Doctoral Dissertation
博士論文

Search for Supersymmetric Partnersof the Top Quark with Leptonic Signatures(レプトニック終状態を用いたトップクォークの超対称性パートナーの探索)

A Dissertation Submitted for the Degree ofDoctor of Philosophy
April 2020
令和２年４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

Tomohiro Yamazaki
山﨑友寛Abstract

Supersymmetry (SUSY) is one of the most elegant theories that can provide
solutions to the problems in the Standard Model. Natural SUSY models favor light scalar top quarks (stops) and higgsinos. This dissertation presents
two searches for the direct productions of stops using collision data at a cen√ter of mass energy of s = 13 TeV collected with the ATLAS detector at theLarge Hadron Collider. The first search is performed using data collected in
2015–2016, corresponding to an integrated luminosity of 36 fb−1 . The lightest
supersymmetric particle (LSP) is assumed to be a higgsino-like particle, and alarge mass-splitting between the stop and the LSP is considered. This is the firstsearch where the three decay modes of the stop decaying into the higgsino-like
LSP are taken into account. The second search targets a small mass difference
between the stop and the LSP, referred to as “compressed signal,” using datacollected in 2015–2018, corresponding to an integrated luminosity of 139 fb−1 . In
order to increase the acceptance of the compressed signal, a novel identification
technique for low momentum b-hadrons (soft b-tagging) has been developed.
The soft b-tagging is an algorithm based on the secondary vertex reconstruction. It shows an improvement by a factor of 10 in the identification efficiency
for low momentum b-hadrons compared to the standard b-hadron identification
algorithm in ATLAS. In both searches, no significant excess over the Standard
Model expectation is observed. Exclusion limits at 95% confidence level arederived for comprehensive decay scenarios. For the large mass-splitting in the
higgsino-like LSP scenario, stop masses up to 800 GeV are excluded for the LSP
mass of 150 GeV. In the compressed case with the stop four-body decay, theexclusion limit is extended by 240 GeV for the stop mass from the previous
results, and stop masses up to 640 GeV for the LSP with a mass of 580 GeV
are excluded.

Acknowledgements

First, I would like to express my deepest gratitude to my supervisor, Prof.
Junichi Tanaka, for his continuous support, guidance, and encouragement. I
would also like to express my appreciation to my former supervisor, Prof. Tatsuo Kawamoto. I appreciate the careful review and discussion during the defense
by the reviewers: Prof. Yoshinari Hayato, Prof. Yutaka Ushiroda, Prof. Takeo
Moroi, Prof. Wataru Ootani, and Prof. Hidetoshi Yamaguchi. I wish to pay
my special regards to Keisuke Yoshihara, who supported me in all topics in thisdissertation. Without him, I could not have obtained these results. I was luckythat I was able to start the analysis with SUSY third-generation experts, Takashi
Yamanaka and Till Eifert, before starting my Ph.D. course. I learned a lot when
I was working on my first stop search with 36 fb−1 data, thanks to the powerful analysis organization by Javier Montejo Berlingen and Sophie Pataraia, theexcellent analysis framework from Jan Kuechler and Daniela Boerner, and thehiggsino team with Christian Herwig and Kouta Onogi. The development of thesoft b-tagging was super exciting, though, to be honest, I thought it would not
be possible to make such a powerful tool. I wish to thank Hideyuki Oide for thetechnical support, and the soft b-tag co-developers: Iacopo Vivarelli, Francesca
Ungaro, Samuel Jones, Mario Spina, and Peter Mcnamara. I spent a really enjoyable time to work on the full Run 2 analysis with the stop1L team. I thankMichaela Queitsch-Maitland and Frederik Ruehr, Sara Strandberg, Christophe
Clement, Paola Arrubarrena Tamae, David Handl, Stefio Yosse Andrean, Prim
Pasuwan, Laura Pereira Sanchez, and Julian Wollath for sharing the work andmany discussions. We couldn’t have done all these works without careful reviews from the SUSY (sub-)conveners: Zach Marshall, Federico Meloni, Rosa
Simoniello, and Calum Macdonald. There were many useful discussions in theTokyo ICEPP group with Yuji Enari, Tatsuya Masubuchi, Ryu Sawada, Yasuyuki Okumura, Koji Terashi, Tomoyuki Saito, and Takuya Nobe. Last but
not least, I would like to recognize the invaluable support from my family.

v

Contents
1 Introduction

1

2 Theoretical Background

4

2.1
2.2

The Standard Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4

2.1.1

Problems of the Standard Model . . . . . . . . . . . . . . . . . . . .

4

Supersymmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7

2.2.1

MSSM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

8

2.2.2

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

10

2.2.3

SUSY Breaking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

11

2.2.4

Neutralinos and Charginos . . . . . . . . . . . . . . . . . . . . . . .

12

2.2.5

Scalar Top Quarks . . . . . . . . . . . . . . . . . . . . . . . . . . . .

13

2.2.6

Natural SUSY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

14

3 Experimental Apparatus

17

3.1

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

17

3.2

The ATLAS Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

18

3.2.1

Coordinate System . . . . . . . . . . . . . . . . . . . . . . . . . . . .

19

3.2.2

Inner Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

20

3.2.3

Calorimeters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

22

3.2.4

Muon Spectrometer . . . . . . . . . . . . . . . . . . . . . . . . . . .

23

3.2.5

Magnet System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

25

3.2.6

Luminosity Detector . . . . . . . . . . . . . . . . . . . . . . . . . . .

25

3.2.7

Trigger and Data Acquisition System

26. . . . . . . . . . . . . . . . .

4 Data and Simulation

28

4.1

Data Acquisition in LHC Run 2 . . . . . . . . . . . . . . . . . . . . . . . . .

28

4.2

Monte Carlo Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

31

4.2.1

Description of pp Collisions . . . . . . . . . . . . . . . . . . . . . . .

31

4.2.2

Simulation Samples . . . . . . . . . . . . . . . . . . . . . . . . . . .

32vi

5 Event Reconstruction

35

5.1

Tracks and Primary Vertex . . . . . . . . . . . . . . . . . . . . . . . . . . .

35

5.2

Topological Clusters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

36

5.3

Jets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

37

5.4

b-tagging. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

39

5.5

Muons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

43

5.6

Electrons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

45

5.7

Missing ET . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

47

5.8

Overlap Removal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

48

6 Stop Search Strategies

49

6.1

Signal Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

50

6.2

Background Events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

54

6.3

Discriminating Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

56

6.4

Background Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

58

6.5

Systematic Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

59

6.5.1

Experimental Uncertainty . . . . . . . . . . . . . . . . . . . . . . . .

59

6.5.2

Theoretical Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . .

61

6.6

Statistical Treatments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

62

6.7

Previous Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

64

6.7.1

Higgsino-like LSP Model . . . . . . . . . . . . . . . . . . . . . . . . .

64

6.7.2

Simplified Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

65

7 Search for Stop with Large ∆m(t̃1 , χ̃01 ) Scenarios

68

7.1

Event Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

68

7.2

Background Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

75

7.3

Systematic Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

85

7.4

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

86

8 Soft b-tagging for Compressed Signatures

93

8.1

Targets of Soft b-tagging . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

93

8.2

Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

95

8.2.1

Track Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

95

8.2.2

Vertex Fitting. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

96

8.2.3

Vertex Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

97

8.3

Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

102

8.4

Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

105

vii

9 Search for Stop with Small ∆m(t̃1 , χ̃01 ) Scenarios

112

9.1

Event Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

112

9.2

Background Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

118

9.3

Systematic Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

126

9.4

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

127

10 Discussion

133

10.1 Bino-Higgsino Mixed LSP Scenario . . . . . . . . . . . . . . . . . . . . . . .

133

10.2 Comparison of Results with CMS Results . . . . . . . . . . . . . . . . . . .

135

10.3 Fine-tuning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

136

10.4 Comparison with Searches for the Direct Higgsino Production . . . . . . . .

137

11 Conclusion

139

A Contributions of Signal Regions to Exclusion Limits

142

Bibliography

145

viii

Preface
This dissertation is based on my work in the ATLAS experiment during my Ph.D. programat The University of Tokyo in 2016-2020. I started physics analysis in 2016 for stop searches
focusing on one-lepton final state (a.k.a. stop1L). Since then, I had opportunities to contribute to three publications: the stop1L analysis with data collected in 2015–2016 [1], thedevelopment of the soft b-tagging algorithm [2], and stop1L analysis with the full Run 2
data [3]. Here, I briefly describe my contribution to these publications.
Stop search analysis
I joined the stop1L analysis group in 2016. My contributions to the first publication [1]are as follows. I studied a new data-driven background estimation for tt̄ with a lepton(electron or muon) and a hadronic tau, by replacing a lepton with a jet in di-leptonictt̄ events in data. I designed new higgsino-like LSP and bino-higgsino mixed signal
models with Keisuke Yoshihara (was in UPenn, now in Iowa State) and ChristianHerwig (was in UPenn, now in Fermilab), and generated signal MC samples. Targetingthe stop-to-higgsino model with a b-quark and a chargino in final states, I designed
an analysis by defining a set of regions (signal regions, control regions, and validation
regions). I have also contributed to the evaluation of systematic uncertainties andsignal acceptance in all regions in this publication. Furthermore, I have contributed
to the development of a package called the stop-polarization tool. This is an essential
tool to correct for spin polarization of particles emitted from the stop decay and toensure the line shape of the angular distributions of stop signals.
For the analysis with the full Run 2 dataset [3], I played an essential role as a developer of the analysis software and produced common skimmed datasets for the wholeanalysis group. I have contributed to the generation of the stop four-body signals. I
have designed a signal region (bffN softb) using the soft b-tagging and also studied
the background estimation. I implemented the signal regions in a truth-based framework (SimipleAnalysis). I performed statistical treatments for the four-body signal
regions and implemented a statistical combination of two signal regions. I combinedix

all two-, three-, and four-body stop decay results and derived an exclusion limit forthe paper.
Flavor tagging
I have contributed to the identification of heavy flavor hadrons (flavor tagging). I
conducted a study of the b-tagging efficiency for c-jets which are misidentified as bjets, using D∗± → D0 (→ K ∓ π ± )π ± decays. This method cross-checked the standard

c-jet calibration results measured by tt̄ with the W → cs decay. I have been qualified
as an ATLAS author with this work.

The development of the soft b-tagging algorithm [2] is a major contribution to thecollaboration during my Ph.D. This is the first b-tagging algorithm targeting low
momentum b-hadrons. I developed the Track-based Low pT Vertex Tagger (T-LVT)
algorithm, including the track selection, vertex fitting, and vertex selection, as well
as new variables used in these steps. I evaluated the performance of the algorithm,
together with the other soft b-tagging algorithms, which was published as a Conference
Note [2]. Finally, I have proposed the calibration strategy of the T-LVT algorithm
and performed the calibration, and validated the calibration in the context of the stop
searches and applied the soft b-tagging in the analysis.
Detector upgrade
I had been working on the R&D of Micromegas detectors during the master course
at The University of Tokyo in 2014-2016 [4]. I performed several irradiation tests
for prototype detectors and evaluated the tracking performance at test beams for the
New Small Wheel upgrade in ATLAS. I have also contributed to the quality controlof the resistive anode foils of the Micromegas detector.

xChapter 1

Introduction
The smallest unit of matter is one of the fundamental questions in science. As of today,
it is called an elementary particle, and the best knowledge on the elementary particles iswell described by the Standard Model (SM) of particle physics [5–8]. The SM is the mostsuccessful achievement of particle physics in the 20th century and explains many experimental results with remarkable precision. The discovery of the Higgs boson in 2012 [9, 10]
was a notable achievement in this century, and it was the final piece of the undiscovered SM
particles. As the precision of experimental results improved, some observations that cannot
be explained by the SM have appeared. For example, the existence of dark matter (DM) is
strongly supported by the observation of the universe [11–15], but no SM particle satisfies
the properties of DM. The masses of neutrinos should not be zero to explain the neutrino
oscillations [16–18], but the masses of neutrinos are exactly zero in the SM due to thelack of right-handed neutrinos. The model itself also contains mysteries of particle physics.
There are four forces that interact between particles: the strong, weak, electromagnetic,
and gravitational forces. The SM is a framework that summarizes the former three forces
but does not contain the gravitational force. There is a huge gap between the energy scaleof gravity and the mass of the Higgs boson. It is difficult to explain the unnatural gap in
the regime of the SM, and this problem is called the hierarchy problem.
The next target of particle physics is to find new physics beyond the SM that solves these
problems. An extension of the SM is strongly believed to account for these observations thatcannot be explained in the framework of the SM. There are many theories that could explainthese mysteries, but none of them is confirmed by an experimental result. A discovery
of a non-SM particle could be a smoking gun of a new physics model beyond the SM.
Supersymmetry (SUSY) [19–25] is one of the leading candidates among theories beyond
the SM. SUSY is a symmetry between bosons and fermions and predicts a boson (fermion)
partner for each fermion (boson) particle. SUSY was proposed in the 1970s based on thequantum field theory, and it is now a well-established theory in particle physics though no1

evidence of SUSY has been found. Despite the lack of experimental evidence, SUSY has
been an attractive theory because it provides an elegant solution to the hierarchy problem
and DM candidates, and the Grand Unification could be possible if SUSY exists [26–29].
According to the Naturalness [30, 31], the supersymmetric partners of the top quark and
Higgs boson, the scalar top quark (stop) and higgsinos, respectively, are considered to belight [32,33]. If the mass of the stop is smaller than around 1 TeV, the Large Hadron Collider(LHC) with the center-of-mass-energy of 13 TeV has the potential to produce enough stop
pairs for discovery. Experimental evidence of at least one of these new particles as an excess
over the prediction of the SM processes in data would indicate the existence of new physics.
This dissertation presents searches for the stop production at the LHC, mainly focusing
on a scenario where the lightest neutral higgsino is the lightest supersymmetric particle(LSP). In this scenario, the stop produced in pp collisions decays into the higgsino-like LSP,
which is a stable particle that does not interact with the detector, and SM particles. Twosearches are performed to cover the scenario widely. The first search [1] targets a scenario
with a large mass difference between the stop and LSP (∆m(t̃1 , χ̃01 )) using data collected in
2015–2016. The higgsino-like LSP scenario is characterized by small mass-splittings (∆m)
between three higgsino states. The small ∆m emits low-momentum particles, which makes
the search difficult. The analysis extends the search sensitivity by exploiting low-momentum
leptons. In the context of the stop searches, final states often contain b-hadrons. b-hadrons
are identified by the b-tagging technique exploiting the long lifetime of b-hadrons. In thecompressed stop scenario, where the mass difference between the stop and LSP is small
such as 20 GeV, the final states contain low-momentum b-hadrons. Since the standard
b-tagging algorithm in ATLAS is sub-optimal for such low-momentum b-hadrons, a new
b-tagging algorithm optimized for low-momentum b-hadrons (soft b-tagging) [2] has beendeveloped. The second stop search [3] aims for the small ∆m(t̃1 , χ̃01 ) signature with thenovel soft b-tagging. This analysis is performed with the data collected in 2015–2018, andoptimized using a simplified stop signal model [34–36], where a stop decays into the LSP
without considering other SUSY particles.
The theoretical framework of the SM and SUSY is reviewed in Chapter 2. The experimental apparatuses, the LHC and ATLAS, are reviewed in Chapter 3. The data and Monte
Carlo (MC) simulation used in this dissertation are explained in Chapter 4. The standard reconstruction algorithms used in ATLAS are documented in Chapter 5. The generalstop analysis strategy is explained in Chapter 6 before discussing details of the individual
analyses. The stop search targeting higgsino-like LSP with large ∆m(t̃1 , χ̃01 ) is describedin Chapter 7. The details of the soft b-tagging for the small ∆m(t̃1 , χ̃01 ) are explained in
Chapter 8, which is then applied to the analysis targeting the compressed scenario described2

in Chapter 9. The results of the two searches are discussed in Chapter 10. At the end, aconclusion is presented in Chapter 11.

3

Chapter 2Theoretical Background
2.1

The Standard Model

The Standard Model (SM) is a quantum field theory that describes behavior of elementary
particles. The theory is based on SU (3)C × SU (2)L × U (1)Y . The Lagrangian of the SM is/
L = ψ i ∂ψ1
/ − B µν Bµν− g1 ψ Bψ41/ ψ − W µν Wµν− g2 ψ W
41 µν/ − G Gµν
− g3 ψ Gψ
4+ ψ i yij ψj φ + h.c.

+ |Dµ φ|2 − V (φ),(2.1)

with a fermion field ψ, a Higgs field φ, electroweak gauge fields B µν and W µν , and a gluon
field Gµν . The first line describes the kinetic term of fermions, and the second, third,
and forth lines show interactions between gauge fields and fermions, and interactions of
the gauge fields themselves. The fifth and sixth lines are related to the Higgs field with apotential V (φ). The g1 , g2 , g3 , and yij are the coupling constants in each interaction. The
Lagrangian of the SM is determined from the gauge symmetry, requiring invariant of the
Lagrangian under gauge transformations.
The particles in the SM are listed in Tables 2.1–2.2. The last piece of the SM particles,
the Higgs boson, was discovered at the LHC in 2012 [9, 10].

2.1.1

Problems of the Standard Model

Nature has two typical energy scales, the electroweak scale at the order of 102 GeV and the
Planck scale at the order of 1019 GeV. The light masses of the gauge bosons and quarks
4

Table 2.1: List of the SM fermions. All listed particles have a spin of 1/2. The masses aremeasured values taken from reference [37].
quarkselectric charge

mass

leptons

electric charge

mass

u
d

+2/3
−1/3

2.2 MeV
4.7 MeV

e
νe

−1
0

511 keV< 225 eV

c
s

+2/3
−1/3

1.3 GeV
93 MeVµνµ−10106 MeV
0.19 MeV

t
b

+2/3
−1/3

173 GeV
4.2 GeV

τ
ντ

−1
0

1.78 GeV< 18.2 MeV

Table 2.2: List of the SM bosons. The masses are measured values taken from reference [37].
particles

electric charge

spin

mass

g
γ
W±
Z
H

0
0
±1
0
0

1
1
1
1
0

0
0
80.4 GeV
91.2 GeV
125.1 GeVare explained by the local gauge symmetry and chiral symmetry in the SM. However, there
is no symmetry in the SM that keeps the Higgs mass at the electroweak scale. The huge
gap between the Higgs mass and the Planck scale is considered unnatural, which is known
as the hierarchy problem. The correction to the Higgs mass contains a loop effect shownin Figure 2.1 left. This loop correction, which induces a quadratic divergence of the Higgs
mass contains a term
∆m2h = const. × g 2 Λ2 ,(2.2)

where g is a coupling strength between the Higgs boson and a fermion, and Λ is a cutoff
parameter which corresponds to an energy scale from which new physics at the high energy
scale needs to be considered.
The strong, weak, and electromagnetic forces could unify to one force at the grandunification scale of 1016 GeV. The gap between the EW scale of 102 GeV and the grandunification scale introduces a problem because of the quadratic divergent correction. When
Λ in equation (2.2) is at the grand unification scale, the correction is an order of 1032 GeV2 ,while the square of the bare Higgs mass is an order of 104 GeV2 . The mass of the Higgs
boson is given by the correction, which is 28 orders of magnitude larger than the tree-level
5

et

t
H

H
<latexit sha1_base64="wZ/rWYsLg6GeaercpdKTZersokk=">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</latexit><latexit sha1_base64="1mB6FC/RtrJkRc7MphH1jUsQ9FI=">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</latexit>t

Figure 2.1: Loop corrections to the Higgs mass. The left diagram is the fermion loopthat induces the quadratic divergence of the Higgs mass. The right diagram is a bosoniccounterpart of the fermion loop, which has an opposite sign of the fermion term, resulting
in the cancellation of the divergence.

term. A huge fine-tuning is needed to achieve this correction, and it is not natural. The
fine-tuning problem is caused by the fermion loop in the Higgs mass. In order to avoid the
problem, one possible solution is to cancel the fermion loop by introducing a boson loopwith the same coupling and an opposite sign to the fermion loop, as shown in Figure 2.1
right.
Cosmological observations have revealed that visible material that can be observed bytelescopes is not enough to account for the material in the universe, and there is moreinvisible matter than the known visible material. The invisible matter is called dark matter(DM). Figure 2.2 shows two pieces of evidence of DM. The first evidence of DM is therotation velocity of the galaxy shown in Figure 2.2 left [38]. The expected rotation velocity
from the visible disk around the galaxy has a peak at a certain distance from the center(R), and then decreases as a function of R. However, the rotation velocity observed using
the 21 cm line emitted from hydrogen atoms shows the different feature, and that indicates
additional invisible material around the galaxy (halo). The density of the invisible halo is
consistent with the non-relativistic dark matter models (cold dark matter). The right image
in Figure 2.2 shows the observation of a bullet cluster [39], which consists of two colliding
clusters of galaxies, by two methods, X-ray and gravitational lensing effect. The distributionof gaseous material observed by detecting X-rays is shown in red, while the gravitationallens observation is sensitive to massive material shown in blue. As can be seen in the image,the two distributions do not agree with each other. This can be explained by the existenceof DM. The visible gas interacts with the gas of the other galaxy, so that the distributionof the gas remains around the collision area, while DM mostly passes through due to the6feeble interaction of DM. In the SM, there is no candidate particle that is consistent withthese observations.

Figure 2.2: Evidences of the DM. (left) The rotation velocity of the galaxy M33 as afunction of the distance from the center of the galaxy [38]. The points show the observed
M33 rotation curve with the best fit model (solid line). The contribution of the halo (dasheddotted line), stellar disk (short dashed line) and gas (long dashed line) are shown together.
(right) Image of Bullet Cluster 1E0657-558 [39]. Image of the bullet cluster observed by
X-ray is shown in red and the cluster observed by gravitational lensing effect is shown in
blue.

2.2

Supersymmetry

Supersymmetry is a symmetry between bosons and fermions, which provides boson partners
to fermion particles of the SM and vice versa. A supersymmetric operator Q transforms aboson state into a fermion state and vice versa. This can be written as

Q |Bosoni = |Fermioni(2.3)

Q |Fermioni = |Bosoni .

(2.4)

The operator Q satisfies the following anti-commutation and commutation relations,{Q, Q† } = P µ{Q, Q} = {Q† , Q† } = 0[P µ , Q] = [P µ , Q† ] = 0.

(2.5)
(2.6)
(2.7)

Here P µ is a generator of spacetime translations, and Q† is the hermitian conjugate of
Q. The third equation (2.7) indicates that Q is exchangeable with m2 = P µ Pµ , resulting
in that the operator Q does not change the mass. Hence, fermion and boson partners,
7for example, the electron in the SM and its supersymmetric partner, have the same mass.
SUSY particles are partners of the SM particles, and the properties of the SUSY particles
are described by the same expression as that of the SM except for their spin. In the realworld, however, such supersymmetric partners have not been discovered yet; for example,
there is no supersymmetric partner of the electron, which is a boson with me = 511 keV.
Supersymmetry should be broken so that fermion and boson partners have different masses
to account for the fact. The quantum numbers related to SU (3) × SU (2) × U (1) of SUSY

particles are identical to ones of the SM particles, and the pair has the same coupling
constants.
The electroweak theory combines electromagnetic and weak forces. The grand unification theory (GUT) is a theory that combines the electroweak theory and the theory of
the strong force, QCD. These forces have different strengths at the energy scale where thecurrent experiments can reach, but at a much higher energy scale, these interactions could
be unified to a single coupling. The three couplings approach together as the energy scalegoes higher, which raises hopes for the unification. The precise measurements of the coupling strength at the LEP have unveiled the behavior of the couplings running to the higher
scale, as shown in Figure 2.3. Three lines do not cross at a common point, which indicatesthat the GUT cannot happen in the SM. However, if the SUSY breaking scale is around
O(TeV), the three coupling lines share a common point at around 1016 GeV. This indicatesthe possibility of the GUT at that energy scale and above.

2.2.1

MSSM

The Minimal Supersymmetric Standard Model (MSSM) [40, 41] is a minimum supersymmetric extension of the SM. The particles in the MSSM are listed in Table 2.3. Each SM
particle has a supersymmetric partner with a spin which is shifted by 1/2 from that of theSM. The Lagrangian of the MSSM can be split into two parts as
MSSM
LMSSM = LMSSM,
SUSY + Lsoft(2.8)

where the first part LMSSM
SUSY describes the properties of the SUSY particles that are the sameas ones of the SM particles. The second part LMSSM
describes the soft breaking terms ofsoft

the MSSM, which are essential when discussing the phenomenology of the MSSM particles.
The soft breaking Lagrangian can be expanded to

8

60
U(1)

50
40
SU(2)
-1

α 30
20
10 SU(3)
0
2

4

6

8

10

12

14

16

18

Log10(Q/GeV)
Figure 2.3: Renormalization evolution of the inverse gauge couplings [25]. The renormalization group running is calculated, including up to two-loop effects. The dashed lines show
the SM, while the solid lines show the MSSM. The red and blue lines correspond to thethreshold of MSSM particle masses at 750 GeV and 2.5 TeV, respectively.


1M3 g̃g̃ + M2 W̃ W̃ + M1 B̃ B̃ + c.c.
2
˜ Q̃H − ẽa L̃H + c.c.
− ũa Q̃H − da

=−
LMSSM
soft

u

u

d

d

e

d

†
˜ 2d
˜† − ẽm 2 ẽ†− Q̃† m2Q Q̃ − L̃† m2L L̃ − ũmu2 ũ − dmed− m2Hu Hu∗ Hu − m2Hd Hd∗ Hd − (bHu Hd + c.c.).

(2.9)

Here u, d, and e are supermultiplets of right handed fermions, and Q and L are left-handed
supermultiplets. A supermultiplet contains a pair of SM and SUSY particles. The symbols
for SUSY particles are the same as the ones for the SM particles but a tilde (˜) is added
for SUSY particles. The first line represents the gaugino masses. The masses of the gluino,wino, and bino are given by M3 , M2 , and M1 , respectively. The second line shows thetrilinear couplings, which describes Yukawa coupling where left-handed and right-handed
scalar particles are involved. The third line describes the mass terms of squarks and sleptons,
and here m2Q , m2L , mu2 , m2d , and m2e are complex 3 × 3 matrices, which correspond to themasses of the particles. The last line corresponds to the Higgs potential in the MSSM.

The name of the supersymmetric particles with a spin 1/2 is given by adding -ino to
the end of the SM particle’s name, and the name of the spin 0 particles is given by adding
scalar on top of the SM particle’s name. The scalar particles are also called by adding s9

to the SM particle’s name. For example, the supersymmetric partner of the top quark iscalled scalar top (quark ), or stop.
If SUSY exists, at least two Higgs doublets (Hu and Hd ) are required while the SM has
a Higgs doublet [42]. The ratio between the two vacuum expected values of vu = hHu i and

vd = hHd i,tan β =

vuvd

(2.10)

is an important parameter that governs the phenomenology. The neutral Higgs boson that
corresponds to the Higgs boson with mH = 125 GeV is a linear combination of Hu0 and Hd0 .
Table 2.3: List of supersymmetric partners with the SM particles [25]. For quarks, leptons,
squarks, and sleptons, only the first generation is listed.

namequarksleptonsHiggs
gluon
W bosonB boson

2.2.2

SM
particle(uL , dL )uR
dR(eL , νL )eR
νR
(Hu+ , Hu0 )(Hd− , Hd0 )g±
W , W0
B0

spin
1/2
1/2
1/2
1/2
1/2
1/2
0
0
1
1
1

SUSY
name
particle(ũL ,d˜L )squarksũRd˜R(ẽL ,ν̃L )sleptonsẽRν̃R
higgsinos (H̃u+ ,H̃u0 )(H̃d− ,H̃d0 )gluinog̃±winoW̃ , W̃ 0
bino
B̃ 0

spin
0
0
0
0
0
0
1/2
1/2
1/2
1/2
1/2

R-parity

It is possible to add terms that violate either lepton number or baryon number conservation
to the potential in the SUSY Lagrangian as can be written as
1
W∆L=1 = λijk Li Lj ek + λ0ijk Li Qj dk + µ0i Li Hu ,2
1 00ijkW∆B=1 = λui dj dk .
2

(2.11)(2.12)In these expressions, λijk , λ0ijk , λ00ijk , and µ0i are coupling constants of each term.
However, in many theories, these terms are considered to be small, mainly due to two
reasons. First, there is no experimental observation that supports the violation of thesenumbers. The fact that the proton decay has not been discovered implies the non-violationof baryon and lepton number conservation since the process of the proton decay changes both10

lepton and baryon numbers by a unit of one. The second reason is that introducing theseterms is not favored in terms of DM. It becomes difficult to explain a dark matter candidate
within the framework of the SUSY including one of these violation terms. To conserve
baryon and lepton numbers, a new symmetry called R-parity has been introduced [43] as
R = (−1)3(B−L)+2s ,(2.13)

where B, L, and s are the baryon number, lepton number, and spin of the particle, respectively. All particles in the SM have R = 1, while all SUSY particles have R = −1. If the

R-parity is conserved, SUSY particles must be produced in a pair, and decay into particles
in which an odd number of SUSY particles are included. Hence the lightest supersymmetricparticle (LSP) must be stable. Due to its stability and weakness of the interaction, the LSP
is a leading candidate for DM. From the cosmological constraints, DM cannot have a coloror an electric charge; thus, the LSP is considered to be one of the neutral SUSY particles.
In many models, the lightest neutralino is the LSP. The neutralino is electrically neutraland does not have colors; hence like neutrinos, the neutralino LSP cannot be detected by
the detector in collider experiments.

2.2.3

SUSY Breaking

As mentioned earlier, SUSY must be broken in order to explain the absence of SUSY
particles with the same masses as the ones of SM particles. There are some models that
describe mechanisms of the SUSY breaking. In these models, the SUSY breaking occurs
in a hidden sector, and the effect is propagated to the MSSM sector via a mediator, which
depends on the model.
Gravity-mediated supersymmetry breaking (Supergravity, SUGRA)The supergravity (SUGRA) model [44–46] is the most popular model which describes
SUSY breaking with a small number of parameters. The minimal SUGRA model(mSUGRA) is a simplified model that contains five parameters: the scalar mass (m0 )and gaugino mass (m1/2 ) at the GUT scale, tan β, trilinear coupling A0 , and the signof the higgsino mass sign (µ). The masses of the particles at a lower energy scale
can be obtained by the renormalization group equations from the masses at the GUT
scale, as shown in Figure 2.4.
Gauge-mediated supersymmetry breaking (GMSB)
The gauge-mediated supersymmetry breaking (GMSB) model [47–49] consists of ahidden sector where the SUSY is broken, and a messenger sector with messenger
particles, and the MSSM sector. In this scenario, the gauge interactions transfer the11

SUSY breaking effects from the messenger sector to the MSSM sector. In this model,
the LSP is the supersymmetric partner of the graviton, gravitino, which is considered
to be light, such as an order of keV or lower.
Anomaly-mediated supersymmetry breaking (AMSB)In the anomaly-mediated supersymmetry breaking (AMSB) [50, 51] model, the SUSY
breaking occurs on a brane, which is separated from the brane where the MSSM lies,
and the breaking is mediated via supergravity effects. In this model, a wino-like LSP
is favored.
2500

Mass [GeV]

2000
Hd

1500

2

2 1/2

(µ +m0 )

Hu
M3

m1/2

M2

1000

M1

squarks500

sleptons

0
2

4

6

8
10
12
14
Log10(Q/1 GeV)

m0

16

18

Figure 2.4:
Renormalization evolution of the mass parameters in the MSSM with amSUGRA scenario [25]. The scalar and gaugino masses are given by common masses
at the GUT scale, m0 and m1/2 respectively, and the running to lower scale is determinedby the renormalization group equations.

2.2.4

Neutralinos and Charginos

The electroweak gauginos and higgsinos mix with each other and form mass eigenstates.
The four neutral particles (H̃u0 , H̃d0 , B̃, and W̃ 0 ) form neutralinos and the charged states(H̃u+ /H̃d− and W̃ ± ) form charginos. The neutralinos are denoted by χ̃01 , χ̃02 , χ̃03 , and χ̃04 ,±while the charginos are denoted by χ̃±
1 and χ̃2 . In these expressions, the numbers in thesubscript of χ̃ are assigned in ascending order of their masses. By definition, the LSP isdenoted by χ̃01 when a neutralino is the LSP. The mass matrix of the neutralinos is given as

12



M1

0
MÑ =  −cβ sW mZ
sβ sW mZsβ sW mZ−sβ sW mZ 
,

−µ
0

−cβ sW mZ
cβ sW mZ0−µ0M2cβ cW mZ−sβ cW mZ(2.14)

where sβ = sin β, cβ = cos β, sW = sin θW , and cW = cos θW with the electroweak mixing
angle θW . The masses of the neutralinos are obtained by diagonalizing the mass matrix
MÑ . Similarly, the mass matrix for charginos is given by
MC̃ =



0 XT
X 0



,

(2.15)

with
X=

2.2.5



√ M2
2cβ mW√2sβ mWµ.

(2.16)

Scalar Top Quarks

Similar to the mixing in neutralinos and charginos, the right- and left-handed squarks arealso mixed. A large mixing could happen for the stop case due to the large Yukawa couplingof the top, while the mixing is negligible for the first and second generation squarks. The
Lagrangian of the stop mass term is given as
Lmassstop =

t̃∗L

t̃∗R



m2t̃



t̃L
t̃R



(2.17)

with the stop mass matrixv(A∗t sin β − µyt cos β)
m2Q3 + m2t + ∆ũL
2
mt̃ =
,
v(At sin β − µ∗ yt cos β)
m2u3 + m2t + ∆ũR
with ∆ũL =2
1
2
2 − 3 sin θWcos(2β)m2Z and ∆ũR =2
2
3 sin θW



(2.18)

cos(2β)m2Z , and At is thestop trilinear coupling. The mass eigenstates of the stop are obtained by diagonalizing themass matrix, as


t̃1
t̃2



=



ct̃ −st̃∗st̃ ct̃∗



t̃L
t̃R



,

(2.19)

with a condition |st̃ |2 + |ct̃ |2 = 1. The off-diagonal terms of the stop mass matrix tend to

induce a large mixing. Because of that, the mass of the lighter stop (t̃1 ) is typically light,
and many models predict that t̃1 is the lightest squark.

13

2.2.6Natural SUSYIn the MSSM, the mass of the Z boson at the tree level with large tan β can be written as−m2Z= |µ|2 + m2Hu ,2(2.20)

with the higgsino mass parameter µ and the mass of the up-type Higgs boson mHu [52].
In the natural SUSY scenario, the right terms should not be too large compared to theleft side; otherwise, a large cancellation between the two terms on the right side would beneeded. That indicates that the higgsino should be light, and the mass is expected to beat the same order as mZ . There is a contribution from the stop mass to the mHu at the
one-loop level. The mHu can be split into two parts, the tree level and radiation correction,
as m2Hu = m2Hu |tree + m2Hu |rad. . The stop mass contributes to the mHu at the one-loop order.
The second term can be written as

3y 2
m2Hu |rad = − t28πm2Q3 + m2U3 + |At |2



ln



Λ
mt̃



.

(2.21)

Here mQ3 and mU3 are the masses of the left-handed and right-handed third generationsquarks, respectively, and Λ is the scale at which SUSY particles are generated [52]. In
order to avoid too large radiative correction, the mQ3 and mU3 should not be too large
compared to the Z boson mass scale. Similarly, there is also a gluino mass contribution
to the second loop correction to Equation (2.21), which implies that the gluino is not too
heavy. The expected masses spectrum from the natural SUSY requirement is summarized
in Figure 2.5.
On the other hand, the discovered Higgs boson indicates that too light stop is notfavored. The mass of the Higgs boson also provides information for the SUSY particles.
The Higgs mass is described as

3 m4
m2h ∼ m2Z cos2 2β + 2 2t
4π v

(

m2t̃

X2
ln 2 + t
mt̃2
mt

Xt2
1−
12m2t̃

!),(2.22)

where Xt = At − µ cot β is the stop mixing parameter [53]. At the tree level, the observed

Higgs boson with a mass of 125 GeV cannot be achieved by the term m2Z cos2 2β. Hence,the second term must be large to account for the observed mass. In the case of heavy stops,
the first term in the brace contributes to lift up the Higgs mass. The second term becomes√maximum when |Xt | = 6mt̃ , which is the so-called maximal mixing case. Figure 2.6
shows the Higgs mass calculated with Suspect [54] and FeynHiggs [55] packages. The green
and purple areas surrounded by the two lines are rough estimates of uncertainty because
the two packages have different renormalization prescriptions. If the stop mixing is zero,14

L̃i , ẽi

B̃W̃Q̃1,2 , ũ1,2 , d˜1,2

b̃R

g̃
t̃L
b̃L

t̃R

H̃

natural SUSY

decoupled SUSY

Figure 2.5: Typical mass spectrum with naturalness constrains in the MSSM [52]. The
particles on the left side are considered to be light in natural SUSY models, while the other
SUSY particle on the right side can be heavy. Light higgsinos, stops, left-handed sbottom,
and gluino are expected.

the observed Higgs mass cannot be explained with a light stop below a few TeV, but the
maximal mixing scenario gives a solution where a light stop below 1 TeV is possible.
The main target of this dissertation is a natural SUSY scenario where the mass of thelightest stop is below 1 TeV, and the stop decays to the higgsino-like LSP, as shown in
Figure 2.5.

15

MSSM Higgs Mass
140

mh @GeVD

130

Xt =

6 mt

mh = 124-126 GeV

120
110
Xt = 0

100
90
200

300

500

700

Suspect
FeynHiggs

1000

1500 2000

3000

mt1 @GeVD
Figure 2.6: The Higgs mass as a function of the lightest stop mass in the MSSM [56] Twocalculation packages are used: Suspect in red lines and FeynHiggs in blue. In both colors,
the maximal and zero stop mixing parameters are shown. The green (purple) area shows
the difference between the Suspect and FeynHiggs calculations at the maximal (zero) stop
mixing.

16

Chapter 3

Experimental Apparatus
3.1

Large Hadron Collider

Figure 3.1: The accelerator complex at CERN [57].

The Large Hadron Collider (LHC) is a proton-proton accelerator located in Geneva,
Switzerland. It accelerates protons using its 27 km circumference to a 6.5 TeV beam energy.
The accelerator complex is shown in Figure 3.1. The LHC is one part of the accelerator
complex at CERN. The proton acceleration starts from an injection of hydrogen atoms into
Linear accelerator 2 (Linac 2). At the beginning of Linac 2, the hydrogen passes throughan electric field to strip off the electrons in the atoms, and only protons are injected into
17

Linac 2. In Linac 2, pulses of the protons are generated, and the protons are accelerated
to the energy of 50 MeV. The accelerated pulse of the protons is extracted from Linac 2
and injected into the Proton Synchrotron Booster (PSB). The protons are accelerated to
1.4 GeV in the Booster for the injection into the Proton Synchrotron (PS). The Booster
enhances the number of protons that can be injected into the PS by accelerating protons
in advance. The PS takes the protons to the energy of 25 GeV with its 277 electromagnets
in a circumference of 628 m. The next step is the Super Proton Synchrotron (SPS). The
SPS was originally used as a main ring to collide proton and antiproton beams, and it was
the historical place where the W and Z bosons were discovered in 1983. Today, the SPS is
used as the last part of the supply chain before the LHC main ring, and accelerates protons
to 450 GeV in its nearly 7 km circumference. The LHC is the main ring of the complex
and exploits the tunnel that was used for the LEP and LEP2 experiments. Two proton
beams with opposite directions are injected from the SPS, and accelerated to the energy of
6.5 TeV. Superconducting magnets are used in the LHC, and the dipole magnets provide
an 8 T magnetic field. The LHC has four interaction points, and four major detectors:
ATLAS, CMS, ALICE, and LHCb, are installed in these points. The LHC beam has abunch stricture in which about 1011 protons are contained. The interval between bunches
is 25 ns at the interaction point except for empty bunches in the chain of bunches.

3.2

The ATLAS Detector

Figure 3.2: ATLAS detector overview [58]The ATLAS detector is a multi-purpose particle detector designed to cover various
18physics programs at the LHC, including the Higgs boson and new physics searches, andprecision measurements of the SM. The ATLAS detector is located at Point 1 of the LHC,
which is one of the interaction points of the LHC. Figure 3.2 shows the image of the
ATLAS detector. It has a cylindrical shape, and the size of the detector is 44 m in heightand 25 m in diameter. The side of the cylindrical shape is called the barrel, and the capof the cylinder is called the endcap to describe the parts of the detector. The ATLAS
detector consists of several subsystems. A tracking system is placed in the most inner partof the ATLAS detector, which consists of the silicon pixel detector, silicon strip tracker(SCT), and Transition Radiation Tracker (TRT) from the inner to outer order. These
detectors are used to provide charged particle trajectories, called tracks in the following. The
tracking subsystem is surrounded by the solenoid magnet, which provides a magnetic field
for the tracking detectors to measure the momenta of tracks using the track curvature. The
next outer subsystem is the calorimeter subsystem, which consists of the electromagnetic
calorimeter and hadronic calorimeter. The energies of jets, electrons, and photons aremeasured by the calorimeters. The outermost part of the detector is the muon spectrometer(MS). Together with the muon spectrometer, toroid magnets are installed in both the barrel
and endcap regions to provide the magnetic field to measure the momentum of muons. The
details of the subsystems are described in the following sections.

3.2.1

Coordinate System

A right-handed coordinate system is used in ATLAS. The center of the coordinate system
is defined as the interaction point (IP) at the center of the ATLAS detector, and the x-axis
points from the IP to the center of the LHC ring. The y-axis points upwards, and thenthe z-axis is defined along to the beamline at the IP, pointing to the direction to Geneva
International Airport. Polar coordinates are also useful to describe the detector or positions
and momentum of particles from the IP. The polar angle φ is defined as the angle in thex-y plane (transverse plane) starting from the positive x-axis, and the azimuthal angle
θ is defined as the angle from the positive z-axis to the negative z-axis. In the collider
experiments, the pseudorapidity η is often used instead of θ asθ
η = − ln tan
.
2

(3.1)

According to this definition, θ = 0, π/2, and π correspond to η = ∞, 0, and −∞, respectively. In order to describe the distance of two positions in the η − φ plane,p∆R = ∆η 2 + ∆φ2(3.2)

is often used, where ∆η and ∆φ are the differences between the two positions in the η andφ coordinates, respectively.
19

3.2.2

Inner Detector

The Inner Detector (ID) consists of four trackers: Insertable B-Layer (IBL), Pixel detector,
Silicon Strip Tracker (SCT), and Transition Radiation Tracker (TRT). The layout of the
ID is shown in Figures 3.3–3.4. In the region of the ID, a 2 T magnetic field is provided
by the surrounding solenoid magnet. The magnetic field is parallel to the beam axis, sothat charged particles are bent in the transverse plane. In each tracker, different shapesof the layers are used in the barrel and endcap regions to provide tracking information in|η| < 2.5.

Figure 3.3: An illustration of the Inner Detector [58]. Both barrel and endcap regions areshown.

Insertable B-Layer (IBL)The IBL is a single pixel layer detector located at 33 mm from the beamline. It was installed
during the shutdown of the LHC between Run 1 (2011–2013) and Run 2 (2015–2018) inorder to improve the performance of the tracking, especially the resolution of the impact
parameter.
Pixel Detector
The pixel detector provides the hit position of tracks of charged particles with high precision.
With its pixel structure, the 2D hit position is measured on each layer. It has a higher
granularity than the SCT modules to provide precise hit positions, because the hit position
measurement on the pixel detector is more important than that on the outer layers in termsof the reconstruction of the primary vertices and b-tagging. Typically three layers of the
pixel detector are crossed by each track in both barrel and endcap regions. In total, 80.4 M

20

Figure 3.4: The positions of the IBL, Pixel, SCT, and TRT layers in the barrel region [58].
A typical track crosses one IBL, three pixel, and eight SCT layers, and 36 TRT tubes.

readout channels are used in the pixel detector. The nominal size of the pixel is 50×400 µm,
and the thickness of the sensors is 250 µm.
Semiconductor Tracker (SCT)The SCT is a semiconductor detector with a strip structure. One SCT layer provides 1D
hit positions. Two layers attached in a module are not placed in parallel with each other,but inclined by 40 mrad. By placing the two layers with the stereo angle, the SCT module
can provide 2D hit positions by combining the 1D information from the stereo and nominal
SCT layers. Each track typically crosses eight layers. The intrinsic accuracy of hit positions
on the SCT modules is 17 µm for (R − φ) direction in both barrel and endcap, and 580 µm
for z (R) direction in the barrel (endcap). Strip structure with a pitch of 80 µm is used tocollect signals, and the thickness of the sensors is 285 µm.
Transition Radiation Tracker (TRT)The TRT [59] is made up of proportional drift tubes (straws) with a diameter of 4 mm. It
provides continuous tracking in |η| < 2.0. The straw tube wall is made of Kapton coatedwith aluminum and graphite-polyamide. Tungsten wires plated with gold are used as anodes
and supported at the ends of the straw tubes. The straws are filled with 70 % Xe, 27%

CO2 and 3% O2 . For modules in which gas leakage is observed, Ar is filled instead of Xe.
The TRT has the ability of electron identification by exploiting transition radiation photons
21because the intensity of the transition radiation depends on the Lorentz γ factor. Tracks
produce typically 36 hits per track, which have an intrinsic accuracy of 130 µm per straw
in R − φ.

3.2.3

Calorimeters

Figure 3.5: An overview of the ATLAS calorimeter system [58]. The calorimeter covers|η| < 4.9 using different types of modules. The electromagnetic calorimeters are surroundedby the hadronic calorimeters.

The calorimeter was designed to measure the energy and identify particle types forelectrons, photons, taus, and jets. It also plays an important role in measuring missing
transverse energy. The electromagnetic calorimeter is placed in small radii, surrounded by
the hadron calorimeter, as shown in Figure 3.5.
Electromagnetic Calorimeter
The main role of the electromagnetic (EM) calorimeter is precise measurements and particle
identification of electrons and photons. It covers the barrel (|η| < 1.475) and endcap(1.375 < |η| < 3.2) regions. It is a sampling calorimeter in which liquid Ar (LAr) andlead are used as active material and absorber plates, respectively. The lead absorber hasan accordion shape, as shown in Figure 3.6, to cover the full range in φ without azimuthal
cracks. The thickness of the EM calorimeter corresponds to ∼ 22 (24) radiation length
in the barrel (endcap) region. The designed energy resolution of the EM calorimeter is√
σE /E = 10%/ E ⊕ 0.7% for the measured energy of E (GeV).

22

Hadronic Calorimeter
The hadronic calorimeter is divided into three parts: the tile calorimeter in the range
of |η| < 1.0, the LAr hadronic endcap calorimeter (HEC) located behind the endcap EM

calorimeter, and the LAr forward calorimeter (FCal) in 3.1 < |η| < 4.9. The tile calorimeteris a sampling calorimeter with scintillating tiles as active material and steel as absorbers,
as shown in Figure 3.6 right. The HEC and FCal are sampling calorimeters using liquidargon as active media. As absorbers, copper (copper-tungsten) plates are used in the HEC(FCal). Copper was chosen for the good heat removal and resolution, and tungsten wasused in the outer FCal modules to minimize the lateral spread of hadronic showers. The
total thickness of the detector is 9.7 (10) interaction length in the barrel (endcaps).
Cells in Layer 3∆ϕ×∆η = 0.0245×0.05

Photomultiplier

TriggerTower∆η = 0.
1

2X0

Wavelength-shifting fibre
Scintillator

47

0m

m

η=0

Steel

16X0
TriggerTower∆ϕ = 0.
09

82

0m

m

4.3X0

15
0

1.7X0
∆ϕ=0.
0245x436.8m
mx4=147.3mm

ϕ

Square cells in
Layer 2∆ϕ = 0.

0245
Sourcetubes∆η = 0.
025
m/8 =
4.
∆η = 0. 69 mm
0031
Strip cells in Layer 1

37.5m

η

Figure 3.6: Illustrations of the LAr calorimeter (left) and tile calorimeter (right) in thebarrel region [58]. The LAr EM calorimeter has three layers with different sizes of segments in ∆η × ∆φ. In the Tile hadron calorimeter, signals in the scintillators are read byphotomultipliers installed at the edge of the detector.

3.2.4

Muon Spectrometer

The muon spectrometer (MS) [58, 60] is the outermost part of the ATLAS detector andidentifies muons and measures their momenta in |η| < 2.7. Figure 3.7 shows the muon

spectrometers together with the toroid magnets, which provide a magnetic field for themuon momentum measurements. The four muon chambers are divided into two types by

their purposes. The Monitored Drift Tubes (MDT) and Cathode Strip Chambers (CSC)
are detectors used for precise measurements of the muon momentum. The Resistive Plate
Chambers (RPC) and Thin Gap Chambers (TGC) are mainly used online for the trigger
decision. The trigger chambers also contribute to the determination of the second coordinates in the offline muon reconstruction to complement the MDT’s 1D measurements in23

Figure 3.7: ATLAS muon spectrometers: MDT, CSC, RPC, and TGC [58]. The toroid
magnets are shown in yellow.

the bending direction. The MS is designed to provide a transverse momentum with a resolution of 10% for 1 TeV muon tracks. The muon chambers in the barrel are placed in three
concentric cylindrical shells around the beam axis at R = 5, 7.5, and 10 m. The chambersin the endcaps that form big wheels are placed at |z| = 7.4, 10.8, 14, and 21.5 m.
Monitored Drift Tube (MDT)The MDT is used in both barrel and endcap regions to provide high precision tracking formuons. The spatial resolution of the track position in the z direction is 35 µm. The MDT
consists of three to eight layers of drift tubes with a diameter of 3 cm filled with Ar (93%)
and CO2 (7%) at 3 bar. At the center of the tubes, a tungsten-rhenium wire is used as an
anode of the drift chamber.
Cathode Strip Chamber (CSC)
The CSC is used as a precision muon tracker in the innermost forward region (2 < |η| < 2.7)

instead of the MDT because the CSC provides better tracking performance than the MDT

in the high-hit-rate environment. The CSC consists of a set of multi-wire proportional
chambers. The cathode plane is divided into strips in the orthogonal direction to the wires
to provide 2D hit positions. The resolution of the CSC is 40 µm in the bending plane and5 mm in the transverse plane.

24Resistive Plate Chamber (RPC)
The RPC works as a trigger chamber in the barrel (|η| < 1.05) region. The RPC is a gaseousparallel electrode-plate detector with a 2 mm distance between the two electrodes. The
pick-up strips are connected to the electrodes capacitively. The signal is read out throughreadout strips via capacitive coupling, and electrodes are separated by PET foils. The
readout strips in both sides are placed in the orthogonal direction so that 2D information of
the hit position is available. A mixture of C2 H2 F4 /Iso-C4 H4 /SF6 is filled in the chambers.
Thin Gap Chamber (TGC)
In the endcap region (1.05 < |η| < 2.4), the TGC provides muon track information for the
online trigger decision. The TGC is made up of multi-wire proportional chambers with a

2.8 mm gap between graphite coated FR4 plates, as the name suggests. Copper strips on
the other side of the plate provide azimuthal position measurements. In the middle of thegap, anode wires are arranged with a wire-to-wire distance of 1.8 mm. A highly quenchinggas mixture of CO2 /n-pentane is used to prevent continuous current.

3.2.5

Magnet System

As mentioned with the ID and muon spectrometer, the ATLAS detector has solenoid andtoroid magnets. The former provides the 2 T magnetic field for the ID, while the latterprovides approximately 0.5 T and 1 T for the muon detectors in the barrel and endcap
regions, respectively. The solenoid magnet is installed between the ID and EM calorimeterin the barrel, and the inner and outer radii are 2.46 m and 2.56 m, respectively. The nominal
operating current is 7.7 kA, which corresponds to the stored energy of 40 MJ. The solenoid
is designed to keep as thin as possible to reduce material in front of the calorimeters. An
Al-stabilized NbTi conductor is surrounded by a single-layer coil. The barrel toroid consistsof eight coils installed between muon detectors. The conductor of the barrel and endcap
toroid magnets is made up of Al-stabilized Nb/Ti/Cu. The endcap toroid is placed between
the inner and middle layers of the endcap muon wheels.

3.2.6

Luminosity Detector

LUCID-2
The luminosity recorded in ATLAS is monitored by the luminosity detectors during all datataking periods. The LUCID-2 detector [61] consists of several sets of Cherenkov detectors
installed at the forward region of the ATLAS detector. The LUCID-2 detector measures therelative luminosity, which is used to extrapolate from the absolute luminosity measurements25

to the luminosity of the data for physics analyses. In each side of the ATLAS detector, 16
photomultiplier tubes (PMT) are installed surrounding the beam pipe at approximatelyz = ±17 m and detect Cherenkov light produced in the quartz window of the PMTs. Four
additional PMTs are installed on the muon shielding to detect Cherenkov light from quartz
fibers situated around the beam pipe as Cherenkov medium.

3.2.7

Trigger and Data Acquisition System

Calorimeter detectors
TileCalMuon detectors

Level-1 Calo

Endcapsector logic

JEP (jet, E)
CMX

Barrelsector logic

MUCTPI

L1TopoCTPCTPCORE

Level-1 Accept

Preprocessor
nMCM
CP (e,γ,τ)CMX

Detector
Read-Out

Level-1 Muon
FE

FE

ROD

ROD

...

FE

ROD

DataFlow
Read-Out System (ROS)

Level-1

RoI

Fast TracKer(FTK)

Pixel/SCTCTPOUT

Central Trigger

High Level Trigger(HLT)
AcceptData Collection Network

Data Storage

Processors O(28k)

Event
Data

Tier-0Figure 3.8: The ATLAS trigger and data acquisition system [62]. The trigger system consists of two stages: Level-1 and HLT. The hardware-based Level-1 trigger uses informationfrom the calorimeter and muon detectors, and issues Level-1 Accept and provides region ofinterest (ROI) information to the HLT. The software-based HLT issues final accept signals
to record events using offline-like reconstruction algorithms.

At the interaction point, proton bunches collide in every 25 ns, which corresponds to
40 MHz bunch crossings. Since it is not possible to record all collision data due to the hugecollision rate, the ATLAS trigger system performs an online selection of the collision datain two steps: the Level 1 (L1) and High Level Trigger (HLT). An overview of the trigger
and data acquisition system is shown in Figure 3.8. The L1 trigger is a hardware-based
26

trigger, which reduces the trigger rate from 40 MHz to about 100 kHz. The informationfrom the calorimeters and muon trigger detectors (RPC and TGC) is used for the trigger
decision. If an event satisfies a certain trigger requirement, an L1 Accept signal is issued
by the Central Trigger Processor (CTP), and the data is transferred to the downstream.
The HLT is a software-based trigger system, which reduces the trigger rate from 100 kHz
to about 1 kHz. The selected events by the HLT trigger processor are then recorded in thestorage.

27

Chapter 4

Data and Simulation
4.1

Data Acquisition in LHC Run 2

This dissertation uses pp collisions at a center-of-mass energy of√s = 13 TeV recordedwith the ATLAS detector during LHC Run 2 in 2015–2018. A subset of the data recorded
in 2015–2016 is used in the search discussed in Chapter 7, while the full Run 2 data is usedin Chapters 8–9.
From 2015 to 2016, the total integrated luminosity delivered by LHC is 42.7 fb−1 , and39.5 fb−1 pp collision data was recorded by ATLAS. During the full Run 2 period, 156 fb−1
data was delivered, and 147 fb−1 data was recorded by ATLAS. Figure 4.1 shows the historyof the integrated luminosity in Run 2. The total good quality data in 2015–2016 (2015–2018) corresponds to 36.1 (139.0) fb−1 . Figure 4.2 shows the mean number of interactions
per event (hµi). LHC Run 2 started with a low instantaneous luminosity in 2015, and theluminosity was increased as the LHC and ATLAS became in stable condition.

Luminosity measurement
The LUCID 2 detector measures a visible interaction rate per bunch crossing µvis [63]. The
per-bunch instantaneous luminosity is

Lb =µvis fr
,
σvis

(4.1)

where fr is the LHC revolution frequency, which is defined as the ratio of the speed of lightto the circumferences of the LHC (11246 Hz). The visible cross section σvis is a calibration
constant, which is specific to the luminosity calibration algorithm. Here Lb σvis = µvis fr

corresponds to the number of visible pp collisions by a given bunch crossing pair. With
LHC beam parameters, a per-bunch instantaneous luminosity is given byLb =fr n1 n2,2πΣx Σy28(4.2)

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

2/19 calibration

Total Integrated Luminosity fb-1

160

20
0

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

Month in Year
Figure 4.1: Integrated luminosity recorded with ATLAS in LHC Run 2 [57]

where n1 and n2 are the numbers of protons in the beam-1 and beam-2 colliding bunches,and Σx (Σy ) is the horizontal (vertical) convoluted beam width. The width Σx and Σy aremeasured by the van de Meer (vdM) method [64, 65], in which the beam position in thetransverse plane is scanned in a special vdM run once per year. The n1 n2 is determinedbased on the measurement of beam-gas event rates by the LHCb experiment [66].

Triggers
In SUSY searches in Chapters 7 and 9, data recorded by the missing transverse momentum
miss ) trigger are used. The soft b-tagging study in Chapter 8 uses data recorded by the(ETsingle muon or single electron trigger. The threshold of the triggers are summarized inTable 4.1. The trigger thresholds were raised as the instantaneous luminosity increased.
The same trigger conditions are implemented in the simulation. In the offline selection, amiss or lepton transverse momentum (p ) cut is required to avoid the uncertainty
higher ET
Tmiss . In SUSY searches, E miss > 230 GeV
associated with the resolution of the lepton pT or ET
T

is required and in soft b-tagging study leptons with pT > 27 GeV are used.

29

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

2/19 calibration

Recorded Luminosity [pb-1/0.1]

600

100
0
0

10

20

30

40

50

60

70

80

Mean Number of Interactions per Crossing
Figure 4.2: Mean number of interactions per crossing (hµi) distribution [57].

miss trigger is used
Table 4.1: Overview of online trigger thresholds in each year. The ET
in stop searches, and the single electron or single muon trigger is used in the soft b-tagging
study.

2015
2016
2017
2018

miss (GeV)ET

electron pT (GeV)

muon pT (GeV)70
90 − 11090 − 110110

20
24 − 26
26
26

24
24 − 26
26
26

30

4.2

Monte Carlo Simulation

The Monte Carlo (MC) simulation is of great importance in collider experiments in almost
all aspects, such as designing experiments and detectors, developing algorithms, and estimating signal and background processes in analyses. In this section, MC simulation for SM
background processes, as well as SUSY signal processes used in the following chapters, areexplained [67].

4.2.1

Description of pp Collisions

The simulation of pp collisions is split into two parts in terms of the energy scale of theprocess. Processes at high energy scale are calculated using perturbation theory at a fixedorder of αS . Processes at low energy scale are described by models parameterized byexperimental results, because it is difficult to calculate low energy QCD processes due tonon-perturbative effects with large αS . A cross section of a process with a final state n is
described asσ=XZ

dxa dxba,bZ

fap1 (xa , µF )fbp2 (xb , µF )dσ̂ab→n (µF , µR ),

(4.3)

1
|Mab→n |2 (Φn ; µF , µR ).
2ŝ

(4.4)

with
dσ̂ab→n (µF , µR ) = dΦn

The fapi (xa , µF ) is a parton distribution function (PDF), which describes distributions ofquarks and gluons in an incoming proton pi , (i = 1, 2) as shown in Figure 4.3. It is a functionof the momentum fraction xa , which is a fraction of the momentum of the parton a, withrespect to the momentum of the proton. The PDF also depends on a factorization scale µF ,which is an energy scale splitting the low- and high-energy for the PDF and perturbative
calculation. The parton-level cross section is described as σ̂ab→n (µF , µR ), which is a crosssection of initial partons a and b to a final state n. The factor 1/2ŝ = 1/(2xa xb s) is theparton flux, where s is the parton level center of energy squared, and Φn is the phase spaceof the final state n. Mab→n represents the matrix element (ME) of ab → n process, whichcorresponds to a sum over Feynman diagrams. It depends on µF and the renormalization
scale µR . The total cross section σ is obtained by summing up all initial partons in proton
p1 and p2 , and integrating over the phase space of the final state n as well as the momentum
fraction of the partons a and b.
Figure 4.4 shows a schematic view of a pp collision. The ME calculation does not take
into account low energy scales to avoid divergence in soft and collinear limits. Parton
shower s (PS) perform an evolution from the energy scale of initial and final state partons
31

11

11
NNPDF3.1
NNPDF3.1(NNLO)(NNLO)

0.9
0.9

g/10
g/10
0.9
0.9

2 =10GeV
xf(x,
xf(x,
µµ2=10
GeV2)2)

0.8
0.8
0.7
0.7

44
2 =10
xf(x,
xf(x,
µµ2=10
GeV
GeV2)2)

ss
0.8
0.8

g/10
g/10

0.7
0.7
dd

0.6
0.6

0.6
0.6

uu
vv

0.5
0.5

0.5
0.5

0.4
0.4

0.4
0.4

0.3
0.3

dd
vv

ss

0.3
0.3

0.2
0.2
uu

0.1
0.1

cc
uu
vv
uu
bb

dd
vv

0.2
0.2

dd

0.1
0.1

cc
00
−3−3
10
10

10
10−2−2xx

1010−1−1

00
−3−3
10
10

11

10
10−2−2xx

1010−1−111

Figure 4.3: Parton distribution functions from NNPDF3.1 at Q2 = 10 GeV2 (left) andQ2 = 104 GeV2 [68].

towards a hadron confinement scale at an order of 1 GeV, taking into account all effects
of higher orders. Below that scale reached after the evolution by the PS, the perturbation
theory does not work. The low energy non-perturbation treatment is performed by thehadronization, which describes the confinement of QCD to generate colorless hadrons fromcolored partons.

4.2.2

Simulation Samples

Two sets of MC samples are used in this dissertation. The first set sampleA summarizedin Table 4.2 is used in the analysis for large ∆m(t̃1 , χ̃01 ) in Chapter 7. The second set
sampleB in Table 4.3 is used in the soft b-tagging study in Chapter 8 and analysis targeting small ∆m(t̃1 , χ̃01 ) in Chapter 9. The tt̄ and single top samples were generated with
Powheg-Box (at next leading order (NLO) accuracy) interfaced to Pythia 6 [70] andPythia 8 [71] for PS in sampleA and sampleB, respectively. The cross sections of tt̄ andsingle top were calculated at next-to-next-to-leading order (NNLO) with the resummationof soft gluon emission at next-to-next leading-logarithm (NNLL) accuracy. The W +jets
and Z+jets samples were generated with Sherpa 2.2.0 [69] for sampleA and Sherpa 2.2.1
for sampleB at NLO, and the cross sections were calculated up to NNLO [72]. The multiboson samples were generated with Sherpa 2.2.1–2.2.2, and merged with Sherpa PS [73].
The cross sections of the multiboson processes were calculated at NLO. The Sherpa sam32

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Figure 4.4: A schematic view of a pp collision [69]. From protons coming from left andright sides, gluons and quarks in blue are produced according to the PDF. The big red blob
represents the hard scatter interaction, which emits outgoing particles of the hard process.
ISR (FSR) radiation shown in blue (red) is produced below (above) the hard process blob.
Hard QCD radiations are also shown in red, and hadronization occurs in the light green
blobs. The dark green blobs are hadrons produced in the hadronization step, and photon
radiation in yellow occurs at any step. The purple blob shows a secondary interaction(underlying event) generated by the same proton.

ples used Comix [74] and OpenLoops [75], and were merged with Sherpa PS using the
ME+PS@NLO prescription [76]. The SUSY signals in sampleA were generated at leading
order with MG5 aMC@NLO2.3.3 [69] interfaced to Pythia 8 PS, and the cross section is
calculated up to NLO and NLL for soft gluon emission. The signals in sampleB were generated with MadGraph2.6.2 [69], and Pythia 8 PS was used. The stop four-body samples
were decayed with MadSpin [77], and the cross sections were calculated at NNLO+NNLL
accuracy. The P2012 [78] and A14 [79] tuning for the underlying events (UE), which are secondary scattering interactions from beam remnants, are used with Pythia 6 and Pythia
8 PS, respectively.
The Geant 4 [80] simulation framework is used to describe interactions of particles and33

the ATLAS detector [81]. In the signal samples, the fast simulation [81] is used for theshower evolution in the calorimeters.
Table 4.2: Overview of the MC samples (sampleA) used in the analysis for large ∆m(t̃1 , χ̃01 )(Chapter 7).
Process

ME event generator

PDF

PS andharmonization

UE tuneCross-section
calculationtt̄Single-top
t-channels- and W t-channel
V +jets (V = W/Z)
Multiboson
SUSY signal

Powheg-Box v2 [82]CT10 [83]Pythia 6 [70]P2012 [78]

NNLO+NNLL [84–89]

Powheg-Box v1
Powheg-Box v2
Sherpa 2.2.0 [69]Sherpa 2.1.1 – 2.2.1
MG5 aMC@NLO 2.2 – 2.4

CT104f [83]CT10
NNPDF3.0 [93]CT10/NNPDF3.0
NNPDF2.3 [94]Pythia 6
Pythia 6
SherpaSherpaPythia 8 [71]

P2012
P2012
Sherpa default
Sherpa default
A14 [79]

NNLO+NNLL [90]NNLO+NNLL [91, 92]
NNLO [72]NLO
NLO+NLL [95]Table 4.3: Overview of the MC samples (sampleB) used in the soft b-tagging study (Chapter 8) and analysis for small ∆m(t̃1 , χ̃01 ) (Chapter 9).
Process

ME event generator

PDF

PS andharmonization

UE tuneCross-section
calculationtt̄Single-top
t-channels- and W t-channel
V +jets (V = W/Z)
Multiboson
SUSY signal

Powheg-Box v2

NNPDF3.0

Pythia 8

A14

NNLO+NNLL [84–89]

Powheg-Box v1
Powheg-Box v2
Sherpa 2.2.1
Sherpa 2.2.1 – 2.2.2
MadGraph 2.3.3

NNPDF3.0
NNPDF3.0
NNPDF3.0
NNPDF3.0
NNPDF2.3

Pythia 8
Pythia 8
SherpaSherpaPythia 8

A14
A14
Sherpa default
Sherpa default
A14

NNLO+NNLL [90]NNLO+NNLL [91, 92]
NNLO [72]NLO
NNLO+NNLL [96, 97]34

Chapter 5

Event Reconstruction
5.1

Tracks and Primary Vertex

Trajectories of charged particles, tracks, are reconstructed from hit information in theID [98]. Tracks themselves are not directly used in many physics analyses, but they arebasic objects as a seed of higher-level reconstruction such as the b-tagging, τ identification,
muons, and electrons. It is also used to measure low pT activities such as the soft term of
miss ) and the isolation of leptons. Tracks are reconthe missing transverse momentum (ETstructed and track parameters: the pT , η, φ, d0 , z0 , and charge of tracks, are measured
using the magnetic field provided by the solenoid magnet. The d0 and z0 are transverseand longitudinal impact parameters, respectively. They are defined as the distances fromthe beam spot to the perigee of the track in the transverse plane and z direction.
The first step of the tracking algorithm starts with the clustering of Pixel and SCT hits
to define three-dimensional coordinates (space points) on each layer of the tracker. On thelayers of the Pixel detector, adjacent hits are assembled, and a space point is obtained. On
the SCT layer, two sensor layers on both sides of the SCT module are used to estimate a
3D position. From three space points created in the clustering, track seeds are formed. Inorder to limit the number of track seeds and increase purity, a set of criteria is applied. The
track seeds are extended by incorporating additional space points on the IBL, the Pixel,
and the SCT using Kalman filter [99, 100], and track candidates are reconstructed. At thisstage, the collection of the track candidates still contains overlaps of track candidates thatare incorrectly assigned. This ambiguity is solved by the track selection using the scoring of
tracks in a reward/penalty schema, considering the properties of the track candidates suchas shared hits and holes of the ID sensors. In the ambiguity solver, the track candidates
are required to satisfy the basic quality criteria, such as pT > 500 MeV, |η| > 2.5, andrequirements on the transverse and longitudinal impact parameters, and the numbers of
pixel and SCT holes and shared clusters. For the track candidates that pass the ambiguity

35

solving process, a high-resolution fit is performed to measure the track parameters precisely.
The high-resolution fit utilizes all available information, such as the position and uncertainty
of clusters of hits determined by the artificial neural network (NN). The NN is also consulted
to identify the merged clusters that are formed by multiple particles. Finally, the track
candidates found in the silicon detectors are extended into the TRT, which are then usedin the high-level reconstruction algorithms, as explained in the following.
The interaction points of the pp collisions are reconstructed from the reconstructed
tracks [101, 102]. The vertex is reconstructed by the adaptive vertex fitter [103], using thebeam spot as a seed position in the transverse plane. The resolution of the vertex position isabout 30 µm in the longitudinal direction and of the order of 10 µm in the transverse plane.
The vertex with the highest sum of squared pT of the tracks is selected as the hard scatteredvertex, which is considered as a production position of the physics process of interest. In
the following, the hard scatter vertex is referred to as the primary vertex (PV), and theother vertices of pp collisions are referred to as pile-up vertices.

5.2

Topological Clusters

Energy deposits in the calorimeters are clustered, collecting the measured energies in neighboring cells, and topological clusters, or topo-clusters are formed [104, 105]. The reconstruction of topo-clusters uses the three-dimensional distribution of energy deposits in thecalorimeter cells. The energy of an input particle is calculated by summing all the energies
in these cells, and the direction of the input particle is also calculated. Topo-clusters are
EM , which is defined as the measured energy
formed based on the cell signal significance ςcellin the cell divided by the average level of the noise in the cell,
EM
ςcell
=

EM
Ecell
EM
σnoise,cell

.

(5.1)

EM is the energy measured in the calorimeter cell and σ EM
Here Ecellnoise,cell is the noise of thecell. Both of them are measured by the EM energy scale. The measured calorimeter signal
is converted to the energy for electrons and photons (EM scale) by recovering the energy
loss of these particles due to the detector response. The energy of hadrons is different fromthe EM energy scale due to the different responses between the EM showers and hadron
showers. The reconstruction of topo-clusters starts with the reconstruction of proto-cluster s
as follows.
EM > 4.
1. The proto-cluster reconstruction starts from a seed cell with ςcell
EM > 0, the cells are
2. If the neighboring cells of the cell have significant energy with ςcell

added to the proto-cluster.
36

EM > 2, step 2 is done for the cell, and3. If a cell contained in the proto-cluster has ςcell

step 3 is repeated.
The proto-clusters reconstructed by the procedure above can be too large compared to theshower structure to measure the energy and direction of incoming particles. To provide
fine structures of showers, a proto-cluster is split if it has two or more local maxima interms of the cell energy. The split cluster is then used as a topo-cluster. The direction of a
topo-cluster is calculated from the weighted average of positions of cells in η and φ.

5.3

Jets

Quarks and gluons produced at the interaction point are not observed as themselves. In
the hadronization process, quarks and gluons form hadrons. Hadrons interact with thedetector material, which spread in the transverse plane of the travel direction, resulting inshower-shaped structures, called jets. In order to obtain the four-momentum of the original
quark or gluon, the anti-kt algorithm [106] is used, and the jet energy is scaled to recover
the energy loss due to the detector response or invisible particles. The jet reconstruction is
performed within the FastJet software package [107].
In the anti-kt algorithm, jets are formed from topo-clusters using the distance between
two topo-clusters defined as
dij = min11,
p2T,i p2T,j

!

2
∆Rij
,
R2

(5.2)

where pT,i and pT,j are the pT of the i-th and j-th topo-clusters and ∆Rij is the angulardistance between the two topo-clusters. The parameter R controls the cone size of thejets, and in the following analyses, R = 0.4 is used. The algorithm proceeds by merging
two topo-clusters, which have the smallest dij , and the merged object is then treated asanother cluster and this step is repeated. When the minimum dij becomes equal to 1/p2T,i ,the iteration stops, and the i-th object is called as a jet, and the clusters used are removed
from the topo-cluster collection. As the negative power of the pT is used in the distancedefinition, the algorithm prioritizes the highest pT object and the soft objects around thehighest pT object are merged into the hard cluster. Therefore, the shape and pT of the jets
are not sensitive to soft radiation.
The energy of jets needs to be calibrated from the EM-scale, which is measured forthe topo-cluster, to the particle-level energy. The sequence of the calibration steps below
corrects the jet energy and angles using the MC and data [108].

37

Origin correction
The four momentum of each jet is recalculated so that it points to the hard-scatter
vertex rather than the center of the detector to improve the resolution of the jetangles.
Pile-up correction
The effect of the pile-up is corrected [109] aspcorr= precoT
T − ρ × A − α × (Nvtx − 1) − β × µ,(5.3)

where precois the reconstructed jet pT at the EM scale. The second term correspondsTto the area-based pile-up subtraction. ρ is the pT density, which is the pile-up contribution to the jet pT per unit area, and A is the area of the jet. The third and fourthterms refer to the residual correction based on the number of reconstructed vertices(Nvtx ), and the mean number of additional pp collisions per bunch crossing (µ), and
α and β are coefficients used in the correction.
Absolute MC-based calibration
The jet energy is scaled to the particle-level energy by applying the average energy
response, which is defined as the mean of the Gaussian fit to the E reco /E truth distributions binned in E truth and η. E reco is the EM-scale energy calculated from the
topo-clusters, and E truth is the energy of the truth jet that matched to the reco jet.
Truth jets are reconstructed using final-state particles from MC generators as input.
Global sequential calibration
The calorimeter response is sensitive to the fluctuation of the particles in jets. Dueto the different numbers of color charges for quarks and gluons, a jet originating froma quark tends to have hadrons with higher pT and fewer soft particles than a gluoninitiated jet. In order to correct the dependence on the fraction of constituents, theenergy response is corrected using the fractions of the jet energy measured in the lastlayer of the EM calorimeter and the first layer of the hadron calorimeter, the numberof tracks associated with the jet, the average transverse distance of these tracks withrespect to the jet axis, and the number of the muon track segments.
In situ calibration
As the last step, the difference between data and MC is corrected in the in situ
calibration. In the in situ calibration, the data and MC differences are quantified by
the pT ratio of a jet to other well-measured reference objects. The response Rin situ isdefined as the average ratio of jet pT to the pT of the reference object binned in the38reference pT . The ratio of the Rin situ between data and MC is used to correct the pT ofjets as a function of jet pT and η. In order to utilize good reference objects balancing
to the jet that is being calibrated, Z boson, photon, and multijet events are used.
The uncertainties in the in situ calibration are mainly arising from the mismodelingof physics effects and the pT balance, and measurement of the kinematics of thereference objects.
The calibration steps above correct the mean of the response of the calorimeter, but it isalso needed to calibrate the width of the response, the jet energy resolution (JER) [110].
The JER is parameterized as
σpT
N
S
=
⊕ √ ⊕ C,
pT
pT
pT

(5.4)

where N refers to the pile-up and electronic noise, S is the statistical Poisson fluctuationsin the sampling nature of the calorimeters, and C is the constant term. The calibrationof JER is to measure these parameters and it is performed with Z+jets, γ+jets, and dijet
events.
Jet Vertex Tagger (JVT) [109], which is a likelihood discriminating algorithm that rejects
jets originating from pile-up vertices using tracks and the PV, is used for 20 GeV < pT <120 GeV. Jets that are likely produced by non-collision backgrounds such as the beam
remnant or detector noise are removed by the jet cleaning [111] using the signal pulse shapein the LAr calorimeters, energy ratios in the calorimeter cells, and track-based variables.

5.4

b-taggingJets originating from b-quarks, b-jets, are identified by the b-tagging algorithm [112, 113],
which is one of the most powerful tools in physics analyses in ATLAS. The signature ofb-hadrons in the detector is characterized by the long flight distance compared to the otherquarks or the gluon, due to their long lifetimes of about 1.5 ps, which correspond to cτ =450 µm. The flight distance l is larger than cτ due to the boost factor (βγ) of the particle,
resulting in l = βγcτ of a few mm. In this section, the standard b-tagging algorithm, which
is based on the reconstructed jets, is described. The low-pT b-tagging, which is a key of thisdissertation, is written in Chapter 8.
The b-tagging algorithm is applied to jets, utilizing tracks ghost-associated [114]1 withthe jet, and returns a score for each jet, which describes how likely the jet is a b-jet. Theb-tagging score is evaluated by a high-level tagger based on Boosted Decision Tree (BDT),
1

Tracks are associated to a jet as ghost particles with negligible momentum by the jet reconstruction
algorithm.

39

which is one of the multi-variate analysis tools. The input variables of the high-level tagger
are provided by low-level algorithms. There are three low-level algorithms, which make useof the properties of long-lived particles. The characteristics of long-lived b-hadrons are thepresence of a displaced vertex with a few mm distance from the PV, large impact parametersof tracks originating from the displaced vertices, and multiple displaced vertices producedin the cascade decay of b-hadrons.
The presence of a secondary vertex (SV) displaced from the PV can be clear evidenceof a long-lived particle. The SV1 [115] algorithm reconstructs one secondary vertex in ajet. All possible pairs of tracks are used to fit two-track vertices, and tracks that are notassociated with a good two-track vertex are rejected. Two-track vertices that are consistent
with an SV of Ks , Λ, photon conversion, or hadronic interaction with the detector material
are removed by exploiting the invariant mass of the two tracks or the detector layout. The
final good-quality vertices are reconstructed using the set of tracks associated with thetwo-track vertices.
Two impact parameter-based algorithms, IP2D and IP3D [116], are used as another lowlevel tagger. The former algorithm uses the signed transverse impact parameter significanced0 /σd0 , while the latter utilizes signed transverse and longitudinal impact parameter significance (d0 /σd0 and z0 sin θ/σz0 sin θ ) accounting for their 2D correlation. A positive sign of the
impact parameter d0 is assigned if the perigee of the track is in front of the PV with respect
to the jet direction. Probability density functions (pdf) of the track impact parameters on
a per-track basis are constructed from simulated b-, c-, and light-flavor jets separately. For
Peach flavor of jets, a log-likelihood ratio is calculated e.g., track log(pb /pu ), where pb andpu are the per-track pdfs under the b- and light-flavor hypothesizes, respectively.

In most cases, a b-hadron decays into a c-hadron, and the c-hadron decays into shadron via the weak interaction. Since these downstream particles also have long lifetimes,
though they are shorter than that of b-hadrons, a b-hadron and its cascade decay can
produce multiple displaced vertices. In order to find a common line on which the primary,secondary, and tertiary vertices lie, the JetFitter algorithm [117] is used. It is a modified
Kalman filter, which provides eight discriminant variables related to vertices and the tracks
associated with the vertices to the high-level tagger.
A BDT-based high level tagger, called MV2c10 [116], is used to classify jets as a signal(b-jet) or background (light-flavor jet, or c-jet). The BDT is trained with simulated tt̄ events
for jets with pT < 250 GeV, while Z 0 events are used for the jet pT above 250 GeV. In the
training sample, the fraction of the c-jets (light-flavor jet) is set to 7% (93%). The kinematic
variables, pT and η, are included in the input variables for the BDT to account for theircorrelation with the discriminant variables. From the output of SV1, eight discriminant40

Event fraction

1

ATLAS Simulations = 13 TeV, tt

b-jetsc-jets10−1Light-flavour jets

10−2

10−3

jet p >20 GeV, |η|<2.5
T−1−0.8 −0.6 −0.4 −0.2

0

0.2

0.4

0.6

0.8

1

MV2c10 BDT output distribution
Figure 5.1: MV2c10 distribution of b-jets, c-jets, and light-flavor jets [118]. The histograms
are normalized to unity. Scores close to one are given to b-jet-like jets, while jets with lowscores are less likely b-jets.

variables related to the SV, such as the vertex mass2 , the number of associated tracks, thedistance between the primary and secondary vertex and its significance, are included in
the input of MV2c10. Three variables from IP2D and IP3D, the per-jet likelihood ratios
between b-, c-, and light-flavor jets, log(Pb /Plight ), log(Pb /Pc ), and log(Pc /Plight ), are added.
From JetFitter, variables that describe properties of the cascade decay, such as thenumber of vertices, the total number of tracks, and the vertex mass, are used. The MV2c10
distributions of b-jet, c-jets, and light-flavor jets are shown in Figure 5.1. The performanceof the MV2c10 classifier evaluated with MC simulation is shown in Figure 5.2. Along theline showing the MV2c10 performance, working points (WPs) are defined by selecting acertain threshold of the MV2c10 score above which the b-jet candidates are taken. The WP
with 77% b-tagging efficiency is used in this dissertation. In the 77% WP, the rejection
factors3 for the light-flavor and c-jets are 110 and 4.9, respectively.
The b-tagging efficiency in data is measured for b-, c-, and light-flavor jets, in terms ofthe generator-level flavor composition. The b-jet tagging efficiency (b ) is measured using
di-leptonic tt̄ events selecting an electron and a muon with opposite charges and exactly2

The vertex mass is defined as the invariant mass calculated from the attached tracks using the charged
pion mass for each track.
3
a rejection factor of 100 means that 1% of jets are misidentified as b-tagged.

41

ATLAS Simulations = 13 TeV, tt

104c-jet rejection

Light-flavour jet rejection105

Jet pT ≥ 20 GeV, |η| ≤ 2.5

MV2
DL1
IP3D
SV1
JetFitter

ATLAS Simulations = 13 TeV, tt
102

Jet pT ≥ 20 GeV, |η| ≤ 2.5

MV2
DL1
IP3D
SV1
JetFitter

103

102

10

10

2
1.5
1
0.5
0
0.5

0.6

0.6

0.7

0.7

0.8

0.8

0.9

0.9

1

1
0.5

0.6

0.7

1

2
1.5
1
0.5
0
0.5

0.6

0.7

Ratio to MV2

Ratio to MV2

10.5

b-jet tagging efficiency

0.8

0.9

1

0.8

0.9

1

b-jet tagging efficiency

Figure 5.2: The performance of the low- and high-level taggers [112]. The light fakerejection factor (left) and charm rejection factor (right) as a function of the efficiency are
shown. The DL1 algorithm is not used in this dissertation.

two jets, which are candidates of b-tagged jets [112]. The b-tagging efficiency is extractedusing a likelihood fit. The scale factor (SF) is defined as the ratio of the b in data to theb in MC. The SF for the 77% efficiency WP is shown in Figure 5.3. The uncertainties in
the measurement is dominated by the systematic uncertainties in the modeling of the tt̄
and single top, as well as the statistics of data. The c-jet mistag efficiency (c ) is measured
using tt̄ events with a W boson decaying into charm and strange quarks [119]. Charmjets are extracted by KLFitter [120], which assigns reconstructed jets to quarks of the tt̄
process, exploiting the decay topology of tt̄ events. In order to measure the light-flavor
mistagging efficiency, a high-purity light-flavor sample is needed. A light flavor jet could
be mistagged when the jet contains tracks with large impact parameter significance d0 /σd0
with the positive sign due to the finite resolution of the impact parameters. In order toevaluate the mistag rate, the sign of the track impact parameter is flipped, and the flippedversion of the tracks is used as the input of the b-tagging algorithm [121]. For c and light ,events that contain charm or light-flavor jets are fitted with the efficiency as a parameterof interest.

42

b-jet tagging efficiency SF

1.15
1.1

ATLAS s = 13 TeV, 80.5 fb-1
MV2, εb = 77% single-cut OP

1.05
1
0.95
0.9
Scale factor (stat. unc.)
Scale factor (total unc.)

0.85
0.8
30 40

102

2×102

Jet p [GeV]T

Figure 5.3: b-tagging scale factor as a function of jet pT for b-jets [112].

5.5

Muons

The signature of muons is characterized by the long trajectory penetrating the detector due
to the small energy deposit dE/dx. Depending on the use of the ID, MS, and calorimetercomponents, muons are classified as follows [122].
Combined (CB) muon
Muon candidate tracks are reconstructed in the ID and MS separately, and then thecandidate tracks from each detector are combined as a single muon (combined muon)by a global refit using the hits from the ID and MS together.
Segment-tagged (ST) muon
Segment-tagged muons are used when the muon track is not fully reconstructed in the
MS due to its low pT or inefficiency of the MS. An ID track is labeled as an ST muon
if the extrapolated track from the ID is associated with at least one track segment in
the MDT or CSC.
Calorimeter-tagged (CT) muon
In order to recover the muon reconstruction inefficiency at |η| < 0.1, which is not fully

covered by the muon detectors due to the detector support structure, CT muons arereconstructed from ID tracks and energy deposits in the calorimeters. If the ID track
matches energy deposit in the calorimeter which is compatible with the minimum
ionizing energy loss of a particle, the ID track is identified as a CT muon.
Extrapolated (ME) muon
ME muons are reconstructed using only MS tracks. The muon track parameters are43

estimated, taking into account the energy loss in the calorimeters. ME muons aremainly used in the forward region where ID tracks cannot be reconstructed due to theacceptance of the ID.
Muons mainly required in physics analyses are prompt muons produced directly fromdecays of W/Z bosons or BSM particles. The background muons mainly from pion or
kaon decays are suppressed at the muon identification step. Since background muons areproduced from in-flight decays of long-lived particles, the difference between the track parameters measured in the ID and MS are used to suppress background muons. The qualityof the combined track fit based on χ2 is also used to suppress background tracks with inconsistent ID and MS measurements. Depending on the tightness of the muon identification,
several working points (e.g., Loose, Medium, Tight) are provided, and an appropriate working point is selected in each analysis. The muon efficiency with the Medium identification
WP is shown in Figure 5.4.
Muons originating from heavy particles such as W /Z bosons or BSM are isolated, whilemuons from semi-leptonic decays of the heavy hadrons (b- or c-hadrons) often have otherparticles around the muon track. To reduce these background muons from hadron decays,
the following isolation variables are used.
• pvarcone30
is the scalar sum of the pT of the tracks with pT > 1 GeV in a cone of sizeT
∆R = min(10 GeV/pT (GeV), 0.3) around the muon track.

topocone20is the scalar sum of the transverse energy of topological clusters measured• ET

in the calorimeters in a cone of size ∆R = 0.2 around the muon. The contribution of
the muon itself is subtracted.

The isolation working points used in this dissertation are shown in Table 5.1. The
analysis with 2015–2016 data in Chapter 7 uses WP1, while the analysis with 2015–2018
data in Chapter 9 uses WP2.
Table 5.1: The definitions of muon isolation working points
Working Point

Calorimeter-based isolation

Track-based isolation

WP1
WP2

topocone20
ET/pT < 0.15–

pvarcone30/pT < 0.04
T
varcone30
pT/pT < 0.06

44Efficiency

1

0.98
J/ ψ →µµ Data
J/ ψ →µµ MC
Z→µµ Data
Z→µµ MC

ATLAS

0.96

s = 13 TeV, 3.2 fb-1

Data / MC

Medium muons, |η|>0.1

1.02

6 7 8 910

20

30
40 50 60
100
Stat only
Sys ⊕ Stat

6 7 8 910

20

30

1
0.98
102
40 50 60
p [GeV]T

Figure 5.4: Muon efficiency for the Medium muon ID WP as a function of muon pT [122].
The efficiency of high pT muon is measured with Z → µµ while J/ψ → µµ is used for low
pT . The efficiencies measured with data and MC agree within 0.5%.

5.6

Electrons

An electron produced at the IP passes through the ID creating hits and forms a showerin the EM calorimeter. Figure 5.6 shows an illustration of an electron trajectory passing
through the detectors. The electron reconstruction [124] is based on three components:
the track reconstruction, cluster reconstruction, and track-cluster matching. On top of the
track fit presented in Section 5.1, an additional fit is tried if the first fit fails. Due to the pion
hypothesis used in the primary fit, the energy loss of the electron tracks in the inner detectors
is not considered in the first fit. In the second fit attempt, the bremsstrahlung losses fromelectrons are considered by an additional degree of freedom using a Gaussian-sum filter(GSF) [125] to recover the inefficiency for the electrons. Clusters of the calorimeter cells arereconstructed using the topo-cluster algorithm. In the electron reconstruction, the energy
from cells in the EM calorimeter is used except for the transition region of 1.37 < |η| < 1.63.

Figure 5.6 shows the electron reconstruction efficiency. Electrons with pT > 4.5 GeV are
used in physics analyses, and the low pT electron reconstruction is limited by the cluster
finding and cluster-track matching efficiency.
The reconstructed electron candidates need to satisfy the identification criteria to enhance the purity of the prompt electrons. Likelihood-based criteria are applied with dis45

hadronic calorimeter

third layer∆η×∆φ = 0.05×0.0245

second layer∆η×∆φ = 0.025×0.0245

first layer (strips)

electromagnetic
calorimeterη∆η×∆φ = 0.0031×0.098

presamplerφ

TRT (73 layers)
SCT
beam axis

pixelsbeam spotd0
insertable B-layer

Figure 5.5: An illustration of the electron trajectory [123]criminating variables such as the fraction of the energy in each layer of the calorimeter, thelateral spread of the calorimeter shower, and the intensity of the transition radiation in the
TRT.
The isolation requirements are also applied to the electrons. The isolation variables
for electrons are similar to the ones for muons. For electrons, pvarcone20/pT < 0.06 andTtopocone20
ET/pT < 0.06 are required, where these variables are calculated around the electron

track in the same way as for muons, but the maximum cone size for the track-based isolation(pvarcone20) is set to 0.2 for the electron isolation.
T

46

Reconstruction efficiency

1

0.8

ATLAS Simulation
Cluster

0.6

Track
Cluster and track
Electron candidate

0.4

0.2

0
0

5

10

15

20

25
true
ET [GeV]Figure 5.6:
Electron reconstruction efficiency as a function of the electron truth energy [124]. Electron identification or isolation is not applied. The total efficiency shown inpurple is mainly limited by the cluster efficiency in red and also cluster-track matching.

5.7

Missing ET

Particles that do not interact with detector materials are observed as missing energy [126]in the ATLAS detector. Due to the momentum conservation before and after the collision,
the sum of the transverse momenta of the particles must be zero. Only the transverse
momentum is considered in the hadron detector because the initial momenta of the partons
are unknown. The momentum of the invisible particles, like neutrinos or neutralinos, is~ miss ). The magnitude of the E~ miss ismeasured as the missing transverse momentum (ETTmiss . The E~ miss is reconstructed as the negativereferred to as missing transverse energy ETTsum of the reconstructed objects as
miss~T~ miss,hard + E~ miss,soft ,
E
=E
T
T

(5.5)

with
~ miss,hard = −ET~ miss,soft = −E
TXelectrons

p~T e −

X

muons

p~T

unused tracks

47

X

track

.

p~T µ −X

p~T jet ,

(5.6)

jets

(5.7)

The hard objects have their lower pT threshold so low pT activities are not considered in themiss hard term. The soft activity from the hard-scatter vertex is therefore included in theETmiss soft term. The soft term is calculated using the vectorial sum of the tracks that areET

not associated with any hard objects. Tracks emerging from the hard-scatter vertex is usedin the soft term, but tracks associated with the hard objects are removed. The particles
miss calculation are calibrated in the dedicated calibrations for each object.
added to the ET

Hence, the systematic uncertainties related to the hard objects are not directly shown as
miss uncertainties, but they are included in the uncertainties in each hard object.
ET

5.8

Overlap Removal

The reconstructed objects described above can be overlapped. To avoid double-counting
the same detector signal as more than one objects, the overlap needs to be removed. In theoverlap removal procedure, a shared track, ghost matching [114], or distance between thetwo objects based on ∆Ry are used as matching criteria. In the overlap removal procedure,
E+pz
the angular distance between the two objects ∆Ry is calculated with rapidity y = 12 ln E−pZ

instead of pseudorapidity η. If an electron and jet are separated by ∆R < 0.2, then thejet is discarded, and the electron is retained. If a muon is ghost-associated with a jet andthe jet is muon-like (ntrack < 3 or pµT /pjT > 0.7), then the jet is discarded and the muon is10
kept4 . If a jet and a lepton are overlapped within ∆R < min(0.4, 0.04 + p` /GeV), then theT

lepton is removed and the jet is retained.

4

In the analysis in Chapter 7, this is not applied if the jet is b-tagged.

48

Chapter 6

Stop Search Strategies
In the following chapters, the searches for the stop direct production in pp collisions arepresented. The searches are performed by looking for excesses over the SM prediction in
the collected data. In order to predict the SM events, we rely on the MC simulation bymaking use of the established knowledge of the SM. The observed data is compared to theSM background prediction estimated from the MC with scale factors, which correct theimperfect modeling of the MC simulation. The analyses are performed as follows.
• Signal models are constructed for the considered scenario. Signal and background MC
events are generated.

• Good discriminating variables for extracting the signal events from overwhelming
background events are selected.

• Signal regions (SRs) are defined to maximize the sensitivity for a benchmark signal.
The signal region is determined based on the MC simulation, and the data in thesignal regions are blinded to avoid human biases in the selection.
• Control regions (CRs), in which MC yields are scaled to data yields, are defined toestimate background events in the SRs. In validation regions (VRs), the backgroundestimation strategy is validated.

• Experimental and theoretical systematic uncertainties are evaluated.
• Signal regions are unblinded. Hypothesis tests are performed to discover or exclude
the signals.

Given that our analysis strategy is common in the stop searches described in Chapters 7–
9, the common details are written in this section before individual analyses are presented.

49pp, s = 13 TeV, NLO+NLL - NNLOapprox+NNLL

104
102
cross section [pb](higgsino)

gg
gq
qq *
tt * , bb *+1 1 (wino)± 0
1 2 (wino)
L, R L, R

100
10 2
10 4
10 6

250

500

750
1000 1250
particle mass [GeV]

1500

1750

2000

Figure 6.1: Cross sections of SUSY signals as a function of the mass of the particle [97,127–130]. The cross sections are calculated at the NNLO + NNLL precision for the squarks
and gluino productions, and the NLO+NLL precision for the electroweak productions. Fora pair of different types of particles, the two particles are assumed to have the same mass.
The colored bands show the uncertainties on the cross sections estimated from the variationof renormalization and factorization scales and the PDF.

6.1

Signal Models

The target signal of this dissertation is the direct production of a t̃1 pair in the R-parity
conserved scenario with neutralino LSPs. Figure 6.1 shows the production cross sections of√
SUSY particles in pp collisions at s = 13 TeV. The cross sections depend on the masses of
the SUSY particles. Decay branching ratios (BRs) and types of particles in the final state
depend on the masses of the t̃1 and χ̃01 , as well as the presence of other SUSY particles into
which the t̃1 can decay. Figure 6.2 shows the mass spectra of SUSY particles in two models
considered in this dissertation.

Simplified model
When there is only one SUSY particle involved in the t̃1 decay, the particle must be the LSP
and the decay modes can be simplified as shown in Figure 6.3. In the simplified model [34–36], the possible decay modes of t̃1 are t̃1 → tχ̃01 , t̃1 → bW χ̃01 , and t̃1 → bf f 0 χ̃01 , where f50

sparticle masses

00t̃1 , b̃1 , ˜01 , ˜±
1 , ˜2 , ˜300t̃1 , b̃1 , ˜01 , ˜±
1 , ˜2 , ˜3a) simplified model

00t̃1 , b̃1 , ˜01 , ˜±
1 , ˜2 , ˜300t̃1 , b̃1 , ˜01 , ˜±
1 , ˜2 , ˜3b) higgsino LSP model<latexit sha1_base64="efBFOAC6jnE0Q3MiW2FbCh8G8V0=">AAACHXicbVDLSsNAFJ34rPUVdelmsAq6KUkVdFl047KCfUBbymRy0w6dScLMRCih/QB/wl9wq3t34lbc+iVO2iy09cDA4Zx7OXeOF3OmtON8WUvLK6tr64WN4ubW9s6uvbffUFEiKdRpxCPZ8ogCzkKoa6Y5tGIJRHgcmt7wJvObDyAVi8J7PYqhK0g/ZAGjRBupZx93PJHijiB6IEVKziZYMWGCAwY+nojIBz4e9+ySU3amwIvEzUkJ5aj17O+OH9FEQKgpJ0q1XSfW3ZRIzSiHcbGTKIgJHZI+tA0NiQDVTae/GeMTo/g4iKR5ocZT9fdGSoRSI+GZyexsNe9l4r+eJ+aSdXDVTVkYJxpCOgsOEo51hLOqsM8kUM1HhhAqmbkd0wGRhGpTaNGU4s5XsEgalbJ7Xq7cXZSq13k9BXSIjtApctElqqJbVEN1RNEjekYv6NV6st6sd+tjNrpk5TsH6A+szx8pZKLa</latexit><latexit sha1_base64="9wqZ2LgxlSbHzD61LGSthyxWqBY=">AAACHXicbVC7SgNBFJ31GeNr1dJmMArahN0oaBm0sbCIaB6QLGF2drIZMo9lZlYIS/IB/oS/YKu9ndiKrV/i5FFo4oELh3Pu5d57woRRbTzvy1lYXFpeWc2t5dc3Nre23Z3dmpapwqSKJZOqESJNGBWkaqhhpJEognjISD3sXY38+gNRmkpxb/oJCTiKBe1QjIyV2u5hK+QZbHFkuopn4cmwS+NYUyGHN3eVIZcRYYNB2y14RW8MOE/8KSmAKSpt97sVSZxyIgxmSOum7yUmyJAyFDMyyLdSTRKEeygmTUsF4kQH2fibATyySgQ7UtkSBo7V3xMZ4lr3eWg7R2frWW8k/uuFfGaz6VwEGRVJaojAk8WdlEEj4SgqGFFFsGF9SxBW1N4OcRcphI0NNG9D8WcjmCe1UtE/LZZuzwrly2k8ObAPDsAx8ME5KINrUAFVgMEjeAYv4NV5ct6cd+dj0rrgTGf2wB84nz/GoKM6</latexit>

Figure 6.2: Mass spectra of considered scenarios. In the simplified model (left), t̃1 always
decays into χ̃01 and SM particles. The higgsino-like LSP scenario (right) has three higgsino
states shown in green, and the branching ratio of the t̃1 decay depends on the MSSM parameters. The higgsino-like LSP is characterized by the small splittings among the higgsino
states.

and f 0 denote fermions1 . The diagrams of these decay models are shown in Figure 6.4. The
region where mt̃1 < mχ̃01 is not considered, as the lightest neutralino is assumed as the LSP(through this dissertation). The decay modes depend on the mass difference between t̃1
and χ̃01 (∆m(t̃1 , χ̃01 )). When ∆m(t̃1 , χ̃01 ) > mt , t̃1 directly decays into the same flavor SM
particle, top quark, with the LSP (t̃1 → tχ̃01 ). If ∆m(t̃1 , χ̃01 ) is smaller than mt , then the t̃1

decay becomes the three-body decay, via an off-shell top quark. For the most compressedcase where ∆m(t̃1 , χ̃01 ) < mW + mb , the four-body decay is observed via an off-shell W

boson. For each decay modes, 100% branching ratios are considered.

Higgsino LSP
The higgsino-like LSP scenarios is favored by the naturalness as discussed in Section 2.2.6.
There are three higgsino states: two neutralinos (χ̃02 and χ̃01 ) and a chargino (χ̃±
1 ). Thesignature is characterized by small mass-splittings among the higgsino states, which are
typically below 5 GeV. This dissertation targets two scenarios: ∆m(t̃1 , χ̃01 ) > mt and∆m(t̃1 , χ̃01 ) < mt .
∆m(t̃1 , χ̃01 ) > mt
In this case, three t̃1 decay modes are considered: t̃1 → tχ̃01 , t̃1 → tχ̃02 , t̃1 → bχ̃±
1 . The0
diagram of t̃1 → bχ̃±
1 decay is shown in Figure 6.5. The diagram of t̃1 → tχ̃2 is similar
1

A flavor changing decay t̃1 → cχ̃01 is not considered in this dissertation.

51

m > mt̃1
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˜
t˜1
m 1
!
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 100m>0

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

Figure 6.3: Possible decay modes in the simplified model. The decay modes depends on∆m(t̃1 , χ̃01 ), and in each phase space, 100% branching ratio is assumed.

to that of the tχ̃01 decay, except for an additional decay of χ̃02 . If t̃1 decays into χ̃02 or χ̃±1,these intermediate SUSY particles further decay into the LSP and SM particles. Due to the0small mass-splitting, the SM particles from the χ̃±
1 or χ̃2 decay tend to have low momenta.

The branching ratio of these decays depend on MSSM parameters. In order to cover a wide
range of possible scenarios, three models summarized in Table 6.1 with different branchingpratios are considered. To build the three models, M3 = 2.2 TeV, MS = t̃1 t̃2 = 1.2 TeV,
and M1 = M2 ∼ 1.5 TeV are assumed. The t̃1 branching ratios depends on the t̃R and t̃Lcomposition of the t̃1 . When t̃1 is composed of mainly t̃L , tχ̃01 and tχ̃02 decays are favored,
while bχ̃±
1 is favored when t̃1 is mainly composed of t̃R in the small tan β case. When tan β islarge and t̃1 ∼ t̃L , the three decay modes have similar branching ratios, which is consideredin the third scenario.

Table 6.1: Higgsino LSP scenarios. The branching ratios are fixed in all signal points foreach scenario.
Scenario
mostly left
mostly rightlarge tan β

Left/Rightt̃1 ∼ t̃L
t̃1 ∼ t̃Rt̃1 ∼ t̃L

tan β
20
20
60

BR (tχ̃01 , tχ̃02 , bχ̃±1)45 : 45 : 10
25 : 25 : 50
33 : 33 : 33

For each scenario, two 2D plane signal grids are generated as follows:• mχ̃± –mχ̃01 plane with a fixed ∆m(t̃1 , χ̃01 ) of 5 GeV.
1

52

b

b

`

p

ν
t̃

p

χ̃01
p

q
b

p

q

b
ν

W
t̃

χ̃01

t̃

`
p
t̃

χ̃01
χ̃01

t̃

q

W
b

t̃
p

q

t

t

`
ν

W

χ̃01
χ̃01

W

q
b

q

Figure 6.4: Diagrams of t̃1 decaying into χ̃01 . The four-body decay (left) is the mostcompressed case where the ∆m(t̃1 , χ̃01 ) is too small to decay via an on-shell W boson. In
the three-body decay (middle), t̃1 decays into a b-quark, an on-shell W boson and a χ̃01 . If∆m(t̃1 , χ̃01 ) is large enough to decay to an on-shell top quark, the two-body decay (right) is
considered.

±0• mt̃1 –∆m(χ̃±
1 , χ̃1 ) plane with a fixed χ̃1 mass of 150 GeV.
0
In both planes, ∆m(χ̃02 , χ̃01 ) = 2 × ∆m(χ̃±
1 , χ̃1 ) is assumed. The branching ratios and themass relations are fixed over the signal grids. A stop and higgsino search based on thismodel is performed in the analysis in Chapter 7.

±
Figure 6.5: A diagram of t̃1 decaying into a b-quark and a χ̃±
1 . The χ̃1 decays into the LSP0(χ̃1 ). The momentum of the W boson and its decay products depends on the mass-splitting0
between χ̃±
1 and χ̃1 .

∆m(t̃1 , χ̃01 ) < mt
If the decay of t̃1 into tχ̃01 or tχ̃02 is kinematically forbidden due to a small mass-splitting
between t̃1 and χ̃01 (∆m(t̃1 , χ̃01 ) < mt ), the decay of t̃1 becomes simple. Only possible decay±(∗) χ̃0 . In this case, the final state is similar toof t̃1 is t̃1 → bχ̃±
1
1 with χ̃1 decaying into W

that in the simplified model. The compressed scenario search is presented in Chapter 9,
using the simplified model. In particular, the most compressed region where t̃1 decays into
four-body (t̃1 → bf f 0 χ̃01 ) is considered.

53

6.2

Background Events

In this dissertation, the stop searches are performed by requiring exactly one lepton andmiss in final states. The presence of b-hadrons in the final states is also one of the distinctive
ETfeatures of the stop signals. Background processes in the stop searches with one lepton final
states are explained below and Feynman diagrams of main processes are shown in Figure 6.6.
The cross sections of the SM background processes are summarized in Figure 6.7. Comparedto the cross section of the targeting t̃1 production, which is an order of pb or lower, the SM
background processes have significantly higher cross sections. To reduce these overwhelming
backgrounds, a variety of discriminating variables are introduced in the following chapters.

g

t

g

t

<latexit sha1_base64="ogX0Fa6f5TM3jrBf5hImkFH9Xr0=">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</latexit>

g

q

q

W±

<latexit sha1_base64="BO99nxxIwUQol+jOOZ6p/6v/bHI=">AAADinicfZLbbtNAEIY3NocSCqRwBzcWCVJBVmQbqQVxUwEXXBaJNJWSEK03Y2fVPZjddaRo5UfgAXkA3oAHYO0ENYeWkSzNzjf/jPVr0oJRbaLoV8vz79y9d//gQfvh4aPHTzpHTy+0LBWBAZFMqssUa2BUwMBQw+CyUIB5ymCYXn2q+XABSlMpvpllAROOc0EzSrBxpelR6+c4hZwKm/Esowwqm8FS5AoX86odBNewKb2pjuM4Ck+i146tYuwYg8xYmoQ0rrbqiuZzY2USyh1gc1ZKUVkah4sNtGKp1DVbOFmyI8tAcdoIk3BxK1zE+wuvYbK/kuEUmO396NWDb2Z5zf6jk7ew4Xc7LnhVd7jJtaMgZht+tv+9G/Pb00436kdNBPtJvE66aB3n087v8UySkoMwhGGtR3FUmInFylBSDxyXGgpMrnAOI5cKzEFPbHM3VfDKVWZBJpX7hAma6qbCYq71kqeuk2Mz17usLt7ERqXJ3k0sFUVpQJDVoqxkgZFBfYTBjCoghi1dgomi7l8DMscKE+NOdWtLfY28qJwv8a4L+8lF0o/f9pOvSffs49qhA/QCvUTHKEan6Ax9QedogEjrj/fc63o9/9BP/Pf+h1Wr11prnqGt8D//BfOiDZU=</latexit>

b

t

g

W

<latexit sha1_base64="pE+WgINYl7kizgv1ZIhCACPHl1c=">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</latexit>

Figure 6.6: Feynman diagrams of the main background processes: tt̄ (left), W +jets (middle), and single top (right).

tt̄
In many signal regions, the top pair production (tt̄) is the dominant background promiss , including off-shell top cases.
cess because a typical stop signal topology is tt̄ + ET√
The cross section of the tt̄ process at s = 13 TeV is 818 pb [132]. The tt̄ backgroundis classified into three categories in terms of the decay modes of the top quarks. Whenboth top quarks decay hadronically (t → bW (→ qq)), it is called full-hadronic tt̄, andtt̄ with two leptonically decaying tops (t → bW (→ `ν)) is referred to as di-leptonic tt̄.

When one top decays hadronically and another top decays leptonically, the event iscategorized in the semi-leptonic tt̄. Both semi-leptonic and di-leptonic tt̄ enter in themiss originating from neutrinos. Despite the exactly one
signal regions because of ET

lepton requirement, the di-leptonic tt̄ is a dominant background in some cases when
one of the leptons is lost due to the inefficiency of the lepton ID or the lepton is outof acceptance.
W +jets
The W boson production associated with jets has a large cross section at54√

s = 13 TeV,

R

L dt
Standard Model Total Production Cross Section Measurements Status:
November 2019
−1

[fb ]

σ = 96.07 ± 0.18 ± 0.91 mb (data)

pp
W
Z
tt̄
tt−chan
WW
H
Wt
WZ
ZZ
ts−chan
tt̄W
tt̄Z
tZj
WWW
WWZ

COMPETE HPR1R2 (theory)σ = 95.35 ± 0.38 ± 1.3 mb (data)
COMPETE HPR1R2 (theory)σ = 190.1 ± 0.2 ± 6.4 nb (data)
DYNNLO + CT14NNLO (theory)σ = 112.69 ± 3.1 nb (data)
DYNNLO + CT14NNLO (theory)σ = 98.71 ± 0.028 ± 2.191 nb (data)
DYNNLO + CT14NNLO (theory)
σ = 58.43 ± 0.03 ± 1.66 nb (data)
DYNNLO+CT14 NNLO (theory)σ = 34.24 ± 0.03 ± 0.92 nb (data)
DYNNLO+CT14 NNLO (theory)σ = 29.53 ± 0.03 ± 0.77 nb (data)
DYNNLO+CT14 NNLO (theory)
σ = 818 ± 8 ± 35 pb (data)
top++ NNLO+NLL (theory)σ = 242.9 ± 1.7 ± 8.6 pb (data)
top++ NNLO+NNLL (theory)σ = 182.9 ± 3.1 ± 6.4 pb (data)
top++ NNLO+NNLL (theory)σ = 247 ± 6 ± 46 pb (data)
NLO+NLL (theory)
σ = 89.6 ± 1.7 + 7.2 − 6.4 pb (data)
NLO+NLL (theory)σ = 68 ± 2 ± 8 pb (data)
NLO+NLL (theory)σ = 130.04 ± 1.7 ± 10.6 pb (data)
NNLO (theory)σ = 68.2 ± 1.2 ± 4.6 pb (data)
NNLO (theory)
σ = 51.9 ± 2 ± 4.4 pb (data)
NNLO (theory)
σ = 57 + 6 − 5.9 + 4 − 3.3 pb (data)
LHC-HXSWG YR4 (theory)σ = 27.7 ± 3 + 2.3 − 1.9 pb (data)
LHC-HXSWG YR4 (theory)σ = 22.1 + 6.7 − 5.3 + 3.3 − 2.7 pb (data)
LHC-HXSWG YR4 (theory)σ = 94 ± 10 + 28 − 23 pb (data)
NLO+NNLL (theory)σ = 23 ± 1.3 + 3.4 − 3.7 pb (data)
NLO+NLL (theory)σ = 16.8 ± 2.9 ± 3.9 pb (data)
NLO+NLL (theory)
σ = 51 ± 0.8 ± 2.3 pb (data)
MATRIX (NNLO) (theory)σ = 24.3 ± 0.6 ± 0.9 pb (data)
MATRIX (NNLO) (theory)σ = 19 + 1.4 − 1.3 ± 1 pb (data)
MATRIX (NNLO) (theory)σ = 17.3 ± 0.6 ± 0.8 pb (data)
Matrix (NNLO) & Sherpa (NLO) (theory)
σ = 7.3 ± 0.4 + 0.4 − 0.3 pb (data)
NNLO (theory)σ = 6.7 ± 0.7 + 0.5 − 0.4 pb (data)
NNLO (theory)σ = 4.8 ± 0.8 + 1.6 − 1.3 pb (data)
NLO+NNL (theory)
σ = 870 ± 130 ± 140 fb (data)
Madgraph5 + aMCNLO (theory)σ = 369 + 86 − 79 ± 44 fb (data)
MCFM (theory)σ = 950 ± 80 ± 100 fb (data)
Madgraph5 + aMCNLO (theory)σ = 176 + 52 − 48 ± 24 fb (data)
HELAC-NLO (theory)σ = 620 ± 170 ± 160 fb (data)
NLO+NLL (theory)
σ = 0.65 + 0.16 − 0.15 + 0.16 − 0.14 pb (data)
Sherpa 2.2.2 (theory)
σ = 0.55 ± 0.14 + 0.15 − 0.13 pb (data)
Sherpa 2.2.2 (theory)

−4

10

−3

10

−2

10

−1

10

ATLAS Preliminary

Theory√
LHC pp s = 7 TeV

1

10

10

10

4

10

EPJC 79 (2019) 760

4.6

EPJC 77 (2017) 367

3.2

JHEP 02 (2017) 117

20.2

JHEP 02 (2017) 117

4.6

JHEP 02 (2017) 117

3.2

PLB 761 (2016) 136

20.2

EPJC 74: 3109 (2014)

4.6

EPJC 74: 3109 (2014)

3.2

JHEP 04 (2017) 086

20.3

EPJC 77 (2017) 531

4.6

PRD 90, 112006 (2014)

36.1

EPJC 79 (2019) 884

20.3

PLB 763, 114 (2016)

4.6

PRD 87, 112001 (2013)
PRL 113, 212001 (2014)

36.1

ATLAS-CONF-2017-047

20.3

EPJC 76, 6 (2016)

4.5

EPJC 76, 6 (2016)

3.2

JHEP 01 (2018) 63

20.3

JHEP 01, 064 (2016)

2.0

PLB 716, 142-159 (2012)

36.1
4.6
36.1

PRD 97 (2018) 032005

Data
stat
stat ⊕ syst

20.3

JHEP 01, 099 (2017)

4.6

JHEP 03, 128 (2013)
PLB 735 (2014) 311

20.3

PLB 756, 228-246 (2016)

36.1

PRD 99, 072009 (2019)

20.3

JHEP 11, 172 (2015)

36.1

PRD 99, 072009 (2019)

20.3

JHEP 11, 172 (2015)36.1

PLB 780 (2018) 557

79.8

PLB 798 (2019) 134913

79.8

PLB 798 (2019) 134913

510

Nucl. Phys. B, 486-548 (2014)√
s = 8 TeV

Data
stat
stat ⊕ syst

3

PLB 759 (2016) 601

20.2

20.3

√
LHC pp s = 13 TeV

2

0.081

EPJC 79, 535 (2019)
PLB 761 (2016) 179
PRD 93, 092004 (2016)
PLB 761 (2016) 179
EPJC 72, 2173 (2012)
PLB 761 (2016) 179

Data
stat
stat ⊕ syst

LHC pp1

PLB 761 (2016) 158

8×10−8√Run 1,2 s = 7,8,13 TeV

Reference

50×10−8

6

10

11

10

0.5 1.0 1.5 2.0

σ [pb] data/theory

Figure 6.7: The production cross sections of the SM processes at the LHC [131]. The
measurements at ATLAS are compared to the theoretical prediction.
190 nb [133]. Events with a leptonically decaying W boson pass the one lepton andmiss selection. The W +jets events are strongly suppressed by requirements ofhigh ETb-tagging, but the events with a gluon splitting to bb̄ pair (g → bb̄) from initial or final
state radiation enter the signal regions.

Single top
A process with a single top quark is also a non-negligible background in some signal
regions. In the following searches, the single top production in association with a
W boson (W t) gives a large contribution. The cross section of the W t process is
94 pb [134].
tt̄ + VIn spite of a small cross section, tt̄ + V (V is Z or W ± ) is a tough background process.
In particular, tt̄ + Z with Z → νν is an irreducible background in some signal regions.

Due to the small cross section, the process has not been precisely studied yet in SM
measurements, which makes the background estimation of this process difficult.

55

Multiboson
Events with more than one electroweak bosons (W ± and Z) are not main backgroundprocesses, but still these events account for some fraction of the background in themiss is created by neutrinos from Z → νν or leptonicallysignal regions. Large ET

decaying W bosons. Contributions are mainly from the diboson process, which has

exactly two electroweak bosons.
Z+jetsThe Z boson production is a minor background process in signal regions with one
miss selections. The Z → `` process is suppressed by the one lepton and
lepton and ET

b-tagging requirements.

Multijet
Most pp collisions do not contain leptons produced via electroweak interactions, butthey create quarks and gluons via QCD interactions, resulting in multijet signatures.
The multijet processes do not contain isolated leptons, but some of the tracks orclusters can be misidentified as leptons. When the jet energy is mismeasured, themiss is obtained. The probability
transverse energy does not conserve, and non-zero ET
miss is very small. However,of having a jet mimicking a lepton and creating large ET
miss regions due to the signifievents with a fake lepton are observed mainly in low ET

cantly large cross section of the QCD processes compared to the EW processes. The
contribution of the multijet to the following analyses are found to be negligible since
miss is required in the analyses.
large ET

6.3

Discriminating Variables

The transverse mass mT is defined asqmiss (1 − cos ∆φ(~~ miss )),`, E
mT = 2p`T ET
T

(6.1)

~ miss ) is the angle between the lepton (`) and E miss directions in the transverse
where ∆φ(~`, E
T
T
plane. This quantity corresponds to the transverse component of the invariant mass of theW boson, and is used to discriminate tt̄ and W +jets events exploiting the mass of themiss originating from a W
leptonically decaying W boson. If an event has a lepton and ET
miss from other particles orboson decay and there are no additional contributions to the ET

the pile-up, the mT of the event has an end point at the mass of the W boson (80.4 GeV).
By requiring the high mT , W +jets and tt̄ backgrounds with a leptonic W boson are reduced
significantly.

56

The stransverse mass mT2 [135] is used for decay topology with two branches (a and b in
the following); one branch is fully reconstructed while the other is not fully reconstructed due
to an invisible particle. The measured four-momentum is referred to as p~ = (Ei , p~T,i , pz,i ),while the unmeasured momentum is referred to as ~q = (Fi , ~qT,i , qz,i ). For each branchi ∈ (a, b),
m2Ti =qq
2
2 + m2
p2Ti + m2pi + qTi− (~pTi + ~qTi )2
qi

(6.2)

with m2pi = Ei2 − p~i 2 and m2qi = Fi2 − ~qi 2 . If the invisible momentum and the masses ofthe particles are correctly assigned, the mTi must be smaller than the mass of the pair~ miss is split into ~qTa and ~qTb , andproduced parent. The observed missing momentum ETthen the stransverse mass is defined as
mT2 =

min

~ missq~Ta +~
qTb =ET{max(mTa , mTb )} .

(6.3)

The asymmetric transverse mass (amT2 ) [136–138] is a variation of this variable targetingthe di-leptonic tt̄ with a missing lepton, as shown in Figure 6.8. For branch a, the measured
particle is the b-jet from the top quark decay, and the unmeasured particle is the W bosonwith a missing lepton. For branch b, the measured particles are the b-jet and charged lepton,
while the neutrino is the unmeasured particle. For the masses of the particles needed forthe calculation above, mqa = mW = 80.4 GeV and mqb = mν = 0 GeV are used. According
to the discussion above, the distribution of the amT2 in the di-leptonic tt̄ events has aboundary at the mass of the top quark.

57

Figure 6.8: An illustration of a di-leptonic tt̄ event for the amT2 calculation. The unmeasured particles on the top branch (branch a) form a W boson, i.e., a missing lepton and aneutrino, while the one in the bottom branch (branch b) is a neutrino. The assignment of
the measured b-jets to either branch a or b is unknown, so both assumptions are tested.

6.4

Background Estimation

The background events in SRs are estimated mainly based on the MC simulation. In orderto reduce the uncertainties in the modeling of the MC simulation, the normalization of theMC events is scaled with normalization factors (NF), which are measured ratios of data to
MC in CRs. Each SR has a CR for each dominant background process which contributes
to the SR yields at roughly above 20%. Once a SR selection is defined with a maximum
significance of the signal events as a figure of merit, corresponding CRs are defined withsimilar selections to the one for the SR. VRs are defined to check if the normalization
factors give a proper data/MC normalization in a region which is closer to the SR than the
CR. The SR, CR, and VR are statistically independent with each other. Figure 6.9 shows
how to define these regions. The CRs should have enough statistics of data to minimize
the statistical fluctuation of the normalization factor. The CR selection needs to be as
close as possible to the SR selection so that the normalization factor is obtained in similarphase space. If the CR and SR have different MC modeling, the normalization factor
obtained in the CR would overestimate or underestimate the background yields in the SR.
It is important to design the CR where the contribution of signal events to the total CR
yields is negligible; otherwise the normalization factor would become large due to the signal
contamination if there are signal events. The CRs for all dominant backgrounds are thenfitted simultaneously to obtain the normalization factor for each background process. The
normalization factors are applied to each background in the SRs, CRs, and VRs. The CR
and VR for each process need to have a good purity of the background process that is being

58

Events

Control
RegionValidation
RegionSignalRegionSignalBackground

Variable X

Figure 6.9: An illustration of the background estimation strategy. The SR is defined
to maximize the sensitivity to discover the signal. The CR is defined in the region whereenough background events are available and the signal contamination is negligible. Between
the SR and CR, the VR is defined to validate the extrapolation from the CR to the SR.

normalized. To increase the purity of the process, additional requirements that can enhance
the process or suppress the other are used.

6.5

Systematic Uncertainties

Systematic uncertainties are classified into two types: the experimental and theoreticaluncertainties. The former is generally associated with the calibration of the physics objects,
and the latter is caused by the imperfect modeling of the MC simulation. The impact of
uncertainties on each analysis are described in the following chapters, but details of theuncertainties are explained here. The systematic uncertainties are incorporated in profile
likelihood fits as nuisance parameters.

6.5.1

Experimental Uncertainty

The experimental uncertainties associated with each object come from the uncertainties
in the calibration of each object. The variations of the number of events in the SR, CR,
and VR from each source of uncertainty are included in the fit as nuisance parameters, as
described in Section 6.6.

59

Jets
The jet energy scale (JES) and jet energy resolution (JER) are the main components of theuncertainty in the momentum of jets. As already discussed in Section 5.3, these uncertainties
are associated with the calibration of them. The uncertainties affect the event yields directly
miss . The
from the jet pT cuts or via indirect effects on the magnitude and direction of the ET

uncertainty in the JVT explained in Section 5.3 is also considered.
Leptons
The uncertainties in the electron and muon calibrations: the scale and resolution of the
lepton momentum and the isolation efficiency measurements are considered. The size of the
lepton uncertainties is typically small compared to that for the jet measurements.
Flavor tagging
For the standard b-tagging, the uncertainties in the calibration of the efficiencies for b-, c-,and light-flavor jets in Section 5.4 are treated separately. These uncertainties affect SR
event yields if CR selections have different b-tagging requirements or flavor composition ofa b-tagged jets. The uncertainties in the soft b-tagging are discussed in Section 8.4.
Luminosity
For the minor backgrounds that do not have a dedicated CR and the signal, the uncertainty
in the luminosity measurement is considered. The uncertainties are mainly coming fromthe vdM scan and calibration transfer from the scan to the data for physics analyses. The
uncertainty for the 2015–2016 data is 2.1%, and for the full Run 2 data is 1.7%.
Pile-up reweighting
The distribution of the number of pp interactions per event in the MC simulation isreweighted to match the distribution of data. The uncertainty in the reweighting is included to account for the residual imperfect pile-up modeling in the MC simulation.
miss soft termETmiss originating from hard objects such as jets or leptons are
The uncertainty in the ET

considered in the uncertainties of each hard objects. In addition to them, the data andmiss soft term is evaluated in the E miss calibration with Z → µµ
MC difference of the ETTevents [126]. The uncertainties in the scale and resolution of the soft term from the calibration are included.

60

Normalization
The uncertainties in the NFs of the dominant background processes are originating fromlimited statistics of the data in the CRs.
MC statistics
Due to the tight selections for the SRs, the background and signal MC events are limited
in some cases, which could be one of the main uncertainties.

6.5.2

Theoretical Uncertainty

The main uncertainty in the MC simulation is caused by the limited accuracy of the QCD
perturbation calculation. The missing higher orders cause the uncertainties in the MC
simulation. The treatment of the evaluation depends on the generators used for the process.
The methods used for the evaluation are given below. The uncertainties in the choice of
proton PDFs are evaluated by using different sets of PDF and are found to be negligible.
For the main background processes which have a dedicated CR, the impacts on theextrapolation of the NFs from the CR to the other regions are evaluated. The transfer
factor (TF) is defined as the ratio between the event yields in the CR and the other region
for each main background process. For example, the tt̄ TF which controls the number of tt̄
events in the SR is
tt̄
T FSR
=

tt̄
NSR
,
tt̄
NTCR

(6.4)

tt̄ and N tt̄
where NSR
TCR are the number of tt̄ events in the SR and tt̄ CR, respectively. The

uncertainties are also evaluated for the transfer factors corresponding to the extrapolationfrom the tt̄ CR to the other CRs (e.g., W +jets CR) and VRs. The uncertainties that
affect the overall normalization of the background process are canceled because these effects
are common in all regions. For the systematic uncertainties which have ±1σ variations,the difference between them is taken as the uncertainty. For the systematic uncertainties
which have only one variation, such as the generator comparison, the difference between
the alternative and default settings are taken. For the minor background processes without
a dedicated CR, the direct impact on the event yield in each region is evaluated.
tt̄ modeling
The uncertainty in the hard scatter process is evaluated by comparing generators with different matrix element (ME) calculations. The nominal tt̄ sample with Powheg (ME) andPythia (PS) is compared with an alternative tt̄ sample generated with MG5 aMC@NLO(ME)61and Pythia (PS), and the difference is taken as the uncertainty in the hard scatter. The
uncertainty in the PS is evaluated with an alternative sample with Powheg (ME) and Herwig (PS). Alternative samples with the same generator but with different ISR radiation
hardness are used to evaluate the uncertainty in the ISR jet.
W +jets modeling
The uncertainties in the renormalization and factorization scales are evaluated by varying
these scales from 1/2 to 2 with respect to the nominal scales in the nominal Sherpa sample.
The parameters used for the resummation of the soft gluon emission and the matching
between ME and PS are varied to evaluate the uncertainties in them. In addition to that,the nominal Sherpa sample is compared with MadGraph (ME) + Pythia (PS) sample
to evaluate the uncertainty in the Sherpa PS.
Single top modeling
The uncertainty in the single top process is dominated by the interference between thett̄ and single top W t processes. The uncertainty is evaluated by comparing the diagram
removal (DR) scheme and diagram subtraction (DS) scheme [139], and the difference istaken as the uncertainty. The uncertainties in the hard scatter, PS, and ISR radiation aretaken into account in the same way as for the tt̄ modeling. This treatment is included in theanalysis targeting the higgsino-like LSP scenario, where the contribution of the single top
is visible. Given the small single top contribution to the signal region and control regionsin the analyses with soft b-tagging, a flat 30% uncertainty is added.
Modeling of minor backgrounds
The uncertainties in the production cross sections are taken into account in the minor background processes that do not have a dedicated control region, and the signal processes.
Given the small impact of the uncertainties from the minor backgrounds on the total yields,
flat uncertainties in the event yields in each region is added as an inclusive modeling uncertainty.

6.6

Statistical Treatments

Fitting is performed based on a likelihood function:
!nr
!
Y 1 X
X
Y
i i
i i
L(µ, θ; n) =
µ yr
exp −
µ yr
C(θj ).
nr !
r
i

i

62

j

(6.5)

The first part is a product of the probabilities to observe nr events in a region r, where µi yri
events are predicted for the i-th process in a set of background or signal processes. Theµi is a NF applied to the events predicted by MC (yri ). The µi is fixed to unity for minor
backgrounds that do not have a dedicated CR. Systematic uncertainties are incorporated
into the likelihood as nuisance parameters (NPs). The NPs vary the predicted signal andbackground events. The yields are parameterized with the NPs as
yri = yri0 +Xθj ∆yrij ,

(6.6)

θj ∈θ

where yri0 is the pre-fit yield without systematics, and ∆yrij is a size of the variation of
the yield yri from the effect of the nuisance parameter θj . The ∆yrij corresponds to the 1σvariation of the uncertainty, which is calculated before fitting. If θj = 0, the event yields
are not changed by the j-th NP in all regions. The nuisance parameters are constrained by
the second part of the likelihood. For each nuisance parameter θj , the C(θj ) is a term that
constrains the nuisance parameter typically using a Gaussian form.
In order to discover or exclude certain models like an SM-only prediction or existenceof a new physics beyond the SM, hypothesis tests are performed [140]. In the following, µrefers to the µsignal , the signal strength compared to the theoretically predicted signal yield.
The test statistic for hypothesis tests is defined with as a ratio of the likelihoods
λ(µ) =

ˆL(µ, θ̂)(0 ≤ µ̂ < µ),L(µ̂, θ̂)

(6.7)

ˆ
where a set of µ̂ and θ̂ maximizes L, and θ̂ is the value that maximizes L for a given µ.
The ratio λ(µ) varies between 0 and 1, and a larger value of λ means that the value gives
better description of the observed data. The likelihood ratio is converted toqµ = −2 ln λ(µ),(6.8)

as a test statistic for hypothesis tests.
To quantify the incompatibility of observed data with a hypothesis with a signal strengthµ, a p-value is defined as
pµ =

Z ∞

qµ,obsf (qµ0 |µ)dqµ0 ,(6.9)

where qµ,obs is an observed value of qµ , and f (qµ |µ) is a probability density function of theqµ for a given µ. By definition, a smaller p-value means that the hypothesis with the µ is
more incompatible with the observed data.

63

Background only fit
The background only fit is performed without signal samples to estimate background contribution in SRs and VRs. Only CRs are used in the background only fit, and the obtained µ
values (NPs) for the background processes are applied to the SR and VR yields to estimate
the background yields in these regions.

Model-dependent signal fit (Exclusion fit)
The model-dependent signal fit is a fit to exclude a signal model. The SRs and CRs are usedin the fit, considering a signal contribution in these regions. In the following chapters, signal
regions for the exclusion fit are defined as multi-bin signal regions. The exclusion fit over themulti-bin SR (shape-fit) exploits the shapes of the signal and background distributions sothat the sensitivity to exclude the model is improved by considering the correlation among
the multiple bins. When a signal model contributes to more than one SRs, it is beneficial
to combine these SRs. In that case, a simultaneous fit is performed using these SRs as if
these SRs were a single multi-bin SR so that more powerful exclusion sensitivity is achieved
than the individual SRs.
Using the background only hypothesis and signal and background hypothesis, corresponding to p0 and p1 , respectively, the CLs [141] is defined as
CLs =

p1
.
p0

(6.10)The p-value for the signal plus background hypothesis (p1 ) itself is not used, but a penalty
1/p0 is applied in order to avoid rejecting a signal model when observed data is less likely tothe background only prediction either. A model is considered as excluded at 95% confidence
level (CL) when the CLs is lower than 0.05, which corresponds to the modified probabilityof having a signal model to be below 5%.

6.7

Previous Results

6.7.1

Higgsino-like LSP Model

A similar scenario to the higgsino LSP model with large ∆m(t̃1 , χ̃01 ) was searched in theprevious analysis at ATLAS with Run 1 data corresponding to an integrated luminosity of√
20 fb−1 of pp collisions at s = 8 TeV [142]. A model where t̃1 decays to tχ̃01 or bχ̃±
1 , with∗ 00χ̃±
1 decaying into W χ̃1 was considered. In this analysis, tχ̃2 decay was not considered.
0
For the mass-splitting between χ̃±
1 and χ̃1 , both 5 GeV and 20 GeV mass-splittings wereconsidered. The branching ratios of the t̃1 decay were scanned as the Br(tχ̃01 :bχ̃±1 ) of 75:25,
50:50, and 25:75. Figure 6.10 shows the exclusion limit at 95% CL for each assumption. The
64

miss in the final states. The rightanalysis was performed using two b-jets, a lepton, and ET
0handed t̃1 scenario in Run 2 analysis is similar to the assumption with ∆m(χ̃±
1 , χ̃1 ) = 5 GeV
00
and Br(tχ̃01 :bχ̃±1 ) = (50:50) %, ignoring the difference between tχ̃1 and tχ̃2 decays. In that

scenario, masses of t̃1 up to 515 GeV with χ̃01 = 100 GeV were excluded and the limit
reached to 160 GeV for the mass of χ̃01 . Because of a small excess observed in the Run 1
search, the observed limits were weaker than the expected ones.

6.7.2

Simplified Model

The simplified model has been a benchmark scenario in the stop searches at ATLAS andCMS since the beginning of the experiments [1, 142–163]. Figure 6.11 shows the summaryof ATLAS results as of 2018, including the results in Run 1 and Run 2 in 2015–2016. In
general, the searches have been carried out using the full-hadronic (0L), semi-leptonic (1L)
and di-leptonic (2L) analyses. For the t̃1 → tχ̃01 (2-body) decay region, the 0L and 1L
analyses have strong sensitivities, while in the compressed region with t̃1 → bW χ̃01 /bf f 0 χ̃01

(3-body / 4-body) decays, 1L, and 2L analyses have compatible sensitivities. At the very
miss and acompressed region of the 4-body decay, the mono-jet analysis which utilizes high ET

high pT ISR signature has high sensitivity while the 1L and 2L analyses lose sensitivity due
to the inefficiency of the lepton reconstruction. The bottom right corner of the exclusion
region with large ∆m(t̃1 , χ̃01 ) has been extended up to around 1 TeV stop mass, whilein the compressed region the search sensitivities were lower due to the difficulties of thereconstruction of low pT particles. In the large ∆m(t̃1 , χ̃01 ) region, the t̃1 decay dependon the assumption of the LSP, and the simplified model does not have sufficient power tocover the higgsino like LSP. In addition, the excluded region in the small ∆m(t̃1 , χ̃01 ) was
smaller compared to the large ∆m(t̃1 , χ̃01 ). Therefore, the search in Chapter 9 is performed
targeting the stop in the 4-body region with a new soft b-tagging technique.

65

1

ATLAS

1

1

1

mχ∼0 [GeV]SUSY
Observed limit (± 1 σtheory)-1

s=8 TeV, 20 fb∼ ∼Expected limit (± 1 σexp )∆ m(χ± ,χ0) = 5 GeV
1 1
∼
∼
~
~
BR(t1→ t χ0) = 75 % , BR(t1→ b χ± ) = 25 %

280
260

1

320
300

0
* 0
~~
~
±
t1t1 production, t1 → t ∼χ /b ∼
χ , χ±→ W ∼
χ
1

ATLAS

1
SUSY

280

Observed limit (± 1 σtheory)1

tb analysis

1

tb analysis

240

240

220

220

200

200

180

180

160

160

140

140

120
200

1

s=8 TeV, 20 fb∼ ∼Expected limit (± 1 σexp )∆ m(χ± ,χ0) = 20 GeV
1 1
∼
∼
~
~
BR(t1→ t χ0) = 75 % , BR(t1→ b χ± ) = 25 %

260

1

1

-1

1

300

0
* 0
~~
~
±
t1t1 production, t1 → t ∼χ /b ∼
χ , χ±→ W ∼χ

1mχ∼0 [GeV]

320

120
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650

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550

ATLAS

1

1

1
SUSY
Observed limit (± 1 σtheory)-1

s=8 TeV, 20 fb∼ ∼Expected limit (± 1 σexp )∆ m(χ± ,χ0) = 5 GeV
1 1
∼
∼
~
~
BR(t1→ t χ0) = 50 % , BR(t1→ b χ± ) = 50 %

280
260

1

320
300

1

ATLAS

1

1

1
SUSY

Observed limit (± 1 σtheory)-1

s=8 TeV, 20 fb∼ ∼Expected limit (± 1 σexp )∆ m(χ± ,χ0) = 20 GeV
1 1
∼
∼
~
~
BR(t1→ t χ0) = 50 % , BR(t1→ b χ± ) = 50 %

280
260

1

1

tb analysis

1

tb analysis

240

240

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200

180

180

160

160

140

140

120
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300

350

400

450

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550

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650

200

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300

350

400

450

500

550

ATLAS

1

1

1

mχ∼0 [GeV]SUSY
Observed limit (± 1 σtheory)-1

s=8 TeV, 20 fb∼ ∼Expected limit (± 1 σexp )∆ m(χ± ,χ0) = 5 GeV
1 1
∼
∼
~
~
BR(t1→ t χ0) = 25 % , BR(t1→ b χ± ) = 75 %

280
260

1

320
300

1

ATLAS

1

1

1
SUSY

Observed limit (± 1 σtheory)-1

s=8 TeV, 20 fb∼ ∼Expected limit (± 1 σexp )∆ m(χ± ,χ0) = 20 GeV
1 1
∼
∼
~
~
BR(t1→ t χ0) = 25 % , BR(t1→ b χ± ) = 75 %

280
260

1

1

tb analysis

1

tb analysis

240

240

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200

180

180

160

160

140

140

120
200

650

0
* 0
~~
~
±
t1t1 production, t1 → t ∼χ /b ∼
χ , χ±→ W ∼
χ

1

300

1

600

m~t [GeV]

0
* 0
~~
~
±
t1t1 production, t1 → t ∼χ /b ∼
χ , χ±→ W ∼χ

1mχ∼0 [GeV]

m~t [GeV]
320

650

0
* 0
~~
~
±
t1t1 production, t1 → t ∼χ /b ∼
χ , χ±→ W ∼
χ

1

300

0
* 0
~~
~
±
t1t1 production, t1 → t ∼χ /b ∼
χ , χ±→ W ∼
χ
1

600

m~t [GeV]mχ∼0 [GeV]3201mχ∼0 [GeV]

m~t [GeV]

120
250

300

350

400

450

500

550

600

650

200

m~t [GeV]

250

300

350

400

450

500

550

600

650

m~t [GeV]±
Figure 6.10: Exclusion limits for the tχ̃01 → tχ̃01 /bχ̃±
1 decays with BR(bχ̃1 ) = 25, 50, and±
075% (in descending rows) and ∆m(χ̃1 , χ̃1 ) = 5 (left) and 20 (right) GeV from the Run±∗ 0
1 analysis [142]. Following the t̃1 → bχ̃±
1 decay, χ̃1 decays into W χ̃1 . The analysis was
miss .
performed with one lepton final states requiring two b-jets and high ET

66

May 2018

800

ATLAS Preliminarys=13 TeV, 36.1 fb-1
0L
[1709.04183]
1L[1711.11520]
2L[1708.03247]
Monojet[1711.03301]

0 ~0~t1→ t ∼
χ / t1→ W b ∼
χ
1
1
0 ~
0 ~
0
~
t1→ t ∼
χ / t1→ W b ∼χ / t1→ b f f' ∼
χ
1
1
1
0 ~
0 ~
0
~
∼
∼
∼
t1→ t χ / t1→ W b χ / t1→ b f f' χ
10
10
1
~
~
∼
∼
t1→ c χ / t1→ b f f' χ
1
1
0
~
∼
t→cχ

600

1

1

s=8 TeV, 20 fb-1

Observed limits[1506.08616]

W

m ~
(t ∼
1 ,χ 0
1 )<

m
+

∆

b

m

m ~
(t
1 , χ∼ 0
1 )<

m ~
(t ∼
1 ,χ 01 )<All limits at 95% CL

∆

∆

400

[1805.01649]

Run 1

Expected limits
0

500

c0L

t

700

m

1

0
m(∼
χ ) [GeV]

0 ~
0 ~
0 ~
0
~~
~
t1t1 production, t1→ b f f' ∼
χ1 / t1→ c ∼χ1 / t1→ W b ∼χ1 / t1→ t ∼
χ1

300
c∼
χ1

200

0

0
b f f' ∼
χ1

100
0
W b∼
χ1

0

200

300

400

500

600

700

800

900

1000

~
m(t1) [GeV]
Figure 6.11: Exclusion contours from previous searches at ATLAS [164]. The results of Run
1 analyses [142] and Run 2 analyses [1,143–145] with the data collected in 2015-2016 are displayed. Another scenario in which t̃1 decays into a charm quark and the LSP [165] is overlaid,but it assumes a different model with a flavor-changing neutral-current decay. The dashedlines show the expected exclusion limits while the solid lines show the observed exclusion
limits. The gray dashes lines separate the t̃1 decay modes depending on the mass difference
between t̃1 and χ̃01 . If the on-shell top decay is kinematically allowed (∆m(t̃1 , χ̃01 ) > mt ),t̃1 → tχ̃01 is considered. In the diagonal region where mb + mW < ∆m(t̃1 , χ̃01 ) < mt and∆m(t̃1 , χ̃01 ) < mb + mW , the 3-body decay (t̃1 → bW χ̃01 ) and 4-body decay (t̃1 → bf f 0 χ̃01 )are considered, respectively. For each decay mode, 100% branching ratio is considered.

67

Chapter 7

Search for Stop with Large∆m(t̃1, χ̃01) Scenarios
In this chapter, a stop search with the data recorded in 2015–2016 is presented. The
integrated luminosity of the data that satisfies good quality criteria is 36.1 fb−1 . The main
target of the search is the stop pair production under the higgsino-like LSP scenario. As
discussed in Section 6.1, the higgsino-like LSP scenario is a complicated model where many
decay modes of t̃1 are possible, and the branching ratio depends on the MSSM parameters.
The difficulties of the higgsino-like LSP scenario lies in the compressed mass spectra of
the higgsino states, which generate low pT objects in the final states. Given the small
mass-splitting between χ̃02 and χ̃01 , t̃1 → tχ̃01 and t̃1 → tχ̃02 have similar signatures except

for the soft activity emitted from the decay of χ̃02 . Both decay modes contain high pT top
quarks when t̃1 is sufficiently heavier than χ̃01 /χ̃02 . Hence the signal regions designed for the2t̃1 → tχ̃01 decay1 can be exploited for t̃1 → tχ̃02 as well. In this chapter, t̃1 → bχ̃±
1 decay istargeted so that the whole decay modes of the higgsino signals are covered.

7.1

Event Selection

A benchmark signal, which is used in the optimization of the signal region, is the higgsino0
simplified model with masses of m(t̃1 , χ̃02 , χ̃±
1 , χ̃1 ) = (600, 210, 205, 200) GeV. The mostly

right-handed t̃1 assumption in which the branching fractions of tχ̃01 , tχ̃02 , and bχ̃±
1 are 25%,
25%, and 50%, respectively, are considered, since the signature is not well covered by thetχ̃01 decay searches [1, 142, 146].
As seen in the diagram in Figure 6.5, the final state contains b-jets, LSPs, and soft decay
products from the χ̃±
1 decay via a virtual W boson. A simple selection with only high pT
miss selection, cannot be good for that signal due to overwhelming
objects, like a b-jets and ET
1
2

The diagram of the t̃1 → tχ̃01 decay is the right diagram in Figure 6.4.
The diagram of the t̃1 → bχ̃±
1 decay is shown in Figure 6.5.

68

backgrounds such as Z+jets with a b-quark pair from a gluon. Adding an object on top of
miss selection can suppress the background significantly. In this case, thethe b-quark and ET

additional object is a low pT lepton from the χ̃±
1 decay. The presence of a low pT lepton
can be distinctive for such compressed signatures.
The preselection, which is a set of loose cuts on variables before designing dedicatedsignal selections, for this search is summarized in Table 7.1. The events are collected bymiss trigger. Events that satisfy offline E miss > 230 GeV are selected. Figures 7.1–7.2
the ETT

show comparisons between the data and MC after the preselection.
Table 7.1: Preselection criteria used for the stop search with 2015–2016 data. The lepton
refers to an electron or a muon, including a lepton from a leptonic decay of τ .
Preselection
Trigger
Data quality
Number of leptons
Lepton pT [GeV]
Number of jets
Number of b-tags
miss [GeV]ET~ miss )||∆φ(j1,2 , E
Tmiss triggers onlyET

jet cleaning, primary vertex= 1 lepton> 4 for µ> 5 for e≥ 2 (pT > 25 GeV)
>0
> 230
> 0.4

69

Data
tt 2L
W+jetsMultiboson
Z+jets104

Events / 8 GeV

s = 13 TeV, 36 fb-1
Preselection

Total SM
tt 1L
Single top
ttV

5

10

103

102

102

10

10

1.5
1
0.5

200

300

400

500

600

700

800

s = 13 TeV, 36 fb-1
Preselection

1
0.5

0

Data
tt 2L
W+jetsMultiboson
Z+jets104

Events / 30 GeV

Events / 30 GeV

s = 13 TeV, 36 fb-1
Preselection

Total SM
tt 1L
Single top
ttV

103

Total SM
tt 1L
Single top
ttV

1.5

20

40

60

Emiss
[GeV]
T
105

Data
tt 2L
W+jetsMultiboson
Z+jets104

103

Data / SM

Events / 30 GeV
Data / SM

105

105

80 100 120 140 160
mT [GeV]s = 13 TeV, 36 fb-1
Preselection

Data
tt 2L
W+jetsMultiboson
Z+jets104

Total SM
tt 1L
Single top
ttV

103

102

Data / SM

Data / SM

102
1.5
1
0.5

100

200

300

400

500

600 700
amT2 [GeV]

1.5
1
0.5

200

300

400

500

600

700 800
pW [GeV]T

miss
Figure 7.1: Comparison of data and simulation distributions with the preselection: ET
W(top left), mT (top right), amT2 (bottom left), and pT (bottom right). The statistical andexperimental uncertainties are displayed. The overflow is included in the last bin.
Emiss
[GeV]
T

mT [GeV]70

22 s = 13 TeV, 36 fb
20 Preselection
18
16
14
12
10
8
6
4
2
0

Total SM
tt 1L
Single top

105

s = 13 TeV, 36 fb-1
Preselection104

s = 13 TeV, 36 fb-1
Preselection

10

Data
tt 2L
W+jetsOthersTotal SM
tt 1L
Single top

8

Data / SM

2

1

3

12

4

0.5

2

×103

6

1.5

1

Events / 0.05

Data
tt 2L
W+jetsOthersEvents / 10 GeV

-1

4

5

6
7
8
Jet multiplicity

Data
tt 2L
W+jetsMultiboson
Z+jets

0
1.5
1
0.5

0 20 40 60 80 100 120 140 160 180 200
lepton p [GeV]TEvents / 40 GeV

EventsData / SM×103

Total SM
tt 1L
Single top
ttV

105

104

103

103

102

102

s = 13 TeV, 36 fb-1
Preselection

Data
tt 2L
W+jetsMultiboson
Z+jetsTotal SM
tt 1L
Single top
ttV

Data / SM

Data / SM

10
1.5
1
0.5

0

0.5

1
1.5
lepton p / Emiss
T

1.5
1
0.5

0

100 200 300 400 500 600 700 800
first jet p [GeV]T

T

Figure 7.2: Comparison of data and simulation distributions with the preselection: themiss (bottom left), and leading jet p
jet multiplicity (top left), lepton pT (top right), p`T /ET
T(bottom right). The statistical and experimental uncertainties are displayed. The overflow
is included in the last bin.
lepton p [GeV]

Jet multiplicity

T71

On top of the preselection, a series of cuts are required to define a SR. The selection
is optimized by trying several variables and changing cut values to search for the best
set of selections that maximizes the significance of the benchmark signal yields over the
background prediction. The selection is summarized in Table 7.2, and the SR is namedmissbCsoft med. The pW
T is the magnitude of the vectorial sum of the lepton and ET . Since

the signal tends to have very low pT leptons, the SR is defined in small mT . Figure 7.3 shows
distributions used to define the SR. All selections of the SR definition but the selections of
the variables that are shown are applied in these plots. Since the signature of the signal ismiss created by the LSP, the ratio between thecharacterized by a low pT lepton and large ET
miss tends to be small for the signal, while the lepton p and E miss tend
lepton pT and ET
T
T
miss variable is exploited
to balance in the background processes. The shape of the p`T /ETmiss
to maximize the experimental sensitivity. In the shape fit for the exclusion, the p`T /ETis binned into three bins. The small ∆m(t̃1 , χ̃01 ) signal tends to appear in the small bins,
miss bins. Table 7.3
while the high ∆m(t̃1 , χ̃01 ) signal would be seen in the high plepton/ETTshows the event yields after applying the SR selection, and the fraction of the backgroundcomponents is summarized in Figure 7.4. The background events are dominated by the
W +jets and semi-leptonic tt̄, followed by the single top.
Table 7.2: The event selection for the signal region. The preselection is applied before
the selection shown here. For the pT of jets and b-jets, requirements on the top four (two)miss is performed
highest pT jets (b-jets) are described. For the exclusion, a shape-fit on p`T /ETwith a boundary shown in the bottom row.
bCsoft med
Preselection

Table 7.1

Number of jets
Number of b-jets≥3≥2

Jet pTb-jet pT

> (120, 60, 40, 25) GeV> (120, 60) GeV

miss
ET
mT
amT2
min(∆φ(~pmiss
T , b-jet))pW
T> 230 GeV
< 160 GeV
> 200 GeV
> 0.8
> 400 GeV

miss (single-bin SR)p`T /ET< 0.03

miss (multi-bin SR)p`T /ET[0, 0.015, 0.03, 0.1]

72

20

Total SM
tt 1L
W+jetsSingle top
Others~ ± ∼0m(tR,∼
χ ,χ )=(600,205,200)
1

Events / 50 GeV

Events / 0.01

s = 13 TeV, 36 fb-1

25 bCsoft_med
1

15

14
12

Total SM
tt 1L
Single top

tt 2L
W+jetsOtherss = 13 TeV, 36 fb-1
bCsoft_med~ ± ∼0m(tR,∼
χ ,χ )=(600,205,200)
1

1

10
8
6

10

4
5
0
0

2
0.02

0.04

0.06

0
100 150 200 250 300 350 400 450 500 550 600
amT2 [GeV]

0.08
0.1
lepton p / Emiss
T

24 s = 13 TeV, 36 fb-1
Total SM
22 bCsoft_med
tt 2L
20~ ± ∼0tt 1Lm(tR,∼
χ ,χ )=(600,205,200)
1 1
18
W+jets16
Single top
14
Others
12
10
8
6
4
2
0
200 250 300 350 400 450 500 550 600
pW [GeV]

Events / 0.4

Events / 40 GeV

T

14
12

Total SM
tt 1L
Single top

tt 2L
W+jetsOtherss = 13 TeV, 36 fb-1
bCsoft_med~ ± ∼0m(tR,∼
χ ,χ )=(600,205,200)
1

10

1

8
6
4
2
0
0

0.5

1

1.5

T

2
2.5
3
min ∆φ(b-jet, Emiss)T

Figure 7.3: Distribution of the variables used to define the bCsoft med discovery SR:
miss (top left), amWp`T /ETpmiss
T2 (top right), pT (bottom left), and min(∆φ(~T , b-jet)) (bottom
right). All bCsoft med cuts except the one on the displayed distribution are applied. Only
statistical uncertainty is included. The overflow is added in the last bin.

Table 7.3: Expected number of events in bCsoft med SR with 36.1 fb−1 before applying the
NFs. Only the statistical uncertainty of the MC samples is given. The background yields
0
are compared with that of the benchmark signal with m(t̃1 , χ̃±
1 , χ̃1 ) = (600, 205, 200) GeV
in the higgsino-like LSP model with the mostly right-handed stop assumption.
Process

Background

Eventstt̄ 1Ltt̄ 2LW +jets
Single top
Multiboson
Z+jetstt̄ + VTotal

4.68 ± 0.28
0.59 ± 0.08
4.72 ± 0.41
3.29 ± 0.32
0.31 ± 0.24
0.17 ± 0.05
0.44 ± 0.10
14.21 ± 0.65
25.69 ± 3.98

Benchmark signal

73

s = 13 TeV, 36 fb-1
bCsoft_med

W+jets (33.3%)
tt1L (32.9%)
Singletop (23.2%)
others (10.6%)

Figure 7.4: Breakdown of the individual SM contributions to the signal region. The prefit
background yields are used. The minor backgrounds are merged into “Others.”

74

7.2

Background Estimation

The background estimation follows the strategy discussed in Section 6.4. The numberof background events estimated from the MC simulation is normalized to the data. The
prediction from the MC simulation is scaled by a parameter µ for each main backgroundprocess. To extract the NFs µ for the tt̄, W +jets, and single top, CRs are defined foreach process with accompanied VRs, as summarized in Table 7.4. For the other minor
background processes, the estimation relies on the MC prediction with the theoretical crosssections, i.e., µ = 1. The tt̄ CR (TCR) and VR (TVR) are defined by inverting the amT2
miss condition is inverted forcut for the SR selection to enhance the tt̄ events. The p`T /ET

TCR, while the same value as for the SR is used for the TVR. The W +jets and single top
miss > 0.2 to minimize the signal contamination
CRs (WCR and STCR) are defined as p`T /ETand increase the statistics in the CRs, while VRs (WVR and STVR) are defined as 0.1 <miss < 0.2. Other cut values are also modified from the SR selection in order to enhancep`T /ETthe background process or increase the statistics in the regions, as shown in Table 7.4. The
event yields in these CRs are shown in Table 7.5. In the table, the yield of the benchmark
signal is also shown, and the signal contamination in the CR is found to be negligible. As
shown in Figure 7.5, each CR has a high purity (>∼ 50%) of the corresponding backgroundprocess. The yields in the VRs are also shown in Table 7.6. The selections for the VRs
are close to the ones for the SRs, but the signal contamination in the VRs is suppressed
to a negligible level. The composition of the background processes in each VR is shown in
Figure 7.6.
Table 7.4: Selections for the control and validation regions. The SR definition is also
shown for comparison. The preselection is summarized in Table 7.1. The “–” indicates that
there is no requirement.
SR

TCR/VR

Preselection
Number of (jets, b-tags)
b-tagged jet pT [GeV]

STCR/VR

preselection in Table 7.1(≥ 3, ≥ 2)
> (120, 60)(≥ 3, ≥ 2)
> (120, 60)

Jet pT [GeV]
miss
ET
[GeV]
mT [GeV]pW
T [GeV]missp`T /ET
amT2 [GeV]min(∆φ(~pmiss, b-jet))T∆R(b1 , b2 )WCR/VR(≥ 3, = 1)
> 120(≥ 3, ≥ 2)
> (120, 60)> (120, 60, 40, 25)
> 230
< 160
> 400
< 0.03
> 200
> 0.8
–

> 0.03 / < 0.03
< 200
–
–

75

> 0.2 / [0.1, 0.2]
> 200
[0.8, 2.5]–

> 0.2 / [0.1, 0.2]
> 200
> 0.8
> 1.2

Table 7.5: Pre-fit expected events in bCsoft med CRs for 36.1 fb−1 . Only the statisticaluncertainties of the MC samples are given. The benchmark signal is the higgsino simplified
0model with the masses of m(t̃1 , χ̃±
1 , χ̃1 ) = (600, 205, 200) GeV, and the mostly right-handed
scenario is considered.
TCR

WCR

STCR

tt̄ 1Ltt̄ 2LW +jets
Single top
Multiboson
Z+jetstt̄ + V1086.66 ± 8.36
99.01 ± 3.31
10.26 ± 0.71
73.80 ± 4.03
2.34 ± 0.63
0.39 ± 0.07
11.94 ± 0.55

72.73 ± 1.99
9.19 ± 0.67
156.72 ± 3.38
70.59 ± 1.95
12.93 ± 1.84
1.91 ± 0.24
1.53 ± 0.18

35.79 ± 1.88
4.18 ± 0.43
37.71 ± 1.23
164.75 ± 2.74
7.08 ± 3.25
0.50 ± 0.14
3.02 ± 0.21

Total Background1284.40 ± 9.91

325.60 ± 4.81

253.04 ± 4.84

Benchmark signal

6.56 ± 2.10

1.24 ± 0.74

0.67 ± 0.50

s = 13 TeV, 36 fb-1
bCsoft_med-TCR

tt1L (84.6%)
tt2L (7.7%)
Singletop (5.7%)

s = 13 TeV, 36 fb-1
bCsoft_med-WCR

W+jets (48.1%)
tt1L (22.3%)
Singletop (21.7%)

others (1.9%)

others (7.9%)

s = 13 TeV, 36 fb-1
bCsoft_med-STCR

Singletop (65.1%)
W+jets (14.9%)
tt1L (14.1%)
others (5.8%)

Figure 7.5: Breakdown of the individual SM contributions to the tt̄ (left), W +jets (middle), and single top (right) control regions. The pre-fit yields are displayed. The minor
backgrounds are merged into the “Others” category.
The distributions of some key variables in TCR, WCR, and STCR are shown in Figures 7.7, 7.8, and 7.9, respectively. The NFs obtained by the background only fit in thethree CRs are shown in Table 7.7. The NFs are close to unity for tt̄ and W +jets, while the
NF for the single top is small. In the nominal single top W t process, the DR scheme [139]is used, but the interference term of the W W bb final states between the single top and tt̄ ispoorly modeled in this phase space [166]. The distributions in VRs after applying the NF
are shown in Figures 7.10–7.12. In all validation regions, reasonable agreement between thedata and MC within the uncertainties is observed. The post-fit yields in the CRs and VRs
are summarized in Table 7.8.

76

Table 7.6: Pre-fit expected events in bCsoft med VRs for 36.1 fb−1 . Only the statisticaluncertainty of the MC samples is given. The benchmark signal is the higgsino simplified
0model with the masses of m(t̃1 , χ̃±
1 , χ̃1 ) = (600, 205, 200) GeV, and the mostly right-handed
scenario is considered.
TVR

WVR

STVR

tt̄ 1Ltt̄ 2LW +jets
Single top
Multiboson
Z+jetstt̄ + V35.82 ± 0.68
5.79 ± 0.30
0.99 ± 0.20
3.72 ± 0.64
0.02 ± 0.01
0.05 ± 0.04
0.47 ± 0.12

14.48 ± 0.51
2.29 ± 0.17
46.24 ± 2.02
10.01 ± 0.63
2.87 ± 0.57
0.39 ± 0.10
0.65 ± 0.10

8.01 ± 0.37
1.24 ± 0.19
11.02 ± 0.62
22.41 ± 0.89
0.24 ± 0.11
0.16 ± 0.05
0.77 ± 0.13

Total Background46.86 ± 1.01

76.93 ± 2.26

43.86 ± 1.18

Benchmark Signal

2.04 ± 0.83

1.43 ± 0.98

0.64 ± 0.47

s = 13 TeV, 36 fb-1
bCsoft_med-TVR

tt1L (76.4%)
tt2L (12.3%)
Singletop (7.9%)

s = 13 TeV, 36 fb-1
bCsoft_med-WVR

W+jets (60.1%)
tt1L (18.8%)
Singletop (13.0%)

others (3.3%)

s = 13 TeV, 36 fb-1
bCsoft_med-STVR

others (8.1%)

Singletop (51.1%)
W+jets (25.1%)
tt1L (18.3%)
others (5.5%)

Figure 7.6: Breakdown of the individual SM contributions to the tt̄ (left), W +jets (middle),
and single top (right) validation regions. The pre-fit yields are displayed. The minor
backgrounds are merged into the “others” category.

Table 7.7:
Normalization factors for the main background processes obtained by the
background only fit in the three control regions. The errors of the NFs include statistical,
experimental, and theoretical uncertainties.
Background process

NFtt̄
W +jets
single top

0.92 ± 0.07
1.35 ± 0.24
0.47 ± 0.14

77

200

Events / 20 GeV

Events / 0.1

250

s = 13 TeV, 36 fb-1
bCsoft_med-TCR

Data
Total SM
tt 2L
tt 1L
Others150

160

s = 13 TeV, 36 fb-1
bCsoft_med-TCR

140
120

Data
Total SM
tt 2L
tt 1L
Others

100
80
60

100

40
20

0

Data / SM

Data / SM

50

1.5
1
0.5

0

0.5

1
lepton p / Emiss
T

0
1.5
1
0.5

200 250 300 350 400 450 500 550 600
Emiss
[GeV]
T

200

s = 13 TeV, 36 fb-1

180 bCsoft_med-TCR
160
140

Events / 10 GeV

Events / 10 GeVT

Data
Total SM
tt 2L
tt 1L
Others120

250

s = 13 TeV, 36 fb-1
bCsoft_med-TCR

200

Data
Total SM
tt 2L
tt 1L
Others

150

100
80

100

60
40

50

0

Data / SM

Data / SM

20
1.5
1
0.5

0

20

40

60

80 100 120 140 160
mT [GeV]

0
1.5
1
0.5

80

100 120 140 160 180 200 220
amT2 [GeV]

Figure 7.7: Comparison of data and simulation distributions for the tt̄ CR after applying
miss (top left), E miss (top right), m (bottom left), andthe normalization factors: the p`T /ET
T
T
amT2 (bottom right). The statistical and experimental uncertainties are displayed. The
last bin includes the overflow.
lepton p / Emiss
T

Emiss
[GeV]
T

T

78

s = 13 TeV, 36 fb-1
bCsoft_med-WCR

120
100

Events / 50 GeV

Events / 0.16

140

Data
Total SM
tt 1L
W+jetsSingle top
Others

80

100
80

40

40

20

20
Data / SM

0
1.5
1
0.5

0

0.5

1
1.5
lepton p / Emiss
T

0
1.5
1
0.5

200 250 300 350 400 450 500 550 600 650 700
Emiss
[GeV]
T

s = 13 TeV, 36 fb-1

80 bCsoft_med-WCR

60

Events / 100 GeV

Events / 25 GeV

T

70

Data
Total SM
tt 1L
W+jetsSingle top
Others60

60

Data / SM

s = 13 TeV, 36 fb-1

120 bCsoft_med-WCR

Data
Total SM
tt 1L
W+jetsSingle top
Others50

100
80

s = 13 TeV, 36 fb-1
bCsoft_med-WCR

Data
Total SM
tt 1L
W+jetsSingle top
Others

60

40
40

30
20

20

0

Data / SM

Data / SM

10
1.5
1
0.5

0

50 100 150 200 250 300 350 400
lepton p [GeV]
T

0
1.5
1
0.5

0 100 200 300 400 500 600 700 800 9001000
first jet p [GeV]T

Figure 7.8: Comparison of data and simulation distributions for the W +jets CR after
miss (top left), E miss (top right), lepton p
applying the normalization factors: the p`T /ETT
T(bottom left), and leading jet pT (bottom right). The statistical and experimental uncertainties are displayed. The last bin includes the overflow.
lepton p / Emiss
T

Emiss
[GeV]
T

T

79

s = 13 TeV, 36 fb-1

Events / 16 GeV

Events / 0.16

80

Data
Total SM
tt 1L
W+jetsSingle top
Others70 bCsoft_med-STCR
60
50

50

s = 13 TeV, 36 fb-1
bCsoft_med-STCR

40

Data
Total SM
tt 1L
W+jetsSingle top
Others

30

40
30

20

20
10
0

Data / SM

Data / SM

10
1.5
1
0.5

0

0.5

1
1.5
lepton p / Emiss
T

0
1.5
1
0.5

0

20

40

60

70

s = 13 TeV, 36 fb-1
bCsoft_med-STCR

Events / 50 GeV

Events / 0.5

TData
Total SM
tt 1L
W+jetsSingle top
Others60
50

90

s = 13 TeV, 36 fb-1

80 bCsoft_med-STCR
70
60

80 100 120 140 160
mT [GeV]Data
Total SM
tt 1L
W+jetsSingle top
Others

50

40

40

30

30
20

20
10

0

Data / SM

Data / SM

10
1.5
1
0.5

1.5

2

2.5

3

3.5

4

4.5 5
∆R(b , b2)

0
1.5
1
0.5

400 450 500 550 600 650 700 750 800 850 900
pW [GeV]1

T

Figure 7.9: Comparison of data and simulation distributions for the single top CR after
miss (top left), m (top right), ∆R(b , b )applying the normalization factors: the p`T /ET
1 2
T(bottom left), and pW(bottomright).
The
statisticalandexperimental
uncertainties
areT
displayed. The last bin includes the overflow.
lepton p / EmissTmT [GeV]T80s = 13 TeV, 36 fb-1
bCsoft_med-TVR

20

Events / 60 GeV

Events / 0.005

25

Data
Total SM
tt 2L
tt 1L
Others1530

s = 13 TeV, 36 fb-1
bCsoft_med-TVR

Data
Total SM
tt 2L
tt 1L
Others

25
20
15

10
10
5

0

Data / SM

Data / SM

5

1.5
1
0.5

0

0.01

0
1.5
1
0.5

0.02
0.03
lepton p / Emiss
T

400 450 500 550 600 650 700
Emiss
[GeV]
T

s = 13 TeV, 36 fb-1
bCsoft_med-TVR

20

Events / 20 GeV

25

Data
Total SM
tt 2L
tt 1L
Others

15

25

5

5

0
1
0.5

0

20

40

60

80 100 120 140 160
mT [GeV]Data
Total SM
tt 2L
tt 1L
Others15
101.5

s = 13 TeV, 36 fb-1
bCsoft_med-TVR

20

10Data / SM

Data / SM

Events / 20 GeV

T

0
1.5
1
0.5

80

100

120

140

160

180 200
amT2 [GeV]

Figure 7.10: Comparison of data and simulation distributions for the tt̄ VR after applying
miss (top left), E miss (top right), m (bottom left), andthe normalization factors: the p`T /ET
T
T
amT2 (bottom right). The statistical and experimental uncertainties are displayed. The
last bin includes the overflow.
lepton p / Emiss
T

Emiss
[GeV]
T

T

81

Events / 50 GeV

Events / 0.02

s = 13 TeV, 36 fb-1

Data
Total SM
tt 1L
W+jetsSingle top
Others

30 bCsoft_med-WVR
25
20

50

s = 13 TeV, 36 fb-1
bCsoft_med-WVR

40

Data
Total SM
tt 1L
W+jetsSingle top
Others

30

15
20
10
10

0

Data / SM

Data / SM

5

1.5
1
0.5

0.1

0.12

0.14

0.16
0.18
0.2
lepton p / Emiss
T

0
1.5
1
0.5

200 250 300 350 400 450 500 550 600 650 700
Emiss
[GeV]
T

40

s = 13 TeV, 36 fb-1
bCsoft_med-WVR

Events / 80 GeV

45

Data
Total SM
tt 1L
W+jetsSingle top
Others

35
30

45

35
30

25
20

20

15

15

10

10

5

5

0
1.5
1
0.5

0

20

40

60

80
100 120
lepton p [GeV]Ts = 13 TeV, 36 fb-1

40 bCsoft_med-WVR

25

Data / SM

Data / SM

Events / 12 GeV

T

Data
Total SM
tt 1L
W+jetsSingle top
Others

0
1.5
1
0.5

0

100 200 300 400 500 600 700 800
first b-jet p [GeV]T

Figure 7.11: Comparison of data and simulation distributions for the W +jets VR afmiss (top left), E miss (top right), lepton
ter applying the normalization factors: the p`T /ETT
pT (bottom left), and leading b-jet pT (bottom right). The statistical and experimental
uncertainties are displayed. The last bin includes the overflow.
lepton p / Emiss
T

Emiss
[GeV]
T

T

82

14
12

Events / 60 GeV

Events / 0.02

s = 13 TeV, 36 fb-1

16 bCsoft_med-STVR

Data
Total SM
tt 1L
W+jetsSingle top
Others

10
8
6
4

0

Data / SM

Data / SM

2
1.5
1
0.5

0.1

0.12

0.14

0.16
0.18
0.2
lepton p / Emiss
T

22 s = 13 TeV, 36 fb-1
20 bCsoft_med-STVR
18
16
14
12
10
8
6
4
2
0
1.5
1
0.5

200

300

400

16
14
12

Events / 50 GeV

Events / 100 GeV18

s = 13 TeV, 36 fb-1
bCsoft_med-STVR

500

600

700

800

Emiss
[GeV]
T

T

20

Data
Total SM
tt 1L
W+jetsSingle top
OthersData
Total SM
tt 1L
W+jetsSingle top
Others25
2015

s = 13 TeV, 36 fb-1
bCsoft_med-STVR

Data
Total SM
tt 1L
W+jetsSingle top
Others

10
10

8
6

5

4
0

Data / SM

Data / SM

2
1.5
1
0.5

0 100 200 300 400 500 600 700 800 9001000
first jet p [GeV]
T

0
1.5
1
0.5

400 450 500 550 600 650 700 750 800 850 900
pW [GeV]T

Figure 7.12: Comparison of data and simulation distributions for the single top VR after
miss (top left), E miss (top right), leading jet
applying the normalization factors: the p`T /ETT
pT (bottom left), and pW(bottomright).
The
statisticalandexperimental uncertainties
Tare displayed. The last bin includes the overflow.
lepton p / Emiss
T

Emiss
[GeV]
T

T

83

Table 7.8: Number of observed events and post-fit event yields in the CRs and VRs obtained by the background only fit in the CRs. The statistical, experimental, and theoreticaluncertainties are included. The minor background processes are merged into the “Others”
category.
TCR

WCR

STCR

TVR

WVR

STVR

1155

321

175

47

71

30

Fitted background1155.0 ± 34.0

321.0 ± 17.9

175.0 ± 13.2

42.0 ± 5.8

82.7 ± 7.2

34.6 ± 3.2tt̄
W +jets
Single top
Multiboson
Others1092.7 ± 39.6
12.8 ± 4.0
34.8 ± 19.8
2.3 ± 0.8
12.3 ± 2.0

75.5 ± 13.2
195.6 ± 26.4
33.3 ± 11.0
12.9 ± 4.2
3.4 ± 1.7

36.8 ± 8.0
49.9 ± 12.5
77.7 ± 21.2
7.1 ± 2.4
3.5 ± 0.7

38.3 ± 5.9
1.3 ± 0.5
1.8 ± 1.0
0.0 ± 0.0
0.5 ± 0.1

15.5 ± 2.8
58.6 ± 8.6
4.7 ± 1.7
2.9 ± 0.9
1.0 ± 0.4

8.5 ± 1.9
14.3 ± 4.0
10.6 ± 3.2
0.2 ± 0.2
0.9 ± 0.2

Observed events

84

7.3

Systematic Uncertainties

The experimental systematic uncertainties associated with each object are estimated in thecalibration of each object, as explained in Section 6.5, and the ±1σ variations are includedin the fit. The theoretical uncertainties for each background process, which affect the event
yields in each region are summarized in Table 7.9. The details on these uncertainties aredescribed in Section 6.5.
Table 7.9: Theoretical uncertainties (%) in the tt̄, W +jets, single top, and multiboson processes. The relative uncertainties with respect to the number of events for the backgroundprocess in each region are shown. For tt̄, W +jets, and single top, the uncertainties in thetransfer factors from the control region of the background process to the other regions arecalculated. Due to the lack of the multiboson CR, the uncertainties in the multiboson yields
contain the uncertainty related to the normalization.
tt̄

W +jets

single top

multiboson

SR

14.3

7.3

9.9

32.0

SR1
SR2
SR3

18.5
13.5
13.4

6.8
7.1
4.1

12.0
11.5
14.1

22.9
64.1
11.6

TCR
WCR
STCR

–
14.1
17.2

11.0
–
2.3

48.9
5.2
–

18.2
15.2
14.7

TVR
WVR
STVR

6.5
14.6
17.6

12.4
1.2
2.5

49.4
10.6
9.3

21.8
11.1
20.8

The systematic uncertainties in the background prediction in the SR are summarizedin Table 7.10. The statistical uncertainty which corresponds to the expected number ofbackground events is 28%, and the systematic uncertainty in the background prediction is15%. The largest systematic uncertainty comes from the flavor tagging uncertainty, whichis caused by the b-tagging efficiency measurements. It contains the uncertainties in the b-jet
tagging efficiency, the c-jet and light-jet mistag efficiencies, and the extrapolation of theefficiency to high-pT jets. The main flavor-tagging uncertainty in this analysis is from thecharm mistag calibration. If a c-jet in a tt̄ event is b-tagged, the final state particles arewrongly assigned in the amT2 calculation. In that case, the event tends to have a large
amT2 value and enter the SR. The second largest uncertainty in the bCsoft med SR is theuncertainty in the W +jets normalization, which is mainly from the limited statistics in the
W +jets CR.

85

Table 7.10: Summary of the dominant systematic uncertainties (%) in the background
prediction in the bCsoft med SR. The statistical uncertainty is calculated from the expected
number of events in the SR.
SR Uncertainty (%)

bCsoft medpStatistical uncertainty ( Nexp )28

Total systematic uncertainty

15

Flavor tagging
W +jets normalization
miss soft term
ETtt̄ modeling
MC statistics
Single top normalization
W +jets modelingtt̄ normalization
JES
JER

7.4

13.9
8.1
7.8
7.0
4.6
3.4
3.2
2.6
2.6
2.1

Results

Table 7.11 shows the observed events in the SRs. The background events in the SR arenormalized by the NFs obtained by the background only fit. No significant excess overthe expected background yields is observed. The observed p-value for the background-only
hypothesis is p0 = 0.12, which corresponds to 1.17σ. The distributions of key variables after
miss distribution with thethe single-bin SR selection are shown in Figure 7.13. The p`T /ET

shape-fit binning is shown in Figure 7.14.
Table 7.11: Post fit yields in the SRs. The “SR” is the single bin SR, and “SR1-3” are themulti-bin SRs for the exclusion.
SR

SR1

SR2

SR3

19

4

15

57

Fitted Background13.7 ± 2.1

4.9 ± 0.9

8.9 ± 1.3

52.9 ± 6.2

tt̄
W +jets
Single top
Multiboson
Others

4.9 ± 1.5
6.4 ± 2.0
1.6 ± 0.5
0.3 ± 0.2
0.6 ± 0.2

1.4 ± 0.4
2.5 ± 0.8
0.5 ± 0.2
0.4 ± 0.1
0.2 ± 0.1

3.5 ± 1.0
3.9 ± 1.2
1.1 ± 0.4
0.0 ± 0.0
0.4 ± 0.1

16.3 ± 4.0
24.5 ± 6.5
8.6 ± 2.6
1.8 ± 0.7
1.7 ± 0.3

Observed events

Figure 7.15 shows the expected and observed limits from bCsoft med SR as well as
the expected limits from other SRs in reference [1]. Figures 7.16–7.17 show the combined86exclusion contours at 95% CL for the higgsino-like LSP scenario. For the exclusion contours,
other SRs described in reference [1] are also used to cover the whole phase space andbranching ratios3 .
The bCsoft med SR contributes mainly to the mostly-right-handed-stop scenario due to00
the large branching ratio of bχ̃±
1 decay as designed. To cover all decay modes: tχ̃1 , tχ̃2 , and00bχ̃±1 , a hard-lepton SR and a soft-lepton SR are combined so that the tχ̃1 or tχ̃2 branch

can be caught by the hard-lepton SR while the bχ̃±
1 branch is covered by the soft lepton
SRs. The soft-lepton and hard-lepton SRs are then fitted simultaneously. The bCsoft med
SR contributes significantly to the t̃1 ∼ t̃R scenario in which the bχ̃±
1 decay is favored.

All three BR assumptions are well covered, and stop masses are excluded up to 800 GeV
for the LSP mass of 150 GeV. With an assumption of mχ̃± = 150 GeV, the limits reach10∆m(χ̃±
1 , χ̃1 ) ∼ 2 GeV in all three scenarios.

3

In reference [1], hard lepton SRs (tN med, tN high, bC2x diag, bC2x med) and soft lepton SRs(bCsoft med, bCsoft diag, and bCsoft high) and other SRs that are not used for the result in this dissertation are described. The contributions of these SRs to the exclusion limits are shown in Appendix A.

87

s = 13 TeV, 36 fb-1

Data
Total SM
tt 1L
W+jetsSingle top
Others

12 bCsoft_med~ ± ∼0m(tR,∼
χ ,χ )=(600,205,200)
1

10Events / 40 GeV

Events / 0.005

14

1

8
6

10

s = 13 TeV, 36 fb-1
bCsoft_med

Data
Total SM
tt 1L
W+jetsSingle top
Others~ ± ∼0m(tR,∼
χ ,χ )=(600,205,200)

8

1

1

6
4

4
2

2
0
0

0.01

0
200 250 300 350 400 450 500 550 600
amT2 [GeV]

0.02
0.03
lepton p / Emiss
T

16
14

s = 13 TeV, 36 fb-1
bCsoft_med

Data
Total SM
tt 1L
W+jetsSingle top
Others~ ± ∼0m(tR,∼
χ ,χ )=(600,205,200)
1

Events / 2 GeV

Events / 60 GeV

T

1

12
10
8

12

s = 13 TeV, 36 fb-1
bCsoft_med~ ± ∼0m(tR,∼
χ ,χ )=(600,205,200)
1

10

1

8

4

4

2

2
300

400

500

600

700

0
0

800

2

4

6

s = 13 TeV, 36 fb-1

12 bCsoft_med
10~ ± ∼0m(tR,∼
χ ,χ )=(600,205,200)
1

1

8

Data
Total SM
tt 1L
W+jetsSingle top
Others10 12 14 16 18 20
lepton p [GeV]

14
12

Data
tt 1L
Single top

s = 13 TeV, 36 fb-1
bCsoft_med

Total SM
W+jetsOthers~ ± ∼0m(tR,∼
χ ,χ )=(600,205,200)
1

1

10
8

6

6

4

4

2

2

0
0

8

T

Events / 0.4

Events / 20 GeV

Emiss
[GeV]
T
14

Data
Total SM
tt 1L
W+jetsSingle top
Others

6

6

0
200

14

20

40

60

80

100 120 140 160
mT [GeV]

0

1

1.5

2

2.5
3
min ∆φ(b-jet, Emiss)T

Figure 7.13: Distribution of the variables used to define the bCsoft med discovery SR: (leftmiss , E miss , m , (right column) am , lepton p , and min(∆φ(~column) p`T /ET
pmiss
T
T2
T
T
T , b-jet)),in descending rows. The benchmark signal is overlaid.

88Events

120 ATLAS
100
80

Data
tt
W+jetsDibosons = 13 TeV, 36.1 fb-1
bCsoft_med

Total SM
tt+V
Single top~ ± ∼0m(t1, ∼
χ , χ ) = (600,205,200) GeV
1

1

60
40

(n

obs

- nexp)
σtot

20
0

2
0

−2
0

0.02

0.04

0.06

0.08
0.1
miss
lepton p / ET
T

Figure 7.14: The observed data and post-fit background prediction in the shape-fit SRs.
The binning of the plot is the same as the shape-fit binning. On the bottom panel, thedifference between the observed data and predicted yield divided by the total uncertainty
is shown.

89

1

1

2

s = 13 TeV, L= 36.1 fb-1
Limit at 95% CL~
t1 →Expected limit (bCsoft_high)400

Expected limit (Combined)

0

0
0
0
∼
χ →h∼
χ ,Z∼
χ

1

2

1

1

~ ~
t1 ≈ tR

Expected limit (bCsoft_med) (±1 σ exp)

450

±

1

Observed limit (bCsoft_med)

500

1

b∼
χ ,t∼
χ
1
1,2
0
±
∼
χ →W∼
χ

∼0, bχ
∼±, t χ∼0) ≈ (25, 50, 25)%
Br(tχ
2

1

600

~~
Higgsino LSP model: t 1t 1 production, m∼χ± = m∼χ0+5 GeV, m∼χ0 = m∼χ0+10 GeV
1

1

Expected limit (bCsoft_high)400

Expected limit (Combined)

200

150

150
600

0
0
0
∼
χ →h∼
χ ,Z∼
χ
2

1

1

∼0, bχ
∼±, t χ∼0) ≈ (45, 10, 45)%
Br(tχ
2

1

1

0
(t ~
1 , χ∼ 01 )<(t ~1 , χ∼ 0
1 )<
∆m

250

200

500

1

~ ~
t 1 ≈ t L, large tanβ

∆m

300

0

300

400

0

Observed limit (Combined)

350

100

±

Expected limit (tN_med)

Observed limit (Combined)

350
250

1

b∼
χ ,t∼
χ
1
1,2
0
±
∼
χ →W∼
χ
1

Expected limit (bCsoft_med) (±1 σ exp)

450

2

~
t1 →

Observed limit (bCsoft_med)

500

Expected limit (tN_med)1

s = 13 TeV, L= 36.1 fb-1
Limit at 95% CL

550

1

550

~~
Higgsino LSP model: t 1t 1 production, m∼χ± = m∼χ0+5 GeV, m∼χ0 = m∼χ0+10 GeVm∼χ0 [GeV]1m∼χ0 [GeV]

600

700

800

100

900
1000
m~t [GeV]

400

500

600

1

mχ∼0 [GeV]

1

600
550

700

800

900
1000
m~t [GeV]
1~~
Higgsino LSP model: t 1t 1 production, mχ∼± = mχ∼0+5 GeV, mχ∼0 = mχ∼0+10 GeV11

s = 13 TeV, L= 36.1 fb-1
Limit at 95% CL

2

~
t1 →

1

0
±
b∼
χ ,t∼
χ
1
1,2
0
±
∼
χ →W∼
χ
1

500

Observed limit (bCsoft_med)

450

Expected limit (bCsoft_high)400

Expected limit (Combined)

Expected limit (bCsoft_med) (±1 σ exp)

1

0
0
0
∼
χ →h∼
χ ,Z∼
χ
2

1

1

~ ~
t 1 ≈ t L, small tanβ∼ , bχ
∼ , tχ∼ ) ≈ (33, 33, 33)%
Br(tχ
0

±

0

2

1

1

Expected limit (tN_med)

Observed limit (Combined)

250

(t ~
1 , χ∼ 0
1 )<
∆m

300

0

350

200
150
100

400

500

600

700

800

900
1000
m~t [GeV]
1

Figure 7.15: Expected and observed limits obtained from the bCsoft med SR and expected
limits from other SRs in reference [1] (tN med and bCsoft high), for (top left) t̃1 ∼ t̃R , (topright) t̃1 ∼ t̃L , and (bottom) large tan β scenarios. The combined limits are obtained
from the simultaneous fits using a soft-lepton SR (one of bCsoft med, bCsoft high, andbCsoft diag) and the tN med SR. Limits from bCsoft diag SR are not shown because it
does not have sensitivity in the off-diagonal region (∆m(t̃1 , χ̃01 ) > mt ). The choice of theSRs at each mass point is summarized in Appendix A.

90

~~Higgsino LSP model: t1t1 production, m∼χ±1 = m∼χ0+5 GeV, m∼χ0 = m∼χ0+10 GeV

1m∼χ0 [GeV]

1

700
600

ATLAS
s = 13 TeV, 36.1 fb-1
Limit at 95% CL

2

1

0
~
±
t1 → b ∼
χ ,t∼
χ
1

1,2

0
±
∼
χ →W∼
χ
1

1

0
0
0
∼
χ →h∼
χ ,Z∼
χ
2

1

1

0
0
±
B(t∼
χ2, b∼
χ1, t∼
χ1) ≈Observed limit~t L, small tanβ: (45, 10, 45)%~
Expected limit (±1σexp)
t , large tanβ: (33, 33, 33)%~ ~~ ~~ ~ ~Lt1 ≈ tL t1 ≈ tL(large tanβ)t1 ≈ tR t : (25, 50, 25)%
R

500
400

m ∼χ 1
0

300

<
~
mt

mt

+

200
100

400

500

600

700

800

900 1000m ~t [GeV]1

Figure 7.16: Observed (solid lines) and expected (dashed lines) exclusion limit at 95%
CL in the plane of mt̃1 versus the mass of the neutralino LSP (mχ̃01 ). The higgsino-like
LSP model with mχ̃± = mχ̃01 + 5 GeV and mχ̃02 = mχ̃01 + 10 GeV is considered. The three1

scenarios: t̃1 ∼ t̃R (green), t̃1 ∼ t̃L (blue), and large tan β (red) are shown. In the region
below the gray dashed line, the t̃1 is kinematically allowed to decay into an on-shell top
quark and the LSP.

91

ATLASs = 13 TeV, 36.1 fb-1
Limit at 95% CL

25

1

1

∼±, χ
∼0) [GeV]
∆m(χ

30

~~
Higgsino LSP model: t1t1 production, m∼χ±1 = 150 GeV

Observed limit
Expected limit (±1σexp)

20

~ ~
~ ~
t1 ≈ tL
t1 ≈ tR~ ~t1 ≈ tL(large tanβ)

15

0
~
±
t1 → b ∼
χ ,t∼
χ
1

1,2

0
±
∼
χ1 → W ∼
χ1

10

0
0
0
∼
χ2 → h ∼χ1, Z ∼
χ1

0
0
±
B(t∼
χ , b∼
χ , t∼
χ )≈2
1
1~
t L, small tanβ: (45, 10, 45)%~t L, large tanβ: (33, 33, 33)%~t R : (25, 50, 25)%5

0
600 700 800 900 1000 1100 1200 1300 1400
m ~t [GeV]1

Figure 7.17: Observed (solid lines) and expected (dashed lines) exclusion limit at 95%±
0
CL in the plane of mt̃1 versus ∆m(χ̃±
1 , χ̃1 ). The mass of χ̃1 is fixed to 150 GeV. The
higgsino-like LSP model with mχ̃± = mχ̃01 + 5 GeV and mχ̃02 = mχ̃01 + 10 GeV is considered.
1

The three scenarios: t̃1 ∼ t̃R (green), t̃1 ∼ t̃L (blue), and large tan β (red) are shown. In theregion below the gray dashed line, the t̃1 is kinematically allowed to decay into an on-shell
top quark and the LSP.

92

Chapter 8Soft b-tagging for Compressed
Signatures
8.1

Targets of Soft b-tagging

When the mass-splitting between t̃1 and χ̃01 is small, the final state contains low pT bhadrons. The pT of the b-hadrons is typically below 20 GeV. In the standard b-jet tagging
algorithm optimized for higher pT b-hadrons, the reconstruction efficiency for these low-pT
b-hadrons is too low to be useful because the b-tagging algorithm relies on jets reconstructedfrom EM topo clusters (EM topo jets). Due to the difficulties in the reconstruction andcalibration of low pT jets, the EM topo jets are only used in pT > 20 GeV. Furthermore, theMV2c10 algorithm is not optimized for such low pT b-hadrons. In order to expand the ability
to tag b-hadrons in such a low pT regime, a new algorithm without relying on the presenceof reconstructed jets has been developed. The new algorithm targeting low pT b-hadrons
referred to as soft b-tagging in the following, reconstructs secondary vertices of b-hadrons
using tracks outside reconstructed jets. Figure 8.1 shows the pT and the transverse distance
between the PV and SV (Lxy ) of b-hadrons in the stop signal with ∆m(t̃1 , χ̃01 ) = 20 GeV.
Most of the SVs from the signal are populated in the vicinity of the PV, and the goal of
the algorithm is to reconstruct secondary vertices whose distances from the PV are smaller
than 2 mm. Figure 8.2 is an event display of a typical simulated stop signal. In order toreconstruct a SV, at least two charged particles need to be generated at the SV position.
However, about half of the b-hadrons do not satisfy that condition, as can be seen in thisevent, which is one of the main limitations of the soft b-tagging efficiency. The soft b-tag
algorithm is named Track-based Low pT Vertex Tagger (T-LVT) [2], and it is implemented
in the athena software framework [167] for the event reconstruction in ATLAS. In the next
section, the algorithm of T-LVT is presented. After that, the performance of the algorithm
and an ad-hoc calibration method are introduced.

93

Arbitrary units

Arbitrary units

0.15
stop signal~ 0m(t1, ∼
χ )=(450, 430) GeV
1

0.1

0.4
stop signal~ 0m(t1, ∼
χ )=(450, 430) GeV

0.3

1

0.2
0.05
0.1

0
0

5

10

15

20

25

0
0

30

0.5

1

1.5

2

2.5

Truth b-hadron p [GeV]

3

3.5

4

4.5

5

Truth b-hadron Lxy [mm]Ty [mm]

Figure 8.1:
pT (left) and Lxy (right) of the stop four-body signal with m(t̃1 , χ̃01 ) =(450, 430) GeV.

3
2

ATLAS Simulation Internal
primary vertex
b hadronc hadroncharged particle1

neutral particle

0
−1
−2
−3
−3

−2

−1

0

1

2
3
x [mm]

Figure 8.2: A display of a simulated stop signal event with m(t̃1 , χ̃01 ) = (450, 430) GeV
in the transverse plane. The position博士論文審査会
of the PV is shown as the red star. The b-hadrons
1 / 342020/05/13
from the stop decay and the decay products of the b-hadrons are shown, while the otherparticles from the PV or pile-up vertices are not displayed. The green (orange) lines showb(c)-hadrons, and the solid (dashed) lines represent charged (neutral) particles with pT >0.5 GeV.

94

8.2

Algorithm

The soft b-tagging algorithm consists of three steps: the track selection, the vertex fitting,and the vertex selection. The algorithm starts from the selection of reconstructed tracks.
As mentioned in Section 5.1, tracks of charged particles are reconstructed from hits in theID, and the track parameters (q/pT , η, φ, d0 , z0 ) are calculated using Kalman Filter. Tracks
with pT > 500 MeV are used as the input of the soft b-tagging. It is not feasible to use allavailable tracks to find the secondary vertices because the processing time and the numberof fake vertices from random crossings increase explosively as the number of combinationsof track pairs increases. A dedicated track selection is performed before finding secondary
vertices in order to reduce the number of tracks that are used in the vertex fitting. The
algorithm is developed using the stop four-body signal with m(t̃1 , χ̃01 ) = (450, 430) GeV as
a benchmark signal, and W +jets without b- or c-hadrons as background.

8.2.1

Track Selection

There are many tracks reconstructed by the tracking algorithm. Some of them are comingfrom SVs, but many of them are not. There are three types of tracks that are considered as
background in this selection: tracks from the PV, tracks from pile-up vertices, and tracks
reconstructed with a bad quality fit. The track selection is summarized in Table 8.1. Figure
8.3 illustrates the key components of the track selection: the selection of large d0 tracks, theoverlap removal with jets, and the pile-up track suppression. There is no pT requirementin addition to pT > 500 MeV imposed in the track reconstruction. Since particles from thedecay of the stop signal tend to be localized at the central part, i.e., the small η region,
compared to the background tracks, |η| < 2 is required. The tracks from a decay of along-lived b-hadron tend to have large transverse impact parameter (d0 ) and longitudinal

impact parameter (z0 ). The impact parameters of the tracks from the PV are zero if theresolution of the parameter is ignored, but in reality they are non zero due to the finite
resolutions of the parameters. For the longitudinal direction, the z0PV , which is the trackz0 with respect to the z coordinate of the PV, is used. The requirement on d0 and z0 arethus intended to remove tracks from the PV. Tracks with small errors of the parameters are
selected to reduce PV tracks with large impact parameters due to the poor accuracy of theparameters. The significance of the impact parameter is defined as the impact parameter
divided by the error of that. The large impact parameter significance is required to accountfor the parameter itself as well as the error of that. For the pile-up suppression, upper limits
are set for the |z0PV | and |z0PV sin θ|. The loose upper limits on |d0 | and |z0 | are set to remove
tracks produced in the detector materials. To suppress fake tracks that are reconstructed95

from wrong combination of hits, the track quality criteria based on the χ2 of the track fit
and the number of hits on the Pixel, SCT, and IBL detectors are applied. Since the targetof the soft b-tagging is b-hadrons that are not reconstructed as a jet, tracks overlappingwith a jet are removed. Tracks within ∆R < 0.4 with respect to any EM topo jets withpT > 30 GeV are removed. The threshold of the jet pT is optimized to maximize the signal
efficiency while keeping strong background rejection. Figures 8.4–8.5 show the distributionsof these variables. The tracks from b-hadrons in the benchmark signal and backgroundtracks in the W +jets without heavy flavor hadrons are compared. All cuts used in the
track selection are applied except for the cut on the displayed variable.
Table 8.1: Track selection used in the T-LVT algorithm
VariablepT (MeV)
|η|

Cut
> 500
<2

|d0 | (mm)d0 significanced0 error (mm)∈ (0.05, 10.0)> 1.7< 0.13|z0PV | (mm)z0 error (mm)z0PV significance|z0 | (mm)|z0PV sin θ| (mm)

<2
< 0.3
> 0.5
< 100.0< 1.2

track χ2
Pixel hits
SCT hits
B-Layer hitsmin ∆R(track, jet30 GeV )

8.2.2

< 4.0
≥3
≥1
≥1
> 0.4

Vertex Fitting

The two-track vertex reconstruction is performed for all possible pairs of tracks selected in
the previous section. Using a pair of tracks, an approximate vertex position is estimated bya Kalman Filter based fitting algorithm, VKalVrt [168]. First, track parameters measured
at the perigee with respect to the beam spot are used. If a vertex has a small transverse
radius and small impact parameters of the tracks with respect to the fitted vertex, the vertex
is refitted by a precision fitting using an accurate track extrapolation. Only vertices which
satisfy the fitting quality requirement are used in the following steps. In order to reduce thetracks originating from the PV, the two-track vertex is discarded if the distance between

96

SV
SV

PV

d0

SV

PV

z0PV

Figure 8.3: Illustrations of the key components in the track selection. (left) The tracks
with a large transverse impact parameter (d0 ) are selected. (middle) The tracks within thehigh pT jets are removed (∆R < 0.4). (right) The tracks with a large longitudinal impact
parameter are removed to discard tracks from the pile-up vertices.
the PV and a two-track vertex is smaller than 0.2 mm. The momentum of the vertex isdefined as the vectorial sum of the momenta of the associated tracks, and the direction of
the vertex is defined as the direction from the PV to the two-track vertex. The momentumof the two-track vertex is required to be consistent with the flight direction of the vertex. If
the cosine of the angle between the two-track vertex momentum and the flight direction issmaller than 0.7, the two-track vertex is removed. A track can be used in different two-track
vertices, and a single b-hadron can be reconstructed as multiple two-track vertices. In orderto solve the ambiguity, a set of tracks is created by selecting tracks that share the sametwo-track vertex using incompatibility graph technique [169]. A multi-track vertex is fittedusing the set of tracks used in the two-track vertices. A single track is not allowed to be
used in more than one SV. If a track is shared by multiple multi-track vertices, the trackis assigned to the vertex with the best fitting quality, and it is removed from the othervertices. Finally, vertices are fitted again, and the position and the associated tracks are
stored.

8.2.3

Vertex Selection

The reconstructed vertices still contain backgrounds: fake vertices reconstructed from randomly crossing tracks originating from the PV and the secondary vertices of long-lived lightflavor particles. The vertex selection is defined to reduce such background vertices. The
selection is summarized in Table 8.2. The long-lived SM background is mainly from Ks
meson decaying into a pair of charged pions. This background can be efficiently suppressedby requiring the mass of the reconstructed vertex above 600 MeV, because the mass of Ks
is 498 MeV [37]. The mass of the vertex is calculated from the associated tracks, assuming
all the tracks associated with the vertex are charged pions. The Lxy and the three dimen-

97

1

0.1

Arbitrary unit

Arbitrary unit

~ ∼0
Signal: stop, m(t1, χ)=(450, 430) GeV, Background: W+jets, b/c-hadron veto
Tracks from b-hadron
Tracks from b-hadron (Selected)
Background tracks
Background tracks (Selected)~ ∼0
Signal: stop, m(t1, χ)=(450, 430) GeV, Background: W+jets, b/c-hadron veto1

0.08

Tracks from b-hadron
Tracks from b-hadron (Selected)
Background tracks
Background tracks (Selected)

0.06

0.04

0.05

0.02

0
0

1

2

3

4

5

6

7

0
0

8

1

2

3

4

5

6

7

8

z0 significance wrt PV~ ∼0Signal: stop, m(t1, χ)=(450, 430) GeV, Background: W+jets, b/c-hadron veto1

Arbitrary unit

Arbitrary unit

d0 significanceTracks from b-hadron
Tracks from b-hadron (Selected)
Background tracks
Background tracks (Selected)

0.1

~ ∼0
Signal: stop, m(t1, χ)=(450, 430) GeV, Background: W+jets, b/c-hadron veto1

0.06

Tracks from b-hadron
Tracks from b-hadron (Selected)
Background tracks
Background tracks (Selected)

0.04

0.05

0.02

0
0

0.2 0.4 0.6 0.81

1.2 1.4 1.6 1.8

0
−150

2

−100

−50

0

50

~ ∼0
Signal: stop, m(t1, χ)=(450, 430) GeV, Background: W+jets, b/c-hadron veto1
Tracks from b-hadron
Tracks from b-hadron (Selected)

0.04

Background tracks
Background tracks (Selected)

150

~ ∼0
Signal: stop, m(t1, χ)=(450, 430) GeV, Background: W+jets, b/c-hadron veto1
Tracks from b-hadron
Tracks from b-hadron (Selected)

0.1

Background tracks
Background tracks (Selected)

0.05

0.02

0
0

100

z0 [mm]Arbitrary unit

Arbitrary unit

d0 [mm]

0.05

0.1

0.15

0.2

0.25

d0 error [mm]

0
0

0.1

0.2

0.3

0.4

0.5

0.6

z0 error [mm]Figure 8.4: Track variables used to define the track selection: (top left) the d0 significance,(top right) z0PV significance, (middle left) d0 , (middle right) z0 , (bottom left) d0 error, and(bottom right) z0 error. The red histograms show the tracks from b-hadrons in the stop
signal events, and the blue histograms show the tracks in the W +jets. W +jets events thathave b- or c-hadrons are not used. All cuts described in Table 8.1 are applied, except forthe cut on the variable that is shown in each plot. The shaded part of the histograms shows
the distribution adding the cut on the displayed variable.
sional distance divided by its uncertainty (L3D significance) are variables which describe
the displacement of the SV, and the pT of SV is used to suppress the random combination
backgrounds. A cut on the η of the SV can improve the background rejection. Variables
related to the angle of the SV are used. The cut on the cos θ used in the two-track vertex
selection is tightened in the final vertex selection. The spread of the tracks with respect to98

1

Arbitrary unit

Arbitrary unit

~ ∼0
Signal: stop, m(t1, χ)=(450, 430) GeV, Background: W+jets, b/c-hadron veto
Tracks from b-hadron
Tracks from b-hadron (Selected)
Background tracks
Background tracks (Selected)

0.08

~ ∼0
Signal: stop, m(t1, χ)=(450, 430) GeV, Background: W+jets, b/c-hadron veto1

0.1

Tracks from b-hadron
Tracks from b-hadron (Selected)
Background tracks
Background tracks (Selected)

0.06
0.05

0.04
0.02
0
0

0.5

1

1.5

2

2.5

3

3.5

0
0

4

0.2 0.4 0.6 0.81

1.2 1.4 1.6 1.8

1

Arbitrary unit

Arbitrary unit0

~ ∼0Signal: stop, m(t1, χ)=(450, 430) GeV, Background: W+jets, b/c-hadron veto
Tracks from b-hadron
Tracks from b-hadron (Selected)

0.15

2

|z sinθ| [mm]min dR(track,jet)Background tracks
Background tracks (Selected)~ ∼0
Signal: stop, m(t1, χ)=(450, 430) GeV, Background: W+jets, b/c-hadron veto1

Tracks from b-hadron
Tracks from b-hadron (Selected)

0.1

Background tracks
Background tracks (Selected)

0.1
0.05
0.05

0
0

1

2

3

4

5

6

7

8

9

0
0

10

0.5

1

1.5

2

2.5
|η|

p [GeV]T

Figure 8.5: Track variables used to define the track selection: (top left) the minimum ∆Rbetween the track and EM topo jets with pT > 30 GeV, (top right) |z0PV sin θ|, (bottom
left) pT , and (bottom right) |η|. The red histograms show the tracks from b-hadrons in thestop signal events, and the blue histograms show the tracks in the W +jets. W +jets events
that have b- or c-hadrons are not used. All cuts described in Table 8.1 are applied, except
for the cut on the variable that is shown in each plot. The shaded part of the histograms
shows the distribution adding the cut on the displayed variable.
the vertex direction is measured by∆Rmean =Ptrack ∆R (ptrack , pvtx )Ntrack

,(8.1)

where ptrack , pvtx , and Ntrack are the momentum of the track, momentum of the vertex,
and the number of tracks attached to the secondary vertex. The vertex selection criteria
are optimized to maximize the sensitivity of the stop signal with ∆m(t̃1 , χ̃01 ) = 20 GeV in
the analysis described in Chapter 9. Figures 8.6–8.7 show the distributions of the variables
used in the vertex selection. The reconstructed SVs matched to the truth SV in the stopbenchmark signal and fake SVs in the background events are compared.

99

Table 8.2: Vertex selection used in the T-LVT algorithm
VariableCut~ 0
Signal: stop, m(t1, ∼χ )=(450, 430) GeV, Background: W+jets, b/c-hadron veto1

Arbitrary unit

Arbitrary unit

SV mass (GeV)
SV Lxy (mm)SV L3D significanceSV pT (GeV)
SV |η|
SV cos θ∆Rmeanb-hadron SV
b-hadron SV (Selected)

0.2

Fake SV
Fake SV (Selected)> 0.6∈ (0.5, 5.0)
> 7.0
>3
< 1.5
> 0.95< 1.0~ 0
Signal: stop, m(t1, ∼χ )=(450, 430) GeV, Background: W+jets, b/c-hadron veto10.1

b-hadron SV
b-hadron SV (Selected)
Fake SV
Fake SV (Selected)

0.15
0.05
0.1

0.05

0
0

5

10

15

20

25

30

35

40

45

0
0

50

0.5

1

1.5

2

2.5

3

3.5

~ ∼0
Signal: stop, m(t1, χ)=(450, 430) GeV, Background: W+jets, b/c-hadron veto1b-hadron SV
b-hadron SV (Selected)
Fake SV
Fake SV (Selected)

0.1

0.05

0
0

4

4.5

5

SV Lxy [mm]Arbitrary unit

Arbitrary unit

SV L3D significance~ ∼0
Signal: stop, m(t1, χ)=(450, 430) GeV, Background: W+jets, b/c-hadron veto1b-hadron SV
b-hadron SV (Selected)

0.2

Fake SV
Fake SV (Selected)

0.1

1

2

3

4

5

6

7

8

9

0
0

10

SV p [GeV]

1

2

3

4

5

6

7

SV mass [GeV]T

Figure 8.6: Distributions of the SV variables used in the vertex selection: (top left) theL3D significance, (top right) SV Lxy , (bottom left) SV pT , and (bottom right) SV mass.
All cuts in Table 8.2 are applied except for the cut on the displayed variable. The redhistograms are reconstructed SV that matched to a truth SV in the stop four-body signal
with m(t̃1 , χ̃01 ) = (450, 430) GeV. The blue histograms are reconstructed SV in the W +jets
with no b- or c-hadrons. The shaded part shows the SV accepted by the algorithm.

100

1

0.8

Arbitrary unit

Arbitrary unit

~ ∼0
Signal: stop, m(t1, χ)=(450, 430) GeV, Background: W+jets, b/c-hadron vetob-hadron SV
b-hadron SV (Selected)
Fake SV
Fake SV (Selected)

0.6

~ ∼0
Signal: stop, m(t1, χ)=(450, 430) GeV, Background: W+jets, b/c-hadron veto1

0.06

b-hadron SV
b-hadron SV (Selected)
Fake SV
Fake SV (Selected)

0.04
0.4
0.02
0.2

0
0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

0
−2.5 −2 −1.5 −1 −0.5

1Arbitrary unit

0.4

0

0.5

1

1.5

2

2.5

SV η

SV cosθ~ 0
Signal: stop, m(t1, ∼χ )=(450, 430) GeV, Background: W+jets, b/c-hadron veto1b-hadron SV
b-hadron SV (Selected)

0.3

Fake SV
Fake SV (Selected)

0.2

0.1

0
0

0.5

1

1.5

2

2.5

3

3.5

4

SV ∆R(track,SV) mean

Figure 8.7: Distributions of the SV variables used in the vertex selection: (top left) thecos θ, (top right) SV |η|, and (bottom) ∆Rmean . All cuts in Table 8.2 are applied except forthe cut on the displayed variable. The red histograms are reconstructed SV that matched
to a truth SV in the stop four-body signal with m(t̃1 , χ̃01 ) = (450, 430) GeV. The blue
histograms are reconstructed SV in the W +jets with no b- or c-hadrons. The shaded partshows the SV accepted by the algorithm.

101

8.3

Performance

The performance of the soft b-tagging is evaluated using the MC simulation. The efficiencyof the tagger is defined as the fraction of the tagged b-hadrons using generator level bhadrons (truth b-hadrons). For truth b-hadrons, all the simulated b-hadrons are used, andno pT cut is applied. Only b-hadrons that decay into another flavor are considered to avoid
double counting of b-hadrons with the same origin. The truth matching is based on theangle ∆R between the truth b-hadron and the reconstructed object (the SV for T-LVT
and the b-tagged jet for the standard b-tagging). In the calculation of ∆R, the direction of
the T-LVT SV is defined as the pointing vector from the PV to the SV. For the jet-based
b-tagging, the jet axis is used as the direction. If a reconstructed object is found aroundthe truth b-hadron within ∆R < 0.3, the b-hadron is labeled as tagged. The reconstructedobject cannot be shared by more than one b-hadrons. If multiple truth b-hadrons have thesame reconstructed objects within ∆R < 0.3, the b-hadron with the smallest ∆R is kept
as tagged, and the other b-hadrons are not considered as tagged by that object. Figure 8.8
shows the efficiency of the T-LVT tagger together with that of the standard b-tagging on
the EM topo jets.
Each reconstructed object is also labeled as b-matched, charm-fake, or fake as follows:• If a weakly decaying b-hadrons is found within ∆R < 0.3, the object is labeled asmatched to a b-hadron.

• If the object is not matched as b-hadron, but a weakly decaying c-hadron is foundwith the same criteria, then the object is labeled as a charm fake.

• If the object is not matched to b- or c- hadron, then the object is labeled as a fake.
With this label, the fake rate (charm fake rate) is defined as the average number offake (charm) objects per event. Figure 8.9 shows the efficiency as a function of the fakeor charm rate in two pT ranges of b-hadrons. For the comparison of the T-LVT and thestandard b-tagging, the fake and charm rate are evaluated with the signal events. In bothpT ∈ (5, 15) GeV and pT ∈ (15, 20) GeV, the T-LVT algorithm shows better performance
than the standard b-tagging. It is notable that in the low pT range, the T-LVT efficiency isabout 10 times better than that of the standard b-tagging at the same fake rate.

102

Efficiency

0.6Soft b-tag (T-LVT)

0.5
0.4

Standard b-tag 77% WP~ 0stop signal, m( t1, ∼χ )=(450, 430) GeV
1

0.3
0.2
0.1
0
0

5

10

15

20

25

30

Truth b-hadron p [GeV]
Efficiency

T

0.6
Soft b-tag (T-LVT)

0.5
0.4

Standard b-tag 77% WP~ 0stop signal, m( t1, ∼χ )=(450, 430) GeV
1

0.3
0.2
0.1
0
0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Truth b-hadron Lxy [mm]Figure 8.8: Efficiencies of the soft b-tagging algorithm and the standard b-tagging as afunction of truth b-hadron pT (top) and Lxy (bottom). Weakly decaying b-hadrons in thestop signal are considered. The efficiency is a fraction of b-hadrons which are tagged by theb-tagger based on the truth matching described in the text.

103

~ 0
stop, m(t1, ∼χ )=(450, 430) GeV
1

Efficiency

Efficiency

0.1

Calorimeter-jet-based b-tagging

0.08

Soft b-tagging (T-LVT)
pb-hadron ∈ (5, 15) GeV

0.3

~ 0
stop, m(t1, ∼χ )=(450, 430) GeV
1

Calorimeter-jet-based b-tagging
Soft b-tagging (T-LVT)
pb-hadron ∈ (15, 20) GeV

0.2

T

T

0.06
0.04
0.1
0.02
0
0

0.01

0.02

0.03

0
0

0.04

0.01

0.02

0.1

~ ∼0
stop, m(t1, χ)=(450, 430) GeV
1

Calorimeter-jet-based b-tagging

0.08

0.03

0.04

Number of fakes per event
Efficiency

Efficiency

Number of fakes per event

Soft b-tagging (T-LVT)
pb-hadron ∈ (5, 15) GeV

0.3

~ ∼0
stop, m(t1, χ)=(450, 430) GeV
1

Calorimeter-jet-based b-tagging
Soft b-tagging (T-LVT)
pb-hadron ∈ (15, 20) GeV

0.2

T

T

0.06
0.04
0.1
0.02
0
0

0.01

0.02

0.03

0.04

Number of charm fakes per event

0
0

0.01

0.02

0.03

0.04

Number of charm fakes per event

Figure 8.9: Efficiencies as a function of the average number of fake objects per event (toprow) and average number of charm objects per event (bottom row). The plot in the left
column show the lower-pT region pb−hadron∈ (5, 10) and the right plots are for higher-pTTregion pb−hadron
∈
(15,
20).
The
orangepoint
is the T-LVT working point, and the blueTcurve shows the standard b-tagging performance by changing the cut value on the MV2c10
score.

104

8.4

Calibration

In order to evaluate the data and MC agreement in the soft b-tagging variables, two calibration regions are defined, as shown in Table 8.3. One is a tt̄ region dominated by di-leptonictt̄ events, and the other is a W +jets region. For both regions, events are collected with thesingle lepton trigger. For the tt̄ region, a pair of leptons with opposite sign of their charges
and opposite flavor (e and µ) (OSOF) and exactly one b-jet are required. The W +jets
miss andregion is defined with exactly one lepton and no b-jets, and requirements on the ET

mT are imposed to remove the contribution from multijet events. After the selection, thesimulated tt̄ and W +jets events are normalized to data. Figure 8.10 shows distributions of
the soft b-tagging variables. In both regions, the SV yields are underestimated in the MC
simulation.
Table 8.3: Event selection to define calibration regions
Selectiontt̄ selection

W +jets selection

TriggerNumber of jets
Number of leptons (pT > 27 GeV)b-jets (MV2c10)
miss
ET
mT

single lepton trigger≥ 2 (20 GeV)
= 2 (OSOF)
= 1
=1
=0
–
> 80 GeV–> 30 GeV

It is not feasible to use the SV without any correction in physics analysis due to thepoor modelings, and a calibration is needed to correct the MC before application. For
the standard b-tagging algorithm, the efficiencies of the taggers are measured in both data
and MC, and the scale factor (SF), which is the ratio of the efficiency in data to that in
MC, is measured. The efficiency is defined as the number of jets tagged by the algorithm
over the number of jets, for a given set of jets that contain a truth b-hadron. In thephysics analyses, the b-tagging efficiency in MC is corrected by applying the scale factor.
However, it is difficult to use the same method to calibrate the T-LVT algorithm because thedenominator of the efficiency can not be defined. The efficiency of the standard b-tagging
is the probability to be labeled as b for a given jet, while the T-LVT is not an algorithm
that labels something as b-tagged, but it creates a new object.
In order to reduce the discrepancy between data and MC, the source of the mismodelingis corrected, instead of directly measuring the efficiency of the T-LVT. The main source ofthe discrepancy comes from the mismodeling of tracks in the MC simulation. Figure 8.11
shows the number of selected tracks at the track selection step discussed in the previous

105Events

Events106

Data
Total SMtt
W+jetsSingle top
Multibosons = 13 TeV, 139 fb-1

105
4

107

105

103

104

2

103

10

102
Data / SM

10

1.5
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5000

0

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2

Data
Total SMtt
Single top
Otherss = 13 TeV, 139 fb-1

4000

1.5
1
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SV multiplicity
Events / 0.5 mm

Data / SM

Data
Total SMtt
W+jetsSingle top
Multibosons = 13 TeV, 139 fb-1

106

10

Events / 0.5 mm

108

3000

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×103
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Total SMtt
W+jetsSingle top
Multibosons = 13 TeV, 139 fb-1

70
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s = 13 TeV, 139 fb-1

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SV Lxy [mm]Data
Total SMtt
Single top
Others5000
4000

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0
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Events / 0.5 GeV

Data / SM

10
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100

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s = 13 TeV, 139 fb-1

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Data
Total SMtt
W+jetsSingle top
Multiboson

SV multiplicity
40

3000
2000

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Data / SM

Data / SM

1000
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SV mass [GeV]

0
1.5
1
0.5

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
SV mass [GeV]

Figure 8.10: Distribution of the T-LVT variables: (top) the SV multiplicity, (middle) SV
Lxy , and (bottom) SV mass in (left column) the tt̄ and (right column) W +jets selections.
Only statistical uncertainty is added.
SV Lxy [mm]SV Lxy [mm]106section. The track multiplicity is underestimated in MC, and the discrepancy is more visible
in the W +jets region. Since the T-LVT algorithm relies heavily on the reconstructed tracks,
this mismodeling directly affects the SV yields. To correct the mismodeling observed insimulation, the distribution of the number of selected tracks (Ntrk ) is reweighted. The MC
events are scaled to match the data in each bin of the Ntrk distribution in both tt̄ andW +jets regions separately. Figure 8.12 shows the T-LVT variables after the reweighting.
Compared to the same variables before the reweighting in Figure 8.10, the agreements

×103
80

Data
Total SMtt
Single top
Otherss = 13 TeV, 139 fb-1

70

×106
4
3.5

50

2.5

40

2

30

1.5

20

1

10

0.5

0
1.5
1
0.5

0

2

4

6

8

Data
Total SM
W+jetsOtherss = 13 TeV, 139 fb-1

3

Data / SM

Data / SM

60

EventsEventsbecome much better after the reweighting.

10

0
1.5
1
0.5

0

Number of selected tracks

2

4

6

8

10

Number of selected tracks

Figure 8.11: Number of selected tracks in T-LVT algorithm before the vertex fitting stepin (left) tt̄ and (right) W +jets regions. Only statistical uncertainty is included. The lastbin includes overflow.
Figure 8.13 shows how much the SV yields are scaled by the reweighting for each SV
truth label in tt̄ and W +jets MC samples. The ratio of the post-reweighting number of
events to that before reweighting is taken as the scale factor of the T-LVT algorithm. The
scale factors are derived for the tt̄ and W +jets separately, as summarized in Table 8.4. To
account for the residual discrepancy between data and MC after the reweighting, flat 20%
uncertainty is added on the SF for each flavor and each sample. The size of the uncertainty
is determined to cover the data and MC disagreement in Figure 8.12.
Figure 8.14 shows comparisons of different generators in tt̄ events. These plots indicatethat the modeling of the Ntrk distribution is different between the Sherpa sample and othersamples. In the analysis described in Chapter 9, the tt̄ and single top, and signal samples
are generated with Powheg-Box +Pythia 8 and MadGraph+Pythia 8, respectively,
while the W +jets, Z+jets,
andmultiboson
scaletracks
factors
Numberof selected
tracks are generated with Sherpa.
NumberTheof selectedfrom the tt̄ sample are applied to the former samples, and the ones from the W +jets are107

Table 8.4: Soft b-tagging scale factors derived by the Ntrk reweighting in tt̄ and W +jets
samples. The scale factors are measured for each truth flavor label of the SV.
Selectiontt̄

W +jets

SF (truth b-hadron)
SF (truth c-hadron)
SF (Fake)

1.23
1.21
1.27

1.56
1.36
1.56

applied to the latter. For further cross-checks, Figure 8.15 shows the distribution of the SVvariables in the tt̄ selection, in which the MG5 aMC@NLO+Pythia 8 tt̄ is used insteadof the nominal tt̄. In these plots, the Ntrk reweight factor obtained from the nominal tt̄ isused. The MC and data agree well within the 20% systematic uncertainty.

108

Events

Events106

Data
Total SMtt
W+jetsSingle top
Multibosons = 13 TeV, 139 fb-1

105
104

106

103

105

102

104

10

103
102
Data / SM

Data / SM

Data
Total SMtt
W+jetsSingle top
Multibosons = 13 TeV, 139 fb-1

107

1
1.5
1
0.5

7000

Data
Total SMtt
Single top
Otherss = 13 TeV, 139 fb-1

6000
5000
4000

1.5
1
0.5

−0.5

Events / 0.5 mm−0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
SV multiplicity
Events / 0.5 mm

108

3000

0

0.5

1

1.5

2

2.5 3 3.5
SV multiplicity

×103
100

Data
Total SMtt
W+jetsOtherss = 13 TeV, 139 fb-1

80
60
40

2000
20

Data / SM

0
1.5
1
0.5

Events / 0.5 GeV

0.5

1 1.5

2

2.5

3

3.5

4 4.5 5
SV Lxy [mm]×10310s = 13 TeV, 139 fb-1

8
6

Data
Total SMtt
Single top
OthersSV multiplicity

0
1.5
1
0.5

0.5

Events / 0.5 GeV

Data / SM

1000

1 1.5

2

2.5

3

3.5

4 4.5 5
SV Lxy [mm]

×103
120
100

s = 13 TeV, 139 fb-1

Data
Total SMtt
W+jetsOthers80
SV multiplicity
60

4
40

0
1.5
1
0.5

20
Data / SM

Data / SM2

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
SV mass [GeV]

0
1.5
1
0.5

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
SV mass [GeV]

Figure 8.12: Distribution of the T-LVT variables after the Ntrk reweighting: (top) theSV multiplicity, (middle) SV Lxy , and (bottom) SV mass in (left column) the tt̄ and (rightcolumn) W +jets selections. Only statistical uncertainty is added in the top plots. For SV
Lxy and mass distributions, the uncertainty
includes 20% systematic uncertainty
as well as
SV Lxy [mm]SV Lxy [mm]statistical uncertainty.
109

35
tt selection

30

×103

Entries

Entries×103

100
W+jets selection

reweighted

reweighted

80

no reweighting

25

no reweighting

60

20
15

40

10
20

0

0

1.5

1.5

Ratio

Ratio

5

1
0.5

b-hadronc-hadron

1
0.5

fake

b-hadronc-hadron

fake

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

Event fraction

Event fraction / 10

Figure 8.13: SV truth label before and after applying the Ntrk reweighting for the tt̄
selection (left) and the W +jets selection (right). The ratio on the bottom panel corresponds
to the soft b-tag SF.

PowhegPythia8
aMCAtNLOPythia8
Sherpa

50

100

150

200

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

0

5

10

Number of selected tracks

1.4
1.2
1
0.8
0.6

Ratio

Ratio

Number of PV tracks

PowhegPythia8
aMCAtNLOPythia8
SherpaNumber of PV tracks

1.4
1.2
1
0.8
0.6

Number of selected tracks

Figure 8.14:
tt̄ Generator comparison for the track multiplicity: (left) the number of tracks associated with the PV, and (right) the number of tracks selected in TLVT algorithm. The black nominal Powheg-Box +Pythia 8 tt̄ is compared with the
MG5 aMC@NLO+Pythia 8 in red and the Sherpa in blue. The distributions are normalized to unity. The bottom panels show the ratio to the nominal sample.

110

Events / 0.5 GeV

Data
Total SMtt
Otherss = 13 TeV, 36 fb-1

2000

1000

1000

500

500

0

2

4

6

8 10 12 14 16 18 20 22 24
SV p [GeV]

1800

Data
Total SMtt
Otherss = 13 TeV, 36 fb-1

1600

Events

2000

0
1.5
1
0.5

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
SV mass [GeV]TEvents / 0.5 mm

2000
1500

1.5
1
0.5

Data
Total SMtt
Otherss = 13 TeV, 36 fb-1

2500

1500

Data / SM

Events / 2 GeV
Data / SM

2500

×103
25

Data
Total SMtt
Single top
Otherss = 13 TeV, 36 fb-1

20

1400
1200

15

1000
800

10

600
400

5

0

Data / SM

Data / SM

200
1.5
1
0.5

0.5

1 1.5

2

2.5

3

3.5

4 4.5 5
SV Lxy [mm]

0
1.5
1
0.5

0

2

4

6

8

10

Number of selected tracks

Figure 8.15: Comparison of distributions between data and simulation with the tt̄ selection:(top left) the SV pT , (top right) SV mass, (bottom left) SV Lxy , and (bottom right) the
number of selected tracks in T-LVT. The MG5 aMC@NLOwith Pythia8 tt̄ is used insteadof the nominal tt̄ (Powheg-Box +Pythia 8). The Ntrk reweighting factor calculated with
SV p [GeV]
SV mass [GeV]T
the nominal tt̄ is applied. The 20%
systematic
uncertainty is added.

111

SV Lxy [mm]Number of selected tracks

Chapter 9

Search for Stop with Small∆m(t̃1, χ̃01) Scenarios
In this chapter, a stop search with the data recorded in 2015–2018 is presented. The integrated luminosity of the data which satisfies good quality criteria is 139.0 fb−1 . The searchtargets the most compressed signature, the t̃1 → bf f 0 χ̃01 decay. Under the higgsino-like

LSP assumption, the t̃1 decays to tχ̃01 or tχ̃02 are forbidden kinematically if the ∆m(t̃1 , χ̃01 )∗ 0
0 0
is smaller than mt . The other decay, bχ̃±
1 becomes bW χ̃1 → bf f χ̃1 eventually. In the fol-lowing, this search is presented using the simplified model, which is explained in Section 6.1.

9.1

Event Selection

In this analysis, the stop four-body decay (t̃1 → bf f 0 χ̃01 ) with m(t̃1 , χ̃01 ) = (450, 430) GeV

signal is used as a benchmark signal to define a SR. We use the events with exactly one lepton
miss . The first set of the event selection criteria (preselection) is summarized inwith high ET~ miss , `), lepton charge,
Table 9.1. The distributions of key variables: the E miss , mT , ∆φ(E

T
T
`
miss
number of b-tagged jets, lepton pT , pT /ET , and SV, after the preselection are shown
miss trigger along with thein Figures 9.1 and 9.2. The events are collected with the ET
miss > 230 GeV. The hardest vertex is selected as the PV
requirement of the offline ET

as explained in Section 5.1. The tight jet-cleaning criteria are applied for the leading jet
miss topology due to a fakein order to avoid having events that mimic an ISR + high ET

high-pT jet. The preselection for this search uses muons with pT > 4 GeV and electrons
with pT > 4.5 GeV. Due to the small mass-splitting between t̃1 and χ̃01 in the benchmark
miss which satisfies the E miss trigger andfour-body signal, many events do not have large ET
Tmiss requirement in this search. To improve the signal-to-background ratio, the leading
the ETjet pT is required to be larger than 200 GeV to select boosted topology with a high-pT ISR,
in which the t̃1 pair is recoiled into the opposite hemisphere to the ISR jet. This results
miss from the two LSPs. In order to reduce tt̄ and W +jets events whichin the large ET

112

have a leptonically decaying W boson, mT > 90 GeV is required in the selection. Finally,
miss and leading jet is required to be larger than 0.4 in order tothe |∆φ| between the ET

reduce multijet events produced by QCD processes with a jet that is misreconstructed as a

miss created by misaligned jets. If there are more than one jets, the same
lepton and large ET

requirement is also applied to the second leading jet.
Table 9.1: Preselection criteria.
Preselection
Trigger
Data quality
Number of leptons
Lepton pT [GeV]
Number of jets
miss [GeV]ET
mT [GeV]~ miss )||∆φ(j1,(2) , E
Tmiss triggers onlyET
jet cleaning, primary vertex= 1 lepton> 4 for µ> 4.5 for e≥ 1 (pT > 200 GeV)
> 230
> 90
> 0.4

113

Data
tt 2L
W+jetsMultiboson
tt+V

104

Events / 12 GeV

Events / 30 GeV

s = 13 TeV, 139 fb-1
Preselection

105

Total SM
tt 1L
Single top
Z+jetss = 13 TeV, 139 fb-1
Preselection

Data
tt 2L
W+jetsMultiboson
tt+V

105

Total SM
tt 1L
Single top
Z+jets

104

103
102

103

Data / SM

Data / SM

10
1.5
1
0.5

200

300

400

500

600

700

1.5
1
0.5

800

100

150

200

Events / 0.16

×103
14

s = 13 TeV, 139 fb-1
Preselection

Data
tt 2L
W+jetsOthers12

Total SM
tt 1L
Multiboson

Events

Emiss
[GeV]
T

300
mT [GeV]

×103
60
50

10

250

Data
tt 2L
W+jetsOtherss = 13 TeV, 139 fb-1
Preselection

Total SM
tt 1L
Multiboson

40

8
30
6
20

4

10

0

Data / SM

Data / SM

2
1.5
1
0.5

0

0.5

1

1.5

2

0
1.5
1
0.5

−1.5

2.5
3
miss
∆φ(lep, E )
T

−1

−0.5

0

0.5
1
1.5
lepton charge

Figure 9.1: Comparison of data and simulation for the main discriminating variables before
miss , (top right) m , (bottom left)
fitting MC to data at the preselection level: (top left) ETT~ miss , `), and (bottom right) lepton charge. Statistical and experimental uncertainties∆φ(ET
are displayed. The overflow is includedin the last bin.
missET

mT [GeV]

[GeV]

114

miss

Data
tt 2L
W+jetsMultiboson
tt+V

105

Total SM
tt 1L
Single top
Z+jets4

10

Events / 10 GeV

Eventss = 13 TeV, 139 fb-1
Preselections = 13 TeV, 139 fb-1

Data
tt 2L
W+jetsOthers8000 Preselection
7000

Total SM
tt 1L
Multiboson

6000
5000
4000

103

3000
2000

Data / SM

1000

1.5
1
0.5

Events / 0.1

0

105

1

2

s = 13 TeV, 139 fb-1
Preselection

3

Data
tt 2L
W+jetsMultiboson
tt+V

104

4
Nb-jetTotal SM
tt 1L
Single top
Z+jets

0
1.5
1
0.5

0

50

100

150

200 250 300
lepton p [GeV]TEvents / 0.25 mm

Data / SM

102

450
400
350

s = 13 TeV, 139 fb-1
Preselection

Data
tt 2L
W+jetsOthersTotal SM
tt 1L
Single top

300
250
200

3

10

150
100
50
Data / SM

Data / SM

102

1.5
1
0.5

0

0.5

1

1.5
2
lepton p / Emiss
T

0
1.5
1
0.5

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
SV Lxy [mm]TFigure 9.2: Comparison of data and simulation for the main discriminating variables
before fitting MC to data at the preselection level: (top left) b-jet multiplicity, (top right)
miss , and (bottom right) SV L . Statistical and experimental
lepton pT , (bottom left) p`T /ETxy
uncertainties are displayed. The overflow is included in the last bin.
lepton p [GeV]

Nb-jetT

115

On top of the preselection, tighter selection criteria are applied to define the SR. The SR
targeting the four-body decay using the soft b-tagging technique is named bffN softb. The
event selection for the bffN softb SR is summarized in Table 9.2. The distributions of themiss requirement thanvariables used to define the SR are shown in Figure 9.3. A tighter ET

the preselection is added to enhance the signal-to-background ratio. Since signal events
have low-pT b-hadrons while the tt̄ background has b-hadrons with higher pT , events thathave any b-jets tagged by the standard b-tagging algorithm are rejected. After removing
events with high-pT b-jets, the background processes are dominated by the W +jets process.
In order to select events with low pT b-hadrons, it is required to have at least one secondary
vertex reconstructed by the soft b-tagging algorithm. Since there is no b-hadron in typicalW +jets events, the soft b-tagging requirement significantly reduces the W +jets background.
The remaining background is dominated by W +jets events with low pT b-hadrons produced
miss arefrom a gluon (g → bb̄). In general, the pT of the lepton and the magnitude of ET

miss , tendbalanced in tt̄ and W +jets events because a lepton and a neutrino, which makes ET

to be emitted from the same W boson. The signal events have a low-pT lepton and large
miss . Therefore, p` /E miss is a good estimator to separate the signal from the background.
ET
TT

Two types of SRs are defined: a single-bin SR targeting for a discovery and a shape-fit
SR for excluding signals when there is no discovery. The single-bin SR is defined with
miss < 0.04, while the shape-fit SR has five bins using the p` /E miss distribution. Thep`T /ET
T
T

event yields after applying the single-bin SR selection are shown in Table 9.3 for backgroundand the benchmark signal. The fractions of the background processes before applying the
NFs are displayed in Figure 9.4.
Table 9.2: Overview of the event selection defining the bffN softb SR.
bffN softb
Preselection

Preselection in Table 9.1

miss
ET

> 250 GeV
≥1=0
<2

Number of secondary vertices (NSV )Number of b-jets (pT > 20 GeV)~ miss , `)
∆φ(E
T
miss
p`T /ET< 0.04 (discovery)missp`T /ET[0, 0.015, 0.025, 0.04, 0.06, 0.08] (exclusion)

116

3

10

s = 13 TeV, 139 fb-1
bffN_softb

Total SM
tt 1L
Single top
Z+jets~ 0m(t1,∼χ ) = (450, 430) GeV
1

EventsEvents104

tt 2L
W+jetsMultiboson
tt+V

2

10

10
1
10−1

103
102

1

2

s = 13 TeV, 139 fb-1
bffN_softb~ 0m(t1,∼χ ) = (450, 430) GeV
1

3
4
SV multiplicity
Total SM
tt 1L
Single top
Z+jetsEventsEvents / 10 GeV

0

tt 2L
W+jetsMultiboson
tt+V

20 s = 13 TeV, 139 fb-1
18 bffN_softb~ 016m(t1,∼χ ) = (450, 430) GeV
1
14
12
10
8
6
4
2
0
−0.5 0 0.5 1 1.5 2

104
103

10

Total SM
tt 1L
Single top
Z+jetstt 2L
W+jetsMultiboson
tt+V

Total SM
tt 2L
tt 1L
W+jetsOthers

2.5 3

3.5 4 4.5
Nb-jets = 13 TeV, 139 fb-1
bffN_softb~ 0m(t1,∼χ ) = (450, 430) GeV
1

102

1

10

−1

10

1
20 40 60 80 100 120 140 160 180 200
mT [GeV]1412
10

Total SM
tt 1L
Multiboson
Otherstt 2L
W+jetsZ+jetss = 13 TeV, 139 fb-1
bffN_softb~ 0m(t1,∼χ ) = (450, 430) GeV
1

8
6

0

0.1
lepton p / EmissTs = 13 TeV, 139 fb-1

5 bffN_softb~ 0m(t1,∼χ ) = (450, 430) GeV
1

4

Total SM
tt 1L
Single top
Otherstt 2L
W+jetsMultiboson

3
2

4

1

2
0
0

0.05

T

Events / 100 GeV

Events / 0.4

10−2
0

0.5

1

1.5

2

0
0 100 200 300 400 500 600 700 800 9001000
first jet p [GeV]

2.5
3∆φ(lep, Emiss)T

T

Figure 9.3: Distributions of the variables used to define the bffN softb single-bin SR
after applying all bffN softb cuts, except the one on the displayed distribution: (topleft) the soft b-tag SV multiplicity, (top right) number of b-jets tagged by the standard
miss , (bottom left) ∆φ(E~ miss , `),b-tagging algorithm, (middle left) mT , (middle right) p`T /ETT
and (bottom right) leading jet pT . The events are not scaled by the normalization factors,
and only statistical uncertainty is displayed. The last bin includes the overflow.

117

Table 9.3: Expected number of events in bffN softb for 139 fb−1 before applying the NFs.
Only the statistical uncertainty of the MC samples is given.
Process

Eventstt̄ 1Ltt̄ 2LW +jets
Single top
Multiboson
Z+jetstt̄ + V
Total

Background

1.3 ± 0.2
1.9 ± 0.4
4.6 ± 1.6
0.2 ± 0.1
0.9 ± 0.1
0.5 ± 0.2
0.1 ± 0.1
9.5 ± 1.6
12.3 ± 1.9

Benchmark signal

s = 13 TeV, 139 fb-1
bffN_softb

W+jets (48.0%)
tt 2L (20.5%)
tt 1L (13.6%)
others (17.9%)

Figure 9.4: Breakdown of the individual SM contributions to the signal region. The pre-fit
yields are shown. The minor background processes are merged into “Others.”

9.2

Background Estimation

The dominant backgrounds entering the signal region are W +jets and tt̄ processes. The
single top process is a minor background in this analysis because no amT2 cut is used.
Dedicated CRs and VRs are defined for W +jets, and tt̄. The other minor backgroundprocesses are normalized by their theoretical cross sections. Table 9.4 summarizes theevent selections for the CRs and VRs for W +jets and tt̄, comparing with the SR selection.
miss compared to the SR requirement to increase the
The CRs are defined with high p`T /ET
miss isbackground events and minimize the signal contamination. The intermediate p`T /ET

used for the VR. The same soft b-tag requirement (NSV > 0) is used in all regions to cancel
the soft b-tagging uncertainty for the main background processes. To increase the purityof the background process in each CR and VR, additional requirements on the number of118

the standard b-tag and lepton charge are added. At least one b-jet is required in the tt̄ CR
and VR, which enhances tt̄ events effectively by requiring two b-hadrons by both b-tagging
algorithms. A positive charged lepton is required in W +jets CR and VR, and the opposite
requirement is added in tt̄ regions to enhance the purity of the backgrounds. There are morepositive charged leptons in the W +jets selection than negative ones because of the different
cross sections between ug → W + d and dg → W − u due to the proton property. The event

yields in the tt̄ and W +jets CRs are shown in Table 9.5, and breakdown of the backgroundprocesses are shown in Figure 9.5. Table 9.6 shows the tt̄ and W +jets VR yields, and thebreakdown is shown in Figure 9.6. In all CRs and VRs, the signal contamination is foundto be negligible.
Table 9.4: Overview of the event selections defining bffN softb and the associated control
and validation regions.
SR

TCR/TVR

WCR/WVR

Preselection

Preselection in Table 9.1

miss
ET
NSV
~ miss , `)∆φ(E> 250 GeV
≥1
<2

T

Number of b-jets
Lepton charge
missp`T /ET=0–< 0.04≥1<0∈ (0.12, 0.25)/∈ (0.08, 0.12)=0>0∈ (0.16, 0.32)/∈ (0.08, 0.16)

Table 9.5: Pre-fit expected events in bffN softb TCR and WCR for 139 fb−1 . Only
the statistical uncertainty of the MC samples is given. The benchmark signal is the stopfour-body decay signal with the masses of m(t̃1 , χ̃01 ) = (450, 430) GeV.
TCR

WCR

tt̄ 1Ltt̄ 2LW +jets
Single top
Multiboson
Z+jetstt̄ + V57.5 ± 2.0
74.6 ± 1.7
10.7 ± 1.9
5.9 ± 0.8
2.0 ± 0.3
0.2 ± 0.1
2.0 ± 0.3

22.0 ± 1.2
19.7 ± 0.9
72.7 ± 5.6
6.1 ± 1.1
9.3 ± 1.8
0.9 ± 0.2
0.9 ± 0.1

Total

152.8 ± 3.4

131.5 ± 6.2

< 0.1

< 0.1

Benchmark signal

Comparisons of the distributions of key variables are shown in Figures 9.7–9.8 for tt̄ andW +jets CRs, respectively. The data and MC distributions of variables in tt̄ and W +jets
VRs are shown in Figures 9.9–9.10. The tt̄ and W +jets NFs obtained by the simultaneous119s = 13 TeV, 139 fb-1
bffN_softb-TCR

tt 2L (48.8%)
tt 1L (37.6%)
W+jets (7.0%)

s = 13 TeV, 139 fb-1
bffN_softb-WCR

others (6.6%)

W+jets (55.3%)
tt 1L (16.7%)
tt 2L (15.0%)
others (13.0%)

Figure 9.5: Breakdown of the individual SM contributions to the TCR (left) and WCR(right). The pre-fit yields are shown. The minor background processes are merged into
“Others.”
Table 9.6: Pre-fit expected events in bffN softb TVR and WVR for 139 fb−1 . Only
the statistical uncertainty of the MC samples is given. The benchmark signal is the stopfour-body decay signal with the masses of m(t̃1 , χ̃01 ) = (450, 430) GeV.
TVR

WVR

tt̄ 1Ltt̄ 2LW +jets
Single top
Multiboson
Z+jetstt̄ + V

15.7 ± 1.1
25.8 ± 0.8
5.0 ± 1.3
2.3 ± 0.5
0.6 ± 0.1
0.1 ± 0.1
0.9 ± 0.2

10.7 ± 0.9
12.2 ± 0.7
59.4 ± 6.2
4.4 ± 0.9
4.5 ± 0.9
0.6 ± 0.2
0.2 ± 0.1

Total

50.5 ± 2.0

91.9 ± 6.5

< 0.1

< 0.1

Benchmark signal

fit in both CRs are summarized in Table 9.7, which are applied in the VRs and SR. Table 9.8
is the summary of the post-fit yields in all CRs and VRs.

120

s = 13 TeV, 139 fb-1
bffN_softb-TVR

tt 2L (51.1%)
tt 1L (31.1%)
W+jets (9.9%)s = 13 TeV, 139 fb-1
bffN_softb-WVR

W+jets (64.6%)
tt 2L (13.3%)
tt 1L (11.6%)

others (7.8%)

others (10.5%)

Figure 9.6: Breakdown of the individual SM contributions to the TVR (left) and WVR(right). The pre-fit yields are shown. The minor background processes are merged into
“Others.”

Table 9.7:
CRs.

Normalization factors obtained by the background only fit in tt̄ and W +jets
Background process

NFtt̄
W +jets

0.68 ± 0.10
1.04±+0.22−0.20

Table 9.8: Post-fit yields in the CRs and VRs.

Observed events
Fitted backgroundtt̄
W +jets
Single top
Multiboson
Others

TCR

WCR

TVR

WVR

111

121

38

77

111.1 ± 10.6
89.9 ± 12.2
11.1 ± 3.9
5.9 ± 2.3
2.0 ± 0.6
2.2 ± 1.2

121.0 ± 11.1
28.4 ± 6.0
75.5 ± 13.5
6.1 ± 2.2
9.3 ± 2.9
1.7 ± 0.6

37.5 ± 4.1
28.3 ± 4.6
5.2 ± 2.1
2.3 ± 0.9
0.6 ± 0.2
1.0 ± 0.5

87.2 ± 14.7
15.6 ± 4.0
62.0 ± 15.3
4.4 ± 1.8
4.5 ± 1.4
0.8 ± 0.2121s = 13 TeV, 139 fb-1
bffN_softb-TCR

Data
tt 2L
W+jetsOthers35
30

Events / 40 GeV

Events / 0.03

40

Total SM
tt 1L
Single top

25
20

s = 13 TeV, 139 fb-1

60 bffN_softb-TCR
50

Data
tt 2L
W+jetsOthersTotal SM
tt 1L
Single top

40
30

15
20
10
10

0

Data / SM

Data / SM

5
1.5
1
0.5

0.1

0.15

0.2

0.25
0.3
lepton p / Emiss
T

0
1.5
1
0.5

200 250 300 350 400 450 500 550 600
Emiss
[GeV]
T

s = 13 TeV, 139 fb-1
bffN_softb-TCR

102

Data
tt 2L
W+jetsOthersEvents / 0.2

Events / 10 GeV

T

Total SM
tt 1L
Single top

40

s = 13 TeV, 139 fb-1
bffN_softb-TCR

Data
tt 2L
W+jetsOthersTotal SM
tt 1L
Single top

30
10

20
10

Data / SM

1
Data / SM

50

1.5
1
0.5

100 120 140 160 180 200 220 240
mT [GeV]

0
1.5
1
0.5

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2∆φ(lep, Emiss)T

Figure 9.7: Comparison of data and simulation for the tt̄ CR after applying the normalmiss , (top right) E miss , (bottom left) m , and (bottom
ization factors: (top left) the p`T /ETT
T~ miss , `). Statistical and experimental uncertainties are displayed. The last binright) ∆φ(ET
includes the overflow.
lepton p / Emiss
T

Emiss
[GeV]
T

T

122

Data
tt 2L
W+jetsOthers35

Events / 40 GeV

Events / 0.03

s = 13 TeV, 139 fb-1

45 bffN_softb-WCR
40

Total SM
tt 1L
Multiboson

30
25

70

s = 13 TeV, 139 fb-1
bffN_softb-WCR

Data
tt 2L
W+jetsOthers60

Total SM
tt 1L
Multiboson

50
40

20

30

15

20

10
10

0

Data / SM

Data / SM

5
1.5
1
0.5

0.1

0.15

0.2

0.25
0.3
lepton p / Emiss
T

0
1.5
1
0.5

200 250 300 350 400 450 500 550 600
Emiss
[GeV]
T

40
35

s = 13 TeV, 139 fb-1
bffN_softb-WCR

Data
tt 2L
W+jetsOthers30

Events / 0.5 mm

Events / 10 GeV

T

Total SM
tt 1L
Multiboson

25

50

s = 13 TeV, 139 fb-1
bffN_softb-WCR

Data
tt 2L
W+jetsOthers40

Total SM
tt 1L
Multiboson

30

20
20

15
10

10

0

Data / SM

Data / SM

5
1.5
1
0.5

0

20

40

60

80
100 120
lepton p [GeV]
T

0
1.5
1
0.5

0.5

1 1.5

2

2.5

3

3.5

4 4.5 5
SV Lxy [mm]Figure 9.8: Comparison of data and simulation for the W +jets CR after applying themiss , (top right) E miss , (bottom left) lepton p , andnormalization factors: (top left) the p`T /ETT
T(bottom right) soft b-tag SV Lxy . Statistical and experimental uncertainties are displayed.
The last bin includes the overflow.
lepton p / Emiss
T

Emiss
[GeV]
T

T

123

Events / 40 GeV

Data
tt 2L
W+jetsOthersTotal SM
tt 1L
Single top

Data / SM

Events / 0.01
Data / SM24
s = 13 TeV, 139 fb-1
22 bffN_softb-TVR
20
18
16
14
12
10
8
6
4
2
0
1.5
1
0.5

0.08

0.09

0.1

0.11
0.12
lepton p / Emiss
T

22 s = 13 TeV, 139 fb-1
20 bffN_softb-TVR
18
16
14
12
10
8
6
4
2
0

Data
tt 2L
W+jetsOthers1.5
1
0.5

200 250 300 350 400 450 500 550 600
Emiss
[GeV]
T

s = 13 TeV, 139 fb-1
bffN_softb-TVR

Data
tt 2L
W+jetsOthers25

Events / 0.5 mm

Events / 10 GeV

T

30

Total SM
tt 1L
Single top

20

Total SM
tt 1L
Single top

16
14

s = 13 TeV, 139 fb-1
bffN_softb-TVR

Data
tt 2L
W+jetsOthers12

Total SM
tt 1L
Single top

10
8

15

6

10

4
2

0

Data / SM

Data / SM

5

1.5
1
0.5

0

20

40

60

80
100 120
lepton p [GeV]
T

0
1.5
1
0.5

0.5

1 1.5

2

2.5

3

3.5

4 4.5 5
SV Lxy [mm]Figure 9.9: Comparison of data and simulation for the tt̄ VR after applying the normalizamiss , (top right) E miss , (bottom left) lepton p , and (bottomtion factors: (top left) the p`T /ETT
Tright) soft b-tag SV Lxy . Statistical and experimental uncertainties are displayed. The lastbin includes the overflow.
lepton p / Emiss
T

Emiss
[GeV]
T

T

124

s = 13 TeV, 139 fb-1
bffN_softb-WVR

35
30

Data
tt 2L
W+jetsMultiboson

Events / 40 GeV

Events / 0.02

40

Total SM
tt 1L
Single top
Others25

s = 13 TeV, 139 fb-1

Data
tt 2L
W+jetsMultiboson

50 bffN_softb-WVR
40

Total SM
tt 1L
Single top
Others

30

20
15

20

10
10
0

Data / SM

Data / SM

5
1.5
1
0.5

0.08

0.1

0.12

0.14
0.16
lepton p / Emiss
T

0
1.5
1
0.5

200 250 300 350 400 450 500 550 600
Emiss
[GeV]
T

s = 13 TeV, 139 fb-1

60 bffN_softb-WVR
50
40

Data
Total SM
tt 2L
tt 1L
W+jetsOthersEvents / 0.5 mm

Events / 2 GeVT40

s = 13 TeV, 139 fb-1

Data
Total SM
tt 2L
tt 1L
W+jetsOthers35 bffN_softb-WVR
30
25
20

30

15
20

10
5

0

Data / SM

Data / SM

10

1.5
1
0.5

4

6

8

10 12 14 16 18 20
SV p [GeV]

0
1.5
1
0.5

0.5

T

1 1.5

2

2.5

3

3.5

4 4.5 5
SV Lxy [mm]Figure 9.10: Comparison of data and simulation for the W +jets VR after applying themiss , (top right) E miss , (bottom left) p of the soft
normalization factors: (top left) the p`T /ETT
Tb-tag SV, and (bottom right) soft b-tag SV Lxy . Statistical and experimental uncertainties
are displayed. The last bin includes the overflow.
lepton p / Emiss
T

Emiss
[GeV]
T

T

125

9.3

Systematic Uncertainties

Details of the systematic uncertainty were already discussed in Section 6.5. The theoreticaluncertainties in each region are summarized in Table 9.9. The uncertainties in the transfer
factors from the TCR or WCR to the other regions are estimated by the same method
as for the analysis described in Chapter 7. Due to the small contributions from the otherminor background processes, a flat 30% uncertainty is included for the minor backgroundprocesses which do not have a dedicated CR. For the tt̄ background process, the main
contributions come from the uncertainties in the parton shower and hard scatter. For the
W +jets background, the main contribution comes from the generator comparison with thealternative MadGraph +Pythia 8 sample.
Table 9.9: Theoretical uncertainties (%) in the tt̄ and W +jets processes. The relative
uncertainties with respect to the number of events for the background process in eachregion are shown. The uncertainties in the transfer factors from the control region of the
background process to the other regions are calculated.
tt̄

W +jets

SR

12.8

17.7

SR1
SR2
SR3
SR4

32.4
11.1
14.4
9.0

23.2
28.2
16.1
4.9

TCR
WCR

–
9.9

8.3
–

TVR
WVR

1.9
11.8

11.8
1.8

The uncertainties in the background prediction in the SR are summarized in Table 9.10.
The total statistical uncertainty is 34% for the expected SM events, and the systematic
uncertainty is 27%. The sources of these uncertainties are explained in Section 6.5. The
dominant systematic uncertainty comes from the MC statistical uncertainty for the W +jets
sample due to the tight SR selection. The number of events in the SR is also affected by theuncertainties originating from the jet calibration (JES and JER). The W +jets normalization
uncertainty is caused by the limited statistics in the WCR, and the W +jets modelinguncertainty is the theoretical uncertainty as discussed above.

126

Table 9.10: Summary of the dominant systematic uncertainties in the background prediction in the bffN softb SR.
SR Uncertainty (%)

p
Statistical uncertainty ( Nexp )Total systematic

MC statistics
JES
W +jets normalization
W +jets modeling
JER
LeptonOther modelingtt̄ normalization
miss soft term
ETtt̄ modeling

9.4

bffN softb
34
27
17.2
11.7
11.1
9.7
7.6
4.9
3.7
3.7
3.4
3.3

Results

The observed data in the SR is summarized in Table 9.11, together with the predictedbackground events. No significant excess is found in the SR. The observed p-value for the
background-only hypothesis is p0 = 0.37, which corresponds to 0.34σ. The distributions of
the key variables with the SR selection is shown in Figure 9.11. Since no deviation from the
SM prediction is found, exclusion limits are derived from the shape-fit SR. For the exclusion,
the SR with soft b-tagging (bffN softb) and another SR with the standard b-tagging [3] aresimultaneously fitted. The bffN softb is sensitive to the low ∆m(t̃1 , χ̃01 ) region, while theSR with the standard b-tagging has better sensitivity for ∆m(t̃1 , χ̃01 ) > 40 GeV. Figure 9.12
shows the gain of soft b-tagging comparing the expected exclusion limits with the standard
b-tagging only and the combination of the two b-taggers. For the ∆m(t̃1 , χ̃01 ) = 20 GeV,
the expected limit is improved from 460 GeV to 600 GeV for the mt̃1 by introducing thesoft b-tagging.
In exclusion limits, other signal regions in reference [3] are also used for the 2-body and3-body regions. Figure 9.13 shows the observed and expected exclusion limits at 95% CL
in the mt̃1 versus mχ̃01 plane, and Figure 9.14 shows the same limits with ∆m(t̃1 , χ̃01 ) on thevertical axis. In the four-body decay region (∆m(t̃1 , χ̃01 ) < mb + mW ), the limit reaches
640 GeV in the stop mass, and the limit is lowered to ∆m(t̃1 , χ̃01 ) = 20 GeV owing to thenovel soft b-tagging technique.

127

Table 9.11: Post fit yields in the bffN softb SRs. The “SR” is the single bin SR, while“SR1-5” are the multi-bin SRs for the exclusion.
Observed events
Fitted background eventstt̄
W +jets
Multiboson
Others

SR

SR1

SR2

SR3

SR4

SR5

10

0

2

8

19

25

8.7 ± 2.3

0.4 ± 0.3

1.8 ± 0.7

7.0 ± 1.7

19.4 ± 3.0

25.6 ± 3.4

2.2 ± 0.6
4.8 ± 2.1
0.9 ± 0.3
0.80 ± 0.21

0.0 ± 0.0
0.2 ± 0.2
0.03 ± 0.02
0.10 ± 0.08

0.3 ± 0.1
1.3 ± 0.7
0.15 ± 0.06
0.07 ± 0.04

2.0 ± 0.5
3.6 ± 1.6
0.8 ± 0.3
0.62 ± 0.15

4.1 ± 1.1
11.7 ± 2.6
2.0 ± 0.7
1.01 ± 0.54

6.8 ± 1.7
14.9 ± 3.3
1.9 ± 0.6
2.02 ± 1.06

128

12
10

Data
tt 2L
W+jetsZ+jetsEvents / 100 GeV

Events / 0.01

14

s = 13 TeV, 139 fb-1
bffN_softb

Total SM
tt 1L
Multiboson
Others~ 0m(t1,∼χ ) = (450, 430) GeV
1

8
6

12
10

s = 13 TeV, 139 fb-1
bffN_softb~ 0m(t1,∼χ ) = (450, 430) GeV
1

8

Data
tt 2L
W+jetsZ+jetsTotal SM
tt 1L
Multiboson
Others

6
4

4

2

2
0
0

0.01

0.02

0
200

0.03
0.04
lepton p / Emiss
T

300

400

500

600

s = 13 TeV, 139 fb-1

12 bffN_softb10~ 0m(t1,∼χ ) = (450, 430) GeV
1

Data
tt 2L
W+jetsZ+jetsEvents / 10 GeV

Events / 5 GeVT

14

Total SM
tt 1L
Multiboson
Others8

s = 13 TeV, 139 fb-1

102 bffN_softb~ 0m(t1,∼χ ) = (450, 430) GeV
1

Data
tt 2L
W+jetsZ+jets

700
800
Emiss
[GeV]
T
Total SM
tt 1L
Multiboson
Others

10

6
1

4
2
0
0

10−1
5

10

15

20
25
30
lepton p [GeV]

90

100

110

120

130

14
12

Data
tt 2L
W+jetsZ+jetsTotal SM
tt 1L
Multiboson
Otherss = 13 TeV, 139 fb-1
bffN_softb~ 0m(t1,∼χ ) = (450, 430) GeV
1

10

Events / 1 mm

Events / 0.4

T

8

8

s = 13 TeV, 139 fb-1
bffN_softb~ 0m(t1,∼χ ) = (450, 430) GeV
1

Data
tt 2L
W+jetsZ+jetsTotal SM
tt 1L
Multiboson
Others

6
4

6
4

2

2
0
0

10

140
150
mT [GeV]

0.2 0.4 0.6 0.8

00

1 1.2 1.4 1.6 1.8 2∆φ(lep, Emiss)T

0.5

1 1.5 2

2.5 3

3.5 4 4.5 5
SV Lxy [mm]Figure 9.11: Distribution of the variables used to define the bffN softb discovery SR with
miss , (top right) E miss , (middle left) lepton p , (middle
the SR selection: (top left) the p`T /ET
T
T
miss
~
right) mT , (bottom left) ∆φ(E
,
`),
and
(bottomright)
soft
b-tag
SV
L
.
The NFsxy
T
are applied to the tt̄ and W +jets backgrounds. Statistical, theoretical, and experimental
uncertainties are included. The last bin includes the overflow.

129without soft b-tag
with soft b-tag
ATLAS Data15-16

80

1

1

~ ∼0
∆ m(t , χ
) [GeV]

Expected Limit at 95%

60

40

20
300 350 400 450 500 550 600 650 700 750 800
m~t [GeV]
1

Figure 9.12: Expected exclusion limits at 95% CL in the plane of mt̃1 versus ∆m(t̃1 , χ̃01 ).
The blue line shows the limit obtained from the signal region with the standard b-tagging.
The red line shows the limit from the simultaneous exclusion fit using both soft b-tagging
and standard b-tagging SRs. The gray region shows the previous ATLAS results with datacollected in 2015–2016, which corresponds to 36 fb−1 [1, 143–145].

130

1

ATLAS Preliminary

Observed limit (±1σ th)s = 13 TeV, 139 fb
Limit at 95% CL

ATLAS-CONF-2019-017-1

ATLAS Run-1 20 fb ,

∆m

700

Expected limit (±1σ exp)

W

-1

t

800

1

(t ~
1 , χ∼ 0
~
1 )
(
t
<
∆m
1 , χ∼ 0
0
(t ~
1 )
,
<
∼
1 χ 0
m
1 )
b +
<
m
m

900

1

∆m

1

mχ∼0 [GeV]

1000

~~
~
0 ~
0 ~
0
t1t1 production, t1→bff'∼
χ , t1→bW∼
χ , t1→t∼χRun-2 36 fb-1

600
500
400
300
200
100
0
200

400

600

800

1000

1200

1400

m~t [GeV]
1

Figure 9.13: Expected (black dashed) and observed (red solid) limits at 95% CL in theplane of mt̃1 versus mχ̃01 . The yellow band displays the ±1 σ variation of the expected limit,
and the red dotted lines along the observed line show the uncertainty in the stop crosssection. The gray dashed lines separate the t̃1 decay modes: tχ̃01 (2-body), bW χ̃01 (3-body),
and bf f 0 χ̃01 (4-body). The gray region shows the previously excluded area from the ATLAS
Run 1 and Run 2 with data15–data16 results [1, 142–145]. The green line is the result froma dedicated 3-body analysis [170] with one lepton final states using 139 fb−1 data.

131

ATLAS Preliminarys = 13 TeV, 139 fb-1

1

1

~ 0
∆m(t , ∼χ ) [GeV]

Limit at 95% CL
~~
~
0 ~
0 ~
0
t1t1 production, t1→bff'∼
χ , t1→bW∼
χ , t1→t∼
χ
1

200
180
160
140
120
100
80
60
40
20
200

1

Observed limit (±1σth)
Expected limit (±1σexp)
ATLAS-CONF-2019-017-1
ATLAS Run-1 20 fb ,Run-2 36 fb-1

1

0
t∼
χ
1

0
bW∼
χ
1

0
bff'∼
χ
1

300

400

500

600

700

800

m~t [GeV]
1

Figure 9.14: Expected (black dashed) and observed (red solid) limits at 95% CL in theplane of mt̃1 versus ∆m(t̃1 , χ̃01 ). The yellow band displays the ±1 σ variation of the expected
limit, and the red dotted lines along the observed line show the uncertainty in the stop crosssection. The gray dashed lines separate the t̃1 decay modes: tχ̃01 (2-body), bW χ̃01 (3-body),
and bf f 0 χ̃01 (4-body). The gray region shows the previously excluded area from the ATLAS
Run 1 and Run 2 with data15–data16 results [1, 142–145]. The green line is the result froma dedicated 3-body analysis [170] with one lepton final states using 139 fb−1 data.

132

Chapter 10

Discussion
10.1

Bino-Higgsino Mixed LSP Scenario

In Chapter 7 and Chapter 9, the results of the stop searches for large ∆m(t̃1 , χ̃01 ) and small∆m(t̃1 , χ̃01 ) are presented, respectively. A dedicated higgsino-like LSP model was designedin the former search, while the simplified model is used for the latter. In the compressedregion where only t̃1 → bχ̃±
1 decay is kinematically allowed, the final state particles arealways bf f 0 χ̃01 , which do not depend on the components of the neutralino LSP. Hence,from the two searches, the higgsino-like LSP scenario has been excluded in a wide range of∆m(t̃1 , χ̃01 ), considering all possible decay modes with various branching ratios.
The observed relic density of the DM indicates the cross section of the DM annihilation
process. A large annihilation cross section results in small relic density of DM, and viceversa. From cosmological observations, the relic density1 of the DM is estimated to beΩh2 ∼ 0.1 [171]. Figure 10.1 shows the LSP mass and the DM relic density of the possible

SUSY models after the LHC Run 1 results [172]. In order to achieve Ωh2 ∼ 0.1, scenariosof light higgsino LSP or wino LSP below 1 TeV are not possible for most cases. On theother hand, the pure bino LSP cannot be a good solution due to the small cross section of
the bino-bino annihilation. However, the DM relic density of Ωh2 ∼ 0.1 could be realized if

the LSP is a mixed state of bino-higgsino or bino-wino. This is the so-called well-tempered
neutralino scenario [173].
The result in Chapter 7 is interpreted into the bino-higgsino mixed LSP scenario. Here,

we can use the results presented in Chapter 7 to set constraints to the bino-higgsino mixed
LSP scenario. Signal grids are generated with a requirement of 0.10 < Ωh2 < 0.12. The
scanned parameters are M1 and the third generation squark mass, with the fixed parametersof M2 = 2.0 TeV and M3 = 1.8 TeV. A parameter with a large t̃R −t̃L mixing is chosen in
the range of 700−1300 GeV in order to be consistent with the mass of the Higgs boson. Since
1

The relic density is expressed with the density parameter (Ω) and Hubble constant (h).

133t̃L and b̃L have similar masses because they consists of a doublet of the third generationsquarks, the sbottom direct production is also considered when t̃1 ∼ t̃L . In this model, t̃1±000can decay into tχ̃01 , tχ̃02 , tχ̃03 , and bχ̃±
1 , and b̃1 can decay into bχ̃1 , bχ̃2 , bχ̃3 , and tχ̃1 . The

other SRs in reference [1] are also used to set the limits. Figure 10.2 shows the exclusion
limits at 95% CL for the bino-higgsino well-tempered LSP scenario2 .
The observed exclusion contour is weaker than the expected one because of the small
excess of the data in bCsoft med SR, as shown in Table 7.11. In the right-handed stop
scenario, no observed exclusion contour is obtained due to the small excess.
The exclusion limits shown in the higgsino-like LSP and simplified model in Figures 7.16
and 9.13 may give an impression that the stop is strongly excluded for mt̃1 < 800 GeV.
However, such conclusions strongly depend on models. As shown in Figure 10.2, a lightstop or natural SUSY scenarios are still alive when the mass spectrum is more complicated.
The searches for such complicated scenarios like the well-tempered neutralino are important
and will be performed in future analyses of the data from the LHC.

Figure 10.1: The DM relic density and LSP mass of possible models after the ATLAS Run1
results [172]. Wino-like, bino-like, and higgsino-like LSPs are plotted separately. The two
triangle areas in mχ̃01 < 100 GeV correspond to the annihilation of the DM via s-channel ofZ boson and the Higgs boson.

2

The SR in this dissertation mainly contributes to mt̃1 < 700 GeV in the right-handed stop scenario as
shown in Appendix A.

134

2

600

1

m∼χ0 [GeV]~~ ~ ~
00
Bino/Higgsino mix model: t1t1 + b1b1 production, ∆ m(∼χ ,∼χ ) = 20-50 GeV

500
400

1

0
~
±
t1 → b ∼
χ ,t∼
χ
1
1,2,3
~
0
±
∼
∼
b → tχ ,bχATLAS
s = 13 TeV, 36.1 fb-1
Limit at 95% CL

1

1

1,2,3

0
±
∼
χ → W* ∼
χ
1
1,2
0
0
±
∼
∼
χ → W* χ , Z*/h* ∼
χ
3

1

0
0
∼
χ2 → Z*/h* ∼χ1Observed limit
Expected limit (±1σexp)~ ~~ ~t1 ≈ tL
t1 ≈ tR

1,2

300
200
500

600

700

800

900
m ~t [GeV]1

Figure 10.2:
Observed (solid) and expected (dashed) exclusion limits at 95% CL for
the bino-higgsino mixed model in the plane of mt̃1 versus mχ̃01 . Mostly right-handed t̃1(blue) and left-handed t̃1 (red) are considered. The parameters, such as the masses andbranching ratios, are determined by choosing the DM relic density that is consistent withthe observed value. Decay modes and branching ratios of t̃1 decays (tχ̃01 , tχ̃02 , tχ̃03 , and bχ̃±
1)dependontheare determined at each signal point in the plane. The masses of χ̃02 , χ̃03 , χ̃±1signal point. In the left-handed t̃1 scenario, the b̃1 pair production is also included withpossible b̃1 decay modes of bχ̃01 , bχ̃02 , bχ̃03 , and tχ̃±
1.

10.2

Comparison of Results with CMS Results

The analysis presented in Chapter 7 is the first stop search with the higgsino-like LSP
where the three decay modes are considered. The simplified model used in the analysis
for the small ∆m(t̃1 , χ̃01 ) presented in Chapter 9 is also used in the CMS stop searches.
The latest results of searches for the stop four-body signature from CMS is based on thepartial Run-2 data collected in 2015–2016, which corresponds to an integrated luminosity of
35.9 fb−1 . Figure 10.3 shows the expected and observed exclusion limits at 95% confidence
level from the CMS analyses [156]. The results obtained from the one-lepton analysis withthe multivariate analysis technique shown in light green excluded the stop masses up to560 GeV. The best exclusion limit from the CMS is obtained from the combination of the
all-hadronic and one-lepton analyses as shown in dark green, and stop masses up to 600 GeV

135

are excluded. Comparing the limit with the one presented in Chapter 9, it is concluded
that the stringent limit is derived by the analysis in this dissertation.

120

CMS

0
1

m~t - m ∼χ [GeV]~~ ~∼pp → t t, t → ( b f f' / c) χ01

100

July 201835.9 fb-1 (13 TeV)~∼t → b f f ' χ01: 1805.05784, soft 1-lep + 0-lep~∼
t → b f f ' χ01: 1805.05784, soft 1-lep (MVA)~∼t → c χ01: 1707.07274, 0-lep (stop/sbottom)~∼
t → c χ01: 1705.04650, 0-lep (MT2)~∼t → c χ01: 1707.03316, 0-lep (stop)~∼t → c χ01: 1802.02110, 0-lep ( α T )Expected
Observed

m~t = m χ∼ + m W
0
1

80

60

40

20
200 250 300 350 400 450 500 550 600 650 700

m~t [GeV]
Figure 10.3: The latest observed and expected exclusion limits for the simplified modelwith the stop four-body decay from the CMS collaboration [174]. The results for the fourbody signature are shown in dark green and light green [156]. The light green lines show
the exclusion limits obtained from the search using one charged lepton. The dark green
lines are the combined results obtained from the all-hadronic and one-lepton modes. The
other lines show the t̃1 → cχ̃01 decay, which is not considered in this dissertation.

10.3

Fine-tuning

As discussed in Chapter 2, the Natural SUSY is the outcome of small fine-tuning. The
degree of fine-tuning [56] is quantified as the maximum logarithmic derivative of the Higgs
boson mass (mh ) with respect to the fundamental parameters pi ,∆mh = maxi∂ ln m2h.
∂ ln pi(10.1)As the parameter pi , the fundamental parameters at the messenger scale: µ, b, m2Q3 , m2u3 , At ,m2Hu , and m2Hd are taken into account. The fine-tuning measure ∆mh represents how stable
the Higgs boson mass is against the variation of these fundamental parameters. Figure 10.4

136

shows the fine-tuning ∆mh as a function of the stop mass and stop mixing parameter. In√
order to achieve the observed Higgs boson mass, the maximal mixing (|Xt | ∼ 6mt̃ ) gives
the minimal fine-tuning.

Higgs Mass vs. Fine Tuning

Lightest Sto

3000

3000

2500

2500

1000

Suspect
FeynHiggs

SuspecFeynHig

2000
100

1500

mt @GeVDmt @GeVD

2000
500

1000

1000

75

500

1500

1500
1000

50

500
200

500
0
-4

500

Dmh
-2

0

2

4

100

0
-4

Xt mt

Figure 10.4: Contours of fine-tuning ∆mh with the stop mass mt̃ and the stop mixing
parameter Xt [56]. The dashed purple lines show the contours of fine-tuning. The redand blue bands correspond to the observed Higgs boson mass in the range of 124–126 GeV
calculated with Suspect and FeynHiggs, respectively.

In this dissertation, the stop masses up to 800 (640) GeV are excluded for the large√(small) ∆m(t̃1 , χ̃01 ) scenario. Assuming the maximal mixing with Xt /mt̃ = 6 ∼ 2.45, thestop exclusion limits correspond to the exclusion of ∆mh < 200 (100) for the small (large)∆m(t̃1 , χ̃01 ) scenario.

10.4

750

25

200

Comparison with Searches for the Direct Higgsino Production

This dissertation considers the light stop and light higgsinos, which are favored by the
Natural SUSY. The search for the large ∆m(t̃1 , χ̃01 ) in Chapter 7 excluded the LSP masses
up to 200 GeV, and the search for the small ∆m(t̃1 , χ̃01 ) in Chapter 9 excluded the LSP
masses up to 580 GeV. Those searches for the stop decaying into the higgsino-like LSP set
the limits for higher higgsino masses compared with the searches for the direct production
137

-2

0

Xt mt

of higgsinos. Figure 10.5 shows the summary of the higgsino direct production searches.
0
The mass splitting ∆m(χ̃±
1 , χ̃1 ) higher than 1 GeV is covered by the search which exploits

two soft leptons from the χ̃02 → ``χ̃01 decay [175] (2L analysis), while the very small mass

splitting ∆m(t̃1 , χ̃01 ) < 0.3 GeV is searched by the disappearing track analysis [176]. The
2L analysis excluded the higgsinos up to 150 GeV, and the disappearing track analysis also
excluded the higgsinos up to 150 GeV for the pure higgsino model. Comparing the direct
production limits and the LSP mass limits obtained in this dissertation, the stop search
results set limits for higher higgsino masses by exploiting the large cross sections of stop
direct production and the distinctive signatures of the stop decays.

0∆m(χ̃±
1 , χ̃1) [GeV]July 20190Soft 2`, 139 fb−1 , CONF-2019-014, m(χ̃02 ) = m(χ̃01 ) + 2∆m(χ̃±
1 , χ̃1 )−10Disappearing track, 36.1 fb , PHYS-PUB-2017-019, m(χ̃2 ) = m(χ̃01 )LEP2 χ̃±
1 excluded
Theoretical prediction for pure Higgsino

50
20
10
5
2

ATLAS Preliminary
√

1
0.5
0.2

s = 13 TeV

± 0
0 0
+ −
pp → χ̃02 χ̃±
1 , χ̃2 χ̃1 , χ̃1 χ̃1 , χ̃1 χ̃1 (Higgsino)

All limits at 95% CL
Observed limits

100

120

140

160

Expected limits

180

200

m(χ̃±
1 ) [GeV]
Figure 10.5: The excluded region obtained by the searches for the direct higgsino production [164]. The gray regions shows the exclusion of light charginos by LEP2 [177].
The search with two soft leptons [175] excluded the blue area and the disappearing track0
search [176] excluded the orange area below ∆m(χ̃±
1 , χ̃1 ) < 0.3 GeV.

The mass-splitting below 1 GeV but above the disappearing track coverage has not been
covered by searches at the LHC. The 2L search loses the sensitivity due to the inefficiency ofthe very low-pT lepton reconstruction. The disappearing track search loses the sensitivity
due to the short flight length of the charginos. This uncovered region is expected to be
searched in the future with new ideas such as a search with soft displaced tracks [178].

138

Chapter 11

Conclusion
This dissertation presents the searches for the stop direct production using the data collectedwith the ATLAS detector at the LHC, using pp collisions at a center of mass energy of√s = 13 TeV. Natural SUSY models suggest a light stop and higgsinos, and the stop mass
below 1 TeV can be consistent with the mass of the observed Higgs boson in the case of the
maximal mixing. Two searches are performed targeting large and small mass differences
between the stop and LSP (∆m(t̃1 , χ̃01 )).
The first search is performed for large ∆m(t̃1 , χ̃01 ) using data corresponding to an integrated luminosity of 36 fb−1 collected in 2015–2016, in which three decay modes are
considered: t̃1 → tχ̃01 , tχ̃02 , and bχ̃±
1 . The stop branching ratios depend on the MSSM

parameters, hence the three scenarios: t̃1 ∼ t̃L , t̃1 ∼ t̃R , and large tan β, are considered tocover wide phase space. The signature of bχ̃±
1 decay is characterized by a low pT lepton
miss from neutralinos. Since the traditional
produced from the χ̃±
1 decay, as well as large ET

signal regions with a high pT lepton is not sensitive to the bχ̃±
1 decay, a signal region is
optimized for the t̃1 → bχ̃±
1 decay. The signal region is defined using the discriminating

miss , number of b-tagged jets, and am . The SM background prevariables such as p`T /ET
T2

diction is estimated by normalizing the main background processes (tt̄, W +jets, and single
top) in CRs. No significant excess over the SM prediction is observed, and the exclusion0
limits are derived. For ∆m(χ̃±
1 , χ̃1 ) = 5 GeV, the stop mass is excluded up to 800 GeV

for the LSP mass of 150 GeV in all three scenarios. This is the first result for a realistic
higgsino-like LSP model in which all decay modes are considered.
In the case of the small ∆m(t̃1 , χ̃01 ), the final state contains low pT b-hadrons. Since
the standard ATLAS b-tagging algorithm is not optimal for such low pT hadrons, a newsoft b-tagging algorithm has been developed. The algorithm utilizes the secondary vertex
reconstruction. Due to a large number of tracks in an event, the track selection is essential
in this new algorithm. Dedicated requirements for the low pT b-hadrons are used, such as
the loose requirements on the impact parameter or overlap removal between tracks and high139

pT jets. The fake rate is reduced by removing the tracks overlapping with high pT jets. The
efficiency of the soft b-tagging is about 10 times higher than that of the standard b-tagging
at the same fake rate for b-hadron pT between 5 and 15 GeV. The track-based reweighting
method is developed and performed to correct the imperfect MC modeling.
Since no significant excess is found in large ∆m(t̃1 , χ̃01 ), the second search is performed
targeting the small ∆m(t̃1 , χ̃01 ) with the data collected in 2015–2018, which corresponds toan integrated luminosity of 139 fb−1 . The stop four-body decay t̃1 → bf f 0 χ̃01 is considered

miss requirement, the soft
as a benchmark signal in the search. In addition to the small p`T /ETb-tagging is used to strongly suppress the W +jets and tt̄ backgrounds. The soft b-tagging±
00
expands the search sensitivity for the small ∆m(χ̃±
1 , χ̃1 ) region, in particular ∆m(χ̃1 , χ̃1 )below 40 GeV. No excess is found in this search either, and the four-body decay is excluded
up to the stop mass of 640 GeV at mχ̃01 = 580 GeV.
Unfortunately, no sign of natural SUSY has been found in the searches. However, theinterpretation of the results also shows that there are still uncovered regions of the phasespace to be searched at the LHC, such as mixed LSP scenarios.

140

Appendix A

Contributions of Signal Regions to
Exclusion Limits
The exclusion limits from the results in the analysis targeting large ∆m(t̃1 , χ̃01 ) are derived
using the bCsoft med SR described in Chapter 7 and other SRs in Reference [1]. Figure A.1
and A.1 show the SRs used for the exclusion contours at each signal mass point. At eachmass point, the SR that has the best expected CLs value is selected and used to draw
the exclusion limits. Figure A.3 shows the same plot for the bino-higgsino mixed scenario
discussed in Chapter 10.

142

~~
Higgsino LSP model: t1t1 production, mχ∼±1 = mχ∼0+5 GeV, mχ∼0 = mχ∼0+10 GeV

700 ATLAS~~
Higgsino LSP model: t1t1 production, mχ∼±1 = mχ∼0+5 GeV, mχ∼0 = mχ∼0+10 GeV

1

1

bCsoft_diag ⊕ tN_med-1

s = 13 TeV, 36.1 fb
Observed limit

bCsoft_high ⊕ tN_med

Expected limit

bCsoft_med ⊕ tN_med

1

600

2

m∼χ0 [GeV]1mχ∼0 [GeV]1500

s = 13 TeV, 36.1 fb

600

2

1

bCsoft_diag ⊕ tN_med-1

Observed limit

bCsoft_high ⊕ tN_med

Expected limit

bCsoft_med ⊕ tN_med

500

400

400

300

<

m

mt

+

0
m ∼χ 1m ∼χ 1
0

300

~t

<

m

200
100

700 ATLAS

mt

+

~t

200
400

500

600

700

800

100

900 1000m ~t [GeV]

400

500

600

1

700

800

900 1000m ~t [GeV]1~~
Higgsino LSP model: t1t1 production, mχ∼±1 = mχ∼0+5 GeV, mχ∼0 = mχ∼0+10 GeV

1m∼χ0 [GeV]

1

700 ATLAS

1bCsoft_diag ⊕ tN_med

s = 13 TeV, 36.1 fb-1

600

2

Observed limit

bCsoft_high ⊕ tN_med

Expected limit

bCsoft_med ⊕ tN_med

500400m ∼χ 1
0

300

<

m

mt

+

~t

200
100

400

500

600

700

800

900 1000m ~t [GeV]1

Figure A.1: The SR with the best CLs value for the higgsino-like LSP scenario in theplane of mt̃1 versus mχ̃01 : (top left) t̃1 ∼ t̃L , (top right) t̃1 ∼ t̃R , and (bottom) large tan βscenarios.

143ATLASs = 13 TeV, 36.1 fb-1

25

Expected limit

20

bCsoft_diag ⊕ tN_med

15bCsoft_high ⊕ tN_med

10

30

~~
Higgsino LSP model: t1t1 production, m∼χ±1 = 150 GeV

ATLAS
s = 13 TeV, 36.1 fb-1

25

Observed limit

1

Observed limit

1

1

∼±, χ
∼0) [GeV]∆m(χ~~Higgsino LSP model: t1t1 production, m∼χ±1 = 150 GeV

1

∼±, χ
∼0) [GeV]∆m(χ30

Expected limit

20

bCsoft_diag ⊕ tN_med

15bCsoft_high ⊕ tN_med

10bCsoft_med ⊕ tN_med

bCsoft_med ⊕ tN_med

550
600 700 800 900 1000 1100 1200 1300 1400
m ~t [GeV]

0600 700 800 900 1000 1100 1200 1300 1400
m ~t [GeV]

30

1

ATLAS
s = 13 TeV, 36.1 fb-1

25

Observed limit

1
1

±

0

∼,χ
∼ ) [GeV]
∆m(χ

1

~~
Higgsino LSP model: t1t1 production, mχ∼±1 = 150 GeV

Expected limit

20

bCsoft_diag ⊕ tN_med

15bCsoft_high ⊕ tN_med

10bCsoft_med ⊕ tN_med

5
0
600 700 800 900 1000 1100 1200 1300 1400
m ~t [GeV]1

Figure A.2: The SR with the best CLs value for the higgsino-like LSP scenario in the plane0of mt̃1 versus ∆m(χ̃±
1 , χ̃1 ): (top left) t̃1 ∼ t̃L , (top right) t̃1 ∼ t̃R , and (bottom) large tan βscenarios.

1Bino/Higgsino mix model: ∆ m(∼χ ,∼χ ) = 20-50 GeV

tN_medtN_highbC2x_diagbC2x_medbCsoft_diag ⊕ tN_med
bCsoft_med ⊕ tN_med
bCsoft_high ⊕ tN_med

ATLAS
s = 13 TeV, 36.1 fb-1

500

600

400

300

300

200

200
600

700

800

0

2

1

tN_medtN_highbC2x_diagbC2x_medbCsoft_diag ⊕ tN_med
bCsoft_med ⊕ tN_med
bCsoft_high ⊕ tN_med

ATLAS
s = 13 TeV, 36.1 fb-1

500

400

500

0

1

0

2

m∼χ0 [GeV]

600

0

1

mχ∼0 [GeV]

Bino/Higgsino mix model: ∆ m(∼χ ,∼χ ) = 20-50 GeV

900m ~t [GeV]

500

1

600

700

800

900
m ~t [GeV]1

Figure A.3: The SR with the best CLs value for the bino-higgsino mixed scenario in theplane of mt̃1 versus mχ̃01 : (left) t̃1 ∼ t̃L , (right) t̃1 ∼ t̃R .

144

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