Search for top squarks in events with one lepton
in pp collisions at! = 13 TeV13 TeV
1 



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Search for top squarks in events with one leptonpin pp collisions at s = 13 TeV

Tatsuya Mori
Department of Physics, Faculty of Science & Graduate School of Science, The University of Tokyo

December, 2016

Abstract
This thesis presents the results of a search for the top squark (stop), the supersymmetric partnerof the top quark, in events with one lepton. The search uses the datasets of the 2015 andp2016 LHC pp collisions at s = 13 TeV recorded by the ATLAS detector, which amount to an
integrated luminosity of 28.0 fb 1 . The analysis targets a direct pair production of stops where0each stop decays into the top quark and the lightest neutralino (t̃1 ! t ˜1 ), the W boson from oneof the two top quarks decays to an electron or muon (either directly or via a ⌧ lepton), and the
W boson from the other top quark decays hadronically. Since the signal event topology highly
depends on the mass di↵erence between the stop and the lightest neutralino, three analyses
are performed which are optimized to Boosted, Resolved, and Diagonal topologies of the signal
0
events. In Boosted topology ( m(t̃1 , ˜1 ) & 3mt ), top quarks are highly boosted so that bqq 0 from0

hadronic top decay forms one large-R jet. In Resolved topology ( m(t̃1 , ˜1 ) ⇠ 2mt ), the hadronic
top decay products are not merged into one large-R jet but resolved into three smaller-radius
0
jets because pT of top quark is relatively medium. In Diagonal topology ( m(t̃1 , ˜1 ) ⇠ mt ),0

the behavior of hadronic top decay is the same as Resolved region but ˜1 and t from t̃1 decay
are nearly collinear with respect to t̃1 momentum. The detector signature of the signal events
is similar to that of a top quark pair produced in association with large missing transverse
momentum, which is highly suppressed by dedicated variables in Boosted and Resolved analyses
and precisely estimated by a 2-dimensional shape fit in Diagonal analysis.
No significant excess from the Standard Model background-only hypothesis is observed, andexclusion limits on a plane of stop and lightest neutralino masses are set at 95% confidence
level. The results extend the ATLAS and the CMS exclusion limits for stop pair production
model obtained with data of 13.2 fb 1 . The Resolved result doesn’t newly exclude but enlarges
the expected CLs contour up to (mt̃1 , m ˜01 ) ⇠ (700 800, 400) GeV. The Boosted result newly
0
excludes the t̃1 ! t ˜1 model with the mt̃ . 980 GeV for m ˜0 . 300 GeV and (mt̃ , m ˜0 ) = (900,
1

1

1

1

350) GeV. The Diagonal result is reinterpreted to set exclusion limits on the model where stop0
decays to bottom quark, W -boson, and lightest neutralino (t̃1 ! bW ˜1 ), and newly excludes

00
the t̃1 ! t ˜1 and t̃1 ! bW ˜1 models with 200 GeV < m ˜01 < 240 GeV and (mt̃1 , m ˜01 ) ⇠ (430,250) GeV near a Diagonal line of mt̃1 = mt + m ˜01 .

Contents
1 Introduction

4

1.1

The Standard Model

4

1.2

Hierarchy Problem

5

1.3

Supersymmetry

6

1.4

Top Squark

9

1.5

Neutralino

10

1.6

Stop Search

11

1.6.1

Boosted13

1.6.2

Resolved

14

1.6.3

Diagonal

14

2 ATLAS Experiment

16

2.1

Large Hadron Collider

16

2.2

ATLAS Detector

18

2.2.1

Inner Detector

20

2.2.2

Electromagnetic Calorimeter and Hadronic Calorimeter

22

2.2.3

Muon Spectrometer

28

2.3

Trigger and Data Acquisition30

3 Data and Monte Carlo Samples

31

3.1

Data and Trigger

31

3.2

Monte Carlo Samples

33

3.2.1

Signal

33

3.2.2

tt̄

34

3.2.3

Single Top

34

3.2.4

W/Z+jets

35

3.2.5

tt̄ + W/Z

35

3.2.6

tt̄ +

35

3.2.7

Diboson36

4 Physics Object Definition

37

4.1

Primary Vertex

38

4.2

Electron

38

4.3

Muon

38

4.4

Photon

39

4.5

Jet

39

4.6

Missing Transverse Momentum

40
1

4.7

Overlap Removal

40

4.8

Large-Radius Jet

41

5 Event Selection
5.1

42

Event Preselection

42

5.1.1

Stransverse Mass

42

5.2

Resolved Signal Region

46

5.3

Boosted Signal Region

51

5.4

Diagonal Base Event Selection

55

6 Background Estimation

57

6.1

Resolved and Boosted Control Regions

58

6.2

Resolved and Boosted Control Regions For tt̄ + Z

73

6.3

Resolved and Boosted Validation Regions

76

6.4

2-D Shape Fit for Diagonal85

7 Hypothesis Test Procedures

89

7.1

Hypothesis Test for New Particle Search

89

7.2

Binned Maximum Likelihood Fit

90

7.3

Model Parameterization

91

7.4

Profile Likelihood Ratio as Test Statistic

95

8 Systematic Uncertainties

96

8.1

Experimental Sources

97

8.2

tt̄

101

8.3

Single Top

101

8.4

W +jets

102

8.5

Diboson102

8.6

tt̄ + V102

8.7

Signal103

9 Results

104

9.1

Results for Resolved and Boosted

104

9.2

Results from Diagonal

113

9.3

Combined Results

129

9.4

Future Prospects

132

10 Conclusion

134

Appendix

137

A Validation Fit for Diagonal

137

B Asymptotic Formulae for Hypothesis Test

153

C Systematic Uncertainty Plots for Diagonal

155

2

D Upgrading Trigger Readout of LAr Calorimeter

166

D.1 Supercell

166

D.2 New High-End Electronics for Supercell Toward Phase-I Upgrade

167

D.3 Demonstrator System

169

D.4 Performance Results from the Demonstrator System

170

3Chapter 1

Introduction
The final goal of elementary particle physics is to discovery an ultimate law of nature that is theorigin of all physics phenomena in the universe. As one of the steps, elementary particle physicists have constructed the Standard Model (SM), successfully describing physics of elementary
particles in a high energy scale called electroweak scale (around W /Z-boson mass, 100 GeV).
However, the SM is not perfect and has many problems. One of the most important problems is‘hierarchy problem’, which points out why the electroweak scale is much di↵erent from the grandunification theory (GUT) scale (1016 GeV) or Planck scale (1019 GeV). The di↵erence results inan extremely large quantum correction to the Higgs mass. The other problem is that there is no
appropriate candidate for dark matter in the SM. Furthermore, the grand unification cannot bederived from the SM.
These problems can be solved by introducing ‘supersymmetry’, one of the most compelling
extension of the SM. If supersymmetry is true, there should be superpartner of top quark named
top squarks (or stops). Since the stop mass is the most important key to solve the hierarchy problem, searching for stop could be a powerful test of supersymmetry. Furthermore, if the hierarchy
problem is solved by supersymmetry, then stop mass is predicted ⇠ 1 TeV at maximum, whichis small enough to be searched for in the LHC-ATLAS experiment. This thesis presents a search
for top squarks (stops) using pp-collisions data of 28.0 fb 1 in the LHC-ATLAS experiment.
In this Chapter 1, the SM and supersymmetry are briefly overviewed to support the following
sections where motivations of stop search and outline of the analysis are introduced.

1.1

The Standard Model

The Standard Model (SM) [1] is essentially based on three types of elementary particles (leptons,
quarks, and gauge-bosons). Figure 1.1 and 1.2 show all the particles and possible interactions in
the SM. Interaction of fermions (leptons or quarks) via photon, W /Z-boson and gluon are called
electromagnetic, weak and strong interaction, respectively.
The electrically neutral part of the SM Higgs field is a complex scalarwith a classicalpotential:

1 2 2 1
µ | | +
| |4 .
(1.1)
2
4
Figure 1.3 illustrates the global Higgs potential before/after electroweek spontaneous symmetry
V =breaking (EWSB). Above a certain extremely high energy, energy on ground state of the global

4

Figure 1.1: All particles described in the Standard Model [1]. In each block for each particle, its
mass, spin, and electro-charge are shown.
Higgs field or vacuum expectation value (VEV, v) is considered zeroq (left of Figure 1.3), andbelow the high energy threshold, the EWSB happens and then v !

µ2, experimentally known

1

as approximately 246 GeV (right of Figure 1.3) . After the EWSB, the transformation from theglobal to the local Higgs field (H) is denoted by

p , and then a mass term of the local= v+H
2

Higgs field can be expressed with , v or µ:m2H 2
H = v2 H 2 =2

1.2µ2 H 2(1.2)

Hierarchy Problem

In the SM, each fermion that couples to the Higgs field has a Yukawa couplingf . The interaction

term between fermion and Higgs is denoted by:
LYukawa =¯

f f Hfwhere f is the Dirac Field. The mass of a fermion after the EWSB is deduced to:v
mf = p2f(1.3)

Equation 1.3 means that the Higgs boson is most likely to couple to the heaviest fermion, namely
top quark, witht ⇠ 1.

Then if one considers the loop-correction to the Higgs mass shown in

Figure 1.4(a) and the following Equation 1.4, the most significant correction comes from top
quark:| f |2 2⇤ + ....
(1.4)
8⇡ 2 UV
where ⇤UV is an ultraviolet momentum cuto↵ used to regulate the loop integral, which shouldm2H =be interpreted as at least the threshold of energy scale above which the SM is not valid and new
physics appears.
1 The mass of W -boson, M

MW
ve
e2
1
W , after the EWSB can be expressed by 2 sin ✓w , where 4⇡ ⇠ 137 and cos ✓w = M .
Z

All the parameters to calculate v have been measured and therefore v can be determined ⇠246 GeV.

5

Figure 1.2: Possible interactions between particles in the SM [1].
The problem is that if ⇤UV is at the order of the grand unification energy scale 1016 GeV,
where electromagnetic, weak, and strong forces are unified into one force, this quantum correction
to m2H is some 24 orders of magnitude larger than the value of m2H =(125 GeV)2 . This iscalled ‘hierarchy problem’ [2–6]. The hierarchy problem is just for the Higgs boson mass. Indeed
the quantum corrections to fermion and gauge boson masses do not have the quadratic term of⇤UV because of symmetries.
In addition, since the Higgs mass is a parameter determined only through measurement atleast in the SM, the problem can be also interpreted as a criterion that a future theory of particle
physics, where the Higgs mass will be calculable, must be constructed without any excessive finetunings of the Higgs mass.

1.3

Supersymmetry

SM Particle TypeParticle

SymbolSpin

R-Parity

Superpartner

SymbolSpin

R-parity

Fermions

Quark

q

1
2

+1

Squarkq̃

0-1

Lepton`1
2+1

Slepton

`˜

0

-1

W

W

1

+1

Wino

W̃

1
2

-1

B

B

1

+1

Bino

B̃

1
2

-1
-1
-1

Bosons

Higgs bosons

Gluon

g

1

+1

Gluino

g̃

1
2

Higgs

Hu , Hd0+1

HiggsinoH̃u , H̃d

1
2

Table 1.1: The SM particles and their superpartners introduced by the supersymmetry. Symbol,
Spin and R-Parity of each particle are shown.

6

Figure 1.3: Illustration of the Higgs potential. The left/right figure shows the Higgs potential
before/after electroweek spontaneous symmetry breaking (EWSB) and the center shows thetransition. The parameters are> 0 and µ2 > 0 before the EWSB, and> 0 and µ2 < 0 after

the EWSB.

Figure 1.4: Feynman diagrams for loop correction to the Higgs mass m2H from a fermion (a) andthe correction from a scalar (b)Supersymmetry (SUSY) or Supersymmetric Standard Model [6–12] is a well motivated extension of the SM that provides a natural solution [13, 14] to the hierarchy problem.
The supersymmetry assumes that there exists a symmetry between fermions and bosons byintroducing an operator Q carrying spin angular momentum 1/2 that transforms from a bosonicstate into a fermionic state, and vice versa such as:
Q |Bosoni = |Fermioni , Q |Fermioni = |Bosoni(1.5)

A minimal incorporation of the supersymmetry into the SM requires that there should exist supersymmetric partner (superpartner) particles to each of the SM particles as shown in Table 1.1,
respectively. The superpartner of fermion is a scalar particle with spin 0 (Sfermion), and thesuperpartner of boson is a fermion particle with spin 12 (Bosino). Each superpartner particle
has the same mass as its partner unless the supersymmetry be broken. Each sfermion also has
the same multiplet structure of its partner, SU (3)C ⌦ SU (2)L ⌦ U (1)Y , so there are also leftand right-handed spinors for each sfermion. This extension of fermion multiplet is called ‘chiralsupermultiplet’ and summarized in Table 1.2.
Furthermore, the couplings of fermion and sfermion to the Higgs are assumed to be exactly
the same, namely

2
S = | f | , where

S is a Yukawa coupling constant for sfermion. Therefore,

the Feynman diagram of the loop correction from the sfermion to the Higgs mass is described asshown in Figure 1.4(b) and the correction is denoted by:
S
m2H = 2 ⇥⇤2
2m2S ln (⇤UV /mS )... ,16⇡ 2 UV

7

(1.6)

NamesSpinor Notationsquarks, quarks

Q(⇥3 families)ūd¯

sleptons, leptons(⇥3 families)⇣

spin 0⌘ũL d˜Lspin 1/2

SU (3)C , SU (2)L , U (1)Y(uL dL )3, 2, 16

ũ⇤R
d˜⇤

u†R

3̄, 1,

Rd†R

3̄, 1,L(˜⌫L ẽL )(⌫L eL )

1, 2,

ē

ẽ⇤R

e†R

2
3
1
3
1
2

(1, 1, 1)

Table 1.2: Chiral supermultiplet and notation of left- and right-handed spinors for each fermionand each sfermion.
where mS is mass of a sfermion. A remarkable thing is that the correction is positive2 andcompletely cancels the huge loop correction from fermion to the Higgs mass in Equation 1.4.
However, since the sfermion cancellation also leaves its own logarithmic correction proportional
to m2S (the second term in Equation 1.6), the mass of the sfermion with the largest Yukawa
coupling must be, at most, at the order of ⇠ 1 TeV so thatm2H does not become too large.

This series of extensions of the SM is called Minimal Supersymmetric Standard Model(MSSM) and its logic or property to solve the hierarchy problem is called ‘naturalness’.
In the MSSM, baryon number and lepton number get no longer conserved by all of therenormalizable couplings, but this conservation breaking must be very small in order not toconflict with the experimental upper limit on the proton life time [15]. To solve this, the MSSM
requires that ‘R-parity’ should be conserved in the MSSM interactions. The R-parity is definedby:PR = ( 1)3(B L)+2s(1.7)

where B and L are baryon and lepton number and s is spin, respectively. As shown in Table 1.1,
PR = +1 for the SM particles and PR =1 for the superpartners. If R-parity conservation istrue, this provides three important phenomenological consequences [16]:• The lightest sparticle (LSP) with PR =1 must be stable. If the LSP is electricallyneutral, it interacts only weakly with ordinary matter. Then the LSP can be an attractive
candidate for the ‘Dark Matter’ [17, 18].

• Each sparticle except for the LSP must eventually decay into a state that contains an odd
number of LSPs (usually just one).

• In collider experiments, sparticles can only be produced in even numbers at one collision(usually two at one collision).

In addition to naturalness and dark matter, ‘gauge coupling unification’ is also one of thetheoretical motivations of the MSSM. By introducing the supersymmetric particles, it modifies
the energy dependence of the three running coupling constants, making possible their perfectconvergence at the scale of grand unification theory (GUT), ⇤GUT ⇠ 1016 GeV [6, 19–21].
Figure 1.5 shows the three running coupling constants in the SM and MSSM.

2 This is due to a spin-statistics theorem meaning that fermions will have a negative contribution and bosons

a positive contribution.

8

Figure 1.5: Two-loop renormalization group evolution of the inverse gauge couplings ↵a 1 (Q) in
the SM (dashed lines) and the MSSM (solid lines) [6]. The dependency on the threshold energy oftransition from the SM to the MSSM is indicated by blue line (500 GeV) and red line (1.5 TeV).

1.4

Top Squark

Up to the present time, a superpartner particle that has the same mass as its normal partner
has not been discovered, hence the supersymmetry breaking must occur so that superpartner
particles get heavier than their normal partners.
Unlike the light-flavor squarks in the first and second generation, the stop has a non-negligible
left-right mixing due to its large Yukawa coupling [22] 3 . The left-right mixing is described by ahermitian 2 ⇥ 2 mass matrix:
Lt̃M =(t̃⇤L , t̃⇤R )

Mt̃2LLMt̃2LR

Mt̃2RL

Mt̃2RR

!

t̃L
t̃R

!

,

(1.8)

with
2
Mt̃2LL = MQ̃+ (Tt3
3

Qt sin2 ✓W ) cos 2 m2Z + m2t

Mt̃2RR = Mt̃2 + Qt sin2 ✓W cos 2 m2Z + m2t⇣⌘
3
Mt̃2RL = (Mt̃2LR )⇤ = mt At̃ µ⇤ (tan ) 2Tt(1.9)

where mt , Qt and Tt3 are the mass, electric charge and weak isospin of top quark, respectively.
✓W denotes the weak mixing angle, tan= vu /vd with vu (vd ) being the vacuum expectation
00value of the Higgs field Hu (Hd ). MQ̃3 is the mass of left-handed squark spinor of third generation⇣⌘(Q̃3 = t̃L , b̃L ), and Mt̃ is the mass of right-handed spinor of stop. At̃ is a trilinear coupling
constant of stop. In case parameters µ and At̃ are complex, the o↵-diagonal elements Mt̃2RL =(Mt̃2LR )⇤ are also complex with a phase of
h
i
h
2
=
arg
M
=
arg
At
t̃
t̃RL

i
3
µ⇤ (tan ) 2Tt .

3 The sbottom also has a non-negligible left-right mixing in the same way.

9

(1.10)

Finally, the stops in the mass eigenstates are written such ast̃1 = ei t̃ cos ✓t̃ t̃L + sin ✓t̃ t̃R(1.11)sin ✓t̃ t̃L + e i t̃ cos ✓t̃ t̃R

t̃2 =
where
cos ✓t̃ = r

Mt̃2
LR

Mt̃2LR⇣2+ m2t̃

Mt̃2
LL

1⌘ , sin ✓t̃ = r
2

Mt̃2
LR

Then the mass eigenvalues can be deduced to:1
m2t̃1,2 =2⇣

Mt̃2LL + Mt̃2RR

⌘

r⇣

⌥

Mt̃2

Mt̃2LL m2t̃1
⇣
⌘2 .
2
2
2
+ mt̃
Mt̃

Mt̃2

LL

RR

1

⌘2

(1.12)LL+ 4 Mt̃2

LR2!

(1.13)

where mt̃1 < mt̃2 .

1.5

Neutralino

The higgsinos and electroweak gauginos mix each other because of the e↵ects of the EWSB. The
neutral higgsinos (H̃u0 and H̃d0 ) and the neutral gauginos (B̃, W̃ 0 ) are combined to form four0mass eigenstates called ‘neutralinos’. The neutralino mass eigenstates are denoted by ˜1,2,3,4 .
By convention, they are labeled in ascending order; m ˜01 < m ˜02 < m ˜03 < m ˜04 . The lightest
0
neutralino ˜1 is usually assumed to be the LSP or the dark matter candidate.
In the gauge-eigenstate basis

0= (B̃, W̃ 0 , H̃d0 , H̃u0 ), the neutralino mass term of the La-

grangian is

1 0 T( ) M ˜02

Lneutralino mass =
where

0

B
B
M ˜0 = BB@

0+ c.c.,

M1

0c sW mZ

0

M2

c c W mZ

c sW mZc c W mZ

0s sW mZ

s cW mZµ(1.14)

s s W mZ

1C
s c W mZ C
C.
C
µ
A
0

(1.15)

M1 and M2 are bino and wino mass, µ is higgsino mass, and s = sin , c = cos , sW = sin ✓W ,and cW = cos ✓W . The mass matrix M ˜0 can be diagonalized by a unitary matrix N to obtain
mass eigenstates:
˜0 i = N ij
so thatN ⇤ M ˜0 N

1

0

B
B
=B
B
@

0
j

(1.16)

m ˜01

0

0

0

0

m ˜02

0

0

0

0

m ˜03

0

0

0

0

m ˜04

0

0

0

1
C
C
C
C
A

0

(1.17)

has real positive values on the diagonal. Although ˜1 (and ˜2 , ˜3 , ˜4 ) is basically a mixture of0B̃, W̃ 0 , H̃d0 , H̃u0 , ˜1 could be in a pure state, such as:0• Pure Bino: M1 ⌧ M2 , µ =) ˜1 ⇡ B̃0

• Pure Wino: M2 ⌧ M1 , µ =) ˜1 ⇡ W̃ 0•0Pure Higgsino: µ ⌧ M1 , M2 =) ˜1 ⇡

⇣

0
H̃u
±H̃d0
p
2

10

⌘

1.6

Stop SearchThis thesis aims at searching for the lighter stop (t̃1 ). As described in Section 1.3, if the naturalness is true, the sfermion with the largest Yukawa coupling, namely stop, must have the massof the order of ⇠ 1 TeV [23, 24]. This mass range can be explored sufficiently in the LHC, aphadron collider providing pp collisions at s = 13 TeV. Stops can be produced through strong
interactions and therefore can be produced in pp collisions. Because of the R-parity conservation,
two stops are directly produced at one collision.

00(b) stop three-body decay (t̃1 ! bW ˜1 )(a) stop two-body decay (t̃1 ! t ˜1 )Figure 1.6: Feynman diagram of the direct pair production of t̃1 particles and their two types
00of decays, t̃1 ! t ˜1 (a) and t̃1 ! bW ˜1 (b). For simplicity, no distinction is made between
00particles and antiparticles. The t̃1 ! t ˜1 and t̃1 ! bW ˜1 decay modes can be allowed if00mt̃m ˜0 ⌘ m(t̃1 , ˜1 ) > mt and mt > m(t̃1 , ˜1 ) > mW , respectively.
1

1

The stop can decay into a variety of final states, depending on the SUSY particle mass
spectrum, in particular on the masses of the stop and lightest neutralino. The analysis presented
0in this thesis targets t̃1 ! t ˜1 decay mode illustrated in Figure 1.6(a) where mt̃m ˜0 ⌘
1

1

0
0m(t̃1 , ˜1 ) > mt , and focuses on the events with one lepton, where each t̃1 decays as t̃1 ! t ˜1 ,the W boson from one of the two top quarks decays to an electron or muon (either directly or via

a ⌧ lepton) and the W boson from the other top quark decays hadronically. The final state can00
be denoted by t̃1 t̃1 ! [bqq ˜1 ][b`⌫ ˜1 ] (with no distinction between particles and antiparticles).
Thus, the dominant SM background events are:• tt̄• a top quark and a W boson (single top, W t)
• tt̄ + Z(! ⌫ ⌫¯)• W bosons and jets (W +jets)• two bosons (diboson)
In the analysis, the contribution of multijet events is found to be negligible from an data-driven
0
estimation using a fake-factor method [25, 26]. In addition, since the t̃1 ! t ˜1 search is somewhat
11

0

sensitive to t̃1 ! bW ˜1 decay mode shown in Figure 1.6(b) where mt >0
results are also interpreted in the t̃1 ! bW ˜1 decay mode scenario.

The signal kinematic topology highly depends on the model parameter0m(t̃1 , ˜1 ) > mW , the0m(t̃1 , ˜1 ), therefore

there are three analyses individually optimized to three types of kinematic topologies, Boosted
000( m(t̃1 , ˜1 ) & 3mt ), Resolved ( m(t̃1 , ˜1 ) ⇠ 2mt ), and Diagonal ( m(t̃1 , ˜1 ) ⇠ mt ). Figure 1.7

and 1.8 illustrate the three topologies and territories of the three topologies in a (mt̃1 , m ˜01 ) plane.
0
For a scenario of m(t̃1 , ˜1 ) & 3mt , the topology would be Boosted (Figure 1.7(a)), where thethree jets from the t decay forms one large-R jet and a significantly large missing transverse energy
0
0
miss
(ET
) arises from the two ˜1 ’s with very high pT . For a scenario of m(t̃1 , ˜1 ) ⇠ 2mt , thetopology would be Resolved (Figure 1.7(b)), where the three jets are not merged into one large-R
00
missjet but resolved and a large ET
arises from the two ˜1 ’s. For a scenario of m(t̃1 , ˜1 ) ⇠ mt ,0

the topology would be Diagonal (Figure 1.7(c)), where the three jets are resolved and ˜1 and t
from t̃1 decay are nearly collinear with respect to t̃1 momentum. The latter tendency results in0
missa large cancellation of ET
contributions from the two ˜1 ’s.
In a preceding study using the data of 13.2 fb 1 , which uses events with one lepton in the
final state, there were some excesses of CLb = 2.2

3.3

in several signal regions which aresomewhat kinematically overlapped with each other [27]. The search in this thesis covers a part ofthe phase spaces with the excesses. For this reason, Resolved and Boosted analyses in this thesis
are similar to those of Ref. [27]. The originality in this thesis is that a new analysis is developed
and performed to search a stop mass region, named Diagonal, which is very important to solve
the hierarchy problem naturally. The key technique newly developed for Diagonal analysis is abackground estimation using ‘2-dimensional shape fit’, which greatly expands the search regionof Diagonal. In the following sections, Boosted, Resolved, and Diagonal analysis strategies are
outlined.

0(b) Resolved ( m(t̃1 , ˜1 ) ⇠ 2mt )0(a) Boosted ( m(t̃1 , ˜1 ) & 3mt )0(c) Diagonal ( m(t̃1 , ˜1 ) ⇠ mt )Figure 1.7: Illustration of three types of the signal kinematic topologies, Boosted, Resolved, and0
Diagonal, categorized by m(t̃1 , ˜1 ). The dashed lines indicate particles completely invisible to
ATLAS detector. The cones indicate jets. The detail is explained in the main text.

12Figure 1.8: Illustration of all the mass points used in the analysis with categorization of the signal
0kinematic topologies. The red circle and the blue cross indicate the decay modes, t̃1 ! t ˜1 and
0t̃1 ! bW ˜1 , respectively. The red and blue dashed lines are the boundaries of the decay modes.

The cyan, purple, and orange regions are generally Diagonal, Resolved, and Boosted topology,
respectively. The benchmark mass points to optimize Diagonal, Resolved, and Boosted analyses
are indicated by cyan, purple, and orange stars, respectively.

1.6.1

Boosted

Boosted analysis aims at signal events with0m(t̃1 , ˜1 ) & 3mt as indicated by the orange re-gion in Figure 1.8. The benchmark mass point to optimize Boosted analysis is (mt̃1 , m ˜01 ) =(1000, 1) GeV.
In Boosted region, as shown in Figure 1.7(a), top quarks are highly boosted so that bqq 0 fromhadronic top decay forms one large-R jet. If one approximates its

R by

R of W and b fromtop decay, then it can be written as the following equation;
R⇡

2mt
,
pT

(1.18)

where pT is for top quark. In Boosted region, the top quark pT can be approximately deduced
to pT ⇠

m2t̃

1

m2t

2mt̃1

, hence pT in Boosted region is typically more than ⇠ 300 GeV and therefore

R of the large-R jet is less than ⇠ 1.2. Figure 1.9 shows distribution of

R between the W

and b from top quark decay as a function of the top quark pT and indicates that

R for topquarks with pT = 300 GeV is mostly less than 1.2. From this fact and an optimization study, a
reclustering jet algorithm is used in Boosted analysis that reconstructs large-R jets from small-R
jets using anti-kT algorithm with a jet radius parameter R = 1.2 [28]. Section 4.8 describes thealgorithm in detail.
0
The ˜1 ’s pT is also very high and thus Boosted topology tends to provide larger missing
13

miss
transverse energy (ET, see Section 4.6) than Resolved and Diagonal topologies and the SM
missevents. The dominant background remaining after a large ET
requirement is tt̄ and tt̄ + Z(⌫⌫)

event.

Figure 1.9:

R between the W and b from top quark decay as a function of the top quarkpT [29]. The distributions in every pT bins are normalized to 1. the color coding corresponds tothe fraction of considered top quarks at a pT bin. The distribution corresponds to the particle
information at the generator level after the emission of initial and final state radiation and arepobtained from tt̄ decays in pp collisions at s = 8 TeV simulated using Powheg +Pythia.

1.6.2

Resolved

Resolved analysis aims at signal events with0m(t̃1 , ˜1 ) ⇠ 2mt as indicated by the purple re-gion in Figure 1.8. The benchmark mass point to optimize Resolved analysis is (mt̃1 , m ˜01 ) =(600, 300) GeV.
In Resolved region, as shown in Figure 1.7(b), the hadronic top decay products are not merged

into one large-R jet but resolved into three smaller-radius jets because pT of top quark is relatively0
medium. Since the ˜1 ’s pT is also relatively medium, Resolved topology tends to provide larger
missET
than Diagonal topology and the SM events. The dominant background remaining after
missa large ET
requirement is tt̄ ! [b`⌫][b`lost ⌫] event where `lost is a lost lepton due to outside
miss
acceptance, and thus contributes to increase ET. Section 5.2 describes an event selection to

suppress the tt̄ ! [b`⌫][b`lost ⌫] event and the other backgrounds.

1.6.3

Diagonal0

Diagonal analysis aims at signal events with m(t̃1 , ˜1 ) ⇠ mt as indicated by the cyan region
0in Figure 1.8. In Figure 1.8, m(t̃1 , ˜1 ) = mtop is equivalent to the red dashed line of the00transition from t̃1 ! t ˜1 to t̃1 ! bW ˜1 decay mode, and thus it is called ‘(top-mass) diagonal
0line’. Diagonal analysis is also sensitive to t̃1 ! bW ˜1 scenario because it is similar to the
14

0

0

t̃1 ! t ˜1 event topology, although the analysis is optimized just only to t̃1 ! t ˜1 scenario. The
benchmark mass point to optimize Diagonal analysis is (mt̃1 , m ˜01 ) = (400, 200) GeV.

In the region near the diagonal line, as shown in Figure 1.7(c), the behavior of hadronic top
0
decay is the same as Resolved region. Figure 1.7(c) also indicates that ˜1 and t from t̃1 decay0

are nearly collinear with respect to t̃1 momentum, because momenta of t and ˜1 at the center of0mass system of t̃1 ! t ˜1 are nearly 0. In addition, since t̃1 pair is produced typically back-to0

back, the directions of the two ˜1 ’s also tend to be almost back-to-back. This results in a large0
misscancellation of ET
contributions from the two ˜1 ’s, and therefore Diagonal topology tends tomissprovide a little bit larger ET
than the SM events4 .

Since the di↵erence between Diagonal topology and tt̄ event topology is smaller than Boosted
and Resolved, the dominant background is tt̄ event and it is very challenging to suppress them
missby event selection. For this reason, Diagonal analysis exploits a 2-dimensional (ET,mT ) shape

fit that provides a precise background estimation, which is described in Section 6.4.
In the following chapters, the Boosted, Resolved, and Diagonal analyses are described indetail. Chapter 2 introduces outlines of the LHC and the ATLAS detector. Chapter 3 describes
dataset and Monte Carlo samples used in the analyses. Chapter 4 defines physics objects andChapter 5 defines event selections using the physics objects. Chapter 6 describes backgroundestimations. Chapter 7 introduces hypothesis test procedures used to provide quantitative resultsof stop search. Chapter 8 describes systematic uncertainties used in the background estimations.
Chapter 9 presents the stop search results. Chapter 10 is the conclusion of this thesis.

4 If there is an initial or final state radiation from pp ! t̃ t̃ process, the two
1 1
miss also can arise.
state and then a relatively large ET15

˜01 ’s are not in back-to-backChapter 2

ATLAS Experiment
2.1

Large Hadron Collider

The Large Hadron Collider (LHC) [30] at the European Organization for Nuclear research(CERN) is a circular proton-proton (pp) collider. It is located in a tunnel with a 27 km circumference at a depth below ground of between 45 m (around lake Geneva) - 170 m (at the footof the Jura mountains), which was excavated in the 1980s. In 8.33 T magnetic fields provided bysuperconducting dipole electromagnets, the proton beams circulate in opposite direction in two
separate beam pipes in an ultra-high vacuum. Before being injected into the LHC, proton beams
pass through a chain of pre-accelerators shown in Figure 2.1. First of all, the hydrogen atoms

Figure 2.1: The CERN accelerator complex [31]. The LHC is the last ring (dark blue line) in acomplex chain of particle accelerators.
with valence electrons stripped o↵ are accelerated in the linear accelerator 2 (LINAC2) up to 50
MeV, and are injected afterwards into the Proton Synchrotron Booster (PSB). This first circular
pre-accelerator increases the energy of the protons up to 1.4 GeV. After that, the protons are16

accelerated to 25 GeV in the Proton Synchrotron (PS) and then injected into the Super Proton
Synchrotron (SPS), where they are accelerated up to 450 GeV and then piped to the LHC. At
the LHC, the protons are further accelerated up to the maximum achievable energy and are thencollided at each of the four interaction points where the four main LHC experiments are hosted,
the ATLAS, CMS, ALICE and LHCb experiments.

p
In the physics runs from 2010 to 2012 (Run-1), the center of mass energy of pp collisions sp
was 7-8 TeV. From 2015, LHC started with approximately 2 times higher energy s = 13 TeV(Run-2). Figure 2.2 shows the peak and average instantaneous luminosity as a function of date in2016. The max peak instantaneous luminosity in 2016 was 13.7⇥1033 cm 2 s 1 . The frequency ofthe bunch crossing is 40 MHz (in other words, the time between colliding bunches is 25 ns). The
number of average interactions per bunch crossing is measured as shown in Figure 2.3. Since theinstantaneous luminosity gradually increased during 2016, the number of the average interactionsin 2016 is larger than 2015.

Figure 2.2: Peak and average instantaneous

Figure 2.3: Observed number of the aver-luminosity as a function of date in 2016.

age interactions per bunch crossing.
2015 dataset (3.2 fb(33.3 fb

1

The

) and the 2016 dataset) are shown in the plot (amount to36.5 fb 1 ).

17

1

2.2

ATLAS Detector

ATLAS (A Toroidal LHC ApparatuS) detector [32] is a multipurpose particle physics detector
with nearly 4⇡ coverage in solid angle at the collision point.
In the ATLAS experiment, a right-handed coordinate system where the reference point is
set at the nominal interaction point in the center of the detector and the z-axis is set along thebeam pipe. The x-axis is set to point from the interaction point to the center of the LHC ring,and the y-axis points upward vertically. Cylindrical coordinates (r, ) are also used in the x-yplane, whereis the azimuthal angle around the z-axis. The pseudorapidity is defined using thepolar angle ✓ as ⌘ = ln tan(✓/2).
p
R ⌘ ( ⌘)2 + ( )2 .

and ⌘ are also used to measure angular distance defined as

From inside to outside, particles traverse the inner detector (tracking of charged particles), theelectromagnetic calorimeter (measuring energies of electron and photon), the hadronic calorimeter (measuring energies of hadrons), and the muon spectrometer (identifying muon and measuring
its momentum) as illustrated in Figure 2.4 and 2.5.

Figure 2.4: Cut-away view of the ATLAS detector [32]. The dimensions of the detector are 25 m
in height and 44 m in length. The overall weight of the detector is approximately 7000 tonnes.

18Figure 2.5: Illustration of particle detection in the sub-detectors of the ATLAS detector in
R- cut-away view. From inside to outside, particles traverse the inner tracking detector, theelectromagnetic calorimeter, the hadronic calorimeter, and the muon spectrometer. Trajectories
indicated by dashed lines are invisible to the sub-detectors. For example, photons are invisible tothe inner tracking detector but visible to the electromagnetic calorimeter. Neutrinos are invisible
to all the sub-detectors.

19

2.2.1

Inner Detector

Figure 2.6: R- cross-sectional view of barrel part of the ATLAS inner detector, including the
new insertable B-layer (IBL) [33]. The distances to the interaction point are also shown.
Approximately 1000 particles are produced from the collision point every 25 ns within |⌘| <2.5, and make a very high track density in the detector. The inner detector (ID) is designed

to achieve robust track-pattern recognition and precision measurements of tracks and vertices.
Figure 2.6 and 2.7 show the R- cross-sectional view of the ID barrel part and the R-z crosssectional view of the ID, respectively. The ID is immersed in a uniform 2 T magnetic field
generated by the central solenoid, which extends over a length of 5.3 m with a diameter of 2.5 m.
The ID consists of 4 discrete sub-detectors, from inside to outside, silicon pixel detector (Pixel),semi-conductor tracker (SCT), and transition radiation tracker (TRT).
The precision tracking detectors (Pixel and SCT) cover the region |⌘| < 2.5. In the barrel

region, Pixel and SCT are arranged on concentric cylinders around the beam axis. In the end-cap
regions, Pixel and SCT are located on disks perpendicular to the beam axis.
The Pixel achieves the high granularity around the vertex region. The Pixel layers are locatedsuch that each track typically crosses four pixel layers. The innermost layer, named insertable Blayer (IBL) [33], consists of 14 staves equipped with planar and 3D silicon pixel sensor technologythat are arranged in turbine-like fashion. The pixel size of the IBL is 50 ⇥ 250 µm2 in R- ⇥ z.
The pixel sensors in the three outer layers have a minimum pixel size of 50 ⇥ 400 µm2 in R-⇥ z. The intrinsic accuracies in the barrel are 10 µm (R- ) and 115 µm (z) and in the disks are
10 µm (R- ) and 115 µm (R).

For the SCT, eight strip layers are crossed by each track and reconstruct four space points.
In the barrel region, the SCT uses small-angle (40 mrad) stereo strips and locate one set of strips

20

Figure 2.7: R-z cross-sectional view of the layout of the ATLAS Inner Detector for Run-2 [34].
The top panel shows the whole Inner Detector, whereas the bottom panel shows a magnified
view of the Pixel detector region.
in each layer parallel to the beam axis in order to measure R- coordinates. The layers consistof two 6.4 cm long daisy-chained sensors with a strip pitch of 80 µm. In the end-cap region, theSCT has a set of strips running radially and a set of (40 mrad) stereo strips. The average pitchof the strips is approximately 80 µm. The intrinsic accuracies in the barrel are 17 µm (R- ) and580 µm (z) and in the disks are 17 µm (R- ) and 580 µm (R).
The TRT provides typically 36 hits per track by its 4 mm diameter straw tubes and covers|⌘| < 2.0. The TRT only provides R-

information and the intrinsic accuracy is 130 µm per

straw. In the barrel region, the straws are 144 cm long and are parallel to the beam axis. In theend-cap region, the straws are 37 cm long and are arranged radially in wheels. The combinationof the Pixel and the SCT with the TRT gives very robust pattern recognition and very highprecision in both R- and z coordinates. The TRT contribute significantly to the momentum
measurement because of the large number of measurements and the longer measured track length.
In order to identify electron, the tracking measurements in the ID system are also usedwith the precision measurements of the electromagnetic calorimeter. The electron identification
capabilities are enhanced by the detection of transition-radiation photons in the xenon-based gas
mixture of the TRT straw tubes. The Pixel and SCT also allow impact parameter measurements
and vertexing for b-jet and ⌧ lepton tagging. The performance of secondary vertex measurement
is enhanced by the innermost layer of the Pixel at a radius of 33.5 mm.

21

2.2.2

Electromagnetic Calorimeter and Hadronic Calorimeter

Figure 2.8: A cut-away view of the ATLAS calorimeter [35].
Figure 2.8 shows a cut-away view of the calorimeters. These calorimeters cover the range |⌘|< 4.9, using di↵erent techniques suited to the various requirements of the physics processes ofinterest and of the radiation environment over this large ⌘-range. Over the ⌘ region matchedto the inner detector, |⌘| < 2.5, the fine granularity of the electromagnetic (EM) calorimeter isideally suited for precision measurements of electrons and photons. The coarser granularity of

the rest of the calorimeter is enough to satisfy the physics requirements for jet reconstruction
and missing transverse energy measurements. Table 2.1 shows granularity versus |⌘| of all thecalorimeters.

Calorimeters are required to stop electromagnetic and hadronic showers in themselves, andsuppress punch-through into the muon system. The total thickness of the EM calorimeter is atleast 22 radiation lengths (X0 ) in the barrel and at least 24 X0 in the end-caps. The approximate
9.7 nuclear interaction lengths ( ) of hadronic calorimeter in the barrel (10are adequate to provide good resolution for high energy jets,
The total thickness (including 1.3

in the end-caps)p3%.
E /E = 50%/ E/GeV

from the outer support) is 11

at |⌘| = 0 and is enough toreduce punch-through of jets significantly (although muons can pass). This thickness also ensures

a good missing transverse energy measurement, which is important for many physics analyses
especially for SUSY particle searches. Figure 2.9 and 2.10 summarize radiation and interaction
lengths of the ATLAS calorimeters.
The ATLAS Calorimeter consists of 4 types of calorimeters:
Liquid Argon (LAr) Calorimeter
It is a lead-LAr detector with accordion-shaped kapton electrodes and lead absorber plates.
The accordion geometry provides complete
22

symmetry without azimuthal cracks. The

EM Calorimeter
BarrelEnd-cap

Granularity⌘⇥

versus |⌘|Presampler

0.025 ⇥ 0.1|⌘| < 1.52

0.025 ⇥ 0.1

1.5 < |⌘| < 1.8

Calorimeter 1st layer

0.025/8 ⇥ 0.1|⌘| < 1.40

0.050 ⇥ 0.1

1.375 < |⌘| < 1.425

0.025 ⇥ 0.025

1.40 < |⌘| < 1.475

0.025 ⇥ 0.1

0.025/8 ⇥ 0.1
0.025/6 ⇥ 0.1
0.025/4 ⇥ 0.1
0.025 ⇥ 0.1

Calorimeter 2nd layer

Calorimeter 3rd layer

0.025 ⇥ 0.025|⌘| < 1.40

0.075 ⇥ 0.025

1.40 < |⌘| < 1.475

0.050 ⇥ 0.025|⌘| < 1.35

0.1 ⇥ 0.1

0.050 ⇥ 0.025
0.025 ⇥ 0.025
0.1 ⇥ 0.1

0.050 ⇥ 0.025

1.425 < |⌘| < 1.5
1.5 < |⌘| < 1.8
1.8 < |⌘| < 2.0
2.0 < |⌘| < 2.4
2.4 < |⌘| < 2.5

2.5 < |⌘| < 3.2

1.375 < |⌘| < 1.425

1.425 < |⌘| < 2.5
2.5 < |⌘| < 3.2
1.5 < |⌘| < 2.5

LAr Hadronic End-cap (HEC)
Granularity⌘⇥

versus |⌘|Calorimeter 1st layer

0.1 ⇥ 0.1

1.5 < |⌘| < 2.5

0.2 ⇥ 0.2

2.5 < |⌘| < 3.2

0.1 ⇥ 0.1

Calorimeter 2nd layer
Calorimeter 3rd layer

1.5 < |⌘| < 2.5

0.2 ⇥ 0.2

Calorimeter 4th layer

2.5 < |⌘| < 3.2

LAr Forward Calorimeter (FCal)
Granularityx⇥y (cm) versus |⌘|3.0 ⇥ 2.6

Calorimeter 1st layer⇠ four times finer
Calorimeter 2nd layer

3.10 < |⌘| < 3.15
4.30 < |⌘| < 4.83

3.3 ⇥ 4.2

3.24 < |⌘| < 4.50

5.4 ⇥ 4.7

3.32 < |⌘| < 4.60

⇠ four times finer
Calorimeter 3rd layer

3.15 < |⌘| < 4.30

⇠ four times finer

3.20 < |⌘| < 3.24
4.50 < |⌘| < 4.81

3.29 < |⌘| < 3.32
4.60 < |⌘| < 4.75

Scintillator Tile Calorimeter
Granularity⌘⇥

versus |⌘|BarrelCalorimeter 1st layer
Calorimeter 2nd layer
Calorimeter 3rd layer

Extended Barrel

0.1 ⇥ 0.1|⌘| < 1.0

0.1 ⇥ 0.1

0.8 < |⌘| < 1.7

0.2 ⇥ 0.1|⌘| < 1.0

0.2 ⇥ 0.1

0.8 < |⌘| < 1.7

0.1 ⇥ 0.1|⌘| < 1.0

0.1 ⇥ 0.1

0.8 < |⌘| < 1.7

Table 2.1: Granularity versus |⌘| in each layer of each calorimeters.

23

X0

X0

12

45

10

Before accordion

40

Before presampler

358

Before scintillator
Barrel accordion
Before barrel accordion
Before barrel presampler

End-cap accordion
Before end-cap accordion
Before end-cap presampler

30
25

6

20
4

15
10

2

5
1

1.5

2

0

2.5
3
Pseudorapidity

1.4

1.45

1.5

1.55

1.6

1.65
1.7
Pseudorapidity

X0

0.5

X0

0
0

Layer 3Layer 2
Layer 1
Before accordion

40
35

45
40

Layer 3Layer 2
Layer 1
Before accordion

35

30

30

25

25

20

20

15

15

10

10

5

5

0
0

0.2

0.4

0.6

0.8

1

0

1.2
1.4
Pseudorapidity

1.6

1.8

2

2.2

2.4

2.6

2.8
3
3.2
Pseudorapidity

Figure 2.9: Cumulative amounts of material in front of and in the electromagnetic calorimeters,in units of radiation length X0 , as a function of |⌘|. The top left-hand plot shows separately the

total amount of material in front of the presampler layer and in front of the accordion for thefull ⌘-coverage. The top right-hand plot shows the details of the crack region between the barrel
and endcap cryostats. The two bottom figures show the thicknesses of each accordion layer aswell as the amount of material in front of the accordion, for the barrel (left) and end-cap (right)
part, respectively.
lead thickness in the absorber plates has been optimized as a function of ⌘ in terms of EM
calorimeter performance in energy resolution. The EM calorimeter is divided into a barrel
part (|⌘| < 1.475) and two end-cap components (1.375 < |⌘| < 3.2). The barrel calorimeterconsists of two identical half-barrels, separated by a small gap (4 mm) at z = 0. Each endcap calorimeter is mechanically divided into two coaxial wheels; an outer wheel covering theregion 1.375 < |⌘| < 2.5, and an inner wheel covering the region 2.5 < |⌘| < 3.2. Over theregion devoted to precision physics (|⌘| < 2.5), the EM calorimeter is segmented in three
sections in depth. Furthermore, in the region of |⌘| < 1.8, a presampler detector is used
to correct for the energy lost by electrons and photons upstream of the calorimeter. The

presampler consists of only an active LAr layer of thickness 1.1 cm (0.5 cm) in the barrel(end-cap) region. Figure 2.11 and 2.12 show a module in the barrel and the accordionshaped structure. With Run-1 full datasets, the energy resolution for electron and photon
has been studied and is shown in Figure 2.13.
Tile Calorimeter
It is a hadronic calorimeter located just outside the EM calorimeter envelope. Its barrel
covers the region |⌘| < 1.0, and its two extended barrels 0.8 < |⌘| < 1.7. It is a sampling calorimeter using steel as the absorber and scintillating tiles as the active material.

24Interaction lengths

20
18
16
14
12

HEC3

10
Tile3

HEC2

6 Tile2

HEC1

8

4 Tile1
0
0

0.5

1

1.5

FCal2

HEC0

EM calo

2

FCal3

FCal1
2

2.5

3

3.5

4
4.5
5
Pseudorapidity

Figure 2.10: Cumulative amount of material, in units of interaction length, as a function of |⌘|.
The total amount of material in front of the electromagnetic calorimeters and in front of the firstactive layer of the muon spectrometer (up to |⌘| < 3.0) are also shown (dusty yellow and light
blue respectively).

Figure 2.14 shows structure of a barrel module of the tile calorimeter. The barrel andextended barrels are divided azimuthally into 64 modules. Radially, the tile calorimeter
extends from an inner radius of 2.28 m to an outer radius of 4.25 m. It is segmented in
depth in three layers, approximately 1.5, 4.1 and 1.8 nuclear interaction lengths ( ) for thebarrel and 1.5, 2.6, and 3.3

for the extended barrel. The total detector thickness at theouter edge of the tile-instrumented region is 9.7

at |⌘| = 0.

LAr Hadronic End-cap Calorimeter (HEC)
It consists of two independent wheels per end-cap located behind the end-cap electromagnetic calorimeter. The HEC covers the range 1.5 < |⌘| < 3.2.
LAr Forward Calorimeter (FCal)
It covers 3.1 < |⌘| < 4.9. In order to reduce the amount of neutrons in the inner detector

cavity, the front face of the FCal is 1.2 m behind the EM calorimeter front face as shownin Figure 2.15. This severely limits the depth of the calorimeter and therefore calls for ahigh-density design. The FCal is approximately 10 interaction lengths deep, and consistsof three modules in each end-cap; the first, made of copper, is optimized for electromagnetic measurements, while the other two, made of tungsten, measure mainly the energy ofhadronic interactions. As shown in Figure 2.16, each module consists of a metal matrix,
with regularly spaced longitudinal channels filled with the electrode structure consisting ofconcentric rods and tubes parallel to the beam axis. The LAr in the gap between the rod
and the tube is the sensitive medium.
25

Figure 2.11: Sketch of a barrel module in the LAr

Figure 2.12: Accordion structure of the barrel [36].

calorimeter where the di↵erent layers are clearly visi-

The top figure is a view of a small sector of the barrel

ble with the accordion-shaped kapton electrodes [36].

calorimeter in R- plane.

The granularity in⌘⇥of the cells of each of thethree layers is also shown.

(a) Energy resolution for electron(b) Energy resolution for photon

Figure 2.13: Energy resolution for electron and photon as function of ET [37].

26

Photomultiplier

Wavelength-shifting fibre
Scintillator

Steel

Sourcetubes

Figure 2.14: Sketch of a barrel module of the tile calorimeter.

R

R (cm)

LAr gap

60

HEC

HEC
(back)(front)

50

EMEC
r

40

20

FCal 1

FCal 2

FCal 3

(EM)

(Had)

(Had)

Moderator shielding

Beampipe

sh LA
ie r
ld C
in al
g or
pl im
ug e
te

30

Warm
wall

10

Superinsulation
Cold
wall

Pump
0
350

400

450

500

550

600

650

z (cm)

Figure 2.15: A schematic diagram showing

Figure 2.16: Electrode structure of the FCal

the three FCal modules located in the end-

1st layer with the matrix of copper plates andcap cryostat. The material in front of thethe copper tubes and rods with the LAr gap

FCal and the shielding plug behind it are also

for the electrodes. The Moliere radius, RM , isshown. The black regions are structural parts

represented by the solid disk.

of the cryostat. For clarity, the vertical scaleis enlarged in the diagram.

27

2.2.3

Muon Spectrometer

Figure 2.17: Cut-away view of the ATLAS muon system.
The Muon Spectrometer (MS) is the outermost and largest part of the ATLAS detector
as shown in Figure 2.17. The MS is based on the magnetic deflection of muon tracks in thelarge superconducting air-core toroid magnets and consists of separate trigger and high-precision
tracking chambers. Figure 2.18 shows geometry of the air-core toroid magnets. The use of air-coretoroid magnets can minimize the degradation of resolution due to multiple scattering. Figure 2.19
shows a R-z cross-sectional view of the MS. For |⌘| < 1.4, magnetic bending is provided by thelarge barrel toroid. For 1.6 < |⌘| < 2.7, muon tracks are bent by two smaller end-cap magnets
which are inserted into both ends of the barrel toroid. The range of 1.4 < |⌘| < 1.6 is usuallyreferred to as the transition region where magnetic deflection is provided by a combination of
barrel and end-cap fields and the field is mostly orthogonal to the muon trajectories.
For |⌘| < 2.7, a precision measurement of the track coordinates is provided by Monitored

Drift Tubes (MDT’s). The mechanical separation in the drift tubes of each sense wire from its
neighbors assures a robust and reliable operation. For 2.0 < |⌘| < 2.7, Cathode Strip Chambers(CSC’s) are used, which are multiwire proportional chambers with cathodes segmented into strips
with higher granularity.
The trigger system of the MS covers the pseudorapidity range |⌘| < 2.4. As trigger chambers,

Resistive Plate Chambers (RPC’s) are used in the barrel and Thin Gap Chambers (TGC’s) areused in the end-cap regions. The trigger chambers provide bunch-crossing identification, provide
well-defined pT thresholds, and measure the muon momentum in z-axis.

28

Figure 2.18: Geometry of air-core toroid magnets. The Tile calorimeter steel is also shown asa reference. The eight barrel toroid coils and the end-cap coils inserted into both ends of thebarrel toroid are visible.

Figure 2.19: R-z cross-sectional view of the muon system. Infinite-momentum muons would
propagate along straight trajectories which are illustrated by the dashed lines and typicallytraverse three muon stations.

29

2.3

Trigger and Data Acquisition

pp collisions in the LHC produce too many events to record all of them, most of which are
not interesting in physics analyses, for example, low pT multi-jet events. The cross section ofthese events is about 100 mb while that of new physics events is typically at the order of 1 fb.
Therefore, by using a two-level trigger system, the only interesting events are recorded as many
as possible with rejecting unimportant events. Figure 2.20 shows a schematic of the trigger anddata acquisition (TDAQ) system. The first level is a hardware-based system named ‘Level 1
Trigger (L1)’ and uses information of the calorimeter1 and the the muon spectrometer to reduce
the accepted rate to 100 kHz. The second level is a software-based system named ‘High Level
Trigger (HLT)’ that reduces the rate of event records to 1 kHz. There are many types of triggers
for several physics purposes [38], which are called ”trigger menus”. The trigger menu must bechanged depending on the instantaneous luminosity.

Figure 2.20: The ATLAS trigger and data acquisition (TDAQ) system in Run-2 [39]. Newfeatures with respect to the Run-1 system are indicated with orange boxes.

1

There is a long-term project of upgrading trigger readout of the calorimeter, which is aimed at ‘High-

Luminosity LHC (HL-LHC)’ that will start from 2024 with an ultimate peak instantaneous luminosity of L ⇠5 ⇥ 1034 cm

2 s 1 . See Appendix D.

30

Chapter 3

Data and Monte Carlo Samples
This chapter introduces datasets and Monte Carlo (MC) samples used in the analysis. The
datasets are described in Section 3.1 with the detail of triggers used in the analysis. MC samples
are used to model events of the SM background and signal processes in ATLAS. The MC samples
are summarized in Section 3.2.

3.1

Data and Trigger

In this thesis, ATLAS data collected in proton-proton (pp) collisions at a center-of-mass energy ofps = 13 TeV in 2015 and 2016 are used. The data is required to have been recorded in the stateof stable beam and stable detector operation with no issue. In 2016, data taking has continued
until 26 October and finally amounts to 33.3 fb 1 . In this thesis, the 2015 data (3.2 fb 1 ) andthe data taken until 9 September in 2016 (24.8 fb 1 ) are used, and therefore the total amountis 28.0 fb 1 .
missResolved and Boosted analyses use events recorded by a ET
trigger that accepts events with
miss
an ET
threshold at trigger level 80 GeV for the 2015 dataset and 100 and 110 GeV for an

early and a late part of 2016 dataset, respectively1 .
missDiagonal analysis uses events recorded by the same ET
trigger as the Resolved and Boosted
misscase, three single-electron triggers, or two single-muon triggers. If ET
reconstructed at themisso✏ine level (see Section 4.6) is larger than 200 GeV, the ET
trigger and the single-electron

and the single-muon triggers are considered; otherwise only those lepton triggers are considered.
The three single-electron triggers record an event if an electron has pT at the trigger level larger
than 24, 60, and 120 GeV for the 2015 dataset and 26, 60, and 140 GeV for the 2016 dataset.
The two single-muon triggers record an event if a muon has pT at the trigger level larger than
20 and 50 GeV for the 2015 dataset and 26 and 50 GeV for the 2016 dataset. The singleelectron and single-muon triggers with lower pT threshold impose tighter electron and muon
quality requirements. Table 3.1 summarizes the trigger configurations for Resolved, Boosted, andDiagonal.

1 As the instantaneous luminosity increases, pileup events increase so that trigger thresholds must be tighten

to keep the total L1 trigger rate 100 kHz.

31

TriggerThreshold2015

early-2016

late-2016

For Resolved, Boosted, and Diagonal
MET

80 GeV
100 GeV110 GeVFor Diagonal Only

Single Electron

24 GeV + Medium ID
26 GeV + Tight ID + Loose Isolation
60 GeV + Medium ID
120 GeV + Loose ID
140 GeV + Loose ID

Single Muon

20 GeV + Loose Isolation
26 GeV + Medium Isolation
50 GeV

Table 3.1: Trigger configurations for Resolved, Boosted, and Diagonal. For Diagonal, events are
miss
miss
recorded by the ET
or the single-lepton triggers, and the ET
triggers are used only whenmisso✏ine ET> 200 GeV; otherwise single-lepton triggers are used only. The single-electron andsingle-muon triggers with lower pT threshold impose tighter electron and muon quality and/or
isolation requirements.

32

3.2

Monte Carlo Samples

The nominal MC samples used in this analysis are summarized in Table 3.2. All samples,
except for the signal and tt̄ +sample, are processed with the full simulation of the ATLAS

detector [40] based on Geant4 [41]. The signal samples and the tt̄ +sample are processedwith a fast simulation [42] of the ATLAS detector, where a parameterized shower simulation isused for the calorimeter and other parts are the same as the full simulation.
The signal, tt̄ + W/Z (for Resolved and Boosted), and tt̄ +sample that are generated atleading order (LO), while other samples and tt̄ + W/Z (for Diagonal) are generated at nextto-leading order (NLO). To simulate these events more realistically, additional radiations are
generated by Pythia 8 in the parton showering process.
All samples are produced with varying the number of minimum-bias events following the
expected pileup distributions, where the minimum-bias events simulated from Pythia 8 areadded to a hard-scattering simulated event to account for pileup from multiple pp interactionsin the same or nearby bunch crossings. Then, the number of average interactions per bunch
crossing is reweighted to match the distributions in data. In addition, all the MC samples are
reweighted to account for small di↵erences in the efficiencies of physics-object reconstruction andidentification with respect to those measured in data.
The detail of the nominal MC sample is described in the following sections, while the setups
to estimate and model the impact of theoretical uncertainties are discussed in Chapter 8.
Process

ME generator

ME
PDF

decay, PS, andHadronization

UE
tune

Cross-section
order

tt̄
Single top
W/Z+jets
Dibosontt̄ + W/Ztt̄ +SignalPowheg-Box v2
Powheg-Box v1/v2
Sherpa 2.2
Sherpa 2.1.1
MG5 aMC@NLO 2.2.2
MG5 aMC@NLO 2.2.3
MG5 aMC@NLO 2.2.2

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

Pythia 6
Pythia 6
SherpaSherpaPythia 8
Pythia 8
Pythia 8

P2012
P2012
SherpaSherpaA14
A14
A14

NNLO+NNLL [43–48]
NNLO+NNLL [49–51]
NNLO [52]NLO
NLO [53]
NLO [53]
NLO+NLL [54]Table 3.2: Summary of setups of the nominal MC samples. All the MC samples are normalized
to the highest-order (in ↵S ) cross section available as indicated in the last column.

3.2.1

SignalThe signal samples are based on a simplified model [55, 56], assuming that the branching ratio of00t̃1 ! t ˜1 is 100%. The ˜1 is taken to be a pure bino as a benchmark model. The signal samples
are generated at LO with MG5 aMC@NLO 2.2.2 [53] as a matrix element (ME) generator of

pp ! t̃1 t̃1 process, accompanied by NNPDF2.3 [57] PDF (Parton Distribution Function) set

along with the A14 [58] set of underlying-event tuned parameters (UE tune). For decay, parton
shower (PS), and hadronization, Pythia 8 [59] generator is used. Since the kinematics of signal
0
events highly depend on the masses of t̃1 and ˜1 , the signal samples are generated in a grid0

across the plane of t̃1 and ˜1 masses (from (mt̃1 , m ˜01 ) = (200,12) GeV to (1000,600) GeV) witha spacing of 50 GeV for most of the plane. The grid spacing around the ‘Diagonal’ region wheremt̃1 approaches mt + m ˜01 is finer. All the mass points produced are shown in Figure 1.8. The
produced samples are normalized to the cross sections at NLO also including resummation ofsoft gluon emission up to next-to-leading logarithmic (NLL), which are shown in Figure 3.1.
33

Figure 3.1: NLO and NLL cross section of the signal event as a function of mt̃1 [54], to which all
signal samples are normalized. The cross section just only depends on mt̃1 and not depend on00either m ˜0 or decay mode (t̃1 ! t ˜1 or t̃1 ! bW ˜1 ). The band indicates theoretical uncertainty
1taken from an envelopment of systematic error on PDF sets and factorization and renormalization
scales, as described in [60].

3.2.2

tt̄

tt̄ samples are generated at NLO with Powheg-Box v2 [61–65] as ME generator, accompanied
by CT10 [66] NLO PDF set along with the P2012 [67] set of UE-tuned parameters. For PS andhadronization, Pythia 6 [68] generator is used. The cross section is normalized to the crosssection at NNLO and NNLL, 831.78 pb [43–48]. More details can be seen in [69].

3.2.3Single Top

Figure 3.2 shows 3 types of single top events, s-channel, t-channel, and W t associated production.
Single top samples are produced with the same generator combination as tt̄ sample, except that
ME generator for electroweak t-channel single top events is Powheg-Box v1 generator insteadof Powheg-Box v2 generator. The cross section is normalized to the cross section at NNLO
and NNLL, 145.45 pb (s-channel: 3.35 pb, t-channel: 70.43 pb, W t associated production:
71.67 pb) [49–51]. More details can be seen in [69]. The dominant remaining process after event
selections is W t channel because its event topology is similar to the signal.

34

Figure 3.2: Feynman diagrams of s-channel (a), t-channel (b), and W t associated production (c)of single top events.

3.2.4

W/Z+jets

W/Z+jets samples are generated at NLO by Sherpa 2.2 [70] ME generator along with Comix [71]and OpenLoops [72] ME generators. For W/Z+jets samples, a simplified scale setting prescription in the multi-parton matrix elements is used to improve the event generation speed. A
theory-based re-weighting of the jet multiplicity distribution is applied event by event that isderived from event generation with a strict scale prescription [73]. The PDF set is NNPDF 3.0
NNLO [74] along with the default UE tune provided by the authors of Sherpa. Sherpa is also
used as decay, PS, and hadronization generator [75]. The cross sections are normalized to thecross sections at NNLO, 60180.48 pb and 17662.80 pb for W +jets and Z+jets, respectively [52].
More details can be seen in [76]. Since Z+jets process provides two leptons, it can be highly
reduced by requiring exact one lepton. Therefore, mainly W +jets remains after event selections.

3.2.5

tt̄ + W/Z

Figure 3.3(a)-3.3(d) shows tt̄ + W/Z events. tt̄ + W/Z samples are generated with at LO for
Resolved and Boosted and at NLO for Diagonal. with MG5 aMC@NLO 2.2.2 [53] as ME
generator, accompanied by NNPDF2.3 [57] PDF set along with the A14 [58] set of UE tune.
For decay, PS, and hadronization, Pythia 8 [59] generator is used. For LO samples, the crosssections is normalized to the cross sections at NLO, 0.61 pb and 0.87 pb for tt̄ +W and tt̄ +Z,
respectively [53]. More details can be seen in [77]. The dominant remaining process after event
selections is tt̄ + Z(! ⌫ ⌫¯) channel (its NLO cross section produced by its branching ratio is0.17 pb) because its event topology is similar to the signal.

3.2.6
tt̄ +

tt̄ +
samples are generated at LO with the same configuration as tt̄ + W/Z samples exceptthat MG5 aMC@NLO 2.2.3 and CTEQ6L1 [78] LO PDF set are used. The cross section isnormalized to the cross sections at NLO, 4.38 pb [53]. More details can be seen in [69]. tt̄ +events are used to estimate tt̄ + Z(! ⌫⌫) background by regarding

as the Z ! ⌫ ⌫¯ branch

shown in Figure 3.3(b)-3.3(d)2 . The detail and the systematic uncertainty of the estimation are
described in Section 6.2 and Section 8.6.
2 For Diagonal, tt̄ +is not used and tt̄ + Z(! ⌫ ⌫¯) is predicted by MC only.

35

ℓ

ν
Z

W−

d

u
ν̄

ν̄

u

u
t

t

ū

ū
t̄

t̄

(a) tt̄ + Wg(b) tt̄ + Z(! ⌫ ⌫¯) (1/3)
g

t̄

t̄
ν

ν

Z

Z
ν̄
ν̄
g

g

t

(c) tt̄ + Z(! ⌫ ⌫¯) (2/3)t(d) tt̄ + Z(! ⌫ ⌫¯) (3/3)

Figure 3.3: Feynman diagrams of tt̄ + W (! `⌫) (a), tt̄ + Z(! ⌫ ⌫¯) (b)-(d).

3.2.7

DibosonDiboson samples (W W , W Z, ZZ) are generated at NLO by Sherpa 2.1.1 [70] ME generator
along with Comix [71] and OpenLoops [72] ME generators. The o↵-shell bosons are also considered in the generation. The PDF set is CT10 [66] NLO PDF set along with the UE tune
provided by authors of Sherpa. Sherpa is also used as PS and hadronization generator [75].
The cross section at NLO provided by the generator, 136.78 pb, is used. More details can beseen in [79].

36Chapter 4

Physics Object Definition
This chapter introduces definition of physics objects, which is commonly used in Boosted, Resolved, and Diagonal analyses. In this thesis, ‘physics object’ means a reconstructed particle (ora reconstructed 4-momentum) with a label like electron, muon, photon, jet, b-jet, ⌧-jet, etc. Since
the reconstruction and the labeling are based on measurements with a limited detector acceptance in a high-density environment, for example, an electron in a signal event is sometimes notreconstructed due to outside acceptance or a b from W decay is sometimes labeled as not b-jet
but jet due to a limitation of b-tagging algorithm. These e↵ects are not negligible and therefore
considered in the definitions of physics objects and event selections.
In the analysis, electrons and muons from W -boson decay must be reconstructed and labeledcorrectly, but electrons and muons from the other sources not. For example, leptons from c/b-jet
are not important. To distinguish them, generally the former is called isolated lepton and thelatter is called non-isolated lepton. To pick up only isolated ones, electron and muon definitionsin the analysis include ‘isolation’ requirement [80] as described in Section 4.2 and 4.3.
In the labeling of physics objects, there are two levels called baseline and signal. The signallevel physics objects are defined by the tighter requirements than baseline-level physics objects,
thus the efficiency of baseline-level labeling is higher than signal-level labeling, but the fake rateof signal-level labeling is lower than baseline-level labeling. Therefore, baseline objects are used
to compute the missing transverse momentum and to apply a second-lepton veto to suppress
events with tt̄ dileptonic event. Because of the reliability of signal-level labeling, signal objects
are mostly used in the event selection.
Since there is no priority among all the labeling (identification) algorithms by default, sometimes physics objects could have more than one label. To avoid physics objects to have morethan one label, an overlap removal procedure described in Section 4.7 is applied just after all thereconstruction and the labeling. All baseline and signal objects are also required to survive theoverlap removal procedure.
Section 4.1 introduces the definition of a primary vertex, which is used for definitions of
the other physics objects. Section 4.2-4.6 introduce the definitions of electron, muon, photon,
jet, and missing transverse momentum. Section 4.7 describes the overlap removal procedure.
Section 4.8 explains the definition of a large-R jet.

37

4.1

Primary Vertex

The primary vertex is defined by a reconstructed vertex with the highestP2i2T pT i , where T isa set of all tracks used to reconstruct the vertex. Furthermore, the primary vertex is required tohave at least two tracks with pT > 400 MeV. In order to confirm that there is at least one hard
pp collision in an event, all events are required to have at least one primary vertex. The primaryvertex is also used as a reference point of impact parameters of electron and muon candidates.

4.2

ElectronElectron candidates are reconstructed from electromagnetic calorimeter cell clusters that arematched to tracks reconstructed in the ID system. Baseline electrons are required to havepT > 7 GeV, |⌘| < 2.47, and satisfy ‘VeryLoose’ likelihood identification criteria describedin [81].

Signal electrons in Resolved and Boosted are required to pass all baseline requirements andhave pT > 25 GeV, satisfy ‘Loose’ likelihood identification criteria [81], and have impact parameters with respect to the reconstructed primary vertex along the beam axis (z0 ) and in
the transverse plane (d0 ) that satisfy |z0 sin ✓| < 0.5 mm and |d0 |/ d0 < 5, whered0

is theuncertainty of d0 . Furthermore, the signal electrons in Resolved and Boosted must pass ‘LooseTrackOnly’ isolation criteria. The LooseTrackOnly isolation criteria use track-based information
to obtain a 99% efficiency that is independent of pT . These values are estimated from Z ! ``MC samples and confirmed in data [80].

Signal electrons in Diagonal are required to pass all baseline requirements and also havepT > 27 GeV, satisfy ‘Tight’ likelihood identification criteria [81], and have the same impact
parameter requirements as the signal electrons in Resolved and Boosted. Furthermore, the signal
electrons in Diagonal must pass ‘GradientLoose’ isolation criteria. The GradientLoose isolation
criteria use both caloriemter-cell and track-based information to obtain a 95(99)% efficiency
at pT = 25(60) GeV. These values are estimated from Z ! `` MC samples and confirmed indata [80].

The reason why the signal electrons in Diagonal are more tightly defined than Resolved and
Boosted is that single electron triggers are used in Diagonal strategy and not used in Resolved or
Boosted. Therefore, a little bit tighter definition is required to use the triggers introduced in
Section 3.1.

4.3

Muon

Typically, a muon is reconstructed from a track reconstructed by combining two tracks in the ID
and the MS. In order to improve the muon reconstruction efficiency, a track in the ID matched
to a track segment in the MS, a track in the MS not matched to any tracks in the ID, or a trackin the ID matched to an energy deposit in the calorimeter compatible with a minimum-ionizing
particle (referred to as calo-tagged muon) [82] is also used to reconstruct a muon. Baseline muons
are required to have pT > 6 GeV, |⌘| < 2.6, and satisfy ‘Loose’ identification criteria describedin [82].

Signal muons must pass all baseline requirements and also have pT > 25 GeV, and have38

impact parameters |z0 sin ✓| < 0.5 mm and |d0 |/ d0 < 3. Furthermore, the signal muons must
pass ‘LooseTrackOnly’ isolation criteria like the signal electrons.

4.4

PhotonPhoton identification is not used in the main event selection, and therefore photons are labeled
as extra jet or electron candidates. Photons are identified only when the tt̄ +sample is used
1

for the data-driven estimation of the tt̄ + Z background in Resolved and Boosted . In this case,photons are reconstructed from calorimeter cell clusters and must have pT > 145 GeV and|⌘| < 2.37, excluding the barrel-endcap calorimeter transition in the range 1.37 < |⌘| < 1.52.

Photons are also required to satisfy ‘Tight’ identification criteria described in [83] and ‘Tight’
isolation criteria based on both track and calorimeter information. For recording tt̄ +events,a single photon trigger is used that records events with a photon passing Loose identification
criteria with pT > 140 GeV. The photon definition is tighter than the trigger requirements, hence
all events with at least one photon defined here are ⇠100% recorded by the trigger.

4.5

Jet

Jets are reconstructed from topological clusters [84, 85] in the calorimeters using the anti-kt
algorithm with angular distance parameter of R = 0.4 [28]. Jets are corrected for contaminationfrom pileup events using the jet area method [86–88], and then jet energy calibration to accountfor the detector response [89, 90] is performed. Furthermore, jets in data are calibrated based onin situ measurements of the jet energy scale. Baseline jets are required to have pT > 20 GeV and|⌘| < 4.9 to precisely reconstruct missing transverse momentum described in Section 4.6. Signal

jets must have pT > 25 GeV and |⌘| < 2.5. For signal jets with pT < 60 GeV, ‘Jet Vertex Tagger(JVT)’ criteria is applied to them, which is designed to reject jets stemmed from pileup eventsusing vertex information [88]. Events containing a jet that does not pass specific jet quality
criteria are rejected in the analysis to suppress detector noise and non-collision backgrounds [91,92].
Jets resulting from b-quarks (called b-jets) are identified using the MV2c10 b-tagging algorithm, which exploits one of machine learning techniques, boosted decision tree (BDT) [93], anduses quantities such as impact parameters and distances between primary and secondary vertices [94–96]. This algorithm outputs a b-jet likelihood score (or b-tagging weight), and then jets
exceeding a threshold of the weight are b-tagged. In the analysis, the threshold is relatively loose
in order to increase b-tagging efficiency, resulting in 77% b-tagging efficiency and fake rates of⇠1/134 for light-quark flavors and gluons and ⇠1/6 for c-jets in simulated tt̄ events.

In the event selections of Resolved and Boosted, some variables such as mtop , amT2 , andtopness require at least 2 b-jets by definition. Even if there is only one b-tag jet in an event,anti-b-tag jet with the second highest b-tagging weight is temporarily regarded as the secondb-tag jet in the calculation.
Hadronically decaying ⌧ leptons are identified by using a BDT [93] technique which uses
quantities such as number of tracks in a jet and shape of the jet. The analysis uses the ‘Loose’
1

The photon candidates are not used in Diagonal and tt̄ + Z background is estimated with MC only inDiagonal

39

criteria described in [97, 98] which provides 60% and 50% efficiencies for identifying ⌧ leptons
decaying into one and three charged pions, respectively. For ⌧ candidates, a dedicated energy
calibration [98] is applied. The ⌧ candidates must have pT > 20 GeV, |⌘| < 2.5, and one or three
tracks with total electric charge opposite to that of the signal lepton.

In this thesis, if ‘jet’ is mentioned without any specification such as ‘(anti-) b-tag’, the two
types of jets are implicitely included in the context. For example, the word ‘number of signal
jets’ means number of signal anti-b-tag jets and signal b-tag jets. In this thesis, ⌧ candidates
are categorized as ⌧ , not jet. However, the analysis doesn’t remove overlap between ⌧ candidate
and the parent jet, and therefore ⌧ object and the parent jet object are used independently
in the analysis. As described in Section 5.1, the analysis rejects events with at least one tau
candidate that fail in m⌧T2 criteria. In some of the events passing the criteria, the tau candidates
are regarded as not ⌧ . Since the tau candidate should be regarded as jet in the case, the overlap
between ⌧ candidate and jet is not removed although this is confusing.

4.6

Missing Transverse Momentum

miss
The missing transverse momentum, p~miss(or ET⌘ p~miss), is defined by the negative vectorTT

sum of the transverse momenta of baseline leptons, baseline jets, and a soft-term which is built

from high-quality tracks associated with the primary vertex but not with the baseline objects [99,100]. The norm of missing transverse momentum is called missing transverse energy denoted by
missET. Basically, photons and hadronically decaying ⌧ leptons contribute to p~missas jets orTelectrons or via the soft-term. In the event selections requiring photons, transverse momenta of
the photons2 are also added to p~miss
T .

4.7

Overlap Removal

To avoid physics objects to have more than one label, an overlap removal procedure is applied
after all the reconstruction and the labeling. The procedure is optimized to this analysis bysimulation. Table 4.1 summarizes the procedure. Given a set of objects passing at least baseline
definition3 , the procedure checks for overlap based on either a shared track, ghost-matching [87],or a minimal distanceR between objects. For example, if

R between a baseline electron anda baseline jet is less than 0.2, then the electron is retained (as indicated in the ‘Precedence’ row)and the jet is discarded, unless the jet is b-tagged (as indicated in the ‘Condition’ row) in whichcase the electron is expected to originate from a heavy-flavor decay and then discarded while
the b-tagged jet is retained. If the matching requirement in Table 4.1 is not satisfied, the bothobjects are kept. The procedure shown in the columns in Table 4.1 is executed from left to right.
The second (ej) and the third (µj) steps of the procedure ensure that

R between leptons andjets is at least 0.2. Therefore, the fourth step (`j) is considered only for

R > 0.2. The steps

involving a photon are applied only for the event selection requiring photons. All baseline objects
are required to survive the overlap removal procedure, and all signal objects are the survivors
that also pass signal definition.
2 There is no baseline/signal labeling for photon as described in Section 4.4.
3 Therefore, some of them may pass signal requirements, but the overlap removal procedure does not check

whether objects pass signal definition or not.

40

Object 1

e

e

µ

`

Object 2

µ

j

j

j

Matching
criteria
Condition

shared trackcalo-tagged µ

Precedencee

R < 0.2

j not b-tagged

ghost-matched and✓

R < 0.2(j not b-tagged) andnjtrack < 3 or

e

µ

pT
j

pT

> 0.7

◆

µ

R < min⇣

10
0.4, 0.04 + p` /GeV
T

–
j

⌧
⌘

j

e

e

R < 0.2

R < 0.1

R < 0.1

–

–

–

e

e

Table 4.1: A summary of overlap removal procedure. The procedure is executed from left toright. The first two rows (Object 1, Object 2) indicate the types of overlapping objects: electrons(e), muons (µ), electron or muon (`), jets (j), photons ( ), and hadronically decaying ⌧ lepton(⌧ ). The procedure is applied only to baseline objects except forand ⌧ where there is no

distinction between baseline and signal definition. The third row (Matching criteria) defines thecriteria to consider that an object pair is overlapping. If there is the overlap, the object shownin the last row (Precedence) is retained and the other is discarded. If a condition is described in
the fourth row (Condition) and if the condition is not satisfied, then the precedence is inversed.

4.8

Large-Radius Jet

Large-radius jets are used only in Boosted that are clustered from all signal jets using the anti-kt
algorithm with R = 1.2. To reduce the impact of soft radiation and pileup events, the largeradius jets are groomed using reclustered jet trimming, where the constituent signal jets withpT less than 5% of the ungroomed jet pT are removed [101–104]. Leptons are not included in
the reclustering procedure, because it was found that including them increases the backgroundacceptance more than the signal efficiency. Since the signal jets pass the overlap removal procedure by definition, the large-radius jets are not used in the overlap removal procedure. The
Boosted analysis uses a large-radius jet mass reconstructed from four-vectors of the constituent
signal jets.

41

Chapter 5

Event Selection
This chapter introduces definition of event selection that specifies a phase space where the signal
events are enhanced and the SM backgrounds are suppressed so that the signal contribution canbe seen explicitly in the number of the observed event if stop truly exists. The specified phasespace is named ‘signal region’ (SR), and the number of observed events in SR is used to precisely
determine (or measure) the parameter of interest µsig (Chapter 7). Event selection is a seriesof requirements using dedicated variables discriminating signal and backgrounds, which are also
explained. Section 5.1 introduces an event preselection commonly used in Resolved, Boosted,and Diagonal. Section 5.2 and 5.3 describe the event selections of SR for Resolved and Boosted.
Since Diagonal strategy exploits a shape fit for background estimation described in Chapter 6,
there are multiple SRs for Diagonal topology. For this reason, Section 5.4 describes a base event
selection for the shape fit in Diagonal.

5.1

Event Preselection

The topology of the signal events as explained in Section 1.6 is as follows.
• one lepton• 4 jets including 2 b-jets
0• missing energy (due to neutrinos and ˜1 ’s)
To ensure a basic topology of the signal event, all the SRs for Resolved, Boosted, and Diagonalcommonly require events to have one signal lepton, no additional baseline lepton, at least four
signal jets, where at least one of them should be b-tag jet. After this selection, events withhadronically decaying tau lepton (⌧h ), especially tt̄ ! [b`⌫][b⌧h ⌫] events1 , still remain and thus
they are suppressed by using m⌧T2 variable, which is introduced in Section 5.1.1.

5.1.1

Stransverse Massm⌧T 2 is a type of ‘stransverse mass’, mT2 [105], which targets a topology where there are two
branches of particle decay chains labeled here as a and b in an event. Figure 5.1(a) illustrates
1 Only hadronically decaying tau lepton is considered because it is very challenging to suppress events withleptonically decaying tau lepton (⌧` ) because of its short lifetime in the ATLAS experiment.

42the tt̄ event topologies targeted by m⌧T2 . In each branch, there are visible (measured) andinvisible (unmeasured) particles. The vector sum of the measured momenta in branch i 2 {a, b}
is denoted by pi = (Ei , p~Ti , pzi ) and the vector sum of the unmeasured momenta is denoted byqi = (Fi , ~qTi , qzi ). With m2pi = Ei2

p~i2 and m2qi = Fi2~qi2 , the mT of the particles in branch i

is given by
m2Ti =⇣q

p2Ti + m2pi +q⌘2
2 + m2
qTi
qi

2

(~
pTi + ~qTi ) .

(5.1)

The stransverse mass, mT 2 , is defined as a minimum quantity of the maximum of mTa and mTbover the allocation of p~missbetween ~qTa and ~qTb ;
T
mT2 ⌘

min

q
~Ta +~
qTb =~pmissT{max(mTa , mTb )}(5.2)

where an assumption of mqa and mqb is required in the computation of mT a and mT b . The
result of the minimization is the minimum parent mass which doesn’t kinematically contradict
the observed event topology.
For m⌧T2 , the configuration is as follows;
Branch Start Points:• Branch a: W -boson decaying as W ! ⌧h ⌫.
• Branch b: W -boson decaying as W ! `⌫.
Measured particles:• Branch a: the ⌧ candidate defined in Section 4.5.
• Branch b: the signal lepton.
Unmeasured particles:• Branch a: the two neutrinos from W ! ⌧h ⌫ and from ⌧h ! ⌫ + jet.
• Branch b: the neutrino.
Input masses:• Branch a: mqa = 0 GeV.
• Branch b: mqb = m⌫ = 0 GeV.
For tt̄ ! [b`⌫][b⌧h ⌫] events, the endpoint of m⌧T2 is the W boson mass, whereas the signal events
can exceed this bound.

Events with ⌧h are vetoed exploiting the m⌧T2 variable in the following way;
1. Not veto events which do not have a reconstructed ⌧ that passes the ‘Loose’ identification
criteria with pT > 20 GeV, 1 or 3 tracks,

R > 0.1 from the signal lepton and charge

opposite to the signal lepton.
2. Otherwise, veto events if the leading2 ⌧ candidate results in m⌧T 2 < 80 GeV.
2 ‘Leading’ means that the physics object has the highest p

the event.

43

T among physics objects with the same label in(a) tt̄ ! [b`⌫][b⌧h ⌫] event targeted by m⌧T2(b) tt̄ ! [b`⌫][b`lost ⌫] event targeted by amT2

Figure 5.1: Illustration of of m⌧T2 (left) and amT2 (right) variables, which are used to discriminate
against tt̄ ! [b`⌫][b⌧h ⌫] event (left) and tt̄ ! [b`⌫][b`lost ⌫] where `lost is an undetected (lost)

lepton or ⌧h due to outside acceptance. The objects surrounded by the dashed lines are assumed
to be undetected (lost) in the calculation of the two variables.
Figure 5.2 shows the m⌧T2 distribution. In this thesis, tt̄ events are categorized into the following
final states;
1. tt̄ ! [b`⌫][b`⌫] (2L),
2. tt̄ ! [b`⌫][bqq] (1L),
3. tt̄ ! [b`⌫][b⌧h ⌫] or [b⌧` ⌫][b⌧h ⌫] (1L1⌧h ),4. tt̄ ! others (Other).
⌧h and ⌧` denote hadronically and leptonically decaying taus, respectively. From the top to
the bottom, they are labeled as 2L, 1L, 1L1⌧h , and Other. As shown in Figure 5.2, most tt̄
(1L1⌧h ) events cannot exceed W -boson mass. Most of the surviving tt̄ (1L1⌧h ) events have no ⌧hcandidate because the ⌧h ’s are undetected (lost) due to outside acceptance, which are suppressedby dedicated variables in Resolved and Boosted (Section 5.2 and 5.3) or precisely estimated by ashape fit in Diagonal (Section 5.4).

44

Event fraction / 10 GeV

0.5
0.4

tt 1L1τh
tt 2L
~ 0
m(t,∼
χ1)=(1000,1) GeV

0.3
0.2
0.1
0
0

20 40 60 80 100 120 140 160 180 200mτT2 [GeV]

Figure 5.2: m⌧T2 distribution after the event preselection without m⌧T2 > 80 GeV requirement(Section 3.1). Each event is normalized to one and required to have a ⌧ candidate that passes the‘Loose’ identification criteria with pT > 20 GeV, 1 or 3 tracks,

R > 0.1 from the signal leptonand charge opposite to the signal lepton. Events passing the m⌧T2 requirement are indicated by
the arrow.

45

Resolved Signal Region

5.2

miss
As described in Section 3.1, the ET
trigger is used. Since the momenta of jets in the signal

events are harder than the backgrounds, the leading to fourth leading jets ordered by pT are
required to have pT of at least 80, 50, 40, 40 GeV, respectively. As shown in Figure 5.3 shows
miss
miss
miss
ET
distribution, the signal events make larger ET
than the backgrounds, and thus ET
missis required to be larger than 260 GeV. To enhance the signal events, HT,sig, which is a signal-

object-based missing transverse momentum divided by the per-event resolution, is defined by
missHT,sig=~ miss |
|H
T

M

,

(5.3)

~ miss ||HT~ miss is the sum of the signal jets and signal lepton transverse momenta. The
where HT

~ miss | is|HTcomputed in a sampling method using jet energy resolution [106], while the lepton is assumed to
be well-measured. The parameter M is a characteristic ‘scale’ of the background, which is fixedat 100 GeV determined by optimization studies [107, 108]. As shown in Figure 5.4, the signal

×103
25 Simulations = 13 TeV, 28.0 fb-1

20

~ 0m(t ,∼
χ1)=(600,300) GeV σ×100

Total SM
W+jetsZ+jetsDibosonEvents / 2

Events / 20 GeV

miss
miss
events can provide higher HT,sig
than the backgrounds, and thus HT,sig
is required at least 14.

tt
Single top
tt+V

~ 0
m(t ,∼
χ )=(1000,1) GeV σ×1000
1

Total SM
W+jetsZ+jetsDiboson

Simulation

6000 s = 13 TeV, 28.0 fb-1
~ 0
m(t ,∼
χ1)=(600,300) GeV σ×100

5000

tt
Single top
tt+V

~ 0
m(t ,∼
χ )=(1000,1) GeV σ×1000
1

4000

15

3000

10

2000
5

1000

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

0
0

5

10

15

20

25 30 35 40
HmisssignificanceT

missFigure 5.3: ET
distribution after the event prese-

miss
Figure 5.4: HT,sig
distribution after the event prese-

misslection described in Section 5.1 plus ET> 200 GeV
missprecut and the ET
trigger requirement. Events
misspassing the ET> 260 GeV requirement are in-misslection described in Section 5.1 plus ET> 260 GeV

dicated by the arrow.

arrow.

missand the ET
trigger requirement. Events passing
missthe HT,sig> 14 requirement are indicated by the

For comparison, the cross

For comparison, the cross sections of sig-

sections of signal events with (mt̃1 , m ˜01 ) = (600,nal events with (mt̃1 , m ˜01 ) = (600, 300) GeV (red300) GeV (red dashed-line) and (1000, 1) GeV (bluedashed-line) and (1000, 1) GeV (blue dashed-line) aredashed-line) are scaled up by a factor of 100 and 1000,

scaled up by a factor of 100 and 1000, respectively.

respectively.
miss
To suppress events providing large ET
due to mis-measurement of jet energy, |for i 2 {1, 2} are required larger than 0.4. As shown in Figure 5.5,

(jeti , p~missT )|R(b, `), where b is the lead-ing b-jet in the event, discriminates W +jets events from the signal events. To suppress W +jets
events,R(b, `) are required smaller than 3.0.

To suppress tt̄ (1L) and W +jets events, a ‘transverse mass’ denoted by mT is used. mT is areconstructed mass using the signal lepton transverse momenta p~` and p~miss , defined byqmiss 1mT = 2 · p`T · ET
46

T

cos

(p~`T , p~miss
T ) .

T

(5.4)

As shown in Figure 5.6, for tt̄ (1L) and W +jets events, mT tends to be below the W boson mass.
For events with more than one invisible particle like the signal event, mT can go above the W

Events / 20 GeV

Events / 0.2

boson mass. Therefore, mT is required larger than 170 GeV.
Total SMtt
108 Simulation
W+jetsSingle top
28.0 fb-1
107 s = 13~TeV,
Z+jetstt+V0m(t,∼χ )=(600,300) GeV
6
Diboson1
10~∼ 0m(t,χ )=(1000,1) GeV
1
105
104
103
102
10
1
10−1
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5∆R(b-jet, lepton)

Figure 5.5:

106

Simulations = 13 TeV, 28.0 fb-1

105

~ 0
m(t,∼
χ )=(600,300) GeV
1
~ 0
m(t,∼
χ )=(1000,1) GeV

104

Total SM
tt 1L1τhtt OtherSingle top
tt+V

tt 1L
tt 2L
W+jetsZ+jetsDiboson

1

103
102
10
1
−1

10

0

100

200

300

400

500
600
mT [GeV]R(b, `) distribution after the event pre-Figure 5.6: mT distribution after the event prese-missselection described in Section 5.1 plus the ET>
miss
260 GeV and the ET trigger requirements. Events

misslection described in Section 5.1 plus the ET>

passing thepassing the mT > 170 GeV requirement are indicatedmiss
260 GeV and the ET
trigger requirements. Events

R(b, `) < 3.0 requirement are indicatedby the arrow.

by the arrow.

In order to ensure a hadronically decaying top in each event and to suppress events without
hadronically decaying top, 3 jets are selected by the following
2=

mj1 ,j2 ,bi

mtop

2mj1 ,j2 ,bi

2+

mj1 ,j2

mW

2
mj1 ,j2

2

minimization;2, where i = 1 or 2.

(5.5)

b1 and b2 are the two jets which have the highest b-tagging weights, j1 and j2 are jets with thehighest pT in the event excluding b1 and b2 , and
2
2
2
2
2
mj1 ,j2 ,bi = mj1 ,j2 ,bi (rj1 + rj2 + rbi )22
2
2
mj1 ,j2 = mj1 ,j2 (rj1 + rj2 ).

ri is the fractional pT resolution for jet i determined by dedicated studies [106]. Especially, themass of this2-base hadronic top, mj1 ,j2 ,bi , is denoted by mtop in this thesis. mtop is required

smaller than 270 GeV. Figure 5.7 shows mtop distribution.
In order to suppress tt̄ (2L) and (1L1⌧h ) events where one lepton or one ⌧h from one W decay
is undetected (lost) due to outside acceptance, amT2 , another type of stransverse mass shownin Figure 5.1(b), is exploited. amT2 is an asymmetric form of mT2 [109–111] where one of thetwo W bosons is considered invisible because its lepton or ⌧h is assumed lost due to outside
acceptance (denoted by `lost ). Then the parameters for amT2 are determined as follows;
Branch Start Points:• Branch a: top quark decaying as t ! bW ! b`lost ⌫• Branch b: top quark decaying as t ! bW ! b`⌫
Measured particles
47• Branch a: the b-jet.
• Branch b: the b-jet and the signal lepton.
The two b-jets are identified based on the highest b-tagging weights. Since there are two
combination in the b-jet assignment to branches a and b, mT2 is calculated for each andthe minimum one is used as the final discriminant.
Unmeasured particles• Branch a: the W boson decaying as W ! `lost ⌫.
• Branch b: the neutrino.
Input masses• Branch a: mqa = mW = 80 GeV.
• Branch b: mqb = m⌫ = 0 GeV.
For the tt̄ (2L) and (1L1⌧h ) events with one `lost , amT2 is mostly smaller than the top quark
mass, while for the signal events, amT2 can exceed the top quark mass as shown in Figure 5.8.
miss
In case the `lost is an electron, its energy deposit is included in the ET
calculation as a jet.

Then amT2 in tt̄ events can be larger than the top quark mass, but this variable is still useful to

9000

s = 13 TeV, 28.0 fb-1

Simulation

8000

Total SM
tt 1L1τhtt OtherSingle top
tt+V

7000
6000

Events / 25 GeV

Events / 10 GeV

distinguish between signal and background. Therefore, amT2 is required larger than 175 GeV.

tt 1L
tt 2L
W+jetsZ+jetsDiboson~ 0m(t ,∼
χ )=(600,300) GeV σ×1001~ ∼0m(t ,χ )=(1000,1) GeV σ×1000
1

5000
4000
3000

7000 Simulations = 13 TeV, 28.0 fb-1

6000
5000

~ 0
m(t ,∼
χ1)=(600,300) GeV σ×100~ 0m(t ,∼
χ )=(1000,1) GeV σ×1000

Total SM
tt 1L1τhtt OtherSingle top
tt+V

tt 1L
tt 2L
W+jetsZ+jetsDiboson

1

4000
3000
2000

2000

1000

1000
0
100

150

200

0
0

250
300
350
χ2 based mt,had [GeV]

50 100 150 200 250 300 350 400 450 500
amT2 [GeV]

Figure 5.7: mtop distribution after the event preselec-

Figure 5.8: amT2 distribution after the event prese-

misstion described in Section 5.1 plus ET> 260 GeV
miss
and the ET trigger requirements. Events passing

misslection described in Section 5.1 plus ET> 260 GeV

the mtop < 270 GeV requirement are indicated by

the amT2 > 175 GeV requirement are indicated by

the arrow. For comparison, the cross sections of sig-

the arrow. For comparison, the cross sections of sig-

nal events with (mt̃1 , m ˜01 ) = (600, 300) GeV (rednal events with (mt̃1 , m ˜01 ) = (600, 300) GeV (reddashed-line) and (1000, 1) GeV (blue dashed-line) aredashed-line) and (1000, 1) GeV (blue dashed-line) are

scaled up by a factor of 100 and 1000, respectively.

scaled up by a factor of 100 and 1000, respectively.

miss
and the ET
trigger requirements. Events passing

For the further suppression of the tt̄ (2L) and (1L1⌧h ) events, topness is defined [112]. The
topness is a2function which indicates the similarity of the event to tt̄ (2L) and (1L1⌧h ) eventswith one lepton (including ⌧h ) assumed lost like the amT2 variable. The topness is defined as48

ln(min S), where S is a2function defined as

S(pW,x , pW,y , pW,z , p⌫,z ) =

+

⇣
⇣

m2W

m2t

(p` + p⌫ )2

a4W
(pb2 + pW )
a4t

⌘2

2

⌘2

+

+

⇣

m2t

⇣

(pb1 + p` + p⌫ )
a4t

4 m2t

(⌃i pi )
a4CM

2

⌘2

2

⌘2

(5.6)

.

pW,x , pW,y , and pW,z are the 3-momentum of the invisible W boson. p⌫,z is the longitudinal
momentum of the neutrino from the other W boson decay where the lepton is not lost. ⌃i pi is
the sum of 4-vectors of all the 5 assumed final state particles. aW , at and aCM are the constantvalues suggested by the authors [112]; aW = 5 GeV, at = 15 GeV, aCM = 1 TeV. The four
arguments of S are varied to find the minimum of S. The minimization is constrained such thatthe observed missing transverse momentum is assumed to stem from the unobserved W boson(decaying into a lost lepton and a neutrino) and a neutrino from the other top decay branch. To
find all four arguments of S, the neutrinos and the invisible W boson are assumed to be on-shell.
Two combination of b-jets are evaluated in this minimization. If there is only one b-tagged jet,the leading or subleading anti-b-tagged jet is temporarily regarded as the second b-jet (in thiscase, a total of four possible jet assignments is evaluated). Figure 5.9 shows topness distribution
and indicates that the lower topness region is populated by the tt̄ events and the signal eventsare enhanced at the higher topness region. Therefore, topness is required larger than 6.5. All
the selection described is summarized in Table 6.1. After all the Resolved selections, numbers of
the benchmark signal events with (mt̃1 , m ˜01 ) = (600, 300) GeV and the total SM-background
events are 38 (efficiency = 0.77%) and 46 events, respectively, for the data of 28.0 fb 1 . The

dominant background in the SR is tt̄ which occupies 37% of the total background events. For
the detail of background yields, see Table 9.1.

49

Eventss = 13 TeV, 28.0 fb-1

7000 Simulation
Total SM
tt 1L1τhtt OtherSingle top
tt+V

6000
5000

~ 0
m(t ,∼
χ )=(600,300) GeV σ×100

tt 1L
tt 2L
W+jetsZ+jetsDiboson1~ 0m(t ,∼
χ )=(1000,1) GeV σ×1000
1

4000
3000
2000
1000
0
−10

−5

0

5

10

15
20
topness

Figure 5.9: topness distribution after the event presemiss
lection described in Section 5.1 plus ET> 260 GeV
miss
and the ET
trigger requirements. Events passing

the topness > 6.5 requirement are indicated by thearrow.

For comparison, the cross sections of sig-

nal events with (mt̃1 , m ˜01 ) = (600, 300) GeV (reddashed-line) and (1000, 1) GeV (blue dashed-line) are
scaled up by a factor of 100 and 1000, respectively.

50

5.3

Boosted Signal Region

missCompared to Resolved topology, Boosted topology provides larger ET
as shown in Figure 5.10.
missTherefore, Boosted signal region requires the tighter cut, ET> 450 GeV. As described in
missSection 3.1, the ET
trigger is used. Since the momenta of jets in the signal events are larger

than the backgrounds, the leading to fourth leading jets ordered by pT are required to have pT
missof at least 120, 80, 50, 25 GeV, respectively. To enhance the signal events, HT,sig
described in

106 Simulation-1

s = 13 TeV, 28.0 fb

~ 0
m(t,∼
χ )=(600,300) GeV
1
~ 0
m(t,∼
χ )=(1000,1) GeV

5

10

104

Total SM
W+jetsZ+jetsDibosonEvents / 2

Events / 25 GeV

missSection 5.2 is required at least 22. Figure 5.11 shows HT,sig
distribution.

ttSingle top
tt+V

1

103

s = 13 TeV, 28.0 fb-1

Simulation500

Total SM
W+jetsZ+jetsDiboson400

tt
Single top
tt+V

~ 0
m(t ,∼
χ )=(600,300) GeV σ×50
1

~ 0m(t ,∼
χ )=(1000,1) GeV σ×100
1

300

102
200

10
1

100

−1

10

0
0

200 300 400 500 600 700 800 900 1000
Emiss
[GeV]
T

5

10

15

20

25 30 35 40
HmisssignificanceT

missFigure 5.10: ET
distribution after the event prese-

miss
Figure 5.11: HT,sig
distribution after the event prese-

misslection described in Section 5.1 plus ET> 200 GeV

misslection described in Section 5.1 plus ET> 450 GeV

missprecut and the ET
trigger requirement. Events

missand the ET
trigger requirements. Events passing

misspassing the ET> 450 GeV requirement are indi-

missthe HT,sig> 22 requirement are indicated by thecated by the arrow.

arrow.

For comparison, the cross sections of sig-

nal events with (mt̃1 , m ˜01 ) = (600, 300) GeV (reddashed-line) and (1000, 1) GeV (blue dashed-line) are
scaled up by a factor of 50 and 100, respectively.
miss
For suppressing events with large ET
due to mis-measurement of jet energy, |(jeti , p~missT )|for i 2 {1, 2} are required larger than 0.4. Since the leptonically decaying top in Boosted topology
is highly boosted,R(b, `) of Boosted topology tends to be smaller than tt̄, W +jets, and single

top events as shown in Figure 5.12. To enhance the signal events,

R(b, `) are required smaller

than 2.4. In order to suppress tt̄ (1L) and W +jets events, mT described in Section 5.2 is requiredlarger than 210 GeV. Figure 5.13 shows mT distribution.
In order to suppress tt̄ (2L) and (1L1⌧h ) events with one `lost , amT2 described in Section 5.2
is required larger than 175 GeV. Figure 5.14 shows amT2 distribution.
To ensure the Boosted-specific event topology, at least one large-R jet with pT > 290 GeV
and mass > 70 GeV is required. The pT of 290 GeV is nearly the threshold for a hadronicallydecaying top to form large-R jet with R = 1.2 as described in Section 1.6.1, and then the massof 70 GeV is used because the selected large-R jet should come from a top or at least a W-boson
from a top decay. Figure 5.15 and 5.16 show pT and mass distributions of the leading large-R
jet.
miss
Furthermore, a perpendicular missing transverse energy, ET,?
, is used to suppress tt̄ (1L)
missevents surviving from all the criteria described up to here. A schematic view of ET,?
is shown

51

Total SM
W+jetsZ+jetsDibosons = 13 TeV, 28.0 fb-1

300

~ 0
m(t ,∼
χ1)=(600,300) GeV σ×50

Events / 20 GeV

Events / 0.2

350 SimulationttSingle top
tt+V

~ 0
m(t ,∼
χ )=(1000,1) GeV σ×100

250

1

200

104
103

Simulations = 13 TeV, 28.0 fb-1

~ 0
m(t,∼
χ )=(600,300) GeV
1
~ 0
m(t,∼
χ )=(1000,1) GeV

Total SM
tt 1L1τhtt OtherSingle top
tt+V

tt 1L
tt 2L
W+jetsZ+jetsDiboson

1

102
10

150

1

100

−1

10

50

10−2

0
0

0.5

Figure 5.12:

1 1.5 2

2.5 3

3.5 4 4.5 5∆R(b-jet, lepton)

0R(b, `) distribution after the event

200

300

400

500
600
mT [GeV]Figure 5.13: mT distribution after the event preselec->

misstion described in Section 5.1 plus ET> 450 GeV

miss
450 GeV and the ET
trigger requirements. Events

missand the ET
trigger requirements. Events passing

passing theR(b, `) requirement are indicated by

the mT > 210 GeV requirement are indicated by

the arrow. For comparison, the cross sections of sig-

the arrow. For comparison, the cross sections of sig-

nal events with (mt̃1 , m ˜01 ) = (600, 300) GeV (rednal events with (mt̃1 , m ˜01 ) = (600, 300) GeV (reddashed-line) and (1000, 1) GeV (blue dashed-line) aredashed-line) and (1000, 1) GeV (blue dashed-line) are

scaled up by a factor of 50 and 100, respectively.

scaled up by a factor of 50 and 100, respectively.

preselection described in Section 5.1 plus

miss
ET

100

in Figure 5.17. In the tt̄ background passing a series of the stringent cuts, the boost of the
leptonic top tends to align the neutrino with the leptonic top direction. After reconstructing thehadronic top through the2minimization described in Section 5.2, the remaining b-jet and themisssignal lepton are used to reconstruct the leptonic top3 . After boosting the leptonic top and ET
missinto the tt̄ rest frame, the perpendicular component of the ET
with respect to the leptonic top
miss
is calculated. This ET,?
is expected to be smaller for the tt̄ background because the dominant
miss
miss
contribution to ET
is the neutrino in this case. From optimization studies [27], ET,?
is setmiss
to be larger than 180 GeV. Figure 5.18 shows ET,?
distribution. All the selection describedis summarized in Table 6.1. After all the Boosted selections, numbers of the benchmark signal
events with (mt̃1 , m ˜01 ) = (1000, 1) GeV and the total SM-background events are 7 (efficiency =4.1%) and 7 events, respectively, for the data of 28.0 fb 1 . The dominant background in the SR
is tt̄ + Z(! ⌫⌫) which occupies 36% of the total background events. For the detail of backgroundyields, see Table 9.2.

3 The contribution of neutrino from the leptonic top decay is ignored here.

The reconstructed 4-momentumof leptonic top is just the sum of 4-momenta of the remaining b-jet and the signal lepton.

52

Events / 25 GeV

s = 13 TeV, 28.0 fb-1

700 Simulation
600
500

Total SM
tt 1L1τhtt OtherSingle top
tt+V

~ 0
m(t ,∼
χ )=(600,300) GeV σ×50

tt 1L
tt 2L
W+jetsZ+jetsDiboson1~ 0m(t ,∼
χ )=(1000,1) GeV σ×100
1

400
300
200
100
0
0

50 100 150 200 250 300 350 400 450 500
amT2 [GeV]

Figure 5.14: amT2 distribution after the event presemiss
lection described in Section 5.1 plus ET> 450 GeV
miss
and the ET
trigger requirements. Events passing

the amT2 > 175 GeV requirement are indicated by
the arrow. For comparison, the cross sections of signal events with (mt̃1 , m ˜01 ) = (600, 300) GeV (reddashed-line) and (1000, 1) GeV (blue dashed-line) ares = 13 TeV, 28.0 fb-1

400 Simulation
350
300

Total SM
W+jetsZ+jetsDibosonEvents / 10 GeV

Events / 20 GeV

scaled up by a factor of 50 and 100, respectively.

ttSingle top
tt+V

~ 0
m(t ,∼
χ )=(600,300) GeV σ×50
1

~ 0m(t ,∼
χ )=(1000,1) GeV σ×100
1

250
200
150

300 Simulation250

Total SM
W+jetsZ+jetsDibosons = 13 TeV, 28.0 fb-1
tt
Single top
tt+V

~ 0
m(t ,∼
χ )=(600,300) GeV σ×50
1

~ 0m(t ,∼
χ )=(1000,1) GeV σ×100
1

200
150
100

100
50

50
0

200

300

400

500

0
0

600 700 800
large-R jet p [GeV]

50

T

100

150

200 250 300 350
large-R jet mass [GeV]

Figure 5.15: pT distribution of the leading large-R jet

Figure 5.16: mass distribution of the leading large-

after the event preselection described in Section 5.1

R jet after the event preselection described in Sec-

miss
miss
plus ET> 450 GeV and the ET
trigger require-

miss
miss
tion 5.1 plus ET> 450 GeV, the ET
trigger,ments. Events passing the pT > 290 GeV require-

and the leading large-R jet pT > 290 GeV require-ment are indicated by the arrow. For comparison,ments. Events passing the m > 70 GeV require-the cross sections of signal events with (mt̃1 , m ˜01 ) =ment are indicated by the arrow. For comparison,(600, 300) GeV (red dashed-line) and (1000, 1) GeV

the cross sections of signal events with (mt̃1 , m ˜01 ) =(blue dashed-line) are scaled up by a factor of 50 and(600, 300) GeV (red dashed-line) and (1000, 1) GeV

100, respectively.

(blue dashed-line) are scaled up by a factor of 50 and
100, respectively.

53

miss
miss
Figure 5.17: The schematic view of ET,?
variable. (a) In the tt̄ (1L) events, the neutrino (ET)

is orientated in the same direction as the leptonically decaying top quark when it gets boosted.
miss(b) In the stop events, the neutralinos also contribute to the ET
and they are not collinear tothe leptonically decaying top quark, thus the perpendicular component tends to be larger than

Events / 60 GeV

the ones in tt̄ events.

Simulation

350 s = 13 TeV, 28.0 fb-1
300

~ 0m(t ,∼
χ1)=(600,300) GeV σ×50

Total SM
W+jetsZ+jetsDibosontt
Single top
tt+V

~ 0
m(t ,∼
χ )=(1000,1) GeV σ×100
1

250
200
150
100
50
0
0 100 200 300 400 500 600 700 800 900
perp. Emiss [GeV]T

miss
Figure 5.18: ET,?
distribution after the event presemiss
lection described in Section 5.1 plus ET> 450 GeV
miss
and the ET
trigger requirements. Events passing
missthe ET,?
> 180 GeV requirement are indicated by

the arrow. For comparison, the cross sections of signal events with (mt̃1 , m ˜01 ) = (600, 300) GeV (reddashed-line) and (1000, 1) GeV (blue dashed-line) are
scaled up by a factor of 50 and 100, respectively.

54

5.4

Diagonal Base Event Selection

Variable

Selection

TriggermissET
OR lepton trigger

Leptonexactly one signal lepton (e, µ), no additional baseline leptons

Number of (jets, b-tags)
Hadronic ⌧ veto

(

4,

1)

veto events with a hadronic ⌧ decay and m⌧T2 < 80 GeV

1st to 4th Jet pT > [GeV](60 60 40 25)

miss
ET
[GeV]

> 100⇤

mT [GeV]
p
miss
ET
/ HT

> 60⇤

|

>5

(jeti , p~missT )| for i 2 {1, 2}> 0.4

Table 5.1: Summary table of the base event selection for Diagonal. (⇤ ) indicates the lowest edge
missof the (ET, mT ) shape fit (see Figure 6.24).

As described in Section 1.6.3, the dominant background is tt̄ event and it is very challenging tosuppress them by event selection, because the di↵erence between Diagonal topology and tt̄ event
topology is smaller than Resolved and Boosted. Therefore, the base event selection is designed tojust ensure a basic topology of the signal event. Table 5.1 summarizes the selection for Diagonal.
miss
Since events with ET< 200 GeV are also utilized to improve background estimation in
missDiagonal described in Section 6.4, ET
trigger and lepton trigger are used as described in

Section 3.1. Since the momenta of jets in the signal events are harder than the backgrounds,
the leading to fourth leading jets ordered by pT are required to have pT of at least 60, 60,
miss40, 25 GeV, respectively. ET
and mT is required at least 100 GeV and 60 GeV to ensure
missa basic signal topology, respectively. Figure 5.19 and 5.20 show ET
and mT distributions.
miss
miss
The bump at ET= 200 GeV in Figure 5.19 arises because ET
trigger is also used if o✏ine
missET> 200 GeV (see Section 3.1). As shown in Figure 5.20, the main background in high-mT

region is tt̄ (1L1⌧h ) event. As shown in Figure 5.21, the number of tt̄ (1L1⌧h ) events passingm⌧T2 requirement (Section 5.1) is around 10000, most of which comes from the first bin of them⌧T2 distribution where there is no ⌧h candidate to calculate m⌧T2 . The reason is that ⌧h tends
to be undetected due to outside acceptance. However, since most events failing in the m⌧T2
requirement are also tt̄ (1L1⌧h ) events, those events are used for the background estimation(explained in Section 6.4).
miss
For suppressing events with large ET
due to mis-measurement of jet energy, |(jeti , p~miss
T )|

miss
for i 2 {1, 2} are required larger than 0.4. Because of the same reason, ET
significance
p
miss
miss
denoted by ET / HT is used. The denominator is approximately the resolution of ET
miss
miss
and is expected to be smaller if the main contribution to ET
comes from ET
resolution.
p
missTherefore, ET/ HT is required at least 5 and larger.

55

miss
Figure 5.19: ET
distribution after Diagonal base

Figure 5.20: mT distribution after Diagonal base

event selection.

event selection.

Figure 5.21: m⌧T2 distribution after Diagonal base
event selection without m⌧T2 > 80 GeV requirement.
In events at the first bin, there are no ⌧ candidate tocalculate m⌧T2 . Events passing the m⌧T2 requirement
are indicated by the arrows.

56

Chapter 6

Background Estimation
This chapter introduces background estimations in the SRs. Background estimation is mainly
based on a simultaneous fit of numbers of events in SR and in the other phase spaces near SR. The
phase space near SR is named ‘control region’ (CR). CRs are kinematically similar to the SRs,
but a few key requirements are changed in order to significantly enhance the yield and purityof a specific background event and to reduce signal contamination. In case each backgroundis significantly enhanced in each CR, the simultaneous fit can measure the normalization of
background from data and the uncertainties on the normalization can become smaller thanthose evaluated by MC samples. As explained in Section 7.3, the fitted parameters are total
normalization scale factors1 , µsig and µbkg for signal and backgrounds, respectively. Each µparameter scales up or down its total yield over SR and all CRs by its value, while all the yieldratios between SR and CRs are unchanged. For example, if µttbar (2 µbkg ) is fitted to 1.1, eachof tt̄ yields in SR and all CRs is scaled up by 1.1 from the nominal yield expected by MC. Since
each CR includes each background with higher purity and statistics than SR, µbkg are precisely
determined from the statistical constrait of CRs in the simultaneous fit, and then the backgroundcontamination in SR can be estimated from the fitted µbkg .
To check validity of the simultaneous fit before checking data at SRs, validation regions (VRs)are prepared, which are not overlapped with either CRs or SRs. Number of events in a VR,
expected by µbkg fitted in a ‘background-only fit’, is compared to the observed one to confirm
there is no significant problem in the procedure of background estimation. The background-only
fit is a fit with a background-only model (µsig is fixed to 0) and using only CRs, not SRs. VRs
never contribute to the background-only fit result (or never a↵ect the likelihood used in the fit),hence VRs provide a statistically independent test of the background estimation with the CRs.
In the background-only fit, number of the observed events at SRs had been blinded until it has
been concluded by checking the VRs that the fit configuration and modeling are fine. The VRs
are prepared for Resolved and Boosted in this analysis.
miss
The background estimation for Diagonal analysis exploits a 2-dimensional (ET,mT ) shapefit. Since suppression of tt̄ events is very challenging as discussed in Section 5.4, the Diagonal
analysis gains signal sensitivity with a very precise background estimation achieved by the 2-D
missshape fit. Since the (ET,mT ) shapes of signal and backgrounds are quite di↵erent, the shape fit

can be stable and background can be estimated with small uncertainties. In Diagonal, instead of
1 Parameters of systematic uncertainties (↵) are also fitted but not explained in this section. See Chapter 7.

57

Figure 6.1: A schematic diagram of the signal regin (SR), control region (CR), and validation
region (VR) used in Resolved and Boosted. Solid lines are boundaries of mT and amT2 while
dashed lines indicate that there is no upper boundary for the region. The initials of the regions,
T, ST, W, and TZ, mean tt̄, single top, W +jets, and tt̄ + Z, respectively. The low mT edge of
SR is 170 GeV and 210 GeV for Resolved and Boosted.
preparing VRs, a test fit is used to validate the 2-D shape fit, which is described in Appendix A.
Section 6.1 describes CRs used for Resolved and Boosted with showing data/MC distributions
after the background-only fit. Section 6.2 is dedicated to the description of tt̄ + Z(! ⌫⌫)CR (TZCR) for Resolved and Boosted and shows distributions after the background-only fit.
Section 6.3 describes VRs used for Resolved and Boosted with showing distributions after the
background-only fit. Section 6.4 is dedicated to Diagonal background estimation and describes
missthe (ET,mT ) shape fit with showing data/MC distributions without any fit.

6.1

Resolved and Boosted Control Regions

Figure 6.1 illustrates SR and CRs for Resolved and Boosted. CRs for tt̄, W +jets, single top, andtt̄ + V backgrounds are prepared for Resolved and Boosted, labeled as TCR, WCR, STCR, and
TZCR, respectively. SRs, TCR, WCR and STCR are summarized in Table 6.1 while TZCR is
explained in Section 6.2. The TCRs and WCRs are prepared by changing the mT selection to be awindow, upper edge of which is near the W boson mass. A requirement of amT2 = [100, 200] GeV
is also applied to the TCRs to enhance tt̄ events and to be separated from the STCRs. The STCRs
requires amT2 larger than 200 GeV to strongly reduce tt̄ events. Some other requirements are
removed or loosened to enhance the background yields in the CRs. The WCRs are the same as
the TCRs except that b-jet requirement changes into a b-jet veto and the amT2 requirement isloosened to increase the statistics of the WCR.
The STCRs also require at least two b-tagged jets to reduce the W +jets contamination.
Furthermore, the STCRs requireR(b1 , b2 ) > 1.2 where b1 and b2 are the two highest-pT b-

tagged jets. This is because the tt̄ events can exceed the amT2 kinematic bound when one of thetwo b-tagged jets used in the calculation of amT2 is a charm quark from the W decay misidentified58

as a b-tagged jet, but

R(b1 , b2 ) in those events tends to be smaller than W t events.

Figure 6.4-6.11 show variables after the background-only fit in CRs compared to the observed
data.

59

Common event selection
TriggermissETtrigger

Leptonexactly one signal lepton (e, µ), no additional baseline leptons

Jets

at least four signal jets, and |Hadronic ⌧ veto(jeti , p~missT )| > 0.4 for i 2 {1, 2}veto events with a hadronic ⌧ decay and m⌧T2 < 80 GeVResolved

Variable
1st to 4th Jet pT > [GeV]SR

TCR / WCR

STCR

(80 50 40 40)(80 50 40 40)(80 50 40 40)

miss
ET
[GeV]
miss
HT,sig

> 260

> 200

> 200

> 14

>5

>5

mT [GeV]> 170[30,90][30,120]

amT2 [GeV]> 175[100, 200] / > 100> 200

topness

> 6.5

> 6.5

> 6.5

mtop [GeV]

< 270

< 270

< 270

R(b, `)

< 3.0

–

–

R(b1 , b2 )

–

–

> 1.2

1/=0

2

SR

TCR / WCR

STCR

Number of b-tags

1
BoostedVariable
1st to 4th Jet pT > [GeV](120 80 50 25)(120 80 50 25)(120 80 50 25)

miss
ET
[GeV]
miss
ET,?
[GeV]
miss
HT,sig

> 450

> 300

> 250

> 180

> 160

> 160

> 22

> 15

> 10

mT [GeV]> 210[30,90][30,120]

amT2 [GeV]> 175[100, 200] / > 100> 200

R(b, `)

< 2.4

–

–

R(b1 , b2 )

–

–

> 1.2

1

1/=0

2

Leading large-R jet pT [GeV]

> 290

> 290

> 290

Leading large-R jet mass [GeV]

> 70

> 70

> 70

Number of b-tags

Table 6.1: Summary of the signal region (SR) and the tt̄ (TCR), W +jets (WCR), and W t(STCR) control regions each for Resolved and Boosted. TZCRs are described in Section 6.2
because TZCRs are very di↵erent from the other CRs,

60

Data
tt
W+jetssingletops = 13 TeV, 28.0 fb-1

500
400

Total SMZ+jetstt+V
Diboson

300

20
60

70

0
30

80
90
mT [GeV]
Data / MC

2
1.5
1
0.5
0

1600
1400

Data
tt
W+jetssingletops = 13 TeV, 28.0 fb-1

1200

Total SMZ+jetstt+V
Diboson

800

70

80
90
mT [GeV]

2
1.5
1
0.5
0

Data
tt
W+jetssingletop

300 s = 13 TeV, 28.0 fb-1
250

obs_x_TCR_tN_high_mt1000

Total SMZ+jetstt+V
Diboson

200

100

400

50

200
0
30

40

50

60

70

0
30

80
90
mT [GeV]
Data / MC

2
1.5
1
0.5
0

(c) mT at WCR of Resolved

180-1
160 s = 13 TeV, 28.0 fb

140
120

Data
tt
W+jetssingletop

40

50

60

70

80
90
mT [GeV]

2
1.5
1
0.5
0

(d) mT at WCR of Boosted

obs_x_WCR_SR1_mt1000

Events / 10 GeV

Data / MC

60

150

600

Events / 10 GeV50(b) mT at TCR of Boosted

1000

Total SMZ+jetstt+V
Diboson

100
80

50

s = 13 TeV, 28.0 fb-1

40

Data
tt
W+jetssingletop

obs_x_WCR_tN_high_mt1000

Total SMZ+jetstt+V
Diboson

30
20

60
40

10

20
0
30

40

obs_x_TCR_SR1_mt1000

Events / 10 GeV

Data / MC50

Total SMZ+jetstt+V
Diboson

60

100
40

Data
tt
W+jetssingletops = 13 TeV, 28.0 fb-1

8040(a) mT at TCR of Resolved

40

50

60

70

80

0
30

90 100 110 120
mT [GeV]

2
1.5
1
0.5
0

Data / MC

Data / MC

100

200

0
30

Events / 10 GeV

Events / 10 GeV

Events / 10 GeV

600(e) mT at STCR of Resolved

40

50

60

70

80

90 100 110 120
mT [GeV]

2
1.5
1
0.5
0

(f) mT at STCR of Boosted

obs_x_STopCR_SR1_mt1000

obs_x_STopCR_tN_high_mt1000

Figure 6.2: mT distributions at TCR (top), WCR (middle), and STCR (bottom), respectively. The left and rightcolumns correspond to Resolved and Boosted, respectively. The background-only fit results are applied to the
distributions. The uncertainty band includes statistical and systematic error.
61

Data
tt
W+jetssingletops = 13 TeV, 28.0 fb-1

400

Events / 10 GeV

Events / 10 GeV

500

Total SMZ+jetstt+V
Diboson

300

80
70
60
40
30
20
10

0
100 110 120 130 140 150 160 170 180 190 200
amT2 [GeV]

2
1.5
1
0.5
0

2
1.5
1
0.5
0

Data / MC0
100 110 120 130 140 150 160 170 180 190 200
amT2 [GeV]

Events / 10 GeV(a) amT2 at TCR of Resolved

450
400

Data
tt
W+jetssingletops = 13 TeV, 28.0 fb-1

350
300

(b) amT2 at TCR of Boosted

obs_x_TCR_SR1_amt2

Events / 20 GeV

Data / MC100

Total SMZ+jetstt+V
Diboson250

120 s = 13 TeV, 28.0 fb-1
100

200

60

150
100

40

Data
tt
W+jetssingletop

Total SMZ+jetstt+V
Diboson

300

350
400
amT2 [GeV]

20
150

200

250

300

0
100

350
400
amT2 [GeV]
Data / MC

2
1.5
1
0.5
0

(c) amT2 at WCR of ResolvedData220
s = 13 TeV, 28.0 fb-1
tt
200
W+jets180
singletop
160
140
120
100
80
60
40
20
0
200
250
300
350
400

150

200

250

2
1.5
1
0.5
0

(d) amT2 at WCR of Boosted

obs_x_WCR_SR1_amt2

Events / 50 GeV

Data / MC0100

obs_x_TCR_tN_high_amt2

8050Total SMZ+jetstt+V
Diboson120 s = 13 TeV, 28.0 fb-1
100

obs_x_WCR_tN_high_amt2

Datatt
W+jetssingletop

Total SMZ+jetstt+V
Diboson

400

450
500
amT2 [GeV]

80
60
40
20
0
200

450
500
amT2 [GeV]

2
1.5
1
0.5
0

Data / MCEvents / 20 GeV

Total SMZ+jetstt+V
Diboson50

200

Data / MCDatatt
W+jetssingletops = 13 TeV, 28.0 fb-1(e) amT2 at STCR of Resolved

250

300

350

2
1.5
1
0.5
0

(f) amT2 at STCR of Boosted

obs_x_STopCR_SR1_amt2

obs_x_STopCR_tN_high_amt2

Figure 6.3: amT2 distributions at TCR (top), WCR (middle), and STCR (bottom), respectively. The left andright columns correspond to Resolved and Boosted, respectively. The background-only fit results are applied tothe distributions. The uncertainty band includes statistical and systematic error.
62

Data
tt
W+jetssingletops = 13 TeV, 28.0 fb-1

800

EventsEvents1000

Total SMZ+jetstt+V
Diboson

600
400
200
4

5

6

7

8

9

10 11 12
Jet multiplicity

Data / MC

2
1.5
1
0.5
0

Events / 25 GeV(a) jet multiplicity
Datatt
W+jetssingletop-11000 s = 13 TeV, 28.0 fb

800

Total SMZ+jetstt+V
Diboson

400
200
50

100

150

200

250 300 350
lepton p [GeV]
Data / MC

Data / MC

T

2
1.5
1
0.5
0

(c) pT `3

Figure 6.4: Jet and b-jet multiplicity, signal lepton pT , and

2
1.5
1
0.5
0

R(b, `)

obs_x_TCR_SR1_dr_bjet_lep

R(b, `) distributions at TCR of Resolved after the

background-only fit. The uncertainty band includes statistical and systematic error.

63

obs_x_TCR_SR1_n_bjet

DataTotal SM450 s = 13 TeV, 28.0 fb-1
tt
Z+jets400
W+jetstt+V350
singletop
Diboson
300
250
200
150
100
50
0
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5∆R(b-jet, lepton)(d)

obs_x_TCR_SR1_lep_pt_1_1000

Total SMZ+jetstt+V
Diboson4
5b-jet multiplicity(b) b-jet multiplicity

600

0

Data
tt
W+jetssingletop

2
1.5
1
0.5
0

obs_x_TCR_SR1_n_jet

Events / 0.2

Data / MC

01800 s = 13 TeV, 28.0 fb-1
1600
1400
1200
1000
800
600
400
200
0
1
2

700

s = 13 TeV, 28.0 fb-1

600

Data
tt
W+jetssingletop

EventsEvents / 20 GeV

800

Total SMZ+jetstt+V
Diboson-1
350 s = 13 TeV, 28.0 fb

300

500

250

400

200

300

150

200

100

100

50

0
200 250 300 350 400 450 500 550 600 650 700
miss

Events / 10 GeV

600
500

400

300

300

200

200

100

100

0
100 120 140 160 180 200 220 240 260
χ2 based mt,had [GeV]

0

2
1.5
1
0.5
0

Data / MC

Data / MC

500

400

(c) mtop25miss(b) HT,sig

Total SMZ+jetstt+V
Dibosons = 13 TeV, 28.0 fb-1

7

8

9

30

significanceobs_x_TCR_SR1_ht_sig

Datatt
W+jetssingletop

Total SMZ+jetstt+V
Diboson

10 11 12 13 14 15 16
topness

2
1.5
1
0.5
0

(d) topness

obs_x_TCR_SR1_m_top_chi2

Total SMZ+jetstt+V
Diboson

2
1.5
1
0.5
0

obs_x_TCR_SR1_met1000

Data
tt
W+jetssingletop

20
missData / MCs = 13 TeV, 28.0 fb-1

15

HT

2
1.5
1
0.5
0
miss
(a) ET

10[GeV]

EventsData / MC

ET

0
5

Data
tt
W+jetssingletop

obs_x_TCR_SR1_topness

miss
miss
Figure 6.5: ET, HT,sig, mtop , and topness distributions at TCR of Resolved after the background-only fit. The

uncertainty band includes statistical and systematic error.

64

2000

Events / 25 GeV

Events

2500

Data
tt
W+jetssingletops = 13 TeV, 28.0 fb-1

Total SMZ+jetstt+V
Diboson

1500

500

500
5

6

7

8

9

0

10 11 12
Jet multiplicity
Data / MC

1600 s = 13 TeV, 28.0 fb-1
1400
1200

Data
tt
W+jetssingletop

50

100

150

200

2
1.5
1
0.5
0

(b) pT `obs_x_WCR_SR1_n_jet

Total SMZ+jetstt+V
Diboson800 s = 13 TeV, 28.0 fb-1
700
600

1000

500

800

400

600

300

400

200

200

100

0
200 250 300 350 400 450 500 550 600 650 700

0
5

10

15

Data / MC

2
1.5
1
0.5
0

Events / 10 GeV

900-1800 s = 13 TeV, 28.0 fb

700
600

Total SMZ+jetstt+V
Diboson1800
1600

s = 13 TeV, 28.0 fb-1

1400
1200
1000

400

800

300
200

600
400

100

200

0
100 120 140 160 180 200 220 240 260
χ2 based mt,had [GeV]

0

2
1.5
1
0.5
0

Data / MC

Data / MC

Total SMZ+jetstt+V
Diboson

20

25

miss
(d) HT,sig

500(e) mtopDatatt
W+jetssingletop

30

2
1.5
1
0.5
0

obs_x_WCR_SR1_met1000

Data
tt
W+jetssingletop

obs_x_WCR_SR1_lep_pt_1_1000

miss
HT significanceEventsData / MCmissET [GeV]

miss(c) ET

250 300 350
lepton p [GeV]
T

2
1.5
1
0.5
0

EventsData / MC4

Total SMZ+jetstt+V
Diboson

1500
1000(a) jet multiplicity

Events / 20 GeV

2000

1000

0

Data
tt
W+jetssingletop

2500 s = 13 TeV, 28.0 fb-1

7

8

9

obs_x_WCR_SR1_ht_sig

Datatt
W+jetssingletop

10 11 12 13 14 15 16
topness

2
1.5
1
0.5
0

(f) topness

obs_x_WCR_SR1_m_top_chi2

Total SMZ+jetstt+V
Dibosonobs_x_WCR_SR1_topness

miss
miss
Figure 6.6: jet multiplicity, signal lepton pT , ET
, HT,sig, mtop , and topness distributions at WCR of Resolved

after the background-only fit. The uncertainty band includes statistical and systematic error.
65

Data
tt
W+jetssingletops = 13 TeV, 28.0 fb-1

200

EventsEvents250

Total SMZ+jetstt+V
DibosonDatatt
W+jetssingletop-1
700 s = 13 TeV, 28.0 fb

600

Total SMZ+jetstt+V
Diboson

500

150

400
300

100

200
50
4

5

6

7

8

9

Data / MC

2
1.5
1
0.5
0

(a) jet multiplicity

Events / 25 GeV

0

10 11 12
Jet multiplicity

240
220 s = 13 TeV, 28.0 fb-1
200
180
160
140
120
100
80
60
40
20
0
50
100 1502

Datatt
W+jetssingletop

34(b) b-jet multiplicity

Total SMZ+jetstt+V
DibosonDatatt
W+jetssingletop-1
300 s = 13 TeV, 28.0 fb

250

obs_x_STopCR_SR1_n_bjet

Total SMZ+jetstt+V
Diboson

200
150
100
50

200

0
0

250 300 350
lepton p [GeV]

0.5

1 1.5 2

2.5 3

T

2
1.5
1
0.5
0

Data / MC

Data / MC5b-jet multiplicity

2
1.5
1
0.5
0

obs_x_STopCR_SR1_n_jet

Events / 0.5

Data / MC0100(c) pT `

2
1.5
1
0.5
0

(d)

obs_x_STopCR_SR1_lep_pt_1_1000

Figure 6.7: Jet and b-jet multiplicity, signal lepton pT , andR(b, `)

obs_x_STopCR_SR1_dr_bjet_lep

R(b, `) distributions at STCR of Resolved after the

background-only fit. The uncertainty band includes statistical and systematic error.

66

3.5 4 4.5 5∆R(b-jet, lepton)

miss

Data
tt
W+jetssingletop

Total SMZ+jetstt+V
Diboson

60
40
20
0
5

10

15

20

25
miss

[GeV]

HT
Data / MC

2
1.5
1
0.5
0
miss
(a) ET30

significance

2
1.5
1
0.5
0
miss
(b) HT,sig

obs_x_STopCR_SR1_met1000

obs_x_STopCR_SR1_ht_sig

0
100 120 140 160 180 200 220 240 260
χ2 based mt,had [GeV]

240
Data
Total SM220 s = 13 TeV, 28.0 fb-1
tt
Z+jets200
W+jetstt+V
180
singletop
Diboson
160
140
120
100
80
60
40
20
0
7 8 9 10 11 12 13 14 15 16
topness

2
1.5
1
0.5
0

2
1.5
1
0.5
0

160
140

s = 13 TeV, 28.0 fb-1

120

Data
tt
W+jetssingletop

Total SMZ+jetstt+V
Diboson

100
80
60
40

Data / MC

20

Data / MC

100 s = 13 TeV, 28.0 fb-1
80

EventsData / MCET

Events / 10 GeV

EventsEvents / 20 GeV

200
Data
Total SM-1
180 s = 13 TeV, 28.0 fbtt
Z+jetsW+jetstt+V160
singletop
Diboson
140
120
100
80
60
40
20
0
200 250 300 350 400 450 500 550 600 650 700(c) mtop(d) topness

obs_x_STopCR_SR1_m_top_chi2

obs_x_STopCR_SR1_topness

miss
miss
Figure 6.8: ET, HT,sig, mtop , and topness distributions at STCR of Resolved after the background-only fit.

The uncertainty band includes statistical and systematic error.

67

140

Data
tt
W+jetssingletops = 13 TeV, 28.0 fb-1

120

EventsEvents160

Total SMZ+jetstt+V
Diboson

250

Data
tt
W+jetssingletops = 13 TeV, 28.0 fb-1

200

100

Total SMZ+jetstt+V
Diboson

150

80
100

60
40

50

20
4

5

6

7

8

9

Data / MC

2
1.5
1
0.5
0

(a) jet multiplicity

Events / 100 GeV

010 11 12
Jet multiplicity

450-1
400 s = 13 TeV, 28.0 fb

350
300

Data
tt
W+jetssingletop2

3

Total SMZ+jetstt+V
Diboson

2
1.5
1
0.5
0

Data
tt
W+jetssingletop

120 s = 13 TeV, 28.0 fb-1
100

obs_x_TCR_tN_high_n_bjet

Total SMZ+jetstt+V
Diboson

80

200

60

150

40

100

20

50

0
0

100 200 300 400 500 600 700 800
lepton p [GeV]

0.5

1 1.5 2

2.5 3

T

2
1.5
1
0.5
0

Data / MC

Data / MC45b-jet multiplicity(b) b-jet multiplicity

250

0

1

obs_x_TCR_tN_high_n_jet

Events / 0.5

Data / MC0(c) pT `

2
1.5
1
0.5
0

(d)

obs_x_TCR_tN_high_lep_pt_1_1000

Figure 6.9: Jet and b-jet multiplicity, signal lepton pT , andR(b, `)

obs_x_TCR_tN_high_dr_bjet_lep

R(b, `) distributions at TCR of Boosted after the

background-only fit. The uncertainty band includes statistical and systematic error.

68

3.5 4 4.5 5∆R(b-jet, lepton)

Data
tt
W+jetssingletops = 13 TeV, 28.0 fb-1

70
60

EventsEvents / 20 GeV

80

Total SMZ+jetstt+V
Diboson

80

50
30

40

20

20

10
0
300 350 400 450 500 550 600 650 700 750
miss

80

Total SMZ+jetstt+V
Diboson

40
20
150

200

250
300
350
large-R jet mass [GeV]

24

26

28

30

significance

2
1.5
1
0.5
0

90 s = 13 TeV, 28.0 fb-1
80
70
60
50
40
30
20
10
0
200 300 400 500

obs_x_TCR_tN_high_ht_sig

Datatt
W+jetssingletop

Total SMZ+jetstt+V
Diboson

600 700 800 900
large-R jet p [GeV]T

Data / MC

2
1.5
1
0.5
0

(c) mlarge-R jet

22

miss
(b) HT,sig

60

100

20

miss

obs_x_TCR_tN_high_met1000

Data
tt
W+jetssingletop

18

HT
Data / MC

100 s = 13 TeV, 28.0 fb-1

16

[GeV]

2
1.5
1
0.5
0
miss
(a) ET

Events / 25 GeV

0Events / 50 GeV

Data / MCET

Data / MC

Total SMZ+jetstt+V
Diboson

60

40

0

Data
tt
W+jetssingletop-1
100 s = 13 TeV, 28.0 fb

2
1.5
1
0.5
0

(d) pT large-R jet

obs_x_TCR_tN_high_fatjet_R12_L0_m_1_1000

obs_x_TCR_tN_high_fatjet_R12_L0_pt_1_1000

miss
miss
Figure 6.10: ET, HT,sig, and large-R jet mass and pT distributions at TCR of Boosted after the background-only

fit. The uncertainty band includes statistical and systematic error.

69

Data
tt
W+jetssingletops = 13 TeV, 28.0 fb-1

600
500

Events / 100 GeV

Events700

Total SMZ+jetstt+V
Diboson

400

1200

Data
tt
W+jetssingletops = 13 TeV, 28.0 fb-1

1000
800

Total SMZ+jetstt+V
Diboson

600

300
400

200

200

100
4

5

6

7

8

9

Data / MC

300

Data
tt
W+jetssingletops = 13 TeV, 28.0 fb-1

250
200

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

2
1.5
1
0.5
0

(a) jet multiplicity

Events / 40 GeV

010 11 12
Jet multiplicity

2
1.5
1
0.5
0

(b) pT `obs_x_WCR_tN_high_n_jet

EventsData / MC0

Total SMZ+jetstt+V
Dibosonobs_x_WCR_tN_high_lep_pt_1_1000

200-1
180 s = 13 TeV, 28.0 fb
160
140
120
100
80
60
40
20
0
16
18 20
22

150
100
50
0
300 350 400 450 500 550 600 650 700

Datatt
W+jetssingletop

24

Data / MC

2
1.5
1
0.5
0

200 s = 13 TeV, 28.0 fb-1
180
160
140
120
100
80
60
40
20
0
100
150
200

Data
tt
W+jetssingletop

miss(d) HT,sig

Total SMZ+jetstt+V
Diboson

250
300
350
large-R jet mass [GeV]30

220
s = 13 TeV, 28.0 fb-1
200
180
160
140
120
100
80
60
40
20
0
200 300 400 500

obs_x_WCR_tN_high_ht_sig

Datatt
W+jetssingletop

Total SMZ+jetstt+V
Diboson

600 700 800 900
large-R jet p [GeV]
T

2
1.5
1
0.5
0

(e) mlarge-R jet

28

2
1.5
1
0.5
0

obs_x_WCR_tN_high_met1000

Data / MC

Data / MCEvents / 25 GeV

miss(c) ET

26

miss
HT significanceEvents / 50 GeV

Data / MCmissET [GeV]

Total SMZ+jetstt+V
Diboson

2
1.5
1
0.5
0

(f) pT large-R jet

obs_x_WCR_tN_high_fatjet_R12_L0_m_1_1000

obs_x_WCR_tN_high_fatjet_R12_L0_pt_1_1000

miss
miss
Figure 6.11: Jet multiplicity, signal lepton pT , ET
, HT,sig, and large-R jet mass and pT distributions at WCRof Boosted after the background-only fit. The uncertainty band includes statistical and systematic error.
70

Data
tt
W+jetssingletops = 13 TeV, 28.0 fb-1

70

EventsEvents90
80

Total SMZ+jetstt+V
Diboson

250

Data
tt
W+jetssingletops = 13 TeV, 28.0 fb-1

200

Total SMZ+jetstt+V
Diboson

60
150

50
40

100

30
20

50

10
4

5

6

7

8

9

Data / MC

2
1.5
1
0.5
0

(a) jet multiplicity

Events / 100 GeV

010 11 12
Jet multiplicity

2

3

4

(b) b-jet multiplicity

Data
Total SM200 s = 13 TeV, 28.0 fb-1
tt
Z+jets180
W+jetstt+V160
singletop
Diboson
140
120
100
80
60
40
20
0
100 200 300 400 500 600 700 800
lepton p [GeV]

120
100

Data
tt
W+jetssingletops = 13 TeV, 28.0 fb-1

80

Total SMZ+jetstt+V
Diboson

40
20
0
0

0.5

1 1.5 2

2.5 3

TData / MC

Data / MC

obs_x_STopCR_tN_high_n_bjet

60

2
1.5
1
0.5
0

(c) pT `5b-jet multiplicity

2
1.5
1
0.5
0

obs_x_STopCR_tN_high_n_jet

Events / 0.5

Data / MC

0

2
1.5
1
0.5
0

(d)

obs_x_STopCR_tN_high_lep_pt_1_1000

Figure 6.12: Jet and b-jet multiplicity, signal lepton pT , andR(b, `)

obs_x_STopCR_tN_high_dr_bjet_lep

R(b, `) distributions at STCR of Boosted after the

background-only fit. The uncertainty band includes statistical and systematic error.

71

3.5 4 4.5 5∆R(b-jet, lepton)

Data
tt
W+jetssingletops = 13 TeV, 28.0 fb-1

70
60

Total SMZ+jetstt+V
Diboson60
50

Total SMZ+jetstt+V
Diboson

40
30

30
20

20

10

10

0
250 300 350 400 450 500 550 600 650 700

010 12 14 16 18 20 22 24 26 28 30
miss

[GeV]

HT

2
1.5
1
0.5
0

Data / MC

Data / MCDatatt
W+jetssingletops = 13 TeV, 28.0 fb-1

40

miss

miss
(a) ET80

s = 13 TeV, 28.0 fb-1

70
60

Data
tt
W+jetssingletopmiss(b) HT,sig

Total SMZ+jetstt+V
Diboson50
40

50

s = 13 TeV, 28.0 fb-1

40

obs_x_STopCR_tN_high_ht_sig

Datatt
W+jetssingletop

Total SMZ+jetstt+V
Diboson

30
20

20

10

10
0

significance

2
1.5
1
0.5
0

obs_x_STopCR_tN_high_met1000

30

100

150

200

0
200

250
300
350
large-R jet mass [GeV](c) mlarge-R jet

300

400

500

600 700 800 900
large-R jet p [GeV]
T

2
1.5
1
0.5
0

Data / MC

Data / MC

70

50

ET

Events / 25 GeV

Events / 2

80

Events / 50 GeV

Events / 50 GeV

90

2
1.5
1
0.5
0

(d) pT large-R jet

obs_x_STopCR_tN_high_fatjet_R12_L0_m_1_1000

obs_x_STopCR_tN_high_fatjet_R12_L0_pt_1_1000

miss
miss
Figure 6.13: ET, HT,sig, and large-R jet mass and pT distributions at STCR of Boosted after the background-

only fit. The uncertainty band includes statistical and systematic error.

72

6.2

Resolved and Boosted Control Regions For tt̄ + Z

Control regions for tt̄ + Z (TZCRs) are prepared for Resolved and Boosted in a dedicated way
di↵erent from the other CRs. tt̄ production with radiation of a Z boson decaying into neutrinos
is an irreducible background2 .
A CR using Z boson decays to charged leptons doesn’t work well because of the limited data
statistics due to the small branching ratio to leptons. Instead, a CR using tt̄ +events is used

where the Z boson is emulated by the . The CR is defined to minimize the di↵erences betweentt̄ + Z and tt̄ +processes to reduce the theoretical uncertainties in the emulation of tt̄ + Z.

The main di↵erence arises from the fact that the Z boson mass is much larger thanmass. This

causes di↵erence in kinematic distributions. Furthermore, at LHC energies, the bremsstrahlungrate of Z boson from top quark is lower than that offrom top quark and its decay products.

These di↵erences can be reduced if the boson pT is larger than the Z boson mass. In thelimit, the kinematical impact of the mass di↵erence on the phase space is reduced, and thebremsstrahlung rate of photon is suppressed [113]. For this reason, photon objects are required
to have pT larger than 145 GeV as described in Section 4.4. In this condition, the uncertainty fromphoton radiations has turned out to be subdominant compared to the uncertainties described in
Section 8.6 and therefore can be neglected [26].
The event selection for the TZCRs requires at least one photon, exactly one signal lepton, no
additional baseline lepton, and at least four signal jets, at least one of which must be b-tagged.
Furthermore, the TZCRs are required to have the same jet pT thresholds as the corresponding
SRs. To emulate the Z ! ⌫ ⌫¯ decay, the photon with the highest pT is vectorially added to p~miss
T

miss
miss
and this sum is used to construct an emulated ET
denoted by ẼT
⌘ |~
pmiss
+ p~T |. Then,
T

miss
miss
m̃T and H̃T,sig
are also calculated by regarding ẼT
as the normal missing transverse energy.

In order to make the region kinematically closer to the SRs, event in the TZCRs must satisfy
miss
miss
miss
ẼT
> 120 GeV, m̃T > 100 GeV, and H̃T,sig> 5. Finally, ET< 200 GeV is required to makethe TZCR statistically orthogonal to the other CRs and SRs.
Figure 6.14-6.15 show variables after the background-only fit in CRs compared to the observed
data.

2 The expected yields of tt̄ + W in the SRs are less than 10% of the expected yields of tt̄ + Z, and hence thetwo processes are combined in the analysis.

73s = 13 TeV, 28.0 fb-1

120
100

Data
tt+γ
Z+jetstt+V
DibosonEvents / 20 GeV

Events / 20 GeV

140

Total SMtt
W+jetssingletop

80
60

40

[GeV]
Data / MC

2
1.5
1
0.5
0
miss
(a) ET

250 s = 13 TeV, 28.0 fb-1
200

Data
tt+γ
Z+jetstt+V
DibosonTotal SMtt
W+jetssingletop

90
80

50

20
10
0
0
Data / MC

2
1.5
1
0.5
0
miss
(c) H̃T,sig

Data
tt+γ
Z+jetstt+V
DibosonTotal SMtt
W+jetssingletop

2
1.5
1
0.5
0

50 100 150 200 250 300 350 400 450 500~miss
ET = Emiss
with photon added [GeV]Tmiss(d) ẼT

obs_x_ttZCR_SR1_ht_sig_photon

obs_x_ttZCR_SR1_photon_mt1000

50
40
30

20
25
30
~miss
HT significances = 13 TeV, 28.0 fb-1

70
60

100

15

200
300
400
500
600
~ = m with photon added [GeV]m
TT(b) m̃T

150

10

100

2
1.5
1
0.5
0

obs_x_ttZCR_SR1_met1000

Events / 20 GeV

Data / MC500050 100 150 200 250 300 350 400 450 500
miss

Events / 5

60

Total SMtt
W+jetssingletop

10

ET

Data / MC

70

Data
tt+γ
Z+jetstt+V
Diboson

20

20

0
5

s = 13 TeV, 28.0 fb-1

30

40

0
0

80

obs_x_ttZCR_SR1_photon_met1000

miss
miss
miss
Figure 6.14: ET, m̃T , H̃T,sig, and ẼT
distributions at TZCR of Resolved after the background-only fit. The

uncertainty band includes statistical and systematic error.

74

120
100

Data
tt+γ
Z+jetstt+V
DibosonEvents / 20 GeV

Events / 20 GeV

140 s = 13 TeV, 28.0 fb-1

Total SMtt
W+jetssingletop

80

[GeV]
Data / MC

2
1.5
1
0.5
0
miss
(a) ETs = 13 TeV, 28.0 fb-1

200

Data
tt+γ
Z+jetstt+V
DibosonTotal SMtt
W+jetssingletop

100
50
15

20
25
30
~miss
HT significance
Data / MC

2
1.5
1
0.5
0
miss
(c) H̃T,sig

200
300
400
500
600
~ = m with photon added [GeV]m
TT(b) m̃T

150

10

100

2
1.5
1
0.5
0

obs_x_ttZCR_tN_high_met1000

Events / 20 GeV

Data / MC00

50 100 150 200 250 300 350 400 450 500
miss

Events / 5

50

10

ET

Data / MC60

Total SMtt
W+jetssingletop

20

20

0
5

70

Data
tt+γ
Z+jetstt+V
Diboson

30

40

250

s = 13 TeV, 28.0 fb-1

40

60

0
0

80

Data

Total SM90 s = 13 TeV, 28.0 fb-1
tt+γtt
Z+jetsW+jets80
tt+V
singletop
70
Diboson
60
50
40
30
20
10
0
0 50 100 150 200 250 300 350 400 450 500~miss
ET = Emiss
with photon added [GeV]
T

2
1.5
1
0.5
0

miss
(d) ẼT

obs_x_ttZCR_tN_high_ht_sig_photon

obs_x_ttZCR_tN_high_photon_mt1000

obs_x_ttZCR_tN_high_photon_met1000

miss
miss
miss
Figure 6.15: ET, m̃T , H̃T,sig, and ẼT
distributions at TZCR of Boosted after the background-only fit. The

uncertainty band includes statistical and systematic error.

75

6.3

Resolved and Boosted Validation Regions

Each SR has two VRs, TVR (tt̄) and WVR (W +jets). These are constructed with the same
selection as the TCR and the WCR except that mT is required to be between 90 and 120 GeV3 .
The signal contamination in the VRs is checked for all the signal mass points shown in Figure 1.8,
and found to be negligible. Figure 6.18-6.23 show variables after the background-only fit in VRs
compared to the observed data. These VR plots show that there is no significant problem in the
background estimation procedure developed in this section.

3 Since the m

T range in the STCR is already extended upward to 120 GeV to increase statistics, a W t VR is

not defined.

76

160

Data
tt
W+jetssingletops = 13 TeV, 28.0 fb-1

140

Events / 10 GeV

Events / 5 GeV

180

Total SMZ+jetstt+V
Diboson120
100

45 s = 13 TeV, 28.0 fb-1
40
35
30
25
20
15
10
5
0
90
100

80
60
40
20
95

100

105

110

Data / MC

2
1.5
1
0.5
0

(a) mT at TVR of Resolved

Events / 5 GeV

115
120mT [GeV]

350
300

Data
tt
W+jetssingletops = 13 TeV, 28.0 fb-1

250(b) mT at TVR of Boosted

Total SMZ+jetstt+V
Diboson200

80

s = 13 TeV, 28.0 fb-1

70
60

Data
tt
W+jetssingletop

obs_x_TVR_tN_high_mt1000

Total SMZ+jetstt+V
Diboson

50
30

100

20

50

10
95

100

105

110

0
90

115
120
mT [GeV]

2
1.5
1
0.5
0

Data / MC

Data / MC

120mT [GeV]

40

150

0
90

110

Total SMZ+jetstt+V
Diboson

2
1.5
1
0.5
0

obs_x_TVR_SR1_mt1000

Events / 10 GeV

Data / MC

0
90

Data
tt
W+jetssingletop(c) mT at WVR of Resolved

100

110

120
mT [GeV]

2
1.5
1
0.5
0

(d) mT at WVR of Boosted

obs_x_WVR_SR1_mt1000

obs_x_WVR_tN_high_mt1000

Figure 6.16: mT distributions at TVR (top) and WVR (bottom), respectively. The left and right columns
correspond to Resolved and Boosted, respectively. The background-only fit results are applied to the distributions.
The uncertainty band includes statistical and systematic error.

77

Events / 20 GeV
Data / MC50

Total SMZ+jetstt+V
Diboson

30

180
200
amT2 [GeV]

0
100

350
400
amT2 [GeV]

2
1.5
1
0.5
0

s = 13 TeV, 28.0 fb-1

obs_x_TVR_tN_high_amt2

Datatt
W+jetssingletop

Total SMZ+jetstt+V
Diboson300

400
amT2 [GeV]155(c) amT2 at WVR of Resolved

160

20

10
300

140

25

10

250

120

2
1.5
1
0.5
0

20

200

Total SMZ+jetstt+V
Diboson(b) amT2 at TVR of Boosted

30

150

Data
tt
W+jetssingletop15

obs_x_TVR_SR1_amt2

40

0
100
Data / MCDatatt
W+jetssingletops = 13 TeV, 28.0 fb-1

20

0
100

Data / MCEvents / 10 GeV60

s = 13 TeV, 28.0 fb-1

5

2
1.5
1
0.5
0

(a) amT2 at TVR of Resolved

25

10

Events / 60 GeV

Events / 10 GeV
Data / MC

Data
Total SM90 s = 13 TeV, 28.0 fb-1
tt
Z+jets80
W+jetstt+V70singletop
Diboson
60
50
40
30
20
10
0
100 110 120 130 140 150 160 170 180 190 200
amT2 [GeV]

200

2
1.5
1
0.5
0

(d) amT2 at WVR of Boosted

obs_x_WVR_SR1_amt2

obs_x_WVR_tN_high_amt2

Figure 6.17: amT2 distributions at TVR (top) and WVR (bottom), respectively. The left and right columns
correspond to Resolved and Boosted, respectively. The background-only fit results are applied to the distributions.
The uncertainty band includes statistical and systematic error.

78

Data
tt
W+jetssingletop-1
160 s = 13 TeV, 28.0 fb

140
120

EventsEvents180

Total SMZ+jetstt+V
Diboson

250

80

150

60

100

40

50

20
5

6

7

8

9

Data / MC(a) jet multiplicity

Events / 25 GeV

0

10 11 12
Jet multiplicity

140

Data
tt
W+jetssingletops = 13 TeV, 28.0 fb-1

120

2

3

2
1.5
1
0.5
0

Total SMZ+jetstt+V
DibosonDatatt
W+jetssingletop

160 s = 13 TeV, 28.0 fb-1
140120

obs_x_TVR_SR1_n_bjet

Total SMZ+jetstt+V
Diboson

100

80

80

60

60

40

40

20

20
50

100

150

200

0
0

250 300 350
lepton p [GeV]

0.5

1 1.5 2

2.5 3

T

2
1.5
1
0.5
0

Data / MC

Data / MC45b-jet multiplicity(b) b-jet multiplicity

100

0

1

obs_x_TVR_SR1_n_jet

Events / 0.5

Data / MC

4

2
1.5
1
0.5
0

160

Total SMZ+jetstt+V
Diboson

200

100

0

Data
tt
W+jetssingletop

300 s = 13 TeV, 28.0 fb-1(c) pT `

2
1.5
1
0.5
0

(d)

obs_x_TVR_SR1_lep_pt_1_1000

Figure 6.18: Jet and b-jet multiplicity, signal lepton pT , andR(b, `)

obs_x_TVR_SR1_dr_bjet_lep

R(b, `) distributions at TVR of Resolved after the

background-only fit. The uncertainty band includes statistical and systematic error.

79

3.5 4 4.5 5∆R(b-jet, lepton)

140
120

Data
tt
W+jetssingletop

Total SMZ+jetstt+V
Diboson

70
60

80

40

60

30

40

20

20

10

0
200 250 300 350 400 450 500 550 600 650 700

0
5

Data
tt
W+jetssingletops = 13 TeV, 28.0 fb-1

Total SMZ+jetstt+V
Diboson

80

25

miss
(b) HT,sig

Total SMZ+jetstt+V
Diboson30

significance

2
1.5
1
0.5
0

obs_x_TVR_SR1_met1000

Data
tt
W+jetssingletop

20
missData / MC

120

15

HT

EventsData / MCmiss(a) ET

10

[GeV]

2
1.5
1
0.5
0

100

s = 13 TeV, 28.0 fb-1

50

miss

-1
120 s = 13 TeV, 28.0 fb

100

obs_x_TVR_SR1_ht_sig

Datatt
W+jetssingletop

Total SMZ+jetstt+V
Diboson

80
60

60

40

40

20

20

0
100 120 140 160 180 200 220 240 260
χ2 based mt,had [GeV]

0

2
1.5
1
0.5
0

Data / MC

Data / MC

80

100

ET

Events / 10 GeV

EventsEvents / 20 GeV

160 s = 13 TeV, 28.0 fb-1(c) mtop

78

9

10 11 12 13 14 15 16
topness

2
1.5
1
0.5
0

(d) topness

obs_x_TVR_SR1_m_top_chi2

obs_x_TVR_SR1_topness

miss
miss
Figure 6.19: ET, HT,sig, mtop , and topness distributions at TVR of Resolved after the background-only fit.

The uncertainty band includes statistical and systematic error.

80

300

Data
tt
W+jetssingletops = 13 TeV, 28.0 fb-1

250

Events / 25 GeV

Events350

Total SMZ+jetstt+V
Diboson

200

250

Data
tt
W+jetssingletops = 13 TeV, 28.0 fb-1

200

Total SMZ+jetstt+V
Diboson

150

150

100

100
50

50
4

5

6

7

8

9

0

10 11 12
Jet multiplicity(a) jet multiplicity

100

150

200

(b) pT `Events

100 s = 13 TeV, 28.0 fb-1
80

0
5

10

15

20

25

30

miss
HT significance

Data / MC

2
1.5
1
0.5
0
miss
(d) HT,sig

obs_x_WVR_SR1_met1000

EventsData / MCEvents / 10 GeV

Total SMZ+jetstt+V
Diboson20

0
100 120 140 160 180 200 220 240 260
χ2 based mt,had [GeV]
2
1.5
1
0.5
0

2
1.5
1
0.5
0

80

Total SMZ+jetstt+V
Dibosonobs_x_WVR_SR1_ht_sig

DataTotal SM200 s = 13 TeV, 28.0 fb-1
tt
Z+jets180
W+jetstt+V160
singletop
Diboson
140
120
100
80
60
40
20
0
7 8 9 10 11 12 13 14 15 16
topness-1
100 s = 13 TeV, 28.0 fb

60
40

Data / MC

20

Data / MCDatatt
W+jetssingletop

40

2
1.5
1
0.5
0

Data
tt
W+jetssingletop

obs_x_WVR_SR1_lep_pt_1_1000

60

miss
ET [GeV]

miss(c) ET

250 300 350
lepton p [GeV]

2
1.5
1
0.5
0

obs_x_WVR_SR1_n_jet

240
Data
Total SM220 s = 13 TeV, 28.0 fb-1
tt
Z+jets200
W+jetstt+V
180
singletop
Diboson
160
140
120
100
80
60
40
20
0
200 250 300 350 400 450 500 550 600 650 700

Events / 20 GeV

50

T

2
1.5
1
0.5
0

Data / MC

Data / MC0(e) mtop(f) topness

obs_x_WVR_SR1_m_top_chi2

obs_x_WVR_SR1_topness

miss
miss
Figure 6.20: Jet multiplicity, signal lepton pT , ET
, HT,sig, mtop , and topness distributions at WVR of Resolved

after the background-only fit. The uncertainty band includes statistical and systematic error.
81

Data
tt
W+jetssingletops = 13 TeV, 28.0 fb-1

20

EventsEvents25

Total SMZ+jetstt+V
Diboson

40

Data
tt
W+jetssingletops = 13 TeV, 28.0 fb-1

35
30

15

Total SMZ+jetstt+V
Diboson

25
20

10

15
10

5

5
4

5

6

7

8

9

Data / MC

2
1.5
1
0.5
0

(a) jet multiplicity

Events / 100 GeV

010 11 12
Jet multiplicity

50

s = 13 TeV, 28.0 fb-1

40

Data
tt
W+jetssingletop

Total SMZ+jetstt+V
Diboson20
10
100 200 300 400 500 600 700 800
lepton p [GeV]
Data / MC

Data / MC

T

2
1.5
1
0.5
0

(c) pT `23

45b-jet multiplicity(b) b-jet multiplicity

30

0

1

2
1.5
1
0.5
0

obs_x_TVR_tN_high_n_jet

Events / 0.5

Data / MC

0

22
Data
Total SM-1
20 s = 13 TeV, 28.0 fbtt
Z+jets18
W+jetstt+Vsingletop
Diboson
16
14
12
10
8
6
4
2
0
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5∆R(b-jet, lepton)
2
1.5
1
0.5
0

(d)

obs_x_TVR_tN_high_lep_pt_1_1000

Figure 6.21: Jet and b-jet multiplicity, signal lepton pT , andR(b, `)

obs_x_TVR_tN_high_dr_bjet_lep

R(b, `) distributions at TVR of Boosted after the

background-only fit. The uncertainty band includes statistical and systematic error.

82

obs_x_TVR_tN_high_n_bjet

20

Events / 3

Events / 50 GeV

25

Data
tt
W+jetssingletops = 13 TeV, 28.0 fb-1

Total SMZ+jetstt+V
Diboson

20

5

10

0
300 350 400 450 500 550 600 650 700

0
15

miss

18
16
14

miss

Data / MCs = 13 TeV, 28.0 fb-1

miss(b) HT,sig

Total SMZ+jetstt+V
Diboson

12
10
8

18
16
14

6
4
2
150

200

0
200

250
300
350
large-R jet mass [GeV]

Total SMZ+jetstt+V
Diboson

300

400

500

600 700 800 900
large-R jet p [GeV]T

Data / MC

2
1.5
1
0.5
0

(c) mlarge-R jet

Datatt
W+jetssingletop

10
8

4
2
100

s = 13 TeV, 28.0 fb-1

obs_x_TVR_tN_high_ht_sig

12

6

0

30
significance

2
1.5
1
0.5
0

obs_x_TVR_tN_high_met1000

Data
tt
W+jetssingletop

25
HT

2
1.5
1
0.5
0
miss
(a) ET

20[GeV]

Events / 50 GeV

Data / MC40

Total SMZ+jetstt+V
Diboson30

ET

Events / 25 GeV

Datatt
W+jetssingletops = 13 TeV, 28.0 fb-1

15
10

Data / MC

50

2
1.5
1
0.5
0

(d) pT large-R jet

obs_x_TVR_tN_high_fatjet_R12_L0_m_1_1000

obs_x_TVR_tN_high_fatjet_R12_L0_pt_1_1000

miss
miss
Figure 6.22: ET, HT,sig, and large-R jet mass and pT distributions at TVR of Boosted after the background-only

fit. The uncertainty band includes statistical and systematic error.

83

Data
tt
W+jetssingletops = 13 TeV, 28.0 fb-1

50

Events / 100 GeV

Events60

Total SMZ+jetstt+V
Diboson

40
30

80

Data
tt
W+jetssingletops = 13 TeV, 28.0 fb-1

70
60

Total SMZ+jetstt+V
Diboson

50
40
30

20

20
10
4

5

6

7

8

9

30

Data / MCDatatt
W+jetssingletops = 13 TeV, 28.0 fb-1

25

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

2
1.5
1
0.5
0

(a) jet multiplicity

Events / 50 GeV

010 11 12
Jet multiplicity

2
1.5
1
0.5
0

(b) pT `obs_x_WVR_tN_high_n_jet

Events / 3

Data / MC

0

10Total SMZ+jetstt+V
Diboson20

50

obs_x_WVR_tN_high_lep_pt_1_1000

Datatt
W+jetssingletops = 13 TeV, 28.0 fb-1

40

Total SMZ+jetstt+V
Diboson

30

15

20

10
10

5
0
300 350 400 450 500 550 600 650 700

0
15

20

25

Data / MC

2
1.5
1
0.5
0

20
18
16
14
12
10
8
6
4
2
0

s = 13 TeV, 28.0 fb-1

2
1.5
1
0.5
0
miss
(d) HT,sig

obs_x_WVR_tN_high_met1000

Data
tt
W+jetssingletop

Total SMZ+jetstt+V
Diboson25

s = 13 TeV, 28.0 fb-1

20

obs_x_WVR_tN_high_ht_sig

Datatt
W+jetssingletop

Total SMZ+jetstt+V
Diboson

15
10
5

100

150

200

0
200

250
300
350
large-R jet mass [GeV](e) mlarge-R jet

300

400

500

600 700 800 900
large-R jet p [GeV]
T

2
1.5
1
0.5
0

Data / MC

Data / MCEvents / 25 GeV

miss(c) ET

30

miss
HT significanceEvents / 50 GeV

Data / MCmissET [GeV]

2
1.5
1
0.5
0

(f) pT large-R jet

obs_x_WVR_tN_high_fatjet_R12_L0_m_1_1000

obs_x_WVR_tN_high_fatjet_R12_L0_pt_1_1000

miss
miss
Figure 6.23: Jet multiplicity, signal lepton pT , ET
, HT,sig, and large-R jet mass and pT distributions at WVRof Boosted after the background-only fit. The uncertainty band includes statistical and systematic error.
84

6.4

2-D Shape Fit for Diagonal

missFigure 6.24: Binning configuration for the 2-dimensional (ET, mT ) binned shape fit in the

Diagonal analysis. Each yield at each bin is used in the binned maximum likelihood fit. Coloredbins indicate that they enhance a specific process to control its normalization. (red:signal,
blue:tt̄ ! [b`⌫][bqq], cyan:tt̄ ! 1`1⌧h ).
After the base event selection described in Section 5.4, the selected events are divided into 4
missET
slices, [100,150], [150, 200], [200, 250], [250, inf] GeV, and subsequently divided into 9mT slices, [60, 90], [90, 120], [120, 150], [150, 180], [180, 210], [210, 240], [240, 270], [270, 300],
miss[300, inf] GeV. The binning configuration of the 2-dimensional (ET,mT ) shape fit is shown in

Figure 6.24.
missFigure 6.25 shows each mT distribution at each ET
slice. To show how well the backgroundMC samples can describe data, Figure 6.25 also shows data points while those in the region
misswhere ET> 150 GeV and mT > 120 GeV are blinded. The signal events are enriched in themisshigh-ETand high-mT region, where, however, 1L1⌧h events are also enriched and become thedominant background. The hadronically decaying tau in 1L1⌧h events after the base selection
misstends to be outside acceptance and thus contributes to ET
and mT as an invisible object likeneutrino. Therefore 1L1⌧h events have also high mT . To precisely estimate the 1L1⌧h events,‘TAUCR’ is prepared, which enriches 1L1⌧h events by requiring events to pass the base selection
with the tau-veto requirement ‘inversed’ and have mT > 120 GeV. Figure 6.26 shows each mT
miss
miss
distribution at TAUCR at each ET
slice. TAUCR is not divided into ET
and mT slices but

remains just one bin in the fit because it is enough for 1L1⌧h to be controlled well and because of
simplicity of the fit. The subdominant background is 1L events, which can be precisely estimatedmissby mT shape at low-ET
slice. All other small backgrounds are determined from simulationand normalized to the most accurate theoretical cross-section available.
Instead of preparing VRs like Resolved and Boosted, the 2-D shape fit has been validated
missby a test fit, called ‘validation fit’, in which bins in the region where ET> 150 GeV andmT > 120 GeV are not used and blinded as shown in Figure A.1. The purpose of the validation
fit is to assure that the SM-background model can describes data at background-enhanced regions

85

well without any significant issues. As a goodness of fit, CLb has been calculated and the result
is 0.436 (0.160 ). The result has concluded that there is no insanity in the fit configuration andmodeling. For the validation studies, see Appendix A. After confirming by the tests that there
is no significant issue in the fit configuration and modeling, the ‘unblind’ fit has been done andthe results are shown in Section 9.2.

86

miss
(a) mT at ET= [100, 150] GeV.

miss(b) mT at ET= [150, 200] GeV.

miss(c) mT at ET= [200, 250] GeV.

miss(d) mT at ET= [250, inf] GeV.

miss
miss
Figure 6.25: mT distributions at each ET
slice. Data points are blinded in the region where ET> 150 GeV

and mT > 120 GeV. The uncertainty band includes statistical error.

87

miss
(a) mT at TAUCR at ET= [100, 150] GeV.

miss(b) mT at TAUCR at ET= [150, 200] GeV.

miss(c) mT at TAUCR at ET= [200, 250] GeV.

miss(d) mT at TAUCR at ET= [250, inf] GeV.

miss
Figure 6.26: mT distributions at TAUCR at each ET
slice. The mT > 120 GeV requirement is not applied in

the plots. The uncertainty band includes statistical error.

88

Chapter 7

Hypothesis Test Procedures
In this chapter, hypothesis test procedures used in the analysis are introduced. Section 7.1
outlines hypothesis test dedicated to new particle search in high energy physics. Section 7.2
introduces a maximum binned likelihood fit with a description of likelihood form used in the fit
to determine a parameter of interest and nuisance parameters. This is needed to calculate a test
statistic used in the analysis, profile likelihood ratio, introduced in Section 7.4. This likelihood
fit is applied at signal and control regions as shown in Chapter 6 and 9.
Section 7.3 describes the actual likelihood form for each strategies, Resolved, Boosted, andDiagonal. Section 7.4 introduces calculation of probability distribution of the test statistic byasymptotic formulae instead of a traditional MC sampling method. The probability distribution
is needed to calculate p-values used to quantitatively declare discovery or exclusion of new theory.

7.1

Hypothesis Test for New Particle Search

In high energy physics, to declare discovery of a new particle and exclusion of its existence,a hypothesis test is used that compares two hypotheses: a new particle doesn’t exists (called
null-hypothesis) and truly exists (called alternative-hypothesis). The hypothesis test provides
p-values, quantitative measures about how well null-hypothesis or alternative-hypothesis arematched to observed data. To do the hypothesis test, first one must calculate posterior probability each for the two hypotheses, and then must construct probability distributions of a test
statistic in each assumption that either null- or alternative-hypothesis is actually true. The test
statistic is a variable as a function of observed data that indicates which hypothesis is plausible,
so the test statistic should be chosen to be highly sensitive to null- or alternative-hypothesis.
Then, the probability distribution of the test statistic is integrated to calculate p-value. In the
recent high energy experiments, mainly two types of p-values are used, called CLb and CLs [114],
which are used for discovery and exclusion declaration of new theory, respectively.
CLb is defined as:
CLb =

Z 1

P rob(t|µsig = 0)dt,

(7.1)

tobs

where t is a test statistic, tobs is the one for observed data, P rob(t|µsig = 0) is a probability density
as function of t in the assumption that null-hypothesis is true, which is denoted by µsig =0, andµsig is a scale factor of signal cross section. When µsig = 1, it indicates that nominal signal
cross section predicted by a new theory is assumed, and when µsig = 0, it indicates signal cross89

section is assumed 0 (in other words assumes there is no new particle), so CLb is a probability
indicating how often the observation could happen if null-hypothesis is true. In high energy
and cosmological physics experiments, when one obtains CLb < 2.87 ⇥ 10 7 from a hypothesis

test, it is conventionally called ‘discovery’ of a new particle because the value indicates that theobserved data happened with an unnatural probability just only 2.87 ⇥ 10 7 if null-hypothesis istrue. Since the value 2.87⇥10 7 is sometimes inconvenient, p-value is conventionally transformed

to z-value. z-value is a quaintly of standard Gaussian distribution and p-value is expressed withz-value as follows:
p=

Z 1

1
p e
2⇡

z

x2
2

dx

For p-value (CLb ) = 2.87 ⇥ 10 7 , z-value = 5 , called 5(7.2)
discovery.

When observed CLb is relatively large (typically around 0.5), the null-hypothesis is considered

to be reasonable. Then, CLs value [114] is used to quantitatively declare how much alternativehypothesis could be realistic, which is defined as:
CLs+b
,
1 CLb

CLs =

(7.3)

where CLs+b is a posterior probability for the alternative-hypothesis defined as:
Z tobsCLs+b =
P rob(t|µsig = 1)dt.

(7.4)

1

In earlier times, CLs+b was a standard measure of exclusion of new theories, but this is not a goodmeasure when observed data has downward fluctuation with respect to background expectationand the signal expectation is relatively smaller than the background. CLs can be robust to theissue although CLs somewhat sacrifices the characteristic as probability in a mathematical sense.
When CLs < 0.05 is observed, one can declare that the alternative-hypothesis, the new theory
is excluded with 95% confidence level. The z-value for CLs = 0.05 corresponds to 1.64 .
Since µsig is a parameter that represents which hypothesis is assumed, it is called parameter ofinterest (POI). All parameters in the test statistic except for POI, called ‘nuisance parameters’,must be determined or marginalized by, for example, a profiling technique (see Section 7.4),
otherwise p-values cannot be calculated.

7.2

Binned Maximum Likelihood Fit

In the analysis, the observable is a set of number of events at each bin1 , and the observable ismodeled to consist of the SM events (backgrounds) and the signal events from a new theory.
Then, a binned likelihood form for the observable, which is frequently used in the analysis, isdenoted byL(n|µsig , µbkg , ↵) =Y

b2all histogram bins

P (nb |⌫b (µsig , µbkg , ↵)) ⇥Y

syst (↵i ),

(7.5)

i2↵

where n is a vector of each number of observed events at each bins (nb is b-th component of
the n), ↵ is a vector of the systematic parameters2 , µbkg is a vector of each scale factors of
1 For Resolved and Boosted, the observable is a set of number of events at SR, TCR, WCR, STCR, TZCR.
miss , m )For Diagonal, it is a set of number of events at each bin, all of which constitute the 2-dimensional (ETT

distribution.
2 The systematic parameters are standardized as ↵

i =

90

(↵raw
i

raw,mean

↵i

↵raw
i

)

.

each background cross section, P (nb |⌫b (µsig , µbkg , ↵)) is a poisson distribution of number of
events with the expected mean ⌫b (µsig , µbkg , ↵) at b-th bin, andsyst (↵) is a standard gaussian

distribution.
To perform a maximum likelihood fit to the observed data, ‘MINUIT’ [115] is used in theanalysis. The error and correlation of fitted parameters are calculated from hessian matrix ofthe log likelihood3 . One remarkable thing is that the uncertainty from the systematic e↵ect is
automatically propagated into the POI µsig with consideration of correlation among systematicparameters.
Another important characteristic of fit with the likelihood is that systematic parameter ↵i
is included in both its gaussian term and poisson term, meaning that systematic parameters
can be also correlated with observed number of events and thus can be constrained by not
only its gaussian term but also the poisson term. If a systematic e↵ect estimated before fit isstatistically too large compared to the observation, then the poisson term reduces the likelihoodscore drastically, resulting in a narrower error width of a systematic parameter after fit than
before fit. This e↵ect is called ‘profile e↵ect’4 and gets larger as the expected number of events
increases, so it can be interpreted such that the systematic e↵ect estimated before fit5 is more
precisely estimated by measurement (fit) with higher statistics.

7.3

Model Parameterization

In this section, the actual form of ⌫b (µsig , µbkg , ↵) in Equation 7.5 each for Resolved, Boosted,and Diagonal is introduced. For Resolved and Boosted, ⌫b (µsig , µbkg , ↵) can be explicitly written
down such as⌫b = ⌫bsig+ ⌫bttbar+ ⌫bwjets+ ⌫bsingletop+ ⌫bttV+ ⌫bzjets+ ⌫bdiboson

⇥
⇥
⇥
⇥
⇥
⇥
⇥

Y

sig
⌘i,b
(↵i )

⇥ µsig⌘ 0 i,b (↵i )ttbar⇥ µttbarwjets⇥ µwjets

i2↵

Y

i2↵

Y

⌘ 0 i,b (↵i )i2↵Ysingletop⌘ 0 i,b

(↵i )

i2↵

Y

ttV

⌘ 0 i,b (↵i )i2↵

Y⇥ µsingletop(7.6)⇥ µttV

zjets
⌘i,b
(↵i )

i2↵

Y

diboson
⌘i,b
(↵i )

i2↵

3 In the assumption that likelihood can be approximated by a multivariate gaussian distribution, log[L] /1(✓
2

ˆ T H(✓✓)

ˆ where ✓ is a vector of all model parameters and H =✓),the covariance matrix of parameters, V̂ = H

1.

@ 2 log L(n|✓ )@✓2, one can estimate✓ =✓ˆThe numerical calculation of hessian is done by ‘HEESE’

implemented in MINUIT [115].
4 In a di↵erent context, the word ‘profile’ is also used for a marginalization of all parameters except for POI
in a test statistic, described in Section 7.4.
5 Typically, the systematic e↵ect has been estimated with an early dataset that has lower statistics than thepdata stored up to now. It is also estimated with an extrapolation from measurement with Run-1 s = 7, 8 TeV
dataset but tends to have large uncertainty due to the extrapolation. The systematic parameters estimated inthese ways tend to be profiled.

91

for any b 2 SR, TVR, WCR, STCR, and just for TZCR:
Y sig
sig
⌫TZCR = ⌫TZCR⇥⌘i,TZCR (↵i )⇥ µsigi2↵

ttbar+ ⌫TZCRwjets+ ⌫TZCR

singletop+ ⌫TZCR
ttgamma+ ⌫TZCRzjets+ ⌫TZCR
diboson+ ⌫TZCR

where

⇥
⇥
⇥
⇥
⇥
⇥

Y

ttbar

⇥ µttbarwjets⇥ µwjets

singletop⇥ µsingletop⌘ 0 i,TZCR (↵i )i2↵

Y⌘ 0 i,TZCR (↵i )i2↵

Y⌘ 0 i,TZCR (↵i )i2↵

Yttgamma⌘ 0 i,TZCR (↵i )

i2↵

Y

(7.7)

⇥ µttVzjets⌘i,TZCR
(↵i )

i2↵

Y

diboson⌘i,TZCR
(↵i )

i2↵

X

ttbar

⌘ 0 i,b (↵i ) = 1

b2SR, TVR, WCR, STCR, TZCR

X

wjets

⌘ 0 i,b (↵i ) = 1

b2SR, TVR, WCR, STCR, TZCR

X

singletop⌘ 0 i,b(7.8)(↵i ) = 1

b2SR, TVR, WCR, STCR, TZCR

X

ttV

ttgamma⌘ 0 i,b (↵i ) + ⌘ 0 i,TZCR (↵i ) = 1

b2SR, TVR, WCR, STCR

for any i 2 ↵. Each of ⌫bsig , ⌫bttbar , ⌫bwjets , ⌫bsingletop , ⌫bttV , ⌫bdiboson is an expected mean yield for the

event at b bin, which is estimated with each MC sample. Each of µsig , µttbar , µwjets , µsingletop , µttV
ttbar

wjets

sig
is a scale factor shared at all bins for each event type6 . Each of ⌘i,b(↵i ), ⌘ 0 i,b (↵i ), ⌘ 0 i,b (↵i ),singletop⌘ 0 i,bttV

diboson(↵i ), ⌘ 0 i,b (↵i ), ⌘i,b(↵i ) is a scale factor at b bin for the event as a function of astandardized systematic parameter ↵i shared at all bins. The ⌘i,b (↵i ) function is modeled continuously with respect to ↵i by using an interpolation among three points: ⌘i,b (↵i = +1), ⌘i,b (↵i =0), ⌘i,b (↵i =1), which can be estimated by preparing three MC samples in each conditionof ↵i = 0, ↵i =1, and ↵i = +1. The interpolation used in the analysis is implemented in

HistFactory [116]. Figure 7.1 shows four types of interpolation implemented in HistFactory, anda combination of polynomial interpolation (inside ±1 ) and exponential extrapolation (outside±1 ) is used in the analysis (green line in Figure 7.1).

Equation 7.8 means that each systematic variation of tt̄, W +jets, singletop, and tt̄ + V /samples never changes total yield (sum of yields at all bins) of the sample by itself. Althoughsystematic e↵ects of course could change the total yield of the event, those changes are absorbed(or integrated) into the µ-parameters of the samples. This µ-absorption also reduces local minima
in the likelihood and makes fit more stable, so if precise measurement of total normalization ofa sample (or a bin that strongly constrains it) is possible, this µ-parameter technique should
be used7 . For Resolved and Boosted, TCR, WCR, STCR, and TZCR are prepared, and then6 Note that µ

at TZCR.
ttV is also shared by tt̄ +7 The reason why the signal term includes not only the scale factor µ

sig but also the unconserved systematic

sig
variations ⌘i,b(↵i ), not the conserved one, is that if systematic e↵ects on total yield of the signal are integrated

into µsig , then there is no way to invert the signal cross section from µsig and the hypothesis test doesn’t makesense in the case.

92

Figure 7.1: Comparison of the four interpolation options implemented in HistFactory [116] for
four di↵erent models (a)-(d). ⌘(↵) is a scale factor of expected mean of number of events at ahistogram bin as function of a standardized systematic parameter ↵. The given (modeled) sets of⌘(±1) before the interpolation are (a) ⌘( 1) = 0.8, ⌘(+1) = 1.2, (b) ⌘( 1) = 1.1, ⌘(+1) = 1.5,(c) ⌘( 1) = 0.2, ⌘(+1) = 1.8, (d) ⌘( 1) = 0.95, ⌘(+1) = 1.5. In this analysis, the combinationof polynomial-interpolation and exponential-extrapolation (green line) is used.

93

µttbar , µwjets , µsingletop , µttV are available. For diboson and Z+jets, it is a little bit difficult toprepare their control regions, but their contribution is very small, and hence their µ-parameters
are not provided.
In the same context, the model Parameterization for Diagonal can also be written down suchas:⌫b = ⌫bsig⇥+ ⌫bttbar1L⇥+ ⌫bttbarTau⇥+ ⌫bwjets⇥+ ⌫bsingletop⇥+ ⌫bttV⇥+ ⌫bdiboson

⇥

Y

sig
⌘i,b
(↵i )

⇥ µsigi2↵

Yttbar1L⌘ 0 i,b⇥ µttbar1L

(↵i )

i2↵

Y

ttbarTau⌘ 0 i,b

(↵i )

i2↵

Y

wjets
⌘i,b
(↵i )

(7.9)

i2↵

Y

⇥ µttbarTau

singletop
⌘i,b
(↵i )

i2↵

Y

ttV
⌘i,b
(↵i )

i2↵

Y

diboson
⌘i,b
(↵i )

i2↵

for any b 2 all histogram bins
where

X

ttbar1L⌘ 0 i,b(↵i ) = 1b2all histogram bins

X

ttbarTau⌘ 0 i,b

(7.10)(↵i ) = 1b2all histogram bins

for any i 2 ↵As discussed in Section 6.4, the dominant and subdominant backgrounds are tt̄ ! [b`⌫][bqq]and tt̄ ! [b`⌫][b⌧h ⌫], and their total normalizations can be determined precisely by TAUCR andmissthe mT shape at low ET
slices. Therefore there are µttbar1L and µttbarTau for tt̄ ! [b`⌫][bqq]and tt̄ ! [b`⌫][b⌧h ⌫]8 . In Diagonal, µwjets is dropped o↵ because from the fit tests with µwjets

configuration with WCR-like bins, it has turned out that the sensitivity doesn’t change withor without µwjets . This can be interpreted such as the contribution of W +jets events are verysmall in the signal-enhanced bins, and then the reduction of W +jets yield uncertainty by themeasurement (or fit) of µwjets is negligible. The contribution of singletop and tt̄ + V events arealso small in Diagonal, hence they are also not let have their µ scale factors. For Diagonal, thecontribution of Z+jets is ignorable and thus dropped o↵.
For implementation of the model described until here, HistFitter [117] has been used, which
provides a human-friendly interface to HistFactory [116] and RooStats [118]. The model building
is based on HistFactory, and the hypothesis test is based on RooStats.
8 The contributions of the other tt̄ decay modes is small, but their (E miss ,TmT ) shapes are relatively similar

to tt̄ ! [b`⌫][b⌧h ⌫]. Therefore, although the notation of ‘ttbarTau’ is used also for ⌫ and ⌘-parameter, they aremodeled by tt̄ samples excluding tt̄ ! [b`⌫][bqq] decay mode.

94

7.4

Profile Likelihood Ratio as Test Statistic

In the case where one compares just only two hypotheses each of which has neither unknown nor
undetermined parameters, choosing as a test statistic a ratio of ‘likelihood for the alternativehypothesis (µsig = 1)’ to ‘likelihood for the null-hypothesis (µsig = 0)’ is justified by NeymanPearson lemma [119] that assures that such a test statistic has the highest power for the test:=

L (n|µsig = 1).
L (n|µsig = 0)

(7.11)

Although including undetermined nuisance parameters in the likelihoods is required to model
the observable and therefore the likelihood ratio cannot be directly applied in the analysis, theundetermined nuisance parameters can be marginalized by using ‘profile likelihood ratio (PLR)’
defined as:(µsig ) =⇣⌘ˆˆ (µsig )ˆ bkg (µsig ), ↵L n µsig , µ̂ˆ)L (n |µ̂sig , µ̂bkg , ↵.

(7.12)

where parameters with single-hat mean that they are simply the best fitted values in the likelihood(Equation 7.5) and parameters with double hats mean that they are the best fitted values in acondition that µsig is fixed to a given value in the fit, practically 0 or 1. For a protection against
the unphysical µ̂sig , a modified PLR is defined as:
8 ✓◆ˆ bkg (µsig ),↵ˆ>L n µsig ,µ̂ˆ(µsig )
>
>
>
✓
◆
>
<
ˆ bkg (0),↵ˆ
L n 0,µ̂ˆ (0)˜ (µsig ) =✓◆>ˆ bkg (µsig ),↵ˆ>L n µsig ,µ̂ˆ (µsig )
>
>
⇣
⌘
>
:
L n µ̂sig ,µ̂bkg ,↵ˆ(µ̂sig < 0)(7.13)(µ̂sig0)

Probability distribution of the modified PLR can be analytically deduced from ‘asymptotic

formulae [120]’, which doesn’t need a traditional MC sampling method, so called Toy MC. In
Appendix B, the deduction of probability distribution from the asymptotic formulae is summarized. Finally, the probability distribution of the modified PLR is used in Equation 7.1 and 7.4
to calculate CLb and CLs+b , and then CLs in Equation 7.3 is also calculated.

95

Chapter 8

Systematic Uncertainties
This chapter introduces systematic uncertainties. Systematic uncertainties in the signal andthe SM-background models arise from experimental and theoretical sources. Those systematic
uncertainties are included as nuisance parameters in the likelihood fits as described in Section 7.2. Practically, the systematic uncertainties are incorporated into the analysis by modeling⌘-functions in Equation 7.6, 7.7, and 7.9 using MC samples with ↵ parameters varied to ±1
one by one. In this chapter, systematic e↵ects are directly indicated by ⌘-functions for Re-

solved and Boosted SRs. Since Diagonal analysis exploits the shape fit, in other words, multiple
missSR-like bins, this chapter only picks up a ⌘-function for MET3 3 bin (ET:[250, inf] GeV,mT :[150, 180] GeV) indicated in Figure 6.24, which is the most sensitive bin to the benchmark
signal model, (mt̃1 , m ˜01 ) = (400, 200) GeV. The detailed descriptions on ⌘-function modelingfor Diagonal are shown in Appendix C.
Since Resolved and Boosted analyses use only five regions (one SR and four CRs) and the
expected number of events in the regions are relatively small, constraints on systematic uncertainties via profile e↵ect is small as described in Section 7.2. From this reason, systematic sources
with small e↵ects on the observable are integrated into one enveloped systematic source1 . This
envelopment simplifies the fit and reduces numerical calculation cost.
Compared to Resolved and Boosted strategies, Diagonal strategy exploits 2-D shape fit to datawith relatively high statistics, and therefore some systematic uncertainties could be reduced
via the profile e↵ect described in Section 7.2. For exploiting the profile e↵ect properly, theenvelopment of systematic sources is avoided as much as possible in Diagonal strategy.
For the estimation of theoretical uncertainties, the MC samples without detector simulation
are produced to determine ⌘-functions at 0, ±1 because of limitation of computing resources. For
Diagonal, the MC samples for tt̄, single top, and W +jets events could be processed with detector

simulation thanks to some technical updates. Basically, ⌘(↵ = ±1) for theoretical uncertainties
are symmetrized, but only tt̄ theoretical uncertainties for Diagonal are not symmetrized2 .

MC statistical uncertainty on total expected events at each bin is also considered in the fit.
For a detailed description of the implementation, see Ref. [116].
1 The ‘enveloped’ systematic uncertainty is defined to be sum of systematic uncertainties in quadrature.
2 There are two technical reasons for symmetrization of theoretical uncertainties. For theoretical uncertainties

evaluated using samples without detector simulation, the larger deviation from ⌘(↵ = 0) is taken to make a symmetrized ⌘(↵ = ±1) for conservativeness. For relatively small systematic uncertainties, they are also symmetrized
in the same way to avoid having local minima in the fit.

96Section 8.1 describes uncertainties arising from experimental sources. Section 8.2-8.7 describes theoretical uncertainties specific to tt̄, single top, W +jets, diboson, tt̄ + V , and the signal
events, respectively. For theoretical uncertainties specific to tt̄ and single top, the estimation isbased on a dedicated study [69].

8.1

Experimental Sources

The dominant experimental uncertainties stem from imperfect knowledge of the jet energy scale(JES) and jet energy resolution (JER) [90], calibrations of the b-tagging efficiencies for b, c
missand light-flavor jets [121, 122], and the contribution of the ET
soft term, which is composedof tracks not associated with any reconstructed objects and not identified as originating frompileup.
For JES, there are 77 nuisance parameters (NPs) mainly arising from di↵erences among
in-situ JES measurements [89, 90]:
• 65 NPs for in-situ JES measurements using Z+jet, +jet, and multijet events.
• 3 NPs for pseudorapidity calibration.
• 1 NP for the behavior of high-pT jets in propagation of single hadron to jet.
• 4 NPs for pileup.
• 1 NP for b-jet response.
• 1 NP for lighter-flavor-jet response.
• 1 NP for lighter-flavor-jet composition.
• 1 NP for punch-through of jet.
For Diagonal, the 12 NPs described from the second to the last items are directly used, but the
65 NPs in the first item are enveloped and formed into 7 NPs (5 dominant eigenvectors and 2
residual terms). Furthermore, for Resolved and Boosted, these 77 NPs are combined into 4 NPs
as discussed in [123].
For JER, there are 9 NPs mainly arising from extrapolation from Run-1 JER measurements
to estimate Run-2 JER [90]:• 1 enveloped NP from in-situ JER measurements using di-jet and multijet events in Run-1.
• 7 NPs from Run-1 and Run-2 cross calibrations.
• 1 NP from Run-1 calibration of forward region.
For Diagonal, all the 9 NPs are directly used. For Resolved and Boosted, the 9 NPs are combined
into 1 NP.
For calibrations of the b-tagging efficiency, there are 25 NPs enveloping efficiency measurements at each jet pT bin as derived in [121, 122]:• 5 NPs for efficiency for b-jet.
• 1 NP for extrapolated efficiency for high-pT b-jet.
97• 4 NPs for efficiency for c-jet.
• 1 NP for extrapolated efficiency for high-pT c-jet.
• 14 NPs for efficiency for lighter-flavor-jet.
For Diagonal, all the 25 NPs are directly used. For Resolved and Boosted, 1 enveloped NP
combining the 5 NPs for b-jet, 1 enveloped NP combining the 4 NPs for c-jet, and 1 enveloped
NP combining the 14 NPs for lighter-flavor-jet are used, and the high-pT b/c-jet NPs are directly
used.
miss
For ETsoft term, there are 3 NPs:

• 1 NP for perpendicular resolution• 1 NP for parallel resolution• 1 NP for energy scale
For all the strategies, they are directly used. These experimental uncertainties for the dominantbackgrounds, tt̄ (Resolved), tt̄ + Z (Boosted), and tt̄ (1L1⌧h ) (Diagonal) events, are summarizedin Table 8.1.
Other sources of experimental uncertainty are the modeling of lepton-related sources (efficiencies of reconstruction, identification, and isolation), photon identification, hadronic-tau-related
sources (energy scale and efficiency of identification), and the uncertainty in the integrated luminosity. However, their impacts on the final results are found negligibly small. For Diagonal,
they are still included while are not consider for Resolved and Boosted.

98

Table 8.1: ⌘-functions with respect to JES, JER, b-tagging, and ETmiss soft term uncertainties at ↵ = ±1

for dominant backgrounds, tt̄ in Resolved SR, tt̄ + Z in Boosted SR, and tt̄ (1L1⌧h ) event in Diagonal
MET3 3 bin. The values are rounded o↵ to three decimal places.
sourceResolved SRtt̄⌘ 0 (↵ = ±1)

Boosted SR
tt̄ + Z

1[%]
JES

⌘ 0 (↵ = ±1)

Diagonal MET3 3 bintt̄ (1L1⌧h )

1[%]⌘ 0 (↵ = ±1)

1[%]

Enveloped NP 1--

Enveloped NP 2--

1.40 / + 0.99

Enveloped NP 3--

0.49 / + 0.29

Enveloped NP 4--

0.79 / + 0.47

Enveloped NP 5--

0.02 / + 0.05

+2.25 /

2.91

Enveloped NP 6--

0.04 /

Pseudorapidity Calibration 1--

0.24 / + 0.29

0.15

Pseudorapidity Calibration 2--

0.18 /

Pseudorapidity Calibration 3--0.26 / + 0.01

High-pT Jet--+0.00 / + 0.00

Pileup 1--

0.77 / + 0.48

Pileup 2--

0.29 / + 0.32

Pileup 3--+0.18 / + 0.05

Pileup 4--+0.16 /

0.35

0.62

B-Jet Response--+0.00 / + 0.00

Lighter-Flavor-Jet Response--+0.37 /

Lighter-Flavor-Jet Composition--

Punch Through--Strongly Enveloped NP 1

+1.90 / + 4.04

0.75

-

Strongly Enveloped NP 2

3.37 / + 3.43

+0.69 / + 1.90-

Strongly Enveloped NP 3

0.47 / + 2.74

+0.48 / + 1.41-

Enveloped NP--

Cross Calibration 1--

Cross Calibration 2--+1.20 / + 0.47

Cross Calibration 3--0.32 / + 0.44

Cross Calibration 4--

Cross Calibration 5--+0.13 /

Cross Calibration 6--+0.16 / + 0.17

Cross Calibration 7--0.28 / + 0.74

+1.66 /

0.76

1.50 / + 1.48
+0.03 /

0.09

JER

Forward Region
Strongly Enveloped NP+4.99 /

+3.34 /

0.39

0.78 /

0.44

0.08 / + 0.15

5.27

+4.02 /

+1.05 /
3.50

0.64

0.34

-

B-Tag
B-Jet 1--0.34 / + 0.32

B-Jet 2--0.14 / + 0.14

B-Jet 3--0.10 / + 0.10

B-Jet 4--0.08 / + 0.08

B-Jet 5
Enveloped B-Jet+0.43 /

0.03

+1.57 /

table continued on next page99

0.00 / + 0.01
1.64-

source

Resolved SR

Boosted SRtt̄
High-pT B-Jet⌘ 0 (↵ = ±1)+1.33 /

tt̄ + Z1[%]0.71

⌘ 0 (↵ = ±1)+0.36 /

Diagonal MET3 3 bintt̄ (1L1⌧h )

1[%]
0.24

⌘ 0 (↵ = ±1)+0.17 /

1[%]
0.17

C-Jet 1--

C-Jet 2--+0.01 /

0.01

C-Jet 3--+0.01 /

0.01

C-Jet 4--

Enveloped C-Jet+0.18 / + 0.50

+0.26 /

0.10-

High-pT C-Jet+0.00 / + 0.68

+0.00 / + 0.17

+0.06 /

0.06

Lighter-Flavor-Jet 1--+0.23 /

0.24

Lighter-Flavor-Jet 2--

0.00 / + 0.00

Lighter-Flavor-Jet 3--

0.02 / + 0.02

Lighter-Flavor-Jet 4--

0.01 / + 0.01

Lighter-Flavor-Jet 5--

0.01 / + 0.01

Lighter-Flavor-Jet 6--+0.00 /

0.00

Lighter-Flavor-Jet 7--+0.01 /

0.00

Lighter-Flavor-Jet 8--+0.00 /

0.00

Lighter-Flavor-Jet 9--

Lighter-Flavor-Jet 10--+0.00 /

0.00

Lighter-Flavor-Jet 11--+0.00 /

0.00

Lighter-Flavor-Jet 12--+0.00 /

0.00

Lighter-Flavor-Jet 13--+0.00 / + 0.00

Lighter-Flavor-Jet 14--+0.00 / + 0.00

+0.10 / + 0.06-

Enveloped Lighter-Flavor-Jet+1.84 /

1.25

0.02 / + 0.01

0.00 / + 0.00

0.00 / + 0.00

missET
soft term

Parallel Resolution+0.49 /

0.48

+0.37 /

0.37

0.49 / + 0.49

Perpendicular Resolution+0.64 /

0.63

+0.12 /

0.12

0.47 / + 0.46

Energy Scale+0.25 / + 0.37

100

+0.32 / + 0.03

0.48 /

0.13

8.2

tt̄

The uncertainty of radiation modeling is estimated by varying factorization scale, renormalization
scale and resummation damping factor hdamp in Powheg-Box + Pythia63 . This uncertainty
includes uncertainties due to missing higher order terms in NLO MC samples. The uncertaintyof hadronization modeling is estimated by a comparison of the nominal configuration PowhegBox + Pythia6 and Powheg-Box + Herwig++ sample. For Diagonal, this uncertainty is
not taken into account because this e↵ect is relatively smaller than others. The uncertainty ofparton shower tuning and ME+PS matching is studied by comparing Powheg-Box + Pythia6
to Powheg-Box + Pythia8 samples. Table 8.2 shows ⌘-functions of tt̄ at ↵ = ±1 for Resolved
and Boosted SRs and Diagonal MET3 3 bin.

sourceResolved SR

Boosted SR

tt̄

tt̄

0

⌘ (↵ = ±1)

Radiation
Hadronization
Parton Shower

Diagonal MET3 3 bin

1[%]

±9.1

tt̄ (1L1⌧h )0⌘ (↵ = ±1)

1[%]

±10.2

±7.7

0

⌘ (↵ = ±1)+19.2 /

±7.4-

tt̄ (1L)
0⌘ (↵ = ±1)

1[%]
4.5

+13.5 / + 4.5--+1.3 /

1[%]

1.6+4.4 /

5.1

Table 8.2: ⌘-functions of tt̄ at ↵ = ±1 for Resolved and Boosted SRs and Diagonal MET3 3 bin. The values arerounded o↵ to three decimal places.

8.3

Single Top

Systematic uncertainties of radiation and hadronization tuning are estimated in the same wayof tt̄. Additionally, an uncertainty on interference between W t and tt̄ [124] is estimated by comparing the nominal tt̄ and W t sample with an W W bb sample generated via MG5 aMC@NLO.
Table 8.3 shows ⌘-functions of single top at ↵ = ±1 for Resolved and Boosted SRs and Diagonal
MET3 3 bin.

sourceResolved SR
0

Radiation
Hadronization
Interference⌘ (↵ = ±1)

±9.2

1[%]

Boosted SR0⌘ (↵ = ±1)

1[%]

±25.2

±9.0

±11.2

±34.6

±62.2

Diagonal MET3 3 bin⌘(↵ = ±1)

1[%]

±3.3
-

±69.5

Table 8.3: ⌘-functions of single top at ↵ = ±1 for Resolved and Boosted SRs and Diagonal
MET3 3 bin. The values are rounded o↵ to three decimal places.

3 For the low radiation tuning, factorization scale, renormalization scale, and an resummation damping factor

hdamp are simultaneously varied by a factor of 2, 2, and 1, respectively, and for the high radiation tuning, 0.5, 0.5,
and 2, respectively. hdamp controls the ME/PS matching in Powheg-Box and e↵ectively regulates the high-pT
radiation and is set to mtop for the nominal samples. The configurations of the high/low radiation tunings are
determined so that di↵erences between data and MC can be explained by radiation tuning as discussed in Ref.[69].

101

8.4

W +jets

For W +jets, the samples to estimate systematic uncertainties have been generated with Sherpa.
By varying renormalization scale, factorization scale, resummation scale and CKKW scale 4 bya factor of 2 and 0.5, respectively, these 4 systematic uncertainties are estimated. These 4
systematic uncertainties are integrated into one enveloped systematic uncertainty for Resolved
and Boosted. Table 8.3 shows ⌘-functions of W +jets at ↵ = ±1 for Resolved and Boosted SRs
and Diagonal MET3 3 bin.
sourceResolved SR0

CKKWFactorization
Renormalization
Resummation
Enveloped⌘ (↵ = ±1)

±1.4

1[%]

Boosted SR0⌘ (↵ = ±1)

±0.8

±3.4

±0.5

±3.1

±0.0

±0.7

±0.4

±4.9

±1.0

1[%]

Diagonal MET3 3 bin⌘(↵ = ±1)

1[%]

±13.4
±13.8
±36.0
±11.5
-

Table 8.4: ⌘-functions of W +jets at ↵ = ±1 for Resolved and Boosted SRs and Diagonal MET3 3bin. The values are rounded o↵ to three decimal places.

The W +jets background is normalized in WCR requiring b-veto in Resolved and Boosted. The
W +heavy-flavor components are coherently scaled by the whole W +jets process modeled by MC.
Therefore, an uncertainty on fraction of yields of W +light, W + c(c) and W + b(b) is additionallyimposed for Resolved and Boosted because the b-veto region is used in these strategies. This
uncertainty has been set to 30% on Resolved and Boosted SRs and is used independently of theenveloped uncertainty [126, 127].

8.5

DibosonDiboson samples are generated via Sherpa, and uncertainties from renormalization, factorization
and resummation scale are evaluated in the same way of W/Z+jets. Diboson samples are notnormalized in a control region, but use the predicted cross section. Hence the cross section
uncertainty 6% is considered, which has been estimated from a Run-1 measurement of crosssection [128]. For Resolved and Boosted, these uncertainties are integrated into one enveloped
systematic uncertainty. Table 8.5 shows diboson theoretical uncertainties for all signal regions.

8.6

tt̄ + VThe method to estimate tt̄ + Z background described here comes from a dedicated study [26].
Since the tt̄+Z background is normalized using tt̄+ at the TZCR, the uncertainties are evaluatedby simultaneously varying parameters of tt̄+ and tt̄+Z samples. An uncertainty due to radiation
tuning is estimated by simultaneously varying the renormalization and factorization scales of
4 CKKW is a scheme of merging between matrix-element and parton-shower [125] used in Sherpa generator,

and the parameter defines which phase-space regions are populated by matrix elements and which ones by parton
showers102

source
Factorization

Resolved SR⌘(↵ = ±1)

1[%]

±3.8

Renormalization

Boosted SR⌘(↵ = ±1)

±6.7

±19.1

±19.0

±6.0

±6.0

±9.3

Resummation
Cross-section⌘(↵ = ±1)

±1.1

±22.4

Enveloped

1[%]

Diagonal MET3 3 bin

±23.5

1[%]

±10.7
±26.8
±7.3
±6.0
-

Table 8.5: ⌘-functions of diboson at ↵ = ±1 for Resolved and Boosted SRs and Diagonal MET3 3bin. The values are rounded o↵ to three decimal places.

tt̄ + Z and tt̄ + events generated at LO by a factor of 2 and 0.5. The impact of the scale choices
is di↵erent between tt̄ + Z and tt̄ +for high-pT bosons, leading to a 10% uncertainty. Since thenominal samples are generated at LO, an uncertainty due to NLO corrections is estimated froma study of the kinematic dependency of the ratio between tt̄ + Z and tt̄ +cross-section factors.

The kinematic dependency of the ratio is studied by calculating a cross-section factor for thett̄ + Z and tt̄ +processes using MG5 aMC@NLO and Sherpa + OpenLoops as a function of

the boson pT , comparing the nominal generator setup with a series of variations, resulting in a
5% uncertainty. Comparing the results using the NNPDF and the CT14 [129] PDF varies ratioof the cross-section factor by less than 2%. An additional uncertainty due to an EW correction
is 5%, which is estimated from a di↵erence in two ratios of cross-section factor for tt̄ +and

tt̄ + Z between MG5 aMC@NLO and Sherpa + OpenLoops when the same scale and PDF
set is used.
These uncertainties are integrated into one enveloped uncertainty amount to 12% on Resolved
and Boosted SRs (⌘ 0 (↵ = ±1)
For Diagonal, tt̄ +1 = ±0.12).

is not used to estimate tt̄ + Z background. Therefore the theoreticaluncertainty simply stems from tt̄ + Z modeling. The uncertainty on radiation and factorization
scales is estimated by varying a factor of 2 and 0.5, resulting in ⌘(↵ = ±1)
Diagonal MET3 3 bin.

8.7

1 = ±5.80% at

SignalThe signal cross-section uncertainties shown in Figure 3.1 are considered but not via ⌘-functions.
The hypothesis test is done three times with fixing cross-section at nominal, +1 , and1

conditions, respectively. For the three conditions, three CLs exclusion contours are drawn. For
example, CLs = 0.05 contour with the +1 condition is drawn by interpolating CLs values at
all mass points which are calculated in the +1 condition.

103

Chapter 9

Results
This chapter presents results of Resolved, Boosted, and Diagonal analyses. For each analysis, theresults of background-only fit described in Chapter 6 are shown in detail, and then CLs exclusion
limits at 95% confidence level (95% CL) are presented in the (mt̃1 , m ˜01 ) plane. Contours of 95%
CL are derived by interpolating CLs values evaluated at all the signal points shown in Figure 1.8
Section 9.1 describes Resolved and Boosted results. Section 9.2 presents Diagonal results. Section 9.3 shows CLs limits combining Resolved, Boosted, and Diagonal results. Finally, Section 9.4
discusses future prospects of this study.

9.1

Results for Resolved and Boosted

The parameters and correlations after the background-only fit1 in Resolved and Boosted areshown in Figure 9.1

9.4. As indicated in Figure 9.1 and 9.3, there are no significant issue inthe fitted parameters in Resolved and Boosted, that is, uncertainties obtained from the fit arealmost the same as the input values and background normalization factor µsig are determined
properly from CRs.
One thing to be noted is that the fitted µttV is around 1.5. Although there are some correlations between µttV and other parameters as shown in Figure 9.2 and 9.4, all the systematicparameters shown in Figure 9.1 and 9.3 are almost at 0, therefore such a large value could not be
due to these parameters. Since there is no significant evidence of mis-modeling of the shapes ofthe various distributions and their deviations from the expectation are within uncertainties, thisissue is not significant for the data with 28.0 fb 1 . but may be a future problem to be solved in
an analysis with higher statistics.
The number of observed events for Resolved and Boosted are shown in Table 9.1 and 9.2, andthe SRs with the VRs are also shown in Figure 9.5. The prediction of number of background
events is obtained using the background-only fit configuration. In Resolved (Boosted) SR, 63 (8)events are observed and the mean of total number of background events predicted by the fit is
51 ± 7 (8 ± 3), and poisson upward/downward fluctuation from the mean is +8/ 7 (+4/ 3).
1 As described in Chapter 6, the background-only fit is a fit with a background-only model (µsig is fixed to 0)

and only CRs. The fit results are applied in the plots in Chapter 6 that shows distributions at CRs and VRs for
Resolved and Boosted. As shown in Section 6.3, there is no significant insanity in distributions at VRs after the
background-only fit and then it has concluded that the SRs can be unblinded.

104

miss
Figure 9.6 shows mT , ET
, and amT2 distributions at Resolved and Boosted SRs after the

background-only fit.
To evaluate how plausible the prediction of the background-only fit is, CLb and its z-value
are calculated by a model independent discovery hypothesis test [117]. Since the choice of the(modified) PLR (Equation 7.13) as test statistic in the analysis requires the best fitted valueof µsig (µ̂sig ), a dummy signal model is used, which is defined to expect just one signal event
at SR for µsig = 1. Since the dummy signal model is incorporated into the likelihood without
any systematic uncertainties on the dummy signal model, the µsig is treated as a measure of adi↵erence between data and the SM-only model at SR. From this context, it is called modelindependent test. The model-independent test is only valid for CLb calculation because of thedummy signal model. This cannot be applied to the shape fit of Diagonal (or a fit with more than
two SRs) because it is impossible to define model-independent shape of a dummy signal model.
The observed CLb and its z-value obtained by the model independent discovery hypothesis test
are 0.098 and 1.29

for Resolved, and 0.487 and 0.032

for Boosted. This concludes that there

is no significant deviation from the SM-only model in Resolved and Boosted analyses.
To evaluate how much the signal models are excluded, CLs exclusion limits at 95% CL arederived each from the Resolved and Boosted analyses, shown in Figure 9.7 and 9.9. In the
exclusion test of Resolved, µ̂sig for the benchmark mass point, (mt̃1 , m ˜01 ) = (600, 300) GeV, is0.37 ± 0.28, and the CLs value and the z-value are 0.0063 and 2.50

(excluded at 99.37% CL). In

the exclusion test of Boosted, µ̂sig for the benchmark mass point, (mt̃1 , m ˜01 ) = (1000, 1) GeV, is0.01 ± 0.45, and the CLs value and the z-value are 0.0619 and 1.54

(excluded at 93.81% CL).

The mass points used to draw the contours are shown with the observed CLs values in Figure 9.8
and 9.10. The mass points with stop mass lower than 400 GeV are not used for Resolved and
Boosted but for Diagonal, because Diagonal analysis explicitly provides the better results aroundthe region. For Resolved and Boosted, the observed CLs limit is almost within the ±1 band of

the expected CLs . The Resolved result excludes up to (mt̃1 , m ˜01 ) = (700, 350) GeV, which is00
the excluded t̃1 ! t ˜1 model with the highest ˜1 mass in Resolved region. The Boosted result0
excludes the t̃1 ! t ˜1 model with the mt̃1 . 980 GeV for m ˜01 . 300 GeV and (mt̃1 , m ˜01 ) =(900, 350) GeV,105

Resolved channel

TCR

WCR

STCR

TZCR

TVR

WVR

SR

Observed events

1861

4664

545

363

345

523

63

Fitted bkg events

1860.99 ± 43.34

4663.72 ± 68.91 545.09 ± 23.30 362.94 ± 19.08 317.56 ± 29.69 546.52 ± 72.12 51.01 ± 5.38

Fitted tt̄ events

1512.55 ± 54.36

915.39 ± 170.48 251.07 ± 23.47

12.55 ± 2.03 266.02 ± 28.35 128.43 ± 27.62 17.93 ± 2.79

129.10 ± 31.03

119.32 ± 46.30 220.41 ± 43.57

5.98 ± 1.85

Fitted W +jets events
Fitted single top events
Fitted tt̄ + Z events
Fitted diboson events
Fitted Z+jets events
Fitted tt̄ +events

174.39 ± 30.94 3327.66 ± 237.60
25.94 ± 2.00

13.57 ± 2.73

16.73 ± 1.47

25.14 ± 22.39

0.65 ± 0.58

17.49 ± 3.83

262.64 ± 55.44

0.00 ± 0.00

0.00 ± 0.00

1.52 ± 1.38

50.92 ± 11.51

5.30 ± 1.30

0.17 ± 0.06

20.37 ± 4.98 349.10 ± 60.50

3.61 ± 0.31

6.14 ± 0.74

0.27 ± 0.06
0.32 ± 0.29

0.00 ± 0.00 340.03 ± 19.23

5.12 ± 2.07

22.92 ± 5.75

17.29 ± 6.93

2.00 ± 0.44

45.52 ± 9.84

2.55 ± 0.83

0.00 ± 0.00

0.00 ± 0.00

0.00 ± 0.00

0.11 ± 0.10

6.21 ± 2.78

2.58 ± 0.68 17.94 ± 2.79
3.61 ± 3.30

1.25 ± 1.14

MC exp. SM events

1855.61 ± 72.04 5818.76 ± 270.24 548.06 ± 50.66 244.45 ± 13.50 312.14 ± 31.52 665.82 ± 93.62 46.01 ± 5.33

MC exp. tt̄ events

1452.96 ± 51.28

879.58 ± 154.86 241.51 ± 26.83

12.06 ± 1.81 255.31 ± 28.03 123.28 ± 25.77 17.24 ± 2.65

128.96 ± 4.17

119.42 ± 20.81 220.14 ± 20.36

6.01 ± 1.62

17.52 ± 3.86

262.41 ± 55.79

0.00 ± 0.00

0.00 ± 0.00

MC exp. W +jets events
MC exp. single top events
MC exp. tt̄ + Z events
MC exp. diboson events
MC exp. Z+jets events
MC exp. tt̄ +events237.65 ± 25.78 4523.42 ± 138.70
17.02 ± 0.54
1.51 ± 1.39

69.48 ± 10.63

8.91 ± 1.55

10.98 ± 0.79

25.02 ± 22.53

0.65 ± 0.59

5.30 ± 1.31

0.24 ± 0.07

27.75 ± 5.48 474.42 ± 72.34

2.37 ± 0.21

4.03 ± 0.35

0.27 ± 0.06
0.31 ± 0.29

0.00 ± 0.00 223.18 ± 11.41

6.98 ± 2.64

22.94 ± 2.11

17.33 ± 3.58

2.00 ± 0.45

45.52 ± 9.90

2.56 ± 0.84

0.00 ± 0.00

0.00 ± 0.00

0.00 ± 0.00

0.11 ± 0.10

6.20 ± 2.32

1.70 ± 0.40 11.76 ± 1.60
3.57 ± 3.29

1.25 ± 1.15

Table 9.1: Number of observed events and the mean of background yields predicted before andafter fit in Resolved for an integrated luminosity of 28.0 fb 1 . The mean values are obtained
from the associated control regions (TCR, WCR, STCR, TZCR) using the background-only fit.
Uncertainties on the mean values are shown and calculated by linearly propagating uncertainties
of all the model parameters (for fitted events, correlations calculated by the fit are also considered). Uncertainties on the fitted yields are symmetric by construction, where the negative error
is truncated when reaching to zero event yield.

Boosted channel

TCR

WCR

STCR

TZCR

TVR

WVR

SR

Observed events

309

902

174

369

39

68

8

Fitted bkg events

309.05 ± 17.58

902.17 ± 30.12

174.04 ± 13.13

369.21 ± 19.24

30.60 ± 6.21

73.79 ± 18.33

8.11 ± 1.52

Fitted tt̄ events

229.86 ± 26.35

73.38 ± 23.40

54.57 ± 10.22

11.22 ± 2.09

24.11 ± 5.66

6.44 ± 2.22

1.10 ± 0.44

26.45 ± 20.70

91.73 ± 20.06

8.09 ± 3.04

2.32 ± 1.94

2.85 ± 2.28

1.20 ± 0.89

4.17 ± 1.33

69.44 ± 20.72

2.08 ± 0.72

0.00 ± 0.00

0.00 ± 0.00

Fitted W +jets events
Fitted single top events
Fitted tt̄ + Z events
Fitted diboson events
Fitted Z+jets events
Fitted tt̄ +eventsMC exp. SM events
MC exp. tt̄ events
MC exp. W +jets events
MC exp. single top events
MC exp. tt̄ + Z events
MC exp. diboson events
MC exp. Z+jets events
MC exp. tt̄ +events32.12 ± 11.16

727.66 ± 50.20

5.71 ± 0.81

2.09 ± 0.49

37.07 ± 16.57

0.13 ± 0.12

328.65 ± 20.76
249.96 ± 9.58

3.15 ± 2.81

0.19 ± 0.18

3.44 ± 0.31
0.27 ± 0.08
0.31 ± 0.28

2.65 ± 0.99

56.76 ± 18.35

1.06 ± 0.22

0.28 ± 0.09

0.45 ± 0.23
0.01 ± 0.00

345.69 ± 19.48

1129.83 ± 58.04

161.76 ± 19.38

253.47 ± 13.58

32.58 ± 5.76

79.79 ± 22.56

59.40 ± 8.06

12.22 ± 1.65

26.17 ± 4.86

20.11 ± 13.21

70.37 ± 8.10

6.25 ± 1.69

1.76 ± 1.46

955.88 ± 37.74

3.83 ± 0.51

1.40 ± 0.30

4.19 ± 1.34

69.50 ± 20.87

0.00 ± 0.00

0.00 ± 0.00

0.13 ± 0.12

5.88 ± 0.93

0.19 ± 0.06

0.00 ± 0.00

42.22 ± 13.61
28.32 ± 9.13

19.58 ± 7.53

3.14 ± 2.83

25.77 ± 9.08
3.95 ± 0.60
2.08 ± 0.72
0.19 ± 0.18
0.00 ± 0.00

0.25 ± 0.07
2.31 ± 0.22
0.27 ± 0.08
0.31 ± 0.28

231.86 ± 11.45

0.00 ± 0.00

6.96 ± 2.12
0.51 ± 0.46
0.00 ± 0.00

0.06 ± 0.06
0.00 ± 0.00

6.99 ± 2.12

1.20 ± 0.42

2.15 ± 1.52

0.91 ± 0.61

0.71 ± 0.14

0.19 ± 0.06

0.00 ± 0.00

1.28 ± 0.56

6.95 ± 1.42

74.37 ± 23.23

0.01 ± 0.00

3.67 ± 0.69

91.17 ± 24.03

3.48 ± 1.19

0.45 ± 0.23

0.78 ± 0.39

6.97 ± 2.13
0.50 ± 0.46
0.00 ± 0.00

1.02 ± 0.47
2.46 ± 0.42
1.29 ± 0.56
0.06 ± 0.06
0.00 ± 0.00

Table 9.2: Number of observed events and the mean of background yields predicted before andafter fit in Boosted for an integrated luminosity of 28.0 fb 1 . The mean values are obtained
from the associated control regions (TCR, WCR, STCR, TZCR) using the background-only fit.
Uncertainties on the mean values are shown and calculated by linearly propagating uncertainties
of all the model parameters (for fitted events, correlations calculated by the fit are also considered). Uncertainties on the fitted yields are symmetric by construction, where the negative error
is truncated when reaching to zero event yield.

106

µ(singletop)-1µ(wjets)-1µ(ttbar)-1µ(ttV)-1

ttbar+Z Modelingw+jets Heavy-Flavour Extrapolation

w+jets Modelingsingletop Interference

ttbar Hadronization

ttbar & singletop Radiation

T

B-Tag Enveloped Lighter-Flavor-Jet

B-Tag High-p C-Jet

T

B-Tag Enveloped C-Jet

B-Tag High-p B-Jet

Energy Scale

B-Tag Enveloped B-Jet

miss

ET

Parallel Resolution

miss
ET Perpendicular Resolution

ET

miss

JER Strongly Enveloped NP

JES Strongly Enveloped NP 3

JES Strongly Enveloped NP 2

JES Strongly Enveloped NP 1

Uncertainty After Fit

2
1.5
1
0.5
0
−0.5
−1
−1.5
−2

Figure 9.1: Model parameters and their uncertainties after the background-only fit for Resolved.
The vertical dashed-dotted line divides into two categories: standardized systematic parameters(left) and normalization scale factors (right). The naming rule of systematic parameters follow
Table 8.1 8.5. For the detailed explanation on the fit configuration, see Section 7.2.

h_corr_reduced (threshold 20 precent)1

JES Strongly Enveloped NP 1

1.00

0.00

0.00

0.00

0.00

-0.00

-0.00

-0.00

0.06

B-Tag Enveloped B-Jet

0.00

1.00

0.00

0.00

0.00

-0.00

0.00

-0.00

-0.26

0.04

0.56

-0.47

B-Tag High-p B-Jet

0.00

0.00

1.00

0.00

0.00

-0.00

0.00

-0.00

-0.04

-0.13

0.16

-0.24

B-Tag Enveloped C-Jet

0.00

0.00

0.00

1.00

-0.00

-0.00

0.00

-0.00

-0.01

-0.24

0.19

-0.18

T

-0.21

0.11

-0.01

B-Tag Enveloped Lighter-Flavor-Jet

0.00

0.00

0.00

-0.00

1.00

-0.00

0.00

-0.01

0.11

-0.27

0.40

-0.48

ttbar & singletop Radiation

-0.00

-0.00

-0.00

-0.00

-0.00

1.00

0.00

0.00

0.02

0.25

-0.53

-0.46

0.00

0.00

0.00

0.00

0.00

1.00

0.00

0.00

-0.36

-0.06

0.10

0.09

-0.12

0.10

-0.02

0.06

µ (ttbar)

-0.21

0.04

-0.13

-0.24

-0.27

0.25

-0.36

-0.46

0.10

1.00

-0.35

-0.03

µ (wjets)

0.11

0.56

0.16

0.19

0.40

-0.53

-0.06

0.09

-0.02

-0.35

1.00

-0.30

µ (singletop)

-0.01

-0.47

-0.24

-0.18

-0.48

-0.46

0.10

-0.12

0.06

-0.03

-0.30

1.00
µ (singletop)

-0.46

1.00

µ (wjets)

0.02

0.02

µ (ttbar)

1.00

0.00

µ (ttV)

0.00

0.02

w+jets Heavy-Flavour Extrapolation

0.00

0.11

singletop Interference

-0.01

-0.01

ttbar & singletop Radiation

-0.00

-0.04

B-Tag Enveloped Lighter-Flavor-Jet

-0.00

-0.26

B-Tag Enveloped C-Jet

-0.00

0.06

B-Tag High-p B-Jet-0.00µ (ttV)

B-Tag Enveloped B-Jet-0.00

JES Strongly Enveloped NP 1

singletop Interference
w+jets Heavy-Flavour Extrapolation

0.8
0.6
0.4
0.2
0
−0.2

T

−0.4

Figure 9.2: Correlations among model parameters after the background-only fit for Resolved.
Only parameters with at least one correlation of more than 0.2 are shown. The naming rule ofsystematic parameters follow Table 8.1 8.5. For the detailed explanation on the fit configuration,see Section 7.2.

107

µ(singletop)-1µ(wjets)-1µ(ttbar)-1µ(ttV)-1

ttbar+Z Modelingw+jets Heavy-Flavour Extrapolation

w+jets Modelingsingletop Interference

ttbar Hadronization

ttbar & singletop Radiation

T

B-Tag Enveloped Lighter-Flavor-Jet

B-Tag High-p C-Jet

T

B-Tag Enveloped C-Jet

B-Tag High-p B-Jet

Energy Scale

B-Tag Enveloped B-Jet

miss

ET

Parallel Resolution

miss
ET Perpendicular Resolution

miss

ET

JER Strongly Enveloped NP

JES Strongly Enveloped NP 3

JES Strongly Enveloped NP 2

JES Strongly Enveloped NP 1

Uncertainty After Fit

2
1.5
1
0.5
0
−0.5
−1
−1.5
−2

Figure 9.3: Model parameters and their uncertainties after the background-only fit for Boosted.
The vertical dashed-dotted line divides into two categories: standardized systematic parameters(left) and normalization scale factors (right). The naming rule of systematic parameters follow
Table 8.1 8.5. For the detailed explanation on the fit configuration, see Section 7.2.

h_corr_reduced (threshold 20 precent)1

B-Tag Enveloped B-Jet

1.00

0.00

-0.00

0.00

0.00

-0.00

0.00

-0.27

-0.14

0.39

-0.43

B-Tag High-p B-Jet

0.00

1.00

-0.00

0.00

0.00

-0.00

0.00

-0.04

0.09

0.19

-0.36

B-Tag Enveloped Lighter-Flavor-Jet

-0.00

-0.00

1.00

0.00

0.00

-0.00

0.00

0.09

-0.06

0.39

-0.37

ttbar & singletop Radiation

0.00

0.00

0.00

1.00

0.00

0.00

-0.00

0.00

0.05

-0.24

-0.08

T

0.8
0.6

singletop Interference

0.00

0.00

0.00

0.00

1.00

0.00

-0.00

0.01

-0.43

-0.22

0.13

w+jets Heavy-Flavour Extrapolation

-0.00

-0.00

-0.00

0.00

0.00

1.00

0.00

0.03

-0.29

0.06

-0.16

diboson Modeling

0.00

0.00

0.00

-0.00

-0.00

0.00

1.00

-0.00

-0.01

-0.23

0.00

0.4

µ (ttV)

-0.27

-0.04

0.09

0.00

0.01

0.03

-0.00

1.00

0.13

0.14

0.00

µ (ttbar)

-0.14

0.09

-0.06

0.05

-0.43

-0.29

-0.01

0.13

1.00

0.01

-0.29

µ (wjets)

0.39

0.19

0.39

-0.24

-0.22

0.06

-0.23

0.14

0.01

1.00

-0.47

µ (singletop)

-0.43

-0.36

-0.37

-0.08

0.13

-0.16

0.00

0.00

-0.29

-0.47

1.00

B-Tag Enveloped B-Jet

B-Tag High-p B-Jet

B-Tag Enveloped Lighter-Flavor-Jet

ttbar & singletop Radiation

singletop Interference

w+jets Heavy-Flavour Extrapolation

diboson Modelingµ (ttV)µ (ttbar)µ (wjets)µ (singletop)

0.2
0

T

−0.2
−0.4

Figure 9.4: Correlations among model parameters after after the background-only fit for Boosted.
Only parameters with at least one correlation of more than 0.2 are shown. The naming rule ofsystematic parameters follow Table 8.1 8.5. For the detailed explanation on the fit configuration,see Section 7.2.

108

Events

104

Data
tt
tt+V
Dibosons = 13 TeV, 28.0 fb-1

103

Total SM
W+jetsWt
Z+jets

102
10

40
2
0
−2

0.1667

Resolved TVR

0.3333

Resolved WVR

0.5

Boosted TVR

0.6667

Boosted WVR

0.8333

Resolved SR

1

Boosted SR

(n

obs

- nexp) / σtot

1

Figure 9.5: Comparison of the expected backgrounds (nexp ) with the observed data (nobs ) in
the SRs and VRs. The nexp is obtained by the background-only fit. The bottom plot shows
significance of the di↵erence between expected backgrounds and data. Here the significance isdefined by (nobs

nexp )/ tot , where

tot is sum of the model uncertainty shown in Table 9.1 andTable 9.2 and the poisson fluctuation from the mean number of events in quadrature.

109

35

Data
tt
W+jetssingletops = 13 TeV, 28.0 fb-1

30

Events / 100 GeV

Events / 100 GeV

40

Total SMZ+jetstt+V
Diboson

25
20

5

5

1
200

300

400

500

0

600
700
mT [GeV]
Data / MC

2
1.5
1
0.5
0

(a) mT at SR of Resolved

25

Data
tt
W+jetssingletop

Total SMZ+jetstt+V
Diboson42

s = 13 TeV, 28.0 fb-1

20

Data
tt
W+jetssingletop

400 600 800 100012001400160018002000
mT [GeV]

2
1.5
1
0.5
0

(b) mT at SR of Boosted

obs_x_SR1_mt1000

Events / 50 GeV

Data / MC

6

10

0

s = 13 TeV, 28.0 fb-1

3

15

Events / 40 GeV

7Total SMZ+jetstt+V
Diboson15

7

s = 13 TeV, 28.0 fb-1

6
5

Data
tt
W+jetssingletop

obs_x_tN_high_mt1000

Total SMZ+jetstt+V
Diboson

4
3

10

2
5
0

1

miss

miss

[GeV]

ET
Data / MC

2
1.5
1
0.5
0
miss
(c) ETat SR of Resolved

40
35
30

s = 13 TeV, 28.0 fb-1

Datatt
W+jetssingletop

miss(d) ETat SR of Boosted

Total SMZ+jetstt+V
Diboson

25
20

6
5

s = 13 TeV, 28.0 fb-1

Datatt
W+jetssingletop

Total SMZ+jetstt+V
Diboson

4

2

10

1

5

0
200 300 400 500 600 700 800 900
amT2 [GeV]

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

2
1.5
1
0.5
0

Data / MC

Data / MC7

obs_x_tN_high_met1000

3

15

0

[GeV]

2
1.5
1
0.5
0

obs_x_SR1_met1000

Events / 100 GeV

Data / MCET

Events / 46.875 GeV

0450 500 550 600 650 700 750 800 850 900 950

300 350 400 450 500 550 600 650 700(e) amT2 at SR of Resolved

2
1.5
1
0.5
0

(f) amT2 at SR of Boosted

obs_x_SR1_amt2

obs_x_tN_high_amt2

missFigure 9.6: mT , ET
, and amT2 distributions at Resolved (left) and Boosted (right) SRs. The background-only

fit result is propagated to the background models at SR. The uncertainty band includes statistical and systematic
error.
1101m∼χ0 [GeV]

700

~~
~
0 ~
0
t1t1 production, t1→t+∼
χ , t1→bW∼χ11Observed limit (±1σth)s = 13 TeV, 28.0 fb-1

600 Limit at 95% CL

Expected limit (±1σexp)

500

0

<

400

~

-m

0

-

mW

∼χ 1
~

-m

0

t
-m

<

0

∼χ 1

m t1

m t1

300
200
100
0
200 300 400 500 600 700 800 900 1000m ~t [GeV]1

Figure 9.7: Resolved: Expected (black dashed) and observed (red solid) CLs exclusion limits at
95% CL in the plane of mt̃1 versus m ˜01 . The dashed red line ( th ) indicates the results with1m∼χ0 [GeV]±1 variation of the signal cross section uncertainty (Figure 3.1).

700

~~
~
0 ~
0
t1t1 production, t1→t+∼
χ , t1→bW∼χ11

s = 13 TeV, 28.0 fb-1

600 obs. CLs
500
400

0.83 0.72

0.72

0.73

~

-m

m t1

300

0

<
W
-m

∼χ 1
~

0

-m

m t1

0

t
-m

∼χ 1

<

0

0.67 0.57 0.58
0.58 0.55 0.44

0.72 0.57 0.28 0.14 0.24 0.34 0.51 0.58 0.61

0.78 0.33 0.05 0.02 0.08 0.11 0.28 0.44 0.57 0.61

0.70 0.21 0.01 0.00 0.01 0.04 0.08 0.21 0.43 0.560.63
0.70 0.18 0.00 0.00 0.00 0.00 0.01 0.07 0.16 0.33 0.56 0.61

200

0.04 0.00 0.00 0.00 0.00 0.00 0.00 0.03 0.12 0.37 0.550.60
0.07
0.00 0.00 0.00

100

0.00 0.01 0.02 0.16 0.31 0.56 0.61

0.00 0.00

0.00 0.00 0.00 0.00 0.02 0.14 0.36 0.510.59

0.00 0.00

0.00 0.00 0.00 0.00 0.04 0.11 0.31 0.560.59

0.00 0.00 0.00 0.00 0.02 0.17 0.40 0.55 0.61
0200 300 400 500 600 700 800 900 1000m ~t [GeV]
0.00 0.00

1

Figure 9.8: Resolved: Mass points used to draw the contours in Figure 9.7. Observed CLs values
without variation of the signal cross section uncertainty are shown on the mass points.

111

1

m∼χ0 [GeV]

700

~~
~
0 ~
0
t1t1 production, t1→t+∼
χ , t1→bW∼χ11Observed limit (±1σth)s = 13 TeV, 28.0 fb-1

600 Limit at 95% CL

Expected limit (±1σexp)

500

0

<

400

~

-m

0

-

mW

∼χ 1
~

-m

0

t
-m

<

0

∼χ 1

m t1

m t1

300
200
100
0
200 300 400 500 600 700 800 900 1000m ~t [GeV]1

Figure 9.9: Boosted: Expected (black dashed) and observed (red solid) CLs exclusion limits at
95% CL in the plane of mt̃1 versus m ˜01 . The dashed red line ( th ) indicates the results with1m∼χ0 [GeV]±1 variation of the signal cross section uncertainty (Figure 3.1).

700

~~
~
0 ~
0
t1t1 production, t1→t+∼
χ , t1→bW∼χ11

s = 13 TeV, 28.0 fb-1

600 obs. CLs
500
400

0.93 0.79

0.61

0.89

~

-m

m t1

300

0

<
W
-m

∼χ 1
~

0

-m

m t1

0

t
-m

∼χ 1

<

0

0.90 0.71 0.61
0.76 0.50 0.49

0.97 0.89 0.64 0.24 0.15 0.14 0.13 0.150.16

0.83 0.72 0.27 0.20 0.04 0.09 0.05 0.04 0.070.14

0.99 0.65 0.37 0.12 0.06 0.02 0.01 0.02 0.03 0.050.16
0.98 0.76 0.55 0.20 0.01 0.00 0.00 0.00 0.00 0.01 0.040.10

200

0.97 0.45 0.12 0.00 0.00 0.00 0.00 0.00 0.00 0.01 0.040.06
0.97
0.35 0.11 0.09

100

0.00 0.00 0.00 0.00 0.00 0.030.07

0.07 0.14

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.020.05

0.06 0.05

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.020.05

0.00 0.00 0.00 0.00 0.00 0.00 0.01 0.020.06
0
200 300 400 500 600 700 800 900 1000m ~t [GeV]
0.03 0.00

1

Figure 9.10: Boosted: Mass points used to draw the contours in Figure 9.9. Observed CLs values
without variation of the signal cross section uncertainty are shown on the mass points.

112

9.2

Results from Diagonal

Before doing the 2-D shape fit shown in Figure 6.24, a test fit has been done to validate theshape fit, which is described in Appendix A. The result has concluded that there is no significant
issue in the fit configuration and modeling, and then the ‘unblind’ fit was performed.
missFigure 9.11 shows the observed mT shape at each ET
slice and TAUCR with the predictedshapes after the background-only fit. The observed shape is within the uncertainties on theprediction of the background-only fit. The other variables not used in the fit are also shown in
Figure 9.12 9.23 under the same condition. There is no remarkable issue in the distributions.
The parameters and correlations after the unblind fit are shown in Figure 9.24 and 9.25.
missThere are correlations of 20 50% for µttbarTau with JER, JES, ET
soft term, and tt̄ and single

top theory uncertainties. Since they are relatively large systematic uncertainties as indicatedin Table 8.1 8.5 and Diagonal analysis exploits the 2-D shape fit with high statistics, thosecorrelations could be stronger than Resolved and Boosted. However, since all the systematicparameters in Diagonal remain within 0.5

line and there is no large excess in the observed

shape, the correlation e↵ect on µttbarTau is not a significant issue for the fit.
To evaluate how plausible the prediction of the background-only fit is, CLb and its z-value arecalculated by discovery hypothesis test with the benchmark signal model ((mt̃1 , m ˜01 ) = (400,200) GeV). The observed CLb and its z-value obtained by the model independent discovery
hypothesis test are 0.221 and 0.770 . The other mass points are also tested, but all the z-values
are within 1 . This concludes that there is no significant deviation from the SM-only model inDiagonal analysis.
To evaluate how much the signal models are excluded, CLs exclusion limits at 95% CL arederived from the Diagonal analysis, shown in Figure 9.26. The mass points used to draw thecontours are shown with the observed CLs values in Figure 9.27. For Diagonal, the observed CLs
0limit is within the ±1 band of the expected CLs . The Diagonal result excludes the t̃1 ! t ˜10model with m ˜01 . 240 GeV and t̃1 ! bW ˜1 model with m ˜01 . 260 GeV near the Diagonal line.

113

miss
(a) mT at ET= [100, 150] GeV.

miss(b) mT at ET= [150, 200] GeV.

miss(c) mT at ET= [200, 250] GeV.

miss(d) mT at ET= [250, inf] GeV.

(e) mT at TAUCR.
miss
Figure 9.11: mT distribution at each ET
slice and TAUCR after the background-only fit with unblind. The

uncertainty band includes statistical and systematic error.
114

miss
(a) jet multiplicity at ET= [100, 150] GeV.

miss(b) jet multiplicity at ET= [150, 200] GeV.

miss(c) jet multiplicity at ET= [200, 250] GeV.

miss(d) jet multiplicity at ET= [250, inf] GeV.

(e) jet multiplicity at TAUCR.
miss
Figure 9.12: jet multiplicity distribution at each ET
slice and TAUCR after the background-only fit withunblind. The uncertainty band includes statistical and systematic error.
115

miss
(a) 1st jet pT at ET= [100, 150] GeV.

miss(b) 1st jet pT at ET= [150, 200] GeV.

miss(c) 1st jet pT at ET= [200, 250] GeV.

miss(d) 1st jet pT at ET= [250, inf] GeV.

(e) 1st jet pT at TAUCR.
miss
Figure 9.13: 1st jet pT distribution at each ET
slice and TAUCR after the background-only fit with unblind.

The uncertainty band includes statistical and systematic error.
116

miss
(a) 2nd jet pT at ET= [100, 150] GeV.

miss(b) 2nd jet pT at ET= [150, 200] GeV.

miss(c) 2nd jet pT at ET= [200, 250] GeV.

miss(d) 2nd jet pT at ET= [250, inf] GeV.

(e) 2nd jet pT at TAUCR.
miss
Figure 9.14: 2nd jet pT distribution at each ET
slice and TAUCR after the background-only fit with unblind.

The uncertainty band includes statistical and systematic error.
117

miss
(a) 2nd jet pT at ET= [100, 150] GeV.

miss(b) 2nd jet pT at ET= [150, 200] GeV.

miss(c) 2nd jet pT at ET= [200, 250] GeV.

miss(d) 2nd jet pT at ET= [250, inf] GeV.

(e) 3rd jet pT at TAUCR.
miss
Figure 9.15: 3rd jet pT distribution at each ET
slice and TAUCR after the background-only fit with unblind.

The uncertainty band includes statistical and systematic error.
118

miss
(a) 2nd jet pT at ET= [100, 150] GeV.

miss(b) 2nd jet pT at ET= [150, 200] GeV.

miss(c) 2nd jet pT at ET= [200, 250] GeV.

miss(d) 2nd jet pT at ET= [250, inf] GeV.

(e) 4th jet pT at TAUCR.
miss
Figure 9.16: 4th jet pT distribution at each ET
slice and TAUCR after the background-only fit with unblind.

The uncertainty band includes statistical and systematic error.
119

miss
(a) lepton pT at ET= [100, 150] GeV.

miss(b) lepton pT at ET= [150, 200] GeV.

miss(c) lepton pT at ET= [200, 250] GeV.

miss(d) lepton pT at ET= [250, inf] GeV.

(e) lepton pT at TAUCR.
miss
Figure 9.17: lepton pT distribution at each ET
slice and TAUCR after the background-only fit with unblind.

The uncertainty band includes statistical and systematic error.
120

miss
(a) 1st b-jet pT at ET= [100, 150] GeV.

miss(b) 1st b-jet pT at ET= [150, 200] GeV.

miss(c) 1st b-jet pT at ET= [200, 250] GeV.

miss(d) 1st b-jet pT at ET= [250, inf] GeV.

(e) 1st b-jet pT at TAUCR.
miss
Figure 9.18: 1st b-jet pT distribution at each ET
slice and TAUCR after the background-only fit with unblind.

The uncertainty band includes statistical and systematic error.
121

p
miss
miss
(a) ET/ HT at ET= [100, 150] GeV.

p
miss
miss
(b) ET/ HT at ET= [150, 200] GeV.

p
miss
miss
(c) ET/ HT at ET= [200, 250] GeV.

p
miss
miss
(d) ET/ HT at ET= [250, inf] GeV.

pmiss(e) ET/ HT at TAUCR.

p
miss
miss
Figure 9.19: ET/ HT distribution at each ET
slice and TAUCR after the background-only fit with unblind.
The uncertainty band includes statistical and systematic error.
122

(a)

miss
R(b, `) at ET= [100, 150] GeV.

(b)

miss
R(b, `) at ET= [150, 200] GeV.

(c)

miss
R(b, `) at ET= [200, 250] GeV.

(d)

miss
R(b, `) at ET= [250, inf] GeV.

(e)

Figure 9.20:

R(b, `) at TAUCR.

miss
R(b, `) distribution at each ET
slice and TAUCR after the background-only fit with unblind.

The uncertainty band includes statistical and systematic error. These plots are just for validations of the 2-D
shape fit, and not used in either the event selection or the fit.
123

miss
(a) mtop at ET= [100, 150] GeV.

miss(b) mtop at ET= [150, 200] GeV.

miss(c) mtop at ET= [200, 250] GeV.

miss(d) mtop at ET= [250, inf] GeV.

(e) mtop at TAUCR.
miss
Figure 9.21: mtop distribution at each ET
slice and TAUCR after the background-only fit with unblind. The

uncertainty band includes statistical and systematic error. These plots are just for validations of the 2-D shapefit, and not used in either the event selection or the fit.
124

miss
(a) amT2 at ET= [100, 150] GeV.

miss(b) amT2 at ET= [150, 200] GeV.

miss(c) amT2 at ET= [200, 250] GeV.

miss(d) amT2 at ET= [250, inf] GeV.

(e) amT2 at TAUCR.
miss
Figure 9.22: amT2 distribution at each ET
slice and TAUCR after the background-only fit with unblind. The

uncertainty band includes statistical and systematic error. These plots are just for validations of the 2-D shapefit, and not used in either the event selection or the fit.
125

miss
(a) topness at ET= [100, 150] GeV.

miss(b) topness at ET= [150, 200] GeV.

miss(c) topness at ET= [200, 250] GeV.

miss(d) topness at ET= [250, inf] GeV.

(e) topness at TAUCR.
miss
Figure 9.23: topness distribution at each ET
slice and TAUCR after the background-only fit with unblind. The

uncertainty band includes statistical and systematic error. These plots are just for validations of the 2-D shapefit, and not used in either the event selection or the fit.
126

JES Enveloped NP 1
JES Enveloped NP 2JES Enveloped NP 3
JES Enveloped NP 4JES Enveloped NP 5JES Enveloped NP 6
JES Pseudorapidity Calibration 1
JES Pseudorapidity Calibration 2
JES Pseudorapidity Calibration 3
JES High-p Jet
T
JES Pileup 1
JES Pileup 2
JES Pileup 3
JES Pileup 4
JES B-Jet Response
JES Lighter-Flavor-Jet Response
JES Lighter-Flavor-Jet Composition
JES Punch ThroughJER Enveloped NP
JER Cross Calibration 1
JER Cross Calibration 2
JER Cross Calibration 3
JER Cross Calibration 4
JER Cross Calibration 5
JER Cross Calibration 6
JER Cross Calibration 7
JER Forward Region
miss
ET Parallel Resolution
miss
ET Perpendicular Resolution
miss
ET Energy Scale
B-Tag B-Jet 1
B-Tag B-Jet 2
B-Tag B-Jet 3
B-Tag B-Jet 4
B-Tag B-Jet 5
B-Tag High-p B-Jet
T
B-Tag C-Jet 1
B-Tag C-Jet 2
B-Tag C-Jet 3
B-Tag C-Jet 4
B-Tag High-p C-Jet
T
B-Tag Lighter-Flavor-Jet 1
B-Tag Lighter-Flavor-Jet 2
B-Tag Lighter-Flavor-Jet 3
B-Tag Lighter-Flavor-Jet 4
B-Tag Lighter-Flavor-Jet 5
B-Tag Lighter-Flavor-Jet 6
B-Tag Lighter-Flavor-Jet 7
B-Tag Lighter-Flavor-Jet 8
B-Tag Lighter-Flavor-Jet 9
B-Tag Lighter-Flavor-Jet 10
B-Tag Lighter-Flavor-Jet 11
B-Tag Lighter-Flavor-Jet 12
B-Tag Lighter-Flavor-Jet 13
B-Tag Lighter-Flavor-Jet 14
ttbar & singletop Radiation
ttbar Parton Shower
singletop Interference
W+jets & diboson CKKW
W+jets & diboson Factorization
W+jets & diboson Renormalization
W+jets & diboson Resummation
ttbar+Z Scaleµ (ttbar1L)-1µ (ttbarTau)-1

Uncertainty After Fit

2
1.5
1
0.5
0
−0.5
−1
−1.5
−2

Figure 9.24: Model parameters and their uncertainties after the 2-D shape fit with unblind.
The vertical dashed-dotted line divides into two categories: standardized systematic parameters(left) and normalization scale factors (right). The naming rule of systematic parameters follow
Table 8.1 8.5. For the detailed explanation on the fit configuration, see section 7.2.

h_corr_reduced (threshold 20 precent)
JES Enveloped NP 1

1.00

-0.08

0.01

-0.12

0.17

-0.07

0.02

0.03

0.01

0.06

0.09

0.16

-0.05

0.04

-0.05

-0.05

-0.27

0.18

JES Pseudorapidity Calibration 1

-0.08

1.00

0.14

-0.09

0.13

-0.15

0.03

-0.04

0.03

-0.18

0.00

0.11

-0.13

-0.23

-0.02

-0.01

-0.02

0.03

JES Lighter-Flavor-Jet Response

0.01

0.14

1.00

0.02

-0.32

0.04

-0.02

0.07

-0.02

0.01

0.02

-0.02

-0.02

0.06

-0.06

0.04

0.16

-0.22

JES Lighter-Flavor-Jet Composition

-0.12

-0.09

0.02

1.00

0.12

-0.09

0.06

0.03

0.01

0.12

0.13

0.20

-0.02

0.05

-0.06

-0.08

-0.36

0.25

JER Enveloped NP

0.17

0.13

-0.32

0.12

1.00

0.05

0.21

-0.01

0.15

-0.16

-0.09

-0.17

0.24

-0.03

0.13

0.10

0.05

0.53

JER Cross Calibration 3

-0.07

-0.15

0.04

-0.09

0.05

1.00

0.28

0.28

-0.05

-0.10

-0.36

-0.02

0.15

-0.05

-0.06

-0.06

-0.10

-0.49

JER Cross Calibration 4

0.02

0.03

-0.02

0.06

0.21

0.28

1.00

-0.02

-0.03

-0.14

-0.02

-0.08

-0.02

-0.02

-0.05

-0.00

-0.02

0.05

JER Cross Calibration 5

0.03

-0.04

0.07

0.03

-0.01

0.28

-0.02

1.00

0.02

-0.08

0.00

-0.03

-0.07

-0.01

0.04

0.02

0.04

0.07

JER Cross Calibration 7

0.01

0.03

-0.02

0.01

0.15

-0.05

-0.03

0.02

1.00

0.02

-0.00

-0.05

0.08

-0.04

-0.02

-0.02

-0.02

0.21

Parallel Resolution

0.06

-0.18

0.01

0.12

-0.16

-0.10

-0.14

-0.08

0.02

1.00

-0.28

-0.26

-0.17

0.09

-0.15

-0.01

-0.09

-0.21

Perpendicular Resolution

0.09

0.00

0.02

0.13

-0.09

-0.36

-0.02

0.00

-0.00

-0.28

1.00

-0.21

0.12

0.05

0.01

-0.01

-0.01

0.33

Energy Scale

0.16

0.11

-0.02

0.20

-0.17

-0.02

-0.08

-0.03

-0.05

-0.26

-0.21

1.00

0.25

-0.03

0.01

-0.04

-0.23

0.13

ttbar & singletop Radiation

-0.05

-0.13

-0.02

-0.02

0.24

0.15

-0.02

-0.07

0.08

-0.17

0.12

0.25

1.00

0.10

-0.02

0.20

0.24

0.34

ttbar Parton Shower

0.04

-0.23

0.06

0.05

-0.03

-0.05

-0.02

-0.01

-0.04

0.09

0.05

-0.03

0.10

1.00

0.07

0.12

0.23

0.28

miss

ET
miss

ET

miss

-0.06

-0.06

0.13

-0.06

-0.05

0.04

-0.02

-0.15

0.01

0.01

-0.02

0.07

1.00

-0.05

0.44

0.33

-0.01

0.04

-0.08

0.10

-0.06

-0.00

0.02

-0.02

-0.01

-0.01

-0.04

0.20

0.12

-0.05

1.00

0.58

0.18

-0.27

-0.02

0.16

-0.36

0.05

-0.10

-0.02

0.04

-0.02

-0.09

-0.01

-0.23

0.24

0.23

0.44

0.58

1.00

0.24

µ (ttbarTau)

0.18

0.03

-0.22

0.25

0.53

-0.49

0.05

0.07

0.21

-0.21

0.33

0.13

0.34

0.28

0.33

0.18

0.24

1.00

JES Pseudorapidity Calibration 1

JES Lighter-Flavor-Jet Response

JES Lighter-Flavor-Jet Composition

JER Enveloped NP

JER Cross Calibration 3

JER Cross Calibration 4

JER Cross Calibration 5

JER Cross Calibration 7

Energy Scalettbar & singletop Radiation

ttbar Parton Shower

singletop Interference

W+jets & diboson Renormalizationµ (ttbar1L)µ (ttbarTau)

ET

miss

miss

ET

ET

miss

-0.02

-0.05

Perpendicular Resolution-0.05µ (ttbar1L)

Parallel Resolution

singletop Interference
W+jets & diboson Renormalization

JES Enveloped NP 1

ET

1
0.8
0.6
0.4
0.2
0
−0.2
−0.4

Figure 9.25: Correlations among model parameters after the 2-D shape fit with unblind. Onlyparameters with at least one correlation of more than 0.2 are shown. The naming rule of systematic parameters follow Table 8.1 8.5. For the detailed explanation on the fit configuration,
see section 7.2.

1m∼χ0 [GeV]

700

~~
~
0 ~
0
t1t1 production, t1→t+∼
χ , t1→bW∼χ11Observed limit (±1σth)s = 13 TeV, 28.0 fb-1

600 Limit at 95% CL

Expected limit (±1σexp)

500

<

400

~

-m

m t1

0

-

0

mW

∼χ 1
~

-m

0

t
-m

<

0

∼χ 1

m t1

300
200
100
0
200 300 400 500 600 700 800 900 1000m ~t [GeV]1

Figure 9.26: Diagonal: Expected (black dashed) and observed (red solid) CLs exclusion limits
at 95% CL in the plane of mt̃1 versus m ˜01 . The dashed red line ( th ) indicates the results with1m∼χ0 [GeV]±1 variation of the signal cross section uncertainty (Figure 3.1).

700

~~
~
0 ~
0
t1t1 production, t1→t+∼
χ , t1→bW∼χ11

s = 13 TeV, 28.0 fb-1

600 obs. CLs
500

<

-m

-m

400

m

300
200
100
0.00
0.03
0.01

0.22
0.00
0.07 0.00
0.00 0.00
0.00 0.00 0.00
0.00
0.00 0.00
0.00
0.00
0.00
0.00

0.82 0.78

0.92
0.77
0.84 0.73
0.73
t 0.73
W 0.80
0.71
0.69
0.65
0
0
0.54
∼
0.65
∼χ 1
χ1
0.81 0.47 0.64
0.62 0.44 0.35
~t 1 0.55
~t 1
0.50
0.48
0.70 0.22 0.37
0.29 0.11 0.12
0.23 0.40
0.67 0.07 0.48
0.30 0.10 0.02 0.02 0.04
0.06 0.16
0.08
0.01 0.07 0.01 0.00 0.00 0.00 0.01
0.04
0.01
0.02 0.00 0.00 0.00 0.00 0.00 0.01
0.00
0.00 0.00 0.00
0.00

0

-m

<

-m

m

0

0.79
0.69 0.65 0.68
0.53 0.52
0.27 0.38 0.49 0.57 0.67 0.71
0.18 0.29 0.39 0.52 0.620.70
0.09 0.25 0.32 0.51 0.630.70
0.07 0.17 0.30 0.45 0.580.69
0.03 0.11 0.21 0.43 0.590.68
0.03 0.09 0.24 0.41 0.540.67

0.00 0.00

0.00 0.00 0.00 0.01 0.10 0.23 0.39 0.540.67

0.00 0.00

0.00

0.00 0.01 0.08 0.19 0.38 0.560.67

0200 300 400 500 600 700 800 900 1000m ~t [GeV]
0.00 0.00

0.00 0.00 0.00 0.01 0.08 0.23 0.43 0.570.67

1Figure 9.27: Diagonal: Mass points used to draw the contours in Figure 9.9. Observed CLs
values without variation of the signal cross section uncertainty are shown on the mass points.

128

9.3

Combined Results

As shown in Figure 9.7, 9.9, and 9.26, Resolved, Boosted, and Diagonal results exclude their target
regions individually. Figure 9.28 shows CLs exclusion limits at 95% CL obtained by combining
Resolved, Boosted, and Diagonal results, where the exclusion limits are obtained by selecting oneof the three strategies, which gives the lowest expected CLs value, for each mass point. As acomparison, Figure 9.29 shows the exclusion limits obtained by the latest search results using
13.2 fb 1 of LHC pp collision data collected in the ATLAS and CMS experiments. Resolved,
Boosted, and Diagonal results using the data of 28.0 fb 1 enlarges the exclusion contours in00
Figure 9.29 for t̃1 ! t ˜1 and t̃1 ! bW ˜1 decay model with 100% BR.
00

The Diagonal result newly excludes the t̃1 ! t ˜1 and t̃1 ! bW ˜1 model with mt̃1 from 200 to

240 GeV and (mt̃1 , m ˜01 ) ⇠ (430, 250) GeV near the Diagonal line. The Resolved result doesn’t
newly exclude but enlarges the expected CLs contour up to (mt̃1 , m ˜01 ) ⇠ (700

800, 400) GeV.

The Boosted result newly enlarges the expected and observed limits up to mt̃1 . 980 GeV for0m ˜0 . 300 GeV and (mt̃ , m ˜0 ) = (900, 350) GeV, which is the highest ˜1 mass excluded in1

1

1

Boosted region.
For a fair comparison of performance, the expected CLs exclusion limits of the combination of
Resolved, Boosted, and Diagonal on the assumption of 13.2 fb 1 are evaluated and compared tothe ones of ATLAS and CMS analyses with 13.2 fb 1 in Figure 9.30. Figure 9.30 indicates that
as well as the Diagonal analysis with 28.0 fb 1 , the analysis with 13.2 fb 1 can also provide thebest performance at 200 GeV < mt̃1 < 240 GeV and at (mt̃1 , m ˜01 ) ⇠ (430, 250) GeV, comparedto the other ATLAS and CMS analyses with 13.2 fb 1 .

129

600

1

m∼χ0 [GeV]

~~
~
0 ~
0
t t production, t1→t+∼
χ , t1→bW∼
χ

700 1 11

1

Observed limit (±1σth)s = 13 TeV, 28.0 fb-1
Limit at 95% CL

500
400

~

-m

0

<
W
-m

0

-m

∼χ 1

m

m t1

Expected limit (±1σexp)

0

t
-m

<

0

∼χ 1

~t 1

300
200
100
0
200 300 400 500 600 700 800 900 1000m ~t [GeV]1

Figure 9.28: The expected (black dashed) and observed (red solid) CLs exclusion limits at 95%
CL in the plane of mt̃1 versus m ˜01 derived by combining Resolved, Boosted, and Diagonal results.
The exclusion limits are obtained by selecting one of the three strategies, which gives the lowest
~~
~
0 ~
0
t t production, t1→t+∼
χ , t1→bW∼
χ

700 1 11

1This Thesis 28.0 fb

600

1m∼χ0 [GeV]

expected CLs value, for each mass point before checking the observed CLs value.

500

Limit at 95% CL-1

ATLAS 1L 13.2 fb [CONF-2016-050]
-1

obs.
exp.

400

-1

-1

ATLAS 0L 13.2 fb [CONF-2016-077]
ATLAS 2L 13.2 fb [CONF-2016-076]-1

ATLAS Run-1 (8 TeV) 20.3 fb [1506.08616]

<
-m

~
m t1

-m
0

W

m

~t 1

∼χ 1

0

-m

-m
0

t

<

0

-1

CMS 1L 12.9 fb [SUS-16-028]

∼χ 1

300
200
100
0
200 300 400 500 600 700 800 900 1000m ~t [GeV]1

Figure 9.29: Comparison of the combined results of Resolved, Boosted, and Diagonal (red line) tothe dedicated ATLAS and CMS searches for stop pair production. The green, orange, and violet
lines correspond to searches based on 13.2 fb 1 of pp collision data taken by the ATLAS detectorp
at s = 13 TeV using events with no lepton [130], one lepton [27], and two leptons [131],
respectively. The blue line corresponds to the CMS result based on 12.9 fb 1 data taken atps = 13 TeV using events with one lepton [132]. The observed limit obtained by the ATLASp
Run-1 search with 20.3 fb 1 at s = 8 TeV [133] is also indicated by the gray region. Exclusion
limits at 95% CL are shown in the (mt̃1 , m ˜01 ) plane. The solid and dashed lines show theobserved and expected limits, respectively, which include all uncertainties except the theoreticalsignal cross section uncertainty.

130

1

1
-1

13.2 fb (This Thesis)

6001m∼χ0 [GeV]

700

~~
~
0 ~
0
t1t1 production, t1→t+∼
χ , t1→bW∼
χ

500
400

-1

Limit at 95% CL

ATLAS 0L 13.2 fb [CONF-2016-077]-1

ATLAS 1L 13.2 fb [CONF-2016-050]
-1

obs.
exp.

ATLAS 2L 13.2 fb [CONF-2016-076]-1

ATLAS Run-1 (8 TeV) 20.3 fb [1506.08616]

<
-m

-m
0

W

m

~t 1

∼χ 1

~
m t1

0

-m

-m
0

t

<

0

-1

CMS 1L 12.9 fb [SUS-16-028]

∼χ 1

300
200
100
0
200 300 400 500 600 700 800 900 1000m ~t [GeV]1

Figure 9.30: Comparison of the expected CLs exclusion limits obtained by the combination of
Resolved, Boosted, and Diagonal on the assumption of 13.2 fb 1 (red line) with the ones obtainedby the ATLAS results with 13.2 fb 1 using events with no lepton [130], one lepton [27], and two
leptons [131] and the CMS result with 12.9 fb 1 using events with one lepton [132]. As a reference,p
the observed limit obtained by the ATLAS Run-1 search with 20.3 fb 1 at s = 8 TeV [133]is also indicated by the gray region. The expected limits include all uncertainties except thetheoretical signal cross section uncertainty.

131

9.4

Future Prospects

Figure 9.31 shows a schedule of the LHC operation with center-of-mass energy and integrated
luminosity indicated. Run-2 is planned to continue until 2018 and provide 100⇠150 fb 1 . In
the shutdown period from 2019 to 2020 (LS2), LHC and some detectors will be upgraded andreplaced to increase instantaneous luminosity by a factor of two. Run-3 is planned to operatefrom 2021 to 2023 and provide 300 fb 1 . In the shutdown period from 2024 to mid-2026 (LS3),
LHC and several detectors will be upgraded and replaced, and the upgraded LHC is called ‘High
Luminosity Large Hadron Collider (HL-LHC)’. HL-LHC increases instantaneous luminosity bya factor of 5 to 7 and is planned to operate from mid-2016 to 2037 and provide 3000 fb 1 .
As one of future prospects, the expected exclusion limits are evaluated by assuming higher
integrated luminosity in the future, which is shown in Figure 9.32, where systematic uncertainties
are assumed to be not changed. Run-2 and Run-3 are expected to exclude most of mass points
with up to m ˜01 ⇠ 400 to 500 GeV2 . The HL-LHC will reach most of mass points with up
to m ˜01 ⇠ 500 to 600 GeV. The analysis needs to be improved to search mass points withm ˜01 > 600 GeV.

miss
As integrated luminosity increases, the larger ET
region will be more important because
missthe signal events tend to provide larger ET
than the backgrounds. Therefore, adding larger
missET
bins (for example, [250, 300], [300, 350] GeV) would improve sensitivity.

Focusing on ISR jet from signal event is also interesting. The signal events with one ISR jet
miss
can provide larger ET
because the existing of the ISR jet weakens back-to-back state of the stop
misspair and also the neutralino pair. This characteristics is indirectly exploited in the (ET,mT )shape fit in this thesis, but the direct use of ISR-related variables may improve sensitivity suchas the stop analysis with no lepton [130]. Application of multivariate analysis such as machinelearning techniques [93] or matrix element likelihood method [134] to the signal events with one
ISR jet is also interesting as a longer-term study. There were dedicated studies using matrix
element likelihood method where matrix element of the signal event is used at the LO precision
without any ISR jets [135, 136] and such studies indicate that the likelihood based on the matrix
element without ISR jets are not good enough to improve sensitivity. It indicates that at least
matrix element without any ISR jets doesn’t work well and therefore considering ISR jets could
be one of motivated studies for the further improvement of the analysis.

2 A region of mt̃1 > 1 TeV was not evaluated because samples with such high mass points were unavailable.

132

~~
~
0 ~
0
t t production, t1→t+∼
χ , t1→bW∼
χ

700 1 1600

1m∼χ0 [GeV]

Figure 9.31: A schedule of the LHC and HL-LHC operation [137].

500
400

1

1

Limit at 95% CL
obs.
exp.

<

~

-m

m t1

0

-

0

mW

∼χ 1
~

-m

0

t
-m

<

0

∼χ 1

m t1

300
200
100

13.2 fb-1

28.0 fb-1

100 fb-1

300 fb-11000 fb-1

3000 fb-1

0
200 300 400 500 600 700 800 900 1000m ~t [GeV]1

Figure 9.32: Evolution of the expected exclusion limits at 95% CL due to increment of integrated
luminosity. The expected limits are evaluated by assuming integrated luminosity of 13.2 (earlyRun-2, Moriond 2016), 28.0 (this thesis), 100 (late-Run-2), 300 (Run-3), 1000 (early-HL-LHC),and 3000 (HL-LHC) fb 1 . Resolved, Boosted, and Diagonal results are combined as describedin Section 9.3. The dashed lines show the expected limits including all uncertainties except thetheoretical signal cross section uncertainty. For 28.0 fb 1 , the observed limit (solid line) is also
shown as a reference. The systematic uncertainties are assumed to be not changed. A region ofmt̃1 > 1 TeV was not evaluated because samples with such high mass points were unavailable.

133Chapter 10

Conclusion
This thesis presents a search for top squarks in events with one lepton in pp collisions atps=

13 TeV. Top squark (stop) is a new particle predicted by supersymmetry, which is an extensionof the SM. Stop is the key particle to naturally solve the hierarchy problem of the Higgs mass
correction (naturalness). The analysis targets a direct pair production of stops where each stop0
decays into the top quark and the lightest neutralino (t̃1 ! t ˜1 ), the W boson from one of thetwo top quarks decays to an electron or muon (either directly or via a ⌧ lepton), and the Wboson from the other top quark decays hadronically. The lightest neutralino is a candidate ofdark matter and this is also one of motivations of supersymmetry.
0
Since the analysis optimized to t̃1 ! t ˜1 is also sensitive to a model where stop directly0

decays into the b-quark, W -boson, and the lightest neutralino (t̃1 ! bW ˜1 ), the analysis result0
is reinterpreted for t̃1 ! bW ˜1 model. The search uses 28.0 fb 1 of LHC pp collision datacollected in the ATLAS experiment in 2015 and 2016.

Since the signal event topology highly depends on the mass di↵erence between the stop andthe lightest neutralino, three analyses are performed which are optimized to Diagonal, Resolved,0
and Boosted topologies of the signal events. In Boosted topology ( m(t̃1 , ˜1 ) & 3mt ), top quarks
are highly boosted so that bqq 0 from hadronic top decay forms one large-R jet. In Resolved
0
topology ( m(t̃1 , ˜1 ) ⇠ 2mt ), the hadronic top decay products are not merged into one large-R
jet but resolved into three smaller-radius jets because pT of top quark is relatively medium. In
0Diagonal topology ( m(t̃1 , ˜1 ) ⇠ mt ), the behavior of hadronic top decay is the same as Resolved
0

region but ˜1 and t from t̃1 decay are nearly collinear with respect to t̃1 momentum.

In a preceding study using the data of 13.2 fb 1 , which uses events with one lepton in the
final state, there were some excesses of CLb = 2.2

3.3

in several signal regions which aresomewhat kinematically overlapped with each other [27]. The search in this thesis covers a partof the phase spaces with the excesses. For this reason, Resolved and Boosted analyses in thisthesis are similar to those of Ref. [27]. The originality in this thesis is the Diagonal analysis
which is newly developed and performed to search the Diagonal region which is more importantfrom the view of naturalness. The key technique newly developed for Diagonal analysis is abackground estimation using ‘2-dimensional shape fit’, which greatly expands the search regionof Diagonal.
The analysis starts from defining physics object, which is a four-momentum reconstructedfrom the detector signature with a tag such as electron, muon, jet, b-jet, etc. The defined physics

134objects are used in the event selection which specifies a phase space named ‘signal region (SR)’,
where the signal events are enhanced and background events are suppressed. Since there iscontamination of background events in the SR, they are estimated by using ‘control region (CR)’defined as a SR with some key requirements changed to enhance purity and yield of a specificbackground in the region. Number of events in SR and CRs are used in a simultaneous fit,
where the fitted parameters are total normalization scale factors for signal and backgrounds.
The total normalization scale factors are determined from the statistical constraint of CRs in
the simultaneous fit, and then the background contamination in SR can be estimated from thefitted µbkg . Experimental and theoretical uncertainties are also considered by incorporating
the systematic parameters with gaussian constraints into likelihood used in the simultaneous fit.
Finally, CLb and CLs values are calculated in the hypothesis test which compares null-hypothesis(background-only scenario) to alternative-hypothesis (background + signal scenario) using the
fit result.
The detector signature of the signal events is similar to that of a top quark pair (tt̄) producedin association with large missing transverse momentum, which becomes the main backgroundin the analyses. The event selection and background estimation are optimized to Diagonal,
Resolved, and Boosted analyses, individually. Resolved and Boosted analyses exploit the conventional cut-and-count methods and the dedicated event selections which highly suppress the
misstt̄ events. Diagonal analysis exploits the dedicated 2-dimensional (ET,mT ) shape fit newly

developed in this thesis, which precisely estimates the tt̄ events in the signal region.
The analysis concludes that there is no significant excess over the SM background expectationin Diagonal, Resolved, and Boosted signal regions. Exclusion limits at 95% CL are derived for stop00pair production models for the assumptions of BR(t̃1 ! t ˜1 ) = 100% and BR(t̃1 ! bW ˜1 ) =100% with di↵erent hypotheses of the mass splitting between the stop and the lightest neutralino.
These results extend the latest ATLAS and CMS exclusion limits with an integrated luminosity0
of 13.2 fb 1 for stop pair production model. The Diagonal result newly excludes the t̃1 ! t ˜10

and t̃1 ! bW ˜1 models with 200 GeV < m ˜01 < 240 GeV and (mt̃1 , m ˜01 ) ⇠ (430, 250) GeV
near the Diagonal line. The Resolved result doesn’t newly exclude but enlarges the expected
CLs contour up to (mt̃1 , m ˜01 ) ⇠ (700

800, 400) GeV. Although there was the excess of CLb

in the Resolved analysis with 13.2 fb 1 reported in Ref. [27], the excess decreases to0
CLb = 1.29 in this thesis. The Boosted result newly excludes the t̃1 ! t ˜1 model with the= 2.2

mt̃1 . 980 GeV for m ˜01 . 300 GeV and (mt̃1 , m ˜01 ) = (900, 350) GeV.

135

Acknowledgements
I thank CERN for the very successful operation of the LHC, as well as the support sta↵ fromcollaborating institutions without whom ATLAS could not be operated efficiently.
I thank Keita Hanawa who was a sta↵ sharing a workplace with me and gives me manyadvices about analysis technique (and very funny jokes). I thank Shimpei Yamamoto who wasa sta↵ helping my understanding statistics in high energy physics. I also thank Chikuma Kato
who is my friend sharing a workplace with me and makes my life at CERN enjoyable and gives
me hints helping my analysis that stem from his experience of Higgs analysis.
In particular, I thank Takashi Yamanaka and Junichi Tanaka very much.
Takashi Yamanaka is my supervisor who kindly supports this study and gives me a lot ofpenetrating advices in aspects of SUSY theory and analysis techniques. Without his helps, I
would have not resolved many analysis stoppers.
Junichi Tanaka is my boss who sincerely supports my life and computing at CERN and gives
me many helpful advices about analysis that comes from his thick experiences in physics analyses
and about strategies or behaviors in working at CERN, which will be very helpful in the works
in a big group (my next job is just the case).
They also have given many comments on this thesis. Without it, this thesis could have notbeen submitted.
Finally, I thank my family, Chikako Mori, Atsushi Mori and Eiko Mori very much for greatly
supporting basis of my study and life. Without the dedicated supports, I could have not studied
with my full e↵ort.
Thanks again!

136

Appendix A

Validation Fit for Diagonal

Figure A.1: Binning configuration for the validation fit in Diagonal. Slashed bins are ‘blinded’
bins that had not been either used until this validation fit has confirmed that there is no issue
misswith respect to the (ET,mT ) shape fit configuration.

In this appendix, results of a validation fit for Diagonal are shown. In the context of Diagonal,
the validation fit means the 2-D shape fit with the blinded bins indicated in Figure A.1 and thesignal model dropped away from fit. The purpose of the validation fit is to check how well thebackground models (or the SM-only model) can explain the observed data and to confirm there
missis no issue in the fit. Figure A.2 shows variable distributions after validation fit at each ET

slice and at TAUCR. The variables not used in the selection,

R(b, `), mtop , amT2 , and topness,

are also checked and shown in Figure A.3-A.14. The parameters and correlations after fit are
shown in Figure A.15 and A.16. The observed CLb obtained by a discovery hypothesis testwith the benchmark signal model in Diagonal where (mt̃1 , m ˜01 ) = (400, 200) is 0.436 (0.160 )1 ,concluding that there is no significant deviation from the SM-only prediction and thus the SMonly model is plausible.
From the validation fit results, it has been concluded that there is no significant issue in the
1 The terminology of hypothesis test is summarized in Section 7.

137

2-D shape fit and unblind fit can be done with a confidence in this context. The unblind fit
results are shown in Section 9.2.

138

miss
(a) mT at 1st ET
slice [100, 150] GeV.

miss(b) mT at 2nd ET
slice [150, 200] GeV.

miss(c) mT at 3rd ET
slice [200, 250] GeV.

miss(d) mT at 4th ET
slice [250, inf] GeV.

(e) mT at TAUCR.
miss
Figure A.2: mT distribution with blind at each ET
slice after the validation fit. The uncertainty band includes

statistical and systematic error.
139

miss
(a) jet multiplicity at 1st ET
slice [100, 150] GeV.

miss(b) jet multiplicity at 2nd ET
slice [150, 200] GeV.

miss(c) jet multiplicity at 3rd ET
slice [200, 250] GeV.

miss(d) jet multiplicity at 4th ET
slice [250, inf] GeV.

(e) jet multiplicity at TAUCR.
miss
Figure A.3: jet multiplicity distribution at each ET
slice after the validation fit. The uncertainty band includes

statistical and systematic error.
140

miss
(a) 1st jet pT at 1st ET
slice [100, 150] GeV.

miss(b) 1st jet pT at 2nd ET
slice [150, 200] GeV.

miss(c) 1st jet pT at 3rd ET
slice [200, 250] GeV.

miss(d) 1st jet pT at 4th ET
slice [250, inf] GeV.

(e) 1st jet pT at TAUCR.
miss
Figure A.4: 1st jet pT distribution at each ET
slice after the validation fit. The uncertainty band includes

statistical and systematic error.
141

miss
(a) 2nd jet pT at 1st ET
slice [100, 150] GeV.

miss(b) 2nd jet pT at 2nd ET
slice [150, 200] GeV.

miss(c) 2nd jet pT at 3rd ET
slice [200, 250] GeV.

miss(d) 2nd jet pT at 4th ET
slice [250, inf] GeV.

(e) 2nd jet pT at TAUCR.
miss
Figure A.5: 2nd jet pT distribution at each ET
slice after the validation fit. The uncertainty band includes

statistical and systematic error.
142

miss
(a) 2nd jet pT at 1st ET
slice [100, 150] GeV.

miss(b) 2nd jet pT at 2nd ET
slice [150, 200] GeV.

miss(c) 2nd jet pT at 3rd ET
slice [200, 250] GeV.

miss(d) 2nd jet pT at 4th ET
slice [250, inf] GeV.

(e) 3rd jet pT at TAUCR.
miss
Figure A.6: 3rd jet pT distribution at each ET
slice after the validation fit. The uncertainty band includes

statistical and systematic error.
143

miss
(a) 2nd jet pT at 1st ET
slice [100, 150] GeV.

miss(b) 2nd jet pT at 2nd ET
slice [150, 200] GeV.

miss(c) 2nd jet pT at 3rd ET
slice [200, 250] GeV.

miss(d) 2nd jet pT at 4th ET
slice [250, inf] GeV.

(e) 4th jet pT at TAUCR.
miss
Figure A.7: 4th jet pT distribution at each ET
slice after the validation fit. The uncertainty band includes

statistical and systematic error.
144

miss
(a) lepton pT at 1st ET
slice [100, 150] GeV.

miss(b) lepton pT at 2nd ET
slice [150, 200] GeV.

miss(c) lepton pT at 3rd ET
slice [200, 250] GeV.

miss(d) lepton pT at 4th ET
slice [250, inf] GeV.

(e) lepton pT at TAUCR.
miss
Figure A.8: lepton pT distribution at each ET
slice after the validation fit. The uncertainty band includes

statistical and systematic error.
145

miss
(a) 1st b-jet pT at 1st ET
slice [100, 150] GeV.

miss(b) 1st b-jet pT at 2nd ET
slice [150, 200] GeV.

miss(c) 1st b-jet pT at 3rd ET
slice [200, 250] GeV.

miss(d) 1st b-jet pT at 4th ET
slice [250, inf] GeV.

(e) 1st b-jet pT at TAUCR.
miss
Figure A.9: 1st b-jet pT distribution at each ET
slice after the validation fit. The uncertainty band includes

statistical and systematic error.
146

p
miss
miss
(a) ET/ HT at 1st ET
slice [100, 150] GeV.

p
miss
miss
(b) ET/ HT at 2nd ET
slice [150, 200] GeV.

p
miss
miss
(c) ET/ HT at 3rd ET
slice [200, 250] GeV.

p
miss
miss
(d) ET/ HT at 4th ET
slice [250, inf] GeV.

pmiss(e) ET/ HT at TAUCR.

p
miss
miss
Figure A.10: ET/ HT distribution at each ET
slice after the validation fit. The uncertainty band includes
statistical and systematic error.
147

(a)

miss
R(b, `) at 1st ET
slice [100, 150] GeV.

(b)

miss
R(b, `) at 2nd ET
slice [150, 200] GeV.

(c)

miss
R(b, `) at 3rd ET
slice [200, 250] GeV.

(d)

miss
R(b, `) at 4th ET
slice [250, inf] GeV.

(e)

Figure A.11:

R(b, `) at TAUCR.

miss
R(b, `) distribution at each ET
slice after the validation fit. The uncertainty band includes

statistical and systematic error. These plots are just for validations of the 2-D shape fit, and not used in either
the event selection or the fit.
148

miss
(a) mtop at 1st ET
slice [100, 150] GeV.

miss(b) mtop at 2nd ET
slice [150, 200] GeV.

miss(c) mtop at 3rd ET
slice [200, 250] GeV.

miss(d) mtop at 4th ET
slice [250, inf] GeV.

(e) mtop at TAUCR.
miss
Figure A.12: mtop distribution at each ET
slice after the validation fit. The uncertainty band includes statisticaland systematic error. These plots are just for validations of the 2-D shape fit, and not used in either the event
selection or the fit.
149

miss
(a) amT2 at 1st ET
slice [100, 150] GeV.

miss(b) amT2 at 2nd ET
slice [150, 200] GeV.

miss(c) amT2 at 3rd ET
slice [200, 250] GeV.

miss(d) amT2 at 4th ET
slice [250, inf] GeV.

(e) amT2 at TAUCR.
miss
Figure A.13: amT2 distribution at each ET
slice after the validation fit. The uncertainty band includes

statistical and systematic error. These plots are just for validations of the 2-D shape fit, and not used in either
the event selection or the fit.
150

miss
(a) topness at 1st ET
slice [100, 150] GeV.

miss(b) topness at 2nd ET
slice [150, 200] GeV.

miss(c) topness at 3rd ET
slice [200, 250] GeV.

miss(d) topness at 4th ET
slice [250, inf] GeV.

(e) topness at TAUCR.
miss
Figure A.14: topness distribution at each ET
slice after the validation fit. The uncertainty band includes

statistical and systematic error. These plots are just for validations of the 2-D shape fit, and not used in either
the event selection or the fit.
151

−1
−1.5
−2

JER_NP0
JER_NP1
JER_NP2
JER_NP3
JER_NP4
JER_NP5
JER_NP6
JER_NP7
JER_NP8
JES_BJES
JES_Eta_Model
JES_Eta_NonClosure
JES_Eta_TotalStat
JES_Flavor_Composition
JES_Flavor_Response
JES_Np1
JES_Np2
JES_Np3
JES_Np4
JES_Np5
JES_Np6
JES_Pileup_OffsetMu
JES_Pileup_OffsetNPV
JES_Pileup_PtTerm
JES_Pileup_RhoTopology
JES_PunchThrough_MC15
JES_SingleParticle_HighPt
Luminosity
MET_Reso_para
MET_Reso_perp
MET_ScaleTES_Detector
TES_Insitu
TES_Model
bextracextraeigen_b0
eigen_b1
eigen_b2
eigen_b3
eigen_b4
eigen_c0
eigen_c1
eigen_c2
eigen_c3
eigen_l0
eigen_l1
eigen_l10
eigen_l11
eigen_l12
eigen_l13
eigen_l2
eigen_l3
eigen_l4
eigen_l5
eigen_l6
eigen_l7
eigen_l8
eigen_l9
elId
jvt
muEffSyst
phId
prw
tauJetId
tauRecotheory_A14
theory_DS
theory_ckkw
theory_fac
theory_qsf
theory_rad
theory_renorm
theory_scale
xsec_diboson
mu_ttbar1L-1
mu_ttbarTau-1

Uncertainty After Fit

2
1.5
1
0.5
0
−0.5

Figure A.15: Model parameters and their uncertainties after the 2-D shape validation fit. The
vertical dashed-dotted line divides into two categories; standardized systematic parameters (left)
and normalization scale factors (right). The naming rule of systematic parameters follow Table 8.1-8.5. For the detailed explanation on the fit configuration, see Section 7.2.

h_corr_reduced (threshold 20 precent)
JES Enveloped NP 1

-0.02

-0.08

0.15

0.03

0.03

0.03

-0.03

-0.11

-0.03

-0.03

JES Enveloped NP 2

0.04

1.00

0.21

-0.04

0.02

0.11

0.14

-0.04

0.01

-0.06

0.02

0.11

0.02

-0.04

0.18

-0.10

-0.04

0.00

-0.11

-0.24

0.28

0.02

-0.02

0.24

0.07

JES Enveloped NP 3

-0.02

1.00

0.21

0.04

1.00

0.02

-0.02

0.03

-0.02

-0.05

-0.08

0.04

-0.01

0.01

0.03

0.01

0.00

0.02

0.02

-0.05

-0.03

-0.01

-0.01

-0.05

0.02

-0.05

0.01

0.04

0.05

0.02

JES Pseudorapidity Calibration 1

-0.08

-0.04

0.02

1.00

-0.03

-0.17

-0.02

0.15

-0.02

0.02

0.00

0.11

JES Pileup 1

-0.02

0.02

0.03

-0.03

1.00

-0.04

0.08

0.01

0.07

0.00

-0.09

-0.09

-0.01

-0.03

-0.02

0.12

0.07

0.02

-0.03

0.12

0.05

-0.02

-0.00

-0.21

-0.07

JES Pileup 3

-0.05

0.11

-0.02

-0.17

-0.04

1.00

-0.04

-0.02

0.06

-0.05

0.15

-0.01

-0.02

0.05

-0.06

0.03

0.17

0.00

-0.04

-0.03

0.06

-0.01

-0.05

-0.05

0.11

0.06

-0.04

0.01

-0.00

-0.11

-0.19

-0.09

-0.03

0.02

-0.16

-0.08

0.07

-0.06

-0.01

0.02

0.02

-0.13

0.06

0.07

0.12

0.15

-0.00

0.02

-0.12

-0.21

0.04

0.03

-0.01

-0.01

-0.22

0.06

JES Lighter-Flavor-Jet Response

0.04

0.14

-0.08

0.02

0.08

-0.04

-0.08

-0.01

0.07

-0.30

0.08

0.29

JES Lighter-Flavor-Jet Composition

-0.16

-0.04

-0.01

-0.08

0.01

-0.02

0.06

1.00

0.14

0.04

0.01

0.07

0.05

0.04

0.11

0.06

0.12

-0.01

-0.02

-0.03

0.05

-0.04

-0.08

-0.28

0.18

JER Enveloped NP

0.15

0.01

0.01

0.07

0.07

0.06

-0.04

0.14

1.00

-0.13

-0.25

0.15

-0.01

0.07

-0.23

0.00

-0.24

0.07

0.26

0.06

0.22

-0.05

-0.02

0.06

0.28

JER Cross Calibration 2

0.03

-0.06

0.03

-0.02

0.00

-0.05

-0.02

0.04

-0.13

1.00

-0.08

-0.07

-0.03

0.05

-0.07

-0.04

-0.04

-0.02

0.06

JER Cross Calibration 3

-0.06

0.02

0.01

0.15

-0.09

0.15

0.04

0.01

-0.25

-0.08

1.00

-0.19

0.13

0.09

0.11

0.12

0.03

0.02

0.01

-0.06

0.01

0.03

-0.04

0.30

0.51

JER Cross Calibration 4

-0.01

0.11

0.00

0.02

-0.09

-0.01

0.01

0.07

0.15

-0.07

-0.19

1.00

-0.11

0.02

-0.13

0.10

-0.06

-0.02

-0.02

-0.04

0.03

-0.01

-0.01

0.19

0.37

JER Cross Calibration 5

0.03

0.02

0.02

-0.02

-0.01

-0.02

0.01

0.05

-0.01

-0.03

0.13

-0.11

1.00

0.05

-0.07

0.14

-0.00

0.01

0.01

0.16

0.05

-0.00

0.04

0.25

0.43

JER Cross Calibration 7

0.03

-0.00

-0.02

0.04

0.01

-0.05

-0.03

0.04

-0.02

-0.10

0.06

-0.04

0.02

0.02

-0.03

0.05

-0.00

0.04

0.07

0.05

0.09

0.02

0.05

1.00

-0.01

0.03

-0.02

0.01

0.06

0.10

0.02

0.01

0.14

0.29

Parallel Resolution

0.02

0.18

-0.05

-0.13

-0.02

-0.06

-0.11

0.11

-0.23

-0.07

0.11

-0.13

-0.07

-0.01

1.00

-0.32

-0.24

0.01

-0.16

-0.04

-0.14

0.02

0.06

-0.09

-0.19

0.06

-0.10

-0.03

0.07

0.12

0.03

-0.19

0.06

0.00

-0.04

0.12

0.10

0.14

0.03

-0.32

1.00

-0.28

-0.07

0.08

0.09

0.09

0.04

-0.07

-0.04

0.23

Energy Scale

0.12

-0.04

-0.01

0.15

0.07

0.17

-0.08

0.12

-0.24

-0.05

0.03

-0.06

-0.00

-0.02

-0.24

-0.28

1.00

-0.05

0.13

-0.04

0.14

-0.02

-0.04

-0.27

-0.07

-0.05

miss

miss

ET

0.00

0.02

0.02

0.09

0.34

0.18

0.21

0.08

0.03

0.18

0.11

-0.05

0.03

0.05

0.06

-0.09

0.05

0.22

0.06

0.01

0.03

0.05

0.02

-0.14

0.09

0.14

-0.11

0.26

0.21

1.00

-0.05

-0.47

0.12

0.26

0.01

-0.01

-0.02

-0.01

0.04

-0.04

-0.05

-0.02

0.03

-0.01

-0.00

-0.00

0.02

0.04

-0.02

-0.05

0.02

0.08

-0.05

1.00

-0.21

0.14

-0.02

-0.02

0.04

-0.01

-0.00

-0.05

0.08

-0.08

-0.02

-0.10

-0.04

-0.01

0.04

0.01

0.06

-0.07

-0.04

-0.22

0.09

0.03

-0.47

-0.21

1.00

0.23

-0.08

µ(ttbar1L)

-0.22

0.24

0.05

0.00

-0.21

-0.05

0.29

-0.28

0.06

0.06

0.30

0.19

0.25

0.14

-0.09

-0.04

-0.27

0.00

0.34

0.18

0.12

0.14

0.23

1.00

0.48

µ(ttbarTau)

0.06

0.07

0.02

0.11

-0.07

0.11

-0.03

0.18

0.28

0.22

0.51

0.37

0.43

0.29

-0.19

0.23

-0.07

0.02

0.18

0.11

0.26

-0.02

-0.08

0.48

1.00

miss

ET

miss

ET

miss

0.28
0.02

-0.03

Parallel Resolution

0.04
-0.03

Perpendicular Resolution

singletop Interference
W+jets & diboson Factorization
W+jets & diboson Renormalizationµ(ttbar1L)

-0.22

0.26

1.00

µ(ttbarTau)

-0.05

0.03

0.03

W+jets & diboson Factorization

-0.11

1.00

-0.03

W+jets & diboson Renormalization

-0.03

0.01

-0.04

ttbar Parton Shower

0.01

0.13

0.09

singletop Interference

1.00

0.08

-0.04

ttbar & singletop Radiation

-0.07

-0.16

0.10

Energy Scale

0.01

0.06

0.16

B-Tag Lighter-Flavor-Jet 1

0.01

0.01

-0.04

JER Cross Calibration 7

0.01

-0.02

-0.06

JER Cross Calibration 5

-0.02

0.01

-0.02

JER Cross Calibration 4

0.02

-0.04

0.06

JER Cross Calibration 3

-0.03

0.26

-0.03

JER Enveloped NP

0.07

-0.02

-0.30

JER Cross Calibration 2

-0.01

0.07

-0.03

JES Lighter-Flavor-Jet Response

-0.01

-0.04

0.12

JES Lighter-Flavor-Jet Composition

0.00

-0.03

-0.21

JES Pileup 1

0.02

-0.12

0.02

JES Pileup 3

0.02

-0.05

-0.24

JES Enveloped NP 3

-0.01

-0.11

-0.11

JES Pseudorapidity Calibration 1

0.00

-0.03

JES Enveloped NP 1

-0.00

ttbar Parton Shower

JES Enveloped NP 2

B-Tag Lighter-Flavor-Jet 1
ttbar & singletop Radiation

ET

0.8
0.6

0.22

Perpendicular Resolution

ET
miss

ET

1.00

1

0.4
0.2
0
−0.2
−0.4

Figure A.16: Correlations among model parameters after the 2-D shape validation fit. Onlyparameters with at least one correlation of more than 0.2 are shown. The naming rule of systematic parameters follow Table 8.1-8.5. For the detailed explanation on the fit configuration,see Section 7.2.

152

Appendix B

Asymptotic Formulae for
Hypothesis Test
This appendix summarizes the ‘asymptotic formulae [120]’ that analytically deduces probability
distribution of the modified profile likelihood ratio (PLR) in Equation 7.13. The asymptotic
formulae can reduce CPU time drastically compared to a traditional MC sampling method,
therefore it is matched to the analysis where many nuisance parameters must be included in themodel. For usefulness in the later use, two types of test statistics are defined for the purpose of
discovery and exclusion declaration respectively. The test statistic used for discovery is defined
as:
t0 =

8
<0

(µ̂sig < 0)

: 2 ln ˜ (0)(µ̂sig(B.1)

0)

And the test statistic used for exclusion is defined as:
8<0(µ̂sig > 1)t1 =: 2 ln ˜ (1) (µ̂  1)

(B.2)

sig

To construct the probability distribution of t0 (t1 ) to calculate p-values for discovery (exclusion),
the asymptotic formulae [120] are used in the analysis instead of a traditional MC sampling
method. The asymptotic formulae are based on the Wald’s theorem [138] where for the casethere is just one POI, the following approximation of profile likelihood ratio is derived:
2 ln (µsig ) =µ̂sig )2

(µsig

2

p
+ O(1/ N )(B.3)

where N is the number of observed events. From Equation B.3, the test statistic for discovery(Equation B.1) is approximated as:
t0 =
where

8
<0
:

(µ̂sig < 0)µ̂2sig2(µ̂sig(B.4)

0)

is standard deviation of µ̂sig . And the probability of the test statistic for discovery canbe derived as:
P rob(t0 |µ0sig ) =

✓

1

✓

µ0sig

◆◆

1 1
1
(t0 ) + p p exp
2 2⇡ t0
153

"

1
2

✓

p

t0

µ0sig

◆2 #

(B.5)

whereis standard gaussian, µ0sig indicates which hypothesis is assumed true for the probability(µ0sig = 0 and µ0sig = 1 for null- and alternative-hypothesis respectively), and µ̂sig is assumed tofollow a gaussian distribution with mean µ0sig and standard deviation . In the case of the testof null-hypothesis (µ0sig = 0) to calculate CLb , this reduces to:
P rob(t0 |µ0sig = 0) =1
1 1
1(t0 ) + p p e22 2⇡ t0

t02

In the same way, the test statistic for exclusion (Equation B.2) is approximated as:
8>>0(µ̂sig > 1)><2
t1 = (1 µ̂2sig )(0  µ̂sig  1)>>>2µ̂sig:1(µ̂ < 0)
2

+

2

:p

p1 exp2⇡ t1

1
exp
2⇡(2/ )

h

h

(B.7)

sig

2

and the probability of the test statistic for exclusion can be derived as:✓ 0◆µsig 10
P rob(t1 |µsig ) =(t1 )8< 1 p1(B.6)

i

1 µ0sig 2
1 p)
2 ( t1
0
2 2i
(t
(1
2µ
)/
)
sig
1 1
2
(2/ )2(0 < t1  12 )(B.8)

(t1 > 12 )For CLs calculation, CLb and CLs+b can be calculated by integration of P rob(t1 |µ0sig = 0) andP rob(t1 |µ0sig = 1). The hypothesis test with the asymptotic formulae and profile calculation are
implemented in RooStats [118].

154

Appendix C

Systematic Uncertainty Plots for
DiagonalThis appendix shows ⌘ modeling for Diagonal in detail. Since there are too many ⌘ functions(⇠84000), relatively important systematic variations for the dominant background tt̄ (1L1⌧h ) at
misseach ETslice and TAUCR are shown in Figure C.1-C.10.

155

2000

2500

1500

1000

1000

500

500

50

100

150

200

250

300

1.1

JER_NP1Norm Syst
Nom [MCStatError]
JER_NP1Norm HighJER_NP1Norm Low

2000

1500

0

∆ X/X[%]

Entries

JER_NP1Norm Syst
JER_NP0Norm Syst
Nom [MCStatError]
JER_NP0Norm HighJER_NP0Norm Low

0350
mt/1000∆ X/X[%]

Entries

JER_NP0Norm Syst
2500

1.05

50

100

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300

350
mt/1000

50

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350
mt/1000

1.04
1.02

1

1

0.95

0.98
0.96

0.9

50

100

150

200

250

300

350
mt/1000(a) JER NP0(b) JER NP1
JER_NP2Norm Syst
Nom [MCStatError]
JER_NP2Norm HighJER_NP2Norm Low

2000

2500

1500

1000

1000

500

500

50

100

150

200

250

300

1.08
1.06
1.04
1.02
1
0.98
0.96
0.94
0.92
0.9

50

100

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300

JER_NP3Norm Syst
Nom [MCStatError]
JER_NP3Norm HighJER_NP3Norm Low

2000

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2500

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mt/1000∆ X/X[%]

Entries

JER_NP2Norm Syst

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mt/1000

50

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mt/1000

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0.98
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350
mt/1000(c) JER NP2(d) JER NP3
JER_NP4Norm Syst
Nom [MCStatError]
JER_NP4Norm HighJER_NP4Norm Low

2000

2500

1500

1000

1000

500

500

50

100

150

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JER_NP5Norm Syst
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2000

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Entries

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2500

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mt/1000∆ X/X[%]

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JER_NP4Norm Syst

1.08
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1.02
1
0.98
0.96
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0.92
0.9

50

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150

200

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300

350
mt/1000

50

100

150

200

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350
mt/1000

1.02
1
0.98
0.96
0.94

50

100

150

200

250

300

350
mt/1000(e) JER NP4(f) JER NP5
JER_NP6Norm Syst
Nom [MCStatError]
JER_NP6Norm HighJER_NP6Norm Low

2000

2500

1500

1000

1000

500

500

50

100

150

200

250

300

1.06

JER_NP7Norm Syst
Nom [MCStatError]
JER_NP7Norm HighJER_NP7Norm Low

2000

1500

0

∆ X/X[%]

Entries

JER_NP7Norm Syst

2500

0

350
mt/1000∆ X/X[%]

Entries

JER_NP6Norm Syst

1.04
1.02
1

50

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150

200

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350
mt/1000

50

100

150

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300

350
mt/1000

1.04
1.02
1
0.98

0.98

0.96

0.96

0.94

0.94

50

100

150

200

250

300

350
mt/1000(g) JER NP6(h) JER NP7

missFigure C.1: Systematic variations of mT [GeV] shape at the 1st ET
slice ([100, 150] GeV) of Diagonal for tt̄

(1L1⌧h ) (1/2). Each error bar indicates MC statistical error. Green and red lines indicate the ⌘(↵ = ±1) values.

156

2000

2500
JES_Flavor_CompositionNorm Syst
Nom [MCStatError]
JES_Flavor_CompositionNorm High

2000

1500

1500

1000

1000

500

500

0

∆ X/X[%]

Entries

JES_Flavor_CompositionNorm Syst
JER_NP8Norm Syst
Nom [MCStatError]
JER_NP8Norm HighJER_NP8Norm Low

50

100

150

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250

300

1
0.99
0.98
0.97
0.96

0

350
mt/1000

1.04
1.03
1.02
1.01

∆ X/X[%]

Entries

JER_NP8Norm Syst
2500

JES_Flavor_CompositionNorm Low

50

100

150

200

250

300

350
mt/1000

50

100

150

200

250

300

350
mt/1000

1.06
1.04
1.02
1
0.98
0.96
0.94

50

100

150

200

250

300

350
mt/1000(a) JER NP8(b) JES Flavor Composition
MET_Reso_paraNorm Syst
Nom [MCStatError]
MET_Reso_paraNorm HighMET_Reso_paraNorm Low

2000

2500

1500

1000

1000

500

500

50

100

150

200

250

300

0

350
mt/1000

1.04
1.02
1
0.98
0.96

50

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300

MET_Reso_perpNorm Syst
Nom [MCStatError]
MET_Reso_perpNorm HighMET_Reso_perpNorm Low

2000

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∆ X/X[%]

Entries

MET_Reso_perpNorm Syst

2500

∆ X/X[%]

Entries

MET_Reso_paraNorm Syst

50

100

150

200

250

300

350
mt/1000

50

100

150

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250

300

350
mt/1000

1.04
1.03
1.02
1.01
1
0.99
0.98
0.97
0.96

350
mt/1000(c) MET Reso para(d) MET Reso perp
theory_A14Norm Syst
Nom [MCStatError]
theory_A14Norm Hightheory_A14Norm Low

2000

2500

1500

1000

1000

500

500

50

100

150

200

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300

1.12
1.1
1.08
1.06
1.04
1.02
1
0.98
0.96
0.94
0.92

theory_radNorm Syst
Nom [MCStatError]
theory_radNorm Hightheory_radNorm Low

2000

1500

0

∆ X/X[%]

Entriestheory_radNorm Syst

2500

0

350
mt/1000∆ X/X[%]

Entriestheory_A14Norm Syst

50

100

150

200

250

300

350
mt/1000

50

100

150

200

250

300

350
mt/1000

1.1
1.05
1
0.95
0.9

50

100

150

200

250

300

350
mt/1000(e) theory A14(f) theory rad

missFigure C.2: Systematic variations of mT [GeV] shape at the 1st ET
slice ([100, 150] GeV) of Diagonal for tt̄

(1L1⌧h ) (2/2). Each error bar indicates MC statistical error. Green and red lines indicate the ⌘(↵ = ±1) values.

157

JER_NP1Norm Syst
Entries

Entries

JER_NP0Norm Syst
1000
JER_NP0Norm Syst
Nom [MCStatError]
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800

1000
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Nom [MCStatError]
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900
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mt/1000∆ X/X[%]∆ X/X[%]

50

1.1
1.08
1.06
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1.02
1
0.98
0.96
0.94

50

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350
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50

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1
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250

300

350
mt/1000(a) JER NP0(b) JER NP1
JER_NP3Norm Syst
Entries

Entries

JER_NP2Norm Syst
1000
JER_NP2Norm Syst
Nom [MCStatError]
JER_NP2Norm HighJER_NP2Norm Low

900
800

JER_NP3Norm Syst
Nom [MCStatError]
JER_NP3Norm HighJER_NP3Norm Low

900
800

700

700

600

600

500

500

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200
100

100
100

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mt/1000∆ X/X[%]

50∆ X/X[%]

1000

1.07
1.06
1.05
1.04
1.03
1.02
1.01
1
0.99

50

100

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mt/1000

50

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mt/1000

1.08
1.06
1.04
1.02
1
0.98
0.96
0.94

50

100

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250

300

350
mt/1000(c) JER NP2(d) JER NP3
JER_NP5Norm Syst
Entries

Entries

JER_NP4Norm Syst
1000
JER_NP4Norm Syst
Nom [MCStatError]
JER_NP4Norm HighJER_NP4Norm Low

900
800
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500

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100
100

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mt/1000∆ X/X[%]

50

1.05
1.04
1.03
1.02
1.01
1
0.99
0.98
0.97
0.96

JER_NP5Norm Syst
Nom [MCStatError]
JER_NP5Norm HighJER_NP5Norm Low

900
800

100

∆ X/X[%]

1000

50

100

150

200

250

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mt/1000

50

100

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mt/1000

1.06
1.04
1.02
1
0.98

50

100

150

200

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300

0.96

350
mt/1000(e) JER NP4(f) JER NP5
JER_NP7Norm Syst

1000

Entries

Entries

JER_NP6Norm Syst
JER_NP6Norm Syst
Nom [MCStatError]
JER_NP6Norm HighJER_NP6Norm Low

900
800

JER_NP7Norm Syst
Nom [MCStatError]
JER_NP7Norm HighJER_NP7Norm Low

900
800

700

700

600

600

500

500

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200

200

100

100
100

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250

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1.04
1.03
1.02
1.01
1
0.99
0.98
0.97

350
mt/1000∆ X/X[%]

50∆ X/X[%]

1000

50

100

150

200

250

300

350
mt/1000

50

100

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300

350
mt/1000

1.06
1.04
1.02
1
0.98

50

100

150

200

250

300

350
mt/1000(g) JER NP6(h) JER NP7

missFigure C.3: Systematic variations of mT [GeV] shape at the 2nd ET
slice ([150, 200] GeV) of Diagonal for tt̄

(1L1⌧h ) (1/2). Each error bar indicates MC statistical error. Green and red lines indicate the ⌘(↵ = ±1) values.

158

JES_Flavor_CompositionNorm Syst
Entries

Entries

JER_NP8Norm Syst
1000
JER_NP8Norm Syst
Nom [MCStatError]
JER_NP8Norm HighJER_NP8Norm Low

900
800

JES_Flavor_CompositionNorm Syst

900

JES_Flavor_CompositionNorm High

700

700

600

600

500

500

400

400

300

300

200

200

JES_Flavor_CompositionNorm Low

100
100

150

200

250

300

350
mt/1000∆ X/X[%]

50

1.05
1.04
1.03
1.02

50

100

150

200

250

300

350
mt/1000

50

100

150

200

250

300

350
mt/1000

1.06
1.04
1.02

1.01

1

1
0.99

0.98

0.98

Nom [MCStatError]

800

100

∆ X/X[%]

1000

0.96

50

100

150

200

250

300

350
mt/1000(a) JER NP8(b) JES Flavor Composition
MET_Reso_perpNorm Syst

1000

Entries

Entries

MET_Reso_paraNorm Syst
MET_Reso_paraNorm Syst
Nom [MCStatError]
MET_Reso_paraNorm HighMET_Reso_paraNorm Low

900
800

MET_Reso_perpNorm Syst
Nom [MCStatError]
MET_Reso_perpNorm HighMET_Reso_perpNorm Low

900
800

700

700

600

600

500

500

400

400

300

300

200

200

100

100
100

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250

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mt/1000∆ X/X[%]

50∆ X/X[%]

1000

1.02
1.01
1
0.99
0.98

50

100

150

200

250

300

350
mt/1000

1.04
1.03
1.02
1.01
1
0.99
0.98
0.97
0.96

50

100

150

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250

300

350
mt/1000

50

100

150

200

250

300

350
mt/1000(c) MET Reso para(d) MET Reso perp
theory_radNorm Syst
Entries

Entriestheory_A14Norm Syst
1000
theory_A14Norm Syst
Nom [MCStatError]
theory_A14Norm Hightheory_A14Norm Low

800

1000
theory_radNorm Syst
Nom [MCStatError]
theory_radNorm Hightheory_radNorm Low

900
800
700
600

600

500
400

400

300
200

200

100

1.08
1.06
1.04
1.02
1
0.98
0.96
0.94
0.92
0.9
0.88

100

150

200

250

300

350
mt/1000∆ X/X[%]∆ X/X[%]

50

50

100

150

200

250

300

350
mt/1000

50

100

150

200

250

300

350
mt/1000

1.05
1
0.95
0.9
0.85

50

100

150

200

250

300

350
mt/1000(e) theory A14(f) theory rad

missFigure C.4: Systematic variations of mT [GeV] shape at the 2nd ET
slice ([150, 200] GeV) of Diagonal for tt̄

(1L1⌧h ) (2/2). Each error bar indicates MC statistical error. Green and red lines indicate the ⌘(↵ = ±1) values.

159

JER_NP1Norm Syst
Entries

Entries

JER_NP0Norm Syst
450

JER_NP0Norm Syst
Nom [MCStatError]
JER_NP0Norm HighJER_NP0Norm Low

400

JER_NP1Norm Syst
Nom [MCStatError]
JER_NP1Norm HighJER_NP1Norm Low

400

350

350

300

300

250

250

200

200

150

150

100

100

50

50
100

150

200

250

300

1.06
1.04
1.02

350
mt/1000∆ X/X[%]

50∆ X/X[%]

450

1
0.98
0.96
0.94
0.92

50

100

150

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250

300

50

100

150

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250

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350
mt/1000

50

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350
mt/1000

1.03
1.02
1.01
1
0.99
0.98
0.97
0.96
0.95

350
mt/1000(a) JER NP0(b) JER NP1
JER_NP3Norm Syst
Entries

Entries

JER_NP2Norm Syst
450
JER_NP2Norm Syst
Nom [MCStatError]
JER_NP2Norm HighJER_NP2Norm Low

400

JER_NP3Norm Syst
Nom [MCStatError]
JER_NP3Norm HighJER_NP3Norm Low

400

350

350

300

300

250

250

200

200

150

150

100

100

50

50
100

150

200

250

300

1.08
1.06
1.04
1.02

350
mt/1000∆ X/X[%]

50∆ X/X[%]

450

1
0.98
0.96
0.94

50

100

150

200

250

300

350
mt/1000

50

100

150

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250

300

350
mt/1000

1.08
1.06
1.04
1.02
1
0.98
0.96
0.94

50

100

150

200

250

300

350
mt/1000(c) JER NP2(d) JER NP3
JER_NP5Norm Syst

450

Entries

Entries

JER_NP4Norm Syst
JER_NP4Norm Syst
Nom [MCStatError]
JER_NP4Norm HighJER_NP4Norm Low

400

350

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300

250

250

200

200

150

150

100

100
50
100

150

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mt/1000∆ X/X[%]

50

1.04
1.02
1

50

100

150

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350
mt/1000

50

100

150

200

250

300

350
mt/1000

1.04
1.02
1

0.98

0.98

0.96
0.94
0.92

JER_NP5Norm Syst
Nom [MCStatError]
JER_NP5Norm HighJER_NP5Norm Low

400

350

50

∆ X/X[%]

450

0.96

50

100

150

200

250

300

350
mt/1000(e) JER NP4(f) JER NP5
JER_NP7Norm Syst
Entries

Entries

JER_NP6Norm Syst
450
JER_NP6Norm Syst
Nom [MCStatError]
JER_NP6Norm HighJER_NP6Norm Low

400

350

300

300

250

250

200

200

150

150

100

100
50
100

150

200

250

300

350
mt/1000∆ X/X[%]

50

1.06
1.04
1.02

50

100

150

200

250

300

350
mt/1000

50

100

150

200

250

300

350
mt/1000

1.02
1
0.98

1

0.96

0.98
0.96

JER_NP7Norm Syst
Nom [MCStatError]
JER_NP7Norm HighJER_NP7Norm Low

400

350

50

∆ X/X[%]

450

0.94

50

100

150

200

250

300

0.92

350
mt/1000(g) JER NP6(h) JER NP7

missFigure C.5: Systematic variations of mT [GeV] shape at the 3rd ET
slice ([200, 250] GeV) of Diagonal for tt̄

(1L1⌧h ) (1/2). Each error bar indicates MC statistical error. Green and red lines indicate the ⌘(↵ = ±1) values.

160

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Entries

Entries

JER_NP8Norm Syst
450
JER_NP8Norm Syst
Nom [MCStatError]
JER_NP8Norm HighJER_NP8Norm Low

400

JES_Flavor_CompositionNorm Syst
Nom [MCStatError]

400

JES_Flavor_CompositionNorm HighJES_Flavor_CompositionNorm Low

350

350

300

300

250

250

200

200

150

150

100

100

50

50
100

150

200

250

300

350
mt/1000∆ X/X[%]

50∆ X/X[%]

450

1.04
1.02
1
0.98
0.96

50

100

150

200

250

300

50

100

150

200

250

300

350
mt/1000

50

100

150

200

250

300

350
mt/1000

1.02
1.01
1
0.99
0.98
0.97
0.96
0.95

350
mt/1000(a) JER NP8(b) JES Flavor Composition
MET_Reso_perpNorm Syst
Entries

Entries

MET_Reso_paraNorm Syst
450
MET_Reso_paraNorm Syst
Nom [MCStatError]
MET_Reso_paraNorm HighMET_Reso_paraNorm Low

400

MET_Reso_perpNorm Syst
Nom [MCStatError]
MET_Reso_perpNorm HighMET_Reso_perpNorm Low

400

350

350

300

300

250

250

200

200

150

150

100

100
50

50
100

150

200

250

300

350
mt/1000∆ X/X[%]

50∆ X/X[%]

450

1.03
1.02
1.01
1
0.99
0.98
0.97

50

100

150

200

250

300

50

100

150

200

250

300

350
mt/1000

50

100

150

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250

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350
mt/1000

1.02
1.015
1.01
1.005
1
0.995
0.99
0.985
0.98

350
mt/1000(c) MET Reso para(d) MET Reso perp
theory_radNorm Syst

500

Entries

Entriestheory_A14Norm Syst
theory_A14Norm Syst
Nom [MCStatError]
theory_A14Norm Hightheory_A14Norm Low

450
400

theory_radNorm Syst
Nom [MCStatError]
theory_radNorm Hightheory_radNorm Low

450
400

350

350

300

300

250

250

200

200

150

150

100

100

50

50
100

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mt/1000∆ X/X[%]

50∆ X/X[%]

500

1.2
1.1
1
0.9

50

100

150

200

250

300

350
mt/1000

50

100

150

200

250

300

350
mt/1000

1.25
1.2
1.15
1.1
1.05
1
0.95
0.9

0.8
0.7

50

100

150

200

250

300

350
mt/1000(e) theory A14(f) theory rad

missFigure C.6: Systematic variations of mT [GeV] shape at the 3rd ET
slice ([200, 250] GeV) of Diagonal for tt̄

(1L1⌧h ) (2/2). Each error bar indicates MC statistical error. Green and red lines indicate the ⌘(↵ = ±1) values.

161

JER_NP1Norm Syst
Entries

Entries

JER_NP0Norm Syst
350
JER_NP0Norm Syst
Nom [MCStatError]
JER_NP0Norm HighJER_NP0Norm Low

300

250

250

200

200

150

150

100

100

50

50
100

150

200

250

300

350
mt/1000∆ X/X[%]∆ X/X[%]

50

1.1
1.08
1.06
1.04
1.02
1
0.98
0.96

JER_NP1Norm Syst
Nom [MCStatError]
JER_NP1Norm HighJER_NP1Norm Low

300

50

100

150

200

250

300

350
mt/1000

50

100

150

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350
mt/1000

1.08
1.06
1.04
1.02
1
0.98
0.96
0.94

50

100

150

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250

300

350
mt/1000(a) JER NP0(b) JER NP1
JER_NP3Norm Syst
Entries

Entries

JER_NP2Norm Syst
JER_NP2Norm Syst
Nom [MCStatError]
JER_NP2Norm HighJER_NP2Norm Low

300

250

250

200

200

150

150

100

100

50

50
100

150

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300

1.12
1.1
1.08
1.06
1.04
1.02
1
0.98
0.96

350
mt/1000∆ X/X[%]

50∆ X/X[%]

JER_NP3Norm Syst
Nom [MCStatError]
JER_NP3Norm HighJER_NP3Norm Low

300

50

100

150

200

250

300

350
mt/1000

50

100

150

200

250

300

350
mt/1000

1.06
1.04
1.02
1
0.98
0.96
0.94

50

100

150

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300

350
mt/1000(c) JER NP2(d) JER NP3
JER_NP5Norm Syst
Entries

Entries

JER_NP4Norm Syst
JER_NP4Norm Syst
Nom [MCStatError]
JER_NP4Norm HighJER_NP4Norm Low

300

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250

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200

150

150

100

100

50

50
100

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1.12
1.1
1.08
1.06
1.04
1.02
1
0.98
0.96
0.94

350
mt/1000∆ X/X[%]

50∆ X/X[%]

JER_NP5Norm Syst
Nom [MCStatError]
JER_NP5Norm HighJER_NP5Norm Low

300

50

100

150

200

250

300

350
mt/1000

50

100

150

200

250

300

350
mt/1000

1.06
1.04
1.02
1
0.98
0.96
0.94

50

100

150

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250

300

350
mt/1000(e) JER NP4(f) JER NP5
JER_NP7Norm Syst
Entries

Entries

JER_NP6Norm Syst
JER_NP6Norm Syst
Nom [MCStatError]
JER_NP6Norm HighJER_NP6Norm Low

300

250

250

200

200

150

150

100

100

50

50
100

150

200

250

300

1.06
1.04

350
mt/1000∆ X/X[%]

50∆ X/X[%]

JER_NP7Norm Syst
Nom [MCStatError]
JER_NP7Norm HighJER_NP7Norm Low

300

1.02
1
0.98
0.96
0.94

50

100

150

200

250

300

350
mt/1000(g) JER NP6

100

150

200

250

300

350
mt/1000

50

100

150

200

250

300

350
mt/1000

1.02
1
0.98
0.96
0.94
0.92

0.92

50

1.06
1.04

(h) JER NP7

missFigure C.7: Systematic variations of mT [GeV] shape at the highest ET
slice ([250, inf] GeV) of Diagonal for tt̄

(1L1⌧h ) (1/2). Each error bar indicates MC statistical error. Green and red lines indicate the ⌘(↵ = ±1) values.

162

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Entries

Entries

JER_NP8Norm Syst
JER_NP8Norm Syst
Nom [MCStatError]
JER_NP8Norm HighJER_NP8Norm Low

300

Nom [MCStatError]
JES_Flavor_CompositionNorm HighJES_Flavor_CompositionNorm Low

250

250

200

200

150

150

100

100

50

50
100

150

200

250

300

350
mt/1000∆ X/X[%]

50∆ X/X[%]

JES_Flavor_CompositionNorm Syst

300

1.1
1.08
1.06
1.04
1.02
1
0.98
0.96
0.94

50

100

150

200

250

300

350
mt/1000

50

100

150

200

250

300

350
mt/1000

1.04
1.02
1
0.98
0.96

50

100

150

200

250

300

350
mt/1000(a) JER NP8(b) JES Flavor Composition
MET_Reso_perpNorm Syst
Entries

Entries

MET_Reso_paraNorm Syst
MET_Reso_paraNorm Syst
Nom [MCStatError]
MET_Reso_paraNorm HighMET_Reso_paraNorm Low

300

250

250

200

200

150

150

100

100

50

50
100

150

200

250

300

1.03

350
mt/1000∆ X/X[%]

50∆ X/X[%]

MET_Reso_perpNorm Syst
Nom [MCStatError]
MET_Reso_perpNorm HighMET_Reso_perpNorm Low

300

1.02
1.01
1

1
0.995
0.99
0.985
0.98

0.99
0.98
0.97

50

100

150

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250

300

350
mt/1000

50

100

150

200

250

300

350
mt/1000

50

100

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200

250

300

350
mt/1000

1.02
1.015
1.01
1.005

(c) MET Reso para(d) MET Reso perp
theory_radNorm Syst
Entries

Entriestheory_A14Norm Syst
theory_A14Norm Syst
Nom [MCStatError]
theory_A14Norm Hightheory_A14Norm Low

300

400
theory_radNorm Syst
Nom [MCStatError]
theory_radNorm Hightheory_radNorm Low

350
300

250

250
200
200
150
150
100

100
50

50
100

150

200

250

300

350
mt/1000∆ X/X[%]∆ X/X[%]

50

1.15
1.1
1.05
1
0.95
0.9
0.85
0.8

50

100

150

200

250

300

350
mt/1000

50

100

150

200

250

300

350
mt/1000

1.3
1.2
1.1
1
0.9

50

100

150

200

250

300

0.8

350
mt/1000(e) theory A14(f) theory rad

missFigure C.8: Systematic variations of mT [GeV] shape at the highest ET
slice ([250, inf] GeV) of Diagonal for tt̄

(1L1⌧h ) (2/2). Each error bar indicates MC statistical error. Green and red lines indicate the ⌘(↵ = ±1) values.

163

JER_NP1Norm Syst
Entries

Entries

JER_NP0Norm Syst
1850

JER_NP0Norm Syst
Nom [MCStatError]
JER_NP0Norm HighJER_NP0Norm Low

1840

JER_NP1Norm Syst
Nom [MCStatError]
JER_NP1Norm HighJER_NP1Norm Low

1806

1830

1804

1820

1802

1810

1800

1800

1798

1790

1796

1780

1794
120

140

160

180

200

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260

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120
mt/1000

1.04∆ X/X[%]∆ X/X[%]

1808

1.03
1.02

140

160

180

200

240

260

280

300
mt/1000

1.01
1.005

1.01

1

1

0.995

0.99

120

140

160

180

200

220

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260

280

0.99

300
mt/1000

120

140

160

(a) JER NP0

180

200

220

240

260

280

300
mt/1000(b) JER NP1
JER_NP3Norm Syst
Entries

JER_NP2Norm Syst
Entries

220

1.015

JER_NP2Norm Syst
Nom [MCStatError]
JER_NP2Norm HighJER_NP2Norm Low

1815

1808
JER_NP3Norm Syst
Nom [MCStatError]
JER_NP3Norm HighJER_NP3Norm Low

1806
1804

1810

1802
1805
1800
1800
1798
1796

1795

1794
1790
140

160

180

200

220

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120
mt/1000∆ X/X[%]∆ X/X[%]

120

1.02
1.015
1.01

140

160

180

200

240

260

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Figure C.9: Systematic variations of mT [GeV] shape at TAUCR of Diagonal for tt̄ (1L1⌧h ) (1/2). Each error
bar indicates MC statistical error. Green and red lines indicate the ⌘(↵ = ±1) values.

164JES_Flavor_CompositionNorm Syst
Entries

Entries

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bar indicates MC statistical error. Green and red lines indicate the ⌘(↵ = ±1) values.

Appendix D

Upgrading Trigger Readout of
LAr Calorimeter
This appendix describes upgrade studies of the LAr calorimeter trigger readout. There is along-term project of upgrading trigger readout of the ATLAS LAr calorimeter, which is aimed at‘High-Luminosity LHC (HL-LHC)’ that will start from 2024 with an ultimate peak instantaneous
luminosity of L ⇠ 5 ⇥ 1034 cm 2 s 1 and will deliver an integrated luminosity of ⇠ 250 fb 1 in ayear and up to 3 fb 1 after 12 years of running. Due to its very high instantaneous luminosity,
keeping L1 trigger rate 100 kHz in HL-LHC requires to replace the current trigger readout
electronics with new high-end ones. The new trigger readout system is named ‘supercell’ thatcan provide higher-granularity, higher-resolution and longitudinal shower information from thecalorimeter to the L1 trigger processors [139].
Appendix D.1 describes supercell design. Appendix D.2 outlines new high-end electronics forsupercell. Appendix D.3 introduces ‘demonstrator system’ to do performance tests of the newhigh-end electronics and obtain experiences of supercell installation. Appendix D.4 shows resultsof the performance test with the demonstrator system. My main works were performance testsof ‘demonstrator system’, described in Appendix D.4. Especially, I contributed to the success offirst installation of the demonstrator system by assuring through performance tests that it has
no significant problem.

D.1

Supercell

Figure D.1 illustrates how supercell works with comparison of the current trigger readout system
named ‘trigger tower’ and shows the behavior of the supercell and the trigger tower against
injection of an electron into the barrel part of LAr calorimeter. Although there are four layers
in the barrel part and calorimeter cells with fine granularity as described in section 2.2.2 andTable 2.1, the trigger tower reads out just only sum of energy deposits over a coarser range of⌘⇥= 0.1 ⇥ 0.1 in the four layers all because of limitation of its readout performance. In

the case of supercell, new electronics can provide faster readout and thus the supercell can readout each of 10 energy deposits per the range of trigger tower with granularity of⌘⇥=

0.1 ⇥ 0.1(1st and 4th layers) and 0.025 ⇥ 0.1(2nd and 3rd layers) as illustrated in Figure D.1.
The new trigger readout electronics will be installed into the LAr calorimeter during two terms;

166

Figure D.1: Comparison of the upgraded and the current trigger readout systems, ‘supercell’ (a)and ‘trigger tower’ (b). An electron (with transverse energy of 70 GeV) is injected into the barrel
part of LAr calorimeter, and the behavior of supercell and trigger tower is illustrated.
a long shutdown during 2019 - 2020 (Phase-I upgrade) and the next long shutdown during 2024
- mid-2026 (Phase-II upgrade)[137, 139].

D.2

New High-End Electronics for Supercell Toward PhaseI Upgrade

Figure D.2 shows the new readout system in the Phase-I Upgrade that contains the legacy trigger
tower readout path and the new supercell readout path will be prepared in parallel in order tokeep the legacy trigger path as a fallback. The new high-end electronics for the supercell readout
is prepared for purpose of fast real-time data processing and transfer. In this section, four newcomponents, a new baseplane, a new layer sub board, the LAr Trigger Digitizer Board (LTDB),
and the LAr Digital Processing System (LDPS) are overviewed.
New Layer Sum Board
The current layer sum board (LSB) provides summation of analog signals of the elementary
LAr calorimeter cells over a range of⌘⇥= 0.1⇥0.1 for a given layer of the calorimeter.

During the Phase-I Upgrade, the new LSB processes 4 times finer segments

167

⌘⇥

=

Figure D.2: Schematic diagram of the architecture of the readout electronics after the Phase-I
Upgrade [139]. New components are indicated by red-outlined blocks.
0.025 ⇥ 0.1 for the summation in the 2nd and 3rd layers. The new LSBs are mounted on
the Front-End Board (see the upper left side of Figure D.2).
New Baseplane
In order to allocate new slot for LTDB and to route the analog signal from Front-End
Boards, the current baseplane is replaced. A much larger number of signals can be transferred through the new baseplane. It also routes the legacy trigger signals to the Tower
Builder Board, as is done by the current baseplane.
LAr Trigger Digitizer Board
Primary role of LTDB is to digitize the supercell signals from the new LSB. The 40 MHz
sampling digitization is realized with custom developed 12-bit SAR ADC in 130 nm CMOS
technology, which has a good level of radiation tolerance [140]. The other role is to transmit
the digitized signal to the LDPS. LOCx2 serializer and LOCld optical driver [141] aredeveloped to perform the data transfer at 5.44 Gb/s per fibre; 40 fibers are used in total.
Each of the 124 LTDBs handles up to 320 Super Cell channels.
LAr Digital Processing System
There are three roles assigned to the LDPS. First, the LDPS receives the digitized data
at a total rate of 25 Tb/s. Second, the LDPS reconstructs transverse energies of eachSuper Cell and also calculate energy sums in real time. Finally, the LDPS transmits datacontaining the transverse energy information to the L1 trigger processors. For achieving
these roles, LDPS in design consists of 32 ATCA carrier blades named LAr digital processing blade (LDPB) (see Figure D.3), which carry 4 Advanced Mezzanine Cards (AMC)
each (see Figure D.4). On the AMCs, precise energy reconstruction, pile-up suppression,
168

and identification of the correct bunch crossing time are performed. Each AMC carries
one ALTERA Arria-10 FPGA for the real time processing which handles 320 supercells at
maximum.

Figure D.3: Schematic diagram of LDPB,

Figure D.4: Schematic diagram of an AMC,

which contains four AMCs.

with an ALTERA Arria-10 FPGA on the center.

D.3

Demonstrator System

Figure D.5: The two types of LTDB demonstrators, developed by BNL (left) and LAL/Saclay(right) respectively.
For developing hardware, obtaining the installation experience, and testing and validating theperformance of the supercell, a ‘demonstrator’ system has been installed in the ATLAS detector
in summer 2014. LTDB prototypes, also called LTDB demonstrators, have been installed in oneof front-end crates as shown in Figure D.2. The LTDB demonstrators read out supercells for theregion of a barrel part of the LAr calorimeter, 1.767 << 2.160, 0 < ⌘ < 1.4, and operates inparallel to the regular ATLAS data taking during the LHC Run-2. Figure D.5 shows two typesof demonstrators, developed by BNL and LAL/Saclay. The BNL LTDB uses analog mezzanine
169

and digital main board. The LAL/Saclay LTDB has a design with opposite configuration, digital
mezzanine and analog main board. A commercial product, TI ADS5272, is chosen as ADC in
both LTDBs.

Figure D.6: The pre-prototype LDPB developed in LAPPThe digitized data is transmitted to the pre-prototype LDPB, developed by LAPP (see Figure D.6), which have been installed in USA15 (Backend part of ATLAS). The LDPB is designed
along with a commercial Advanced Telecommunications Computing Architecture (ATCA) system. Its core components are ALTERA R Stratix IV FPGAs. The two front FPGAs receive thedigitized data and format them in ATLAS RAW Event Format. The formatted event data istransferred through the back FPGA, via ATCA fabric interface with IPbus and Internet Control
Message Protocol (ICMP). These three FPGAs are interconnected via XAUI.

D.4

Performance Results from the Demonstrator System

This section shows the results of measurement on the demonstrator system [142]. First, theperformance of the legacy readout is discussed, followed by the demonstrator readout.
Measurements with the Legacy Readout
The purpose of measurements with the legacy readout is for assuring that the LTDB
demonstrator does not degrade the performance of the energy measurement for the current
physics run. First, using a calibration system, we confirmed that there is no dead channel
and adjusted the gain level in each channel. The total noise and coherent noise fractionof front-end boards were measured with the legacy readout. Figure D.7 and D.8 are acomparison of the total noise and the coherent noise fraction of front-end boards for thedemonstrator crate and for neighboring crates. The noise level of the demonstrator crate isconsistent with that of neighboring crates. Figure D.9 shows the total noise on the trigger
170

tower readout. The observed noise level is consistent with the current system.
Measurements with the Demonstrator Readout
We have evaluated the prototype LTDB performance in terms of noise, pulse and linearity.
Figure D.10 shows the RMS of the pedestal run in ADC counts for the LTDB Demonstrator
as function of ⌘. The noise level is as expected between 100 and 250 MeV per supercell.
Figure D.11 shows the responses of four supercells (one from each layer) from the LTDB
demonstrator to injected calibration pulses (DAC = 1000 to each LAr cell). The sizeand shape of pulses are as expected and vary due to di↵erent detector and electronics
properties. Figure D.12 shows pulse shapes of a super cell from the demonstrator for
injected calibration pulses with di↵erent amplitudes. The size and shape of pulses are as
expected and show good linearity up to DAC = 8000, while beyond, analog saturation
occurs upstream of the demonstrator board as expected by the design. In Figure D.13,
the pulse maximum in ADC counts for four di↵erent super cells from the demonstrator asfunction of the amplitude of injected calibration pulse in DAC (left) and transverse energy(right) are shown. The pulse shapes shown in Figure D.12 correspond to blue up triangles
in Figure D.13. In the right part of Figure D.13, one can observe that the linearity is kept
up to sufficiently large values of ET .

171

total noise [ADC counts]

total noise [ADC counts]

9
8
7
6
5
4
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8
7
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PS FEBs
Front FEBs

ATLAS Preliminary

92

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ATLAS Preliminary

Back FEBs

1
0
0

20

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60

80

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Middle FEBs

1

100

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0

120

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20

40

60

80

100

channel number

120

channel number

Figure D.7: The RMS of pedestal run for channels of the Front-End Boards in the demonstrator
crate (left) and same sets in the neighboring crate (right). There are 28 Front-End Boards per
crate, each has 128 channels. The noise levels of the boards vary because di↵erent capacitances
8
7
6
5

FT7

FT8

FT9

FT10

FT11

FT12

Total noise [MeV]

coherent noise fraction [%]and gains are applied to their respective cells [142].

ATLAS Preliminary

180
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4

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3

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110

2

100

1
0

ATLAS Preliminary

90
2

4

6

8

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12

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14

5

10

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25

Trigger tower number

slot number

Figure D.8: The fraction of coherent noise

Figure D.9: The total noise in the trigger

per readout channel (Coherent Noise Frac-

tower readout path on the demonstrator sys-tion, CNF) for feedthroughs (FT) 7-12 on thetem in transverse energy in MeV. Trigger

calorimeter. FT9 and 10 belong to the demon-

tower 1-14 correspond to 0 to 1.4 in ⌘ andstrator crate. FT7, 8, 11, and 12 belong to

16-29 are the same in ⌘, but adjacent in

the neighbor crate. The board in the first slot

The values represented by the full circles werereads out the presampler, the boards in themeasured by a spectrum analyzer, and the val-following seven slots read out the front layer,

ues shown in open circles were measured with

the next two boards the back layer and the lastFlash ADCs [142].

four boards the middle layer of the calorimeter. The last entry is the CNF of the wholehalf crate. The coherent noise fraction was
calculated
according to the following equation,q⇢CNF =

2
P

i2A

2
Ni2A ·< i2A>

Ni2A ·< i2A >, where A is a setof channels, Ni2A is the number of channels
belong to A [142].

172.

ATLAS Preliminary
LAr Demonstrator
φ = 1.82

Back layer
Middle layer
Front layer
Presampler

350
300

ADC

RMS in E T [MeV]

400

250

400
300

ATLAS Preliminary
LAr Demonstrator
φ = 1.82, DAC = 1000

200

Front layer, η = 1.01
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Back layer, η = 1.25
Presampler, η = 0.05

200
100

150
100

0

50
0
0

0.2

0.4

0.6

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1

1.2

−100
0

1.4

100 200 300 400 500 600 700 800 900 1000

ηtime [ns]Figure D.10: Pseudo rapidity dependence of

Figure D.11: Responses of four supercells (onethe RMS of the transverse energy of the su-

from each layer) from the LTDB demonstrator

percells from the demonstrator setup without

to injected calibration pulses (DAC = 1000 to

beam. The jump seen at ⌘ = 0.8 reflects theeach LAr calorimeter cell) [142].

change of absorber thickness, electrodes andcalibration resistors. The noise level is as expected between 100 and 250 MeV per super

ADC

cell [142].
3000
ATLAS Preliminary
LAr Demonstrator
Front layer
φ = 1.82, η = 0.01

2000

DAC = 10000
DAC = 8000
DAC = 6000
DAC = 4000
DAC = 2000

1000

0
0

100 200 300 400 500 600 700 800 900 1000
time [ns]Figure D.12: Pulse shapes of a super cellfrom the demonstrator for injected calibration
3500
3000
2500

ADC

ADC

pulses with di↵erent amplitudes [142].
ATLAS Preliminary
LAr Demonstrator
φ = 1.82

4000
3500
3000

ATLAS Preliminary
LAr Demonstrator
φ = 1.82

2500

2000

2000
1500

1500

1000

0
0

1000

Front layer, η = 1.39
Front layer, η = 0.01
Middle layer, η = 1.39
Middle layer, η = 0.01

500
2000

4000

6000

8000

Front layer, η = 1.39
Front layer, η = 0.01
Middle layer, η = 1.39
Middle layer, η = 0.01

500
0
0

10000

200

400

600

800

1000

1200

E T [GeV]

DAC

Figure D.13: Pulse maximum in ADC counts for four di↵erent super cells from the demonstrator
for injected calibration pulses amplitude in DAC (left) and transverse energy (right) [142].

173

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