLJ pT imbalance
Fig. 7.7 ABCD plane of leading eLJ pimb
T and furthest eLJ Rφ for full Run-2 data. The SR A
is blinded in the data at this stage of the background estimation, with the unblinded data to
be presented in Sec. 9.1.

7.3

Validation of the Background Estimation Method

We validate the ABCD background estimation method using data in sub-regions of the ABCD
plane as shown in Fig. 7.7. Two such regions are constructed from the combination of theB, C, and D regions, namely the BD and the CD sub-planes, which are further divided into
four sub-regions: BD1, BD2, BD3, and BD4 for the BD sub-plane and CD1, CD2, CD3, andCD4 for the CD sub-plane, as illustrated in Fig. 7.8. The prediction of the ABCD method
is tested in the BD1 and CD1 regions, where the vertical (horizontal) boundary is variedin the test of BD (CD) regions. We fix the other ABCD variable in each case at a nominal
value. Specifically, the furthest eLJ Rφ is set to 0.98 in the BD sub-plane, and the leading
imb
eLJ pimb
T is fixed at 0.90 in the CD sub-plane. In each combination of leading eLJ pT and
the furthest eLJ Rφ cut, expected number of BD1 (CD1) is compared with observed numberof BD2×BD3/BD4 (CD2×CD3/CD4).
Fig. 7.9 (a) shows the observed versus expected number of events in BD1 as a functionof the pimb
T cut. Similarly, Fig. 7.9 (b) shows the observed versus expected number in CD1,

92

Background estimation
scan

Rφ

Rφ
BD3

BD4
B

0.98
BD1

CD3

BD2

0.96

CD4
scan

0.96

C

A

A
CD1
pimb
T

0.82

CD2

0.9

0.82

pimb
T

Fig. 7.8 Illustration of sub-region definitions in BD and CD control region.
scanned by the Rφ cut. For values of pimb
T and Rφ around the final SR threshold, the numberof expected and observed events agrees within 1 σ .
The impact of the signal contamination in regions B, C, and D is evaluated by checking
the observed vs expected number of events in BD and CD sub-planes after subtracting thesimulated signal contributions. Fig. 7.10 shows the robustness of the ABCD method under
the assumption of 17 MeV FRVZ γd with BR(H → 2γd + X) of 0.5% signal contamination.
The agreement is better when the signal contamination is subtracted. Therefore, we checkthe impact on the expected limit due to the signal contamination using the fitting framework
as will be described in Sec. 9.3.1.
700
EventsEvents

1000
900

600

800
700
600

500

expected
observed

400

expected
observed

500
300

400
300

200

200
100

02

0.4
1.8

0.5

0.6

0.7

0.8

1.6

0.9
1
Lead eLJ p imbalance
T

1.4
1.2
1
0.8
0.6

02

0.4
1.8

0.5

0.6

0.7

0.8

0.9

1
Sublead eLJ Rφ

0.5

0.6

0.7

0.8

0.9

1

1.6
1.4
1.2
1
0.8
0.6

0.4

0.4

0.2
0
0.4

BDobs / BDexp

BDobs / BDexp

100

0.2
0.5

0.6

0.7

0.8

0.9

1

Lead eLJ p imbalance

0
0.4

T

(a) BD validation

Furthest eLJ Rφ(b) CD validation

Fig. 7.9 Observed and expected values of the number of events in data in the eLJ-eLJ channel
BD and CD sub-planes as a function of the cut on pimb
T and Rφ , respectively.

93

7.3 Validation of the Background Estimation Method
700
EventsEvents

1000
900

600

800
700
600

500

expected
observed

400

expected
observed

500
300

400
300

200

200
100

02
0.4
1.8

0.5

0.6

0.7

0.8

1.6

0.9
1
Lead eLJ p imbalance
T

1.4
1.2
1
0.8
0.6

02

0.4
1.8

0.5

0.6

0.7

0.8

0.9

1
Sublead eLJ Rφ

0.5

0.6

0.7

0.8

0.9

1

1.6
1.4
1.2
1
0.8
0.6

0.4

0.4

0.2
0
0.4

BDobs / BDexp

BDobs / BDexp

100

0.2
0.5

0.6

0.7

0.8

0.9

1

Lead eLJ p imbalance

0
0.4

T

(a) BD validation

Furthest eLJ Rφ(b) CD validation

Fig. 7.10 Observed and expected values of the number of events in data in the eLJ-eLJ
channel BD and CD sub-planes as a function of the cut on pimb
T and Rφ , respectively, after
subtracting the simulated signal contributions of 17 MeV γd with BR(H → 2γd + X) of 0.5%.
In addition to the BD/CD sub-planes closure checks, to further validate the backgroundestimation method, we define three additional validation regions orthogonal to the ABCD
plane used in Fig. 7.7 to confirm the validity of pimb
T and Rφ in all phase spaces including
region A. Each validation region is independently defined as follows:• VR1: 80 GeV < meLJ−eLJ < 100 GeV;
• VR2: |qeLJ | > 0;
• VR3: |η| > 1.5.
Other event selections on SR are applied to these VRs.
As shown in Table 7.4, which summarizes the background compositions of the SR andthree VRs from MC simulations, both the SR and VRs are predominantly composed of
Z+jets events.
Table 7.4 Composition of background processes from MC simulation in SR and VRs.

Region

t t¯

SR
VR1
VR2
VR3

0.30%
0.01%
0.23%
0.10%

single-top W +jets
0.22%
0.00%
0.20%
0.11%

1.98%
0.03%
0.83%
2.10%

Z+jetsMultijets

97.00%
99.95%
98.15%
84.85%

0.50%
0%
0.58%
12.84%

Table 7.5, Table 7.6, and Table 7.7 present the yields in the ABCD plane for the threevalidation regions: VR1, VR2, and VR3, respectively. The deviations between expected NA

94

Background estimation

Table 7.5 Signal and data yields in VR1 defined by requiring the mass of two eLJ to be within
the Z-mass window normally vetoed in the definition of the SR. Signal events weighted witha BR=0.5% for FRVZ and 0.5% for HAHM.
RegionFRVZ

γd mass [GeV]

0.017

NB
NC
ND
NA
NA (expected)

2.43 ± 0.55
2.84 ± 0.63
1.17 ± 0.37
29.88 ± 1.92

0.03

0.06

1.90 ± 0.46 2.04 ± 0.49
2.98 ± 0.61 3.39 ± 0.68
0.38 ± 0.22 0.71 ± 0.29
17.59 ± 1.43 14.49 ± 1.42

HAHM
0.1

0.24

0.64 ± 0.25 0.83 ± 0.32
1.86 ± 0.47 0.57 ± 0.26
0.37 ± 0.21
0±09.46 ± 1.20 3.79 ± 0.67

Run-2 data

0.017

0.1

0.4

0±0
6.59 ± 0.95
0±050.62 ± 2.55

0.12 ± 0.12
4.69 ± 0.74
0±026.61 ± 1.76

0±00.48 ± 0.25
0±01.98 ± 0.48

318
2486
2249
427
352 ± 22

Table 7.6 Signal and data yields in VR2 defined by requiring the charge of the eLJ to bedifferent from zero. Signal events weighted with a BR=0.5% for FRVZ and 0.5% for HAHM.
Region

FRVZ
0.03

0.06

HAHM

γd mass [GeV]

0.017

0.1

0.24

0.017

NB
NC
ND
NA
NA (expected)

0±00±00±0 0±0 0±0
0±0
0±0
0±0
0 ± 0 0 ± 0 0 ± 0 0.23 ± 0.160±0
0±0
0±0 0±0 0±0
0±0
0 ± 0 0.09 ± 0.09 0 ± 0 0 ± 0 0 ± 0 0.64 ± 0.26

0.1

Run-2 data
0.4

0±0
0±0
0±0
0±0
0±0
0±0
0.88 ± 0.33 0 ± 0

44
246
106
101
102 ± 19

and observed NA in the VRs are considered sources of non-closure systematic uncertainties,
which will be explained in Sec. 8.3. Fig. 7.11 illustrate the population of events from theVRs entering the ABCD regions, as defined in Table 7.1.
Moreover, to validate the prediction of the ABCD method, we also compare the expected
number of events with the observed number of events using the scan method for all 3 VRs.
For each VR, we perform a scan of both pimb
T and Rφ , fixing the other variable to the thresholdvalue defined for the SR in Table 7.1. Fig. 7.12, Fig. 7.13, and Fig. 7.14 show the observed
versus expected number of events in VR1, VR2, and VR3, respectively. The expected values
in region A are consistent with the observed numbers.

Table 7.7 Signal and data yields in VR3 defined by reversing the selection on the η of theeLJ. Signal events weighted with a BR=0.5% for FRVZ and 0.5% for HAHM.
Regionγd mass [GeV]
NB
NC
ND
NA
NA (expected)

FRVZ
0.017

0.03

2.78 ± 0.56
2.50 ± 0.53
13.41 ± 1.33 14.38 ± 1.36
0±00.31 ± 0.18
83.25 ± 3.14 69.68 ± 2.90

0.06

HAHM
0.1

0.24

1.56 ± 0.42 1.83 ± 0.46 0.08 ± 0.08
9.96 ± 1.08 11.05 ± 1.12 2.24 ± 0.51
0.14 ± 0.14 0.09 ± 0.09 0.06 ± 0.06
51.11 ± 2.45 45.57 ± 2.37 9.35 ± 1.03

Run-2 data

0.017

0.1

0.4

16.26 ± 1.40
58.56 ± 2.75
2.12 ± 0.64
623.15 ± 8.80

11.82 ± 1.35
48.44 ± 2.47
1.63 ± 0.44
301.41 ± 6.13

1.66 ± 0.44
6.34 ± 0.99
0±031.48 ± 1.94

353
3599
390
2948
3257 ± 245

95

1

B

D

140

0.9
0.8

120

0.7

100

0.6

80

0.5
0.4

Furthest eLJ RφFurthest eLJ Rφ

7.3 Validation of the Background Estimation Method

A

C

0.3

B

1

D

0.9

7

0.8

6

0.7

5

0.6
0.5

60

0.4

40

0.3

0.2

4

A

C

20

0
0
0 0.10.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Lead eLJ pT imbalance

0.1

1

0

0

0 0.10.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Lead eLJ pT imbalance(a)Furthest eLJ Rφ

3
2

0.2

0.1

8

(b)
1

B

D

50

0.9

45

0.8

40

0.7

35

0.6

30

0.5
0.4

25

A

C

20

0.3

15

0.2

10

0.1

5

0

0

0 0.10.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Lead eLJ pT imbalance(c)Fig. 7.11 ABCD plane of leading eLJ pimb
T and furthest eLJ Rφ for (a) VR1 on-shell Z boson
mass window, (b) VR2 |qeLJ | > 0, and (c) VR3 |η| > 1.5 end-cap.

96

Background estimation

1200
EventsEvents

4000
3500

1000
3000
2500

expected
observed

800

2000

expected
observed

600

1500
400
1000
200

02
0.4
1.8

0.5

0.6

0.7

0.8

1.6

BDobs / BDexp

BDobs / BDexp

500

0.9
1
Lead eLJ p imbalance
T

1.4
1.2
1
0.8
0.6

0.5

0.6

0.7

0.8

0.5

0.6

0.7

0.8

0.9

1.6

1
Sublead eLJ Rφ

1.4
1.2
1
0.8
0.6

0.4

0.4

0.2
0
0.4

02

0.4
1.8

0.2
0.5

0.6

0.7

0.8

0.9

0
0.4

1

Lead eLJ p imbalanceT(a) pimb
T scanFurthest eLJ Rφ
0.91(b) Rφ scanFig. 7.12 Observed vs. expected values of the number of events in data in the eLJ-eLJ
channel on-shell Z boson mass window validation region as a function of the cut on pimb
T and
Rφ , respectively.

400
EventsEvents

500
450

350

400
300
350
300

expected
observed

250

250

expected
observed

200

200

150

150
100
100
50

02

0.4
1.8

0.5

0.6

0.7

0.8

1.6

0.9
1
Lead eLJ p imbalance
T

1.4
1.2
1
0.8
0.6

02

0.4
1.8

0.5

0.6

0.7

0.8

0.5

0.6

0.7

0.8

0.9

1.6

1
Sublead eLJ Rφ

1.4
1.2
1
0.8
0.6

0.4

0.4

0.2
0
0.4

BDobs / BDexp

BDobs / BDexp

50

0.2
0.5

0.6

0.7

0.8

0.9

1

Lead eLJ p imbalance

0
0.4

T

(a) pimb
T scanFurthest eLJ Rφ
0.91(b) Rφ scanFig. 7.13 Observed vs. expected values of the number of events in data in the eLJ-eLJ channel|qeLJ | > 0 validation region as a function of the cut on pimb
T and Rφ , respectively.

97

7.3 Validation of the Background Estimation Method

8000

5000
4500

7000

4000
6000
5000

expected
observed

3500
3000

4000

expected
observed

2500
2000

3000

1500
2000
1000

02

0.4
1.8

500
0.5

0.6

0.7

0.8

1.6

0.9
1
Lead eLJ p imbalance
T

1.4
1.2
1
0.8
0.6

02

0.4
1.8

0.5

0.6

0.7

0.8

0.5

0.6

0.7

0.8

0.9

1.6

1
Sublead eLJ Rφ

1.4
1.2
1
0.8
0.6

0.4

0.4

0.2
0
0.4

BDobs / BDexp

BDobs / BDexp

1000

0.2
0.5

0.6

0.7

0.8

0.9

1

Lead eLJ p imbalance

0
0.4

T

(a) pimb
T scanFurthest eLJ Rφ
0.91(b) Rφ scanFig. 7.14 Observed vs. expected values of the number of events in data in the eLJ-eLJ channel|η| > 1.5 end-cap validation region as a function of the cut on pimb
T and Rφ , respectively.

Chapter 8
Systematic Uncertainties
In this chapter, we evaluate the systematic uncertainties. We perform an event counting
experiment on the final yields in the signal region to derive the analysis results. The numberof signal events is obtained from MC simulations, while the number of background events is
estimated using the ABCD data-driven method explained in Chapter 7. Systematic effects
from experimental and theoretical sources, which may affect the expected number of signal
events, are considered. Additionally, we assign a non-closure systematic uncertainty to thebackground estimation method. The likelihood function used to fit the data includes all
systematic uncertainties as nuisance parameters. These parameters are then profiled in the
final fit, as will be explained in Sec. 9.2.

8.1

Experimental Uncertainties

The following experimental sources of uncertainties are considered and evaluated as impacts
on signal yields in the MC simulation for γd mass below 0.24 GeV in the FRVZ model and
0.4 GeV for the HAHM model.

8.1.1

Standard Objects

Per-object scale factors are applied to correct the modeling of electrons in terms of reconstruction efficiency, isolation, and identification by comparing pT and η distribution of signal
and e from Z events [114]. The uncertainties on these scale factors are treated as systematic
uncertainties to the final signal selection efficiencies. The most significant impact is ±1.6%
for mγd = 0.06 GeV hypothesis of the FRVZ model.

100

8.1.2

Systematic Uncertainties

Triggers

The efficiency of single and di-electron triggers listed in Table 5.7 are calibrated by the
Z → ee events [114]. The systematic impact is evaluated to be negligible for the HAHM
model and ±0.2% for the FRVZ model.

8.1.3

Luminosity

The systematic uncertainty on the integrated luminosity of Run-2 data from 2015 to 2018 is
0.8% [104]. The uncertainty is calculated based on the luminosity scale calibrations using
x-y beam separation scans of the LUCID2 detector [115].

8.1.4

Pile-up Reweighting

To account for the multiple interactions per bunch crossing mentioned in Sec. 4.1.4, the pileup distribution in each data-taking period is modeled in the MC simulations and corrected bydata in a pile-up reweighting procedure. The systematic uncertainties associated with pile-up
reweighting are evaluated by shifting the default data scale factor 1/1.03 to up-variation
1/0.99 and down variation 1/1.07. The uncertainties propagate through the event selections
and result in, at most, a ±5.5% effect for mγd = 0.24 GeV hypothesis of the FRVZ model.

8.1.5 eγ energy scale and resolution
The systematic uncertainties concerning the electron kinematic uncertainties arising from theeγ energy scale and resolution are also evaluated. The most significant impact is ±0.95% formγd = 0.1 GeV hypothesis of the FRVZ model.

8.1.6

Jet Energy Scale and Jet Energy Resolution

Systematic uncertainties from JES and JER (see Sec. 4.3.4) are measured by varying a
reduced set of 3 nuisance parameters for JES and 6 nuisance parameters for JER associatedwith the calibration procedures [116]. The most significant impact is ±3.1% for mγd = 0.1
GeV hypothesis of the FRVZ model.

8.1.7

MC Statistics

The uncertainties in the final signal yields due to MC statistics are also considered. These
uncertainties become dominant compared to other systematic effects in the high mass region,

8.2 Theoretical Uncertainties

101

where acceptance is lower. The most significant uncertainty observed is ±9.3% for mγd =0.24 GeV hypothesis of the FRVZ model.

8.2

Theoretical Uncertainties

The theoretical uncertainties for the FRVZ and HAHM signal processes are considered. A
general n-th order perturbation theory computation of inclusive cross section in pp collisions
can be described by:
σ (n) = PDF(x1 , µF , Q) ⊗ PDF(x2 , µF , Q) ⊗ σ̂ (n) (x1 , x2 , µR , Q),(8.1)

σ̂ = αs σ̂ (0) + αs2 σ̂ (1) + ... + αsn σ̂ (n) + O(αsn+1 ).

(8.2)

where

Here µF and µR are the factorization and renormalization scales. The parton distributionfunctions at energy scale Q can be estimated by the DGLAP equations [117] [118] [119]:
dPDF(x, Q2 )/d log Q2 = P(αs )(x, z)PDF(x/z, Q2 ),(8.3)

where the splitting function P(αs ) can be perturbative expanded byP(αs ) = αs p(LO) + αs2 p(NLO) + ...

(8.4)

We consider two sources of theoretical uncertainties from the perturbative QCD crosssection computation.
The remaining uncertainties from higher orders O(αsn+1 ) are estimated by performing scale variations on renormalization and factorization. A 7-point scale variation of{µF , µR } × {0.5, 0.5}, {0.5, 1}, {1, 0.5}, {1, 1}, {1, 2}, {2, 1}, {2, 2} is considered, and the
maximum among these 7 variations is used to evaluate scale uncertainties.
PDFs are extracted from experimental data using global fitting methods. The uncertainties
arising from experimental uncertainties and the choice of functional forms in the PDF fitting
procedures are incorporated by PDF error ensembles. Each ensemble features slight variations
in parameterization. For event generation in both FRVZ and HAHM signal MC simulations,
the NNPDF2.3 [120] set is used, where an ensemble of 101 internal PDF variations is
included. The sample standard deviation from the central value is assigned as the PDF
uncertainty to the final signal yields.

102

Systematic Uncertainties

Table 8.1 Summary table of the systematic uncertainties on the final yield of FRVZ signal
MC events.
mγd
(GeV)
0.017
0.03
0.06
0.10
0.24

ID
(%)
1.5
1.6
1.6
1.5
1.3

Iso
(%)
0.16
0.19
0.18
0.15
0.13

Reco
(%)
0.84
0.88
0.85
0.79
0.72

Trigger
(%)
0.20
0.23
0.21
0.20
0.13

Lumi
(%)
0.8
0.8
0.8
0.8
0.8

PRW
(%)
0.87
2.6
2.9
2.4
5.5

eγ reso
(%)
0.12
0.33
0.78
0.95
0.90

eγ scale
(%)
0.21
0.76
0.68
0.67
0.15

JER
(%)
1.2
0.41
1.5
0.54
1.5

JES
(%)
2.5
2.2
2.2
3.1
2.6

MC stat
(%)
3.1
3.6
4.2
4.7
9.3

PDF
(%)
3.4
3.4
3.4
3.4
3.4

Scale
(%)
5.5
5.7
5.6
5.6
5.5

Total
(%)
7.9
8.5
9.0
9.2
13

Table 8.2 Summary table of the systematic uncertainties on the final yield of HAHM signal
MC events.
mγd
(GeV)
0.017
0.1
0.4

ID
(%)
0.43
0.48
0.42

Iso
(%)
0.031
0.042
0.029

Reco
(%)
0.85
0.80
0.85

Trigger
(%)
0.019
0.026
0.019

Lumi
(%)
0.8
0.8
0.8

PRW
(%)
1.2
0.51
2.5

eγ reso
(%)
0.12
0.091
0.37

eγ scale
(%)
0.056
0.22
0.0012

JER
(%)
0.33
0.69
1.4

JES
(%)
2.2
2.3
2.5

MC stat
(%)
1.1
2.2
5.8

PDF
(%)
3.4
3.4
3.4

Scale
(%)
5.7
5.9
5.6

Total
(%)
7.3
7.7
9.6

Both scale and PDF uncertainties are implemented by a reweighting method, whichapproximates the probability of a sample produced with another PDF:
w=

PDFnew (x1 , µF , Q) ⊗ PDFnew (x2 , µF , Q).
PDFold (x1 , µF , Q) ⊗ PDFold (x2 , µF , Q)

(8.5)

Fig. 8.1 and Table 8.1 summarize the experimental and theoretical systematic uncertainties
for different γd mass hypotheses in the FRVZ benchmark model. Similarly, Fig. 8.2 andTable 8.2 summarize the uncertainties for the HAHM benchmark models.

8.3

Non-closure Uncertainties

In this analysis, we have adapted the entirely data-driven ABCD method for backgroundestimation as explained in Chapter 7. Consequently, the expected background event yield
uncertainty in SR A is affected by statistical uncertainties propagated from CRs B, C, and D,
rather than the theoretical and experimental effects discussed for the signal events. We haveincluded non-closure uncertainties to account for the difference between the predicted andobserved events in the VRs as an additional systematic uncertainty due to the adaption of the
ABCD method.
To evaluate the background estimation method, three VRs with background compositions
similar to the SR have been constructed: VR1, which is within the Z mass window; VR2,
where the eLJ charge requirement is inverted; and VR3, in the end-cap region as explained inSec. 7.3. For each VR, the non-closure uncertainty is determined by the maximum observed

8.3 Non-closure Uncertainties

103

Fig. 8.1 Contributions from the different systematic sources of uncertainties to the signal
yields for the FRVZ benchmark model.

Fig. 8.2 Contributions from the different systematic sources of uncertainties to the signal
yields for the HAHM benchmark model.

Systematic Uncertainties

0.2
0.017 GeV γ FRVZ
d0.18

0.030 GeV γ FRVZ
d

0.060 GeV γ FRVZ
d

0.16

0.1 GeV γ FRVZ
d0.24 GeV γ FRVZ
d

0.14
0.12

Normalized events

Normalized events

104

0.2

0.16

EntriesMean
Std Dev1704
0.89840.09509

0.8

0.9

0.14
0.12

0.1

0.1

0.08

0.08

0.06

0.06

0.04

0.04

0.02

0.02

−0.5

RΦ

0.18

−0.4

−0.3

−0.2

−0.1

0

0.1
0.2
0.3
0.4
0.5
reco p imbalance - truth p imbalance
T

(a)

0

0.1

0.2

0.3

0.4

0.5

T

0.6

0.7

1
RΦ

(b)

imb
Fig. 8.3 (a) Distribution for measured pimb
T - truth pT for events entering the ABCD plane
for the FRVZ benchmark model. The mean σ is 0.11. (b) Distribution for Rφ entering the
ABCD plane for data. The standard deviation is 0.1.

deviation from the expected event yield, calculated as NA = NB × NC /ND , considering
the statistical uncertainties. To account for the resolution of the measured pimb
T shown in
Fig. 8.3 (a), which has an average σ = 0.11, we evaluate within the range 0.71 < pimb
T < 0.93,
while fixing the showering ratio Rφ at the nominal threshold of 0.96. Similarly, we evaluate
the variation of Rφ within the range 0.86 < Rφ < 0.99 while fixing the pimb
T at the nominal
threshold of 0.82. The range is selected based on the standard deviation of 0.1 in theactual data distribution as shown in Fig. 8.3 (b). Fig. 8.4 and Fig. 8.5 show the nonclosure systematic uncertainties evaluated through scans of pimb
T in VR1, VR2, and VR3.
In addition, we perform the closure checks on BD and CD sub-planes by scanning over
0.71 < pimb
T < 0.93 and 0.86 < Rφ < 0.99, respectively, as shown in Fig. 8.6.
The total systematic uncertainty is calculated as the quadratic sum of non-closure systematic uncertainties from maximum deviations observed in each region to 19%. After
implementing the non-closure systematic uncertainties, the expected and observed events in
NA are consistent within a 1 σ .

105

8.3 Non-closure Uncertainties

(a)

(b)

(c)

Fig. 8.4 Ratio of observed NA / expected NA at different pimb
T thresholds around nominal cutof 0.82 for (a) VR1 within the Z mass window, (b) VR2 where the eLJ charge requirement isinverted, and (c) VR3 in the end-cap region. Statistical uncertainties propagated from regions
B, C, and D are shown in purple. Non-closure uncertainties are shown in red.

106

Systematic Uncertainties

(a)

(b)

(c)

Fig. 8.5 Ratio of observed NA / expected NA at different Rφ thresholds around nominal cut of
0.96 for (a) VR1 within the Z mass window, (b) VR2 where the eLJ charge requirement isinverted, and (c) VR3 in the end-cap region. Statistical uncertainties propagated from regions
B, C, and D are shown in purple. Non-closure uncertainties are shown in red.

107

8.3 Non-closure Uncertainties

(a)

(b)

Fig. 8.6 Ratio of observed NA / expected NA for (a) BD sub-plane at different pimb
T thresholds
around the nominal cut of 0.82 (b) CD sub-plane at different Rφ thresholds around thenominal cut of 0.96. Statistical uncertainties propagated from regions B, C, and D are shownin purple. Non-closure uncertainties are shown in red.

Chapter 9
Results and Discussions
9.1

Results

Fig. 9.1 shows the final event distribution of the full Run-2 data in the ABCD plane. The
observed number of events and the expected number of events in SR A is summarized inTable 9.1. Here, the expected number of events in region A is estimated by NA = NB ×NC /ND ,assuming that the ABCD plane is populated by background events only. Overall, the observed
351 events in A are consistent with the expected 303 ± 33 (stat.) ± 58 (syst.) with nosignificant excess observed. Statistical uncertainty of the expected number in A is propagatedfrom the standard error in regions B, C, and D and dominated by the number in B. Systematic
uncertainty of 19% due to non-closure obtained in VRs is described in Sec. 8.3.
Table 9.1 Summary of expected and observed events entering the ABCD plane.
RegionNumber of events

B
125

C
862

D
356

Expected A
303 ± 33 (stat.) ± 58 (syst.)

Observed A
351

As an additional cross-check, Fig. 9.2 shows the eLJ invariant mass distribution in the
final SR, compared with the prediction of MC simulations SM background processes. No
unexpected behavior is observed.

9.2

Likelihood fit

Since the unblinded data does not show any significant excess compared to the estimatedbackground obtained using the background-only ABCD method, we will use these results toestablish exclusion upper limits for the production cross-section times the Higgs branching
fraction σ × B for γd production in both the FRVZ and HAHM processes. We apply a

110

Furthest eLJ RΦ

Results and Discussions

B

1

D

20

0.9

18

0.8

16

0.7

14

0.6

12

0.5

A

0.4

10

C

8

0.3

6

0.2

4

0.1

2

0
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Lead eLJ pT imbalance

top
data

w

Events

tt
qcd

z

tt
qcd

103

103

102

102

10

10

1

1

10− 1

10− 1

2

eLJ mass [MeV]

1.5
1
0.5
0

Data / MC

Data / MCEventsFig. 9.1 Event distribution of the full Run-2 data in the ABCD plane.

top
data

w

2

z

eLJ mass [MeV]

1.5
1
0.5

0

20

40

60

80

100

120

140

160

180

200

0

0

100

200

300

400

500

eLJ invariant mass [MeV]

(a)

600

700

800

900

1000

eLJ invariant mass [MeV](b)

Fig. 9.2 Full Run-2 data to MC simulation comparisons for eLJ invariant mass in the range(a) [0, 200 MeV], and (b) [0, 1000 MeV] in the final SR A. The MC simulations are scaled
to the observed number of data for shape comparison. No unexpected behavior is observed.

111

9.2 Likelihood fit

likelihood-based modified ABCD method, which simultaneously fits signal and backgroundyields in the four regions. The likelihood function that describes the expected number ofsignal and background events is defined by the product of Poisson functions, taking the form:
L (nA , nB , nC , nD |s, b, τB , τC ) =e−Ni Nini,∏
ni !
i=A,B,C,D(9.1)

where nA , nB , nC , and nD are the observed number of events in each region in data. Ni are theexpected number in each region, which are linear combinations of signal and background
events defined as follows:
NA = s + b
NB = sεB + bτB
NC = sεC + bτC
ND = sεD + bτC τB
Here, s and b correspond to the number of signal and background events in region A. The
signal contamination in regions B, C, and D are described by εi , obtained from signal
MC simulations. τB and τC are the nuisance parameters that define the ABCD ansatz forbackground events.
All the parameters s, b, τB , τC are allowed to float to fit the observed data in four regions.
The systematic uncertainties discussed in Chapter 8 are included in the fit as follows: experimental and theoretical effects on the signal yields are included in the nuisance parameter s
by multiplying the fit likelihood with Gaussian probability density functions (PDFs), wherethe variance of these PDFs corresponds to 68% of the systematic uncertainties. Similarly, thenon-closure effects on the observed number of A is similarly implemented to the nuisanceparameter b by multiplying the fit likelihood with Gaussian PDFs.
The upper limit on signal strength µ defined as the ratio of fitted s to input s with
BR(H → 2γd + X)=0.5% is obtained with the CLS method [121] by performing a global
simultaneous fit based on the profile likelihood method [122] to normalize the observed datain all the regions to the signal expectation. The presence of any excess generated by thesignal is then evaluated by comparing the estimated number to the observed number of eventsin SR A.
Possible signal contamination in the CRs is considered by performing the simultaneous
ABCD fit to signal and background. The impact of signal contamination in this analysis will
be investigated in Sec. 9.3.

112

9.3

Results and Discussions

Exclusion Limits

Using the fitting procedures described in Section 9.2, we obtain CLS as functions of thesignal strength for different γd masses in both the FRVZ and HAHM models. The results areshown in Figures 9.3 and 9.4, respectively.
Figure 9.5 presents the upper limit on BR(H → 2γd + X) at the 95% CL for the FRVZ
model, while Figure 9.6 presents the upper limit on BR(H → 2γd ) for the HAHM model.
It is observed that the observed limit is within 1 σ of the expected limit, and the exclusion
power is stronger for lower mass γd in both benchmark models. This is expected since thisanalysis is optimized for collimated eLJ signatures targeting the low mass regime.

9.3.1

Impact of signal contamination

As we saw from Sec. 7.3, the ABCD agreement is better when subtracting the signal
contamination. To study the impact of signal contamination in regions B, C, and D on the
expected limits, simultaneous fitting to signal and background numbers in the ABCD plane
is performed by neglecting the signal contribution in these regions. The result of the fit isshown in Fig. 9.7 for the FRVZ model and Fig. 9.8 for the HAHM model labeled as noleakage. In comparison, the actual limits shown in Fig. 9.5 and Fig. 9.6 are labeled as withleakage. The limit fittings converge for both scenarios, and it is observed that the exclusion
limit, when subtracting the signal contamination, is approximately 1 σ more powerful than
the actual case with leakage. For future developments, the leakage could be optimized to
improve the search power.

9.3.2

Limits from Muon and Mixed Channel

In addition to the electron channel discussed in this thesis, the muon channel (µLJ-µLJ)
and mixed channel (eLJ-µLJ) are exploited to provide exclusion limits in the higher mass
range of [0.24, 10] GeV, as shown in Fig. 9.9 for both the FRVZ and HAHM models. Dueto the excellent mass resolution of µLJ compared with eLJ, the muon channel and mixed
channel perform a bump hunting on the invariant mass of µLJ, leading to a more competitive
exclusion limit in their phase space.

9.3.3

Higgs portal interpretation

Until now, several search efforts for dark photons in the Higgs portal interpretations in thepromptly decaying scenario (cτ < 0.01 mm) have been conducted by the ATLAS [3] [4]113

1
Expected CLs ± 2σ
Expected CLs ± 1σ
Expected CLs
Observed CLs

0.9
0.8
0.7

1

CLs

CLs

9.3 Exclusion Limits

Expected CLs ± 2σ
Expected CLs ± 1σ
Expected CLs
Observed CLs

0.9
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

2

3

4

0

5

0

1

2

3

4

5

6

7

µ

µ

(b) FRVZ 30 MeV γd1Expected CLs ± 2σ
Expected CLs ± 1σ
Expected CLs
Observed CLs

0.9
0.8
0.7

1

CLs

CLs

(a) FRVZ 17 MeV γdExpected CLs ± 2σ
Expected CLs ± 1σ
Expected CLs
Observed CLs

0.9
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

2

4

6

8

0

10

0

2

4

6

8

10

µ

14
µ

(c) FRVZ 60 MeV γd
CLs12(d) FRVZ 100 MeV γd1Expected CLs ± 2σ
Expected CLs ± 1σ
Expected CLs
Observed CLs

0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

0

10

20

30

40

50
µ

(e) FRVZ 240 MeV γdFig. 9.3 CLS as functions of the signal strength µ for different γd masses in the FRVZ
benchmark model. The signal strength µ = 1 refers to BR(H → 2γd + X)=0.5%. The upper
limit at 95% is highlighted in red.

114

1

CLs

CLs

Results and Discussions

Expected CLs ± 2σ
Expected CLs ± 1σ
Expected CLs
Observed CLs

0.9
0.8
0.7

1
Expected CLs ± 2σ
Expected CLs ± 1σ
Expected CLs
Observed CLs

0.9
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

0.1

0.2

0.3

0.4

0.5

0

0.6

0

0.5

1

1.5

2

µ

µ

(a) HAHM 17 MeV γd
CLs

2.5

(b) HAHM 100 MeV γd1Expected CLs ± 2σ
Expected CLs ± 1σ
Expected CLs
Observed CLs

0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

0

5

10

15

20
µ

(c) HAHM 400 MeV γdFig. 9.4 CLS as functions of the signal strength µ for different γd masses in the HAHM
benchmark model. The signal strength µ = 1 refers to BR(H → 2γd )=0.5%. The upper limit
at 95% is highlighted in red.

115

10
observed
expected
expected ± 1 σ
expected ± 2 σ

d95% CL limits on Br(H→ 2γ +X)

9.3 Exclusion Limits1

s=13 TeV, 140 fb-1 95%
CL limitseLJ-eLJ FRVZ

10−1

10−2 br = 1%

10−3

0.05

0.1

0.15

0.2

0.25

mγ [GeV]dd

95% CL limits on Br(H→ 2γ )Fig. 9.5 Expected and observed limits at the 95% CL on BR(H → 2γd + X) for the FRVZ
model promptly decaying γd (cτ < 0.01 mm). Systematic uncertainties are included. For
mγd > 2mµ , the branching ratio of muon decays is also taken into account according to
Fig. 3.6.
101s=13 TeV, 140 fb-1 95%
CL limitseLJ-eLJ HAHM

observed
expected
expected ± 1 σ
expected ± 2 σ

10−1
10−2

br = 1%10−3

br = 0.1%

10−4 00.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4mγ [GeV]dFig. 9.6 Expected and observed limits at the 95% CL on BR(H → 2γd ) for the HAHM model
promptly decaying γd (cτ < 0.01 mm). Systematic uncertainties are included. For mγd > 2mµ ,the branching ratio of muon decays is also taken into account according to Fig. 3.6.

116

Results and Discussions

95% CL limits on FRVZ Br(H 2 d+X)

100

Expected (with leakage)
Expected (no leakage)
Expected ±1 (with leakage)
Expected ±1 (no leakage)

10 1

10 2

10 3

17 30

60

100

240

d mass [MeV]Fig. 9.7 Expected and observed limits at the 95% CL on BR(H → 2γd + X) for the FRVZ
model promptly decaying γd (cτ < 0.01 mm). Systematic uncertainties are included. Signal
contributions in regions B, C, and D are zero in the label no leakage. For mγd > 2mµ , thebranching ratio of muon decays is also taken into account according to Fig. 3.6.

95% CL limits on HAHM Br(H 2 d)100

Expected (with leakage)
Expected (no leakage)
Expected ±1 (with leakage)
Expected ±1 (no leakage)

10 1

10 2

10 3

10 4

17

100

400

d mass [MeV]Fig. 9.8 Expected and observed limits at the 95% CL on BR(H → 2γd ) for the HAHM
model promptly decaying γd (cτ < 0.01 mm). Systematic uncertainties are included. Signal
contributions in regions B, C, and D are zero in the label no leakage. For mγd > 2mµ , thebranching ratio of muon decays is also taken into account according to Fig. 3.6.

117d95% CLs limits on Br(H→ 2γ )d95% CLs limits on Br(H→ 2γ + X)

9.3 Exclusion Limits

10

Observed CLs
Expected CLs
Expected ± 1σ
Expected ± 2 σs=13 TeV, 140 fb-1, FRVZ

1
−1

10

10−2
10−3
10−4
−5

Observed CLs
Expected CLs
Expected ± 1σ
Expected ± 2 σs=13 TeV, 140 fb-1, HAHM

1
−1

10

10−2
10−3
10−4
10−5

10

10−6

10

3×10−11

2

3

4 5 6 7 89
mγ [GeV]10−6

3×10−1

1

2

d

(a)

3

4 5 6 7 89
mγ [GeV]d(b)Fig. 9.9 95% CL exclusion limit (a) on BR(H → 2γd + X) for the FRVZ model, and (b) on
BR(H → 2γd ) for the HAHM model in the µLJ-µLJ and eLJ-µLJ combined channel of fullrun-2 pp collision data collected in the ATLAS experiment. Resonant states are blinded.
and CMS [5] experiments at the LHC, and the excluded phase-spaces are limited to γdmass larger than 0.25 GeV. By exploring signatures of γd s that promptly decay into themore challenging electron final states, this analysis pushes the search limit to the previously
unexplored [0.017, 0.24] GeV lower mass range benchmarked by the FRVZ and HAHM
models. It provides the first exclusion limit for the Higgs portal in the FRVZ and HAHM
dark sector model, which is way below the BR(H → inv)< 11% constraint. Furthermore,this analysis can potentially be sensitive in interpreting even lower mass range and eventuallylimited by the resolution of ID tracking performance, which is 130 µm in the TRT in the
ATLAS experiment.

9.3.4

Vector portal interpretation

In this analysis, the search results for γd s have been optimized for the promptly decaying
scenarios, specifically where cτ < 0.01 mm. To compare these results with constraints fromother experiments, the exclusion limits are interpreted at 90% CL in the vector portal using
Eq. 3.5, assuming the production of γd s through the Higgs portal in the FRVZ and HAHM
models. Fig. 9.10 shows the exclusion contours as a function of ε and mγd for the FRVZ
model, while Fig. 9.11 shows them for the HAHM model. It is shown that this analysis
extends the exclusions to unsearched regions of ε ∼ 10−3 in the vector portal through the
Higgs portal in both the FRVZ and HAHM models, compared with other vector-portal-only
experiments and the displaced search in ATLAS which focuses on decaying of γd outside theinner detector. Note that cτ < 0.01 mm is a conservative estimate, and this analysis could besensitive to γd s with longer lifetimes (smaller ε). For future improvements, we can performVector portal coupling ε118

Results and Discussions

10−2

FRVZ Model
H→2γ +X

10−3dmH = 125 GeV
90% CL observed limits

10−4

Run-2 Prompt (140 fb-1)
B=10.0%
B=5.0%
B=1.0%

10−5

Run-1 Prompt (20.3 fb-1)
JHEP 02 (2016) 062

10−6

B=10%
Run-2 displaced (139 fb-1)
arXiv:2311.18298

10−7

B=10%
B=5%
B=1%

10−8

Non-ATLAS searches−1

10

JHEP 06 (2018) 004

1
10
Dark Photon mass [GeV]

Vector-Portal-only limits

Fig. 9.10 90% exclusion contours as a function of ε and mγd for the FRVZ model in theassumption of γd decay length cτ < 0.01 mm. The limits are obtained by assuming a decay branching ratio of Higgs boson into γd s
ranging between 10% to 1%, where the darker colors correspond to stronger choices ofbranching ratio. The figure also shows previous ATLAS Run-1 prompt [4], ATLAS Run-2
dispaced [53], and other vector-portal-only limits.
lifetime reweighting to extrapolate signal efficiency using samples generated with different γdmean decay lifetimes, which will fully exploit the limits of this analysis in the vector portal.

9.4

Future developments

The work in this thesis lays the groundwork for future analyses at the LHC. By utilizing
the scenario of merged clusters with separate tracks, which provide a rich phenomenology,
we can access and probe collimated decays of dark photons and other new physics particles.
A potential improvement comes from the intermediate scenario where electrons from dark
photon decays are close but not merging in the calorimeter. As shown in this thesis, constructing such objects using standard definitions results in lower efficiency. In future upgrades
like HL-LHC, dedicated triggers targeting such signatures could be developed based on theunique shower shapes and tracking information. Additionally, cluster reconstruction and119

Vector portal coupling ε

9.4 Future developments

10−2

HAHM Model
H→2γ

10−3

d

mH = 125 GeV
90% CL observed limits

10−4

Run-2 Prompt (140 fb-1)
B=10.0%
B=5.0%
B=1.0%
B=0.5%
B=0.1%

10−5

Run-2 displaced (139 fb-1)−6

JHEP 06 (2023) 153

10

B=10%
B=5%
B=1%

10−7

Non-ATLAS searches
JHEP 06 (2018) 004

Vector-Portal-only limits

10−8
10−1

1
10
Dark Photon mass [GeV]

Fig. 9.11 90% exclusion contours as a function of ε and mγd for the HAHM model in theassumption of γd decay length cτ < 0.01 mm. The limits are obtained by assuming a decaybranching ratio of Higgs boson into γd s ranging between 10% to 0.1%, where the darker
colors correspond to stronger choices of branching ratio. The figure also shows previous
ATLAS Run-2 dispaced [53], and other vector-portal-only limits.

120

Results and Discussions

isolation criteria can be further optimized. While this analysis focuses on promptly decaying
scenarios (ε ≳ 10−3 ), studying the effects of vertex fitting from ID tracks can help bridge thegap between prompt and displaced analyses (ε ≲ 10−4 ).

Chapter 10
Conclusion
In this thesis, we have presented a search for dark photons that promptly decay into electron
final states with a decay length cτ < 0.01 mm in 140 fb−1 of pp collision data collected at√
s = 13 TeV with the ATLAS detector. The search investigates evidence of dark sector Higgs
portal and vector portal production of γd s using the FRVZ and HAHM models. Specifically,in the FRVZ model, the sensitivity is explored under the assumption that the masses of HLSP
and fd are a few GeV, with the condition that mHLSP + mγd < m fd (detailed mass parameters
are summarized in Table 5.2). Similar assumptions are made in other experiments [4] [53].
The analysis targets the physics-motivated low-mass dark photons by exploiting uniquesignatures from collimated electron pairs in the ATLAS detector. Utilizing the resolutiondifference between the inner detector and the calorimeter, we have developed an innovative
criterion for LJ reconstruction from merged clusters associated with separate tracks. Thisextends the Higgs portal sensitivity limit from 0.25 GeV in previous ATLAS and CMS efforts
to 17 MeV. Vector portal is also interpreted for γd s in the FRVZ and HAHM Higgs portal
production. Compared with other vector-portal-only experiments, we have set exclusions to
unexplored regions around ε ∼ 10−3 .
No significant excess of events is observed compared to the expected number of background events, and upper limits are set on the branching fractions of Higgs productions ofγd s for the models of FRVZ and HAHM. The first prompt dark photon exclusion with a limitof 0.7% BR(H → 2γd + X) for the FRVZ model, and 0.07% BR(H → 2γd ) for the HAHM
model at mγd = 17 MeV is set, which is far below the BR(H → inv)= 11%.

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