論文 / 著書情報
Article / Book Information
題目(和文)ATLAS検出器を用いたヒッグスを介し崩壊するチャージーノ・ニュー
トラリーノ対の直接生成事象探索

Title(English)

Search for direct production of charginos and neutralinos decaying via
Higgs boson with the ATLAS detector

著者(和文)

留目和輝

Author(English)

Kazuki Todome

出典(和文)

学位:博士(理学),学位授与機関:東京工業大学,
報告番号:甲第10929号,
授与年月日:2018年9月20日,
学位の種別:課程博士,
審査員:陣内 修,久世 正弘,河合 誠之,中村 隆司,山口 昌英

Citation(English)

Degree:Doctor (Science),
Conferring organization: Tokyo Institute of Technology,
Report number:甲第10929号,
Conferred date:2018/9/20,
Degree Type:Course doctor,
Examiner:,,,,

学位種別(和文)

博士論文

Type(English)

Doctoral Thesis

Powered by T2R2 (Tokyo Institute Research Repository)

Ph.D Thesis

Search for direct production of charginos andneutralinos decaying via Higgs boson with the
ATLAS detector

Kazuki Todome
Tokyo Institute of Technology, Department of Physics
Jinnouchi Lab.

August, 2018

i

Abstract
The basic model for particle physics, the Standard Model (SM), gives precise predictions, whichhave been verified by various experiments in past years. However, there are some problems whichcannot be explained by the SM, such as the hierarchy problem and dark matter. In order to give
solutions to the problems, various types of beyond the standard models have been proposed. One ofsuch models is the SUperSYmmetry (SUSY). This thesis presents a search for the direct production
0of charginos χ̃±
1 and neutralinos χ̃2 which are the super partners of the gauge bosons predicted by
the SUSY model.
In this thesis, the events where charginos decay via W boson and second lightest neutralinos decay
via Higgs, and then Higgs decays to diphoton and W decays to ℓν, such as0000pp → χ̃02 + χ̃±
1 → χ̃1 + h + χ̃1 + W → χ̃1 + γ + γ + χ̃1 + ℓ + ν

is chosen as the target process. In this channel, some of background processes are strongly suppressedby using a mass reconstructed by diphoton. Therefore, although expected signal yields are relatively
lower than other channels, high significance is expected
due to the scarce backgrounds.
√−1
The analysis is performed with 36.1 fb of s = 13 TeV proton-proton collision data collectedby the ATLAS detector at LHC in 2015 and 2016. The background sources which can be suppressedby the diphoton mass cut are classified as non-peaking background, and the background sources
which have Higgs in their process are classified as peaking background. The yield of non-peaking
background is evaluated by data-driven method using data out of the signal region. And the yields
of peaking background and signals are evaluated using simulation samples.
√
The analysis procedure has been constructed based on the previous analysis performed with s =8 TeV proton-proton collision data. A new selection criterion, b-jet veto, is introduced, in orderto suppress one major background, tt̄h process. This new selection improves sensitivity by ∼ 10%.
Then, defined signal region is further optimized by dividing into two regions, SRa and SRd, instead to
use tight criteria. Using the divided signal regions, significance is improved by ∼ 300% at maximum.
Based on the optimized signal region, expected limit on excluded model parameters is evaluated.
Evaluated limit is distributed around mχ̃± ,χ̃0 = 180 GeV, which is improved from mχ̃± ,χ̃0 = 160 GeV
12
12
of the limit evaluated in the 8 TeV analysis.
After the study above have been performed, the data is unblinded to compare with the expectation.
There are two events in SRa and nine events in SRd, which 0.36 ± 0.22 events and 5.35 ± 0.95 eventsare expected in SRa and SRd respectively. This mild excess is equivalent to 1.93σ deviation in
SRa and 1.36σ deviation in SRd. Model dependent upper limits on the signal cross section areevaluated for all model assumed in the analysis. All the evaluated upper limits on the cross section
are larger than the assumed model. Therefore, no model assumed in the analysis were excluded.
Model independent upper limits on the signal yields are evaluated as 5.7 fb in SRa and 10.4 fb in
SRd. These results suggest importance of further study with more data statistics expected in the
on-going and future experiments.

iii

Contents
Chapter 1
1.1
1.2
1.3

Introduction
Standard Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Supersymmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Author’s contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1
1
4
9

Chapter 2
2.1
2.2

Large Hadron Collider and The ATLAS detector
LHC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
ATLAS detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

11
11
14

Chapter 3
3.1
3.2

Data and Simulation samples
Data samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Simulation samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

25
25
26

Chapter 4
4.1
4.2

Object Reconstruction
Term definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

31
31
32

Chapter 5
5.1
5.2
5.3

Event selection
Overview of development of analysis procedure . . . . . . . . . . . . . . . . . .
Overview of event signatures . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Signal region definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

41
41
41
42

Chapter 6
6.1
6.2

Signal and background modeling
Non-peaking Backgrounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Signal and Peaking Background . . . . . . . . . . . . . . . . . . . . . . . . . .

51
51
55

Chapter 7
7.1
7.2
7.3
7.4

Optimization of Signal regions
Idea of optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Statistical definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Procedure of optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Optimization results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

57
57
57
62
62

Chapter 8
8.1
8.2
8.3
8.4

Systematic and statistical uncertainty
Non-peaking Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Peaking Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Expected exclusion upper limit . . . . . . . . . . . . . . . . . . . . . . . . . . .

69
69
69
72
73

Chapter 9
9.1
9.2
9.3

Results
Observed events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Observed upper limit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

77
77
77
79

iv
Chapter 10

Contents
Conclusion

85

Acknowledgements

87

AppendixA93

Kinematic distributions in signal region

1

Chapter 1

Introduction
The Standard Model (SM) of the particle physics was established in the late ’60. It precisely describes
the particles phenomena, and most of the observations and measurements from the experiments agreewith the predictions by the SM so far. However, there are some facts that cannot be explained by
the SM. In order to explain those, many extended models are proposed, which are known as Beyond
Standard Models (BSM). One of the promissing BSM is the SUperSYmmetry (SUSY) theory. In
this chapter, theoretical and experimental backgrounds of the particle physics are reviewed.

1.1 Standard Model
The Standard Model (SM) is the basic theoretical framework for the particle physics. The SM gives
predictions about interactions and behaviour of elementary particles. The SM assumes twelve flavorof fermions, which have 1/2 of spin and consist “matter”, and three types of interactions via bosons.
Table 1.1 shows the summary of the fermions. As shown in the table, the fermions consist of six
types of quarks and six types of leptons. Both of them are categorized into three generations. The
type is denoted as “flavor”.
The interaction between those fermions are mediated by the propagation of the vector bosons
following gauge theory. The bosons assumed in the SM are summarized in Table 1.2. As shownin the table, interactions in the SM are explained by two theories; the Quantum ChromoDynamics(QCD), which has SU (3)C symmetry, and the Glashow-Weinberg-Salam (GWS) theory, which has
SU (2)L × U (1)EM symmetry.
The QCD explains the strong interactions between “coloured” particles such as quarks and gluons
which are force carrier particles in the strong interaction [1]. Since gluons themselves have colour,

Table1.1 Fermions in Standard Model

Category
Quarks
Leptons

1stup (u)
down (d)electron (e)electron neutrino (νe )Generations
2ndcharm (c)strange (s)muon (µ)
mu neutrino (νµ )Charge3rd
top (t)bottom (b)tauon (τ )tau neutrino (ντ )

+2/3
-1/3
-1
0

Table1.2 Bosons in Standard Model

Name
Gluon
photonWeak boson(g)(γ)(W ± )(Z 0 )

Interactions
StrongElectromagnetic
Wek

Charge00±10TheoryQuantum Chromodynamics
Glashow-Weinberg-Salam theory

2

Chapter 1 Introduction

the potential between coloured particles is increased in proportion to the distance between particles.
From increased potential, another pair of coloured particles are generated. As a result, coloured
particles cannot be observed directly and only colour singlet hadrons can be observed. This is called“colour confinement”.
The GWS theory explains the unified electroweak interaction [2, 3, 4]. At first, two fields are
introduced; SU (2)L gauge field (Wµ ) and U (1)EM gauge field (Bµ ). Those fields under the gauge
symmetries expect mass less bosons. Then, after the spontaneous symmetry breaking, often called
as the Brout-Englert-Higgs mechanism, those two fields are mixed as following:1
Wµ± = √ (Wµ1 ∓ iWµ2 )23Zµ = Wµ cos θW − Bµ sin θW
Aµ = Wµ3 sin θW + Bµ cos θW

(1.1)
(1.2)
(1.3)

where θW is Weinberg angle, defined as:sin θW =

e
g

(1.4)

where e is the coupling constant of Aµ or the elementary charge, and g is the coupling constant of
Wµ . The gauge particles quantized by those gauge fields are listed in Table 1.2; γ is from Aµ , W ± isfrom Wµ± and Z 0 is from Zµ . The Brout-Englert-Higgs mechanism predicts the existence of a scalarboson, called Higgs boson (h).

1.1.1 Standard Model in LHC experiment
In last decades, many collider experiments have been conducted to verify the SM, and to search for
the BSMs.
Figure 1.1 shows the observed and the prediction for the cross section of various physics processes.
The data points are measurements by the LHC experiment, which is used in this thesis. Detail ofthe experiment will be described in next chapter. The theoretical prediction, given as gray bandin the figure, is from 10−3 to 1011 pb. Since those processes have origin of proton-proton collision,
higher yields from QCD activities are expected than the yields from the electroweak activities. Since
particles generated from the QCD have colour, it decays to bunch of hadrons and constructs “jet”
in the detector. As expected, jet processes have the next-to-highest yields as shown in the figure*1 .
Although the range of predicted cross section is wide, almost all experimental measurements are
consistent with the theoretical predictions.
One of the remarkable experimental results in the LHC experiment is the discovery of the Higgs
particle. After the discovery of tau neutrino in 2000, the Higgs particle was the last missing elementin the SM. It was discovered at the ATLAS and the CMS experiment in 2012 [6, 7]. Later it was
confirmed that the characteristic of the discovered particle is consistent with the SM prediction
about the Higgs particle. The mass of the Higgs particle was measured as 124.97 ± 0.24 GeV [8].
The discovery of the Higgs particle completes the SM.

1.1.2 Hierarchy problem and dark mater
Although the SM gives predictions for most of the physics processes with high accuracy, which areverified by various experiments, there are some issues that cannot be explained by the SM. In thissection, two such issues are introduced; the hierarchy problem and dark matter.
The hierarchy problem can be seen in the calculation of the Higgs mass. As described in theprevious section, the Higgs mass is experimentally measured as 125 GeV. On the other hand, the*1 The highest process is the inelastic scattering of proton-proton collision.

1.1 Standard Model3

σ [pb]

Standard Model Production Cross Section Measurements

Status: July 2018

total (2x)1011

ATLAS Preliminary

inelastic

106

Run 1,2

incl√

Theorys = 7,8,13 TeV
LHC pp

Data 4.5 − 4.9 fb−1

dijets105

pT > 25 GeV

104

LHC pppT > 125 GeV

LHC ppnj ≥ 1

102

Data 3.2 − 79.8 fb−1WWnj ≥ 1WZ
nj ≥ 2

Wt

10

ZZ

nj ≥ 2nj ≥ 2

1

t -channj ≥ 1nj ≥ 1nj ≥ 3nj ≥ 4nj ≥ 31
nj ≥ 6

WW
WZ

WW
total

WZ

ggF

ZZ ZZ

nj ≥ 3nj ≥ 3nj ≥ 5nj ≥ 5nj ≥ 4H→WWnj ≥ 4nj ≥ 4nj ≥ 6nj ≥ 5nj ≥ 7

VH

H→ττ
tZj

nj ≥ 5WγH→bbs -chan

Zγ

VBF

H→WW

nj ≥ 610−1√
s = 13 TeV

nj ≥ 0total

pT > 100 GeVnj ≥ 2√
s = 8 TeV
Data 20.2 − 20.3 fb−1

nj ≥ 0103√
s = 7 TeVnj ≥ 8nj ≥ 6nj ≥ 710−2

H→γγnj ≥ 7nj ≥ 7

H→ZZ →4`

W ±W ±

10−3

WZ

pp

Jets

γ

W

Z

tt̄

t

VV

tot.

tot.

γγ

H

WV Vγ tt̄W tt̄Z tt̄H tt̄γ γγγ Wjj Zjj WWZγγWγγWWγ ZγjjVVjj
EWK

tot. tot. tot.

EWK Excl.

EWK

tot.

Figure1.1 Summary of several Standard Model total and fiducial production cross section
measurements, corrected for leptonic branching fractions, compared to the corresponding theoretical expectations. All theoretical expectations were calculated at NLO or higher. The
luminosity used for each measurement is indicated close to the data point. Some measurements have been extrapolated using branching ratios as predicted by the Standard Model for
the Higgs boson. Uncertainties for the theoretical predictions are quoted from the original
ATLAS papers. They were not always evaluated using the same prescriptions for PDFs andscales. The Wgamma and Zgamma theoretical cross-sections have non-perturbative corrections
applied to the NNLO fixed order calculations (PRD 87, 112003 (2013)). Not all measurements
are statistically significant yet. The figure is cited from [5]mass can be calculated from the quantum field theory. The theoretical calculation explains theexperimentally measured mass m2h as:
m2h = m2h0 + δm2h

(1.5)

where mh0 is the Higgs bare mass and δmh is the quantum correction. mh0 is free parameter in thetheory. However, the quantum correction is calculated asδmh = −

|λf |2 2
Λ − O(log(Λ2 )) + · · ·
8π 2

(1.6)

where λf is the Yukawa coupling of the fermion f and Λ is the cut-oﬀ scale parameter meaning
upper limit of the energy scale that the SM is valid. If only the SM is considered, Λ is expected tobe O(1019 ) GeV, which is the Planck scale. Since mh is measured as 125 GeV, mh0 is required to be

4

Chapter 1 Introduction

O(1019 ) GeV and two huge terms have to cancel out unnaturally to the level of O(102 ) GeV. This
unnatural “tuning“ is called hierarchy problem.
The other issue introduced in this section, dark matter, was obtained from the observation in theastrophysics. From the precise measurements by the Planck satellite [9], it is suggested that the SMparticles can explain only 4.9% of energy of the whole universe. The rest is covered by dark matter,
which is unknown to be massive particles, covering 26.8%, and dark energy, which is unknown energy
accelerating the expansion of the universe, covering 68.3%. Since dark matter is not directly detected
yet, the interaction between the SM particles and the dark matter must be very small.
The issues introduced above cannot be explained by the SM alone. In order to explain those, manyextended models have been constructed, which are known as the Beyond Standard Model (BSM).
One of the BSM is the Supersymmetry. It can explain both hierarchy and dark matter problems. It
is explained in the next section.

1.2 Supersymmetry
1.2.1 Mechanism of Supersymmetry
The basic idea of SUperSYmmetry (SUSY) is to introduce a new symmetry between bosons andfermions[10]. SUSY assumes “supperpartner” for all the SM particles. The new particles are called
SUSY particles. The SUSY particles are summarized in Table 1.3. As shown in the table, supperpartners of quark and lepton are called squark and slepton respectively. Supperpartners of bosons
are called Gluino, Wino, Bino and Higgsino. Within a framework of the SM + SUSY, the operator
transforming fermions and bosons are
Q |Fermion⟩ = |Boson⟩ , Q |Boson⟩ = |Fermion⟩(1.7)

and should not retain the symmetry.
The SUSY model can explain the hierarchy problem. The hierarchy problem is caused by thedominant quantum corrections of fermions. In SUSY model, all fermions have boson supperpartners
which are supposed to have the same mass. And correction term of boson have opposite sign to
the fermion correction and vice versa. Therefore, the correction terms are naturally cancelled and“tuning” is not needed anymore.
Because the SUSY particles are not discovered yet, the SUSY is broken in the our universe.
However, even after the symmetry breaking, quantum corrections for higgs mass must be cancelled
out naturally. In order to achieve such symmetry braaking, “soft” SUSY breaking is introduced as:
L = LSUSY + LSUSY(1.8)

where LSUSY contains all of the gauge and Yukawa interactions and preserves SUSY invariance,and Lsoft violates SUSY but contains only mass terms and coupling parameter with positive mass
Table1.3 SUSY particles

name˜ s̃, b̃)Squarks (ũ, c̃, t̃, d,spin
0Sleptons (ẽ, µ̃, τ̃ , ν˜e , ν˜µ , ν˜τ )Quarks (u, c, t, d, s, b)
Leptons (e, µ, τ, νe , νµ , ντ )Gluino (g̃)
Wino (W̃ )corresponding SM particles

Gluon (g)1/2
Weak boson (W, Z) and photon (γ)

Bino (B̃)
Higgsino (H̃)

1/2

Higgs (h)1.2 Supersymmetry5¯
Figure1.2 Proton decay via SUSY particle (s̃).

dimension, which are known as terms not to lead quadratic divergence even after symmetry breaking.
Because of the Lsoft , supperpartners are expected to be heavier than the SM particles. Even after
the symmetry breaking due to the Lsoft , there are no quadratic divergence shown in Equation 1.6.
The introduction of SUSY allow violations of baryon number (B) or lepton number (L). A famous
process to violate the baryon number is the proton decay. With introduced SUSY particles, a proton
may decay via a squark into a lepton and a meson, as shown in Figure 1.2. However, it is known thatsuch violations are extremely small from severe experimental constraints [11]. In order to explainsuch observation, new symmetry, R-parity, is introduced. It is defined as
R = (−1)2S+3B−L(1.9)

where S is spin. The SM particles have a positive R-parity, and the SUSY particles have a negative
R-parity. R-parity is expected to be conserved*2 . Because of R-parity conservation, SUSY particles
are expected to be generated by pair production and the Lightest SUSY Particle (LSP) cannot decay
to SM particles. Since LSP is not discovered yet, it is expected to be neutral and not to have colour.
Among the SUSY particles shown in Table 1.3, Wino, Bino, and Higgsino are mixed. They
are called electroweak gauginos. They are represented as mass eigenstates by χ̃0i (i = 1, 2, 3, 4)
0(neutralino) for neutral particles and χ̃±i (i = 1, 2) (chargino) for charged particles. χ̃1 satisfies the
expected conditions about the LSP described above.
Regarding dark matter, the LSP can be a good candidate. As described above, the LSP cannot
decay to any other particle. And the expected interaction between LSP and the SM particles isonly the weak interaction, which is extremely diﬃcult for the direct detection. This expectation can
explain the reason why dark matter has not been discovered yet. Those characteristics are ideal forthe dark matter candidate.
The soft SUSY breaking term Lsoft can be defined by 105 parameters. However, many of thoseparameters are strongly constrained by experimental observations such as neither CP-violation nor
flavor changing neutral currents. By assuming first and second generation universality, free input
parameters are only 19, which are:
• The ratio of the vacuum expectation value of the two higgs fields (1 parameter)• The mass of the pseudoscalar higgs boson (1 parameter)• The higgs-higgsino mass parameter (1 parameter)• The bino, wino, and gluino mass parameters (3 parameters)• The squarks and sleptons masses (10 parameters)• The third generation trilinear couplings (3 parameters)
This model is called Phenomenological Minimal Supersymmetric Standard Model (pMSSM) [13].
The study described in this thesis is based on the pMSSM.

*2 There are some models assuming R-parity violation. But from the fact that proton decay is not observed so far,there are upper limit on the R-parity violating couplings [12].

6

Chapter 1 Introduction

Figure1.3 Cross sections for SUSY particle production at
figure is cited from [14]√s = 8 TeV and 13、14 TeV. The

1.2.2 SUSY searches in LHC experiment
In the LHC experiment, many types of SUSY searches have been performed. Because mass hierarchyof SUSY depends on the SUSY modeling parameters, many types of the pair production modes are
candidates for the searches. Figure 1.3 shows the expected cross sections for SUSY particle pair
production at the diﬀerent center of mass energies in proton-proton collisions. As shown in the figure,gluino or squarks, which are generated by QCD interaction, have large cross sections. Therefore,
if QCD production mode is accessible by experiment, it is expected to be observed in early stageof LHC experiment. However, as seen in Figure 1.4, even after the analysis using ∼ 20 fb−1 of
8 TeV data, experimental hints for the existence of SUSY particles have not been seen so far. Thissuggests that SUSY pair production may occur via QCD interaction but it is not accessible yet
simply due to their high masses, or the production mode accessible by experiments is not QCD butelectroweak interaction, such as the pair production of charginos and/or neutralinos. In this thesis,
electroweak interaction is assumed as a production mode accessible by experiments, and we searchfor pair production of electroweak gauginos.

1.2.3 Electroweak gauginos
The search for pair production of electroweak gauginos is generally performed with the model socalled “simplified” model. As described in Section 1.2.1, electroweak gauginos are expected to bemixed. However, in the simplified model, “pure” LSP and Next-to-Lightest SUSY Particle (NLSP)
are assumed. In this thesis, LSP is assumed to be the bino, and NLSP is assumed to be thedegenerated wino triplet. And the other supperpartners are assumed to be heavy and decoupled*3 .
The direct search for general neutral LSP has been performed as a general search for dark matter,such as [16]. However, such study is challenging because similar event kinematics can be seen in many
SM process, and therefore large background contributions are expected. Hence, searches for direct*3 For the cross section calculation, all other supperpartners except for wino and bino are assumed to have 100

TeV mass. And mixing angles and trilinear couplings are assumed to be zero.

1.2 Supersymmetry

7
ATLAS√ Preliminary

ATLAS SUSY Searches* - 95% CL Lower Limits
Status: July 2015
Model

miss Re, µ, τ, γ Jets E
T

MSUGRA/CMSSM

GGM (bino NLSP)GGM (higgsino-bino NLSP)GGM (higgsino-bino NLSP)GGM (higgsino NLSP)
Gravitino LSP0b̃1 b̃1 , b̃1 →bχ̃1±b̃1 b̃1 , b̃1 →tχ̃1±t˜1 t˜1 , t˜1 →bχ̃100t˜1 t˜1 , t˜1 →Wbχ̃1 or tχ̃10t˜1 t˜1 , t˜1 →cχ̃1t˜1 t˜1 (natural GMSB)t˜2 t˜2 , t˜2 →˜t1 + Z

Long-lived
particles

EW
direct

3rd gen.
g̃ med.

0g̃g̃, g̃→bb̄χ̃10g̃g̃, g̃→t¯t χ̃10g̃g̃, g̃→t¯t χ̃1+g̃g̃, g̃→b¯tχ̃1

3rd gen. squarks
direct production

Inclusive Searches

0q̃q̃, q̃→qχ̃10q̃q̃, q̃→qχ̃1 (compressed)
0q̃q̃, q̃→q(ℓℓ/ℓν/νν)χ̃10g̃g̃, g̃→qq̄χ̃1±0g̃g̃, g̃→qqχ̃1 →qqW ± χ̃10g̃g̃, g̃→qq(ℓℓ/ℓν/νν)χ̃1
GMSB (ℓ̃ NLSP)000-1 e, µ0-1 e, µRPV

3b7-10 jets
3b
3b

20.3
20.3
20.3
20.3
20.3
20
20
20.3
20.3
20.3
20.3
20.3
20.3

F1/2 scale

Yes
Yes
Yes
Yes

20.1
20.3
20.1
20.1

g̃
g̃
g̃
g̃

Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes

20.3
20.3
20.3
20.3
20.3
20.3
20.3
20.3

W̃

+ −
±
Disapp. trk
1 jet
Direct χ̃1 χ̃1 prod., long-lived χ̃1+ −±dE/dx trk
Direct χ̃1 χ̃1 prod., long-lived χ̃1Stable, stopped g̃ R-hadron
1-5 jets0
Stable g̃ R-hadron
trk
0
GMSB, stable τ̃, χ̃1 →τ̃(ẽ, µ̃)+τ(e, µ) 1-2 µ002γGMSB, χ̃1 →γG̃ , long-lived χ̃10
displ. ee/eµ/µµg̃g̃, χ̃1 →eeν/eµν/µµν
0displ. vtx + jets
GGM g̃g̃, χ̃1 →ZG̃

Yes
Yes
Yes
Yes
-

20.3
18.4
27.9
19.1
19.1
20.3
20.3
20.3

χ̃±1
χ̃±1
g̃
g̃
χ̃01
χ̃01
χ̃01
χ̃01

Yes
Yes
Yes
Yes
-

20.3
20.3
20.3
20.3
20.3
20.3
20.3
20.3
20.3

ν̃τ
q̃, g̃
χ̃±1
χ̃±1
g̃
g̃
g̃
t̃ 1
t̃ 1

Yes

20.3

c̃

χ̃+1 χ̃−1 , χ̃+1 →W χ̃01 , χ̃01 →eeν̃µ , eµν̃eχ̃+1 χ̃−1 , χ̃+1 →W χ̃01 , χ̃01 →ττν̃e , eτν̃τg̃g̃, g̃→qqq
00g̃g̃, g̃→qχ̃1 , χ̃1 → qqqg̃g̃, g̃→˜t1 t, t˜1 →bst˜1 t˜1 , t˜1 →bst˜1 t˜1 , t˜1 →bℓ
0

Scalar charm, c̃→cχ̃1eµ,eτ,µτ
2 e, µ (SS)0-3 b4 e, µ3 e, µ + τ
6-7 jets
0
6-7 jets
02 e, µ (SS)0-3 b
2 jets + 2 b
02 e, µ
2b
0

2c

ℓ̃
χ̃±1
χ̃±1
χ̃±1 , χ̃02
χ̃±1 , χ̃02
χ̃±1 , χ̃02χ̃02,310−1√

s = 7 TeV

s = 7, 8 TeV
References = 8 TeV

1.8 TeV m(q̃)=m(g̃)
0

850 GeV
100-440 GeV
780 GeV
1.33 TeV
1.26 TeV
1.32 TeV
1.6 TeV
1.29 TeV
1.3 TeV
1.25 TeV
850 GeV
865 GeVm(χ̃1 )=0 GeV, m(1st gen. q̃)=m(2nd gen. q̃)0m(q̃)-m(χ̃1 )<10 GeV
0m(χ̃1 )=0 GeV
0m(χ̃1 )=0 GeV
0±0m(χ̃1 )<300 GeV, m(χ̃ )=0.5(m(χ̃1 )+m(g̃))
0m(χ̃1 )=0 GeV
tanβ >20cτ(NLSP)<0.1 mm
0m(χ̃1 )<900 GeV, cτ(NLSP)<0.1 mm, µ<00m(χ̃1 )<850 GeV, cτ(NLSP)<0.1 mm, µ>0m(NLSP)>430 GeVm(G̃)>1.8 × 10−4 eV, m(g̃)=m(q̃)=1.5 TeV

1407.0600
1308.1841
1407.0600
1407.0600

01308.2631
1404.2500
1209.2102, 1407.0583m(χ̃1 )<90 GeV±
0m(χ̃1 )=2 m(χ̃1 )±
0
0m(χ̃1 ) = 2m(χ̃1 ), m(χ̃1 )=55 GeV0χ̃m( 1 )=1 GeV
0m(t˜1 )-m(χ̃1 )<85 GeV
0m(χ̃1 )>150 GeV
0m(χ̃1 )<200 GeV

100-620 GeV
275-440 GeV
230-460 GeV
210-700 GeV
150-580 GeV
290-600 GeV

0m(χ̃1 )=0 GeV
0±0m(χ̃1 )=0 GeV, m(ℓ̃, ν̃)=0.5(m(χ̃1 )+m(χ̃1 ))0±
0m(χ̃1 )=0 GeV, m(τ̃, ν̃)=0.5(m(χ̃1 )+m(χ̃1 ))
±
0
0
±
0
m(χ̃1 )=m(χ̃2 ), m(χ̃1 )=0, m(ℓ̃, ν̃)=0.5(m(χ̃1 )+m(χ̃1 ))±0
0m(χ̃1 )=m(χ̃2 ), m(χ̃1 )=0, sleptons decoupled±00m(χ̃1 )=m(χ̃2 ), m(χ̃1 )=0, sleptons decoupled
0
0
0
0
0
m(χ̃2 )=m(χ̃3 ), m(χ̃1 )=0, m(ℓ̃, ν̃)=0.5(m(χ̃2 )+m(χ̃1 ))cτ<1 mm90-325 GeV
140-465 GeV
100-350 GeV
700 GeV420 GeV
250 GeV
620 GeV124-361 GeV

0

±

±

m(χ̃1 )-m(χ̃1 )∼160 MeV, τ(χ̃1 )=0.2 ns±0±m(χ̃1 )-m(χ̃1 )∼160 MeV, τ(χ̃1 )<15 ns
0m(χ̃1 )=100 GeV, 10 µs<τ(g̃)<1000 s

270 GeV482 GeV832 GeV
1.27 TeV

10<tanβ<50537 GeV435 GeV02<τ(χ̃1 )<3 ns, SPS8 model0
7 <cτ(χ̃1 )< 740 mm, m(g̃)=1.3 TeV0
6 <cτ(χ̃1 )< 480 mm, m(g̃)=1.1 TeV

1.0 TeV
1.0 TeV
1.7 TeV
1.35 TeV

λ′311 =0.11, λ132/133/233 =0.07m(q̃)=m(g̃), cτLS P <1 mm
0±m(χ̃1 )>0.2×m(χ̃1 ), λ121 ,00±m(χ̃1 )>0.2×m(χ̃1 ), λ133 ,0BR(t)=BR(b)=BR(c)=0%

750 GeV450 GeV917 GeV
870 GeV
850 GeV0m(χ̃1 )=600 GeV

100-308 GeV
0.4-1.0 TeV

BR(t˜1 →be/µ)>20%0m(χ̃1 )<200 GeV

490 GeV

11507.05525
1405.7875
1507.05525
1503.03290
1405.7875
1507.05525
1501.03555
1407.0603
1507.05493
1507.05493
1507.05493
1503.03290
1502.01518

0m(χ̃1 )<400 GeV
0m(χ̃1 ) <350 GeV
0m(χ̃1 )<400 GeV
0m(χ̃1 )<300 GeV

1.25 TeV
1.1 TeV
1.34 TeV
1.3 TeVb̃1b̃1t̃ 1 110-167 GeVt̃ 1
90-191 GeVt̃ 1
90-240 GeV
t̃ 1
t̃ 2

0
0
0
0-2 jets
0-2 b
0
-

√

Mass limitq̃, g̃
q̃
q̃
q̃
g̃
g̃
g̃
g̃
g̃
g̃
g̃
g̃

Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes

0
20.1
2b
Yes
2 e, µ (SS)
20.3
0-3 b
Yes
1-2 e, µ1-2 b
Yes 4.7/20.3
0-2 e, µ 0-2 jets/1-2 b Yes
20.3
mono-jet/c-tag Yes
020.3
2 e, µ (Z )
20.3
1b
Yes
3 e, µ (Z )
1b
Yes
20.3

0
2 e, µℓ̃L,R ℓ̃L,R , ℓ̃→ℓχ̃1
χ̃+1 χ̃−1 , χ̃+1 →ℓ̃ν(ℓν̃)
2 e, µχ̃+1 χ̃−1 , χ̃+1 →τ̃ν(τν̃)
2τ±03 e, µχ̃1 χ̃2 →ℓ̃L νℓ̃L ℓ(ν̃ν), ℓν̃ℓ̃L ℓ(ν̃ν)
2-3 e, µχ̃±1 χ̃02 →W χ̃01 Z χ̃01
±
0
0
0
e,
µ, γ
χ̃1 χ̃2 →W χ̃1 h χ̃1 , h→bb̄/WW/ττ/γγ
χ̃02 χ̃03 , χ̃02,3 →ℓ̃R ℓ
4 e, µ1 e, µ + γ
GGM (wino NLSP) weak prod.

LFV pp→ν̃τ + X, ν̃τ →eµ/eτ/µτBilinear RPV CMSSM

Other

0-3 e, µ /1-2 τ 2-10 jets/3 b
2-6 jets0mono-jet
1-3 jets
2 e, µ (off-Z )2 jets
2-6 jets
00-1 e, µ
2-6 jets
2 e, µ0-3 jets
1-2 τ + 0-1 ℓ 0-2 jets
2γ
γ
1b
γ
2 jets2 e, µ (Z )2 jetsmono-jet0

L dt[fb−1 ]1506.08616
1407.0608
1403.5222
1403.5222
1403.5294
1403.5294
1407.0350
1402.7029
1403.5294, 1402.7029
1501.07110
1405.5086
1507.05493
1310.3675
1506.05332
1310.6584
1411.6795
1411.6795
1409.5542
1504.05162
1504.05162
1503.04430
1404.2500
1405.5086
1405.5086
1502.05686
1502.05686
1404.250
ATLAS-CONF-2015-026
ATLAS-CONF-2015-015
1501.01325

Mass scale [TeV]*Only a selection of the available mass limits on new states or phenomena is shown. All limits quoted are observed minus 1σ theoretical signal cross section uncertainty.

Figure1.4 Mass reach of ATLAS searches for Supersymmetry achieved at July 2015, before√
collecting collision data with s = 13 TeV. The figure is cited from [15]pair production of NLSPs, using event characteristics which are rare in SM process, are relatively
more promising than searches for direct production of LSPs. As direct pair productions of wino like+−
0*5
NLSP*4 , two types of pair production can be expected; χ̃±
1 , χ̃2 production or χ̃1 , χ̃1 production
±
0
±
0
0
0
χ̃1 can decay to χ̃1 + W , and χ̃2 can decay to χ̃1 + Z or χ̃1 + h. All of these combinations had
been studied with 8 TeV data by the ATLAS experiment. The results are shown in Figure 1.5.
−
±
+
−
0
*6
Because of small cross section of χ̃+
1 , χ̃1 comparing to χ̃1 , χ̃2 [17] , the exclusion reach of χ̃1 , χ̃1±0
is smaller than the one for χ̃1 , χ̃2 . Comparing the results via W Z and via W h, the analysis via W Z
seems to be strong in excluding the model from the figure. However, this depends on the assumptionof branching fraction of χ̃±
1 . Both analyses with 8 TeV data via W Z [18] and via W h [19] assume
the branching fraction χ̃02 → χ̃01 + Z/h to be 100%. From the tree-level calculation with input ofwino mass = 175 GeV and LSP mass = 0 GeV, Br(χ̃02 → χ̃01 + h) is greater than Br(χ̃02 → χ̃01 + Z), if
Higgsino mass is assumed to be much larger than the masses of other electroweak gauginos [20]. Thissuggests that analysis via W h can be powerful to search for electroweak gauginos pair production.
Therefore, in this thesis, target physics process is determined to be decay via W h. As having been
done in the analysis with 8 TeV data, 100% branching ratios to W and h are assumed to simplify*4 Pair productions of wino like NLSP and bino like LSP are strongly suppressed because direct coupling between

them is prohibited.
*5 χ̃0 , χ̃0 production is also a possible mode. However, such process is produced only from neutral weak currents,22which is quite small, meaning production cross section is also quite small.
*6 This is mainly due to the proton PDF.

8

Chapter 1 Introduction−±
0
Figure1.5 The 95% CL exclusion limits on χ̃+
1 + χ̃1 and χ̃1 + χ̃2 production with SM-boson±
00mediated decays, as a function of the χ̃1 , χ̃2 and χ̃1 masses. The production cross-section is−± 0
for pure wino χ̃+1 χ̃1 and χ̃1 χ̃2 . The plot is cited from [21]the analysis.
There are further categorization using decay mode of W and h. Figure 1.6 shows the results ofelectroweak gaugino search decaying via W and h using 8 TeV data. As showing in the figure, there
were four channels;• 3ℓ channel: assuming W → ℓν and h → ℓℓ*7
• ℓ± ℓ± channel: assuming W → ℓν and h → ℓνqq *8• ℓγγ channel: assuming W → ℓν and h → γγ
• ℓbb channel: assuming W → ℓν and h → bb
In this thesis, the third channel, W (→ ℓν)h(→ γγ) process is chosen as a target, which is called“diphoton” channel. Figure 1.7 shows the diagram of this channel. As shown in Figure 1.6, thediphoton channel is expected to have high exclusion performance because of following reasons. Oneof the big advantage of this channel is the characteristic of diphoton mass. Since diphoton are decay
products from the Higgs, reconstructed mass of those two photons is expected to have keen peakaround the Higgs mass. Such characteristic cannot be seen for most of the backgrounds. Therefore,
by just limiting diphoton mass close to the Higgs mass, most of the backgrounds can be suppressed.
In the case of 3ℓ channel, since h decays to two leptons and missing object, background suppression
using di-lepton mass is not promising. This is further discussed in Section 3.2.1.
The lack of the expected QCD activities is also a strong motivation of this channel. Since thecollected data is from proton-proton collisions, large QCD background are expected. Therefore,
the channels assuming objects generated by QCD in the final state, such as ℓbb channel and ℓ± ℓ±*7 It is assuming to decay via h → W W/ZZ → ℓℓνν or h → τ τ → ℓℓ+missing.
*8 It is assumed to decay via h → W W . And signals decay via h → ZZ or τ τ also have contribution if there are

misidentified objects.

1.3 Author’s contributions

9

Figure1.6 Observed (solid line) and expected (dashed line) 95% CL exclusion regions in themass plane of mχ̃0 vs. mχ̃± ,χ̃0 in the simplified model, using 8 TeV data. The dotted lines1
2
1
around the observed limit represent the results obtained when changing the nominal signal
SUSY
theoretical uncertainty. The solid band around thecross section up or down by the ±1σtheory
expected limit shows the ±1σexp uncertainty band where all uncertainties, except those on thesignal cross sections, are considered. The figure is cited from [19]channel, are expected to suﬀer huge QCD background. In addition, because estimation of the QCD
backgrounds have large uncertainties, accuracy of the background estimation is limited.
Diphoton channel has advantages as described above. However, the diphoton channel has a difficulty as well. The major one is the expected low statistics. Since Br(h → γγ) is only 0.23%,
the yields of signal is expected to be small compared to the other channels. Therefore, during thedevelopment of the analysis, more weights are put on keeping acceptance of the signal yields, andthe sophisticated treatments on the small statistics in the signal region.

1.3 Author’s contributions
As described above, this thesis presents the analysis on searching for a direct pair production of00
charginos and neutralinos using decay channel χ̃02 → χ̃01 h → χ̃01 γγ and χ̃±
1 → χ̃1 W → χ̃1 ℓν withdata collected with the ATLAS detector. The motivation for this search is described in this chapter.
In Chapter 2, experimental setup is described. The author contributed to the data acquisition
system for the pixel detector, described in Section 2.2.1. Because of the update of center-of-massenergy, which is described in Section 2.1.2, it was expected that the bandwidth of some part of thedata acquisition system of the pixel detector is going to reach the limit within the experiment from2016. To avoid such situation, the data acquisition system for the outer most layer of the pixel
detector was fully replaced at the beginning of 2016 [22]. The author developed the firmware for the
new data acquisition system.
In Chapter 3, data and simulation samples used in the analysis are introduced. Those samples areprocessed and physics objects are reconstructed as described in Chapter 4. The author processed the10Chapter 1 Introduction

Figure1.7 Feynman diagram of diphoton channel.

signal samples and the updated background samples as described in Section 3.2.1. The author also
verified the “isolation” definition for photon and electron, which is described in Section 4.2.1. As
described in Equation 4.2, isolation criteria depend on the expected energy of the photon candidate.
The author confirmed that this expected energy is close enough to the truth photon or electronenergy, and there are no deviation which may be the source of bias of the selection.
From Chapter 5, analysis procedure and study performed for this search are discussed. The author
contributed as the main analyzer for this search. All the figures used in those chapters are producedby the author. In Chapter 5, event selection criteria are described. As described in that chapter,the criteria optimization was started from the criteria used in previous work. All the criteria are
confirmed and tuned as necessary by the author. In Chapter 6, procedure for the evaluation of
backgrounds are described and verified. All the evaluation and the study described in this chapter
was performed by the author. In Chapter 7, optimization of the signal region definition to improvesignificance is described. The topic described in this chapter is a major improvement from theprevious work. The author performed the study described in this chapter and proposed optimized
signal region. In Chapter 8, uncertainties and their eﬀects are explained. The author evaluatedthose and found that the systematical eﬀect is small enough compared to the statistical eﬀect. In
Chapter 9, observed events are statistically evaluated. All the interpretations have been performedby the author. In Chapter 10, all the studies described in this thesis are summarized.

11

Chapter 2

Large Hadron Collider and The ATLAS
detector
The Large Hadron Collider (LHC) is the largest circular hadron collider in the world. The ATLAS
detector is one of the multiple purpose detectors for the LHC. In this chapter, the experimental
setup is described. The LHC is overviewed in Section 2.1, and the ATLAS detector is overviewed in
Section 2.2.

2.1 LHC
The Large Hadron Collider (LHC) is a circular collider, which is made of two rings of superconducting hadron accelerators, constructed at the European Organization for Nuclear Research (Conseil
Européen pour le Recherche
Nucléaire, CERN). It is designed to collide proton beams at a total√
center-of-mass energy s = 14 TeV. The construction was started by replacing the experimental
setup for the Large Electron Positron collider (LEP) while reusing the tunnel for the accelerator
located underground from 45 m to 170 m, around the border of Switzerland and France. Aroundthe tunnel, of which length is 26.7 km, several detectors were constructed for the measurement of
the collisions.
The proton beam for the collisions is accelerated by several types of the injectors step by step
before the injection into the LHC. In Section 2.1.1, those LHC injector chains are overviewed. Then,the design of the LHC is explained in Section 2.1.2.

2.1.1 LHC injector chain
Figure 2.1 shows the full chain of the LHC injector. The chain is constructed as following order: Linear accelerator 2, Proton Synchrotron Booster, Proton Synchrotron and Super Proton Synchrotron
before the LHC.
The Linear accelerator 2 (Linac2) generates proton sources from hydrogen gas by passing throughthem into an electric field to remove their electrons and injects them into the Proton Synchrotron
Booster (PSB) as 50 MeV beams. The PSB, which consists of four super-imposed synchrotronrings distributed along 157 m length of circumference, accelerates the beam to 1.4 GeV and injects
them into the Proton Synchrotron (PS). The PS, which is a synchrotron made by 277 conventional
electromagnets distributed along 628 m length of circumference, accelerates the beam to 25 GeV,
and injects them into the Supper Proton Synchrotron (SPS). The SPS is the last accelerator before
the injection to LHC. It contains 1425 magnets distributed along 6.9115 km length of circumference
and accelerates beam up to 450 GeV.
The proton beam in the LHC is accelerated in a form of bunches. It is designed so that 2808
bunches are filled in 3564 bunch places in LHC beam line with 25 nsec bunch spacing. The proton
beam injected with 450 GeV is accelerated up to 7 TeV. More detail about the LHC is described in
the next section.

12

Chapter 2 Large Hadron Collider and The ATLAS detector

Figure2.1 The accelerator comples at CERN. The figure is cited from [23].

2.1.2 LHC design
The LHC is developed for the search for new physics. Event yield of new physics is a key of theexperiment. The expected number of events per second generated in LHC collisions is given by:
Nevent = Lσevent(2.1)

where σevent is the cross section for the target event, and L is the machine luminosity. The machine
luminosity can be written for a Gaussian beam distribution as:
L=

Nb2 nb frev γrF
4πϵn β ∗(2.2)

where Nb is the number of particles per bunch, nb is the number of bunches per beam, frev isthe revolution frequency, γr is the relativistic gamma factor, ϵn is the normalized transverse beamemittance, β ∗ is the beta function at the collision point, and F is the geometric luminosity reduction
factor due to the crossing angle at the interaction point:
(
F =

1+

(

θc σz
2σ ∗

)2 )−1/2(2.3)

θc is the full crossing angle at the interaction point, σz is the RMS bunch length, and σ ∗ is thetransverse RMS beam size at the interaction point, under the assumption of σz ≪ β ∗ [24]. The

137
s = 13 TeV

Peak Luminosity per Fill [1033 cm-2 s-1]

ATLAS Online Luminosity

6

LHC Stable Beams
Peak Lumi: 5.0 × 1033 cm-2 s-1

5
4
3
2
1
0
25/05

23/06

23/07

21/08

20/09

19/10 17/11
Day in 201518

ATLAS Online Luminosity

16

LHC Stable Beams

14

s = 13 TeV

Peak Lumi: 13.8 × 1033 cm-2 s-1

12
10
8
6
2/17 calibration

Peak Luminosity per Fill [1033 cm-2 s-1]

2.1 LHC4
2

0
11/04 12/05 12/06 13/07 13/08 13/09 15/10 15/11
Day in 2016

Figure2.2 Peak luminosity at ATLAS as a function of time

design values of those parameters are summarized in Table 2.1 with actual operation values shownin the right columns. With design parameters, L is expected to achieve 1034 cm2 s−1 .
Until 2012, the LHC was operated with 3.5 and 4 TeV proton beam. After that operation, there
were two years of long shutdown to upgrade beam energy to 6.5 TeV. Then, finally from 2015, first
operation with 6.5 TeV proton beam started. The experiment performed until 2012 is called Run 1,
and experiment performed from 2015 is called Run 2. This analysis is using the data collected from2015 to 2016.
Figure 2.2 shows the peak luminosity within those periods. At the beginning of the operationin 2016, it was found that there were unexpected objects in the beam pipe. Due to those objects,
observed peak luminosity in early period of 2015 was lower than the design value. The peak luminosity increased mainly due to reduced full crossing angle θc after September 2015. In 2016, the peakluminosity further increased mainly due to reduced β ∗ . With those setups, integrated luminosity
achieved 4.2 fb−1 in 2015 and 38.5 fb−1 in 2016.
Table2.1 Design and Operational parameters of LHC. Interaction point is assumed to be at
the ATLAS detector. In September 2015, the full crossing angle was reduced from 370 µm to
280 µm. In later 2016, the beta function was reduced from 40 cm to 33 cm.

Parameters
Beam energy [TeV]
Bunch spacing [nsec]
2
Peak luminosity L [1034 cm s−1 ]Number of particles per bunch Nb [1011 per bunch]
Number of bunches per beam nb
Revolution frequency frev
Normalized transverse beam emittance ϵn [µm]Beta function at the ATLAS β ∗ [cm]Full crossing angle at the ATLAS θc [µrad]
RMS bunch length at the ATLAS σz [cm]Transverse RMS beam size at the ATLAS σ ∗ [µm]

Design
7
25
1
1.15
2808
3.75
55
285
7.55
1.67

2012
4
50
0.75
1.65
1374

2015
6.5
25
1.4
1.1
2220
11.2 kHz
2.5
2.2
60
40
290
370 → 280

2016
6.5
25
1.7
1.2
2556
2.2
40 → 33300

14

Chapter 2 Large Hadron Collider and The ATLAS detector

Figure2.3 Cut-away view of the ATLAS detector. The dimensions of the detector are 25 m
in height and 44 m in length. The overall weight of the detector is approximately 7000 tonnes.
The figure is cited from [25].

2.2 ATLAS detector
There are four detectors at LHC. Two general purpose detectors are the ATLAS and the CMS. Oneof the other detectors is LHCb, which is for the studies of b-physics. The last one is ALICE detector
too, which is for heavy-ion collision experiments. In this section, the ATLAS detector, which is usedin this analysis, is described.
The ATLAS, which stands for A Troidal LHC ApparatuS, is a general purpose detector for protonproton collisions. Figure 2.3 shows the cut-away view of the ATLAS detector. As shown in the figure,its height is 25 m and its length is 44 m. It consists of following sub-detector systems from innerside:• Inner Detector: The tracking system, described in Section 2.2.1. It consists of the pixel
detector, the semiconductor tracker and the transition radiation tracker.
• Calorimeter: The detector to measure particle energy, described in Section 2.2.2. It consistsof the electromagnetic calorimeter and the hadron calorimeter.
• Muon spectrometer: The subsystem for muons, which are particles that penetrate thecalorimeter. It is described in Section 2.2.3. It consists of the thin gap chambers, resistive
plate chambers, monitored drift chambers and cathode strip chambers.
The detector is constructed so that the center of the detector is located at the LHC collision
point. Due to its shape shown in Figure 2.3, a cylindrical coordinate system is nominally used in
the ATLAS experiment, while the beam direction defines the z-axis and x-y plane is transverse to
the beam direction. The angle around z axis is measured by ϕ, and the polar angle θ from thebeam axis is often interpreted to the pseudorapidity η = − ln[tan(θ/2)]. The distance ∆R in the2.2 ATLAS detector

15

Figure2.4 Schematic x-y coross section view of a detailed layout of the Inner Detector (ID),including the new Insertable B-Layer (IBL). The figure is cited from [26]√pseudorapidity-azimuthal angle space, which is defined as ∆η 2 + ∆ϕ2 , is also often used. The
region where the detector constructed in parallel to z-axis, is called “barrel“ region, and the region
where the detector constructed in x-y plane, is called “end-cap” region.
The detector has two magnet systems: a thin superconducting solenoid magnet surrounding theinner detector, and three large surrounding toroids arranged with an eight-fold azimuthal symmetryaround the calorimeters. The magnet surrounding the inner detector provides 2 T solenoidal field tothe tracking volume. Due to the field, momentum of charged particles in x-y plane, called transverse
momentum pT , can be measured by their tracks. In order to measure transverse momentum in highresolution, the resolution in ϕ direction is more important than that in η direction.

2.2.1 Inner Detector
Figure 2.4 shows the schematic x-y cross section view of the Inner Detector (ID). Figure 2.5 shows ther-z cross section view of it. As shown in the figures, the ID is made of the Pixel, the SemiConductor
Tracker (SCT) and the Transition Radiation Tracker (TRT). Each sub-detector is described below.
Pixel detector
The pixel detector is installed in the inner most layer close to the beam line. The sensors of the pixel
detector are made of n-type wafers with readout pixels on the n+ -implanted side of the detector.
It has four barrel layers, covering 33.5 < r < 122.5 mm and |z| < 400.5 mm, and three end-cap
layers, covering 88.8 < r < 149.6 mm and 495.0 < |z| < 650 mm. The inner most barrel layer, whichis called IBL, was installed after the run in 2012. The typical pixel size of the IBL is 50 µm (rϕ) × 250 µm (z), while that of the other pixel layers is 50 µm (r-ϕ)× 400 µm (z)Figure 2.6 shows the typical structure of the pixel “module”, which is an unit of the pixel detector.
The module is made of the sensor containing 46080 readable channels in 63.4 × 24.4 mm2 , connected
to 16 of the read-out Front End (FE) chips which detect analog signal from the sensor and digitize it
for read-out, and the specific flex which is shown in the top of the figure. The flex contains Module

16

Chapter 2 Large Hadron Collider and The ATLAS detector

Figure2.5 The r-z cross section view of the layout of a quadrant of the ATLAS inner detector
for Run 2. The figure is cited from [27]. The top panel shows the whole inner detector, whereas
the bottom-left panel shows a magnified view of the pixel detector region. Compared to Run
1, the IBL (shown in orange in the bottom-left panel) and its services, together with the newbeam pipe, were added.

Control Chip (MCC), which is controlling 16 of FEs, NTC thermistors for the temperature control
and High-Voltage (HV) elements to supply HV to the sensor. The flex is connected to readoutcabling via the connector on the “pigtail” shown as yellow plane in the figure.
In case of the IBL, FE has a role of MCC. Only two FEs are used to readout whole sensors in amodule, while number of channels per module is 53760.
The pixel detector contains over 92 million pixels in total. For the barrel pixel layer, individual
layer resolution of 10 µm in the ϕ direction and 115 µm in z direction are achieved.
Semiconductor Tracker
The SemiConductor Tracker (SCT) is the second inner most tracker, next to the pixel detector.
The sensors of the SCT is single-sided p-in-n silicon strip sensor in 80 µm pitch. Since one SCT
sensor has high resolution only in one direction, two sensors are glued back-to-back with a 40 mradrotation around the geometrical center of the sensors. Each side of the sensor has 768 readable stripsof which length is 6 cm. Owing to this angle, the module achieves resolution of 580 µm in the z
direction, while 17 µm in ϕ direction is achieved. Although the resolution in z direction is worse
than that of the pixel sensor, this concept can reduce readout channel significantly, as 6 × 12.6 cm
space is covered by 768 × 2 readout strips while for Pixels 46080 readout channels are needed tocover 63.4 × 24.4 mm2 . Therefore, the inner-most region, where it is requested to measure tracks
in high resolution, is covered by the pixel detector, and outer region, which has large surface area

2.2 ATLAS detector

17

Figure2.6 Schematic view of a barrel pixel module illustrating the major pixel hybrid andsensor elements, including the MCC (module-control chip), the front-end (FE) chips, the NTC
thermistors, the high-voltage (HV) elements and the Type0 signal connector. On the bottomof the module, there is a Thermal Management Tile (TMT). The figure is cited from [25].

needed to be covered, is covered by the SCT. There are 15912 strips for the barrel region.
Figure 2.7 shows the typical structure of the SCT “module”, which is an unit of the SCT detector.
The module is made of the two glued sensors, connected to 6 of the read-out Front End (FE) chips
which are mounted on the hybrid assembly. The module is constructed on the baseboad made bythermal pyrolytic graphite (TPG), which has high conductivity providing a thermal path between
the coolant and the sensors. The board has beryllia facings which are interfaced to the coolingsystem.
The SCT has four barrel layers, covering 299.0 < r < 514.0 mm and |z| < 749.0 mm, and nine
end-cap layers, covering 275.0 < r < 560.2 mm and 853.8 < |z| < 2720.2 mm. The detail geometry
is shown in Figure 2.5.
Transition Radiation Tracker
The Transition Radiation Tracker (TRT) is the tracker located in the outer-most layer of the ID.
The sensors of the TRT is polyimide drift straw tubes with a diameter of 4 mm, with the tungsten
wire with diameter of 31 µm plated with 0.5–0.7 µm gold, supported at the end of the straw by an
end-plug. The straws were cut to 144 cm for the barrel and 37 cm for the end-caps, and filled by
the gas mixture with 5–10 mbar over-pressure. The design value of the gas mixture is 70% Xe, 27%
CO2 and 3% O2 , which achieves 2.5 × 104 gain with 1530 V. The position resolution of this sensor
in r − ϕ plane is 120 µm in the barrel region. The tubes are installed in parallel to the beam line in
the barrel region, and in parallel to the r direction in the end-cap region.
The TRT has three types of the modules in barrel, covering 563.0 < r < 1066.0 mm and |z| <712.0 mm, and two types of module in the end-caps, covering 644.0 < r < 1004.0 mm and 848.0 <|z| < 2710.0 mm. Each module layer has several layers of straws. The structure is designed so that
all charged tracks with pT > 5 GeV in |η| < 2.0 must pass through at least 36 straws except in
the barrel-end-cap transition region, which is 0.8 < |η| < 1.0. Even in the barrel-end-cap transition
region, charged particles pass at least 22 straws.

18

Chapter 2 Large Hadron Collider and The ATLAS detector

Figure2.7 Drawing of a barrel module, showing its components. The thermal pyrolytic
graphite (TPG) base-board provides a high thermal conductivity path between the coolant
and the sensors. The figure is cited from [25].

2.2.2 Calorimeter
Figure 2.8 shows the cut-away view of the ATLAS calorimeter system. As shown in the figure, the calorimeter system is made of the LAr electromagnetic calorimeter and three types ofhadronic calorimeters, the tile calorimeter, the LAr hadronic end-cap calorimeter and the LAr forward calorimeter.
Those detectors were designed to provide containment for electromagnetic and hadronic showers. Therefore, radiation length (X0 ) and interaction length (λ) are important parameters for thecalorimeter. In the calorimeter, energy is measured using energy deposits from showers. In order togenerate showers eﬃciently, several types of absorbers are used in the ATLAS detector, as explainedin the following sections. The electromagnetic calorimeter has thickness > 22X0 in the barrel, andthickness > 24X0 in the end-caps. The hadronic calorimeter has thickness > 9.7λ in the barrel andthickness > 10λ in the end-caps.
Further detail about each sub-detector is described below.
Electromagnetic calorimeter
Figure 2.9 shows a sketch of a part of the ElectroMagnetic (EM) calorimeter in the ATLAS detector.
This type of the EM calorimeter covers |η| < 1.475. It consists of accordion shape lead absorbers
and liquid argon (LAr) as the active detector medium. The shape of the absorbers is chosen to makeseveral active layers in depth.
The first layer has strip cells to distinguish two collimated photons decayed from π 0 and photons
form collisions.The second layer is the main detector to measure the energy. The last layer is tocollect energy leaking from the second layer.
The end-cap region is covered by two wheels of LAr ElectroMagnetic End-cap Calorimeter(EMEC); inner one covering 1.375 < |η| < 2.5 and the other covering 2.5 < |η| < 3.2. Those
calorimeters have same structure with the EM calorimeter. In front of the detector described above,
there is detector called PreSamplers (PS), which has only 11 mm depth of active layer to measure
the energy lost in front of the calorimeters, covering |η| < 1.8.

2.2 ATLAS detector

19

Figure2.8 Cut-away view of the ATLAS calorimeter system. The figure is cited from [25].

The geometry of the detector is summarized in Table 2.2. Since 1.37 < |η| < 1.52 is intermediate
region between the barrel and the end-caps, this region is called the crack region.
Hadronic calorimeter
The three types of hadronic calorimeter are located outside of the EM calorimeter.
The calorimeter placed outside of the EM calorimeter is the tile calorimeter. It consists of steel
absorbers and scintillating tiles as the active detector medium. The main part covers |η| < 1.0, andtwo extended parts cover 0.8 < |η| < 1.7.
Further high η region is covered by the LAr Hadronic End-cap Calorimeter (HEC) located behindthe end-cap EM calorimeter. It consists of flat shape copper absorbers and liquid argon as the active
detector medium. It covers 1.5 < |η| < 3.2.
The most forward region is covered by the Forward Calorimeters (FCal), which has three layers.
The first layer consists of flat shape copper absorbers and liquid argon as the active detector medium.
The other layers consist of tungsten absorbers and liquid argon as the active detector medium. Due
to high particle fluxes in this region, the gap for liquid argon is smaller than 0.6 mm, in contrast to
the 2 mm gap for the EM calorimeter. It covers 3.1 < |η| < 4.9.

2.2.3 Muon Spectrometer
Figure 2.8 shows the cut-away view of the ATLAS muon system. The system consists of four types of
sub detectors and large toroid magnets arranged with an eight-fold azimuthal symmetry around thez axis. The barrel toroid magnet provides 1.5 to 5.5 Tm of magnetic field to the region 0 < |η| < 1.4,
and the end-cap toroid magnets provide 1 to 7.5 Tm of magnetic field to the region 1.6 < |η| < 2.7.
The sub detectors are following; the Monitored Drift Tubes (MDT), the Cathode Strip Chambers

20

Chapter 2 Large Hadron Collider and The ATLAS detector
Cells in Layer 3∆ϕ×∆η = 0.0245×0.05
Trigger Towe∆η = 0 r
.1

2X0

47
0m

m

η=0

16X0
TriggeTow r∆ϕ = 0er
.0982

m

m

4.3X0

15
00

1.7X0
∆ϕ=0.0245x36.8m 4mx
=147.3 4mm

ϕSquare cells in
Layer 2∆ϕ = 0.0245∆η = 0.025
m/8 =4∆η = 0 .69 mm.0031
Strip cells in Layer 1

37.5m

η

Figure2.9 Sketch of a barrel module of the electromagnetic calorimeter where the diﬀerent
layers are clearly visible with the ganging of electrodes in phi. The granularity in eta and phiof the cells of each of the three layers and of the trigger towers is also shown. The figure iscited from [25].

Table2.2 Geometry of EM calorimeter

LayersPresampler in barrel
Presampler in end-caps
1st layer of EM calorimeter in barrel
1st layer of EM calorimeter in end-cap

2nd layer of EM calorimeter in barrel
2nd layer of EM calorimeter in end-cap

3rd layer of EM calorimeter in barrel
3rd layer of EM calorimeter in end-cap

Granularity (∆η × ∆ϕ)
0.025 × 0.1
0.025 × 0.1
0.025/8 × 0.1
0.025 × 0.025
0.050 × 0.1
0.025 × 0.1
0.025/8 × 0.1
0.025/6 × 0.1
0.025/4 × 0.1
0.025 × 0.1
0.1 × 0.1
0.025 × 0.025
0.075 × 0.025
0.050 × 0.025
0.025 × 0.025
0.1 × 0.1
0.050 × 0.025
0.050 × 0.025

Covering η|η| < 1.52
1.5 < |η| < 1.8|η| < 1.4
1.40 < |η| < 1.4
1.375 < |η| < 1.425
1.425 < |η| < 1.5
1.5 < |η| < 1.8
1.8 < |η| < 2.0
2.0 < |η| < 2.4
2.4 < |η| < 2.5
2.5 < |η| < 3.2|η| < 1.4
1.40 < |η| < 1.475
1.375 < |η| < 1.425
1.425 < |η| < 2.5
2.5 < |η| < 3.2|η| < 1.35
1.5 < |η| < 2.5

2.2 ATLAS detector

21

Figure2.10 Cut-away view of the ATLAS muon system. The figure is cited from [25].

(CSC), the Resistive Plate Chambers (RPC) and the Thin Gap Chambers (TGC). Figure 2.11 shows
the cross-section of the muon system. Each sub-detector shown in the figure is described below.
Monitored Drift Tubes
The Monitored Drift Tubes (MDT) is the main detector to measure momentum precisely. The sensor
of the MDT is drift tubes with a diameter of 29.970 mm, with the gold-plated tungsten-rhenium
wire with a diameter of 50 µm. The tube is filled by the gas mixture with 3 bar. The design valueof the gas mixture is 93% Ar and 7% CO2 , which achieves 2 × 104 gain with 3080 V. The position
resolution of this sensor in transverse direction is 60-80 µm per tube. From the precise position
measured by this detector, tracks are reconstructed and used to measure precise momentum.
This detector is shown in the figure with following naming:• First character shows the location, barrel (B) or end-cap (E).
• Second character shows the layer, inner (I), middle (M), outer (O) or Extra (E).
• Last character shows the sector, large (L) or small (S).
As shown in the figure, it covers |η| < 2.7, except for the inner most layer which covers |η| < 2.0.
Cathode Strip Chambers
The Cathode Strip Chambers (CSC) covers the inner most layer of the forward region, where highcounting rate is expected so the MDT cannot be used safely. The gap of the CSC is filled withthe gas mixture of 80% Ar and 20% CO2 , which achieves 6 × 104 gain with 1900 V. The position

22

Chapter 2 Large Hadron Collider and The ATLAS detector

Figure2.11 Cross-section of the muon system in a plane containing the beam axis (bending
plane). Infinite-momentum muons would propagate along straight trajectories which are illustrated by the dashed lines and typically traverse three muon stations. The figure is citedfrom [25].

resolution of this sensor is 60 µm per CSC plane. It covers the inner most layer of 2.0 < |η| < 2.7.
Resistive Plate Chambers
The Resistive Plate Chambers (RPC) is for trigger system in barrel region. The detector consistsof parallel 2 mm plastic plates with a 2 mm gap. The gap is filled with the gas mixture of 94.7%
C2 H2 F4 , 5% Iso-C4 H10 and 0.3% SF6 , which achieves the detection eﬃciently greater than 98.5%
per layer with 1900 V. It covers |η| < 1.05.
Thin Gap Chambers
The Thin Gap Chambers (TGC) is for trigger system in end cap region. The TGC is multi-wire
proportional chamber. The wire to chamber distance is 1.4 mm, and the wire to cathode distanceis 1.4 mm. The gap is filled with the gas mixture of 55% CO2 and 45% n-pentane, which achieves
3 × 105 gain with 2900 V. It covers 2.0 < |η| < 2.7.

2.2.4 Trigger system
As described in Section 2.1.1, the bunch space of the LHC is 25 nsec. Hence, collision rate is detected
in 40 MHz. However, most of the detected events are background events. Because of limited resource
for the data acquisition, all events cannot be recorded. Therefore, the trigger system, which filters
only interesting events, is used in the ATLAS experiment. Figure 2.12 shows the overview of thetrigger system. There are two types of trigger system used in the ATLAS experiment; the Level 1(L1) trigger and the high level trigger, as described below.

2.2 ATLAS detector

23

Figure2.12 The ATLAS trigger and data acquisition system in Run 2 with emphasis on thecomponents relevant for triggering, cited from [28]L1 trigger
The L1 trigger is hardware-based trigger. This trigger gives decision based on the information fromthe calorimeter and the muon system, for the barrel region and the end-cap region individually. The
information related to muon is processed at the level-1 Muon system, and calorimeter information
is processed at the level-1 Calo system, by a new FPGA-based multi-chip module (NMCM). Thenthe Cluster Processor (CP) identify electron/photon and tau, and Jet/Energy-sum Processor (JEP)
identify jets and missing transverse momentum. The outputs from the level-1 muon system isprocessed at the Muon-to-CTP interface (MUCPTI). The outputs from the level-1 Calo system
and MUCPTI are used at Level 1 Topological trigger (L1Topo) to combine the objects. All those
information are processed at the Central Trigger Processor (CTP), which submits L1 trigger basedon dedicated trigger menu. L1 trigger is accepted by the Read Out Driver (ROD).
Only when L1 trigger is accepted, the ROD for all the detector starts read out data from the Front
End (FE) chips. The L1 trigger menu is designed to achieve ∼100 kHz of read out.
High Level Trigger
The next step of the trigger is the High Level Trigger (HLT). This is software-based trigger.
The data taken by L1 triggers are buﬀered in the Read-Out System (ROS). Then, based on
the L1 trigger information, the Region-of-Interest (RoI) is used at the HLT processors. Online
reconstructions are performed only for the objects in the RoI, and the dedicated HLT algorithm isapplied.
Only events accepted by the HLT are recorded in the Data Storage. The HLT menu is designed
to achieve ∼1 kHz of data recording.

25

Chapter 3

Data and Simulation samples
The search for new physics is generally performed as a search for the deviation from the expectation
based on the SM. The events expected by the SM are background for such search, and the events
expected by new physics are signal. In order to search for the deviation, it is important to understandthe characteristics of the background and the signal. Both expectation, based on the SM and new
physics, can be provided by simulated samples. In this chapter, details of collected data and simulated
samples are introduced.

3.1 Data samples√
The LHC has been operated at s = 13 TeV from 2015. The dataset used in this analysis is collectedusing the ATLAS detector in 2015 and 2016. Figure 3.1 shows the integrated luminosity in 2015
and 2016. Because of the DAQ ineﬃciency and the start up time for the electronics of the tracking
detectors, not all of the delivered luminosity can be recorded, as shown in the figures.
Total recorded integrated luminosity is 3.9 fb−1 in 2015 and 35.6 fb−1 in 2016. However, some ofthose data were recorded when a sub detector system had a trouble. The largest eﬀect in 2015 is that
the IBL was turned oﬀ for two runs, corresponding to 0.2 fb−1 . And the largest eﬀect in 2016 is thatthe toroid magnet was oﬀ for some runs, corresponding to 0.7 fb−1 . The data collected when somesub detector had a trouble are removed and not used in the analysis. Total integrated luminosity usedin the analysis is 3.2 fb−1 in 2015, and 32.9 fb−1 in 2016. Therefore, overall integrated luminosity
used in the analysis is 36.1 fb−1 .

3.1.1 Trigger
As described in Section 2.2.4, data is collected using prepared triggers. In this analysis, the used
dataset is collected by diphoton trigger, which is dedicated for the events contain two or more
photons. Among several types of the diphoton triggers developed in the ATLAS experiment,
HLT g35 LOOSE g25 LOOSE, which is the loosest type of trigger, is used for this analysis. This
trigger is dedicated for the events containing leading photons with greater than 35 GeV transverse
momentum and sub-leading photons with greater than 25 GeV transverse momentum. The eﬃcientlyof this trigger for the target diphoton events are closest to 100% [30].

3.1.2 Blind analysis
The collected data is used not only for the estimations of the existence of new physics, but also
for the evaluations of the backgrounds. At first background estimations have been performed, thenobserved data is compared with the expected backgrounds. Within the procedure of the backgroundestimation, collected numbers of events or distributions of data, which are used for the estimation of
the existence of new physics, are hidden, in order to avoid artificial bias, such as under estimation of
the background. This procedure is called “blind” analysis, and the hidden region is called blindedATLAS Online Luminosity5

s = 13 TeV

LHC Delivered
ATLAS Recorded

4

Total Delivered: 4.2 fb-1
Total Recorded: 3.9 fb-1

3
2
1
0
23/05

20/06

18/07

15/08

12/09

10/10 07/11
Day in 2015

Total Integrated Luminosity [fb-1]

Chapter 3 Data and Simulation samples

50

ATLAS Online Luminositys = 13 TeV

LHC Delivered

40
30

ATLAS Recorded
Total Delivered: 38.5 fb-1
Total Recorded: 35.6 fb-1

20
10

2/17 calibration

Total Integrated Luminosity [fb-1]

26

0
18/04 16/05 13/06 11/07 08/08 05/09 03/10 31/10
Day in 2016

Figure3.1 Total integrated luminosity in 2015 (left) and 2016(right) versus time. Delivered
integrated luminosity is shown in green, and recorded integrated luminosity is shown in yellow.
The figures are cited from [29].

region, which is equivalent to the signal region described in Table 5.1. The background estimations
described up to Chapter 8 have been performed with blinded data, and the blinded region is opened
in Chapter 9. Instead of using data in the signal region, the simulation samples described in thenext section is used as expected distributions.

3.2 Simulation samples
Monte Carlo (MC) simulation samples are produced for background estimation and evaluation of thesignificance of the signals. Event generators are used to simulate proton-proton inelastic scattering,
parton shower, and hadronization. As an input to the simulation, prepared Parton Distribution
Function (PDF) set is used. Non-perturbative parameters for the simulation, which cannot be determined from theories, are “tuned” to reproduce the observed event. Depending on the physics
process, several types of generators, PDFs and tunes are used. Those are explained in this section. The generated events are used as inputs to simulator for the detector system based on the
GEANT4 [31, 32]. Outputs of the detector simulation contain energy deposits, hit timing, etc. indetector elements. These are further transformed to the digital outputs from detector components
through digitization process. These data are in the same format as the ones from the data from realdetector.
The MCs for the backgrounds are explained in Section 3.2.1. The MCs for the signals are explainedin Section 3.2.2.

3.2.1 Backgrounds
miss
) are
As described in Figure 1.7, two photons, one lepton and the missing transverse energy (ETexpected in the final state of the signal. Some types of the events predicted in the SM have the same
final state with signal. Therefore, those are expected as background sources.
Those backgrounds sources are classified into two types. The backgrounds including a SM higgs
particle within their process is classified as “peaking backgrounds”, which are W h, Zh, tt̄h, VBFhand ggh. And the other type of the backgrounds is “non-peaking backgrounds”, which are W γγ,
Zγγ, W γ, Zγ, γγ, tt̄, and single photon. All samples are summarized in Table 3.1.
As described in Section 6.1, MC samples for the non-peaking backgrounds are not used for theestimation of their contributions. Instead, the estimation for the non-peaking backgrounds has been

3.2 Simulation samples

27

performed with data-driven method. Those MC samples are only used for the comparison between
the data used in the data-driven method and the SM expectation. On the other hand, the MC
samples for the peaking backgrounds are directly used for the backgrounds estimation. Because ofthis reason, two types of MC samples for W h and Zh are used in the analysis.
The non-peaking backgrounds except for the tt̄ are generated using the leading order (LO) generator SHERPA v2.1.1 simulation package [33] with the CT10 PDF set [34]. The tunes have been
done inside SHERPA.
The tt̄ is generated using the NLO generator POWHEG [35] for the hard scatterings and
PYTHIA6 [36] for the rest with the CT10 PDF set. For the tunes, the Perugia2012 [37] tune isused.
The first set of the W h and Zh samples are called “LO samples”, since those samples are generator with the LO generator. Those are generated using the LO generator PYTHIA8 [38] with
the NNPDF2.3LO PDF set [39, 40]. For the tune, the A14 [41] tune is used. The LO samples areused with the early selections, which are introduced in Section 5.1, for the optimization and somevalidations.
The next set of the W h and Zh samples are called “NLO samples”, since those samples are
generator with the next-to-leading order (NLO) generator. Those are generated using the NLO
generator POWHEG+MiNLO for the hard scatterings and PYTHIA8 for the rest with the CT10
and CTEQ6L1 [42] PDF sets. For the tunes, the AZNLO tune [42] is used. The total cross section
for the normalization is calculated with NNLO QCD and NLO EW. Then, the correction for EW at
NLO is applied by the reweighting factor based on the truth transverse momentum of W or Z.
The LO samples are used in the early stage of analysis. The NLO samples are used mainly forthe statistical evaluation of the results. The eﬀect of the diﬀerence of the sample is evaluated in
Section 7.4.2 as negligible level.
The VBFh and ggh are generated using the LO generator PYTHIA8 with the CTEQ6L1 PDF
set. For tune, the AZNLO tune is used. The processes are calculated with LO, then scaled to NNLO
by applying scaling factor called k-factor.
The tt̄h are generated using aMcAtNlo [43] for the hard scatterings Herwigpp V2.7.1 [44] for the
rest with the CT10 and CTEQ6L1 PDF sets. For the tune, the CTEQ6L1-UE-EE-5 tune [45] isused.

3.2.2 Signals
The signal samples are created under the assumptions described in Section 1.2.3. The only freeparameters are the mass of LSP (mχ̃01 ) and the mass of NLSP and the lightest chargino (mχ̃± ,χ̃0 ).
1
2
Figure 3.2 shows the points of the values of the created signal points in the mχ̃01 versus mχ̃± ,χ̃0
1
2
parameters space. As shown in the figure, there is a theoretical limitation about mχ̃01 and mχ̃± ,χ̃0 .
1
2
Since χ̃02 → χ̃01 h is assumed, mχ̃± ,χ̃0 − mχ̃01 must be larger than the Higgs mass. This is shown as a
1

2

Table3.1 Simulation samples used in this analysis.

processtt̄
All other non-peaking
backgrounds
W h and Zh LO samples
W h and Zh NLO samples
VBFh and ggh
tt̄hgenerator
POWHEG + PYTHIASHERPA

PDF
CT10
CT10

tune
Perugia2012
SHERPAPYTHIAPOWHEG + MiNLO+ PYTHIAPYTHIAaMcAtNlo + Herwigpp

NNPDF2.3LO
CT10 and CTEQ6L1

A14
AZNLO

CTEQ6L1
CT10 and CTEQ6L1

AZNLO
CTEQ6L1-UE-EE-5

Chapter 3 Data and Simulation samples
Number of points = 80

120

100

1

m∼χ0 [GeV]

28

80

60

40

20

0
100

150

200

250

300

350

400

450

500

550

m∼χ0, m∼± [GeV]2

χ

1

Figure3.2 Assumed signal sample points in (mχ̃± ,χ̃0 , mχ̃0 ) space. The diagonal line shows1
12mχ̃± ,χ̃0 − mχ̃0 = 125 GeV.
121

diagonal line in the figure.
All the signal samples are generated using MG5 aMC@NLO v2.3.3 [46] for the matrix element
calculation for the hard process part and PYTHIA8 for the rest with the NNPDF23LO PDF set [39].
For the tune, the A14 tune is used. The fast simulation (Atlfast-II [47]) is used for the simulation of
the detector response, instead of the “full” simulation used for the other samples. The cross sections
for those samples, which depend on mχ̃± ,χ̃0 , are summarized in Table 3.2.
12

3.2 Simulation samples

29

Table3.2 Cross sections of assumed signal sample points.

mχ̃± ,χ̃0 [GeV]
1
2
150
152.5
162.5
165
175
177.5
187.5
190
200
202.5
212.5
215
225
227.5
237.5
240
250
262.5
275
287.5
300
312.5
325
337.5
350
375
400
425
450
475
500

Cross sections [fb]5.18094.87893.87183.6621
2.95332.80372.29272.18371.8074
1.72611.4431
1.3815
1.16511.11800.91370.91370.78250.64940.54300.45700.38690.32950.28190.24250.20940.15810.12100.09380.07340.0581
0.0464

31

Chapter 4

Object Reconstruction
Events in collected data and generated simulations contain hit information on the detector. From
those, candidates of the physics objects, such as photons, leptons, jets, which are a collimated spray of
misshadrons coming from QCD activities, and missing transverse momentum (ET), are reconstructed.
Then, specific selection criteria for each type of object are applied. In this chapter, reconstruction
procedures for each object are described.

4.1 Term definitions
Hit information on the detector are interpreted as tracks and deposit energies, and then reconstructed
as physics objects. Before the introductions about the reconstruction procedures, which are describedin the next section, some terms used in the explanations are defined in this section.

4.1.1 ET and pT
Tracks of charged particles are reconstructed by hit information on the ID [48]. As described in
Section 2.2, 2 T solenoidal magnetic field is provided to the tracking volume. Because of the field,
charged particle draws curved path in the ID. From the curvature radius in x-y plane, transverse
momentum pT can be measured. In this chapter, pT means the transverse momentum measured bytrack. Hit information on the calorimeters are interpreted as deposit energy. In this chapter, it isdenoted as ET (transverse energy).
ET and pT have relation such as√
ET = m2 + p2T .
(4.1)
Since mass m is negligible comparing to scale of ET and pT , ET of correctly reconstructed object isequal to pT . After this chapter, assuming all objects are correctly reconstructed, all momentum orenergy are denoted by pT .

4.1.2 Primary vertexes and µ
The other term used in this chapter is the primary vertex. Since the ATLAS collects collisionsof proton beams, there are multiple interactions expected in a beam crossing. The number ofinteractions in a beam crossing is denoted as µ*1 . The point of each interaction is denoted as
primary vertex.
The primary vertex is reconstructed by track information. Reconstructed tracks are extrapolated
to the beam spot center, then the z coordinate of the primary vertex is evaluated. The tracks sharing
the primary point are used to determine the vertex position. More detail are described in [49].
*1 This is used in Table A.2

32

Chapter 4 Object Reconstruction

Figure4.1 Photon and electron candidates classification workflow.

4.2 Objects
4.2.1 Photons and Electrons
Reconstruction of candidates
Due to their simulator characteristics in the detector, a photon object and an electron object arereconstructed in the same workflow described in following.
At first, electromagnetic clusters of the cells of the second EM calorimeter layer are reconstructed.
For this reconstruction, η × ϕ = 3 × 5 cells of the window are used for the scan of the local maximumof the total ET . If ET of the cluster is greater than 2.5 GeV, it is used as a seed of the object. Then,the energy collected around the seed are used as inputs to the clustering algorithm [50] to constructtopological cluster.
When a cluster is constructed at EM calorimeter, candidates of the associated tracks are definedby the tracks reconstructed by the inter detector that are matched to the cluster by the extractionof the track. If a vertex for two associated tracks are reconstructed, it is saved as a candidate forthe photon conversion vertex.
By using those information, object are classified as a photon, an electron or an “ambiguous” object
which could be a photon or an electron. Only when object is surely not considered to be an electron(photon), it is classified as a photon (electron) candidate respectively. Figure 4.1 shows the overview
of the classification algorithm, which is described below.
In the following cases, the object is classified as a photon.

4.2 Objects

33• There are no tracks.
• There are no tracks with at least 4 hits in silicon layers (the pixel detector and the SCT).
• There is a vertex reconstructed by two tracks which have hit on the silicon layers but no hit
in the pixel layers. In this case, the object is considered as a converted photon.
When the object is not classified as a photon, the object is checked about following criteria:• ET /pT < 10. Otherwise, the object is not likely an electron since pT of an electron measured
by the track should be close to its ET .
• pT > 2.0 GeV. Otherwise, the object has too low momentum to conclude it is an electron
candidate.
• There is a track with a hit on the pixel layers. Otherwise, the object is not likely an electron
since it is rare for an electron track.
In the cases that the object cannot pass at least one of the criteria listed above, the object is classified
as an ambiguous object, since it is not classified as a photon, nor an electron.
The object, which is not classified as a photon or an ambiguous object, is classified as an electron
candidate in the following cases:• There are no vertices.
• There is a vertex but it is due to accidental vertex with cosmic ray or noise. To confirm it, avertex must pass one of following criteria:– It is not reconstructed by two tracks having a hit on the pixel layers.
– It is reconstructed by two tracks having a hit on the pixel layers, but only one track has
a hit on the inner most pixel layer.
The object which dose satisfy any criteria above is classified as an ambiguous object. The ambiguous
objects are used as both photon and electron candidates in the following selection procedure.
Selection of photon candidates
The dedicated criteria for the photon candidates and for the electron candidates are applied to theclassified objects. The ambiguous objects are used as both candidates in this step, and overlap isremoved later.
For the photon candidates, following criteria are applies:• passing “Tight” photon IDentification (ID)• |η| < 2.37 excluding the crack region of 1.37 < |η| < 1.52 (See Section 2.2.2)• passing “FixedCutTightCaloOnly” isolation criterion• ET > 27 GeV
An important purpose of those requirements is to reduce fake candidates mostly due to π 0 mesons
decaying to two photons. Two photons decayed from a π 0 with high momentum are collimated andgeometrically close at the EM calorimeters. Therefore, the cluster at the second EM calorimetercan be merged into one cluster. Since the signal detected at the second EM calorimeter is due tophotons, even if it is originally from π 0 , it is diﬃcult to distinguish it from truth prompt photons.
The criteria described above are designed to reduce such fake candidates, as following.
The photon ID is developed in the ATLAS experiment to distinguish truth photons from fake photons, as described in [51]. It is based on the energy deposits in the first and second EM calorimeter,
and the leakage into the hadronic calorimeter. The ID was tuned to provide about 85% eﬃciency at
40 GeV.
The first EM calorimeter provides useful information in the photon ID definition. As described in
Section 2.2.2, it has fine segmentation to detect two photons from π 0 separately. In order to ensure
the quality of the photon ID, the requirement on the η measured by the first EM calorimeter isapplied.
The isolation requirement is a diﬀerent approach to reduce fake candidates. In general, mesons,

34

Chapter 4 Object Reconstruction

Figure4.2 Schematics of topoEtcone40. Images shows the cells of the second EM calorimeter
layer. Left image is for photon, and right image is for π 0 decayed into diphoton. There are
pileup eﬀects for both cases. For π 0 case, there are jet contributions also. topoEtcone40 is
calculated from total deposits energy (ΣR<0.40 ET ) within R = 0.4 cone, which is shown as a
blue circle. In order to remove contribution of photon, deposits energy within η × ϕ = 5 × 7
5x7 corewindow (ET), which is shown as red cells, is subtracted. Then, expected deposits energy
5x7 coreleaked from the window (fleak (ET, η)), which is shown as purple cells, is calculated andsubtracted. Finally, pileup eﬀect (ρ(η)), which is shown as gray cells, is subtracted. topoEtcone40 for photon is close to 0. On the other hand, topoEtcone40 for π 0 can be large value
due to jet contributions shown as green cells.

such as π 0 , are generated by the strong production, while photons are generated by the electroweak
production. Therefore, other QCD activities, such as jets, are expected to be around a meson, which
are not expected for a truth photon. The isolation requirement is suppressing objects with such jets
activities. Several types of the criteria are developed in the ATLAS experiment.
In this analysis, “FixedCutTightCaloOnly” is used as the isolation criterion. This is the requirement on the calorimeter isolation energy, represented by topoEtcone40. Figure 4.2 shows theschematic of the topoEtcone40 definition. Idea of topoEtcone40 is total energy deposits aroundphoton candidates. It is evaluated from the total energy deposits within an η − ϕ cone of a radius∆R = 0.40 around the center of the cluster of the photon candidate (ΣR<0.40 ET ). ΣR<0.40 ET include energy deposits of photon candidate and pileup eﬀect also. In order to evaluate energy deposits
inside cone except for photon, energy deposits of photon is evaluated separately and subtracted. It
5x7 coreis evaluated from deposits energy within η × ϕ = 5 × 7 window (ET) at first. Then, expected
5x7 coredeposits energy leaked from the window is calculated using a dedicated function of ETand η
5x7 core(fleak (ET, η)). Pileup eﬀect (ρ(η)) is also evaluated as a function of η. Then, topoEtcone40
can be defined as:
5x7 core
5x7 core
topoEtcone40 = ΣR<0.40 ET − ET− fleak (ET, η) − ρ(η)(4.2)

5x7 coreDue to uncertainty on the fleak (ET, η), the width of the topoEtcone40 become wider with
5x7 corelarger ET. Therefore, the threshold of “FixedCutTightCaloOnly” is tuned as a function of thephoton transverse energy, as following:

topoEtcone40 < 2.45GeV + 0.22 × ET

(4.3)

The last criterion is on photon transverse energy. In this analysis, further selections are appliedin the signal region requirement. This is discussed in Section 5.3.2.
Selection of electron candidates
For the electron candidates, following criteria are applied:4.2 Objects

35• passing “TightLLH” electron IDentification (ID)• |η| < 2.47 excluding the crack region of 1.37 < |η| < 1.52
• passing “gradient loose” isolation criterion• |z0 sin θ| < 0.5 mm• |d0 /σd0 | < 5.0• pT > 15 GeV
In the case of the electron candidates, main source of the fake are hadronic jets and photons converting to electron positron pairs. Electrons in hadronic jets or converted from the photon can beelectron candidates, even if they are not prompt electrons.
The “TightLLH” electron ID is developed based on the log likelihood (LLH) with the multivariate
analysis (MVA) technique [52]. The definition of the “TightLLH” uses information from the hadronic
calorimeter, the EM calorimeter and the inner detectors.
The η cut is based on the range where the four momentum of the electron can be calculated basedon the track measured by the inner detectors.
The isolation requirement is to suppress hadronic jets, as it is for the photon isolation. For theisolation requirement, two discriminating variables are used: a calorimetric isolation energy and a
track isolation. The calorimetric isolation energy is evaluated by topoEtcone20, which is the samewith topoEtcone40 except for the size of the radius for the calculation which is ∆R = 0.20 insteadof 0.40. The track isolation is represented by ptvarcone40. It is defined as the sum of transverse
momentum of all the track within a cone of ∆R = min(0.40, 10GeV/ET ) around the candidate
electron track, excluding the electron associated track. The track used in this calculation are only
those which pass following criteria:• pT > 1 GeV• 7 or more hits in the silicon layers• 2 or less missing hits in the silicon layers• 1 or less missing hits in the pixel layers• 1 or less hits in the silicon layers assigned to more than one track• |z0 sin θ| < 0.3 mm
The “gradient loose” criterion is tuned to provide 95% of the total eﬃciency for 25 GeV electrons,
and 99% total eﬃciency at 60 GeV. The thresholds for calorimetric isolation energy and track
isolation are not fixed values. The total eﬃciency is evaluated by using simulation of Z → ee.
The selection for z0 and d0 is to request that the origin of the track is close to the primary vertex,
which is the common origin for the high-quality reconstructed tracks. Those parameters are called
impact parameters, which are showing distance from the primary vertex to the track, as shown in
Figure 4.3. d0 is the closest distance from the track to the primary vertex in the (x, y) plane. z0 is
the z intercept in the (z, direction of pT ) plane. d0 is divided by uncertainty on d0 and requested
that the size of d0 is within 5σ. z0 is weighted by sin θ, where θ is track angle from the z axis. z0 sin θmeans distance from the track to the primary vertex in the (z, direction of pT ) plane.
The last criterion is on electron momentum. In this analysis, further selections are applied in thesignal region requirement. This is discussed in Section 5.3.3.

4.2.2 Muons
Reconstruction of candidates
Muon candidates are reconstructed using the information from the inner detectors and the muon
spectrometer (MS).
At first stage of the reconstruction, muon candidates are reconstructed by the inner detectors andthe muon spectrometer individually. The reconstruction with the inner detector is performed as didfor other charged particles. On the other hand, the reconstruction with the muon spectrometer isperformed as following steps:

36

Chapter 4 Object Reconstruction

Figure4.3 Image of the impact parameters. Left image shows an image of d0 . Charged particle
draw an arc in the (x, y) plane as shown as an orange arrow. d0 is closest distance from thetrack to the primary vertex in the (x, y) plane, which is shown as a red arrow. Right image
shows an image of z0 sin θ. z0 is the z intercept in the (z, direction of pT ) plane, which is shown
as a blue arrow. With weight of sin θ, where θ is is track angle from the z axis, closest distancefrom the track to the primary vertex in the (z, direction of pT ) plane (z0 sin θ) is evaluated, as
shown as z0 sin θ.

• Hit patterns for the muon track candidates are searched inside each muon chamber in the MS.
• The track candidates are reconstructed by fitting hits on diﬀerent layers. The fit is performed
from the seeds generated from the hit segments in the middle layers of the detector, and thenextended to the inner and outer layers.
• If there are segments used by several track candidates, an overlap removal algorithm is applied.
The algorithm selects the best assignment of the segment to a single track or two tracks as ashared segment.
• The hits associated with each track candidate are fitted using a global χ2 fit to remove low
quality tracks from the candidates.
After the individual reconstruction by the inner detectors and the muon spectrometer, those
information are combined in several ways. Depending on which subdetectors are used in the reconstruction, four types of the muons are defined [53]. In this analysis, only following two types of themuon are used as muon candidates.
• Combined muons: A combined track is formed from the tracks reconstructed by the innerdetectors and the muon spectrometer using global refit. Most of the muons are reconstructedby the pattern recognition from the muon spectrometer and then extrapolating to the trackin inner detectors.
• Extrapolated muons: a muon track is reconstructed only using the track in the muon spectrometer with a loose requirement on compatibility with originating from the interaction point
when extrapolating the track. This is to extend the acceptance for muon reconstruction into
the region 2.5 < |η| < 2.7, which is not covered by the inner detectors.
Selection of muon candidates
For the reconstructed muon candidates, following criteria are applied:• passing “medium” muon IDentification (ID)

4.2 Objects

37• |η| < 2.7• passing “gradient loose” isolation criterion• |z0 sin θ| < 0.5 mm• |d0 /σd0 | < 3.0• pT > 10 GeV
Those criteria are to suppress background, mainly from pion and kaon decays, while keeping higheﬃciency for the prompt muons and guaranteeing a robust momentum measurement,
The “medium” muon ID is developed as the default selection for muons in the ATLAS experiment,
to minimize the systematic associated with muon reconstruction and calibration. Individual criteria
for the Combined muons and for the Extrapolated muons are defined in [53], based on the informationfrom the muon spectrometer and the inner detectors. The reconstruction eﬃciency of the muon withthis muon ID is greater than 95%. The η cut is based on the region covered by three layers of
MDTs. Since the Combined muon candidates are reconstructed within the inner detector coverage(|η| < 2.5), and the Extrapolated muon candidates are reconstructed in 2.5 < |η| < 2.7, this cut
does not aﬀect the candidates.
The isolation requirement is to suppress muon from semileptonic decays in hadronic jets. As in
the case of electron, muons originating from the decay of heavy particles, such as W , Z or higgs
are often produced with isolation from other particles, unlike the muons from semileptonic decays.
As discriminating variables for the muon isolation, topoEtcone20 and ptvarcone30 are used. The
definitions of them are the same with the ones for the electron isolation, expect for the cone size ofptvarcone30, which is ∆R = min(0.30, 10GeV/ET )The “gradient loose” criterion is tuned to provide 95% of the total eﬃciency for 25 GeV muons,
and 99% total eﬃciency at 60 GeV, which are the same working point as the case of the electrons.
The total eﬃciency is evaluated by using simulation of Z → µµ.
The selection for z0 and d0 is, again as it is for the electron, to request that the origin of the trackis close to the primary vertex.
The last criterion is on muon momentum. In this analysis, further selections are applied in thesignal region requirement. This is discussed in Section 5.3.3.

4.2.3 Jets
Reconstruction of candidates
Quarks and gluons generated by proton-proton collision immediately transform into bunch of
hadrons, as described in Section 1.1.1. It is detected as a “jet” in the detector.
The candidates of the jet objects are reconstructed using the anti-kT algorithm [54] with a distanceparameter R = 0.4. The input to the algorithm is the topological clusters [55] at the calorimeters.
Several topological clusters are combined as following:
∆2

−2
ij
• For all the combination of the topological clusters i and j, distances dij = min(p−2Ti , pTj ) R2
22
2
and diB = p−2
Ti are calculated, where ∆ij = (yi − yj ) + (ϕi − ϕj ) and pTi , yi , ϕi are thetransverse momentum, rapidity and azimuthal angle around z-axis of the cluster i.
• The minimum distance is searched.
– If diB is the minimum, the cluster i is classified as a jet and removed from the list of theclusters.
– If dij is the minimum, the cluster i and the cluster j are combined into one cluster.
• The steps described above are repeated until all the clusters are combined and classified as
jets.

With this algorithm, clusters within the distance parameter R are combined into one cluster. If
there are several clusters within R, the cluster with high momentum has priority to be combined.

38

Chapter 4 Object Reconstruction

Selection of candidates
To all the candidates of jets, two acceptance cuts, pT > 30 GeV and |η| < 2.8, are applied. Inorder to suppress the contributions from pile-up jets, the Jet Vertex Tagger (JVT) cuts are applied.
JVT is likelihood that the jet is hard scatter jet [56]. Jets are rejected if they have pT < 60 GeV,
|η| < 2.4, and JVT < 0.59.
The selections described above are all for the jet candidates. However, the jet candidates are used
to vetoing event also, which is called bad-jet veto. Bad jet due to the noise in the calorimeter or
cosmic ray can be a jet candidate. The quality of the event which contains such object cannot be
guaranteed. Therefore, such event is vetoed by tagging the object as bad jet [57]. If such object
exists even after the overlap removal, which is described in Section 4.2.4, the event is removed fromthe analysis.
The other type of tag for jet used in this analysis is the b-jet tagging, which is used in Section 5.3.7.
A jet originating from b-hadron decay, which is called b-jet, can be identified using its characteristics.
In ATLAS experiment, following three types of inputs are used [58]:• Secondary Vertex: Due to its relatively long life time, the decay point of b-hadron is notmatching to the primary vertex. Such point is called secondary vertex. In the b-jet tagging
algorithm, the secondary vertex is reconstructed, and its characteristics is used for the tagging.
• Impact Parameter: Even without finding the secondary vertex, tracks in the b-jet have diﬀerent characteristics, since some of them are originating from secondary vertex. Based on thisapproach, likelihood of b-jet or other jets are calculated using impact parameter of tracks andused for the tagging.
• Decay Chain Multi-Vertex Algorithm (JetFitter [59]): The JetFitter algorithm tries to reconstruct the topological structure from the priority vertex to b-hadron and c-hadron. The
reconstructed information are used for the tagging.
Using the inputs discussed above, a boosted decision tree algorithm to discriminate b-jet from otherjets are trained. The trained algorithm, called MV2c20*2 , provide the output shown in Figure 4.4.
In this analysis, the working point providing 77% eﬃciency for b-jet is used. This tag is used in
Section 5.3.7

4.2.4 Overlap removal
Just after the reconstruction of the physics objects described above, some of the objects can be double
counted as several physics objects. One possible reason of such reconstruction is misidentification for
one of the object. Muon track can be misidentified as an electron or a converted photon. Converted
photon can be misidentified as an electron. Energy deposit on the calorimeter by electron and photon
can be misidentified as a jet. When one of the reconstructed object is jet, there is another possibility
that overlapped object is part of jet. Muon, photon, and electron can be a part of jet. Such overlap
is removed in the following order in this analysis:• If an electron and a muon share a track, it is used for a track for the muon.
• If a jet and an electron are found within ∆R < 0.2, the object is interpreted as an electron
and the overlapping jet is removed from the event.
• If a jet and an electron are found within 0.2 < ∆R < 0.4, the object is interpreted as jet andthe electron is removed.
• If a jet and a muon are found within ∆R < 0.4, the object is interpreted as jet and the muonis removed from the event.
• If a jet and a photon are found within ∆R < 0.2 the object is interpreted as photon and the*2 The name came form the composition of background sample for the training, which is 20% c-jets and 80%

light-flavour jets.

4.2 Objects

39

Figure4.4 The MV2c20 output for b- (solid green), c- (dashed blue) and light-flavour (dottedred) jets in tanti-t events. The figure is cited from [58].

overlapping jet is removed from the event.
• If a jet and a photon are found within 0.2 < ∆R < 0.4, the object is interpreted as a jet andthe overlapping photon is removed from the event.
• If a electron and a photon are found within ∆R < 0.4, the object is interpreted as electron
and the overlapping photon is removed from the event.
• If a muon and a photon are found within ∆R < 0.4, the object is interpreted as muon andthe overlapping photon is removed from the event.

4.2.5 Missing transverse energy
After the overlap removal, one more physics object is reconstructed, which is the missing transverse
energy (Emiss
T ). Because of the momentum conservation in transverse plane, the total momentum
or the invisible particles, can be estimated by negative vector sum of the detected objects. In thisanalysis, a neutrino decayed from W boson and two χ̃01 are expected as sources of Emiss
T .
miss
ET is defined as following:
miss emiss γ
miss jetmiss µmiss Soft Term
(Emiss,T )x(y) = (ET )x(y) + (ET )x(y) + (ET )x(y) + (ET )x(y) + (ET )x(y)(4.4)

where each term is computed from the negative vector sum of calibrated reconstructed objects in
the respective category. The last term is for objects called soft term, which is calculated from thereconstructed tracks which are not associated to any physics object [60, 61].

4.2.6 Skimming sample
For establishment of the analysis procedure, collected data is expected to be analyzed several times.
In order to analyze data eﬃciently, skimming of events is performed. The skim has been performed
just after the reconstruction of physics object candidates, before the selection of them. At that stage,
the events not passing following criteria are removed.

40

Chapter 4 Object Reconstruction• The dataset is included in the good run list, which is the list of good quality dataset commonlyused in the ATLAS experiment.
• The event is associated with a primary vertex. Otherwise the event can come from cosmic
muon or noise.
• The event is not used if one of the following problems occurred:– Noise burst at the LAr calorimeter.
– Recovery from the trip of the low voltage power supply for the tile calorimeter.
– DAQ had been done during the recovery procedure for single event upsets in the SCT.
• The event dose not include more than one muon with a |z0 | > 1 mm or |d0 | > 0.2 mm, which
is likely cosmic muon.
• The event passes at least one of following selections*3 :– The event contains more than one photon candidate with greater than 30 GeV transverse
energy.
– The event contains at least one photon candidate with greater than 30 GeV transverse
energy and at least one electron candidate with greater than 30 GeV momentum.
– The event contains more than one electron candidate with greater than 30 GeV momentum.

The events passing the criteria above are used in the analysis described in the following chapters.

*3 These selections are applied as loose pre-selections.

41

Chapter 5

Event selection
As described in Section 1.2, the relative yield of new physics to the SM physics is expected to besmall. Therefore, it is important to suppress the contributions of the SM events, while keeping
acceptance of the contributions of the new physics.
In this chapter, the signal region is defined. At first, overall development of the analysis procedures
are overviewed in Section 5.1. In Section 5.2, the signatures of the signals and the backgrounds are
overviewed. Based on the described signatures, the signal region is defined in Section 5.3.

5.1 Overview of development of analysis procedure
At first, the signal region is defined based on the previous study. The selection criteria used in earlystage of the development are denoted as “early selections”. Using the early selections, procedures toevaluate yields are established, as described in the next chapter. Then rough uncertainties on theevaluated yields are evaluated. Using those procedures and rough uncertainties, the signal region isfurther optimized, as described in Chapter 7. After the optimization, some selections and samples
are changed. The selections used after this change are denoted as “final selections”. The diﬀerence
between the early selections and the final selections are evaluated in Section 7.4.2. With the final
selections and the optimized signal regions, uncertainties are re-evaluated, then the expected upper
limit is evaluated in Chapter 8.

5.2 Overview of event signatures
miss
) are
As described in Figure 1.7, two photons, one lepton and the missing transverse energy (ETexpected in the final state of the signal. Therefore, exactly two photons, exactly one lepton, and a
missrequirement on the missing transverse energy, which is ET> 40 GeV , are requested as the basic
selections. Only electron or muon is considered as a lepton in the final state in this analysis. In thecase of tau, it decays immediately. Only when tau decays into leptons, the event is used as signal inthis analysis.
The backgrounds which can pass the basic requirements are classified into two types, as introducedin Section 3.2.1. The backgrounds including a SM higgs particle within their process is classified as
peaking background. The other type of the backgrounds is non-peaking backgrounds. Since those
two types of the backgrounds have diﬀerent signatures, those are considered separately.

5.2.1 Peaking backgrounds
The peaking backgrounds are mainly from W with associated SM higgs, which is called SM W h. In
contrast to the large missing transverse energy in the signal events, the missing transverse energy inthe peaking backgrounds events is relatively small due to lack of the LSP particles. Therefore, thevariables related to the missing transverse energy are the key to suppress peaking backgrounds.

42

Chapter 5 Event selection

Figure5.1 Image of mγγ distributions. In contrast to the peaking backgrounds and signals(shown as a blue region) which have mγγ close to 125 GeV because of the higgs particles
within their processes, the non-peaking backgrounds (shown as an orange region) have wide
range of mγγ .

5.2.2 Non-peaking backgrounds
The non-peaking backgrounds are mainly from W or Z associated with diphoton. Due to the same
reason with the peaking backgrounds, the non-peaking background events have relatively small
missing transverse energy.
Additionally, invariant mass of the diphoton system (mγγ ) is an important variable to suppress
non-peaking backgrounds. Figure 5.1 shows a conceptual drawing of mγγ distribution. As shown in
the figure, for the signal and the peaking backgrounds, two photons are from the SM higgs decay.
Therefore, reconstructed mγγ is close to the mass of the SM higgs particle (125 GeV). On the other
hand, mγγ of the non-peaking background events may not be close to the mass of the SM higgs
particle. Therefore, the non-peaking backgrounds can be suppressed by the cut on mγγ .

5.3 Signal region definitions
After the basic selection described in the previous section, further cuts are applied to reduce backgrounds. In this section, the requirements for the signal region are described.
In order to show their discrimination power, the distributions of discriminating variables are shownin the following sub section. All the distributions shown in this section are after the basic selections
and the mγγ requirement, which is 105 < mγγ < 160 GeV. The region 120 < mγγ < 130 GeV
is called Higgs window and it blinded. The region out of the Higgs window are called sideband
region. Since only the higgs window is used as the signal region, the contributions of the nonpeaking backgrounds, which is distributed in both the sideband and higgs window, are scaled by
10/55 which is the ratio of mγγ width between the higgs window and the sideband window*1 . Detailabout the window width is described in Section 5.3.5.
In this analysis, most of the requirements are the same with the 8 TeV analysis [19]. Eachrequirement threshold is reconsidered by using distributions shown in this section, and some of them
are updated to improve the sensitivity to the signal.

5.3.1 Signal focus points
Most of the kinematic distributions of signals depend on the assumed mass of LSP and NLSP. In
the optimization and the evaluation of the backgrounds steps, three focus points are used.
One of the focus points is a signal assuming (mχ̃± ,χ̃0 , mχ̃01 ) = (150, 0) GeV, called low-mass signal.
1*1 For this scaling,

Section 6.1.2.

2

it is assumed that non-peaking backgrounds have linear mγγ shape. This is validated in

43

8
-1

7

s = 13 TeV, 36.1 fb , with the basic selections
signal-150-0
signal-250-25
signal-250-100
sideband data

6

γ +jet2γ
tt
SM higgs

Wγ
Zγ
Wγ γ
Zγ γ

EventsEvents

5.3 Signal region definitions
16
-1

14

10

4

8

3

6

2

4

1

2
20

40

60

80

100 120 140 160 180 200
γ1
pT [GeV]0γ +jet2γ
tt
SM higgs

signal-150-0
signal-250-25
signal-250-100
sideband data

12

5

0

s = 13 TeV, 36.1 fb , with the basic selections

10

20

30

40

50

60

70

80

Wγ
Zγ
Wγ γ
Zγ γ

90

100

γ2
pT [GeV]γ2
Figure5.2 pγ1T (left) and pT (right) distributions with the basic selections, which are exactly
miss
two photons, exactly one lepton, and ET> 40 GeV. Contributions of non-peaking backgrounds are scaled by 10/55, which is the ratio of mγγ width between the higgs window andthe sideband window. Data (black points) are shown only for those distributed out of higgs
window, and are scaled by 10/45. Shown uncertainty is only statistical error on sideband data.

This signal had been excluded by the 8 TeV analysis. This point is used to ensure that the significancein low mass parameter space of the model is kept.
The other type of focus points are called high-mass signals. Those are signals assuming(mχ̃± ,χ̃0 , mχ̃01 ) = (250, 25) GeV and (mχ̃± ,χ̃0 , mχ̃01 ) = (250, 100) GeV. Those two signals are chosen
12
12
to evaluate typical signatures of signal event in high mass parameter space of the model. The
optimization has been performed to improve sensitivity to the high-mass signals.

5.3.2 Photon selection
The two photons passing the object selections described Section 4.2.1 are sorted by their transverse
momentum, and called leading photon or sub-leading photon. Figure 5.2 shows their momentum.
Unless otherwise noted, the plots shown in this section are after the basic selection:• Exactly two photons.
• Exactly one lepton.
miss
• ET
> 40 GeV
Regarding data, for those distributed in the sideband windows are shown, and for those distributedin the Higgs window are blinded. Then, the contributions of the non-peaking backgrounds arewidth of the higgs window in GeV
scaled by 10
55 =width of the sideband in GeV . Also, the contributions of sideband data are scaled bywidth of the higgs window in GeV
10
55−10 = width of the sideband in GeV−width of the blinded Higgs window in GeV . The contributions of peaking
backgrounds are merged as “SM higgs”, and all the backgrounds are shown as a stacked histogram.
Regarding uncertainty, only statistical fluctuation of sideband data are shown as black bars, which
are calculated based on Poisson function.
γ2
As described in Section 3.1.1, diphoton trigger is used to collect data with pγ1
T > 35 GeV and pT >25 GeV. As described in Section 4.2.6, event must pass at least one of the conditions for skimming
described below;• Event contains more than one photon candidate with greater than 30 GeV momentum.
• Event contains at least one photon candidate with greater than 30 GeV momentum and at
least one electron candidate with greater than 30 GeV momentum.
• Event contains more than one electron candidate with greater than 30 GeV momentum.
Therefore, events shown in Figure 5.2 are only passing the pre-selections on photon momentumChapter 5 Event selection
4
-1

3.5

s = 13 TeV, 36.1 fb , with the basic selections
γ +jet2γ
tt
SM higgs

signal-150-0
signal-250-25
signal-250-100
sideband data

3

Wγ
Zγ
Wγ γ
Zγ γ

2.5

EventsEvents44

6-1

s = 13 TeV, 36.1 fb , with the basic selections
signal-150-0
signal-250-25
signal-250-100
sideband data

5

γ +jet2γ
tt
SM higgs

Wγ
Zγ
Wγ γ
Zγ γ

4

2

3

1.5
2

1

1

0.5
20

40

60

80

100

120

140
pel [GeV]
T

20

40

60

80

100 120 140 160 180 200
pmu [GeV]
T

Figure5.3 peT (left) and pµT (right) distributions with the basic selections, which are exactly two
missphotons, exactly one lepton, and ET> 40 GeV. Contributions of non-peaking backgrounds
are scaled by 10/55, which is the ratio of mγγ width between the higgs window and the sideband
window. Data (black points) are shown only for those distributed out of higgs window, andare scaled by 10/45. Shown uncertainty is only statistical error on sideband data.

described above.
In the 8 TeV analysis, pγ2
T > 20 GeV was applied [19]. The right plot in Figure 5.2 shows thatsignals are distributed to lower momentum region. Therefore, it is recommended to set the thresholdfor pγ2
T as low as possible to keep signal acceptance.
For the leading photon, pγ1
T > 40 GeV is applied as in the 8 TeV analysis. For the sub-leading
photon, two types of selection thresholds are used in this analysis. When the optimization study
described in Section 7 and the validations of the method to evaluate non-peaking backgrounds
described Section 6.1 are performed, pγ2
T > 27 GeV are applied. However, this requirement can be asource of bias since this threshold is lower than the threshold applied at the skimming step describedabove. Therefore, the threshold for pγ2
T is increased to 31 GeV after those studies. This is discussed
in more detail in Section 7.4.2. The requirements before changing the threshold for pγ2
T are noted as
the early selections, and the requirements after the change are noted as the final selections.

5.3.3 Lepton selection
Figure 5.3 shows the momentum distributions of electrons and muons. For both leptons, 25 GeV
is applied as the threshold for their transverse momentum. The isolation criterion for the electron
applied in the object selection described in Section 4.2.1 is tuned to provide more than 95% of
eﬃciency for Z → e+ e− events from this threshold.

5.3.4 Missing transverse energy selection
Figure 5.4 shows the missing transverse energy distribution. As described in Section 5.2, the distrimiss
bution is after applying ET> 40 GeV as a part of the basic selections.
Figure 5.4 suggests that both type of the backgrounds can be suppressed by increasing threshold formissET
as expected. However, the acceptance for the low-mass signal decreased with higher threshold
miss
miss
for ET . Therefore, further requirement on ET
is not applied in the signal region requirements.
Instead, this discriminating variable is used for the optimization, which is dividing the signal region
to improve significance, described in Chapter. 7

Events

5.3 Signal region definitions

45
9

-1

s = 13 TeV, 36.1 fb , with the basic selections
γ +jet2γ
tt
SM higgs

signal-150-0
signal-250-25
signal-250-100
sideband data

8
7

Wγ
Zγ
Wγ γ
Zγ γ

6
5
4
3
2
1
0

50

100

150

200

250

300

Emiss
[GeV]
T

EventsFigure5.4 Missing transverse energy distribution with the basic selections, which are exactly
miss
two photons, exactly one lepton, and ET> 40 GeV. Contributions of non-peaking backgrounds are scaled by 10/55, which is the ratio of mγγ width between the higgs window andthe sideband window. Data (black points) are shown only for those distributed out of higgs
window, and are scaled by 10/45. Shown uncertainty is only statistical error on sideband data.
10-1

s = 13 TeV, 36.1 fb , in SR

γ +jet2γ
tt
SM higgs

signal-150-0
signal-250-25
signal-250-100
sideband data

8

Wγ
Zγ
Wγ γ
Zγ γ

6
4
2

110

120

130

140

150

160

mγ γ [GeV]

Figure5.5 mγγ distribution with the signal region selections except for mγγ cut, which aresummarized in Table 5.1. Scaling applied to the other plot is not applied to this plot. Data
(black points) are shown only for those distributed out of higgs window. Data distributed in
the Higgs window are blinded. Shown uncertainty is only statistical error on sideband data.

5.3.5 Diphoton invariant mass
As described in Section 5.2.2, the invariant mass of the diphoton system (mγγ ) is an importantvariable to suppress the non-peaking backgrounds. mγγ is defined as following:√mγγ =2ETγ1 ETγ2 (cosh ∆η − cos ∆ϕ)Figure 5.5 shows mγγ distribution. For this figure, not the basic selection but the inclusive singal
regon requirements summarized in Table 5.1 are applied. Scaling factors on non-peaking backgrounds
and sideband data are not applied. Data distributed in the Higgs window are blinded.
As described at the beginning of Section 5.3, 105 < mγγ < 160 GeV is required for the sideband
region, and 120 < mγγ < 130 GeV is required for the signal region. *2*2 The sideband range is validated in Section 6.1.2 in detail.

Chapter 5 Event selection
Events46
6-1

s = 13 TeV, 36.1 fb , with the basic selections
signal-150-0
signal-250-25
signal-250-100
sideband data

5

γ +jet2γ
tt
SM higgs

Wγ
Zγ
Wγ γ
Zγ γ

4
3
2
1
2

2.2

2.4

2.6

2.8

3

3.2

3.4
∆ϕ(Wh)

Figure5.6 ∆ϕ(W, h) distribution with the basic selections, which are exactly two photons,
missexactly one lepton, and ET> 40 GeV. Contributions of non-peaking backgrounds are scaledby 10/55, which is the ratio of mγγ width between the higgs window and the sideband window.
Data (black points) are shown only for those distributed out of higgs window, and are scaledby 10/45. Shown uncertainty is only statistical error on sideband data.

The non-peaking backgrounds are uniformly distributed *3 in the sideband region as shown in
Figure 5.5. In contrast, the signals and the peaking backgrounds are distributed only in the higgs
window. Therefore, the ratio between higgs window width and sideband window width is applied
as a scaling factor to evaluate the contribution of the non-peaking backgrounds in the higgs window
for the kinematic distribution except for mγγ distribution.

5.3.6 W boson and higgs systems
The “W boson object” is reconstructed from the missing transverse energy and the lepton *4 . The
higgs object is reconstructed from the two photons. Since all objects in the final states of the signals
and the SM W h can be reconstructed as a higgs object or a W object, those two objects are expected
to fly away back-to-back in lab frame. On the other hand, additional objects and miss-reconstructedobjects are expected in final state of non-peaking backgrounds. Therefore, the angular distribution
between the W object and the higgs object can be smaller than the case of the signal and SM W h.
In order to suppress the non-peaking backgrounds using the angular information, ∆ϕ(W, h) is
defined as ϕ separation between the W object and the higgs object. Figure 5.6 shows the ∆ϕ(W, h)distribution. As expected above, the signals and the peaking backgrounds are distributed in high∆ϕ(W, h) region. And distributions of the non-peaking backgrounds are relatively flat. As a signal
region requirement, ∆ϕ(W, h) > 2.25 is applied, as applied in the 8 TeV analysis.
Because of the contribution of the LSPs to the missing transverse energy, reconstructed masses ofthe W object and a photon object can be discriminating variables. In this analysis, the transverse
masses reconstructed with the missing transverse energy, the lepton, and one of the photons are usedas the discriminating variables in the signal region requirement. The transverse mass reconsideredwith the missing transverse energy and the lepton without using photon objects is used for the
optimization described in Chapter 7. The transverse mass reconstructed with leading photon (γ1 )is noted as MTWγ1 . And the transverse mass reconstructed with sub-leading photon (γ2 ) is noted as
MTWγ2 . The transverse mass reconstructed without using photon objects is noted as MTW . Definition*3 The shape of mγγ distribution of the non-peaking background is validated in Section 6.1.2 in detail.
*4 W object is not always truth W boson. In the case of signal, it includes two LSPs.

6

47
EventsEvents

5.3 Signal region definitions-1

s = 13 TeV, 36.1 fb , with the basic selections
γ +jet2γ
tt
SM higgs

signal-150-0
signal-250-25
signal-250-100
sideband data

5

Wγ
Zγ
Wγ γ
Zγ γ

4

3

3

2

2

1

1
150

200

250

300

350

400

450

signal-150-0
signal-250-25
signal-250-100
sideband data

5

4

100

-1

s = 13 TeV, 36.1 fb , with the basic selections

6

500

50

100

150

γ1
mW
[GeV]
T

200

γ +jet2γ
tt
SM higgs

250

Wγ
Zγ
Wγ γ
Zγ γ

300

350

γ2
mW
[GeV]
T

EventsFigure5.7 MTWγ1 (left) and MTWγ2 (right) distributions with the basic selections, which are
missexactly two photons, exactly one lepton, and ET> 40 GeV. Contributions of non-peaking
backgrounds are scaled by 10/55, which is the ratio of mγγ width between the higgs window
and the sideband window. Data (black points) are shown only for those distributed out ofhiggs window, and are scaled by 10/45. Shown uncertainty is only statistical error on sideband
data.
9

-1

s = 13 TeV, 36.1 fb , with the basic selections
signal-150-0
signal-250-25
signal-250-100
sideband data

87

γ +jet2γ
tt
SM higgs

Wγ
Zγ
Wγ γ
Zγ γ

6
5
4
3
2
1
0

20

40

60

80

100 120 140 160 180 200mW
T [GeV]

Figure5.8 MTW distribution with the basic selections, which are exactly two photons, exactly
miss> 40 GeV. Contributions of non-peaking backgrounds are scaled by
one lepton, and ET
10/55, which is the ratio of mγγ width between the higgs window and the sideband window.
Data (black points) are shown only for those distributed out of higgs window, and are scaledby 10/45. Shown uncertainty is only statistical error on sideband data.

of those transverse masses are following:
MTW γi =

MTW =

√
√

(5.1)
γi ℓ
miss (1 − cos ∆ϕℓ miss (1 − cos ∆ϕmiss ) + 2E E
miss ) + 2E
2ETγi ET
γi,ET
ℓ,ET
T T
T ET (1 − cos ∆ϕγi,ℓ )
miss (1 − cos ∆ϕmiss )
2ETℓ ET
ℓ,ET

(5.2)

Figure 5.7 shows the MTWγ1 distribution and the MTWγ2 distribution respectively. In this analysis,
MTWγ1 > 150 GeV and MTWγ2 > 80 GeV are used for the signal region requirements, as applied in
the 8 TeV analysis. Figure 5.8 is the MTW distribution.

Chapter 5 Event selection
Events

48
20
18

-1

s = 13 TeV, 36.1 fb , with the basic selections
signal-150-0
signal-250-25
signal-250-100
sideband data

16
14

γ +jet2γ
tt
SM higgs

Wγ
Zγ
Wγ γ
Zγ γ

3.5

4.5

12
10
8
6
4
2
0

0.5

1

1.5

2

2.5

3

4

5

b-jet multipulisity

Figure5.9 Distribution of the number of b-jets with the basic selections, which are exactly two
missphotons, exactly one lepton, and ET> 40 GeV. Contributions of non-peaking backgrounds
are scaled by 10/55, which is the ratio of mγγ width between the higgs window and the sideband
window. Data (black points) are shown only for those distributed out of higgs window, andare scaled by 10/45. Shown uncertainty is only statistical error on sideband data.

5.3.7 B-jet
Figure 5.9 shows the distribution of the number of b-jets. Most of the signal events have no b-jets,
while non-negligible background events have one or more b-jet. Non-peaking background eventswith b-jets are mainly from tt̄ events, and peaking background events with b-jets are mainly fromtt̄h events.
The diﬀerence between the signal and two type of the backgrounds suggests that significance canbe improved by vetoing events with b-jets (b-jet veto). The improvement with the b-jet veto is
estimated with the asymptotic formulae of the expected significance Z assuming the nominal signal
hypothesis [62] and only statistical uncertainty, defined as√s
Z = 2((s + b) ln(1 + ) − s),bwhere s is the expected yields of the signal and b is the expected yields of all the backgrounds. Fors, high-mass focus points were assumed.
From the calculation of significance Z using the yields evaluated by MCs, ∼ 10% improvement of
the significance is evaluated while keeping the acceptance of the signal yields. Therefore, the b-jet
veto is introduced into signal region requirements.

5.3.8 Subdivision of the signal region
In Table 5.1, all the requirements for the signal region are summarized.
As a result of the optimization described in Chapter 7, the signal region defined above are subdivided to four subsets noted from SRa to SRd. Since those subsets are mentioned in the following
chapter, only the definitions of those subsets are shown in the Table 5.2 The subdividing thresholds
are shown in Figure 5.10.

5.3 Signal region definitions

49

Figure5.10 Subdivided signal regions in (MTWγ2 , MTW ). z axis showns the yield of the peaking
background. SRb, which is not shown in the figure, is complement to SRa + SRc.

Table5.1

Requirements of the inclusive signal region.

Number of photon
pγ1
T
pγ2
T
Number of leptons
peT or pµT
miss
ET
mγγ
∆ϕ(W, h)
MTWγ1
MTWγ2
Number of b-jets

Table5.2

Exactly two> 40 GeV> 27 GeV(> 31 GeV after the optimization)
Exactly one (electron or muon)> 25 GeV> 40 GeV> 120 GeV and < 130 GeV> 2.25> 150 GeV
> 80 GeV
Exactly zero

Definitions of the subsets of signal region. SRb and SRc are subsets of SRd.

SRa
SRb
SRc
SRd

MTWγ2 > 140 GeV and MTW > 110 GeV
MTWγ2 < 140 GeV or MTW < 110 GeV
excluding SRc
MTWγ2 < 140 GeV and 60 < MTW < 90 GeV
MTWγ2 < 140 GeV or MTW < 110 GeV

51

Chapter 6

Signal and background modeling
The signal region defined in the previous chapter is further optimized in the next chapter. For the
optimization, reliable yields expectation of the signal and background are needed. In this chapter,the procedures to estimate the yields of signal and background are described. For the non-peaking
backgrounds, the yields are evaluated using data-driven method, as described in Section 6.1. The
others are evaluated by MCs, as described in Section 6.2.

6.1 Non-peaking Backgrounds
The non-peaking backgrounds are widely distributed in signal region and sideband regions. Thus,
the yields of the non-peaking backgrounds in the signal region can be estimated by interpolating theshape of the distribution from the sideband region.

6.1.1 Yields evaluation method
As shown in Figure 5.5, the sideband region is dominated by non-peaking backgrounds. Assuming
no contribution of the peaking backgrounds and the signal to the sideband region and continuous
mγγ shape of the non-peaking backgrounds, yields of non-peaking backgrounds in the signal region
can be evaluated by using data distributed in the sideband region. Because of the limited statistics
in the sideband region, a simple assumption is chosen as the shape of mγγ distribution, which is theconstant function*1
The yields are evaluated as following. At first, data in sideband region of each subset of thesignal region are fitted with a constant function. The fitted distributions are shown in Figure 6.1
and Figure 6.2. From the fitted functions, the yields in the subsets are evaluated. Since all themγγ distributions are plotted in 5 GeV bin width, the yields in the 10 GeV of higgs window can beevaluated by a twice the fitted constant value. The results are shown in Table 6.1. In the table, thestatistical uncertainties are also shown, which are evaluated in Section 8.1. The results are with thefinal selections.
Table6.1 Estimated yields of the non-peaking backgrounds with statistical uncertainty, by
fitting constant function to the mγγ sideband data, for each subset of the signal region. The
yields expected from MCs and their statistical uncertainty are aslo shown.

Subsets of the signal region
SRa
SRb
SRc
SRd

Estimated yields from the fitting
0.22 ± 0.22
2.44 ± 0.67
0.89 ± 0.45
3.33 ± 0.90

*1 This assumption is discussed in Section 6.1.2.

MC expectation
0.41 ± 0.11
2.02 ± 0.41
0.86 ± 0.42
2.88 ± 0.59

Chapter 6 Signal and background modeling5

EventsEvents52-1

s = 13 TeV, 36.1 fb , in SRa

γ +jet2γ
tt
SM higgs

signal-150-0
signal-250-25
signal-250-100
sideband data

4

Wγ
Zγ
Wγ γ
Zγ γ

10

6

2

4

1

2

120

130

140

150

160

γ +jet2γ
tt
SM higgs

signal-150-0
signal-250-25
signal-250-100
sideband data

8

3

110

-1

s = 13 TeV, 36.1 fb , in SRb

110

120

130

140

Wγ
Zγ
Wγ γ
Zγ γ

150

mγ γ [GeV]160

mγ γ [GeV]

5

EventsEventsFigure6.1 mγγ distributions in SRa (left) and in SRd (right). Data (black points) are shown
only for those distributed out of higgs window. Shown uncertainty is only statistical error on
sideband data.
-1

s = 13 TeV, 36.1 fb , in SRc

γ +jet2γ
tt
SM higgs

signal-150-0
signal-250-25
signal-250-100
sideband data

4

Wγ
Zγ
Wγ γ
Zγ γ

10

6

2

4

1

2

120

130

140

150

160

mγ γ [GeV]

γ +jet2γ
tt
SM higgs

signal-150-0
signal-250-25
signal-250-100
sideband data

8

3

110

-1

s = 13 TeV, 36.1 fb , in SRd

110

120

130

140

Wγ
Zγ
Wγ γ
Zγ γ

150

160

mγ γ [GeV]

Figure6.2 mγγ distributions in SRc (left) and in SRd (right). Data (black points) are shown
only for those distributed out of higgs window. Shown uncertainty is only statistical error on
sideband data.

6.1.2 Validations of the method
Fitting function dependence
In order to verify about the mγγ shape, the study is performed with toy samples, which is the pseudodata generated under simple assumptions. This study is performed with the early selections. Dueto lack of statistics in the subsets of the signal region, the study is performed only for the inclusive
signal region.
For the study, two types of assumptions are considered; the genuine shape of the non-peaking
backgrounds do not depend on the mγγ (constant function), or it has linear dependence on mγγ(linear function). At first, observed sideband data are fitted by the assumed function. Because of
the large statistical fluctuation of the sideband data, the slope of the linear function is evaluated by
the MC distributions, and the function is scaled to the sideband data while fixing the slope. Then,the fitted functions are assumed as genuine probability density function. Based on the two fitted
functions, two types of toy samples are generated. For this study, 10,000 of toy samples for each
assumption are generated.
After generating the toy samples, those are re-fitted with a constant and a linear function in
the same manner to evaluate expected yield for each toy sample. Finally, mean and RMS of the6.1 Non-peaking Backgrounds

53

re-evaluated yields for each type of toy samples are calculated. The results are shown in Table 6.2.
The results suggest that there are no dependence on the assumption of the shape, considering thelarge statistical error.
Fitting range dependence
Since the expected yields rely on the distribution of the data in sideband, they could be aﬀectedby the definition of sideband range. In order to verify the eﬀect, several fittings to the data in the
inclusive signal region has been performed with various definitions of the sideband range. This study
is performed with the early selections.
Table 6.3 shows the results. Although small tendency can be seen in the results, the eﬀect is muchsmaller than the statistical uncertainty. Therefore, this dependence is not considered further.
Leakage from signal region
The studies described above are based on the assumption that all the data distributed in the sideband
region are non-peaking backgrounds. This assumption is satisfied if there are no leakage of the signal
or the peaking backgrounds from the signal region. It is confirmed with the mγγ distribution shownin Figure 5.5. From the distribution, the evaluated leakages to sideband region are smaller than 0.3
events. The leakages are much smaller than the yields of the non-peaking backgrounds expected by
MCs. Therefore, the possibilities that the leakages aﬀect the fitting results or the validation studies
are negligible and not considered here.

6.1.3 Further validation about mγγ shape
The validations described in the previous subsection had been performed in early stage of the development of analysis procedure. In final stage of the development, further study about mγγ has been
performed because of mild “slopes” around higgs window shown in Figure 5.5. The slopes seem to
be wide tails leaked from the higgs window. It is expected to be statistical fluctuation, so the study
is performed to guarantee that expectation. This study is performed with the final selections.
If the slopes are due to statistical fluctuation, similar fluctuation may be seen in other region.
Since the used range of mγγ is too narrow for discussion, mγγ requirement is relaxed from [105,160] GeV to [0,300] GeV. Because of wide range of mγγ , bin width is changed from 5 GeV to
10 GeV. The distribution is shown in Figure 6.3 As shown in the figure *2 , data points are fluctuated

Table6.2 Results of the toy study. The nominal assumption is shown in third row. The
diﬀerences between evaluated yields are small comparing to their error.

Toy assumption
constant
linearconstant
linearfitted functions
linearlinearconstant
constantevaluated yields
4.70 ± 1.00
4.70 ± 1.00
4.88 ± 1.03
4.89 ± 1.03

Table6.3 Results of the sideband range study. The nominal range is shown in third row. The
diﬀerences between evaluated yields are small comparing to the error on the nominal yield.

Sideband range
110 < mγγ < 160 GeV
107.5 < mγγ < 160 GeV
105 < mγγ < 160 GeV
105 < mγγ < 157.5 GeV
105 < mγγ < 155 GeV

evaluated yields
5.25
5.18
4.88 ± 1.03
4.71
4.50

Chapter 6 Signal and background modeling
Events

54
20
18

-1

s = 13 TeV, 36.1 fb , in SR relaxed mγ γ cut
γ +jet2γ
tt
SM higgs

signal-150-0
signal-250-25
signal-250-100
sideband data

16
14

Wγ
Zγ
Wγ γ
Zγ γ

12
10
8
6
4
2
0

50

100

150

200

250

300

mγ γ [GeV]

EventsFigure6.3 mγγ distributions in the inclusive SR with relaxed mγγ requirement, which is[0, 300] GeV. Data (black points) are shown only for those distributed out of higgs window.
Shown uncertainty is only statistical error on sideband data. Since W γγ sample is generating
only mγγ > 80 GeV, there are deviation between data and MCs below 80 GeV region.
20

miss

s = 13 TeV, 36.1 fb , in SR relaxed ET& ∆ϕ(Wh) cut

110

150

-1

γ +jet2γ
tt
SM higgs

signal-150-0
signal-250-25
signal-250-100
sideband data

18
16

Wγ
Zγ
Wγ γ
Zγ γ

14
12
10
8
6
4
2
120

130

140

160

mγ γ [GeV]missand ∆ϕ(W, h) requireFigure6.4 mγγ distributions in the inclusive SR with relaxed ET
ments, which are 20 GeV and 0, respectively. Data (black points) are shown only for those
distributed out of higgs window. Shown uncertainty is only statistical error on sideband data.

around the MC expectation, not only around the higgs window. The points around the higgs window
accidentally have positive fluctuations, but the sizes of the fluctuations are reasonable to be statisticalfluctuations.
One more study is performed by relaxing the selection. If the slopes are not due to statisticalfluctuation, that shape is stable even with large statistics. In order to avoid eﬀect to mγγ shape,
miss
miss
, thresholdand ∆ϕ(W, h) are relaxed. For ET
criteria on relatively non related discriminants, ET
is relaxed from 40 GeV to 20 GeV. And ∆ϕ(W, h) cut, which is ∆ϕ(W, h) > 2.25, is removed. The
result is shown in Figure 6.4 As expected, size of deviation from data to MCs becomes small. The
data point of [130, 135] GeV is below the MC expectation.
Both of those study suggest that the mild slopes seen around the higgs window are due to statisticalfluctuations.

*2 It is seen that overall mγγ distribution has mild slope.

But it is confirmed that the assumption of slope dose
not aﬀect evaluation because of low statistic, as shown in the previous subsection.

6.2 Signal and Peaking Background55

6.2 Signal and Peaking BackgroundIn contrast to the non-peaking backgrounds, it is diﬃcult to separate the peaking backgrounds fromthe signal. All the kinematic variables introduced in the previous section are considered to eﬃciently
separate them, but no variable could isolate only the peaking backgrounds with cut-base selection.
Even though isolating those two components are diﬃcult, by dividing the signal region, an improvement of the significance was achieved using the “ratio” of yields between divided regions, as
described in Chapter 7. For the evaluation of improvement, yield evaluations of signal and peaking
backgrounds are important. In this section, the yields evaluated by MCs are explained.

6.2.1 Evaluated yields
Table 6.4 shows the yields expected by MCs. Those are evaluated with the final selections. Owing
to the b-jet veto newly introduced in this analysis, tt̄h is suppressed to ∼ 10%.As shown in the table,
the dominant source of the peaking background is the SM W h.

Table6.4 Expected yields of the peaking backgrounds and the focus point signals for thesubsets of the signal region.

Process
SM W hSM ZhSM tt̄hggh
VBFh
Total peaking background(mχ̃± ,χ̃0 , mχ̃01 ) = (150, 0)12(mχ̃± ,χ̃0 , mχ̃01 ) = (250, 25)12(mχ̃± ,χ̃0 , mχ̃01 ) = (250, 100)
1

2

SRa
0.094 ± 0.014
0.011 ± 0.002
0.033 ± 0.005< 0.001< 0.0010.138 ± 0.021
2.87
1.36
0.95

SRb
1.504 ± 0.226
0.067 ± 0.010
0.099 ± 0.015< 0.001
0.001 ± 0.001
1.672 ± 0.251
5.90
0.86
0.84

SRc
0.315 ± 0.047
0.010 ± 0.002
0.014 ± 0.002< 0.001< 0.001
0.338 ± 0.051
0.68
0.04
0.06

SRd
1.818 ± 0.273
0.077 ± 0.012
0.113 ± 0.017< 0.001
0.001 ± 0.001
2.010 ± 0.302
6.57
0.90
0.90

57

Chapter 7

Optimization of Signal regions
In this chapter, the defined signal region is further optimized. As an introduction, the idea of the
optimization is described in Section 7.1. Some statistical definitions that are used for the optimizationand the interpretation of the results are described in Section 7.2. The detail of the procedure of
the optimization is described in Section 7.3, and the results of the optimization is described in
Section 7.4.

7.1 Idea of optimization
As seen in Section 5.3, the signals and the backgrounds have diﬀerent shapes in some kinematic
variables, However, it is not possible to isolated only the signal using those variables. In otherwords, when the signal region is subdivided, both subsets have non negative yields of the signals
and the backgrounds, such as shown in top of Figure 7.1. Since there are diﬀerent shapes of somekinematic variables, the ratios of the yields between the two subsets subdivided by appropriate
thresholds can be significantly diﬀerent between the signal and the backgrounds. This information
is useful to evaluate if there are any contributions of the signals in observed events; if there are only
contributions of the backgrounds, the ratio between the two subsets must be close to the ratio of the
backgrounds, such as shown in the bottom left of Figure 7.1. Otherwise, that could be due to thecontributions of the signal, such as shown in the bottom right of Figure 7.1.
In order to evaluate the contributions of the signal, number of the observed events in both subdivided regions are fitted simultaneously by expected yields while fixing the ratio between the regions.
It is called simultaneous fit. The merit of this procedure is that signal acceptance can be kept since
the overall signal region is not changed.
The subdividing thresholds are defined by the optimization study described in this chapter. Since
the purpose of this analysis is searching for un-discovered particles, the optimization has been performed by maximizing expected discovery significance defined in Section 7.2.3, by scanning thesubdividing thresholds.

7.1.1 Distributions of discriminating variables
miss, MTW . MTWγ1 and MTWγ2 are considered as candidates of the subdividing variables in theET
optimization study. Figure 7.2 and Figure 7.3 show those distributions with the final selections.

7.2 Statistical definitions
Some statistical tools are used to search for the optimal subdivision and for the interpretation of theobserved data in this analysis. In this section, the statistical tools used in this analysis are defined.

58

Chapter 7 Optimization of Signal regions

2.5

EventsEventsFigure7.1 Idea of optimization. As shown in the top two images, background is expected
miss
miss
region, in contrast to
region rather than high ET
to have large contribution in low ET
miss
miss
region. In casesignal which has large contribution in high ET region rather than low ET
that observed data includes only background, the ratio between the two regions is close to the
expected ratio of background yields, as shown in the left bottom image. If there are contributionof signal in observed data, the ratio is diﬀerent from the expected ratio of background yields,
as shown in the right bottom image.

-1

s = 13 TeV, 36.1 fb , in SR
signal-150-0
signal-250-25
signal-250-100
sideband data2

γ +jet2γ
tt
SM higgs

Wγ
Zγ
Wγ γ
Zγ γ

2.5

1.5

1

1

0.5

0.5

50

100

150

200

250

signal-150-0
signal-250-25
signal-250-100
sideband data

2

1.5

0

-1

s = 13 TeV, 36.1 fb , in SR

300

Emiss
[GeV]
T

0

20

40

60

80

γ +jet2γ
tt
SM higgs

Wγ
Zγ
Wγ γ
Zγ γ

100 120 140 160 180 200mW
T [GeV]

Figure7.2 Missing transverse energy (left) and MTW (right) distributions in the signal region.
Contributions of non-peaking backgrounds are scaled by 10/55, which is the ratio of mγγ width
between the higgs window and the sideband window. Data (black points) are shown for only
for those distributed out of higgs window, and are scaled by 10/45. Shown uncertainty is only
statistical error on sideband data.

2.5

59
EventsEvents

7.2 Statistical definitions-1

s = 13 TeV, 36.1 fb , in SR

γ +jet2γ
tt
SM higgs

signal-150-0
signal-250-25
signal-250-100
sideband data

2

Wγ
Zγ
Wγ γ
Zγ γ

2.5

1.5

1

1

0.5

0.5

150

200

250

300

350

400

450

signal-150-0
signal-250-25
signal-250-100
sideband data

2

1.5

100

-1

s = 13 TeV, 36.1 fb , in SR

500

50

100

150

γ1
mW
[GeV]
T

200

γ +jet2γ
tt
SM higgs

250

Wγ
Zγ
Wγ γ
Zγ γ

300

350

γ2
mW
[GeV]
T

Figure7.3 MTWγ1 (left) and MTWγ2 (right) distributions in the signal region. Contributions of
non-peaking backgrounds are scaled by 10/55, which is the ratio of mγγ width between the
higgs window and the sideband window. Data (black points) are shown for only for those
distributed out of higgs window, and are scaled by 10/45. Shown uncertainty is only statisticalerror on sideband data.

7.2.1 Likelihood
In this analysis, binned likelihood (L) is used. As described above chapters, the yields of nonpeaking backgrounds (bi ), peaking backgrounds (hi ), and signals (si ) are evaluated in each subsetof the signal regions. Using those yields and their relative uncertainties which are σb,i , σh and σs
respectively, L is defined as
L = exp(−

θs 2
θh 2
e−λi λi Ni
θb,i 2) exp(−
)Πi
exp(−
),
2
2
Ni !
2

(7.1)

where λi = µ(1 + θs σs )si + (1 + θh σh )hi + (1 + θb,i σb,i )bi ). Here i shows a subset of the signal region.
Therefore, it runs from “a” to “d”. θs , θh and θb,i are nuisance parameters associated with theuncertainties of the signal, the peaking and the non-peaking backgrounds. µ is the signal strength.
Ni is the observed number of events in each subset of the signal region. This likelihood is definedby the product of a Poisson function and constraint terms for the nuisance parameters. The Poisson
function part provides high values when the total yields (λi ) is close to the observed number of theevents. The constraint terms are to limit fitted yields within size of the uncertainties.
As described in Chapter 8, dominant source of uncertainty is the statistical uncertainty for nonpeaking backgrounds. On the other hand, σh and σs are mainly from systematical uncertainty on
MC. Therefore, individual nuisance parameter is defined for each subset of the signal region for the
non-peaking backgrounds. For the signal and the peaking backgrounds, one nuisance parameter isshared among all subsets of the signal region.
In the optimization study, σh = 13.8% and σs = 15% are used as tentative values. Those values
are evaluated by rough estimation described in Section 8.2 and 8.3. The eﬀect of the fluctuation of
those uncertainties are discussed in Section 7.4.1, and the precise evaluation of them are discussed in
Chapter 8. For σb,i , the uncertainties shown in Table 6.1 are used, which is evaluated in Section 8.1.

60

Chapter 7 Optimization of Signal regions

Figure7.4 Image of qµ distribution and definition of pµ . This image is case of the assumptionof µ = 0. With this assumption, backgrounds only like events show small qµ , and signal +background like events show large qµ . pµ is defined as probability to observe qµ larger thanqµ,obs . as shown as a green area.

7.2.2 Test statistic
In order to do statistical hypothesis tests, the test statistic is also defined with given signal strengthµ asˆ−2 ln L(µ,θ̂)(µ̂ < 0),L(0,θ̂(0))
qµ =
(7.2)
ˆ
−2 ln L(µ,θ̂)
(µ̂
≥
0),
L(µ̂,θ̂(µ))ˆˆ
L(µ,θ̂)This is based on the likelihood ratio L(µ̂,, where θ̂ is the nuisance parameters maximizing L with
θ̂(µ))

given µ. µ̂ and θ̂ are the combination of the signal strength the nuisance parameters maximizing
L. Since negative signal strength is not considered in this analysis, when µ̂ is negative, µ̂ is fixed tozero and θ̂ is re-evaluated with that setup.
When given µ describes well the observed events, the likelihood ratio is close to 1, and qµ is close
to 0. Large qµ means inconsistency between given µ and the observed events. In order to evaluate
the inconsistency, the p-value is defined as∫ ∞pµ =f (qµ |µ)dqµ(7.3)
qµ,obswhere f (qµ |µ) is the probability density function of qµ under the assumption that given µ describes
the physics. qobs is calculated qµ with the observed numbers of the events. Image of f (qµ |µ) and qµ
are drawn in Figure 7.4. The meaning of the p-value is the possibility that qµ greater than qobs isobserved when given µ is correct.
In most of the cases in this analysis, f (qµ |µ) function is evaluated by using toy samples as following.
First, background only model or background plus new physics model are assumed. Next, many toy
sample in each signal region subset are generated, assuming that their probability density functions
are Poisson functions which give the expected yields as their averages. Then, qµ is evaluated witheach generated toy sample, and the normalized distribution of evaluated qµ is used as f (qµ |µ).

7.2 Statistical definitions

61

Since the evaluation with toy samples takes long time, the optimization has been performed withthe asymptotic method described as following. The asymptotic method is under the assumption of
the Wald appropriation [62]. With this assumption, f (qµ |µ) is given as11
f (qµ |µ) = √ √ e−qµ /2 .
2π qµ

(7.4)

This method is useful to evaluate p-value in short time, but it is known that there is inconsistency
between evaluated p-value with this method and the toy method, especially when the yields of signals
and backgrounds are small. As shown in the previous chapter, the yields are expected to be small.
Therefore, the asymptotic method is used only at the optimization study, and toy method is used
for the other studies.
The evaluated p-value pµ is interpreted as a significance (Zµ ) with following function:Zµ = Φ−1 (1 − pµ ),(7.5)

where Φ−1 is the inverted function of the standard Gaussian. In the ATLAS experiment, typically 5σ(p-value = 2.87 × 10−7 ) is required for the discovery of new physics, and 3σ (p-value = 1.35 × 10−3 )is required for the evidence of new physics. For the discussion of the exclusion, when (1− p-value)is larger than the confidence level, the assumed model is excluded. Typically, 5% p-value (95%
confidence level) is used as the threshold.

7.2.3 Significance for discovery
When observed number of events is greater than the yields expected by the SM, it could be due tothe contribution of new physics. In that case, the significance for discovery is calculated as following.
When such events are observed, qµ is calculated under the assumption of µ = 0. Evaluated significance from p0 is called the discovery significance. It shows the probability that the inconsistency
between the expectation and the data is larger than the experimentally observed case, under theassumption that there are no new physics.
In order to evaluate the significance with blinded information, the most probable significance fordiscovery is evaluated as expected discovery significance. For the evaluation, instead of qobs , themost probable qexp is used, which is the mean of the probability density function of qµ under theassumption of µ = 1 with the focus point signal models (f (qµ |µ = 1)). Therefore, the evaluated p0
shows the expected p0 value when the assumed model is completely correct.
In the optimization, the expected p0 values are used as the figure of merit. If expected p0 is large,
it means that no statistical diﬀerences from the SM expectation can be seen even if the assumed
new physics exists. Therefore, this value can be used to estimate the range in the parameter space
where the signal event can be discovered if it exists.

7.2.4 Significance for exclusion
When observed number of events is close to the yields expected by the SM, the results can beinterpreted as the exclusion of some of the physics models which expect large signal yields. For thistype of discussion, pµ is calculated as a function of µ. Evaluated significance from pµ is called theexclusion significance. If pµ evaluated with µ = 1 is smaller than (1− confidence level), assumed
model is excluded by “confidence level”.
The upper limit of the signal strength µ is also evaluated from pµ . Typically, larger µ leads tosmaller pµ . µ which provides qµ equal to (1− confidence level) is the upper limit of the signal
strength. The product of the upper limit on the signal strength and the expected yields of signal isconsidered as the upper limit on the expected yields of the signal. By dividing the upper limit on
the expected yields of signal by collected luminosity, the upper limit on the signal cross section canbe evaluated.

62

Chapter 7 Optimization of Signal regions

In order to evaluate expected significance with blinded information for the exclusion, qexp is
evaluated from the mean of the probability density function of qµ under the assumption of µ = 0(f (qµ |µ = 0)). Therefore, the evaluated pµ under this assumption shows expected pµ value when
there are no new physics.

7.2.5 Model independent significanceSignificance evaluation under assumptions about the signal can be biased. To avoid such bias, model
independent significance is evaluated. At this evaluation, since the expected signal yields (si ) cannot
be assumed, overall signal yields (S) is used instead of si µ Since the ratio of the signal yields between
diﬀerent signal regions cannot be assumed, this type of significance is evaluated in individual signal
region.
For the interpretation of the results to the discovery significance, this model independent significance is used. By using model independent significance for exclusion, upper limits on the yield andthe cross section of new physics can be evaluated without assuming any specific physics models.

7.3 Procedure of optimization
As described in Section 7.1, the optimization has been performed by maximizing the expecteddiscovery significance. The procedure is described below.
First, discriminating variables for the subdivision are defined. In this study, one or two variables
are used. For each chosen combination of the variables, the thresholds dividing signal region arescanned and expected discovery significance is evaluated with three focus points. Scan range andstep are summarized in Table 7.1. Then, the thresholds achieving highest significances are chosen
as the best thresholds for the scanned discriminating variables.
For the decision of the best thresholds, root mean square of the two high-mass signals is considered.
This is because the low-mass signal has been excluded by the 8 TeV analysis, and owing to its large
signal yield high enough significance is expected even without the optimization. The expectedsignificance for the low-mass signal is only used for the verification of the high expected significanceafter the optimization.
This study has been performed with the early selections.

7.4 Optimization results
Table 7.2 shows the achieved significances and the best thresholds with one discriminating variable.
Table 7.3 shows those with two discriminating variables. In order to see the improvement, original
expected significances without subdividing signal region are shown in the top row of the tables,
and the improvement ratios against the originals are shown in the Gain column. Those results are
obtained with the early selections.
As shown in the tables, the optimization with two discriminating variables can achieve higher
significances than the optimization with one discriminating variable. From Table 7.3, it is found thatmiss) achieved similarly highest significances.
the subdivisions using (MTWγ2 ,MTW ) and using (MTW ,ET
Table7.1 Optimization range and step

Discriminating variables
miss
ET
MTW
MTWγ1
MTWγ2

Ranges [GeV][40, 110][0, 160][150, 300]
[80, 150]

Steps [GeV]
10
10
10
10

7.4 Optimization results

63

Since the achieved results with the two high-mass signals are similar, expected discovery significances with all the signal samples are evaluated with those two subdivisions to conclude which
combination is the best. The results are shown in Figure 7.5 and 7.6. In those figures, expectedsignificances for some of the higher mass signals cannot be evaluated since the evaluated p-value
is too high. Although those two results are similar, (MTWγ2 ,MTW ) combination is chosen since it
missachieved slightly better significances than (MTW ,ET). The region above the thresholds is called
SRa, and the complement region is called SRd.
Figure 7.7 and Figure 7.8 show the (MTWγ2 , MTW ) distributions of the peaking backgrounds andthe three focus points, which defined in Section 5.3.1.
As shown in Figure 7.7, the peaking backgrounds are mainly distributed MTW ∼ 80 GeV andlow MTWγ2 region, as expected from the main source of the peaking backgrounds which is the SM
miss
W h. Since the SM W h has only neutrino as a source of ET, the W object is expected to bereconstructed from a neutrino and a lepton only, without contributions of LSPs. Thus, MTW is
missexpected to be around the W mass (80 GeV). Due to the lack of the contributions of LSPs, ET
misscan be relatively lower than ETof the signal events. This leads to relatively low MTWγ2 value.
From the tendency described above, further subdivision is suggested. The idea is isolating thepeaking backgrounds by subdividing SRd into SRc (the peaking backgrounds is mainly distributed)
and SRb (the complement to SRc in the SRd). The definitions of the subsets are summarized inTable 5.2 and Figure 5.10. The expected significances are evaluated with the combination of SRa
and SRb and SRc, and the combination of SRa and SRc also. Those results are shown in Figure 7.9
and 7.10. Comparing those results with Figure 7.6, obviously the original combination of SRa and
SRd shows the best results. Therefore, the combination of SRa and SRd is chosen as the signal
region subsets.

Table7.2 Best thresholds and achieved significances with one discriminating variable

Discriminating
variables
Original
miss
ET
MTW
MTWγ1
MTWγ2

Thresholds
(GeV)
—
90
120
270
40

(mχ̃± ,χ̃0 , mχ̃01 )(GeV) =1

2(150, 0)
2.92
2.87
3.05
2.75
3.22

Gain
—
0.98
1.04
0.94
1.10

(250, 25)
0.47
0.64
0.88
0.72
0.65

Gain
—
1.37
1.88
1.55
1.40

(250, 100)
0.21
0.34
0.59
0.33
0.37

Gain
—
1.59
2.77
1.54
1.74

Table7.3 Best thresholds and achieved significances with two discriminating variables

Discriminating
variables
Original
MTWγ1 ,MTWγ2
MTWγ1 ,MTW
miss
MTWγ1 ,ET
Wγ2
MT ,MTW
miss
MTWγ2 ,ETW
miss
MT ,ET

Thresholds(GeV)—(240,140)(190,120)(220,90)(140,110)(140,70)(100,70)(mχ̃± ,χ̃0 , mχ̃01 )(GeV) =1

2(150, 0)
2.92
2.93
3.07
2.96
3.01
2.97
2.94

Gain
—
1.00
1.05
1.01
1.03
1.01
1.01

(250, 25)
0.47
0.74
0.87
0.73
0.90
0.73
0.93

Gain
—
1.57
1.87
1.56
1.92
1.56
1.98

(250, 100)
0.21
0.41
0.59
0.37
0.64
0.41
0.62

Gain
—
1.95
2.78
1.74
3.03
1.93
2.92

Chapter 7 Optimization of Signal regions

120

3
0.51

1

mχ 0 [GeV]

64

0.58

100

0.22 0.03

2.5

0.60
0.88 0.60 0.61

80

21.07 0.95 0.68 0.40

0.32 0.07

1.59 1.12 0.95 0.66 0.4760

1.41 1.09 0.73 0.56

1.5

0.35 0.11

1.77

40
2.19

1.82

2.09

20 2.83

1.38 0.92 0.69 0.52

1.75 1.24 0.90 0.56

1

0.21

0.31 0.15

0.5

2.42 1.95

1.48 0.94 0.71 0.45

0.23 0.08

0 3.08 2.31 1.69 1.15 0.82 0.55 0.31 0.09
150
200
250
300
350

400

450

500
mχ 0/ χ ± [GeV]2

0

1

Significances in (mχ̃± ,χ̃0 ,mχ̃0 ) parameter space for the subdivision based on the
1
2
1
miss
W
= 100 GeV.
values MT = 70 GeV and ET

120

3
0.47

1

mχ 0 [GeV]

Figure7.5

0.47

100

0.07

2.5

0.65
0.85 0.54 0.48

80

20.99 0.90 0.60 0.35

0.19

1.54 1.09 0.83 0.50 0.32

60

1.43 0.96 0.61 0.39

1.5

0.22 0.00

1.81

40
2.18

20 2.94

1.66

2.14

1.23 0.80 0.54 0.38

1.62 1.12 0.79 0.42

2.41 1.85

10.09

0.26 0.03

0.5
1.36 0.81 0.61 0.33

0.12

0 3.01 2.25 1.65 1.10 0.71 0.43 0.19 0.00
150
200
250
300
350

400

450

500
mχ 0/ χ ± [GeV]
2

Figure7.601Significances in (mχ̃± ,χ̃0 ,mχ̃0 ) parameter space for the subdivision based on the
1
1
2
Wγ2
values MT= 140 GeV and MTW = 110 GeV.

7.4 Optimization results

65

higgs bkg

signal 150 0
0.16

250

mW
T [GeV]

300mW
T [GeV]

300

0.12

250

0.14
0.1
0.12

200

200
0.08

0.1
150

150
0.08

0.06

0.06

100

100
0.04

0.04
50

50

0.02

0.02
0
0

50

100

150

200

250

300

350

400

450
500
Wγ 2
mT [GeV]

0

0
0

50

100

150

200

250

300

350

400

450
500
Wγ 2
mT [GeV]0

Figure7.7 (MTWγ2 , MTW ) distribution of peaking background (left) and the (mχ̃± ,χ̃0 , mχ̃0 ) =1
1
2(150, 0) GeV (right) in the signal region.
signal 250 25

signal 250 100

300
0.08

250

0.07

mW
T [GeV]mW
T [GeV]

300

0.025

250
0.02

0.06
200

200

0.05
150

0.015
150

0.04

0.01

0.03

100

100

0.02
50

0.005

50

0.01

50

100

150

200

250

300

350

400

450
500
Wγ 2
mT [GeV]

0

0
0

50

100

150

200

250

300

350

400

450
500
Wγ 2
mT [GeV]Figure7.8 (MTWγ2 , MTW ) distribution of the (mχ̃± ,χ̃0 , mχ̃0 ) = (250, 25) GeV signal point (left)
1
2
1
and the (mχ̃± ,χ̃0 , mχ̃0 ) = (250, 100) GeV signal point (right) in the signal region.
1

1

2

120

3
0.44

1

mχ 0 [GeV]

0
0

0.48

100

0.13

2.5

0.64
0.80 0.61 0.52

80

21.03 0.92 0.60 0.39

0.21

1.49 1.06 0.87 0.58 0.36

60

1.35 0.98 0.64 0.48

1.5

0.28 0.05

1.71

40
2.20

1.72

2.00

20 2.80

1.27 0.81 0.62 0.47

1.57 1.17 0.83 0.43

2.29 1.79

10.12

0.25 0.07

0.5
1.47 0.89 0.66 0.39

0.17 0.01

0 2.88 2.13 1.69 1.12 0.77 0.48 0.26 0.04
150
200
250
300
350

400

450

500
mχ 0/ χ ± [GeV]
2

Figure7.901Signal significance across the (mχ̃± ,χ̃0 ,mχ̃0 ) grid with SRa, SRb and SRc.
1

2

1

0

Chapter 7 Optimization of Signal regions
120

3
0.27

1

mχ 0 [GeV]

66

0.36

100

0.12

2.5

0.42
0.49 0.44 0.4280

20.67 0.77 0.55 0.32

0.16

1.04 0.80 0.70 0.51 0.29

60

1.07 0.79 0.54 0.40

1.5

0.20

1.05

40
1.31

1.23

1.31

1.05 0.71 0.49 0.41

1.31 1.04 0.73 0.41

1

0.11

0.20 0.04

20 1.55

0.5

1.48 1.42

1.20 0.80 0.58 0.32

0.14

0 1.82 1.52 1.36 0.96 0.67 0.43 0.19
150
200
250
300

350

400

450

500
mχ 0/ χ ± [GeV]
2

Figure7.10

1

Signal significance across the (mχ̃± ,χ̃0 ,mχ̃0 ) grid with SRa and SRc.
1

2

1

120

3
0.57

1

mχ 0 [GeV]

0

0.64

100

0.39 0.28 0.22

2.5

0.72
0.86 0.71 0.67

80

21.06 1.03 0.76 0.55

0.43 0.31 0.22 0.19

0.12 0.08

1.48 1.14 0.97 0.70 0.53

60

1.70

40
2.09

1.72

1.99

20 2.68

1.42 1.08 0.76 0.63

0.47 0.33 0.25 0.17

1.36 0.95 0.73 0.61

1.63 1.24 0.94 0.63

1.5
0.12 0.09 0.07

1

0.39

0.46 0.35 0.26 0.18

0.13 0.08 0.06 0.05

0.5

2.24 1.85

1.49 0.99 0.78 0.57

0.41 0.30

0 2.84 2.11 1.74 1.20 0.87 0.63 0.47 0.33 0.25 0.18 0.12 0.09 0.06 0.05 0.03
150
200
250
300
350
400
450
500
mχ 0/ χ ± [GeV]
2

Figure7.11

01

Expected exclusion significances with σh = 13.8% and σs = 8%.

7.4.1 Eﬀect of uncertainties
The optimization study described above has been done with tentative values. In order to evaluate
eﬀect from fluctuation of the uncertainties, exclusion significances were evaluated with uncertainty
on the peaking backgrounds σh from 8% to 20%. The results are shown in Figure 7.11 to 7.13. From
those figures, there are no visible eﬀect due to the fluctuation of σh . It is expected that this is due
to large uncertainties on non-peaking backgrounds. This study suggests that significance cannot be
improved even if uncertainties on peaking backgrounds or signals can be reduced from the precise
evaluations. Therefore, the conservative evaluations have been done in Chapter 8.

67

120

3
0.56

1

mχ 0 [GeV]

7.4 Optimization results

0.63

100

0.39 0.28 0.22

2.5

0.71
0.85 0.70 0.66

80

21.04 1.01 0.75 0.54

0.42 0.31 0.22 0.19

0.12 0.08

1.45 1.12 0.96 0.69 0.53

60

1.39 1.06 0.75 0.62

1.5

0.46 0.32 0.24 0.17

0.11 0.09 0.07

1.66

40
2.02

1.68

1.93

20 2.56

1.33 0.94 0.73 0.61

1.59 1.22 0.92 0.62

1

0.38

0.46 0.34 0.26 0.18

0.13 0.08 0.06 0.05

0.5

2.16 1.80

1.46 0.98 0.77 0.57

0.40 0.30

0 2.71 2.05 1.70 1.18 0.86 0.62 0.47 0.33 0.25 0.18 0.12 0.09 0.06 0.05 0.03
150
200
250
300
350
400
450
500
mχ 0/ χ ± [GeV]2

1

Expected exclusion significances with σh = 13.8% and σs = 15%.

120

3
0.56

1

mχ 0 [GeV]

Figure7.12

0

0.62

100

0.39 0.28 0.22

2.5

0.70
0.83 0.69 0.66

80

21.02 0.99 0.74 0.54

0.42 0.30 0.22 0.19

0.12 0.08

1.42 1.10 0.94 0.68 0.52

60

1.36 1.04 0.74 0.61

1.5

0.46 0.32 0.24 0.17

0.11 0.09 0.07

1.61

40
1.95

1.63

1.87

1.30 0.93 0.72 0.60

1.55 1.20 0.91 0.62

1

0.38

0.45 0.34 0.26 0.17

0.13 0.08 0.06 0.05

20 2.440.5

2.08 1.75

1.43 0.96 0.76 0.56

0.40 0.30

0 2.58 1.98 1.65 1.16 0.85 0.61 0.46 0.32 0.25 0.18 0.12 0.09 0.06 0.05 0.03
150
200
250
300
350
400
450
500
mχ 0/ χ ± [GeV]
2

Figure7.13

01

Expected exclusion significances with σh = 13.8% and σs = 20%.

7.4.2 Eﬀect of updates of setup
The optimization studies described above have been performed with 27 GeV threshold on pγ2
T . After
those studies, the threshold is increased to 31 GeV. At the same period, a few more updates havebeen done as following:• σh is updated from 13.8% to 15% according to the study described in Section 8.2• σs is updated from 15% to 8% according to the study described in Section 8.3• SM W h and SM Zh samples are updated from LO samples to NNLO samples

Chapter 7 Optimization of Signal regions
120

3
0.56

1

mχ 0 [GeV]

68

0.62

100

0.39 0.28 0.22

2.5

0.70
0.83 0.69 0.66

80

21.02 0.99 0.74 0.54

0.42 0.30 0.22 0.19

0.12 0.08

1.42 1.10 0.94 0.68 0.52

60

1.36 1.04 0.74 0.61

1.5

0.46 0.32 0.24 0.17

0.11 0.09 0.07

1.61

40
1.95

1.63

1.87

1.30 0.93 0.72 0.60

1.55 1.20 0.91 0.62

1

0.38

0.45 0.34 0.26 0.17

0.13 0.08 0.06 0.05

20 2.44
2.08 1.75

0.5
1.43 0.96 0.76 0.56

0.40 0.30

0 2.58 1.98 1.65 1.16 0.85 0.61 0.46 0.32 0.25 0.18 0.12 0.09 0.06 0.05 0.03
150
200
250
300
350
400
450
500
mχ 0/ χ ± [GeV]
2

Figure7.14

01

Expected exclusion significances with σh = 13.8% and σs = 20% with the updated setup.

As described in Section 5.3.2, the requirements before this change are early selections, and thoseafter the change are noted as final selections.
Since the optimization has been performed with the early selections, in order to evaluate the eﬀectof those changes, expected exclusion significances is re-evaluated with final selections, as shown in
Figure 7.14. From the comparison between Figure 7.12 and 7.14, it is concluded that there are no
significant eﬀects due to this update. Therefore, the same optimized results are used with the final
selections.

69

Chapter 8

Systematic and statistical uncertainty
In this chapter, the uncertainties on the three types of the events, namely the non-peaking backgrounds, the peaking backgrounds, and the signals, are described.
The yields of the non-peaking backgrounds are evaluated from the sideband data. Therefore, it isaﬀected by statistical fluctuation of the sideband data. This is discussed in Section 8.1.
In contrast, the peaking backgrounds and the signals are evaluated from the MCs. Therefore, it
is aﬀected by uncertainty on the MCs. This is discussed in Section 8.2 and 8.3.
The evaluation has been performed for SRa to SRd in this chapter. The uncertainties used in the
optimization study has been evaluated in the same manner.

8.1 Non-peaking BackgroundAs described in Section 6.1.1, the non-peaking backgrounds are evaluated by the sideband fit. Dueto the low statistics of the data in the sideband region, large statistical fluctuation is expected. It isevaluated by using the toy sample.
The evaluation procedure is shown in Figure 8.1 It has been performed as following. At first,
sideband data is fitted with a constant function. Then, toy samples are generated using Poisson
function which has the fitted result as its mean. Next, each generated sample is fitted by a constantfunction and yield is re-evaluated. Finally, the statistical uncertainties are evaluated from those
distributions.
The distributions of re-evaluated yields for the overall toy samples are shown in Figure 8.2 andFigure 8.3. The uncertainty is defined as 1σ equivalent width of the distribution. However, as shownin the distributions, re-evaluated yields are discretely distributed. This is because generated toy
samples have discrete number of events for each bin. Due to their discreteness, the width exactly
equivalent to 1σ cannot be defined. Therefore, in this analysis, the wider side of the width closest
to 1σ equivalent width is chosen as shown in the figures.
In the case that the evaluated uncertainties for upper side and lower side are diﬀerent, conservativeside, i.e. with larger one, is chosen as an uncertainty. The evaluated uncertainties are summarizedin Table 6.1. Due to low statistics in the sideband region, the evaluated uncertainties are large as
expected.

8.2 Peaking BackgroundAs described in Section 7.4.1, the results are not aﬀected by the uncertainties on peaking backgrounds
and the signals due to the large uncertainties on the non-peaking backgrounds. Therefore, in thisanalysis, conservative uncertainties are evaluated and used.
At first, the experimental uncertainties are evaluated. Since the yields are evaluated by the MCs,the evaluation of the uncertainties also relies on the MCs. The uncertainties include errors on event
generator and detector performance.
In the ATLAS experiment there are many sources of the experimental uncertainties. They are

70

Chapter 8 Systematic and statistical uncertainty

9000
8000

SRa: 0.22

Number of toy

Number of toy

Figure8.1 Conceptual drawing of uncertainty evaluation procedure for non-peaking backgrounds. From left side, sideband data fit, toy sample generation, re-evaluation of yields of toy
samples, and distribution of re-evaluated yields is shown. From the width of the distribution,
uncertainty is evaluated.

+0.22 (1.43 σ)-0.22 (0.00 σ)

7000

2500

SRb: 2.44+0.67 (1.06 σ)-0.66 (-1.05 σ)

2000
6000
5000

1500

4000
1000

3000
2000

500
1000
0
0

0.2

0.4

0.6

0.8

1

1.2

0
0

1.4
Evaluated yields

1

2

3

4

5

6
Evaluated yields

4500
4000

SRc: 0.89

Number of toy

Number of toy

Figure8.2 Distributions of re-evaluated yields in SRa (left) and in SRb (right).

+0.45 (1.24 σ)-0.44 (-1.33 σ)

3500

2200

SRd: 3.32+0.90 (1.16 σ)-0.88 (-1.06 σ)

2000
1800
1600

3000

1400
2500
1200
2000

1000

1500

800
600

1000

400
500
0
0

200
0.5

1

1.5

2

2.5

3
Evaluated yields

0
0

1

2

3

4

5

Figure8.3 Distributions of re-evaluated yields in SRc (left) and in SRd (right).

6

7
8
Evaluated yields

8.2 Peaking Background71

classified into the groups which are not correlated to each other. In this analysis, following groups
are taken into account.
• photon ID eﬃciency• b-tag scale factor• photon energy resolution• photon energy scale factor• 3 groups of jet energy scale factors*1• jet energy resolution
miss
• ET
resolution
miss
• ET
scale factor• photon isolation eﬃciency
All of systematics have both positive and negative variations on the sources except for the photon
isolation eﬃciency*2 .
For the evaluation of eﬀects from those uncertainties to the evaluated yields, specific MC sample isdeveloped for each group in the ATLAS experiment. Those samples are generated with a performanceparameter shifted for 1σ. Taking diﬀerences between nominal sample and those systematical samples,systematical uncertainties on the yields can be evaluated. In table 8.1, the evaluated yields andsystematics with the various specific samples are summarized. In order to evaluate total experimental
uncertainties, quadratic sum of the those uncorrelated systematics are calculated in SRa and SRd.

Table8.1 Yields and systematics of the peaking backgrounds evaluated by systematic MCs.
In the case that the absolute value of evaluated systematic is smaller than 0.001, it is shown
as 0.

Sources
Nominalph-totSF-eﬀ-id-up
ph-totSF-eﬀ-id-down
jet-totBtagSF-up
jet-totBtagSF-down
SYST-EG-RESOLUTION-ALL-1down
SYST-EG-RESOLUTION-ALL-1up
SYST-EG-SCALE-ALL-1down
SYST-EG-SCALE-ALL-1up
SYST-JET-GroupedNP-1-1down
SYST-JET-GroupedNP-1-1up
SYST-JET-GroupedNP-2-1down
SYST-JET-GroupedNP-2-1up
SYST-JET-GroupedNP-3-1down
SYST-JET-GroupedNP-3-1up
SYST-JET-JER-SINGLE-NP-1up
SYST-MET-SoftTrk-ResoPara
SYST-MET-SoftTrk-ResoPerp
SYST-MET-SoftTrk-ScaleDown
SYST-MET-SoftTrk-ScaleUp
SYST-PH-Iso-DDonoﬀ

SRa Yield
0.111
0.113
0.109
0.111
0.111
0.108
0.107
0.106
0.108
0.102
0.122
0.107
0.112
0.105
0.113
0.119
0.106
0.104
0.113
0.103
0.111

SRa systematics
0.002-0.00200-0.003-0.004-0.005-0.003-0.0090.011-0.0040.001-0.0060.002
0.008-0.005-0.0070.002-0.0080

SRd Yield
2.09
2.12
2.05
2.09
2.09
2.08
2.06
2.05
2.07
2.11
2.05
2.08
2.07
2.09
2.07
2.08
2.07
2.07
2.07
2.07
2.09

SRd systematics
0.03
-0.04
0
0
-0.01
-0.03
-0.04
-0.02
0.02
-0.04
-0.01
-0.02
0
-0.02
-0.01
-0.02
-0.02
-0.02
-0.02
0

*1 There are 88 nuisance parameters (NP) related to this factor. But those are reduced to 3 groups.
*2 The photon isolation is corrected using a data-driven method with single photon and single electron events. The

uncertainty is evaluated by turning oﬀ this correction. Therefore, only one systematic sample is evaluated forthis factor.

72

Chapter 8 Systematic and statistical uncertainty

For the systematic sources which have positive and negative variations, only larger eﬀects are chosen
for the calculation. The results are 13.3% in SRa, and 3.9% in SRd. The conservative one, 13.3%,
is used as a total experimental uncertainty in the following discussion.
Then, the theoretical uncertainty is discussed. There are two types of the theoretical uncertainties;
one aﬀects the overall normalization. The other aﬀects the shape of the kinematic distribution.
The theoretical uncertainties which aﬀect the overall yields are related to the cross-section calculation. Following sources of the uncertainties related to the cross-section are taken into account.
• Eﬀect from higher order QCD term (0.7% [63])• PDFs and QCD scale uncertainty (0.7% [63])• Branching fraction from H to diphoton (2.0% [64])The total eﬀect, which is evaluated by quadratic sum, is 3.6%. The quadratic sum of the overall
experimental uncertainty (13.3%) and the overall theoretical uncertainty (3.6%) is the value (13.8%)
used for the early selections.
The theoretical uncertainties which aﬀect the shape of kinematic distributions are related tothe modeling uncertainty. Those are evaluated by using MCs with the specific correction function
described below. The sources taken into account are:
• PDFs uncertainty• QCD scale factor• Underlying event parton shower (UEPS)• NLO electroweak corrections
The yields with those sources can be evaluated with the correction factor, which is a function oftruth momentum of the vector boson. This type of uncertainty is evaluated only for the contributionof SM W h, which is the main source of the peaking backgrounds (∼ 90%). The evaluated yields andthe systematics are summarized in Table 8.2. The overall uncertainty on the modeling, evaluated byquadratic sum, is 4.1%.
Finally, overall uncertainty, which is calculated by quadratic sum of three types of the uncertainties
described above, is evaluated as 14.4%. Since it is confirmed that the uncertainties on the peaking
backgrounds does not aﬀect the results, rounded value, 15%, is chosen as the total uncertainties andused for the final selections.

8.3 Signal
For the uncertainty on the yields of the signals, only experimental uncertainty is taken into account.
With the same manner described in the previous section, the experimental uncertainty is evaluated.
First, the experimental uncertainties on the high-mass focus points are evaluated with LO samples.
Since the results are around 6.4% to 8.6%, 15%, which is around twice of the estimated values, isused as a conservative tentative value. The tentative value is used for early selections.
Then, the same calculations have been performed for all the used signals with NLO samples, as
shown in Figure 8.4 and 8.5. The evaluated uncertainties are distributed from 2% to 14%. No

Table8.2 Yields and systematic of SM W h valuated by MCs with correction factors. In thecase that the absolute value of evaluated systematic is smaller than 0.001, it is shown as 0.

Sources
Nominal
QCD
PDF
UEPS
NLO electroweak

SRa Yield
0.094
0.092
0.094
0.097
0.095

SRa systematics-0.0020+0.003-0.001

SRd Yield
1.816
1.783
1.809
1.861
1.843

SRd systematics-0.033-0.007+0.045+0.027

73

25

120

05
8

03
6

0.

04
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0.

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6

100

6

1

mχ 0 [GeV]

8.4 Expected exclusion upper limit

500mχ 0/ χ ± [GeV]
2

0

0

0

0.02

0.04

0.06

0.08

0.1

0.12

1

0.14
relative error

Figure8.4 Evaluated conservative uncertainty for the signal points with SRa selections in(mχ̃± ,χ̃0 , mχ̃0 ) space (left) and the projection of the evaluated values (right).
1

2

25

120

03
0.

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4 0
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74
02
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mχ 0 [GeV]1500mχ 0/ χ ± [GeV]
2

0

1

0

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14
relative error

Figure8.5 Evaluated conservative uncertainty for the signal points with SRd selections in(mχ̃± ,χ̃0 , mχ̃0 ) space (left) and the projection of the evaluated values (right).
12

1

tendency related to LSP or NLSP mass is appeared in the 2D plots. Therefore, the information issummarized into 1D plots. From these 1D plots, it is suggested that relative uncertainties around
14% are outliers. Since 97% of the signals show relative uncertainties lower than 8%, 8% is chosen
as the relative uncertainties on all signal samples and used for the final selections.

8.4 Expected exclusion upper limit
With the uncertainties described above, the upper limit of the excluded region is expected as following. The expected exclusion significances are re-evaluated with the final selections and with the
toy method for all signal points, and then plotted to (mχ̃± ,χ̃0 , mχ̃01 ) space. The intermediate spaces
1
2
between the used signal points are complemented by interpolation. Then, the contour line corresponding to the confidence level is taken from the plot as the expected upper limit of the exclusion
region. In this analysis, standard 95% is used as the confidence level, which corresponds to 1.64σ.
In the same manner, the error band is evaluated by replacing input numbers from mean to mean ±1σ. The result is shown in Figure 8.6.

Chapter 8 Systematic and statistical uncertainty
0 ±
0 0
∼
χ2∼
χ1 → Wh ∼
χ1∼
χ1

160

1

m∼χ0 [GeV]

74

140
120

s=13 TeV, 36.1 fb-1

All limits at 95% CL

Wh diphoton
Expected limit (±1 σexp)

100
80
60
40
20
0
150

200

250

300

350

400

450
500
m∼χ±/ ∼χ0 [GeV]1

2

Figure8.6 Estimated expected exclusion upper limit for σh = 15% and σs = 8%. Expected
95% CL exclusion regions in the (mχ̃± ,χ̃0 , mχ̃0 ) space in the simplified model, using 13 TeV
1
1
2
data. The solid band around the expected limit shows the ±1σexp uncertainty band where all
uncertainties including σh = 15% and σs = 8%.

8.4.1 Comparison with 8 TeV analysis
Figure 8.7 shows the expected limit evaluated in 8 TeV analysis. As shown in the figure, theexpected upper limit in the 8 TeV analysis is distributed around mχ̃± ,χ̃0 = 160 GeV with 20.3 fb−1
12
data. On the other hand, the expected upper limit in the 13 TeV analysis is distributed aroundmχ̃± ,χ̃0 = 180 GeV with 36.1 fb−1 data, as shown in Figure 8.6. This improvement on the expected12limit is smaller than the naive expectation.
In order to understand this, the expected yields are normalized to the yields per fb−1 . The
compared result is shown in Table 8.3. The yields in the 8 TeV analysis are taken from the high MT
region described in [19], which has similar definitions with the inclusive signal region in the 13 TeV
analysis. The yields in the 13 TeV analysis is evaluated with the early selections. As shown in thetable, the ratio of the yields per fb−1 is 1.3 between two analyses. However, the ratio is expected to
be around two from the cross sections with the 8 TeV and the 13 TeV center of mass energies.
After the investigation about this diﬀerence, three possible sources were found. One is the diﬀerences on the used selection criteria. Although almost all criteria are the same between the 8 TeV
analysis and the 13 TeV analysis, some criteria are tightened in the 13 TeV analysis, such as theisolation criterion for photon, the threshold on the momentum of sub-leading photon, the trigger
and the b-jet veto. In order to evaluate the eﬀect of those criteria, the yield of the low-mass signal
in inclusive signal region in the 13 TeV analysis is re-evaluated with the criteria relaxed to the level
used in 8 TeV analysis specifically as following:• The isolation criterion was changed from topoEtcone40 < 2.45 GeV + 0.022 × pT (γ) to topoEtcone20 < 0.065 × pT (γ) & ptcone20 < 0.05 × pT (γ)

1mχ∼0 [GeV]

8.4 Expected exclusion upper limit

75

70

ATLAS
60

SUSY

Observed limit (± 1 σtheory)s = 8 TeV, 20.3 fb-1
Expected limit (± 1 σexp)50ℓγγ channel
0
0
± 0
∼
χ ∼
χ → W± ∼
χ h∼
χ
1

40

2

1

All limits at 95% CL

1m∼χ± = m∼χ0
1

2

30
0

-m

<
0

mh

∼χ 1

m ∼χ 2

20

10

0

130

140

150

160

170

180

190

mχ∼0, χ∼± [GeV]2

1

Figure8.7 Observed (solid line) and expected (dashed line) 95% CL exclusion regions in themass plane of mχ̃0 vs. mχ̃± ,χ̃0 in the simplified model, using 8 TeV data, only for the dipho1
12
ton channel. The dotted lines around the observed limit represent the results obtained when
SUSYchanging the nominal signal cross section up or down by the ±1σtheory
theoretical uncertainty.
The solid band around the expected limit shows the ±1σexp uncertainty band where all uncertainties, except those on the signal cross sections, are considered. The figure is cited from [19]• The threshold on pγ2
T was changed from 27 GeV to 20 GeV• The b-jet veto and the trigger requirement were removed
Then, the yield per fb−1 of the low-mass signal in the 13 TeV analysis is increased from 0.313 to0.364. With this yield, the ratio between two analyses is calculated as 1.5, which is still lower than
2.0 of theoretical expectation. Although these relaxed criteria achieve higher acceptance on signal,these cannot be used in the 13 TeV analysis due to much dense environment of events than the
8 TeV analysis.

Table8.3 Comparison between the 8 TeV and 13 TeV analyses of the numbers of expected
events, per fb−1 of accumulated data, for peaking backgrounds, non-peaking backgrounds andfocus-point signal events for the inclusive signal region.

Process
SM W hOther peaking backgrounds
Non-peaking background(mχ̃± ,χ̃0 , mχ̃01 ) = (150, 0) GeV
1

2

8 TeV Analysis, per fb−1
0.044
0.003
0.030
0.240

13 TeV Analysis, per fb−1
0.061
0.006
0.135
0.313

Ratio
1.4
2.0
4.5
1.3

76

Chapter 8 Systematic and statistical uncertainty

The second possible sources is the signal cross section used in the 8 TeV analyses. The MC samples
for signals used in the 8 TeV analysis were generated without the hadronic tau decays where thetau is from W . However, the cross section used for the normalization was calculated by including
it. This lead 30% over estimation on the yields of the signals in the 8 TeV analysis. If the yield of
low-mass signal in the 8 TeV analysis is corrected for this over estimation factor, it becomes 0.185
from 0.240. With this corrected yield, the ratio between two analyses becomes 2.0 which is equivalent
to the theoretical expectation.
The last possible source to make the improvement small is found on the evaluation of the nonpeaking backgrounds. It is evaluated with sideband fit based on the observed events in higher orlower mγγ region than the signal region in both the 8 TeV and the 13 TeV analyses. With MTWγ1
and MTWγ2 cuts are applied, 47% of the sideband events pass the selection in the 13 TeV analysis.
On the other hand, only 17% of the events could pass the same selection in the 8 TeV analysis.
According to the 8 TeV analysis, 48% of the events in the MC samples passed the same selection,
which is the eﬃciency close to the eﬃciency of the 13 TeV data. This suggests that there are large
down fluctuation in data in the 8 TeV analysis. Since the evaluation of the non-peaking backgrounds
depends on the sideband data, the yield of the non-peaking backgrounds used in the calculation of
the expected and the observed limits is smaller than the expectation from MC. Such inconsistency
between data and MC is not seen in the 13 TeV analysis, thus the ratio of the yields of non-peaking
backgrounds between two analyses are larger than the other components, as shown in Table 8.3.
The possible sources about the signal cross section and the estimation on non-peaking backgrounds
suggests over estimation on the expected limit in the 8 TeV analyses. And it is possible that theover estimation is a part of the reasons of the relatively small improvement comparing to the naive
expectation.

77

Chapter 9

Results
In this chapter, observed data in the signal region is shown. The observed data is compared withthe expected backgrounds described in the previous chapters. The observed events are described in
Section 9.1. The statistical evaluation for those observed events are performed in Section 9.2.

9.1 Observed events
After the estimation of the background described in above chapters, the blinded data in the signal
region is opened. mγγ distributions with unblinded data are shown in Figure 9.1 and 9.2. The
numbers of observed events in the signal region are summarized in Table 9.1 with the expected
yields. As shown in the table and the figures, two events in SRa and nine events in SRd areobserved, while 0.36 events are expected in SRa and 5.35 events are expected in SRd. Therefore,
the observed data in both signal regions are greater than the expected total yields of background.
In order to see the characteristics of the events in the SRs, their kinematic distributions arecompared with the expectations. All details are shown in Appendix A. No strong bias which suggeststhat the excesses are due to miss modelling can be seen in the kinematic distributions.
The inconsistency between the SM expectations and the observed numbers is interpreted in two
ways under following assumptions; it is due to the statistical fluctuation of the SM background, or
it is due to the contributions of new physics. The former leads to the interpretation in terms of
the exclusion limit of the model. The later leads to the interpretation in terms of the statisticalsignificances. Those two interpretations are discussed in the next sections.

9.2 Observed upper limit
At first, the inconsistency is interpreted in terms of the statistical significances as following. The
significances is evaluated by p0 described in Section 7.2.3. In order to avoid any biases from themodeling of the signal, model independent p0 is evaluated in SRa and SRd individually.
The evaluated p0 is 2.7% in SRa and 8.6% in SRd, which are equivalent to 1.93σ in SRa and 1.36σ
in SRd. From those evaluations, it is concluded that the inconsistency between the observed eventand the expected yields of the backgrounds are not statistically significant. This is expected to be
due to the large statistical uncertainty on non-peaking backgrounds. In other words, the mild excess
is within a level of the statistical fluctuation.
Next, the interpretation in terms of the exclusion limit of the model is performed as following.
pµ with µ = 1 is calculated with all signal points as described in Section 7.2.4. However, nosignals assumed in this analysis could be excluded, due to the observed excess. Therefore, insteadof excluding any signal models, the upper limit of the cross sections are evaluated for each signal
point. The results are shown in Figure 9.3. In the figure, the upper limits of the cross section are
shown by text, and the expected upper limit of the excluded model is also shown.
The model independent exclusion limit is calculated too. The results are interpreted to the upper
limit on the signal yields (S 95 ) and the production of the cross section of the new physics and the

78

Chapter 9 Results

Table9.1 Expected numbers of peaking background, non-peaking background, and focus-point
signal events for SRa and SRd. Here, the peaking background is fully broken down into its
potential contributing components. Non-peaking-background uncertainty is dominated by thestatistical uncertainty on the side-band fits. The peaking background uncertainties include boththeoretical (production rate) and experimental (detector eﬀect) contributions, as described in
the text. The uncertainties on the “WH” and “Other peaking” backgrounds are taken to be
fully correlated. Also shown are the observed numbers of events in SRa and SRd.

Process
SM W hSM ZhSM tt̄hggh
VBFh
Total peaking backgroundNon-peaking backgroundTotal background
Observed events(mχ̃± ,χ̃0 , mχ̃01 ) = (150, 0)12(mχ̃± ,χ̃0 , mχ̃01 ) = (250, 25)12(mχ̃± ,χ̃0 , mχ̃01 ) = (250, 100)

Events

1

5

2

SRa
0.094 ± 0.014
0.011 ± 0.002
0.033 ± 0.005< 0.001< 0.0010.138 ± 0.021
0.22 ± 0.22
0.36 ± 0.22
2
2.87
1.36
0.95

SRd
1.818 ± 0.273
0.077 ± 0.012
0.113 ± 0.017< 0.001
0.001 ± 0.001
2.010 ± 0.302
3.33 ± 0.90
5.34 ± 0.95
9
6.57
0.90
0.90

-1

s = 13 TeV, 36.1 fb , in SRa

γ +jet2γ
tt
SM higgs

signal-150-0
signal-250-25
signal-250-100
sideband data
data in window

4

Wγ
Zγ
Wγ γ
Zγ γ

3
2
1

110

120

130

140

150

160

mγ γ [GeV]
Figure9.1 mγγ distribution of data and expected background and signals with SRa selection.

79

Events

9.3 Discussions10-1

s = 13 TeV, 36.1 fb , in SRd

γ +jet2γ
tt
SM higgs

signal-150-0
signal-250-25
signal-250-100
sideband data
data in window

8

Wγ
Zγ
Wγ γ
Zγ γ

6
4
2

110

120

130

140

150

160

mγ γ [GeV]
Figure9.2 mγγ distribution of data and expected background and signals with SRd selection.

acceptance for that signal (⟨ϵσ⟩95 ). In Table 9.2, those results calculated with the number of observed
events, and with the SM expected number are summarized with the discovery significances.
If the mild excesses came from new physics, it is going to be clear with higher statistical data.

9.3 Discussions
9.3.1 Best fit µ
The mild excess seen in Section 9.1 can be interpreted in terms of signal models with some assumed
masses. With an assumption of the signal model, expected yields in SRa and SRd are estimated. The
signal model which has expected yields close to the mild excess is considered as a “preferred” signal
model. Such preferred signal model can be searched using the signal strength µ, which is definedin Section 7.2.1. µ is the normalization factor for signal model. If assumed model well explains themild excess, best fit µ (µ̂), which is the µ value after fitting to data without any constraints, should
be consist with 1.
SM
Table9.2 Summary of the number of events expected from SM sources (Nexp), and the observed number of events (Nobs ), for each SR. Also shown is the derived model-independent
95
95% CL limit (Sobs) on the number of possible events from new physics, as well as both the95
observed (⟨ϵσ⟩obs ) and expected (⟨ϵσ⟩95exp ) 95% CL limit on the visible cross section from newphysics, assuming an integrated luminosity of 36.1 fb−1 .

Signal Region Nobs
SRa
SRd

2
9

SM
Nexp

95
Sobs

95
Sexp

⟨ϵσ⟩95
obs [fb]⟨ϵσ⟩95exp [fb]

Significance (p0 value)

0.36 ± 0.22
5.34 ± 0.95

5.7
10.4

3.8+0.3−0.1
6.1+3.2
−1.0

0.158
0.288

0.105+0.008−0.0030.169+0.089−0.0281.93 (0.027)
1.36 (0.086)

Chapter 9 Results160

s=13 TeV, 36.1 fb-1

Numbers give 95% CL excluded model cross sections [fb]

0 ±
0 0
∼
χ2∼
χ1 → Wh ∼
χ1∼
χ1

1

m∼χ0 [GeV]80

All limits at 95% CL

Wh diphoton

140
120

Expected limit (±1 σexp)
5.3

100

4.7

5.9

80

4.6

6.4
5.0

6.0

60

5.2

6.4

40
20

4.5

5.6

5.5

7.0
5.9

6.8

0 6.8
150

6.6

4.6
5.0

5.5

3.7

4.4

4.2

200

3.5

3.9

4.0

2.5

3.0

2.7

2.5

2.0

2.1

2.0

2.9

2.6

2.3

2.3

2.1

1.9

1.8

2.5

2.2

2.1

1.9

2.1

1.9

1.7

2.3

2.1

2.0

1.9

1.8

1.7

3.1
3.3

3.5
3.4

3.8
4.1

3.6

3.9

3.8

2.9

3.6
4.0

4.3

3.2

2.7
3.3

3.2
3.6

250

2.8
2.9

2.9
3.2

2.7
2.8

300

2.4
2.6

350

400

1.7

450
500
m∼χ±/ ∼χ0 [GeV]1

2

Figure9.3 Observed 95% CL upper limit on the cross section for wino-like gaugino productionin the context of the model described in Section 1.2.3. Also shown is the expected 95% CL
exclusion region. Due to the observed excesses in both SRa and SRd, no region in the parameter
space of the model is excluded by the analysis.

Figure 9.5 shows calculated µ̂ for all signal models. From the figure, the region mχ̃± ,χ̃0 ∼ 200 GeV
12
seems to be preferred.
However, there is large fitting error on µ̂ due to large statistical uncertainty. Deviations of µ̂ from
1 are divided by fitting error ((µ̂ − 1)/(error on µ̂)) and summarized in Figure 9.6. As shown in the
figure, most of points are within ±1. Those points are consistent with µ̂ = 1 within its fitting error.
Therefore, preferred signal “region” spreads around from mχ̃± ,χ̃0 = 150 GeV to mχ̃± ,χ̃0 = 350 GeV.
12
1
2
Because of large statistical error, the preferred signal region spreads widely. However, Figure 9.5
and Figure 9.6 show some expected tendency; From light mχ̃± ,χ̃0 to heavy mχ̃± ,χ̃0 , µ̂ is increased.
1212This tendency came from the cross section diﬀerences described in Section 3.2.2.
Although it is hard to see in Figure 9.5, Figure 9.6 shows another clear tendency; The points ofmχ̃± ,χ̃0 ∼ 250 GeV shows (µ̂ − 1)/(error on µ̂) from around 0.4 to 0.9. Since cross section, which
12depends on mχ̃± ,χ̃0 , is similar for those points, this tendency came from the ratio of yields. In
12
missgeneral, heavy mχ̃01 leads to high yields in SRd because of large ET. In the case of mχ̃± ,χ̃0 ∼1
2
250 GeV, light mχ̃01 is preferred rather than heavy mχ̃01 .

81

95% CL Limit on σ/ σ

SUSY

9.3 Discussions-1

s = 13 TeV, 36.1 fb
Wh diphoton, m 0 = 0 GeV
χ

10

1

Observed
Expected
±1σ
±2σ

1

150

200

250

300

350

400

450
500
mχ0/ χ± [GeV]
2

1

120

5

3

22
4.

82
3.

07
3.

10

3

4

1

48
7.

1

92
5.

4

51
4.

6

36
4.

3.

47

5

54

3

2.

92

5
49
2.
5

0

0

25
8.

98
6.

6

5

26
6.

99
4.

4.

00

1

2.

3
95

4

8

96

9.

8.

74
7.

6

6

59
5.

8

85
4.

81
3.

09
2.

1.

62

6

1.

99

7

2.

18

2
12
2.

61
1.
6
46

2
3

03
.2

13
12

.2

3
49

450

10

15

1
8.

400

7.

6

6

83
5.

80

7

350

4.

95
3.

37

6

3.

45

6

300

3.

7

2.

91

8
72
2.

23

6

2.

37

6

250

2.

79

0

1.

88

5
1.

40

0

1.

60

5
8
93

200

1.

1.

11

0
0.
1
0.

81
0.

150

92

4
75
0.
2
58
0.

0

4

0.

20

63

40

8

6

5 0.
84
0.
3 1.
87
01
7 1.
3
00
4
1.
1.
02
22
3 1.
9
26
9 1.
1.
32
53
8 1.
6
68
8 1.
1.
64
98
1 2.
8
05
2.
9 2.
26
28
3 2.
4
19
7 2
2.
.7
76
27
5 3.
10
5 3.
3.
22
40
4
8

1.

60

1.

20

4

1.

60

7

80

4

1.

85

0

2.

13

100

0

0 2
.4
2.
23
29
6

12

1

mχ 0 [GeV]

Figure9.4 Observed 95% CL upper limit on the cross section for wino-like gaugino productionin the context of the model described in Section 1.2.3 for mχ̃0 = 0 GeV points. Also shown is1
the expected 95% CL exclusion limits with overall uncertainty.

500mχ 0/ χ ± [GeV]20

1

Figure9.5 µ̂ for wino-like gaugino production in the context of the model described in Section 1.2.3.

Chapter 9 Results

9

3

00
1.

5

00
1.

92

5
0.
81
1
0.
77
3

0.

83

100

1
0.

1 0
.9
0.
22
82
7

120

1

mχ 0 [GeV]

82

1.
08
1
1.
11
8

0.
91
1
0.
94
7
1.
03
0
0.
99
9

0.
74

350

1.
10
6
1.
10
3
1.
12
2
1.
05
4
1.
14
3
1.
14
3
1.
14
1

450

17
8

15
4

13
0

11
5

06
6

400

1.

300

1.

250

1.

200

−1
1.

150

−0.5

1.

-1

0

.2

20

0

-0
.9
05 -0
79 -0
.5
.3
42 -0
-0
1 0
.3
.2
77 -0
30 0 2 .02
.0
2
.1
07
34
-0
0.
0.
.0
03
29
98 0
4 0.
2
.1
32
52 0
1
0.
0
.3
.5
41
58 0
23
4 0.
.5
53
87 0
5 0.
0.
.
61
54
72
6 0.
0 0.
6
64
71
0.
7 0.
8 0.
76
76
78
2 0.
5 0.
4
79
73
2 0
5 0
0.
.8
.8
86
70 0
62
4 0.
.9
86
2
7 0.
0 0.
0.
94
91
94
0 0.
6
0
93
5 0.
0.
0.
97
96
99
7
4
6
1.
1.
1.
03
04
04
5
2
7

60

40

0.5

0.
27
2
0.
49
4
0.
55
5
0.
73
0
0.
83
1

0.
60
9
0.
56
7
0.
71
8
0.
83
8

80

500
mχ 0/ χ ± [GeV]2

1

Figure9.6 (µ̂ − 1)/(error on µ̂) for wino-like gaugino production in the context of the model
described in Section 1.2.3.

9.3.2 Expected observations in other channel
In case the mild excess is a sign of new physics, excess can be seen in other channel introduced in
Section 1.2.3. As shown in Figure 1.6, the 3ℓ channel provided the second largest limit. In thissection, expected observations in 3ℓ channel with the same data set is discussed.
For this discussion, following points are assumed:• Signal acceptance is the same between 8 TeV analysis and 13 TeV analysis.
• Number of backgrounds is increased following the ratio of luminosity and the ratio of crosssection of dominant process, which is tt̄.
• The signal model is (mχ̃± ,χ̃0 , mχ̃01 ) = (187.5, 12.5) GeV
1

2

Regarding the signal model, this point is chosen as the point of µ̂ closest to 1. As discussed in theprevious subsection, the preferred region is from mχ̃± ,χ̃0 = 150 GeV to mχ̃± ,χ̃0 = 350 GeV. The
12
12
cross section is decreased from 5.2 fb to 0.2 fb. The point assumed in this discussion have the crosssection of 2.3 fb. Therefore, the estimation can be move from twice to 1/10.
In 3ℓ channel with 8 TeV data described in [65], the signal region called SR2τ b is the typical signal
region for W h-mediated signal. The numbers used in that analysis is summarized in Table 9.3*1 As
shown in the table, expected signal (backgrounds) yields with 13 TeV√ data set is calculated as 6.44
(42.2) respectively. With those yields, asymmetric significance S/ B = 0.99 which is lower thanthat of the diphoton channel. It is caused by the large number of backgrounds in the 3ℓ channel.
However, expected signal yield is larger than diphoton channel. Therefore, if backgrounds can besuppressed while keeping signal acceptance by improvement of the analysis procedure, significancecan be larger than the diphoton channel. For 2σ observation only by the 3ℓ channel with 13 TeV
data set, backgrounds need to be reduced below 10.4 events.

*1 5 events were observed in this region in 8 TeV analysis.

When 7.2 backgrounds are expected, the probability
that 5 or less events are observed is 28% from Poisson distribution. Therefore this mass point was not excluded
in 8 TeV analysis.

9.3 Discussions

83

Table9.3 Acceptance, cross sections and luminosity used in 3ℓ channel with 8 TeV data [65].
Cross sections with 13 TeV is also shown. Expected yields for 13 TeV data set are calculated
from other numbers. For the calculations, signal acceptance with 13 TeV is assumed to besame with 8 TeV case. And expected yield of backgrounds is scaled using cross section ratiosof tt̄ and luminosity.

process
signalbackgrounds√s [TeV]813
813cross section [pb]
1.035
2.293
0.247 (tt̄)
0.816 (tt̄)

luminosity [fb−1 ]
20.3
36.1
20.3
36.1

acceptance
7.78 × 10−5–––expected yields
1.63
6.44 (calculated)
7.2
42.2 (calculated)

85

Chapter 10

Conclusion
A search for direct production of electroweak gauginos decaying√ via Higgs boson and W boson is−1
performed using 36.1 fb of proton-proton collision data at s = 13 TeV collected by the ATLAS
detector at the LHC in 2015 and 2016. In this thesis, the channel where Higgs decays to diphoton
and W decays to ℓν, such as0000pp → χ̃02 + χ̃±
1 → χ̃1 + h + χ̃1 + W → χ̃1 + γ + γ + χ̃1 + ℓ + ν(10.1)

is sought. Because of characteristics that mass reconstructed by diphoton is expected to have keen
peak around the Higgs mass, expected SM backgrounds can be suppressed by the cut on diphoton
mass. The background sources which can be suppressed by the diphoton mass cut are classified as
non-peaking background, and the background sources which have Higgs in their process, meaning
they cannot be suppressed by the diphoton mass cut, are classified as peaking backgrounds. Due tothe low branching ratio from higgs to diphoton, expected signal yields are relatively low comparing
to the other channels of electroweak gauginos searches. Therefore, statistical treatment is the key ofthis analysis.
For the event selection, exactly expected numbers of the reconstructed objects are required, suchmiss
as exactly two photons, exactly one lepton and large missing transverse energy (ET). Selection
misscriteria related to ET are useful to suppress backgrounds since only signal event is expected to have
miss
miss
miss
cut, but also MTWγ1 cut and MTWγ2 are applied.
, not only ET
bacause of χ̃01 . Using ET
large ET
In order to suppress non-peaking backgrounds as described above, mγγ cut is applied. Regarding
missand lepton, and higgs
non-peaking backgrounds, W boson objects, which is reconstructed from ET
object, which is reconstructed from diphoton, may not flay away back-to-back because of additional
objects and miss-reconstructed objects. Therefore, ∆ϕ(W, h) cut is applied to reduce contributionsof non-peaking backgrounds. One new criterion, b-jet veto is introduced. It can reduce one of the
major peaking background sources, SM tt̄h background. This new criterion improves significance by∼10%.
After the event selection, yields of the backgrounds and the signals are evaluated. In order to avoid
uncertainty from MC simulations, the non-peaking backgrounds are evaluated using sideband datawith data-driven method, The method is validated based on possible assumptions and confirmed forits stability. The yields of the peaking backgrounds and signals are evaluated using MC simulations.
Because of large statistical error on the non-peaking backgrounds, systematical uncertainty of theevaluations using MCs are confirmed to be small enough not to aﬀect the results.
Based on the evaluated yields, the signal region is further optimized. Because of very similar
kinematical characteristics of signals and SM W h background, typical cut-base selection cannot
improve significance. In order to enhance significance without losing signal acceptance, the signal
region is divided into two regions, SRa and SRd. The optimization of the dividing thresholds is
performed by maximizing expected discovery significances. This optimization achieves ∼ 300% of
improvement in significance at maximum.
The expected limit of model exclusion is evaluated using the optimized signal region. Evaluatedlimit is distributed around mχ̃± ,χ̃0 = 180 GeV. This is improved form mχ̃± ,χ̃0 = 160 GeV of the
1

2

1

2

86

Chapter 10 Conclusion

limit evaluated in the 8 TeV analysis. The improvement is not significant. It is suggested that there
are possible sources of over estimation in the 8 TeV analysis found out by the detailed comparisons
between this and the 8 TeV analyses.
After setting the expected limit, collected data is compared with the expectation in the signal
region. There are two events in SRa and nine events in SRd, while 0.36 ± 0.22 and 5.35 ± 0.95 eventsare expected in SRa and SRd respectively. This mild excess is equivalent to 1.93σ deviation and1.36σ deviation in SRa and SRd respectively. Those statistical values suggest that there are mildexcesses in both signal regions, but the mild excess is within a level of the statistical fluctuation. On
the other hand, due to these mild excesses, any signal model points assumed in this analysis cannot
be excluded. Instead, upper limit of the cross section of the wino-like gaugino pair productions arecalculated. Also, model independent exclusion limit on the signal yields is evaluated. The evaluatedupper limit of yields are 5.7 fb in SRa and 10.4 fb in SRd. The dominant uncertainty is statisticalerror on the non-peaking background.
This result may suggest that there are still a room for the new physics assumed in this thesis. If
it exists and the mild excess is from such physics, the mild excess between the expectation and data
would be clear with more luminosity.
If the mild excess is interpreted as a sign of new physics, the preferred signal model evaluatedfrom the best fit µ (µ̂) are from mχ̃± ,χ̃0 = 150 GeV to mχ̃± ,χ̃0 = 350 GeV. The wide region is due
12
12
to large statistical uncertainty.
The mild excess is used to predict the expectation of the 3ℓ channel with 13 TeV data set.
This calculation is performed by extrapolating the 8 TeV analysis results. Expected asymmetricsignificance is 0.99σ.

87

Acknowledgements
I would like to express the deepest appreciation to my supervisor, Associate Professor Osamu Jinnouchi. I joined his laboratory 6 years ago. But even before that period, he showed me how physics
is attractive through an interview he kindly accepted. After I joined his laboratory, he gave me many
challenging topics. Without those experiences, I could not learn the skills I have acquired so far.
And especially the study described in this thesis would not have been finished. It was so challenging
because of the small analysis group and limited time. He spent so much time for the discussion withme about this topic, and suggested so many great ideas. His kind help drives the analysis.
I would like to express my gratitude to Professor Bruce Schumm, who is the convener of thediphoton analysis group. He collected the results to form a paper and suggested what we need. Also
his pointed question changed stacked situation many times. Thanks to his help, the analysis is going
to be published. I would like to thank the members of the diphoton analysis group.
I would like to thank to Dr. Alberto Cervelli and Dr. Jeanette Lorenz, who are the convenersof the Wh analysis group. They helped discussions about analysis procedure. And their technicalhelps are necessary for the analysis.
I would like to show my appreciation to Dr. Yohei Yamaguchi, who was a staﬀ of Jinnouchi Lab.
Especially during my stay at CERN, he supervised me so kindly. I believe my stay could not gosmooth without him.
I would like to thank Assistant Professor Yosuke Takubo, who is a Pixel project leader, for his
help about my tasks related to the inner detector from when I was a master student. He supervisedme about detector study, and also invited me for many joyful events. His kind help is one of thereasons I decided to dive into academic world.
I would like to thank Professor Masahiro Kuze who is my sub-supervisor, for his interesting lectureand suggestive discussion.
I would like to thank all the members of Jinnouchi Lab for joyful lab life. Especially to Dr. Daiki
Yamaguchi, Dr. Ryo Nagai, Dr. Nora Pettersson and Dr. Kazuki Motohashi.
I would like to thank house mates at CERN, Satoshi Higashino, Dr. Shunsuke Honda, Takuya
Honda and Kosuke Takeda. They gave me many good memories.
This work was supported by JSPS KAKENHI Grant Number JP16J0774.
Finnally, I would like to thank my family for their supports, I would like to thank Ai Shitaba, whois my fiancée, for making my life so happy.

89

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AppendixA

Kinematic distributions in signal region

TableA.1 Photon characteristics for the 11 signal events (GeV and mm units). The first two
events fell into SRa and the final nine in SRd. “Iso” refers to the value of the topEtCone40
variable. Rconv shows the radius of conversion vertex. For converted photons, it is classified as
type 1 (one track only with Si hits), type 2 (one track only with no Si hits), type 3 (two tracks
both with Si hits), or type 5 (two tracks and only one with Si hits).

Run
282712303892280423300863301973302380303208304008309640310341310863

Event
922772599
4127378101
81213163
1002432542
567913060
473324458
5060330829
2769513232
4285889264
1548645619
337227316

pT
155.5
98.0
85.9
68.0
74.4
171.2
71.9
133.4
104.0
77.8
122.9

Leading Photon(η,ϕ)
Rconv (Type)(0.3,-0.9)
297 (1)(0.3,-1.0)
48 (3)(1.1,-1.3)
632 (2)(0.8,1.5)
Unconv(-0.6,1,1)
630 (2)(-0.7,-3.0)
Unconv(-0.4,-0.8)
Unconv(0.7,2.6)
Unconv(-0.5,0.8)
Unconv(0.9,-2.7)
Unconv(-1.7,1.1)
Unconv

Iso
5.38
0.55
-1.24
1.50
1.49
-2.17
1.98
1.09
-1.24
-2.55
2.14

pT
72.3
32.2
69.0
36.7
56.8
94.0
32.5
94.5
51.3
55.1
52.9

Subleading Photon(η,ϕ)
Rconv (Type)(0.0,-2.1)
Unvonv(1.7,-2.9)
320 (5)(0.0,-2.6)
Unconv(-0.2,-1.2)
Unconv(-1.1,-1.4)
Unconv(-0.3,2.4)
Unconv(1.1,2.6)
Unconv(0.1,-2.7)
49 (3)(0.1.,2.7)
Unconv(-0.6,2.7)
Unconv(-1.8,2.9)
Unconv

Iso
0.21
0.04
0.02
-0.95
2.52
0.36
-2.04
2.95
1.32
-0.08
-0.03

TableA.2 Lepton,jet and event characteristics for the 11 signal events (GeV units). The firsttwo events fell into SRa and the final nine in SRd.

Run
282712303892280423300863301973302380303208304008309640310341310863

Event
922772599
4127378101
81213163
1002432542
567913060
473324458
5060330829
2769513232
4285889264
1548645619
337227316

Type
e
e
e
µ
e
µ
e
µ
µ
µ
µ

LeptonpT(η,ϕ)
26.6 (-0.4,-2.3)
99.0(2.0,1.6)
67.9(1.7,0.9)
33.8(-0.7,2.4)
38.9(-1.0,3.0)
120.4 (-0.5,-0.3)
35.7 (-0.7,-2.1)
158.0(0.8,0.1)
55.7(1.7,-2.1)
25.9(1.0,-1.0)27.9(0.7,-2.6)

Leading jet
pT
(η,ϕ)
78.0
(1.4,1.8)——
34.7(1.8,0.4)
66.6(2.6,0.1)————
38.5 (-1.0,0.4)——
125.7 (-1,5.1.0)——
210.2 (0.1,1.7)

Subleading Jet
pT(η,ϕ)
43.8 (2.6,-1.5)
—
—
—
—
—
—
—
—
—
—
—
—
—
—
50.9 (-2.7,-2.4)
—
—
—
—

miss
ET
163.4
66.4
58.8
82.4
66.9
143.0
54.4
64.6
64.8
115.5
253.8

⟨µ⟩
14.8
16.6
16.9
22.5
25.4
27.8
16.6
23.4
23.6
29.3
41.9

AppendixA Kinematic distributions in signal region

9

EventsEvents94-1

s = 13 TeV, 36.1 fb , in SR

γ +jet2γ
tt
SM higgs

signal-150-0
signal-250-25
signal-250-100
sideband data

8
7

Wγ
Zγ
Wγ γ
Zγ γ

6

-1

s = 13 TeV, 36.1 fb , in SR
signal-150-0
signal-250-25
signal-250-100
sideband data

5

γ +jet2γ
tt
SM higgs

Wγ
Zγ
Wγ γ
Zγ γ

6
4

5
4

3

3

2

2
1

1
2

2.2

2.4

2.6

2.8

3

3.2

0

3.4

50

100

150

200

250

300

Emiss
[GeV]
T

∆ϕ(Wh)

5

EventsEventsmiss
FigureA.1 Signal region distribution in ∆ϕ(W, h) and ET.

-1

s = 13 TeV, 36.1 fb , in SR

γ +jet2γ
tt
SM higgs

signal-150-0
signal-250-25
signal-250-100
sideband data

4

Wγ
Zγ
Wγ γ
Zγ γ

8
-1

7

s = 13 TeV, 36.1 fb , in SR
signal-150-0
signal-250-25
signal-250-100
sideband data

6

γ +jet2γ
tt
SM higgs

Wγ
Zγ
Wγ γ
Zγ γ

5
3
4
3

2

2
1
1
100

150

200

250

300

350

400

450

500

50

100

150

200

250

γ1
mW
[GeV]
T

300

350

γ2
mW
[GeV]
T

8
-1

7

s = 13 TeV, 36.1 fb , in SR
signal-150-0
signal-250-25
signal-250-100
sideband data

6

γ +jet2γ
tt
SM higgs

Wγ
Zγ
Wγ γ
Zγ γ

EventsEventsFigureA.2 Signal region distribution in MTWγ1 and MTWγ2

8
-1

7

5

4

4

3

3

2

2

1

1
20

40

60

80

100 120 140 160 180 200

signal-150-0
signal-250-25
signal-250-100
sideband data

6

5

0

s = 13 TeV, 36.1 fb , in SR

0

20

40

60

80

mW
T [GeV]

FigureA.3 Signal region distribution in MTW and pγ1
T .

γ +jet2γ
tt
SM higgs

Wγ
Zγ
Wγ γ
Zγ γ

100 120 140 160 180 200
pγT1 [GeV]9

EventsEvents95-1

s = 13 TeV, 36.1 fb , in SR

γ +jet2γ
tt
SM higgs

signal-150-0
signal-250-25
signal-250-100
sideband data

8
7

Wγ
Zγ
Wγ γ
Zγ γ

5

-1

s = 13 TeV, 36.1 fb , in SR

γ +jet2γ
tt
SM higgs

signal-150-0
signal-250-25
signal-250-100
sideband data

4

Wγ
Zγ
Wγ γ
Zγ γ

6

3

5
4

2

3
2

1

1
0

10

20

30

40

50

60

70

80

90

20

100

40

60

80

100

120

γ2
pT [GeV]140pel [GeV]T5-1

s = 13 TeV, 36.1 fb , in SR
signal-150-0
signal-250-25
signal-250-100
sideband data

4

γ +jet2γ
tt
SM higgs

Wγ
Zγ
Wγ γ
Zγ γ

EventsEventse
FigureA.4 Signal region distribution in pγ2
T and pT .

10

6

2

4

1

2

40

60

80

100 120 140 160 180 200

γ +jet2γ
tt
SM higgs

signal-150-0
signal-250-25
signal-250-100
sideband data

8

3

20

-1

s = 13 TeV, 36.1 fb , in SR

0

1

2

3

Wγ
Zγ
Wγ γ
Zγ γ

4

pmu [GeV]

5
Njets

T

FigureA.5 Signal region distribution in pµ
T and the number of jets.

TableA.3 Lepton vertex characteristics for the 11 signal events. The first two events fell into
SRa and the final nine in SRd. The perfect agreement between the z positions of the lepton
and primary vertices indicated that the lepton reference vertex was always found to be thereconstructed primary vertex.

Run
282712303892280423300863301973302380303208304008309640310341310863

Event
922772599
4127378101
81213163
1002432542
567913060
473324458
5060330829
2769513232
4285889264
1548645619
337227316

z of PV (mm)
-8.32
-5.30
88.43
63.69
65.80
-11.91
-9.82
25.65
18.58
-15.55-25.10z of lepton vertex (mm)
-8.32
-5.30
(NA*1 )
63.69
65.80
-11.91
-9.82
25.65
18.58
-15.55-25.10d0 (µm)
-8.87
26.02
6.68
10.98
-9.21
0.70
5.190
-8.83
2.49
-0.24
1.60

d0 sig-0.490
0.904
0.140
0.936
-0.3000.060.320-0.8970.231-0.0190.143

z0-0.051-0.023
0.271
0.066
0.021
0.048
0.043
0.006
-0.075-0.0050.006

z0 sin θ
0.046-0.006
0.097
0.051
0.014
0.042
0.034
0.004
-0.025-0.0030.005

97

List of Figures
1.1

1.2
1.3
1.4
1.5

1.6

1.7
2.1
2.2
2.3

2.4
2.5

Summary of several Standard Model total and fiducial production cross section measurements, corrected for leptonic branching fractions, compared to the corresponding theoretical expectations. All theoretical expectations were calculated at NLO
or higher. The luminosity used for each measurement is indicated close to the data
point. Some measurements have been extrapolated using branching ratios as predicted by the Standard Model for the Higgs boson. Uncertainties for the theoreticalpredictions are quoted from the original ATLAS papers. They were not always
evaluated using the same prescriptions for PDFs and scales. The Wgamma andZgamma theoretical cross-sections have non-perturbative corrections applied to the
NNLO fixed order calculations (PRD 87, 112003 (2013)). Not all measurements are
statistically significant yet. The figure is cited from [5] . . . . . . . . . . . . . . . .
¯ . . . . . . . . . . . . . . . . . . . . . . . . . . .
Proton decay via SUSY particle (s̃).
√
Cross sections for SUSY particle production at s = 8 TeV and 13、14 TeV. The
figure is cited from [14] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Mass reach of ATLAS searches√ for Supersymmetry achieved at July 2015, before
collecting collision data with s = 13 TeV. The figure is cited from [15] . . . . . .
−±0
The 95% CL exclusion limits on χ̃+
1 + χ̃1 and χ̃1 + χ̃2 production with SM-boson±
00mediated decays, as a function of the χ̃1 , χ̃2 and χ̃1 masses. The production cross−± 0
section is for pure wino χ̃+1 χ̃1 and χ̃1 χ̃2 . The plot is cited from [21] . . . . . . . .
Observed (solid line) and expected (dashed line) 95% CL exclusion regions in themass plane of mχ̃01 vs. mχ̃± ,χ̃0 in the simplified model, using 8 TeV data. The
1
2
dotted lines around the observed limit represent the results obtained when changing
SUSY
the nominal signal cross section up or down by the ±1σtheory
theoretical uncertainty.
The solid band around the expected limit shows the ±1σexp uncertainty band where
all uncertainties, except those on the signal cross sections, are considered. The figure
is cited from [19] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Feynman diagram of diphoton channel. . . . . . . . . . . . . . . . . . . . . . . . . .
The accelerator comples at CERN. The figure is cited from [23]. . . . . . . . . . . .
Peak luminosity at ATLAS as a function of time . . . . . . . . . . . . . . . . . . . .
Cut-away view of the ATLAS detector. The dimensions of the detector are 25 m
in height and 44 m in length. The overall weight of the detector is approximately
7000 tonnes. The figure is cited from [25]. . . . . . . . . . . . . . . . . . . . . . . .
Schematic x-y coross section view of a detailed layout of the Inner Detector (ID),including the new Insertable B-Layer (IBL). The figure is cited from [26] . . . . . .
The r-z cross section view of the layout of a quadrant of the ATLAS inner detector
for Run 2. The figure is cited from [27]. The top panel shows the whole innerdetector, whereas the bottom-left panel shows a magnified view of the pixel detector
region. Compared to Run 1, the IBL (shown in orange in the bottom-left panel) andits services, together with the new beam pipe, were added. . . . . . . . . . . . . . .

3
5
6
7

8

9
10
12
13

14
15

16

98
2.6

2.7

2.8
2.9

2.10
2.11

2.12

3.1

3.2

List of Figures
Schematic view of a barrel pixel module illustrating the major pixel hybrid and sensor
elements, including the MCC (module-control chip), the front-end (FE) chips, theNTC thermistors, the high-voltage (HV) elements and the Type0 signal connector.
On the bottom of the module, there is a Thermal Management Tile (TMT). The
figure is cited from [25]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Drawing of a barrel module, showing its components. The thermal pyrolytic graphite(TPG) base-board provides a high thermal conductivity path between the coolant
and the sensors. The figure is cited from [25]. . . . . . . . . . . . . . . . . . . . . .
Cut-away view of the ATLAS calorimeter system. The figure is cited from [25]. . .
Sketch of a barrel module of the electromagnetic calorimeter where the diﬀerent
layers are clearly visible with the ganging of electrodes in phi. The granularity in
eta and phi of the cells of each of the three layers and of the trigger towers is also
shown. The figure is cited from [25]. . . . . . . . . . . . . . . . . . . . . . . . . . .
Cut-away view of the ATLAS muon system. The figure is cited from [25]. . . . . .
Cross-section of the muon system in a plane containing the beam axis (bending
plane). Infinite-momentum muons would propagate along straight trajectories which
are illustrated by the dashed lines and typically traverse three muon stations. The
figure is cited from [25]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The ATLAS trigger and data acquisition system in Run 2 with emphasis on thecomponents relevant for triggering, cited from [28] . . . . . . . . . . . . . . . . . . .
Total integrated luminosity in 2015 (left) and 2016(right) versus time. Delivered
integrated luminosity is shown in green, and recorded integrated luminosity is shownin yellow. The figures are cited from [29]. . . . . . . . . . . . . . . . . . . . . . . .
Assumed signal sample points in (mχ̃± ,χ̃0 , mχ̃01 ) space. The diagonal line shows12mχ̃± ,χ̃0 − mχ̃01 = 125 GeV. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1

4.1
4.2

4.3

4.4

2

Photon and electron candidates classification workflow. . . . . . . . . . . . . . . . .
Schematics of topoEtcone40. Images shows the cells of the second EM calorimeter
layer. Left image is for photon, and right image is for π 0 decayed into diphoton.
There are pileup eﬀects for both cases. For π 0 case, there are jet contributions
also. topoEtcone40 is calculated from total deposits energy (ΣR<0.40 ET ) within
R = 0.4 cone, which is shown as a blue circle. In order to remove contribution of
5x7 core), which is shown
photon, deposits energy within η × ϕ = 5 × 7 window (ETas red cells, is subtracted. Then, expected deposits energy leaked from the window
5x7 core, η)), which is shown as purple cells, is calculated and subtracted.
(fleak (ETFinally, pileup eﬀect (ρ(η)), which is shown as gray cells, is subtracted. topoEtcone40
for photon is close to 0. On the other hand, topoEtcone40 for π 0 can be large value
due to jet contributions shown as green cells. . . . . . . . . . . . . . . . . . . . . .
Image of the impact parameters. Left image shows an image of d0 . Charged particle
draw an arc in the (x, y) plane as shown as an orange arrow. d0 is closest distancefrom the track to the primary vertex in the (x, y) plane, which is shown as a redarrow. Right image shows an image of z0 sin θ. z0 is the z intercept in the (z,direction of pT ) plane, which is shown as a blue arrow. With weight of sin θ, whereθ is is track angle from the z axis, closest distance from the track to the primaryvertex in the (z, direction of pT ) plane (z0 sin θ) is evaluated, as shown as z0 sin θ.
The MV2c20 output for b- (solid green), c- (dashed blue) and light-flavour (dottedred) jets in tanti-t events. The figure is cited from [58]. . . . . . . . . . . . . . . . .

17

18
19

20
21

22
23

26
28
32

34

36
39

99
5.1

5.2

5.3

5.4

5.5

5.6

5.7

5.8

5.9

Image of mγγ distributions. In contrast to the peaking backgrounds and signals(shown as a blue region) which have mγγ close to 125 GeV because of the higgs
particles within their processes, the non-peaking backgrounds (shown as an orange
region) have wide range of mγγ . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
γ2pγ1
T (left) and pT (right) distributions with the basic selections, which are exactly
miss
two photons, exactly one lepton, and ET> 40 GeV. Contributions of non-peaking
backgrounds are scaled by 10/55, which is the ratio of mγγ width between the higgs
window and the sideband window. Data (black points) are shown only for those
distributed out of higgs window, and are scaled by 10/45. Shown uncertainty is only
statistical error on sideband data. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
peT (left) and pµT (right) distributions with the basic selections, which are exactly
miss
two photons, exactly one lepton, and ET> 40 GeV. Contributions of non-peaking
backgrounds are scaled by 10/55, which is the ratio of mγγ width between the higgs
window and the sideband window. Data (black points) are shown only for those
distributed out of higgs window, and are scaled by 10/45. Shown uncertainty is only
statistical error on sideband data. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Missing transverse energy distribution with the basic selections, which are exactly
miss
two photons, exactly one lepton, and ET> 40 GeV. Contributions of non-peaking
backgrounds are scaled by 10/55, which is the ratio of mγγ width between the higgs
window and the sideband window. Data (black points) are shown only for those
distributed out of higgs window, and are scaled by 10/45. Shown uncertainty is only
statistical error on sideband data. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
mγγ distribution with the signal region selections except for mγγ cut, which aresummarized in Table 5.1. Scaling applied to the other plot is not applied to this plot.
Data (black points) are shown only for those distributed out of higgs window. Data
distributed in the Higgs window are blinded. Shown uncertainty is only statisticalerror on sideband data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
∆ϕ(W, h) distribution with the basic selections, which are exactly two photons, exmiss> 40 GeV. Contributions of non-peaking backgrounds
actly one lepton, and ET
are scaled by 10/55, which is the ratio of mγγ width between the higgs window andthe sideband window. Data (black points) are shown only for those distributed outof higgs window, and are scaled by 10/45. Shown uncertainty is only statistical error
on sideband data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
MTWγ1 (left) and MTWγ2 (right) distributions with the basic selections, which aremiss> 40 GeV. Contributions of nonexactly two photons, exactly one lepton, and ET
peaking backgrounds are scaled by 10/55, which is the ratio of mγγ width between
the higgs window and the sideband window. Data (black points) are shown only for
those distributed out of higgs window, and are scaled by 10/45. Shown uncertainty
is only statistical error on sideband data. . . . . . . . . . . . . . . . . . . . . . . . .
MTW distribution with the basic selections, which are exactly two photons, exactly
miss
one lepton, and ET> 40 GeV. Contributions of non-peaking backgrounds are
scaled by 10/55, which is the ratio of mγγ width between the higgs window and thesideband window. Data (black points) are shown only for those distributed out ofhiggs window, and are scaled by 10/45. Shown uncertainty is only statistical error
on sideband data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Distribution of the number of b-jets with the basic selections, which are exactly
miss
two photons, exactly one lepton, and ET> 40 GeV. Contributions of non-peaking
backgrounds are scaled by 10/55, which is the ratio of mγγ width between the higgs
window and the sideband window. Data (black points) are shown only for those
distributed out of higgs window, and are scaled by 10/45. Shown uncertainty is only
statistical error on sideband data. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

42

43

44

45

45

46

47

47

48

100
5.10

6.1

6.2

6.3

6.4

7.1

7.2

7.3

7.4

7.5
7.6
7.7
7.8
7.9

List of Figures
Subdivided signal regions in (MTWγ2 , MTW ). z axis showns the yield of the peaking
background. SRb, which is not shown in the figure, is complement to SRa + SRc. .
mγγ distributions in SRa (left) and in SRd (right). Data (black points) are shown
only for those distributed out of higgs window. Shown uncertainty is only statisticalerror on sideband data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
mγγ distributions in SRc (left) and in SRd (right). Data (black points) are shown
only for those distributed out of higgs window. Shown uncertainty is only statisticalerror on sideband data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
mγγ distributions in the inclusive SR with relaxed mγγ requirement, which is[0, 300] GeV. Data (black points) are shown only for those distributed out of higgs
window. Shown uncertainty is only statistical error on sideband data. Since W γγ
sample is generating only mγγ > 80 GeV, there are deviation between data andMCs below 80 GeV region. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
missmγγ distributions in the inclusive SR with relaxed ETand ∆ϕ(W, h) requirements, which are 20 GeV and 0, respectively. Data (black points) are shown only for
those distributed out of higgs window. Shown uncertainty is only statistical error on
sideband data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Idea of optimization. As shown in the top two images, background is expected
miss
miss
to have large contribution in low ET
region rather than high ET
region, in
misscontrast to signal which has large contribution in high ET region rather than low
missregion. In case that observed data includes only background, the ratio betweenET
the two regions is close to the expected ratio of background yields, as shown in theleft bottom image. If there are contribution of signal in observed data, the ratio is
diﬀerent from the expected ratio of background yields, as shown in the right bottom
image. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Missing transverse energy (left) and MTW (right) distributions in the signal region.
Contributions of non-peaking backgrounds are scaled by 10/55, which is the ratioof mγγ width between the higgs window and the sideband window. Data (black
points) are shown for only for those distributed out of higgs window, and are scaledby 10/45. Shown uncertainty is only statistical error on sideband data. . . . . . . .
MTWγ1 (left) and MTWγ2 (right) distributions in the signal region. Contributionsof non-peaking backgrounds are scaled by 10/55, which is the ratio of mγγ width
between the higgs window and the sideband window. Data (black points) are shownfor only for those distributed out of higgs window, and are scaled by 10/45. Shown
uncertainty is only statistical error on sideband data. . . . . . . . . . . . . . . . . .
Image of qµ distribution and definition of pµ . This image is case of the assumptionof µ = 0. With this assumption, backgrounds only like events show small qµ , andsignal + background like events show large qµ . pµ is defined as probability to observeqµ larger than qµ,obs . as shown as a green area. . . . . . . . . . . . . . . . . . . . .
Significances in (mχ̃± ,χ̃0 ,mχ̃01 ) parameter space for the subdivision based on the val1
2
missues MTW = 70 GeV and ET= 100 GeV. . . . . . . . . . . . . . . . . . . . . . . .
Significances in (mχ̃± ,χ̃0 ,mχ̃01 ) parameter space for the subdivision based on the val1

49

52

52

54

54

58

58

59

60
64

2

ues MTWγ2 = 140 GeV and MTW = 110 GeV. . . . . . . . . . . . . . . . . . . . . . .
(MTWγ2 , MTW ) distribution of peaking background (left) and the (mχ̃± ,χ̃0 , mχ̃01 ) =1
2(150, 0) GeV (right) in the signal region. . . . . . . . . . . . . . . . . . . . . . . . .
(MTWγ2 , MTW ) distribution of the (mχ̃± ,χ̃0 , mχ̃01 ) = (250, 25) GeV signal point (left)
1
2
and the (mχ̃± ,χ̃0 , mχ̃01 ) = (250, 100) GeV signal point (right) in the signal region. .
1
2
Signal significance across the (mχ̃± ,χ̃0 ,mχ̃01 ) grid with SRa, SRb and SRc. . . . . . .
1

2

64
65
65
65

101
7.10
7.11
7.12
7.13
7.14

8.1

8.2
8.3
8.4
8.5
8.6

8.7

9.1
9.2
9.3

9.4

9.5
9.6

A.1
A.2
A.3
A.4
A.5

Signal significance across the (mχ̃± ,χ̃0 ,mχ̃01 ) grid with SRa and SRc. . . . . . . . . .
1
2
Expected exclusion significances with σh = 13.8% and σs = 8%. . . . . . . . . . .
Expected exclusion significances with σh = 13.8% and σs = 15%. . . . . . . . . . .
Expected exclusion significances with σh = 13.8% and σs = 20%. . . . . . . . . . .
Expected exclusion significances with σh = 13.8% and σs = 20% with the updated
setup. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Conceptual drawing of uncertainty evaluation procedure for non-peaking backgrounds. From left side, sideband data fit, toy sample generation, re-evaluation ofyields of toy samples, and distribution of re-evaluated yields is shown. From thewidth of the distribution, uncertainty is evaluated. . . . . . . . . . . . . . . . . . .
Distributions of re-evaluated yields in SRa (left) and in SRb (right). . . . . . . . .
Distributions of re-evaluated yields in SRc (left) and in SRd (right). . . . . . . . . .
Evaluated conservative uncertainty for the signal points with SRa selections in(mχ̃± ,χ̃0 , mχ̃01 ) space (left) and the projection of the evaluated values (right). . . .
1
2
Evaluated conservative uncertainty for the signal points with SRd selections in(mχ̃± ,χ̃0 , mχ̃01 ) space (left) and the projection of the evaluated values (right). . . .
1
2
Estimated expected exclusion upper limit for σh = 15% and σs = 8%. Expected
95% CL exclusion regions in the (mχ̃± ,χ̃0 , mχ̃01 ) space in the simplified model, using
1
2
13 TeV data. The solid band around the expected limit shows the ±1σexp uncertainty
band where all uncertainties including σh = 15% and σs = 8%. . . . . . . . . . . .
Observed (solid line) and expected (dashed line) 95% CL exclusion regions in themass plane of mχ̃01 vs. mχ̃± ,χ̃0 in the simplified model, using 8 TeV data, only
1
2
for the diphoton channel. The dotted lines around the observed limit represent theresults obtained when changing the nominal signal cross section up or down by the
SUSY±1σtheory
theoretical uncertainty. The solid band around the expected limit shows
the ±1σexp uncertainty band where all uncertainties, except those on the signal crosssections, are considered. The figure is cited from [19] . . . . . . . . . . . . . . . . .
mγγ distribution of data and expected background and signals with SRa selection.
mγγ distribution of data and expected background and signals with SRd selection.
Observed 95% CL upper limit on the cross section for wino-like gaugino productionin the context of the model described in Section 1.2.3. Also shown is the expected
95% CL exclusion region. Due to the observed excesses in both SRa and SRd, noregion in the parameter space of the model is excluded by the analysis. . . . . . .
Observed 95% CL upper limit on the cross section for wino-like gaugino productionin the context of the model described in Section 1.2.3 for mχ̃01 = 0 GeV points. Also
shown is the expected 95% CL exclusion limits with overall uncertainty. . . . . . .
µ̂ for wino-like gaugino production in the context of the model described in Section 1.2.3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(µ̂ − 1)/(error on µ̂) for wino-like gaugino production in the context of the model
described in Section 1.2.3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
miss
Signal region distribution in ∆ϕ(W, h) and ET. . . . . . . . . . . . . . . . . . .
Wγ1Wγ2Signal region distribution in MT
and MT. . . . . . . . . . . . . . . . . . . . .
Signal region distribution in MTW and pγ1.
.
.
.
. . . . . . . . . . . . . . . . . . . .
T
γ2eSignal region distribution in pT and pT . . . . . . . . . . . . . . . . . . . . . . . . .
Signal region distribution in pµT and the number of jets. . . . . . . . . . . . . . . .

66
66
67
67
68

70
70
70
73
73

74

75
78
79

80

81
81
82
94
94
94
95
95

103

List of Tables
1.1
1.2
1.3

Fermions in Standard Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Bosons in Standard Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
SUSY particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.1

2.2

Design and Operational parameters of LHC. Interaction point is assumed to be at
the ATLAS detector. In September 2015, the full crossing angle was reduced from
370 µm to 280 µm. In later 2016, the beta function was reduced from 40 cm to 33 cm. 13
Geometry of EM calorimeter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.1
3.2

Simulation samples used in this analysis. . . . . . . . . . . . . . . . . . . . . . . . .
Cross sections of assumed signal sample points. . . . . . . . . . . . . . . . . . . . .

27
29

5.1
5.2

Requirements of the inclusive signal region. . . . . . . . . . . . . . . . . . . . . . .
Definitions of the subsets of signal region. SRb and SRc are subsets of SRd. . . . .

49
49

6.1

Estimated yields of the non-peaking backgrounds with statistical uncertainty, by
fitting constant function to the mγγ sideband data, for each subset of the signal
region. The yields expected from MCs and their statistical uncertainty are aslo shown. 51
Results of the toy study. The nominal assumption is shown in third row. The
diﬀerences between evaluated yields are small comparing to their error. . . . . . . . 53
Results of the sideband range study. The nominal range is shown in third row. The
diﬀerences between evaluated yields are small comparing to the error on the nominal
yield. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
Expected yields of the peaking backgrounds and the focus point signals for thesubsets of the signal region. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

6.2
6.3

6.4

7.1
7.2
7.3

Optimization range and step . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Best thresholds and achieved significances with one discriminating variable . . . . .
Best thresholds and achieved significances with two discriminating variables . . . .

8.1

Yields and systematics of the peaking backgrounds evaluated by systematic MCs.
In the case that the absolute value of evaluated systematic is smaller than 0.001, it
is shown as 0. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Yields and systematic of SM W h valuated by MCs with correction factors. In thecase that the absolute value of evaluated systematic is smaller than 0.001, it is shownas 0. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Comparison between the 8 TeV and 13 TeV analyses of the numbers of expected
events, per fb−1 of accumulated data, for peaking backgrounds, non-peaking backgrounds and focus-point signal events for the inclusive signal region. . . . . . . . .

8.2

8.3

1
1
4

62
63
63

71

72

75

104
9.1

9.2

9.3

A.1

A.2
A.3

List of Tables
Expected numbers of peaking background, non-peaking background, and focus-point
signal events for SRa and SRd. Here, the peaking background is fully broken down
into its potential contributing components. Non-peaking-background uncertainty isdominated by the statistical uncertainty on the side-band fits. The peaking background uncertainties include both theoretical (production rate) and experimental(detector eﬀect) contributions, as described in the text. The uncertainties on the“WH” and “Other peaking” backgrounds are taken to be fully correlated. Also
shown are the observed numbers of events in SRa and SRd. . . . . . . . . . . . . .
SM
Summary of the number of events expected from SM sources (Nexp), and the observed
number of events (Nobs ), for each SR. Also shown is the derived model-independent
95
95% CL limit (Sobs) on the number of possible events from new physics, as well as
95
both the observed (⟨ϵσ⟩95obs ) and expected (⟨ϵσ⟩exp ) 95% CL limit on the visible crosssection from new physics, assuming an integrated luminosity of 36.1 fb−1 . . . . . .
Acceptance, cross sections and luminosity used in 3ℓ channel with 8 TeV data [65].
Cross sections with 13 TeV is also shown. Expected yields for 13 TeV data set arecalculated from other numbers. For the calculations, signal acceptance with 13 TeV
is assumed to be same with 8 TeV case. And expected yield of backgrounds is scaled
using cross section ratios of tt̄ and luminosity. . . . . . . . . . . . . . . . . . . . . .
Photon characteristics for the 11 signal events (GeV and mm units). The first two
events fell into SRa and the final nine in SRd. “Iso” refers to the value of the
topEtCone40 variable. Rconv shows the radius of conversion vertex. For converted
photons, it is classified as type 1 (one track only with Si hits), type 2 (one track onlywith no Si hits), type 3 (two tracks both with Si hits), or type 5 (two tracks andonly one with Si hits). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Lepton,jet and event characteristics for the 11 signal events (GeV units). The firsttwo events fell into SRa and the final nine in SRd. . . . . . . . . . . . . . . . . . .
Lepton vertex characteristics for the 11 signal events. The first two events fell into
SRa and the final nine in SRd. The perfect agreement between the z positions of the
lepton and primary vertices indicated that the lepton reference vertex was always
found to be the reconstructed primary vertex. . . . . . . . . . . . . . . . . . . . .

78

79

83

93
93

95