Doctoral Dissertation

博士論文

Search for the scalar top quark in the final statewith jets and missing transverse momentum
with the ATLAS detector at the LHC

実験におけるジェットと消失横運動量を持つ終状態を用いたスカラートップクォークの探索)

08/01/2021

CERN-THESIS-2020-309(LHC-ATLASA Dissertation Submitted for the Degree ofDoctor of Philosophy
November 2020
2 11

令和 年 月博士（理学）申請

Department of Physics, Graduate School of Science,
The University of Tokyo東京大学大学院理学系研究科物理学専攻
Yi-Lin Yang

楊易霖

Abstract
Supersymmetry theory (SUSY) can explain unsolved problems in theStandard Model of particle physics, such as, dark matter observed in
the universe, the unification of coupling constants of the electromagnetic,
weak, and strong interactions and hierarchy problem of the mass of the
Higgs boson. The 125 GeV mass of the Higgs boson, which was observedat the LHC, is too light for the naturalness in the Standard Model unless
new mechanism to stabilize the Higgs mass is introduced. The superpartners of the top quarks, which are called scalar top quarks, can provide
a key solution for the observed Higgs mass according to the predictionof natural SUSY, but they have not been observed so far. The search
for the scalar top quarks has been performed at the ATLAS. The scalar
top quark decays into a top quark and a neutralino if it is kinematicallyallowed. In the hadronic final states of top quarks, the method of the
top reconstruction is one of the principal features in the analysis for the
production of boosted tops due to the large mass difference of a scalar top
quark and a neutralino. The top reconstruction is performed in two steps:
to reconstruct jets of top-quark decay products and to identify top-quarks,
called top-quark tagging, using the reconstructed jets. In this thesis, a new
method, DNN top tagger, is introduced for both the jet reconstruction andtop-quark tagging, optimized for the high-mass scalar top quarks. The
new method shows high top-tagging efficiencies and good backgroundrejections, which help significantly improve 27% of the significance forsignal models where the final states top-quarks are highly boosted. The√
search uses at 139 fb−1 of s = 13 TeV data of proton-proton collisionsat Large Hadron Collider recorded by the ATLAS. No significant excess
over the Standard Model predictions is observed. The exclusion of themass of the scalar top quark is extended up to 1.4 TeV for the mass of theneutralino below 200 GeV at 95% confidence level.

1

Contents
1

Introduction

7

2

Theory10

2.1

Brief introduction of the Standard Model . . . . . . . . . . . . . . . . .

10

2.1.1

Symmetry transformation . . . . . . . . . . . . . . . . . . . . . .

10

2.1.2

Gauge theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10

2.1.3

Spontaneous symmetry breaking of electroweak theory . . . . .

12

2.1.4

Naturalness of Higgs mass . . . . . . . . . . . . . . . . . . . . .

12Supersymmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

13

2.2.1

Minimal supersymmetric Standard Model (MSSM) . . . . . . .

13

2.2.1.1

R-parity conservation . . . . . . . . . . . . . . . . . . .

14

2.2.1.2

Soft supersymmetry breaking . . . . . . . . . . . . . .

14

2.2.1.3

Higgs mass in the MSSM . . . . . . . . . . . . . . . . .

16

Problems in the Standard Model . . . . . . . . . . . . . . . . . .

16

2.2.2.1

Hierarchy problem . . . . . . . . . . . . . . . . . . . . .

16

2.2.2.2

Unification of coupling constants . . . . . . . . . . . .

172.2.2.3

Dark matter . . . . . . . . . . . . . . . . . . . . . . . . .

17

Properties of scalar top quarks . . . . . . . . . . . . . . . . . . . . . . .

18

2.2

2.2.2

2.3

3

LHC and ATLAS detector

22

3.1

Large Hadron Collider . . . . . . . . . . . . . . . . . . . . . . . . . . . .

22

3.2

ATLAS detector overviews . . . . . . . . . . . . . . . . . . . . . . . . . .

24

2

3.3

Coordinate system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

24

3.4

Magnet system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

26

3.5

Inner detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

26

3.5.1

Pixel detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

26

3.5.2

Silicon micro-strip tracker (SCT) . . . . . . . . . . . . . . . . . .

27

3.5.3

Transition radiation tracker (TRT) . . . . . . . . . . . . . . . . .

28

Calorimetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

28

3.6.1

29

3.6

Liquid argon calorimeter (LAr) . . . . . . . . . . . . . . . . . . .
3.6.1.1

Barrel electromagnetic calorimeter (EMB) and end-cap
electromagnetic
calorimeter (EMEC) . . . . . . . . . . . . . . . . . . . .

29

3.6.1.2

Hadronic end-cap calorimeter (HEC) . . . . . . . . . .

30

3.6.1.3

Forward calorimeter (FCal) . . . . . . . . . . . . . . . .

31

Tile calorimeter . . . . . . . . . . . . . . . . . . . . . . . . . . . .

32

Muon spectrometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

32

3.7.1

Precision tracking chambers . . . . . . . . . . . . . . . . . . . . .

33

3.7.1.1

Monitored Drift Tube (MDT) . . . . . . . . . . . . . . .

33

3.7.1.2

Cathode-Strip Chamber (CSC) . . . . . . . . . . . . . .

34

Trigger chambers . . . . . . . . . . . . . . . . . . . . . . . . . . .

35

3.7.2.1

Resistive Plate Chambers (RPC) . . . . . . . . . . . . .

35

3.7.2.2

Thin Gap Chambers (TGC) . . . . . . . . . . . . . . . .

35

3.8

Forward Detector for Luminosity measurement . . . . . . . . . . . . .

36

3.9

Trigger and Data Acquisition (TDAQ) . . . . . . . . . . . . . . . . . . .

36

3.9.1

36

3.6.2
3.7

3.7.2

Level-1 trigger . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3

3.9.24

37

Samples and event reconstruction

38

4.1

Data and Monte Carlo simulation . . . . . . . . . . . . . . . . . . . . . .

38

4.1.1

Data selections and triggers . . . . . . . . . . . . . . . . . . . . .

38

4.1.1.1

Monte Carlo simulation . . . . . . . . . . . . . . . . . .

40

Event reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

44

4.2.1

Track reconstruction . . . . . . . . . . . . . . . . . . . . . . . . .

44

4.2.2

Primary vertex . . . . . . . . . . . . . . . . . . . . . . . . . . . .

45

4.2.3

Electron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

46

4.2.4

Muon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

49

4.2.5

Jet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

50

4.2.6

VR Track jets . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

54

4.2.7

Flavor tagging . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

55

4.2.8

Hadronic tau . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

56

4.2.9

Overlap removal . . . . . . . . . . . . . . . . . . . . . . . . . . .

57

4.2.10 ETmiss and object-based ETmiss significance . . . . . . . . . . . . . .

57

4.2

5

High level trigger . . . . . . . . . . . . . . . . . . . . . . . . . . .

DNN top taggers and their calibration

59

5.1

Large-R jet labeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

59

5.2

Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

60

5.3

Network model of the taggers . . . . . . . . . . . . . . . . . . . . . . . .

64

5.4

Calibration of the taggers . . . . . . . . . . . . . . . . . . . . . . . . . .

65

5.4.1

65

Region definitions . . . . . . . . . . . . . . . . . . . . . . . . . .

4

6

5.4.2

Scale factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

66

5.4.3

Systematic uncertainties on the scale factor estimation . . . . .

71

5.4.4

Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

72

Data analysis and results

74

6.1

Analysis overviews . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

74

6.2

Preselections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

74

6.3

Signal region definitions . . . . . . . . . . . . . . . . . . . . . . . . . . .

77

6.3.1

Signal region A (mT2,χ2 > 450 GeV) . . . . . . . . . . . . . . . . .

79

6.3.2

Signal region B (mT2,χ2 < 450 GeV) . . . . . . . . . . . . . . . . .

80

Background estimations . . . . . . . . . . . . . . . . . . . . . . . . . . .

86

6.4.1

Control regions . . . . . . . . . . . . . . . . . . . . . . . . . . . .

87

6.4.1.1

tt̄Z control region (CRttZ) . . . . . . . . . . . . . . . . .

87

6.4.1.2

Z+jets control region (CRZ) . . . . . . . . . . . . . . . .

89

6.4.1.3tt̄ control region (CRT) . . . . . . . . . . . . . . . . . . .

89

Validation regions . . . . . . . . . . . . . . . . . . . . . . . . . .

91

6.4.2.1

tt̄Z validation region (VRttZ) . . . . . . . . . . . . . . .

91

6.4.2.2

Z+jets validation region (VRZ) . . . . . . . . . . . . . .

95

6.4.2.3tt̄ validation region (VRT) . . . . . . . . . . . . . . . . .

95

6.4

6.4.2

6.5

6.6

Systematic uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
6.5.1

Experimental uncertainties . . . . . . . . . . . . . . . . . . . . . 101

6.5.2

Theoretical uncertainties . . . . . . . . . . . . . . . . . . . . . . . 103

Statistical model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
6.6.1

Fit strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
5

6.6.2
6.7

7

8

Statistical test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
6.7.1

Background-only fit . . . . . . . . . . . . . . . . . . . . . . . . . 110

6.7.2

Discussion of data in signal regions . . . . . . . . . . . . . . . . 112

6.7.3

Model-dependent signal fit . . . . . . . . . . . . . . . . . . . . . 117

6.7.4

Model-independent signal fit . . . . . . . . . . . . . . . . . . . . 118

Discussion

120

7.1

Exclusion limit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

7.2

Comparison with the results of reclustering method . . . . . . . . . . . 120
7.2.1

Regions with the reclustering method . . . . . . . . . . . . . . . 120

7.2.2

Signal regions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

7.2.3

Performance comparison . . . . . . . . . . . . . . . . . . . . . . 123

7.2.4

Comparison of Results . . . . . . . . . . . . . . . . . . . . . . . . 124

7.3

Comparison with CMS results . . . . . . . . . . . . . . . . . . . . . . . . 127

7.4

Comparison with results in one/two-lepton final states . . . . . . . . . 128

Conclusion

129

Reference

130

Appendices

143

A Discussion on the physical objects used in the event reconstruction

143

B Impact on the extrapolation of signal scale factors of DNN top taggers

145

6

1

Introduction

The achievements of the particle physics theories and experiments establish the description of the four forces in our world, which are electromagnetic force, weak force,strong force, and gravitational force. The Standard Model describes the interactionof three forces except for the gravitational force. Although it is the outstandingachievement in the Standard Model, the hierarchy problem, the unification of coupling constants, and the dark matter still cannot be explained in the Standard Model.
The Higgs mass has been measured to be 125.10±0.14 GeV as the average of theresults from the ATLAS and CMS [1]. The mass is too light in the Standard Model if
we believe in the so-called naturalness. The Higgs mass is partly contributed fromthe self-coupling λ, which results in quadratic divergence. If the Standard Modelholds up to the Planck scale, which is the scale of unification of gravity, the Higgs baremass will also run up to the Planck scale. The bare mass largely depends on the cutoff scale. Since the Higgs mass is 125 GeV, there must be a fine-tuning between baremass and radiation corrections, which has no theoretical motivation in the Standard
Model. This is known as the problem of the fine-tuning.
Supersymmetry (SUSY) is one of the Beyond the Standard Model (BSM) theory.
There are many new particles which are predicted in the supersymmetry theory. In
the minimal supersymmetric Standard Model (MSSM) with two Higgs doublets, theobserved Higgs boson at the LHC can be considered as the lower mass Higgs boson,
h0 . The h0 mass no longer depends on the self-coupling λ and only the radiative
corrections contribute to the h0 mass in the MSSM. The radiative corrections of h0
largely depend on the stop (scalar top) mass and top mass due to the large Yukawa
coupling to the top quark. The stop is the superpartner of the top with spin 0
predicted in the supersymmetry theory. The contributions from the other quarks
are usually not considered since their Yukawa coupling constants are smaller thanthe Yukawa coupling of top quarks. Therefore, the stop mass can be the smallest one
among all the superpartners of the quarks.
In the recent searches for the stop with full hadronic final states, Figure 1 summarizes the search results at 36 fb−1 of the LHC Run2 data (2015-2016). Figure 1 (a)shows the exclusion limit of the stop mass mt̃ at the low neutralino mass mχ̃0 is
1extended around 1020 GeV by the CMS [2]. The mχ̃0 has been excluded up to 420 GeV,
1

which depends on the mt̃ . Figure 1 (b) shows the results from the ATLAS [3]. The
limit of the mt̃ at the low mχ̃0 is around 1000 GeV, and the limit of the mχ̃0 is up to
1

1

7

102

200

10−2

100
0

200

400

600

800

1000

1200

10−3

1

700

s=13 TeV, 36.1 fb-1

ATLAS 20 fb-1, s=8 TeVLimits at 95% CL

mt +SRA+SRB+SRC+SRD+SRE

1

m

χ∼ 0

600

300

1

W +

m

400

b

+

m

χ∼ 0

t

1

m~

<

500

m

10−1

300

SUSY

Expected limit (±1 σexp)

<

t

m~

400

Observed limit (±1 σtheory)

ATLAS

t

1

m
t +

1

=m

500

800

~
(*) ∼0) = 100%
Top squark pair production, B(t1 → t χ
1

1

10

χ∼ 0

600

mχ∼0 [GeV]

Observed ± 1 σtheory
Expected ± 1 σexperiment

700

95% CL upper limit on cross section [pb]~~ ~∼pp → t t, t → t χ01 NLO+NLL exclusion

900

m~

35.9 fb-1 (13 TeV)

CMS

0
1

m∼χ [GeV]

800

200
100
0

200

400

600

800

1000
1200
m~t [GeV]

m~t [GeV]

1

(a)

(b)

Figure 1: Exclusion limits of the mt̃ and mχ̃0 with 36 fb−1 of 2015 and 2016 dataset
1
published by (a) CMS collaboration [2] and (b) ATLAS collaboration [3].
400 GeV, which depends on the mt̃ .
qbLarge ΔR

q

b

W

q

q

t W

t

W
t

q

q

q

W

q

b
Small ΔR

(a)

t

b

(b)

Figure 2: Schematics of pair production of stops in the fully hadronic final states
00with (a) ∆m(t̃1 , χ̃1 ) close to top mass and (b) ∆m(t̃1 , χ̃1 ) much larger than top mass.
∆R is the separation of decay products of a top quark (see Eq. (29) for the definition).
The stop mass can be as low as several hundred GeV if the mixing of righthanded stop t̃R and left-handed stop t̃L is large, which is needed to be 125 GeV Higgs
mass. Since the lower mass limit of the stop quark has reached up to about 1 TeV,
it is naturally important to explore even higher mass region. In this thesis, we focus
0on the search in the t̃ → tχ̃ channel with the hadronic decay of the top quarks in0

the boosted region, where the ∆m(t̃1 , χ̃1 ) is much larger than the top mass. The top
can be fully reconstructed from the decay products in the absence of ETmiss , and theboosted topology allows us to exploit small angular separation of the decay products
for the top reconstruction (see Figure 2). The decay products of top quarks with small
8

angular separation can be reconstructed as jets with a large radius, which are called“large-R jet”. The feature of substructure in the large-R jets, which is introduced
as substructure variables, is useful to identify the top jets and reject quark/gluoninitiated jets. To maximize the discriminant power of the substructure variables, adeep neutral network (DNN) algorithm with a set of the substructure variables isused for the development of the tagging techniques, which can efficiently distinguishthe top jets from the quark/gluon-initiated jets. The DNN top taggers are validatedwith the measurement of data efficiencies for the top jets and quark/gluon-initiatedjets. The presence of the stop signals is tested by a fit to a representative kinematic
observable after the selections are applied. In case no signal is found, the upper limitof the signal yields is evaluated, and then the lower limit of mass is considered.
We briefly introduce the theory of the Standard Model related to the unsolved
problems and the theory of the MSSM in Chapter 2. The structure of the LHC and the
ATLAS detector are described in Chapter 3. The samples and event reconstruction
are in Chapter 4. A new method for the top-tagging is introduced in Chapter 5. The
data analysis for the search for the stop using the full Run2 data of 139 fb−1 will
be shown in Chapter 6. The ATLAS collaboration has published the new results at
139 fb−1 with an alternative method in the paper. The results with two different
approaches, and the comparison with CMS results at 137 fb−1 of the full Run2 data
are discussed in Chapter 7. Finally, all works are summarized in Chapter 8.

92Theory2.1

Brief introduction of the Standard Model

The Standard Model of particle physics includes three different gauge symmetries,
which are denoted as SU(3)C × SU(2) L × U(1)Y . In the Standard Model, there are six

quarks separated into the up-type and the down-type, and three generations of eachpair of the up-type and the down-type quarks. There are also six leptons classified
into three generations. These particles are spin 1/2 fermions and also have their own
anti-particles. In addition, there are also particles, which are bosons with spin-0 or
spin-1. A photon γ is a particle, which propagates the electromagnetic force. The

W ± and Z are spin-1 bosons, which propagate the weak force, and the W ± bosons
only interact with left-handed particles. The gluons are massless bosons with spin 1,
which propagate the strong force. The last one is the Higgs boson with spin 0, whichmakes the other particles massive. All particles are summarized in the Standard
Model section of Figure 3 (left).

2.1.1

Symmetry transformation

To describe the behavior of the particles, the conservation law must be obeyed. The
conservation law is given by some physical invariance. The symmetry transformations based on the invariance are represented by changes between different states.
This is important for describing the dynamics of the particles. The infinitesimalchanges of continuous transformations provide the description of the transformations by using the unitary or anti-unitary operator U with the identity and infinitesimal transformation:
U = I + iδξG,(1)where I is the identity operator, and δξ indicates an infinitesimal change of a parameter. G is an operator which is the generator of the symmetry transformation.

2.1.2

Gauge theory

Gauge theory can describe physics with the global symmetry and local symmetry.
For example, in the case of the isospin of a proton and a neutron, the symmetrytransformation of isospin affects all the protons and neutrons in the universe. The
10

Standard Model particles

Superpartners of SM particles

2.2MeV

1.28GeV

173.1GeV

0

u

c

t

g

125.10GeV

H

ũ

c̃

t̃

g̃

H̃

up

charm

top

gluon

Higgs

sup

scharmstop

gluinohiggsino

4.7MeV

96MeV

4.18GeV

0

d

s

b

γ

d˜

s̃

b̃

γ̃

down

strangebottomphotonsdown

sstrangesbottomphotino0.511MeV

105.66MeV

1.7768GeV

91.19GeV

e

µ

τ

Z

ẽ

µ̃

τ̃

W̃

electron

muon

tau

Z bosonselectron

smuon

stau

wino

<0.17MeV<0.17MeV<18.2MeV

80.39GeV

νe

νµ

ντ

W

ν̃e

ν˜µ

ν˜τ

Z̃

electronneutrino

muon
neutrinotau
neutrino

W bosonselectron
neutrino

smuon
neutrino

stau
neutrino

zino

Figure 3: The elementary particles of the Standard Model (left) and theirsuperpartners (right) in the supersymmetry theory.
symmetry is called global symmetry. However, the physics which we are dealing
with changes locally. The effect from an event cannot propagate out of the spacetime of the light cone (causality). This means the transformations can only happen
independently. This kind of symmetry is called local symmetry. The first gauge
theory with local symmetry is Maxwell’s theory. The vector potential A and electricalpotential V can be expressed by the form similar to the Eq. (1) with a gauge field,
A0 = A + ∇ f , V0 = V −

∂f
.
∂t

(2)

In quantum field theory, the gauge theory can be built with an abelian group or a
non-abelian group, expressed using the commutation relation of the generators as:[ T i , T j ] = i f ijk T k ,(3)where T represents the generators, and f ijk is known as the structure constant. If
f ijk =0, the T belongs to the abelian group. For example, in quantum electrodynamics(QED), the generator of U(1) symmetry transformation is abelian. The symmetrytransformation happens in the charge field. If f ijk is not zero, the T is non-abelian.
For example, the weak interaction has non-abelian SU(2) symmetry for the weakisospin. In addition, the generators which have SU(3) symmetry transformations in
the color space in quantum chromodynamics (QCD) are also non-abelian.

112.1.3

Spontaneous symmetry breaking of electroweak theory

The electroweak theory is a theory for the unification of electromagnetic and weakinteraction [4]. The gauge symmetry is SU(2) L × U(1)Y . To introduce the gauge the-ory into the weak interaction, the gauge boson of weak interaction must be massive

since the range of the interaction is short. On the other hand, the gauge boson forthe photon should be massless. Since the properties of electromagnetic and weakinteractions differ from each other at a low energy scale, the local symmetry of theelectroweak must be broken. The Higgs mechanism is involved in the spontaneous
symmetry breaking, making the vacuum expectation value of the Higgs field nonzero. The symmetry transformation cannot remain invariant. The SU(2) L × U(1)Y

breaks into U(1)em . In addition, the masses of fermions are also given by the broken
symmetry. The Higgs fields are defined as one doublet scalar fields φ. The Higgs
potential is introduced as a formula as:V ( φ ) = + µ2 φ † φ + λ ( φ † φ )2 ,(4)

where µ2 is the mass parameter, and λ is the Higgs self-coupling. To minimize theh0|φ|0i, we can consider two conditions for µ2 . For µ2 > 0, the vacuum expectation

value ν = 0, which is not what we expect for the symmetry breaking. For µ2 < 0, thevacuum expectation value is not zero and can be calculated from the Fermi coupling√
constant υ2 = ( 2GF )−1 = (246 GeV)2 . Then, we can have the Higgs mass M H fromthe vacuum expectation value and the Higgs self-coupling.
M2H = 2υ2 λ.

2.1.4

(5)

Naturalness of Higgs mass

In the previous section, the Higgs mass is obtained at the tree level. Now, we consider
Higgs bare mass m H with one-loop precision before the renormalization [5],(m2H = M2H − 2g2

m2f
3 M2H
1
1
(1 − n)( + 2 ) −
+∑ 2
2
2 4cw
4 MW
f MW

)

Λ2
,
16π 2

(6)

where n is the number of the poles, g is the coupling constant, m f is the mass of thefermion, Λ is the cut-off energy scale, MW is the W mass, and cw is the cosθw . The
second term of the RHS is from the one-loop contribution and depends on the cut-off
scale. This is known to cause a quadratic divergence, which is mainly contributed
12

from the integral of the propagators containing the poles. The renormalization also
needs to have the cut-off dependence to match the Higgs mass obtained from theexperimental results.

2.2

Supersymmetry

Supersymmetry is a spacetime symmetry which transforms fermionic (bosonic) fields
into bosonic (fermionic) fields by using fermionic generators (Q, Q† ) of supersymmetry transformations under the usual bosonic spacetime coordination, x µ , and the four
fermionic superspace, θ and θ † (two-component spinor for each). The generators arealso known as supercharges. The anticommutation relations of the generators withtwo different Dirac spinors, α and β, form as:{ Qα , Q†α̇ } = −2σαα̇ Pµ ,µ

{ Qα , Q β } = 0, { Q†α̇ , Q†β̇ } = 0,(7)where σ is the Pauli matrix, and Pµ is a four-vector momentum operator. The firstline of Eq. (7) shows the transformation of the spacetime. Those new particles
are superpartners of the Standard Model particles. The spin of the superpartner isdifferent by a half. The spin half fermions become spin-0 bosons while the spin1 gauge bosons become spin- 21 gauge fermions. For example, a top quark in theStandard Model has its own superpartner, which is called the scalar top or the stop.
The elementary particles predicted in supersymmetry are shown in Figure 3 (right).

2.2.1

Minimal supersymmetric Standard Model (MSSM)

In the MSSM, only the simple symmetry N = 1, which means there is only one setof the supercharges, is used. There are two types of representations, chiral andvector supermultiplets. A chiral supermultiplet contains one complex scalar field
φ, one two-component chiral fermionic field Φ, and a complex scalar auxiliary field
F. A vector supermultiplet contains a spin 1 vector gauge boson field Aµa , a twocomponent Weyl fermion gaugino λ a , and a real scalar auxiliary field D. The auxiliary fields make the closure of the supersymmetry off-shell.
The Higgs sector in the Standard Model is a single doublet field, which is mentioned in section 2.1.3. In the MSSM, the two doublet Higgs fields, Hu and Hd , arerequired for the holomorphic property of the superpotential. The Hu couples only to13the up-type quarks and the Hd to the down-type quarks, and charged lepton. Therefore, the superpotential for the quark and lepton masses in the MSSM is expressedas:¯ d QHd − ēyd LHd + µHu Hd ],W = eαβ [ūyu QHu − dy(8)where ū, d,¯ ē are the up-type quark superfield, down-type quark superfield, andcharged lepton superfield, respectively. The eαβ corresponds to the weak isospin
with indexes. The yu , yd , and ye are the Yukawa couplings. The Yukawa matrices
determine the mass and CKM mixing angles of the quarks and leptons if the Hu andHd have their vacuum expectation value. The Yukawa couplings in supersymmetry
are required to be the same as the couplings in the Standard Model.

2.2.1.1

R-parity conservation

In supersymmetry, additional renormalizable terms violate the baryon number B
and lepton number L, which causes the short lifetime of protons. To eliminate theviolations, a new symmetry is introduced in the supersymmetry called R-parity,
which is expressed as:
R = (−1)3( B− L)+2s ,(9)where s is the spin of the particle. The R-parity is defined to be +1 for particles inStandard Model and -1 for their superpartners. This property is important for the
existing of the lightest supersymmetry particles (LSPs). In the MSSM, the R-parity
is conserved. Therefore, the supersymmetry particles must be produced in pair, andthe final states contain a pair of the LSPs. The LSPs are also considered as candidates
for the dark matters since they are massive, and weakly interact with the Standard
Model particles. In this thesis, the R-parity conservation is assumed.

2.2.1.2

Soft supersymmetry breaking

Since the supersymmetry particles are not observed so far, the supersymmetry mustbe broken. The Higgs mass term in the MSSM is non-negative. This causes a minimum at Hu0 = Hd0 = 0 if a supersymmetry-breaking squared-mass soft term is not14

included. The soft Lagrangian given in Ref. [6] is expressed as:1
Lso f t = − ( M3 g̃ g̃ + M2 W̃ W̃ + M1 B̃ B̃ + c.c.)2˜¯a Q̃H − ē˜a L̃H + c.c.)− (ū˜ a u Q̃Hu − da
e
d
d
d
†
† 2
† 2
2
˜¯m 2 d˜¯† − ē˜m 2 ē˜†
− Q̃ m Q̃ − L̃ m L̃ − ū˜ m ūu ū˜ − dm
ēe

(10)

L
Q
d̄d
2
∗
2
∗
− m Hu Hu Hu − m Hd Hd Hd − (bHu Hd + c.c.).

All the quantities in Lso f t have the radiative corrections, which result in the cut-off

dependence and can be renormalized. The M3 , M2 , and M1 are the gluino, wino,
and bino mass terms, respectively. The a u , a d , and a e are 3x3 matrices corresponding
to the Yukawa couplings and usually assumed to be proportional to the Yukawa
couplings. The gluino cannot mix with the other particles in the MSSM due to thecolor octet. The other gauginos and higgsino with the same electrical charge can mix
together. There are two mixed charged supersymmetry particles called charginos χ±and four neutral mixed particles called neutralinos χ0 . The above quantities dependon the tanβ = h Hu i / h Hd i, which is also a key variable in the experiments. The tanβ
is also constrained by the Yukawa couplings and thus can be between ∼1 and 60.

The symmetry can be broken only if either the F term or the D term is not
zero. For the D term breaking, a Fayet-Iliopoulos term is needed to be added into
the Lagrangian. However, this breaks gauge invariance, and the mass terms of thesquarks and sleptons disappear. The D term breaking mechanism is still unclear now.
On the other hand, the F term breaking is called O’Raifeartaigh model. The supersymmetry breaking is also considered as a hidden sector. If it couples to visible sector
directly, the gauge has no mass since there are no scalar-gaugino-gaugino couplings,
and some predictions are already ruled out by experiments. Hence, there must be
some mediating interactions between the hidden sector and the visible sector. If themediating interaction is flavor-blind, the parameters in the MSSM have relations asfollows:

m 2Q = m2Q 1 , m 2ūu = m2ū 1 , m 2d̄d = m2d¯1 , m 2L = m2L 1 , m 2ēe = m2ē 1 ,a u = Au0 y u , a d = Ad0 y d , a e = Ae0 y e .

(11)

There are different mechanisms of the soft breaking, such as, gravity mediatedsymmetry breaking, gauge mediated symmetry breaking (GMSB), and anomaly mediated symmetry breaking (AMSB).

15

2.2.1.3

Higgs mass in the MSSM

From the contributions of the superpotential of Eq. (8), the soft Lagrangian in the
Eq. (10), and Kähler D terms, the scalar Higgs potential is expressed as:
g2 + g 02 †g2
( Hd Hd − Hu† Hu )2 + | Hd† Hu |2 + |µ|2 ( Hd† Hd + Hu† Hu )
8
2
2
†
2
†
+ (m Hd Hd Hd + m Hu Hu Hu ) − (bHu Hd + h.c.),

VHiggs =(12)

where b is a complex parameter. The Higgs potential in the MSSM is much more
complicated than the Higgs potential in the Standard Model. Owing to two doublet Higgs fields, the Higgs bosons have two mass states, Mh and M H . The Mh isgenerally referred to as the smaller mass. The Mh at tree level is given by:



1
(0) 2
Mh
=
2



M2A + M2Z −q( M2A − M2Z )2 + 4M2A M2Z sin2 (2β)


,

(13)

where M2A is b(tanβ + cotβ). The Mh is smaller than MZ even if the decoupling
limit of M A  MZ is considered, which causes the large difference of the Higgs
mass between the prediction at tree level and the observation. Hence, the radiative
corrections are needed, which is explained below.

2.2.2

Problems in the Standard Model

2.2.2.1

Hierarchy problem
t

h

t̃

h

h

t̃

h
h

t

h

t̃

(a)

(b)

Figure 4: The Higgs self-energy contributed from the (a) top loop and (b) scalar top
quark loop in the MSSM.
As discussed in the section of the Standard Model, the cut-off dependence of themass is unnatural. In the MSSM, thanks to the contributions of the supersymmetry
particles at the loop level, the divergence of the Higgs bare mass can be reduced
16

before the renormalization. Since the Yukawa coupling of the top quark is largest
among the other quarks, the contribution from the stop is also larger than the othersquarks. The divergence contributed from top quarks (see Figure 4 (a)) can be cancelled out by introducing the scalar top quark loops (see Figure 4 (b)). The massdifference between tree level and 1-loop level is given by:
#
"
2
2
4
2
m
X
m
X
3
t
t
) ,
∆Mh2 ∼
ln 2t̃ + t (1 −2
2mt̃2
12mt̃2
4π υ
mt

(14)

where Xt = at − µcotβ is the stop mixing parameter.
2.2.2.2

Unification of coupling constants

In the Standard Model, the different forces are described in the different symmetries.
These symmetries also can be considered as subgroups of a larger symmetry. In the
grand unification theory, a SU(5) or SO(10) is used to unify the strong and electroweak interactions. Figure 5 shows the inverse of the running gauge coupling α−1 .
The energy scale for the grand unification is up to 1015 GeV. In the Standard Model,
the coupling constants α(SU(3)) and α(SU(2)) become weaker, and the α(U(1))
becomes stronger as the energy scale increases. However, the unification of coupling
constants will not be seen in the Standard Model. With the supersymmetry, only theα(SU(3)) becomes weaker, and both the α(SU(2)) and the α(U(1)) become stronger
as the energy scale increases. The unification can be possible around the GUT (Grand
Unification Theory) scale.

2.2.2.3

Dark matter

The presence of dark matter is strongly believed from the cosmological studies. In
the early studies on the galaxy clusters and the galactic rotation curves, there must
be missing mass in the space. Someone may argue that the mass can be from known
matters, which cannot be detected from the earth. Thanks to the fitting results ofthe cosmic microwave background (CMB) according to the Λ CDM predictions, theabundance of the interstellar deuterium can be correctly estimated, which can constrain the baryonic matter in the universe. According to the recent results with thedata of baryon acoustic oscillations from the Planck project, the universe is made of
26.06±0.30% of the cold dark matter [7]. In this thesis, we are interested in the can-didates of supersymmetry particles, which belong to the weakly interacting massive
17

Figure 5: α−1 ( Q) with two-loop radiative corrections as a function of the energy
scale [6]. The dashed line is the inverse of the coupling constants in the SM. The
blue and red lines show the constants, which are from the masses of sparticles at
750 GeV and 2.5 TeV, respectively.
particles (WIMPs). The WIMPs weakly interact with other particles, so it is hard to
detect. With R-parity conservation, the LSPs may match the properties, which arerequired for the dark matter. The detectable mass states of the LSP can be the mixing
states of the superpartners of the gauge bosons. The search for the LSP is modeldependent since a different soft symmetry breaking model predicts a different LSP.
The LSP in the GMSB is the gravitino and the wino in the AMSB.

2.3

Properties of scalar top quarks

Due to the chirality, the stop sector has a right-handed stop t̃R and a left-handed stopt̃L . The t̃R and t̃L can mix together, which causes that the t̃R and t̃L are not the mass
eigenstates of the stop. The Lagrangian of the stop mass is as follows:

L = − t̃∗L t̃∗R m 2t̃t
wherem 2t̃t =m2Q3 + m2t + ∆ū L

υ( at sinβ − µ∗ yt cosβ)

t̃ L
t̃ R

!
,

υ( a∗t sinβ − µyt cosβ)m2ū3 + m2t + ∆ūR

(15)

!
.

(16)

The top mass mt , the ∆ from the electroweak symmetry breaking, and the Yukawa
coupling yt in the Standard Model contribute to the stop mass. The at from the soft18

breaking sector, the vacuum expectation value (VEV) υ of Hd , and β from tanβ in the
MSSM also contribute to the stop mass. The mass eigenstates can be obtained fromthe mixing of t̃L , and t̃R with the mixing angle θt̃ :
t̃1
t̃2

!

=

cosθt̃ −sinθt̃
sinθt̃

cosθt̃

!

t̃L
t̃R

!
,

(17)

where the stop with the smaller mass is assigned as t̃1 and the one with the larger
mass is t̃2 .

Figure 6: The contours show (Left) the fine tuning of the Higgs mass ∆mh (purple
dash line) and (Right) lightest stop mass mt̃1 (green dash line) as a function of thestop mixing parameter Xt within the Higgs mass 124∼126 GeV by using simulation
software, Suspect (Red) and FeynHiggs (Blue), at tanβ = 20 in the MSSM [8].
Figure 6 shows the results obtained by Lawrence et al. [8], who studied the relations of Higgs mass and the mixing of the stops. The Xt is the stop mixing parameter.
The zero means there is no mixing between t̃R and t̃L . Two public programs, Suspectand FeynHiggs, are used in this thesis. The calculations include radiative corrections
up to the two-loop level. The Higgs mass is derived under the decoupling limit. If
the mixing of the stop is not considered, the stop mass will not be below 3 TeV. The
mass scale of 3 TeV or higher will not be reachable at LHC. However, the mass of√t̃1 can be 300−500 GeV if Xt = 6. This mass scale will allow us to search at LHC of√s = 13 TeV.
In this thesis, the simplified model [10, 11] is used for the search for the stop. In
the simplified model, we do not need to scan the large set of MSSM parameters. The
mass spectrum of the SUSY particles is more important, and the parameters can belargely reduced. The gluino mass is assumed to be much higher than the stop mass.
19m = mt̃1
m
>
m
0
1

t˜
!
t˜1

!

t˜1

!

c˜

1

0

mt̃1 < m ˜01

m ˜01

t

b

m bf
> f 0m m
m ˜ 0> >
W1
m 0
+ t˜1
t˜1
m
!
m b
bW > m m >
m
>
˜0 W
m 0
+ t˜1
1
m

m > mW + mb

t˜1

m0
[GeV]
0 100 200 300
˜01 [GeV]
200m300t̃1 100

m>0
m > mt̃1

0 100 200 3000 100 200 300
0 100 200 300
0 100 200
1 [GeV] mm ˜300t̃1 [GeV]
0

Figure 7: Decay channels with respect to the mass regions [9]. Two-body decay, t̃1 →000tχ̃1 , occurs in ∆m(t̃1 , χ̃1 ) > mt . Three-body decay, t̃1 → bW χ̃1 , occurs in mW + mb <000∆m(t̃1 , χ̃1 ) < mt . Four-body decay, t̃1 → b f f 0 χ̃1 , occurs in ∆m(t̃1 , χ̃1 ) < mW + mb .
0

The decay channels of the t̃1 where the lightest neutralino χ̃1 is directly produced
from the t̃1 decay are shown in Figure 7. Depending on the mass difference between00
the t̃1 and χ̃1 (∆m(t̃1 , χ̃1 )), the decay channels can be classified into two-body, three0

body, and four-body decays. If the ∆m(t̃1 , χ̃1 ) is larger than the top mass, the decay0channel is the two-body decay. If the ∆m(t̃1 , χ̃1 ) is between top mass and W mass, the0decay channel is the three-body decay. Finally, if the ∆m(t̃1 , χ̃1 ) is smaller than the W
mass, the decay channel is the four-body decay. The mt̃ smaller than mχ̃0 is forbidden.
01

In this thesis, we aim for the two-body decays with large ∆m(t̃1 , χ̃1 ), where the top
quarks have high pT and decay hadronically.

Figure 8: Feynman diagrams for the stop production via quark-antiquarkannihilation (first row) and gluon-gluon fusion (second row) at leading order [12].
The pair production of the stops via qq̄ and gg are considered in the calculationof the cross section. Other processes are suppressed by the higher order of the strong
coupling. The cross section at leading order mainly depends on the stop mass since
light squarks do not appear in the Feynman diagrams as shown in Figure 8. In
20

the higher order calculation, the gluinos and light squarks appear in the loop so
the gluino mass and light squark mass affect the stop production. In addition, stop
mixing parameter and other stop mass (mt̃2 ) also appear in high order calculation.

21

3

LHC and ATLAS detector

3.1

Large Hadron Collider

The Large Hadron Collider (LHC) [13] is a circular collider with 27 km in circumference, at the mean depth of 137 m across the France-Swiss border. The beam pipes
are installed in the tunnel which was built for the Large Electron-Position (LEP)
collider [14]. The proton or the lead ion beams go in the counter-rotating direction
in two different beam pipes for the collision. With the high energy of the collisions,
it allows us explore the physics at the TeV scale. The magnet system is a criticaltechnology for the circulation of the beams. There are mainly two types of magnets,
dipole and quadrupole magnets. These magnets are made of the NbTi Rutherford
cables. The magnets provide 8 T field at the temperature below 2 K. The superfluid
helium is used in the cryostat system. The energy of the proton beam is 7 TeV in
the design. In the Run2 (2015-2018), the beam energy is only up to 6.5 TeV due to alimitation of available magnetic field.
The protons from a bottle of hydrogen gas are accelerated by the radio frequency
in the series of accelerators, as shown in Figure 9. The protons are accelerated in
Linac2, and the proton beam energy is up to 50 MeV. After the acceleration in Linac2,
the beam energy is increased to 1.4 GeV in Proton Synchrotron Booster (PSB). The
PSB also acts as the transition to convert the RF harmonics from the Linac2 to Proton
Synchrotron (PS) where the beam energy is increased up to 25 GeV. The beam energy
is further increased to 450 GeV in the Super Proton Synchrotron (SPS) and injected to
the LHC. The proton beams are accelerated in the RF cavities of the LHC. After the
beam energy reaches 6.5 TeV, the proton beams are used in the collisions.
The instantaneous luminosity of the ideal head-on collision of the Gaussian
beams [16] is defined as:
L=

N1 N2 f Nb,
4πσx σy(18)

where N1 and N2 are the number of the particles in one bunch, f is the revolution
frequency, and Nb is the number of bunches in the ring. σx , σy are the parametersdescribed in Gaussian profiles. The additional terms are required to describe the realmachines. The instantaneous luminosity has been achieved up to 2 × 1034 cm2 s−1

at the interaction points of the ATLAS detector and the CMS detector. The instantaneous luminosity in Run2 data taking exceeds the designed instantaneous luminosity

22

The CERN accelerator complex
Complexe des accélérateurs du CERNCMSNorth Area

LHC

GIF++

2008 (27 km)

CENF

ALICE

2015

LHCb

2016

TT20

TT40

TT41

SPS
1976 (7 km)

TI2

TT10

TI8

AWAKE

ATLAS

HiRadMat
2011

2016

TT66

TT2

AD

ELENA

1999 (182 m)

2016 (31 m)

ISOLDEBOOSTER

1992

1972 (157 m)
RIBs
p

p

East Area

2001/2015

n-ToF
2001

IRRAD/CHARM

PSn1959 (628 m)

p

ions

CLEAR

LINAC 2e-

LEIR

LINAC 3Ionsp (protons)

REX/HIE

20172005 (78 m)n (neutrons)

RIBs (Radioactive Ion Beams)– (antiprotons)pe- (electrons)

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

Figure 9: Accelerator complex at CERN [15].

23

of 1.0 × 1034 cm2 s−1 . The standard filling scheme of the LHC is 2808 bunches per

ring. Each bunch contains ∼ 1011 protons in the dimension around 16 µm in widthand few centimeters in length of the interaction point of ATLAS experiment.

3.2

ATLAS detector overviews

Figure 10: The cut-away view of the ATLAS detector [17].
The ATLAS (A Toroidal LHC ApparatuS) detector [18] is located at the point
1 of the LHC. Figure 10 shows the overviews of the ATLAS detector. The ATLAS
detector is designed to have the 4π coverage and comprises several sub-detectors
for a wide spectrum of physics processes. The magnet system makes the trajectories of the charged particles bent so that the momentum and electric charge can bemeasured. The detectors consist of the inner detector, the calorimeter, and the muon
spectrometer from the inside to the outside. All three sub-systems consist of one
barrel part and two end-cap parts.

3.3

Coordinate system

The directions and position in the ALTAS detector can be described in the xyz coordinate system. The origin (0,0,0) is defined at the center of the ATLAS detector. The
z-axis is defined along the beam pipe. The positive z side is called A-side, and the24Figure 11: The geometry of the magnet systems (red) [18]. The tile calorimeter is alsomodelled.
negative z side is called C-side. The positive y-axis is defined in a vertical direction,
pointing upwards. The positive x-axis points to the center of the LHC from the centerof the ATLAS detector.
The magnitude of the momentum in the x-y plane is referred to as the transverse
momentum. The azimuthal angle φ is defined with respect to the x-axis. Instead of
the polar angle θ, the rapidity y is used in the hadron collider experiment:
1
E + pzy = ln,2
E − pz(19)

where E denotes the energy of particles and pz denotes the momentum along thez-axis. This quantity is very useful in high energy physics since the difference inrapidity is Lorentz invariant. For the massless objects, the pseudo-rapidity is used toapproximate rapidity and defined as:θη = −ln tan
.
2

(20)

It is useful since the pseudo-rapidity is directly calculated from the polar angle. To
describe the angular separation of two objects, the ∆R is defined in the η − φ plane

as:

∆R =

q

(∆η )2 + (∆φ)2 ,where ∆η = η1 − η2 , and ∆φ = φ1 − φ2 .

25

(21)

3.4

Magnet system

There are one solenoid and three toroid magnet systems in the ATLAS detector. The
location of the magnets is pointed out in Figure 11. The superconductors are used in
the magnets. The whole magnet systems are contained in the cylindrical space withthe 22 m in diameter and 26 m in length. The energy stored in the system is 1.6 GJ.
The solenoid magnet with 2.46 m in diameter and 5.8 m in length the surrounds theinner detector and provides 2 T axial field. Three toroids around the calorimeters
are arranged with an eight-fold azimuthal symmetry. A Barrel toroid with an innerdiameter of 9.4 m and 25.3 m in axial length in the muon detectors provides ∼0.5 T

magnetic field, and two end-cap toroids with 5.0 m in axial length also provide ∼1 T

magnetic field.

3.5

Inner detector

The inner detector (ID) [19] provides a reconstruction of tracks of charged particles
and vertices from the reconstructed tracks. The momentum can be determined fromthe curvature of the trajectories. The coverage is over the pseudo-rapidity range of|η | < 2.5. The inner detector is inside the solenoid magnet system and consists ofthree sub-detectors, pixel detector close to the beam pipe, silicon micro-strip tracker(SCT) in the middle and transition radiation tracker (TRT) in the outermost layers.

Figure 12 shows the r-z cross-section views of the inner detector. Insertable B-Layer
detector (IBL) [20] was installed during a long shutdown in 2014 before the Run2
to enhance the tracking performance and efficiency of b-tagging. The overall innerdetector is 2.3 m in diameter and 7m in z-direction.

3.5.1

Pixel detector

The pixel detector consists of 1456 barrel modules and 288 disk modules. Four layersof pixel modules are in the barrel regions and three layers in the end-cap region.
A pixel sensor [21] has a 256 µm thick n-bulk. The nominal pixel size is 50 µm(φdirection) × 400 µm (z-direction). The n+ implants are embedded on the readoutside, and the p-n junction is on the back size. The n+ -in-n design allows the operationeven if the type inversion occurs. Each sensor module is composed of 47232 pixel
sensors. The sensors are arranged in 144 columns and 328 rows. In the barrel region,
13 modules are mounted on each stave. The operation temperature is maintained26

Figure 12: The r-z cross-section views of the position of a quadrant of all innerdetectors (upper panel) and the pixel detector (lower left panel). The table shows
the distance range of each sub-detector in r-axis.
within −5∼−10 °C to suppress the annealing effect and the noise.
The IBL is the innermost layer of the pixel detector and consists of 14 carbon fiber
staves. The addition of the IBL improves the track resolution [20]. Two different pixel
sensors are used in each stave. 8 planar sensors are placed in the central region, and4 full 3D sensors are placed on two sides of the stave. The design of the planar sensor
is similar to the original design for the pixel detector but has several improvements.
The 3D sensors have a better tolerance to a high fluence of the non-ionizing particles.

3.5.2

Silicon micro-strip tracker (SCT)The SCT consists of 2112 barrel modules assembled in 4 layers in the barrel region [22], and 1976 end-cap modules assembled in 18 disks in the end-cap region [23].
The sensors of SCT are made by classical single-sided p-in-n technology. A barrel
module contains four sensors. On each end, two sensors are connected in a daisy
chain to form 768 strips of approximately 12 cm in length. On the other side, theidentical sensors are glued back-to-back. The two identical sensors on both sides
are aligned with a stereo angle of 4 mrad. Each module is mounted at an angle of
11° to the tangent to the cylinder in the inner two layers and 11.5° in the outer twolayers. There are three different types of end-cap modules with trapezoidal sensors.
27

The modules with daisy-chained sensors are used in the outer and middle rings.
The modules with one sensor on each side are used in the inner rings. All end-cap
modules are similar to barrel modules. Two identical sensors are glued back-to-back.

3.5.3

Transition radiation tracker (TRT)The TRT also consists of barrel modules and end-cap modules in the total coverage
up to |η | < 2.0. The gas for the ionization is flowed in the straws. The radiators madeby the polypropylene are placed outside of the straw. The length of straws is 144
cm in barrel modules and 37 cm in end-cap modules. The tube wall is made in themultilayer, including a layer of aluminium as the cathode. The gold-plated tungsten
wires with the diameter of 31 µm kept at ground potential are in the center of the
straws.
For the barrel part, total of 96 modules are assembled into three layers of rings
from the inside to the outside. Each ring contains 32 modules. For the end-cap
module [24], the straws placed radially in a wheel with layers. Between straw layers,
layers of 15 µm thick polypropylene foils are filled. There are two different sets ofwheels. The set close to the barrel contains 12 wheels. Each wheel has 8 layers ofstraws spaced by 8 mm. The outer set contains eight wheels. Each wheel has 8 layersof straws spaced by 15 mm.
The standard gas mixture is 70% Xe, 27% CO2 , and 3% O2 . During Run2, as thegas leak in some modules was large, the gas mixture of 70% Ar, 27% CO2 , and 3% O2
is used instead. Although argon gas has much lower efficiency to be ionized by TR
photons, the tracking capacity is similar to the xenon gas.

3.6

Calorimetry

The calorimeters have wide coverage in the range of |η | < 4.9 and are designed tomeasure the energy of both neutral and charged particles. Two different technologies are used in the calorimeters. The liquid argon calorimeters [25] provides themeasurements of particles like electrons, positrons, photon, and hadronic particles.
The tile calorimeters [26][27] provide the measurements of hadronic particles. The
Liquid argon calorimeters (LAr) is located in the inner side of tile calorimeters in therange of |η | < 1.7, as shown in Figure 10.

28

Cells in Layer 3∆ϕ×∆η = 0.0245×0.05
Trigger Tow∆ η = er
0.1

2X 0

47

0

m

m

η =0

16X 0
Trigge
r
Tower
∆ϕ =
0.

0982

15

00

m

m

4.3X 01.7X 0∆ ϕ =0.0245x 436.8m
m=147.3 x 4mm

Square cel l s i n
L ay er 2

∆ϕ =
37.5m

m /8 =∆ η = 4.69 m m m
0.0031ϕ∆η =0.02450.025

Stri p cel l s i n L ay er 1
Cells in PS∆η×∆ϕ = 0.025 ×0.1
η

(a)

(b)

Figure 13: (a) Accordion structure of electrode plates and absorber plates. The lower
figure shows the details of the layers of plates and liquid argon gaps [28]. (b) A
schematic of cells in accordion electrons divided into three layers [29].
3.6.1

Liquid argon calorimeter (LAr)

The particle through the liquid argon causes the ionization of argon atoms. The freeelectrons drift in the electrical field. Since liquid argon needs low temperature andgood thermal insulation, the barrel part of the electromagnetic calorimeter (EMB) is
sealed inside of the barrel cryostat. Three sub-systems, an electromagnetic end-cap
calorimeter (EMEC), a hadronic end-cap calorimeter (HEC), and a forward calorimeter (FCal) [30] are in the end-cap cryostat for both sides. The EMB cover the range of|η | < 1.475. The EMEC covers the range of 1.375 < |η | < 3.2. The HEC covers in therange of 1.5 < |η | < 3.2. The FCal provides the coverage in the range of 3.1 < |η | < 4.9.
3.6.1.1

Barrel electromagnetic calorimeter (EMB) and end-cap electromagnetic
calorimeter (EMEC)

The absorbers in the calorimeters are lead plates glued between the two sheets ofthe stainless steel. The electrodes are three-layer copper-polyimide (Kapton) printed
circuit boards [31]. Both absorbers and electrodes are bent in an accordion geometry
to provide full coverage of absorbers and active material in the path of the particle.
The cylindrical detector is made of the absorbers interleaved with the electrodes andthe honeycomb spacer for the 2mm LAr gap (see Figure 13 (a)). The accordionshaped electrodes are divided into three layers: the front layer, the middle layer,
and the back layer (see Figure 13 (b)). The presamplers (PS) [32] are in front of the

29

(a)

(b)

Figure 14: (a) Cutout view of a HEC module [18]. (b) A schematic of the electrodes in
the gap between copper plates [18].
electromagnetic calorimeters in the range of |η | < 1.8 for the improvement of theenergy resolution. Except for the transition region between EMB and EMEC, thecells in the front layer have the finest granularity in η direction of the EMB (η × φ =0.003 × 0.1) but variable sizes in the EMEC to provide γ/π 0 separation. The cells in

the middle layer have the medium granularity in η direction (η × φ = 0.025 × 0.025

in EMB and EMEC). The cells in the back layers have the largest granularity (η × φ =0.05 × 0.025 in EMB and EMEC).
3.6.1.2

Hadronic end-cap calorimeter (HEC)

The hadronic end-cap calorimeter provides the measurements for the energy of hadronic
particles. The absorbers in the hadronic end-cap calorimeter are the copper plates
instead of the lead plates. Front wheels (HEC1) and rear wheels (HEC2) are oneach side of the end-cap. Each wheel is composed of 32 modules (see Figure 14 (a)).
Except for the front and rear copper plates which have only half of the thicknesses,
the thicknesses of the copper plates in the HEC1 and the HEC2 are 25 mm and 50
mm, respectively. The copper plates are bolted together by the stainless steel tie rods
and the annular spacers on the tie rods to maintain the 8.5 mm gap between two
copper plates (see Figure 14 (b)). Three electrode boards are arranged in the 8.5 mm
30

R

LAr gap

Beampipe
Warm
wall
Superinsulation
Cold
wall

(a)

(b)

Figure 15: (a) The array structure of anode rods, cathode tubes, and the LAr gaps
in the FCal1 module [18]. The magenta disk represents the Molière radius. (b) The
array of electrodes and the tungsten alloy slugs surrounded for the hadronic forward
calorimeters [18].
gap between copper plates and separated by honeycomb spacers. The honeycomb
spacers maintain the LAr gap of 1.8 mm between boards. The middle board contains
a layer of the copper as a read-out electrode.

3.6.1.3

Forward calorimeter (FCal)

The FCal modules are surrounded by the end-cap cryostats. Three modules on eachside are named as FCal1, FCal2, and FCal3 from the module close to the interaction
point. The FCal1 is designed as an electromagnetic calorimeter, and the FCal2 andFCal3 are hadronic calorimeters. The electrode rods for the readout are parallel to thebeam pipe and placed in the copper tube with PEEK fiber wrapped. The gap between
the copper tube and rod is filled with the LAr. Since the FCal modules are close to thebeam pipe, the high rate of the ionization is expected. To reduce the accumulation of
the charge, the LAr gaps of the FCal1, FCal2, and FCal3 are smaller than the nominal
LAr gap (∼2 mm), and they are 0.269 mm, 0.376 mm, and 0.508 mm, respectively.
For the FCal1, the material used in the rods and the matrix of the absorbers are thesame. The absorbers are copper plates with holes for the electrodes, as shown in
Figure 15 (a). For the FCal2 and FCal3, the rods are made by pure tungsten, but theabsorber slugs (see Figure 15 (b)) are made by the tungsten alloy (97% tungsten, 2%
nickel, and 1% iron).

31Photomultiplier

Wavelength-shifting fibre
Scintillator

Steel

Sourcetubes

Figure 16: A schematic of the structure of absorbers and scintillators in a tile
calorimeter module [18].
3.6.2

Tile calorimeter

The tile calorimeter [27, 33] consists of steel plates as the absorber and polystyrene
tiles as the scintillator. The scintillator is inserted in the pockets which are formed
between the master plates with trapezoidal shape divided by steel tiles, as shownin Figure 16. The scintillators are connected to the wavelength shifting fibers which
guide the light to the PMTs in the girder. The modules are installed side by side toform a cylinder.

3.7

Muon spectrometer

The muon spectrometer (MS) contains the barrel part and end-cap part. The muon
spectrometer covers the pseudorapidity range of |η | < 2.7. There are two purposesof the muon spectrometers. First, the precision momentum measurements are measured by the precision tracking chambers, which are the Monitored Drift Tube (MDT)
and the Cathode-Strip Chamber (CSC). Second, the trigger chambers provide muontracking information to the L1 trigger system. The Resistive Plate Chambers (RPC)
and the Thin Gap Chambers (TGC) are the trigger chambers.

32

Figure 17: The schematic of r-z cross-section view of the muon spectrometer [18]. The
dash lines show the muon trajectories with the infinite momentum.
3.7.1
3.7.1.1

Precision tracking chambers
Monitored Drift Tube (MDT)The cathode of the sensor is the aluminium tube with an inner diameter of 30 mm.
The gold-plated tungsten-rhenium wire (97% W and 3% Re) with a diameter of 50µm is the anode at the center of the aluminium tube, which is the cathode. The
tube is filled with 3 bara of Ar gas with a mixture of 93% Ar, 7% CO2 , and a few
hundred ppm of water vapor. The HV is applied between the anode and the cathode.
When the muon passes through the tube, the gas molecules are ionized, and theelectron avalanche occurs. The drift time of the electrons is up to 700 ns. The readout electronics is connected at the opposite end of the HV supply.
The MDT chambers are designed in three layers in the barrel region and threelayers in the end-cap region and cover in a range of |η | < 2.7. The layout of an

MDT chamber used in the barrel region is shown in Figure 17. The chambers arerectangular in the barrel region but trapezoidal in the end-cap region. There are twogroups of multi-layers in each chamber. In the innermost layer of chambers, there
are four tube layers for each group. In the middle and outer layers, three tube layers
are used. The four-tube-layer structure is used to enhance the performance of thepattern recognition.

33

Figure 18: The schematic of a module of Monitored Drift Tubes [18]. Four alignment
rays are used for monitoring the internal geometry. RO and HV mean the side ofconnection of readout electronics and the side for applying high voltage.
3.7.1.2

Cathode-Strip Chamber (CSC)

The CSC is located in the ATLAS small wheel behind the end-cap cryostats. The CSC
covers the pseudorapidity range of 2.0 < |η | < 2.7. In this region, the counting rate isover the limit of 150 Hz/cm2 for the MDT. The rate of CSC can deal with up to 1000

Hz/cm2 .
The CSC contains multiple anode wires and cathode strips, as shown in Figure 19. The wires which are the same material used in the MDT are in the radial
direction of the ATLAS detector. There are two types of the cathode planes in a CSC.
First, the cathode strips lie in the direction orthogonal to the anode wires. This setup
is targeting the space resolution of the η direction. Second, the cathode strips are in
the same direction of the wires to enhance the resolution of the φ direction. There
are also the small and the large chambers. The anode pitches are 5.3 mm in the smallchambers and 5.6 mm in the large chambers. The strip width is 1.5 mm in the smallchambers and 1.6 mm in the large chambers. The inter-strip gaps are the same. It is
0.25 mm. The gas mixture for the ionization is 80% Ar and 20% CO2 .

34

Figure 19: The cutoff views of the CSC design [18].
3.7.2
3.7.2.1

Trigger chambers
Resistive Plate Chambers (RPC)

The three layers of the RPC at the radius 7 m, 8 m 10 m from the interaction point
are in the barrel region and cover in the range of |η | < 1.05. There are two units ina layer. Each unit contains two gas volumes for the discharge. The plate is made ofphenolic-melaminic plastic laminate glued with graphite layers as electrodes. The
gas mixture of 94.7% C2 H2 F2 , 5% isobutane, and SF6 as the high resistive insulator isflushed through the gas volume. 9.8 kV is applied to the electrodes with 2mm gap.

3.7.2.2

Thin Gap Chambers (TGC)

The TGC is installed in the end-cap region for the muon trigger and compensationof the measurement of the MDT in azimuthal coordinate. TGC consists of multiple
wires with a diameter of 50 µm in the middle of 2.8 mm gap. Wire pitch is 1.8 mm.
The wall of the gap is coated with a graphite layer. The ionizing gas mixture of
55% CO2 and 45% n-pentane is flushed through the gas volume. The high voltage isapplied on the wire, and the graphite layer is grounded.
The outer ring of the TGC covers the range of 1.05 < |η | < 1.92. The inner ring of

the TGC covers the range of 1.92 < |η | < 2.4. The outer ring consists of one layerof triplet modules and two layers of the doublet modules to form a seven-layer
35structure. The inner ring of TGC only consists of one layer of double modules. The
honeycomb paper is used for the separation of the chambers.

3.8

Forward Detector for Luminosity measurement

The LUCID-2 detector (LUminosity measurement using Cerenkov Integrating Detector) [34] provides the main measurement of the instantaneous luminosity and theintegrated luminosity for the p-p scattering. The LUCID-2 is the upgraded versionof the LUCID detector described in the ATLAS detector paper [18]. The PMT withquartz window as Cherenkov medium is used. Four groups of 5 PMTs surround thebeam pipe at 14 m of both A-side and C-side. For each group, there is one MODIFIED
detector with reduced acceptance (φ = 7 mm but φ = 10 mm for the nominal one), one
LED detector for the calibration with LED signals, one BI detector for the calibration
with 207 Bi sources, and one SPARE detector with the same configuration of the LED
detector.

3.9

Trigger and Data Acquisition (TDAQ)

The trigger and data acquisition system plays an important role in the collider experiments. Only the data with interesting phase space is collected. The useful data
is identified online by the trigger system and stored to be analyzed offline. Trigger system at ATLAS consists of the hardware-based Level-1 trigger (L1) and thesoftware-based high level trigger (HLT) (see Figure 20).

3.9.1

Level-1 trigger

The decision of the L1 trigger are made by the Central Trigger Processor (CTP). The
CTP receives the signals from the L1 calorimeter (L1Calo) trigger, L1 muon (L1Muon)
trigger, L1 topological (L1Topo) trigger for the identified objects, signals from the
Minimum Bias Trigger Scintillators (MBTS), LUCID-2, and zero-degreecalorimeters (ZDC) [36].
The L1Calo trigger receives the signals from the calorimeters. The preprocessor
system digitizes and calibrates the analog signals from front-end boards and passes
the outputs to the Cluster Processor (CP) and Jet/Energy-sum Processor (JEP) in
parallel. The clusters of trigger towers are identified by the preprocessor system.
36

Calorimeter detectors
TileCalLevel-1 Calo

Detector
Read-Out

Level-1 Muon

Preprocessor

Endcapsector logic

Barrelsector logic

FE

FE

ROD

ROD

...

FE

Muon CTP
Interface(MUCTPI)
L1TopoCentralTrigger
Processor(CTP)

Central Trigger

Level-1
RoI

Fast TracKer(FTK)

Level-1 Accept

JEP (jet, E)

Pixel/SCT

CP (e,γ,τ)Muon detectors

High Level Trigger(HLT)
AcceptROD

DataFlow
Read-Out System (ROS)

Data Collection Network

Data Storage

Processors

Event
Data

Tier-0Figure 20: The schematics of the ATLAS TDAQ system in Run 2 with L1 trigger, HLT,
and read-out data flow [35]. The Fast Tracker project was closed in 2019 due to thelack of person power.
The CP system identifies the electron, photon, and τ candidates. The JEP system
identifies the jet candidates and produces the ETmiss . The L1Muon trigger identifies
the muon candidates by using the hits in the RPCs and TGCs if the coincidence of thehits satisfies the logic. The L1Topo trigger combines the geometry and kinematics of
the identified objects from the L1Calo or L1Muon systems. The rate of Level-1 trigger
reduces to the rate up to the maximum of 100 kHz from the bunch crossing rate ofabout 40 MHz. The latency of the process is less than 2.5 µs. The readout of thefront-end electronics is sent to ReadOut Drivers (ROD) for the initial processing andformatting. The data is buffered in the ReadOut System (ROS).

3.9.2

High level trigger

The software based high level trigger is the second stage of the trigger systems andcomposed of the computer farm of about 40,000 Processing Units. The HLT receives
the Region of Interests from the L1 trigger. The data rate is further reduced to 1.2 kHz
after the HLT. The events accepted by the HLT are sent to the permanent storage forthe offline analysis and exported to the Tier-0 facility at CERN’s computing center.

37

4

Samples and event reconstruction

For the search for the stops, with the R-parity conservation, the stops are produced0
in pair in the events. For both stops, the two-body decay channel, t̃1 → tχ̃1 , where0t → bW → bqq0 , is the target in this thesis. That is, the ∆m(t̃1 , χ̃1 ) is larger than mt

in this region. The final state contains four light quark jets, two b quark jets, andmissing transverse momentum.

4.1

Data and Monte Carlo simulation

4.1.1

Data selections and triggers

The full ATLAS Run2 data collected in 2015-2018 with 33.7 of the average number√of interactions per bunch crossing hµi at s = 13 TeV in the p-p collision is used inthis analysis. Figures 21 (a) and 21 (b) summarize the data collection in the full Run2.
The data is reprocessed offline for the use of physical analysis. All data is recordedin lumi blocks (one lumi block is 1 min). The final integrated luminosity of selected
data is 139 ± 2 fb−1 [38].
The events which pass the ETmiss triggers for the high ETmiss requirement in signal
regions and control regions or the single lepton triggers for the control regions [39]are used. The used triggers in the ATLAS Run2 change between data years and aresummarized in Tables 1 and 2, where the names include hardware-based first-level

ATLAS
140 Preliminary120

LHC Delivered
ATLAS Recorded100

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

Good for Physics

80
60
40
20

ATLAS Online, 13 TeV
500∫Ldt=146.9 fb-1

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

400
300
200
100
0
0

0

Jan

600

2/19 calibration

Recorded Luminosity [pb-1/0.1]

160

2/19 calibration

Total Integrated Luminosity fb-1

triggers (L1) and software-based high-level triggers (HLT).

'15 ul '15 an '16 ul '16 an '17 ul '17 an '18 ul '18
J
J
J
J
J
J
J

10

20

30

40

50

60

70

80

Mean Number of Interactions per Crossing

Month in Year

(a)

(b)

Figure 21: (a) Integrated luminosity and (b) hµi distribution during all the Run2
period [37].
38Table 1: Lowest unprescaled missing transverse energy trigger chains used for 2015,2016, 2017, and 2018 0- and 1-lepton selections [40].
Trigger chain names

2015

HLT_xe70_mht

X

2016

2017

2018

X
X
X

HLT_xe90_mht_L1XE50 (A-D3)
HLT_xe100_mht_L1XE50 (D4-F1)
HLT_xe110_mht_L1XE50 (F2-end)

XX

HLT_xe110_pufit_L1XE55 (B1-D5)
HLT_xe110_pufit_L1XE50 (D6-end)

XX

HLT_xe110_pufit_xe70_L1XE50 (B-C5)
HLT_xe110_pufit_xe65_L1XE50 (C6-end)

Table 2: Lowest unprescaled single lepton trigger chains used for 2015, 2016, 2017,and 2018 2- and 3-lepton selections [41][42]. A logical OR is performed between thevarious chains for a given year.
Trigger chain names

2015

HLT_e24_lhmedium_L1EM20VH

X

HLT_e26_lhtight_nod0_ivarloose

2016

2017

2018

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

HLT_e60_lhmedium
HLT_e60_lhmedium_nod0

X

HLT_e120_lhloose
HLT_e140_lhloose_nod0

X

HLT_mu20_iloose_L1MU15
HLT_mu26_ivarmedium

X

HLT_mu40
HLT_mu50

39

•Condition of the first level trigger (L1)

In L1 trigger, for example, “L1XE50” in Table 1 represents the met trigger with athreshold of 50 GeV. “L1MU15” in Table 2 represents the muon trigger with a threshold of 15 GeV. “EM” means the energy calculation is from electromagnetic calorimeters. The H denotes the veto of hadronic calorimeters for the electron candidates.
The absorption length depends on η for the material in front of the calorimeters. V
denotes the compensation of the effect by varying ET as a function of η.
•

Condition of the high level trigger (HLT)

Table 2 summaries the trigger chains with the HLT following the L1. The names ofparticle type are “xe” for the ETmiss , “e” for the electrons and “mu” for the muons. For
the ETmiss triggers [40], the number in the trigger names shows the transverse energy,
and three algorithms are used for the reconstruction of the ETmiss . First, the most basic
algorithm, “cell”, is to sum over all the calorimeter cells with the energy larger than
two times of the noise level. Second, a “mht” algorithm means the ETmiss is calculated
from the sum of all R=0.4 jets by using the anti-kt algorithm without the calibration.
Third, a “pufit” algorithm represents a fit to the signals below ET thresholds for thepile-up. The signals above the ET threshold are corrected by using the fit results. For
example, “HLT_xe110_pufit_xe65” denotes ETmiss threshold of 110 GeV in the “pufit”
algorithm and 65 GeV in the “cell” algorithm. Figure 22 shows the efficiencies of
the ETmiss triggers. For the electron triggers [41], the number shows the pT of theelectron. The “lhloose”, “lhmedium”, and “lhtight” denote working points of thelikelihood discriminant of the multivariate techniques. The “nod0” means the impact
parameter d0 and its significance are not included in the selections. The “ivarloose”
is an additional requirement for the track-only isolation for the electrons. In muon
triggers [42], the HLT_mu26_ivarmedium is designed to select low pT muon withthe loose isolation. The trigger rate is in control, and the efficiency remains high. The
HLT_mu20_iloose_L1MU15 is the lowest unprescaled version in 2015.

4.1.1.1

Monte Carlo simulation

A Monte Carlo (MC) method is used for the simulation of expected backgroundand signal samples. The nominal MC background samples are all produced by thefull ATLAS detector simulation modelled by GEANT4 [43], and some systematics
40

Same rate efficiency

1.2
ATLAS

1

Data 2018, s=13 TeV

0.8
0.6
L1 Emiss> 50 GeVT
Z→µ µ events

0.4

miss

ET (cell) > 92 GeV
miss

ET (pufit) > 116 GeV

0.2
0

miss

ET (cell) > 65 GeV andmiss
ET (pufit) > 110 GeV

0

50

100

150

200

250

300 350p (µµ) [GeV]T

Figure 22: Trigger efficiency in the 2018 data of Z→ µµ events as a function of offline
ETmiss [40]. Three different HLT algorithms, the “cell” algorithm alone, the “pufit”
algorithm, and the combination of the “cell” algorithm and “pufit” algorithm, areshown.
samples and signal samples are produced by the ATLFAST-II [44]. For the ATLFASTII, the electromagnetic and hadronic showers are parametrized in the longitudinaland lateral shower shapes in the calorimeters.
The real data contains multiple pp collisions, which are called pile-up, in one
bunch crossing. To simulate such pileup conditions, the MC samples are produced
for matching the pileup condition of the data. The pileup events are added withoverlaid minimum bias interactions generated by using P YTHIA 8 [45, 46] with A3
set of tuned parameters [47] and NNPDF2.3 LO PDF set [48].
Tables 3 and 4 summarize the generators, PDF, tunes for underlying events (UE),and the order of the perturbative calculations for the cross-sections of all MC nominal
samples used in the study of the stop analysis and DNN top taggers in Chapter 5. The
stop signal samples are generated with M AD G RAPH 5_aMC@NLO 2.6.2 [49] at the
next-to-leading order (NLO) in QCD. The parton showering and the hadronization
are simulated in P YTHIA 8, and the decay of c-hadrons and b-hadrons is modeledusing E VT G EN 1.6.0 [50]. The mixing of t̃L and t̃R is set to the maximum in thesignal samples. Each signal sample has its own pair of the stop mass and neutralinomass. Figure 23 shows the signal samples in the mt̃ -mχ̃0 plane. The Z/W+jets and1

diboson samples are generated by using S HERPA 2.2.1 [51] with NLO NNPDF2.3 set
for up to two jets at NLO and up to four jets at LO and the parton showering at NLO
level for the first and second jet and LO for the third and fourth jet. The tt̄W/Z, tZ,
tWZ, and tt̄H are generated by using MG5_aMC@NLO 2.3.3 (MG5_aMC@NLO 2.3.3
for tt̄H) interfaced to P YTHIA 8.230 (P YTHIA 8.212 for tWZ) with A14 set of tuned
41

~~
~
0
t t production : t → t∼
χ11mχ∼0 [GeV]

1000
800
600
400
200
0

400

600

800

1000

1200

1400
m~t [GeV]

Figure 23: Signal samples in the the mt̃ -mχ̃0 plane. Orange circles represent signal
1
mass points.
parameters and NLO NNPDF3.0 set. Both tt̄ and single top samples are generated
by using Powheg-Box v2 [52] interfaced to P YTHIA 8.230 with A14 set of tuned
parameters and NNLO NNPDF3.0 set. Alternative tt̄ samples are generated by using P OWHEG interfaced to H ERWIG 7 with H7UE tune [53] and aMC@NLO [49]interfaced to P YTHIA 8 with the A14 tune for the alternative parton showering andgenerator. Finally, multijet samples are generated by using P YTHIA 8.230 with LO
NNPDF2.3 set and A14 tune.
For MC samples used in DNN top tagger studies (see Chapter 5), Z 0 → tt̄ eventswith inclusive final state are generated by using P YTHIA 8 with A14 set of tunable

parameters and LO NNPDF2.3 PDF set. The resonant mass is set to 2 TeV, and thecross-section is reweighed to flat distribution in the 200 GeV < pT < 3 TeV. γ+jet
samples are generated by S HERPA 2.1.1 with NLO CT10 set. Vγ samples with V → qq0

states are generated by S HERPA 2.1.1 with LO CT10 set. tt̄+γ samples are generated
by MG5_aMC@NLO 2.2.3 interfaced to P YTHIA 8 with A14 set of tunable parametersand LO NNPDF2.3 set.

42

Table 3: Overview of the nominal simulated samples used in the stop analysis.
Process

ME event generator

ME PDFPS andhadronisation

UE tuneCross-section
calculation

Z+jets, W+jets
tt̄Z, tt̄W
tZ
tWZ
tt̄H

S HERPA 2.2.1
MG5_aMC@NLO 2.3.3
MG5_aMC@NLO 2.3.3
MG5_aMC@NLO 2.3.3
MG5_aMC@NLO 2.2.3

NNPDF3.0 NNLO
NNPDF3.0 NLO
NNPDF3.0 NLO
NNPDF3.0 NLO
NNPDF3.0 NLO

S HERPAP YTHIA 8.230
P YTHIA 8.230
P YTHIA 8.212
P YTHIA 8.230

Default
A14 [48]
A14
A14
A14

tt̄

Powheg-Box v2

NNPDF3.0 NNLOP YTHIA 8.230

A14Single top

Powheg-Box v2

NNPDF3.0 NNLOP YTHIA 8.230

A14

DibosonMultijet

S HERPA 2.2.1-2.2.2
P YTHIA 8.230

NNPDF3.0 NNLO
NNPDF2.3 LO

S HERPAP YTHIA 8.230

Default
A14

NNLO [54]
NLO [49, 55]
NLO [49]
NLO [49, 55]
NLO [49]
NNLO+NNLL[56, 57, 58, 59, 60, 61]
NNLO+NNLL[62, 63, 64]
NLO [49, 65]
NLO [66]

Stop signal

MG5_aMC@NLO 2.6.2

NNPDF2.3 NLO

P YTHIA 8.230

A14

NNLO [67, 68, 12, 69]

Table 4: Overview of the nominal simulated samples used in DNN top taggers.
Process

V+jets (V = W/Z )tt̄
Single top
DibosonMultijet
γ+jet
Vγ
tt̄γ
Z 0 → tt̄ME event generator

ME PDFPS andhadronisation

UE tuneCross-section
calculation

S HERPA 2.2.1
S HERPA 2.1.1
Powheg-Box v2
Powheg-Box v2
S HERPA 2.2.1
P YTHIA 8.230
S HERPA 2.1.1
S HERPA 2.1.1
MG5_aMC@NLO 2.3.3

NNPDF3.0 NNLO
CT10 NLO [70]
NNPDF3.0 NNLO
NNPDF3.0 NNLO
NNPDF3.0 NNLO
NNPDF2.3 LO
CT10 NLO
CT10 NLO
NNPDF2.3 LO

S HERPAS HERPAP YTHIA 8.230
P YTHIA 8.230
S HERPAP YTHIA 8.230
S HERPAS HERPAP YTHIA 8.212

Default
Default
A14
A14
Default
A14
Default
Default
A14

NNLO
NNLO
NNLO+NNLL
NNLO+NNLL
NLO
NLO
NLO [49]
NLO [49]
NLO [49]

P YTHIA 8.230

NNPDF2.3 LO

P YTHIA 8.230

A14

NLO [49]

43

4.2

Event reconstruction

In this section, the definitions of physical objects used in this thesis are introduced:
electrons, muons, taus, jets, and ETmiss . In our interested events, the final states arejets and ETmiss , and the leptons are vetoed.

4.2.1

Track reconstruction

Charged particles pass through the inner detector and produce signals in each layerof sensors. The trajectories of the charged particles are reconstructed as tracks. The
reconstruction of tracks is performed in three stages [71]:•

Clusterization

Charge particles usually produce signals in multiple pixel sensors of each layer.
These signals are clustered into clusters. The positions of the clusters are referredto three-dimensional “space-points”.
•

Iterative combinatorial track finding

Track finding starts from tracks seeds, which are sets of three space-points. To distinguish the track quality, the purity of tracks is introduced by categorizing the spacepoints in SCT-only, pixel-only or mixed detectors. A combinatorial Kalman filter [72]is used to reconstruct the preliminary tracks in the pixel and SCT detectors. Very highefficiency for the track reconstruction is achieved but there are also track candidates
with the space-points, which overlaps with other track candidates or are incorrectly
assigned.
•

Ambiguity solving

The quality of track candidates is determined by introducing a “track score”. The
track score of a track candidate depends on the weight of assigned clusters and holes
in the expected trajectory of the track. A χ2 fit for each track is also considered in
the track score. After the score is calculated, the track candidates with bad scores are
rejected, but the rest of track candidates also need to satisfy the following minimum
criteria:44

• pT > 500 MeV, |η | < 2.5,
• |d0 | < 2 mm, |∆z0 sinθ | < 3 mm,• Number of silicon clusters ≥ 7,
• Number of shared modules ≤ 1,
shared + N shared /2. N shared is the number(The shared module is defined as the NPix
SCT
Pixshared is the number of SCT clustersof pixel clusters shared by multiple tracks. NSCT

shared by multiple tracks)• Number of holes in silicon detectors ≤ 2,
• Number of holes in the pixel detector ≤ 1.
The d0 and z0 denote the transverse and longitudinal impact parameters with respect to the beam-line position and the primary vertex (see the next section). The
transverse impact parameters are defined as the shortest distance between the tracks
and the reference in the x-y plane. The longitudinal impact parameters are definedas the distance projected in the z-axis between the reference and the point with theshortest distance in the x-y plane.

4.2.2

Primary vertex

Event data of a bunch-crossing contains multiple inelastic pp interactions which canbe reconstructed as the primary vertices. The additional interactions are usually
soft-QCD interactions which are considered as pile-up events. The number of theinteractions per bunch crossing follows a Poisson distribution with the mean value

hµi, which can be estimated by using the instantaneous luminosity. Primary vertices

are constructed by fitting the track information of charged particles. The selected
tracks have to pass the stage of ambiguity solving with the following minimum
criteria:• pT > 500 MeV,
• |d0 | < 4 mm, σ (d0 ) < 4 mm, σ(z0 ) < 10 mm,• Number of silicon clusters ≥ 9,
• Number of SCT clusters ≥ 4,45

Average number of reconstructed vertices

60
50

ATLAS Preliminary
data 2018, s = 13 TeV
cyApril 〈µ 〉=45.5

40

n

co

n

re

tio
ac

r

20

te

%

0
0

io
ct

ef

tru
ns

30

10

n
ie

fic

June 〈µ 〉=47.1

in

0
10

10

20

30

40

50

60

70

80

Average number of interactions per bunch crossing

Figure 24: Distribution of the longi- Figure 25: Performance of the recontudinal impact parameter of the re- struction of primary vertices shown asconstructed tracks in the simulated a function of the average number ofH (130) → 4` events [73]. Signal primary interactions per bunch crossing with2018 data. The grey line shows 100%vertex is marked with a red arrow.
efficiency of the reconstruction.
• Number of holes in the pixel detector = 0,
where the definitions of d0 and z0 are different from the previous section, which
denote the transverse and longitudinal impact parameters with respect to the centerof the luminous region. σ (d0 ) and σ(z0 ) are the corresponding uncertainties.
The vertex seeds are identified by an iterative vertex finding algorithm [73]. The
global maximum of the number of tracks in the z-direction is selected as a vertex seed(see Figure 24). The adaptive vertex fitting algorithm [74] is used to fit the positionof the vertex seed and tracks around the seed by the χ2 method. The tracks with thedeviation of more than 7 σ are removed and used for the construction of the newvertex seeds. Figure 25 shows the average number of reconstructed primary vertices
as a function of hµi. The interactions, which can be estimated from the instantaneous

luminosity, are not fully reconstructed as the primary vertices. A hard-scattering
vertex is defined from a primary vertex with the highest sum of p2T of the tracks.

4.2.3

ElectronElectrons are reconstructed in the range of |η | < 2.47, where the inner detector isavailable. Electrons pass through the inner detector and reach the calorimeter leave
hits in the inner detector, and energy deposits in the calorimeter. The clusters ofcalorimeter cells are found by the topological-clustering algorithm [75]. The tracks
are reconstructed in three steps: pattern recognition, ambiguity resolution, and TRT46

extension. The reconstructed tracks are matched with the clusters by requiring the|ηcluster − ηtrack | < 0.05 and one of two selections of −0.1 < ∆φ < 0.05 and −0.1 <∆φres < 0.05. ∆φ and ∆φres are calculated as −q × (φcluster − φtrack ) where q is the signof the charge of the particle, and the momentum of the track is rescaled to the energyof the matched topo-cluster for ∆φres . The energy loss due to the path in the innerdetector is estimated by the Gaussian Sum Filter [76], and the correction is applied tothe clusters. The tracks with no pixel hit and associated with the conversion tracks
from the photon conversion reconstruction [77] are considered as the electrons fromthe conversion of a photon.
Electron identification is performed by the likelihood ratio method. The several
variables corresponding to the information of the calorimeters and tracking are considered in the PDF of the likelihood function. The detail of the variables can be foundin Table 5.
isol ) based on theElectron isolation is calculated by the “ET cone” observable (ET,conecalorimeter energy cluster and the “pT cone” observable (pTisol ) based on the tracks toestimate the activity in the vicinity of the electron candidates. For ET cone, the energy
contributed from other clusters in the vicinity is summed in the range of ∆R < 0.2
with the leakage and pile-up corrections. For pT cone, the pT of the surrounding
charged particle is summed. The cone in the inner detector is chosen to be the smaller
one due to the small size of sensors. The cone varies with pT and has the upper limitof 0.2. The energy thresholds are optimized in the bins of η and ET .
The energy and efficiency calibrations are performed with the samples of J/ψ →ee and Z → ee. J/ψ → ee samples are used in the derivation of scale factors1 in the

low pT region (4.5 GeV∼ 20 GeV). Z samples are used in the high pT range ( > 15
GeV).

Baseline electrons are reconstructed in the range of |η | < 2.47 and have the pT >4.5 GeV. The identification has to pass LooseAndBLayer criteria with the track-tovertex association (|z0 sinθ | < 0.5 mm) applied. The LooseAndBLayer criteria have arequirement of the likelihood discriminant, at least two hits in the pixel detector, a
hit in the IBL and total seven hits in the pixel and silicon strip detectors. The baseline
electrons are used in the requirement of lepton-veto to define the signal regions.
The definitions of signal electrons are based on the baseline electrons and used
for the control regions. Tight identification criteria, which is a tighter selection of
1 The scale factors are the ratios of the energy (efficiency) in data to the energy (efficiency) in MC.

47

Table 5: Variables used for the likelihood discriminant [78].
Type

Name

Description

Hadronic leakage

Rhad1

Ratio of ET in the first layer of thehadronic calorimeter to ET of the EM
cluster (used in |η | < 0.8 or |η | > 1.37)
Ratio of ET in the hadronic calorimeterto ET of the EM cluster (used in 0.8 <|η | < 1.37)

Rhad

Third layer of EM calorimeterf3

Ratio of the energy in the third layer tothe total energy in the EM calorimeter(used in ET < 80 GeV and |η | < 2.37)

Second of layer of EM calorimeterwη 2

Lateralq

RφRη

First layer of EM calorimeter

Eratiof1
Track conditions

d0|d0 /σ(d0 )|
∆p/p

TRT
Track-cluster matching

showerwidth,(∑ Ei ηi2 )/(∑ Ei ) − ((∑ Ei ηi )/(∑ Ei ))2 ,where Ei is the energy of the cell i withthe pseudorapidity η and the sum ofenergy is calculated within a windowof 3×5 cells
Ratio of the total energy in a windowof 3×3 cells to the total energy in awindow of 3×7 cells
Ratio of the total energy in a windowof 3x7 cells to the total energy in awindow of 7×7 cells
Ratio of the difference between the
maximum energy deposit and secondary energy deposit in the cluster
to sum of maximum and secondary
energyRatio of the energy in the first layer tothe total energy in the EM calorimeterTransverse impact parameter withrespect to the beam line
Significance of transverse impact parameter
Momentum loss divided by the momentum in a track. Momentum loss
is defined as the difference between
the perigee and the last measurement
point

eProbabilityHT

Likelihood probability based on transition radiation in the TRT∆η1∆η between the first layer of thecluster and the extrapolated track

φresq∆φ where q sign of electric charge and∆φ between the second layer of thecluster and momentum-rescaled track48

the likelihood discriminant, without the requirement of a hit in the IBL are further
isol /papplied. In addition, the Fix (Loose) isolation, which passes ET,cone
T < 0.20 andisol /ppT,var
T <0.15, is also required. The track-to-vertex association, d0 significance(d0 /σd0 ) < 5, is also applied.

4.2.4

Muon

The reconstruction of muons is available in the range of |η | < 2.7, where the muon

spectrometer has coverage, and are based on several reconstruction methods [79].
A combined (CB) muon is reconstructed from the refit of tracks in both ID and MS.
The hits in the MS can be added or removed in the refit process to improve the fit
quality. A segment-tagged (ST) muon is reconstructed from a track in the ID and an
associated local track in a segment of the CSC or the MDT. A calorimeter-tagged (CT)muon is reconstructed from a track in the ID and the associated deposited energy inthe calorimeters with the minimum-ionizing particle. An extrapolated (ME) muonis reconstructed from a track in the MS and a loose requirement of the interaction
points and is used in the range of 2.5 < |η | < 2.7.
For CB tracks, the requirements of significance of a ratio of the charge and momentum (q/p significance), the absolute value of pT difference in the ID and the MS
divided by CB muon pT (ρ’), and normalized χ2 fit are applied to guarantee a goodquality in the fit. Several thresholds are defined for different working points.
The track-based isolation and calorimeter-based isolation are considered in themuon isolation. The track-based isolation variable, pTvarcone30 , depends on a variable
cone size ∆R = min(10 GeV/pTu , 0.3) with pT > 1 GeV. The method of calorimeterµbased isolation is the same as the electron isolation. The variable, ETvarcone20 , is used
to estimate the activity in the range of ∆R < 0.2.
The Z → µµ and J/ψ → µµ are used for the calibration of the transverse mo-mentum and the efficiencies. The pT range of the calibration is available down to 4
GeV.
Baseline muons are reconstructed in the range of |η | < 2.7 and have pT > 4 GeV.

The identification has to pass the Medium criteria. Medium muons are identified byusing the CB and ME tracks. More than or equal to 3 hits in at least two MDTs layers
are required in CB tracks except for the |η | < 0.1 where at least one MDT layer but nomore than one hole in the MDT layers are accepted in the CB tracks. For ME tracks,49

hits in at least three MDT/CSC layers are required in the 2.5 < |η | < 2.7. The |z0 sinθ |< 0.5 mm is also applied.

Signal muons have to pass the same criteria of the baseline muon. In addition,
the isolation working point is required to be FixedCutLoose (FCLoose), which satisfiesµµpTvarcone30 /pT < 0.15, pTvarcone20 /pT < 0.30. The track-to-vertex association, d0 significance < 3, is also applied.
BadMuon is also defined to veto a muon with a significantly bad momentum
resolution. For the combined muon, the fit is performed with hits in the inner detector and muon spectrometer. The misalignment between two sub-detectors may notproperly be taken into account. If muons satisfy[σ(q/p)/(q/p)] ID[σ(q/p)/(q/p)] MS< 0.8 or< 0.8,[σ(q/p)(q/p)]CB[σ(q/p)(q/p)]CB(22)

which indicates that the resolution of the combined muon is much worse than the
resolution in the inner detector and muon spectrometer, the muons are labelled as
BadMuon. This kind of reconstructed muons causes a non-negligible impact on theanalysis. The events with the “BadMuon” muons are vetoed.
“Cosmic muons” are defined to satisfy |d0 | > 0.2 mm, |z0 | > 1 mm or |σ (q/p)/(q/p)| >0.2. The events with cosmic muons are vetoed.

4.2.5

Jet

Jets are reconstructed in two stages. First, the signals of calorimeter cells are clusteredby using the topological-clustering algorithm [75]. Second, the topo-clusters are
clustered into jets by using the anti-k t algorithm [80].
•Topo-clusters
A calorimeter cell with the absolute energy above 4σ of cell noise is treated asa seed. The expansion of a seed is performed to build a cluster if the energy ofneighborhood cells exceeds 2σ of the cell noise, but the expansion stops in the neighborhood cells with no more than zero σ of the cell noise. A negative energy of the cells
is possible since the cell signals are collected in the bipolar shape with a pedestal levelsustaining for several bunch crossings. The negative energy can be caused by thepile-up and the electronic noise and used in the clustering to cancel the contributionof the out-of-time pile-up. A cluster with two or more local maximums is split into50

clusters to keep the jet substructure and high quality of ETmiss reconstruction.
To deal with the nature of showering and the signal loss due to the strategy
of clustering, there are three corrections of the energy applied for the cell signals.
First, the cell signals are weighted with different scales, which are considered during
the reconstruction of topo-clusters for the different types of the showering. The
electromagnetic scale (EM scale) is set the weight to 1 since the electromagnetic
showering directly responds to the ionization of the argon. The local cluster weighting (LCW) is applied if the signals are from the hadronic showering. Second, thereconstruction of clusters may not contain whole energy of particles creating a single
shower. The out-of-cluster correction is taken into account that the signals is notin the neighborhood cells, and the shared signals are from other clusters. Third, thedead material correction is to compensate for the energy deposits in the dead material
in front of calorimeters or in the calorimeters.
•

Small-R jets
The topo-clusters with the EM scale correction are further reclustered to the R =0.4 jets by the anti-k t algorithm. The jet pT is required to be larger than 20 GeV andin the range of |η | < 2.8. The jet needs to be associated with the hard-scattering

vertex. The J ET V ERTEX TAGGER (JVT) algorithm [81] is used to veto jets from pile-up
vertices. The multivariate discriminant of the associated tracks with |η | < 2.5 is usedin the JVT. The JVT requirements are applied for the jets with pT < 120 GeV due to the
low rate of pile-up jets with pT > 120 GeV. The efficiency with JVT > 0.59 (|η | < 2.4)
and JVT > 0.11 (2.4 < |η | < 2.5) is 89 (95) % at 20 (60) GeV.

The jets can be originated from in non-collision background or the noise in thecells of the calorimeters [82], which are called fake jets. The relations between energy
depositing in the calorimeters and the energy from the tracks and the quality ofcell signals, for example, the pulse shape in comparison with the reference, in thecalorimeters are used as the discriminant for the signal jets and the fake jets. The jets
which do not pass the criteria are tagged as bad jets.
•

Large-R jets
The topo-clusters with LCW scale correction are further reclustered to reconstruct

jets with radius R = 1.0 by the anti-k t algorithm. The jets are called large-R jets. The
clusters inside a large-R jet, which are called “constitutes”, are reclustered to R = 0.2“subjets” by using k t algorithm. The grooming technique called “trimming” [83] isapplied to the large-R jets to reduce the effect of the pileup and soft radiations. If an
R = 0.2 subjet inside a large-R jet has pT smaller than 5% of large-R jet pT , the subjet
is removed from the jet. The large-R jets are required in the range of |η | < 2.0.
51

EM-scale jets

Origin correction

Jet area-based pileup correction

Residual pile-up
correction

Jet finding applied totopological clusters at
the EM scale.

Changes the jet direction
to point to the hard-scatter
vertex. Does not affect E.

Applied as a function of
event pile-up pT density
and jet area.

Removes residual pile-up
dependence, as afunction of 𝜇 and NPV.

Absolute MC-based
calibration

Global sequential
calibration

Residual in situ
calibration

Corrects jet 4-momentum
to the particle-level energy
scale. Both the energy anddirection are calibrated.

Reduces flavor dependence
and energy leakage effects
using calorimeter, track, andmuon-segment variables.

A residual calibration
is derived using in situ
measurements and isapplied only to data.

Figure 26: Full calibration stages for the jet energy scale in the small-R jets [84].
•Jet energy calibration
Figure 26 summarizes all the stages in the small-R jet calibration. The recon-

structed small-R jets need to be calibrated for energy based on truth information andthe location of hard-scattering vertex, which is often shifted from the center of thedetector. The jet axis is also corrected with respect to the hard-scattering vertex.
The pile-up correction is one of the most important corrections in the jet calibration. The MC samples are used for the pile-up estimation. The pile-up contributionof jet pT is derived by using the jet area estimated from the ghost-association [85] andmultiplying the jet area by the pT density of pile-up. There is still a residual pile-up
contribution after the aforementioned correction is performed. The residual pile-up
is corrected as a function of the number of primary vertices and hµi.
Next, jets need to be calibrated to the energy in the truth particle level (truth
particles which contribute energy deposits in the detector). The reconstructed jets arecompared to truth jets for the estimation of pT response. The truth jets are definedwith the stable truth particles with cτ > 10 mm. The muons and neutrinos are notincluded in the truth jets. The pT response is derived as a function of η since thetransition of detector structure causes biases on the jet reconstruction.
The global sequential calibration (GSC) further includes the information of muon
spectrometers and associated tracks to improve the jet energy resolution.
Finally, the pT correction derived with data events (in-situ calibration) is alsoneeded as the detector description used in the MC is not perfect. The four methods [84, 86] are used to calibrate the jet pT . The Z/γ+jet in low pT range and multijetbalance in high pT range are used for the jet in the central region. The pT of a recoiled
jet is corrected by the well-calibrated physical objects. For the η-calibration, the wellcalibrated jet in the central region is used to calibrate the jets in higher η region. The
relative small-R jet responses for the in-situ calibration are shown in Figure 27.
52

1.2

ATLAS
s = 13 TeV, 3.2 fb-1
anti-k t R = 0.4, EM+JES
115 < p avg < 145 GeV

Relative jet response

Relative jet response

1.3

Data
Powheg+Pythia
Sherpa

T

1.1

1.05
1
0.95
0.9

1.2

ATLAS
s = 13 TeV, 3.2 fb-1
anti-k t R = 0.4, EM+JES
1.2 < η < 1.5

Data
Powheg+Pythia
Sherpadet

1.1
1MC / data

MC / data

1

1.3

−4

−3

−2

−1

0

1

2

3

1.05
1
0.95

4
η

30 40

102

2×102

det

103
2×103
Jet p [GeV]
T

(a)

(b)

Figure 27: Relative jet response of small-R jets as a function of (a) η in 115 GeV <avg
avg
pT < 145 GeV and (b) pT in 1.2 < ηdet < 1.5 [84]. pT is the average pT between areference jet and a probed jet in the η-calibration. The lower panel shows the ratios
for the in-situ calibration smoothed by using the sliding Gaussian kernel.
For the large-R jets, the pile-up correction and GSC are not applied, but the MCbased and in-situ calibrations are applied. The methods of the in-situ calibration are
similar to the calibration for the small-R jets. The relative large-R jet responses forthe in-situ calibration are shown in Figure 28.
•

Large-R jet mass (mcomb )For a jet including the decay products of a massive particle, the decay products

may spread in a comparable scale of the granularity of the calorimeter cells. Combined mass (mcomb ) benefits from the measurement of energy in the calorimeter andthe finer angular resolution of tracking. The mcomb is the combination of the calo mass
(mcalo ) and track-assisted mass (m TA ) and defined as:
mcomb =

−2
σcalomcalo +
−2

−2
σcalo
+ σTA

−2
σTA

−2
−2
σcalo
+ σTA

m TA .

(23)

The calo mass is defined with the energy and momentum of the clusters as:
m

calo

=

s

→
( ∑ Ei )2 − ( ∑ −p i )2 .
i ∈jet(24)

i ∈jet

The track-assisted mass is defined with the ratio of the calo pT and track pT times
track mass (mtrack ) as:m TA =

pTcalopTtrack

mtrack ,(25)

where pTcalo is the transverse momentum of the large-R jet, and mtrack and pTtrack are theinvariant mass and the transverse momentum from four-vector sum of all associatedtracks in a jet. Both mcalo and m TA are calibrated with truth jet mass after the jet
53550 ≤ p

ATLAS
-1

avg
T

Relative jet response, R rel

Relative jet response, R rel

1.2< 700 GeV

s = 13 TeV, 36.2 fb , dijets
1.1

Trimmed anti-k t R = 1.0 (LCW+JES+JMS)

1

Powheg+Pythia

Data

SherpaMC / data

MC / data

1.1

s = 13 TeV, 36.2 fb-1, dijets

det< -0.4

Trimmed anti-k t R = 1.0 (LCW+JES+JMS)

1

Data

Powheg+Pythia

Sherpa

1.05

1.05
1

0.95
0.9
−2.5

1.1

0.9

0.9

-0.6 ≤ η

ATLAS

1

0.95

−2

−1.5

−1

−0.5

0

0.5

1

1.5

2

η

2.5

3×102

4×102

5×102

103

Large-R jet p [GeV]

det

T

(a)

(b)

Figure 28: Relative jet response of large-R jets as a function of (a) η in 550 GeV ≤avg
avg
pT < 700 GeV and (b) pT in -0.6 ≤ ηdet < -0.4 [86]. pT is the average pT between areference jet and a probed jet in the η-calibration. The lower panel shows the ratios
for the in-situ calibration smoothed by using the sliding Gaussian kernel.
energy scale is applied. The σcalo and σTA are the resolutions of the mcalo and m TA
obtained from the correction of jet mass between the truth jets and reconstructed jets.

4.2.6

VR Track jets

Variable Radius (VR) track jets are used only in the calibration of top taggers. VR
track jets are reconstructed from the tracks identified in the inner detector by theanti-k t algorithm. The track candidates must pass minimum criteria but with norequirements on the transverse impact parameter. The VR track jets are also required
to be originated from the hard-scattering vertex by using |∆z0 sinθ | < 3 mm. The
radius of the VR track jets depends on the jet pT [87]:ρ, Rmax
R → Re f f ( pT ) = max Rmin , min
pT


,

(26)

where the parameter ρ is used to optimize the performance and set to 30 GeV. Rminand Rmax are the range for the variation of the radius and set to 0.2 and 0.4, respectively. The VR track jets are required to satisfy pT > 5 GeV and |η | < 2.5.

54

4.2.7

Flavor tagging

The b-tagging is applied to small-R jets and VR track jets. The b-tagging algorithm isperformed in two levels [88] with the properties of the tracks.
At the first level, three types of low-level algorithms are performed. Tracks
matching with a small-R jet by requiring a ∆R as a function of the jet pT (0.45 for
pT = 20 GeV and 0.26 for jet pT = 150 GeV) or tracks in the VR track jets are used in
all algorithms. IP2D and IP3D algorithms are based on the impact parameters. The
IP2D uses the signed significance of the transverse impact parameter of the tracks
to construct the likelihood functions. The IP3D uses both the signed significanceof the transverse and longitudinal impact parameters. The likelihood ratios of bjet to light jet or c-jet are built for the discriminant. The secondary vertex tagging
algorithm (SV1) [89] uses each pair of tracks to reconstruct the vertex by the χ2
method. The likelihood ratio between b-jet and other jets is also used in this algorithm. Finally, the topological multi-vertex algorithms, JetFitter [90], uses tracks
to reconstruct the secondary vertices, which provides the topological variables toconstruct the likelihood functions for the b-tagging.
At the second level, a high-level MV2 algorithm which is a Boosted Decision
Tree (BDT) algorithm is used with the output of three low-level algorithms. The
weight of the BDT output is the final discriminant, as shown in Figure 29. The cuton the output weights is optimized for different cut-based working points of theefficiencies. Alternative DL1 algorithm based on a deep feed-forward neural network(NN) is also used for the second level. The working points of DL1 b-tagging are also
optimized based on the weight of the output.
The b-tagged small-R jets with MV2 selections in the stop analysis are required to
be in the range of |η | < 2.5 and pT > 20 GeV. A 77% efficiency of the selections derived

from the b-jets from t → Wb are used in the search for the stop. The backgroundrejections derived from the inversion of the efficiencies are 110 for light jets and 5 forcharm jets. The b-tagged VR track jets with a 77% efficiency of DL1 selections areused in the calibration of top taggers. The scale factors from the efficiency calibration
are derived from the tt̄ MC events.

55

Fraction of jets / 0.05

10

ATLAS Simulations = 13 TeV, tt

b-jetsc-jetsLight-flavour jets

1

10−1

10−2

10−3

10−4−1 −0.8 −0.6 −0.4 −0.2

0

0.2

0.4

0.6

0.8

1

DMV2

0.3

Simulation

0.25

tt events

Normalized

Normalized

Figure 29: Distribution of the output of the MV2 algorithm for the small-R jets fromb-jets, c-jets and light jets in the tt̄ simulated events.
τ jetsnon-τ jets

0.45
0.4

Simulation

0.35

tt events

τ jetsnon-τ jets

0.3

0.2

0.25

0.15

0.2
0.15

0.1

0.1
0.05
0
0

0.05
0.5

1

1.5

2

2.5

0

3

∆φ(jet,E

miss
T

0

2

4

6

8

)

10

12

14

16

18
Ntrk

(a)

(b)

Figure 30: Distributions of (a) ∆φ( ETmiss , jet) and (b) the number of tracks N trk forthe τ jets and non-τ jets in the particle level in the tt̄ events selected by using thepreselections in Table 10. The black arrows show the cut values for the hadronic tau
candidates.
4.2.8

Hadronic tau

Hadronic taus are also considered in the search for the stop since they can be reconstructed as jets. The hadronic tau candidates are selected from the small-R jetswith no b-tagging in the range of |η | < 2.5 and associated with four tacks or fewer.
The candidates also need to satisfy ∆φ( ETmiss , jet) < π/5 for the events with W →τν. Figure 30 shows the distributions of the ∆φ( ETmiss , jet) and the number of tracks

for the τ jets and non-τ jets with cut values for the identification of hadronic tau
candidates.

56

4.2.9Overlap removal

Muons, electrons, and jets are independently reconstructed. This can cause thatthe same low-level reconstructed objects may be identified as the different physicalobjects. To prevent the possible overlapping physical objects, the procedures ofoverlap removal are applied in order after each kind of objects is defined. The ∆Rbetween objects are used as the metric. The b-tagging working point in the overlap
removal is 85% to remove the electrons more aggressively. The hadronic taus andlarge-R jets, which are considered in the optimization of signal regions are not usedin the overlap removal.

•

Electron-jet
The energy of electrons depositing in the calorimeters may also be reconstructed

as a jet. If a non-b-tagged jet matches with an electron within ∆R < 0.2, the jet isremoved. To preserve the semi-leptonic b-jets which may also produce the electrons,
if an electron matches with a b-tagged jet within ∆R < 0.04 + 10 GeV/pelectronor ∆R <
T
0.4, the electron is removed.
•

Muon-jet
The π ± and K ± in the hadronic showering may produce the muons in-flight,

which is identified as a muon in the reconstruction stage. Also, as above, in theelectron-jet, a b-jet may also produce a muon. A muon with very high energy may
produce the electromagnetic showering in the calorimeters and is misidentified asa jet. To remove the overlapping, if a non-b-tagged jet with the number of tracks
smaller than three matches with a muon within ∆R < 0.2, the jet is removed. If a b-jet
matches with a muon within ∆R < 0.04 + 10 GeV/pmuon
or ∆R < 0.4, the muon isTremoved.

4.2.10ETmiss and object-based ETmiss significanceThe imbalance of the vector sum of the transverse energy of objects is defined as themissing transverse energy (ETmiss ) [91]. The ETmiss in the direction along x-axis andy-axis is defined as:jet

so f t,TST

eExmiss(y) = −( Ex (y) + Ex (y) + Ex (y) + Ex (y)
µ

57

),

(27)

A photon is not reconstructed as a photon object but treated as a jet in the calculation.
The well-reconstructed objects like electrons, muons, and jets are considered as thehard terms. The hard terms also need to pass the overlap removal. The tracks or theenergy deposits in the calorimeters which do not match the hard terms are includedin the soft term called Track-based soft term (TST). TST can remove the out-of-time
pile-up in the calorimeters, but the neutral particles are not included in the soft term.
Since the large ETmiss significance2 cannot be explained by the momentum resolution of hard terms which produce the imbalance of the transverse momentum andsuch large ETmiss significance can be produced by invisible particles in the detector,
object-based ETmiss significance [92] is introduced. This variable is based on the likelihood ratio of the probability of non-zero true ETmiss to the probability of zero true
ETmiss . The significance can be written as:sS=| ETmiss |2,
σL2 (1 − ρ2LT )(28)

with the relatively total longitudinal resolution (σL ) and the correlation factor between total longitudinal and transverse relative resolution (ρ2LT ) of all the objects.

2 Emiss significance is defined as Emiss /T
TqσEmiss .
T58

5

DNN top taggers and their calibration

The reconstruction of boosted objects becomes more important as the mass of interestof the stop search goes higher. In the final state of the production of a top anda neutralino from the stop with no lepton, it is possible to fully reconstruct top
quark decay products into a large-R jet. A multivariate Deep neural network (DNN)
algorithm is used to identify boosted objects reconstructed by using large-R jets. Thisis called a DNN top tagger.
The top taggers are trained with the Monte Carlo simulation samples. The truth
information of the large-R jets needs to be defined for both signal jets which arefrom top decay and background jets which are quark or gluon-initiated jets (q/g jets)
to develop top taggers. Large-R jet labeling is introduced in Section 5.1. Variables
used in the development as the inputs of the taggers to distinguish signal jets frombackground jets are explained in Section 5.2. A network model of DNN is describedin Section 5.3. The performance of top taggers is calibrated with signal jets andbackground jets in data. The results of the scale factors are shown in Section 5.4.

5.1

Large-R jet labeling

The size of the spread of the decay products (∆R) follows the relation of pT and massof the parent particle:
∆R ≈

2m
.
pT

(29)

When the mass is fixed, the ∆R becomes smaller as the pT goes higher. Figure 31
shows the study on the containment of a top decay at the truth level. When the
top pT is higher than 500 GeV, the large-R jet containing all the decay products
dominates. In the pT range of 200 GeV < pT < 500 GeV, the qb and qq are thedominant components. Below 200 GeV, the single b or single q becomes dominating.
To define a top in the jet at reconstruction level, the following criteria are required.
First, the R = 1 truth jet and large-R jet need to pass a criterion of ∆R( Jreco , Jtruth ) <0.75. Second, a top needs to pass the criterion of ∆R(top, Jtruth ) < 0.75 [94]. Then,a jet satisfies these criteria is labeled as “inclusive top.” A jet labeled as “contained
top” needs to pass, in addition to those, the selection of the truth jet mass larger than
140 GeV and one b-hadron in the jet with the ghost-association [85]. These criteria

59Top Quark Jet Labelling Efficiency

ATLAS Simulation
truth t → b q 1 q 2
anti-k t R =1.0 truth jets
1.4 |ηtrue| < 2

Top Jet Contains
b and q 1 and q 2
b and only q 1 or q 2
only q 1 and q 2
only bonly q 1 or q 2
none

1.6

1.2
1
0.8
0.6
0.4
0.2
0
0

500

1000

1500 2000 2500 3000
Truth Top Quark p [GeV]T

Figure 31: Ratio of the containment of top quark decay products in a matched anti-k t
R = 1.0 truth jet with respect to the top pT [93].
are generator-independent3 and can be applied to the samples generated from thedifferent generators.

5.2

Variables

The topology of topo-clusters inside a large-R jet is called “substructure”. The jet
substructure efficiently distinguish signal jets from the background jets since the top
0

decay produces separated constituents, corresponding to t → bqq , while a quark or
a gluon produces a single dense constituent surrounded by the soft radiation in ajet. Many studies show how to use the variable to describe the substructure. There
are 13 jet substructure variables used as the inputs of the DNN algorithm. Table 6
summaries all the variables.
Except for pT and combined mass mcomb , other 11 variables are explained asfollows:(i) N-subjettiness and its ratio
The N-subjettiness is defined as a function of the sum over pT of all the constituents multiplied by ∆R between constituents and the closest subjet among the
3 S HERPA does not contain the truth information of W bosons in truth level.

It is not possible tolabel a large-R jet based on the truth level partons. The ghost-associated b-hadron can be applicablefor all the MC samples.

60

Table 6: Summary of the variables used as the input of the DNN algorithm. β angularexponent is set to 1.
Observables
Jet kinematics
N-subjettiness and its ratio
Energy correlation ratios
Splitting scales
W reconstruction

variables

ReferencepT , mcomb
τ1 , τ2 , τ3 , τ21 , τ32, D2√e3 , C2√
d12 , d23
Qw

[95][96, 97][98, 99, 100]
[101, 102]
[103]

leading N subjets (defined in Chapter 4.2.5):
τN = ∑ pTi min{∆R1,i , ∆R2,i , · · ·, ∆R N,i },
β

β

β

β

(30)

i

where β is the angular weighting exponent analogous to the parameter in angularities [104]. β = 1 is found to contribute to the identification of the boosted
objects [97]. The jets with τN ≈ 0 are considered as jets with N (or fewer) subjets

since all the constituents are aligned with one of the leading N subjets. On theother hand, the jets with large τN represent at least N+1 subjets in the jets sincesome constituents distribute away from the selected subjets. Figure 32 shows all
the N-subjetttness variables used as inputs. q/g jets from multijet events distributein low τ2 and τ3 but high τ1 . Top jets have high τ1 and τ2 but low τ3 . Therefore, theτ2 shows good discrimination between top jets and q/g jets.
The N-subjettiness ratios are defined as:
τ21 =

τ2
,
τ1

τ32 =

τ3
,
τ2

(31)

which further enhance the discrimination.
(ii) Energy correlation function ratios
An energy correlation function (ECF) is a function of pT of the subjet and ∆R
between subjets within leading N subjets:
β

e2 =

∑

1≤ i < j ≤ N

zi z j ∆Rij
β

(32)

and
β

e3 =

∑

1≤ i < j < k ≤ N

zi z j zk ∆Rij ∆R jk ∆Rik
β

61

β

β

(33)

top jets
q/g jets

Simulation

0.07
0.06
0.05

Normalized

Normalized

Normalized

0.09
0.08

0.14
0.12

top jets
q/g jets

Simulation

0.1

0.3

top jets
q/g jets

Simulation

0.25
0.2

0.08

0.04

0.35

0.15

0.06

0.03
0.04

0.1

0.02

0.05

0.02
0.01
0
0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0
0

1

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

τ1

0.12

top jets
q/g jets

Simulation
0.1

0.08

0.1

0.1

0.04

0.04

0.02

0.02

0.3

0.4

0.2

0.25

0.5

0.6

0.7

0.8

0.9

0.35

τ3

top jets
q/g jets

Simulation

0
0

1

0.3

0.08

0.06

0.2

0.15

(c)

0.06

0.1

0.05

(b)
Normalized

Normalized

(a)

0
0

0
0

0.5

τ2

0.1

0.2

0.3

0.4

0.5

0.6

τ21

0.7

0.8

0.9

1

τ32

(d)

(e)

Figure 32: Comparison of shapes of (a) τ1 , (b) τ2 , (c) τ3 , (d) τ21 , and (e) τ32 in large-R
jets with simulated tt̄ samples (red) and multijet samples (blue). The contained top
definition is used for the identification of top jets. Angular weighting exponent, β, isset to 1. The truth jet mass is required within 140 GeV < mass < 200GeV.
with
zi =

pT,i
,
∑ j∈ N pT,j(34)

where β is the angular exponent. The C2 and D2 is defined as:
β

β

β
C2 =

e3
β

( e2 ) 2

,

β
D2 =

e3
β

( e2 ) 3.

(35)

The energy correlations are similar to the N-subjettiness. As a result, the energy correlations like en+1 are close to zero in the jets with n subjets, which is also the casein the N-subjettiness. Those variables show good separations of jets from QCD andZ bosons [105]. This is also the case in top quarks, as shown in Figure 33 (a) (b) (c).
(iii) k t Splitting Scales
The splitting scales (qdij ) are used in the k t jet algorithm. It is defined as:
s
q

dij =

R2ij
2
2
min( pT,i , pT,j ) 2 ,R(36)

with the reclustered jet radius R (R = 0.2 inside large-R jets) and pT,i of subjets.

62Normalized

Normalized

0.12

top jets
q/g jets

Simulation
0.1

0.08

0.12

0.08

0.06

0.06

0.04

0.04

0.02

0.02

0
0

top jets
q/g jets

Simulation
0.1

0.01

0.02

0.03

0.04

0.05

0.06

0
0

0.07

0.1

0.2

0.3

0.4

0.5

0.6

e3

C2

(b)
Normalized

Normalized

(a)
0.25

top jets
q/g jets

Simulation
0.2

0.15

0.24
0.22

top jets
q/g jets

Simulation

0.2
0.18
0.16
0.14
0.12
0.1

0.1

0.08
0.06
0.05

0.04
0.02

0
0

0.5

1

1.5

2

2.5

3

0
0

3.5

20

40

60

80

100

120

D2

160

180

200

Qw [GeV](d)Normalized(c)Normalized

140

0.14

top jets
q/g jets

Simulation
0.12
0.1

0.18
0.16

top jets
q/g jets

Simulation

0.14
0.12

0.08

0.1

0.06

0.08
0.06

0.04
0.04
0.02
0
0

0.02
20

40

60

80

100

120

140

160

180

0
0

200

10

20

30

40

d12 [GeV]

50

60

70

80

d23 [GeV]

(e)

(f)

√
Figure33:
Comparisonofshapes
of
(a)
e
,
(b)
C
,
(c)
D
,
(d)
Q
,
(e)
d12 , and (f)
w
3
2
2
√
d12 in large-R jets with simulated tt̄ samples (red) and multijet samples (blue). The
contained top definition is used for the identification of top jets. Angular weighting
exponent, β, is set to 1. The truth jet mass is required within 140 GeV < mass <200GeV.

63

Background rejection (1/ εbkg )200

ATLAS Simulation Preliminarys = 13 TeV
Trimmed anti- k t R = 1.0 jetsp > 350 GeV, |η| < 2.0

150

TTop tagger:
Contained, εsig = 50%
Contained, εsig = 80%
Inclusive, εsig = 50%
Inclusive, εsig = 80%

100

50

0

500

1000

1500 2000 2500 3000 3500

4000

Jet p [GeV]T

Figure 34: Background rejections as a function of jet pT for the contained andinclusive top taggers with both 50% and 80% efficiencies in multijet events [109].
Rejection is defined as the inversion of tagging efficiencies on background jets.
Figures 33 (e) and 33 (f) show the distributions of top and multijet samples. Morediscrimination power is observed in splitting scales between subleading and third
jets.
(iv) W reconstruction
The subjets reconstructed by using the k t jet algorithm are paired to reconstruct
the invariant mass of two subjets. The minimum mass is defined as the Qw . The
peak around W mass is observed in top jets, as shown in Figure 33 (d).

5.3

Network model of the taggers

The deep neural network is a fully-connected feedforward neural network trained in
the Keras framework [106] with the Theano backend [107] and Adam optimizer [108].
The detail of the DNN algorithm is described in Table 7. The jets passing mcomb > 40
GeV and N const ≥ 3 are used in the training. The input of jet truth pT is ranged from
200 GeV to 4 TeV. The truth pT is reweighted into a flat distribution to remove thebias of kinematics between the signal and background samples. The efficiency of
the taggers is determined by the cut value of the DNN output as a function of pT .
The taggers with 80% and 50% efficiencies of top-tagging in both definitions of thecontained top and inclusive top are developed in the ATLAS. Figure 34 shows the
background rejections of four taggers in multijet events.

64

Table 7: Parameters and architecture used in the training of the top taggers [93].
DNN top taggers
SoftwareLayer type
Number of hidden layers
Architecture
Activation function
Optimizer
Learning
L1 regulariser
NN weight initialization
Batch size
Batch normalization
Number of epochs

5.4

Keras 1.0.8 [106] with Theano backend [107], lwtnn 2.0 [110]Dense
518, 16, 14, 10, 5
Rectified linear unit (ReLU)
Adam [108]0.00005
0.001
Glorot uniform
200X
100 with early stopping

Calibration of the taggers

The top-tagging algorithm is trained using MC simulation, but it is calibrated using
data and MC to evaluate the deviation of efficiencies between the data and MC. The
scale factors of signal and background for the individual tagger are introduced forquantifying the deviations. The signal scale factors are derived in the events with thehigh purity of the semi-leptonic tt̄ events. The background scale factors are derived
in two different event selections. A set of selections that enhances γ+jet fraction isused for the low jet pT region. The selections to enhance the multijet fraction is used
for the high jet pT region. Baseline large-R jets used in the calibration are required tosatisfy pT > 200 GeV, |η | < 2.0, and mcomb > 40 GeV.
5.4.1

Region definitions

The selections for semi-leptonic tt̄ events are defined in Table 8. Only events containing exactly one muon and at least one large-R jet are used. A small-R jet is required
to be close to the muon for the b-jet from leptonic decay of the top quark. A b-tagged
VR track jet is also required to be in the leading large-R jet for the rejection of thejets from W bosons. The requirement of ETmiss is to select events with neutrinos. For
the events with low ETmiss , the selection on the transverse mass of the muon andETmiss can reduce the events with the significant mismeasurements of jet energies. The
data/MC distributions of important variables are shown in Figure 35. This method
covers the pT range from 350 GeV to 1000 GeV. The scale factors and uncertainties are
extrapolated from the last bin for the jet with 1000 GeV < pT < 3000 GeV due to low
65Table 8: Selections for the tt̄ events with one muon.
Variables
Trigger
N muon (pT > 30 GeV)
N electron (pT > 25 GeV)
ETmissETmiss +mWT
N small - R jet, pT >25 GeV, ∆R(jet,muon)<1.5
N large - R jet, pT >200 GeV
N b - tagged VR track jet∆R(leading large - R jet, b - tagged VR jet)single muon trigger
1
0>20 GeV> 60 GeV
≥1
≥1
≥1
< 1.0

statistics in high pT range.
To cover the full range of the jet pT , two selections of γ+jet and multijet events
are required, as shown in Table 9. A photon in the γ+jet events also needs to satisfy
pT > 155 GeV and the loose isolation for the region of high efficiencies in the single
photon trigger. At least one large-R jet is required for the jet calibration in the γ+jet
events. A leading large-R jet with pT > 500 GeV is required in the multijet events
duo to the high efficiencies of the single large-R jet trigger. Additional large-R jets
are considered as objects recoiled from the leading large-R jet. Due to the limited
statistics of the data events, the scale factors derived from γ+jet samples cover theleading large-R pT range from 350 GeV to 500 GeV, and the multijet region covers
the range from 500 GeV to 2500 GeV. Figures 36 and 37 show the data and MC
distributions of both regions. The significant deviations of P YTHIA γ+jet samples
are due to a bug in the MC production, which results in the overestimation of themodelling uncertainties.
Table 9: Definition of γ+jet region and multijet region.
Variables
Trigger
N large - R jet
N large - R jet, pT >500 GeV
N photon, pT >155 GeV

5.4.2
•

γ+jet

multijetsingle photon≥1≥1

single large-R jet≥2≥1-

Scale factors

Signal scale factors

66

104
3

10

1600

1200
1000
800

10

600

1

400

10−1

200

200 400
1.5

600

800 1000 1200 1400 1600 1800 2000

1
0.5
200 400

600

Data 2015-2017
t t (top)t t (W )t t (other)Single Top (W )Single Top (other)W + jets
VV , Z + jets
Total uncert.
Stat. uncert.
t t modelling uncert.

1400

102

Data/Pred.

Data/Pred.

Events / 5 GeV

Events / GeV

Data 2015-2017
t t (top)t t (W )t t (other)Single Top (W )Single Top (other)W + jets
VV , Z + jets
Total uncert.
Stat. uncert.
t t modelling uncert.

s = 13 TeV, 80.4 fb-1
Trimmed anti-k t R =1.0 jets5

10

800 1000 1200 1400 1600 1800 2000
Leading large-R jet p [GeV]

0
1.5

50

100

50

100

0

200

250

150
200
250
Leading large-R jet m comb [GeV](b)
Events / 0.02

Events / 0.12

3000

150

1

(a)
3500

T

0.5

T

4000

s = 13 TeV, 80.4 fb-1
Trimmed anti-k t R =1.0 jets
∆ R (large-R jet, b -jet) < 1.0
p > 350 GeV

Data 2015-2017
t t (top)t t (W )t t (other)Single Top (W )Single Top (other)W + jets
VV , Z + jets
Total uncert.
Stat. uncert.
t t modelling uncert.

s = 13 TeV, 80.4 fb-1
Trimmed anti-k t R =1.0 jets
∆ R (large-R jet, b -jet) < 1.0
p > 350 GeV
T

2500

1800
1600
1400
1200
1000

2000

Data 2015-2017
t t (top)t t (W )t t (other)Single Top (W )Single Top (other)W + jets
VV , Z + jets
Total uncert.
Stat. uncert.
t t modelling uncert.

s = 13 TeV, 80.4 fb-1
Trimmed anti-k t R =1.0 jets
∆ R (large-R jet, b -jet) < 1.0
p > 350 GeV
T

800
1500
600
1000

400

0
1.5

200
0.5

1

1.5

2

2.5

3

3.5

4

Data/Pred.

Data/Pred.

500

1
0.5
0

0.5

1

1.5

2

2.5
3
3.5
4
Leading large-R jet D 2

0
1.5

0.1

0.2

0.3

0.4

0.5

0.1

0.2

0.3

0.4

0.5

0.9

0.6 0.7 0.8 0.9
Leading large-R jet τ 32(d)
Events / 0.025

Events / 0.025

0.8

1

0

4000

3000

0.7

0.5

(c)
3500

0.6

Data 2015-2017
t t (top)t t (W )t t (other)Single Top (W )Single Top (other)W + jets
VV , Z + jets
Total uncert. (excl. tagger)
Stat. uncert.
t t modelling uncert.

s = 13 TeV, 80.4 fb-1
Trimmed anti-k t R =1.0 jets
∆ R (large-R jet, b -jet) < 1.0
p > 350 GeV
T
m comb > 40 GeV

2500
2000
1500

3000
2500
2000

Data 2015-2017
t t (top)t t (W )t t (other)Single Top (W )Single Top (other)W + jets
VV , Z + jets
Total uncert. (excl. tagger)
Stat. uncert.
t t modelling uncert.

s = 13 TeV, 80.4 fb-1
Trimmed anti-k t R =1.0 jets
∆ R (large-R jet, b -jet) < 1.0
p > 350 GeV
T
m comb > 40 GeV

1500
1000

1000
500

0
1.5

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Data/Pred.

Data/Pred.

500

1
0.5
0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
1
Leading large-R jet DNN top contained discriminant

0
1.5

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1
0.5
0

(e)

0.1

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
1
Leading large-R jet DNN top inclusive discriminant(f)Figure 35: Distributions of leading large-R jet (a) pT , (b) combine mass, (c)D2 , (d) τ32 , (e) DNN discriminant for the 80% contained top tagger, and (f) DNN
discriminant for the 80% inclusive top tagger in tt̄ event selections for both data andMC predictions.
67

1012

Data
Pythia8 (× 1.70)
Sherpa (× 2.23)
W+jetsZ+jetsall-had tt
Stat. uncert.
Total uncert.

-1

s = 13 TeV, 79.8 fb
Trimmed anti-k t R =1.0
Multijet Selectionp > 500 GeV

11

10

1010
9

10

Events / 8 GeV

Events / 50 GeV

1013

T

108

109

Data
Pythia8 (× 1.70)
Sherpa (× 2.23)
W+jetsZ+jetsall-had tt
Stat. uncert.
Total uncert.

-1

s = 13 TeV, 79.8 fb
Trimmed anti-k t R =1.0
Multijet Selectionp > 500 GeV

108

T

107
106

107
6

10

105

105
104

104

103

103

1.5
Data/Pred

Data/Pred

102
10
1.5

1.25
1
0.75
0.5
500

1000

1.25
1
0.75
0.50

1500
2000
2500
3000
Leading Trimmed large-R jet p T [GeV]

50

100

150

(a)
×10

Events / 0.02

Events / 0.1

Data
Pythia8 (× 1.70)
Sherpa (× 2.23)
W+jetsZ+jetsall-had tt
Stat. uncert.
Total uncert.

-1

3

300

350

×10

6

4.5

3.5

250

(b)

6

4

200

Leading Trimmed large-R jet combined mass [GeV]s = 13 TeV, 79.8 fb
Trimmed anti-k t R =1.0
Multijet Selectionp > 500 GeV
T

2.5

Data
Pythia8 (× 1.70)
Sherpa (× 2.23)
W+jetsZ+jetsall-had tt
Stat. uncert.
Total uncert.

6
5
4

2

3

1.5

2

-1

s = 13 TeV, 79.8 fb
Trimmed anti-k t R =1.0
Multijet Selectionp > 500 GeV
T

1
1

0.5

Data/Pred

1
0.75
0.50

Events / 0.02

1.5

0.5

1

1.5

2

108
107

3.5

0.50

4

Data
Pythia8 (× 1.70)
Sherpa (× 2.23)
W+jetsZ+jetsall-had tt
Stat. uncert.
Total uncert.

s = 13 TeV, 79.8 fb
Trimmed anti-k t R =1.0
Multijet Selectionp > 500 GeV
Tmcomb > 40 GeV

0.3

0.4

0.5

1010

0.6

0.7

0.8

0.9

108

106

105

105

104

104

3

103

s = 13 TeV, 79.8 fb
Trimmed anti-k t R =1.0
Multijet Selectionp > 500 GeV
Tmcomb > 40 GeV

1.5
Data/Pred

1.5

Data
Pythia8 (× 1.70)
Sherpa (× 2.23)
W+jetsZ+jetsall-had tt
Stat. uncert.
Total uncert.

-1

109

107

10

Data/Pred

0.2

(d)

106

1.25
1
0.75
0.50

0.1

(c)
-1

10

3

1
0.75

Leading Trimmed large-R Jet τ 32

1010
9

2.5

1.25

Leading Trimmed large-R Jet D 2

Events / 0.02

Data/Pred

1.5
1.25

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.25
1
0.75
0.50

1

Leading large-R jet DNN contained top tag discriminant

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Leading large-R jet DNN inclusive top tag discriminant

(e)

(f)

Figure 36: Distributions of (a) pT , (b) mass, (c) D2 , (d) τ32 , (e) DNN discriminant
for the 80% contained top tagger, and (f) DNN discriminant for the 80% inclusive
top tagger of the leading large-R jets in multijet selection for both data and MC
predictions. The ratios to the S HERPA and P YTHIA are the scale factor to the yields
from N data − N V + jets − N tt̄ .
68

Data
Sherpa γ + jet (× 1.51)
Pythia8 γ + jet (× 1.16)
Sherpa W/Z + γ
MG tt + γ
Stat. uncert.
Total uncert.

s = 13 TeV, 79.8 fb-1
Trimmed anti-k t R =1.0
γ + jet selection

108
107

Events / 5 GeV

Events / 40 GeV

109

6

10

107

Data
Sherpa γ + jet (× 1.51)
Pythia8 γ + jet (× 1.15)
Sherpa W/Z + γ
MG tt + γ
Stat. uncert.
Total uncert.

s = 13 TeV, 79.8 fb-1
Trimmed anti-k t R =1.0
γ + jet selection

106
105

105
104

104

3

10

103

102

102

10

1.5
Data/Pred

Data/Pred

1.5
1.25
1
0.75
0.5
200

400

600

1.25
1
0.75
0.550

800 1000 1200 1400 1600 1800 2000
Leading Trimmed large-R jet p T [GeV]

100

150

(a)
×10

Events / 0.02

Events / 0.1

300

350

×10

3

400

300

250

(b)

3

350

200

Leading Trimmed large-R jet combined mass [GeV]

Data
Sherpa γ + jet ( × 1.52)
Pythia8 γ + jet ( × 1.16)
Sherpa W/Z + γ
MG t t + γ
Stat. uncert.
Total uncert.

s = 13 TeV, 79.8 fb-1
Trimmed anti-k t R =1.0
γ + jet selection

250

Data
Sherpa γ + jet (× 1.51)
Pythia8 γ + jet (× 1.15)
Sherpa W/Z + γ
MG tt + γ
Stat. uncert.
Total uncert.

450
400
350
300

s = 13 TeV, 79.8 fb-1
Trimmed anti-k t R =1.0
γ + jet selection

250

200

200
150
150
100

100

50

50

Data/Pred

1
0.75
0.50

Events / 0.02

1.5

0.5

1

1.5

2

2.5

10

0.50

4

Data
Sherpa γ + jet (× 1.51)
Pythia8 γ + jet (× 1.16)
Sherpa W/Z + γ
MG tt + γ
Stat. uncert.
Total uncert.

-1

s = 13 TeV, 79.8 fb

7

106

109

0.5

0.6

0.7

0.8

0.9

106

10

104

103

103

2

10

102

10

10
1

−1
10
1.5

−1
10
1.5

Data/Pred

1

1.25
1
0.75
0.4

0.5

0.6

0.7

0.8

0.9

Data
Sherpa γ + jet (× 1.51)
Pythia8 γ + jet (× 1.16)
Sherpa W/Z + γ
MG tt + γ
Stat. uncert.
Total uncert.

s = 13 TeV, 79.8 fb-1

107
105

0.3

0.4

108

4

0.2

0.3

1010

105

0.1

0.2

(d)

108

0.50

0.1

(c)

10

Data/Pred

3.5

1
0.75

Leading Trimmed large-R Jet τ 32

1010
9

3

1.25

Leading Trimmed large-R Jet D 2

Events / 0.02

Data/Pred

1.5
1.25

1.25
1
0.75
0.50

1

Leading large-R jet DNN contained top tag discriminant

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Leading large-R jet DNN inclusive top tag discriminant

(e)

(f)

Figure 37: Distributions of (a) pT , (b) mass, (c) D2 and (d) τ32 , (e) DNN discriminant
for the 80% contained top tagger, and (f) DNN discriminant for the 80% inclusive top
tagger in the γ+jet selections for both data and MC predictions. The ratios next to the
S HERPA and P YTHIA are the scale factor to the yields from N data − N Vγ − N tt̄γ .
69

The signal jets which satisfy truth top labels (either contained tops or inclusive tops)
are from not only in tt̄ events but also the single top events with a hadronic decay
top. The jets with no truth top definitions in tt̄ events or single top events are treatedas non-tt̄ backgrounds. To derive the scale factors, the MC efficiency of tt̄ events inthe pT bin i is defined as:

passedeiMC =

Ni,signal
Total
Ni,signal.

(37)

The large-R jets tagged as top candidates are put in a pass category. If they are nottagged, they are put in a fail category. The simultaneous fit between pass and failcategories is performed in each pT bin independently by using the χ2 method. The
data efficiencies are defined as:
passedeidata =Ni, f itted signal
Ni,Totalf itted signal

,

(38)

where the number of fitted signal events are used. Hence, the scale factor for thepT bin i is defined as:

eidata

SFi =

•

eiMC

.

(39)

Background scale factors
The scale factors are derived as a function of pT and ln(mcomb /pT ) to reduce thescale factor uncertainties along with the top mass due to the correlation between jet
pT and mass. The MC efficiencies in each pT -ln(mcomb /pT ) bin are defined as:taggede MC =

Ndijet/γ+ jet
total
Ndijet/γ
+ jet

.

(40)

The data efficiencies are derived from the data events subtracted by other minor
physics process using MC samples,taggededata =

Ndata

tagged− NMC,others

total − N total
NdataMC,others

The scale factor is defined as a ratio of edata to e MC .

70

.

(41)

5.4.3

Systematic uncertainties on the scale factor estimation

Several theoretical and experimental uncertainties are considered for the uncertainties of scale factors. The theoretical uncertainties include the uncertainties of theprediction estimated by using a few different generators for the physics processes
and the varying the scales of parameters. The experimental uncertainties are uncertainties of the detector response dependent on the truth objects. The major sourcesof the uncertainties are described as follows:•

Jet energy scale uncertainties for large-R jets
The uncertainties on the jet energy scale (JES) from the jet response are needed tobe considered. The Rtrk method [111] is used to derive the large-R jet uncertainties.
The double ratio of the response of the jet moment in data and MC prediction is used,
and the response is defined as the ratio of the calorimeter to the matched track jet.
•Background modelling
The modelling uncertainties used in multijet and γ+jet events vary the back-ground scale factors. Alternative S HERPA samples for the multijet events and P YTHIA
samples for the γ+jet events is used to derive the uncertainties of background modelling that accounts for the effect on the different generators and parton showering.
•tt̄ modelling
The uncertainties of hard-scattering, parton showering, and QCD radiation are

considered in the tt̄ modelling. The alternative samples of P OWHEG interfaced to
H ERWIG 7 are used for the derivation of uncertainties of the parton showering. The
samples of aMC@NLO with the same showering configuration as the nominal samples are used to determine the uncertainties of the hard-scattering. The uncertainties
of initial/final state radiation are derived by varying the renormalization scale (µ R )for strong coupling at m Z , the factorization scale (µ F ) for the parton density function [112], and the parameters for the initial state radiation.
•

Flavor-tagging uncertainties
The uncertainties of both theoretical and experimental uncertainties are consid-

ered in the calibration of the DL1 b-tagging algorithm. There are nuisance parametersof the uncertainties provided from the calibration with true b-jets, c-jets, and light jets
and the extrapolation to high pT for true b-jets and c-jets.

71Data 2015-2017
PowhegPythia8
Total uncert.

0.5
600

800

1000

600
800
1000
Leading large-R jet p [GeV]T

Signal efficiency (∈sig)

Data/MC

1.5 400
1
0.5
400

1

s = 13 TeV, 80.5 fb-1µ+jets selection
Trimmed anti-k t R =1.0 jets
|η| < 2.0
Top tagger (∈sig = 80%): contained

1.5

Data/MC

Signal efficiency (∈sig)

1.5

1.5 400
1
0.5
400

1

s = 13 TeV, 80.5 fb-1µ+jets selection
Trimmed anti-k t R =1.0 jets
|η| < 2.0
Top tagger (∈sig = 80%): inclusive (incl.)

Data 2015-2017
PowhegPythia8
Total uncert.

0.5
600

800

1000

600
800
1000
Leading large-R jet p [GeV]
T

(a)

(b)

Figure 38: Signal efficiencies and scale factors (lower panel) of DNN (a) contained top
tagger and (b) inclusive top tagger with 80% efficiencies are derived as a function oflarge-R jet pT . The total uncertainties are evaluated in the quadratic sum.
5.4.4

Results

Figure 38 shows the results of the scale factors of DNN top taggers. JES uncertainties
for large-R jets and tt̄ modelling uncertainties are the dominated uncertainties of thescale factors. The scale factors are consistent with 1 within total uncertainties which
are around 6∼16%. The results show a good modelling of the signal jets in the MC

samples.

Figure 39 shows the background scale factors and total JES uncertainties, which
are the dominated uncertainties, in the two-dimensional plane. The empty bins arefilled by the average of their neighbors. The 2D Gaussian smoothing is applied to thescale factors and the uncertainties to reduce the fluctuation of statistics among bins.
The high scale factor uncertainties of ∼ 80% in the low ln(mcomb /pT ) of Figure 39 (c)and are mainly from the one variation of JES uncertainties, although the variation
contributes only ∼ 8% shift in the large-R pT . This has been verified by checking

the event migration. By shifting in pT , mass or both of pT and mass, it is foundthat the trained taggers are sensitive to the changing in mcomb /pT , which results
in propagated uncertainties become very high. For the DNN algorithm with 80%
efficiency on tagging contained top, the uncertainties are up to 80% in the low mass
region but the less than 20% around the true top mass in the range pT < 1 TeV. The
scale factors are around 0.9 ∼ 1.1.

72

−0.5

T

ln(m/p )Tln(m/p )

2

0

1.8

-1

s = 13 TeV, 79.8 fb

−1

1.6

−1.5

1.4

−2

2

0
−0.5

s = 13 TeV, 79.8 fb

−1

1.6

−1.5

1.4

1.2

−2

1.2

−2.5

1

−2.5

1

−3

0.8

−3

0.8

−3.5

0.6

−3.5

0.6

−4

0.4

−4

0.4

−4.5

0.2

−4.5

0.2

−5

−5

0
500 1000 1500 2000 2500 3000 3500 4000

500 1000 1500 2000 2500 3000 3500 4000

Leading large-R jet p [GeV]

T

(a)
T

ln(m/p )

T

(b)

0
−0.5

1.4

s = 13 TeV, 79.8 fb-1

−1

1.2

−1.5

0
−0.5

1.4

s = 13 TeV, 79.8 fb-1

−1

1.2

−1.5

1

−2

1

−2

0.8

−2.5
−3

0.8

−2.5
−3

0.6

−3.5

0.6

−3.5

0.4

−4

0.4

−4

0.2

−4.5
−5

0

Leading large-R jet p [GeV]Tln(m/p )1.8-1

500 1000 1500 2000 2500 3000 3500 4000

0.2

−4.5
−5

0

Leading large-R jet p [GeV]

500 1000 1500 2000 2500 3000 3500 4000

0

Leading large-R jet p [GeV]

T

T

(c)

(d)

Figure 39: Background scale factors of (a) contained top tagger and (b) inclusive top
tagger with 80% efficiencies and uncertainties of the scale factors propagated from
JES uncertainties with (c) contained top tagger, and (d) inclusive top tagger with 80%
efficiencies as a function of pT and ln(mcomb /pT ). “1” in uncertainty means a 100%
uncertainty of a scale factor. The red lines indicate the top mass.

73

6

Data analysis and results

6.1

Analysis overviews

The events are preliminary selected by using preselections based on the feature ofstop signals. After the event selections are applied by using the signal signatures,
further selections are considered to enhance the purity of stop signals and increase
the search sensitivity. Signal regions (SRs) are defined for the phase space expected
to contain more stop signals and less SM backgrounds to maximize the sensitivitiesof the search for the stop.
The backgrounds in the SRs need to be correctly estimated by introducing thecontrol regions (CRs) for each background process. By selecting a CR dominatedby a given background process and contaminated with the negligible signal, we cancontrol the background by comparing with the data sample in the CR. The topology
in the CRs is as close as possible to the topology in SRs. We can assume the same
behavior between the SRs and the CRs to apply the extrapolation from the CRs to theSRs. The validation regions (VRs) are used to validate the background estimations
from CRs. The VRs are defined in the phase space close to the SRs and have relatively
low signal contamination. The presence of the signal can be examined by using asimultaneous fit to the SRs and CRs.
The preselections are introduced in Section 6.2. The definitions of SRs are introduced in Section 6.3. The CRs and VRs are introduced in Section 6.4 for backgroundestimations. The statistical method and fit configurations are explained in Section 6.6.
The fit results are presented in Section 6.7.

6.2

Preselections
0

A stop (t̃) decays into a top quark and a neutralino (χ̃1 ), and our target channel isthe channel in which the top quark decays hadronically. There are two unknown
masses, mt̃ and mχ̃0 , in this channel. The decay topology and the optimal search
100strategy depend on the ∆m(t̃1 , χ̃1 ). In the region of medium to high ∆m(t̃1 , χ̃1 ), thefinal state is characterized by the existence of multiple small-R jets, large-R jets, btagged jets, high ETmiss and zero lepton. The large-R jets with DNN top taggers are a
key for the top-tagging, which are used in the definition of signal regions.
74

The preselections for the topology signatures are defined in Table 10. The first
five selections are required for all the regions in this analysis. The GoodRunLists
is the list of the recorded data with good conditions of detector operations. The
events affected by the noise of the detector signals or the incomplete information
are removed in Event Cleaning. Bad jets and bad muons (Chapter 4.2) are also
removed from the events. The requirement of the primary vertex is to ensure thehard-scattering in the events. Since the channel for the search is defined in the zero
lepton, the QCD backgrounds also need to be carefully taken into account. The
ETmiss > 250 GeV, min[∆φ( j1−4 , ETmiss )] > 0.4, and object-based ETmiss significance >5 suppress the QCD background. Figures 40 (a), 40 (b), and 40 (c) are the N−1

plots4 for min[∆φ( j1−4 , ETmiss )], object-based ETmiss significance and ETmiss . Owing to

the selections of three variables, the multijet background (orange in Figure 40) is
below 2% of total SM background in the event selections. The Njets ≥ 4 (the numberj2

of small-R jets in Figure 40 (e)), pT (subleading small-R jet pT in Figure 40 (f)),
j4

and pT (4th leading small-R jet pT ) are required to satisfy the criteria in the table
for the rejection of the backgrounds and retaining signal events. The Nb - jet ≥ 1(Figure 40 (d)) is also used for the rejection of the backgrounds with no b quarks.
The dominant backgrounds that remain after these preselections are tt̄Z, Z+jets, andtt̄. Diboson, single top, and W+jets are minor backgrounds.
Table 10: Definition of preselections based on the common signal signatures andevent cleaning
Variables

Preselection

GoodRunLists
Event Cleaning
Bad jet veto
Bad muon vetoNPV
baseline `ETmiss trigger
ETmissmin[∆φ( j1−4 , ETmiss )]Object-based ETmiss sig.
Njets
j
pT2
j
pT4
Nb - jet

X
X
X
X
≥1

0
X
> 250 GeV
> 0.4
>5
≥4
> 80 GeV> 40 GeV≥1

4 N-1 means all selections are applied except for the selections shown in the plots.

75

data
multijet
ttbar
Z+jetsW+jetsttZSingle Top
Diboson
Other

-1

1013

s=13 TeV, 36.2 fb~ ∼0m(t ,χ
)=(1100,1)~ 01
m(t ,∼
χ )=(1300,1)~ ∼ 01m(t ,χ 1 )=(700,400)

1011
10

9

EventsEvents

1015

107

1013

~ ∼0
m(t ,χ
)=(1100,1)~ 01
m(t ,∼
χ )=(1300,1)~ ∼ 01m(t ,χ 1 )=(700,400)

109
10

data
multijet
ttbar
Z+jetsW+jetsttZSingle Top
DibosonOther

s=13 TeV, 36.2 fb-1

1011

7

105

105
103

103

10

10

10− 1

Emiss
[GeV]
T

0.2
0.1
00

200

400

600

800

1000

1200

Emiss
[GeV]
T

Signal/SM

Signal/SM

10−1∆φ(jet

0.04
0.02
00

0.2

~ ∼0
m(t ,χ
)=(1100,1)~ ∼ 01m(t ,χ
)=(1300,1)~ ∼ 01m(t ,χ )=(700,400)

9

1

107

Events

109

1

107
105
103

10

10

10− 1

10− 1

miss

Object-based E

T

5

10

15

20

25

~ ∼0
m(t ,χ
)=(1100,1)~ ∼ 01m(t ,χ
)=(1300,1)~ ∼ 01m(t ,χ )=(700,400)

1011

3

0.3
0.2
0.1
00

Sig.

30

35

Object-based Emiss
Sig.
T

0.06
0.04
0.02
0

0

2

4

~ 0
m(t ,∼
χ )=(1100,1)~ ∼ 01m(t ,χ
)=(1300,1)~ 01
m(t ,∼
χ )=(700,400)
1

107

Signal/SM

Events

1013
1011
109

103

10

10

10− 1

10− 1

Njets
4

6

8

10

12

14

16

18

Njets

(e) Njets~ 0m(t ,∼
χ )=(1100,1)~ ∼ 01m(t ,χ
)=(1300,1)~ 01
m(t ,∼
χ )=(700,400)
1

105

2

data
multijet
ttbar
Z+jetsW+jetsttZSingle Top
DibosonOther

s=13 TeV, 36.2 fb-1

107

3

0.15
0.1
0.05
0 0

10

Nb-jet

105
10

8

1015

Signal/SM

Events1096(d) Nb - jetdata
multijet
ttbar
Z+jetsW+jetsttZSingle Top
DibosonOther

s=13 TeV, 36.2 fb-1

1011

1.2

Nb-jet(c) Object-based ETmiss sig.
1014
1013

1

data
multijet
ttbar
Z+jetsW+jetsttZSingle Top
DibosonOther

s=13 TeV, 36.2 fb-1

1013

105
10

Signal/SM

1015

Signal/SM

Events10

data
multijet
ttbar
Z+jetsW+jetsttZSingle Top
DibosonOther

s=13 TeV, 36.2 fb-1

1011

0.8

(b) min[∆φ( j1−4 , ETmiss )]

1015
10

0.6

miss

,ET )

∆φ(jet0~3,Emiss)
T(a) ETmiss
13

0.4

0~3

0.06
0.04
0.02
00

j2

p [GeV]
T

200

400

600

800

1000

1200

pj2T [GeV]j2(f) pT

Figure 40: Data/MC N-1 plots for the preselections. N-1 means the all selections
are applied except for the selections shown in the plots. The last bin contains theevents in overflow bin. The lower panel shows the ratios of signals of (mt̃ ,mχ̃0 ) =1(700,400) GeV (orange), (1100,1) GeV (purple), and (1300,1) GeV (pink) to the total
SM prediction.
76

6.3

Signal region definitions
0

To characterize the properties of the signal with varying ∆m(t̃1 , χ̃1 ) values, the benchmark points of signals (mt̃ , mχ̃0 ) = (1300,1) GeV, (1100,1) GeV, and (700,400) GeV are
1

used. Two signal points, (mt̃ , mχ̃0 ) = (1300,1) GeV and (1100,1) GeV, are chosen for
10

the large ∆m(t̃1 , χ̃1 ) regions, and one signal point, (mt̃ , mχ̃0 ) = (700,400) GeV, is for the10

medium ∆m(t̃1 , χ̃1 ). (1100,1) GeV is the point close to the exclusion limit of ATLAS
results at 36 fb−1 [113]. (1300, 1) GeV and (700,400) GeV are expected to be close to
the limit boundaries at 139 fb−1 .
The mT2 algorithm [114, 115] is used to reconstruct the stop transverse mass. In
general, the mT2 is expressed as:m T2 (mt , mχ̃0 , ~t1 , ~t2 , 6 ~p T ) =1min {max[ MT (mt , ~t1 ; mχ̃0 , p~1 ), m T (mt , ~t2 ; mχ̃0 , p~2 )]}, (42)~p1 +~p2 =6 p~T1

1

where the transverse mass m T is defined as:sm T (mt ,~t; mχ̃0 , ~p) =1

m2t + m2χ̃0 + 2
1

qm2t + |~t|2rm2χ̃0 + |~p|2 − 2~t · ~p.

(43)

1

mt and mχ̃0 represent top and neutralino mass, respectively. ~t(1/2) is the transverse
1

momentum of the top quark, and ~p(1/2) is the transverse momentum of the neutralinos. ~6 p is the Emiss vector. A top candidate is reconstructed by a vector sum of aTTb-tagged jet and one or two small-R light jets treated as a W boson. For only one
b-tagged jet in an event, the second b-tagged jet is selected from a light jet with thehighest b-tagging weight. The optimal combination of jets for two top candidates isdecided by the minimization of χ2 -like function:
χ2 =

2
2
true )2
true )2(mtop,1 − mtrue(mtop,2 − mtrue(mW,1 − mW
(mW,2 − mW
top )
top )
+
+
+
.
true
true
true
mW
mtrue
m
m
top
top
W
(44)

The true masses of the W boson and top quark are set to 80.4 GeV and 173.2 GeV,
respectively. The neutralino mass is set to 1 GeV. The mT2 based on the top candidates selected by the aforementioned χ2 -like function is expressed as the mT2,χ2 . The
0mT2,χ2 shows good separation of the signal points at large ∆m(t̃1 , χ̃1 ) ((1100,1)
0

GeV and (1300,1) GeV) and medium ∆m(t̃1 , χ̃1 ) ((700,400) GeV), as shown in Fig0
ure 41. At the boundary of 450 GeV, the signal point with medium ∆m(t̃1 , χ̃1 ) and77

Events

1011
1010

data
multijet
ttbar
Z+jetsW+jetsttZSingle Top
DibosonOther

s=13 TeV, 139 fb-1

109
108
107
106

~ 0
m(t ,∼
χ )=(1100,1)~ 01
m(t ,∼
χ )=(1300,1)~ ∼ 01m(t ,χ 1 )=(700,400)

105
104
103
102
10
1

Signal/SM

10− 1

1.5
1
0.5
00

mχT2 [GeV]
2

200

400

600

800

1000

1200

2
mχT2 [GeV]

Figure 41: mT2,χ2 distribution after the event selections with signal samples, (mt̃ , mχ̃0 )1= (700,400) GeV, (mt̃ , mχ̃0 ) = (1100,1) GeV, and (mt̃ , mχ̃0 ) = (1300,1) GeV, at 139 fb−1 .
1
1
The ratio of (mt̃ , mχ̃0 ) = (700,400) GeV is multiplied by 3. “Other” includes tZ, tWZ,
1
tt̄W, and tt̄H. Lower panel shows ratios of individual signals to total SM predictions.
0the signal points with large ∆m(t̃1 , χ̃1 ) are separated according to the optimal signal
0
significance. The signal of medium ∆m(t̃1 , χ̃1 ) with the upper cut of mT2,χ2 has better
signal significance than those without the upper cut. Owing to this behavior of thesignals, we define the signal region A (SRA) in large mT2,χ2 > 450 GeV region and thesignal region B (SRB) in mT2,χ2 < 450 GeV region.
The SRA has a highly boosted topology since the top quark is boosted due to0
the large ∆m(t̃1 , χ̃1 ). Figures 42 show the correlation between the maximal ∆R of
the daughter quarks (two quarks from W and one b quark) from the hadronicallydecaying top and the pT of top quark. The top quarks produced in the (1300,1)
GeV sample tend to have higher pT , and the ∆R of the final state particles becomes
smaller.
The top candidates from the DNN contained top tagger, and the inclusive top
tagger are used to categorize the signal regions. All the signal regions are required
to contain at least one contained top candidate due to higher background reduction.
Three categories, TT, TW, and T0, are designed to cover the possible topologies ofthe second top candidate to maximize the acceptance of the signals. “T” denotes thecontained top. “W” denotes the inclusive top, which is not identified as a contained78s = 13 TeV, 139 fb-1

Simulation

4.5∆Rmax(daughters)∆Rmax(daughters)s = 13 TeV, 139 fb-1

25

4
3.5

20

3
15

2.5
2

10

1.5
1

Simulation

4.5

0.7

4

0.6

3.5
3

0.5

2.5

0.4

2

0.3

1.5

0.2

1

5

0.5

0.1

0.5

0
0
0 100 200 300 400 500 600 700 800 9001000

000 100 200 300 400 500 600 700 800 9001000

top pTruth [GeV]

top pTruth [GeV]

T

T

(a)

(b)

Figure 42: The correlation plots of maximal ∆R of quarks from top decay and top
truth pT for the signal samples of (a) (mt̃ , mχ̃0 ) = (700,400) GeV and (b) (mt̃ ,mχ̃0 ) =1
1(1300,1) GeV.
top. “0” denotes that no second top candidate is identified.
The signal regions are also categorized by the number of the b-tagged jets tomaximize the sensitivity. Two categories, one for exactly one b-tagged jet and theother one for two or more than two b-tagged jets, are defined. The high backgroundrejection of the DNN top tagger enables us to use only one b-tagged jet region that
contributes to the sensitivity of the search.

6.3.1

Signal region A (mT2,χ2 > 450 GeV)

Table 11 shows the definitions of all six signal regions categorized by the top candidates and the number of b-tagged jets, which are optimized with the object based
ETmiss significance. The ETmiss is expected to be higher in the boosted regions so that the
cut value of object-based ETmiss significance is large. For the cut value optimization,
Figure 43 shows the N−1 plots with the expected discovery significance Z0,A basedon the profiled likelihood ratio test and Asimov approximation [116]:

v
"
#
"
#
u
2)
2s
2
u
(
s
+
b
)(
b
+
σ
σ
b
√
b
b
Z0,A = q0,A = t2((s + b)ln
) − 2 ln 1 +,b2 + (s + b)σb2
σbb(b + σb2 )(45)

where s denotes the total signal yield, b denotes the total background yield, and σb2
denotes the uncertainty of the total background. The lower panel of the plots shows
the significance calculated by integrating signal and background yields from therightmost bin to the current bin. The cut values are optimized with the significanceand the statistics to maximize the sensitivity. Tables 12 and 13 show the expected79

Table 11: Definitions of the signal region A in addition to the event selections inTable 10
Variables

SRATT

mT2,χ2NDNNFCtop80
Excl. NDNNInctop80
Nb - jetObject-based ETmiss sig.
τ veto

SRATW

SRAT0

> 450 GeV
≥2
1
1
≥1
0
≥2
1
≥2
1
≥2
1
> 20 > 22 > 20 > 22 > 28 > 28
X

Table 12: Signal region A with the number of b-tagged jets greater than or equal to
2 at 139 fb−1 . “Other” includes tZ, tWZ, tt̄W, and tt̄H. The relative ratios of eachbackground to the total background are shown in parentheses.
Regions

SRATT-2b

SRATW-2b

SRAT0-2bZ+jetstt̄Ztt̄
W+jetssingle top
dibosonothers0.14 ± 0.12 (17.3%)
0.45 ± 0.25 (56.2%)
0.07 ± 0.11 (8.8%)
0.04 ± 0.03 ( 5.1%)
0.06 ± 0.04 ( 7.2%)
0.00 ± 0.00 ( 0.0%)
0.04 ± 0.03 ( 5.4%)

0.53 ± 0.15 (24.2%)
0.80 ± 0.26 (36.1%)
0.34 ± 0.36 (15.5%)
0.17 ± 0.09 ( 7.9%)
0.28 ± 0.09 (12.6%)
0.02 ± 0.00 ( 0.8%)
0.07 ± 0.02 ( 3.1%)

1.24 ± 0.27 (46.8%)
0.50 ± 0.27 (19.0%)
0.11 ± 0.12 (4.2%)
0.41 ± 0.15 (15.4%)
0.32 ± 0.17 (12.2%)
0.05 ± 0.05 ( 1.9%)
0.01 ± 0.01 ( 0.4%)

0.00 ± 0.00
4.75 ± 1.86
2.01 ± 0.74

0.18 ± 0.19
4.87 ± 1.22
1.79 ± 0.51

0.00 ± 0.00
4.25 ± 1.01
1.96 ± 0.50

Total SM(mt̃ ,mχ̃0 )=(700,400)
1(mt̃ ,mχ̃0 )=(1100,1)
1(mt̃ ,mχ̃0 )=(1300,1)
10.81 ± 0.40

2.21 ± 0.49

2.65 ± 0.57

yields of the signals and backgrounds. The main backgrounds are tt̄Z and Z+jets.

6.3.2

Signal region B (mT2,χ2 < 450 GeV)To enhance the background rejection in the SRB, more variables are considered. The∆R (b1 , b2 ) is ∆R between the two b-tagged jets with the highest b-tagged weights.
This variable is used to remove the b-tagged jets from gluon-splitting, which is expected to have small ∆R (b1 , b2 ). The criteria of mTb,min and mTb,max aim to reduce thesemi-leptonic decay of the tt̄ events. If an unidentified lepton exists, the lepton is
expected to be merged into the ETmiss . The transverse mass of the b-tagged jet and theETmiss can be considered as the transverse mass of a top. The formula of transverse

80

10

~ ∼0
m(t ,χ
)=(1100,1)~ 01
m(t ,∼
χ )=(1300,1)~ ∼ 01m(t ,χ 1 )=(700,400)

10EventsEventsttbar
Z+jetsW+jetsttZSingle Top
DibosonOther

s=13 TeV, 139 fb-1
2

10

10− 1

miss

Object-based E

T

ZA

10− 1

ZA

1

Sig.

2
00

~ ∼0
m(t ,χ
)=(1100,1)~ 01
m(t ,∼
χ )=(1300,1)~ ∼ 01m(t ,χ 1 )=(700,400)

10

1

4

miss

Object-based E

2

T

5

10

15

20

25

30

00

35

Object-based ET

5

10

102

~ ∼0
m(t ,χ
)=(1100,1)~ ∼ 01m(t ,χ
)=(1300,1)~ ∼ 01m(t ,χ )=(700,400)
1

10

103

1

10− 1

ZA

miss

Object-based E

T

20

25

30

ZA

10− 1

15

~ ∼0
m(t ,χ
)=(1100,1)~ ∼ 01m(t ,χ
)=(1300,1)~ ∼ 01m(t ,χ )=(700,400)

10

1

10

Sig.
35

1.5
1
0.5
00

miss
T

5

10

15

ttbar
Z+jetsW+jetsttZSingle Top
DibosonOther~ 0m(t ,∼
χ )=(1100,1)~ ∼ 01m(t ,χ
)=(1300,1)~ 01
m(t ,∼
χ )=(700,400)

105
104

1

103

108

106

~ 0
m(t ,∼
χ )=(1100,1)~ ∼ 01m(t ,χ
)=(1300,1)~ 01
m(t ,∼
χ )=(700,400)

105

1

104
103

35

102

10

10
1

10− 1

10− 1

miss

Object-based E

2

T

5

10

15

20

25

30

ZA

1

ZA

30

ttbar
Z+jetsW+jetsttZSingle Top
DibosonOther

s=13 TeV, 139 fb-1

107

102

1
00

25

(d) SRATW-1b
EventsEvents

10

20

Sig.

Object-based Emiss
Sig.
T(c) SRATW-2b
s=13 TeV, 139 fb-1

35

Object-based E

Object-based Emiss
Sig.
T

6

30

ttbar
Z+jetsW+jetsttZSingle Top
DibosonOther

s=13 TeV, 139 fb-1

102

1

5

25

(b) SRATT-1b

ttbar
Z+jetsW+jetsttZSingle Top
DibosonOther

s=13 TeV, 139 fb-1

20

Object-based Emiss
Sig.
T

EventsEvents

103

15

Sig.

(a) SRATT-2b

107

Sig.

1

miss

3
2
1
00

ttbar
Z+jetsW+jetsttZSingle Top
DibosonOther

s=13 TeV, 139 fb-1
2

Sig.

miss

1

Object-based E

T

0.5
00

35

Object-based Emiss
Sig.
T

5

10

15

20

25

30

Sig.
35

Object-based Emiss
Sig.
T(e) SRAT0-2b(f) SRAT0-1b

Figure 43: N−1 plots of object-based ETmiss significance for the signal region A withthe cut value where the red arrows indicate. Full selections are applied except for theobject-based ETmiss significance at 139 fb−1 . “Other” includes tZ, tWZ, tt̄W, and tt̄H.
Signal samples, (mt̃ , mχ̃0 ) = (700,400) GeV, (mt̃ , mχ̃0 ) = (1100,1) GeV, and (mt̃ , mχ̃0 ) =1
1
1(1300,1) GeV are shown in the plots.
81

Table 13: Yields of the signal region A with one b-tagged jet at 139 fb−1 . “Other”
includes tZ, tWZ, tt̄W, and tt̄H. The relative ratios of each background to the total
background are shown in parentheses.
Regions

SRATT-1b

SRATW-1b

SRAT0-1b

Z+jetstt̄Ztt̄
W+jetssingle top
dibosonothers0.35 ± 0.22 (42.8%)
0.21 ± 0.09 (25.8%)
0.06 ± 0.07 ( 7.1%)
0.04 ± 0.02 ( 4.6%)
0.12 ± 0.07 (14.8%)
0.01 ± 0.01 ( 1.1%)
0.03 ± 0.02 ( 3.8%)

1.38 ± 0.41 (46.1%)
0.33 ± 0.13 (11.5%)
0.15 ± 0.13 ( 4.9%)
0.24 ± 0.12 ( 8.0%)
0.51 ± 0.13 (17.1%)
0.32 ± 0.16 (10.6%)
0.05 ± 0.01 ( 1.7%)

3.87 ± 1.05 (61.2%)
0.47 ± 0.36 ( 7.5%)
0.25 ± 0.12 ( 4.0%)
0.81 ± 0.44 (13.0%)
0.33 ± 0.46 ( 5.3%)
0.53 ± 0.10 ( 8.5%)
0.03 ± 0.01 ( 0.5%)

0.00 ± 0.00
2.39 ± 0.93
1.14 ± 0.56

0.29 ± 0.07
2.74 ± 0.81
1.16 ± 0.32

0.00 ± 0.00
2.83 ± 0.78
1.51 ± 0.38

Total SM0.82 ± 0.32

(mt̃ ,mχ̃0 )=(700,400)
1(mt̃ ,mχ̃0 )=(1100,1)
1(mt̃ ,mχ̃0 )=(1300,1)
1

3.00 ± 0.60

6.25 ± 1.88

Table 14: Definitions of the signal region B in addition to the event selections inTable 10
Variables

SRBTT

mT2,χ2NDNNFCtop80
Excl. NDNNInctop80
Nb - jet∆R (b1 , b2 )mTb,minmTb,max
Object-based ETmiss sig.
τ veto

SRBTW

SRBT0

< 450 GeV
≥2
1
1
≥1
0
≥2
1
≥2
1
≥2
1
> 1.4
> 1.4
> 1.4
> 200 GeV > 200 GeV > 200 GeV> 150 GeV
> 150 GeV
> 12
> 12
> 12
> 12
> 20
> 20
X

mass is as follows:
mb,min/max
=
T

q


2pbT ETmiss 1 − cos max / min[∆φ(b, ETmiss )] .

(46)

The four variables, including object-based ETmiss significance, are considered in the
optimization of the sensitivities (see the cut value in Figures 44 and 45). The definitions of six regions are summarized in Table 14. Tables 15 and 16 show expected
yields of the signal and backgrounds. The main backgrounds are tt̄ and Z+jets.

82ttbarZ+jetsW+jetsttZSingle Top
DibosonOther

s=13 TeV, 139 fb-1
102

EventsEvents103~ ∼0m(t ,χ
)=(1100,1)~ 01
m(t ,∼
χ )=(1300,1)~ ∼ 01m(t ,χ 1 )=(700,400)

10

103

10

1

10− 1

10− 1

miss

Object-based E

T

5

10

15

20

25

30

ZA

ZA

~ ∼0
m(t ,χ
)=(1100,1)~ 01
m(t ,∼
χ )=(1300,1)~ ∼ 01m(t ,χ 1 )=(700,400)

102

1

3
2
1
00

Sig.
35

1.5
1
0.5
00

miss

Object-based E

T

5

10

15

Object-based Emiss
Sig.
T

~ ∼0
m(t ,χ
)=(1100,1)~ ∼ 01m(t ,χ
)=(1300,1)~ ∼ 01m(t ,χ )=(700,400)

EventsEvents

102

1

10

25

30

35

(b) SRBTT-1b

ttbar
Z+jetsW+jetsttZSingle Top
DibosonOther

s=13 TeV, 139 fb-1

20

Sig.

Object-based Emiss
Sig.
T(a) SRBTT-2b
103

ttbar
Z+jetsW+jetsttZSingle Top
DibosonOther

s=13 TeV, 139 fb-1

104

s=13 TeV, 139 fb-1

103

~ ∼0
m(t ,χ
)=(1100,1)~ ∼ 01m(t ,χ
)=(1300,1)~ ∼ 01m(t ,χ )=(700,400)

102

ttbar
Z+jetsW+jetsttZSingle Top
Diboson
Other

1

10
1
1

10− 1

miss

1.5
1
0.5
00

Object-based E

T

5

10

15

20

25

30

ZA

ZA

10− 1

Sig.
35

0.6
0.4
0.2
00

miss

Object-based E

T

5

10

15

Object-based Emiss
Sig.
T

~ 0
m(t ,∼
χ )=(1100,1)~ ∼ 01m(t ,χ
)=(1300,1)~ 01
m(t ,∼
χ )=(700,400)

106
10

5

1

104

EventsEventsttbar
Z+jetsW+jetsttZSingle Top
Diboson
Other

107

103

30

35

(d) SRBTW-1b

109

s=13 TeV, 139 fb-1

25

Object-based Emiss
Sig.
T(c) SRBTW-2b
108

20

Sig.

1011
1010
10

ttbar
Z+jetsW+jetsttZSingle Top
DibosonOther

s=13 TeV, 139 fb-1

9

~ 0m(t ,∼
χ )=(1100,1)~ ∼ 01m(t ,χ
)=(1300,1)~ 01
m(t ,∼
χ )=(700,400)

108
107
106

1

105
10

4

103

102

102

10

10
1

1

1.5
1
0.5
00

10− 1

miss

Object-based E

T

ZA

ZA

10− 1

Sig.

miss

Object-based E

0.4

T

Sig.

0.2
5

10

15

20

25

30

00

35

Object-based Emiss
Sig.
T

5

10

15

20

25

30

35

Object-based Emiss
Sig.
T(e) SRBT0-2b(f) SRBT0-1b

Figure 44: N−1 plots of object-based ETmiss significance for the signal region B withthe cut value where the red arrows indicate. Full selections are applied except forthe object-based ETmiss significance. “Other” includes tZ, tWZ, tt̄W, and tt̄H. Signal
samples, (mt̃ , mχ̃0 ) = (700,400) GeV, (mt̃ , mχ̃0 ) = (1100,1) GeV, and (mt̃ , mχ̃0 ) = (1300,1)
1
1
1
GeV are shown in the plots.
83

102

s=13 TeV, 139 fb

ttbar
Z+jetsW+jetsttZSingle Top
Diboson
Other

-1

~ ∼0
m(t ,χ
)=(1100,1)~ 01
m(t ,∼
χ )=(1300,1)~ ∼ 01m(t ,χ 1 )=(700,400)

10

103

EventsEvents

103

102

1

10− 1

mb,min
[GeV]
T
200

400

600

800

1000

ZA

10− 1

ZA

~ ∼0
m(t ,χ
)=(1100,1)~ 01
m(t ,∼
χ )=(1300,1)~ ∼ 01m(t ,χ 1 )=(700,400)

10

1

3
2
1
00

ttbar
Z+jetsW+jetsttZSingle Top
DibosonOther

s=13 TeV, 139 fb-1

1200

3
2
1
00

∆R(b,b)
0.5

1

1.5

2

2.5

3

3.5

4

(b) SRBTT-2b ∆R (b1 , b2 )ttbar
Z+jetsW+jetsttZSingle Top
DibosonOther

s=13 TeV, 139 fb-1

102

EventsEvents(a) SRBTT-2b mTb,min

103

~ 0
m(t ,∼
χ )=(1100,1)~ ∼ 10m(t ,χ
)=(1300,1)~ ∼ 01m(t ,χ
)=(700,400)
1

10

103

~ 0
m(t ,∼
χ )=(1100,1)~ ∼ 10m(t ,χ
)=(1300,1)~ ∼ 01m(t ,χ
)=(700,400)
1

10

1

10− 1

mb,min
[GeV]
T
200

400

600

800

1000

ZA

10− 1

ZA

ttbar
Z+jetsW+jetsttZSingle Top
DibosonOther

s=13 TeV, 139 fb-1

102

1

1.5
1
0.5
00

1200

1.5
1
0.5
00

∆R(b,b)
0.5

1

1.5

2

2.5

3

3.5

4

(d) SRBTW-2b ∆R (b1 , b2 )(c) SRBTW-2b mTb,min
ttbar
Z+jetsW+jetsttZSingle Top
DibosonOther

s=13 TeV, 139 fb-1

102

EventsEvents

104

3

~ ∼0
m(t ,χ
)=(1100,1)~ 01
m(t ,∼
χ )=(1300,1)~ ∼ 01m(t ,χ 1 )=(700,400)

10

103

~ ∼0
m(t ,χ
)=(1100,1)~ 01
m(t ,∼
χ )=(1300,1)~ ∼ 01m(t ,χ 1 )=(700,400)

10

1

mb,min
[GeV]
T
200

400

600

800

1000

1200

ZA

10− 1

10− 1

ZA

ttbar
Z+jetsW+jetsttZSingle Top
DibosonOther

s=13 TeV, 139 fb-1

102

1

1.5
1
0.5
00

4.5

∆R(b,b)mb,min
[GeV]
T

10

4.5

∆R(b,b)mb,min
[GeV]
T

1.5
1
0.5
00

∆R(b,b)
0.5

1

1.5

2

2.5

3

3.5

(e) SRBT0-2b mTb,min

4

4.5∆R(b,b)mb,min[GeV]T(f) SRBT0-2b ∆R (b1 , b2 )Figure 45: N−1 plots of ∆R (b1 , b2 ) and mTb,min for the signal region B with the
cut value where the red arrows indicate. Full selections are applied except for the∆R (b1 , b2 ) (right side) or mTb,min (left side). “Other” includes tZ, tWZ, tt̄W, and tt̄H.
Signal samples, (mt̃ , mχ̃0 ) = (700,400) GeV, (mt̃ , mχ̃0 ) = (1100,1) GeV and (mt̃ , mχ̃0 ) =1
1
1(1300,1) GeV are shown in the plots.
84

Table 15: Yields in the signal region B with the number of b-tagged jet greater than orequal to 2 at 139 fb−1 . “Other” includes tZ, tWZ, tt̄W, and tt̄H. The relative ratios ofeach background to the total background are shown in parentheses.
Regions

SRBTT-2b

SRBTW-2b

SRBT0-2bZ+jetstt̄Ztt̄
W+jetssingle top
dibosonothers0.10 ± 0.04 ( 5.4%)
1.10 ± 0.29 (57.2%)
0.25 ± 0.29 (13.2%)
0.07 ± 0.03 ( 3.5%)
0.14 ± 0.03 ( 7.5%)
0.09 ± 0.03 ( 4.7%)
0.16 ± 0.04 ( 8.5%)

0.19 ± 0.11 ( 5.3%)
1.58 ± 0.41 (44.6%)
0.78 ± 0.53 (22.2%)
0.23 ± 0.09 ( 6.6%)
0.48 ± 0.30 (13.5%)
0.14 ± 0.04 ( 3.9%)
0.13 ± 0.03 ( 3.8%)

1.01 ± 0.36 (25.9%)
0.72 ± 0.38 (18.5%)
1.59 ± 0.35 (40.8%)
0.14 ± 0.12 ( 3.5%)
0.36 ± 0.15 ( 9.3%)
0.03 ± 0.04 ( 0.8%)
0.04 ± 0.04 ( 0.9%)

4.55 ± 1.89
1.25 ± 0.52
0.24 ± 0.11

3.30 ± 1.57
1.25 ± 0.41
0.30 ± 0.10

3.17 ± 2.11
0.62 ± 0.19
0.17 ± 0.05

Total SM(mt̃ ,mχ̃0 )=(700,400)
1(mt̃ ,mχ̃0 )=(1100,1)
1(mt̃ ,mχ̃0 )=(1300,1)
1

1.92 ± 0.50

3.53 ± 0.77

3.09 ± 0.84

Table 16: Yields of the signal region B with one b-tagged jet at 139 fb−1 . “Other”
includes tZ, tWZ, tt̄W, and tt̄H. The relative ratios of each background to the total
background are shown in parentheses.
Regions

SRBTT-1b

SRBTW-1b

SRBT0-1b

Z+jetstt̄Ztt̄
W+jetssingle top
dibosonothers0.60 ± 0.45 (13.7%)
0.97 ± 0.34 (21.5%)
2.12 ± 1.48 (48.7%)
0.37 ± 0.18 ( 8.5%)
0.08 ± 0.03 ( 1.9%)
0.10 ± 0.02 ( 2.3%)
0.14 ± 0.04 ( 3.3%)

3.41 ± 1.18 (20.5%)
0.90 ± 0.29 ( 5.4%)
6.89 ± 2.64 (41.5%)
3.41 ± 1.18 (20.5%)
0.92 ± 0.67 ( 5.6%)
1.11 ± 0.47 ( 6.7%)
0.30 ± 0.04 (1.8%)

8.63 ± 1.65 (40.8%)
1.27 ± 0.45 ( 6.0%)
5.35 ± 1.64 (25.3%)
3.62 ± 2.19 (17.1%)
0.61 ± 0.75 ( 2.9%)
1.60 ± 0.58 ( 7.6%)
0.06 ± 0.02 ( 0.3%)

3.27 ± 1.12
1.05 ± 0.47
0.26 ± 0.14

3.33 ± 1.54
1.32 ± 0.38
0.36 ± 0.12

3.64 ± 1.32
0.80 ± 0.27
0.18 ± 0.05

Total SM(mt̃ ,mχ̃0 )=(700,400)
1(mt̃ ,mχ̃0 )=(1100,1)
1(mt̃ ,mχ̃0 )=(1300,1)
1

4.35 ± 1.88

85

16.62 ± 3.13

21.14 ± 3.70

6.4

Background estimations

The background estimation using Monte Carlo simulation may be imprecise due topossible mismodelling in the simulation. To correctly estimate the background in
signal regions, the control regions of individual background components are definedand used to account for the discrepancies between the data and the simulation.
From Tables 12, 13, 15, and 16, we can conclude that there are three main backgrounds, tt̄Z, Z+jets, and tt̄. The control regions are defined to be orthogonal to thesignal regions, and the phase space of control regions is chosen as close as possible tothe signal regions. Three floating parameters, µtt̄Z , µ Z , and µtt̄ , are introduced as thenormalization factors of tt̄Z, Z+jets, and tt̄, respectively. The normalization factors
are determined by the simultaneous fit to all the control regions with the data (seeBackground-only fit in Chapter 6.6).
To validate the background estimations, the validation regions are also defined
as close as possible to the signal regions. The normalization factors are applied tocorrect the background yields in the validation regions and the corrected backgroundyields are compared with the data to confirm the fit results.
Figure 46 summarizes the control regions and validation regions by the numberof b-tagged jets and the number of leptons. The tt̄Z, Z+jets, and tt̄ backgrounds in all
the plots shown in this chapter are normalized with the normalization factors fromthe background-only fit, which is discussed in Chapter 6.7.

Nb - tagged jets

≥2
1

VRttZ

SRs
VRZ
VRT

CRT-2b
CRT-1b

CRZ

0

1

2

CRttZ

3

N leptons

Figure 46: Region definitions in the plane with a vertical axis of the number of btagged jets and a horizontal axis of the number of leptons. The SRs are the signal
regions. The VRZ and VRT are the validation regions of Z+jets and tt̄, respectively.
The CRT-1b and CRT-2b are tt̄ control regions defined in only one b-tagged regionand ≥ 2 b-tagged region, respectively. The CRZ is a Z+jets control region. The VRttZ
and CRttZ are a validation region and a control region for the tt̄Z, respectively.

86

q

q̄

q

0

0

W+ b

W+ b

t

t
g

q̄

g

ν̄

g

¯l

g

g

g
t̄

t̄

t̄ Z
b̄

W−

q

q̄

t̄ Z

ν

b̄

W−

0

l

(a)

l

ν̄

(b)

Figure 47: Diagrams of tt̄Z decay chains with (a) zero lepton and (b) three leptons.
6.4.1
6.4.1.1

Control regions
tt̄Z control region (CRttZ)

The tt̄Z events with Z → νν and fully hadronic tt̄ in the signal regions result in

the final states with high ETmiss and zero lepton. The tt̄Z is the main backgroundin the TT2b and TW2b regions and sub-dominant background in the TT1b region.
Figure 47 (a) shows the diagram of the dominant channel of tt̄Z in the signal region.
The control region of tt̄Z is defined by using three lepton region in which tt̄Z process
dominates (see Figure 47 (b)). To emulate the topology in the signal regions, the two
opposite-sign same-flavor leptons are required and the mass of two leptons should bein the mass window of Z boson (81GeV < m(`, `) < 101GeV). The ETmiss in three lepton
region is treated as a jet pT . The extra one lepton is also treated as a jet. Therefore,
the selection variables relative to jets, Njets and jet pT , contain the ETmiss and lepton
pT . The definition of variables is listed in Table 17. The number of DNN top tagged
jets, which reduces the data statistics significantly, is not considered in the definitionof the control region. For the boosted topologies in the tt̄Z control region, the pT andmass selections of leading Large-R jet are needed. Figure 48 shows the post-fit plots
for some variables. No significant mismodelling is found.

87s = 13 TeV, 139 fb
4

10

Data
tt
Z+jetsW+jetsttZSingle top
Dibosons
Others
SM

-1

CRttZ
PostFit103

EventsEvents

105

102

105
104
3

10

1

10−1

10−1

1.5

1.5

Data/SM1

Data/SM

10

1

50

100

150

200

250

300

CRttZ
PostFit

102

10

0.5
0

Data
tt
Z+jetsW+jetsttZSingle top
Dibosons
OthersSM

s = 13 TeV, 139 fb-1

350

1
0.5

400

400

500

600

700

800

900

mJ :R=1.0 [GeV](b) Leading large-R jet pT
EventsEvents

105

3

10

Data
tt
Z+jetsW+jetsttZSingle top
Dibosons
OthersSM

s = 13 TeV, 139 fb-1
CRttZ
PostFit

102

104

10−1

10−1

1.5

1.5

Data/SM1

Data/SM

1

1

84

86

88

90

92

94

96

98

PostFit

102
10

82

Data
tt
Z+jetsW+jetsttZSingle top
Dibosons
OthersSM

s = 13 TeV, 139 fb-1
CRttZ

103

10

0.5
80

1
0.5
0

100 102

100

200

300

400

500

600

700

(d) pT``
EventsEvents

105

10

Data
tt
Z+jetsW+jetsttZSingle top
Dibosons
OthersSM

s = 13 TeV, 139 fb-1
CRttZ
PostFit

102

105
104
103

10−1

10−1

1.5

1.5

Data/SM1

Data/SM

1

1

6

7

8

9

10

CRttZ
PostFit

102
10

5

Data
tt
Z+jetsW+jetsttZSingle top
Dibosons
OthersSM

s = 13 TeV, 139 fb-1

10

0.5
4

900 1000
T(c) m(`, `)3800

pll [GeV]m(l,l) [GeV]

104

1200

[GeV]

T

(a) Leading large-R jet mass

1041000 1100
J :R=1.0

p1

1

11

1
0.5
0

12

1

2

3

Njets

4

5

6

Nb-jet(e) Njets(f) Nb - jet

Figure 48: Post-fit plots for the tt̄Z control region. µ Z = 0.93 ± 0.12, µtt̄Z = 0.77 ±
0.22, and µtt̄ = 0.83 ± 0.04 are applied to Z+jets, tt̄Z, and tt̄, respectively. The shaded
area in the lower panel shows total uncertainties including systematic and statisticaluncertainties.
88Table 17: Definitions of tt̄Z control region in three lepton region.
Variables
signal `additional baseline `single lepton trigger

CRttZ
3, 2 with same flavor / sum of charge=±10Xm(`, `)
Njets
j
pT2
j
pT4
Leading pT`
Third pT`ETmissNb - jet
NDNNFCtop80
Leading Large-R jet pT
Leading Large-R jet masspT``
6.4.1.2[81,101] GeV≥ 4 (ETmiss included)> 80 GeV> 40 GeV> 27 GeV> 20 GeV≥1> 350 GeV
> 40 GeV> 150 GeV

Z+jets control region (CRZ)

The control region of Z+jets is defined in a region with two lepton events. The
events are selected using a single muon or single election triggers. The two oppositesign same flavor (OSSF) leptons are required. The leading lepton pT is required tobe larger than 27 GeV. The mass of two leptons is in the mass window between
81 GeV and 101 GeV. The muons or electrons from Z bosons are treated like the0neutrinos from Z bosons. Therefore, the pT of the dilepton system is used for ETmiss =+−|~pT`` | =|~pT` + ~pT` | in the Z+jets control region. The Z+jets with two leptons has

no true ETmiss since all the final states are detectable in the ATLAS detector. The
upper cut of ETmiss is required to reduce the other background contamination. The
requirement of Z+jets control region is in Table 18. The only-one b-tagged jet makes
CRZ orthogonal to the tt̄Z validation region. Figure 49 shows post-fit plots for somevariables. The data and MC predictions are in agreement after the normalization
factors are applied.

6.4.1.3tt̄ control region (CRT)

The tt̄ control region is defined to be dominated by tt̄ events with a lepton (seeFigure 50) since the fully-hadronic tt̄ is removed by requiring high ETmiss . Most of

89

104
103

EventsEvents

105

Data
tt
Z+jetsW+jetsttZSingle top
Dibosons
OthersSM

s = 13 TeV, 139 fb-1
CRZ
PostFit

102

105
104

PostFit

102

1

10−1

10−1

1.5

1.5

Data/SM1

Data/SM

10

1

82

84

86

88

90

92

94

96

98

CRZ

103

10

0.5
80

Data
tt
Z+jetsW+jetsttZSingle top
Dibosons
OthersSM

s = 13 TeV, 139 fb-1

1
0.5
200

100 102

300

400

500

600

700

800

0

(b) pT`` (ETmiss )EventsEvents

104

Data
tt
Z+jetsW+jetsttZSingle top
Dibosons
OthersSM

s = 13 TeV, 139 fb-1
CRZ
PostFit

103
102

105
104
103

1

10−1

10−1

1.5

1.5

Data/SM1

Data/SM

10

1

0.5

1

1.5

2

2.5

3

3.5

4

Data
tt
Z+jetsW+jetsttZSingle top
Dibosons
OthersSM

s = 13 TeV, 139 fb-1
CRZ
PostFit

102

10

0.5
0

4.5

1
0.5
0

5

10

20

30

103

EventsEvents

104

Data
tt
Z+jetsW+jetsttZSingle top
Dibosons
OthersSM

CRZ
PostFit

102

105
104

102

10−1

10−1

1.5

1.5

Data/SM1

Data/SM

1

1

6

7

8

9

10

11

12

CRZ
PostFit

10

5

60

Data
tt
Z+jetsW+jetsttZSingle top
Dibosons
OthersSM

s = 13 TeV, 139 fb-1

103

10

0.5
4

50

(d) ETmiss(c) NDNNFCtop80
s = 13 TeV, 139 fb-1

40

Emiss
[GeV]
T

NDNNFCtop80

105

1000

T

(a) m(`, `)
105

900

pll [GeV]m(l,l) [GeV]

13

1
0.5

14

10

15

20

25

30

Object-based Emiss Sig.

Njets

T

(f) Object-based ETmiss sig.

(e) Njets

Figure 49: Post-fit plots for the Z control region. µ Z = 0.93 ± 0.12, µtt̄Z = 0.77 ±
0.22, and µtt̄ = 0.83 ± 0.04 are applied to Z+jets, tt̄Z, and tt̄, respectively. The shaded
area in the lower panel shows total uncertainties including systematic and statisticaluncertainties.
90

Table 18: Definitions of Z+jets control region in two lepton region.
Variables

CRZX
2, same flavor / opposite sign0

single lepton trigger
signal `additional baseline `Leading pT`
Subleading pT`m(`, `) 

1−4min ∆φ jet00, ETmiss> 27 GeV> 20 GeV[81,101] GeV
> 0.4



ETmissETmiss
Njets
j
pT2
j
pT4
Nb - jet
NDNNFCtop80
0
Object-based ETmiss sig.

> 250 GeV
< 50 GeV≥4> 80 GeV> 40 GeV
1≥1> 12

W bosons decay into a τ and a neutrino in signal regions where the τ has pT lower
than 20 GeV since the tau-veto is also required in the signal regions. In the tt̄ control
region, the ETmiss trigger is used. One baseline lepton is required. The lower boundof the baseline lepton pT is very low (4.5 GeV for muons and 5 GeV for electrons).
The pT of muons or electrons is required to be lower than 20 GeV so that muons orelectrons in the control region can mimic τs in the signal regions. The definitions of
the tt̄ control region are in Table 19. To account for the effect due to the requirementof a different number of b-tagged jets in the signal regions, the 1b and 2b regions aredefined. Figures 51 and 52 show the post-fit plots for the variables. The fit works
well, and no significant mismodelling is found.

6.4.2
6.4.2.1

Validation regions
tt̄Z validation region (VRttZ)

The tt̄Z is the main background in SRAs but it is difficult to find a tt̄Z validation region with high statistics of tt̄Z in the zero lepton final states. Therefore, the tt̄Z validation region is finally defined with two lepton events (see Table 20). The single lepton
trigger is used. The OSSF leptons with the dilepton mass falling in the window (81
GeV < m(`, `)< 101 GeV) are required to select events with a Z boson. The number of
91

q̄

0

q
b
W+
g

g

t̄
t

g

b̄
W−
l

ν̄

Figure 50: Diagram of semi-leptonic tt̄.

Table 19: Definitions of tt̄ control region with one lepton. CRT-1b and CRT-2b are
defined in the region with only one b-tagged jet and more than two b-tagged jets.
Variables

CRT-1b

CRT-2b

ETmiss trigger
baseline `p`TX1< 20 GeV

Njets
j
pT2
j
pT4
NDNNFCtop80
mT `, ETmiss
Object-based ETmiss sig.
∆R (b1 , b2 )Nb - jet≥4> 80 GeV> 40 GeV≥1< 120 GeV
> 12
> 1.4
1
≥2

92

105
104

s = 13 TeV, 139 fb

EventsEvents

106

Data
tt
Z+jetsW+jetsttZSingle top
Dibosons
OthersSM-1

CRT-1b
PostFit

3

10

2

10

106
105
104

102

10−1

10−1

1.5

1.5

Data/SM1

Data/SM

1

1

400

600

1
0.5
0

800 1000 1200 1400 1600 1800 2000
Emiss
[GeV]
T

CRT-1b
PostFitEventsEvents

103
102

105

102

10−1

1.5

1.5

Data/SM

10−1
Data/SM

1

1

3

4

5

6

7

8

PostFit

103

1

2

50

9

1
0.5
0

10

2

4

6

8

10

12

14

16

NDNNFCtop80

EventsEvents104

s = 13 TeV, 139 fb
CRT-1b
PostFit

103
102

105

s = 13 TeV, 139 fb-1
CRT-1b
PostFit

3

10

102

Data
tt
Z+jetsW+jetsttZSingle top
Dibosons
Others
SM

10

1

1

−1

−1

10

10

1.5

Data/SM

Data/SM

106

104

10

1
0.5
0

20

(d) Njets
Datatt
Z+jetsW+jetsttZSingle top
Dibosons
Others
SM

-1

18

Njets

(c) NDNNFCtop80
105

60

Data
tt
Z+jetsW+jetsttZSingle top
Dibosons
OthersSM

s = 13 TeV, 139 fb-1
CRT-1b

104

10

1

40

106

10

0.5
0

30

T

Data
tt
Z+jetsW+jetsttZSingle top
Dibosons
OthersSM

s = 13 TeV, 139 fb-1
10420(b) Object-based ETmiss sig.

106
10

10

Object-based Emiss Sig.

(a) ETmiss

5

PostFit

10

10

200

CRT-1b

3

10

0.5
0

Data
tt
Z+jetsW+jetsttZSingle top
Dibosons
OthersSM

s = 13 TeV, 139 fb-1

20

40

60

80

100

1.5
1
0.5
0

120

200

400

600

800 1000 1200 1400 1600 1800 2000

mT(l,Emiss) [GeV]

mT2,χ2 [GeV]

T


miss

(e) mT `, ET(f) mT2,χ2

Figure 51: Post-fit plots for the tt̄ control region with one b-tagged jet. µ Z = 0.93
± 0.12, µtt̄Z = 0.77 ± 0.22, and µtt̄ = 0.83 ± 0.04 are applied to Z+jets, tt̄Z, and tt̄,
respectively. The shaded area in the lower panel shows total uncertainties including
systematic and statistical uncertainties.
93

105
104

s = 13 TeV, 139 fb

EventsEvents

106

Data
tt
Z+jetsW+jetsttZSingle top
Dibosons
OthersSM-1

CRT-2b
PostFit

3

10

106
105

CRT-2b
104
10

102

10

10

1

1

10−1

10−1

1.5

1.5

Data/SM

Data/SM

1
0.5
0

200

400

600

1
0.5
10

800 1000 1200 1400 1600 1800 2000
Emiss
[GeV]
T

CRT-2b104

PostFitData
tt
Z+jetsW+jetsttZSingle top
Dibosons
Others
SM

103

105

10−1

1.5

1.5

Data/SM

10−1
Data/SM

1

1

4

5

24

26

28

6

7

8

PostFit

9

1
0.5
0

10

2

4

6

8

10

12

14

16

NDNNFCtop80

EventsEvents104

CRT-2b
PostFit

103
102

104

s = 13 TeV, 139 fb-1
CRT-2b
PostFit

3

10

102

Data
tt
Z+jetsW+jetsttZSingle top
Dibosons
Others
SM

10

1

1

−1

−1

10

10

1.5

Data/SM

Data/SM

106
105

10

1
0.5
0

20

(d) Njets
Datatt
Z+jetsW+jetsttZSingle top
Dibosons
OthersSM

s = 13 TeV, 139 fb-1

18

Njets

(c) NDNNFCtop80
105

30

Data
tt
Z+jetsW+jetsttZSingle top
Dibosons
OthersSM

s = 13 TeV, 139 fb-1

102

1

3

22

103

10

2

20

CRT-2b

10

1

18

106

104

102

0.5
0

16

(b) Object-based ETmiss sig.

s = 13 TeV, 139 fb-1

10

14

T

EventsEvents5

12

Object-based Emiss Sig.

(a) ETmiss
106

PostFit

3

10

2

Data
tt
Z+jetsW+jetsttZSingle top
Dibosons
OthersSM

s = 13 TeV, 139 fb-1

20

40

60

80

100

1.5
1
0.5
0

120

200

400

600

800 1000 1200 1400 1600 1800 2000

mT(l,Emiss) [GeV]

mT2,χ2 [GeV]

T


miss

(e) mT `, ET(f) mT2,χ2

Figure 52: Post-fit plots for the tt̄ control region with equal to or more than two btagged jet. µ Z = 0.93 ± 0.12, µtt̄Z = 0.77 ± 0.22, and µtt̄ = 0.83 ± 0.04 are applied
to Z+jets, tt̄Z, and tt̄, respectively. The shaded area in the lower panel shows total
uncertainties including systematic and statistical uncertainties.
94

Table 20: Definitions of tt̄Z validation region.
Variables

VRttZ

X
2, same flavor / opposite sign0

single lepton trigger
signal `additional baseline `Leading pT`
Subleading pT`m(`, `) 

1−4min ∆φ jet, ETmiss> 27 GeV> 20 GeV[81,101] GeV> 0.4< 50 GeV> 150 GeV
≥4> 80 GeV> 40 GeV
≥1
≥1
>5
> 1.4



ETmiss0
ETmiss
Njets
j
pT2
j
pT4
Nb - jet
NDNNFCtop80
0
Object-based ETmiss sig.
∆R (b1 , b2 )b-tagged jets (Nb - jet ) is the key selection for the orthogonality with CRZ and increasing the purity of tt̄Z. The tt̄Z validation region is still largely contaminated by theZ+jets. Figure 53 shows the post-fit plots of the variables. No significant deviation isfound but the validation in the VRttZ is significantly affected by the Z+jet events.

6.4.2.2

Z+jets validation region (VRZ)

The two Z+jets validation regions are defined in Table 21 since the statistics is allowed to validate two different topologies of SRA and SRB. For the SRA, the validation region, VRZA, is designed in the zero top-tagged large-R jet, but the pT and massof large-R jet are required to mimic the boosted topologies. The VRZB for the SRB isdefined in the inversion of ∆R (b1 , b2 ) and largely contaminated by tt̄. The validationin the VRZB is also affected by the tt̄ events. Figures 54 and 55 show the post-fit plotsof the variables. No significant deviation is found in the both regions.

6.4.2.3tt̄ validation region (VRT)The tt̄ validation region is defined in a region with zero lepton events. The ETmiss trigger is used. The inversion of object-based ETmiss significance is chosen for the high
95

Data
tt
Z+jetsW+jetsttZSingle top
Dibosons
OthersSM

s = 13 TeV, 139 fb-1
104
3

10

EventsEvents105

VRttZ
PostFit

102

105
10

103

1

10−1

10−1

1.5

1.5

Data/SM1

Data/SM

10

1

82

84

86

88

90

92

94

96

98

VRttZ
PostFit

102

10

0.5
80

Data
tt
Z+jetsW+jetsttZSingle top
Dibosons
OthersSM

s = 13 TeV, 139 fb-1
4

1
0.5
0

100 102

100

200

300

400

500

600

700

(b) pT``103

EventsEvents

104

Data
tt
Z+jetsW+jetsttZSingle top
Dibosons
OthersSM

s = 13 TeV, 139 fb-1
VRttZ
PostFit

102

105
104

102

10−1

10−1

1.5

1.5

Data/SM1

Data/SM

1

1

20

30

40

VRttZ
PostFit

10

10

Data
tt
Z+jetsW+jetsttZSingle top
Dibosons
OthersSM

s = 13 TeV, 139 fb-1

103

10

0.5
0

50

1
0.5
0

60

1

2

3

4

5

6

7

Object-based Emiss Sig.

3

10

Data
tt
Z+jetsW+jetsttZSingle top
Dibosons
OthersSM

s = 13 TeV, 139 fb-1
VRttZ
PostFit102

105

s = 13 TeV, 139 fb-1

104

VRttZ
PostFit

102

1

10−1

10−1

1.5

1.5

Data/SM1

Data/SM

10

1

2

4

6

8

10

12

14

16

10

Data
tt
Z+jetsW+jetsttZSingle top
Dibosons
Others
SM

103

10

0.5
0

9

(d) NDNNFCtop80
EventsEvents(c) Object-based ETmiss sig.

104

8

NDNNFCtop80

T105

900 1000
T(a) m(`, `)
105

800

pll [GeV]m(l,l) [GeV]

18

1
0.5
0

20

1

2

3

4

5

Njets

6

7

8

9

10

Nb-jet(e) Njets(f) Nb - jet

Figure 53: Post-fit plots for the tt̄Z validation region. µ Z = 0.93 ± 0.12, µtt̄Z = 0.77 ±
0.22, and µtt̄ = 0.83 ± 0.04 are applied to Z+jets, tt̄Z, and tt̄, respectively. The shaded
area in the lower panel shows total uncertainties including systematic and statisticaluncertainties.
96

5

10

Data
tt
Z+jetsW+jetsttZSingle top
Dibosons
OthersSM

s = 13 TeV, 139 fb-1
VRZA

104

EventsEvents106

PostFit

3

10

2

10

106
10

VRZA
PostFit

4

10

103
102

10

10

10−1

1.5

1.5

Data/SM1

10−1
Data/SM

1

1
0.5
0

200

400

600

1
0.5
0

800 1000 1200 1400 1600 1800 2000
Emiss
[GeV]
T

104

s = 13 TeV, 139 fb

Datatt
Z+jetsW+jetsttZSingle top
Dibosons
OthersSM-1

VRZA
PostFit

102

VRZA
104

PostFit

103
102

10−1

10−1

1.5

1.5

Data/SM1

Data/SM

1

1

600

700

800

900

1000 1100
J :R=1.0

p1

0.5
0

1200

VRZA
104

PostFit

3

10

2

10

10

4

10

400

500

600

Data
tt
Z+jetsW+jetsttZSingle top
Dibosons
OthersSM

s = 13 TeV, 139 fb-1
VRZA
PostFit

103
102
10

1

1

−1

−1

10

10

1.5

Data/SM

Data/SM

106
5

10

1
0.5
0

300

(d) Leading large-R jet massData
tt
Z+jetsW+jetsttZSingle top
Dibosons
OthersSM

s = 13 TeV, 139 fb-1

200

1

EventsEvents106

100

mJ :R=1.0 [GeV](c) Leading large-R jet pT

10

60

1

[GeV]

T

5

50

Data
tt
Z+jetsW+jetsttZSingle top
Dibosons
OthersSM

s = 13 TeV, 139 fb-1

105

10

500

40

106

10

400

30

(b) Object-based ETmiss sig.

103

0.5

20

T

EventsEvents10

10

Object-based Emiss Sig.

(a) ETmiss
5

Data
tt
Z+jetsW+jetsttZSingle top
Dibosons
OthersSM

s = 13 TeV, 139 fb-1

5

2

4

6

8

10

12

14

16

18

1.5
1
0.5
0

20

1

2

3

4

5

Njets

6

7

8

9

10

Nb-jet(e) Njets(f) Nb - jet

Figure 54: Post-fit plots for the Z+jets validation region, corresponding to signal
region A. µ Z = 0.93 ± 0.12, µtt̄Z = 0.77 ± 0.22, and µtt̄ = 0.83 ± 0.04 are applied
to Z+jets, tt̄Z, and tt̄, respectively. The shaded area in the lower panel shows total
uncertainties including systematic and statistical uncertainties.
97

104

EventsEvents

105

Data
tt
Z+jetsW+jetsttZSingle top
Dibosons
OthersSM

s = 13 TeV, 139 fb-1
VRZB
PostFit

103
102

105
104

PostFit

102

1

10−1

10−1

1.5

1.5

Data/SM1

Data/SM

10

1

200

400

600

1
0.5
0

800 1000 1200 1400 1600 1800 2000
Emiss
[GeV]
T

Data
tt
Z+jetsW+jetsttZSingle top
Dibosons
OthersSM

s = 13 TeV, 139 fb-1
VRZB
PostFit

102

105
104
103

1

10−1

10−1

1.5

1.5

Data/SM1

Data/SM

10

1

2

3

4

5

40

50

6

7

8

VRZB
PostFit

9

1
0.5
0

10

2

4

6

8

10

12

14

16

NDNNFCtop80

EventsEvents104

VRZB
PostFit

103
102

105
104

102

10−1

10−1

1.5

1.5

Data/SM1

Data/SM

1

1

2

3

4

5

6

7

8

VRZB
PostFit

10

1

Data
tt
Z+jetsW+jetsttZSingle top
Dibosons
OthersSM

s = 13 TeV, 139 fb-1

103

10

0.5
0

20

(d) Njets
Datatt
Z+jetsW+jetsttZSingle top
Dibosons
OthersSM

s = 13 TeV, 139 fb-1

18

Njets

(c) NDNNFCtop80
105

60

Data
tt
Z+jetsW+jetsttZSingle top
Dibosons
OthersSM

s = 13 TeV, 139 fb-1

102

10

1

30

(b) Object-based ETmiss sig.

103

0.5
0

20

T

EventsEvents104

10

Object-based Emiss Sig.

(a) ETmiss
105

VRZB

103

10

0.5
0

Data
tt
Z+jetsW+jetsttZSingle top
Dibosons
OthersSM

s = 13 TeV, 139 fb-1

9

1
0.5
0

10

100

200

300

400

500

600

700

800

900 1000

mb,min[GeV]
T

Nb-jet(f) mTb,min(e) Nb - jet

Figure 55: Post-fit plots for the Z+jets validation region, corresponding to signal
region B. µ Z = 0.93 ± 0.12, µtt̄Z = 0.77 ± 0.22, and µtt̄ = 0.83 ± 0.04 are applied toZ+jets, tt̄Z, and tt̄, respectively. The shaded area in the lower panel shows total
uncertainties including systematic and statistical uncertainties.
98

Table 21: Definitions of Z+jets validation regions with zero lepton. VRZA and VRZB
are the validation regions for SRA and SRB, respectively.
Variables

VRZA

ETmiss trigger
baseline `

VRZB

X
0

≥4
> 80 GeV> 40 GeVmin ∆φ jet1−4 , ETmiss> 0.4
τ vetoX
mT2,χ2> 450 GeV < 450 GeVNDNNFCtop80
0
≥1
miss
Object-based ET sig.
> 20
> 12
∆R (b1 , b2 )< 1.4
Nb - jet
≥1
≥2
b,min
mT
> 200 GeV
Leading Large-R jet pT> 350 GeV
Leading Large-R jet mass > 40 GeV
Njets
j
pT2
j
pT4

purity of tt̄ events. Since the lower object-based ETmiss significance cut is used in
the SRB, the selection of object-based ETmiss significance is between 5 and 12. The
NDNNFCtop80 and Nb - jet are required to be larger than or equal to one. Figure 56
shows the post-fit plots for the variables. No significant deviation is found.

99

106
105

EventsEvents

107

Data
tt
Z+jetsW+jetsttZSingle top
Dibosons
OthersSM

s = 13 TeV, 139 fb-1
VRT
PostFit

104
103

107
106

s = 13 TeV, 139 fb-1

105

VRT

104

102

10

10

1.5

1.5

Data/SM1
10−1

Data/SM

1
10−1

1

200

400

600

1
0.5
0

800 1000 1200 1400 1600 1800 2000
Emiss
[GeV]
T

VRT
PostFitEventsEvents

103

106
5

10

4

10

40

50

VRT
PostFit

102
10

10

1
10−1

1.5

1.5

Data/SM

1
10−1

1

1

2

3

4

5

6

7

8

9

1
0.5
0

10

2

4

6

8

10

12

14

16

NDNNFCtop80

105

VRT

EventsEventss = 13 TeV, 139 fb-1

Datatt
Z+jetsW+jetsttZSingle top
Dibosons
OthersSM

PostFit

103

107
106

s = 13 TeV, 139 fb-1

105

VRT

104

10

102

10

10

1.5

1.5

Data/SM1
10−1

Data/SM

1
10−1

1

1

2

3

4

5

6

7

8

Data
tt
Z+jetsW+jetsttZSingle top
Dibosons
OthersSM

PostFit

103

2

0.5
0

20

(d) Njets

107
106

18

Njets

(c) NDNNFCtop80

104

60

Data
tt
Z+jetsW+jetsttZSingle top
Dibosons
OthersSM

s = 13 TeV, 139 fb-1

103

102

Data/SM

30

T

Data
tt
Z+jetsW+jetsttZSingle top
Dibosons
OthersSM

s = 13 TeV, 139 fb-1

104

0.5
0

20

(b) Object-based ETmiss sig.

107

105

10

Object-based Emiss Sig.

(a) ETmiss
106

PostFit

103

102

0.5
0

Data
tt
Z+jetsW+jetsttZSingle top
Dibosons
Others
SM

9

1
0.5
0

10

100

200

300

400

500

600

700

800

900 1000

mb,min[GeV]
T

Nb-jet(f) mTb,min(e) Nb - jet

Figure 56: Post-fit plots for the tt̄ validation region. µ Z = 0.93 ± 0.12, µtt̄Z = 0.77 ±
0.22, and µtt̄ = 0.83 ± 0.04 are applied to Z+jets, tt̄Z, and tt̄, respectively. The shaded
area in the lower panel shows total uncertainties including systematic and statisticaluncertainties.
100Table 22: Definitions of tt̄ validation region.
Variable

VRT

ETmiss trigger
baseline `

X
0

Njets
j
pT2
j
pT4



min ∆φ jet1−4 , ETmissτ vetomT2,χ2NDNNFCtop80
Object-based ETmiss sig.
Nb - jet

6.5≥4> 80 GeV> 40 GeV> 0.4
X≥1[5, 12]≥1

Systematic uncertainties

Experimental uncertainties are those originating from the experiment, for example,
the calibration of each physical object. Theoretical uncertainties are from the uncertainties of the simulation and the calculation, for example, the choice of the modelling, and cross section of signal and background processes.

6.5.1
•

Experimental uncertainties

Jet energy scale (JES) for small-R jets
The uncertainties of jet energy scale originate from the jet energy calibration

explained in Chapter 4.2.5 [84]. The uncertainties are derived as a function of pT andη. Total 77 components of uncertainties are extracted from the 4 in-situ method,pile-up, jet-flavor, punch-through, fast simulation and single-particle response forthe jets with pT larger than 2 TeV [117]. The pile-up uncertainties originate from the
MC mismodelling of NPV , µ, ρ, and the dependence of residual pT . The jet flavor
accounts for the difference due to jets originating from light quarks, gluons, and b
quarks. Strongly reduced scenario of the uncertainties is used, which reduces the full77 nuisance parameters (NP) into 7 NPs only via an eigenvector decomposition [84,118]. The uncertainties of the total SM predictions are 8∼52% for the signal regions.
•Jet energy resolution (JER) for small-R jets
The jet energy resolution is parametrized by using the function of the relative101

energy resolution in the calorimeters [117]. The function with pT dependence isexpressed as:
σpT
N
S
=
⊕ √ ⊕ C,
pT
pT
pT

(47)

where the first term in the right-hand side is the noise term, the second term is thestochastic term, and C is the constant term. JER measurement is derived by the
dijet balance method [117]. The asymmetry of two leading jets forms the Gaussian
distribution with the standard deviation as the JER. The noise term is derived by
the random cone method to measure the fluctuation due to the pile-up. The JER
uncertainties are obtained by the fit to JER measurement with the template of Eq.
(47). The nuisance parameters are also reduced via the eigenvector decomposition.
The uncertainties of the total SM predictions are 3∼36% for the signal regions.
•

JES for large-R jets and DNN top tagger uncertainties (Large-R jet + DNN)
The jet energy scale for the large-R jets and the uncertainties of scale factors of

DNN top taggers are already explained in Chapter 5. The propagated JES uncertainties of large-R jets after the DNN taggers are correlated with the original JES
uncertainties for the large-R jets. The uncertainties of the total SM predictions are
14∼88% for the signal regions.
•

Jet vertex tagger
The uncertainties are estimated from the calibration of the mis-tagged efficiencies

on the pile-up jets with Z → µµ+jets events [81]. The difference of mis-tagged effi-

ciencies between data and MC samples and the difference of hard-scatter efficiencies

between two different simulation generators are included. The uncertainties of thetotal SM predictions are 5∼21% for the signal regions.
•b-tagging
Scale factors of the efficiencies between data and MC samples are applied tocorrect the efficiency of the b-tagging on the small-R jets [90]. The uncertainties ofscale factors include the modelling uncertainties, JES uncertainties and other sources.
The final nuisance parameters are reduced via eigenvector decomposition. The uncertainties of the total SM predictions are 3∼8% for the signal regions.
•ETmiss soft-term resolution and scale
The ETmiss uncertainty is derived from the hard components and soft term in Eq.

(27) [91]. For the hard components, their uncertainties are propagated to the ETmiss uncertainty directly. On the other hand, the uncertainties of the soft term include
102sof t,k

p~T

p~Tsof t

p~Tsof t,⊥∆~pT−~pThard

p~Thard~ miss = ∆~pT
E
T

Figure 57: Projection of the soft term vector with respect to the vector sum of the hardterms [91].
the parallel scale, the parallel resolution and the transverse resolution. Figure 57
shows the definition of direction of the soft term [91]. The reference direction isdefined in the direction of the vector sum of pT of hard components. The data/MC
difference in the Z → `` events are used as the uncertainties of the soft term. The

uncertainties of the total SM predictions are 1∼20% for the signal regions. The
ETmiss trigger uncertainties can be ignored due to high ETmiss requirement in the offline

selection, where the efficiencies of ETmiss trigger are higher than 99%.
•

Lepton reconstruction and identification
The electrons and muons are calibrated for the energy scale, energy resolution

and efficiencies [78, 79]. The uncertainties are applied to backgrounds. The scale
factors of lepton trigger and trigger uncertainties are also applied due to the control
regions with leptons.
•

Pile-up reweighting
The pile-up reweighting is the correction of an average number of interactions

per bunch crossing hµi on the MC samples [119]. The hµi in the MC sample isrescaled by 1.03 to match the data. The uncertainties are accounted for the shifts
in the nominal scale factor by changing the scale factors from 1.03 to 1.0 and 1.18.

6.5.2
•

Theoretical uncertainties

Z/W+jet modelling
The Z/W+jet samples with Sherpa event generator are produced with a simpli-

fied scale prescription [120]. The matrix element matching (CKKW) provides the calculation for the overlap between jets from the matrix element and the parton shower.
The nominal value is 20 GeV and varied to 15 GeV and 30 GeV. The renormalization103

scale (renorm) for the running strong coupling constant, the factorization scale (fac)for the parton density functions, and the resummation scale(qsf) for the resummationof soft gluon emission are varied to 2 and 1/2 with respect to the nominal value.
The uncertainties of the total SM predictions are 3∼20% for the signal regions. A

30% uncertainty is assigned to the extrapolation between the control regions andsignal regions to account for the uncertainty associated with Z/W+heavy flavor jet
modeling because the extrapolation relies on the number of b-tagged jets.
•tt̄ modelling
The tt̄ modelling can be referred to Chapter 5.4.3. The uncertainties of the total

SM predictions are 2∼35% for the signal regions.
•Single top modelling
The single top production is dominated by the Wt process in the signal andcontrol regions. There is an issue on the diagram of the NLO calculation. Whenthe invariant mass of a W and an extra b at NLO is close to top mass, the interference
to the tt̄ events becomes significant. There are two methods, a diagram removal (DR)and diagram subtraction (DS) [121], to remove the effect on cross-section calculation.
The DR is used as the baseline method for the simulation. The DS is used as analternative sample for the estimation of the correction on the interference. The difference between DR and DS is considered as a single top modelling uncertainty. The
uncertainties of the total SM predictions are 1∼17% for the signal regions.
•tt̄Z modelling
The 6 point variations in the factorization scale and renormalization scale and the

Var3c envelope [48] are used for the evaluation of the parton shower and radiation
uncertainties. The envelope of all difference is used in the fit. The uncertainties of
the total SM predictions are 1∼19% for signal regions.
•

Signal uncertainties
The variation of factorization scale for the PDF, renormalization scale for thestrong coupling, merging scale between the matrix element and parton shower, andVar3c envelop are evaluated for the uncertainties. The uncertainties of signal yields
are 5% for the SRA and 12% for the SRB.
•

Monte Carlo statistics
The statistics of simulation events can affect the results significantly due to thelimited computing power in some regions. The uncertainties of the total SM predictions are 26∼49% for the TT regions and 19∼30% for the other regions.
104

6.6

Statistical modelWith the region definitions, event yields of signals and the individual backgroundcan be estimated. The statistical model of the analysis is built by using HistFactory [122]. The tool is developed based on the RooStats [123] and RooFit [124]. The
minimization of the minus log-likelihood is performed by MINUIT, which is implemented in ROOT. In this analysis, each region is described as a single channel. The
probability density function (PDF) in each region c (channel) is a Poisson distribution
with expected events νc and observed events nc , where the νc is described as:νc = µsig νc + ∑ µbkg,i νc
sig

bkg,i

,

(48)

i

where µsig is the signal strength, and µbkg,i is the normalization factor of a backgroundprocess i. When we include the nuisance parameters and normalization factors, thelikelihood template can be written into a formula as:
L (n , θ 0 |µsig , µ bkg , θ ) =∏c∈channels

Pois(nc |λc (µsig , µ bkg , α )) · ∏ G (θ 0p |θ p ),

(49)

p

where p denotes parameters, θ p denotes nuisance parameters associated to the systematics and θ 0p is an auxiliary measurement used to constrain θ p . The expectation
value λc of the Poisson distribution is described as a function of signal strength, normalization factors of background processes and nuisance parameters. The G (θ 0p |θ p )is the constraint term for other nuisance parameters by using the Gaussian function
with a standard deviation ∆θ = 1.

6.6.1

Fit strategy

All the fit strategies are provided in the HistFitter framework [125]. Figure 58 summaries the procedures to get the upper limits on the cross section for the stop signal.
Three types of fitting are used for different purposes. A background-only fit is performed for the validation of background estimations and unblinded results in theSRs. A model-dependent fit and a model-independent fit are used to evaluate theupper limits on the cross section if there is no significant excess in the unblindedresults.
•

Background-only fit

105Total PDF
CRs+VRs+SRs
PDF
CRs+VRs

PDF
CRs+SRs

PDF
CRs

Extrapolation

Extrapolation

PDF
CRs+SRs

Model-independent
fit

Model-dependent
fit

Upper limit
for discovery

Upper limit
for exclusion

Background-onlyfit
Validation

UnblindFigure 58: Overviews of the fit strategy for background estimations and the upper
limits of the signals.
The dominant backgrounds in the SRs and VRs are estimated by the backgroundonly fit in all the CRs. Only the likelihood models of all the CRs are included in
the statistical model. The normalization factor of each background is set as a freeparameter in the fit. The simultaneous fit among all the CRs is performed to take
into account the contamination of other backgrounds in a certain CR which aims forhigh purity of a specific background sample.
The fitted normalization factors are applied to the VRs to check the fit results.
If there is no significant mismodelling in the VRs, the fit results are considered to bevalidated, and the normalization factors are applied to the backgrounds in the SRs.
The same fitted normalization factor of each dominant background is applied to thecorresponding background obtained from MC samples in SRs.
The minor backgrounds in the SRs are estimated by using MC predictions, andthe impacts due to constraints on the backgrounds in CRs are not considered since
they are minor.
•

Model-dependent signal fit

The signal model with the signal strength µsig and background models with normalization factors are included in the model-dependent signal fit. In case of no excess
found in SRs, the model-dependent fit is used for the exclusion of a given signal
model. In contrast, if the excess is found in SRs, the model-dependent fit can be used
for measurement of the signal strength. The fit is performed in all the SRs and CRs
simultaneously. The signal contamination in the CRs can be taken into account. Since106the multiple SRs are statistically independent, the combination of the SRs in the fit
should provide a better expected exclusion sensitivity.
•

Model-independent signal fit

For the search for new physics, upper limits of event yields or cross sections of any
signal models are set in each SR. The model-independent fit is performed in only
one signal region with all the CRs. In case of model-dependent signal fit, the signal
can potentially spread across the multiple SRs. This is not considered for the case ofmodel-independence. A dummy signal model is used in the fit to estimate the upper
limit of the signal cross section (see Section 6.7.4). In this fit, no signal contaminationin the CRs is assumed. The background-only hypothesis test is also performed forquantifying the significance of any observed excess of events in each SR.

6.6.2

Statistical test

For the search for new physics, we need to define what is known and what we wantto know. The Standard Model processes are defined as a null hypothesis, H0 , anddescribed as a background model. The new physics is defined as an alternative
hypothesis, H1 , and described as a signal model. To quantify the agreement between
data and the background hypothesis, we calculate the p-value based on the hypotheses to estimate the incompatibility of the observation in a certain region. A p-value isusually converted into a significance Z. For discovery of new physics, Z is required
to be at least 5, which means p = 2.87 × 10−7 . For an exclusion limit, p = 0.05 is often

used, which is equivalent to Z = 1.64 for one sided test.

The parameter of interest, µsig , provides the key information for both hypotheses. The profiled likelihood ratio is usually used for quantifying the observation, anddefined as:λ(µsig ) =L (µsig , θ̂θˆ )L (µ̂sig , θ̂θ )

,

(50)

where the quantity θ̂θˆ denotes the value of nuisance parameter θ with a given µsig ,and the µ̂ and the θ̂θ are the maximum likelihood (ML) estimators, which maximize
the likelihood function. The profiled likelihood ratio is a ratio of the conditional
maximum likelihood to the maximum likelihood as a function of µsig with a value
between 0 and 1. If the λ(µsig ) is close to 1, it implies that the data is consistent withsignal plus background model with the given µsig . A natural logarithmic form is107usually used as a test statistic,
qµsig = −2ln(λ(µsig )).

(51)

To quantify the observation in both null hypothesis and alternative hypothesis, thep-value from the probability density function of the test statistic is required. From
Wald’s work [126], the test statistic with a single parameter can be expressed as:√(µsig − µ̂sig )2
+
O
(
1/
N ),
σ2

qµsig = −2ln(λ(µsig )) =

(52)

0

where the µ̂sig is a Gaussian distribution with a mean µsig and a standard deviation
σ, and N denotes the data sample size. The second term can be ignored if the data
sample size is large. Then, the PDF of the test statistic can be expressed as a noncentral χ2 function:1
1√ ×
f (qµsig ; Λ) = p
2 qµsig 2π



√ 2
√ 2 
1 p
1 p, (53)
exp − ( qµsig + Λ) + exp − ( qµsig − Λ)22where the non-centrality parameter Λ is defined as:0Λ=(µsig − µsig )2
σ2

.

(54)

0

For the case of µsig = µsig , the distribution becomes a χ2 distribution and depends
only on qµsig .
For the unknown Λ, Asimov data set [127] is defined for both signal regions andcontrol regions in the assumption of the partial derivatives of likelihood function
with respect to the nuisance parameters equal to zero. The profiled likelihood ratio
from the Asimov data set can be used for the approximation of the Λ:qµsig ,A = −2lnλ A (µsig ) ≈(µsig − µ̂sig )2
= Λ.
σ2

(55)

Then, σ is obtained from this expression.
There are two test statistics used in the analysis with the approximation from the
Asimov data set: discovery and upper limit. q0 is defined for the discovery, which108

rejects the null hypothesis with µsig = 0. The definition is as follows:q0 =µ̂2 /σ2 ,µ̂sig ≥ 0,0,µ̂sig < 0.

sig

(56)

Only the positive signal is taken into account. The downward fluctuation of data
below the background-only hypothesis is assumed as the effect from the systematic
uncertainties.
q̃µsig is defined for the upper limit by rejecting the µ̂sig > µsig and models with
µsig ≥ 0 by requiring maximum likelihood at 0 if µ̂sig < 0. The definition of q̃u isexpressed as:µ2 /σ2 + 2µsig µ̂sig /σ2 ,


 sig
q̃µsig = (µsig − µ̂sig )2 /σ2 ,



0,

µ̂sig < 0,(57)

0 ≤ µ̂sig ≤ µsig ,µ̂sig > µsig .

0

S+B Model
B Modelf(q |1)0
f(q |0)q1

f(~qµ|µ')

f(q |µ')Figure 59 shows examples of q0 and q̃µsig distributions including the signal plus

0,A

S+B Model
B Model
~ |1)
f(q
~µ|0)
f(q
µ

~
q

1

µ,A

0

CLS+B

10−1

1-CLB

10−1
CLS+B

1-CLB
10−2

10−2

10−3

0

2

4

6

8

10

12

14

16

10−3

18

0

2

4

6

8

q

0

(a)

10

12

14

16

18

~
qµ

(b)

Figure 59: Example of the probability density function of profiled likelihood ratiofor (a) the discovery and (b) the upper limit with models background only (red) andsignal plus background (blue). The black line shows the median value of q0,A andq̃µ,A for the evaluation of p-values for the background only (1 − CLB ) and for thesignal plus background (CLS+B ).
background model and background only model made by using the toy experiments
generated by the Monte Carlo method, which are showed as the histograms. The
approximated distributions from the Asimov data set are shown as dashed lines,
which have good agreement with the distributions from the toy experiments. The
p-values of the observation for both models (shaded area) are easily obtained fromthe non-central χ2 function without consuming the large computing power.
109

The CLS method [128] is used for the upper limit to prevent the exclusion in thealternative hypothesis with no or little sensitivity. The CLS is defined as:
CLS ≡

CLS+B
,
1 − CLB(58)

where the CLS+B and 1 − CLB can be referred in Figure 59. The one-sided p-value of
the CLS at 95% confidence level (CLS < 0.05) is used to reject the alternative hypoth-

esis.

6.7

Results

Signal regions, control regions and validation regions are defined as mentioned in theprevious sections. All the experimental and theoretical systematic uncertainties areused in the statistical model of the likelihood function. Based on the fit configurations
introduced in the previous section, all three types of fits have been performed.

6.7.1

Background-only fitµ Z , µtt̄Z , and µtt̄ , which are the normalization factors of Z+jets, tt̄Z, and tt̄, are thefloating parameters in the fit. Table 23 summaries the normalization factors of eachdominated background. The statistics of data affect the uncertainties of the normalization factors in the tt̄Z control region since the yields are relatively low. Figure 60
summarizes the data and MC in both control regions and validation regions after thenormalization factors are applied. There are no significant deviations between thedata and MC predictions in all regions. The data and MC agreement in both 1b and2b regions of tt̄ control regions with only one normalization factor of tt̄ indicates thenormalization is not affected by the b-tagging.
Table 23: Floating parameters for the background-only fit with the initial value equal
to 1 and final values.
Floating Parameter

Final Value

µZ
µtt̄Z
µtt̄

0.93 ± 0.12
0.77 ± 0.22
0.83 ± 0.04

The breakdown of dominant systematic uncertainties in background estimations is shown in Table 24 in the percentage of total systematic uncertainties. For
110

Table 24: Systematic uncertainties in percentage of the total SM predictions larger
than 1 % within SRA and SRB. The floating normalization factors, µtt̄ , µtt̄Z , and µ Z aredetermined by simultaneous fit to all the control regions with data. The uncertainties
are estimated by simultaneous fit to all the control regions and each signal region
with normalization factors. Single top modelling is negligible after the fit.
Nb - jet

SRATT
≥2
1

SRATW
≥2
1

SRAT0
≥2
1

SRBTT
≥2 1

SRBTW
≥2
1

SRBT0
≥2
1

Total syst. unc.

50

40

21

21

21

29

28 41

23

18

21

16

tt̄ modellingtt̄Z modelling
Z modelling
W modelling

12
15
4
3

6
7
6
1

12
5
4
4

3
1
7
2

2
8
7
5

1
3
10
4

12 27
5 2
1 1
1 3

11
3
1
2

10
<1
1
6

5
2
4
1

4
<1
6
5

µtt̄
µtt̄+ZµZ<1 < 1
14
6
2
5

1
9
3

<1 <1 <1
3
4
2
6
6
8

1
15
1

3
5
2

1
11
1

2
1
2

2
5
3

1
1
5

Small-R JER
Small-R JES
Large-R jet + DNN
b-tagging
ETmiss soft term
LeptonPile-up
MC statistics

21
3
32
3
2
4
<1
18

3
1
3
4
1
3
2
11

7
3
5
3
1
4
1
15

8 9
1 3
13 26
4 3
<1 3
3 3
4 2
12 10

5
6
11
3
1
2
1
9

5
3
10
2
1
3
1
5

13
8
4
4
6
4
1
8

12
5
3
2
2
3
<1
4

9
9
29
1
1
5
2
17

111

9
2
5
5
3
5
2
11

23
3
10
2
3
7
2
6

the experimental uncertainties, the Large-R jet + DNN and JER for the small-R jets
are dominant systematic uncertainties. The Large-R jet + DNN contributes to theuncertainties mostly in TT regions of both SRA and SRB (over 30% in SRATT). The
JER for small-R jets is dominant in T0 regions and subdominant in TT regions. The
Large-R jet + DNN in the Z+jets event is well controlled by the CRZ, which results in small uncertainties of the Large-R jet + DNN when the Z+jets dominates.
For theoretical uncertainties, the tt̄Z uncertainty is dominant in the SRATT due tomain backgrounds in SRATT. The tt̄ modelling is non-negligible in most of the signal
regions and dominant in SRBTT and SRBTW. The Z modelling does not affect theuncertainties significantly. The fit results in Figure 61 show the nuisance parameters
belonging to the theoretical uncertainties of the main backgrounds, the dominant
experimental uncertainties and normalization factors of tt̄, tt̄Z, and Z+jets. Mostof the nuisance parameters show no significant deviation between pre-fit and postfit except for the tt̄ modelling due to two tt̄ control regions with one normalization
factor.

Events

1010
109
108
107
106

data
ttbar
ttZ
Z+jetsW+jetssingle top
dibosonothers = 13 TeV, 139 ± 2.4 fb-1
PostFit
CRVRs

105
104
103
102
10
1

Data/SM10−1 0

1

2

3

tZ

CRZ

CRT

1.5

4

5

6

7

8

1
0.5

CRt

C
V
VRZ
VRT
-1b RT-2b RZA
B

VRt

tZ

Figure 60: Summary plots for control regions and validation regions. All the SM
backgrounds are included with the band of the total uncertainties.

6.7.2

Discussion of data in signal regions

Tables 26 and 27 show the yields after the normalization factors are applied. No
excess is found in all the signal regions. Figure 62 summarizes all the signal regions. No events are observed in the SRATT2b and SRATT1b. The SM predictions112

µ_Zjetsµ_ttZµ_ttbar

0.6 0.7 0.8 0.9

1

1.1

µ

DNNSFDijet_Modelling
DNNSFDijet_Stat
DNNSFGammajet_Modelling
DNNSFGammajet_Stat
DNNSFttbar_Modelling_bTagLightDNNSFttbar_Modelling_hadronisation
DNNSFttbar_Modelling_highPt
DNNSFttbar_Modelling_matrixElement
DNNSFttbar_Modelling_radiation
DNNSFttbar_Stat
JET_JER_DataVsMC
JET_JER_EffectiveNP_1
JET_JER_EffectiveNP_2
JET_JER_EffectiveNP_3
JET_JER_EffectiveNP_4
JET_JER_EffectiveNP_5
JET_JER_EffectiveNP_6
JET_JER_EffectiveNP_7restTerm
JET_Rtrk_Baseline_pT
JET_Rtrk_Modelling_pT
JET_Rtrk_TotalStat_pT
JET_Rtrk_Tracking_pT
Z_Theo_HF
Z_fac
Z_qsf
Z_renorm
ttbar_FSR
ttbar_Hadronization
ttbar_HardScatter
ttbar_Radiation

−1

−0.5

0

0.5

1

α

Figure 61: Results of fit parameters α and normalization factors µ of main
backgrounds (upper panel) from the background-only fit to all control regions. α =(θ − θ 0 )/∆θ, where θ 0 and ∆θ are the initial mean values and standard deviations forindividual parameters, and θ is final value after the fit. Only the nuisance parameters
belong to main backgrounds with significant uncertainties and the normalization
factors are shown. The details of the nuisance parameters can be found in Table 25.
The tt̄Z modelling is not included in the background-only fit to all the control regions
since the errors are assigned directly to µtt̄Z . The shaded area refers to the initial valueof nuisance parameters, which are set to 0±1.

113

Table 25: Nuisance parameters with major contributions of the systematic
uncertainties.
Uncertainties

Jet energy resolution

Large-R jet + DNN

tt̄ modelling

Z+jets modelling

Parameters

Description

JET_JER_EffectiveNP_1
JET_JER_EffectiveNP_2
JET_JER_EffectiveNP_3
JET_JER_EffectiveNP_4
JET_JER_EffectiveNP_5
JET_JER_EffectiveNP_6
JET_JER_EffectiveNP_7restTerm
JET_JER_DataVsMC

7 NPs including the uncertainties propagated from JES
uncertainties and random cone method and 1 NP for the
non-closure between the data and MC

JET_Rtrk_Tracking_pT
JET_Rtrk_TotalStat_pT
JET_Rtrk_Modelling_pT
JET_Rtrk_Baseline_pT

4 NPs for jet response from the Rtrk method

DNNSFttbar_Stat
DNNSFttbar_Modelling_radiation
DNNSFttbar_Modelling_matrixElement
DNNSFttbar_Modelling_highPt
DNNSFttbar_Modelling_hadronisation
DNNSFttbar_Modelling_bTagLight

6 NPs for signal scale factors of DNN top tagger

DNNSFGammajet_Stat
DNNSFGammajet_Modelling
DNNSFDijet_Stat
DNNSFDijet_Modelling

4 NPs for background scale factors of DNN top tagger

ttbar_Radiation
ttbar_HardScatter
ttbar_Hadronization
ttbar_FSR

Uncertainty in the initial state radiation
Uncertainty in different generators
Uncertainty in the parton showing
Uncertainty in the final state radiation

Z_ckkw
Z_fac
Z_qsf
Z_renorm
Z_Theo_HF

Uncertainty in the matrix element matching
Uncertainty in the factorization scale
Uncertainty in the resummation scale
Uncertainty in the renormalization scale
Uncertainty in the Z+heavy flavor jetsin the SRATW2b and SRAT02b are slightly higher than the observed events, but the
SM predictions of SRATW1b and SRAT01b are in agreement with the data whichhave higher statistics than those in the SRATW2b and SRAT02b. This could be simply caused by the fluctuation of low statistics data. The SRB shows better agreement between data and SM predictions. Figure 63 shows the post-fit distributionsof mT2,χ2 , Njets , mTb,min , ETmiss , mTb,max , and object-based ETmiss significance in SRATW1b,
SRAT01b, SRBTW2b, SRBTW1b, SRBT02b, and SRBTT1b, respectively.
Table 26: Fit results for the SRA with background corrections, for an integrated
luminosity of 139 fb−1 . The total uncertainties are shown. “Other” includes tZ, tWZ,
tt̄W, and tt̄H.
Regions
Observed events
SM events
tt̄ events
tt̄Z events
W+jets events
Z+jets events
Single top events
Diboson events
Other events

SRATT2b

SRATW2b

SRAT02b

SRATT1b

SRATW1b

SRAT01b

0

1

1

0

3

7

0.7 ± 0.3

1.9 ± 0.4

2.4 ± 0.5

0.7 ± 0.3

2.8 ± 0.6

5.8 ± 1.7

0.1 ± 0.1
0.3 ± 0.1
0.2 ± 0.1
1.3 ± 0.4
0.5 ± 0.1
0.3 ± 0.2
0.1 ± 0.0

0.2 ± 0.1
0.4 ± 0.3
0.8 ± 0.4
3.6 ± 1.0
0.4
0.3+
−0.3
0.5 ± 0.1
0.0 ± 0.0

0.1
0.1+
−0.1
0.4 ± 0.2
0.0 ± 0.0
0.1 ± 0.1
0.1 ± 0.0
0.0 ± 0.0
0.0 ± 0.0

0.3 ± 0.2
0.6 ± 0.3
0.2 ± 0.1
0.5 ± 0.2
0.3 ± 0.1
0.0 ± 0.0
0.1 ± 0.0

0.1
0.1+
−0.1
0.4 ± 0.2
0.4 ± 0.2
1.2 ± 0.3
0.3 ± 0.2
0.1 ± 0.0
0.0
0.0+
−0.0

114

0.1
0.0+
−0.0
0.2 ± 0.1
0.0 ± 0.0
0.3 ± 0.2
0.1 ± 0.1
0.0 ± 0.0
0.0 ± 0.0

Events

25
data
ttbar
ttZ
Z+jetsW+jetssingle top
dibosonother~ ∼0m(t ,χ 1 )=(1100,1)~ ∼0m(t ,χ 1 )=(1300,1)~ ∼0m(t ,χ 1 )=(700,400)

s = 13 TeV, 139 ± 2.4 fb-1
PostFit
SRs

20

15

10

5

Data/SM

0

2

1.5

4

6

8

10

12

1
0.5 SR SR SR SR SR SR SR SR SR SR SR SR
ATT ATW AT0 ATT ATW AT0 BTT BTW BT0 BTT BTW BT0-2b -2b -2b -1b -1b -1b -2b -2b -2b -1b -1b -1b

Figure 62: Summary plots for all the signal regions with data unblinded. All the SM
backgrounds with the shaded band of the total uncertainties are included. (mt̃ ,mχ̃0 )1= (1300,1), (mt̃ ,mχ̃0 ) = (1100,1), and (mt̃ ,mχ̃0 ) = (700,400) are also shown.
1

1

Table 27: Fit results for the SRB with background corrections, for an integrated
luminosity of 139 fb−1 . The total uncertainties are shown. “Other” includes tZ, tWZ,
tt̄W, and tt̄H.
Regions
Observed events
SM events
tt̄ events
tt̄Zevents
W+jets events
Z+jets events
Single top events
Diboson events
Other events

SRBTT2bSRBTW2b

SRBT02b

SRBTT1b

SRBTW1b

SRBT01b

2

4

3

4

12

18

1.6 ± 0.5

3.0 ± 0.7

3.4 ± 0.7

3.7 ± 1.5

15.0 ± 2.7

19.3 ± 3.0

0.7 ± 0.4
1.2 ± 0.5
0.2 ± 0.1
0.2 ± 0.1
0.5 ± 0.3
0.1 ± 0.0
0.1 ± 0.0

1.3 ± 0.3
0.6 ± 0.3
0.1 ± 0.1
0.9 ± 0.4
0.4 ± 0.2
0.0
0.0+
−0.0
0.0 ± 0.0

1.8 ± 1.2
0.7 ± 0.3
0.4 ± 0.2
0.6 ± 0.4
0.1 ± 0.0
0.1 ± 0.0
0.1 ± 0.0

5.7 ± 2.2
0.7 ± 0.3
3.4 ± 1.1
2.9 ± 1.0
0.9 ± 0.7
1.1 ± 0.5
0.3 ± 0.0

4.4 ± 1.2
1.0 ± 0.4
3.6 ± 2.1
8.1 ± 1.8
0.7
0.6+
−0.6
1.6 ± 0.6
0.1 ± 0.0

0.2
0.2+
−0.2
0.8 ± 0.3
0.1 ± 0.0
0.1 ± 0.0
0.1 ± 0.0
0.1 ± 0.0
0.2 ± 0.0115

5

s = 13 TeV, 139 fb
SRATW-1b
PostFitEventsEvents6Datatt
Z+jetsW+jetsttZSingle top
Dibosons
OthersSM~ ∼0m(t ,χ
)=(1300,1)

-1

4
3

9
8
7
6

Data
tt
Z+jetsW+jetsttZSingle top
Dibosons
OthersSM~ ∼0m(t ,χ
)=(1300,1)

s = 13 TeV, 139 fb-1
SRAT0-1b
PostFit

5
4

1

1

3

2

2
1
1
0

600

800

0
4

1000 1200 1400 1600 1800 2000

5

6

7

8

9

10

11

12

13

mT2,χ2 [GeV](b) Njets in SRAT01b

65s = 13 TeV, 139 fb
SRBTW-2b
PostFitEventsEvents(a) mT2,χ2 in SRATW1b
Datatt
Z+jetsW+jetsttZSingle top
Dibosons
OthersSM~ ∼0m(t ,χ
)=(700,400)

-1

4
3

30
25
20

Data
tt
Z+jetsW+jetsttZSingle top
Dibosons
OthersSM~ ∼0m(t ,χ
)=(700,400)

s = 13 TeV, 139 fb-1
SRBTW-1b
PostFit

15

1

1

2

10

1

5

0
200

300

400

500

600

700

800

0

900 1000

300

400

500

600

700

800

mb,min
[GeV]
T

3
2.5
2

EventsEvents

4
3.5

1000

(d) ETmiss in SRBTW1b5
s = 13 TeV, 139 fb-1
SRBT0-2b
PostFit

900

Emiss
[GeV]
T

(c) mTb,min in SRBTW2b
4.5

14

Njets

Data
tt
Z+jetsW+jetsttZSingle top
Dibosons
OthersSM~ ∼0m(t ,χ
)=(700,400)

7
6
5

Data
tt
Z+jetsW+jetsttZSingle top
Dibosons
OthersSM~ ∼0m(t ,χ
)=(700,400)

s = 13 TeV, 139 fb-1
SRBTT-1b
PostFit

4
3

1

1.5

1

2

1
1

0.5
0
0

100 200 300 400 500 600 700 800 900 1000

0
10

12

14

16

18

20

22

24

26

28

30

Object-based Emiss Sig.

mb,max[GeV]TT(f) Object-based ETmiss sig. in SRBTT1b(e) mTb,max in SRBT02b

Figure 63: Post-fit plots for the signal regions. All the SM backgrounds are included
with the band of the total uncertainties. (mt̃ ,mχ̃0 ) = (1300,1) is shown in (a) and (b).
1(mt̃ ,mχ̃0 ) = (700,400) is shown in (c), (d), (e), and (f).
1116

6.7.3Model-dependent signal fit

Since no significant excess from total SM predictions is found, a model-dependent
signal fit is performed in each signal point of (mt̃ , mχ̃0 ) to extract the lower limits on
1

the masses. Although the results are changing in different signal models, the most
relevant results are the benchmark point (mt̃ , mχ̃0 ) = (1300,1) GeV. All control regions
1

for tt̄Z, tt̄, and Z+jets and all signal regions (SRAs and SRBs) are included in PDFs
for the total likelihood function. The breakdown of the systematic uncertainties isshown in Table 28. Comparing to Table 24 for the background-only fit, most of thedominant uncertainties remain the same. The uncertainty for µsig is large in SRATT2b
due to the signal yield being large in the SRATT2b. The results of fit parameters forthe model-dependent signal fit are shown in Figure 64. Slight deviations between
pre-fit and post-fit are observed in the model-dependent signal fit since the data are
not matched well the SM predictions.
Table 28: Systematic uncertainties in percentage of the total SM predictions larger
than 1 % within SRA and SRB. The uncertainties are estimated by using simultaneous
fit to the all signal regions and control regions in data and MC with fixed
normalization factors (µtt̄ , µtt̄Z , and µ Z ) from the background-only fit and floatingµsig . The signal samples (mt̃ , mχ̃0 ) = (1300,1) GeV is used as signal model. Single top
1
modelling is negligible after the fit.
Nb - jet

SRATT
≥2
1

SRATW
≥2
1

SRAT0
≥2
1

SRBTT
≥2
1

SRBTW
≥2
1

SRBT0
≥2
1

Total syst. unc.

42

26

19

18

17

21

24

31

19

13

17

12

tt̄ modellingtt̄Z modelling
Z modelling
W modelling

12
16
5
3

6
7
8
2

10
5
5
3

3
2
9
3

2
8
9
6

1
3
13
4

11
5
1
1

28
2
1
4

9
3
1
3

7
<1
1
8

6
2
5
1

5
1
7
6

µsig
µtt̄
µtt̄+Z
µZ

19
9
<1 <1
14
6
2
5

6
1
9
3

3
5
2
<1 <1 <1
3
4
2
5
6
7

1
1
14
1

<1
3
5
2

1
1
11
1

<1 <1 <1
2
2
1
1
5
1
2
3
5

Small-R JER
Small-R JES
Large-R jet + DNN
b-tagging
ETmiss soft term
LeptonPile-up
MC statistics

19
3
20
3
2
4
<1
6

3
1
3
4
1
3
2
7

6
3
3
4
1
4
1
10

8
1
8
4
<1
3
4
11

9
3
15
3
3
3
2
9

5
5
7
4
1
2
1
8

8
10
15
2
1
5
2
8

9
2
5
5
3
5
2
7

117

20
3
8
2
3
6
2
5

5
3
5
2
1
2
1
5

12
7
4
4
5
4
1
8

10
5
3
2
2
3
<1
4

µ_sigµ_Zjetsµ_ttZµ_ttbar0

0.2 0.4 0.6 0.8

1µ

DNNSFDijet_Modelling
DNNSFDijet_Stat
DNNSFGammajet_Modelling
DNNSFGammajet_Stat
DNNSFttbar_Modelling_bTagLightDNNSFttbar_Modelling_hadronisation
DNNSFttbar_Modelling_highPt
DNNSFttbar_Modelling_matrixElement
DNNSFttbar_Modelling_radiation
DNNSFttbar_Stat
JET_JER_DataVsMC
JET_JER_EffectiveNP_1
JET_JER_EffectiveNP_2
JET_JER_EffectiveNP_3
JET_JER_EffectiveNP_4
JET_JER_EffectiveNP_5
JET_JER_EffectiveNP_6
JET_JER_EffectiveNP_7restTerm
JET_Rtrk_Baseline_pT
JET_Rtrk_Modelling_pT
JET_Rtrk_TotalStat_pT
JET_Rtrk_Tracking_pT
Z_Theo_HF
Z_fac
Z_qsf
Z_renorm
ttbar_FSR
ttbar_Hadronization
ttbar_HardScatter
ttbar_Radiation−1.5 −1 −0.5 0

0.5

1 1.5
α

Figure 64: Results of fit parameters α and normalization factors µ of main
backgrounds and a signal (upper panel) from the model-dependent signal fit to allcontrol regions and signal regions with signal model (mt̃ ,mχ̃0 ) = (1300,1) GeV. α =1(θ − θ 0 )/∆θ, where θ 0 and ∆θ are the initial mean values and standard deviations forindividual parameters, and θ is final value after the fit. Only the nuisance parameters
belong to main backgrounds with significant uncertainties and the normalization
factors are shown. The details of the nuisance parameters can be found in Table 25.
The tt̄Z modelling is not included in the model-dependent fit since the errors are
assigned directly to µtt̄Z . The shaded area refers to the initial value of nuisanceparameters, which are set to 0±1.
6.7.4

Model-independent signal fit

By performing the model-independent signal fit, we can extract the probability ofsignals and the upper limit on the visible cross section for new physics. Since nosignal model is considered, the fit is performed separately for each signal region.
Table 29 shows the results of the fit. The visible cross section is defined as the productof the cross section, acceptance, and efficiency for the selection criteria used in theanalysis. Four SRA regions in the top rows of the table show the lowest upper limits
on the visible cross section, which is 0.02 fb−1 .

118

Table 29: 95% CL upper limits on the visible cross section (heσ i95
obs ) and on the number
95 ) shows the 95%
95
of signal events (Sobs ) for each signal region. The third column (Sexp
CL upper limit on the number of signal events, given the expected number (and ±1σ
excursions on the expectation) of background events. The last two columns indicate
the CLB value, i.e. the confidence level observed for the background-only hypothesis,
the discovery p-value (p(s = 0)), and the significance (Z). The p-value is truncatedto 0.5 if the data is less than the MC predictions.
Signal Region
SRATT2b
SRATW2b
SRAT02b
SRATT1b
SRATW1b
SRAT01b
SRBTT2bSRBTW2b
SRBT02b
SRBTT1b
SRBTW1b
SRBT01b95
heσi95
obs [fb] Sobs

0.02
0.02
0.02
0.02
0.04
0.06
0.03
0.04
0.03
0.05
0.06
0.08

2.3
3.3
3.3
2.3
5.0
8.0
4.4
6.0
4.8
6.7
8.0
10.9

119

95
Sexp

CLB

p(s = 0) (Z)

2.0
3.0+
−1.1
2.5
4.2+
−1.4
2.5
4.5+
−1.5
2.1
3.1+
−1.1
2.7
4.9+
−1.6
3.5
7.0+
−2.2
2.4
4.0+
−1.4
2.8
5.0+
−1.7
2.8
5.2+
−1.7
3.0
6.5+
−1.9
4.6
10.0+
−3.0
5.3
12.0+
−3.6

0.28
0.29
0.23
0.26
0.54
0.63
0.58
0.66
0.43
0.53
0.27
0.41

0.50 (0.00)
0.50 (0.00)
0.50 (0.00)
0.50 (0.00)
0.46 (0.11)
0.35 (0.38)
0.39 (0.27)
0.31 (0.48)
0.50 (0.00)
0.46 (0.10)
0.50 (0.00)
0.50 (0.00)

7Discussion

7.1

Exclusion limit

Exclusion limits with the DNN top taggers are shown in Figure 65 in the cross section
as a function of mt̃ at mχ̃0 = 100 GeV and Figure 66 in the mt̃ -mχ̃0 plane. The expected11limit of mt̃ is extended to ∼1300 GeV at low mχ̃0 . The observed limit with the DNN
1

top tagger is extended to ∼1400 GeV. The expected (observed) limit of mχ̃0 reaches up
1

to 540 (610) GeV. The mt̃ region below 400 GeV is not considered in the analysis since
the mass region is already excluded in the previous ATLAS results at 36 fb−1 [3].
The deviation between expected limit and observed limit around mt̃ = 1300-1400
GeV is due to the smaller number of observed events in the SRAs with respect tothe background expectation.

7.2

Comparison with the results of reclustering method

The search for the scalar top quark in the boosted regions in the paper [129] is briefly
introduced, and the results are compared to the results with DNN top tagger method
obtained in this thesis. The paper shows the results of the four signal regions, SRA,
SRB, SRC, and SRD. The SRC focuses on the compressed region of two-body andthree-body decays (see Figure 7). The SRD covers the three-body and four-bodydecays. The SRA and SRB aim for the same mass region as this thesis (DNN top
tagger method). The critical difference between this thesis and the paper is themethod of top reconstruction. The reclustering jets are used in the paper.

7.2.1

Regions with the reclustering method

Due to different methods of top reconstruction, the design of the regions is also
different. Here, we briefly summarize signal regions and top-tagging method usedin the paper.

7.2.2

Signal regions

The reclustering is the alternative method of the top reconstruction used in the stop
search in the final state with jets and ETmiss [3]. The decay products of hadronically
120

~~
~
0
t1 t1 production ; t1 → t ∼χ
13

σ [pb]

10

s = 13 TeV, 139 ± 2.4 fb-1
m∼χ0 = 100 GeV

2

10Expected cross section ± 2 σ
Expected cross section ± 1 σ

1Expected cross section

10

Theoritical cross section
Observed cross section

1
10−1
10−2
10−3
10−4

400

600

800

1000

1200

1400
m~t [GeV]1

1m∼χ0 [GeV]

Figure 65: Observed (black solid line) and expected (black dot-dashed line) limits asa function of mass of the scalar top quarks on the production cross section at 95%
confidence level with 139 fb−1 of full Run2 dataset. The theoretical cross sections areshown as the red line.

1200

1000

0
0
~~
~
t1 t1 production ; t1 → t ∼χ /bW ∼
χ1

1-1

s=13 TeV, 139 fb , 95% CL

>

m~t 1

m ∼χ 1
0

mt
mt
<
>
∼0 )
∼0 )
~t , χ 1~t , χ 1
(
(
m 1
m 1
∆
∆

Expected Limit (± 1 σexp)
SUSY

Observed Limit (± 1 σtheory)

800

-1

ATLAS ttbarMET0L, 36.1 fb

600

400

200

0

400

600

800

1000

1200

1400

m~t [GeV]
1

Figure 66: Observed (red line) and expected (black dash line) exclusion limit at 95%
confidence level with 139 fb−1 of full Run2 dataset. ±1σ of expected limit (yellowband) is also shown. Observed exclusion limit is also shown in grey area for thecomparison. Grey dash-dotted lines indicate the mass regions of the two-body andthree/four-body decays.

121

ATLAS
Simulation
0.04

s = 13 TeV~ 0χ 1 ) = (1000,1) GeV( t 1,∼

600

Fraction of events

m 1jet, R =1.2 [GeV]

800

400

TT

0.02

200

0

TW
T0
200

400

600

800

0.00

m 0jet, R =1.2 [GeV]

Figure 67: The categories of the signal regions based on the mass of leading R = 1.2
reclustered jets (m0jet, R=1.2 ) and subleading R = 1.2 reclustered jets (m1jet, R=1.2 ) [3].
The simulation sample of (mt̃ , mχ̃0 ) = (1000,1) GeV is used and loose preselections are1
applied. The black line shows the mass requirements of the categories.
decaying top quarks can be mostly reconstructed using small-R jets. These smallR jets are reclustered into R = 1.2 and R = 0.8 jets separately by using the anti-k t
algorithm. No further grooming techniques are applied during the reclustering. The
categories of the signal regions are based on the masses of the leading and subleading
R = 1.2 reclustered jets. Figure 67 shows the two-dimensional mass distributions of
the leading and subleading reclustered jets, with the three prominent populations
visible in the mass plane (The leading jet and the subleading jet are defined as 0 and
1 in the paper with the 36 fb−1 data but they are defined as 1 and 2 in the paper withthe 139 fb−1 data. Here, we use 1 and 2 for the leading jet and the subleading jet.).
All the signal regions are defined by using the leading R = 1.2 jets with the jet masslarger than 120 GeV (m1jet,R=1.2 > 120 GeV). The “TT” category, which means two top
candidates, is defined by using subleading R = 1.2 reclustered jets with the mass >120 GeV. The “TW” category means one top candidate and one W candidate in themass region of 60 GeV <m2jet,R=1.2 < 120 GeV. Finally, the “T0”, which means only
one top candidate is found, is defined with m2jet,R=1.2 < 60 GeV. Both SRA and SRB
consist of these three categories but are separated by using the mT2,χ2 > 450 GeV for
the SRA and mT2,χ2 < 450 GeV for the SRB. In SRA, the mass requirement of the R = 0.8
reclustered jet and b-tagged jet matched with the leading R = 1.2 reclustered jet byusing ∆R < 1.2 are additionally applied. The signal regions are optimized by using∆R (b1 , b2 ), mTb,min , mTb,max , and object-based ETmiss significance, which are also used in
the DNN top tagger method. All the regions are defined in the region with more than
two b-tagged jets. Other variables in Table 30 have been mentioned in the previous
chapters.
122

Table 30: Definition of the SRA and SRB using the reclustered jets and othervariables [129]. The dash line indicates no selection is applied.

Variable/SR

SRA-TT

SRA-TW

SRA-T0

SRB-TT

SRB-TW

SRB-T0> 120 GeV 60–120 GeV< 60 GeV

Trigger

ETmissETmiss> 250 GeV

Nleptons

exactly 0

Njets

≥4

p2T
p4T

> 80 GeV> 40 GeV∆φ jet1−4, ETmiss



> 0.4
≥2

Nb - jetmTb,min> 200 GeV

τ-vetoX

m1jet,R=1.2
m2jet,R=1.2
m1jet,R=0.8
j1R=1.2 (b)j2R=1.2 (b)> 120 GeV

∆R (b, b)> 120 GeV 60–120 GeV> 60 GeV

–

X

–

X

–

> 1.0
–

> 200 GeV

> 25

> 14

> 450 GeV

< 450 GeV

Object-based ETmiss sig.

7.2.3

> 1.4

–

mTb,maxmT2,χ2< 60 GeV

Performance comparison

Figure 68 (a) shows the top-tagging efficiencies of both reclustered jets and DNN
contained top tagged jets as a function of leading large-R jet pT in pT > 350 GeV. The
leading large-R jets are selected by requiring ∆R (large-R jet labelled as a contained
top, R = 1.2 reclustered jet) < 1.0. The reclustering method shows excellent efficiencies close to 100%. The efficiencies of the DNN contained top tagger are around 80%
as expected. Figure 68 (b) shows the background rejection of both methods for themain background process of Z→ νν. The DNN contained top tagger has ∼5 times
better background rejection than the reclustering method. The reclustering method
has essentially no ability of rejecting background in high pT range. This can explain
why reclustering method has the signal efficiency of nearly 100%.
Based on the performance of two methods, most of the signal regions withreclustering method are defined with the tighter selections. The mTb,min , mTb,max , and
123

1.6
1.4
1.2

s = 13 TeV, 139 ± 2.4 fb
Simulation~ ∼0m(t ,χ
)=(1100,1) GeV
1-1

Rejection

Efficiency

2
1.8

RC jet

DNN top tagger

20
18
16
14

1

10
8

0.6

6

0.4

4

0.2

2
400

500

600

700

800

RC jet

DNN top tagger

12

0.8

0

s = 13 TeV, 139 ± 2.4 fb-1
Simulation
Z+jets

900

1000

1100

1200

Leading Large-R Jet p [GeV]

0

400

500

600

700

800

900

1000

1100

1200

Leading Large-R Jet p [GeV]

T

T

(a)

(b)

Figure 68: Performance of the DNN contained top tagger and reclustered jet on (a)the signal efficiencies derived in the simulation sample of (mt̃ , mχ̃0 ) = (1100,1)
1
GeV and (b) the background rejection derived in the simulation samples of Z → νν.
A RC jet is referred to the a reclustered jet.
Table 31: Observed data and fitted SM yields of the reclustering method in SRAs
and SRBs after the background-only fit [3]. The uncertainties include MC statisticaluncertainties, the experimental uncertainties and theoretical uncertainties.
SRA-TT
Observed
Total SMZ + jets
Single top
tt̄
tt̄+Z
W + jetsOther

4
3.2 ± 0.5
1.35 ± 0.28
0.50 ± 0.31
0.08 ± 0.07
1.05 ± 0.29
0.16 ± 0.07
0.080 ± 0.020

SRA-TW
SRA-T0
SRB-TT SRB-TW
SRB-T0
8
11
67
84
292
5.6 ± 0.7 17.3 ± 1.7 46 ± 7
81 ± 7276 ± 243.2 ± 0.4 10.5 ± 1.3 15.6 ± 3.3 28.7 ± 3.4 117 ± 140.59 ± 0.29 1.9 ± 0.8
3.5 ± 1.2
7.0 ± 3.0
31 ± 15
0.16 ± 0.10 0.4 ± 0.4 10 ± 5
20 ± 672 ± 190.74 ± 0.17 1.50 ± 0.34 9.9 ± 1.9 12.5 ± 2.5
22 ± 40.53 ± 0.20 1.7 ± 0.6
4.9 ± 1.98 ±422 ± 90.34 ± 0.24 1.32 ± 0.22 2.4 ± 0.4
4.7 ± 2.3
10.4 ± 1.3∆R (b1 , b2 ) are not used in the SRA with the DNN top tagger method. The selectionsof object-based ETmiss significance with reclustering method are tighter than the selections with DNN top tagger method except for T0 regions. In addition, the regionswith only one b-tagged jet can be used only for using the DNN top tagger method
since only one b-tagged region has too many background events for the reclustering
method.

7.2.4

Comparison of Results

The fit strategy is basically the same as the strategy mentioned in Chapter 6.6.1.
The background-only fit estimates corrections of the normalization factors of backgrounds by using the simultaneous fit to all the control regions. The five floating
normalization factors are set for Z+jets, tt̄Z, tt̄, single top, and W+jets for the fitting.

124

SRBT0

290

2

SRBTW

83

1

SRBTT

61

SRAT0

10

SRATW

8

SRATT

4

250
2

Events

Reclusterings = 13 TeV 139 ± 2.4

200

4

150

1

100
50
1

Not Matched

Not

0
SRA
SRA
S
S
S
S
TW RAT02 RBTT2 RBTW RBT02
che TT2b
2b
2b
b
b
b
d

Mat

DNN top tagger

Figure 69: Comparison of the observed data between DNN top tagger method andreclustering method in the regions with ≥ 2 b-tagged jets. “Not matched” shows theevents are found only in only one method.
Table 31 shows the observed data and fitted SM backgrounds after the backgroundonly fit. No significant excess is found in the results except for the ∼ 1.9σ in the

SRBTT. Comparing with the sensitivity for the signal (mt̃ ,mχ̃0 ) = (1300,1) GeV using1

the DNN top tagger method, the expected significance is improved by 14% with the
DNN top tagger method if only the signal regions with at least two b-tagged jets
are considered. Furthermore, the DNN top tagger method improves the expectedsignificance by 27% over the reclustering method if signal regions with both one andat least two b-tagged jets are considered.
Figure 69 shows the correlation of observed data between the DNN top tagger
method and reclustering method. Since no events are found in the SRATT2b, theSRATT2b bins are empty. Most of the events in DNN top tagger method can befound in the reclustering method except for one in the SRATW2b. The event in
the SRATW2b contains the leading large-R jet being tagged as an inclusive top andthe subleading large-R jet being as a tagged contained top. The leading large-R jet
matches the leading reclustered jet with mass less than 120 GeV. Therefore, the event
does not pass the criteria in the reclustering method. The data migration is found in
the SRB. The TT goes to the TW, and the TW goes to T0. This is expected due to thetighter selections applied to the top candidates.
Figure 70 shows the exclusion limit in the mt̃ -mχ̃0 plane with full Run2 1391

fb−1 dataset for both reclustering method and DNN top tagger method. For the
reclustering method, the yellow band and black dashed line are the expected limit
with ±1σ uncertainties. The expected and observed exclusion limits of mt̃ are ex125

tended to ∼1250 GeV at low neutralino mass. The expected (observed) exclusion
limit of mχ̃0 is extended to ∼510 (490) GeV around mt̃ = 1100 GeV. The expected1

exclusion area is largely improved for the results at 139 fb−1 . For the DNN top
tagger method, the expected (observed) limit of mt̃ at low neutralino mass is 50(150) GeV higher than the reclustering method and the expected (observed) limit ofmχ̃0 is 30 (120) GeV higher in two-body region. It is clearly seen that the search at the1boosted region can benefit from the DNN top tagger method. On the other hand, theregion containing more resolved top signals benefits from the reclustering methodwith larger radius jets and loose selections. Such selections with the reclustering
method will result in higher sensitivity in the region close to the compressed region
below mt̃ = 800 GeV.
Due to the excess in SRBTT with the reclustering method, the observed limit
around (mt̃ ,mχ̃0 ) = (900,400) GeV is not excluded. However, the excess is not found in1

the DNN top tagger method, and the signal point is excluded by the DNN top tagger

1mχ∼0 [GeV]

method.
1200

1000

0
0
0
~~
~
t1 t1 production ; t1 → t ∼χ /bW ∼
χ /bff'∼
χ
1

1

1

>

-1

s=13 TeV, 139 fb , 95% CL

m~t 1

0
m ∼χ 1

Expected Limit (±1 σ exp) (RC)
Expected Limit (±1 σ exp) (DNN)
Observed Limit (RC)
Observed Limit (DNN)-1
ATLAS ttbarMET0L, 36.1 fb

800

mt
mt
<
>
∼0 )
∼0 )
~t , χ 1~t , χ 1
(
(
m 1
m 1
∆
∆

600

400

200

0

400

600

800

1000

1200

1400

m~t [GeV]
1

Figure 70: Observed and expected exclusion limit at 95% confidence level with
139 fb−1 of full Run2 dataset in the mt̃ -mχ̃0 plane for both DNN top tagger method1
and reclustering method. “RC” represents the reclustering method and “DNN”
represents the DNN top tagger method. The results of reclustering method include0
the search for a compressed region of two-body decay (∆m(t̃1 , χ̃1 ) > mt ) and0
three/four-body decay (∆m(t̃1 , χ̃1 ) < mt ). Both targeting regions are also sensitive
to three-body decay. Observed exclusion limit is also shown in a grey area for thecomparison.

126

7.3

Comparison with CMS results

Figure 71: Observed and expected exclusion limit at 95% confidence level with 137
fb−1 of full Run2 dataset in the mt̃ -mχ̃0 plane [130].
1

Figure 71 shows the exclusion contour of mt̃ and mχ̃0 , where the scalar top quarks
1decay in the two-body and three-body, with 137 fb−1 of full Run2 data recorded by
the CMS detector. The mt̃ is excluded up to 1220 GeV for the expected limit and 1200
GeV for the observed limit. The mχ̃0 is excluded up to 520 GeV for the expected limit1

and 580 GeV for the observed limit. CMS collaboration uses mT2 inclusive search for
the SUSY particles including gluinos, light-flavor, bottom and top squarks. The mT2 isreconstructed by selecting the ETmiss and the two jets with the highest dijet invariant
mass. Total 282 signal regions are categorized by the number of jets, the number ofb-tagged jets, the scalar sum of jet pT and mT2 . In the DNN top tagger method andreclustering method, we aggressively select boosted top candidates in SRA regions
and SRB regions to get higher sensitivity at high mt̃ . However, CMS collaboration
has better results near the compressed region, for example, the (mt̃ , mχ̃0 ) = (700, 450)
1

GeV, which is not excluded by either the DNN top tagger or reclustering method. In
this region, the top quarks are not boosted so that the decay products may spreadwidely. The reconstruction of resolved top quarks can be a key for the improvementof the sensitivity.
In summary, CMS results show better limits in the compressed region near0∆m(t̃1 , χ̃1 ) ∼ mt . The results of DNN top tagger method show better limits in highmt̃ region, which is our target in this thesis.

127Comparison with results in one/two-lepton final statess = 8,13 TeV, 20.3-139 fb -1

July 2020
Observed limits

W

m

70
60
50
40
30
20
10
0 180

Expected limits

Data 15-18, s = 13 TeV, 139 fb -1
~
∼0 ~
∼0 ~
∼0
0L, t1 → t χ / t1 → bWχ / t1 → bff' χ
1

200

1

1

220

1

1

[ATLAS-CONF-2020-003,
ATLAS-CONF-2019-017]
~
∼0 ~
∼0 ~
∼0
2L, t1 → t χ / t1 → bWχ / t1 → bff' χ
1

1

1

∆

500

1

[2004.14060]
~
∼0 ~
∼0 ~
∼0
1L, t1 → t χ / t1 → bWχ / t1 → bff' χ

t

600

+

700

Limits at 95% CLb~~t1t1 production
∆
m ~
m ~
(t
(t
1 , χ∼ 0
1 , χ∼ 0
1 )=
1 )=
m
m

800

0

ATLAS Preliminarym ~(t
1 , χ∼ 0
1 )=

0
m(∼
χ 1) [GeV]

900

∆

7.4

[ATLAS-CONF-2020-046]

400

Data 15-16, s = 13 TeV, 36.1 fb -1
~
∼0 ~
∼0 ~
∼0
t1 → t χ / t1 → bWχ / t1 → bff' χ
1

300

1

1

[1709.04183, 1711.11520,
1708.03247, 1711.03301]~∼0
tt, t1 → t χ

200

1[1903.07570]

100

Data 12, s = 8 TeV, 20.3 fb -1
~
∼0 ~
∼0 ~
∼0
t1 → t χ / t1 → bWχ / t1 → bff' χ1

1

1[1506.08616]

200

400

600

800

1000 1200~m( t1 ) [GeV]

Figure 72: Observed and expected exclusion limit of all channels at 95% confidence
level with 139 fb−1 of full Run2 dataset in the mt̃ -mχ̃0 plane [131].
1

Figure 72 shows the exclusion contour of mt̃ and mχ̃0 with 139 fb−1 of full Run2
1

data recorded by the ATLAS detector. The expected (observed) limit of the stop mass
is extended up to 970(1000) GeV for the two-lepton channel and 1200(1200) GeV
for the one-lepton channel. In the analysis of two-lepton channel [132], the reconstruction of top candidates is not considered. Instead, the mT2 algorithm with the
inputs of two leptons and ETmiss is used for the rejection of background leptonic decayof W bosons if the ETmiss is mainly contributed from neutrinos. In the one-lepton
channel [133], two methods are used for the top reconstruction in the medium and0high ∆m(t̃1 , χ̃1 ). First, the topness variable [134] is used for the rejection of dileptonictt̄, which one of the two leptons is not identified. The variable is determined by minimizing the χ2 -like function based on the top mass and W boson mass. Second, thereslustered jets with a variable radius are used for the hadronic decay of top quarks,
which the initial radius is 3.0. The larger radius can provide the reconstruction of
top candidates with lower pT . However, the identification of boosted top candidates
shows better sensitivity in the high stop mass region since the limit of the stop massin the zero-lepton channel is higher than the limit in the one-lepton channel.
In summary, the identification of boosted top candidates in the hadronic final
states plays a key role in the search for the stop with the high mass.
128

8Conclusion

A new method for the top reconstruction, DNN top tagger, has been introduced in
the search for the scalar top quark with fully hadronic final states. This search is√
performed with an integrated luminosity of 139 fb−1 of s = 13 TeV proton-proton
collision data acquired at the ATLAS. The direct pair production of the scalar top
quarks is assumed in the signal scenario. A scalar top quark is expected to decay
into a top and a neutralino. The target for the improvement is the boosted region
0with large ∆m(t̃1 , χ̃1 ). The number of the top quark candidates from the DNN top
tagger provides good categorization to maximize the acceptance of the stop signals
and reduce the backgrounds. The signal regions with high sensitivity are defined andoptimized for the full Run 2 dataset. The main backgrounds in the signal regions arecarefully estimated using the control regions defined for each main background andvalidated in the validation regions. The performance of top taggers is also validated
by evaluating the top-quark tagging efficiency and background rejection using dataenriched in hadronic top jets and background jets.
The comparison between the reclustering method used in the ATLAS paper andthe DNN top tagger method used in this thesis is also presented. The reclustering
method shows very high tagging efficiencies but low background rejections. The
DNN top tagger method has the comparable tagging efficiencies (80%) with fivetimes higher background rejections. The new method exploits the jet substructure
variables and the deep learning algorithm to gain the background rejection, resulting
in the restoration of the sensitivity in certain signal regions, otherwise dominated by
the background. Owing to the improved background rejection, the signal regionswith only 1 b-tagged jet are newly introduced to the search for the scalar top quark
signals. As a result, the DNN top tagger method improves the 27% higher sensitivity
over the reclustering method in the search for the scalar top quark in the boosted
regions.
No significant excess is found in the stop search using the DNN top tagger
method. Exclusion limits at 95% confidence level are evaluated as a function ofmt̃ and mχ̃0 . The exclusion of the mt̃ is extended up to 1.4 TeV for the mχ̃0 below 200
1

1

GeV. Model-independent limits are also derived for each signal region. The lowest
cross section bound for new physics phenomena is down to 0.02 fb.

129

Reference[1] M. Tanabashi et al. “Review of Particle Physics”. Phys. Rev. D 98 (3 2018),
p. 030001. DOI: 10 . 1103 / PhysRevD . 98 . 030001. URL: https : / / link . aps .

org/doi/10.1103/PhysRevD.98.030001 (cit. on p. 7).
[2] Albert M Sirunyan et al. “Search for supersymmetry in proton-proton collisions at 13 TeV using identified top quarks”. Phys. Rev. D 97.CMS-SUS-16-050,
CERN-EP-2017-269 (2018), p. 012007. DOI: 10 . 1103 / PhysRevD . 97 . 012007.
arXiv: 1710.11188 [hep-ex] (cit. on pp. 7, 8).
[3] Morad Aaboud et al. “Search for a scalar partner of the top quark in the√jets plus missing transverse momentum final state at s=13 TeV with the
ATLAS detector”. JHEP 12.CERN-EP-2017-162 (2017), p. 085. DOI: 10.1007/

JHEP12(2017)085. arXiv: 1709.04183 [hep-ex] (cit. on pp. 7, 8, 120, 122, 124).
[4] Steven Weinberg. “A Model of Leptons”. Phys. Rev. Lett. 19 (21 1967), pp. 1264–
1266. DOI: 10.1103/PhysRevLett.19.1264 (cit. on p. 12).
[5] M. J. G. Veltman. “The Infrared - Ultraviolet Connection”. Acta Phys. Polon.
B12.Print-80-0851 (MICHIGAN) (1981), p. 437 (cit. on p. 12).
[6] Stephen P. Martin. “A Supersymmetry primer”. FERMILAB-PUB-97-425-T (1997).
[Adv. Ser. Direct. High Energy Phys.18,1(1998)], pp. 1–98. DOI: 10 . 1142 /9789812839657_0001. arXiv: hep-ph/9709356 [hep-ph] (cit. on pp. 15, 18).
[7] Y. Akrami et al. “Planck 2018 results. I. Overview and the cosmological legacyof Planck” (2018). arXiv: 1807.06205 [astro-ph.CO] (cit. on p. 17).
[8] Lawrence J. Hall, David Pinner, and Joshua T. Ruderman. “A natural SUSY
Higgs near 125 GeV”. Journal of High Energy Physics 2012.4 (2012), p. 131. ISSN:
1029-8479. DOI: 10.1007/JHEP04(2012)131 (cit. on p. 19).
[9] ATLAS collaboration. “Search for direct top squark pair production in the 3body decay mode with a final state containing one lepton, jets, and missing√
transverse momentum in s = 13TeV pp collision data with the ATLAS detector”. ATLAS-CONF-2019-017 (May 2019) (cit. on p. 20).
[10] Johan Alwall, Philip Schuster, and Natalia Toro. “Simplified Models for aFirst Characterization of New Physics at the LHC”. Phys. Rev. D 79 (2009),
p. 075020. DOI: 10.1103/PhysRevD.79.075020. arXiv: 0810.3921 [hep-ph](cit. on p. 19).

130

[11] Claus Horn. “A Bottom-Up Approach to SUSY Analyses”. J. Phys. G 36 (2009),
p. 105005. DOI: 10 . 1088 / 0954 - 3899 / 36 / 10 / 105005. arXiv: 0905 . 4497

[hep-ex] (cit. on p. 19).
[12] Wim Beenakker et al. “Supersymmetric top and bottom squark production at
hadron colliders”. JHEP 08.CERN-PH-TH-2010-142, ITFA-2010-015, ITP-UU10-17, NIKHEF-2010-016, TTK-10-33 (2010), p. 098. DOI: 10.1007/JHEP08(2010)098. arXiv: 1006.4771 [hep-ph] (cit. on pp. 20, 43).
[13] Lyndon Evans and Philip Bryant. “LHC Machine”. JINST 3 (2008), S08001.
DOI : 10.1088/1748-0221/3/08/S08001 (cit. on p. 22).

[14] CERN. “LEP Design Report: Vol.2. The LEP Main Ring”. CERN-LEP-84-01(June 1984) (cit. on p. 22).
[15] Esma Mobs. “The CERN accelerator complex - August 2018. Complexe desaccélérateurs du CERN - Août 2018”. OPEN-PHO-ACCEL-2018-005 (2018).
General Photo. URL: http://cds.cern.ch/record/2636343 (cit. on p. 23).
[16] Werner Herr and B Muratori. “Concept of luminosity” (2006). DOI: 10.5170/

CERN- 2006- 002.361. URL: https://cds.cern.ch/record/941318 (cit. on
p. 22).
[17] Joao Pequenao. “Computer generated image of the whole ATLAS detector”.
2008. URL: https://cds.cern.ch/record/1095924 (cit. on p. 24).
[18] G. Aad et al. “The ATLAS Experiment at the CERN Large Hadron Collider”.
JINST 3 (2008), S08003. DOI: 10.1088/1748-0221/3/08/S08003 (cit. on pp. 24,
25, 30–36).
[19] ATLAS collaboration. “ATLAS inner detector: Technical design report. Vol. 1”.
CERN-LHCC-97-16, ATLAS-TDR-4 (Apr. 1997) (cit. on p. 26).
[20] M. Capeans et al. “ATLAS Insertable B-Layer Technical Design Report”. CERNLHCC-2010-013, ATLAS-TDR-19 (Sept. 2010) (cit. on pp. 26, 27).
[21] G. Aad et al. “ATLAS pixel detector electronics and sensors”. JINST 3 (2008),
P07007. DOI: 10.1088/1748-0221/3/07/P07007 (cit. on p. 26).
[22] A. Abdesselam et al. “The barrel modules of the ATLAS semiconductor tracker”.
Nucl. Instrum. Meth. A 568.ATL-COM-INDET-2006-009, ATL-INDET-PUB-2006005 (2006), pp. 642–671. DOI: 10.1016/j.nima.2006.08.036 (cit. on p. 27).
[23] A. Abdesselam et al. “The ATLAS semiconductor tracker end-cap module”.
Nucl. Instrum. Meth. A 575 (2007), pp. 353–389. DOI: 10.1016/j.nima.2007.

02.019 (cit. on p. 27).
131

[24] E. Abat et al. “The ATLAS TRT end-cap detectors”. JINST 3 (2008), P10003.
DOI : 10.1088/1748-0221/3/10/P10003 (cit. on p. 28).

[25] ATLAS collaboration. “ATLAS liquid argon calorimeter: Technical design report”. CERN-LHCC-96-41 (Dec. 1996) (cit. on p. 28).
[26] ATLAS collaboration. “ATLAS tile calorimeter: Technical design report”. CERNLHCC-96-42 (Dec. 1996) (cit. on p. 28).
[27] J. Abdallah et al. “The Production and Qualification of Scintillator Tiles for the
ATLAS Hadronic Calorimeter”. ATL-COM-TILECAL-2007-026, ATL-TILECALPUB-2007-010 (Dec. 2007) (cit. on pp. 28, 32).
[28] G. Aad et al. “Drift time measurement in the ATLAS liquid argon electromagnetic calorimeter using cosmic muons”. J. Phys. Conf. Ser. 293 (2011), p. 012050.
DOI : 10.1088/1742-6596/293/1/012050 (cit. on p. 29).

[29] I. Wingerter-Seez. “Particle Physics Instrumentation”. Proceedings, 2nd AsiaEurope-Pacific School of High-Energy Physics (AEPSHEP 2014): Puri, India, November 04–17, 2014. 2017, pp. 295–314. DOI: 10 . 23730 / CYRSP - 2017 - 002 . 295.
arXiv: 1804.11246 [physics.ins-det] (cit. on p. 29).
[30] A. Artamonov et al. “The ATLAS forward calorimeters”. JINST 3 (2008), P02010.
DOI : 10.1088/1748-0221/3/02/P02010 (cit. on p. 29).

[31] Bernard Aubert et al. “Development and construction of large size signal
electrodes for the ATLAS electromagnetic calorimeter”. Nucl. Instrum. Meth. A
539.CERN-PH-EP-2004-019 (2005), pp. 558–594. DOI: 10.1016/j.nima.2004.

11.005 (cit. on p. 29).
[32] M.L Andrieux et al. “Construction and test of the first two sectors of the
ATLAS barrel liquid argon presampler”. Nucl. Instrum. Meth. A 479 (2002),
pp. 316–333. DOI: 10.1016/S0168-9002(01)00943-3 (cit. on p. 29).
[33] J. Abdallah et al. “Mechanical construction and installation of the ATLAS tile
calorimeter”. JINST 8 (2013), T11001. DOI: 10.1088/1748-0221/8/11/T11001(cit. on p. 32).
[34] G. Avoni et al. “The new LUCID-2 detector for luminosity measurement andmonitoring in ATLAS”. Journal of Instrumentation 13.07 (2018), P07017–P07017.
DOI : 10.1088/1748-0221/13/07/p07017 (cit. on p. 36).

[35] Georges Aad et al. “Operation of the ATLAS trigger system in Run 2”. CERNEP-2020-109 (July 2020). arXiv: 2007.12539 [physics.ins-det] (cit. on p. 37).

132

[36] Peter Jenni, Marzio Nessi, and Markus Nordberg. Zero Degree Calorimeters for
ATLAS. Tech. rep. CERN-LHCC-2007-001. LHCC-I-016. Geneva: CERN, 2007.
URL : https://cds.cern.ch/record/1009649 (cit. on p. 36).

[37] ATLAS collaboration. LuminosityPublicResultsRun2. https://twiki.cern.ch/

twiki/bin/view/AtlasPublic/LuminosityPublicResultsRun2 (cit. on p. 38).
√[38] ATLAS collaboration. “Luminosity determination in pp collisions at s = 13
TeV using the ATLAS detector at the LHC”. ATLAS-CONF-2019-021 (June2019) (cit. on p. 38).
[39] Morad Aaboud et al. “Performance of the ATLAS Trigger System in 2015”.
Eur. Phys. J. C 77.CERN-EP-2016-241 (2017), p. 317. DOI: 10 . 1140 / epjc /s10052-017-4852-3. arXiv: 1611.09661 [hep-ex] (cit. on p. 38).
[40] Georges Aad et al. “Performance of the missing transverse momentum triggers for the ATLAS detector during Run-2 data taking”. JHEP 08.CERN-EP2020-050 (2020), p. 080. DOI: 10.1007/JHEP08(2020)080. arXiv: 2005.09554[hep-ex] (cit. on pp. 39–41).
[41] G. Aad et al. “Performance of electron and photon triggers in ATLAS during
LHC Run 2”. The European Physical Journal C 80.1 (2020). ISSN: 1434-6052. DOI:

10.1140/epjc/s10052-019-7500-2 (cit. on pp. 39, 40).
[42] Georges Aad et al. “Performance of the ATLAS muon triggers in Run 2”.
JINST 15.CERN-EP-2020-031 (2020), P09015. DOI: 10.1088/1748- 0221/15/

09/p09015. arXiv: 2004.13447 [hep-ex] (cit. on pp. 39, 40).
[43] S. Agostinelli et al. “Geant4 - a simulation toolkit”. Nuclear Instruments andMethods in Physics Research Section A: Accelerators, Spectrometers, Detectors andAssociated Equipment 506.3 (2003), pp. 250–303. DOI: 10.1016/S0168-9002(03)01368-8 (cit. on p. 40).
[44] ATLAS collaboration. “The simulation principle and performance of the ATLAS fast calorimeter simulation FastCaloSim”. ATL-PHYS-PUB-2010-013, ATLCOM-PHYS-2010-838 (Oct. 2010) (cit. on p. 41).
[45] Torbjörn Sjöstrand, Stephen Mrenna, and Peter Z. Skands. “PYTHIA 6.4 Physics
and Manual”. JHEP 05 (2006), p. 026. DOI: 10.1088/1126-6708/2006/05/026(cit. on p. 41).
[46] Torbjörn Sjöstrand, Stephen Mrenna, and Peter Z. Skands. “A Brief Introduction to PYTHIA 8.1”. Comput. Phys. Commun. 178 (2008), pp. 852–867. DOI:

10.1016/j.cpc.2008.01.036 (cit. on p. 41).

133

[47] ATLAS collaboration. “The Pythia 8 A3 tune description of ATLAS minimum
bias and inelastic measurements incorporating the Donnachie-Landshoff diffractive model”. ATL-PHYS-PUB-2016-017 (Aug. 2016) (cit. on p. 41).
[48] ATLAS collaboration. “ATLAS Pythia 8 tunes to 7 TeV datas”. ATL-PHYSPUB-2014-021 (Nov. 2014) (cit. on pp. 41, 43, 104).
[49] J. Alwall et al. “The automated computation of tree-level and next-to-leading
order differential cross sections, and their matching to parton shower simulations”. JHEP 07 (2014), p. 079. DOI: 10 . 1007 / JHEP07(2014 ) 079 (cit. on
pp. 41–43).
[50] D.J. Lange. “The EvtGen particle decay simulation package”. Nucl. Instrum.
Meth. A 462 (2001). Ed. by S. Erhan, P. Schlein, and Y. Rozen, pp. 152–155. DOI:

10.1016/S0168-9002(01)00089-4 (cit. on p. 41).
[51] T. Gleisberg et al. “Event generation with SHERPA 1.1”. JHEP 02.FERMILABPUB-08-477-T, SLAC-PUB-13420, ZU-TH-17-08, DCPT-08-138, EDINBURGH2008-30, IPPP-08-69, MCNET-08-14 (2009), p. 007. DOI: 10.1088/1126-6708/

2009/02/007. arXiv: 0811.4622 [hep-ph] (cit. on p. 41).
[52] Simone Alioli et al. “A general framework for implementing NLO calculations in shower Monte Carlo programs: the POWHEG BOX”. JHEP 06.DESY10-018, SFB-CPP-10-22, IPPP-10-11, DCPT-10-22 (2010), p. 043. DOI: 10.1007/

JHEP06(2010)043. arXiv: 1002.2581 [hep-ph] (cit. on p. 42).
[53] Johannes Bellm et al. “Herwig 7.0/Herwig++ 3.0 release note”. Eur. Phys. J.
C76.4 (2016), p. 196. DOI: 10.1140/epjc/s10052-016-4018-8 (cit. on p. 42).
[54] Stefano Catani et al. “Vector boson production at hadron colliders: a fully
exclusive QCD calculation at NNLO”. Phys. Rev. Lett. 103 (2009), p. 082001.
DOI : 10.1103/PhysRevLett.103.082001. arXiv: 0903.2120 [hep-ph] (cit. on

p. 43).
[55] ATLAS collaboration. “Modelling of rare top quark processes at√

s = 13 TeV

in ATLAS”. ATL-PHYS-PUB-2020-024 (Sept. 2020) (cit. on p. 43).
[56] Michał Czakon, Paul Fiedler, and Alexander Mitov. “Total Top-Quark PairProduction Cross Section at Hadron Colliders Through O(α4S )”. Phys. Rev.

Lett. 110.CERN-PH-TH-2013-056, TTK-13-08 (2013), p. 252004. DOI: 10.1103/

PhysRevLett.110.252004. arXiv: 1303.6254 [hep-ph] (cit. on p. 43).

134

[57] Michal Czakon and Alexander Mitov. “NNLO corrections to top pair production at hadron colliders: the quark-gluon reaction”. JHEP 01.CERN-PH-TH2012-286 (2013), p. 080. DOI: 10 . 1007 / JHEP01(2013 ) 080. arXiv: 1210 . 6832

[hep-ph] (cit. on p. 43).
[58] Michal Czakon and Alexander Mitov. “NNLO corrections to top-pair production at hadron colliders: the all-fermionic scattering channels”. JHEP 12.CERNPH-TH-2012-181 (2012), p. 054. DOI: 10.1007/JHEP12(2012)054. arXiv: 1207.

0236 [hep-ph] (cit. on p. 43).
[59] Peter Bärnreuther, Michal Czakon, and Alexander Mitov. “Percent Level Precision Physics at the Tevatron: First Genuine NNLO QCD Corrections to qq̄ →tt̄ + X”. Phys. Rev. Lett. 109.CERN-PH-TH-2012-092 (2012), p. 132001. DOI:

10.1103/PhysRevLett.109.132001. arXiv: 1204.5201 [hep-ph] (cit. on p. 43).
[60] Matteo Cacciari et al. “Top-pair production at hadron colliders with next-tonext-to-leading logarithmic soft-gluon resummation”. Phys. Lett. B710.CERNPH-TH-2011-277, TTK-11-54 (2012), pp. 612–622. DOI: 10.1016/j.physletb.

2012.03.013. arXiv: 1111.5869 [hep-ph] (cit. on p. 43).
[61] Michal Czakon and Alexander Mitov. “Top++: A Program for the Calculationof the Top-Pair Cross-Section at Hadron Colliders”. Comput. Phys. Commun.
185.CERN-PH-TH-2011-303, TTK-11-58 (2014), p. 2930. DOI: 10.1016/j.cpc.

2014.06.021. arXiv: 1112.5675 [hep-ph] (cit. on p. 43).
[62] Nikolaos Kidonakis. “Next-to-next-to-leading-order collinear and soft gluon
corrections for t-channel single top quark production”. Phys. Rev. D83 (2011),
p. 091503. DOI: 10.1103/PhysRevD.83.091503. arXiv: 1103.2792 [hep-ph](cit. on p. 43).
[63] Nikolaos Kidonakis. “Two-loop soft anomalous dimensions for single top quark
associated production with a W − or H − ”. Phys. Rev. D82 (2010), p. 054018.
DOI : 10.1103/PhysRevD.82.054018. arXiv: 1005.4451 [hep-ph] (cit. on p. 43).

[64] Nikolaos Kidonakis. “NNLL resummation for s-channel single top quark production”. Phys. Rev. D81 (2010), p. 054028. DOI: 10 . 1103 / PhysRevD . 81 .

054028. arXiv: 1001.5034 [hep-ph] (cit. on p. 43).
[65] ATLAS collaboration. “Multi-Boson Simulation for 13 TeV ATLAS Analyses”.
ATL-PHYS-PUB-2017-005 (May 2017) (cit. on p. 43).
[66] ATLAS collaboration. “Multijet simulation for 13 TeV ATLAS Analyses”. ATLPHYS-PUB-2019-017 (2019) (cit. on p. 43).

135

[67] Wim Beenakker et al. “NNLL-fast: predictions for coloured supersymmetricparticle production at the LHC with threshold and Coulomb resummation”.
JHEP 12.MS-TP-16-17, NIKHEF-2016-037, TTK-16-28 (2016), p. 133. DOI: 10.

1007/JHEP12(2016)133. arXiv: 1607.07741 [hep-ph] (cit. on p. 43).
[68] W. Beenakker et al. “Stop production at hadron colliders”. Nucl. Phys. B 515.RALTR-97-056, DESY-97-214, CERN-TH-97-177 (1998), pp. 3–14. DOI: 10 . 1016 /S0550-3213(98)00014-5. arXiv: hep-ph/9710451 (cit. on p. 43).
[69] Wim Beenakker et al. “NNLL resummation for stop pair-production at the
LHC”. JHEP 05.MS-TP-16-01, TTK-16-01, NIKHEF-2016-002 (2016), p. 153. DOI:

10.1007/JHEP05(2016)153. arXiv: 1601.02954 [hep-ph] (cit. on p. 43).
[70] Hung-Liang Lai et al. “New parton distributions for collider physics”. Phys.
Rev. D 82.MSUHEP-100707, SMU-HEP-10-10 (2010), p. 074024. DOI: 10.1103/

PhysRevD.82.074024. arXiv: 1007.2241 [hep-ph] (cit. on p. 43).
[71] M. Aaboud et al. “Performance of the ATLAS Track Reconstruction Algorithms in Dense Environments in LHC Run 2”. Eur. Phys. J. C 77.CERN-EP2017-045 (2017), p. 673. DOI: 10 . 1140 / epjc / s10052 - 017 - 5225 - 7. arXiv:

1704.07983 [hep-ex] (cit. on p. 44).
[72] R. Fruhwirth. “Application of Kalman filtering to track and vertex fitting”.
Nucl. Instrum. Meth. A 262.HEPHY-PUB-87-503 (1987), pp. 444–450. DOI: 10.

1016/0168-9002(87)90887-4 (cit. on p. 44).
[73] G. Piacquadio, Kirill Prokofiev, and A. Wildauer. “Primary vertex reconstruction in the ATLAS experiment at LHC”. J. Phys. Conf. Ser. 119 (2008), p. 032033.
DOI : 10.1088/1742-6596/119/3/032033 (cit. on p. 46).

[74] R. Fruhwirth, W. Waltenberger, and P. Vanlaer. “Adaptive vertex fitting”. J.
Phys. G 34.CERN-CMS-NOTE-2007-008, CMS-NOTE-2007-008 (2007), N343.
DOI : 10.1088/0954-3899/34/12/N01 (cit. on p. 46).

[75] ATLAS Collaboration. “Topological cell clustering in the ATLAS calorimeters
and its performance in LHC Run 1”. Eur. Phys. J. C 77.CERN-PH-EP-2015-304(2017), p. 490. DOI: 10.1140/epjc/s10052- 017- 5004- 5. arXiv: 1603.02934[hep-ex] (cit. on pp. 46, 50).
[76] ATLAS collaboration. “Improved electron reconstruction in ATLAS using theGaussian Sum Filter-based model for bremsstrahlung”. ATLAS-CONF-2012047 (May 2012) (cit. on p. 47).

136

[77] Georges Aad et al. “Electron and photon performance measurements with
the ATLAS detector using the 2015–2017 LHC proton-proton collision data”.
JINST 14.CERN-EP-2019-145 (2019), P12006. DOI: 10.1088/1748- 0221/14/

12/P12006. arXiv: 1908.00005 [hep-ex] (cit. on p. 47).
[78] Morad Aaboud et al. “Electron reconstruction and identification in the ATLAS√
experiment using the 2015 and 2016 LHC proton-proton collision data at s
= 13 TeV”. Eur. Phys. J. C 79.CERN-EP-2018-273 (2019), p. 639. DOI: 10.1140/

epjc / s10052 - 019 - 7140 - 6. arXiv: 1902 . 04655 [physics.ins-det] (cit. on
pp. 48, 103, 143).
[79] Georges Aad et al. “Muon reconstruction performance of the ATLAS detector√
in proton–proton collision data at s =13 TeV”. Eur. Phys. J. C 76.CERN-EP2016-033 (2016), p. 292. DOI: 10 . 1140 / epjc / s10052 - 016 - 4120 - y. arXiv:

1603.05598 [hep-ex] (cit. on pp. 49, 103, 144).
[80] Matteo Cacciari, Gavin P. Salam, and Gregory Soyez. “The anti-k t jet clustering algorithm”. JHEP 04.LPTHE-07-03 (2008), p. 063. DOI: 10 . 1088 / 1126 -6708/2008/04/063. arXiv: 0802.1189 [hep-ph] (cit. on p. 50).
[81] ATLAS collaboration. “Tagging and suppression of pileup jets”. ATLAS-CONF2014-018 (May 2014) (cit. on pp. 51, 102).
[82] ATLAS collaboration. “Selection of jets produced in 13TeV proton-proton collisions with the ATLAS detector”. ATLAS-CONF-2015-029 (July 2015) (cit. on
p. 51).
[83] David Krohn, Jesse Thaler, and Lian-Tao Wang. “Jet Trimming”. JHEP 02 (2010),
p. 084. DOI: 10.1007/JHEP02(2010)084. arXiv: 0912.1342 [hep-ph] (cit. on
p. 51).
[84] M. Aaboud et al. “Jet energy scale measurements and their systematic uncer√
tainties in proton-proton collisions at s = 13 TeV with the ATLAS detector”.
Phys. Rev. D 96.CERN-EP-2017-038 (2017), p. 072002. DOI: 10.1103/PhysRevD.

96.072002. arXiv: 1703.09665 [hep-ex] (cit. on pp. 52, 53, 101).
[85] Matteo Cacciari, Gavin P. Salam, and Gregory Soyez. “The Catchment Area ofJets”. JHEP 04.LPTHE-07-02 (2008), p. 005. DOI: 10.1088/1126- 6708/2008/

04/005. arXiv: 0802.1188 [hep-ph] (cit. on pp. 52, 59).
[86] Morad Aaboud et al. “In situ calibration of large-radius jet energy and massin 13 TeV proton–proton collisions with the ATLAS detector”. Eur. Phys. J. C
79.CERN-EP-2018-191 (2019), p. 135. DOI: 10.1140/epjc/s10052-019-6632-8.
arXiv: 1807.09477 [hep-ex] (cit. on pp. 52, 54).
137

[87] David Krohn, Jesse Thaler, and Lian-Tao Wang. “Jets with Variable R”. JHEP
06 (2009), p. 059. DOI: 10.1088/1126- 6708/2009/06/059. arXiv: 0903.0392[hep-ph] (cit. on p. 54).
[88] Georges Aad et al. “ATLAS b-jet identification performance and efficiency√
measurement with tt̄ events in pp collisions at s = 13 TeV”. Eur. Phys. J. C
79.CERN-EP-2019-132 (2019), p. 970. DOI: 10.1140/epjc/s10052-019-7450-8.
arXiv: 1907.05120 [hep-ex] (cit. on p. 55).
[89] ATLAS collaboration. “Secondary vertex finding for jet flavour identification
with the ATLAS detector”. ATL-PHYS-PUB-2017-011 (June 2017) (cit. on p. 55).
[90] ATLAS collaboration. “Topological b-hadron decay reconstruction and identification of b-jets with the JetFitter package in the ATLAS experiment at the
LHC”. ATL-PHYS-PUB-2018-025 (2018) (cit. on pp. 55, 102).
[91] ATLAS collaboration. “ETmiss performance in the ATLAS detector using 20152016 LHC p-p collisions”. ATLAS-CONF-2018-023 (June 2018) (cit. on pp. 57,
102, 103).
[92] ATLAS collaboration. “Object-based missing transverse momentum significance in the ATLAS detector”. ATLAS-CONF-2018-038 (July 2018) (cit. on
p. 58).
[93] Morad Aaboud et al. “Performance of top-quark and W-boson tagging withATLAS in Run 2 of the LHC”. Eur. Phys. J. C 79.CERN-EP-2018-192 (2019),
p. 375. DOI: 10.1140/epjc/s10052-019-6847-8. arXiv: 1808.07858 [hep-ex](cit. on pp. 60, 65).
[94] Amal Vaidya et al. Optimisation procedure for two-variable top, W and Z substructure taggers for the ATLAS detector. Tech. rep. ATL-COM-PHYS-2017-033.
Geneva: CERN, 2017. URL: https://cds.cern.ch/record/2242865 (cit. on
p. 59).
[95] ATLAS collaboration. “Jet mass reconstruction with the ATLAS Detector inearly Run 2 data”. ATLAS-CONF-2016-035 (July 2016) (cit. on p. 61).
[96] Jesse Thaler and Ken Van Tilburg. “Identifying Boosted Objects with N-subjettiness”.
JHEP 03.MIT-CTP-4191 (2011), p. 015. DOI: 10.1007/JHEP03(2011)015. arXiv:

1011.2268 [hep-ph] (cit. on p. 61).
[97] Jesse Thaler and Ken Van Tilburg. “Maximizing Boosted Top Identification
by Minimizing N-subjettiness”. JHEP 02.MIT-CTP-4287 (2012), p. 093. DOI:

10.1007/JHEP02(2012)093. arXiv: 1108.2701 [hep-ph] (cit. on p. 61).

138

[98] Andrew J. Larkoski, Gavin P. Salam, and Jesse Thaler. “Energy Correlation
Functions for Jet Substructure”. JHEP 06.MIT-CTP-4446, CERN-PH-TH-2013066, LPN13-026 (2013), p. 108. DOI: 10.1007/JHEP06(2013)108. arXiv: 1305.

0007 [hep-ph] (cit. on p. 61).
[99] Andrew J. Larkoski, Ian Moult, and Duff Neill. “Analytic Boosted Boson Discrimination”. JHEP 05.MIT-CTP-4681 (2016), p. 117. DOI: 10.1007/JHEP05(2016)

117. arXiv: 1507.03018 [hep-ph] (cit. on p. 61).
[100] Ian Moult, Lina Necib, and Jesse Thaler. “New Angles on Energy Correlation
Functions”. JHEP 12.MIT-CTP-4825 (2016), p. 153. DOI: 10.1007/JHEP12(2016)

153. arXiv: 1609.07483 [hep-ph] (cit. on p. 61).
[101] S. Bethke et al. “New jet cluster algorithms: Next-to-leading order QCD andhadronization corrections”. Nucl. Phys. B 370.CERN-TH-6222-91 (1992). [Erratum: Nucl.Phys.B 523, 681–681 (1998)], pp. 310–334. DOI: 10. 1016/0550 -

3213(92)90289-N (cit. on p. 61).
[102] Stephen D. Ellis and Davison E. Soper. “Successive combination jet algorithm
for hadron collisions”. Phys. Rev. D 48.CERN-TH-6860-93 (1993), pp. 3160–
3166. DOI: 10.1103/PhysRevD.48.3160. arXiv: hep-ph/9305266 (cit. on p. 61).
[103] Jesse Thaler and Lian-Tao Wang. “Strategies to Identify Boosted Tops”. JHEP
07 (2008), p. 092. DOI: 10.1088/1126- 6708/2008/07/092. arXiv: 0806.0023[hep-ph] (cit. on p. 61).
[104] Carola F. Berger, Tibor Kucs, and George F. Sterman. “Event shape / energy
flow correlations”. Phys. Rev. D 68.YITP-SB-03-06 (2003), p. 014012. DOI: 10.

1103/PhysRevD.68.014012. arXiv: hep-ph/0303051 (cit. on p. 61).
[105] Andrew J. Larkoski, Ian Moult, and Duff Neill. “Power Counting to Better Jet
Observables”. JHEP 12.MIT–CTP-4588 (2014), p. 009. DOI: 10.1007/JHEP12(2014)009. arXiv: 1409.6298 [hep-ph] (cit. on p. 62).
[106] François Chollet et al. Keras. https://keras.io. 2015 (cit. on pp. 64, 65).
[107] The Theano Development Team et al. Theano: A Python framework for fast computation of mathematical expressions. 2016. arXiv: 1605.02688 [cs.SC] (cit. on
pp. 64, 65).
[108] Diederik P. Kingma and Jimmy Ba. Adam: A Method for Stochastic Optimization.
2014. arXiv: 1412.6980 [cs.LG] (cit. on pp. 64, 65).
[109] ATLAS collaboration. “Boosted hadronic vector boson and top quark tagging
with ATLAS using Run 2 data”. ATL-PHYS-PUB-2020-017 (Aug. 2020) (cit. on
p. 64).
139

[110] Daniel Hay Guest et al. lwtnn/lwtnn. Version Release for athena v21. 2017 (cit.
on p. 65).
[111] Georges Aad et al. “Performance of jet substructure techniques for large-R jets√
in proton-proton collisions at s = 7 TeV using the ATLAS detector”. JHEP
09.CERN-PH-EP-2013-069 (2013), p. 076. DOI: 10 . 1007 / JHEP09(2013 ) 076.
arXiv: 1306.4945 [hep-ex] (cit. on p. 71).
[112] G. Ridolfi and S. Forte. “Renormalization and factorization scale dependenceof observables in QCD”. J. Phys. G 25 (1999). Ed. by R. Devenish and W.James
Stirling, pp. 1555–1556. DOI: 10.1088/0954-3899/25/7/351 (cit. on p. 71).
[113] ATLAS Collaboration. “Search for a scalar partner of the top quark in the√jets plus missing transverse momentum final state at s=13 TeV with the
ATLAS detector”. JHEP 12.CERN-EP-2017-162 (2017), p. 085. DOI: 10.1007/

JHEP12(2017)085. arXiv: 1709.04183 [hep-ex] (cit. on p. 77).
[114] C. G. Lester and D. J. Summers. “Measuring masses of semi-invisibly decaying particle pairs produced at hadron colliders”. Phys. Lett. B 463 (1999),
pp. 99–103. DOI: 10.1016/S0370-2693(99)00945-4. arXiv: hep-ph/9906349(cit. on p. 77).
[115] Christopher G. Lester and Benjamin Nachman. “Bisection-based asymmetric MT2 computation: a higher precision calculator than existing symmetricmethods”. Journal of High Energy Physics 2015.3 (2015), p. 100. ISSN: 1029-8479.
DOI : 10.1007/JHEP03(2015)100 (cit. on p. 77).

[116] Cowan G. “Discovery sensitivity for a counting experiment with backgrounduncertainty” (2012). URL: http://www.pp.rhul.ac.uk/~cowan/stat/medsig/

medsigNote.pdf (cit. on p. 79).
[117] Georges Aad et al. “Jet energy scale and resolution measured in proton-proton√
collisions at s = 13 TeV with the ATLAS detector”. CERN-EP-2020-083 (July2020). arXiv: 2007.02645 [hep-ex] (cit. on pp. 101, 102).
[118] Georges Aad et al. “Jet energy measurement and its systematic uncertainty in√proton-proton collisions at s = 7 TeV with the ATLAS detector”. Eur. Phys. J.
C 75 (2015), p. 17. DOI: 10.1140/epjc/s10052-014-3190-y. arXiv: 1406.0076[hep-ex] (cit. on p. 101).
[119] William Buttinger. Using Event Weights to account for differences in Instantaneous
Luminosity and Trigger Prescale in Monte Carlo and Data. Tech. rep. ATL-COMSOFT-2015-119. Geneva: CERN, 2015. URL: https://cds.cern.ch/record/

2014726 (cit. on p. 103).
140

[120] John Kenneth Anders and Monica D’Onofrio. V+Jets theoretical uncertainties
estimation via a parameterisation method. Tech. rep. ATL-COM-PHYS-2016-044.
Geneva: CERN, 2016. URL: https://cds.cern.ch/record/2125718 (cit. on
p. 103).
[121] Chris D. White et al. “Isolating Wt production at the LHC”. JHEP 11.NIKHEF2009-013, CERN-TH-2009-136, ITF-UU-09-31, CP3-09-33 (2009), p. 074. DOI:

10.1088/1126-6708/2009/11/074. arXiv: 0908.0631 [hep-ph] (cit. on p. 104).
[122] Kyle Cranmer et al. HistFactory: A tool for creating statistical models for use with
RooFit and RooStats. Tech. rep. CERN-OPEN-2012-016. New York: New YorkU., 2012. URL: https://cds.cern.ch/record/1456844 (cit. on p. 105).
[123] Lorenzo Moneta et al. “The RooStats Project”. PoS ACAT2010 (2010). Ed. by
T. Speer et al., p. 057. DOI: 10.22323/1.093.0057. arXiv: 1009.1003 (cit. on
p. 105).
[124] Wouter Verkerke and David P. Kirkby. “The RooFit toolkit for data modeling”. eConf C0303241.CHEP-2003-MOLT007 (2003). Ed. by L. Lyons and Muge
Karagoz, MOLT007. arXiv: physics/0306116 (cit. on p. 105).
[125] M. Baak et al. “HistFitter software framework for statistical data analysis”.
The European Physical Journal C 75.4 (2015), p. 153. ISSN: 1434-6052. DOI: 10.

1140/epjc/s10052-015-3327-7 (cit. on p. 105).
[126] Walter W. Hauck and Allan Donner. “Wald’s Test as Applied to Hypotheses
in Logit Analysis”. Journal of the American Statistical Association 72.360 (1977),
pp. 851–853. ISSN: 01621459. URL: http://www.jstor.org/stable/2286473(cit. on p. 108).
[127] Glen Cowan et al. “Asymptotic formulae for likelihood-based tests of new
physics”. Eur. Phys. J. C 71 (2011). [Erratum: Eur.Phys.J.C 73, 2501 (2013)],
p. 1554. DOI: 10 . 1140 / epjc / s10052 - 011 - 1554 - 0. arXiv: 1007 . 1727 (cit.
on p. 108).
[128] Alexander L. Read. “Modified frequentist analysis of search results (The CL(s)method)”. Workshop on Confidence Limits. CERN-OPEN-2000-205. Aug. 2000,
pp. 81–101 (cit. on p. 110).
[129] Georges Aad et al. “Search for a scalar partner of the top quark in the all√hadronic tt̄ plus missing transverse momentum final state at s=13 TeV with
the ATLAS detector”. Eur. Phys. J. C 80.CERN-EP-2020-044 (2020), p. 737. DOI:

10 . 1140 / epjc / s10052 - 020 - 8102 - 8. arXiv: 2004 . 14060 [hep-ex] (cit. on
pp. 120, 123).
141

[130] Albert M Sirunyan et al. “Searches for physics beyond the standard modelwith the MT2 variable in hadronic final states with and without disappearing√
tracks in proton-proton collisions at s = 13 TeV”. Eur. Phys. J. C 80.CMSSUS-19-005, CERN-EP-2019-180 (2020), p. 3. DOI: 10.1140/epjc/s10052-019-

7493-x. arXiv: 1909.03460 [hep-ex] (cit. on p. 127).
[131] ATLAS Collaboration. SUSY July 2020 Summary Plot Update. Tech. rep. ATLPHYS-PUB-2020-020. Geneva: CERN, 2020. URL: http : / / cds . cern . ch /record/2725258 (cit. on p. 128).
[132] ATLAS Collaboration. Search for new phenomena in events with two opposite√
charge leptons, jets and missing transverse momentum in pp collisions at s =13 TeV with the ATLAS detector. Tech. rep. ATLAS-CONF-2020-046. Geneva:
CERN, 2020. URL: http://cds.cern.ch/record/2728056 (cit. on p. 128).
[133] ATLAS Collaboration. Search for new phenomena with top quark pairs in final
states with one lepton, jets, and missing transverse momentum in pp collisions at√
s = 13 TeV with the ATLAS detector. Tech. rep. ATLAS-CONF-2020-003. Geneva:
CERN, 2020. URL: https://cds.cern.ch/record/2711489 (cit. on p. 128).
[134] Michael L. Graesser and Jessie Shelton. “Hunting Mixed Top Squark Decays”.
Phys. Rev. Lett. 111.12 (2013), p. 121802. DOI: 10 . 1103 / PhysRevLett . 111 .

121802. arXiv: 1212.4495 [hep-ph] (cit. on p. 128).

142

AppendicesA

Discussion on the physical objects used in the event
reconstruction

The reconstruction of the physical objects is limited by the performance and coverageof the sub-detectors. The coverage of the inner detector is in the range of |η | <2.5,

which affects all the reconstruction requiring the track information.

In the reconstruction of the electrons, all the electron candidates need tracks
matched with topo-clusters, which results in the requirement of |η | <2.47 for the
precision measurements. The lowest pT (4.5 GeV) of the electron candidates is limited by the calibration of the efficiency and energy by using J/Ψ → ee and Z → ee

samples. If the pT is smaller than 4.5 GeV, the Monte Carlo simulation cannot be
trusted. Figure 73 (a) shows the efficiencies of three working points, Loose, Medium,and Tight. LooseAndBLayer is required for the baseline electrons. Loose shows thehighest efficiencies. The additional requirement of the hit in the innermost layer
for the LooseAndBLayer criteria reduces the background from photon conversions.
The signal electrons require Tight criteria for the identification and Fix (Loose) for theisolation. Tight criteria have 5 times higher background rejection against the multijet
production. Fix (Loose) shows the flat efficiencies above 20 GeV as shown in Figure

1

Efficiency

Efficiency

73 (b).

0.95
0.9
0.85

1
0.9
0.8

0.8
0.7

0.75

ATLAS
-1

s = 13 TeV, 37.1 fb

0.7

0.6

Loose
MediumTight

0.6

s = 13 TeV, 37.1 fb-1

0.5
0.4

Data / MC

0.55

Data / MC

Data isolation efficiency εiso

ATLAS

Data identification efficiency εid

0.65

1.1
1
0.9
20

40

60

80

100

120

140

Fix (Loose)Fix (Tight, Track Only)
Fix (Calo only)
Fix (Track Rmax = 0.4)
Fix (Tight)

1.04
1.02
1
0.98
0.96
20

40

60

ET [GeV]

80

100

120

140
ET [GeV](a)(b)

Figure 73: Data (a) identification and (b) isolation efficiency as a function of pT [78].

143Table 32: Efficiency for the prompt muons from W decays and non-prompt muonfrom the hadronic decays with four working points by using tt̄ MC samples [79].

Selection
Loose
MediumTight
High-pT

4 < pT < 20 GeVMCµ [%] MC
Hadrons [%]
96.7
95.5
89.9
78.1

20 < pT < 100 GeVMCµ [%] MC
Hadrons [%]

0.53
0.38
0.19
0.26

98.1
96.1
91.8
80.4

0.76
0.17
0.11
0.13

In the reconstruction of the muons, the coverage of pseudorapidity in the muon
spectrometers is up to 2.7. Therefore, the reconstruction of muon can be in the range
of |η | <2.7. The lowest pT (4 GeV) of the muon candidates is due the calibration of
the efficiency and energy by using J/Ψ → µµ and Z → µµ samples. Table 32 showsthe efficiencies of the identification of prompt muons and the misidentification of
non-prompt muon from hadronic decays. Medium criteria show high efficiencies in
low and high pT region and good background rejection in high pT region, which isthe best choice for the boosted topology with zero lepton. FixedCutLoose keeps highefficiency of prompt muons and high rejection of non-prompt muon in the high pT
region. Figure 74 shows the efficiencies and scale factors of FixedCutLoose isolation

Efficiency

with Medium criteria.
ATLAS
s = 13 TeV, 3.2 fb-1

FixedCutLoose isolation

1
0.98
Z µµ

0.96

Data
MC

Data / MC

0.94

1
Stat only

0.98
20

30 40 50

100

Sys ⊕ Stat

200 300
p [GeV]T

Figure 74: Data and MC efficiencies of the FixedCutLoose isolation with the Medium
criteria in Z → µµ events [79].
For the reconstruction of small-R jets, the jet response in the central region (|η | <3.2) is well understood as shown in Figure 27 (a). By taking the radius of small-R

jets into account, the pseudorapidity is required to be smaller than 2.8. The available
pT is also limited from the calibration of jet energy scale by Z+jets samples. For thisthesis, we are aiming for the boosted topology. The requirement of 20 GeV is notcritical in the stop analysis.

144

B

Impact on the extrapolation of signal scale factors of
DNN top taggers

The uncertainties of the signal scale factors evaluated in Chapter 5 are evaluated in
the large-R jet pT range up to 1 TeV. The extrapolation from 1 TeV is directly from theinformation of the last bin. In this section, the impact on the stop analysis from theextrapolation is estimated. The signal region A and benchmark signal point (mt̃ ,mχ̃0 )1= (1300,1) GeV are used for the high stop mass region. The post-fit results of theyields and uncertainties are shown in Tables 26 and 24. In Table 24, the “Large-R jet+ DNN” represents the uncertainties of the scale factors and JES for the large-R jets.
To test the signal scale factors in high pT range, the “Large-R jet + DNN” uncertainties
of events with leading large-R jet pT higher than 1 TeV are replaced into 100%. The
modified uncertainties of signal scale factors are only applied to tt̄, tt̄Z, and single
top samples. The effect on the uncertainties of the signal scale factors is estimated byusing expected discovery significance as shown in Eq. 45.
Table 33 shows the results with the original and modified uncertainties. The correlation of nuisance parameters is not considered in this study. The total uncertainties
are calculated in the root of the quadratic sum. SRATT-1b shows the 12% differenceof total uncertainties, but Z0,A shows the only 5% difference, which affects the upper
limit of the cross section for the stop production. By using the quadratic sum ofsignificance in each region, the values of the total significance are 2.55 for the original
uncertainties and 2.51 for the modified uncertainties. Less than 2% decrease is found.
If the modified uncertainties are included in the fit, the impact can be neglected.

145

Table 33: Comparisons of the results between original and modified “Large-R jet+ DNN” uncertainties. “Signal yields” column shows the yields of (mt̃ ,mχ̃0 ) =1(1300,1) GeV. “SM yields” shows the total SM background predictions. “Events(> 1 TeV)” shows the yields with the leading large-R jet pT over 1 TeV. “Systematics”
column shows uncertainties in yields with original and modified “Large-R jet +DNN” uncertainties. “Z0,A ” column shows expected discovery significance withoriginal and modified “Large-R jet + DNN” uncertainties. The numbers in theparenthesis indicate the percentage based on the total SM yields.
Signal regions
SRATT-2b
SRATW-2b
SRAT0-2b
SRATT-1b
SRATW-1b
SRAT0-1bSignal yields
2.01
1.79
1.96
1.14
1.16
1.51

SM yields
0.69
1.94
2.44
0.74
2.80
5.83

Events (> 1 TeV)
0.05 (7%)
0.01 (1%)
0.11 (5%)
0.14 (19%)
0.27 (10%)
0.16 (3%)

146

Z0,A

Systematics
Original

Modified

0.34 (49%)
0.42 (22%)
0.54 (22%)
0.29 (39%)
0.61 (22%)
1.78 (31%)

0.37 (54%)
0.42 (22%)
0.58 (24%)
0.38 (51%)
0.71 (25%)
1.84 (32%)

Orignal Modified
1.61
1.08
1.05
1.03
0.61
0.47

1.58
1.08
1.04
0.98
0.60
0.47