Doctoral Dissertation
博士論文
Search for gluinos in final states with jetsand missing transverse√ momentum inp p collisions at s =13 TeV(重心系エネルギー13 TeVの陽子·陽子衝突における終状態にジェットと横方向消失運動量をもつ
超対称性粒子グルイーノ探索)

A dissertation Submitted for the Degree of Doctor of Philosophy
令和元年12月博士（理学）申請

December 2019
Department of Physics, Graduate School of Science
東京大学大学院理学系研究科
物理学専攻

The University of Tokyo
Kenta Uno
宇野 健太

Ph.D Thesis
Search for gluinos in final states with jetsand missing transverse√ momentum inp p collisions at s =13 TeV

Kenta Uno
1

The University of Tokyo

Abstract
Standard Model (SM) provides a successful description in the current particle physics
and it is consistent with almost all experimental results. However, there are problems
such as an existence of dark matter and a hierarchy problem, which cannot be explainedin the SM. Hence, the extension of the SM is needed. One of the promising extension
is to introduce Supersymmetry (SUSY), which is a symmetry between fermions andbosons. When SUSY is considered, partners of all the SM particles (super-partners) areintroduced and these particles have been searched. This thesis describes a search forgluino, which is the super-partner of gluon at the LHC ATLAS experiment. In the pp
collision, the cross section of gluino is relatively large due to strong interaction and thegluino search is one of the most important physics programs.
The result of a search for gluinos in final states with jets and missing transverse momentum√
at s =13 TeV with the ATLAS detector is presented. This thesis uses data collected
in 2015-2018 corresponding to the integrated luminosity of 139 fb−1 . Compared to thepast search, a machine learning technique as a new approach is introduced and allows thesensitivity to heavier gluino which has not been looked into before, to be improved well.
No significant excess over the background prediction is observed and the gluino mass is
excluded up to 2.2 TeV and the lightest neutralino mass is excluded up to about 1.2 TeV at
95% confidence level.
This research shows the first result of the gluino search using the machine learning,which is published from ATLAS. This thesis has been proved that the machine learningtechnique is applicable to SUSY search.

Contents

1 Introduction
1.1 Remaining problem
1.1.1 Hierarchy problem
1.1.2 Dark Matter problem
1.2 Supersymmetry
1.2.1 R-parity conservation
1.3 Constraints on SUSY particles via indirect search
1.4 Constraints on SUSY particles via direct search
1.5 Target SUSY particles
1.6 Strategy of gluino search

9
9
9
10
11
13
13
16
17
20

2 LHC-ATLAS experiment
2.1 Large Hadron Collider (LHC)
2.2 ATLAS detector
2.2.1 Inner detector
2.2.2 Calorimeter2.2.3 Muon Spectrometer
2.3 Trigger and Data Acquisition system

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3 Dataset and Monte-Calro sample
3.1 Dataset
3.2 Trigger
3.3 Monte-Carlo sample
3.3.1 Background MC sample
3.3.2 Signal MC sample
3.3.3 Detector and pileup simulation

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35
36

4 Object reconstruction and identification
4.1 Charged tracks
4.2 Jet4.2.1 Reconstruction
4.2.2 Calibration
4.2.3 Jet Vertex Tagging
4.2.4 Flavor Tagging
4.2.5 Jet in this analysis
4.3 Electron

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46
47

5

Contents
4.4
4.5
4.6

Muon
Missing transverse momentum
Overlap removal

48
48
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5 Event selection with machine learning
5.1 Jet cleaning
5.2 Treatment of dead tile modules
5.3 Preselection
5.4 Discriminating variables
5.5 Boosted Decision Tree (BDT)
5.6 Approach of BDT analysis
5.6.1 BDT classifier training
5.6.2 Application of BDT classifier
5.6.3 Optimization of BDT classifier
5.6.4 Determination of input variables
5.7 Signal region (SR) definition

53
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6 Background estimation
6.1 Background composition
6.2 Background estimation strategy
6.3 Z+jets background estimation
6.4 W+jets background estimation
6.4.1 Definition of CR
6.4.2 Properties of W →µν events
6.4.3 Adjustment of cut in CRW
6.5 Top background estimation
6.6 Validation region

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7 BDT validation
7.1 Overtraining
7.2 Difference of two BDT score distribution
7.3 Correlation of input variables
7.4 Profile distribution in BDT score
7.5 Summary of BDT validation

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105

8 Statistical analysis
8.1 Likelihood function
8.2 Hypothesis test
8.3 Systematic uncertainty
8.3.1 Experimental uncertainty
8.3.2 Theoretical uncertainty
8.3.3 MC statistical uncertainty
8.3.4 CR statistical uncertainty
8.3.5 SUSY signal
8.3.6 Summary of systematic uncertainties

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6

Contents
9 Results
9.1 Results from background-only fit
9.2 Model-independent fit
9.3 Model-dependent fit
9.3.1 Target signal models
9.3.2 Other signal models
9.3.3 Cross section upper limits
9.4 Discussion
9.4.1 Comparison to the convensional approach
9.4.2 Comparison to the CMS experiment9.4.3 Impact of the result to SUSY models

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10 Conclusion

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A Input variable distribution137

B Input variable distribution

141

C Trigger readout electronics upgrade of the LAr calorimeter
C.1 LAr calorimeter upgrade at Run 3 experiment
C.2 New trigger readout scheme

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7

1 Introduction
Elementary particles are the most fundamental building blocks of the universe. Figure 1.1 shows allelementary particles in the Standard Model (SM) [1]. They are composed of three types: fermions withthe spin 1/2, gauge bosons with spin 1 and Higgs boson with spin 0. The SM provides a successful
description of these particles and their interactions. It is also consistent with almost all experimental
results. However, the SM is not a perfect theory because it cannot explain many problems. In the next
section, two representative problems are discussed: the hierarchy problem [2] and the existence of thedark matter. Then, Supersymmetry (SUSY), which solves these problems, is introduced.

Figure 1.1: Elementary particles in the Standard Model [3]. The quarks (u, d, c, s, t and b) and leptons (e− , νe ,µ− , νµ , τ − and ντ ) are spin 1/2 particles. All matters are made up of these fermions. There are antiparticles of¯ c̄, t¯, b̄, e+ , ν̄e , µ+ , ν̄µ , τ + and ν̄τ . The gauge bosons (g, Z 0 , W ± and γ) are spin 1
quarks and leptons: ū, d,particles and carry interactions. The Higgs boson is a spin-zero particle and generates the masses of all particles.

1.1 Remaining problem
1.1.1 Hierarchy problem
The Higgs boson is discovered by both the ATLAS and CMS experiments at the Large Hadron
Collider (LHC) in 2012 [4, 5]. They have been measuring properties of the Higgs boson. It is aparticle with spin 0 and the mass of 125.09 ± 0.21 (stat) ± 0.11 (syst) GeV [4, 5], which is much lighter
than Planck scale (∼1019 GeV). The other particles in the SM (fermions and gauge bosons) have also
light masses but the symmetries in the SM (gauge invariance and chirality conservation) allow them9

Introduction
to have such light masses [6, 7]. However, there is no symmetry for particles with spin 0 in the SM.
Since the Higgs boson is only a particle with spin 0 as shown in Figure 1.1, it is an open question why
the energy scale of the Higgs boson (O(102 ) GeV) is much less than the Planck scale [2].
The mass of the Higgs boson is theoretically expressed as Eq. 1.1:
2
2
mh,obs= mh,bare
−

2y 2f

λS2

16π

16π 2

Λ2 +
2

Λ2 + ...

(1.1)

where mh,obs (mh,bare ) is the observed (bare) Higgs boson mass, Λ is the cut-off scale of the loop
calculation and y f (λS ) is the Higgs coupling with a fermion (boson) [8]. The second and third terms
are the contribution of the one-loop quantum corrections from the fermion ( f ) and boson (S) as shownin Figure 1.2.
S
f
H

H

H

H

f¯

Figure 1.2: The one-loop quantum correction to the Higgs boson mass due to fermion (left) and boson (right).

If the SM is applicable to the Planck Scale, the Λ scale should be the same order. In order to beconsistent with the observed Higgs boson mass, the difference between the bare Higgs boson andquantum corrections, which contain the fermion and boson loops in Eq. 1.1, has to be tuned at thelevel of 10−34 . This adjustment is quite unnatural, which is called "Fine tuning problem" [2].

1.1.2 Dark Matter problem
There are cosmological observations which indicate the existence of dark matter. An example is themeasurement of the galaxy rotation curve [9]. It measures the rotational velocity, which is the orbital
velocity of a star or gas in the galaxy as a function of the distance from the center of the galaxy to theorbiting object (r). Generally, the rotational velocity would expect v(r) ∝ √1r in the outer side of thegalaxy. However, the measured velocity is approximately constant in the large value of r as shown in
Figure 1.3. It means an existence of massive material, which is not luminous. Such a massive material
is called "Dark Matter" (DM).

10

1.2 Supersymmetry

Figure 1.3: The M33 galaxy rotational curve [9]. The x-axis is the distance from the center of the galaxy to
the orbiting object and y-axis is the rotational velocity. The filled circles are the measured data points. The
solid line is the best fit model considered on the halo contribution (dashed line), stellar disk contribution (shortdashed line) and gas contribution (long dashed line).

The DM is generally assumed to be composed of elementary particles. In order to explain
observations, these particles should have the following properties:• They do not have strong and electromagnetic interaction.
• They are stable.
• They have a finite mass.
Among the SM particles, the neutrinos have these properties. However, since the mass of the neutrinos
is too light (for example, νe <2 eV) [10], that is, the neutrinos are so-called hot DMs, the universe
would not have a large scale structure in the astronomical survey [11]. Therefore, there is no candidatein the SM to explain the dark matter.

1.2 Supersymmetry
One of the promising solution of these problems is SUSY, which is a symmetry between fermions andbosons [12–17]. There are several SUSY models, but this thesis focuses on Minimal SupersymmetricStandard Model (MSSM), which introduces minimal particle contents and degrees of freedom toSM [18, 19]. In the MSSM, two Higgs doublets model is introduced unlike the SM. This doublets
model extends one Higgs boson particle to five particles: CP even neutral Higgs bosons (h and H),
CP odd neutral Higgs boson (A) and charged Higgs bosons (H ± ). In order to provide the symmetry
between fermions and bosons, partners of all the SM particles (super-partners) have to be introduced
as shown in Figure 1.4. The super-partners of the SM fermions are called "sfermions" and have spin 0:"squarks" are the super-partners of the quarks and "sleptons" are the super-partners of the leptons.

11Introduction
The super-partners of the SM gauge and higgs bosons are called "gauginos" ("winos", "binos" and"gluinos") and "higgsinos" with spin 1/2, respectively. The charged gauginos (W̃ ± , H̃ ± ) would mix
each other and give the mass eigenstates, which are called "chargino". They are denoted as χ̃1± and χ̃2±in order starting with the lightest mass. The neutral gauginos ( Z̃ 0 , γ̃, H̃u ,H̃d ) are mixed as the sameas the charged gauginos. They are called "neutralinos" and denoted as χ̃10, χ̃20, χ̃30 and χ̃40 in order
starting with the lightest mass.

Figure 1.4: All the particles in the MSSM [20]. Two charged and neutral Higgs bosons are added in the SMparticles in addition to the observed Higgs boson in this theory. Therefore, five Higgs bosons are considered in
the SM particles (left figure). Furthermore, a set of the partners of the SM particles are introduced (right figure).

SUSY can provide an elegant solution to the remaining problems. For the fine tuning of the Higgs
boson mass described in Sec. 1.1.1, since the super-partners of the SM fermions (bosons) are particles
with spin 0 (spin 1/2), the one-loop corrections of SUSY particles are added the opposite sign tocorresponding SM particles. The one-loop correction including in SUSY particles is expressed as
Eq. 1.2:
2
mh,obs = mh,bare
−

2y 2f
16π

Λ +
2
2

y 2f˜
16π

Λ2 +
2

λS2
16π

Λ2 −
2

2λS̃2
16π 2

Λ2 ...

(1.2)

where y f˜ (λS̃ ) is the Higgs coupling with a sfermion (gaugino). If the masses of SUSY particles areexactly the same as those of SM particles, equations of 2y f = y f˜ and λS = 2λS̃ can be obtained 1 . It
leads that the Λ contributions can be cancelled and thus the fine tuning is not needed.
1 Since no super-partner of any SM particles has been observed, the mass of SUSY particles is not the same as SM particles.

It means that SUSY must be a mechanism for breaking the symmetry at some higher energy scale [21]. In this case, somefine tuning is needed to explain the Higgs boson mass but SUSY models are still motivated because the order of the finetuning can be significantly reduced.

12

1.3 Constraints on SUSY particles via indirect search

1.2.1 R-parity conservation
An important conservation is introduced: R-parity conservation [18, 19, 22]. This conservation isrequired to explain experimental results of proton decay. The proton decays have been searched for inseveral experiments, but it is not observed until now. The proton decay experiments have establishedthe upper limit of the proton lifetime, τp > 1.6 × 1034 years [23].
SUSY can easily have proton decay, for example, via p → e+ π 0 as shown in Figure 1.5 and in orderto prohibit such a proton decay, a new quantum number, R-parity is introduced
R := (−1)3(B−L)+2S ,(1.3)

where B (L) is the baryon (lepton) number and S is the spin. Under this definition, SM particles
have R-parity of +1, while the SUSY particles have R-parity of -1. If R-parity is conserved, SUSY
particles must be produced in pair from SM particles. Therefore, the process in Figure 1.5 is forbidden.
R-parity-conserving SUSY is consistent with the experiment results. From the R-parity conservation,SUSY can provide a contribution of dark matter. It will be explained in the next section.

e+

u
d˜j

p
d

ū

u

u

π0

Figure 1.5: p → e+ π 0 decay via SUSY particle, d˜j .

1.3 Constraints on SUSY particles via indirect search
For the indirect search, theoretical and experimental constraints have been considered on SUSY
particles. The Higgs boson mass in the MSSM can be expressed as Eq. 1.4:
mh2 = m2Z cos2 2β + δt2(1.4)

where mh (m Z ) is the Higgs (Z) boson mass, tanβ is the ratio of the vacuum expectation valuesof up and down type Higgs boson and δt is the contribution from loops of top quarks and top
squarks (stop) [24]. Since Z boson mass is lighter than the Higgs boson mass, a large radiation
correction (δt ) is needed to reach up to the 125 GeV. Figure 1.6 shows the Higgs boson mass as afunction of the stop mass considering on up to the two-loop correction in the MSSM.

13

Introduction

Figure 1.6: The Higgs boson as a function of the lightest stop mass in the MSSM [24]. The red (blue) lines arecomputed using the Suspect [25] (FeynHiggs [26]) packages, which have each renormalization prescriptions.
tanβ = 20 is considered here.

This figure implies two things. First, the stop mass would be above 3 TeV in case the left- andright-handed stops do not mix with each other at all (Xt =0). In this case, a large fine tuning isnecessary. Second, the stop mass
√ would be 300∼1000 GeV with the mildly fine tuning in case the stop
mixing is maximized (Xt = 6 mt̃ ).

The results of flavor mixing and CP violation can also set the constraints of SUSY particles. The
squark masses can be estimated from K 0 − K¯0 oscillation; the d s̄ and s d¯ states can exchange into eachother via weak boson as shown in Figure 1.7(a) [27]. The physical mass eigenstates are called Ks0 andK L0 and there is a very small mass difference between them in the SM. However, the mass difference
can be enhanced due to loop contributions of the SUSY particles as shown in Figure 1.7(b). The
current measurement of the mass difference is 3.5×10−15 GeV [28], so a constraint of mixing term
between s̃ and d˜ is obtained [27]W−sū, c̄, t̄

d¯

d

g̃

u, c, t
W+

(a)

s̃R

s

s

d¯

d˜∗R

×
×

d˜R

d
g̃

s̃∗R

s̄

(b)

Figure 1.7: Example of the Feynman diagrams for K 0 − K¯0 mixing. The flavor can exchange into each other via
only weak boson in the SM (a), but the oscillation can be enhanced via SUSY particles in the MSSM (b). The
symbol "×" corresponds to the violation of the strangeness.

141.3 Constraints on SUSY particles via indirect search
0.04 for mg̃ = 0.5mq̃



m
q̃
s̃ R d̃ R.
(1.5)<
× 0.10 for mg̃ = mq̃
mq̃
1000 GeV  0.22 for mg̃ = 2mq̃In the MSSM, squarks are allowed to mix between different generations. In order to suppress theK 0 − K¯0 oscillation, the mixing term (Re[(m2)2 ]| 1/2 ) has to be small. From Eq. 1.5 and the currents̃ R d̃ Rmeasurement, the squark masses are expected to be heavy (> 10 TeV).
|Re[(m2)2 ]| 1/2

In addition, the properties of neutralino can be constrained from the relic density of the DM [29]. In
the early universe (thermal universe), the DM would be produced and annihilated in pair at the samerate and thus the DM particles and SM particles are balanced at the thermodynamic states. However,these processes are not occurred at the same rate and the number of the DM particles are decreased as
the universe is inflating. As a result, the universe is cooled and the relic density of the DM would keep
the constant due to the low rate of the processes in the current universe. Since the density depends onthe cross section of the processes, the relic density can be estimated.
The recent cosmological experiments on the cosmic microwave background (CMB) radiation
measure the relic density of the DM with:ΩDM h2 = 0.120 ± 0.001(1.6)

where ΩDM is the relic density of the DM and h is the Hubble constant in units of 100 km/(s·Mpc) [30].
In the R-parity conservation, a SUSY particle should decay to a lighter SUSY particle. In the end, thelightest SUSY particle ( χ̃10 ) is stable. It is called the Lightest Supersymmetric Particle (LSP) and is acandidate of the dark matter. Since each neutralino has a different cross section, the LSP type can beconstrained as shown in Figure 1.8 [31]. To satisfy the measured relic density of Eq. 1.6, the uppermass bound of pure wino (higgsino) is found to be about 2 (1) TeV from Figure 1.8.

15

Introduction

Figure 1.8: Relic density of the dark matter as a function of LSP mass in the pMSSM [32, 33], which assumes
some parameters in the MSSM [31]. The colors correspond to LSP types:W̃ (wino), B̃ (bino) and H̃ (higgsino).

1.4 Constraints on SUSY particles via direct search
The direct search for SUSY particles has been performed in several experiments such as LEP,
Tevatron, CMS or ATLAS experiments. Figures 1.9 show SUSY searches in ATLAS, which use data√collected in 2015-2016 at s = 13 TeV corresponding to the integrated luminosity of 36.1 fb−1 : (a)the squark decays into quark and neutralino, (b) the gluino decays into two quarks and neutralino, (c)the stop decays into top quark and neutralino and (d) the chargino decays into two or three lepton andneutralino [34–36].
No significant excess over the SM predictions is observed and the exclusion limits for these SUSY
particles (squarks, gluinos, stop and electroweak gaugino) are set. The masses of the squarks (gluinos)
are excluded up to 1.6 (2.0) TeV and stop (chargino) are excluded up to 1000 (580) GeV in case of
massless neutralino.

16

1.5 Target SUSY particles

(a)

(b)

(d)
(c)
Figure 1.9: The summary of the search for SUSY particles at the ATLAS experiment. The x-axis is (a) squark
mass [34], (b) gluino mass [34], (c) top squark mass [35] and (d) chargino mass [36]. The y-axis is the neutralinomass

1.5 Target SUSY particles
This thesis focuses on the gluino as a target SUSY particle. The gluino search is still one of mostimportant physics programmes at the LHC because there are four reasons as follows.
(i) Since the stop mass is excluded up to 1 TeV as shown in Figure 1.9(c), there is a possibility thatthe stop mass would be heavy (>1 TeV). If the stop mixing is small, the stop mass would be afew TeV from the constraints of the Higgs boson mass calculation (Figure 1.6) and it is difficult
to search for such a heavy stop in the LHC with the current center-of-mass energy.

17Introduction(ii) The squark mass would be heavy (> 10 TeV) from the constraints of K 0 − K¯0 mixing. Therefore,
it is also difficult to search for such a heavy squark in the LHC.
(iii) The cross section of slepton or electroweak production is relatively low as shown in Figure 1.10
and their searches might be difficult with the current data statistics.
(iv) The cross section of gluino production is relatively large due to strong interaction (LHC is a
proton-proton machine) as shown in Figure 1.10.
Under the R-parity conserving models in the MSSM, the gluinos can be produced in pair (g̃ g̃) as
shown in Figure 1.11. In this thesis, the next two processes are considered:(i) Gluino direct decay (GGd): the process decays through g̃ → qq χ̃10 to the lightest neutralino,χ̃10 , assumed to be the LSP as shown in Figure 1.12(a). This is the simplest process in all thegluino processes and the broad search for gluinos can be performed. Hence, the process having
this decay chain is the primary target in this thesis. For this purpose, the final states without
leptons are required.
(ii) Gluino one-step decay (GGo): the process decays to the chargino (neutralino) throughg̃ →qq 0 χ̃1± (g̃ →qq χ̃20 ) where q and q 0 are different flavor quark. As shown in Figure 1.12(b)and (c), the chargino (neutralino) decays to the lightest neutralino via χ̃1± →W ± χ̃10 ( χ̃20 →Z χ̃10 ).
For this process, there are some analyses depending on the number of leptons. The final states
without leptons have the highest sensitivity in a region where the gluino is heavy and thus thisprocess is also considered in this thesis.
The search for these two processes is the main target in this thesis. Since the χ̃10 in Figures 1.12 cannot
be detected in any detectors, an observed event topology is multiple jets and large missing transverse
momentum.

18

1.5 Target SUSY particles√
Figure 1.10: The production cross section in SUSY particles at proton-proton collider at s = 13 TeV [37].
The calculation includes in the resummation of soft gluon emission at the next-to-leading logarithmic accuracy.

q

g

g̃

q
q̃

q̄

g

g̃

g

g̃

q̄

g̃

g̃

g

g̃
g̃

g

g̃

g

g̃

Figure 1.11: Feynmann diagrams of gluino pair production in the LHC.

19

Introduction

q

q
q

p
g̃

p
g̃

χ̃01
χ̃01

g̃
p

q

p

g̃

χ̃±
1
χ̃∓
1

χ̃01
W∓

q

q
(a)

q̄ 0
W± p
χ̃01

(b)

q̄

p

q

q
Z

g̃

χ̃01

χ̃02
χ̃02

g̃

χ̃01
Z

0

q

q

(c)

Figure 1.12: The decay topologies of gluino pair production with (a) direct decays and (b,c) one-step decay.

1.6 Strategy of gluino search
In the previous result of gluino search in final states without leptons at the ATLAS [34], morethan 25 signal regions are prepared in order to search for all gluino mass points. Each signal region
is determined applying cuts on discriminating variables such as the transverse momentum of jets or
missing transverse momentum. The search for higher gluino mass becomes more difficult because
the production of the cross section is smaller as the gluino mass is higher: the number of events issmall. The sensitivity is not significantly improved if this conventional approach is used. Hence, newapproach instead of the conventional approach would be needed for the gluino search.
In this thesis, a machine learning approach is introduced. It can improve the separation between
signals and SM backgrounds using correlations of variables. Since the correlations are not considered
explicitly in the previous result, it allows the sensitivities to be improved well. The machine learning
approach has mainly two difficulties. The kinematics of signal processes depends on SUSY masses
which will be explained in Section 3.3, so the determination of training samples considering
kinematics is very crucial; the choice to improve the sensitivities of all mass points is required. This is
first difficulty to use the machine learning in SUSY search. Second, the estimation of background ismore complicated than the conventional approach because the machine learning approach utilizes
correlations. The development of the background estimation considering the correlations is needed toapply the machine learning to data. Solutions of these difficulties are given in this thesis.

This thesis is organized as follows. Chapter 2 provides the overview of the experiment in thisanalysis. Chapter 3 explains the overview of dataset and simulation used in this analysis. Chapter 4
describes the reconstruction of objects such as jet, electron, muon or missing transverse momentum.
Chapter 5 describes the analysis using the machine learning in detail. Chapter 6 describes the
background estimation in detail. Chapter 7 describes the validation of the machine learning approach.
Chapter 8 describes the statistical treatment in this analysis. Chapter 9 provides the result anddiscussion.

20

2 LHC-ATLAS experiment
2.1 Large Hadron Collider (LHC)The LHC [38] is a particle accelerator of about 27 km-circumference. It is located undergroundbetween 50 m and 175 m depth from the surface in Geneva area. Figure 2.1 shows overview of theaccelerator. In order to obtain accelerated protons, hydrogen atoms are first ionized. Then, the protons
with 50 MeV are injected in the linear accelerator (LINAC 2). Then, they are accelerated to 1.4
GeV with the BOOSTER, Proton Synchrotron (PS) and Super Proton Synchrotron (SPS). Finally, theaccelerated protons are injected in the LHC main ring. It is possible to perform direct searches for
new physics at the TeV scale. In the LHC, there are four main experiments: ATLAS (A Toroidal LHC
Apparatus) [39], CMS (Compact Muon Solenoid) [40], LHCb (Large Hadron Collider beauty) [41]and ALICE (A Large Ion Collider Experiment) [42]. The ATLAS and CMS experiments perform
proton-proton (pp) collisions in the LHC.

Figure 2.1: The schematic view of the CERN accelerator complex [43].

21

LHC-ATLAS experiment
The LHC ATLAS Run 1 experiment performed pp collisions from 2010 to 2012. Its center-of-mass√√energy is s = 7, 8 TeV. The ATLAS detector has been recorded about 5 fb−1 for s = 7 TeV and 20√
fb−1 for s = 8 TeV after requiring the data quality. The LHC ATLAS Run 2 experiment performed√
pp collisions from 2015 to 2018. Its center-of-mass energy is s = 13 TeV. The ATLAS detector has
been recorded 147 fb−1 and then data of 139 fb−1 is used for physics analysis after requiring the data
quality as shown in Figure 2.2.

Figure 2.2: The integrated luminosity delivered to LHC (green) and ATLAS (yellow) at Run 2 experiment [44].
The blue shows the integrated luminosity after requiring the data quality and the data is used in an offline
analysis.

In case of pp collision in LHC, the instantaneous luminosity is expressed as:L=frev nb Nb 2 γrF
4π βx,y(2.1)

where frev is the revolution frequency, nb is the number of bunches per revolution, Nb is the numberof protons per bunch,  is the initial geometric rms emittance, βx,y is the beam size in x-y plane and
F is the geometric luminosity reduction factor. The overview of these parameters for each year isshown in Table 2.1.
Under the condition, a pileup is observed. The pileup is categorized to two types: in-time pileup
and out-of-time pileup. The in-time pileup is caused by pp interactions in the same bunch crossing due
to the dense proton bunches as shown in Table 2.1. In the LHC, the mean number of pp interactions
per bunch crossing (µ) is 10-70 as shown in Figure 2.3 and many events with in-time pileup is
occurred. The out-of-time pileup is caused by pp interactions in the different bunch crossing due tohigh frequency of collisions as shown in Table 2.1.

22

2.2 ATLAS detector√
Table 2.1: Parameters for pp collisions at s = 13 TeV in 2015-2018 [45]. In 2017 run, the LHC runs with two
conditions (nb = 2544, Nb = 1.1 × 1011 and nb = 1909, Nb = 1.2 × 1011 )Parameter
frev [Hz]nb
Nb (1011 protons)
 [m]β x,y [µm]
F

2015
11253
2232
1.1
0.3
0.8
0.94

2016
2017
11253
11253
2208 2544/1909
1.1
1.1/1.2
0.3
0.3
0.4
0.3
0.94
0.94

2018
11253
2544
1.1
0.3
0.3-0.25
0.94

Figure 2.3: Mean number of pp interactions per bunch crossing in 2015-2018 period [44].

2.2 ATLAS detector
The ATLAS detector [39] is a general purpose detector with a symmetric cylindrical geometry on
the LHC ring. It covers nearly covered 4π steradian of solid angle and has 44 m in length, 25 m inheight and 7000 tons in weight.
The ATLAS uses a right-handed coordinate system with its origin at the nominal interaction pointin the center of the detector. The positive x-axis is defined by the direction from the interaction
point to the center of the LHC ring, with the positive y-axis pointing upwards. The z-axis is definedby the beam direction. Cylindrical coordinates (r, φ) are used in the transverse plane, φ being theazimuthal angle around the z-axis. The pseudorapidity η is defined as η = − ln tan(θ/2), where θ isthe polar angle. The rapidity y is defined as y = (1/2) ln[(E + pZ )/(E − pZ )], where E is the energy
and pZ is the longitudinal momentum. The transverse momentum pT = psinθ and transverse energy

23

LHC-ATLAS experiment
ET = Esinθ are defined in the x-y plane.
The ATLAS detector mainly consists of three subdetectors as shown in Figure 2.4: inner detector,
calorimeter and muon spectrometer. In the following subsections, each subdetector is introduced.

Figure 2.4: Overview of the ATLAS detector[39].

2.2.1 Inner detector
The inner detector (ID) consists of pixel, silicon microstrip and transition radiation tracker (TRT),
which cover the pseudorapidity region |η| < 2.5 as shown in Figure 2.5. The aim of this subdetector isto reconstruct a track of charged particles and measure the transverse momentum (pT ).
Silicon pixel detector (Pixel)
Pixel detector has four layer structure and is the closest to the interaction point. The layers except
the innermost layer, which is called the insertable B-layer (IBL), cover the region |η| < 2.5 [47, 48].
They are segmented in R-φ and z direction. All pixel sensors have 400 × 50 µm2 in R-φ × z. The IBL
is newly introduced since Run 2 experiment and has 250×50 µm2 pixel sensors.
Semiconductor Tracker (SCT)SCT detector has four layer structures at the outside of the Pixel detector. The sensors are segmented
into strips a pitch of 80 µm. In order to obtain two dimensional information, two strip layers areclosely laid at 40 mrad stereo angle.

242.2 ATLAS detector

Figure 2.5: Overview of the inner detector [46].

Transition Radiation Tracker (TRT)TRT detector [49] has a structure of straw drift tubes, which is about 150 cm long at the outside of
the SCT detector. The radius of the tube is about 4 mm and operated with a gas mixture of Xe, O2
and CO2 . This gas is ionized by incident charged particles and the ionized electrons are measured.
This effect depends on the relativistic factor γ = E/m, so this detector can provide an identification
between electron and charged pion.

2.2.2 Calorimeter
There are two calorimeters in the ATLAS detector as shown in Figure 2.6: electromagnetic (EM)calorimeter for an electron and a photon and hadronic calorimeter for a hadron. These calorimeters
cover with the range |η| < 4.9.
Electromagnetic calorimeter (EM calorimeter)
The electromagnetic calorimeter is a sampling calorimeter with lead absorber and liquid argon (LAr)detector. The detector covers the range |η| ≤ 3.2. The accordion structure is adopted in order to becontinuous in azimuth direction. When an electron or a photon goes through the detector, the leadabsorber induces an EM shower, which is a cascade of secondary particles. This EM shower ionizes
in the LAr detector and then the ionized particles are measured. The number of ionized particles is
proportional to the total energy of the incident particle.
The LAr calorimeter has four layer structures as shown in Figure 2.7. They are called presampler,
front, middle and back layers, which are segmented in pseudorapidity η and azimuth φ directions.

25

LHC-ATLAS experiment

Figure 2.6: Overview of the calorimeter [50].

The presampler layers cover the range |η| ≤ 1.8 and perform to correct the energy lost in front of
the calorimeter. The front layer has a finer granularity in η directions (∆η = 0.0031) to allow for
the identification between a single photon and a π 0 (→ γγ). The middle layer is the main sampling
one to measure the energy. The back layer is needed to reconstruct a high energy electron or
photon (ET > 50 GeV), which traverses the outside of the middle layers.

Hadronic calorimeter
The hadron calorimeter consists of the Tile Calorimeter (TileCal), the Hadronic End-cap
Calorimeter (HCAL) and the Forward Calorimter (FCAL), which are also sampling calorimeters.
The TileCal covers the region |η| ≤ 1.7 and has three layers with the iron absorber and the plastic
scintillator detector. The HCAL covers the region 1.7 ≤ |η| ≤ 3.2 and has four layers with the copper
absorber and the LAr detector. The FCAL covers the region 3.2 ≤ |η| ≤ 4.9 and has three layers; The
front layer uses the copper absorber and the second and the third layers use the tungsten absorber.
Since the FCAL is close to the beam pipe, the straw tube structures instead of the accordion structures
are adopted.

2.2.3 Muon Spectrometer
The muon spectrometer (MS) is used to measure the momentum and position of muons, whichpass through the calorimeters. The MS is the outermost subdetectors and consists of Monitored
Drift Tube (MDT), Cathod Strip Chamber (CSC), Resistive Plate Chamber (RPC) and Thin Gap

26

2.2 ATLAS detector

Figure 2.7: The structure of the LAr calorimeter at η = 0 region [50].

Chamber (TGC). The MDT and CSC are used for precision measurements of muons. The RPC and
TGC are used for triggering muons.

Monitored Drift Tube (MDT)The MDT has three layers, which consist of drift tubes and covers the region η ≤ 2.0. The drift
tubes have 30 mm diameter and use a mixture of Ar and CO2 . The position resolution is about 80µm.

Cathod Strip Chamber (CSC)

The CSC uses multi-wire proportional chambers (MWPC) and covers the region 2.0 ≤ |η| ≤ 2.7.
They can be operated under a high occupancy. The position resolution is about 60 µm.

27LHC-ATLAS experiment
Resistive Plate Chamber (RPC)
The RPC covers the region |η| ≤ 1.05 and consists of 2 mm gas gap with parallel electrode plates.
The time resolution is about 2.0 ns and position resolution is about 10 mm.
Thin Gap Chamber (TGC)
The TGC uses the MWPC with a gas mixture of CO2 :n-C5 H12 and covers the region 1.05 ≤ |η| ≤ 2.4.
Since the width of the anode wire is about 1.8 mm, the better time resolution is obtained (4 ns). The
position resolution is about 5 mm.

2.3 Trigger and Data Acquisition system
In the Run 2 experiment, the pp collisions are occurred at 40 MHz. Since all the events cannot berecorded, the trigger system, which judges whether each event should be recorded or not, is required.
The ATLAS has two trigger systems as shown in Figure 2.8: the First Level Trigger (L1 trigger) andthe High Level Trigger (HLT) [51–54].
The information of detectors are first buffered in the Readout Drivers (ROD) to wait the judgmentof the L1 trigger. The L1 trigger uses the information of calorimeters and muon spectrometers. In
order to process the judgment quickly, the hardware-based trigger is adopted as the L1 trigger. The
event rate is reduced from 40 MHz to 100 kHz in a limited and fixed latency of 2.5 µs. An event
accepted by L1 is processed in the ROD and then buffered in the Read Out System (ROS) to wait the
HLT accept. The HLT is a software-based trigger so that it can perform similar selections to an offline
data analysis. The HLT would recover the objects, which are not identified in the L1 trigger, by using
the whole detectors. The event rate with HLT accepts is about 1 kHz and the event is transmitted tothe data storage for an offline process system.

28

2.3 Trigger and Data Acquisition system

Figure 2.8: The flow of the trigger system in the Run 2 experiment [51].

29

3 Dataset and Monte-Calro sample
3.1 Dataset√
This analysis uses data collected in 2015-2018 at s = 13 TeV and 25 ns collision rate. The
corresponding integrated luminosities with beam and detector data-quality requirements [44] aresummarized in Table 3.1. The total integrated luminosity is 139 fb−1 . The uncertainty in the combined
2015–2018 integrated luminosity is 1.7 % [55], obtained using the LUCID-2 detector [45] for the
luminosity measurements.
Table 3.1: Summary of integrated luminosities for each period.

period
2015
2016
2017
2018
Total

integrated luminosity [fb−1 ]
3.22
33.0
44.3
58.5
139

3.2 Trigger
Since SUSY signal events in this analysis have large missing transverse momentum, the missing
transverse momentum is mainly used for triggering data. In order to maximize data statistics, the lowest
unprescaled triggers (ETmiss trigger) in each data taking period are used as shown in Table 3.2 [51–54].
Each data taking period has the different pileup condition as shown in Figure 2.3, so the thresholdof ETmiss triggers is changed in order to keep the same trigger rate. In addition, the electron, muonand photon triggers are used for a background estimation as discussed in Chapter 6. The single
lepton (photon) trigger selects the event with at least one electron or muon (photon) satisfying the pT
threshold as shown in Table 3.3 [51–54].
In order to measure the ETmiss trigger efficiency, the tag and probe method with W → µν event isused. First, events with a single muon, which has the single lepton triggers as shown in Table 3.3, areselected. Then, the transverse mass (mT ) cut with 30 GeV < mT < 100 GeV is applied in order toenhance the purity of W boson events. The remaining events are called "tag" events. The transverse
mass is defined as:q
mT = 2p`T ETmiss (1 − cos[∆φ(`, ETmiss )])
(3.1)

31

Dataset and Monte-calro sample

Table 3.2: Summary of ETmiss triggers used in this analysis.

Year
2015
2016
2016
2016
2017
2017
2017
2018
2018

Period
All
A-D3
D4-F1
F2B
C
DB
C-

L1 threshold
50 GeV
50 GeV
50 GeV
50 GeV
50 GeV
50 GeV
50 GeV
50 GeV
50 GeVHLT threshold
70 GeV90 GeV
100 GeV110 GeV90 GeV
100 GeV110 GeV110 GeV110 GeV

Table 3.3: Summary of single lepton (e, µ) and photon (γ) triggers used in this analysis.

Year
2015
2016 - 2018

HLT threshold (e)26 GeV
26 GeVHLT threshold (µ)
20 GeV
24 GeVHLT threshold (γ)
120 GeV140 GeV

where pT ` is the transverse momentum of the lepton, ∆φ(`, ETmiss ) is the angular difference between
the lepton and ETmiss . Finally, it is checked whether the tag events pass the ETmiss triggers or not,depending on the reconstructed ETmiss , which is called "Probe". Figures 3.1 show the trigger efficiency
as a function of ETmiss for each period using the tag and probe method. Since the muon momentum
is not considered in L1 ETmiss trigger, the L1 ETmiss trigger can be emulated by subtracting muon
contribution in offline ETmiss calculation. The efficiency of the ETmiss trigger is more increased as theETmiss is larger and the efficiency reaches to 100% above 300 GeV. In this analysis, ETmiss > 300 GeV isrequired as the preselection, so that the passed events are not biased due to the triggers; no corrections
are needed.

32

3.3 Monte-Carlo sample

Figure 3.1: Trigger efficiencies as a function of offline ETmiss after subtracting the muon momentum in2015 (left-top), 2016 (right-top), 2017 data (left-bottom) and 2018 (right-bottom). The lepton veto, a leading
jet with pT > 200 GeV, a second leading jet with pT > 100 GeV and ∆φ( j1,2,(3), ETmiss ) min > 0.4 selections,which are defined in Section 5.4, are applied.

3.3 Monte-Carlo sample
This analysis uses simulated samples, which are generated by Monte-Carlo (MC) method, in orderto evaluate signal and background processes and to compute with the data. They are called MC
samples in this thesis.

3.3.1 Background MC sample
Events of W/Z bosons associated with jets are simulated using Sherpa 2.2.1 generator, whereas
γ+jets events are simulated with Sherpa 2.2.2 generator [56]. Matrix elements are calculated for up
to two partons at next-to-leading order (NLO) and four partons at leading order (LO) [57, 58] using
the Comix [59] and OpenLoops [60, 61] matrix element generators. Then, they are merged with the
Sherpa parton shower [62] using Meps@NLOprescription [58, 63–65]. The NNPDF3.0NNLO setof parton distribution functions (PDFs) [58] is used in the Sherpa parton shower. The W/Z boson
samples are normalized to the cross section at next-to-next-to-leading order (NNLO) prediction [57].
The γ+jets samples are normalized to the cross section at next-to-leading order (NLO) prediction.

33

Dataset and Monte-calro sample
For the generation of t t¯ events, the Powheg-box [66–69] v2 generator is used at NLO with
NNPDF3.0NLO set of PDFs [58]. In the ATLAS, a hdamp parameter in Powheg-box [70, 71]
is set to 1.5 times the mass of the top quark (mtop = 172.5 GeV). The events are interfaced withPythia 8.230 [72] using the A14 tune [73] and the NNPDF2.3LO set of PDFs in order to model
the underlying event, parton showering and fragmentation. The samples are normalized to the crosssection prediction at next-to-next-to-leading order (NNLO) in QCD including the resummation of
next-to-next-to-leading logarithmic (NNLL) soft-gluon terms calculated using TOP++2.0 [74–80].
For the generation of single-top processes in the Wt, s and t-channels, the Powheg-box [67–69, 81] v2
generator is used at NLO with NNPDF3.0NLO set of PDFs [58]. The events are interfaced withPythia 8.230 [72] using the A14 tune [73] and the NNPDF2.3LO set of PDFs. The samples in Wt,
s-channels are normalized to the cross section at NLO+NNLL prediction. The samples in s-channels
are normalized to the cross section NLO prediction. For the generation of t t¯ in association withelectroweak boson (t t¯+W/Z) or Higgs boson and four-top events, the Madgraph_aMC@NLO 2.3.3
generator [82] at NLO with the NNPDF3.0NLO [58] set of PDFs. The samples are normalized
to the cross section prediction at NLO prediction. The events are interfaced with Pythia 8.210
parton-shower model, with up to two extra partons included in the matrix element. For these processes,
the top quarks are decayed using MadSpin [83, 84] to preserve spin correlations. The properties ofthe bottom and charm hadron decays are simulated using the EvtGen v1.2.0 program [85].

Diboson processes (WW, W Z, Z Z, W γ, Zγ) are simulated using the Sherpa 2.2.1 [56] generator
with NNPDF3.0PDF set [58]. Matrix elements are calculated for no or one parton at NLO and up to
three partons at LO using the Comix and OpenLoops matrix element generators and merged with
the Sherpa parton shower [62]. The samples are normalized to the cross section prediction at NLO
prediction.

A summary of all background MC samples used in this analysis is listed in Table 3.4.
Table 3.4: All background MC samples used in this analysis. The generators, the order in αs of cross-section
calculations used for yield normalization, PDF sets for the parton shower, parton showers and tunes used for theunderlying event are shown.
Physics process

Generator

Cross-section
normalization

PDF setParton shower

Tune

W (→ `ν) + jets
¯ + jetsZ/γ ∗ (→ ` `)γ + jetst t̄
Single top (W t-channel)
Single top (s-channel)
Single top (t-channel)t t̄ + W /Z/Ht t̄ + WW
WW , W Z, Z Z, Wγ, Zγ

Sherpa 2.2.1
Sherpa 2.2.1
Sherpa 2.2.2
Powheg-box v2
Powheg-box v2
Powheg-box v2
Powheg-box v2
Madgraph_aMC@NLO 2.2.3
Madgraph_aMC@NLO 2.2.2
Sherpa 2.2.1

NNLO
NNLO
NLO
NNLO+NNLL
NNLO+NNLL
NLO
NLO
NLO
NLO
NLO

NNPDF3.0NNLO
NNPDF3.0NNLO
NNPDF3.0NNLO
NNPDF2.3NLO
NNPDF2.3LO
NNPDF2.3LO
NNPDF2.3LO
NNPDF2.3LO
NNPDF2.3LO
NNPDF3.0NNLO

SherpaSherpaSherpaPythia 8.230
Pythia 8.230
Pythia 8.230
Pythia 8.230
Pythia 8.210
Pythia 8.210
SherpaSherpaSherpaSherpa
A14
A14
A14
A14
A14
A14
Sherpa34

3.3 Monte-Carlo sample

3.3.2 Signal MC sample
Masses of SUSY particles are needed to prepare signal MC samples and determined from morethan 100 parameters in the SUSY. However, most of parameters do not affect kinematics of the signal
SUSY processes because the kinematics is mainly determined by the SUSY mass spectra. The signal
MC samples are generated depending on the SUSY masses, but there are still several parameters. In
order to reduce the parameters, a simplified model [86–88] are used in the SUSY search. This model
assumes that the masses of all SUSY particles are set to large values except the few SUSY particles
involved in the decay chain of interest. It means only one decay chain of interest is considered andall other decay chains are ignored. In this case, the kinematics of the signal SUSY processes is only
determined by the production of particle masses and cross sections and the model can be described bya few parameters, which is the benefit of simplified models.
Two processes of gluino direct decay and gluino one-step decay as described in Section 1.5 are
generated as signal MC samples.
Gluino direct decay The process is simulated using the Madgraph_aMC@NLO 2.2.3
generator [82] at NLO and interfaced with Pythia 8.230. In order to focus on the decay chain,gluino and lightest neutralino are only considered: other sparticles are assumed to be decoupled. The
0composition of the χ̃1 is assumed to be purely bino. The signal MC samples are generated per agluino and neutralino mass. Figure 3.2(a) shows the generated MC sample for gluino direct decay
process. 143 signal points are generated in total 1 . Since four flavour squarks (ũ, d,˜ c̃, s̃) are nearly
degenerated in the MSSM, the quarks in final states assume to be light-flavour quarks (u, d, c, s).
Gluino one-step decay The process is simulated using the Madgraph_aMC@NLO 2.2.3 generator
at NLO and interfaced with Pythia 8.230. In order to focus on the decay chain, gluino, chargino
and lightest neutralino are only considered for gluino one-step decay via W boson ( χ̃1± →W ± χ̃10 )and gluino, neutralino and lightest neutralino are only considered for gluino one-step decay via Z
0boson ( χ̃20 →Z χ̃10 ): other sparticles are assumed to be decoupled. The composition of χ̃1 ( χ̃1±, χ̃20 ) is
assumed to be purely bino (wino). This thesis considers the following mass spectra for gluino one-step
decay.
• Primary model: the chargino mass (neutralino) is fixed at m χ̃1± = (mg̃ + m χ̃0 )/2 (m χ̃0 =1
2(mg̃ + m χ̃0 )/2).
1• Secondary model: the neutralino mass is fixed at 60 GeV (m χ̃0 ∼ mh /2) in order to explain the1relic density, while avoiding all the current constraints [89].
Figures 3.2(b) and 3.2(c) shows the generated MC sample for gluino one-step decay process. 73 signal
points for primary model and 78 signal points for secondary model are generated in total 2 . Since four
flavour squarks (ũ, d,˜ c̃, s̃) are nearly degenerated in the MSSM, the quarks in final states assume to belight-flavour quarks (u, d, c, s).
1 There are no signal points with a region where the gluino mass is below 1800 GeV and the neutralino mass is below 500

GeV, but the region is already excluded in the previous result of gluino search [34].
2 The secondary model is only considered for gluino one-step decay via W boson in this thesis.

35

1

Number of generated points: 143

2000

1600

1

1800

1400

1200

1200

1000

1000

800

800

600

600

400

400

200

2

1

1

2

1

Number of generated points: 72

1600

1400

0

0
± 0
0 0
± 0
~
g~
g production, B (~g → qq ∼χ /∼χ → qq W±/Z ∼χ )=100%, m(∼χ /∼χ )=(m(~g) + m(∼χ ))/2

0

1800

0
~
g~
g production, B (~g → qq ∼χ )=100%1m(∼χ ) [GeV]

20000∼1) [GeV]m(χDataset and Monte-calro sample

200
600

800

1000

1200

1400

1600

1800

2000

2200

0

2400 2600m(~g) [GeV]

600

800

1000

1200

1

0
0

1800

2000

2200

2400 2600m(~g) [GeV]

1.4~∼± → qq W± χ∼0)=100%, m(χ∼0)=60 GeVg~
g production, B (~g → qq χ1

1

1

Number of generated points: 78
1.2

1
1

±

1600

(b)

~, χ
∼,χ
∼ )/∆ m(g∼)
x=∆ m(χ

(a)

1400

1
0.8
0.6
0.4
0.2
0
1200

1400

1600

1800

2000

2200

2400
2600
m(~
g) [GeV](c)
Figure 3.2: Generated MC signal points in the neutralino mass versus gluino mass for the gluino direct
decay (top-left), gluino one-step decay with primary model (top-right) and gluino one-step decay with secondarymodel (bottom) on a simplified model.

In addition to these two processes, three signal MC samples are generated to evaluate the sensitivity
discussed in Section 9.3. First, the gluino direct decay with heavy flavour (b or t) as shown in
Figures 3.3 are considered. The processes are generated with the same generator as gluino direct decay.
00144 signal points for g̃ →bb χ̃1 and 152 signal points for g̃ →tt χ̃1 are generated in total. Next, themodels with inclusive production of squarks and gluinos are considered. Figures 3.4 show the decay
topologies in the models. There are three productions in the models: gluino pair production, squarkand gluino production and squark pair production. The cross section of each production depends
on the squark and gluino masses. For simplicity, the neutralino mass is fixed to 0 GeV and gluino
and squark masses are varied. All other supersymmetric particles, including the squarks of the third
generation, have set to their masses, so the particles are effectively decoupled from the squarks, gluinos
and lightest neutralinos. The processes are generated under the same generator as gluino direct decay.
42 signal points are generated in total.

3.3.3 Detector and pileup simulation
All background MC samples are passed through full ATLAS detector simulation [90] using
Geant4 [91], while SUSY signal samples are passed through a fast simulation [92], which uses a
parameterized simulation for response of the calorimeter systems. The generation of the simulated36

3.3 Monte-Carlo sample

b̄

t̄
p

p

t
g̃

g̃

χ̃01
χ̃01

g̃
p

b
χ̃01
χ̃01

g̃
p

t

b
b̄

t̄

Figure 3.3: The decay topologies of gluino pair production with direct decays via t quarks (left) and b
quarks (right).

q

q

q

p
g̃

p

χ̃01

χ̃01

χ̃01

g̃
p

q

χ̃01

q̃
g̃

q

p

q

q

q
p
q̃

χ̃01

q̃

χ̃01

p
q
Figure 3.4: The decay topologies of the models with inclusive production of squarks and gluino for direct
decays. There are three productions in the models: gluino pair production (top-left), squark and gluino
production (top-right) and squark pair production (bottom). The cross section of each production depends on
the squark and gluino masses.

37

Dataset and Monte-calro sample
event samples includes the effect of multiple pp interactions per bunch crossing, as well as the effecton the detector response due to pileup events. Then, reconstruction algorithms used for the data, which
will be explained in Chapter 4 are applied to the MC samples. Finally, the generated MC samples
are reweighted to match the observed pileup distribution. Then, a scale factor (1/0.99) is applied
to MC samples to realize the observed mean number of pp interactions per bunch crossing (hµi).
However, the number of primary vertex (NPV ) distribution in data is not described by the MC samples
in this case. If the scale factor (1/1.07) is applied to MC samples, an agreement of number of primaryvertex distribution is observed. In order to take into account both distributions (NPV and hµi), thescale factor (1./1.03), which is the middle value of them is applied to MC samples as a nominal. The
up-type (down-type) scale factor is 1/1.07 (1/0.99).

38

4 Object reconstruction and identification
This analysis uses electrons, muons, photons, jets and missing transverse momenta. This chapter
describes their reconstruction, identification and calibration from the information of the ATLAS
detector described in Section 2.2.

4.1 Charged tracks
When charged particles traverse the inner detectors, energy is deposited as hits on different layers
in the pixel and silicon detectors. In order to reconstruct tracks there are three steps. First, clusters
from the raw measurements in pixel and SCT detectors are assembled from hits using a connectedcomponent analysis [93]. Then, three-dimensional measurements referred to space-points are createdfrom these clusters and seed tracks are formed from three space-points. Finally, track candidates
are built from the seed tracks by performing a Kalman filter [94]. After applying this filter, highefficiencies of the track reconstruction are obtained. However, some track candidates have overlapping
space-points or are incorrectly assigned. Hence, a track score is calculated by considering clusters
assigned to a track in each track candidate. Track candidates with bad track scores are rejected. The
detail of track reconstruction is found in Ref. [95].
From these tracks, vertices are reconstructed using a vertex finding algorithm [96]. This vertex
finding algorithm is iterated until all tracks are associated to vertices, which have at least two tracks.
Then, the sum of transverse momentum of tracks is calculated per vertex and the vertex with thelargest value is used as a primary vertex (PV), which is considered as the vertex of hard scatter.

4.2 Jet4.2.1 Reconstruction
In order to reconstruct jets, the clusters of calorimeters cells are needed. A cell with the mostsignificant energy deposit is the start of cluster reconstruction (seed cell). Then, clusters are formed togather neighbor cells to the seed cell. They are called "topo-clusters" [97].
Jets are reconstructed using an anti-k t jet clustering algorithm [98, 99], which performs
four-momentum recombination of the topo-clusters. The algorithm combines two topo-clusters
based on the distance, di, j , which is defined as−2 ∆Ri, j
di, j = min(pT −2
i , pT j )
2

r

2

(4.1)

39

Object reconstruction and identification
where pT i is the transverse energy of topo-clusters with index i and r is the distance parameter, which
is set to r = 0.4 in this analysis. ∆Ri, j is the distance in η-φ plane defined as∆Ri, j =q(ηi − η j )2 + (φi − φ j )2 .

(4.2)

The anti-k T jet algorithm first calculates the smallest di, j and di,B = pT −2
i . Then, the two topo-clusters
are merged into one cluster if di, j is smaller than di,B and recalculates di, j and di,B . This iteration
continues until di,B becomes the smallest. Figure 4.1 shows the overview of a sample parton-level
event clustered with anti-k t jet clustering algorithm. For this algorithm, the topology of hard jets is
circular with the distance parameter.

Figure 4.1: Example of a sample parton-level event clustered with anti-k t jet clustering algorithm with the
distance parameter R = 1.0 [98].

4.2.2 Calibration
The energy measured in the calorimeters is calibrated in EM scale, which measures the energy
deposited in the calorimeter by particles produced in electromagnetic showers. Since reconstructedjets contain components of the hadronic interaction, an additional calibration should be performed toobtain their proper energy. It is called jet energy scale (JES) calibration [100]. A series of calibrations
is derived from MC simulation and data as shown in Figure 4.2. The details of each calibration stage
are explained below.
Origin correction
The four-momentum of jets is defined with respect to a center of the detector. The "origin
correction" recalculates their four-momentum to point to a hard scatter vertex keeping the jet energy.
This correction improves the η resolution of jets: the difference between reconstructed jets and truth
jets would be small.

40

4.2 Jet

Figure 4.2: Calibration stages for jets measured in the calorimeters [100]. Corrections except "Residual in situ
calibration" are performed using MC simulation. The Residual in situ calibration is performed using the data.

Pileup corrections: Jet area-based pileup correction
The contributions of in-time and out-time pileup are removed using two corrections: jet area-based
correction and residual pileup correction. The jet area-based correction subtracts pileup contributions
event by event. The residual pileup correction subtracts pileup contributions using the number ofreconstructed primary vertex (NPV ) and the average number of interactions per bunch crossings (µpileup ).
The momenta corrected by two corrections (pT reco ) are expressed as:
pT corr = pT reco − ρ × A − α × (NPV − 1) − β × µpileup(4.3)

where pT reco is transverse momentum of a reconstructed jet before pileup corrections and ρ is themean of transverse momentum density of jets in the η-φ plane. A is jet area calculated using ghost
association [101]. The α and β parameters depend on the truth jet pT and η in MC simulation and aredetermined by linear fits.
Absolute MC-based calibration
Since the ATLAS detector has the inactive region such as the transition between calorimeters,reconstructed jets are biased; there is a difference between reconstructed jets and truth jets. The"absolute MC-based calibration" accounts the bias and corrects the four-momentum of jets using MC
sample. The bias is corrected using an average energy response in MC simulation. It is defined as theratio of reconstructed jets and truth jets (ETreco /ETtruth ). The difference between reconstructed jets andtruth jets is appeared in the detector gap and transitions between calorimeters as shown in Figure 4.3(a).
The η bias of jets is also corrected using the relative difference as a function of reconstructed jet |η| asshown in Figure 4.3(b).
Global sequential calibration
Even though the calibrations described above have been applied, the residual dependencies of thejet energy scale on longitudinal and transverse features of the jets are still observed. They are related

41

Object reconstruction and identification

(a)

(b)

Figure 4.3: (a) Average energy response as a function of reconstructed jet η for jets of ETtruth = 30, 60, 110, 400
and 1200 GeV [100]. (b) Relative difference between truth jet ηtruth and reconstructed jet ηreco as a function ofreconstructed jet |ηdet | [100].

to the particle composition and the shower shape of a jet. In order to correct such differences, thecorrection for five independent observables are sequentially applied to the jets: fTile0 , fLAr3 , ntrk , Wtrk
and nsegments . fTile0 is the fraction of jet energy measured in the first layer of the Tile calorimeter. fLAr3
is the fraction of jet energy measured in the third layer of the LAr calorimeter. ntrk is the number oftracks with pT >1 GeV in the jet. Wtrk is the average pT -weighted transverse distance in η-φ plane
between the jet axis and all tracks with pT >1 GeV. nsegments is the number of muon track segments inthe jet. Figures 4.4 show an average transverse momentum response in MC simulation. It is definedtruth
as the ratio of reconstructed jets and truth jets (preco
T /pT ). Small deviations in these variables areobserved, so the calibration is applied to correct the deviations. This procedure is called "Global
sequential calibration".

In situ calibration

Since MC simulation does not describe the detector response perfectly, there are differences between
data and simulation. "In situ calibration" corrects the differences. Difference between data and MC
simulation is quantified by balancing the pT of a jet against other well-measured reference objects
such as Z boson, photon and multi-jet.

Systematic uncertainty in calibration

The final calibration includes more than 100 systematic uncertainties on the energy scale andresolution. All systematic uncertainties are listed in Ref [100]. The majority of uncertainties comefrom in situ calibrations as shown in Figure 4.5.

42

4.2 Jet

Fractional JES uncertainty

Figure 4.4: The average transverse momentum response as a function of the five independent observables forthree ranges of the transverse momentum of truth jet: (a) fTile0 , (b) fLAr3 , (c)ntrk , (d)Wtrk and (e)nsegments [100].

0.1

0.08

ATLAS Preliminary

Data 2015-2017, s = 13 TeV
anti-k t R = 0.4, EM+JES
jet
p = 60 GeV

Total uncertainty
Absolute in situ JES
Relative in situ JES
Flav. composition, inclusive jets
Flav. response, inclusive jets
Pile-up, average 2015-2017 conditions
Punch-through, average 2015-2017 conditions

T

0.06

0.04

0.02

0

−4

−3

−2

−1

0

1

2

3

4
η

(a)

(b)

Figure 4.5: Fractional jet energy scale uncertainty components as a function of transverse momentum of jets at
η=0.0 (a) and η of jets at pT =60 GeV (b) [102].

43

Object reconstruction and identification

4.2.3 Jet Vertex Tagging
The subtraction of pileup jets, which does not come from the primary vertex, is crucial to focus
on only a hard scatter event. In order to suppress the contribution of pileup jets, two variables are
introduced: a corrected Jet Vertex Fraction (corr.JVF) and RpT [103]. The corr.JVF variable is definedasÍ
trk k (PV )
0
k pT
(4.4)
corr.JVF = Í
Í
Í
PU )
trk
trk
i
(PV0 ) + n≥1 k pT k (PVn )/(κ · nntrk
i pTÍwhere k pT trkk (PV0 ) is the scalar pT sum of the tracks, which are associated with a jets in all hardÍÍscatter event (PV) [103]. The term n≥1 k pT trkk (PVn ) is the scalar pT sum of the associated tracks
originating from any of the pileup interactions. This term depends on the total number of pileup tracks
PU and thus the factor κ · nPU with κ = 0.01 are applied. The R
ntrk
pT is defined as
ntrk
RpT =

Í

trk k (PV )0pT jet

k pT

(4.5)

where pT jet is the fully calibrated jet pT [103].
Figures 4.6 show the distributions of these two variables for hard scatter and pileup jets with 20 <pT < 30 GeV. In order to utilize these variables, the Jet Vertex Tagger (JVT), which combines them bya multivariate techniques, is made. The JVT has the strong separation power between the hard scatterand pileup jets as shown in Figure 4.7. In this analysis, the JVT cut is applied to all jets:• JVT>0.59 with pT <120 GeV and |η| <2.4
• JVT>0.11 with jet pT <120 GeV and 2.4< |η| <2.5.

(a)

(b)

Figure 4.6: Distributions of corr.JVF (a) and RpT (b) for hard scatter and pileup jets with 20 < pT < 30
GeV [103].

44

4.2 Jet

Figure 4.7: Distribution of JVT for hard scatter and pileup jets with 20 < pT < 30 GeV [103].

4.2.4 Flavor Tagging
Jets containing b-hadrons can be identified by a b-tagging algorithm, which uses the tracks ofcharged particles [104, 105]. There are three sub-algorithms to identify b-jets in the ATLAS: theimpact parameter based algorithm, the inclusive secondary vertex reconstruction algorithm and the
decay chain multi-vertex reconstruction algorithm. The outputs of these algorithms are combined to
one output by multivariate analysis.

Impact Parameter based algorithm
Since B-meson has a long lifetime of hadrons (cτ ∼450 µm), there is at least one vertex displaced
from the interaction point of the hard scatter events. It would have a large transverse impact
parameter (d0 ), which is defined as the closest distance of a track to the primary vertex in the r-φplane. In addition, it would also have a large longitudinal impact parameter (z0 sin θ), which is definedas the closest distance of a track to the primary vertex in longitudinal plane. In order to consider
the correlation of them, a log likelihood ratio discriminant is computed as the sum of the per-trackcontributions.

Inclusive secondary vertex reconstruction algorithm
The secondary vertex finding algorithm explicitly reconstructs a displaced secondary vertex using
tracks satisfying a quality selections. All track pairs are tested for a two track vertex hypothesis.
Two track vertices, which originate from the decay of a long lived particle such as Ks or Λ, photon
conversions or hadronic interactions with a detector material, are also found, but they are rejected.

45

Object reconstruction and identification
Then, the remaining two track vertex candidates are required to be significantly displaced from theprimary interaction vertex.

Decay chain multi-vertex reconstruction algorithm
The decay chain multi-vertex reconstruction algorithm exploits the topological structure of weak band c-hadron decays within a jet. In order to reconstruct a full b-hadron decay chain, a Kalman filter
is used. This algorithm finds a common line on which the primary vertex and the bottom and charm
vertices approximating the b-hadron flight path and their positions.

Multivariate algorithm (MV2)
Outputs of these three algorithms are combined into one output by a Boosted Decision Tree (BDT),
which is explained in Section 5.5. A large statistics of t t¯ sample is used for the training in BDT. In
order to consider the rejection power of c-quark, the c-jet fraction in the training sample is composedof 10%: the light-flavour fraction is composed of 90%. The produced output by the BDT classifier iscalled "MV2c10 BDT Output" and it has the strong separation between b jets and light-flavour jets orc jets as shown in Figure 4.8. This analysis uses the working point at 77% b jet efficiency.

Figure 4.8: MV2c10 BDT output distribution for b jets (blue), c jets (green) and light-flavour
jets (light-flavour) [104, 105].

4.2.5 Jet in this analysis
This analysis uses the following selections for jets as below.

46

4.3 Electron• pT >20 GeV and |η| <2.8 for inputs to a missing transverse momentum calculation and overlap
removal.
• pT >50 GeV, |η| <2.8 and the JVT cut for requiring a jet.
The additional requirement of b-tagging is performed to identify b jets.

4.3 Electron
Electrons mainly deposit their energy due to bremsstrahlung. Then, radiated photons may convert
into electron-positron pairs. By continuing the processes, electromagnetic showers are constructed.
The reconstruction of electrons can use three algorithms, which utilize the information of the innerdetectors and calorimeters [106, 107].
The reconstruction efficiency of electrons is measured by Z →ee events. Figure 4.9 shows thereconstruction efficiency as a function of the reconstructed electron transverse energy. The efficiency
is more than 97% for ET > 20 GeV and a good agreement between data and MC simulation isobserved. In the reconstruction, pions in the jets are reconstructed as electrons. In order to suppress

Figure 4.9: The reconstruction efficiency as a function of reconstructed electron transverse energy ET obtained
from Z →ee events. The black dot (white) line is data (MC simulation) [106].

the fake electrons, a likelihood based (LH) identification is performed [106, 107]. Inputs to the LH
identification is measurements from the inner detectors and calorimeters such as electron leakage inthe hadronic calorimeters. Depending on the electron efficiency, three working points are prepared:
Loose, Medium and Tight as shown in Figures 4.10 [106]. This analysis was Loose (Tight) working
point, corresponding to 93% (80%) efficiency at ET = 40 GeV.
This analysis uses two selections for an electron, which are defined as below.
• Loose working point with pT > 7 GeV, |η| < 2.47 in case of vetoing electron and input tooverlap removal.
• Tight working point with pT > 7 GeV, |η| < 2.47 in case of requiring electron in order tosuppress fake electrons.

47

Object reconstruction and identification

Figure 4.10: Identification efficiencies in Z →ee events for Loose (blue), Medium (red) and Tight (black)working points as a function of the reconstructed electron ET (left) and η (right). The data of 37.1 fb−1 is usedin this measurement [106, 107].

4.4 Muon
Muon reconstruction is performed in the inner detector and muon spectrometer independently
and then, muon tracks are formed by combining them [108]. In order to keep the muon efficiency
and reject fake muon from pion and kaon, a muon identification is applied. There are four working
points in the muon identification: Loose, Medium, Tight and High-pT . This analysis uses Medium
working point, which minimizes the systematic uncertainties associated with muon reconstruction andcalibration.
The reconstructed efficiency is measured by Z →µµ events. Figure 4.11 shows the reconstruction
efficiency as a function of muon η. The efficiency is more than 98% except |η| < 0.1. In this η region,
the reconstruction efficiency is low due to instruments of the muon spectrometers.
This analysis uses two selections for an muon, which are defined as below.
• Medium working point with pT > 6 GeV, |η| < 2.7 in case of vetoing electron and input tooverlap removal.
• Medium working point with pT > 6 GeV, |η| < 2.47 and track quality in case of requiring
electron in order to suppress fake muons.
– Track quality: |z0PV · sin θ| < 0.5mm and |d0PV |/σ(d0PV ) < 3

4.5 Missing transverse momentum
Since the transverse momentum of initial states is zero in the LHC, the conservation of the transverse
momentum can be used. The energy and direction of each particle such as neutrinos cannot be directly48

4.6 Overlap removal

Figure 4.11: Muon reconstruction efficiency as a function of muon η using Z →µµ events at the Medium
working point [108].

measured, but a vector sum of these particles can be estimated from this conservation. Missing
transverse momentum (ETmiss ) is defined as the negative vectorial sum of transverse momenta of all
physics objects and all tracks, which are not associated with these objects (soft term):
Õ
Õ
Õ
Õ
Õ
jet
γ
µ
term
Emiss
=−
ET −
ETe −
ET −
ET −
Esoft
(4.6)
T
T
γ

µ

where ET , ETe , ET and ET are the transverse momentum of jet, electron, photon and muon. The soft
term
term Esoft
is calculated from tracks in the inner detector, which are not reconstructed in objects,T
but matched to the primary vertex [109]. By considering soft term, the pileup contamination of ETmiss
can be minimized and thus the resolution is not sensitive to the number of primary vertex as shown in
Figure 4.12.
jet

The systematic uncertainties on the missing transverse momentum considers the energy response
and resolution. In the ATLAS, the systematic uncertainties for the hard terms such as jet, electron,
photon and muon entering ETmiss reconstruction are assumed to be uncorrelated [109]. Hence, thesystematic uncertainties of the soft term are evaluated in this case. In order to evaluate the systematic
term
uncertainties, the parallel (E k ) and perpendicular (E⊥ ) projections of Esoft
are defined as shownTin Figure 4.13 Two projections between data and MC simulation as a function of the transverse
momentum of the hard terms are compared and the systematic uncertainties are assigned in order tocover all differences between data and MC simulation [109].

4.6 Overlap removal
Since each object reconstruction is performed in parallel, there is a possibility to reconstruct single
particle as multiple objects. For example, electrons and jets are calorimetric objects so that it is not

49

Object reconstruction and identification

Figure 4.12: ETmiss resolution RMS in x-direction and y-direction using Z →µµ sample as a function of numberof primary vertex without jets with pT >20 GeV [109].

term
Figure 4.13: Schematic view of the parallel (E k ) and perpendicular (E⊥ projections of Esoft
for Z →µµT
missevents without genuine ET for a final state without any jets. If there is no mismeasurement of reconstruction,
the E k is zero and the E⊥ is transverse momentum of Z boson (pT Z ).

uncommon for an electron to be also reconstructed as a jet or vice versa. In order to avoid double
counts of single particle, an "overlap removal" procedure
is applied. Most of the criteria in thep2
procedure are based on a simple geometric ∆R = ∆φ + ∆η2 variable.
First, the overlap removal between the electron and muon is performed. If a baseline electron andbaseline muon share the same ID track, the electron is ignored. Then, if a baseline electron and a jet
are found within ∆R < 0.2, the object is interpreted as an electron. The overlapping jet is ignored.
Then, if they are found within ∆R < min(0.4, 0.04 + 10[GeV]/pTe )[GeV], the object is interpreted
as a jet. The nearby electron is ignored. Then, if a muon and a jet are found within ∆R < 0.2, theobject is treated as a muon. In case that the number of tracks with pT >500 MeV associated to theoverlapping jet is less than three, the jet is ignored. Finally, if a muon and a jet are found within

50

4.6 Overlap removalµ∆R < min(0.4, 0.04 + 10[GeV]/pT [GeV]), the object is treated as a jet and the overlapping muon isremoved.

51

5 Event selection with machine learning
First, this chapter discusses a jet cleaning and a treatment of the dead tile module. Then, thischapter discusses a search strategy of this analysis and explains selections in detail. Since the SUSY
particles are not found in the search, the strategy which covers all mass ranges of the SUSY particles
is described.

5.1 Jet cleaningThis search should be performed with well understood "good" data, which do not contain bad
events such as noise bursts or beam-induced background (BIB). The noise bursts are the bursts ofcoherent noise over a large region of subdetectors. The detector response may not be normal andthe measurement performed over this period would not be reliable. The BIB is observed due toproton losses upstream of the interaction point. They induce secondary particles (muon) and reachto the ATLAS detector. The energy depositions created by them in the ATLAS detector would bemeasured and reconstructed as fake jets. In addition, muons from non-collision would be observed
when cosmic-ray showers overlap with collision events.
Since these events, which contain noise bursts and the BIB, would have high jet pT and ETmiss , thoseare potentially signal like events and not included in MC samples. In order to eliminate these effects,
an event cleaning criterion is introduced. The summary of the criteria and efficiencies for the event
cleaning is shown in Table 5.1.
Table 5.1: Summary of event cleaning efficiencies for data and Z+jets MC sample.

Selection
Loose bad jet veto
Tight bad jet veto for 1st &2nd jets
Jet timing cut

Data
99.0
92.7
97.7

Efficiency [%]MC sample (Z+jets)
99.8
99.5
100

There are two selections using the information from calorimeters, which are described in Ref. [110]:"Loose bad jet" and "Tight bad jet". In order to identify bad jet in this analysis, the selection oftight bad jet is applied to leading and subleading jets and loose bad jet is used for other jets. The
events which have any bad jets are vetoed to reject event contaminated by noise burst. The jet timing
measurement, which is relative timing difference of jet and pp collision, is also used to reduce the
BIBs. Figures 5.1 show the jet timing distributions for collision events and non-collision events, whichis affected by BIBs. In order to visualize these events, a special criterion is applied. The collision

53

Event selection with machine learning
events are selected by single jet triggers and the selection of tight bad for the leading and subleading
jets is required. The non-collision events are selected by the ETmiss trigger and requiring that at least
one of the first two leading jets has the tight bad jet. The jet distribution has a peak around 0 ns forcollision events, whereas the broad distribution is observed in the non-collision events as shown in
Figures 5.1. The BIBs can be reduced by applying the jet timing cut (4 ns).
Most of event cleaning criteria have small loss of events (below 1%) in both data and Z+jets MC as
shown in Table 5.1. No efficiency loss on the SUSY signal event due to these criteria is also observed.

Figure 5.1: Jet timing distributions for 2016 (top-left), 2017 (top-right) and 2018 (bottom) data period. The
selection, ETmiss ≥300 GeV (ETmiss ≤300) GeV is applied to collision events (non-collision events) in order toincrease purity of the event.

5.2 Treatment of dead tile modules
Some modules in the tile calorimeters were having issues in data periods accidentally. These
modules are called dead tile modules. If the jets point close to the dead tile modules, part of theenergy of the jets cannot be measured, which is added to the missing transverse momentum. In these
events, both the jet and the missing transverse momentum would be mismeasured. Since the dead tilemodules are not implemented in the MC simulation, such a event has to be vetoed in data for signal
and background estimations.

54

5.2 Treatment of dead tile modules
Since period and location of the dead tile modules are recorded, the following approach is adopted
in this analysis. If jets point to a region around dead tile modules, the energy of jets would be lost.
Therefore, jet pT ordering would be changed. Figures 5.2 show two dimensional distribution ofsubleading jet φ and η. Because of the dead tile module, leading jet would become subleading jet, whichmakes clear excess in the plots. The missing transverse momentum is increased by the mismeasurementof the energy of jets, so the azimuth direction of the missing transverse momentum (φ (ETmiss )) becomesto be correlated with the dead tile module as shown in Figure 5.3(a). In order to minimize the effectdue to the dead tile module, the events, which have the jets around the dead tile modules, are treatedas follows. If an angular difference between jets and ETmiss is small (<0.3), events are affected by thedead tile modules and vetoed. Fiducial cuts of the dead tile module listed in Table 5.2 are applied inthis analysis. By applying the cuts to data and all MC samples, the φ (ETmiss ) distribution does nothave any peaks correlated with the dead tile modules as shown in Figure 5.3(b).

55Event selection with machine learning

Figure 5.2: The two dimensional distribution of the subleading jet φ (x-axis) and subleading jet η (y-axis) for
2015-2016 (top-left), 2017 (top-right) and 2018 (bottom) data period. The z-axis indicates the number of events.
The energy of the jet around the dead tile modules would be decreased compared to the original one, so thenumber of the subleading jet in the region is significantly increased.

56

5.2 Treatment of dead tile modules

(a)

(b)

Figure 5.3: Distribution of the azimuth direction of the missing transverse momentum (φ(ETmiss )) before (a)and after (b) applying the dead tile module cuts in the data and MC simulation. The dead tile module cuts areapplied to both data and MC simulation. The MC samples are normalized to cross section times integrated
luminosity of 139 fb−1 . The bottom panel is the ratio of the observed data and the sum of SM backgrounds
from simulation. The hatched red error bands indicate the statistical uncertainties of background prediction
based on MC samples.

Table 5.2: The definition of the dead tile module cut.

Data period
2015
2016
2017
2018
kinematic cuts
jet pT∆φ(jet, ETmiss )The cuts of all jets for the dead tile module( 0 < η < 0.9 and 0.8 < φ < 1.0 ) or ( −1.6 < η < −0.9 and 1.9 < φ < 2.1 )( 0 < η < 0.9 and − 1.33 < φ < −1.13 ) or ( −0.9 < η < 0. and 0.34 < φ < 0.54 )( −0.9 < η < 0. and − 0.25 < φ < −0.05 ) or ( 0.8 < η < 1.7 and 0.14 < φ < 0.34 )( 0 < η < 0.9 and 2.7 < φ < 3.0 for 350310 ≤ Run number ≤ 352514( 0. < η < 0.9 and (φ > 3.0 or φ < −3.0 ) for 355261 ≤ Run number ≤ 364292≥ 50 GeV< 0.3

57

Event selection with machine learning

5.3 Preselection
A preselection, which is defined as Table 5.3, is applied to all signal regions (SRs). The preselection
is applied in distributions which is shown in this chapter. The preselection except the number of
leptons is applied for control regions (CRs) and validation regions (VRs), which will be explainedlater. Figures 5.4 show the distribution of the leading jet pT and ETmiss after applying the preselection.
Since the target signals as shown in Figures 1.12 would have the high energy scales compared to theSM backgrounds, the large leading jet pT and ETmiss is expected as shown in Figures 5.4.

Table 5.3: Preselection using ETmiss , Nj (number of jet with pT ≥50 GeV), leading jet pT and number of leptons.

Jet cleaning
Dead Tile Module cut
ETmiss [GeV]Nj
Leading jet pT [GeV]
Number of leptons

See Section 5.1
See Section 5.2
≥ 300
≥4
≥ 200
=0

Figure 5.4: Distribution of the leading jet pT (left) and ETmiss (right) with the preselection. The signals in theplot are gluino direct decay. The last bin includes the overflow. The MC samples are normalized to crosssection times integrated luminosity of 139 fb−1 . The bottom panel is the ratio of the data and the sum of SM
backgrounds. The hatched red error bands indicate the statistical uncertainties of background prediction basedon MC samples.

After applying the preselection, the remaining backgrounds are Z+jets, W+jets, t t¯, single top,
diboson and multi-jets. As discussed in Section 3.3, the cross section is computed at the NLO or
NNLO level. Even if the NLO or NNLO cross section is used for normalizing SM backgrounds, theMC samples do not describe data well. This causes the mismodelling on the description of the objects,

585.4 Discriminating variables
such as the leading jet pT or ETmiss as shown in Figures 5.4. In this analysis, dedicated corrections areapplied on the MC samples based on the data as discussed in Chapter 6.

5.4 Discriminating variables
Before going to the search strategy, the discriminating variables between SUSY signals and SM
backgrounds are listed as follows.
• HT : HT is defined as the scalar sum of pT of all jets with pT ≥50 GeV.
• Effective mass (meff ): Effective mass (meff ) is defined as the scalar sum of ETmiss and pT of alljets with pT ≥50 GeV (HT ):meff ≡nÕ|pT(i) | + ETmiss = HT + ETmiss .

(5.1)

i=1

Events / 100

It approximately corresponds to the gluino mass. The distribution of the effective mass in thesignals has a broad peak, while the backgrounds are smoothly decreasing as shown in Figure 5.5.
10

6

10

5

Data
SM Total
Multijet
Z+jetsW+jetstt(+EW) & single top
Diboson∼(~g, χ∼0)=(2200, 400)(~g, χ10)=(2200, 1000)

s=13 TeV, 139 fb-1

104
10

3

1

102
10
1

Data/MC

1000

1500

2000

2500

3000

3500

4000

4500

5000

1500

2000

2500

3000

3500

4000

4500

5000

2
1.5
1
0.5
0

1000

meff [GeV]

Figure 5.5: Distribution of the effective mass with the preselection. The signals in the plot are gluino direct
decay. The last bin includes the overflow. The MC samples are normalized to cross section times integrated
luminosity of 139 fb−1 . The bottom panel is the ratio of the data and the sum of SM backgrounds. The hatched
red error bands indicate the statistical uncertainties of background prediction based on MC samples.

59Event selection with machine learning• ∆φ(jet1,2,(3) , E®Tmiss )min and ∆φ(jeti>3 , E®Tmiss )min : The variables of ∆φ(jet1,2,(3), E®Tmiss )min and∆φ(jeti>3, E®Tmiss )min are introduced in order to suppress multi-jet events. They are defined as thesmallest azimuthal difference between the missing transverse momentum and the momentumof the jets. Up to three leading jets are considered in case of ∆φ(jet1,2,(3), E®Tmiss )min . Other
jets with pT ≥50 GeV are considered in case of ∆φ(jeti>3, E®Tmiss )min . The requirements of∆φ(jet1,2,(3), E®Tmiss )min and ∆φ(jeti>3, E®Tmiss )min can suppress the multi-jet background in which amismeasurement of the jet energy generates the missing transverse momentum. The distributionsof ∆φ(jet1,2,(3), E®Tmiss )min and ∆φ(jeti>3, E®Tmiss )min are shown in Figures 5.6.

Figure 5.6: Distribution of the smallest azimuthal difference between the missing transverse momentum and themomentum of the jets: ∆φ(jet1,2,(3), E®Tmiss )min considers up to three leading jets (left) and ∆φ(jeti>3, E®Tmiss )minconsiders other jets with pT ≥50 GeV (right). The signals in the plot are gluino direct decay. The MC samples
are normalized to cross section times integrated luminosity of 139 fb−1 . The bottom panel is the ratio of thedata and the sum of SM backgrounds. The hatched red error bands indicate the statistical uncertainties ofbackground prediction based on MC samples.

• Aplanarity: The information of event topology is also useful to separate the signal frombackgrounds. An aplanarity is a variable designed to provide event topological information
about the full momentum tensor of an event. It is defined as 3/2λ3 , where λ3 is the smallest
eigenvalue of the normalized momentum tensor calculated using the momenta of the jets withpT ≥50 GeV in an event [111]. The values near zero indicate relatively planar event shape,
which is background-like events. Signal events tend to have high aplanarity values because they
are more spherical event shape than background events. This is because multiple objects havehigh momentum emitted in the heavy SUSY particle decays. In case of Z+jets background, theselected Z boson is boosted since the large missing transverse momentum is required as shownin Table 5.3. There are several jets via initial state radiation, which are at the opposite directionof the Z boson. The event topology is a planar rather than spherical and the distribution of theaplanarity is different from the signal as shown in Figure 5.8.

60

5.4 Discriminating variables

Figure 5.7: The event topology between the gluino decay (left) and Z+jets (right).

Figure 5.8: Distribution of the aplanarity with the preselection. The signals in the plot are gluino direct decay.
The last bin includes the overflow. The MC samples are normalized to cross section times integrated luminosityof 139 fb−1 . The bottom panel is the ratio of the data and the sum of SM backgrounds. The hatched red error
bands indicate the statistical uncertainties of background prediction based on MC samples.

61

Event selection with machine learnings=13 TeV, 139 fb-1
1400

T

Subleading jet P [GeV]

In these discriminating variables, the effective mass has the strongest separation power between
the signals and backgrounds. However, it gets weaker as the mass difference between gluino andneutralino (∆m(g̃, χ̃10 )) is smaller. If the mass difference is small, the transverse momentum of the jetin the final state is small. As a result, the effective mass is also small and the distribution is shifted to
the low energy scale as shown in Figure 5.5. It is difficult to extract the signal from the backgroundfor the small ∆m(g̃, χ̃10 ) as far as this analysis relies on the effective mass. The new discriminating
variable is needed for the further improvement.
In order to utilize the feature of the discriminating variables, the variable correlation is newly
considered. Figure 5.9 shows the two dimensional distribution of the leading jet pT and subleading
jet pT with the preselection. Since the gluino is produced in a pair and decays to the jets and theneutralino, the properties of the leading jet and subleading jet are similar. On the other hand, thebackground does not have the correlation between them and the obvious difference is observed. The
two dimensional distribution between the effective mass and the aplanarity can also separate thesignal from the background as shown in Figure 5.10. If the effective mass is large for the signals, thesignal events also have jets from initial state radiations and are close to planar event shape. Hence,
the broad aplanarity distribution is obtained for large missing transverse momentum as shown in
Figure 5.10. If the non-linear cut can be performed to these distribution, the separation between thesignal and background would be efficiently improved. Therefore, the non-linear cut considered on
the variable correlation (non-linear correlation) is introduced in this analysis. In order to obtain thecut, the machine learning is adopted. This thesis focuses on the Boosted Decision Tree (BDT) in themachine learning.

1200

SM background∼(~g, χ0)=(2200, 400)
1

3

10

10−1

1000
800

102
10−2

600
400

10

200
10−3
0
0

200

400

600

800

1000

1200

1
1400 0

200

400

600

800

1000 1200 1400

Leading jet P [GeV]T

Figure 5.9: Two dimensional distribution of the leading jet pT and subleading jet pT with the preselection. The
last bin includes the overflow. The left figure shows the distribution in the SM background and the right figure
shows the distribution in the gluino direct decay signal with (mg̃, m χ̃1 )=(2200, 400) GeV.
0

62

Ap

5.5 Boosted Decision Tree (BDT)

0.5

s=13 TeV, 139 fb-1
104

0.45
0.4

SM background

0.35

1

∼
(~
g, χ0)=(2200, 400)
1

103
10−1

0.3
0.25

102

0.2
10−2

0.15
10

0.1
0.05
0
0

1
500 1000 1500 2000 2500 3000 3500 4000 4500 5000
0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

meff [GeV]
Figure 5.10: Two dimensional distribution of the effective mass and the aplanarity with the preselection. The
last bin includes the overflow. The left figure shows the distribution in the SM background and the right figure
shows the distribution in the gluino direct decay signal with (mg̃, m χ̃1 )=(2200, 400) GeV.
0

5.5 Boosted Decision Tree (BDT)
BDT is one of the most famous multivariate analysis (MVA) methods in particle physics [112,113]. This is a binary tree structured classifier and one of ensemble learnings. The ensemble learning
is composed of many "weak" learners and constructs one learner, which is called "strong learner".
Outputs of the strong learner are obtained from majority vote of weak learners considering weights.
In the BDT, a decision tree as shown in Figure 5.11 is used as the weak learners and the weights
are updated by "Boosting" algorithm. A classification criteria of the decision trees is determined byresidual sum of squares, entropy information or Gini coefficient: this analysis uses entropy information
to determine a classification criteria of the decision trees. By using many decision trees, the phase spacecan be split into several regions and each region is classified as signal or background. This analysis
uses 800 decision trees in order to make strong learner. The considering weights are determined by"Gradient Boosting" algorithm.
The two orthogonal samples are needed in the BDT: training and testing samples. The training
sample is provided to calculate the entropy information and determine the classification criteria ofdecision trees. The strong learner produced by the training samples is called "BDT classifier" andconsiders the non-linear correlation as shown in Figure 5.12. The output of the BDT classifier iscalled "BDT score". This BDT score is applied to the testing sample and used in the analysis.

63Event selection with machine learning

Figure 5.11: Schematic view of one decision tree [113]. In a decision tree, there is a sequence of binary splits
using the discriminating variables (xi , x j and xk ) starting from the root node. The discriminating variables are
determined to give the best separation between signal and background at each node. The final nodes in thedecision tree are labelled as "S" for signal and "B" for background. They are determined from the majority
events in the final node.

Figure 5.12: The illustration of the non-linear correlation between variable x1 and x2 . The red point corresponds
to the signal and the blue point corresponds to the background. The most appropriate cut is the green line and it
can be produced by using BDT classifier.

64

5.6 Approach of BDT analysis

5.6 Approach of BDT analysis
5.6.1 BDT classifier training
Since all mass points of the target signals have to be probed, it is not evident how the training of the
BDT classifier is performed. The simplest approach is to prepare all the signal samples and performthe training per signal point. It means the infinite training samples would be needed and this approachis not realistic.
In order to avoid the training per the mass point, the signals with the similar kinematics are mixed in
the training. The jet activity in final states depends on ∆m(g̃, χ̃10 ) as shown in Figure 5.13. Therefore,
the approach of mixing signals in the training with a similar ∆m(g̃, χ̃10 ) is adopted. Similar kinematic
distribution in these signals is observed as shown in Figure 5.14. In this analysis, eight training
categories are prepared such that they can cover the signals with ∆m(g̃, χ̃10 )≥ 200 GeV1 : four training
categories each for the gluino direct decay (indicated as GGdi, i = 1 ∼ 4) and the gluino one-step
decay (GGoi, i = 1 ∼ 4) as shown in Figure 5.15. For gluino one-step decay, the primary modelwith m χ̃1± = (mg̃ + m χ̃0 )/2, as discussed in Section 1.5, is used in the training sample. In addition,1
the gluino one-step decay via W boson as shown in Figure 1.11(b) has the similar kinematics to thegluino one-step decay via Z boson as shown in Figure 1.12(c), and thus the gluino one-step decay via
W boson is only used.2 The training of BDT uses all background components of Z+jets, W+jets, t t¯,single top and diboson except multi-jet in this analysis.

Figure 5.13: Normalized distribution of the effective mass applying the preselection for gluino direct decay
signals with (mg̃ ,m χ̃0 )=(2000, 200) (black line), (2000, 1000) (red line) and (1400, 100) (blue line) GeV. The
1last bin includes the overflow.

1 This thesis does not focus on the signals with ∆m(g̃, χ̃ 0 )≤ 200 GeV. In Ref. [114], another approach is adopted to search1

for this region.
2 There is an idea to mix two signal models for the training, but this thesis uses one signal models in order to simplify thetraining.

65

Event selection with machine learning

Figure 5.14: Distribution of the effective mass (top-left), the missing transverse momentum (top right) andNj (bottom) in four gluino direct decay signals with (mg̃ ,m χ̃0 )=(2200, 1400) (black line), (2400, 1600) (red1line), (2200, 0) (blue line) and (2400, 200) (green line) GeV. The last bin includes the overflow.

66~∼0)=100%g~
g production, B (~g → qq χ11m(∼χ ) [GeV]

2200

1800
1600
1400

2200

BDT-GGd1
BDT-GGd2
BDT-GGd3
BDT-GGd4
Moriond2017.Excl

1800
1600
1400

1200

1200

1000

1000

800

800

600

600

400

400

200
0
0

~
∼± → qq W± χ∼0)=100%, m(χ∼±)=(m(~∼0))/2g~
g production, B (~g → qq χg) + m(χ
1

1

1

1

2000

0

2000

0

1
m(∼
χ ) [GeV]

5.6 Approach of BDT analysis

BDT-GGo1
BDT-GGo2
BDT-GGo3
BDT-GGo4
Moriond2017.Excl

200
500

1000

1500

2000

2500

3000
m(~
g) [GeV](a) GG direct

0
0

500

1000

1500

2000

2500

3000
m(~
g) [GeV](b) GG one-step

Figure 5.15: Illustration of training categories for gluino direct decay (a) and gluino one-step decay (b). For
gluino direct decay (gluino one-step decay), the red point corresponds to GGd1 (GGo1), the magenta point
corresponds to GGd2 (GGo2), the gold point corresponds to GGd3 (GGo3) and the light blue point corresponds
to GGd4 (GGo4) training category. The blue dotted line shows the expected exclusion limit on the previous
ATLAS result with the data of 36.1 fb−1 [34].

5.6.2 Application of BDT classifier
The training samples should not be used for the evaluation of signal and background events. This isbecause a BDT score is built from the training sample and there is a possibility that the BDT scoreobtained from the training sample can be biased. Therefore, each sample is normally divided into
two samples (training sample and testing sample) and the testing sample is only used to evaluate theperformance and to obtain the BDT score. However, it would decrease MC statistics to the half in the
final fit. In order to avoid it, a method as shown in Figure 5.16 is adopted:• MC samples are randomly divided into two data sets: the former set (half sample 1) is used astraining sample and the latter set (half sample 2) is used as input for signal and backgroundestimations.
• The training is also performed using the half sample 2 as well. In total, two kinds of BDT scoreare produced.
• The BDT classifier, which is obtained using the half sample 1, is applied to the half sample 2,
and vice versa.
• Both half sample 1 and half sample 2 are used for the background estimation discussed in
Chapter 6 (No loose of MC statistics).
This method is also applied to the data. Events in the data are divided in half and the BDT score is
obtained from one of BDT classifiers. The validation of this method is discussed in Chapter 7.

5.6.3 Optimization of BDT classifier
With the preselection as listed in Table 5.3, the additional cuts are applied before the training to
reduce background contributions beforehand and focus on the separation between the signal and the67

Event selection with machine learning

Training

Apply

Half
sample 1

BDT score1

Halfsample 2

Halfsample 2

BDT score2

Halfsample 1

Fit input

Figure 5.16: A schematic view of sample division into two sets randomly: for BDT training and for score usage,
respectively. Half sample 1 is the first half of all MC events and half sample 2 is the second half.

background in the training. Table 5.4 show the cuts applied in the training samples.
Table 5.4: The definition of cuts per each training category for gluino direct decays (top) and gluino one-step
decays (bottom), respectively.

68

Nj∆φ( j1,2,(3), pmissT ) minmiss∆φ( ji>3, pT ) min
ETmiss /meff
meff [GeV]0∆m(g̃, χ̃1 ) [ GeV ]

GGd1
≥4
≥0.4
≥0.4
≥0.2
≥1400
1600 – 1900

GGd2
≥4
≥0.4
≥0.4
≥0.2
≥1400
1000 – 1400

GGd3
≥4
≥0.4
≥0.4
≥0.2
≥800
600 – 1000

GGd4
≥4
≥0.4
≥0.4
≥0.2
≥800
200 – 600

Nj
∆φ( j1,2,(3), pmissT ) min∆φ( ji>3, pmissT ) minmiss
ET /meff
meff [GeV]0∆m(g̃, χ̃1 ) [ GeV ]

GGo1
≥6
≥0.4
≥0.4
≥0.2
≥1400
1400 – 2000

GGo2
≥6
≥0.4
≥0.4
≥0.2
≥1400
1200 – 1400

GGo3
≥5
≥0.4
≥0.4
≥0.2
≥800
600 – 1000

GGo4
≥5
≥0.2
≥0.2
≥0.2
≥800
200 – 400

5.6 Approach of BDT analysis

5.6.4 Determination of input variables
In order to maximize the sensitivity, the following variables are checked as the candidate of input
variables.
• Information of each jet: 1st - 6th jet pT , η and φ.
• Information of event scale: meff and ETmiss• Information of event topology: Aplanarity, ∆φ(jet1,2,(3), E®Tmiss )min and ∆φ(jeti>3, E®Tmiss )min
The variable Nj is not the candidate of input variables in this analysis. Figures 5.17 show Nj
distributions and the mismodeling is observed in CR, which will be explained in Section 6.2. When
this variable is used, the background estimation is difficult. Therefore, this variable is not used in thecandidate of input variables.
As the number of input variables is larger, the BDT classifier is more complicated. It causesthat the validation of variable correlations discussed in Section 7.3 is difficult. Hence, if there is
no impact on the sensitivities by adding the variables, the variables are not used in input variables.
Under the decision criteria, the variables, which have the improvement of sensitivity, are selected.
The determination of the input variables are based on the best sensitivity reach. The sensitivity (Zn ) isdefined as below:
r h
o
n
oi
n


σ 2 (n−b)n(b+σ)2
b2


−
ln
1
+
n>b
+
2
nln


b 2 +nσ 2σ2b(b+σ 2 )
r
Zn =
(5.2)
h
n
o
n
oi

n(b+σ)2σ 2 (n−b)

b2

−
2
nln
−
ln
1
+
n
<
b

b 2 +nσ 2σ2b(b+σ 2 )
where n is the number of signal and background and b ± σ is the number of background eventswith statistic and systematic errors [115]. Following the previous publication [34], 20% systematic
uncertainties are also assumed in this study. The sensitivity for all the signal points is calculated byapplying the BDT score cut. In order to check impacts on input variables, 3σ sensitivity contour isevaluated by adding the variable one by one.
Figure 5.18(a) shows the 3σ sensitivity contours in the GGd1 category to check the impact on
1st-4th jets pT . The black line corresponds to the contour when 1st-4th jets η, effective mass, missing
transverse momentum and aplanarity (default variables) are used in input variables. The red line
corresponds to the contour with the default variables and 1st jet pT , the blue line corresponds to thecontour with the default variables and 1st-2nd jets pT , the green line corresponds to the contour withthe default variables and 1st-3rd jets pT , and the magenta line corresponds to the contour with thedefault variables and 1st-4th jets pT . By adding the the variable one by one, the 3σ sensitivity contours
are improved as shown in Figure 5.18(a). Figure 5.18(b) shows the breakdown of the sensitivities
with four signal points in the GGd1 training category: (mg̃ ,m χ̃0 )=(2200, 600), (2200, 0), (2200, 700)1and (2000, 800) GeV. The correlations between jet pT are effective as shown in Figure 5.9 and thesensitivity for gluino direct signal with (mg̃ ,m χ̃0 )=(2000, 800) GeV is improved by ∼50% when 1st-4th
1
jets pT are used.
Figure 5.19(a) shows the 3σ contours in GGd1 category to check the impact on the variables ofaplanarity, ∆φ(jet1,2,(3), E®Tmiss )min , ∆φ(jeti>3, E®Tmiss )min and 1st-4th jets φ. The black line corresponds

69Events / 1

Event selection with machine learning

107
10

6

10

5

s=13 TeV, 139 fb-1

Data
SM Total
Multijet
Z+jetsW+jetstt(+EW) & single top
Diboson∼(~g, χ∼0)=(2200, 400)(~g, χ01)=(2200, 1000)

104
10

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Data/MC

2
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0

Number of jet with P ≥50 GeV (N )
T

j

1800

~
∼0)=100%g~
g production, B (~g → qq χ
1

Significance [σ]1mχ∼0 (GeV)

Figure 5.17: Left figure shows the distribution of the number of jet with pT ≥50 GeV (Nj ) with the preselection.
Right figures shows the Nj with the preselection in CR, which will be explained in Section 6.2. The signals in
the plot are gluino direct decay. The MC samples are normalized to cross section times integrated luminosity of
139 fb−1 . The bottom panel is the ratio of the data and the sum of SM backgrounds. The hatched red error
bands indicate the statistical uncertainties of background prediction based on MC samples.

GGd1: default

1600

-1

L = 139 fb

s=13 TeV

GGd1: + 1st jet pT

GGd1: + 2nd jet p

1400

T

GGd1: + 3rd jet p

1200

T

default: 1st-4th jet,η, m , Emiss
, Ap
T
eff

GGd1: + 4th jet p

T

1000

Training point

2.8

s=13 TeV, 139 fb-1

2.6 default = 1st-4th jet η, m , Emiss, Ap
T
eff
2.4
2.2

~, χ∼0)=(2200, 600)(g1~, χ∼0)=(2200, 0)(g1~, χ∼0)=(2200, 700)(g1~, χ∼0)=(2000, 800)
(g
1

2

800

1.8

600

1.6
400

1.4
200

1.2
0
1400

1600

1800

(a)

2000

2200

2400
m~g (GeV)

default+1st jet pT+2nd jet pT+3rd jet pT+4th jet p

T(b)

Figure 5.18: The left figure is 3σ sensitivity contours in the GGd1 training category. The x-axis indicates thegluino mass and y-axis indicates the lightest neutralino mass. Each line corresponds to the contours with thedifferent sets of input variables (see the text). The right figure is the breakdown of the sensitivities with four
signal points in the GGd1 training category: (mg̃ ,m χ̃0 )=(2000, 800), (2200, 0), (2200, 700) and (2000, 800)
1
GeV. The x-axis indicates the used input variables and y-axis indicates the significance. By adding the variableof jet pT , the sensitivity can be improved and these variables are used.

70

5.6 Approach of BDT analysis

1800

0
~
g~
g production, B (~g → qq ∼χ1)=100%

GGd1: default + Aplanarity

1600

-1

L = 139 fb

s=13 TeV

1400

miss
GGd1: default + ∆φ(jet,E )1,2,(3) T

GGd1: default + ∆φ(jet ,ET

miss

i>3

1200

default: 1st-4th jet p , η, m , Emiss
T
T)

GGd1: default + 1st-4th jet φ

eff

1000

Significance [σ]1mχ∼0 (GeV)

to the contour when 1st-4th jets pT , η, effective mass and missing transverse momentum (default
variables) and aplanarity are used in input variables. The red line corresponds to the contourwith the default variables and ∆φ(jet1,2,(3), E®Tmiss )min , the blue line corresponds to the contour withthe default variables and ∆φ(jeti>3, E®Tmiss )min , and the green line corresponds to the contour withthe default variables and 1st-4th jets φ. Since the aplanarity uses the information of the jets φefficiently, the impact on ∆φ(jeti>3, E®Tmiss )min and jet φ is smaller than the aplanarity. The impact on∆φ(jet1,2,(3), E®Tmiss )min is almost same as the aplanarity as shown in Figure 5.19(b), so it is enough to
add either ∆φ(jet1,2,(3), E®Tmiss )min or aplanarity. The aplanarity is only used in this analysis.
3.53~, χ∼0)=(2200, 600)(g~, χ∼10)=(2200, 0)(g~, χ∼10)=(2200, 700)(g~, χ∼10)=(2000, 800)(gs=13 TeV, 139 fb-1
default = 1st-4th jet P , η, m , ET

miss

T

eff

2.5

1

2

Training point

800

1.5

600

1
400

0.5

200
0
1400

1600

1800

(a)

2000

2200

2400
m~g (GeV)

0+Aplanarity+∆φ(j,Emiss)T

1,2,(3)+∆φ(j ,Emiss)T+1st-4th jet φ

i>3

(b)

Figure 5.19: The left figure is 3σ sensitivity contours in the GGd1 training category. The x-axis indicates thegluino Mass and y-axis indicates the lightest neutralino mass. Each line corresponds to the contours with thedifferent sets of input variables (see the text). The right figure is the breakdown of the sensitivities with four
signal points in the GGd1 training category: (mg̃ ,m χ̃0 )=(2200, 600), (2200, 0), (2200, 700) and (2000, 800)
1
GeV. The x-axis indicates the used input variables and y-axis indicates the significance. For GGd1 category, theapalanarity is only used.

Figure 5.20(a) shows the 3σ contours in GGd1 category to check the impact on jet η. The blackline corresponds to the contour when 1st-4th jets pT , effective mass, missing transverse momentum
and aplanarity (default variables) is used in input variables. The red line corresponds to the contourwith the default variables and 1st-4th jets η. The 3σ sensitivity contour with 1st-4th jets φ are similar
to the contour without 1st-4th jets φ. However, the sensitivity for the heavy gluino (mg̃ >2400 GeV) is
improved by ∼15% when 1st-4th jets η are used as shown in Figure 5.20(b). Therefore, the variablesof jets η are kept in this analysis.

71

1800

0
~
g~
g production, B (~g → qq ∼χ1)=100%

1600-1

L = 139 fb

GGd1: default

s=13 TeV

1400
1200

GGd1: default + 1st-4th jet η

default: 1st-4th jet,η, m , Emiss
, Ap
T
eff

Training point

1000

Significance [σ]1mχ∼0 (GeV)

Event selection with machine learning

3.5
3

s=13 TeV, 139 fb-1
default = 1st-4th jet P , η, m , ET , Aplanarity
miss

T

eff

2.5

~, χ∼0)=(2400, 100)(g~, χ∼01)=(2400, 200)(g~, χ∼01)=(2200, 200)(g~, χ∼01)=(2200, 600)
(g
1

2

800

1.5

600

1
400

0.5

200
0
1400

1600

1800

(a)

2000

2200

2400
m~g (GeV)

0+1st-4th jets η

default(b)

Figure 5.20: 3σ sensitivity contours in the GGd1 training category with different sets of input variables. The
x-axis indicates the gluino Mass and y-axis indicates the lightest neutralino mass. Each line corresponds tothe contours with the different sets of input variables (see the text). The right figure is the breakdown of thesensitivities with four signal points in the GGd1 training category: (mg̃ ,m χ̃0 )=(2400, 800), (2200, 0), (2200,
1700) and (2000, 800) GeV. The x-axis indicates the used input variables and y-axis indicates the significance.
For GGd1 category, 1st-4th jets η are used.

72

5.7 Signal region (SR) definition
Tables 5.5 and 5.6 are the summary of input variables in all the training categories. For GGd2,
GGo1, GGo2 and GGo3, the impact on the missing transverse momentum is small (< 10%), so it
is removed from input variables to reduce the number of input variables. For GGd4 and GGo4, theimpact on the aplanarity is small (< 10%) because the signals in these categories have a planar event
shape. Up to 12 variables are selected among ETmiss , meff , aplanarity, pT and η of selected jets, andused in the training for the eight categories.
Table 5.5: Input variables for the gluino direct decay. Circle ( ) indicates the variable is used in input variables.
The hyphen (-) indicates the variable is not used in input variables.

Input variables
ETmiss [GeV]pT (j) [GeV]η(j)Aplanarity
meff [GeV]
Total number of input variables

GGd1

GGd3

GGd4

1st-4th
1st-4thGGd2
1st-4th
1st-4th

1st-4th
1st-4th

1st-4th
1st-4th
-

11

10

11

10

Table 5.6: Input variables for the gluino one-step decay. Circle ( ) indicates the variable is used in input
variables. The hyphen (-) indicates the variable is not used in input variables.

Input variables
ETmiss [GeV]pT (j) [GeV]η(j)Aplanarity
meff [GeV]
Total number of input variables

GGo1
1st -5th
1st - 5thGGo2
1st - 4th
1st - 4thGGo3
1st - 3rd, 5th - 6th
1st - 3rd, 5th - 6th

12

10

12

GGo4
1st - 4th
1st - 4th10

5.7 Signal region (SR) definition
The BDT scores are close to -1 for background-like events, while they are close to 1 for signal-likeevents. As shown in Figure 5.21, BDT scores have a good separation power between the target
signals and backgrounds. The BDT score cut is required to define signal regions (SRs) This cut is the
final discriminating variable. The SRs are defined for each training category to cover all gluino andneutralino masses. In order to determine the optimized BDT score cut per each training category,the expected significance defined in Eq. 5.2 is calculated for each SR as shown in Figure 5.22. The
optimized cut is chosen to maximize the significance but some of the BDT cuts are loosened from theoptimal cuts to have enough background statistics in terms of background estimation as discussed in
Chapter 6. The summary of all SRs are listed in the Table 5.7.

73

107
10

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10

5

10

4

10

3

s=13 TeV, 139 fb-1
GGd1

Events / 0.1

Events / 0.1

Event selection with machine learning
Data
SM Total
Multijet
Z+jetsW+jetstt(+EW) & single top
Diboson∼(~g, χ0)=(2200, 400)

107
10

6

10

5

10

102
10

1
− 0.6

−0.4

− 0.2

0

0.2

0.4

0.6

0.8

−1

1

Data/MC

Data/MC

1
− 0.8

2
1.5
1
0.5

−1

1

3

10

0

Data
SM Total
Multijet
Z+jetsW+jetstt(+EW) & single top
Diboson∼(~g, χ0)=(2200, 1000)

104

1

102

−1

s=13 TeV, 139 fb-1
GGd2

− 0.8

− 0.6

−0.4

− 0.2

0

0.2

0.4

0.6

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0

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−0.8 −0.6−0.4 −0.20s=13 TeV, 139 fb-1
GGd3

0.2

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−1

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Data
SM Total
Multijet
Z+jetsW+jetstt(+EW) & single top
Diboson~, χ∼0)=(2000, 1200)
(g

104
10

−0.8 −0.6

107
10

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10

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− 0.8

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Data/MC

Data/MCData
SM Total
Multijet
Z+jetsW+jetstt(+EW) & single top
Diboson~, χ∼0)=(1300, 900)
(g

3

10

1.5
1
0.5

−1

s=13 TeV, 139 fb-1
GGd4

104

102

0

− 0.8

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−0.8 −0.6

Events / 0.1

Events / 0.1

s=13 TeV, 139 fb-1
GGo1

Data
SM Total
Multijet
Z+jetsW+jetstt(+EW) & single top
Diboson∼ ∼(~g, χ± , χ0)=(2200, 1300, 400)

107

5

10

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10

3

10

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Data
SM Total
Multijet
Z+jetsW+jetstt(+EW) & single top
Diboson∼ ∼(~g, χ± , χ0)=(2000, 1400, 800)
1

1

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− 0.8

− 0.6

−0.4

− 0.2

0

0.2

0.4

0.6

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−1

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Data/MC

Data/MC

s=13 TeV, 139 fb-1
GGo2

104

1

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1.5
1
0.5

− 0.8

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−0.8 −0.6−0.4 −0.20s=13 TeV, 139 fb-1
GGo3

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−0.8 −0.6

BDT score

10

6

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Data
SM Total
Multijet
Z+jetsW+jetstt(+EW) & single top
Diboson∼ ∼(~g, χ± , χ0)=(1100, 1060, 1020)
1

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102
10

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− 0.8

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Data/MC

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1.5
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s=13 TeV, 139 fb-1
GGo4

104

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107

10

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102

−1

0.8

1.5

0

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Data
SM Total
Multijet
Z+jetsW+jetstt(+EW) & single top
Diboson∼ ∼(~g, χ± , χ0)=(1600, 1300, 1000)

104
10

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Events / 0.1

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107

0.8

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0

0.2

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1

BDT score0−1−0.8 −0.6

BDT score

Figure 5.21: BDT score distributions for all categories. The signals in the plot are gluino direct decay for
GGd1-4 and gluino one-step decay via W boson for GGo1-4. The MC samples are normalized to crosssection times integrated luminosity of 139 fb−1 . The bottom panel is the ratio of the data and the sum of SM
backgrounds. The hatched red error bands indicate the statistical uncertainties of the MC samples.

74Significance [σ]5.7 Signal region (SR) definition

3.5

0
~
g~
g production, B (~g → qq ∼χ )=100%
1

3
2.5
2
s=13TeV, 139 fb-1

1.5

BDTSR-GGd1: (~g, ∼χ ) = (2200,800)010BDTSR-GGd2: (~g, ∼χ ) = (2000,1000)
10

1

BDTSR-GGd3: (~g, ∼χ ) = (1700,1100)
10

BDTSR-GGd4: (~g, ∼χ ) = (1500,1100)
1

0.5

The optimized BDT score cut

Significance [σ]

0
0.5

3

0.55

0.6

0.65

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0.75

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0.9
0.95
1
Cut value on BDT score

0
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±
±
~
g~
g production, B (~g → qq ∼χ → qq W± ∼χ )=100%, m(∼
χ )=(m(~g) + m(∼χ ))/21

1

1

1

s=13TeV, 139 fb-1
0±
BDTSR-GGo1: (~
g, ∼
χ ,∼
χ ) = (2200,1300,400)
1
±

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BDTSR-GGo2: (~
g, ∼
χ ,∼
χ ) = (2000,1500,1000)

2.5

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±
BDTSR-GGo3: (~
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χ ,∼
χ ) = (1800,1500,1200)
1

1

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±
BDTSR-GGo4: (~
g, ∼
χ ,∼
χ ) = (1400,1200,1000)

2

Optimized BDT score cut

1.5

1

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0.5

0.55

0.6

0.65

0.7

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0.9
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1
Cut value on BDT score

Figure 5.22: The expected sensitivities as a function of BDT score cut in all categories for gluino direct (top)and one-step (bottom) decay signals, respectively. These signal masses are one of the target masses for eachtraining category. The final optimized BDT score cuts are highlighted by large solid circles per the categories.

75Event selection with machine learning

Table 5.7: Definition of signal region with the benchmark signal model parameters (∆m(g̃, χ̃1 )) for gluino direct
decays (top) and gluino one-step decays (bottom), respectively.
0

76

Nj
∆φ( j1,2,(3), pmissT ) min∆φ( ji>3, pmissT ) minmiss
ET /meff
meff [GeV]
BDT score0∆m(g̃, χ̃1 ) [ GeV ]

GGd1
≥4
≥0.4
≥0.4
≥0.2
≥1400
≥ 0.971600 – 1900

GGd2
≥4
≥0.4
≥0.4
≥0.2
≥1400
≥ 0.941000 – 1400

GGd3
≥4
≥0.4
≥0.4
≥0.2
≥800
≥ 0.94600 – 1000

GGd4
≥4
≥0.4
≥0.4
≥0.2
≥800
≥ 0.87200 – 600

Nj
∆φ( j1,2,(3), pmissT ) min∆φ( ji>3, pmissT ) min
ETmiss /meff
meff [GeV]
BDT score0∆m(g̃, χ̃1 ) [ GeV ]

GGo1
≥6
≥0.4
≥0.4
≥0.2
≥1400
≥ 0.96
1400 – 2000

GGo2
≥6
≥0.4
≥0.4
≥0.2
≥1400
≥ 0.871200 – 1400

GGo3
≥5
≥0.4
≥0.4
≥0.2
≥800
≥ 0.92
600 – 1000

GGo4
≥5
≥0.2
≥0.2
≥0.2
≥800
≥ 0.84200 – 400

6 Background estimation
The SRs in this analysis are defined in corners of phase space with large meff , leading jet pT and
ETmiss . In addition, the variable correlations are used in this analysis. Therefore, background estimationis challenging. The MC simulation is not modeled well as described in Section 5.4, thus MC samples
need to be corrected properly. This chapter discusses the data driven MC sample correction for each
SM background.

6.1 Background composition
The following SM processes are considered to be background processes in this analysis:• Z+jets: Since large missing transverse momentum is required as shown in Table 5.3, theremaining process of Z boson is Z(→ν ν̄)+jets as shown in Figure 6.1.
ν
Z

q

ν̄

q
g

q

Figure 6.1: Feynman diagram of Z + q, Z →ν ν̄.

• W +jets: Events of W+jets with the leptonic decay W →eν, µν and τν remain in SRs as shownin Figure 6.2. Figures 6.3 show the composition of W+jets background as a function of BDT
score. The majority of the remaining events from W+jets is W →τν with ∼ 70% and others are
W →µν with ∼ 25% and W →eν with ∼ 5%. There are two reasons why the leptonic decaysof W+jets remain in SRs. One is that the lepton is misidentified and reconstructed as a jet.
The other is that the lepton is not selected due to low pT or out of η acceptance. The detail isdiscussed in Section 6.4.
W−

q
q
g

e−, µ−, τ −ν̄e, ν̄µ, ν̄τqFigure 6.2: Feynman diagram of leptonic decays of W boson.

77

Background estimation

Figure 6.3: The composition of W+jets background in GGd1 and GGo1 as a function of BDT score. The
bottom panel of the plots shows the relative fraction of W →τν events.

• Top: The dominant production process with top quark of this analysis is top and anti-top pair
production (t t¯) as shown in Figure 6.4. A top (anti-top) quark decays to a b (b̄) quark with
W + (W − ) boson, which are called "t t¯+EW". In order to obtain a large missing transverse
momentum, the two W bosons have different decays: one is the leptonic decay W →`ν andthe other is the hadronic decay W →qq The events remain in SRs by failing one lepton. The
subdominant process is the single top production as shown in Figure 6.5. The fraction in the top
background processes are ∼ 85% with the t t¯ and ∼ 15% with the single top.
W+
q

g

t

νe, νµ, ντ
b
q

W−
q̄

e+, µ+, τ +

t̄

q̄
b̄

Figure 6.4: Feynman diagram of t t¯ production.
b

t
W−

q

q′

Figure 6.5: Feynman diagram of single top production.

• Diboson: The diboson production has two bosons as shown in Figure 6.6. Considered on therequirement of large missing transverse momentum, the dominant remaining process in thediboson production is W(→`ν)Z(→νν) with additional jets.

786.2 Background estimation strategy
q

V
q

q

V

Figure 6.6: Feynman diagram of diboson production. V indicates the boson (Z, W, γ)• Multi-jet: The multi-jet production has multi jets in the final states as shown in Figure 6.7 andthe cross section is larger than other background processes. When the energy of these jets is
mismeasured, a fake missing transverse momentum is generated and the multi-jet events remainin the SRs. As discussed in Section 5.4, these events are suppressed by ∆φ(jet1,2,(3), E®Tmiss )minand ∆φ(jeti>3, E®Tmiss )min cuts.
g
g

g
g

g

g

q
q

g

q

g
g

Figure 6.7: Main Feynman diagram of multi-jet production.

Figure 6.8 shows the breakdown of expected background components in each SR after applying
selections as shown in Table 5.7. The most dominant component is Z+jets except GGo4 SR because of
the requirement of large missing transverse momentum. For GGo4 SR, t t¯ and single top components
are dominated. The W+jets component is subdominated in all SRs. The diboson contribution isless than 15%. The multi-jet contribution is negligible (<1%) by applying ∆φ(jet1,2,(3), E®Tmiss )min and∆φ(jeti>3, E®Tmiss )min cuts.

6.2 Background estimation strategy
Since MC simulation cannot perfectly describe the data, it should be corrected by using the data.
This analysis1 uses control regions (CRs) to make correction for each background as follows. First,
CRs for each background are designed to be kinematically close but orthogonal to corresponding SRs.
Then, MC samples are normalized to data in CRs. Finally, their normalization factors are applied to
MC samples in their corresponding SR. With this procedure, the number of background events in
SR (NSR ) is expressed as:
NCR dataMC
NSR = NSR ×,(6.1)
NCR MC
where NCR data is the number of the observed events in CR and NSR MC (NCR MC ) is the number of theevents from MC samples in SR (CR). This approach assumes the mismodeling in CRs is the same as
1 Each SR has a single-bin.

79

Fraction [%]Background estimation140

s=13 TeV, 139 fb-1

tt(+EW) & single top
Z+jets120

DibosonW+jetsMulti-jet

100
80
60
40

GGo4

GGo3

GGo2

GGo1

GGd4

GGd3

GGd2

0

GGd1

20

Figure 6.8: Breakdown of the SM components in each SR.

their SRs and it means that differences between the data and MC samples are the same in both SRs
and CRs. This assumption is tested using a validation regions (VRs) as discussed in Section 6.6. CRs
for Z+jets, W+jets and top (t t¯ and single top) components are prepared and discussed below. The MC
samples of diboson and multi-jet are used for the estimation without any corrections. The validity ofthese MC samples are checked by the VRs.

6.3 Z+jets background estimation
In order to control the Z+jets background, the γ+jets event is used as CR, which is called CRY.
The kinematics is expected to closely resemble those of Z(→ν ν̄)+jets events in case the transverse
momentum of Z boson is significantly greater than m(Z) = 91.2 GeV as shown in Figure 6.9. Therefore,
a cut on the high transverse momentum of the reconstructed photon, pTγ > 150 GeV is applied in CRY.
γ
A vector of pTγ is added to the ETmiss vector (ETmiss0 = |Emiss+ pT |) because a photon is consideredT
to be a Z boson and the transverse momentum of the neutrinos from Z boson is measured as ETmiss .
After the modification, the ETmiss in CRY is similar to corresponding SR as shown in Figure 6.10 and
CRY can provide an estimation of the pT of the Z boson decaying to neutrinos in SRs.
By using the events, the kinematic selections in CRY are a little bit optimized in order toobtain the similar BDT score distribution to SR. The selections are same with SRs except GGo1
and GGo2. For GGo1 and GGo2, the number of remaining data events in the CRY is very80

6.3 Z+jets background estimation

Figure 6.9: The schematic view of Z(→ν ν̄) and γ+jets eventsγ

Figure 6.10: Comparison of the distribution between ETmiss of Z+jets in SR and ETmiss0 = |Emiss+ pT | of γ+jets
Tin CRY. The selection, Njet ≥4 is applied in the left figure and Njet ≥6 is applied in the right figure. The last bin
includes the overflow. The bottom panel is the ratio of the MC sample in SR and CRY. The total number of
events in each CRY is normalized to that in the SR in each plot. The black error bar is the relative statisticaluncertainty in SR. The hatched red error bands indicate the statistical uncertainties of background prediction
based on MC samples in CRY.

81

Background estimationlows due to the tight selection. It causes large statistical uncertainties of the normalization
factor and the precise estimation would not be performed despite the main background in the
SR. Therefore, the selections in the CRY are changed. Figures 6.11 show the distributions of threevariables (∆φ(jet1,2,(3), E®Tmiss )min ,∆φ(jeti>3, E®Tmiss )min ,ETmiss /meff ). These variables do not have any
slope in the ratio of data and MC samples so that the normalization factor would not be biased even if
the selections of these variables are removed. In GGo1 and GGo2, the cuts on these variables are notrequired in CRY.

Figure 6.11: ∆φ(jet1,2,(3), E®Tmiss )min , ∆φ(jeti>3, E®Tmiss )min and ETmiss /meff distributions in the CRY. The same
selections as GGo1 SR except ∆φ(jet1,2,(3), E®Tmiss )min , ∆φ(jeti>3, E®Tmiss )min , ETmiss /meff and BDT score are applied.
The MC samples are normalized to data in order to visualize the shape of distribution. The bottom panel is theratio of the observed data and the MC simulation. The black bar is the relative statistical uncertainty in data. The
hatched red error bands indicate the statistical uncertainties of background prediction based on MC samples.

Figures 6.12 show the comparison of BDT score distribution between SRs and CRYs in MC
simulation and the shape in CRY is similar to the corresponding SR within the statistical uncertaintyof MC samples. Therefore, the designed CRYs are suitable for the estimation of Z+jets background.

82

6.3 Z+jets background estimation

Figure 6.12: Comparison of BDT score distribution between Z+jets in SRs (black lines) and γ+jets in CRYs (redlines) in MC simulation. The bottom panel is the ratio of the MC sample in SR and CRY. The total number of
events in each CRY is normalized to that in the SR in each plot. The black error bar is the relative statisticaluncertainty in SR. The hatched red error bands indicate the statistical uncertainties of the MC samples in CRY.

83

Background estimation

6.4 W +jets background estimation
As explained in Section 6.1, events of W+jets with the leptonic decay W →eν, µν and τν remain in
SRs. For W →eν events, the electron is misidentified and reconstructed as a jet in SRs. For W →µν
events, the muon is not selected due to low pT , out of η acceptance (|η| >2.5) and low efficiencies at|η| ∼ 0 as shown in Figure 4.11. For W →τν events, the tau decays hadronically so that this tau isreconstructed as a jet. When a tau decays leptonically (τ →eνe ντ , µνµ ντ ), events having such a tau
are considered in W →eν or W →µν.

6.4.1 Definition of CR
In order to estimate the W+jets background in SRs, W(→ `ν)+jets events by requiring an electron
or a muon are used as CR, which is called CRW. The event topology in W →eν in SRs is similar to
W →τν in SRs because the electron and tau are reconstructed as a jet. W →eν events are CRs for
W →eν and W →τν, and W → µν events are a CR for W →µν but they are combined and considered
as one CR because all the event topologies are similar after a procedure explained below is applied.
The same ETmiss trigger as SRs is used to select the CRW events. This makes it possible to accessa low pT muon region, which is closer to the SR phase space for W →µν events. Additionally, arequirement of the transverse mass defined in Eq. 3.1, 30 GeV< mT < 100 GeV is applied and theb quark is vetoed to enhance the purity of W+jets events against t t¯ events. Figures 6.13 show thecomparison of the ETmiss distribution between SRs and CRWs in MC sample for each decay mode.
Good agreement is already observed in W →eν and τν but disagreement is observed in W →µν. In
order to have similar event topologies in SR, the following procedure for electron and muon in CRW
is performed.
• A lepton is treated as a jet if the lepton is identified as an electron.
• A lepton is treated as a jet if the lepton is identified as a muon with |η| > 0.2.
• A lepton is added to the ETmiss vector (ETmiss0 = |Emiss+ p`T |) if the lepton is identified as a muonTwith |η| < 0.2.
Using this procedure, good agreement of ETmiss distributions for each decay mode between SRs and
CRWs is observed within the statistical uncertainties as shown in Figure 6.14. In the next subsection,
the third bullet is explained in details.

6.4.2 Properties of W →µν events
Figures 6.15 show the truth kinematic distribution of muons in SR. First, the truth muon pT
distribution has a sharp peak at low values, so the majority of the muons is failed due to lepton pT
threshold cut. Figure 6.16 is the distribution of the difference between truth and reconstructed ETmiss
for the events where the muon pT is failed due to the lepton pT threshold cut. The difference is small,so the reconstructed ETmiss is hardly affected when the muon pT is low.

84

6.4 W+jets background estimation

Figure 6.13: Comparison of the ETmiss distribution between W(→eν)+jets in SR and CRW (top-left),
W(→τν)+jets in SR and CRW (top-right) and W(→µν)+jets in SR and CRW (bottom). Njet ≥4 is applied in all
the figures. The last bin includes the overflow. The bottom panel is the ratio of the MC sample in SR and CRW.
The total number of events in each CRW is normalized to that in SR in each plot. The black error bar is therelative statistical uncertainty in SR.T he hatched red error bands indicate MC statistical uncertainties in CRW.

85

Background estimation

Figure 6.14: Comparison of the ETmiss distribution between W(→eν)+jets in SR and CRW (top-left),
W(→µν)+jets in SR and CRW (top-right) and W(→τν)+jets in SR and CRW (bottom). The selection,
Njet ≥4 is applied to all the figures and the missing transverse momentum is modified under the treatment. The
last bin includes the overflow. The bottom panel is the ratio of the MC simulation in SR and CRW. The total
number of events in each CRW is normalized to that in the SR in each plot. The black error bar is the relative
statistical uncertainty in SR. The hatched red error bands indicate the statistical uncertainties of background
prediction based on MC samples in CRW.

86

6.4 W+jets background estimation
Next, the truth muon η distribution has three peaks : η > 2.5, η < −2.5 and η ∼ 0. When themuon traverses the region of η > 2.5 or η < −2.5, the muon is not reconstructed due to the out ofη acceptance in the muon spectrometer. Such a muon causes the difference between the truth andreconstructed ETmiss as shown in Figures 6.17. However, since this contribution in the SRs is small (lessthan 15%) in W →µν+jets events, there is almost no impact in the ETmiss distribution in CRWs. Whenthe muon traverses the region with η ≈ 0, the muon identification efficiency is rather low (∼ 60%)
compared to other regions as shown in Figure 4.11. Since such an undetected muon would have very
high pT , it makes a large difference between the truth and reconstructed ETmiss as shown in Figures 6.18.
This is the reason why a muon at |η| ∼ 0 is added to the missing transverse momentum instead ofbeing treated as a jet.

Figure 6.15: Distributions of the truth muon pT (left) and η (right) in GGd1 SR. The hatched black error bands
indicate the statistical uncertainties of background prediction based on MC samples.

6.4.3 Adjustment of cut in CRW
In order to pass the requirement of large missing transverse momentum, a large momentum of theneutrino from W boson is needed. In this case, the W boson must be boosted. As a result, the lepton
from the W boson has large momentum and the direction of the lepton and the neutrino is similar.
Therefore, the variable of ∆φ(jet1,2,(3), E®Tmiss )min is small for the lepton which is treated as a jet andsuch events would be rejected due to the selection of this variable. In other words, W boson with very
high pT would have small ∆φ(jet1,2,(3), E®Tmiss )min in CRW. If these events are rejected, the kinematics
of remaining events in CRWs is biased and the difference of BDT score distribution between W+jets
in SRs and W+jets in CRWs becomes large as shown in Figure 6.19(a). In order to avoid this bias, thecut of ∆φ(jet1,2,(3), E®Tmiss )min is not required in CRWs, so good agreement of BDT score distribution
between W+jets in SRs and W+jets in CRWs is observed as shown in Figure 6.19(b). The same biases
are observed in all other CRWs. For GGo1, GGo2, GGo3 and GGo4, the number of remaining data
events in the CRW is very low due to the tight selection. Like the CRY, it causes the large statisticaluncertainties of the normalization factor. Therefore, the cut on ∆φ(jeti>3, E®Tmiss )min is not required.

87

Background estimation

Figure 6.16: Distribution of the difference between truth and reconstructed ETmiss for events where the muon pT
is below the muon pT threshold (<6 GeV) in GGd1 SR. The hatched black error bands indicate the statisticaluncertainties of background prediction based on MC samples.

Figure 6.17: Distribution of the difference between truth and reconstructed ETmiss in case of the outside ofη acceptance (|η| > 2.5). The hatched black error bands indicate the statistical uncertainties of background
prediction based on MC samples.

886.4 W+jets background estimation

Figure 6.18: Distribution of the difference between truth and reconstructed ETmiss in case of the region withη ≈ 0. The hatched black error bands indicate the statistical uncertainties of background prediction based on
MC samples.

Figure 6.20 show distributions of ∆φ(jeti>3, E®Tmiss )min . This variable does not have any slope in theratio of data and MC samples so that the normalization factor would not be biased. Figures 6.21 show
the comparison of BDT score distributions between SRs and CRWs in MC simulation after applying
these procedures. The distributions in CRs are well modeled to describe those in SRs within thestatistical uncertainty of MC samples.

89

Background estimation

(a)

(b)

Figure 6.19: Comparison of BDT score distribution in GGd3 between W+jets in SR (black lines) and CRW (redlines). ∆φ(jet1,2,(3), E®Tmiss )min >0.4 is applied in the left figure, but is not applied in the right figure. The bottom
panel is the ratio of the MC simulation in SR and CRW. The total number of events in each CRW is normalized
to that in the SR in each plot. The black error bar is the relative statistical uncertainty in SR. The hatched rederror bands indicate the statistical uncertainties of background prediction based on MC samples in CRW.

Figure 6.20: Distribution of ∆φ(jeti>3, E®Tmiss )min in the CRW. The same selections as GGo1 (GGo3) SR except∆φ(jet1,2,(3), E®Tmiss )min , ∆φ(jeti>3, E®Tmiss )min and BDT score are applied to left figure (right figure). The MC
samples are normalized to data in order to visualize the shape of distribution. The bottom panel is the ratioof the observed data and the MC simulation. The black bar is the relative statistical uncertainty in data. The
hatched red error bands indicate the statistical uncertainties of background prediction based on MC samples.

90

6.4 W+jets background estimation

Figure 6.21: Comparison of all the BDT score distributions between W+jets in SR (black lines) and CRW (redlines). The bottom panel is the ratio of the MC simulation in SR and CRW. The total number of events in each
CRW is normalized to that in the SR in each plot. The black error bar is the relative statistical uncertainty in SR.
The hatched red error bands indicate the statistical uncertainties of MC samples in CRW.

91

Background estimation

6.5 Top background estimation
In order to estimate the top (t t¯ and single top) background in SRs, the top events are selected as
CR (called CRT) as follows. Like CRW, the same ETmiss triggers as SRs are applied, an electron or amuon is required and a requirement of the transverse mass defined in Eq. 3.1 is applied to enhance thepurity of W boson (30 GeV< mT < 100 GeV). Since an event from top background should have atleast one b quark, an additional criteria of at least one b-jet is required. The treatment of the electron
and the muon in CRTs is the same as CRWs.
The cut of ∆φ(jet1,2,(3), E®Tmiss )min is removed from the selection as discussed in Section 6.4.3. In
addition to the variable, the cut of ∆φ(jeti>3, E®Tmiss )min is removed in order to increase the statistics of
CRTs. Figures 6.22 show the comparison of all the BDT score distributions between top events in SRs
and CRTs. For GGo1 and GGo2, the visible difference is appeared. The observed differences are 50%
for GGo1 and GGo2. Therefore, the systematic uncertainties are assigned so that the differences arecorrected. However, the contribution of the top events is relatively small ( 9% for GGd1 and 12% for
GGo2) as shown in Figure 6.8, thus the total background estimation is almost unchanged.
There are known mismodeling on the t t¯ background [116]. This effect is observed in some variablesin this analysis, such as meff and leading jet pT as shown in Figures 6.23. In order to avoid theeffect in the background estimation, the cuts of these variables in CR are designed to be same as SR.
This background estimation is checked by using validation region (VR), which is explained in next
section.

92

6.5 Top background estimation

Figure 6.22: Comparison of all the BDT score distributions between top events in SR (black lines) and CRT (redlines). The bottom panel is the ratio of the MC simulation in SR and CRT. The total number of events in each
CRT is normalized to that in the SR in each plot. The black error bar is the relative statistical uncertainty in
SR. The hatched red error bands indicate the statistical uncertainties of background prediction based on MC
93
samples in CRT.

10

6

10

5

Data
SM Total

s=13 TeV, 139 fb-1
GGd1

tt(+EW) & single top
W+jets104
10

Events / 50 GeV

Events / 100 GeV

Background estimation

DibosonZ+jets

3

107
10

6

10

5

10

Data
SM Total
tt(+EW) & single top
W+jetsDibosonZ+jets

104

102

3

102

10

10

1
1500

1
2000

2500

3000

3500

4000

4500

5000

2
1.5
1
0.5
0

1500

200

Data/MC

Data/MC

s=13 TeV, 139 fb-1
GGd1

400

600

800

1000

400

600

800

1000

1200

1400

2
1.5
1
0.5

2000

2500

3000

3500

4000

4500

5000

meff [GeV]

0

200

1200

1400

Leading jet P [GeV]T

Figure 6.23: Distribution of the effective mass meff (left) and the leading jet pT (right) with the GGd1 cut except
BDT score cut in CRT. The last bin includes the overflow. The bottom panel is the ratio of the observed data
and the MC simulation. The black error bar is the relative statistical uncertainty in the data. The hatched rederror bands indicate the statistical uncertainties of background prediction based on MC samples.

94

6.6 Validation region

6.6 Validation region
In order to check the results of these background estimation, a further set of regions, called
Validation Region (VR), is designed. They are determined with the same strategy as the CR. In thisanalysis, five VRs are introduced.
Z+jets validation region Z+jets events with two electrons or muons are used as VR, which iscalled VRZ as orthogonal region to SRs and CRYs. In order to emulate the transverse momentum ofneutrinos from Z boson, the reconstructed pT from two leptons is added to the ETmiss vector (ETmiss0 =|Emiss+ pTZ→`` |). After the modification, the missing transverse momentum distribution in VRZT
can be similar to the corresponding SR. The Z(→``) events do not have the large ETmiss , so the ETmiss
triggers cannot be used. Hence, the events are selected by lowest unprescaled single lepton triggers
instead of the ETmiss triggers. In order to enhance the purity of the events, two leptons of the same
flavour and opposite sign with pT (`1 ) > 27 GeV and pT (`2 ) > 7 GeV, are required. Furthermore, thecut of invariant mass in the dilepton system, 66 GeV < m`` <116 GeV is applied. Depending on theselection criteria, three VRZs are prepared:• VRZf is defined with the exact same cuts as the SRs.
• VRZLdPhi is defined with the same cuts as the SR, but the cuts of ∆φ(jet1,2,(3), E®Tmiss )min and∆φ(jeti>3, E®Tmiss )min are loosened.
• VRZLBDT is defined with the same cuts as the SR, but the cut of BDT score is loosened.
W +jets and top validation region Events of VRs for W+jets and top events (VRW and VRT)
are the same as CRW and CRT but the requirements on the variables ∆φ(jet1,2,(3), E®Tmiss )min ,∆φ(jeti>3, E®Tmiss )min and BDT score are changed.
• VRWf, VRTf: In addition to the CRW and CRT selection criteria, the same cut values are usedfor ∆φ(jet1,2,(3), E®Tmiss )min and ∆φ(jeti>3, E®Tmiss )min as SR.
• VRWLBDT, VRTLBDT use the same criteria as the CR, but cut on BDT score is loosened.
Diboson validation region There is no CR for the diboson background, but one VR is prepared asorthogonal region to SRs to check if the MC simulation can model the data well. For this purpose,the process of W(→`ν)Z(→``) is used as VR, which is called VR3L. The events are selected bylowest unprescaled single lepton triggers and three leptons with pT (`1 ) > 27 GeV, pT (`2 ) > 7 GeV
and pT (`3 ) > 7 GeV are required. In order to enhance the purity of the event, the cuts about W bosonand Z boson are required: invariant mass in the dilepton system with 66 GeV < m`` <116 GeV andtransverse mass with 30 GeV< mT < 100 GeV and vetoing the b quark. In the VR3L, the transverse
momentum of the leptons from the Z boson is added to the ETmiss vector. The lepton from the W bosonis treated as a jet. The VR3L is defined as follows.
• VR3LBDT is defined with the same cuts as the SR, but cuts on BDT score are removed.

95

Background estimation
0 lepton validation region Unlike other VRs, a VR0L is prepared as orthogonal region to SRs inorder to test all backgrounds in 0 lepton channel. Two VR0Ls are defined as follow.
• VR0Lmetmeff is defined with the same cuts as the SR, but the cut on ETmiss /meff isinverted (ETmiss /meff <0.2).
• VR0LdPhi is defined with the same cuts as the SR, but the cut on ∆φ(jet1,2,(3), E®Tmiss )min is
inverted (∆φ(jet1,2,(3), E®Tmiss )min <0.4).
Table 6.1 shows the list of selection criteria which is different from SR (Table 5.7). The selectionof ∆φ(jet1,2,(3), E®Tmiss )min , ∆φ(jeti>3, E®Tmiss )min , ETmiss /meff and BDT score are changed, depending on
the VRs. These results are discussed in Section 9.1. In VRXLBDT (X=Z,W,T,3), the BDT score cuts
are loosened to obtain enough statistics.
Table 6.1: Summary of the validation regions for all the categories. The selection criteria which is different
from SR is only listed. The selection criteria which is not listed is the same as SR.

∆φ(jet1,2,(3), E®Tmiss )min∆φ(jeti>3, E®Tmiss )min
ETmiss /meff

Loosened BDT score96≥ 0.2 : VRXLdPhi (X=Z)< 0.4 : VR0LdPhi≥ 0.2 : VRXLdPhi (X=Z)< 0.2 : VR0Lmetmeff≥ 0.6 : VRXLBDT (X=Z,W,T) for GGd1-GGd4≥ 0.0 : VRXLBDT (X=Z,W,T) for GGo1
≥ 0.2 : VRXLBDT (X=Z,W,T) for GGo2
≥ 0.4 : VRXLBDT (X=Z,W,T) for GGo3
≥ 0.5 : VRXLBDT (X=Z,W,T) for GGo4≥-1.0 : VR3LBDT

7 BDT validation
The BDT score is not a quantity directly related to measurements, but an output value from amachine learning technique explained in Section 5.5. The BDT score is a useful variable to efficiently
separate signal and background events. It is important to check carefully if the BDT score has the
expected response in both data and MC samples. This chapter discusses several checks in order tovalidate the response.

7.1 Overtraining
If the statistics in the training sample is low or the number of the training parameters is large, BDT
classifiers could extract the local information of the sample in the training. This is called overtraining.
If the overtraining is observed, the BDT score cut for the testing sample is not optimal. Figure 7.1
shows the signal and background distributions for training and testing samples, respectively. Since a
difference between the training and testing samples is observed in the signals, the optimal BDT score
cuts would be different from training and testing samples. If two distributions are similar, the BDT
score cut which is optimized to testing sample is optimal and thus "no overtraining" is very important.

(1/N) dN / dx

TMVA overtraining check for classifier: BDTG
1.8
1.6

Signal (test sample)

Signal (training sample)

Background (test sample)

Background (training sample)

Kolmogorov-Smirnov test: signal (background) probability = 0.024 (0)

1.4
U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%

1.2
1
0.8
0.6
0.4
0.2
0

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

BDTG response

Figure 7.1: BDT score distribution for signals (blue) and backgrounds (red). The dot (filled) histograms are forthe training (testing) samples [113]. Since a difference between the training and testing samples is observed in
the signals, the different sensitivities are obtained when the same BDT score cut is applied.

97

BDT validation
In order to check the overtraining, the comparison of BDT score distribution between the training
sample and testing sample in each SR is performed as shown in Figures 7.2. A ratio of training
and testing samples is checked to quantify the level of a consistency between two distributions. For
the background, the BDT score distributions in the training sample are similar to the testing sample
because the ratio is almost 1 within the MC statistical uncertainty. For the signal, disagreement of
BDT score distributions is appeared with low BDT score (< −0.5) due to the MC statistics in training
sample. They are slightly affected by the overtraining. However, the optimal BDT score cut in the
training sample is similar to the testing sample because there are following reason. As shown in
Figures 7.2, these signals are almost have the positive BDT score and the ratio in the positive BDT
score is almost 1. It means that the signal efficiency of testing sample is almost same as training
sample until the BDT score cut is more than 0.0. In this analysis, all the regions only use the high
BDT scores, so the optimal BDT score cut in the training sample is similar to testing sample.
From the check, the sensitivity of target signals are maximized by the optimized BDT score cuts as
defined in Table 5.7.

7.2 Difference of two BDT score distribution
The training method illustrated in Figure 5.16 assumes that there are no differences between two
BDT classifiers If the statistics in the training is large enough, both BDT score distributions should bestatistically the same and the sensitivity is maximized. In order to validate this, the comparison of
BDT score distributions between first- and second-half training samples is performed on signal andbackground components, respectively. The BDT score in the first-half sample shows good agreementwith that in second-half sample for both signal and background components because the ratio oftraining and testing is almost 1 within the MC statistical uncertainty as shown in Figure 7.3.

98

7.2 Difference of two BDT score distribution

Figure 7.2: Normalized BDT score distributions between the signal (blue) and background (red) component.
The histogram indicates the training sample and the dot point indicates the testing sample. The bottom panel isthe ratio of the training and testing sample.

99

BDT validation

Figure 7.3: Normalized BDT score distributions in the signal (blue) and background (red) component. The
histogram indicates the first-half sample and the dot point indicates the second-half sample. The bottom panel
is the ratio of the first-half and second-half sample.

100

7.3 Correlation of input variables

7.3 Correlation of input variables
The BDT scores are produced by taking into account the correlation of variables. Hence, thevariable correlations in the MC samples need to be described by the data in order to use BDT scoresbuild by MC simulation to data. Additionally, since the normalization factors calculated in CRs isapplied to SRs, the correlations in CRs should have similar tendencies as SRs.
In order to check them, the correlation coefficient values are calculated for the input variables. The
correlation coefficients of two variables, x, y are defined as:(xi − hxi) · (yi − hyi)
σx σy
ÍN
ÍN
yi
i xi
hxi =
, hyi = i
N
Nv
v
u
u
t
t
N
N
1 Õ 2
1 Õ 2
σx =
xi , σy =
yi
N i
N i

corr(x, y)i =

(7.1)
(7.2)
(7.3)

where N is the total number of events, hxi, hyi are the mean of the variable and σx , σy are theRMS. If two variables are uncorrelated, the distribution of correlation coefficient becomes a gaussian
distribution centered at zero. This distribution would be distorted if there is the correlation of two
variables. The features of the correlations can be extracted from the distribution. Figures 7.4-7.5
show the distributions of correlation coefficients between meff and leading jet pT for SRs. Since meffis defined as Eq. 5.1, they are positively correlated so that the positive tails in the distribution are
observed. Good agreement of data and MC samples is observed within the MC statistical uncertainty.
Figures 7.6 show the mean of the distributions of correlation coefficients as a matrix (hcorr(x, y)i i) for
the signals, MC samples and data in GGd1 SR. Compared to the signals and SM backgrounds, theclear difference between the leading jet pT and subleading jet pT (0.49 for signals and 0.24 for SM
backgrounds) as explained in Section 5.4. The matrix of the data has similar tendency. Figure 7.7
shows the difference of correlation coefficients between the data and MC samples and The value
corresponds to the difference. All the correlations in MC samples show agreement with those of thedata within 10% level and all correlations are modeled well by MC samples The similar tendencies
are also observed in CRY, CRW and CRT as shown in Figures 7.8.

101

BDT validation

Figure 7.4: Correlation coefficients of meff and leading jet pT with the selection criteria in all SRs except BDTscore cut. All MC samples are normalized to the data of 139 fb−1 . The last bin includes the overflow. The
bottom panel is the ratio of the data and the MC simulation. The black error bar is statistical uncertainty in thedata. The hatched red error bands indicate MC statistical uncertainties.

102

7.3 Correlation of input variables

Figure 7.5: Correlation coefficients of meff and leading jet pT with the selection criteria in GGd1 CRY (left),
CRW (center) and CRT (right) except BDT score cut. All MC samples are normalized to the data of 139 fb−1 .
The last bin includes the overflow. The bottom panel is the ratio of the data and the MC simulation. The black
error bar is statistical uncertainty in the data. The hatched red error bands indicate MC statistical uncertainties.

Figure 7.6: Matrix of all correlations in gluino direct decay signals with (mg̃ ,m χ̃0 )=(2000, 400) (top-left), MC
1samples (top-right) and data (bottom) applying the selection criteria in GGd1 SR without BDT score cut. The
value corresponds to the mean of each correlation coefficient. The x- and y-axes indicate input variables.

103

BDT validation

Figure 7.7: Matrix of the difference of the mean correlation coefficients between the data and MC samples
applying the selection criteria in GGd1 SR without BDT score cut. The value corresponds to the difference ofeach correlation coefficient between the data and MC simulation. The x- and y-axes indicate input variables.

Figure 7.8: Matrix of all correlations in data (left) and MC simulation (center) for GGd1 CRY (top), CRW (center)and CRT (bottom) without BDT score cut. The value corresponds to the mean of each correlation coefficient.
The difference of the correlation coefficient between the data and MC simulation is shown in the right figures.
The x- and y-axes indicate input variables.

1047.4 Profile distribution in BDT score

7.4 Profile distribution in BDT score
As discussed in Section 7.3, the correlations of input variables are modeled by MC simulation. If
the BDT classifier utilizes these correlations in the separation between signal and background, theproduced BDT scores should have the expected dependence of input variables. For example, BDTscore should become larger as the effective mass is larger if the feature of signals is extracted correctly.
For this purpose, the dependence on each input variable to the BDT score is checked by calculating themean value of input variables per BDT score bin (profile). Figures 7.9 show profile distributions forthe effective mass. It is observed that the effective mass is larger as the BDT score is larger. Since theeffective mass of the signals is large as discussed in Section 5.4, the signals can be survived with thetight BDT score cuts. It implies that the signals remain in SRs even though the signals are different
from the training samples. Additionally, an agreement of the profile distribution between the data
and MC simulation is observed within 10% in SR, CRY and CRW as shown in Figures 7.9 and 7.10.
Since there is the mismodeling on the t t¯ background, an agreement within 15% in CRT is observed.
The behavior of the BDT score distributions are well modeled.

7.5 Summary of BDT validation
Three validations discussed in this Chapter are summarized.
• Overtraining: The produced BDT scores are not biased as shown in Figures 7.2 and 7.3 andthe cuts on BDT score in the Table 5.7 are optimal cuts, which allows the sensitivity of thetarget signals to maximize.
• Correlation of input variables: The correlation of input variables in the MC samples, which
the BDT classifier takes into account, is described by the data within 10% level as shown in
Figures 7.4-7.8. It implies that the BDT scores are the well-understood variables.
• Profile distribution in BDT score: The produced BDT scores have the expected behavior as
shown in Figures 7.9 and 7.10. The effective mass is larger as the BDT scores are larger andsignals having large effective mass are selected. It means that even if the properties of eventsare different from the signals used as training sample, the BDT scores can catch the events up tolarge effective mass is large. Hence, the search for the general signal like events having large
effective mass can be performed.

It has been proved that the BDT classifiers are applicable to both data and MC samples from theseresults. In addition to the method of designing CRs as discussed in Section 6.2, the backgroundestimation using the machine learning has been established in gluino search. It is the important andunique point in this thesis. Based on the framework, the first preliminary result of the gluino searchusing the machine learning was published from ATLAS1 , which is shown in next chapter.
1 It is the preliminary results in a public note of the ATLAS Collaboration, prepared for conferences in 2019. It will be

submitted to a journal in early 2020.

105

BDT validation

Figure 7.9: Average of meff value in each BDT score bin in all SRs without BDT score cut. The black dot
indicates the data and the red dot indicates the MC simulation. The bottom panel is the ratio of the data and theMC simulation.

Figure 7.10: Average of meff value in each BDT score bin for GGd1 CRY (left), CRW (center) and CRT (right).
The black dot indicates the data and the red dot indicates the MC simulation. The bottom panel is the ratio ofthe data and the MC simulation.

106

8 Statistical analysis
A fit to estimate the expected number of events in the SR is performed under a given hypothesis
using a profile Log Likelihood Ratio (LLR) approach. The profile LLR is computed a SR and aset of CRs in three kind of fits: background only fit, model-dependent fit and model-independent
fit [117]. This chapter describes the definition of the likelihood function and the treatment of systematic
uncertainties.

8.1 Likelihood function
The likelihood function is defined as a product of Poisson probability density for SR, and allconsidered CRs and the Gaussian probability density for the systematic uncertainties:
L(n|µ, s, b, θ) =PSR × PCRW × PCRT × PCRY × CSyst(8.1)

where PSR , PCRY , PCRW and PCRT are Poisson probability distributions in each region. CSyst is the
product of Gaussian probability distributions of systematic uncertainties. Each Poisson probability
density distribution Pi uses the observed number of events ni and the expected number of events λi ina given region:
λknk −λPk = P(nk |λk ) =
e k
(8.2)
nk !
The λk is expressed as:Õλk (µ, sk , b, θ) = sk (θ) · µs + (bk, j (θ) · µ j ) + bk,Diboson (θ) + bk,Multi-jet (θ)(8.3)
jwhere each parameter is defined as followings:• k refers to a region (SR, CRY, CRW, CRT).
• j refers to a physics process (Z+jets, W+jets or Top).
• sk is the expected number of signal events from MC simulation in a region k.
• bk, j is the expected number of background events of physics process j from MC simulation in aregion k.
• bk,Diboson is the expected number of background events of diboson process from MC simulation,
which does not have a dedicated CR.
• bk,Multi-jet is the expected number of background events of multi-jet process from MC simulation,
which does not have a dedicated CR.

107

Statistical analysis• µs is the free normalization factor of a signal process and called signal strength.
• µ j is the free normalization factor of a background process j. These are set to the normalization
factors calculated from each CR: Ndata,CR /NMC,CR• θ is a set of the nuisance parameters, which parametrizes systematic uncertainties.
The systematic uncertainties Csyst is expressed as:ÖCsyst =
G(θ i )

(8.4)

i ∈SU

where SU is a set of systematic uncertainties and G is the standard gaussian probability with thenuisance parameter θ i . The mean of standard deviation of all probability density distributions is set to
0 and thus θ = +1 (θ = −1) corresponds to +1σ (−1σ) variations. Since s and b are a function of θ,
the likelihood function is denoted as L(µ, θ) from next section.

8.2 Hypothesis test
The profile likelihood ratio [118] is defined as:
LLR(µs ) =ˆL(n| µs , θ̂)(8.5)

L(n| µ̂s , θ̂)ˆ is the maximized likelihood function for a given parameter µ (conditional
where L(n| µs , θ̂)smaximum-likelihood function). θ̂ˆ corresponds to θ for the conditional maximum-likelihood function.
On the other hand, L(n| µ̂s , θ̂) is the maximized likelihood function (unconditional maximum-likelihood
function). The parameters of ( µ̂s , θ̂) correspond to the parameters of (µs , θ) for the unconditional
maximum-likelihood function.
A test statistics qµs [118] is defined as(qµs = −2log(LLR(µs )) =s ,θ̂)−2log(LLR(µs )) = −2log L(µL(µ̂s ,θ̂)
0Then, a p-value is defined aspµ s =ˆ∫ ∞f (qµs | µs )dqµsµs ≥ µ̂s
0 < µs < µ̂s

(8.6)

(8.7)

qµ s ,obs

where qµs ,obs is the observed value qµs and f (qµs | µs ) is the probability density function of the qµs
under the signal strength µs [118]. The probability density function is defined as





1
1
1 √
µs − µ̂s 2
1 √µs − µ̂s 2
f (qµs | µs ) = √exp − ( qµs +) + exp − ( qµ −
)
(8.8)
√
2 qµs 2π2σ2σwhere σ is the standard deviation of µ̂s [118]. Under the assumption of the signal plus backgroundcase, the probability density function is obtained with µs = 1: f (qµs | µs = 1). On the other hand,1088.3 Systematic uncertainty
under the assumption of the background only case, the probability density function is obtained with
µs = 0: f (qµs | µs = 0).
In order to claim the exclusion of a signal hypothesis, CLs+b , CLb and CLs , which are defined as
below, are used [119].
∫ ∞CLs+b =f (qµ | µs = 1)dqµ = p1
(8.9)
qµ ,obsCLb =∫ ∞qµ ,obsCLs =f (qµ | µs = 0)dqµ = p0p1p0(8.10)(8.11)

When a CLs value is less than 0.05, its signal hypothesis is considered to be excluded at the 95%
confidence level.
In this analysis, the fit without the contribution of signal process is first performed to obtain thenumber of background events in SRs: the fit with the signal strength µs = 0 is performed. This fit
is called background-only fit. Then, when there is no excess in SRs over the number of predictedbackground events, the model-independent and model-dependent fits are performed. The aim of themodel-independent fit is to set upper limits on the number of the events Beyond Standard Model (BSM
event) in SRs using asymptotic formulae [118]. The fit is performed in SR and CRs simultaneously.
Under the fit condition, the p-value defined in Eq. 8.7 is calculated, varying the signal strength. Then,the number of expected signal events and observed signal events on the p-value at 0.05 is interpreted.
95 and S 95 . The visible cross section (h σi 95 ) which is defined Eq. 8.12 is also
They are called Sex
p
obs
obs
calculated [119].
S 95
95h σobsi = ∫ obs
(8.12)Ldt
The aim of the model-dependent fit is to set upper limits for the dedicated signal models at the 95%
confidence level [118]. The fit is performed in SR and CRs simultaneously like model-independent fit.
Under the fit condition, the CLs value defined in Eq. 8.11 is calculated at the fixed signal strengthµs = 1.0 for all signal points. Then, the upper limit on the CLs value at 0.05 is evaluated. These
results are discussed in Section 9.2 and 9.3.

8.3 Systematic uncertainty
There are four types of systematic uncertainties in background prediction: experimental uncertainty,
theoretical uncertainty, MC statistical uncertainty and CR statistical uncertainty. In addition, the SUSY
signal uncertainties are considered. The details of all the uncertainties are explained in this section.

8.3.1 Experimental uncertainty
The following experimental uncertainties are considered.

109

Statistical analysis
Jet As discussed in Section 4.2, the uncertainties in JES calibration are assigned on the jet energy
scale and resolution [100]. More than 100 independent uncertainties are prepared, but the uncertainties
with the similar behavior can be combined [100]. This analysis takes 20 nuisance parameters. Since
this analysis focuses on the kinematic edge of jets, the shift of the jet energy would become large effectin all SRs. The uncertainty of JES calibration is the most dominant in all experimental uncertainties.

ETmiss soft term As discussed in Section 4.5, the scale and resolutions of the objects are propagatedto the soft term in the missing transverse momentum. Hence, the uncertainties of the energy scale andresolution with the soft term in the missing transverse momentum are considered [109].

Lepton, photon and b-tagging The uncertainties of calibration and identification of electrons,muons and photons and the efficiency correction of the b-tagging algorithm are assigned [104–108].
Since the effect of these objects is not sensitive in the SRs, these uncertainties are small in thisanalysis.

Luminosity The uncertainty in the combined 2015–2018 integrated luminosity is 1.7 % [55],obtained using the LUCID-2 detector [45] for the primary luminosity measurements.

Pileup Reweight As discussed in Section 3.3, the up-type (down-type) scale factor is 1/1.07 (1/0.99).
If the scale factor is varied from down-type to up-type scale factor, the impact on the event yield isassigned as the systematic uncertainties. Since this analysis requires the large jet pT and missing
transverse momentum, the effect of the pileup is relative small. It means that this analysis is notsensitive for the pileup and the systematic uncertainty is negligible level.
When these systematic sources are varied, the difference of background events from the nominalis evaluated. The systematic uncertainties are calculated to cover the difference. The evaluatedrelative uncertainties of each experimental uncertainty on the background prediction are summarized
in Figure 8.1. The uncertainties related to jets are dominant in the experimental uncertainties andraise up to ∼ 15% for GGo1 region. The kinematic selection in GGo1 region is tightest in all regions
and a shift in jet energy has the impact of the background prediction. The effects of uncertainties
related to ETmiss soft terms and pileup reweight are a few percent level. The lepton, photon, b-tagging
and luminosity uncertainties are negligible (<1%).

8.3.2 Theoretical uncertainty
The theoretical uncertainties of V+jets, top and diboson components are considered. There are
CRs for the V+jets and top components and all the uncertainties are assigned on the transfer factors,MCwhich are NMC
SR /NCR in Eq. 6.1. For the diboson components, there is no dedicated CR, so theuncertainties were determined not only on shape, but also on the cross-section. The treatment ofsystematic uncertainties are based on Refs. [120, 121].

110

Relative uncertainty

8.3 Systematic uncertainty
0.5
0.4

Jet

s=13 TeV, 139 fb-1

miss

ET

0.3

soft term

Pileup Reweight

0.2
0.1
0

−0.1
−0.2
−0.3
−0.4
−0.5 GGd1

GGd2

GGd3

GGd4

GGo1

GGo2

GGo3

GGo4

Figure 8.1: Calculated relative theoretical uncertainties on the background prediction for all the experimental
uncertainties. The red line corresponds to the uncertainties related to jets and the blue line corresponds tothe uncertainties related to ETmiss soft terms. The green line corresponds to pileup reweight uncertainty. The
uncertainties of lepton, photon, b-tagging and luminosity are less than 0.01 and they are not displayed in theplot.

V +jets Since the dominant background is V+jets component, the theoretical uncertainties of V+jets is
crucial. The V+jets components are simulated using Sherpa 2.2.1 generator as shown in Table 3.4 andthe scale variations are performed to evaluate systematic uncertainties. There are four considering scalevariations for the used samples: renormalization, factorization, resummation (qsf) and CKKW1 [65,122]. In order to estimate these uncertainties, the impact on the shift of the envelope with respect
to the nominal samples is evaluated as up-type and down-type. The renormalization, factorizationand qsf scales in up-type (down-type) samples are four (one fourth) times as the nominal sample.
The CKKW scale in nominal sample uses 20 GeV and it varies from 15 GeV (down-type variation)
to 30 GeV (up-type variation). Next, the parton distribution function (PDF) and strong coupling
constant (αs ) uncertainties are considered [120]. The PDF uncertainties are calculated using thecorresponding error sets and taking the standard deviation. αs uncertainties are estimated by using theupsame PDF set evaluated at different αs values (αs = 0.119, αsdown = 0.117).
The evaluated relative uncertainties of V+jets on the background prediction are summarized in
Figures 8.2. The dominant theoretical uncertainty is the scale variation and it typically varies from 2%
to 10%, depending on the region. If the region with softer kinematic cuts, the PDF and αs uncertainties
are negligible, but they raise up to 4% for tight kinematic region (GGo1).
Diboson The diboson process is also simulated using Sherpa 2.2.1 generator as shown in Table 3.4
and the scale variations are considered as similar approach as V+jet samples. The evaluated relative
uncertainties on the background estimation are summarized in Figure 8.3. The dominant uncertainty
in the scale uncertainties is the renormalization and factorization scale variations. They raise up to∼ 30% for GGd4 region.
1 CKKW indicates the boundary of transverse momentum between tree-level matrix elements and parton showers.

111

0.3
0.2

s=13 TeV, 139 fb-1
Z+jetsScale uncertainty

CKKW uncertainty

PDF uncertainty

qsf uncertainty

Relative uncertainty

Relative uncertainty

Statistical analysis

αs uncertainty

0.1
0

0.3
0.2

−0.2

−0.2
GGd3

GGd4

GGo1

GGo2

GGo3

−0.3 GGd1

GGo4

CKKW uncertainty

PDF uncertainty

qsf uncertainty

αs uncertainty

0

−0.1

GGd2

Scale uncertainty

0.1

−0.1

−0.3 GGd1

s=13 TeV, 139 fb-1
W+jets

GGd2

GGd3

GGd4

GGo1

GGo2

GGo3

GGo4

Relative uncertainty

Figure 8.2: Calculated relative theoretical uncertainties on the background prediction for Z+jets samples (left)
and for W+jets samples (right). The red line corresponds to renormalization, factorization scale uncertainties
and the blue line corresponds to PDF uncertainties. The green line corresponds to αs uncertainties, the orange
line corresponds to CKKW uncertainties and the pink line corresponds to resummation (qsf) uncertainties.

0.4

s=13 TeV, 139 fb-1
DibosonScale uncertainty

αs uncertainty

PDF uncertainty

0.2
0

−0.2
−0.4
GGd1

GGd2

GGd3

GGd4

GGo1

GGo2

GGo3

GGo4

Figure 8.3: Calculated relative theoretical uncertainties on the background prediction for diboson samples. The
red line corresponds to renormalization, factorization scale uncertainties, the blue line corresponds to PDF
uncertainties and the green line corresponds to αs uncertainties.

1128.3 Systematic uncertainty
Top As discussed in Section 6.1, the dominant process in the production which includes top quarks
is t t¯ production. Hence, the uncertainties of t t¯ sample are only considered. The modelling of the t t¯process is difficult and known problem [116], so the difference of generated by an alternative generators,
which have different calculation of matrix elements is assigned as theoretical uncertainty. The nominalt t¯ sample is simulated using Powheg-box and the following uncertainties are evaluated:• Hard Scatter: difference between Powheg-box+Pythia8 and MC@NLO+Pythia8 [82].
• Hadronization, showring: difference between Powheg-box+Herwig7 [123] and Powheg-box+
Pythia8.
• Radiation: difference between Powheg-box + Pythia8 and Powheg-box + Pythia8 withdifferent shower parameters.
– Radiation up (RadHigh): the renormalisation and factorisation scales by 0.5 and at thesame time varying the Pythia8 parameter.
– Radiation down (RadLow): the renormalisation and factorication scales by 2 and at thesame time varying the Pythia8 parameter.

Relative uncertainty

The evaluated relative systematic uncertainties on the background prediction are summarized in
Figure 8.4. The meff distribution in MC@NLO generator is significantly softer than in the Powheg-box
0
generator, so the hard scatter uncertainty is large when the target ∆m(g̃, χ̃1 ) is large. The systematic
uncertainty is very large for applying the tight kinematic selection cut such as GGd1, GGd2, GGo1
and GGo2.
0.8
0.6

s=13 TeV, 139 fb-1
Top

Hard Scatter

Radiation

Hadronization, Showring

0.4
0.2
0

−0.2
−0.4
−0.6
−0.8 GGd1

GGd2

GGd3

GGd4

GGo1

GGo2

GGo3

GGo4

Figure 8.4: Calculated relative theoretical uncertainties on the background prediction for t t¯ samples. The redline corresponds to hard scatter uncertainty, the blue line corresponds to hadronization, showering uncertainties
and the green corresponds to radiation uncertainty.

113

Statistical analysis
In addition, the visible difference between SR and CRT is considered as the systematic uncertainty
as discussed in Section 6.5. In order to cover the difference, 50% uncertainty to top yield is considered
for GGo1 and GGo2. Since the contribution of top events is relatively small for GGo1 and GGo2, thissystematic uncertainty does not affect the total background yield.
Multi-jet As discussed in Section 6.1, the multi-jet process is negligible. In this analysis, 100%
uncertainty to the multi-jet yield is considered. This is a conservative uncertainty from the validation
region result discussed in Section 9.1.

8.3.3 MC statistical uncertainty
The MC statistical error to the MC events in all regions is considered. Since this analysis uses theMC samples and the kinematic edge of distributions due to tight cut, the MC statistical uncertainty isimportant source in systematic uncertainties.

8.3.4 CR statistical uncertainty
As discussed in Chapter 6, normalization factors are obtained from the observed data in the CRs.
Since all fits are performed in SR and CRs simultaneously as explained in Section 8.2, the statisticalerrors in CR are considered as the uncertainties of normalization factors. Only the statistical errors in
CRs are taken into account as their systematic uncertainties because of single-bin counting experiment.
The uncertainties of the normalization factors are most dominant in most of SRs because the statistics
is very low due to tight BDT score cut.

8.3.5 SUSY signal
The cross section uncertainty is estimated by changing the renormalization, factorization, PDF
and the strong coupling constant. The fraction on the cross section is varied from ∼ 8.6% (for 600
GeV gluino mass) to ∼ 30% (for 2600 GeV gluino mass) [37]. Experimental uncertainties and MC
statistical uncertainties are also estimated in the same way for the backgrounds, but they are less thana few percent.

8.3.6 Summary of systematic uncertainties
In this analysis, the nuisance parameters are treated as follow.
• Experimental uncertainties are correlated across the different regions (SR, CRY, CRW and
CRT) and the different physics processes (V+jets, top, diboson and multi-jet).
• Theory uncertainties are correlated across the different regions but independent per process.
• MC statistical and CR statistical uncertainties are fully uncorrelated variables.

114

8.3 Systematic uncertainty

Relative error

Figure 8.5 shows the breakdown of the relative systematic uncertainties on the background prediction.
The dominant systematic uncertainty is the statistical uncertainty in CRs. The theoretical uncertaintyof V+jets is subdominant. The dominant experimental uncertainty is the JES uncertainty. The valuesof relative systematic uncertainties for all types are shown in Table 8.1. These systematic uncertainties
are used in both SRs and VRs.
0.4

s=13TeV, 139 fb-1

0.35
0.3
0.25
0.2

Total Uncertainty
MC statistical uncertainty
CR statistical uncertainty
Theoretical uncertainty
Experimental uncertainty

0.15
0.1

GGo4

GGo3

GGo2

GGo1

GGd4

GGd3

GGd2

0

GGd1

0.05

Signal region

Figure 8.5: Breakdown of the relative systematic uncertainties on the background prediction. The individual
uncertainties can be correlated so that the total background uncertainty is not necessarily their sum in quadrature.

Table 8.1: Relative systematic uncertainties on the background estimation.

SR
Experimental uncertainty [%]Theoretical uncertainty [%]MC statistical uncertainty [%]CR statistical uncertainty [%]Total statistical uncertainty [%]

GGd1
8.5
4.2
5.1
12.2
16.4

GGd2
3.6
4.3
3.1
9.2
11.2

GGd3
1.9
4.8
1.5
5.2
7.4

GGd4
3.2
5.3
1.4
4.8
7.9

GGo1
16.5
3.8
9.3
16.4
27.1

GGo2
5.5
4.3
4.9
9.7
13.1

GGo3
4.7
7.3
2.6
6.0
10.5

GGo4
3.5
6.5
3.2
6.1
10.0

115

9 Results
This chapter shows the results of the fit described in the previous Chapter and discusses the resultsin detail.

9.1 Results from background-only fit

GGo4
GGo4

GGo4

GGo3
GGo3

GGo3

GGo2
GGo2

GGo2

GGo1
GGo1

GGo1

GGd4
GGd4

GGd4

GGd3
GGd3

GGd3

GGd1

GGd2
GGd2

GGd2

2
1.5
1
0.5
0

s=13 TeV, 139 fb-1

GGd1

2
1.5
1
0.5
0
2
1.5
1
0.5
0

GGd1

µ(W+jets)µ(Z+jets)µ(Top)The normalization factors determined in each CR of each background component from thebackground-only fit are shown in Figure 9.1. The normalization factors for top background (µ(Top))are smaller than 1.0 in the SR with tight kinematic selection such as GGd1, GGd2, GGo1 or GGo2.
Since there is the mismodelling of the jets at t t¯ system as shown in Figure 6.23, the small normalization
factors are expected. Since the MC simulation of V+jets samples is described well, the normalization
factors for W+jets (µ(W)) and Z+jets (µ(Z)) are closer to 1.0.

Figure 9.1: Fitted normalization factors per component for all the SRs. The vertical size of the colored region
corresponds to the uncertainty of the normalization factor in each background component.

As discussed in Section 6.6, the number of the background events with background-only fit istested by using VRs. In order to evaluate the difference between the prediction and observed data,
the standard deviation (Zn ) is estimated from the p-value (p0 ) defined as Eq. 8.11. Summary of thedeviation in all the VRs are shown in Figure 9.2 and good agreement between the prediction and thedata is observed within Zn < 2.0σ. The comparison of the prediction and the data in each VR is shownin Figures 9.3-9.5. The background estimation discussed in Section 6.2 seems to have worked properly
from these results, so all SRs were unblinded under these setup. Figure 9.6 shows the comparison of
the prediction and the data in all SRs. The event yields are summarized in Tables 9.1-9.8. The MC

117

Results
event yields ("MC exp.") in these Tables indicate the yields without the normalization factors (pre-fit
yields) and the fitted event yields ("Fitted") indicate the yields with the normalization factors (post-fit
yields). The contribution of the Z+jets component is dominant and followed by the W+jets anddiboson component except GGo4. The contribution of the top background is negligible for GGd1,
GGd2, GGo1 and GGo2 where the tight kinematic selections are applied and visible for GGd3, GGd4,
GGo3 and GGo4 where the loose kinematic selections are applied. No significant excess over the
background prediction is observed as shown in Figure 9.6 and Tables 9.1-9.8.

0.4

0.4

-0.4

-0.6

-0.1

-0.9

0.5

1.5

0.9

-0.6

GGd2

-0.1

-0.1

-0.3

-0.4

-0.1

-0.2

1.5

1.5

0.1

-0.3

GGd3

0.7

0.3

1.0

-0.7

1.1

1.9

-0.4

0.5

-0.8

-0.7

GGd4

1.6

1.6

0.8

-0.2

2.1

0.9

1.9

0.5

-0.0

-0.4

GGo1

-1.1

-1.3

-0.8

-0.7

0.6

-0.5

1.0

0.6

0.8

-0.7

GGo2

-0.9

0.0

0.6

-0.2

0.3

-1.2

1.3

0.6

-0.8

-1.0

GGo3

1.8

1.8

1.4

1.2

-0.1

0.2

0.1

0.7

-0.4

-1.0

GGo4

1.5

1.3

-0.6

0.3

-0.0

0.4

0.1

0.5

-0.4

-0.3

VR0LdPhi

VR0Lmetmeff

3
GGd1

2
1

VR3LBDTVRTLBDT

VRTf

VRWLBDT

VRWf

VRZLBDT

VRZLdPhi

VRZf

0
−1

Standard deviation [σ]s=13TeV, 139 fb-1

−2
−3

Figure 9.2: Summary of the standard deviation, which is calculated from the p-value in all the VRs (x-axis) for
each SR (y-axis).

118

Data
SM Total
Z+jetsW+jetstt(+EW) & single top
DibosonMulti-jets=13TeV, 139 fb-1

3

10

Events102

10

BDT VRW

1102

BDT VRW

Events

102

10

10

GGd3

GGd4

GGo1

GGo2

GGo3

GGd3

GGd4

GGo1

GGo2

GGo3

1

GGo4

GGd2

GGd2

1.5

BDT VRZL∆Φ
GGo4

0.5

GGo4

GGo3

GGo2

GGo1

GGd4

GGd3

GGd2

Data/SM

GGo4

GGo3

GGo2

GGo1

GGd4

GGd3

GGd2

GGd1

0.5

GGd1

Data/SMBDT VRT

1

GGd1

1

1
1.5

Data
SM Total
Z+jetsW+jetstt(+EW) & single top
DibosonMulti-jets=13TeV, 139 fb-1

3

10

GGd1

EventsData
SM Total
tt(+EW) & single top
W+jetsZ+jetsDibosonMulti-jets=13TeV, 139 fb-1

3

GGo4

GGo3

GGo2

GGo1

GGd4

GGd3

GGd2

GGd1

0.5

BDT VRZ

10

GGo4

GGo3

GGo2

GGo1

GGd4

GGd3

1.5

GGo4

GGo3

GGo2

GGo1

GGd4

GGd3

GGd2

GGd1

0.5

Data/SM

GGo4

GGo3

GGo2

GGo1

GGd4

GGd3

GGd2

GGd1

BDT VRZ

1

GGd2

1

1

Data/SMData
SM Total
W+jetstt(+EW) & single top
Z+jetsDibosonMulti-jets=13TeV, 139 fb-1

102

10

1.5

3

10

GGd1

Events

9.1 Results from background-only fit

BDT VRZL∆ Φ

BDT VRT

EventsData
SM Total
Z+jetsW+jetstt(+EW) & single top
DibosonMulti-jet

104

s=13TeV, 139 fb-1
3

10

102

3

10

102

10

10

BDT VRWLBDT

1

3

10

BDT VRWLBDTEventsEventsData
SM Total
tt(+EW) & single top
W+jetsZ+jetsDibosonMulti-jets=13TeV, 139 fb-1

GGo4

GGo3

GGo2

GGo1

GGd4

GGd3

GGd2

GGd1

0.5

BDT VRZLBDT

104

GGo4

GGo3

GGo2

GGo1

GGd4

GGd3

GGd2

1.5

GGo4

GGo3

GGo2

GGo1

GGd4

GGd3

GGd2

0.5

Data/SM

GGo4

GGo3

GGo2

GGo1

GGd4

GGd3

GGd2

GGd1

1

BDT VRZLBDT

1

GGd1

Data/SM

1
1.5

Data
SM Total
W+jetstt(+EW) & single top
Z+jetsDibosonMulti-jets=13TeV, 139 fb-1

104

GGd1

EventsFigure 9.3: Comparison of the background prediction and observed data in VRZf (top-left), VRWf (top-right),
VRTf (bottom-left) and VRZLdPhi (bottom-right) regions for each SR.

Data
SM Total
DibosonZ+jetsW+jetstt(+EW) & single top
Multi-jet3

10

s=13TeV, 139 fb-1

102

102
10
10

GGo4

GGo3

GGo2

GGo1

GGd4

GGd3

GGd2

BDT VR3LBDT

1

GGo4

GGo3

GGo2

GGo1

GGd4

GGd3

GGd2

0.5

GGd1

GGo4

GGo3

GGo2

GGo1

GGd4

GGd3

GGd2

BDT VRTLBDT

Data/SM

GGo4

GGo3

GGo2

GGo1

GGd4

GGd3

GGd2

GGd1

GGd1

Data/SMBDT VRTLBDT

1
0.5

1.5

GGd1

1

1
1.5

BDT VR3LBDT

Figure 9.4: Comparison of the background prediction and observed data in VRZLBDT (top-left),
VRWLBDT (top-right), VRTLBDT (bottom-left) and VR3LBDT (bottom-right) regions for each SR.

119

3

EventsEventsResults

Data
SM Total
Z+jetsW+jetstt(+EW) & single top
DibosonMulti-jet10

s=13TeV, 139 fb-1
102

5

10

Data
SM Total
Z+jetsW+jetstt(+EW) & single top
DibosonMulti-jets=13TeV, 139 fb-1

104
3

10

102

10

10

GGo4

GGo3

GGo2

GGo1

GGd4

GGd3

GGd2

BDT VR0Lmetme

1

BDT VR0L∆ Φ

GGo4

GGo3

GGo2

GGo1

GGd4

GGd3

0.5

GGd1

GGo4

GGo3

GGo2

GGo1

GGd4

GGd2

GGd3

0.5

1.5

GGd2

BDT VR0L∆Φ

GGd1

Data/SM

1

GGo4

GGo3

GGo2

GGo1

GGd4

GGd2

GGd3

1
GGd1

1.5

GGd1

Data/SM1

BDT VR0Lmetme

EventsFigure 9.5: Comparison of the background prediction and observed data in VR0LdPhi (left), VR0Lmetmeff (right)
regions for each SR.

104

Data
SM Total
Z+jetsW+jetstt(+EW) & single top
DibosonMulti-jet-1

s=13TeV, 139 fb
3

10

102

10

GGo1

GGo1

GGo4

GGd4

GGd4

GGo3

GGd3

GGd3

GGo2

GGd2

GGd2

GGd1

1

BDT Signal Region
GGo4

GGo3

GGo2

0.5

GGd1

Data/SM1
1.5

BDT Signal Region

Figure 9.6: Comparison of the background prediction and observed data for all the SRs. The event yield for all
the SRs are shown in Table 9.1-9.8.

120

9.1 Results from background-only fit

Table 9.1: Observed and expected event yield in the GGd1 CRT, CRW, CRY and SR for an integrated luminosityof 139 fb−1 . The MC event yield ("MC exp.") indicates pre-fit yield and the the fitted event yield ("Fitted")
indicates post-fit yield. The errors in the fitted event yield are the systematic uncertainties. For the MC event
yield lower than 0.1, the yield is displayed as at 0.0±0.0.
GGd1

CRT

CRW

CRY

SR

4

13

62

34

Fitted

4.0 ± 1.6

13.0 ± 3.7

62.0 ± 7.9

30.0 ± 4.9

Fitted Multijets
Fitted Wjets
Fitted Zjets
Fitted GAMMAjets
Fitted Top
Fitted Diboson

0.0 ± 0.0
3.4 ± 1.5
0.1 ± 0.0
0.0 ± 0.0
+1.9
0.5−0.5+0.8
0.1−0.1

0.0 ± 0.0
11.8 ± 3.9
0.0 ± 0.0
0.0 ± 0.0
0.1+0.5−0.1
1.0 ± 0.3

0.0 ± 0.0
0.6 ± 0.2
0.0+0.0−0.0
61.3 ± 7.9
0.1+0.2−0.1
0.0+0.0−0.0

0.1+0.1−0.1
7.1 ± 2.6
19.8 ± 3.8
0.0 ± 0.0
0.1+0.3−0.1
3.0 ± 0.9

9.6

13.0

58.4

28.6

Observed

MC exp.

Table 9.2: Observed and expected event yield in the GGd2 CRT, CRW, CRY and SR for an integrated luminosityof 139 fb−1 . The MC event yield ("MC exp.") indicates pre-fit yield and the the fitted event yield ("Fitted")
indicates post-fit yield. The errors in the fitted event yield are the systematic uncertainties. For the MC event
yield lower than 0.1, the yield is displaced as at 0.0±0.0.
GGd2

CRT

CRW

CRY

SR

8

24

110

68

Fitted8.0 ± 2.2

24.0 ± 5.0

110.0 ± 10.5

52.1 ± 5.8

Fitted Multijets
Fitted Wjets
Fitted Zjets
Fitted GAMMAjets
Fitted Top
Fitted Diboson

0.0 ± 0.0
5.8 ± 1.7
0.1 ± 0.0
0.0 ± 0.0
1.8+2.6−1.8
0.3+0.3−0.3

0.0 ± 0.0
21.3 ± 5.3
0.1 ± 0.1
0.0 ± 0.0
0.3+0.5−0.3
2.3 ± 1.1

0.0 ± 0.0
0.7 ± 0.2
0.0 ± 0.0
109.1 ± 10.5
0.1+0.1−0.1
0.1 ± 0.0

0.0+0.0−0.0
13.2 ± 3.6
33.3 ± 4.5
0.0 ± 0.0
0.6+0.8−0.6
4.9 ± 1.4

19.9

25.4

113.4

56.3

Observed

MC exp.

121

Results

Table 9.3: Observed and expected event yield in the GGd3 CRT, CRW, CRY and SR for an integrated luminosityof 139 fb−1 . The MC event yield ("MC exp.") indicates pre-fit yield and the the fitted event yield ("Fitted")
indicates post-fit yield. The errors in the fitted event yield are the systematic uncertainties. For the MC event
yield lower than 0.1, the yield is displayed as at 0.0±0.0.
GGd3

CRT

CRW

CRY

SR

Observed

48

78

458

227

Fitted48.1 ± 6.9

78.0 ± 8.8

458.1 ± 21.4

223.4 ± 16.6

Fitted Multijets
Fitted Wjets
Fitted Zjets
Fitted GAMMAjets
Fitted Top
Fitted Diboson

0.0 ± 0.0
15.2 ± 2.9
0.1 ± 0.0
0.0 ± 0.0
31.0 ± 7.9
1.7 ± 1.1

0.0 ± 0.0
65.7 ± 9.7
0.3 ± 0.2
0.0 ± 0.0
5.5 ± 2.0
6.4 ± 2.8

0.0 ± 0.0
2.1 ± 0.4
0.3 ± 0.0452.9 ± 21.4
2.6 ± 1.1
0.3 ± 0.0

0.1+0.1−0.1
47.7 ± 7.8
138.5 ± 13.6
0.0 ± 0.0
15.6 ± 5.2
21.4 ± 5.0

60.2

90.7

514.4

253.2

MC exp.

Table 9.4: Observed and expected event yield in the GGd4 CRT, CRW, CRY and SR for an integrated luminosityof 139 fb−1 . The MC event yield ("MC exp.") indicates pre-fit yield and the the fitted event yield ("Fitted")
indicates post-fit yield. The errors in the fitted event yield are the systematic uncertainties. For the MC event
yield lower than 0.1, the yield is displayed as at 0.0±0.0.
GGd4

CRT

CRW

CRY

SR

Observed

70

83

595

291

Fitted70.2 ± 8.4

82.9 ± 9.1

594.9 ± 24.4

297.8 ± 23.5

Fitted Multijets
Fitted Wjets
Fitted Zjets
Fitted GAMMAjets
Fitted Top
Fitted Diboson

0.0 ± 0.0
15.9 ± 3.0
0.3 ± 0.1
0.0 ± 0.0
52.0 ± 9.2
2.0 ± 0.7

0.0 ± 0.0
67.5 ± 9.6
0.6 ± 0.1
0.0 ± 0.0
7.3 ± 1.8
7.5 ± 0.7

0.0 ± 0.0
1.9 ± 0.4
0.6 ± 0.1
586.6 ± 24.4
5.6 ± 1.9
0.1+0.3−0.1

0.1+0.1−0.1
52.0 ± 8.8
180.4 ± 17.7
0.0 ± 0.0
38.9 ± 11.1
26.4 ± 6.8

94.6

117.3

641.2

348.2

MC exp.

122

9.1 Results from background-only fit

Table 9.5: Observed and expected event yield in the GGo1 CRT, CRW, CRY and SR for an integrated luminosityof 139 fb−1 . The MC event yield ("MC exp.") indicates pre-fit yield and the the fitted event yield ("Fitted")
indicates post-fit yield. The errors in the fitted event yield are the systematic uncertainties. For the MC event
yield lower than 0.1, the yield is displayed as at 0.0±0.0.
GGo1

CRT

CRW

CRY

SR

6

6

34

6

Fitted6.0 ± 2.5

6.0 ± 2.5

34.0 ± 5.8

5.5 ± 1.5

Fitted Multijets
Fitted Wjets
Fitted Zjets
Fitted GAMMAjets
Fitted Top
Fitted Diboson

0.0 ± 0.0
1.9 ± 1.2
0.0 ± 0.0
0.0 ± 0.0
3.9 ± 2.8
0.2 ± 0.1

0.0 ± 0.0
4.9 ± 2.8
0.0 ± 0.0
0.0 ± 0.0
0.3 ± 0.2
0.7+1.1−0.7

0.0 ± 0.0
0.1+0.1−0.1
0.0 ± 0.0
33.7 ± 5.8
0.2+0.3−0.2
0.0+0.0−0.0

0.0+0.0−0.0
0.9 ± 0.5
3.8 ± 1.3
0.0 ± 0.0
0.2 ± 0.2
0.6 ± 0.2

14.2

9.4

42.0

7.3

Observed

MC exp.

Table 9.6: Observed and expected event yield in the GGo2 CRT, CRW, CRY and SR for an integrated luminosityof 139 fb−1 . The MC event yield ("MC exp.") indicates pre-fit yield and the the fitted event yield ("Fitted")
indicates post-fit yield. The errors in the fitted event yield are the systematic uncertainties. For the MC event
yield lower than 0.1, the yield is displayed as at 0.0±0.0.
GGo2

CRT

CRW

CRY

SR

Observed

22

21

74

25

Fitted

22.0 ± 4.7

21.0 ± 4.6

73.9 ± 8.6

18.3 ± 2.5

Fitted Multijets
Fitted Wjets
Fitted Zjets
Fitted GAMMAjets
Fitted Top
Fitted Diboson

0.0 ± 0.0
6.6 ± 2.1
0.1 ± 0.0
0.0 ± 0.0
14.6 ± 5.2
0.6 ± 0.1

0.0 ± 0.0
18.2 ± 5.2
0.1 ± 0.0
0.0 ± 0.0
1.2 ± 0.5
1.5+1.8−1.5

0.0 ± 0.0
0.3 ± 0.1
0.0+0.0−0.0
72.4 ± 8.6
1.1 ± 0.5
0.1 ± 0.0

0.0+0.0−0.0
3.9 ± 1.3
10.9 ± 1.9
0.0 ± 0.0
1.3 ± 1.0
2.2 ± 0.6

41.8

28.5

99.6

24.8

MC exp.

123

Results

Table 9.7: Observed and expected event yield in the GGo3 CRT, CRW, CRY and SR for an integrated luminosityof 139 fb−1 . The MC event yield ("MC exp.") indicates pre-fit yield and the the fitted event yield ("Fitted")
indicates post-fit yield. The errors in the fitted event yield are the systematic uncertainties. For the MC event
yield lower than 0.1, the yield is displayed as at 0.0±0.0.
GGo3

CRT

CRW

CRY

SR

Observed

46

69

120

80

Fitted46.0 ± 6.8

68.9 ± 8.3

120.0 ± 11.0

84.9 ± 9.6

Fitted Multijets
Fitted Wjets
Fitted Zjets
Fitted GAMMAjets
Fitted Top
Fitted Diboson

0.0 ± 0.0
5.6 ± 1.3
0.1 ± 0.1
0.0 ± 0.0
39.2 ± 7.2
1.2 ± 0.5

0.0 ± 0.0
49.7 ± 9.3
0.5 ± 0.1
0.0 ± 0.0
13.8 ± 3.6
4.9 ± 1.4

0.0 ± 0.0
0.4 ± 0.1
0.1 ± 0.0
116.8 ± 11.0
2.7 ± 1.1
0.0+0.1−0.0

0.1+0.1−0.1
15.5 ± 3.8
34.7 ± 5.5
0.0 ± 0.0
28.1 ± 7.8
6.6 ± 2.2

49.6

92.3

182.2

110.9

MC exp.

Table 9.8: Observed and expected event yield in the GGo4 CRT, CRW, CRY and SR for an integrated luminosityof 139 fb−1 . The MC event yield ("MC exp.") indicates pre-fit yield and the the fitted event yield ("Fitted")
indicates post-fit yield. The errors in the fitted event yield are the systematic uncertainties. For the MC event
yield lower than 0.1, the yield is displayed as at 0.0±0.0.
GGo4

CRT

CRW

CRY

SR

Observed

138

53

140

135

Fitted138.0 ± 11.7

53.0 ± 7.3

140.0 ± 11.8

159.1 ± 16.0

Fitted Multijets
Fitted Wjets
Fitted Zjets
Fitted GAMMAjets
Fitted Top
Fitted Diboson

0.0 ± 0.0
10.0 ± 2.9
0.1 ± 0.0
0.0 ± 0.0
125.9 ± 12.4
2.0 ± 0.6

0.0 ± 0.0
36.0 ± 7.8
0.4 ± 0.2
0.0 ± 0.0
12.3 ± 1.8
4.4 ± 1.3

0.0 ± 0.0
0.8 ± 0.6
0.1 ± 0.0
135.0 ± 11.9
4.1 ± 0.7
0.0+0.1−0.0

0.7+0.7−0.7
27.4 ± 6.4
39.3 ± 6.9
0.0 ± 0.0
84.9 ± 14.2
6.8 ± 2.1

141.6

66.2

169.5

177.3

MC exp.

124

9.2 Model-independent fit

9.2 Model-independent fit

In order to set the upper limits on the number of BSM events, the model-independent fit, which
is discussed in Section 8.2, is performed. Figures 9.7 show the p-value as a function of the signal
strength µs with different probability density functions ( f (qµs | µs = 0) and f (qµs | µs = 1)) for GGd2
and GGo2, which have a small excess over the prediction. From these results, the upper limits at 95%
95
95 .
confidence level on the number of events from BSM events for all SRs are calculated: Sobs
and Sexp
The visible cross section defined in Eq. 8.12 is also calculated as shown in Table 9.9.

In all signal regions, no significant excess over the background prediction is observed from p0
values and any indication of SUSY signal in final states with jets and missing transverse momentum
cannot be found. The constraint of the target signal-like events which have multiple jets and large
missing transverse momentum has been set.

Figure 9.7: Expected and observed CLs (red), CLs+b (blue) and CLb (black) as a function of the signal strengthµs for GGd2 (left) and GGo2 (right). The expected CLs value with ±1σ (green band) and ±2σ (yellow band)
are overlaid. The red horizontal line indicates the value at 0.05.
95
95
Table 9.9: 95% CL upper limits on the visible cross section (h σiobs),the number of visible signal events (Sobs)
95
and the number of expected signal event (Sex p ) given the expected number of background events (and ±1σ
excursions of the expectation). The p-values (p0 ) give the probabilities of the observations being consistent withthe estimated backgrounds. For an observed number of events lower than expected, the p-value is displayed as
at 0.5 in asymptotic calculation.

SR
p0
95
Sobs
95
Sex
p
95
h σiobs
[fb]

GGd1
0.30
18
15+6
−4
0.13

GGd2
0.05
34
20+8
−6
0.24

GGd3
0.44
46
+17
43−12
0.33

GGd4
0.50
50
+21
54−15
0.36

GGo1
0.43
7
+2.5
6.6−1.8
0.05

GGo2
0.12
17
11+5
−3
0.10

GGo3
0.50
23
+10
26−7
0.16

GGo4
0.50
25
+14
36−10
0.18

125

Results

9.3 Model-dependent fit
This section shows the upper limits for the dedicated signal models at 95% confidence level using
model-independent fit. First, the upper limits for the target signal models as discussed in Section 1.5
are shown. Then, the interpretation of other models is performed. Finally, cross sections of upper
limits are extracted.

9.3.1 Target signal models
Figures 9.8 show the upper limits in the simplified models with gluino direct and one-step decay.
The gluino mass with the direct decay is excluded up to 2.15 TeV for massless neutralino at the 95%
confidence level and the exclusion limit is extended by 100 (200-300) GeV in higher gluino (neutralino)mass directions comparing to the previous publication at 36 fb−1 [34]. For the gluino one-step decay
via W boson (g̃ → qq 0 χ̃1± ), the gluino mass is excluded up to 2.18 TeV and the exclusion limit
is extended by 200 (300-400) GeV in higher gluino (neutralino) mass directions comparing to the0previous publication at 36 fb−1 [34]. The signals with large χ̃1 mass have complicated kinematics andthe improvement of sensitivities is expected by using BDT classifiers as discussed in Section 5.6. The
large gain in neutralino mass, in particular on the one-step decays are observed as shown in Figure 9.8
and 9.9, For the gluino one-step decay via Z boson (g̃ → qq 0 χ̃20 ), the gluino mass is excluded up to
2.2 TeV as shown in Figure 9.9. In the Ref. [124], there is only exclusion limit in final states with two
leptons (Z →``). Hence, the exclusion limit is highly improved in higher gluino mass direction: 500
GeV (300-400) GeV in gluino (neutralino) mass directions.
~~~∼0)=100%
gg production, B (g → qq χ~~~~∼± → qq W± χ∼0)=100%, m(χ∼± )=(m(g∼0))/2
gg production, B (g → qq χ
) + m(χ1

1Exp. limit (±1 σexp)

1800

Obs. limit (±1 σtheory)SUSY

All limits at 95 % CL

1400
1200

en
dd
bi

1000
800

0L obs. 36 fb -1[arXiv:1712.02332]

ly

al

ic

at

r
Fo

1

s=13 TeV, 139 fb-1
Obs. limit (±1 σtheory)
SUSY

0-leptons, 2-6 jets

1600

All limits at 95 % CL

0L obs. 36 fb -1[arXiv:1712.02332]

1400
1200

n
de

id

rb

lly
ca

1000

Fo

i
at

m

800

m
ne
Ki

600

600

400

400

200
0

1

Exp. limit (±1 σexp)

1800

s=13 TeV, 139 fb-1
0-leptons, 2-6 jets

1600

1

2000

0
m(∼
χ1) [GeV]0m(∼
χ1) [GeV]

2000

ne
Ki

200
600

800

1000 1200 1400 1600 1800 2000 2200 2400 2600m(~g) [GeV]

0
600

800

1000

1200

1400

1600

1800

2000

2200

2400 2600m(~g) [GeV]Figure 9.8: . Expected and observed limits at the 95% confidence level in the neutralino mass versus gluinomass for the gluino-pair production with direct decay (left), one-step decay with W boson (right) on a simplified
model. The expected (observed) exclusion limit is denoted by the dash (solid) red line. The blue shaded area isthe observed exclusion limits from the previous publication corresponding to the integrated luminosity of 36
fb−1 [34].

The other set of gluino one-step decay with the mass spectra with a fixed m χ̃0 =60 GeV is also1
motivated in term of the relic density of the dark matter as discussed in Section 3.3 [89]. Figures 9.10
show the exclusion limits for the gluino one-step decay via W boson and the gluino mass is excluded up

126

9.3 Model-dependent fit~~~~∼0 → qq Z χ∼0)=100%, m(χ∼0)=(m(g∼0))/2
gg production, B (g → qq χ
) + m(χ
2

1

2

1

0
m(∼
χ1) [GeV]

2000
1800

Exp. limit (±1 σexp)

s=13 TeV, 139 fb-1
0-leptons, 2-6 jets

1600

Obs. limit (±1 σtheory)SUSY

All limits at 95 % CL

1400
n

de

1200

id
rb

ly

1000
800

l
ca

Fo

i

at

m

ne

Ki

600
400
200
0
600

800

1000

1200

1400

1600

1800

2000

2200

2400 2600m(~g) [GeV]Figure 9.9: . Left: Expected and observed limits at the 95% confidence level in the neutralino mass versus
gluino mass for the gluino-pair production with one-step decay with Z boson on a simplified model. The
expected (observed) exclusion limit is denoted by the dash (solid) red line. Right: Expected and observed
limits at the 95% confidence level in the neutralino mass versus gluino mass for the gluino-pair production with
one-step decay with Z boson in final states with two leptons on a simplified model for the integrated luminosityof 36 fb−1 [124].

to 2.17 TeV. The exclusion limit are extended by 300 GeV in higher gluino mass directions comparing
to the previous publication at 36 fb−1 [34].

9.3.2 Other signal models

Some other signal models are interpreted in case the event topology is similar to the target signals.
First, the gluino direct decay with heavy flavour quarks (b or t) as shown in Figures 3.3 are evaluated.
Unlike light-flavour squarks, the sbottoms and stops are not degenerated in the MSSM. Hence, thedifferent upper limits from Figures 9.8 are evaluated. Figures 9.11 show the expected and observed
limits for these models and the gluino mass is excluded up to 1.8 (2.15) TeV for massless neutralino at
the 95% confidence level. There are dedicated analyses, which require many b-jets [125]. Since theeffective mass and missing transverse momentum is large in the signals, the SRs can catch the signal
events. Compared to Ref. [125], the expected exclusion limit in Figure 9.11 is improved in higher
gluino mass direction for gluino decay with b quarks. The constraints on gluino decay with heavy
flavour quarks can be set in this analysis.
Next, the signals of the inclusive production of squarks and gluinos with a fixed m χ̃0 =0 GeV are
1considered as shown in Figure 3.4. Figures 9.12 show the expected and observed limits for this model.
0
A upper limit of 2.15 TeV for gluino mass is set with massless χ̃1 if the squark is very heavy (>2TeV). In this case, the dominant production in the signals becomes the gluino pair production and
Figure 1.12(a) is dominant process. If the gluino is heavy (>3 TeV), the dominant production in thesignals becomes the squark pair production. Since the observed event topology is two jets and missing
transverse momentum, the exclusion limit in is not improved compared to the previous result. The
constraints on inclusive production of squarks and gluinos can be set in this analysis.

127

Results

Figure 9.10: Expected and observed limits on the 95% confidence level in the gluino mass vs variable x, which
is defined x = ∆m( χ̃0± - χ̃i0 )/∆m(g̃- χ̃10 ) with fixed neutralino mass of 60 GeV for the gluino-pair production
with one-step decay via W boson on a simplified model. The expected (observed) exclusion limit is denoted by
the dash (solid) red line. The blue shaded area is the observed exclusion limits from the previous publication
corresponding to the integrated luminosity of 36 fb−1 [34].

~~~∼0)=100%
gg production, B (g → tt χ~~~∼0)=100%
gg production, B (g → bb χ1s=13 TeV, 139 fb

1

2000

-1

Exp. limit (±1 σexp)

1800
All limits at 95 % CL
0-leptons, 2-6 jets

1600

Obs. limit (±1 σtheory)
SUSY

n
de

1400
1200

bid

1000
800

600

600

400

400

200

200
1400

1600

1800

2000

2200

2400
x labelObs. limit (±1 σtheory)
SUSY

n

de

800

1200

All limits at 95 % CL
0-leptons, 2-6 jets

1600

1000

0
1000

Exp. limit (±1 σexp)

1800

1200

ne

Ki

s=13 TeV, 139 fb-1

1400

or

yF

all
tic
ma

0
m(∼
χ1) [GeV]0m(∼
χ1) [GeV]

2000

0
1000

bid
or

yF

t
ma

ll
ica

ne

Ki

1200

1400

1600

1800

2000

2200

2400
x labelFigure 9.11: Expected and observed limits at the 95% confidence level in the neutralino mass versus gluino mass
for the gluino-pair production with direct decay via t quarks (left) and b quarks (right). The expected (observed)
exclusion limit is denoted by the dash (solid) red line.

1289.4 Discussion

Figure 9.12: Expected and observed limits on the 95% confidence level in gluino mass vs squark mass for thephenomenological squark-gluino model with fixed neutralino mass of 0 GeV. The expected (observed) exclusion
limit is denoted by the dash (solid) red line. The blue shaded area is the observed exclusion limits from theprevious publication corresponding to the integrated luminosity of 36 fb−1 [34].

9.3.3 Cross section upper limits
In order to cover several signal models, the upper limits on the cross section for the target signals
are obtained. First, the CLs value is calculated, depending on the signal strength µs as discussed in
Section 8.2. Then, the µ95
s is obtained for a result of CLs = 0.05. Finally, the upper limits on the crosssection is calculated from the µ95
s values. Figures 9.13 show the upper limits on the cross section forgluino direct and one-step decays.

9.4 Discussion
9.4.1 Comparison to the convensional approach
The expected signal and background events with the integrated luminosity of 36 fb−1 are estimatedand they are compared to the previous result [34], which uses the convensional approach explainedin Section 1.6. The impact on the machine learning approach is fairly evaluated in this comparison.
Table 9.10 shows the number of gluino direct decay signal with (mg̃, m χ̃1 )=(1950, 650) GeV and0background events for the convensional approach and the machine learning approach. The cuts inthe previous result are tunned to maximize the sensitivity with the integrated luminosity of 36 fb−1 .
For this comparison, the cuts on BDT score is also tunned in order to maximize the sensitivity. The
number of signal events in the machine learning approach is twice than the convensional approach,while the number of backgrounds is almost the same. It means that the non-linear correlation allows

129

Results~~~∼0)=100%
gg production, B (g → qq χ~~~~∼± → qq W± χ∼0)=100%, m(χ∼± )=(m(g∼0))/2
gg production, B (g → qq χ
) + m(χσ95% CL [fb]

1

1

1

1

1

σ95% CL [fb]2500Exp. limit (±1 σexp)

s=13 TeV, 139 fb-1

2200

3

10

0-leptons, 2-6 jets

1500

3.40

14.31

3.21

1.57

3.43

1.66

1.64

n

131.13

de

id
rb

1000

ly

al

ic

at

m
ne

Ki

411.39 114.26

Fo183.5519.00
193.42345.01490.79

21.12
22.49

28.67

16.36
17.91

16.27
4.15

4.85

1.80
1.85

4.27

5.22

3.41
3.70

3.68

2.32

1.36

1.19

1.73

1.64

1.01

1.42

1.23

0.87

2.10
2.13

1.97
2.14

2.35

2.21

132.06

1.21
1.31

500

1.36

1.07
1.11

1.22

0.64
0.75

1.19

800

1000

1200

1400

1600

1800

1.06

0.57

1.37

1.00

0.49

1.16

0.62

0.45

1.05

0.54

0.68

0.49

0.61

0.46

0.56

0.46

0.55

0.44

0.55
0.65

0.70

600

1.89

SUSY
Obs. limit (±1 σtheory)

All limits at 95 % CL

1600
254.171400

145.81

rb

ly
al

1000

2.74

2.95

1.44

1.37

102

3.26

18.84

3.44

1.50

1.44

0.94

3.62

1.55

1.55

1.03

0.48

1.64

1.12

0.54

0.40

0.60

0.43

0.49

0.40

17.37
713.0917.72

10551.95585.484.03

2726.42600 29364.06

330.37

15.81
14.10
15.61
15.77

Fo

ic
at

m

ne
Ki

800
1

en
dd

i

1200
10

5.06

2.00

1

400

2.64

200

0.45

0.53

0.68

2.47

1.23

0.46

0.40

0.46

0.57

2000

3

10

0-leptons, 2-6 jets

1800
102

13.40
13.30

0

14.13

Exp. limit (±1 σexp)

s=13 TeV, 139 fb-1

2000

SUSY
Obs. limit (±1 σtheory)

All limits at 95 % CL

2000

0
m(∼
χ1) [GeV]0m(∼
χ1) [GeV]

2400

10−1

0.46

2200 2400m(~g) [GeV]

1.84

0
600

800

1000

1200

~~
~
~
∼0 → qq Z χ∼0)=100%, m(χ∼0)=(m(g∼0))/2
gg production, B (g → qq χ
) + m(χ
2

1

2

1

0.59

1400

1600

1800

0.48

2000

0.40

2200

2400 2600m(~g) [GeV]10−1

σ95% CL [fb]0m(∼χ1) [GeV]

2400
2200

Exp. limit (±1 σexp)

s=13 TeV, 139 fb-1

2000

0-leptons, 2-6 jets

1800

All limits at 95 % CL

3

10Obs. limit (±1 σtheory)
SUSY

1600
149.91

1400
1200
ly
al
ic
at

1000
800

m
ne

Ki

15.23

rb
Fo

173.66368.34

24.23

1.09

1.19

102

21.10

2.97

1.10

1.29

0.85

2.71

1.16

1.41

0.96

0.38

1.65

0.89

0.47

0.34

0.78

0.36

0.32

0.43

0.33

0.30

0.41

0.30

0.28

3.19

5.15

0.95

10

1

400

2.19

200
0
600

2.35

2.92
2.59

21.96
466.90

600

10.07
9.53
34.47

n
de
id

1.00

0.60

1.12

1.34

800

1000

1200

1400

0.49

1600

1800

0.39

2000

0.37

2200

0.28

2400 2600~) [GeV]m(g10−1Figure 9.13: Excluded upper limits of expected and observed cross section at 95% confidence level in theneutralino mass versus gluino mass for the gluino-pair production with direct decay (top-left), one-step decay
with W boson (top-right) and one-step decay with Z boson (bottom) on a simplified model. The upper limit
values in all signal points are displayed in the figures.

the signals, which does not remain in the convensional approach, to be survived. This is the reason
why the sensitivity in the machine learning approach is better than convensional approach.
Table 9.10: Comparison of the number of expected signal and background events with the integrated luminosityof 36 fb−1 . The gluino direct decay signal with (mg̃, m χ̃1 )=(1950, 650) GeV is used in the comparison. The
0
MC statistical uncertainty is only displayed in the table.

Number of signal
Number of backgroundPrevious result [34] The result with the method in this thesis
8.6 ± 1.0
16.2 ± 0.7
16.5 ± 2.7
19.1 ± 3.0

Figures 9.14 show the comparison of expected exclusion limits with the integrated luminosity of
36 fb−1 at the 95% confidence level between the machine learning and the convensional approach.
For gluino direct decay, the exclusion limit is extended by 100 GeV in higher gluino mass directions
comparing to the convensional approach. For gluino one-step decay, the exclusion limit is extended
by 200 GeV in higher neutralino mass directions comparing to the convensional approach. Since
the training categories are prepared such that they can cover the signals with ∆m(g̃, χ̃10 )≥ 200 GeV,
the exclusion limit in the regions is improved as shown in Figures 9.14. It means that the use of the130

9.4 Discussion
machine learning contributes to the improvement of the results shown in this thesis.

1400

s=13 TeV, 36 fb

Exp. Limit (±1 σexp)

1

1600

0-leptons, 2-6 jets

h

la
rb

All limits at 95 % CL

1200

n
de

o

0L Exp. Limit 36 fb -1

r
Fo

a

ic

at

Ki

lly

1600
1400

1

1

ah
bl

0L Exp. Limit 36 fb -1[arXiv:1712.02332]

i

at

lly

rb
Fo

a

ic

1000
m

ne

800
600

400

400

200

200

1000 1200 1400 1600 1800 2000 2200 2400 2600
m~g [GeV]

en
dd

1

Exp. Limit (±1 σexp)-10-leptons, 2-6 jets

1200

m
ne

800

s=13 TeV, 36 fb

All limits at 95 % CLor

600

0
600

1

1800

[arXiv:1712.02332]

d
bi

1000
800

~~
~
~
∼± → qq W± χ∼0)=100%, m(χ∼± )=(m(g∼0))/2
gg production, B (g → qq χ
) + m(χ1-1mχ∼0 [GeV]1mχ∼0 [GeV]~~~∼0)=100%
gg production, B (g → qq χ

1800

0

Ki

800

1000

1200 1400 1600 1800 2000 2200

2400 2600
m~g [GeV]

Figure 9.14: Expected exclusion limits at the 95% confidence level in the neutralino mass versus gluino mass
for the gluino-pair production with direct decay (left), one-step decay with W boson (right) on a simplified
model. The expected exclusion limit using machine learning approach at the integrated luminosity of 36 fb−1 isdenoted by the dash line. The blue shaded area is the expected exclusion limits from the previous publication
corresponding to the integrated luminosity of 36 fb−1 [34].

9.4.2 Comparison to the CMS experiment
Figures 9.15 show the exclusion limits at 95% confidence level for gluino direct and gluino
one-step decay on the simplified models with the CMS detector [126]. The data collected 2016-2018
corresponding to the integrated luminosity of 137 fb−1 is used in the results. The analysis in the
CMS adopts a multi-bin technique where the signal and background separation is performed bysimultaneously fitting to multiple observables. The gluino mass is excluded up to 2.0 TeV for direct
decay and 2.03 TeV for one-step decay at the CMS experiment. Compared to the CMS analysis,
this research shown in this thesis clearly outperform the expected exclusion limits in a region where
the gluino mass is heavy (mg̃ >1.9 TeV). In particular, the significant superiority is observed in thegluino one-step decay and a impact of the machine learnining is very large. It implies that a machinelearnining approach is superior to the multi-bin approach for gluino one-step decay, which has more
complicated event topologies than gluino direct decay.

131

Observed ± 1 σtheory
Expected ± 1, ± 2 σexperiment
−1

1400

10

1200
1000

10−2

800
600
−3

10

400
200
0

1000

1500

2000

2500

10−4

1800

0
1

1

1

2000

1600

CMSPreliminary 137 fb-1 (13 TeV)~~ ~∼0 Approx NNLO+NNLL exclusion
pp → g g, g → q q V χ1

1

Observed ± 1 σtheory
Expected ± 1, ± 2 σexperiment
10−1

1400
1200
1000

10−2

800
600
−3

10

400
200
0

1000

1500

mg~ [GeV]

2000

2500

10−4

95% CL upper limit on cross section [pb]

1600

~~ ~
∼0 Approx NNLO+NNLL exclusion
pp → g g, g → q q χm∼χ [GeV]

1800

CMSPreliminary 137 fb-1 (13 TeV)
95% CL upper limit on cross section [pb]

2000

0
1

mχ∼ [GeV]

Results

mg~ [GeV]

Figure 9.15: Expected and observed limits at the 95% confidence level in the neutralino mass versus gluinomass for the gluino-pair production with direct decay (left), one-step decay with bosons (right) on a simplified
model [126].

9.4.3 Impact of the result to SUSY models
As explained in Section 1.5, the gluino search is one of most important physics programmes at the
LHC. In addition, the result in this thesis can provide the constraints of SUSY models. For example,
the ratio of gaugino mass parameters in the Anomaly mediated SUSY breaking (AMSB) [127] andminimum supergravity (mSUGRA) models [128–130] is written as
mbino : mwino : mgluino ∼ 3 : 1 : 8 for AMSB

(9.1)

mbino : mwino : mgluino ∼ 1 : 2 : 7 for mSUGRA(9.2)

where mbino is the bino mass, mwino is the wino mass and mgluino is the gluino mass. The lightest
neutralino is expected to be less than a few TeV from the relic density of the dark matter as shown in
Figure 1.8, so the light gluino mass (O(1-10) TeV) is preferable. The gluino mass is also expected
to be light in term of the fine tuning problem [131]. The gluino mass is related to the Higgs boson
mass calculation at higher order and the level of the fine tuning is smaller as the gluino mass is lighter.
Therefore, the search for gluino with a few TeV mass is important considering on the level of the finetuning problem. In this thesis, the search for this important region can be probed. The extension of
the exclusion limit in this thesis has provided new constraint of the heavier gluino and neutralino forthese models which have not been looked into before.

132

10 Conclusion
This thesis presents a search for gluinos in final states with jets and missing transverse momentum√
using pp collision at s =13 TeV with the ATLAS detector. The data is collected in 2015-2018
corresponding to the integrated luminosity of 139 fb−1 . A machine learning technique is introducedin this search to improve the sensitivity of heavier gluino. In order to probe all mass points of signals,
eight training categories are prepared depending on the mass difference between gluino and neutralino.
The sensitivities of all signal masses are improved by using the training categories. The backgroundestimation considering the correlation is carefully performed and it is validated that the estimation isworked properly from results of the validation regions. In all signal regions, no significant excess overthe background prediction is observed and any indication of SUSY signal in final states with jets andmissing transverse momentum cannot be found.
The exclusion limits for some dedicated signal models at 95% confidence level are set. The gluinomass with the direct decay is excluded up to 2.15 TeV for massless neutralino. Compared to theprevious results, it is extended by 100 (200-300) GeV in heavier gluino (neutralino) mass. The gluinomass with the one-step decay is excluded up to 2.2 TeV for massless neutralino and it is extended by
500 (300-400) GeV in heavier gluino (neutralino) mass compared to the previous results. Using themachine learning in this analysis allows the heavier gluino which has not been looked into before toaccess.
In this research, the framework using the machine learning has been established in gluino search.
Based on the framework, the first preliminary result of the gluino search using the machine learning
was published from ATLAS. The constraints of gluino mass are the best in the world. It has been
proved that the machine learning technique is applicable to SUSY search.

133

Acknowledgements
First of all I would like to express my gratitude to my supervisor, Prof. Junichi Tanaka for giving
me such a wonderful research theme and providing the helpful suggestions at all times. He always
leads me to the right direction, so I was able to continue the research. I would like to also express mygratitude to Dr. Yuji Enari for providing the helpful suggestions and discussing the detail of research at
all times. He also gave a support of the research of LAr calorimeter, which is very interested theme forme, and I was able to have a precious experience. I wouild like to appriciate an important suggestion
about SUSY analysis Prof. Shoji Asai gave me. He also gave a support for the research at CERN.
I would like to thank all the members of ATLAS SUSY group. Dr. Yu Nakahama Higuchi,
Dr. Zuzana Rurikova and Prof. Paul Jackson are the analysis contact in my analysis. They always gave
a lot of suggestion and discussed the details in the analysis with me in order to establish this analysis.
Dr. Tomoyuki Saito, Dr. Takuya Nobe, Dr. Shion Chen, Dr. Masahiko Saito and Prof. Ryu Sawada
gave me a technical advice and useful comment for improvement of my analysis. Dr. Emma Sian
Kuwertz, Dr. Julien Maurer, Dr. Jonathan Long and Dr. Teng Jian Khoo are the leaders in the SUSY
strong production group. They gave a lot of suggestion in the meeting and approved my analysis.
Prof. Zachary Lewis Marshall, Dr. Federico Meloni are the leaders in the SUSY group. They helped
me to publish my analysis result in an international conference. In addition, they also gave me someadvice for my new job position.
I would like to thank all the members of ATLAS Japan group and ICEPP, because I was able toenjoy my student life for their support. Prof. Masaya Ishino, Prof. Yasuyuki Okumura, Prof. Tetsuro
Mashimo, Dr. Koji Terachi, Dr. Tatsuya Masubuchi, Dr. Tomoe Kishimoto and Dr. Michiru Kaneda
gave me a support at CERN and maintained the computer I uses for my analysis. In particular,
Prof. Masaya Ishino and Prof. Yasuyuki Okumura gave me a lot of advice for my new job position. I
would like to also express my gratitude to the secretaries in ICEPP. They always supported me, so I
was able to focus on my research.
Finally, I would like to thank my family and friends for their support in my life.

135

A Input variable distribution
Figures A.1, A.2, A.3 and A.4 show pre-fit distribution of input variables used in the BDT
classifier.

Figure A.1: Distribution of leading jet to 4th jet pT and η with the preselection cut. This signals in the plot are
gluino direct decay. The last bin includes the overflow. The hatched red error bands indicate the MC statisticaluncertainties. The bottom panel is the ratio of the observed data and the MC simulation.

137

A Input variable distribution

Figure A.2: Distribution of ETmiss , meff , ETmiss /ETmiss and aplanarity with the preselection cut. This signals in theplot are gluino direct decay. The last bin includes the overflow. The hatched red error bands indicate the MCstatistical uncertainties. The bottom panel is the ratio of the observed data and the MC simulation.

138

Figure A.3: Distribution of leading jet to 6th jet pT and η with the preselection cut and N j ≥5. This signals
in the plot are gluino one-step decay via W boson. The last bin includes the overflow. The hatched red error
bands indicate the MC statistical uncertainties. The bottom panel is the ratio of the observed data and the MC
simulation.

139

A Input variable distribution

Figure A.4: Distribution of ETmiss , meff , ETmiss /ETmiss and aplanarity with the preselection cut and N j ≥5. Thissignals in the plot are gluino one-step decay via W boson. The last bin includes the overflow. The hatched rederror bands indicate the MC statistical uncertainties. The bottom panel is the ratio of the observed data and theMC simulation.

140

B Input variable distribution
Figures B.1,B.2 and B.3 show pre-fit BDT score distributions in CRs for all training categories.
The distributions in CRY and CRW is well-modelled by MC simulation, but the mismodelling isobserved in CRT.

141

B Input variable distribution

Figure B.1: BDT score distributions in CRY for all training categories. The hatched red error bands indicate
the MC statistical uncertainties. The bottom panel is the ratio of the observed data and the MC simulation.

142

Figure B.2: BDT score distributions in CRW for all training categories. The hatched red error bands indicate
the MC statistical uncertainties. The bottom panel is the ratio of the observed data and the MC simulation.

143

B Input variable distribution

Figure B.3: BDT score distributions in CRT for all training categories. The hatched red error bands indicate
the MC statistical uncertainties. The bottom panel is the ratio of the observed data and the MC simulation.

144

C Trigger readout electronics upgrade of the
LAr calorimeter
In addition to the gluino search, an upgrade of trigger readout electronics of the LAr calorimeterhas been worked in order to enhance the sensitivity in the search of SUSY particles. This section
explains the electronic upgrade in details, which is based on Ref. [132, 133].

C.1 LAr calorimeter upgrade at Run 3 experiment
Run 3 experiment is expected to have two times higher instantaneous luminosity, L =3.0×1034 cm−2 s−1 than in Run 2. In order to perform the experiment under the high luminosity environment, theupgrade of LHC and subdetectors is planned for the long shutdown (2019-2020) [134]. For the LAr
calorimeter, a trigger readout upgrade is planned to improve the L1 trigger performance, because
the limitation of L1 trigger rate. The trigger rate of electron and photon object (L1 EM object) is
determined to be 20 kHz in Run 3 experiment. In the current trigger readout scheme, the transverse
momentum threshold has to be about 34 GeV as shown in Figure C.1 in order to keep the trigger rate.
It leads to drop on the acquisition efficiency of W/Z boson, which decays to W →eν or Z →ee. In
order to reduce the threshold, the shower shape information of object is used to separate the EM object
and jet. By utilizing the shower shape information, the trigger rate can be reduced while the transverse
momentum threshold keeps the same level as Run 2 experiment (20 kHz) as shown inFigure C.1.
Hence, the trigger readout scheme is upgraded to use the shower shape information.

C.2 New trigger readout scheme
As explained in Section 2.2, the LAr calorimeter has four layers, which are segmented inpseudo-rapidity η and azimuth φ directions. The current trigger readout, where the unit of the readout
segment is shown in Figure C.2 and it is called a "Trigger Tower". The readout makes analog sums
over cells of the four layers in a range of ∆η × ∆φ = 0.1 ×0.1 at the frontend electronics. Then, thesummed analog signals are transmitted via coaxial cables to the backend electronics, which digitizes
at 40 MHz. The new trigger readout is shown in Figure C.2 and is called "Super Cells". The summed
analog signals are digitized for each layer separately in the frontend electronics. In order to utilize theshower shape information, the range of the summation for the first and middle layers is changed to be
finer, ∆η × ∆φ = 0.025 × 0.1. These signals are transmitted to the backend electronics via opticalfibers. As a result, one Trigger Tower corresponds to ten Super Cells.

145

C Trigger readout electronics upgrade of the LAr calorimeter

Figure C.1: L1 Trigger rate as a function of transverse momentum threshold with EM object (L1 EM ET ) [134].
It assumes that the electron efficiency is 95%. The blue point indicates the current trigger readout scheme. The
red, green, black and white point indicate the new trigger readout scheme for Run 3 experiment with different
selection criteria.

Figure C.2: The readout scheme of the current trigger readout, which is called Trigger Tower (left) and new
trigger readout, which is called Super Cells (right) [134]. These colors indicate the energy deposit for 70 GeVelectron.

In order to change the trigger readout scheme, a frontend and backend electronics are upgraded.
The frontened electronics digitizes the information of Super Cells at 40 MHz to 12 bits and transmits
it into the backend electronics. The backend electronics computes each transverse energy and thebunch crossing where the EM object is deposited to the Super Cells by using a Field Programmablegate array (FPGA) and transmits it into the L1 trigger system.

146

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