学位論

文

Search for Supersymmetry and Universal Extra Dimensions
with Degenerate Mass Spectrumin Proton-Proton Collisions at√
s = 7 TeV

縮退したスペクトラムを持つ超対称性粒子や余剰次元のLHC 7 TeV データを用いた探索平成 24 年 12 月博士 (理学) 申請

東京大学大学院理学系研究科
物理学専攻

山口

博史

Doctoral Thesis

Search for Supersymmetry and Universal Extra Dimensions
with Degenerate Mass Spectrumin Proton-Proton Collisions at√
s = 7 TeV

December 18, 2012

Department of Physics, The University of Tokyo

Hiroshi Yamaguchi

Abstract

Searching for a supersymmetry (SUSY) and extra dimensions with degenerate mass spectrum incollision at a center-of-mass energy of 7 TeV is presented. This search is based on 4.7 fb−1 of datacollected by ATLAS experiment and Large Hadron Collider (LHC).
This analysis focuses on “degenerate model” with the mass diﬀerence of ∆m/m ∼ 5-30% where m
is mass for the heaviest particle and ∆m is mass diﬀerence between the mass of the initially produced
colored particles and the lightest particle in the model. So far, the SUSY searches are targetingmodels with large mass diﬀerence as ∆m/m ∼ 80% and the analyses do not have sensitivity to suchdegenerate model. In this analysis, the degenerate SUSY model and universal extra dimensions(UED) model are searched for by optimizing the event selection. The UED model has a similar
mass spectrum to those of SUSY models and is characterized by three parameters; compactiﬁcation
scale 1/R, cut-oﬀ scale Λ and Higgs boson mass, so that the analysis for the degenerate model are
optimized to both signal models.
The ﬁnal state of such degenerate model is characterized by leptons and jets with low transverse
momentum (soft leptons and soft jets) due to small mass diﬀerence, a large missing transverse energy
from the lightest neutral particles and an additional high transverse momentum jet derived frominitial state radiation. Analyses in a high transverse momentum lepton channels optimized to general
SUSY models are combined with this analysis to improve the sensitivity to the degenerate models.
The results show that the observed data are consistent with the background expectations in eachsignal region. In absence of an excess, 95% conﬁdence level exclusion limits are set for the simpliﬁed
SUSY model and UED model. The gluino pair production of simpliﬁed SUSY model is excluded
in degenerate mass region where the mass of gluino mg̃ and the lightest SUSY particle mLSP areapproximately below 540 GeV and 450 GeV, respectively. The UED model is also excluded below
840 GeV in 1/R space with ΛR = 5.

2

Contents
1 Introduction
4
1.1 The Standard Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2 Grand Uniﬁcation and Hierarchy Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.3 The Beyond Standard Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.3.1 Minimal Supersymmetric Standard Model (MSSM) . . . . . . . . . . . . . . . . . . . . . . 7
1.3.2 Universal Extra Dimension (UED) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2 Event Topology
15∫
2.1 2011 Summer Results at Ldt = 1.0-1.4 fb−1 with Supersymmetry Model . . . . . . . . . . . . . 15
2.2 Analysis Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3 LHC and ATLAS Detector
3.1 Large Hadron Collider (LHC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.1 Injector Chain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.2 LHC Main Ring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 ATLAS Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.1 ATLAS Coordinate System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.2 Magnet System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.3 Inner Detector (ID) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.4 Calorimeter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.5 Muon Spectrometer (MS) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.6 Trigger System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.7 Luminosity Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

19
19
20
20
21
21
22
23
24
28
30
30

4 Data and Monte Carlo samples
4.1 2011 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Monte Carlo (MC) Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.1 Generations of Monte Carlo Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.2 Monte Carlo Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

33
33
34
34
37

5 Object Definition
5.1 Electron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2 Muon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3 Jet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
miss
5.4 Missing Transverse Energy ET. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.5 Deﬁnitions of variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

40
40
40
40
41
43

6 Event Selection
6.1 Event Cleaning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2 Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.3 Signal Region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.3.1 Degenerate Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.3.2 MSUGRA High m1/2 Region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.3.3 MSUGRA High m0 Region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.4 Expected Signiﬁcance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

45
45
46
47
48
51
51
52

1

7 Background Estimation
7.1 Multijets Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.1.1 Identiﬁcation Eﬃciency for Real Leptons . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.1.2 Misidentiﬁcation Eﬃciency for Electrons in High pT Region (peT > 25 GeV) . . . . . . . .
7.1.3 Misidentiﬁcation Eﬃciency for Muon in High pT Region (pµT > 20 GeV) . . . . . . . . . .
7.1.4 Misidentiﬁcation Eﬃciencies for Low pT Leptons (7 < peT < 25 GeV or 6 < pµT < 20 GeV)
7.2 W +jets and tt̄ Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.2.1 Fit Conﬁgurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.2.2 Shape Correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.2.3 Normalizations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.3 Validation Regions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

54
55
56
56
59
60
62
62
63
64
68

8 Uncertainties
8.1 Systematic Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.2 Theoretical Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.3 Signal Cross Section Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.3.1 Factorization and Renormalization Scale Uncertainty . . . . . . . . . . . . . . . . . . . . .
8.3.2 PDF Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.3.3 ISR Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.3.4 Combined Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.4 Total Uncertainties Estimations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

73
73
75
77
77
77
77
78
78

9 Results
9.1 Testing the background-only hypothesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.2 Exclusion Limit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.3 Summary and Prospects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

82
82
86
91

10 Conclusion

92

A MSUGRA and UED Mass Spectrum
A.1 MSUGRA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A.1.1 Gauginos Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A.1.2 Neutralinos Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A.1.3 Charginos Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A.1.4 Squark and Slepton Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A.2 minimal UED . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

94
94
94
94
95
95
97

B Performance100
B.1 Electron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
B.1.1 Electron Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
B.1.2 Electron Identiﬁcation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
B.1.3 Electron Energy Scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
B.1.4 Electron Energy Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
B.1.5 Electron Scale Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
B.2 Muon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
B.2.1 Muon Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
B.2.2 Muon Momentum Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
B.2.3 Muon Reconstruction Eﬃciency and Scale Factor . . . . . . . . . . . . . . . . . . . . . . . 108
B.3 Jet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
B.3.1 Jet Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
B.3.2 Jet Energy Scale Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
B.3.3 b-tag algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
B.3.4 b-tagging Eﬃciency and Scale Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
miss
B.4 Missing Transverse Energy ET. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
B.4.1 Systematic Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
B.5 Luminosity Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

2

C Simultaneous Fit
122
C.1 Proﬁling Likelihood Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
C.2 Asymptotic approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
C.3 Experimental Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
C.4 Fit Conﬁguration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
C.4.1 Fit Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
C.4.2 Fit Conﬁgurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
C.4.3 Fit Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
C.5 Closure Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
C.6 Signal-Strength-Only Fit Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
C.7 Exclusion Region for SUSY models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
D Electromagnetic Scale Calibration in Tile Calorimeter
137
D.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
D.2 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
D.2.1 CTB setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
D.2.2 The Tile calorimeter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
D.3 Reconstruction and Event Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
D.3.1 Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
D.3.2 Event Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
D.3.3 The Monte Carlo simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
D.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
D.4.1 dE/dℓ distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
D.4.2 Data/MC ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
D.4.3 Non uniformity of cell responses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
D.4.4 Systematic uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
D.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
Bibliography

151

3Chapter 1

Introduction
The Standard Model describes three interactions as electromagnetic, weak and strong interactions by gauge
theory, and the electromagnetic and weak interactions are uniﬁed in the model [1,2]. Predictions in the Standard
Model are consistent with results of high energy experiments around electroweak scale (∼ 100 GeV). On basisof the Standard Model, grand uniﬁcation theory (GUT) which uniﬁes the electromagnetic, weak and strong
interactions is expected.
If GUT scale (∼ 1016 GeV) and Planck scale (∼ 1019 GeV) exists, it is diﬃcult for Higgs bosons to bestable due to contribution from Planck scale. To solve the problem, candidate models; supersymmetry (SUSY)
model [3–11] and extra dimensions model [12–15] are proposed.
From 2010, Large Hadron Collider (LHC) and ATLAS experiment started the operation of proton-proton
collision with center-of-mass energy of 7 TeV, and have searched for such models. Most of analyses for SUSY
search are optimized to mass diﬀerence about 80% between the heavist and the lightest particle in the model.
This analysis focuses on a degenerate SUSY model and Universal Extra Dimensions (UED) [16–19] whose massdiﬀerence are 5-20% in ﬁnal states with jets, missing transverse energy and an isolated low transverse momentum
lepton.
In this chapter, the Standard Model, the hierarchy problem and beyond the Standard Model as the SUSY
and the UED model are introduced.

1.1

The Standard Model

The Standard Model (SM) of the electroweak interactions is based on the gauge group SU(2) × U(1), withgauge bosons Wµi , i = 1, 2, 3, and Bµ for the SU(2) and U(1) factors, respectively, and the corresponding gauge
coupling constants g1 and g2 . A complex scalar Higgs doublet, ϕ, is added to the model for mass generation
through spontaneous symmetry breaking with potential given by,
λ2 ( † )2
ϕ ϕ .
(1.1.1)2√
For µ2 negative, ϕ develops a vacuum expectation value, v/ 2, where v ≈ 246 GeV, breaking part of theelectroweak gauge symmetry, after which only one neutral Higgs scalar, H, remains in the physical particle
spectrum.
For these bosons, the covariant deviation Dµ and the Lagrangian density L are described as following
)
(
Y
τa a
(left-handed and scalar particles)(1.1.2)Dµ =∂µ − ig1 Wµ − ig2 Bµ ,
2
2
(
)
Y
Dµ =
∂µ − ig1 Bµ ,(right-handed particles)(1.1.3)2
1
1
2
L = iψ̄γ µ Dµ ψ + |Dµ ϕ| − Wµν · Wµν − Bµν B µν ,(1.1.4)
4
4
V (ϕ) = µ2 ϕ† ϕ +where Y is hyper-charge, τ is isospin triplet, g1 and g2 are coupling strength √for the electromagnetic and weak±1
2interactions, respectively. When the charged
weak
boson
W
=
(W
∓
W
)/
2 term, the vacuum expectation( ) √value v and the scalar potential ϕ = v0 / 2 are substituted, the gauge bosons and scalar potential interaction

4

term in the Lagrangian transfers
(
) 2
τa a
Y
−ig1 Wµ − igW Bµ ϕ
2
2
(
)
(
)
1 2 + −µ1 2( 3g12=v Wµ W+ v Wµ , Bµ
−g1 g22
8−g1 g2
g22

)(

W 3µ
Bµ

)
.

(1.1.5)

Diagonalization can be applied to the second term in the right side of the above equation and the new state Zµ
and Aµ are introduced,
Aµ

=

Zµ

=

mW

=

g2 Wµ3 + g1 Bµ√
g12 + g22

with mA = 0,g1 Wµ3 − g2 Bµ√
g12 + g22
1
vg1 .
2

with mZ =1v
2(1.1.6)√
g12 + g22 ,(1.1.7)(1.1.8)The mW and mZ indicate the W and Z boson mass. Thus when we introduce the interaction between the vectorboson and the scalar ﬁeld, we can unify the electromagnetic and weak interaction by using the g1 and g2 asU(1)Y and SU(2)L coupling constant, respectively. In addition the vector bosons have the mass spontaneously.
The Standard Model predictions for the electroweak precision observable measured by LEP, SLC, andTevatron experiments are fully implemented [21]. Left ﬁgure of Figure 1.1 gives the pull values obtained fromthe diﬀerence between the theory and the measurement in units of the total experimental error [20]. The
parameters in the ﬁgures are described in detail in [22]. The Standard Model parameters relevant for theprediction of the electroweak observables are the coupling constant of the electromagnetic (α), weak (GF ),ΓZ

G fitter SM

MZ

0.2

May 12

May 12

G fitter SM

MZ

49
61 +- 260.1

ΓZ

95 - 23

-1.7

σ0had

94 - 21

-1.1

0
Rlep

98 - 23

AFB

0,l

-0.8

AFB

0,l

26
97 +- 22

Al(LEP)

0.3

Al(LEP)

92 - 24

Al(SLD)-1.8

Al(SLD)29
110 +- 24-0.8

sin Θlept
(Q )
eff
FB

26
92 +- 23

σ0had
0
Rlep

sin Θlept
(Q )
eff
FB
2

0,c

+ 26
+ 25
+ 26

+ 26

2

+ 25

0.9

AFB

0,c

93 - 22

0,b
AFB

2.6

0,b
AFB

30
74 +- 22

Ac

-0.1

Ac

94 - 22

Ab

0.6

Ab

25
94 +- 22

0

0.0

Rc

0

94 - 22

-2.3

0
Rb

95 - 22

AFB

Rc
0
Rb
(5)

+ 25

+ 25
+ 25

(5)

∆αhad(M2)-1.5∆αhad(M2)Z

64
61 +- 38

MW

-1.2

MW

71
106 +- 32

ΓW

0.2

ΓW

25
94 +- 22

mc

-0.0

mc

94 - 22

mb

-0.0

mb

96± 260.3

mt

73
78 +- 33

Z

mt
-3

-2

-1

0

1

2

3

+ 25

20

(O - Omeas) / σmeas

40

60

80 100 120 140 160

MH [GeV]fit

Figure 1.1: Comparing theory with results of experiments: pull values for the complete ﬁt (left), and results for
Higgs boson mass mH from the standard ﬁt excluding the respective measurements from the ﬁt (right) [20].
5and strong interactions (αs ), and the masses of the elementary bosons (mZ , mW , mH ) and fermions (mf ),where neutrino masses are set to zero. State-of-the-art calculations are used, in particular the full two-loop andleading beyond-two-loop corrections for the prediction of the W mass and the eﬀective weak mixing angle, which
exhibit the strongest constraints on the Higgs boson mass. The experimental results used in the pull include theelectroweak precision data measured at the Z pole (Z resonance parameters, partial Z cross sections, neutral
current couplings), their experimental correlations, and the W mass world average mW = 80.399±0.023 GeV [23]and width ΓW = 2.098±0.048 GeV [24]. Furthermore the average of the direct Tevatron top mass measurements
mt = 173.3 ± 0.9 ± 0.6 GeV is used [25].
The ﬁgure indicates that the Standard Model predictions are in agreement with the observables in experiments. In addition, the results imply a Higgs boson whose mass lies 67 < MH < 120 GeV as right of Figure
1.1.

1.2

Grand Unification and Hierarchy Problem

It is natural that this success with uniﬁcation between electromagnetic and weak interaction is extended to thestrong interaction SU(3)C whose coupling constant is g3 . In addition it is preferable to describe the uniﬁcation
model by a single coupling constant since the Standard Model needs two coupling constants g1 and g2 in theelectroweak scale ∼ 100 GeV. The grand uniﬁcation theory (GUT) is advocated to unify the electromagnetic,
weak and strong interactions by a single coupling constant gG . The normalized running coupling constants
α1 (= g12 /4π), α2 (= g22 /4π), α3 (= g32 /4π) are estimated by using the renormalization group equation
(
)
dαi
bi 2
d ( −1 )bi 2= − αi ,αα(1.2.1)
=
dt
2π
dt i
2π i
where t = log Q and Q is running energy scale. The coeﬃcients bi are determined by the gauge group and thematter multiplets to which the gauge bosons couple. The Equation 1.2.1 can be integrated immediately
αi−1 (Q) = αi−1 (Q0 ) +

Q
bi
log
,
2π
Q0

(1.2.2)where the Q0 is energy scale at which running commences. For the SU(N ) gauge theory, the coeﬃcients bi canbe calculated
bN =

1
1
11
N − nf − nS ,3
3
6

(1.2.3)where nf is a number of fermion multiplets (counting two chirality states separately) and ns is a number of(complex) scaler multiplets which couple to the gauge bosons. The coeﬃcient of each gauge coupling in the

Figure 1.2: Coupling constant of the Standard Model and SUSY (MSSM) model as a function of energy scale.
6

Standard Model is((b1 , b2 , b3 ) =)41 19− , ,7 .
10 6

The grand uniﬁcation is calculated by using the Equation 1.2.1 as following()]
mG
10π [ −1=α1 (mZ ) − α2−1 (mZ ) ∼ 33.1.
log
mZ
28

(1.2.4)(1.2.5)This result impliesmG ∼ 1016 GeV.

(1.2.6)This huge discrepancy between the grand uniﬁcation scale (∼ 1016 GeV) and electroweak scale (∼ 102 GeV) is
known as “hierarchy problem”. The hierarchy problem often indicates a discrepancy between the Planck scale(∼ 1019 GeV) where the all interactions are uniﬁed and electroweak scale as well.
Assuming the GUT scale and the Planck scale, very ﬁne tuning is necessary to generate the Higgs potential
around ∼ 100 GeV. If a heavy complex scalar particle S with mass mS exists, the particle couples to the Higgs
with a Lagrangian term −λS |H||S| where H and S are the ﬁeld of the Higgs and the complex scalar particle,
respectively. Radiative correction of Higgs mass due to the complex scalar particle is
[
(
)
]
λS
ΛUV
∆m2H =
Λ2UV − 2m2S log··· .
(1.2.7)16πmS
As well as a correction due to a heavy fermion particle mass mF is(∆m2H = CH TF

g2
16π 2

(
)2 [
)
]
ΛUV
aΛ2UV + 24m2F log+ ··· ,
mF

(1.2.8)where ΛUV is an ultraviolet momentum cut-oﬀ, CH and TF are group theory factors of order 1 and g is anappropriate gauge coupling. Both formulas are sensitive to the heavy particle mass. If the Higgs is stablearound mH ∼ 100 GeV, we can not assume any heavy particles exist and couple with the Higgs ﬁeld. To solve
this hierarchy problem and uniﬁcation, two theories; supersymmetry and extra dimensions are advocated. The
SUSY cancels out the interaction from gauge bosons and fermions to the Higgs boson by the supersymmetricparticles. On the other hand, the extra dimensions predicts the grand uniﬁcation scale and Planck scale arearound TeV scale actually, however they look like huge energy scale since the extra dimensions weaken thegravity interaction.

1.3

The Beyond Standard Model

1.3.1

Minimal Supersymmetric Standard Model (MSSM)

The Minimal Supersymmetric Standard Model (MSSM) consists of superpartners which are replaced from abosonic state to a fermionic state and vice versa with the Standard Model particles. The superpartners areclassiﬁed in Table 1.1. The radiative correction of Higgs mass including the SUSY particles is∆m2H =)1 (λS − λ2f Λ2UV + · · · ,28π(1.3.1)

where the λf is the Higgs coupling strength with fermions. The Equation 1.3.1 implies that the eﬀects offermions are cancelled out by those of the scalar particles. In addition, coeﬃcients of the running coupling
constants for the MSSM model are calculated as following)(
33(1.3.2)(b1 , b2 , b3 ) =− , −1, 3 .
5These coeﬃcients can be extrapolated as the coupling constant from the electroweak scale to the grand uniﬁcation scale and these results are shown as the black lines in Figure 1.2. The lines of each coupling constant arecrossing at 1016 GeV due to the eﬀects of superpartners around TeV scale.

7

Namessquarks(right-handed)squarks(left-handed)
sleptons

gluinos
winos
bino
higgsinos
goldstino
gravitino

NotationsũR , c̃R , t̃Rd˜R , s̃R , b̃RũL , c̃L , t̃Ld˜L , s̃L , b̃LẽR , µ̃R , τ̃RẽL , µ̃L , τ̃L
ν̃L
g̃
W̃
B̃
H̃u+ , H̃u0
H̃d− , H̃d0

SM parteruR , cR , tR
dR , sR , bR
uL , c L , t L
dL , sL , bL
eR , µR , τR
eL , µL , τL
νL
g
W
B
Hu
Hd

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

SU(3)C , SU(2)L , U(1)Y(3,1, 23 )
(3,1,- 13 )(3,2, 16 )
(3,2, 16 )
(1,1, 12 )
(1,2,- 12 )
(1,2,- 12 )
(8,1,0)(1,3,0)(1,1,0)(1,2, 12 )
(1,2,- 12 )

G̃

G

3/2

(1,1,0)

Table 1.1: Table of qualities of SUSY particles corresponding with the Standard Model particles.

The Lagrangian density for the MSSM is described
L = LSUSY + Lsoft ,(1.3.3)where the LSUSY term contains all of the gauge and Yukawa interactions and preserves supersymmetry invariance, and Lsoft term violates the supersymmetry but contains only mass terms and coupling parameters withpositive mass dimension. The superpartners of MSSM corresponding with the Standard Model particles aredescribed below• Squark : q̃Superpartners of quarks are named “squark”. The squarks are spin-0 scalar particles and the anti-particles
have same properties as particles, thus the squarks are Majorana particles. The left-handed squarks cancouple with the all gauge bosons meanwhile the right-handed squarks can not couple with the weak gaugebosons. Consequently, the right-handed squarks are lighter than the left-handed squarks mq̃R <∼ mq̃L .
• Slepton : ℓ̃Superpartners of leptons are named “slepton”. The sleptons are spin-0 and Majorana particles as well as
the squarks. The sleptons can couple with the weak bosons but can not couple with the strong bosons,thus the sleptons are lighter than squarks and gluino mℓ̃ <∼ mq̃ , mg̃ which couple with colored charge.
• Gaugino : g̃, W̃ , B̃Superpartners of gauge bosons are named “gaugino”. Each gaugino has a charge corresponding to theStandard Model partner, thus the gaugino can mediate the each interaction as well as the Standard Modelgauge bosons.
• Higgsino : H̃The SUSY model requires the SU(2)L doublet Hu and Hd since the electroweak symmetry suﬀers froma gauge anomaly if the Higgs chiral supermultiplet is singlet. The superpartners of Higgs are called“higgsino” and consists of four fermionic particles H̃u+ , H̃u0 , H̃d0 , H̃d− . The higgsinos have the same
quantum state with the gauginos therefore the higgsinos, winos and bino are mixed and generate the0000four neutral fermions so-called “neutralino” χ̃1 , χ̃2 , χ̃3 , χ̃4 and four charged fermions so-called “chargino”±±±
0χ̃1 , χ̃2 . These particles are labeled by the order from lighter particle (χ̃01 , χ̃±1 ) to heavier particle (χ̃4 , χ̃2 ).
• Gravitino : G̃Superpartner of graviton is named “gravitino”. If supersymmetry is violated by gravity mediation,
quantum state of gravitino is the same as the goldstino and the gravitino absorbs the goldstino which
is analogous to the Higgs mechanism for the gauge theory. Therefore the gravitino obtains a mass
m3/2 ∼ ⟨F ⟩ /MP ∼ 100 GeV where ⟨F ⟩ is the supersymmetry broken scale. However this supersymmetric particle does not play any role in the collider physics since the gravitino can interact with other8particles through the gravity. If supersymmetry is violated through the gauge particles, the expected
gravitino mass m3/2 is heavier than a keV.
These supersymmetric particles decay into the more lighter supersymmetric particle until there are no lighter
supersymmetric particles due to R-parity conservation. The R-parity is positive for the Standard Model particles
and negative for the supersymmetric particles, and it is supposed that this parity is conserved. The decay chainsdepend on the kinematics and the strengths of gauge coupling are the same as those of the Standard Model.
These decay chains are described below in detail.
1. Gluino g̃ and squark q̃ decay
The colored supersymmetric particles decay into the chargino or neutralino. If kinematics allows, the0gluino decays g̃ → q q̃ as two-body decay. If all squarks are heavier than gluino, the gluino decay g̃ → qq ′ χ̃±or g̃ → qq ′ χ̃1 through an oﬀ-shell squark. If the tan β which is a ratio of vacuum expectation value of
Hu to that of Hd is large, the virtual squarks prefer to the third generation squarks (b̃ and t̃), thus the
decay widths of b̃ and t̃ are made large. For the squarks production, the squark decay q̃ → qg̃ is dominantbecause of the strong coupling when the squarks are lighter than the gluino. If the gluino mass is heavier
0
than the squark, the squark decay into the quark and either the neutralino or the chargino q̃ → q χ̃ or00χ̃±
1 . The right-handed squarks prefer to decay into q̃L → χ̃1 because the χ̃1 is bino-like meanwhile the±±left-handed squarks is in favor to the decay into q̃R → χ̃2 because the χ̃2 is wino-like. Figure 1.3 issummarized above sentences. In the ﬁgures, the double lines show the SUSY particles.
±0

2. Neutralino χ̃ and chargino χ̃ decay
The neutralino and chargino consist of the wino (W̃ ± , W̃ 0 ) and bino (B̃) admixture states. Therefore theχ̃±
1 → ℓ̃L ν decay chain is dominated. If a mass diﬀerence ∆m = mχ̃0 − mχ̃0 or ∆m = mχ̃± − mχ̃0 are
2
1
1
1
larger than Higgs, Z and W bosons masses, the decay chain from the neutralino and the chargino into
the Higgs and the gauge bosons are opened kinematically. Figure 1.4 shows the chargino and neutralino
decay. The decay chains of the center and the right of the ﬁgures are opened when the mass diﬀerences±00
between χ̃2 , χ̃1 and χ̃1 are larger than the Z mass and the W mass.
3. Slepton ℓ̃ decay00
The dominant decay of the slepton is ℓ̃ → χ̃1 ℓ but if the χ̃2 is lighter than slepton, then the decay chain

g~

q

q

g~

q0

q0

q

g~

q0

q~L

q~L

q~R
~1

~02

~01

g̃ → q q̃L±q̃L → q ′ χ̃1g̃ → q q̃L0q̃L → q ′ χ̃2g̃ → q q̃R0q̃R → q ′ χ̃1Figure 1.3: Diagrams of decay chains of the gluino g̃ and squark q̃. If the mg̃ > mq̃ , the mediate squark is real
particle. On the other hand the mediate squark is virtual if mg̃ < mq̃ .
~
1


`

Z

~02

W

~1

`~
L

χ̃±
1 → ν ℓ̃L0ℓ̃L → ℓ± χ̃1

~01

~01

~01

± 0
χ̃±
1 → W χ̃1 ,χ̃02 → Z χ̃01±

0

Figure 1.4: Diagrams of decay chains of the chargino χ̃1 and neutralino χ̃2 .
900of ℓ̃ → χ̃2 ℓ is opened. In this case the left-handed slepton can couple with the χ̃2 meanwhile the right00
handed slepton can not couple with χ̃2 because the χ̃2 is wino-like, thus the decay chain of ℓ̃R prefer to0
the ℓ̃R → χ̃1 ℓ.

In general, the order of the heavy particle for supersymmetry tends the triplet particles with the strong
interaction, doublet particles with the weak interaction and singlet particles with the hypercharge. However
there are the huge kind of model for the supersymmetry. The mass spectrum depends on the such model. In
this analysis, the minimal supergravity (MSUGRA) model and the model independent supersymmetry model(simpliﬁed SUSY model) are employed to search for physics beyond the Standard Model. Conditions of eachmodel are mentioned in next two sections.
Minimal Supergravity SUSY Model (MSUGRA)For the supersymmetry, it is considered that the spontaneous supersymmetry breaking occurs to mediate hidden
sector particles. The hopeful candidates of the hidden sector are two scenarios, the gravity-mediated and gaugemediated. In general the gravity-mediation is often used as a bench-mark for supersymmetry. The minimal
supergravity (MSUGRA) and constrained minimal supersymmetry standard model (CMSSM) which are gravitymediation models are simpliﬁed to constrain the parameters by theoretical assumptions [26,27]. The MSUGRA
is described by ﬁve parameters m0 , m1/2 , A0 , tan β, µ or sign of µ.
1. m0 (universal scalar mass)
The squarks and sleptons have the same mass m0 at the GUT scale.
2. m1/2 (the universal gaugino mass)
The gauginos have the same mass m1/2 at the GUT scale.
3. A0 (trilinear coupling constant)Af˜ is coeﬃcient that a squark or slepton f˜ couples to the scalar particle with a strength Af˜y f˜L ϕf˜R and
all Af˜ runs to the A0 at the GUT scale.
4. tan β = vHu /vHd
tan β is a ratio of the vacuum expectation value of Hu to that of Hd .
5. µ (higgsino mass)¯ H̃.
µ is coeﬃcient as µH̃
These parameters determine the mass spectrum of SUSY particles. In the proton-proton collider, the gluino
or squark pair productions are dominant since the strong coupling constant αs and the colored parton density
are larger than the electromagnetic coupling constant α and electroweak gauge bosons, respectively. Because
the produced SUSY particles cause the cascade decay, the SUSY signal is leptons, quarks and gluons as jets
miss
miss
and neutralino as missing transverse energy ET. Especially the ET
tends to become larger than signalsof the Standard Model since the mass diﬀerence between the produced SUSY particle and decayed particles
are large. In the high m0 region, the gluino mass mg̃ is smaller than the squark mass mq̃ , therefore the gluino
pair production is dominant. Meanwhile in the high m1/2 region mq̃ is smaller than the mg̃ , thus the squark
pair production is dominant. Diagrams of representative cascade decay for MSUGRA are shown in Figure 1.5.
Cross sections of MSUGRA depend on parton distribution function (PDF) and the mass of SUSY particles.
Therefore the dominated SUSY particle in the production and its cross section are diﬀerent between each signal
grid point. The cross sections of the gluino pair production and squark pair production are shown in Figure
1.6. The typical mass spectrums of the MSUGRA in high m0 (at m0 = 2820 GeV and m1/2 = 120 GeV) andhigh m1/2 signal point (at m0 = 580 GeV and m1/2 = 600 GeV) are shown in Figure 1.7. Calculations to themasses of SUSY particles in the MSUGRA are described in Appendix A.1.
Simplified SUSY Model
For the MSUGRA and other SUSY models, the mass spectrum of the particles depends on theory and model
parameters. Simpliﬁed SUSY model is aimed to optimize signal region and physics interpretation of the exclusion
more straightforward [28, 29]. Deﬁnitions of this simpliﬁed model are described as follows.
• Only strong pair production (squarks pair production and gluino pair production).
10

q

q

q~

Z

~02

q

~01

q

q~

g~

q~
g~


W

~
1

q
q~

`

~01

q

q
~
1
q
~
1

q

W

q

~01

e

W



~01

Figure 1.5: Example diagrams of decay chain for the squark pair production (left) and gluino pair production(right).
MSUGRA / CMSSM : tan β = 10, A = 0, µ > 0

104

600

102
400

1
10-2

200

106

0

~
q~
q Production

104

600

102
400

1
10-2

200

10-4
1000

2000

3000

4000
m0 [ GeV ]cross section [ pb ]~g~
g Production

m1/2 [ GeV ]106

0cross section [ pb ]m1/2 [ GeV ]MSUGRA / CMSSM : tan β = 10, A = 0, µ > 0

10-4

10-6

1000

2000

3000

4000
m0 [ GeV ]

10-6

1600
1500
g̃
q̃q̃RL

1400
1300
1200

Mass / GeV

Mass / GeV

Figure 1.6: Cross section of MSUGRA for the gluino pair production (left) and squark pair production (right)
as functions of m0 and m1/2 . The region in which no signal MC samples is shown as white.

b̃t̃22
b̃1

500

400

g̃

1100
t̃1

1000
900
800
700

ν̃L

χ̃2±

χ̃02

χ̃1±

300

200

τ̃1

600
500
400
300

χ̃04

100

χ̃01

200
100
0

χ̃04
χ̃03

χ̃2±

h0
χ̃03
χ̃02

h0

0

χ̃01

χ̃1±

Figure 1.7: Typical mass spectrum of MSUGRA in the high m1/2 region (at m0 = 580 GeV and m1/2 = 600
GeV) (left) and the high m0 region (at m0 = 2820 GeV and m1/2 = 120 GeV) (right).

11• Single production mode and single decay chain for SUSY particles.
• For the squark production, the gluino mass is set to high mass (4.5 TeV) meanwhile the squark mass is
set to high mass (4.5 TeV) for the gluino production.
• The left-handed squark or gluino decays through the one or more mediate SUSY particles and ﬁnally into
the stable particles as LSP.
• Emitted W bosons are allowed to decay into both leptonic and hadronic ﬁnal states.
±0• The chargino (χ̃1 ) and neutralino (χ̃1 ) consist of pure wino and pure bino state, respectively.

• The ﬁrst- and second- generation left-handed squarks (ũL , d˜L , s̃L , c̃L ) are mass-degenerated.
• The mass of the third-generation quarks (b̃, t̃) are set to large value at 4.5 TeV.

±g̃ → qq′χ̃1 ,±χ̃1 → W ± χ̃0 (LSP)±q̃ → q′χ̃1 ,±0
χ̃1 → W ± χ̃ (LSP)

Figure 1.8: Diagrams of the decay chain for the simpliﬁed SUSY model with the squark pair production (left)
and gluino pair production (right).

1000

102

600

1

400

10-2
10-4

200
400

600

800

104

800

102

600

1

400

10-2
10-4

200

-6
1000
1200 10m~g [ GeV ]

106

200

cross section [ pb ]

104

800

200

mLSP [ GeV ]1000

Simplified Model : ~q~q Production, 1-step Decay (x=1/2)

106cross section [ pb ]mLSP [ GeV ]Simplified Model : ~g~g Prodution, 1-step Decay (x=1/2)

400

600

800

-6
1000
1200 10m~q [ GeV ]Figure 1.9: Cross section of simpliﬁed SUSY model with the gluino pair production (left) and squark pair
production (right). No signal MC sample regions are shown as white.

12

Figure 1.10: Radiative correction as a function of the cut-oﬀ scale ΛR (left) and typical mass spectrum for the
UED model (right) [30].
• The mass of the right-handed quarks q̃R are set to inﬁnity because the wino-like chargino is not allowed
to couple with q̃R in this model.
±

00• The other SUSY particles (ℓ̃, ν̃, χ̃2 , χ̃3 , χ̃4 ) have high masses, thus these particles do not contribute thedecay chain.
The simpliﬁed model is performed by only three parameters, the gluino or squark mass (mg̃ or mq̃ ), the LSP
mass (mχ̃01 ) and mass of mediate particle for example chargino (mχ̃± ). Cross sections for the productions are1
determined by the gluino mass or squark mass and the parton distribution function (PDF) with the colliding
protons. Figure 1.8 and Figure 1.9 show the decay chains and cross sections of the gluino pair production andthe squark pair production.

1.3.2

Universal Extra Dimension (UED)

Minimal Universal Extra Dimension

104

40

102

30

1
20

10-2

10
0

900

106

Mass / GeV

50

cross section [ pb ]

ΛR

In 1920s, T.Kaluza and O.Klein advocated that the general relativity is extended to the ﬁve dimensions and theﬁfth dimension is compactiﬁed around a circle of very small radius [12, 13]. The original proposal from Kaluza
and Klein could not solve some problems, but the concepts about the extra dimensions are expected to solve
the hierarchy problem. The Arkani-Hamad Dimopoulos and Dvali (ADD) model [14] or Randall and Sundrum

g(1)

800

(1)

qR

(1)

qL

10-4
400

600

800

1000
1/R [ GeV ]Z(1)0
W (1)+

10-6

(1)

νL(1)
ℓR

700

γ(1)

ℓL(1)

Figure 1.11: Cross section of minimal UED (left) and the mass spectrum of UED at 1/R = 700 GeV and ΛR= 10 (right).

13

(RS) model [15] propose the additional ﬂat or curvature dimensions in which only gravity can propagate, thus
the coupling strength of gravity weakens tremendously compared to the other interactions.
The UED is one of the extra dimensions models [16–19]. The features of this model are that each particle in
UED model has a partner in the Standard Model and these particles propagate to the extra dimensions. The
propagating particles in the extra dimensions are called “KK-particles”. In this analysis, one extra dimension
model i.e. four spaces and one time dimensions so-called “minimal universal extra dimensions (mUED)” isconsidered.
Wave function of the UED particles ψ is described by using the radius of the extra dimension R so-called“compactiﬁcation scale” as follows[]∞ {( ny )( ny )}
√ ∑
1
µ
SM µ
µ
µ
,
(1.3.4)ψ(x , y) = √ψ (x ) + 2
PL ψL,n (x ) cos+ PR ψR,n (x ) sin
R
R
πR
n=0
where PR and PL are coeﬃcients of the wave function for right-handed and left-handed particles, respectively.
This equation implies that the n = 0 state means the Standard Model and n ≥ 1 is UED model including theexciting states. Lagrangian in ﬁve dimensions is
[
]
∫
( M )
1
1
5
2 2
3
L =
d x
(∂M ψ) ∂ ψ − m0 ψ − g5 ψ + · · ·(1.3.5)
2
3!
[
( 2
)
}
∫
∞ {
∑
n
1
2
=
d4 x
(∂µ ψn ) (∂ µ ψn ) −
+
m
(ψ
)
0
n
2
R2
n=0
]
∞
∞
1 ′ ( 0 )2 1 ′ ∑ 0 n 0 1 ′ ∑ n+m n m− g5 ψ
− g5
ψ ψ ψ − g5ψψ ψ + ··· ,(1.3.6)
3!
2 n=1
2 n,m=1
where M = 0, 1, 2, 3, 5 indicate the dimensions, and g5 , g5′ are the coupling constant in the ﬁfth dimension
and g5′ = g5 /(2πR)1/2 . From this equation, the mass of UED particles including the radiative correction are
estimated as following
m2X n =n2
+ m2X 0 + δmX n ,R2(1.3.7)

where the X 0 means the Standard Model particle and δmX n is radiative correction for the particle which is
proportional to a cut-oﬀ scale Λ. The cut-oﬀ scale should be introduced because the couplings in the ﬁfth
dimension become strong and the theory is no longer perturbative. The equation shows the mass diﬀerenceof UED particles are generated by taking the mass diﬀerence between the Standard Model particles and theradiative corrections, thus the mass diﬀerence becomes smaller than other new physics models comparatively.
The large cut-oﬀ parameter indicates that the mass diﬀerence between the UED particles becomes large. Figure
1.10 (left) shows the value of radiative corrections for each KK-particle at 1/R = 500 GeV.
According to above, the UED model can be described by only three parameters, the compactiﬁcation scale
1/R, the cut-oﬀ scale Λ and the Higgs mass mH . These parameters determine the mass of UED particles.
Figure 1.10 (right) shows a mass spectrum of the UED model. This ﬁgure shows that the spectrum is similar
to the SUSY models. The masses of UED particles are calculated in Appendix A.2. The decay chain of UED
model starts from the KK-gluons and ends at KK-photon due to K-parity conservation through the KK-quarks,
KK-bosons and KK-leptons. Figure 1.11 (left) shows the cross section of mUED model as functions of 1/R andΛR, and Figure 1.11 (right) shows the mass spectrum of mUED at 1/R = 700 GeV and ΛR = 10.

14

Chapter 2

Event Topology
2.1

2011 Summer Results at
try Model∫

Ldt = 1.0-1.4 fb−1 with Supersymme-

Analysis results of the SUSY model in 2011 summer are established by using data with integral luminosity
1.0-1.4 fb−1 and the exclusion limits on the MSUGRA and the simpliﬁed SUSY model are shown in Figure
2.1 [31–34]. MSUGRA is excluded m0 ∼ 3000 GeV and m1/2 ∼ 450 GeV in no-lepton channel and m0 ∼ 950
GeV and m1/2 ∼ 340 GeV in one-lepton channel. These analyses were optimized to MSUGRA where massdiﬀerence between the heavist particle and the lightest particle in the model are about 80%, and do not havesensitivity to degenerate mass scenario. Therefore this analysis focuses on the degenerate scenario with thesimpliﬁed SUSY model. For the simpliﬁed SUSY model, the region in degenerated mass diﬀerence corresponds
to the diagonal region in Figure 2.2 which shows mass points of generated Monte Carlo (MC) signal samples ingluino pair production. In the region, the mass diﬀerence between the gluino (or squark) and LSP ∆m/mg̃ or∆m/mq̃ is less than 30%.
On the other hand, the mass diﬀerence of UED model is also expected to be degenerated as ∆m/mKK-gluon ∼5-30%. The UED model have been analyzed in CDF experiment by taking multi-lepton search at integral
luminosity of 87.5 fb−1 [35]. The analysis set an upper limit in 1/R parameter space below 280 GeV at ΛR =20.
This analysis focuses on these diagonal region of the simpliﬁed SUSY model and UED model.

2.2

Analysis Overview

This section describes the features with kinematics of such degenerate model and key points for the searchof the model. Typical kinematics of the degenerate model is illustrated in Figure 2.3. The features with thedegenerate model are the soft leptons and the soft jets derived from the cascade decay. Thus these signals tend
to hide behind the background, or can not overcome transverse momentum (pT ) threshold of each object inreconstructions. On the other hand, productions of SUSY or UED particles need large transfer momentum.
Such transfer momentum is generated by initial state radiation (ISR). Thus the pT of ISR jet becomes larger in
miss
the SUSY and UED particle production and the jet tends to be a leading jet. Consequently, ET
is generated0
miss
due to the heavier neutoralino χ̃1 for SUSY or KK-photon for UED. The ET tends to be in opposite direction
to ISR jet and become larger because of a hard ISR jet and soft decay products. Figure 2.4 (left) shows thelepton pT distribution for the UED model and background when the exact one lepton is required. Figure 2.4(right) shows the leading jet pT distribution coming from both the ISR jets and the decayed particles by using
the MC prediction in UED model at 1/R = 300 GeV and ΛR = 2, here is more degenerate signal point for the
UED model. These ﬁgures indicate the pT of leptons are much smaller than the background and the ISR jet
tend to become the leading jet for the degenerate model.
To summarize these features as following• ISR jet with large pT is emitted to generate large transfer momentum.
miss• Large ET
due to neutoralino or KK-photon in opposite direction to the ISR jet.

• The leptons and jets derived from the cascade particles have low pT .
15

m1/2 [GeV]MSUGRA/CMSSM: tanβ = 10, A 0= 0, µ>0ATLAS0 lepton 2011 combined
CLs observed 95% C.L. limit∫ L dt = 1.04 fb , s=7 TeV-1

LEP2 ∼
χ1±600

CLs median expected limit
Expected limit ±1 σ

D0 ~
g, ~
q, tan β=3, µ <0, 2.1 fb-1
CDF ~
g,~
q, tan β=5, µ <0, 2 fb-1
Theoretically excluded

Reference point2010 data PCL 95% C.L. limit~q (140m1/2 [GeV]

500
0)

~
g (1200)

400500

MSUGRA/CMSSM: tanβ = 10, A = 0, µ>0
0

ATLAS
450

~q (10

Expected CLS
Expected CLS ± 1σ~
g (900 GeV)∼LEP2 χ

±1350~
g (800 GeV)~q (700 GeV)

00)

300

Observed CLS 95% CL

1 lepton, combination~q (900 GeV)400~
g (1000)

int

L = 1.04 fb-1, s=7 TeV

D0 ~
g, ~
q, tanβ=3, µ<0, 2.1 fb-1
CDF ~
g, ~
q, tanβ=5, µ<0, 2 fb-1

300~
g (800)

250
00
~q (6

~
g (600))200~
g (600 GeV)~q (500 GeV)200~
g (500 GeV)~q (400 GeV)

150

1000

1500

2000

2500

3000

3500

200

400

600

800

1000

1-Step Decay, x=1/2

700

~
∼0χ
∼0
g~
g→qqqqWWχ
1 1

ATLAS
2

10

Combination

600

L = 1.04 fb , s=7 TeV

500

Observed 95% CL

400

int

-1

Expected

10

Expected ±1σ

300
1
200

mLSP [GeV]

800

Cross Section Excluded at 95% CL [pb]mLSP [GeV]

m0 [GeV]

1200
1400
m0 [GeV]

800
1-Step Decay, x=1/2

700

~
∼0
∼0χ
q~
q→qqWWχ
1 1

ATLAS
102

Combination

600
500

int

-1

L = 1.04 fb , s=7 TeV
Expected +1σ

10
400
300
1
200

100

100
10-1

0

Cross Section Excluded at 95% CL [pb]500~
g (400 GeV)

300

400

500

600

700

10-1
0

800

mgluino [GeV]

300

400

500

600

700

800

msquark [GeV]

Figure 2.1: Exclusion limits at 95% CL by using 2011 summer data in integral luminosity 1.0-1.4 fb−1 . The
results of CMS no-lepton channel (top-left) [31] and CMS one-lepton channel (top-right) [32], ATLAS no-lepton
channel (middle-left) [33] and ATLAS one-lepton channel (middle-right) [34] for the MSUGRA as functions of
m0 and m1/2 are shown. The bottom two ﬁgures show results of the simpliﬁed SUSY model of the g̃-g̃ and theq̃-q̃ pair production with ATLAS one-lepton channel.

16• The multiplicity of leptons and jets are higher than that of the background, but it is possible that theseobjects can not get over the pT threshold.

mLSP [GeV]

Therefore this analysis is optimized to the kinematics which are the soft one lepton and soft jets, and leading
miss
jet with large pT and large ET.
For the kinematics, irreducible background candidates are W +jets and tt̄ events. These background events
have similar kinematics to the signal and larger cross section than the signal models. The background estimation
for the W +jets and tt̄ employs MC samples corrected by ﬁtting to data in control regions where such background
events are enhanced.
On the other hand, a reducible backgrouond is multijets events. The events consist of three components; 1)a photon conversion; 2) a neutral hadron associated with charged particles; and 3) a heavy ﬂavor processing
leptonic decay. A lepton from a heavy ﬂavor decay and a photon conversion, or a cluster accosiated with tracks
which are derived from hadrons is misreconstructed as a prompt electron or muon. These leptons are called“misidentiﬁed lepton” or “non-prompt lepton”, and its modeling is diﬃcult. In this analysis, the misidentiﬁed
lepton events are estimated by using observed data in control samples where the misidentiﬁed lepton events are
dominant.
Other small backgrounds are estimated by using simulation only.
The signal yields are estimated in signal regions where the signal events are enriched and the background
miss
events are reduced. The cut-based signal regions are determined by using tight ET
and leading jet pT cut
following the features of degenerate models. To discover the signal events or exclude the signal hypothesis, theobserved data is compared with background-only hypothesis and signal-plus-background hypothesis in the signal
regions. When the observed data is consistent with the background-only hypothesis, this analysis concludes theno signal evidence and estimates the exclusion limits for each signal models. If the observed data excesses overthe background-only hypothesis, we conclude to discover a new physics phenomenon and the most probablesignal mass point is estimated.

1200

1000

800

600

400

200

0

200

400

600

800

1000 1200m~g [GeV]

Figure 2.2: Prepared signal grid points with the g̃-g̃ pair production in simpliﬁed SUSY model. Blue squareroughly shows the region with the degenerated mass spectrum. Considered mass degenerate ∆m/mg̃ is 5-30%
approximately.
17

large leading jet

soft jetsoft lepton

misslarge ETsoft jet

103

-1

∫

MC Simulation, L dt = 4.7 fb

UED:1/R=700GeV-1

Total Background
ΛR= 2
ΛR=10
ΛR=40

2

10

= 1 lepton, p

e(µ )
T

∫ L dt = 1pb ]104[ events / 5 GeV /[ events / 1 GeV ]Figure 2.3: Illustration with the kinematics of the degenerate model.

> 7(6) GeV

10
1
10-10

20

40

60

80

MC Simulation

102

ISR origin

10lepton pT [GeV]

Decay Productions origin

1
10-1
10-2

100

s=7TeV, UED:1/R=300GeV,Λ R=2

0

100

200

300

400

leading true colored particle pT [ GeV ]Figure 2.4: Distributions the pT by using MC simulated events of backgrounds and UED at 1/R = 700 GeV
and ΛR = 2, 10, 40 applying one lepton cut (left), and pT distribution of both ISR jet and jet derived fromcasecade decay (right) predicted by MC simulation.

18

Chapter 3

LHC and ATLAS Detector
This chapter describes the overview of LHC accelerator and ATLAS detector. LHC and ATLAS started theoperation from 2010, and the 2011 operation was ﬁnished on October 30th without any crucial problems. In
this section, ﬁrstly the proton injection and magnet with LHC. The next ATLAS detector is introduced.

3.1

Large Hadron Collider (LHC)

LHC is a hadron-hadron collider which is constructed in European Organization for Nuclear Research (CERN),
Geneva, Switzerland [36]. This apparatus is aimed to search for the Higgs boson, SUSY such as between theelectroweak and the TeV scale physics. The LHC main ring is built in tunnel with circumference of 26.7 km
at depth between 45 m and 170 m. LHC are designed that center-of-mass energy is 14 TeV, peak luminosity
is the 1034 cm−2 s−1 and time spacing between proton bunch is 25 ns. A number of inelastic collision events
is estimated to cause about 23 events at peak luminosity. However the operation of LHC and ATLAS in 2011
do not achieve this design. Currently, LHC is driven at center-of-mass energy of 7 TeV, the peak luminosity is
5 × 1033 cm−2 s−1 , time space is 50 ns.

Figure 3.1: A schematic view of LHC and the injector complex

19

3.1.1

Injector Chain

LHC is supplied with protons by injector chain such as LINAC2, Proton Synchrotron Booster (PSB), Proton
Synchrotron (PS) and Super Proton Synchrotron (SPS) as shown in Figure 3.1. At the beginning, hydrogen gas
is injected into duoplasmatron, a metal cylinder which dissociates electron from hydrogen atom and generates
protons with the kinetic energy of 90 keV. Then the protons are sent to a radio frequency quadrupole (QRF)
which is an accelerating component that both speeds up and focuses the particles with RF ﬁeld provided by fourvanes. Spacing of the vanes bunches and accelerates the protons up to 750 keV. The particles are sent to LINAC2
from QRF, a linear accelerator whose tank is a multi-chamber resonant cavity tuned to a speciﬁc frequency
which creates potential diﬀerences in the cavities that accelerate the particles up to 50 MeV. Protons cross
LINAC2 and reaches PSB, a circular accelerator with circumference of 157 m which consists of four identicalrings mounted one above another. The 20 quadrupole magnets focus the beam along the line and 2 bending
and 8 steering magnets direct the beam, PSB accelerates them to 1.4 GeV. Then protons are injected to PS.
PS is a circular accelerator with circumference of 628 m. Protons are accelerated to 25 GeV in it. PS forms
81 bunches packets of protons with 25 ns spacing for LHC. SPS is the ﬁnal link in the injector chain to LHC
with circumference of 7 km. Triplets of 81 bunches formed in PS are injected to SPS. Three or four triplets areaccelerated in SPS to 450 GeV and ﬁnally transferred to LHC.

3.1.2

LHC Main Ring

The LHC main ring consists of eight arcs and eight straight sections called insertions as depicted in Figure 3.1.
The length of each arc is 2.45 km and length of each insertion is 545 m.
Two proton beams are counter-rotate in beam pipes and collide at four out of eight Interaction Points (IP)in which experimental detectors are held. ATLAS detector is placed at point 1. CMS, ALICE and LHCb arelocated at point 5, point 2 and point 8, respectively. On upstream of each experiment, beams are focused byusing three superconducting quadrupole magnets. Proton beams are designed to be focused into transverse
radius of 16.7 µm at ATLAS and CMS, 70.9 µm at point ALICE and LHCb. The proton beams collide withthe crossing angle of 142.5 µrad at ATLAS and CMS, 150 µrad at ALICE and LHCb. The other insertions atpoint 3 and point 7 have a collimation system to protect LHC against unavoidable beam losses by performing
beam cleaning and at point 4 are housed cavities. The main role of the RF cavities is to keep 2808 proton
bunches tightly bunched to ensure high luminosity at the IPs as well as delivering radio frequency power to thebeams during acceleration. LHC uses eight cavity per beam, each cavity is operated at 4.5 K of temperatureand delivering 2 MV accelerating voltage at 400 MHz of frequency.
The LHC ring consists of eight arcs and eight straight sections, and each sector is made of 23 arc cells.
The arc cells are 106.9 m long and contains three 14.3 m long superconducting two-in-one dipole magnet. A
schematic illustration of cross section of the dipole magnet is shown in Figure 3.2. Those dipoles produce themagnet ﬁeld of 8.33 T which bends trajectory of protons to keep them along their orbit during acceleration.

Figure 3.2: The cross section of the LHC two-in-one dipole magnet

20

Besides dipoles, LHC also deploys sextupole, octupole, and decapole magnets in order to correct for nonlinear
movement due to magnetic ﬁeld ﬂuctuation.

3.2

ATLAS Detector

ATLAS detector is described in Figure 3.3. This detector is designed for general purpose, for example, discovery
for the Higgs boson and the SUSY particles, precise measurement for the electroweak and top quark physics
and stringent test of QCD. Size of ATLAS is r × z = 12.5 m × 44 m as radius times length along beam pipe.
This huge size is because of the precise measurement of tracks and complete energy deposition in calorimeters.
In this section, coordinate where ATLAS employs are explained ﬁrst. The next, structure and performance ofeach detector e.g. the magnet system, track detectors, and calorimeters are described.

3.2.1

ATLAS Coordinate System

Origin of the coordinate system for ATLAS is determined at the proton-proton collision point. The z-axis isoriented parallel to the beam line and positive direction of that is the counter-clockwise direction against the
LHC ring. Direction of x-axis is pointing to the center of the LHC ring and the y-axis direction is upward.
Azimuthal angle ϕ is an angle in x-y plane and originating from x-axis and increasing along clockwise. Polar
angle θ is deﬁned as an angle from the beam axis. Pseudo-rapidity η deﬁned as()θη ≡ − ln tan(3.2.1)
2
is used instead of the polar angle θ since state of particles in collider is highly Lorentz√ boosted. Distance between
22

two points in the pseudorapidity-azimuthal angle plane are deﬁned as ∆R = (∆η) + (∆ϕ) . Transverse
momentum and energy are denoted as pT and ET which are in conservation in hadron collider. Missing
misstransverse energy is denoted as ET.

Figure 3.3: Cut-away view of ATLAS detector. Dimensions of the detector are 25 m in height and 44 m inlength. Overall weight of the detector is approximately 7000 tones.

21

Figure 3.4: Structure of eight barrel and end-cap toroid coils and four solenoid layers.

3.2.2

Magnet System

ATLAS features a hybrid system of four large superconducting magnets. This magnetic system is 22 m indiameter and 26 m in length, with a stored energy of 1.6 kJ. The system consists of,• a solenoid which is aligned on the beam axis and provides a 2 T axial magnetic ﬁeld for the inner detector.
• a barrel toroid and two end-cap toroids which produce a toroidal magnetic ﬁeld of approximately 0.5 T
and 1 T for the muon detectors in the central and end-cap regions, respectively.
The structure of magnet system is shown in Figure 3.4. The solenoid and toroid magnets are described infollowing two sections. The strength of magnetic ﬁeld at r = 0.118 m, 0.538 m and 1.058 m with the r and z
components, and the magnetic ﬁeld integral of muons passing from the innermost to the outermost are shownin Figure 3.5.
Solenoid Magnet

2
1.5

Bz at R=1.058 m
Br at R=1.058 m
Bz at R=0.538 m

1

8
Barrel region
6
4

φ=π/8

2

φ=0

Br at R=0.538 m

End-cap
regionBz at R=0.118 m

0.5

Br at R=0.118 m

0

0

-0.5
-3

Transition region∫B dl (T ⋅ m)

Field (Tesla)

The solenoid magnet is located between the inner detector and the calorimeter with inner and outer diameter
2.46 m and 2.56 m and length 5.8 m. The solenoid provides a 2 T homogeneous axial magnetic ﬁeld at nominal

-2

-1

0

1

2

3
z (m)

-2
0

0.5

1

1.5

2

2.5

|η|

Figure 3.5: (Left) : Magnetic ﬁeld components in the inner cavity along r- and z-dependence of the radial (Br)and axial (Bz) at ﬁxed azimuth. The lines are ﬁtting results. (Right) : Predicted integral magnetic ﬁeld asa function of |η| from the innermost to the outermost MDT layer in one toroid octant for inﬁnite momentum
muons. The curves correspond to azimuthal angles ϕ = 0 (red) and ϕ = π/8 (black).
22

ID end-plate

3512

CryostatSolenoid coil
PPF1
R1150

712

Radius(mm)

R1066

848

PPB1

2710
R1004

TRT(end-cap)

TRT(barrel)
1

R563
R514
R443
R371
R299

R122.5
R88.5
R50.5
0

2

3

4

5

6

7

8

9 10 11 12

1

2

3

Cryostat
4

5

6

7

8

R644
R560

SCT(barrel)

SCT (end-cap)

R408

R438.8Pixel
support tube

R337.6

Pixel PP1

R275

R229

Beam-pipe

Pixel

R34.3
1299.9934749
400.5 580
1399.7495 650 853.8 1091.5

01771.42115.22505

2720.2z(mm)Envelopes

Pixel

Pixel

45.5<R<242mm|Z|<3092mm

SCT barrel

255<R<549mm|Z|<805mm

SCT end-cap

251<R<610mm
810<|Z|<2797mm

TRT barrel

554<R<1082mm|Z|<780mm

TRT end-cap

617<R<1106mm
827<|Z|<2744mm

R149.6

R122.5
R88.5

R88.8

R50.5
0
0

400.5

495

580 650

Figure 3.6: Plane view of a quarter-section of the ATLAS inner detector showing each of the major detector
elements with its active dimensions and envelops.

7.730 kA operational current. This magnet is designed to keep material thickness as possible so that total
radiation length of solenoid is suppressed near to 0.66 at nominal incidence. The coil stores an energy of 40 MJ
and the magnet ﬂux is returned through the calorimeters as return yoke.
Toroid Magnet
The toroid magnets consist of eight barrel and eight end-cap toroid coils. Overall size of the barrel toroid
system is 25.3 m in length, with inner and outer diameters of 9.4 m and 20.1 m, respectively. These magnets
provide the magnetic ﬁeld in the cylindrical volume surrounding the calorimeters and the strength of magnetic
ﬁeld is about 0.5 T at 10.5 kA operational current and 4.5 K temperature. The conductor and coil winding
technology is based on winding a pure Al-stabilized Nb/Ti/Cu conductor into pancake-shaped coils, followedby vacuum impregnation. The two end-cap toroids form a magnetic ﬁeld required in the end-cap regions of themuon spectrometer. There magnets cover 1.65 < r < 10.7 m with axial length of 5.0 m. The ﬁeld strength ofthe end-cap toroid is about 1.0 T in operation condition. The conductor and coil winding technology is basicallythe same as the one used for the barrel toroid.

3.2.3

Inner Detector (ID)The ATLAS Inner Detector (ID) is designed to reconstruct tracks and primary and secondary vertex, and tomeasure particle momentum for the charged tracks above a given pT threshold (normally 0.5 GeV). The innerdetectors are composed of three sections; pixel detector (pixel), SemiConductor Tracker (SCT) and Transition
Radiation Tracker (TRT). A cut-way view of the inner detectors is shown in Figure 3.6 and following sections
describes the detectors.

23

Pixel Detector
The pixel detector consists of three high granularity (minimum pixel size is 50 µm × 400 µm) and very thin(250 µm) layers. In barrel region (0 mm < z < 400.5 mm) the three layers of pixel detector surrounds thebeam pipe on ϕ-z plane, while in end-cap region (495 mm < z < 650 mm) three disks of pixel detector coverin r-ϕ plane within 88.8 mm < r < 149.6 mm. Radii of position for each pixel layer are r = 50.5 mm, 88.5mm and 122.5 mm, and z positions of each pixel disk are z = 495 mm, 580 mm and 650 mm, respectively. The
most inner layer in the barrel is called “b-layer” and employed to reconstruct the secondary vertex for b-jets
and distinguish between electron and photon by whether or not the particle hits the layer. Typical position
resolution of the pixel detector is 10 µm in r-ϕ direction and 115 µm in z direction.
SemiConductor Tracker (SCT)
Silicon microstrip detector technology is applied to SCT. The detector consists of four layers in barrel region
and nine disks in end-cap region as well as pixel detectors. Positions of layers are r = 299 mm, 371 mm, 443 mm
and 514 mm in 853.8 mm < z < 2720.2 mm, and the positions of disks are z = 853.8 mm, 934 mm, 1091.5 mm,
1299.9 mm, 1399.7 mm, 1771.4 mm, 2115.2 mm, 2505 mm, 2720.2 mm in 275 mm < r < 560 mm, respectively.
For the SCT layers, strip pitch is 80 µm along z-direction to provide accurate measurement on r-ϕ plane since
the particle tracks curve ϕ direction due to the magnet. Meanwhile, in order to read the z direction position,
the module of SCT consists of two layers and these two layers cross 40 mrad. Therefore the hit position withz direction can be read from the hit strip in both layer and the crossing point of these strips. The position
resolution along r-ϕ is 17 µm and along z-direction is 580 µm. On the other hand, the strip of SCT disks point
to r-direction so that the resolution of r are replaced to that of ϕ-z and vice versa.
Transition Radiation Tracker (TRT)TRT outputs the track information by using ionization and transition radiation, thus this detector prefers toelectrons. The TRT is made of polymide straw tubes with diameter of 4 mm and operated by mixing gas
consisting of Xe : CO2 : O2 = 70 : 27 : 3 and the gas pressure is 5-10 mbar. The TRT with up to 73 tubes
surround the SCT and cover between r = 563-1066 mm and z < 712 mm in the barrel region and the tubes lie
along z-direction. On the other hand, in the end-cap region 160 straw planes are placed between r = 644-1004
mm and z = 848-2710 mm and the straws point toward the r-direction. A charged particle with pT > 5 GeV
is expected to excite at least 36 tubes. On average, 5-10 high-threshold hits due to transition radiation are
expected for a pT > 2 GeV electron, meanwhile the low-threshold hits due to ionization are expected to have 32
hits on average for the same pT electron. To use these hit information, the TRT can reconstruct the continuous
tracks and identify the electron by using the number of high-threshold hits.

3.2.4

Calorimeter

The calorimeter in ATLAS is composed of Liquid Argon Calorimeter (LAr), Tile Calorimeter (Tile), End-cap
calorimeter (EMEC and HEC) and Forward Calorimeter (FCal). The same technology except the absorberis employed for LAr, EMEC, HEC and FCal calorimeters. The electromagnetic calorimeters are the LAr
calorimeter (|η| < 1.475) and EMEC (1.375 < |η| < 3.2) whose absorber medium is lead. The hadronic
calorimeters are tile calorimeter (|η| < 1.7) and HEC (1.5 < |η| < 3.2) whose absorber media are the steel
and copper, respectively. The FCal (3.1 < |η| < 4.9) plays on roles of both electromagnetic and hadronic
calorimeters whose absorber media are copper and tungsten, respectively. Structure of these calorimeters areshown in Figure 3.7 and following two sections describe the calorimeters.
Electromagnetic Calorimeter (LAr)The electromagnetic calorimeter so-called Liquid Argon Calorimeter (LAr) in ATLAS is designed with anaccordion geometry for absorber and electrodes for a full coverage in ϕ without any cracks or dead materials
and fast reading of signal by the electrodes. The particles interacts with the LAr absorber and generates cascadeshowers. The showers propagate through the liquid argon and are measured by the electrodes. A illustration of
shower shape and LAr module is shown in Figure 3.8 [37] and left of Figure 3.9. For the accurate measurementof energy deposit, a lead absorber is used and active detector medium is liquid argon because of intrinsic linear
behaviour and stability response over time. But the read out of this signal took about 400 ns due to drift velocity
about 5 µm/ns, then the signal shape is converted to the bipole signal and it is sampled at ﬁve point in each
25 ns. A right plot of Figure 3.9 shows the shape of detector signal and converted signal of LAr electrodes [38].
24Figure 3.7: The cat-away view of the calorimeter system

The energy deposit in LAr calorimeter is estimated from values of these ﬁve points (yellow circles) by comparing
with sampling model.
The LAr calorimeter is composed of three layers. As features of each layer; (1) the 1st layer has highgranularity (∆η × ∆ϕ = 0.0031 × 0.0245) along η to identify the electron or photon in addition to determine
the direction of the particles; (2) the 2nd layer is long distance along r (∼ 16X0 : X0 is radiation length) andmeasures the most of energy deposit of the particles; (3) the 3rd layer identiﬁes the electrons, photons or the
hadrons by estimating the ratio of energy deposit between 2nd layer and 3rd layer. Total thickness of the
LAr calorimeter module is 22X0 -30X0 in 0 < |η| < 0.8 and 24X0 -33X0 in 0.8 < |η| < 1.3, on the other hand
thickness is approximately 2λ for hadron interaction length λ. Figure 3.10 shows the radiation length X0 as afunction of η in each LAr layer.
Energy resolution estimated by test beam is
σE
10%
=√
⊕ 0.7%.
E
E [GeV]

Figure 3.8: Shower shape in LAr calorimeter and ﬁne structure of it.
25(3.2.2)

Cells in Layer 3∆ϕ×∆η = 0.0245×0.05
Trigger Towe∆η = 0 r
.1

2X0

47

0m

m

η=0

16X0
TriggeTow r∆ϕ = 0er
.0

982

m
m

4.3X0

15

00

1.7X0
∆ϕ=0.0245x36.8m 4mx
=147.3 4mm

detector pulse

Square cells in
Layer 2∆ϕ = 0.0245

ϕshaped and sampled
signal∆η = 0

37.5m

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

ηFigure 3.9: A sketch of LAr barrel module (left) and the raw and converted signal shape of LAr (right).
Hadron Calorimeter

X0

X0

Two type technology are applied to hadron calorimeter, Tile technology in barrel region and LAr technology
in end-cap and forward regions. The LAr technology is mentioned at the previous section but the absorber isdiﬀerent from the electromagnetic calorimeter. Because many radiated particles ﬂy along beam axis, copper isused in end-cap calorimeter and the ﬁrst layer of forward calorimeter to optimize energy resolution and remove
heat, while tungsten is used in the second and third layer of forward calorimeter to contain and minimize lateral
spread of hadronic shower.
In barrel region, the tile calorimeters cover in |η| < 1.7 with inner radius of 2.28 m and outer radius of 4.45
m. This calorimeter consists of three layers and the cells of size of ∆η × ∆ϕ = 0.1 × 0.1 in the ﬁrst and second
layer, 0.2 × 0.1 in the third layer which measure the energy deposit independently. The schema of a moduleand segmentation of the tile calorimeter are shown in right of Figure 3.11 and Figure 3.12. Iron is used for the
sampling absorber, then total thick of tile calorimeter is 9.7λ approximately. Distribution of λ as a functionof η is shown in the left of Figure 3.11. Hadronic shower is detected by scintillators which are installed in the40
35

Layer 3Layer 2
Layer 1
Before accordion

45
40
35

30

30

25

25

20

20

15

15

10

10

5

5

0
0

Layer 3Layer 2
Layer 1
Before accordion

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 3.10: The cumulative amount of material in the unit of radiation length X0 for the electromagnetic
calorimeter in the barrel region (left) and end-cap region (right).

26

Interaction lengths

Photomultiplier

20

Wavelength-shifting fibre

18

Scintillator

Steel

16
14
12

HEC3

10
Tile3

HEC2

6 Tile2

HEC1

4 Tile1

HEC0

8

EM calo

2
0
0

0.5

1

1.5

FCal3
FCal2
FCal1

2

2.5

3

3.5

Source
tubes

4
4.5
5
Pseudorapidity

Figure 3.11: Left : Cumulative amount of material in unit of interaction length λ0 for electromagnetic calorimeter, hadronic calorimeter and total amount of material in front of the ﬁrst active layer of the Muon spectrometer(|η| < 3.0). Right : Schematic of module of tile calorimeter
absorber scintillator lights are collected to the PMT through the wavelength shifting ﬁbres. Energy resolutions
estimated by the test beam are given by
σE
E

=

σE
E

=

σE
E

=

60%
⊕ 6%.
E [GeV]70%√⊕ 6%.
E [GeV]100%√⊕ 10%.
E [GeV]√(Tile Calorimeter)(3.2.3)(Endcap Hadron Calorimeter)(3.2.4)(Forward Hadron Calorimeter)(3.2.5)In tile calorimeter, cluster energy is measured in EM scale which is estimated by taking electron incidences
to calorimeter. The EM scale is validated by using muon events in Combined Test Beam (CTB) results tocompare with a result of cosmic ray in Appendix D.
3865 mm

η=0,0

0,1

0,2

0,4

0,3

0,6

0,5

0,8

0,7

1,0

0,9

1,1

1,2
1,3

D0

D1

D3

D2

D4
D6

D5
BC1 BC2 BC3

BC4

BC5

BC6

BC7

BC8

1,4

C10
B12

B11
B9

E1

A10

E2

B15

B14

B13

1,5

1,6

A1

2280 mm
0

A2 A3
500

A4

A5
1000

A6

A7

A8

A9

1500 mm

A12

A13

A14

A15

A16

E3

~

E4

beam axis

Figure 3.12: Segmentation of tile calorimeter modules in center (left) and extended barrels (right)

27

3.2.5

Muon Spectrometer (MS)Muon Spectrometer consists of four detectors, Monitored Drift Tubes (MDT), Cathode Strip Chambers (CSC),
Thin Gap Chambers (TGC) and Resistive Plate Chambers (RPC). Purpose of MDT and CSC are precise
tracking, meanwhile that of TGC and RPC are ﬁring triggers, providing the bunch-crossing identiﬁcation, welldeﬁned pT thresholds and measuring the muon coordinate in the direction orthogonal to that determined by
the precision-tracking chambers. Conceptual layout of muon spectrometer is shown in Figure 3.13 and eachdetector is described in following sections.
Monitored Drift Tubes (MDT)The MDT consists of three to eight layers of drift tubes and its diameter is 29.97 mm. The layer size is 1-2 m
in width and 1-6 m in length. The layout of MDT module is shown in Figure 3.14. Alignment system which
consists of a set of four optical alignment laser monitors and calibrates the MDT position two times in a day.
The MDT achieves an average resolution of 80 µm per tube or 35 µm per chamber. Therefore for a track
crossing three MDT chambers, a sagitta resolution is expected ∆S = 45 µm corresponding to the momentum
resolution ∆p/p = ∆S × p [TeV]/ 500 µm.
Cathode Strip Chamber (CSC)
Because a limitation of safe operation of the MDT is about 150 Hz/cm2 , CSC which is multi-proportional
chamber with radially-oriented wires are set up in end-cap region instead of the MDT. Layout of CSC is shownin Figure 3.14. The safe operation limit of CSC is up to 1000 Hz/cm2 . As the beam test, position resolution isestimated 45-60 µm at 1 kHz/cm2 , while signal ineﬃciency increases up to 4-10%.
Thin Gap Chamber (TGC)
TGC is one of muon trigger chamber, thus requirements with TGC are; (1) fast and coarse tracking information
to be used in high level trigger stage; (2) bunch-crossing identiﬁcation; (3) robustness against noise due to neu-

Figure 3.13: Cut-away view of ATLAS muon system

28

Figure 3.14: Structure of MDT (left) and CSC (right)

tron and photon background. In addition, the coordinate measurement of trigger system is used to complement
MDT measurement.
The TGC are multi-wire proportional chambers with distance of 1.4 mm between wire and cathode whichis smaller than the distance of 1.8 mm between wire to wire. High voltage around the wires and small distance
between wires leads to very good time resolution. A signal arrives at the wires inside a time window of 25 ns
with 99% probability.
Resistive Plate Chamber (RPC)
The muon trigger system in the barrel region is composed of Resistive Plate Chamber (RPC). Figure 3.15 shows
view of standard barrel sector and location of the RPC which is colored. The RPC of small lever is aimed to

Figure 3.15: Structure of RPC

29

ﬁre the trigger for the low pT muon (6 < pT < 9 GeV) meanwhile that of large lever provides the high pTmuon trigger (9 < pT < 35 GeV). The RPC consists of two plate holding with distance of 2 mm. The RPC is
operated in two modes, avalanche mode and stream mode. In the high background environment the avalanche
mode is oﬀered to receive the high rate signal. At the nominal operating the signal width is about 5 ns andsignal ineﬃciency is smaller than 1%.

3.2.6

Trigger System

The ATLAS trigger system is performed in three stages, Level-1 (L1), Level-2 (L2) and Event Filter (EF). The
structure of trigger system is shown in Figure 3.16. At the L1 trigger, the signal of detectors are selected by
missthe electronics. The electrons, photons, muons, jets, τ leptons decaying into hadron and large ET
and totalpT candidates are searched for by L1 trigger. The L2 is seeded by the Regions of Interest (RoI) where the L1
trigger has identiﬁed the candidates and reconstructs it quickly and roughly by using trigger algorithm. The EF
uses oﬀ-line analysis procedures on fully-built events to further select events to reduce event rates. The trigger
rates are 75 kHz, 3.5 kHz and 200 Hz at L1, L2 and EF trigger, respectively.

3.2.7

Luminosity Detector

An accurate measurement of luminosity is very important to determine sensitivity for signatures of new phenomena. For the luminosity measurements, the ﬁrst a set of detectors calculates the luminosity on a bunch-by-bunchby using either event or hit counting algorithm. The second, it infers the total luminosity (summed over allbunches) by monitoring detector currents which is sensitive to average particle rate over longer time scales.
Although there are many detectors to measure the luminosity, six detectors; (1) inner detectors; (2) MBTS;(3) BCM; (4) LUCID; (5) tile calorimeter; (6) forward calorimeter are employed for the measurement in 2011.

Figure 3.16: ATLAS Trigger system

30

The inner detectors are used to detect the vertices produced in inelastic pp interactions. For both tile and forward
calorimeters, the luminosity is assumed to be linearly proportional to the observed current after correcting forpedestals in non-collision backgrounds. Therefore the integrated luminosity can be estimated by measuring thecurrent in such calorimeters.
This section provides descriptions of MBTS, BCM and LUCID.
MBTS (Minimum Bias Trigger Scintillator)
At low instantaneous luminosity (L < 1033 cm−2 s−1 ), ATLAS is equipped with segmented scintillator counters,
the MBTS, located at z = ±365 cm from the nominal interaction point, and covering 2.09 < |η| < 3.84. Main
purpose of the MBTS is to provide a trigger on minimum collision activity during a pp bunch crossing. Lightemitted by the scintillators is collected by wavelength-shifting optical ﬁbers and guided to photomultiplier tubes.
The MBTS signals, after being shaped and ampliﬁed, are fed into leading-edge discriminators and sent to the
ATLAS trigger system. Figure 3.17 shows the schematic and photo of MBTS.
BCM (Beam Condition Monitor)
The BCM consists of four small diamond sensors, approximately 1 cm2 in cross section, arranged around thebeam pipe in a cross pattern on each side of the interaction point, at distance of 184 cm. The BCM is a fastdevice originally designed to monitor background levels and issue beam-abort requests when beam losses start torisk damaging the ATLAS detectors. The fast readout of the BCM also provides a bunch-by-bunch luminosity
signal at |η| = 4.2 with a time resolution of ≃ 0.7 ns. The horizontal and vertical pairs of BCM detectors areread out separately, leading to two independent luminosity measurements. Figure 3.18 shows the picture of
BCM.
LUCID (LUminosity measurement using Cherenkov Integrating Detector)
LUCID consists of sixteen aluminium tubes surrounding the beam pipe and pointing the interaction point.
Length and diameter of tubes are 1.5 m and 15 mm, and each tube is ﬁlled with C4 F10 gas at a constantpressure of 1.2-1.4 bar providing a Cherenkov threshold of 2.8 GeV for pions and 10 MeV for electrons. Two
LUCID are placed in each end-cap region at a distance of 17 m from the interaction point and radial distance of
10 cm from the beam line, covering the pseudo-rapidity range 5.6 < |η| < 6.0. The Cherenkov photons createdby charged particles in the gas are reﬂected by the tube walls until they reach photomultiplier tubes (PMTs)
situated at the back end of the LUCID tubes. Additional Cherenkov photons are produced in the quartz window
separating the aluminium tubes from the PMTs. The Cherenkov light created in the gas typically produces
60-70 photoelectrons per incident charged particles, while the quartz window adds another 40 photoelectrons tothe signal. If one of LUCID PMTs produces a signal over a preset threshold (≃ 15 photoelectrons), a “hit” isrecorded for that tube in that bunch crossing. LUCID hit pattern is processed by a custom-built electronics card
which contains Field Programmable Gate Array (FPGAs) that can be programmed with diﬀerent luminosity

Figure 3.17: Schematic (left) and photo (right) of MBTS.

31

algorithms and provide separate luminosity measurements for each LHC bunch crossing. Figure 3.19 shows the
pictures of LUCID.

Figure 3.18: Top view of a BCM module in left picture, showing the diamond sensors (left side of picture),
HV supply and signal-transmission lines, two ampliﬁcation stages and signal connector (right side of picture).
Close-up view one BCM station in right picture installed at 184 cm from the center of the pixel detector, which
can be seen at the far end of the picture.

a)

b)
0
150

310 mm

c)

d)

c
on
nst
i
W

252 mm

one

mm

le
nd
bu
e
r
F ib
l i er
ltip
u
m
oto
Ph

mm
15

170 mmFigure 3.19: (a) Picture of the two LUCID vessels fully assembled and ready to be installed in ATLAS; (b) Sketch
of LUCID integrated in the cone supporting the beam pipe; (c) Design of the gas vessel; (d) Expanded view of
the readout area showing the coupling between the 15 mm diameter Cherenkov tubes and the photomultipliertubes.
32

Chapter 4

Data and Monte Carlo samples
In 2011, collected data was 4.7 fb−1 as available integrated luminosity and new particles search is carried out by
using the data. Background and signal events are estimated by using Monte Carlo (MC) samples corresponding
to the ATLAS detector conditions. This section describes the 2011 data and MC samples with its detector
conditions during data taking and corresponding simulation conﬁgurations.

4.1

2011 Data

7
6
5

ATLAS Online Luminositys = 7 TeV

LHC Delivered
ATLAS Recorded
Total Delivered: 5.61 fb-1
Total Recorded: 5.25 fb-1

4
3
2
1
0
28/02

30/04

30/06

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

Total Integrated Luminosity [fb -1]

In 2011 year, LHC had been operated without any fatal problems
and total luminosity of 5.2 ± 0.2fb−1 is√obtained in proton-proton collisions at center-of-mass energy s = 7 TeV. The 2011 data is separated into
four term by taking into account LHC and ATLAS conditions. The integral luminosity, beginning and end ofeach term and the detector conﬁguration are described as follows. The detector conﬁgurations are installed into
geometry on simulation.
∫
1. B2 - D7 ( Ldt = 194.9 pb−1 , 22/3/2011 - 29/4/2011)
Corresponding ∼3% of data, 54 dead pixel modules, 7 dead b-layer modules and 5 dead modules in thetile calorimeter in this term.
∫
2. E1 - H4 ( Ldt = 1036.7 pb−1 , 30/4/2011 - 28/6/2011)
In this term, 6 dead module in the LAr calorimeter, 6 dead modules in tile calorimeter, 56 dead pixel
modules and 7 dead b-layer modules.

4.5
4

ATLAS Online Luminositys = 7 TeVLHC Stable Beams
Peak Lumi: 3.65 × 10 cm-2 s-1
33

3.5
3
2.5
2
1.5
1
0.5
0
28/02 02/04 05/05 08/06 11/07 14/08 16/09 20/10 22/11
Day in 2011

30/08
31/10
Day in 2011

Figure 4.1: Total integrated luminosity (left) and peak luminosity per day (right) in 2011. The ﬁve term
corresponds to ﬁve blocks and blanks between each term are corresponding to stopping beam due to maintenance.
The ﬁrst term corresponds to calibration run and the last four terms are employed for this analysis and describedin Section 4.1.

33

∫
3. I1 - K6 ( Ldt = 1287.9 pb−1 , 13/7/2011 - 22/8/2011)
The 2 modules in LAr calorimeter are dead, 7 dead modules in tile calorimeter, 62 dead pixel modules
and 10 dead b-layer modules.
∫
4. L1 - M10 ( Ldt = 2674.4 pb−1 , 7/9/2011 - 25/10/2011)
The 2 modules in LAr calorimeter are dead, 9 dead modules in tile calorimeter, 63 dead pixel modules
and 10 dead b-layer modules.
Figure 4.1 shows total integrated luminosity (left) and peak luminosity (right) in 2011. During blanks between each term in the ﬁgures, technical maintenances were applied to LHC and ATLAS, therefore performancesof LHC and ATLAS were improved after blanks.

4.2

Monte Carlo (MC) Samples

MC simulation samples are performing important roles to understand the data. This section describes how to
generate the simulated samples and which samples are used.

4.2.1

Generations of Monte Carlo Samples

A simulation process is categorized into two part, event generation and detector simulation. Generators calculate
decay branches until the particles become stable and also four vector of these decay particles. After that, thestable particles are handed oﬀ to the detector simulation and interact with the detector material. The detector
simulation calculates the hit positions in the track detectors and the energy deposits in the calorimeter cells,
and the electric output signals of detectors by using the hit positions and energy deposits. After the detector
simulation, the data and MC samples are treated equally by using the same reconstruction algorithm.
For the event generation, various generators are prepared to correspond with properties of the events. In
this section, the event generation is described in focusing on ALPGEN generator because W +jets and tt̄ MC
samples as dominant backgrounds are generated by this generator.
Event Generation
Event generator takes charge of processes from proton collision to emission of the stable decayed particles. The
processes are classiﬁed into three types, a matrix element calculation, a parton shower process and hadronization.
Figure 4.2 shows a concept of the processes from proton collisions to hadronization on the MC level. The
processes are explained as follows.
1. Matrix element calculation
ALPGEN generates hard-processes using leading order calculation. The generator produces partons whoseenergy scale is larger than factorization scale µF in the collision proton. The other partons whose energy
are smaller than µF are treated by Parton Distribution Function (PDF). Coupling constant αs are deﬁned
by a renormalization scale µR which is usually the same value as the factorization scale µF . The µR is set( )22
to its hard process energy scale, e.g. µ2R = m2W + pW
in the W +jets events and µ2R = m2t + (ptT ) in tt̄
Tevents. In element matrix calculations, ALPGEN includes additional partons in the matrix element, thencross sections are calculated in each additional parton bin. ALPGEN samples are labeled by the numberof partons as Np0, Np1, · · · , Np5.
2. Parton shower
Parton shower program evolves partons generated in the matrix element. The process is introduced
virtuality Q2 deﬁned by transfer momentum Q2 = −q 2 . Parton in hard-process emits parton shower until
the |Q2 | falls down at |Q20 |.
3. Hadronization
After the parton shower, hadronization proceeds by using all partons which are evolved by the parton
shower and the soft gluons coming from partons below the factorization scale. The partons are combinedwith the neighbor partons to be color singlet. The color singlet hadrons are handed to the detector
simulation.

34

Parton Shower

FR

O( s2) QCD Perturbation
Parton Distributions

Matrix Element

Hadronization

Figure 4.2: Procedure of event generation.
To populate the phase space not taken care of by the matrix element generator, it is necessary to interface thematrix element generator with a parton shower program like PYTHIA and HERWIG. Because it is possible fora parton generated by parton shower program to proceed in phase space where the matrix element calculation
already covers. To avoid this, MLM matching scheme described below is applied to these events.
The partons in the matrix element are generated above a given pT threshold pT > pmin
T . The showeredminevents (before hadronization) are processed with a cone algorithm, deﬁned by ET
and Rjet which are energyminthreshold for the cone jet and angle distance thresholds between the cone jets, respectively. Usually ET= 20
GeV and Rjet = 0.7 are employed. Then the partons from the matrix element calculation are matched to jets
and for every parton, the jet with the smallest ∆R(jet, parton) is selected. If ∆R(jet, parton) is smaller than
Rjet , the parton is considered as matched.
ALPGEN generator calculates the cross sections in each number of parton independently. After the diagrams
drawing and cross section calculations are ﬁnalized, the events are generated to follow the diagrams. The events
generated by ALPGEN which is leading order (LO) generator are corrected by using k-factor which is ratioof LO cross section to next-to-leading order (NLO) cross section. Figure 4.3 shows a example of the relation
between the LO, NLO and next-to-next-leading order (NNLO) cross section as a function of the renormalization
scale. The ratio becomes constant depending the renormalization scale µR . The higher order cross sections arereliable but it takes large time to calculate the complicated matrix elements. The k-factors compensate thecross section with the higher order contributions.

Figure 4.3: Cross section of the leading order, next-to-leading order, next-to-next-leading order calculation as
a function of the renormalization scale. Single jet inclusive distribution at ET = 100 GeV, appropriate for Run
I of the Tevatron. Theoretical predictions are shown at LO (dotted magenta), NLO (dashed blue) and NNLO(red). Since the full NNLO calculation is not complete, three plausible possibilities are shown [39].

35Figure 4.4: Sketch of ﬂow for generation of Monte Carlo samples from event generation to analysis.
Detector Simulation

Recorded Luminosity [pb-1 ]The simulation of the detector response is performed by the simulation tool kit GEANT4. The hit position andtime in the track detectors and the energy deposit in the calorimeters are simulated (so-called simulation) andthese information is converted into signals of the detector (so-called digitization). Finally the simulated detector
signals are processed in the same way as the data and reconstructed to objects (so-called reconstruction). The
reconstructed simulation samples are treated the same as real data and the information of objects, hit positions
and calorimeter energy deposits and so on are stored into data ﬁles named ESD (Event Summary Data) or
AOD (Analysis Object Data). In analysis the necessary information are taken out from the data ﬁles.
The ﬂow chart of MC sample generations described above are drawn and summarized in Figure 4.4.

104

ATLAS Online 2011, s=7 TeV

103∫ Ldt=5.2 fb-1

β * = 1.0 m, <µ> = 11.6
β * = 1.5 m, <µ> = 6.3

102
10
1
10-1
10-2
10-3
0

2

4

6

8

10 12 14 16 18 20 22 24

Mean Number of Interactions per Crossing

Figure 4.5: Average number of interactions per bunch crossing for the measurement in the data derived inperiod B-K (left-blue) and L-M (left-red), and diﬀerent setups of minimum-bias events in MC simulation interms (right).

36

Pile-up
The peak instantaneous luminosity delivered by LHC has increased from L = 2.0 × 1032 cm−2 s−1 in 2010
to L = 3.6 × 1033 cm−2 s−1 by the end of 2011. This increase results from both an increased instantaneous
luminosity delivered per bunch crossing and signiﬁcant increase in the total number of bunches colliding. The
average number of interactions per bunch crossing ⟨µ⟩ has also increased from ⟨µ⟩ ∼ 6.3 to ⟨µ⟩ ∼ 11.6, andmaximum inelastic interactions per bunch crossing is approximately 24.
All simulated samples are generated with a range of simulated minimum-bias interactions overlaid on thehard-scattering event to account for the multiple proton-proton interactions in the same beam crossing. The
minimum-bias interactions are called “pile-up”. Figure 4.5 shows the measurement of average number of interactions per bunch crossing (left) and number of simulated minimum-bias events per bunch crossing contained
into the simulated events.

4.2.2

Monte Carlo Samples

Background samples employed in this analysis are generated by ALPGEN, HERWIG, MC@NLO and PYTHIA.
Especially the ALPGEN generator is important since the W +jets and tt̄ events are produced by this generator.
The dibosons and single top events are generated by the HERWIG and MC@NLO, respectively. Generators,
cross sections and order of calculations are summarized in Table 4.2. The features of these samples are explained
simply below.
W +jets and Z+jets Samples
The W +jets events are dominant background for the one lepton channel analysis. The events are generated
by a valence quark and a anti-quark derived from a gluon split, vice versa. Figure 4.6 show the diagrams of
W +jets and W event associated with heavy ﬂavor jets. Z+jets events are produced in the same manner as
W +jets events.
tt̄ and single top Samples
The secondary dominant background processes are tt̄ events, especially the semi-leptonic decay. This has higher
jet multiplicity compared to the W +jets events. Single top events are also considered. The top quark events
can be enhanced by using b-tagging. The decay processes of tt̄ and single top are shown in Figure 4.7.
Dibosons Samples
The dibosons contaminations are smaller than W +jets and tt̄ events. The diagrams of s-channel and t-channel
dibosons events are shown in Figure 4.8.
Signal Samples
The signal Monte Carlo samples are generated by the HERWIG and MADGRAPH. The generator and theorder of calculations are shown in Table 4.2.

Term

PeriodRun Number

Date

1st
2nd
3rd
4th
Total

B2 – D7
E1 – H4
I1 – K6
L1 – M10
B2 – M10178044 – 180481
180614 – 184169
185353 – 187815
188902 – 191933
177531 – 191933

22-Mar-2011 – 29-Apr-2011
30-Apr-2011 – 28-Jun-2011
13-Jul-2011 – 22-Aug-2011
07-Sep-2011 – 30-Oct-2011
2011-Mar-13 – 2011-Oct-30∫

Ldt[pb−1 ]Record195.0
1036.71287.92674.45194.0∫Ldt[pb−1 ]Available
112.7
948.6
1154.32431.4
4713.1

Table 4.1: Term and integral luminosity of ATLAS data preparation in 2011.

37

q

g

q

q

b

g



b



W

q0

`

q0

W
`

Figure 4.6: Diagrams of the W +jets and W +bb samples.

b

g



t
W+

b
g

`+

t

W+

q

W
g

b

q0

t

`

W

b

q
q0



Figure 4.7: Diagrams of the tt̄ samples (left) and single top sample (right).

`+

q

W+

q
=Z


q

q0

q

`+

W

W+

q
W

q0

q0

q0

Figure 4.8: Diagrams of the dibosons samples. The left ﬁgure shows the t-channel (left) and the right ﬁgureshows the s-channel (right) dibosons event

38

Physics processtt̄
W (→ ℓν) + jets
W (→ ℓν) + bb + jets
W (→ ℓν) + cc + jets
W (→ ℓν) + c + jetsZ/γ ∗ (→ ℓℓ) + jets (mℓℓ > 40 GeV)
Z/γ ∗ (→ ℓℓ) + jets (10 GeV < mℓℓ < 40 GeV)
Z/γ ∗ (→ ℓℓ) + bb + jets (mℓℓ > 40 GeV)
Single-top (t-chan)Single-top (s-chan)Single-top (W t-chan)WW
W Z/γ ∗ (mZ/γ ∗ > 60 GeV)
Z/γ ∗ Z/γ ∗ (mZ/γ ∗ > 60 GeV)
Signal Samples
Simpliﬁed SUSY
UED

Generator
ALPGEN 2.13 [40]
ALPGEN 2.13 [40]
ALPGEN 2.13 [40]
ALPGEN 2.13 [40]
ALPGEN 2.13 [40]
ALPGEN 2.13 [40]
ALPGEN 2.13 [40]
ALPGEN 2.13 [40]MC@NLO 4.01 [41]
MC@NLO 4.01 [41]
MC@NLO 4.01 [41]HERWIG 6.5.20 [42]HERWIG 6.5.20 [42]HERWIG 6.5.20 [42]Generator
MADGRAPH5 [43]HERWIG++ 2.5.2 [40]Crosssection (pb)
166.8
10460
130
360
1100
1070
3970
10.3
7.0
0.5
15.7
44.9
18.5
5.96

Region200 ≤ mg̃ ≤ 1200 GeV
300 ≤ 1/R ≤ 1150 GeV
2 ≤ ΛR ≤ 40

Calculation
accuracy
LO×K
LO×K
LO×K
LO×K
LO×K
LO×K
LO×K
LO×K
NLO
NLO
NLO
NLO
NLO
NLO

Calculation
NLO+NNL
NLO

Table 4.2: Simulated background and signal event samples used in this analysis, with the corresponding production cross sections. The notation LO×K indicates that the process is calculated at leading-order and correctedby a factor derived from the ratio of LO to NLO cross sections for a closely related process. The tt̄, W +light-jets and Z+ light-jets samples are normalized using the inclusive cross sections; the values shown for the
W + light-jets and Z+ light-jets samples are for a single lepton ﬂavor. The single-top cross sections are listed
for a single lepton ﬂavor in the s- and t-channels.

39

Chapter 5

Object Definition
missare
In this chapter, deﬁnitions of used objects and kinematics variables by using electron, muon, jet and ET
described. Reconstruction algorithms and performance of each object are described in Appendix B.

5.1

ElectronElectrons are reconstructed with the clusters in the electromagnetic calorimeter matching with charged tracks.
These reconstructed electrons are reﬁned through two steps. First, medium identiﬁcation algorithm is applied
to the reconstructed electrons as preselection by using shower shape and strip-based cut in ﬁrst layer of LAr
calorimeter to separate from pion processes. In addition the preselected electrons are required to be isolatedwith any jets ∆R(e, jets) > 0.4. The preselected electrons are employed for rejection against noise events andscale factor estimation.
Second, the preselected electrons are required to pass signal selection criteria by using ptcone20 < 0.1 × peT
and tight identiﬁcation algorithm which requires larger ratio of number of high-threshold hits to total numberof hits in TRT than a threshold. The ptcone20 is described in Section 5.5. The signal electrons are employed
for event selections.
The deﬁnitions of preselected and signal electrons are summarized in Table 5.1. The reconstruction andidentiﬁcation algorithm, and their qualities are explained in Appendix B.

5.2

Muon

Muons are reconstructed from combined tracks between inner detector and muon spectrometer. The analysis
employs STACO muons and segment tagged muons as follows; 1) the STACO muons are reconstructed byusing combined good track in both inner detector and muon spectrometer; 2) the segment tagged muons arereconstructed from a good track in inner detector and a segment reconstructed in muon spectrometer layer.
Similarly to the electrons, the reconstructed muons are selected through two steps, preselected and signal
muon selection criteria. The preselected muons are reﬁned by requiring additional inner track qualities andan isolation with ∆R(µ, jets) > 0.4. The selected muons are required ptcone20 < 1.8 GeV. The deﬁnitionof preselected and signal muon is tabled in Table 5.2 and reconstruction and performance are described inAppendix B

5.3

Jet

Jets are reconstructed by using clusters in the electromagnetic and the hadronic calorimeters and Anti-kT 4Topo
algorithm with size parameter ∆R = 0.4 [44–46]. The clusters are merged as long as()
2
2
diB < dij = min 1/kTi, 1/kTj· ∆2ij /(0.4)2 ,(5.3.1)
where kT is a transverse momentum of clusters, ∆ij is an angle distance between a cluster i and other cluster j
and diB is calculated by its own cluster. The energy of clusters are given by EM scale in the jet reconstruction.

40

The EM scale is given by using the detector responses corresponding to electron energy in test beam. The momentum of jet is calibrated by using jet energy scale (JES) measured in test beam and jet-photon measurements
and so on.
The reconstructed jets are classiﬁed into the preselected jets with pT > 20 GeV and |η| < 2.5. The jets arealso selected by jet vertex fraction (JVF) which is a fraction of tracks coming from a primary vertex to total
momentum of tracks associated with the jet as following,∑pT (trackkjeti , vertexj )JVF(jeti , vertexj ) = ∑k∑npT (trackljeti , vertexn ),(5.3.2)lwhere the vertexj is selected from the primary vertex where the associated track pT sum is the highest in theevent. Schematic of jet vertex and distribution of the jet vertex fraction are shown in Figure 5.1. For jets, it isrequired that the jet vertex fraction is larger than 0.75.
The b-tagged jets are identiﬁed by using JetFitterCombNN algorithm. The algorithm is a combination of
JetFitterComb algorithm which identiﬁes b-jets, c-jets and light ﬂavor jets by using information of primaryvertex, secondary vertex and particle trajectories, and IP3D algorithm which is based on a likelihood ratio
between the transverse impact parameter d0 /σd0 and longitudinal impact parameter z0 /σz0 . Operating pointof 1.8 is used for the b-tagging where eﬃciency of b-jets is 60% and rejection factor of light ﬂavor is 200-400,
and 7-10 for the charm jets.
The criteria is shown in Table 5.3 and the jet reconstruction algorithm and performance are described inAppendix B.

5.4

Missing Transverse Energy ETmiss

missET
is deﬁned with vectorial sum of the reconstructed objects in each event. The following objects are usedmiss
to calculate ET.

• Electron
Reconstructed electrons satisfy pT > 10 GeV and medium selection criteria.

events• MuonSTACO muons are applied to isolation with respect to the selected jets by using ∆R(µ, jets) > 0.3.

108
107
106

Data 2011 ( s=7 TeV) ATLAS Work in progress
multijets (MC)-1
L dt = 4.7 fb
W+jetsZ+jetstt
single top
Dibosons
Drell-Yan

∫

105
104
103
-1

-0.5

0

0.5

1

jet vertex fraction

Figure 5.1: Depiction of jet vertex fraction discriminant (left) and distribution of its variable (right). JVF=−1
events are that tracks associated with jet pass through |η| > 2.5 region where the inner track detectors do notexist.

41

pT
η
Algorithm
Quality
Isolation
Overlap Removal

hard electron
soft electron
preselectedsignalpreselectedsignalpT > 10 GeV
pT > 25 GeV
pT > 7 GeV
7 < pT < 25 GeV|η clust | < 2.47
0< |η clust | < 1.37, 1.52< |η clust | < 2.47
ElectronElectronmediumtight
mediumtight—ptcone20/pT < 0.10—
ptcone20/pT < 0.10
∆R(e, jets) < 0.2 and ∆R(e, jets) > 0.4

Table 5.1: Deﬁnition of electron selection criteria.

pT
ηAlgorithm
Isolation

Inner Detector
Track Quality

Overlap Removal

hard muon
soft muonpreselectedsignalpreselectedsignalpT > 10 GeV
pT > 20 GeV
pT > 6 GeV
6 < pT < 20 GeV|η| < 2.40
|η| < 2.40
STACO or segment-tagged muon
STACO or segment-tagged muon—
ptcone20 < 1.8 GeV—
ptcone20 < 1.8 GeV
number of pixel hits + number of crossed dead pixel sensors > 1
number of SCT hits + number of crossed dead SCT sensors ≥ 6number of pixel holes + number of SCT holes < 3≥ one b-layer hit when it can be expectedif |η| < 1.9 then nTRT > 5 and noutliers< 0.9nTRT
TRT
if |η| < 1.9 and nTRT > 5 then noutliers< 0.9nTRT
TRT∆R(µ, jets) > 0.4

Table 5.2: Deﬁnition of muon selection criteria. The number of hole is lack of hit on the layers along the track.
nTRT is the total number of TRT hits, and noutlier
TRT
is number of TRT hits not using for track reconstruction.

pT
ηAlgorithm
Jet Vertex Fraction
Overlap Removalb-tag Algorithm

preselectedpT > 20 GeV

selectb-jet
pT > 25 GeV
pT > 25 GeV|η| < 2.5
AntikT , ∆R <0.4, TopoCluster—
JVF > 0.75
∆R(e, jets) > 0.2——
JetFitterCombNN

Table 5.3: Deﬁnition of jet and b-jet selection criteria. Algorithm of JetFitterCombNN are described in Appendix
B.

42

• JetJets are formed from topoclusters by using Anti-kT Topo algorithm with size parameter ∆R = 0.4 calibrated by the EM+JES scale (the topocluster and Anti-kT Topo algorithm are described in Appendix B).
Transverse momentum of the jets is required to be larger than 20 GeV.
• Cell-out
Cell-out term is formed from all topocluster in the calorimeter not to belong to any other objects (electrons,muons and jets). Energy scale is calibrated by the EM scale.
These terms are expressed as following formula
(∑
) ∑
∑
∑
∑
Exmiss = −Exe −Excalo,µ −pµx −Exjet −
ExCell-out
(∑
) ∑
∑
∑
∑
Eymiss = −Eye −Eycalo,µ −pµy −Eyjet −
EyCell-out(5.4.1)(5.4.2)miss
and the ET
is described as follow
miss
ET
=

5.5

√
(
)2
2
(Exmiss ) + Eymiss(5.4.3)

Definitions of variables

miss
Products by cascade decay from SUSY particles are detected as leptons, jets or ET. To reduce the backgroundor enhance the signal yield, some variables are deﬁned as follows√
22• Transverse momentum : pT =(px ) + (py )The transverse momentum is the momentum on the r-ϕ plane and this momentum is conserved in the
proton-proton collisions.
√
(
)2 (
)2
[
(
)]
miss 1 − cos ∆ϕ(ℓ, E miss )• Transverse mass : mT = |pνT | + |pℓT | − pνT + pℓT=
2 · pℓT · ET
T
missThis variable is reconstructed by using transverse momentum of a lepton pℓT and ET
.
∑ ℓ
∑ jet
miss
• Eﬀective mass : meﬀ = pT + pT + ET
missmeﬀ is composed of scalar sum of pT with leptons and jets and ET, thus meﬀ corresponds to the all
products originating from SUSY particles decay. Two diﬀerent versions of the eﬀective mass are considered.
One is minc
eﬀ based on all selected jets. The other meﬀ only uses the number of jets that are required asa minimum in a given signal selection. For example, in 2-jets soft lepton signal region, only two jets areused in meﬀ .
√2
2• Angle distance : ∆R(a, b) =(ηa − ηb ) + (ϕa − ϕb )The ∆R(a, b) means the angle distance between an object a and an object b.

• ptcone
The ptcone is sum of momentum of tracks within the cone ∆R along trajectory of selected electron or
muon, and subtracted its electron or muon momentum. The cone size is determined to optimize for eachanalysis. In this analysis the ptcone20 whose cone size is ∆R = 0.2 is employed. The leptons after
applying the ptcone are named isolation leptons.
• Invariant mass mℓℓ
Invariant mass is calculated by using dileptons events. The formula is
(
)2
2
ℓ2nd
ℓ1st
mℓℓ = ET
− pℓ1st + pℓ2nd+ ET(5.5.1)Z• Generated W boson pT and Z boson pT : generated pW
T and generated pT
The transverse momentum of the generated W and Z boson which are generated particles on the generator
level employs the transverse momentum calculated by the event generator.

43

Z• Reconstructed W boson pT and Z boson pT : pW
T and pTZ
On the data and reconstructed MC objects, the transverse momentum of W boson pW
T and Z boson pTℓmissW
are obtained from transverse momentum of lepton pT and missing transverse energy ET . The pT is
misscalculated by using the vectorial sum of four momentum with the a lepton and ET. As well, the pZT iscalculated by using the vectorial sum of four momentum with the two leptons. The formula is as follows.

( W )2pT( Z )2pT( W )2 ( W )2 ( ℓ
)2 (
)2
px
+ py
= px + Exmiss + pℓT + Eymiss .
)2( )2 ( )2 ()2 (= pZx + pZy = pℓx1st + pℓx2nd + pℓy1st + pℓy2nd .
=44(5.5.2)(5.5.3)

Chapter 6

Event Selection
Optimization of selection and event cleaning are described in this chapter. One lepton channel analysis requires
the exact one electron or muon isolated with jets. A tau lepton is not identiﬁed but the electron and muoncoming from tau decay is identiﬁed as a prompt-lepton.
The signal region is optimized for the degenerate SUSY model and the UED model by using low pT lepton
which corresponds to an electron with 6 < peT1st < 25 GeV and a muon with 6 < pµT1st < 20 GeV. Analysis
using such lepton is called “soft lepton channel”. Also “hard lepton channel” analysis employs a peT1st > 25 GeVµ1stelectron or a pT
> 20 GeV muon. Although the hard lepton channel is optimized to MSUGRA model, resultsof the channel are combined with that of the soft lepton channel and it improves sensitivity to the degenerate
missand jet multiplicity because of a production of heavymodels. Signal region is also required to have large ET
particles and cascade decays in SUSY or UED models.
In this chapter, event selections which remove events triggered by coherent noise or cosmic rays are described.
After that, the signal regions are determined to be optimized by using a signiﬁcance. The end of this chapter,
expected signiﬁcance for the degenerate SUSY model on mg̃ -mLSP plane and UED model on 1/R-ΛR plane areshown.

6.1

Event Cleaning

Calorimeter burst and data with bad status of detectors should be removed as follows. Non-collision data, forexample cosmic ray, are also eliminated by applying some technic written below.
Good Runs Lists :The ATLAS detectors are monitored to preserve data qualities. Data in bad status of ATLAS detector andcombined performance are ﬂagged to corresponding luminosity block, which is a data block for approximately
a minute.
Bad Jet Cleaning :missNoise in calorimeters makes mismeasurement of jet energy and ET. In general, a localized cluster can be
regarded as noise since the clusters derived from particles deposit the energy in some calorimeter cells. To
remove noise, the events as following are eliminated.
• HEC spike noise
Energy fraction in HEC is larger than 0.5 or negative energy in jet is larger than 60 GeV.
• EM coherent noise
Energy fraction in electromagnetic calorimeter is larger than 0.95 in |η| < 2.8.
• Non-collision background and cosmic
Maximum energy fraction in one calorimeter layer is larger than 0.99 in |η| < 2.0.
LAr Hole Veto :From April 30th 2011, some plate controllers of LAr calorimeter of −0.1 < η < 1.5, − 0.9 < ϕ < −0.5 have beenbroken due to an electric power problem. Jets passing through this region are considered to be misreconstructed.

45

To deal with the hole, events where missing energy excesses a threshold is discarded. The estimation of missing
energy is
[
]
(
)
∑
1
E=
pjet
(1
−
f
)
−
1
cos ϕjet − ϕETmiss(6.1.1)EcellT
1 − fEjet
jets in holewhere fEcell and fEjet are fraction of the jet energy corrected by using the neighbor cells assuming the sameenergy density and jet shape comparing with simulation after jet reconstruction, respectively. If E > 10 GeV
miss
and E > 0.1 · ET
, the event is rejected.
Primary Vertex :To ensure the event coming from not non-collision event or cosmic ray but a hard process, primary vertex where
sum of momentum of tracks from the vertex is the most energetic is required to have at least ﬁve tracks in theevent.
Cosmic Muon and Bad Muon :missEvents which contain muons like cosmic ray or muons interfering with ET
are rejected. The cosmic-likemuons are identiﬁed by using the muon trajectory as |z0 | > 1.0 mm and |d0 | > 0.2 mm. On the other hand,
missnon-isolated muon tracks in muon spectrometer are rarely used to calculate ET
term. These events are called“bad muon events” and removed by applying σ(q/p)/|(q/p)| > 0.2 to muons.
Electron Crack Veto (only soft electrons) :In crack region of LAr calorimeter (1.37 < |η| < 1.52), quantities of sampling material are smaller. MC
predictions are good modeling for hard electrons however the MC predictions are not in agreement with data
for soft electrons in this region. Therefore the events where the soft electrons entering the crack region are
rejected.

6.2

Trigger

The hard electron channel, hard muon channel and soft lepton channel are required the electron trigger, muon
trigger and transverse missing energy trigger, respectively. pT threshold of reconstructed objects are determinedthat each trigger eﬃciency becomes a plateau. Trigger algorithm is described in following.
• Electron trigger
The electron trigger algorithm requires the peT > 20 GeV in earlier 2011, and peT > 22 GeV in later2011 to correspond to instantaneous luminosity increasing. Figure 6.1 (top-left) shows the electron trigger
eﬃciency of trigger with peT threshold at 22 GeV in trigger algorithm and the plateau of eﬃciencies arefrom peT > 25 GeV. Therefore the electrons are required peT > 25 GeV.
• Muon trigger
The muon trigger algorithm requires muons with pT > 18 GeV in earlier 2011. In later 2011, the muon
trigger requires a jet with pT > 10 GeV at the level-1 trigger additionally. Figure 6.1 (bottom) show
the muon trigger eﬃciencies of trigger pµT threshold at 18 GeV in barrel region and end-cap region. The
plateau of trigger eﬃciency of muon pT is from 20 GeV.
miss
• Missing transverse energy ET
trigger
miss
miss
miss
ET trigger is applied to the soft lepton channel. ET
trigger algorithm requires ET> 60 GeV on
miss
miss
event ﬁlter level, but level-2 trigger algorithm requires ET > 40 GeV in early 2011, ET> 45 GeVmissmissin middle 2011 and ET> 55 GeV in later 2011, respectively. ET
trigger eﬃciency becomes plateau
miss
miss
at 180 GeV for all ET
trigger conditions. Figure 6.1 (top-right) shows the ET
trigger eﬃciencies for
miss
miss
the ET > 40 GeV at level 2 trigger. When the soft lepton channel is analyzed, ET> 180 GeV isrequired.

The discrepancy of eﬃciencies for both electron and muon trigger between observed data and MC eventsmissare corrected by taking scale factors of trigger eﬃciency. On the other hand, since the eﬃciency of ET
triggermissshows almost 100% and no discrepancy between data and MC in the plateau region, the scale factors for ET
trigger are not needed.

46

6.3

Signal Region

Before optimizations for signal regions, features of the degenerate model and MSUGRA are discussed. The
features of the signal model is described below.
• Degenerate SUSY model and UED
As mentioned already in Section 2.2, for the degenerate model the momentum and energy of decay products
missare small due to small mass diﬀerence in cascade decays. Meanwhile the pT of leading jet and ET
areexpected to become large. That is because the production of large mass particles need a large transfer
momentum Q2 . To generate the large transfer momentum, the collision parton emits ISR jet with high pT
missand the ISR jet is detected as a high pT leading jet. Consequently, ET
is detected in opposite direction
to the leading jet with the approximately same energy as leading jet pT .
• MSUGRA (large m1/2 region)
In the high m1/2 region the squark production is dominant compared to the gluino production sincemq̃ < mg̃ . In the region, the meﬀ approximately corresponding to the squark mass are heavier and thejet multiplicity tend to be a bit smaller than the gluino productions because a squark immediately decays
into the chargino.
• MSUGRA (large m0 region)
In the high m0 region the gluino production is dominant compared to the squark production because ofmg̃ < mq̃ . In the region the gluino decays through the virtual squarks thus the jet multiplicity tends tobe higher.

1

Trigger Efficiency

Trigger Efficiency

To consider these points, the three analysis channel are provided as follows,

0.8
0.6
EF_e22vh_medium1
Data
MC

0.4

0.8
0.6
EF_xe60_noMu
Data
MC

0.4

0.2
0
0

1

0.2

10

20

30

40

0

50

50

100

150

200
ET

1

Trigger Efficiency

Trigger Efficiency

T

0.8
0.6
EF_mu18_barrel
Data
MC

0.4

[ GeV ]

1
0.8
0.6
EF_mu18_endcap
Data
MC

0.4

0.2
0
0

250

miss

electron p [ GeV ]

0.2

10

20

30

40

0
0

50

muon p [ GeV ]

10

20

30

40

50

muon p [ GeV ]

T

T

miss
Figure 6.1: Eﬃciency of electron trigger (top-left), ET
trigger (top-right), muon trigger in barrel region(bottom-left) and muon trigger in end-cap region (bottom-right) as a function of pT of each object. Only
statistical uncertainty is quoted by bi-nominal.

47

soft lepton

hard lepton 3 jets

hard lepton 4 jets

Trigger

Missing ET

lepton trigger

NℓpℓT1stpℓT2nd=1[7,25]([6,20])< 7 (6) GeV=1> 25 (20) GeV< 10 GeV=1> 25 (20) GeV< 10 GeV

N jet
pjet
T
jet4thpT≥2> 130, 25 GeV—≥3> 100, 25, 25 GeV< 80 GeV≥4> 80, 80, 80, 80 GeV
—

miss
ET
mT
minc
eﬀ
miss
/meﬀ
ET

> 250 GeV
> 100 GeV—
> 0.3

> 250 GeV
> 100 GeV
> 1200 GeV> 0.3> 250 GeV
> 100 GeV
> 800 GeV
> 0.2

Table 6.1: Deﬁnition of the selection criteria of each signal region. The pT selections for lepton is given forelectron (muon).
• Soft lepton (2-jets) channel
missExact soft one isolated electron or muon + ≥ 2 jets + ET
(for the degenerate model).
• Hard lepton (3-jets) channel
missExact one isolated electron or muon + ≥ 3 jets + ET
(for the MSUGRA high m1/2 region).
• Hard lepton (4-jets) channel
missExact one isolated electron or muon + ≥ 4 jets + ET
(for the MSUGRA high m0 ).
The 3-jets and 4-jets hard lepton channels are analyzed to combine with soft lepton channel and improve
the sensitivity to the degenerate models.

6.3.1

Degenerate Model

Optimization of the signal region for the degenerate model is described in this section. The distributions ofrepresentative variables for the analysis with some cuts applied which is described following are shown in Figurejet
jet
6.2 and Figure 6.3. The ﬁgures show leading jet pT 1st and second leading jet pT 2nd , jet multiplicity N jet , mT ,
miss
miss
ET
and ET/meﬀ for the Standard Model background and both simpliﬁed SUSY and UED signals by using
MC predictions. The signal points drawn in these ﬁgures are (mg̃ , mLSP ) = (425 GeV, 345 GeV), (425 GeV,
185 GeV) and (515 GeV, 35 GeV) for the SUSY, on the other hand 1/R = 550, 700, 850 GeV which ΛR is ﬁxed
at ΛR = 10 and 1/R = 700 GeV varying ΛR = 2, 10, 40 for the UED model. pT cut (7 < peT1st < 25 GeV or 6
miss
< pµT1st < 20 GeV) for lepton, N jet ≥ 2 and ET> 180 GeV cuts are applied to all ﬁgures in Figure 6.2 andFigure 6.3.
miss
The optimization begins with N jet ≥ 2 and ET> 180 GeV.
• The ﬁrst, jet multiplicity distribution is shown in Figure 6.2 (top-left) and Figure 6.3 (top-left). The ﬁgureshows the tighter mass degenerate models (e.g. mg̃ = 425 GeV at mLSP = 345 GeV for SUSY and 1/R= 700 GeV at ΛR = 2 for UED) tend to be small jet multiplicity, although the peak of the distributionof ΛR ∼ 10 is held around 3-5. Thus the signal region is required jet multiplicity N jet ≥ 2.
• The second, distribution of leading jet pT with the N jet ≥ 2 cut applied are shown in Figure 6.2 (topright) and Figure 6.3 (top-right). Peaks of total background and each signal parameter are located aroundjet
pT 1st ∼ 150 GeV. The leading jet pT is cut at 130 GeV.
• The third, distribution of second leading jet pT to which the above cuts are applied is shown in Figure
6.2 (middle-left) and Figure 6.3 (middle-left). The peak of tighter degenerate models are below 25 GeV.
In addition, the distribution of signals are softer than that of background. Therefore the second leading
jet pT cut is set to 25 GeV.

48

Standard Model

Simulation

4

10

∫

[ events / bin ][ events / bin ]105
simplified SUSY (~g-~
g Prod.)m~g=425GeV, mLSP=345GeV
m~g=425GeV, mLSP=185GeV
m~g=515GeV, m =35GeV-1

L dt = 5.0 fb , s = 7TeV

103

LSP

104
Standard Model

Simulation

103∫

simplified SUSY (~g-~
g Prod.)m~g=425GeV, mLSP=345GeV
m~g=425GeV, mLSP=185GeV
m~g=515GeV, m =35GeV-1

L dt = 5.0 fb , s = 7TeV

LSP

102

102
10
10
1

1
10-1

2

4

6

8

10

10-10

12

200

400

104
Standard Model103∫ L dt = 5.0 fb , s = 7TeV

simplified SUSY (~g-~
g Prod.)m~g=425GeV, mLSP=345GeV
m~g=425GeV, mLSP=185GeV
m~g=515GeV, m =35GeV

-1

LSP

102

104
103

1

300

400

10-1

500

simplified SUSY (~g-~
g Prod.)m~g=425GeV, mLSP=345GeV
m~g=425GeV, mLSP=185GeV
m~g=515GeV, m =35GeV
LSP

1

200

∫ L dt = 5.0 fb , s = 7TeV
-1

102
10

100

Standard Model

Simulation

10

10-10

200

400

600

104
10

∫

[ events / bin ][ events / bin ]T

3Standard Modelsimplified SUSY (~g-~
g Prod.)m~g=425GeV, mLSP=345GeV
m~g=425GeV, mLSP=185GeV
m~g=515GeV, m =35GeV-1

L dt = 5.0 fb , s = 7TeV

800
miss
ET [ GeV ]2nd leading jet p [ GeV ]Simulation

800
T[ events / bin ][ events / bin ]Number of jets

Simulation600

leading jet p [ GeV ]

LSP

102

103
Standard Model

Simulation

2

10

∫

simplified SUSY (~g-~
g Prod.)m~g=425GeV, mLSP=345GeV
m~g=425GeV, mLSP=185GeV
m~g=515GeV, m =35GeV-1

L dt = 5.0 fb , s = 7TeV

LSP

10
10
1

1
10-10

50

100

150

10-10

200

0.2

0.4

0.6

0.8

1
miss

mT [ GeV ]ET/ meffFigure 6.2: Distributions with the Standard Model background and simpliﬁed SUSY of jet multiplicity (topmissleft), leading jet pT (top-right), second leading jet pT (middle-left), ET(middle-right), mT (bottom-left) andmissjet
ET /meﬀ (bottom-right) to which are applied jet multiplicity N≥ 2, lepton pT cut (7 < peT1st < 25 GeV,
miss
6 < pµT1st < 20 GeV), ET> 180 GeV cut and additional cut described in the text in detail, respectively. The
dashed line shows the border of the signal region.

49

Standard Model

Simulation

104[ events / bin ][ events / bin ]105
minimal UED
1/R=550GeV, ΛR=10∫ L dt = 5.0 fb , s = 7TeV
-1

1/R=700GeV, ΛR=10
1/R=850GeV, ΛR=10

3

1/R=700GeV, ΛR=2

10

1/R=700GeV, ΛR=40

104

2

10

1

4

6

8

10

200

[ events / bin ][ events / bin ]103∫ L dt = 5.0 fb , s = 7TeV

102

1/R=700GeV, ΛR=2
1/R=700GeV, ΛR=40

104
103

1

1

200

300

400

10-1

500

∫ L dt = 5.0 fb , s = 7TeV

minimal UED
1/R=550GeV, ΛR=10
1/R=700GeV, ΛR=10
1/R=850GeV, ΛR=10

-1

102
10

100

Standard Model

Simulation

10

10-10

1/R=700GeV, ΛR=2
1/R=700GeV, ΛR=40

200

400

600

103

[ events / bin ][ events / bin ]TStandard Model

Simulation∫ L dt = 5.0 fb , s = 7TeV

minimal UED
1/R=550GeV, ΛR=10
1/R=700GeV, ΛR=10
1/R=850GeV, ΛR=10

-1

102

800
miss
ET [ GeV ]2nd leading jet p [ GeV ]

104

800
T

minimal UED
1/R=550GeV, ΛR=10
1/R=700GeV, ΛR=10
1/R=850GeV, ΛR=10

-1

600

leading jet p [ GeV ]Standard Model

Simulation

1/R=850GeV, ΛR=10

400

Number of jets

104

1/R=700GeV, ΛR=10

1/R=700GeV, ΛR=40

10-10

12

minimal UED
1/R=550GeV, ΛR=10

1/R=700GeV, ΛR=2

10

10

2

∫ L dt = 5.0 fb , s = 7TeV
-1

103

102

1

Standard Model

Simulation

1/R=700GeV, ΛR=2
1/R=700GeV, ΛR=40

103

Standard Model

Simulation∫ L dt = 5.0 fb , s = 7TeV

minimal UED
1/R=550GeV, ΛR=10
1/R=700GeV, ΛR=10
1/R=850GeV, ΛR=10

-1

102

1/R=700GeV, ΛR=2
1/R=700GeV, ΛR=40

10

10
1

1
10-10

50

100

150

10-10

200

0.2

0.4

0.6

0.8

1
miss

mT [ GeV ]ET/ meffFigure 6.3: Distributions with the Standard Model background and UED model of jet multiplicity (top-left),missleading jet pT (top-right), second leading jet pT (middle-left), ET(middle-right), mT (bottom-left) andmissjet
ET /meﬀ (bottom-right) to which are applied jet multiplicity N≥ 2, lepton pT cut (7 < peT1st < 25 GeV,
miss
6 < pµT1st < 20 GeV), ET> 180 GeV cut and additional cut described in the text in detail, respectively. The
dashed line shows the border of the signal region.

50

miss
miss
• The fourth, ET
distribution are shown in Figure 6.2 (middle-right) and Figure 6.3 (middle-right). ET
missdistribution of signals become harder than the background, this indicates that a tight ET cut increases
missthe sensitivity of signal events. In this analysis the ET
cut is set to 250 GeV since the larger than 250
GeV cut decreases the statistic of signal events.

• The ﬁfth, mT distribution are shown in Figure 6.2 (bottom-left) and Figure 6.3 (bottom-left). mT >100 GeV cut is applied to the signal region. The W +jets and tt̄ events are decreased by taking this cut
signiﬁcantly.
miss• Finally, ET/meﬀ distribution is shown in Figure 6.2 (bottom-right) and Figure 6.3 (bottom-right). The
miss
miss
component of meﬀ are almost ET
and leading jet pT , and the amount of ET
is approximately the same
missas leading jet pT in the degenerate models. Therefore the signal events concentrate to ET/meﬀ ∼ 0.5
miss
and width of the signal distribution is narrower than that of background distribution. ET /meﬀ > 0.3
cut is applied to the signal region.

The deﬁnition of the signal region for soft lepton channel is described as following.
1. Exact one soft lepton (7 < peT1st < 25 GeV or 6 < pµT1st < 20 GeV) is required.
jet

2. The leading jet pT 1st > 130 GeV is required.
3. The jet multiplicity and pT are required N jet ≥ 2 and pjet
T > 25 GeV, respectively.
miss
4. The missing transverse energy ET> 250 GeV.

5. The transverse mass mT > 100 GeV to remove the W +jets events.
miss
miss
6. The ratio of ET
to meﬀ is larger than 0.3 : ET/meﬀ > 0.3.

The selection criteria for the degenerate scenario is tabled in Table 6.1 as the soft lepton channel.

6.3.2

MSUGRA High m1/2 Region

The high m1/2 region are dominated the squark pair production (m2g̃ ∼ 2.6m21/2 and m2q̃ ∼ m20 + 6m21/2 ), thus
the jet multiplicity is larger than that of background and the meﬀ is larger. The signal region for high m1/2 isdetermined as 3-jets channel as follows.
1. Exact one hard lepton (peT1st > 25 GeV or pµT1st > 20 GeV) is required.
jet

2. The leading jet pT 1st > 100 GeV is required.
3. The jet multiplicity N jet ≥ 3 with pjet
T > 25 GeV.
jet

4. The 4th leading jet transverse momentum is required pT 4th < 80 GeV due to orthogonal with 4-jets
channel.
miss
5. The missing transverse energy ET> 250 GeV.

6. The transverse mass mT > 100 GeV to remove the W+jets events.
miss
miss
7. The ratio of ET
to meﬀ as ET/meﬀ > 0.3.

8. The eﬀective mass meﬀ > 1200 GeV.

6.3.3

MSUGRA High m0 Region

In the high m0 region, the jet multiplicity is higher than the distribution in high m1/2 region due to the gluino
pair production dominant. In this region the produced gluino mass is smaller than the squark mass, then therequired meﬀ cut is 800 GeV which is smaller than the 3-jets channel. This signal region is determined asfollows.
1. Exact one hard lepton (peT1st > 25 GeV or pµT1st > 20 GeV) is required.
2. The jet multiplicity N jet ≥ 4 with pjet
T > 80 GeV.
51

miss
3. The missing transverse energy ET> 250 GeV.

4. The transverse mass mT > 100 GeV to remove the W +jets events.
miss
miss
5. The ratio of ET
to meﬀ as ET/meﬀ > 0.2.

6. The eﬀective mass meﬀ > 800 GeV.

6.4

Expected Significance

Expected signiﬁcances in the three signal regions are estimated. In this section, a simple likelihood ratio is
employed to estimate the signiﬁcance value. The likelihood function is deﬁned asn

L(µ) =(µs + b) −(µs+b)en!

(6.4.1)

where the s, b, n and µ are number of signal, number of background, total number of events n = µs+b and signal
strength, respectively. The number of events of background-only samples and background-plus-signal samples
are described by using signal strength µ = 0 and µ = 1, respectively. Then the signiﬁcance of signal-plusbackground hypothesis to background-only hypothesis med[Z0 |µ = 1] can be written by using the likelihood
ratio as following.
√L(µ = 0)√med[Z0 |µ = 1] =q0 = −2 log
L(µ = 1)√ ()
n=
2 n log + b − n
b
√ [
(
]
s)
2 (s + b) log 1 +−s .
(6.4.2)=b

800

Simulation :1

1∫ L dt = 5.0 fb , s = 7TeV

3

-1

2.5

soft lepton 2-jets : 1.64 σ

2

600

1.5
400

0.5
400

600

800

1000
m~g [ GeV ]

1 1

800

Simulation :1

1∫ L dt = 5.0 fb , s = 7TeV

2.5

soft lepton 2-jets : 1.64 σ

2

600

1.5
1
0.5

200

0

3

-1

400

1

200
200

∼±χ
∼±, χ
∼± → W±χ∼0)
Simplified Model 1-step x=1/2 (~g~
g → qqqqχ

mLSP [ GeV ]1 1

Ratio of SignificancemLSP [ GeV ]

∼±χ
∼±, χ
∼± → W±χ∼0)
Simplified Model 1-step x=1/2 (~g~
g → qqqqχ

200

Ratio of SignificanceThe signiﬁcance corresponding to the exclusion limit of 95% conﬁdence level indicates med[Z0 |µ = 1] = 1.64
and the signiﬁcance of discovery corresponding to 5σ is med[Z0 |µ = 1] = 5.00, respectively.
Figure 6.5 shows the expected signiﬁcance and exclusion limits in each signal region by MC prediction forthe simpliﬁed SUSY model and UED model. These plots imply the soft lepton channel is optimized for the
diagonal region i.e. degenerate region for the simpliﬁed SUSY model. The exclusion region of 3-jets and 4-jets
channel extend the high mg̃ .
The distributions of ratio of signiﬁcance in soft lepton signal region to that in 3-jets hard lepton signal region
and 4-jets hard lepton signal region are shown in Figure 6.4. The ﬁgures show that the soft lepton signal region
is more sensitive to the region where mass sepectrum is degenerated than the hard lepton signal regions which
is optimized for MSUGRA. The factors become approximately two to three in the region.

400

600

800

1000
m~g [ GeV ]0

Figure 6.4: Ratio of signiﬁcance of 2-jets soft lepton signal region to that of 3-jets hard lepton signal region(left) and 4-jets hard lepton signal region (right), respectively, with simpliﬁed SUSY model in mg̃ -mLSP plane.
52Minimal Universal Extra Dimension

600

1∫ L dt = 5.0 fb , s = 7TeV

5-1

Expected Exclusion Limit : 1.64 σ
soft lepton 2-jets
hard lepton 3-jets
hard lepton 4-jets

4

ΛR

800

Simulation :1

SignificancemLSP [ GeV ]

0

1 1

5

40

4
30

3

3
20

2

400

Significance

∼±, χ
∼±χ
∼± → W±χ∼)
Simplified Model 1-step x=1/2 (~g~
g → qqqqχ

2
Simulation :-1

Expected Exclusion Limit : 1.64 σ

101∫ L dt = 5.0 fb , s = 7TeV

1

soft lepton 2-jets

200

hard lepton 3-jets
hard lepton 4-jets

800

1000
m~g [ GeV ]mLSP [ GeV ]

∼±, χ
∼±χ
∼± → W±χ∼0)
Simplified Model 1-step x=1/2 (~g~
g → qqqqχ
1 1

800

600

Simulation :

∫

1

1

0

500

600

700

800
1/R [ GeV ]

-1

4

5

40

4
30

3

3
20

2

400

0

Minimal Universal Extra Dimension

5

L dt = 5.0 fb , s = 7TeV

Expected Exclusion Limit : 1.64 σ
soft lepton 2-jets
hard lepton 3-jets
hard lepton 4-jets

400

Significance

600

ΛR

400

Significance200

2Simulation :-1

Expected Exclusion Limit : 1.64 σ

101∫ L dt = 5.0 fb , s = 7TeV

soft lepton 2-jets

200

1

hard lepton 3-jets
hard lepton 4-jets

800

1000
m~g [ GeV ]mLSP [ GeV ]

∼±, χ
∼±χ
∼± → W±χ∼0)
Simplified Model 1-step x=1/2 (~g~
g → qqqqχ
1 1

800

600

Simulation :

∫

1

1

0

500

600

700

800
1/R [ GeV ]

-1

4

5

40

4
30

3

3
20

2

400

0

Minimal Universal Extra Dimension

5

L dt = 5.0 fb , s = 7TeV

Expected Exclusion Limit : 1.64 σ
soft lepton 2-jets
hard lepton 3-jets
hard lepton 4-jets

400

Significance

600

ΛR

400

Significance200

2Simulation :-1

Expected Exclusion Limit : 1.64 σ

101∫ L dt = 5.0 fb , s = 7TeV

soft lepton 2-jets

200

1

hard lepton 3-jets
hard lepton 4-jets

200

400

600

800

1000
m~g [ GeV ]

0

400

500

600

700

800
1/R [ GeV ]0

Figure 6.5: Expected exclusion limits estimated by MC. The left ﬁgures are shown the signiﬁcance of thesimpliﬁed SUSY model as functions of mg̃ and mLSP . The right ﬁgures are shown the signiﬁcance of the UED
model as functions of 1/R and ΛR. The top ﬁgures are results of soft lepton channel, the middle are hard lepton
3 jets channel and the bottom ﬁgures are hard lepton 4 jets channel.

53

Chapter 7

Background Estimation

180
160
140
120
100
80
60
40

Multijet Control Region

mT [GeV]This chapter describes how to estimate the background contribution in the signal regions. The dominantbackgrounds are leptonic decays in W +jets processes and semi-leptonic decays in tt̄ processes. Other small
background processes considered are Z+jets, single-top, dibosons and multijets.
For the W +jets and tt̄ events as dominant background, both shape and normalization of distributions arecorrected by using distributions in each control region where the background events are enhanced. In shapecorrection, the events of generated W and Z bosons are reweighted to ﬁt to the data in pT distribution ofreconstructed Z boson assuming that W and Z bosons have a common set of corrections. The normalizations
are corrected to ﬁt the W +jets and tt̄ events to observed data in control regions.
The multijets events become background when a jet or a lepton coming from heavy ﬂavor decay is misidentiﬁed as lepton coming from a primary vertex. These misreconstructed and non-prompt leptons are called
misidentiﬁed leptons. Since the misidentiﬁed lepton event is not well modeled in simulation, the distributions of
the misidentiﬁed lepton events are estimated by using the data. A matrix method, which is one of data-driven
methods, is employed to estimate the multijets events background.
For the single-top and dibosons events, these MC samples are used to estimate the distributions for eachprocess without any corrections because their contributions are small.
Figure 7.1 shows control regions, validation regions and signal region. The deﬁnitions of the W +jets andtt̄ control regions are described in Table 7.1. The ﬁrst, data-driven estimation for the multijets events are
performed and the estimation is extrapolated into all control regions. The second, the shape corrections by
the generated W and Z boson events are performed. Finally the normalization factors are obtained to ﬁt

no b−jetno b−jet

W+j

W+j

top

≥1 b−jettop≥1 b−jetControl Region
Validation Region2000SignalRegionHigh mT

40

80

120 160 200 240 280 320 360
Emiss
[GeV]
T

miss
Figure 7.1: Illustration of control regions, validation regions and signal regions in ET-mT plane.

54

hard lepton

soft lepton

W +jetstt̄

W +jets

tt̄

ℓ

=1

=1

=1

=1

pℓT

> 25 (20) GeV> 25 (20) GeV> [7,25]([6,20]) GeV[7,25]([6,20]) GeV

N jet

≥3

≥3

≥2

≥2

pjet
T
b-jet

> 80, 25, 25 GeV> 80, 25, 25 GeV> 130, 25 GeV> 130, 25 GeV=0≥ 1 (within 3 jets)=0≥ 1 (within 2 jets)

miss
ET
mT
minc
eﬀ

miss
40 < ET< 150 GeV
40 < mT < 80 GeV
minc
eﬀ > 500 GeV

miss
40 < ET< 150 GeV
40 < mT < 80 GeV
minc
eﬀ > 500 GeV

miss
180 < ET< 250 GeV
40 < mT < 80 GeV—

miss
180 < ET< 250 GeV
40 < mT < 80 GeV—

N

N

Table 7.1: Deﬁnitions of selection criteria of W +jets and tt̄ control regions in both hard lepton and soft lepton
channel. The pT selections without (with) parentheses is given for electron (muon).
the W +jets and tt̄ events to observed data in jet multiplicity distributions. The normalization factors are
determined for each number of partons individually and used for the background estimations in the signal
region. The estimated background events are extrapolated into the validation regions and signal regions. In
validation regions, the corrected background distributions are cross-checked by comparing with observed data.
The same way is applied to the signal regions, and the excess of observed data over background expectations ischecked.

7.1

Multijets Background

Multijets events become a background due to misidentiﬁed leptons. Three major sources of such misidentiﬁed
leptons are considered; 1) a process of neutral hadron associated with charged particles; 2) a photon conversion
to a electron; and 3) a heavy ﬂavor process when a real lepton appears as a decay product of hadrons in jets
but is suﬃciently isolated. Such objects are collectively referred to as misidentiﬁed leptons. The multijets
background in the signal region and in both W +jets and tt̄ control regions is measured from data following amatrix method.
The multijets background from the all sources (but separated by lepton ﬂavor) is determined collectively.
The events are enhanced in control samples by relaxing selection criteria for signal leptons and required theseveral kinematics. The selection criteria for signal leptons and its relaxed selection criteria are called tight and
pass
fail
loose selection criteria, respectively. The deﬁnitions are summarized in Table 7.2. Deﬁning Nobs
and Nobs
asthe number of events in such a loose sample passing or failing the ﬁnal lepton selection criteria, and deﬁning
Nreal and Nmisid as the number of real leptons and the number of misidentiﬁed leptons, the following equations
hold
pass
Nobs
fail
Nobs

=
=

loose
ϵreal Nrealloose(1 − ϵreal ) Nreal

loose+
ϵmisid Nmisid
,
loose
,
+ (1 − ϵmisid ) Nmisid(7.1.1)

where ϵreal is the relative identiﬁcation eﬃciency for real leptons, and ϵmisid is the misidentiﬁcation eﬃciency
for misidentiﬁed leptons as deﬁned by using the number of leptons passing the loose selection criteria N loose
and tight selection criteria N tight as follows
ϵreal =

tight
Nreal
,
loose
Nreal

ϵmisid =tight
Nmisid.
loose
Nmisid

(7.1.2)

Solving the equations leads to
pass
loose
Nmisid= ϵmisid Nmisid
=

pass
fail
Nobs
− (1/ϵreal − 1) Nobs.
1/ϵmisid − 1/ϵreal(7.1.3)

pass
This equation indicates the number of misidentiﬁed leptons passing the signal lepton selection criteria Nmisid
pass
fail
can be estimated from the numbers of Nobs and Nobs
in interesting regions and eﬃciencies ϵreal and ϵmisid .

55

electronmuon

loose selection
preselection· medium identiﬁcation
preselection—

tight selection
signal selection· tight identiﬁcation· ptcone20/pT < 0.1
signal selection· ptcone20 < 1.8 GeV

Table 7.2: Deﬁnition of loose electron (muon) and tight electron (muon) in multijets background estimation.
In the eﬃciency measurements, one control sample for real leptons and three control samples for misidentiﬁed
leptons are prepared. The ϵreal is measured from data by using a sample of Z → ℓℓ decays. For the misidentiﬁed
leptons, the eﬃciency measurements are performed by three control samples as high pT electrons, high pT muonsand soft leptons control sample to enhance the multijets events.
The measurements of ϵreal and ϵmisid are described in following sections.

7.1.1

Identiﬁcation Eﬃciency for Real Leptons

The identiﬁcation eﬃciency for real leptons is measured by using Z → ℓℓ events as a control sample. In themeasurement of the identiﬁcation eﬃciency, a tag-and-probe method is employed. The method requires one
tagged lepton in the control sample passing the tight selection criteria and one probe lepton satisfying the loose
selection criteria. The eﬃciency is calculated by taking a ratio of the number of probe leptons passing the tightselection criteria to the number of all probe leptons. The selection criteria for this control sample are deﬁned
as follows• The events must be ﬁred by the electron or muon trigger.
• The events contain at least two leptons isolated with jets : ∆R(ℓ, jets) > 0.4.
• The two leptons satisfy opposite charge, same ﬂavor and loose selection criteria.
• The invariant mass of the two leptons lies the Z mass window (80 < mℓℓ < 100 GeV).
miss
• ET
< 30 GeV.

• One lepton satisﬁes the tight selection criteria and matches the corresponding trigger object.
Figure 7.2 shows the pT distributions of the probe leptons, the probe leptons satisfying the tight selection criteria
and the identiﬁcation eﬃciencies, respectively. The ﬁgures indicate the contaminations of the other processes
in the control sample are negligible (< 1%). The eﬃciencies for electrons and muons are measured to be ϵreal ∼70-95% depending on pT and |η|, and 97%, respectively.

7.1.2

Misidentiﬁcation Eﬃciency for Electrons in High pT Region (peT > 25 GeV)

The control sample of misidentiﬁed electrons with high pT (peT > 25 GeV) is collected as the multijets events
missthat consist of one misidentiﬁed electron and at least one jet. ET
in multijets events tend to be small since
the events do not have the undetected objects. Selection criteria for the control sample is deﬁned as follows.
• The events must be ﬁred by the electron trigger.
• The events contain the probe electron isolated with jets : ∆R(e, jets) > 0.4.
miss
• ET
< 30 GeV.

• At least one jet with pjet
T > 25 GeV.
Since the multijets events are not modeled well, the events are estimated from diﬀerence between the observed
data and real electron events predicted by MC simulations. In estimation of the real electron distribution, MC
prediction except multijets events are assumed to consist of real electrons and be good modeled but their crosssections have 20% uncertainty.
Diﬀerence of the eﬃciency between components of misidentiﬁed electrons are assigned as additional systematic uncertainty. The eﬃciencies of each component of misidentiﬁed electrons are predicted by using MC
56

LooseDatamulitjets
c-,b- multijets
W+jetsZ+jets108
107[ events / bin ][ events / bin ]109

ttsingle top
dibosonDrell-Yan

109
108
107

106

106

105

105

104

104

103

103

0

20

40

60

80

Loose
Data
mulitjets
c-,b- multijets
W+jetsZ+jets

100

0

20

40

electron p [ GeV ]

8

107

tt
single top
dibosonDrell-Yan

109
10

107
106

105

105

104

104

103

103
20

40

60

80

100

Tight
Data
multijetsc-, b- multijets
W+jetsZ+jets

8

106

0

0

20

40

electron p [ GeV ]

∈real

∈real

60

0.9

0.8

0.8
0.00 < | η | < 0.80
1.37 < | η | < 1.52

0.6

2.01 < | η | < 2.50

60

80

100

Data

1.52 < | η | < 2.01

40

80

0.7

0.80 < | η | < 1.37

20

dibosonDrell-Yan

1

0.9

0.5
0

tt
single top

T

1

0.6

100

muon p [ GeV ]

T

0.7

80
T

[ events / bin ][ events / bin ]

10

Tight
Data
multijetsc-, b- multijets
W+jetsZ+jetsdibosonDrell-Yanmuon p [ GeV ]

T

109

60

tt
single top

0.5
0

100

electron p [ GeV ]

20

40

60

80

100

muon p [ GeV ]T

T

Figure 7.2: Distribution of pT of probe leptons satisfying loose selection criteria (top), pT of probe leptons
satisfying tight selection criteria (middle) and identiﬁcation eﬃciencies ϵreal (bottom) in data and MC for theelectron channel (left) and muon channel (right).

57

LooseDatamulitjets
c-,b- multijets
W+jetsZ+jets108
107[ events / bin ][ events / bin ]109

ttsingle top
dibosonDrell-Yan

109
108
107

106

106

105

105

104

104

103

103
40

60

80

100

Loose
Data
mulitjets
c-,b- multijets
W+jetsZ+jets2040

60electron p [ GeV ]

108
107

tt
single top
dibosonDrell-Yan

109

107
106

105

105

104

104

103

103
60

80

100

20

40

60

electron p [ GeV ]dibosonDrell-Yan

80

100
T

1

∈misid∈misidtt
single top

muon p [ GeV ]T

0.00 < | η | < 0.80
0.80 < | η | < 1.37
1.37 < | η | < 1.52

0.8

100

Tight
Data
multijetsc-, b- multijets
W+jetsZ+jets

108

106

40

80
T

[ events / bin ][ events / bin ]

Tight
Data
multijetsc-, b- multijets
W+jetsZ+jetsdibosonDrell-Yanmuon p [ GeV ]

T

109

tt
single top

1
0.8

1.52 < | η | < 2.01
2.01 < | η | < 2.50

0.6

0.6

0.4

0.4

0.2

0.2

0

40

60

80

0
20

100

electron p [ GeV ]

40

60

80

100

muon p [ GeV ]T

T

Figure 7.3: Distribution of pT of leptons passing the loose selection criteria (top), pT of leptons passing thetight selection criteria (middle) and the misidentiﬁcation eﬃciencies (bottom) in the control samples for highpT electrons (left) and high pT muons (right). The multijets events are estimated by subtracting MC events
except multijets MC events from data since the multijets MC events are not reliable and MC events except
multijets MC events consist of real leptons. 20% uncertainty is assigned to cross sections of real lepton events.
Total of statistical and systematic uncertainties are quoted as error bars.

58

events as 34 ± 1% for hadron process, 20 ± 3% for photon conversion events and 37 ± 1% for heavy ﬂavor events,
respectively (the errors are quoted only statistical uncertainty). Additional systematic uncertainty of 10% for
the misidentiﬁcation eﬃciency is therefore assigned as absolute value.
The pT distribution of the probe electrons, that of the probe electrons satisfying the tight selection criteria
and the misidentiﬁcation eﬃciency are shown in Figure 7.3. The misidentiﬁcation eﬃciency for the high pTelectrons is measured to be ϵmisid ∼ 11-32% with uncertainty 1-8% depending on pT and |η|.
For the events containing at least one b-jet in the control sample, the misidentiﬁcation eﬃciency is ∼ 10%
higher than that of nominal control sample. This eﬃciency is shown in Figure 7.4 and used for the estimationof multijets events in the tt̄ control region.

Misidentiﬁcation Eﬃciency for Muon in High pT Region (pµT > 20 GeV)

7.1.3

Since a dominant component in the misidentiﬁed muon events is the heavy ﬂavor process, the trajectories ofsuch muons do not point to the primary vertex. The events are expected to have at least two heavy ﬂavor jets,
thus the selection criteria for the control sample are deﬁned as follows,
1. The events must be ﬁred by the muon trigger.
2. The events contain exact one probe muon satisfying the loose selection criteria and |d0 /σd0 | > 5.
3. The probe muons are isolated with jets : ∆R(µ, jets) > 0.4.
4. The events contain at least one jet with pT > 60 GeV.

1

∈misid∈misidThe d0 is a transverse impact parameter with respect to the primary vertex and σd0 is a standard deviationof transverse impact parameter. The pjet
T > 60 GeV is required to avoid a bias due to muon trigger algorithm
requiring a jet with pT > 10 GeV at level-1 trigger. In the multijets events measurement, the real muon events
predicted by simulations are subtracted from the distribution in the control sample as well as the eﬃciency
measurement for misidentiﬁed electrons. The pT distributions for the probe muon before and after tight selection
applied and the misidentiﬁcation eﬃciency ϵmisid are shown in Figure 7.3. The eﬃciency is measured to beϵmisid ∼ 25-36% with an uncertainty 3-25% depending on pT .

0.00 < | η | < 0.80
0.80 < | η | < 1.37
1.37 < | η | < 1.52

0.8

10.00 < | η | < 0.80
0.80 < | η | < 1.37
1.37 < | η | < 1.52

0.8

1.52 < | η | < 2.01

1.52 < | η | < 2.01

2.01 < | η | < 2.50

0.6
0.4

0.4

0.2

0.2

0
5

10

15

20

2.01 < | η | < 2.50

0.6

0

25

electron p [ GeV ]

40

60

80

100

electron p [ GeV ]T

T

Figure 7.4: Misidentiﬁcation eﬃciency for low pT electrons (left) and high pT electrons (right) in at least one
b-jets events (N b-jet ≥ 1) in the control samples. The multijets events are estimated by subtracting MC events
except multijets MC events from data since the multijets MC events are not reliable and MC events except
multijets MC events consist of real leptons. 20% uncertainty is assigned to cross sections of real lepton events.
Total of statistical and systematic uncertainties are quoted as error bars.

59

Misidentiﬁcation Eﬃciencies for Low pT Leptons (7 < peT < 25 GeV or 6
< pµT < 20 GeV)

7.1.4

For the measurement of misidentiﬁcation eﬃciency in low pT region, the events containing two misidentiﬁed
leptons are collected as control samples to avoid the trigger bias, and the tag-and-probe method is applied tothe sample in the eﬃciency measurement. To enhance the misidentiﬁed leptons, the ﬁrst the tagged lepton
is required to fail to the tight selection criteria. Since the dileptons events are contaminated by Z and J/ψ
events, invariant mass and charge combination are required to enhance the misidentiﬁed lepton events. Figure
7.5 shows the distributions of invariant mass with same sign and opposite sign under the failure in the tightselection criteria for the tagged leptons. In the ﬁgures, the two peaks around mℓℓ = 3 GeV and 90 GeV consistof J/ψ and Z events. Therefore the requirements of mℓℓ > 10 GeV and |mℓℓ − mZ | > 25 GeV are added.
The selection criteria for the control sample is determined as follows.
• The events must be ﬁred by the electron or muon trigger.
• The events contain at least two leptons isolated with jets : ∆R(ℓ, jets) > 0.4.
• The relation between two leptons is required for same sign and same ﬂavor.
• The invariant mass lies mℓℓ > 10 GeV and |mℓℓ − mZ | > 25 GeV.

108
10

Same Sign : electron channel[ events / bin ][ events / bin ]• The tagged lepton fails to the tight selection criteria and the probe lepton satisﬁes the loose selection
criteria.

Datamultijets

7

106
105

c-, b- multijets

ttsingle top

W+jetsdibosons

Z+jetsDrell-Yan

108

Opposite Sign : electron channel

7

multijets

10

106
105

104

104

103

103

102

102

10

10

1
0

20

40

60

80

1
0

100

Data

20

40

c-, b- multijets

ttsingle top

W+jetsdibosons

Z+jetsDrell-Yan

60

108
10

Same Sign : muon channelDatamultijets

7

106
105

c-, b- multijets

ttsingle top

W+jetsdibosons

Z+jetsDrell-Yan

108
10

103

102

102

10

10
60

80

1
0

100

Mµµ [ GeV ]multijets

105

103

40

Data

106

104

20

100

Opposite Sign : muon channel

7

104

1
0

80

Mee [ GeV ][ events / bin ][ events / bin ]Mee [ GeV ]2040c-, b- multijets

ttsingle top

W+jetsdibosons

Z+jetsDrell-Yan

60

80

100

Mµµ [ GeV ]Figure 7.5: Distributions of the invariant mass mℓℓ in the control sample of electrons (top) and the muons(bottom) with the same sign (left) and the opposite sign (right) requirement, respectively.
60

LooseDatamulitjets
c-,b- multijets
W+jetsZ+jets107
106[ events / bin ][ events / bin ]108

tt
single top
dibosonDrell-Yan

108
107
106

105

105

104

104

103

103

102

102

5

10

15

20

25

Loose
Data
mulitjets
c-,b- multijets
W+jetsZ+jets510electron p [ GeV ]

107
106

tt
single top
dibosonDrell-Yan

108

106
105

104

104

103

103

102

102
10

15

20

25

5

10

electron p [ GeV ]dibosonDrell-Yan

15

20
T

1

∈misid∈misidtt
single top

muon p [ GeV ]T

0.00 < | η | < 0.80
0.80 < | η | < 1.37
1.37 < | η | < 1.52

0.8

20

Tight
Data
multijetsc-, b- multijets
W+jetsZ+jets

107

105

5

15
T

[ events / bin ][ events / bin ]

Tight
Data
multijetsc-, b- multijets
W+jetsZ+jetsdibosonDrell-Yanmuon p [ GeV ]

T

108

tt
single top

1
0.8

1.52 < | η | < 2.01
2.01 < | η | < 2.50

0.6

0.6

0.4

0.4

0.2

0.2

0
5

10

15

20

0
5

25

electron p [ GeV ]

10

15

20

muon p [ GeV ]T

T

Figure 7.6: Distribution of pT for probe leptons passing the loose selection criteria (top), pT for the probe
leptons passing tight selection criteria (middle) and the misidentiﬁcation eﬃciencies ϵmisid (bottom) in thecontrol samples for low pT electrons (left) and muons (right). The misidentiﬁcation eﬃciencies are estimatedby subtracting real lepton events predicted by MC.

61

pT distributions of probe leptons, probe leptons satisfying the tight selection criteria and the misidentiﬁcationeﬃciencies ϵmisid in the control samples for the low pT leptons are shown in Figure 7.6, respectively. The same
method is applied to the electrons and the muons. The eﬃciencies are measured to be ϵmisid ∼ 10-30% with<the uncertainty <∼ 6% depending on the electron pT and |η|, and ϵmisid ∼ 44-66% with the uncertainty ∼ 6%
depending on the muon pT . The uncertainty of 10% derived from the diﬀerence of component is added to theeﬃciency of low pT electrons as well as the high pT electrons. The misidentiﬁed eﬃciency for low pT electrons
in the events containing at least one b-jets is shown in Figure 7.4.

7.2

W +jets and tt̄ BackgroundThe dominant source of background are leptonic decays for the W +jets and the products of the semi-leptonic
decay for tt̄. To obtain better modeling of background events, following corrections is applied to the simulated
samples of the dominant background,
1. Correction with the shape of distributions for W +jets and Z+jets events.
2. Correction with the normalization factors for W +jets, Z+jets and tt̄ events.
For the shape correction, pT of the both generated Z bosons and reconstructed Z bosons are used. The
generated Z boson events are reweighted based on a comparison of data with simulation depending on thepT of reconstructed Z boson in a control sample enriched in Z+jets events. The same correction factor isapplied to W production because of an assumption that the process is similar to the Z+jets process. After the
shape correction, normalizations of the dominant backgrounds are corrected. The relative normalization of the
ALPGEN samples (W +jets, Z+jets and tt̄) is adjusted by comparing the jet multiplicity distribution in data
versus simulation in all control regions. Both control region of W +jets and tt̄ samples are deﬁned in Table 7.1.
The control regions are chosen to enhance the W +jets and tt̄ events by requiring 40 < mT < 80 GeV and 40
miss
< ET
< 150 GeV, and similar jet cut to the signal regions. A common set of corrections is obtained for the
W +jets and Z+jets samples, and a set of corrections is obtained for semi-leptonic leptonic tt̄ decays.
First, this section describes a way of ﬁt, second the shape correction and the normalization correction are
described.

7.2.1

Fit Conﬁgurations

Fit results are obtained by using a likelihood function. The likelihood function consists of two parametertype. One is a signal strength µ which is a scale factor of cross section of interesting sample for example asignal process. The other is a nuisance parameter θ which determines deviation of probable density function in
calculation of the most probable value. The systematic uncertainties are treated as the nuisance parameters.
The likelihood function proceeds through two steps to calculate the most probable values for signal strengthand nuisance parameters. First, the likelihood functions are performed by inserting the signal strength andnuisance parameters into a Poisson function in each bin of the histograms. A product of the likelihood functions
L as following is used to calculate the signal strength∏∏∏Pθ (aθ |αθ ),(7.2.1)L =P ois(ncb |νcb ) · G(Lumi|λ, ∆Lumi )θ∈systc∈channels b∈bins

where ncb and νcb are number of observed events and expected events in each histogram bin b in each channelc. The λ is luminosity parameter for a given sample, thus G(Lumi|λ, ∆Lumi ) determines overall normalization
within the uncertainty of luminosity ∆Lumi . The Pθ (aθ |αθ ) is a constraint term describing an auxiliary measurement aθ that constrains the nuisance parameter αθ . The constraint is given by Gaussian function where
the width is obtained from discrepancy between nominal distribution and distributions after applying ±1σ
uncertainties.
The Poisson function P ois are described by using observed number of events ni and expected number of
events ν = µsi + bi ,n

P ois(µ)=(µsi + bi ) i −(µsi +bi )
e
,
ni !

(7.2.2)where si and bi are number of signal events and background events in each bin i. The most probable value forsignal strength µ̂ is given by maximizing the likelihood function.
62

∫

5000

6000

Events / 50 GeV

Events / 50 GeV

6000

Data 2011 ( s=7 TeV)-1

Ldt = 4.7 fb

Total

true W/Z= 0- 50GeV)

W/Z (p= 50-100GeV)

W/Z (p=100-150GeV)

W/Z (p=150-200GeV)

W/Z (p=200-250GeV)

W/Z (p>250GeV)T
true W/Z

4000

T
true W/ZT
true W/ZT
true W/Z

3000

T
true W/Z
T

2000

2000

Data / Exp

Data / Exp
350

400

=200-250GeV)

W/Z (p>250GeV)ttsingle top & dibosons

1300=150-200GeV)

W/Z (pTtrue W/Z

T

0
2

250

=100-150GeV)

W/Z (pTtrue W/Z

02200= 50-100GeV)

W/Z (pTtrue W/Z

1000

150

= 0- 50GeV)

W/Z (pTtrue W/Z

single top & dibosons

100

multijets (data estimate)W/Z (pTtrue W/Z

3000

tt

50

Total

true W/Z

4000

1000

0
0

Data 2011 ( s=7 TeV)

-1

5000

multijets (data estimate)W/Z (p∫ Ldt = 4.7 fb

450 500
pZ [GeV]

1
0
0

50

100

150

200

250

300

350

400

T

∫ Ldt = 4.7 fb

6000

Data 2011 ( s=7 TeV)

-1

5000

Total

W/Z (p= 0- 50GeV)

W/Z (p= 50-100GeV)

W/Z (p=100-150GeV)

W/Z (p=150-200GeV)

W/Z (p=200-250GeV)

W/Z (p>250GeV)T
true W/Z

4000

T
true W/ZT
true W/ZT
true W/Z

3000

T
true W/Z
T

2000∫ Ldt = 4.7 fb

2000

400

Data / Exp>250GeV)ttsingle top & dibosons

Data / Exp
350=200-250GeV)

W/Z (pT

1
300=150-200GeV)

W/Z (pTtrue W/Z

02250=100-150GeV)

W/Z (pTtrue W/Z

3000

0
2

200

= 50-100GeV)

W/Z (pTtrue W/Z

1000

150

= 0- 50GeV)

W/Z (pTtrue W/Z

single top & dibosons

100

multijets (data estimate)W/Z (pTtrue W/Z

4000

tt

50

Total

true W/Z

1000

0
0

Data 2011 ( s=7 TeV)

-1

5000

multijets (data estimate)true W/ZT

Events / 50 GeV

Events / 50 GeV

6000

450 500
pZ [GeV]450 500
pZ [GeV]

1
0
0

50

100

150

200

250

300

T

350

400

450 500
pZ [GeV]T

Figure 7.7: Distribution of reconstructed pZT in the shape correction control sample for the electron channel(top) and muon channel (bottom), and before the generated pZT ﬁtting (left) and after the generated pZT ﬁtting(right).
Next, the covariance matrix Vjk is calculated from the likelihood function as follow[ 2]∂ ln L−1
Vjk = −E,∂θj ∂θk(7.2.3)where the E means a expectation value of deviations of L. Here the signal strength and nuisance parameters
are treated equally, then θ contains the signal strength. The covariance matrix shows the correlation between
the nuisance parameters, and the correlation constrains uncertainties. The uncertainties are estimated from thecovariance matrix by varying the nuisance parameters θ as following
∆θl =

l
∑

−1
∆θj Vjk∆θk ,(7.2.4)j,kwhere ∆θ is the value of diﬀerence from − 12 σ to + 21 σ with each nuisance parameter θ.
The ﬁt conﬁgurations are described in Appendix C in more detail.

7.2.2

Shape Correction

To correct the shape, the simulated events of W +jets and Z+jets are reweighted by using the generated vectorbosons. Common correction factors for the W +jets and Z+jets events are obtained from a Z → ℓℓ sample
63Fitting Scale

1.2
s = 7TeV,∫ L dt = 4.7 fb-1

1

scale factor

0 < pZT < 50 GeV

1.0

50 < pZT < 100 GeV
100 < pZT < 150 GeV
150 < pZT < 200 GeV
200 < pZT

0.8

0.6

0.4

Generated pZT bin

0 - 50 GeV

50 - 100 GeV

100 - 150 GeV 150 - 200 GeV

200 - 250 GeV

250 -0.893 ± 0.043
0.866 ± 0.056
0.737 ± 0.061
0.772 ± 0.079

GeV

W/Z
[ GeV ]
pgeneratedT

Figure 7.8: Fitting results for pZT reweighting as a function of generated pT .
number of parton bin

W /Z+jetstt̄

Np = 01.0 ± 0.2

0.72 ± 0.18

Np = 1
Np = 2

1.0 ± 0.2
1.22 ± 0.13

1.15 ± 0.10
1.10 ± 0.17

Np = 3
Np = 4
Np = 50.85 ± 0.07
0.97 ± 0.06
0.68 ± 0.25

0.94 ± 0.06
0.94 ± 0.06
0.94 ± 0.06

Table 7.3: Fitting results with normalization factors for the W +jets and tt̄ events in each number of partonbin.
because the process of W +jets events are similar to that of Z+jets and the Z sample can reduce the dependence
on a jet energy scale uncertainty. The control sample is deﬁned as follows.
• At least two leptons N ℓ ≥ 2 satisfy opposite charge and same ﬂavor.
• Leading lepton and second leading lepton are required pℓT1st > 25 GeV and pℓT2nd > 10 GeV, respectively.
• Invariant mass for the dileptons event lies Z mass window 81 < mℓℓ < 101 GeV.
• At least two jets N jet ≥ 2 are required.
jet• The second leading jet is larger than pT 2nd > 50 GeV.
miss
• ET
< 50 GeV.

The transverse momentum of the generated Z on the simulation pZT is utilized to estimate the correction factors.
The generated pZT distribution for the sample is separated into ﬁve bins, with the ﬁrst four bins stepped by 50
GeV from 0 GeV to 200 GeV and the last bin integrated above 200 GeV. The reconstructed pZT distribution forthe simulated samples in the control sample is ﬁtted to the data by reweighting the generated Z boson events.
Likelihood function is performed in the ﬁt, and the most probable values give the correction factors. Source of
uncertainties as input are jet energy scale and renormalization scale, both are described in detail in Chapter
8. Figure 7.7 shows the distribution of the reconstructed pZT before and after reweighting by the generated Z
events. The correction factors obtained from the reweighting are shown in Figure 7.8.

7.2.3

Normalizations

After the shape correction, the W +jets and tt̄ events are normalized in the W +jets and tt̄ control regions.
The normalization factors are measured as the ratio of the normalization obtained from the ﬁt results to thenormalization predicted by the theoretical cross section. The factors are evaluated in each number of parton.
64

-1

1800
1600
1400
1200
1000
800
600

EventsEventsData 2011 ( s=7 TeV)
Total
W+jets & Z+jets Np0
W+jets & Z+jets Np1
W+jets & Z+jets Np2
W+jets & Z+jets Np3
W+jets & Z+jets Np4
W+jets & Z+jets Np5
tt Np0tt Np1
tt Np2
tt Np3
tt Np4
tt Np5
single top & diboson
multijets (data estimate)∫ Ldt = 4.7 fb

2000

1600
1400
1200
1000
800
600

0
2

Data / Exp

200

0

2
1
6

7

8

Data 2011 ( s=7 TeV)
Total
W+jets & Z+jets Np0
W+jets & Z+jets Np1
W+jets & Z+jets Np2
W+jets & Z+jets Np3
W+jets & Z+jets Np4
W+jets & Z+jets Np5
tt Np0tt Np1
tt Np2
tt Np3
tt Np4
tt Np5
single top & diboson
multijets (data estimate)∫ Ldt = 4.7 fb

2000

-1

1800

9
10
Number of jets

1600
1400
1200
1000
800
600

1
0
3

800
600

Data / Exp

Data / Exp

0
2

1
8

-1

1000

2

9
10
Number of jets

910
Number of jets

Data 2011 ( s=7 TeV)
Total
W+jets & Z+jets Np0
W+jets & Z+jets Np1
W+jets & Z+jets Np2
W+jets & Z+jets Np3
W+jets & Z+jets Np4
W+jets & Z+jets Np5
tt Np0tt Np1
tt Np2
tt Np3
tt Np4
tt Np5
single top & diboson
multijets (data estimate)∫ Ldt = 4.7 fb

1200

200

7

8

1400

0

6

7

1600

400

5

6

1800

200

4

5

2000

400

0
3

4

Events5

EventsData / Exp

400

200

4

-1

1800

400

0
3

Data 2011 ( s=7 TeV)
Total
W+jets & Z+jets Np0
W+jets & Z+jets Np1
W+jets & Z+jets Np2
W+jets & Z+jets Np3
W+jets & Z+jets Np4
W+jets & Z+jets Np5
tt Np0tt Np1
tt Np2
tt Np3
tt Np4
tt Np5
single top & diboson
multijets (data estimate)∫ Ldt = 4.7 fb

2000

1
0
3

4

5

6

7

8

9
10
Number of jets

Figure 7.9: Distribution of the number of jets in the W +jets control region for the electron channel (top) andmuon channel (bottom) before normalization (left) and after normalization (right).

65

-1

700
600
500
400
300
200

900

-1

700
600
500
400
300
200

0
2

Data / Exp

100

0

2
1
0
3

4

5

6

900

7

∫

800

8

9
10
Number of jets

Data 2011 ( s=7 TeV)
Total
W+jets & Z+jets Np0
W+jets & Z+jets Np1
W+jets & Z+jets Np2
W+jets & Z+jets Np3
W+jets & Z+jets Np4
W+jets & Z+jets Np5
tt Np0tt Np1
tt Np2
tt Np3
tt Np4
tt Np5
single top & diboson
multijets (data estimate)-1

Ldt = 4.7 fb

700
600
500
400
300
200

1
0
3

400
300
200

Data / Exp

Data / Exp
910
Number of jets

910
Number of jets

Data 2011 ( s=7 TeV)
Total
W+jets & Z+jets Np0
W+jets & Z+jets Np1
W+jets & Z+jets Np2
W+jets & Z+jets Np3
W+jets & Z+jets Np4
W+jets & Z+jets Np5
tt Np0tt Np1
tt Np2
tt Np3
tt Np4
tt Np5
single top & diboson
multijets (data estimate)∫ Ldt = 4.7 fb

500

1
8

8

600

0
2

7

7

700

2

6

6

-1

100

5

5

800

0

4

4

900

100

0
3

Data 2011 ( s=7 TeV)
Total
W+jets & Z+jets Np0
W+jets & Z+jets Np1
W+jets & Z+jets Np2
W+jets & Z+jets Np3
W+jets & Z+jets Np4
W+jets & Z+jets Np5
tt Np0tt Np1
tt Np2
tt Np3
tt Np4
tt Np5
single top & diboson
multijets (data estimate)∫ Ldt = 4.7 fb

800

100

Data / Exp
EventsEventsData 2011 ( s=7 TeV)
Total
W+jets & Z+jets Np0
W+jets & Z+jets Np1
W+jets & Z+jets Np2
W+jets & Z+jets Np3
W+jets & Z+jets Np4
W+jets & Z+jets Np5
tt Np0tt Np1
tt Np2
tt Np3
tt Np4
tt Np5
single top & diboson
multijets (data estimate)∫ Ldt = 4.7 fb

800

EventsEvents

900

1
0
3

4

5

6

7

8

9
10
Number of jets

Figure 7.10: Distribution of the number of jets in the tt̄ control region for the electron channel (top) and muonchannel (bottom) before normalization (left) and after normalization (right).

66

Control region
channelW +jets (hard lepton)
electronmuontt̄ (hard lepton)
electronmuon

Observed events

4510

4064

2225

2137

Fitted bkg events

4511.2 ± 67.7

4053.5 ± 61.8

2231.2 ± 40.9

2133.4 ± 39.4

Fitted tt̄ events
Fitted W +jets & Z+jets events
Fitted other bkg events
Fitted multijets events

1073.9 ± 75.6
2762.5 ± 104.0
100.0 ± 13.4
574.8 ± 111.7

1043.7 ± 79.7
2813.0 ± 99.7
94.6 ± 12.3
102.2 ± 55.6

1740.7 ± 51.4
308.1 ± 37.7
109.5 ± 14.7
73.0 ± 38.0

1701.8 ± 53.6
281.8 ± 31.8
109.1 ± 16.0
40.7 ± 33.1

MC exp. SM events

4887.3 ± 713.5

4262.2 ± 647.9

2525.7 ± 434.4

2220.7 ± 393.1

MC exp. tt̄ events
MC exp. W +jets & Z+jets events
MC exp. other bkg events
Data-driven multijets events

1154.0 ± 147.7
3241.9 ± 632.2
110.7 ± 23.4
380.8 ± 111.7

1006.6 ± 138.9
3069.3 ± 589.3
99.5 ± 22.6
86.8 ± 55.6

2012.4 ± 350.2
315.9 ± 126.0
124.1 ± 32.0
73.3 ± 38.0

1816.7 ± 339.7
257.6 ± 106.4
108.5 ± 34.2
37.9 ± 33.1

Control region
channelW +jets (soft lepton)
electronmuontt̄ (soft lepton)
electronmuon

Observed events

633

1092

131

200

Fitted bkg events

641.0 ± 21.7

1093.4 ± 28.5

130.4 ± 9.8

197.5 ± 12.0

Fitted tt̄ events
Fitted W +jets & Z+jets events
Fitted other bkg events
Fitted multijets events

37.3 ± 4.6
576.5 ± 20.3
13.1 ± 1.7
14.1 ± 13.0

68.7 ± 5.9
966.7 ± 35.4
15.9 ± 2.3
42.1 ± 26.3

70.2 ± 6.1
34.9 ± 4.1
11.8 ± 1.7
13.5 ± 10.1

108.9 ± 7.2
50.8 ± 6.0
17.6 ± 2.4
20.2 ± 11.3

MC exp. SM events

679.3 ± 154.2

1091.5 ± 300.2

125.7 ± 42.2

212.8 ± 78.9

MC exp. tt̄ events
MC exp. W +jets & Z+jets
MC exp. other bkg events
Data-driven multijets events

44.3 ± 16.0
597.0 ± 169.0
14.2 ± 5.6
23.9 ± 13.0

72.5 ± 25.7
961.5 ± 277.9
21.0 ± 6.4
36.4 ± 26.3

78.8 ± 34.0
30.3 ± 16.5
11.2 ± 4.0
5.4 ± 10.1

122.6 ± 50.3
50.0 ± 26.7
19.5 ± 5.7
20.7 ± 11.3

Table 7.4: Number of events in control regions. The ﬁt results of background (Fit) consist of the data-driven
multijets and simulated backgrounds. The inputs to the ﬁt (MC) consist of multijets and nominal expectations
from simulation normalized to theoretical cross sections are also shown. The errors shown are the statisticalplus systematic uncertainties.

67

W +jets

hard lepton
tt̄High mT

soft lepton

Nℓ
pℓT

=1
> 25 (20) GeV=1> 25 (20) GeV=1> 25 (20) GeV=1[7,25]([6,20])

N jet
pjet
T
N b-jet≥3> 80, 25, 25 GeV=0≥3> 80, 25, 25 GeV≥ 1 (within 3 jets)≥3> 80, 25, 25 GeV—≥2> 130, 25 GeV
—

miss
ET
mT
minc
eﬀ

miss
150 < ET< 250 GeV
40 < mT < 80 GeV
minc
eﬀ > 500 GeV

miss
150 < ET< 250 GeV
40 < mT < 80 GeV
minc
eﬀ > 500 GeV

miss
40 < ET< 250 GeV
mT > 100 GeV
minc
eﬀ > 500 GeV

miss
180 < ET< 250 GeV
80 < mT < 100 GeV—

Table 7.5: Deﬁnitions of the selection criteria of each validation region. The pT selections for lepton is given
for electron (muon).
The ﬁt is implemented in following conditions.
• The samples of W +jets associated with the heavy ﬂavor process share the same normalization factors as
the light ﬂavor samples in each bin of parton numbers.
• The Z+jets background associated with both light and heavy ﬂavor process are scaled by the common
normalization factors to the W +jets samples in the same parton bin.
• Larger than three parton bins (Nptt̄ ≥ 3) for the tt̄ samples are merged due to a small statistics.
• Normalization factors for the W +jets background in zero and one parton bins (NpW +jets = 0 and NpW +jets= 1) are ﬁxed at a unity due to the small contributions, and 20% uncertainty are assigned to the crosssections.
• The factors of the other backgrounds are ﬁxed at a unity and 20% uncertainty is assigned to the crosssections.
The normalization factors are measured by ﬁtting the backgrounds to data in a jet multiplicity distribution
in both W +jets and tt̄ control regions. Uncertainties as input for the ﬁt are described in Section 8.1 and Section
8.2. The measured normalization factors are shown in Table 7.3. The jet multiplicity distribution in W +jets
and tt̄ control regions before and after ﬁt by applying both shape corrections and normalization factors areshown in Figure 7.9 and Figure 7.10. In addition, the number of events as ﬁt results in each control region aresummarized in Table 7.4.

7.3

Validation Regions

The background correction is cross-checked by counting the number of events in validation regions, situatedbetween the control regions and the signal regions. Distributions in the validation regions are corrected bytaking the shape corrections and normalization factors in the control regions referred to Figure 7.8 and Table
miss
7.3. The deﬁnitions of validation regions are described in Table 7.5 and depicted on ET-mT plane in Figure
7.1.
miss
ET
distribution in soft lepton, W +jets and tt̄ validation regions are shown in Figure 7.12 (electron channel)
and Figure 7.13 (muon channel). The ﬁt results in both the validation regions are shown in Table 7.6. Pull
results which is diﬀerence between observed and predicted number of events divided by total uncertainty arealso shown in Figure 7.11. The distributions before ﬁt are overestimated in the validation regions, and the shapemisscorrection decreases the distributions at high ET
region. The pull result shows χ2 /NDOF = 4.12/4 = 1.03
in electron channel, χ2 /NDOF = 1.67/4 = 0.42 in muon channel and χ2 /NDOF = 5.79/8 = 0.72 in combined
channel. The results are equivalent to probabilities of 39%, 80% and 67% in chi-square statistic, respectively.
The table and pull results show the background estimation corrected by the scale factors are reasonably inagreement with the observed data in each validations region.

68

Validation region
channelW +jets (hard lepton)
electronmuontt̄ (hard lepton)
electronmuon

Observed events

1068

1019

499

427

Fitted bkg events

1001.1 ± 51.8

1015.2 ± 36.6

465.5 ± 23.2

456.9 ± 18.5

Fitted tt̄ events
Fitted W +jets & Z+jets events
Fitted other bkg events
Fitted multijets events

248.9 ± 15.9
719.1 ± 41.6
31.3 ± 4.1
1.8 ± 23.4

239.5 ± 15.8
739.3 ± 38.8
31.8 ± 4.3
4.6 ± 11.6

366.4 ± 18.2
67.4 ± 9.7
31.4 ± 4.7
0.3 ± 12.2

350.3 ± 18.0
76.4 ± 8.5
26.3 ± 3.7
3.8 ± 5.8

MC exp. SM events

1144.1 ± 211.7

1120.2 ± 197.2

558.1 ± 107.7

491.1 ± 93.8

MC exp. tt̄ events
MC exp. W +jets & Z+jets events
MC exp. other bkg events
Data-driven multijets events

280.5 ± 53.6
826.3 ± 211.5
35.4 ± 10.0
1.8 ± 23.4

242.6 ± 44.4
842.2 ± 181.1
30.7 ± 8.4
4.6 ± 11.6

447.6 ± 90.9
70.6 ± 33.8
39.6 ± 11.3
0.3 ± 12.2

386.5 ± 77.7
73.7 ± 32.1
27.1 ± 8.5
3.8 ± 5.8

Validation region
channelHigh mTelectronmuon

soft lepton
electronmuon

Observed events

7692

7075

295

463

Fitted bkg events

7413.8 ± 547.6

7095.4 ± 135.4

337.1 ± 23.7

490.8 ± 27.0

Fitted tt̄ events
Fitted W +jets & Z+jets events
Fitted other bkg events
Fitted multijets events

3127.5 ± 121.8
3619.7 ± 108.0
231.0 ± 29.5
435.5 ± 525.7

3100.6 ± 115.7
3728.8 ± 114.2
230.0 ± 29.6
35.9 ± 85.3

65.3 ± 5.0
246.6 ± 14.3
11.8 ± 1.6
13.4 ± 16.3

77.0 ± 5.2
380.3 ± 16.1
16.1 ± 2.1
17.5 ± 20.4

MC exp. SM events

8002.2 ± 888.2

7396.1 ± 835.8

342.4 ± 95.5

479.2 ± 137.1

MC exp. tt̄ events
MC exp. W +jets & Z+jets events
MC exp. other bkg events
Data-driven multijets events

3376.1 ± 476.0
3961.9 ± 721.1
228.7 ± 65.2
435.5 ± 525.7

3198.4 ± 476.6
3925.5 ± 718.4
236.2 ± 38.7
35.9 ± 85.3

69.5 ± 26.2
247.1 ± 87.7
12.4 ± 4.3
13.4 ± 16.3

80.9 ± 30.2
363.6 ± 122.5
17.1 ± 6.1
17.5 ± 20.4

Table 7.6: Number of events in validation regions. The ﬁt results of background (Fit) consist of the data-driven
multijets and simulated backgrounds. The inputs to the ﬁt (MC) consist of multijets and nominal expectations
from simulation normalized to theoretical cross sections are also shown. The errors shown are the statisticalplus systematic uncertainties.

69

Electron Channel
Muon Channelhigh mT validation region (hard lepton)

W+jets validation region (hard lepton)

Top validation region (hard lepton)

validation region (soft lepton)

-3

-2

-1

0

(n

obs

1

2

3

1

2

3

- npred) / σtot

Electron Channel
Muon Channelhigh mT validation region (hard lepton)

W+jets validation region (hard lepton)

Top validation region (hard lepton)

validation region (soft lepton)

-3

-2

-1

0

(n

obs

- npred) / σtot

Figure 7.11: Summary of ﬁtting results in validation regions before correction (top) and after correction (bottom). Diﬀerence between the observed and predicted number of events divided by the total uncertainty isshown. For the corrected distributions, χ2 /NDOF of the pull results are χ2 /NDOF = 4.12/4 = 1.03 (probability of 39%) in electron channel, χ2 /NDOF = 1.67/4 = 0.42 (probability of 80%) in muon channel andχ2 /NDOF = 5.79/8 = 0.72 (probability of 67%) in combined channel.

70Data 2011 ( s=7 TeV)
Total
W+jets & Z+jets Np0
W+jets & Z+jets Np1
W+jets & Z+jets Np2
W+jets & Z+jets Np3
W+jets & Z+jets Np4
W+jets & Z+jets Np5
tt Np0tt Np1
tt Np2
tt Np3
tt Np4
tt Np5
single top & dibosons
multijets (data estimate)-1

Ldt = 4.7 fb

160
140
120
100
80
60

60
40

Data / Exp

0
2

1
200

210

220

∫

250

230

-1

Ldt = 4.7 fb

200

100

240
250
miss
ET [GeV]

Data 2011 ( s=7 TeV)
Total
W+jets & Z+jets Np0
W+jets & Z+jets Np1
W+jets & Z+jets Np2
W+jets & Z+jets Np3
W+jets & Z+jets Np4
W+jets & Z+jets Np5
tt Np0tt Np1
tt Np2
tt Np3
tt Np4
tt Np5
single top & dibosons
multijets (data estimate)

1
0
180

1
190

200

210

220

∫ Ldt = 4.7 fb

140

-1

120
100

230 240 250
miss
ET [GeV]

Data 2011 ( s=7 TeV)
Total
W+jets & Z+jets Np1
W+jets & Z+jets Np2
W+jets & Z+jets Np3
W+jets & Z+jets Np4
W+jets & Z+jets Np5
tt Np0tt Np1
tt Np2
tt Np3
tt Np4
tt Np5
single top & dibosons
multijets (data estimate)

80
60
40

210

220

200

210

220

∫ Ldt = 4.7 fb-1

40

230 240 250
miss
ET [GeV]

Data 2011 ( s=7 TeV)
Total
W+jets & Z+jets Np0
W+jets & Z+jets Np1
W+jets & Z+jets Np2
W+jets & Z+jets Np3
W+jets & Z+jets Np4
W+jets & Z+jets Np5
tt Np0tt Np1
tt Np2
tt Np3
tt Np4
tt Np5
single top & dibosons
multijets (data estimate)230 240 250
miss
ET [GeV]

Data 2011 ( s=7 TeV)
Total
W+jets & Z+jets Np1
W+jets & Z+jets Np2
W+jets & Z+jets Np3
W+jets & Z+jets Np4
W+jets & Z+jets Np5
tt Np0tt Np1
tt Np2
tt Np3
tt Np4
tt Np5
single top & dibosons
multijets (data estimate)

60

Data / Exp
200

190

80

1
190

180

100

0
2

180

170

120

0
2

170

160

140

20

160

-1

Ldt = 4.7 fb

240
250
miss
ET [GeV]

1
0
150

20

0
150

∫

230

100

0
2

180

220

150

0
2

170

210

200

50

160

200

250

50

0
150

190

300

Data / Exp

Data / Exp

120

80

2

150

Events / 10 GeV

140

20

190

-1

160

0

0
180

Data 2011 ( s=7 TeV)
Total
W+jets & Z+jets Np0
W+jets & Z+jets Np1
W+jets & Z+jets Np2
W+jets & Z+jets Np3
W+jets & Z+jets Np4
W+jets & Z+jets Np5
tt Np0tt Np1
tt Np2
tt Np3
tt Np4
tt Np5
single top & dibosons
multijets (data estimate)∫ Ldt = 4.7 fb

180

20

300

Data / Exp

200

100

Events / 10 GeV

Events / 10 GeV

Data / Exp

40

Events / 10 GeV∫

180

Events / 10 GeV

Events / 10 GeV

200

1
0
150

160

170

180

190

200

210

220

230 240 250
miss
ET [GeV]miss
Figure 7.12: Distributions of the ET
in the soft lepton (top), W +jets (middle) and tt̄ (bottom) validation
region for the electron channel before (left) and after (right) corrections.

71

Data 2011 ( s=7 TeV)
Total
W+jets & Z+jets Np0
W+jets & Z+jets Np1
W+jets & Z+jets Np2
W+jets & Z+jets Np3
W+jets & Z+jets Np4
W+jets & Z+jets Np5
tt Np0tt Np1
tt Np2
tt Np3
tt Np4
tt Np5
single top & dibosons
multijets (data estimate)-1

Ldt = 4.7 fb

160
140
120
100
80
60

60
40

Data / Exp

0
2

1
200

210

220

∫

250

230

-1

Ldt = 4.7 fb

200

100

240
250
miss
ET [GeV]

Data 2011 ( s=7 TeV)
Total
W+jets & Z+jets Np0
W+jets & Z+jets Np1
W+jets & Z+jets Np2
W+jets & Z+jets Np3
W+jets & Z+jets Np4
W+jets & Z+jets Np5
tt Np0tt Np1
tt Np2
tt Np3
tt Np4
tt Np5
single top & dibosons
multijets (data estimate)

1
0
180

1
190

200

210

220

∫ Ldt = 4.7 fb

140

-1

120
100
80
60
40

230 240 250
miss
ET [GeV]

Data 2011 ( s=7 TeV)
Total
W+jets & Z+jets Np0
W+jets & Z+jets Np1
W+jets & Z+jets Np2
W+jets & Z+jets Np3
W+jets & Z+jets Np4
W+jets & Z+jets Np5
tt Np0tt Np1
tt Np2
tt Np3
tt Np4
tt Np5
single top & dibosons
multijets (data estimate)

210

220

200

210

220

∫ Ldt = 4.7 fb

-1

60
40

Data / Exp
200

190

80

1
190

180

100

0
2

180

170

120

0
2

170

160

140

20

160

-1

Ldt = 4.7 fb

230 240 250
miss
ET [GeV]

240
250
miss
ET [GeV]

Data 2011 ( s=7 TeV)
Total
W+jets & Z+jets Np0
W+jets & Z+jets Np1
W+jets & Z+jets Np2
W+jets & Z+jets Np3
W+jets & Z+jets Np4
W+jets & Z+jets Np5
tt Np0tt Np1
tt Np2
tt Np3
tt Np4
tt Np5
single top & dibosons
multijets (data estimate)

1
0
150

20

0
150

∫

230

100

0
2

180

220

150

0
2

170

210

200

50

160

200

250

50

0
150

190

300

Data / Exp

Data / Exp

120

80

2

150

Events / 10 GeV

140

20

190

-1

160

0

0
180

Data 2011 ( s=7 TeV)
Total
W+jets & Z+jets Np0
W+jets & Z+jets Np1
W+jets & Z+jets Np2
W+jets & Z+jets Np3
W+jets & Z+jets Np4
W+jets & Z+jets Np5
tt Np0tt Np1
tt Np2
tt Np3
tt Np4
tt Np5
single top & dibosons
multijets (data estimate)∫ Ldt = 4.7 fb

180

20

300

Data / Exp

200

100

Events / 10 GeV

Events / 10 GeV

Data / Exp

40

Events / 10 GeV∫

180

Events / 10 GeV

Events / 10 GeV

200

230 240 250
miss
ET [GeV]

Data 2011 ( s=7 TeV)
Total
W+jets & Z+jets Np0
W+jets & Z+jets Np1
W+jets & Z+jets Np2
W+jets & Z+jets Np3
W+jets & Z+jets Np4
W+jets & Z+jets Np5
tt Np0tt Np1
tt Np2
tt Np3
tt Np4
tt Np5
single top & dibosons
multijets (data estimate)

1
0
150

160

170

180

190

200

210

220

230 240 250
miss
ET [GeV]miss
Figure 7.13: Distributions of the ET
in the soft lepton (top), W +jets (middle) and tt̄ (bottom) validation
region for the muon channel before (left) and after (right) corrections.

72

Chapter 8

Uncertainties
The systematic uncertainties of energy scales and momentum resolutions with leptons and jets are measured
in beam tests and collision data in detail. The scale factors which correct the MC distributions to agree withdata have the systematic uncertainties as well. Cross sections and distributions for the simulated samples havetheoretical uncertainties derived from modeling and parameters of generators.
In ﬁtting with the background estimation, the uncertainties give widths where the most probable value canbe ﬁtted. For the some of uncertainties, the shape of distributions after applying ±1σ uncertainties are diﬀerent
from that of nominal distribution. As an example, Figure 8.1 shows jet multiplicity distribution for nominal andobtained by applying ±1σ jet energy scale uncertainties to jets with 40 < pT < 100 GeV and with pT > 100 GeV
in W +jets control region. These uncertainties are inputted in bin by bin so that the background expectations
can be described well by varying the shape of distributions. Therefore the uncertainties are classiﬁed into varying
shape and not varying shape. The uncertainties not varying shape are treated as varying the normalization. In
the following sections the uncertainties are summarized and categorized into varying shape labeled [shape] orvarying normalization labeled [normalization].
The systematic uncertainties are substituted into the likelihood function (Equation 7.2.1) as nuisance parameters. The input values of each uncertainties in this chapter are shown. The output from the covariancematrix (Equation 7.2.3) are shown in Table 8.3.

8.1

Systematic Uncertainties

10

6

Simulation

10
10

4

10

3

Jet energy scale∫ L dt = 4.7 fb , s = 7TeV

5eventsevents

Uncertainties of hit positions and energy scales are measured and propagated to the uncertainties of momentum
and energy. The uncertainties with the scale factors of eﬃciencies for lepton identiﬁcations and triggers arealso measured. Estimation method of systematic uncertainties are described in Appendix B. This section lists
and explains the considered systematic uncertainties. The values of uncertainties written in each item below-1(medium : 40 < pjetT< 100 GeV)

10

6

10

5

Simulation+1σ uncertainty
Nominal-1σ uncertainty

10

4

10

3

Jet energy scale∫ L dt = 4.7 fb , s = 7TeV
-1

10

10

1

1

100
50
0
-50
-100

100
50
0
-50
-100

Deviation [%]Deviation [%]> 100 GeV)

hard lepton W+jets control region

102

10

T

-1σ uncertainty

hard lepton W+jets control region

5jet+1σ uncertainty
Nominal1020(high : p

15
Number of jets

0

5

10

15
Number of jets

Figure 8.1: Jet multiplicity distributions of nominal and after applying ±1σ jet energy scale uncertainties. Jet
energy scale uncertainty is applied to jets with 40 < pT < 100 GeV (left) and jets with pT > 100 GeV (right).

73are estimated from deviations with the number of events between nominal distribution and distribution after
applying ±1σ uncertainties in control regions.
• Jet energy scale [shape]
Jet energy scale is the most dominant source of the uncertainties. The uncertainty increases at both large
and small jet pT , and the origin of uncertainty depends on the jet pT . The uncertainty originating fromcalorimeter response is dominant in large pT region while not only it but also modeling of generator aﬀect
the uncertainty in small pT region. Figure B.10 shows the component of uncertainty in detail. Thus whenjet
the uncertainty is applied to jets, jets are binned into three region, pjet
T < 40 GeV, 40 < pT < 100 GeV
jet
and pT > 100 GeV, respectively. The jet energy scale uncertainty is applied to jets in each pjet
T bin
independently to shift ±1σ. The uncertainty is estimated as ∼ ±25%.
misscell-out [shape]• ET
The energy scale uncertainty of cell-out cluster are derived from the dead materials and mismodelingof shower shape in calorimeters on the simulation. The uncertainty contributes to the overall cell-out
missET
term. The numbers of events in control regions is increased or decreased ∼1% from that of nominal
distribution when ±1σ uncertainties are applied to the nominal distribution.
miss
• ET
pile-up uncertainty [shape]
missTo reduce the pile-up contaminations, a cut-oﬀ is set for topocluster energy. This ET
pile-up uncertainty
is derived from the mismodeling with the dead material and the shower shape of soft jets. The numbers ofevents in control regions varies ∼1% from that of nominal distribution when ±1σ uncertainties are applied
to the nominal distribution.

• Electron energy scale uncertainty [normalization]
The electron energy scale uncertainty is estimated by using Z → ee events. The energy scale measurement
is aﬀected from an imperfect knowledge of the material in front of the electromagnetic calorimeter anddiﬀerent response between the high ET and low ET electron measurement. The value of this uncertainty
is about 1%.
• Muon momentum resolution uncertainty (with inner detector) [normalization]
The muon momentum resolution uncertainty in inner detector tracks is estimated by using Z → µµ events.
Diﬀerence of the Z peak ﬁtting results by using a Gaussian function between data and MC simulation aredealt as systematic uncertainty. The value is measured about 1%• Muon momentum resolution uncertainty (with muon spectrometer) [normalization]
The muon momentum resolution uncertainty with the muon spectrometer track is estimated as well as
the inner detector. The value is measured about 1%.
• Trigger eﬃciency uncertainty [normalization]
The eﬃciencies of electron trigger and muon trigger are not modeled by the MC simulation completely
thus the trigger eﬃciencies are corrected by the scale factors measured Z → ℓℓ events in depending on
miss
the pT and η. The uncertainty is measured as about 2 %. The eﬃciency of ET
trigger is estimated
miss
miss
as almost 100% above ET > 180 GeV both data and MC simulation, thus uncertainty of ET
triggereﬃciency is not applied to the soft lepton channel.
• Lepton scale factor uncertainty [normalization]
The eﬃciencies of electron and muon identiﬁcation are also not modelled by the MC simulation completely,
thus the identiﬁcation eﬃciencies are corrected by the scale factors measured Z → ℓℓ events in dependingon pT and η. The uncertainty is measured as about 2 %.
• Luminosity uncertainty [normalization]
The luminosity uncertainty is measured 3.7% derived from a bunch current measurement [47,48]. Methodof luminosity measurement and source of uncertainty are described in detail in Appendix B.
• b-tagging eﬃciency uncertainty [normalization]
The b-tagging is employed when it is separated into the W +jets control region and the tt̄ control region.
The uncertainty of b-tagging scale factor with no b-jets are applied to the events in W +jets control region,
while the uncertainty of b-tagging scale factor with b-jets are applied to the events in tt̄ control region.
About 9% uncertainty in tt̄ control region and 5% in W +jets control region are given.

74

sample

N jet

=3

tt̄
tt̄
W +jets
W +jets

−1σ
+1σ
−1σ
+1σ

-0.1%
+8%
-0.1%
+0.1%

sample

N jet

tt̄
tt̄
W +jets
W +jets

−1σ
+1σ
−1σ
+1σ

sampleHard lepton control region
=4
=5
=6
-0.1%
+5%
-2%
+0.1%

-0.1%
+0.3%
-0.1%
+0.6%

-2%
+0.1%
-0.1%
+6%

=7

=8

=9

-5%
+0.1%
-0.1%
+20%

-0.1%
+0.4%
-0.1%
+2%

-10%
+0.1%
-0.1%
+6%

Soft lepton control region
=2
=3
=4
=5
-0.1%
+0.3%
-0.1%
+3%

-0.1%
+4%
-4%
+0.1%

-1%
+0.1%
-10%
+0.1%

-2%
+0.1%
-14%
+0.1%

signal region
3-jets hard lepton 4-jets hard leptontt̄
W +jets

±12%
±19%

±16%
±8%

=6

=7

-4%
+0.1%
-12%
+0.1%

-0.1%
+11%
-0.1%
+3%

2-jets soft lepton
±2%
±30%

Table 8.1: MLM matching uncertainty for individual jet bin in hard lepton control regions, soft lepton control
regions and signal regions.
• Fitting uncertainty [shape]
The scale factors of shape and normalization corrections contain the uncertainty. Since variations derived
from renormalization and factorization scale uncertainties mostly aﬀect the shape and normalizations, theenergy scale uncertainties in generators are replaced by the uncertainties of ﬁt in the corrections of shapeand normalization of the individual light parton bins. The values are tabled in Figure 7.8 and Table 7.3.
• Multijets events uncertainty [normalization]
For the multijets background estimated by data-driven method, the systematic uncertainty of cross sectionof real lepton events predicted by the simulation is assumed as 20%. In subtraction of the real lepton
events from observed data, the uncertainty propagates to the multijets distribution. The uncertainty
amounts to 15% in soft lepton control regions, on the other hand 1% for hard lepton control regions.

8.2

Theoretical Uncertainties

Some background and signal estimations are performed by using the simulated events, therefore the modelingof generator is important. The parameters in the generator are tuned with collected data at Tevatron and LHC.
In this section, the uncertainties with modeling or parameters for the generators are summarized.
• Renormalization and factorization scale uncertainty [normalization]
The MC samples are generated with renormalization and factorization scale Q0 deﬁned as following∑ ()
Q20 = m2W +m2 + p2T(8.2.1)
partonsfor W +jets event and it is given by
Q20 =

∑ (

m2 + p2T)(8.2.2)partons

for tt̄ event. The factorization and renormalization scale uncertainty is estimated from the deviation ofsamples in which the energy scale is changed upward 2|Q0 | and downward 0.5|Q0 |.

75

• MLM matching [shape]
To avoid parton overlap between the diﬀerent number of parton sample, the MLM matching is applied.
min
The MLM matching is described in Section 4.2.1. In this analysis, the pmin
= 15 GeV, ET= pmin+5
T
T
GeV = 20 GeV and Rjet = 0.7 are employed.
When the threshold pmin
is varied, the number of jets, pjetTT distributions and the cross sections areaﬀected. Deviations from default sample with pmin=
15
GeV
to the samples with pmin
= 20 GeV and 30
TT
GeV in each jet multiplicity bin in control regions and signal region are assigned as the MLM matching
uncertainty. The amounts are shown in Table 8.1.
• Parton shower and hadronization [normalization]
The diﬀerence of parton shower and hadronization model leads to the diﬀerent distributions. The uncertainty is obtained from the diﬀerence of distributions between PYTHIA and HERWIG as the interfaces.
One of the diﬀerence between these generators is a given energy scale Q which determines probabilityof parton emission, PYTHIA uses Q2 ∼ m2 where m is a mass of generated particle, HERWIG uses
Q2 ∼ E 2 θ2 where E and θ are an energy and an open angle for branching particles. The diﬀerent is
missdistributions. Figure 8.2 shows meﬀ distribution of tt̄ events
ﬁtted to a linear function in meﬀ and ET
generated and the diﬀerence between HERWIG and PYTHIA. After ﬁtting, the ﬁt function extrapolates
from the control region to the signal region as follows[ miss]miss∆Had (%) = ±aETmiss × ET(x2 ) − ET(x1 ) ,
(8.2.3)∆Had (%) =±ameff × [meﬀ (x2 ) − meﬀ (x1 )] ,(8.2.4)miss
misswhere the ET(x1 ) and meﬀ (x1 ) are the thresholds of the control regions, and ET(x2 ) and meﬀ (x2 ) are
thresholds of signal regions. Therefore in the 3-jets, 4-jets hard lepton channel and soft lepton channel,meﬀ (x1 ) = 500 GeV and meﬀ (x2 ) = 1200 GeV, meﬀ (x1 ) = 500 GeV and meﬀ (x2 ) = 800 GeV and
miss
miss
ET
(x1 ) = 180 GeV and ET(x2 ) = 250 GeV are substituted into above equation, respectively. ∆Had
are estimated as 0.7% for W +jets events and 1.5% for tt̄ events in both control and signal regions.

• Cross section of W and Z associated with heavy ﬂavour [shape]
For the heavy ﬂavor quark production associated with W and Z boson, the cross section is not well known.
The cross section of W bb̄, W cc̄ and W c events whose diagram is shown in Figure 4.6 are measured in tt̄
charge asymmetry analysis to extract the events from data [49]. The uncertainties of W bb̄ and W cc̄ cross

meﬀ
miss
ET

W +jets and Z+jets
a = −0.0177
a = 0.0111tt̄
a = −0.0220
a = −0.0216

Figure 8.2: Diﬀerence of hadronization interface. Top ﬁgures show distribution of the eﬀective mass (left) andmiss
the ET(right) in the three jet selection for tt̄ events generated with HERWIG (green) and PYTHIA (blue).
Bottom table shows ﬁt results of the diﬀerence and coeﬃcient a.
76

section are estimated as 32% and that of W c is 47%. For Zbb̄ events the uncertainty of cross section isestimated as 25%.
• Cross section of single-top and dibosons [normalization]
The single-top and dibosons events are estimated by taking the simulated events. The cross sections aretreated as 20% uncertainty assigned.

8.3

Signal Cross Section Uncertainties

The cross sections of supersymmetry models are calculated by the two tools, “NLL-fast” and “Prospino”. The
NLL-fast computes the hadron production cross sections including next-to-leading order SUSY QCD corrections
which calculates the gluon or quark radiation by gluon loops and the virtual diagram involving squark and gluino
loops separately and add a re-summation of soft gluon emissions at next-to-leading logarithmic. Prospino
calculates the cross sections of pair production for supersymmetric particles at next-to-leading order (NLO).
The two tools calculate the uncertainties by using some parton density function (PDF) sets and varying bothfactorization and the renormalization scale Q0 . The estimation for theoretical uncertainty is described asfollowing.

8.3.1

Factorization and Renormalization Scale Uncertainty
2

The cross section calculation adopts the same value Q20 = (mk + ml ) for both factorization and renormalization
scale where k or l is squark or gluino mass contributing to the pair production. The cross section uncertainty
derived from the scale is estimated by taking into account the diﬀerence of cross section by shifting the |Q0 |from |0.5Q0 | to |2Q0 |. For the UED model, this uncertainty ∆αs is obtained by using PYTHIA and the value
is given as 9%.

8.3.2

PDF Uncertainty

CTEQ and MSTW PDF sets contain one central PDF value for the lightest ﬁve quarks and ﬁve anti-quarks
and one gluon and 22 variations which span the range of the uncertainties coming from the experimental errors.
This gives another 44 PDFs (up and down variations). The PDF uncertainty is estimated from the diﬀerenceof cross sections between nominal PDF set and each PDF set as follows,
√ ∑
2
=
∆up
{max [wup − w0 , wdown − w0 , 0]}(8.3.1)PDF
PDF sample

√
∆down
PDF =

∑

2

{max [w0 − wup , w0 − wdown , 0]}(8.3.2)

PDF sample(8.3.3)where the wup and wdown are the PDF weight with cross sections of upward and downward at 90% conﬁdence
level of each PDF samples respectively, and w0 is nominal weight. It is employed to the CTEQ6.6 [50] andMSTW2008 [51] as the PDF set. The upward and downward uncertainties are determined by either PDF set
which gives larger uncertainty than the other.

8.3.3

ISR Uncertainty

miss
miss
The ET
trigger is applied to the soft lepton channel, this ET
is generated by the recoil of neutrino or
neutralino against ISR jet. Thus the ISR jet uncertainty is critical for the soft lepton channel. The ISR
uncertainty estimation employs the MADGRAPH generator. The value is obtained from distributions whichis generated to vary the energy scale of parton emission from |0.5Q| up to |2Q|, where |Q| is nominal valueof energy scale for the transfer momentum. Figure 8.3 shows the nominal distribution of leading jet pT for
UED events and that of distributions after applying ±1σ ISR uncertainties. The discrepancy from the nominal77

distribution is from -10% to +20%. The uncertainty of simpliﬁed SUSY model is given as following [52](mdiﬀ )∆ISR =
1−· Norm
(8.3.4) √ 300GeV()
 (0.25)2 + (0.10)2 + 1.0 − mg̃ − 200GeV · 0.25 (mg̃ < 300GeV)
100GeV
Norm =(8.3.5)√ (0.25)2 + (0.10)2(mg̃ > 300GeV)
mdiﬀ

8.3.4

=

mg̃ − mLSP

(8.3.6)

Combined Uncertainty

The combined theoretical uncertainty of simpliﬁed SUSY model and UED model are estimated as the quadraticsummation of scale uncertainty and PDF uncertainty as follows√(8.3.7)∆ = ∆2αs + ∆2PDF + ∆2ISR
The estimated uncertainties of gluino pair production and squark pair production are shown in Figure 8.4.

8.4

Total Uncertainties Estimations[ events / 50 GeV /-1∫ Ldt = 1pb ]Contributions from uncertainties listed above to the signal regions are estimated in each signal region. The
estimation employs the likelihood function (Equation 7.2.1) and covariance matrix (Equation 7.2.3), and theuncertainties listed in Section 8.1-8.2 are substituted into the functions as nuisance parameters. The systematic
uncertainties as inputs are shown in Table 8.2. Number of events in each component of uncertainties and total
uncertainty in each signal region as outputs of the covariance matrix are shown in Table 8.3. Correlations
between nuisance parameters in covariance matrix constrain the uncertainties, therefore the values of outputs
in Table 8.3 are smaller than those of inputs.

10-3

Simulation

s=7TeV, UE D:1/R=700G eV,Λ R=10
ISR up-410Nominal
ISR down
10-5

10-6

10-7

Ratio

2
1
0

0

200

400

600

800

1000

leading jet p [ GeV ]T

Figure 8.3: Distribution of leading jet pT for nominal and the distributions after applying ±1σ ISR uncertainties
for UED signal events at 1/R = 700 GeV and ΛR = 10.
78Inputs to covariance matrix
Signal region
channel√Total statistical ( Nobs )Total background systematic
Jet energy scale (pjetT < 40 GeV)
Jet energy scale (40 < pjet
T < 100 GeV)
Jet energy scale (pjet>
100 GeV)T
misscell-outET
missET
pile-upElectron energy scale (hard electron)
Electron energy scale (soft electron)
Hard muon energy resolution (Inner Detector)
Soft muon energy resolution (Inner Detector)
Hard muon energy resolution (Muon Spectrometer)
Soft muon energy resolution (Muon Spectrometer)
Trigger Eﬃciency (electron)
Trigger Eﬃciency (muon)
Lepton scale factor (hard electron)
Lepton scale factor (hard muon)
Lepton scale factor (soft electron)
Lepton scale factor (soft muon)pZT weight ( 0 - 50 GeV)
pZT weight ( 50 - 100 GeV)
pZT weight (100 - 150 GeV)
pZT weight (150 - 200 GeV)tt̄ N p0 normalizationtt̄ N p1 normalizationtt̄ N p2 normalizationtt̄ N p3 normalization
W +jets N p2 normalization
W +jets N p3 normalization
W +jets N p4 normalization
W +jets N p5 normalization
Multijets (3-jets electron signal region)
Multijets (4-jets electron signal region)
Multijets (2-jets electron signal region)
Multijets (2-jets muon signal region)
MLM matching (tt̄ events)
MLM matching (W +jets events)
Hadronization (tt̄ events)
Hadronization (W +jets events)
W/Z+jets Heavy Flavor
W +jets N p0 cross section
W +jets N p1 cross section
single top & dibosons cross sections
MC statistical uncertainty

hard lepton 3-jets hard lepton 4-jets soft lepton 2-jets
electron muon electron muon electron muon
±1.41
±1.98

±1.00
±0.95

±2.00
±1.92

±1.41
±1.11

±3.32
±3.79

±3.74
±5.64

±0.72
—
±1.58
±0.14
±0.24
±0.18
—
—
—
—
—
±0.01
—
±0.03
—
—
—
—
—
—
±0.11
—
—
±0.05
±0.04
—
±0.12
—
—
±0.38
—
—
—
—
—
±0.11
±0.23
±0.34
—
—
—
±0.67

±0.08
±0.07
±0.35
±0.06
±0.06
—
—
±0.07
—
±0.06
—
—
±0.11
—
±0.01
—
—
±0.02
—
—
±0.15
—
—
±0.02
±0.05
—
±0.05
±0.11
±0.24
—
—
—
—
—
—
±0.08
±0.38
—
—
—
±0.04
±0.70

±1.18
±0.35
±0.72
±0.13
±0.49
±0.11
—
—
—
—
—
±0.03
—
±0.07
—
—
—
—
—
—
±0.12
—
±0.01
±0.09
±0.15
—
—
±0.04
±0.21
—
±0.38
—
—
—
—
±0.50
±0.14
±0.41
—
±0.18
±0.08
±0.81

±0.36
±0.50
±0.57
±0.30
±0.21
—
—
±0.05
—
±0.05
—
—
±0.13
—
±0.01
—
—
±0.05
—
—
—
—
—
±0.10
±0.12
—
—
—
±0.21
—
—
—
—
—
—
±0.32
±0.03
—
—
—
±0.02
±0.44

±0.17
±0.14
±0.22
±0.24
±0.31
—
—
—
—
—
—
—
—
—
—
±0.54
—
—
—
—
±0.41
±0.08
±0.06
±0.23
±0.13
±0.27
±0.26
±0.11
—
—
—
±2.45
—
—
—
±0.09
±1.65
±0.26
—
—
±0.10
±2.14

±0.14
±0.02
±0.47
±0.09
±0.02
—
—
—
±0.05
—
—
—
—
—
—
—
±0.02
—
±0.05
±0.02
±0.71
±0.27
±0.07
±0.19
±0.14
±0.83
±0.18
±0.11
±0.62
—
—
—
±2.43
—
—
±0.08
±3.15
±0.70
—
—
±0.02
±3.67

Table 8.2: Number of events as inputs derived from systematic uncertainties as inputs on background estimatesin the signal regions. Uncertainties not written are negligible.

79Outputs from covariance matrix
Signal region
channel√Total statistical ( Nobs )Total background systematic
Jet energy scale (pjetT < 40 GeV)
Jet energy scale (40 < pjet
T < 100 GeV)
Jet energy scale (pjet>
100 GeV)T
misscell-outET
misspile-upET
Electron energy scale (hard electron)
Electron energy scale (soft electron)
Hard muon energy resolution (Inner Detector)
Soft muon energy resolution (Inner Detector)
Hard muon energy resolution (Muon Spectrometer)
Soft muon energy resolution (Muon Spectrometer)
Trigger Eﬃciency (electron)
Trigger Eﬃciency (muon)
Lepton scale factor (hard electron)
Lepton scale factor (hard muon)
Lepton scale factor (soft electron)
Lepton scale factor (soft muon)pZT weight ( 0 - 50 GeV)
pZT weight ( 50 - 100 GeV)
pZT weight (100 - 150 GeV)
pZT weight (150 - 200 GeV)tt̄ N p0 normalizationtt̄ N p1 normalizationtt̄ N p2 normalizationtt̄ N p3 normalization
W +jets N p2 normalization
W +jets N p3 normalization
W +jets N p4 normalization
W +jets N p5 normalization
Multijets (3-jets electron signal region)
Multijets (4-jets electron signal region)
Multijets (2-jets electron signal region)
Multijets (2-jets muon signal region)
MLM matching (tt̄ events)
MLM matching (W +jets events)
Hadronization (tt̄ events)
Hadronization (W +jets events)
W/Z+jets Heavy Flavor
W +jets N p0 cross section
W +jets N p1 cross section
single top & dibosons cross sections
MC statistical uncertainty

hard lepton 3-jets hard lepton 4-jets soft lepton 2-jets
electron muon electron muon electron muon
±1.41
±0.81

±1.00
±0.75

±2.00
±0.96

±1.41
±0.50

±3.32
±3.29

±3.74
±4.45

±0.21
—
±0.08
±0.01
±0.02
±0.02
—
—
—
—
—
±0.01
—
±0.02
—
—
—
—
—
—
±0.06
—
—
±0.03
±0.03
—
±0.07
—
—
±0.38
—
—
—
—
—
±0.08
±0.10
±0.17
—
—
—
±0.67

±0.01
±0.01
±0.13
±0.02
±0.04
—
—
—
—
—
—
—
±0.04
—
—
—
—
±0.02
—
—
±0.08
—
—
±0.02
±0.02
—
±0.03
±0.07
±0.04
—
—
—
—
—
—
±0.08
±0.19
—
—
—
±0.02
±0.70

±0.53
±0.09
±0.17
±0.05
±0.11
±0.02
—
—
—
—
—
±0.02
—
±0.04
—
—
—
—
—
—
±0.04
—
±0.01
±0.07
±0.12
—
—
—
±0.13
—
±0.38
—
—
—
—
±0.15
±0.05
±0.20
—
±0.01
±0.02
±0.81

±0.06
±0.09
±0.11
±0.03
±0.07
—
—
—
—
—
—
—
±0.03
—
—
—
—
±0.01
—
—
—
—
—
±0.06
±0.09
—
—
—
±0.12
—
—
—
—
—
—
±0.11
±0.02
—
—
—
—
±0.44

±0.08
±0.01
±0.02
±0.07
±0.28
—
—
—
—
—
—
—
—
—
—
±0.35
—
—
—
—
±0.41
±0.04
±0.06
±0.23
±0.12
±0.25
±0.18
±0.08
—
—
—
±2.45
—
—
—
±0.06
±0.04
±0.11
—
—
±0.06
±2.14

±0.04
—
±0.01
±0.02
—
—
—
—
±0.05
—
—
—
—
—
—
—
±0.01
—
±0.05
±0.02
±0.71
—
±0.07
±0.19
±0.14
±0.82
±0.13
±0.08
±0.27
—
—
—
±2.43
—
—
±0.06
±0.09
±0.51
—
—
±0.01
±3.67

Table 8.3: Number of events derived from systematic uncertainties as outputs on background estimates inthe signal regions. Uncertainties not written are negligible. The uncertainties are constrained by taking thecovariance matrix.

80

Figure 8.4: Cross section for g̃-g̃ pair (left) and q̃-q̃ pair (right) production and associated uncertainty derived
from parton density function and renormalization scale [53].

81Chapter 9

Results
In this chapter, the signals of physics beyond the Standard Model are searched for by using the observed
data and background estimations. Distributions before corrections in signal regions are shown in Figure 9.1(simpliﬁed SUSY with mg̃ = 665 GeV and mLSP = 585 GeV) and Figure 9.2 (UED with 1/R = 900 GeV andΛR = 10). The distributions after the shape and normalization corrections in each signal region are shown in
Figure 9.3. The ﬁt results in signal regions are also shown in Table 9.1.
We can conclude discovery and exclusion by testing background-only hypothesis and signal-plus-backgroundhypothesis, respectively. To summarize the outcome of such a search one quantiﬁes the level of agreement of
the observed data with a given hypothesis H by computing a p-value, i.e. a probability, under assumption of
H, of ﬁnding data of equal or greater incompatibility with the predictions of H. In following sections, the test
results of background-only and signal-plus-background hypotheses with simpliﬁed SUSY and UED models aredescribed.

9.1

Testing the background-only hypothesis

In order to evaluate how well the observed data agree with the background prediction and ﬁnd an excess of
events originating from new physics, a statistical test is performed. For the hypothesis test with a given signal

Signal region
channel3-jets hard lepton
electronmuon

4-jets hard lepton
electronmuon

2-jets soft lepton
electronmuon

Observed events

2

1

4

2

11

14

Fitted bkg events

1.7 ± 0.8

2.2 ± 0.7

3.7 ± 1.0

2.1 ± 0.5

14.0 ± 3.3

18.9 ± 4.4

Fitted tt̄ events
Fitted W +jets & Z+jets events
Fitted other bkg events
Fitted multijets events

0.5 ± 0.2
0.8 ± 0.4
0.0 ± 0.0
0.3 ± 0.4

0.5 ± 0.2
1.6 ± 0.5
0.1 ± 0.1
0.0 ± 0.0

2.3 ± 0.5
0.9 ± 0.3
0.2 ± 0.1
0.3 ± 0.4

1.7 ± 0.4
0.3 ± 0.1
0.0 ± 0.0
0.0 ± 0.0

4.1 ± 0.7
5.6 ± 0.9
0.5 ± 0.1
3.8 ± 2.5

4.0 ± 0.8
11.2 ± 2.3
0.1 ± 0.0
3.6 ± 2.5

MC exp. SM events

2.4 ± 3.0

2.8 ± 1.2

5.6 ± 3.2

2.5 ± 1.3

14.2 ± 4.5

18.0 ± 7.9

MC exp. tt̄ events
MC exp. W +jets & tt̄ events
MC exp. other bkg events
Data-driven multijets events

0.9 ± 0.6
1.2 ± 2.6
0.0 ± 0.1
0.3 ± 0.4

0.6 ± 0.3
2.0 ± 1.3
0.2 ± 0.2
0.0 ± 0.0

3.1 ± 1.4
1.7 ± 2.0
0.4 ± 0.6
0.3 ± 0.4

2.0 ± 1.2
0.4 ± 0.4
0.1 ± 0.6
0.0 ± 0.0

4.3 ± 1.5
5.5 ± 3.1
0.5 ± 0.2
3.8 ± 2.5

3.8 ± 1.4
10.5 ± 5.0
0.1 ± 0.1
3.6 ± 2.5

Table 9.1: Number of events in signal regions. The ﬁt results of background (Fit) consist of the data-driven
multijets and simulated backgrounds. The inputs to the ﬁt (MC) consist of multijets and nominal expectations
from simulation normalized to theoretical cross sections are also shown. The errors shown are the statisticalplus systematic uncertainties.

82

12

6

4

Data / Exp

0
2

1
0.2

0.3

30

Events / 200 GeV

6

0
2

0.4

∫

25

0.5

-1

Ldt = 4.7 fb

0.6
0.7
miss
ET / meff

Data 2011 ( s=7 TeV)
Total
SUSY Simplified Model (~g~g)
mg~=665GeV, mLSP=585GeV

W+jets & Z+jets Np2
W+jets & Z+jets Np3
W+jets & Z+jets Np4
W+jets & Z+jets Np5
tt Np0tt Np1
tt Np2
tt Np3
tt Np4
tt Np5
single top & diboson
multijets (data estimate)

20
15
10

1
0
0.1

10

Data / Exp

5

1200

∫ Ldt = 4.7 fb

-1

4.5

1400
1600
minc
eff [GeV]

Data 2011 ( s=7 TeV)
Total
SUSY Simplified Model (~g~g)
mg~=665GeV, mLSP=585GeV

4

W+jets & Z+jets Np1

3.5

W+jets & Z+jets Np4
W+jets & Z+jets Np5

3

tt Np1

2.5

tt Np22

tt Np4

1.5

Data / Exp

Data 2011 ( s=7 TeV)

-1

Total
SUSY Simplified Model (~g~g)

W+jets & Z+jets Np5

3

tt Np2
tt Np3
tt Np4
tt Np5
single top & diboson
multijets (data estimate)

Data / Exp
1400

1400
1600
minc
eff [GeV]

1

1
1300

∫ Ldt = 4.7 fb

3.5

0
2

1200

1200

1.5

2

1100

SUSY Simplified Model (~g~g)
mg~=665GeV, mLSP=585GeV

mg~=665GeV, mLSP=585GeV

0.5

1000

1000

4

0

900

800

5

0.5

0
800

600

4.5

multijets (data estimate)

1

0
400

2

tt Np5
single top & diboson

Data 2011 ( s=7 TeV)
Total

1

2.5

tt Np3

0.6
0.7
miss
ET / meff

W+jets & Z+jets Np1
W+jets & Z+jets Np2
W+jets & Z+jets Np3
W+jets & Z+jets Np4
W+jets & Z+jets Np5
tt Np0tt Np1
tt Np2
tt Np3
tt Np4
tt Np5
single top & diboson
multijets (data estimate)

20

0
2

1000

0.5

∫ Ldt = 4.7 fb

25

0
2

800

0.4

-1

5

600

0.3

30

5

0
400

0.2

15

1

SUSY Simplified Model (~g~g)
mg~=665GeV, mLSP=585GeV

tt Np1
tt Np2
tt Np3
tt Np4
tt Np5
single top & diboson
multijets (data estimate)82

Data 2011 ( s=7 TeV)
Total

W+jets & Z+jets Np2
W+jets & Z+jets Np3
W+jets & Z+jets Np4
W+jets & Z+jets Np5

10

2

0
0.1

-1

12

Events / 200 GeV

Data / Exp

4∫ Ldt = 4.7 fb

14

tt Np0tt Np1
tt Np2
tt Np3
tt Np4
tt Np5
single top & diboson
multijets (data estimate)

8

Data / ExpSUSY Simplified Model (~g~g)
mg~=665GeV, mLSP=585GeV

W+jets & Z+jets Np2
W+jets & Z+jets Np3
W+jets & Z+jets Np4

10

Events / 200 GeV

Data 2011 ( s=7 TeV)
Total

Events-1

Events / 200 GeV

Events∫ Ldt = 4.7 fb

141500 1600
minc
eff [GeV]

1
0
800

900

1000

1100

1200

1300

1400

1500 1600
minc
eff [GeV]

miss
Figure 9.1: Distribution of the ET/meﬀ in soft lepton signal region (top), and meﬀ in 3-jets hard lepton(middle) and 4-jets hard lepton (bottom) signal region in electron channel (left) and muon channel (right)
before shape and normalization corrections. The contribution of simpliﬁed SUSY with mg̃ = 665 GeV andmLSP = 585 GeV is also shown.

83

12
10

6

Events / 200 GeV

6
4

0
2

Data / Exp

0
2

1
0.2

0.3

0.4

∫

25

0.5

-1

Ldt = 4.7 fb

20
15
10

0.6
0.7
miss
ET / meff

Data 2011 ( s=7 TeV)
Total
minimal UED
1/R=900GeV, ΛR=10
W+jets & Z+jets Np2
W+jets & Z+jets Np3
W+jets & Z+jets Np4
W+jets & Z+jets Np5
tt Np0tt Np1
tt Np2
tt Np3
tt Np4
tt Np5
single top & dibosons
multijets (data estimate)

1
0
0.1

20

10

Data / Exp

0
2

5

1000

∫

4.5

1200

1400
1600
minc
eff [GeV]

Data 2011 ( s=7 TeV)-1

Ldt = 4.7 fb

Total
minimal UED

4

1/R=900GeV, ΛR=10
W+jets & Z+jets Np1

3.5

W+jets & Z+jets Np4
W+jets & Z+jets Np5

3

tt Np1

2.5

tt Np22

tt Np4

Data / Exp

Total
minimal UED
1/R=900GeV, ΛR=10
W+jets & Z+jets Np5
tt Np2
tt Np3
tt Np4
tt Np5
single top & dibosons
multijets (data estimate)

Data / Exp
1400

Data 2011 ( s=7 TeV)

1

1
1300

1400
1600
minc
eff [GeV]

-1

3

0
2

1200

∫ Ldt = 4.7 fb

1.5

2

1100

Data 2011 ( s=7 TeV)
Total
minimal UED
1/R=900GeV, ΛR=10
W+jets & Z+jets Np1
W+jets & Z+jets Np2
W+jets & Z+jets Np3
W+jets & Z+jets Np4
W+jets & Z+jets Np5
tt Np0tt Np1
tt Np2
tt Np3
tt Np4
tt Np5
single top & dibosons
multijets (data estimate)

1200

3.5

0.5

1000

1000

4

0

900

800

5

0.5

0
800

600

4.5

multijets (data estimate)

1

0
400

2

tt Np5
single top & dibosons

0.6
0.7
miss
ET / meff

1

2.5

tt Np31.5

0.5∫ Ldt = 4.7 fb

25

0
2

800

0.4

-1

5

600

0.3

30

5

0
400

0.2

15

1

Data 2011 ( s=7 TeV)
Total
minimal UED
1/R=900GeV, ΛR=10
W+jets & Z+jets Np2
W+jets & Z+jets Np3
W+jets & Z+jets Np4
W+jets & Z+jets Np5
tt Np1
tt Np2
tt Np3
tt Np4
tt Np5
single top & dibosons
multijets (data estimate)

8

2

30

Data / Exp

10

2

0
0.1

-1

12

Events / 200 GeV

Data / Exp

4∫ Ldt = 4.7 fb

14

tt Np0tt Np1
tt Np2
tt Np3
tt Np4
tt Np5
single top & dibosons
multijets (data estimate)

8

Events / 200 GeV

Data 2011 ( s=7 TeV)
Total
minimal UED
1/R=900GeV, ΛR=10
W+jets & Z+jets Np2
W+jets & Z+jets Np3
W+jets & Z+jets Np4

Events-1

Events / 200 GeV

Events∫ Ldt = 4.7 fb

141500 1600
minc
eff [GeV]

1
0
800

900

1000

1100

1200

1300

1400

1500 1600
minc
eff [GeV]

miss
Figure 9.2: Distribution of the ET/meﬀ in soft lepton signal region (top), and meﬀ in 3-jets hard lepton(middle) and 4-jets hard lepton (bottom) signal region in electron channel (left) and muon channel (right)
before shape and normalization corrections. The contribution of UED with 1/R = 900 GeV and ΛR = 10 isalso shown.

84

-1

12

Data 2011 ( s=7 TeV)
Total
W+jets & Z+jets Np2

EventsEvents∫ Ldt = 4.7 fb

14∫ Ldt = 4.7 fb

14

-1

12

W+jets & Z+jets Np3

W+jets & Z+jets Np5

tt Np1

tt Np18

tt Np2

tt Np2

tt Np30
2Data / Exp

0
2

1
0.3

30

0.4

0.5

∫ Ldt = 4.7 fb

-1

25

0.6
0.7
miss
ET / meff

Data 2011 ( s=7 TeV)
Total
W+jets & Z+jets Np2
W+jets & Z+jets Np3
W+jets & Z+jets Np4
W+jets & Z+jets Np5

20

tt Np0tt Np1

1
0
0.1

0.2

0.3

0.4

0.5

∫ Ldt = 4.7 fb

-1

25
20

tt Np215

multijets (data estimate)

30

Events / 200 GeV

Data / Exp2

0.2

tt Np5
single top & dibosons

4

multijets (data estimate)

2

0
0.1

tt Np4

6

tt Np5
single top & dibosons

4

Events / 200 GeV

tt Np3

tt Np4

6

tt Np4
tt Np5
single top & dibosons

10

0
2

0
2

Data / Exp

5

1
0
400

600

800

5

1000

∫

4.5

1200

1400
1600
minc
eff [GeV]

Data 2011 ( s=7 TeV)-1

Ldt = 4.7 fb

Total
W+jets & Z+jets Np1

4

W+jets & Z+jets Np4

3.5

W+jets & Z+jets Np5
tt Np1

3

tt Np2

2.5

Events / 200 GeV

Events / 200 GeV

Data / Exp

multijets (data estimate)5

tt Np3

0
400

600

800

5

1000

1200

∫ Ldt = 4.7 fb-1

4

tt Np2
tt Np32.5

tt Np4
tt Np5
single top & dibosons

1.5
multijets (data estimate)

0.5

0.5

0

0
2

Data / Exp

1

Data / Exp

1

2
1
800

1000

1200

Total

3

2

single top & dibosons

600

Data 2011 ( s=7 TeV)

W+jets & Z+jets Np5

multijets (data estimate)

0
400

1400
1600
minc
eff [GeV]

3.5

tt Np5

1.5

Data 2011 ( s=7 TeV)
Total
W+jets & Z+jets Np1
W+jets & Z+jets Np2
W+jets & Z+jets Np3
W+jets & Z+jets Np4
W+jets & Z+jets Np5

1

4.5

tt Np4

2

0.6
0.7
miss
ET / meff

tt Np0tt Np1
tt Np2
tt Np3
tt Np4
tt Np5
single top & dibosons
multijets (data estimate)15

tt Np310

W+jets & Z+jets Np2
W+jets & Z+jets Np4

10tt Np08

Total
W+jets & Z+jets Np3

W+jets & Z+jets Np4

10

Data 2011 ( s=7 TeV)

1400
1600
minc
eff [GeV]

1
0
400

600

800

1000

1200

1400
1600
minc
eff [GeV]

miss
Figure 9.3: Distribution of the ET/meﬀ in soft lepton signal region (top), and meﬀ in 3-jets hard lepton(middle) and 4-jets hard lepton (bottom) signal region in electron channel (left) and muon channel (right) after
the shape and normalization corrections.

85

Signal region⟨ϵσ⟩95
obs [fb]

95
Sobs

95
Sexp

CLb

4.2+2.2−1.5
4.4+2.2−1.2
5.3+2.6−1.3
6.2+2.4−1.4
10.6+4.3−2.8
12.2+4.9
−1.2

0.57

hard electron 3-jets

0.96

4.5

hard muon 3-jets

0.94

4.4

hard electron 4-jets

1.22

5.8

hard muon 4-jets

1.30

6.1

soft electron

1.92

9.0

soft muon

2.34

11.0

0.50
0.63
0.47
0.31
0.21

95
Table 9.2: 95% CL upper limits on the visible cross-section (⟨ϵσ⟩95obs ) and on the observed (Sobs ) and expected
95(Sexp) number of signal events for the various signal regions. The last column indicates the CLb value.

model with µ, a test statistics
λ(µ) =

ˆL(µ, θ̂)L(µ̂, θ̂),(9.1.1)ˆis used, where L(µ̂,θ̂) is the maximized likelihood function by taking θ̂ and µ̂. The quantity θ̂ denotes thenuisance parameter of that maximizes L for the speciﬁed µ. The numerator of this ratio is called proﬁlelikelihood function, and is a function of µ. Since the signal strength must not have a negative value, the test
statistics is then given byˆ
L(µ, θ̂(µ))
(µ̂ < 0) ,
−2 ln

ˆ

{

L(0,
θ̂(0))
−2 ln λ(µ)(µ̂ ≤ µ)ˆq̃µ ==(9.1.2)L(µ, θ̂(µ))
−2ln(0 ≤ µ̂ ≤ µ) ,0(µ̂ > µ)L(µ̂, θ̂(µ̂))




0
(µ̂ > µ) .
The pb -value of the background-only hypothesis is calculated by integrating the probability density distributionof the test statistics with null signal in the range from q̃µ=0,obs to inﬁnity:∫ ∞pb =f (q̃µ=0 |µ = 0) dq̃µ=0 .
(9.1.3)q̃µ=0,obs

Distributions of background-only hypothesis in the signal regions are already shown Figure 9.3. Model
independent limit on the visible cross section derived from the observations in the signal regions are alsomeasured. A µ scan in the soft electron signal region is shown Figure 9.4 and it gives the upper limits on
both observed and expected 95% CLs of non-standard-model event in the signal regions. The number of non95
95
standard-model signal events at 95% CL, Sobs
, Sexpare derived using the CLs . The limits are divided byintegral luminosity to obtain the limits on visible cross sections ⟨ϵσ⟩95
obs . The CLb are taken at the same signal
strength as the 95% CLs . The results in each signal region are shown in Table 9.2. These results show the
CLb ∼ 20-60%, thus the observed data is consistent with the background-only hypothesis.

9.2

Exclusion Limit

In the absence of a signal, speciﬁc models of new physics are included by comparing signal-plus-backgroundhypothesis with the observed data. The p-value of the signal-plus-background hypothesis is calculated as follows:∫ ∞ps+b =f (q̃µ=1 |µ = 1) dq̃µ=1 .
(9.2.1)q̃µ=1,obs

The conﬁdence level of exclusion CLs is given by using the ps+b as CLs+b = 1−ps+b and CLs = CLs+b /(1−CLb ).
The CLs is given by scanning the signal strength µ of speciﬁc signal model. Figure 9.5 shows the scan result86

p value

Observed CLs

1

Observed CLs+b
Observed CLb
Expected CLs - Median
Expected CLs ± 1 σ

0.8

Expected CLs ± 2 σ

0.6

0.4

0.2

0
0

2

4

6

8

10

12

14

16

18

20
22
24
Signal Strength

p value

Figure 9.4: Scan results for signal strength µ with CLs , CLs+b and CLb for observed and expected with nonstandard-model signal in soft electron signal region.

Observed CLs

1

Observed CLs+b
Observed CLb
Expected CLs - Median
Expected CLs ± 1 σ

0.8

Expected CLs ± 2 σ

0.6

0.4

0.2

0
0

0.1

0.2

0.3

0.4

0.5

0.6

0.7
Signal Strength

Figure 9.5: Scan results for signal strength µ with CLs , CLs+b and CLb for observed and expected with UED
model at 1/R = 700 GeV and ΛR = 1087for UED model at 1/R = 700 GeV and ΛR = 10. Both normalizations of dominant background and signal
strength µ are re-ﬁtted in both control regions and signal regions simultaneously corresponding to the scanningsignal strength. When the signal strength µ at 95% CLs is less than 1.0, we conclude that the signal model is
excluded.
In the calculation of the upper limit on the cross-section for a given signal model, the total theoreticaluncertainty of the signal model described in Section 8.3 is treated as increasing and decreasing the signal crosssections upward and downward ±1σ, respectively. The results are treated as the ±1σtheory observed limits. In
following sections, the exclusion limits at 95% CLs for simpliﬁed SUSY model (g̃-g̃ pair production) and UED
model are shown.

88

Simpliﬁed SUSY model (g̃-g̃ Pair Production)

900

~
∼0χ
∼0, x=1/2
g~
g → qqqqWW χ
1 1

mLSP [GeV]mLSP [GeV]

The results of searching for degenerate SUSY model with simpliﬁed SUSY model are shown in Figure 9.6. The
three ﬁgures show the exclusion limits at 95% CLs for the soft lepton channel, the hard lepton channel andcombination of soft lepton and hard lepton channel.
In the diagonal region along the dashed line where the mass spectrums are degenerated, mg̃ space below∼ 300 GeV in degenerate mass region were already excluded in 2011 summer results (Figure 2.1). The below
ﬁgures indicate that mg̃ ∼ 540 GeV and mLSP ∼ 450 GeV in degenerated mass region and mg̃ ∼ 970 GeV andmLSP ∼ 100 GeV in large mass diﬀerence region are excluded at 95% CLs .
In mass degenerated region as (mg̃ − mLSP )/mg̃ ∼ 10%, the exclusion limit of the soft lepton channel (mg̃ ∼460 GeV) advances compared to that of hard lepton channel mg̃ ∼ 400 GeV. The combined result excludes
a point at mg̃ ∼ 540 GeV and mLSP ∼ 450 GeV for simpliﬁed SUSY model. About 250 GeV in mg̃ space isimproved in the degenerate region from the 2011 summer results.

∫ L dt = 4.71 fb , s=7 TeV-1800

Soft Lepton Channel
Expected limit (±1 σexp)

700

900

~
∼0χ
∼0, x=1/2
g~
g → qqqqWW χ
1 1∫ L dt = 4.71 fb , s=7 TeV-1800

Hard Lepton Channel
Expected limit (±1 σexp)

700

Observed limit (±1 σtheory)

600

Observed limit (±1 σtheory)600

All limits at 95% CL s

500

500

400

400

300

300

200

200

300

400

500

600

mLSP [GeV]

100

900

700

800

900

100

1000 1100m~g [GeV]All limits at 95% CL s

300

400

500

600

700

800

900

1000 1100m~g [GeV]~∼0χ
∼0, x=1/2
g~
g → qqqqWW χ
1 1∫ L dt = 4.71 fb , s=7 TeV-1800

Hard and Soft Lepton Combined
Expected limit (±1 σexp)

700

Observed limit (±1 σtheory)600

All limits at 95% CL s

500
400
300
200
100

300

400

500

600

700

800

900

1000 1100m~g [GeV]

Figure 9.6: Exclusion regions at 95% CLs upper limits in simpliﬁed SUSY model in gluino pair production
with X = (mχ̃± − mχ̃01 )/(mg̃ − mχ̃01 ) = 1/2 samples for the soft lepton channel (top-left), hard lepton channel
1(top-right) and combined results (bottom), respectively.

89Universal Extra Dimensions
The exclusion limits of UED model for the soft lepton channel, the hard lepton channel and the combination ofboth channels are shown in Figure 9.7 on 1/R-ΛR plane.
For UED model, the degree of mass degenerate (mKKgluon − mKKphoton )/mKKgluon are less than 25% in theconsidered ΛR region (ΛR = 2-40). Within the degree, the soft lepton channel contributes to the exclusion
limits greatly. The exclusion limits at 95% CL reaches 1/R ∼ 840 GeV at ΛR = 5 in the soft lepton channel,
although the exclusion limit of hard lepton channel reaches 1/R ∼ 630 GeV at ΛR = 5. At large ΛR region(ΛR ∼ 40) corresponding to the large degree of mass degenerate, the hard lepton channel gets sensitivity to themodel however it is more sensitive for soft lepton channel than that of hard lepton channel in this region.
The combination result excludes the 1/R space above 800 GeV, especially the space of 1/R ∼ 840 GeV at
ΛR = 5 is excluded. The upper limit in a space of 1/R = 830 GeV at ΛR = 20 is more impressive result than
Tevatron results which had excluded the model in 1/R parameter space below 280 GeV. This analysis improves
the upper limit greatly.

Minimal Universal Extra Dimension

ΛR

ΛR

Minimal Universal Extra Dimension

40∫ L dt = 4.71 fb , s=7 TeV

40

-1

35

35

Soft Lepton Channel

30

Observed limit (±1 σtheory)30

Expected limit (±1 σexp)

25

25

All limits at 95% CL s

20

20

15

15

10

10

∫ L dt = 4.71 fb , s=7 TeV-1Hard Lepton Channel

5

Observed limit (±1 σtheory)
Expected limit (±1 σexp)

5

All limits at 95% CL s

500

550

600

650

700

750

800

850
900
1/R [GeV]

500

550

600

650

700

750

800

850
900
1/R [GeV]ΛR

Minimal Universal Extra Dimension

40∫ L dt = 4.71 fb , s=7 TeV-1

35

Hard and Soft Lepton Combined

30

Observed limit (±1 σtheory)
Expected limit (±1 σexp)

25

All limits at 95% CL s

20
15
10
5
500

550

600

650

700

750

800

850
900
1/R [GeV]

Figure 9.7: Exclusion regions at 95% CLs upper limits in UED model for soft lepton channel (top-left), hard
lepton channel (top-right) and combined results (bottom), respectively.

90

9.3

Summary and Prospects

In both the soft lepton and hard lepton signal regions, the expected background with the Standard Model isconsistent with the observed data. The signal excesses are not observed with integrate luminosity of 4.7 fb−1 .
The test of background-only hypothesis gives the 95% upper limits on the invisible cross sections, number ofsignal events and CLb in each signal region.
For the test of background-plus-signal hypothesis, exclusion upper limits at 95% CLs are estimated for thesimpliﬁed SUSY and the UED models. The results of hard lepton channel, soft lepton channel and combinationof these channel are summarized in Figure 9.8. The observed upper limits of these results are overlaid in theﬁgures. The results show that only soft lepton channel is sensitive to the new physics in small degree space ofdegenerate (mg̃ − mLSP )/mg̃ or (mKKgluon − mKKphoton )/mKKgluon <∼ 15%. Approximately from 15% to 25%of the degree, the soft lepton channel is more sensitive to such models than the hard lepton channel. For UED
model, the result of soft lepton channel is signiﬁcantly more better than that of hard lepton channel in all ΛRspace since the degree of degenerate whose values are from ∼5% (ΛR = 2) to ∼25% (ΛR = 40) is smaller than
the general SUSY models.

900

~
∼0χ
∼0, x=1/2
g~
g → qqqqWW χ
1 1

Minimal Universal Extra Dimension

ΛR

mLSP [GeV]

In 2012 run, LHC operates at center-of-mass energy of 8 TeV and integral luminosity is expected to reachto 20 fb−1 . Cross sections of SUSY and UED model in 8 TeV are calculated to be approximately twice larger
than that of 7 TeV. The increasing cross section and integral luminosity improve about ﬁve times signiﬁcanceof the models than the 2011 data. Predicted upper limits in 2012 for simpliﬁed SUSY model and UED model
reach mg̃ ∼ 700 GeV in degenerated region and 1/R ∼ 950 GeV, respectively. It is possible to discover thedegenerate SUSY model or UED model in more higher mass region.

∫ L dt = 4.71 fb , s=7 TeV

40

-1

800

Observed limit (±1 σtheory)

700

Observed limit (±1 σtheory)30

Hard-Soft Channel Combined
Hard Lepton Channel

600

Hard-Soft Channel Combined
Hard Lepton Channel

25

Soft Lepton Channel
All limits at 95% CL s

Soft Lepton Channel
All limits at 95% CL s

500

20

400

15

300

10

200
100

∫ L dt = 4.71 fb , s=7 TeV
-1

35

5
300

400

500

600

700

800

900

1000 1100m~g [GeV]

500

550

600

650

700

750

800

850
900
1/R [GeV]

Figure 9.8: Exclusion regions for simpliﬁed g̃-g̃ production SUSY model and UED in the hard lepton channel(blue), the soft lepton (green) channel and the combined results (red).
91Chapter 10

Conclusion
This analysis searches for physics beyond the Standard Model with degenerate mass spectrum in ﬁnal states
misscontaining one isolated lepton, jets and ET. The interesting models are supersymmetry (SUSY) and universal
extra dimensions (UED) where mass diﬀerence between the heaviest and lightest particles in the model areapproximately less than 30%. In addition, a high pT lepton channel for MSUGRA search is also employed forthe analysis to increase the sensitivity to the degenerate models. The collected data in 2011 corresponding toan integrated luminosity of 4.7 fb−1 and center-of-mass energy of 7 TeV are used for the analysis.
The signal region is optimized for the best signiﬁcance with integrated luminosity with 5.0 fb−1 . The
selection criteria of signal region for the degenerate model are determined by using low pT one lepton and at0
missleast two jets coming from cascade decay, and large ET
originating from neutralino χ̃1 or KK-photon, andhigh pT leading jet due to initial state radiation. The signal region is expected to have approximately twice
sensitivity of MSUGRA search in region where the mass spectrum is degenerated.
The background estimations are performed by ﬁtting to observed data in control regions. The W +jets,
Z+jets and tt̄ events as dominant background are estimated by using simulated samples. These events are
ﬁtted the simulated events to observed data in pZT space for shape correction and in control regions where such
events are enriched for normalization correction.
The multijets events are estimated by data-driven method which decomposes the leptons satisfying signal
selection criteria into real leptons and misidentiﬁed leptons by using eﬃciencies of real leptons and misidentiﬁed
leptons. In the eﬃciency measurements, dileptons events are employed to avoid a trigger bias and some selections
are applied to the events to enhance the real or misidentiﬁed lepton events. The multijets events are measured
by applying the eﬃciencies to the number of observed leptons satisfying and failing the signal selection criteria.
The results show that the observed data are in agreement with the Standard Model expectations and there
are no evidences of the beyond standard models. The g̃-g̃ pair production of simpliﬁed SUSY model is excluded
in degenerate mass region where the mg̃ and mLSP are below approximately 540 GeV and 450 GeV at 95% CL.
In addition, UED model is excluded below 840 GeV in 1/R space at ΛR = 5 at 95% CL. For these models,
the result of soft lepton channel contributes greatly compared to that of hard lepton channel which targets
MSUGRA model.

92

Acknowledgements
I would like to express my deepest appreciation to Prof. Shoji Asai for giving me many idea and knowledge
about the experiments. He supports my research life.
Prof. Naoko Kanaya, Prof. Koji Terashi and Prof. Shimpei Yamamoto, they teach me very kindly andprofessionally. I’m the most grateful to them.
Staﬀ members of International Center for Elementary Particle Physics (ICEPP) in the university of Tokyo
and ATLAS-JAPAN, Prof. Tatsuo Kawamoto, Prof. Junichi Tanaka, Prof. Osamu Jinnouchi, Prof. Yousuke
Kataoka, Prof. Susumu Oda, Dr. Taiki Yamamura, Dr. Tatsuya Masubuchi, Dr. Koji Nakamura and Dr.
Takashi Yamanaka, they support and advise me on the analysis.
Member of SUSY in strong production in one and more leptons channel, Prof. Moritz Backes, Prof. DavidCôté, Prof. Mark Hohlfeld, Prof. Max Baak, Prof. Aleksej Koutsman, Prof. George Redlinger, Prof. MarieHelene Genest, Dr. Xin Chen, Dr. Meyer Carsten, Dr. Matthias Lungwitz, Ms. Jeanette Miriam Lorentz, Prof.
Renaud Brunelière, Dr. Otilia Anamaria Docu, Dr. Julian Maurer, they help and teach me greatly. I would
like to express my gratitude to them.
In tile calorimeter group, Prof. Claudio Santoni and Dr. Zhili Weng teach me how to estimate performanceof tile calorimeter. I am very grateful to them.
I deeply appreciate for staﬀs and students in ICEPP, Prof. Tomio Kobayashi, Prof. Hiroshi Sakamoto,Prof. Tetsuro Mashimo, Prof. Yoshizumi Inoue, Prof. Toshio Nanba, Prof. Tomoaki Nakamura, Prof. Kenji
Mishima, Prof. Tomohiko Tanabe, Prof. Akira Ishida, Dr. Taikan Suehara, Dr. Hidetoshi Otono, Dr. Takayuki
Yamazaki, Mr. Nagataka Matsui, and Mr. Hideyuki Oide, Mr. Ryo Katayama, and graduated students Mr.
Junichi Okamura and Mr. Yoshihumi Takeichi.
I would like to thank students of ICEPP as Mr. Ginga Akimoto, Mr. Yuya Azuma, Mr. Kohei Kessoku,
Mr. Yoichi Ninomiya, Mr. Yuichi Sasaki, Mr. Shingo Kazama, Mr. Keisuke Yoshihara, Mr. Yohei Yamaguchi
and Mr. Akira Miyazaki, and members of ATLAS-JAPAN as Dr. Yasuyuki Okumura, Dr. Yuta Takahashi,
Dr. Takashi Hayakawa, Mr. Takeshi Domae, Mr. Minoru Hirose, Mr. Yu Suzuki, Mr. Takayuki Kanno, Mr.
Satoshi Hasegawa, Mr. Tatsuma Meguro, Mr. Matt King, Mr. Ljiljana Morvaj, Mr. Toyonobu Okuyama, Mr.
Wataru Okamura, Ms. Katarina Bendtz, Mr. Takuya Nobe, Mr. Ryo Nagai, Mr. Jun Wakabayashi.
I am thankful to Dr. Takashi Kubota, Dr. Keigo Imai, Ms. Konomi Sakamoto Ms. Asuka Suzuki, Mr.
Tsuyoshi Maeda, Mr. Yusuke Okuno and Mr. Kouzou Mizunuma they supported and encouraged me when I
enrolled in the graduated school.
My deepest appreciation goes to secretaries in department of physics and ICEPP, Ms. Kuniko Kono, Ms.
Masako Shiota, Ms. Yoko Takemoto, Ms. Akiko Miyazono, Ms. Yoshie Teduka, Ms. Megumi Suzuki, Ms.
Cheiko Morita, Ms. Naoko Kataoka and Ms. Ritsuko Anbiru.
I would like to thank Ms. Geraldine Donaldson, Ms. Esther Lutz Donaldson and Mr. John Donaldson who
teach English and take care of me.
Finally, I thank my family, Yukio Yamaguchi, Miyoko Yamaguchi, Tatsuya Yamaguchi, Yuka Yamaguchi,
Yoshiki Yamaguchi and Keiko Yamaguchi.

93Appendix A

MSUGRA and UED Mass Spectrum
A.1

MSUGRA

A.1.1

Gauginos Mass

The gaugino masses mi and coeﬃcients bi are given by the one-loop renormalization group equations in MSSM
from the Equation 1.3.2,
βmi =

d
1
mi =
bi g 2 midt
8π 2 i(i = 1, 2, 3)(A.1.1)

where m1 , m2 and m3 are the mass of bino, wino and gluino, respectively. It implies the three ratios mi /gi2 areconstant,
m1/2
m2
m3
m1
= 2 = 2 = 2 .
(A.1.2)
2
g1
g2
g3
gG
Then
m3 =

α3
3 α3
m2 sin2 θW =m1 cos2 θW ,α
5 α

(A.1.3)where θW is Weinberg angle. This implies the relation between the gauginos near the TeV scale roughly
m1 : m2 : m3 ∼ 1 : 2 : 6.

A.1.2

(A.1.4)

Neutralinos Mass

The neutralino mass part of the Lagrangian is described by using gauge-eigenstate wave function ϕ0 = (B̃, W̃ 0 , H̃d0 , H̃u0 )as following
Lneutralino−mass = −
where



M1

0
Mχ̃0 =  − cos β sin θW mZ
sin β sin θW mZ

1 ( 0 )Tϕ
Mχ̃0 ϕ0 + c.c.,20M2cos β cos θW mZ− sin β cos θW mZ− cos β sin θW mZ
cos β cos θW mZ
0−µ(A.1.5)
sin β sin θW mZ− sin β cos θW mZ 
.

−µ
0

(A.1.6)This mass matrix Mχ̃0 can be diagonalized by a unitary matrix N to obtain the mass eigenstatesχ̃0 i = Nij ψj0 ,so that



mχ̃01
 0
N∗ MN−1 = 
 0
0

0
mχ̃02
0
0
94

(A.1.7)

0
0
mχ̃03
0


0
0 
.
0 
mχ̃04

(A.1.8)0

If mZ ≪ |µ ± M1 | , |µ ± M2 |, then the neutralino mass eigenstates are nearly bino-like χ̃1 ∼ B̃, wino-like√χ̃02 ∼ W̃ and higgsino-like χ̃03 , χ̃04 ∼ (H̃u0 ± H̃d0 )/ 2, with the mass eigenvalues,
mχ̃01

=

mχ̃02

=

mχ̃03 , mχ̃04==

m2Z sin θW (m1 + µ sin 2β)+ ··· ,
µ2 − m21
m2 (m2 + µ sin 2β)
m2 − W 2+ ··· ,
µ − m22()
m2Z (I − sin 2β) µ + m1 cos2 θW + m2 sin2 θW|µ| −+ ··· ,2 (µ + m1 ) (µ + m2 )()
m2 (I + sin 2β) µ − m1 cos2 θW − m2 sin2 θW|µ| − Z
+ ··· .
2 (µ − m1 ) (µ − m2 )m1 −(A.1.9)(A.1.10)(A.1.11)(A.1.12)The m1 and m2 are set to positive and real, and µ is assumed to be real number with sign I = ±1.

A.1.3

Charginos Mass

The chargino mass spectrum is estimated on the analogue to neutralino. The gauge-eigenstate wave function
ϕ± = (W̃ + , H̃u+ , W̃ − , H̃d− ), the chargino mass terms in the Lagrangian are
Lchargino-mass = −where 2 × 2 block form,()
0 XT
Mχ̃± =
,
X 0

(
with

X=

1 ( ± )TMχ̃± ϕ± + c.c.,
ϕ
2

m2
gvd

gvu
µ

)

(
=

√

(A.1.13)m2
2 cos βmW√

2 sin βmWµ)The 2 × 2 matrices U and V relate to the mass eigenstates are introduced
( + )
( − )
)
)
(
(
χ̃1
χ̃1
W̃ +
W̃ −
,
.
=V
=U
χ̃+
χ̃−
H̃u+
H̃d−
2
2

.

(A.1.14)(A.1.15)

There are the eigenvalues of the 4 × 4 matrix M†χ̃± Mχ̃± , or equivalently the eigenvalues of X† X(
VX† XV−1 = U∗ XX† UT =

)

m2χ̃±

0

0

m2χ̃±

1

.

(A.1.16)2

The solutions of this matrix is
m2Z (m2 + µ sin 2β)+ ···1µ2 − m22
m2 I (µ + m2 sin 2β)mχ̃± = |µ| + Z+ ···2µ2 − m22mχ̃± = m2 −A.1.4

(A.1.17)(A.1.18)

Squark and Slepton Mass

The same type squarks and sleptons have the same quantum state, electric charge and color, thus the scalerparticles are mixed in the family. Then squarks and sleptons are separated into four groups, the up-type squarks(ũL , c̃L , t̃L , ũR , c̃R , t̃R ), down-type squarks (d˜L , s̃L , b̃L , d˜R , s̃R , b̃R ), charged sleptons (ẽL , µ̃L , τ̃L , ẽR , µ̃R , τ̃R )and sneutrino (ν̃e , ν̃µ , ν̃τ ).
The squarks and sleptons mass are determined by taking the contributions K1 , K2 , K3 from each renormalization group running coupling proportional to the gaugino masses. The squared masses of scalar particles can

95

t~L


t~L


t~R

t~R

Hu0

Hu0

Hu0

Hu0

t~L

t~L

t~R

t~R

(a)

(b)

(c)

Figure A.1: Some of the scalar interactions with strength proportional to yt2 .
be approximated as following,
1
K1 ,
36
4
m20 + K3
+ K1 ,
9
1
2+ K1 ,
m 0 + K3
91
2
m0
+ K2 + K 1 ,4+ K1 .
m20

m2Q̃

= m20 + K3 + K2 +(A.1.19)m2ũ

=(A.1.20)m2d˜ =
m2L̃

=

m2ℓ̃

=

(A.1.21)(A.1.22)(A.1.23)

The Ki are estimated by integrating the running coupling from the grand uniﬁcation scale QG to the squark or
slepton mass under consideration Q, around TeV scale,



 



0.35m21/2∫ log(QG ) K1   3/5 
1
2
0.5m21/2
K2
3/4
=
× 2
.
(i = 1, 2, 3) (A.1.24)
dtgi2 (t) |mi (t)| ∼  2π log Q (4.5 − 6.5)m2 

K3
4/3
1/2
Besides the renormalization group eﬀects, the electroweak symmetry breaking contributes to the squarks andsleptons hyperﬁne mass splitting. Each squark and slepton ϕ are given as the contribution ∆ϕ ,
∆ϕ =

)(
) (
)
1(
T3ϕ g12 − Yϕ g22 vd2 − vu2 = T3ϕ − Qϕ sin2 θW m2Z cos 2β,2(A.1.25)

where T3ϕ , Yϕ and Qϕ are the third component of weak isospin, the weak hypercharge and the electric chargeof the left-handed chiral supermultiplet to which ϕ belongs, respectively.
For the squarks and sleptons in the third generation, these particles are aﬀected from the Yukawa coupling of the scaler particles. Figure A.1 indicates the mt̃ terms are contributed from Figure A.1 (b) and (c)as yt2 H̃u0∗ H̃u0 t̃∗L t̃L and yt2 H̃u0∗ H̃u0 t̃∗R t̃R . The scalar potential like Figure A.1 (a) contributes the stop mass as−µ∗ yt t̄˜t̃H̃d0∗ . These terms are expressed as the squark mass matrix for the stop squarks in the gauge-eigenstatebasis (t̃L , t̃R ) which is given by()( ∗ ∗ ) 2 t̃L
Lstop-mass = − t̃L , t̃R mt̃
,(A.1.26)
t̃R
where

(
m2t̃ =

m2Q + m2t + ∆ũLv (at sin β − µ∗ yt cos β)v (a∗t sin β − µyt cos β)m2q̄ + m2t + ∆ũR),

(A.1.27)

and the at is a running coupling strength of top quark. This matrix is diagonalized by taking a unitary matrix
to give mass-eigenstates
(
)(
) (
)
t̃1
t̃L
cos θt̃ sin∗ θt̃=(A.1.28)sin θt̃ cos θt̃
t̃2
t̃R
96

Figure A.2: The coupling constant of standard model and SUSY MSSM model as a function of the energy scale.
The t̃1 is made the lightest squark of all due to the t̃R .
Similarly squared-mass matrices for scalar bottom quark and scalar tau lepton are)(v (a∗b sin β − µyb cos β)
m2Q + ∆d˜L,
m2b̃ =v (a∗b sin β − µ∗ yb cos β)m2q̄ + ∆d˜R(
m2τ̃ =

m2L + ∆τ̃L∗v (aτ cos β − µ∗ yτ sin β)v (a∗τ cos β − µyτ sin β)m2τ̄ + ∆τ̃R

(A.1.29)).

(A.1.30)

The mixing between the left-handed and right-handed is determined by taking the tan β. When the tan β is
given as the large value, the mixing is larger, and the lighter squarks and sleptons of third generation are tended
to be the lightest supersymmetric particle (LSP).
Figure A.2 shows the running group evolution of squarks, sleptons and gaugino mass on MSUGRA which
the used parameters are m0 = 200 GeV, m1/2 = 600 GeV, tan β = 10 and sign(µ) = +. The plot indicates thecolored particles are weighted heavier meanwhile the weak and hypercharge particles are lightened in decreasing
the energy scale to TeV scale. The (µ2 + m20 )1/2 term runs to the negative potential because of the eﬀects of
the large top Yukawa coupling and this provokes electroweak symmetry breaking.

A.2

minimal UED

At tree-level, the mass of minimal UED model particles are contributed from the n-th Kaluza-Klein excitationand the Standard Model particles as follows
m2X n =n2
+ m2X 0 + δmX n ,R2(A.2.1)

where X n is the n-th Kaluza-Klein excitation, X 0 is the Standard Model particle and R is the compactiﬁcation
scale, respectively.

97

Figure A.3: Spectrum of ﬁrst level Kaluza-Klein states, including the eﬀective of radiative corrections andboundary terms. A compactiﬁcation scale of 1/R = 500 GeV, Higgs mass of 115 GeV and cut-oﬀ scale of ΛR= 20. [54]The radiative corrections to KK masses should be considered with the loop diagram transverse around theextra dimension, called bulk loop, and the brane-localized kinetic terms which appear on the orbifold boundaries.
These contributions are given by()
g ′2−39 ζ(3) n22
δ(mB (n) ) =−ln ΛR ,
16π 2 R2
2 π2
3
(
)
g2
−5 ζ(3)2
δ(m2W (n) ) =
+
15n
ln
ΛR
,
16π 2 R2
2 π2
(
)
g32
−3 ζ(3)2
δ(m2g(n) ) =
+
23n
ln
ΛR
,
16π 2 R22 π2()
n27 2 1 ′2
2
δ(mQ(n) ) =
6g
+
g
+
g
ln ΛR,(A.2.2)3
16π 2 R2
8
8
( 2
)
n
δ(mu(n) ) =6g3 + 2g ′2 ln ΛR,
22
16π R ()
1 ′2
n2
δ(md(n) ) =6g3 + gln ΛR,
16π 2 R22()
n
8 2 9 ′2
δ(mL(n) ) =g + g
ln ΛR,
16π 2 R2 27
89 ′2ng ln ΛR.
δ(me(n) ) =2
2
16π R 2
Here ζ(3) ∼ 1.2020 · · · is the third zeta function and Λ is the cut-oﬀ scale and the gi are gauge coupling constants(see Section 1.3.2).
After the KK modes of the W and Z bosons acquire masses by eating the ﬁfth components of the gauge
ﬁelds and Higgs KK modes, four scalar states remain at each KK level. These modes have masses given by
m2Hn0

=

m2H ±

=

m2A0n

=

n

n2
+ m2h + δm2Hn ,R2n2+ m2W + δm2Hn ,R2n2+ m2Z + δm2Hn ,R2
98(A.2.3)

where the radiative and boundary term corrections are given by
(
)
n2
3 ′2
2
2
δmHn =
3g + g − 2λH ln ΛR + m̄2H .
16π 2 R2
2

(A.2.4)

where the λH is the Higgs quartic coupling and m̄2H is the boundary mass term for the Higgs mode. Finally,
the additional contribution from the top quark Yukawa coupling yields:
(
)
n
3h2t
Λ2
δht (mQ(n) ) =−ln 2 ,
3
R
64π 2
µ
(
)
2
n
3ht
Λ2
−
(A.2.5)δht (mt(n) ) =ln 2 .
R
32π 2µ
An example of UED mass spectrum at ﬁrst level is shown in Figure A.3 whose parameters are a compactiﬁcation
scale of 1/R = 500 GeV, Higgs mass of 120 GeV and cut-oﬀ scale of ΛR = 20. The one-loop radiative correction
and boundary terms are included.

99

Appendix B

Performance
In this section, the object deﬁnitions and their performance are described.

B.1

Electron

B.1.1

Electron Reconstruction

The electrons are reconstructed by using a track in inner detectors and a cluster in the electromagnetic (EM)calorimeter. The reconstruction algorithm runs through ﬁve steps as follows [55]1. Cluster search
It looks for a longitudinal tower in the EM calorimeter with total transverse energy ET > 2.5 GeV in awindow size 3 × 5 in unit of ∆η × ∆ϕ = 0.025 × 0.025.
2. Track matching
Reconstructed tracks are extrapolated from their last measurement point to the second layer of the EM
calorimeter. A distance between the track impact point and seed cluster is smaller than ∆η < 0.5 and∆ϕ < 0.1.
3. Cluster rebuilt
The seed cluster is rebuilt by using a new window size of 3 × 7 in barrel region or 5 × 5 in end-cap region.
4. Energy determination
The cluster energy is determined by summing the energy deposit from four parts; (1) in material in frontof calorimeters; (2) in the cluster; (3) outside of cluster as lateral leakage; (4) beyond EM calorimeter aslongitudinal leakage. These four terms are parameterized as a function of the measured cluster energies
in the pre-sampler detector and the three EM calorimeter layers based on simulation.
5. Four momentum calculation
The four momentum of the electron is computed by using the ﬁnal cluster and the best matching track.
The eﬃciency of electron reconstruction is expected to be ∼95% at ET = 5 GeV and 100% for the electrons
with >15 GeV derived from W and Z decays in MC simulations.
The loss of acceptance causes due to rejections for bad clusters to keep electron object quality, for example
failures of readout from boards, high voltage problems and isolated cell expected to be noise. The value andthe uncertainty with loss of acceptance are measured to be about 6% and 0.4% per electron, respectively.

B.1.2

Electron Identiﬁcation

The electron identiﬁcation which relies on a cut-based selection and separates the electron candidates into
isolated or non-isolated signal electrons, background electrons and jets faking electrons. The identiﬁcation isclassiﬁed into three categories, “loose”, “medium” and “tight”. The loose selection requires a narrow shower
shape in the middle layer of EM calorimeter and a small hadronic leakage in tile calorimeters. The medium
selection is deﬁned by taking variables of shower width in the ﬁrst layer of the EM calorimeter, track quality
and tighter track-cluster matching. The tight selection satisﬁes the number of high-threshold hits in TRT,b-layer hits to reject photon conversion events and ratio of the cluster energy to the track momentum E/p. The
100

Type
loose selection
Acceptance
Hadronic leakage

DescriptionName|η| < 2.47
Ratio of ET in the ﬁrst layer of the hadronic calorimeter to ET of
the EM cluster (used over the range |η| < 0.8 and |η| > 1.37)
Ratio of ET in the hadronic calorimeter to ET of the EM cluster(used over the range |η| < 0.8 and |η| > 1.37)
Middle layer of Ratio the energy in 3×7 cells over the energy in 7×7 cells centeredEM calorimeter at the electron cluster√
position∑∑∑∑
2
Lateral shower width, ( Ei ηi2 ) / ( Ei ) − (( Ei ηi ) / ( Ei )) ,where Ei is the energy and ηi is the pseudo-rapidity of cell i andthe sum is calculated within a window of 3×5 cells
medium selection (includes loose)√(∑) ∑2Strip layer of Shower width,
Ei (i − imax ) ( Ei ), where i runs over all
EM cluster
strips in a window of ∆η × ∆ϕ ≈ 0.0625 × 0.2, corresponding
typically to 20 strips in η, and imax is the index of the highestenergy strip
Ratio of the energy diﬀerence between the largest and second
largest energy deposits in the cluster over the sum of these energies
Track quality
Number of hits in the pixel detector (≥ 1)
Number of total hits in the pixel and SCT detectors (≥ 7)
Transverse impact parameter (|d0 | < 5 mm)
Track-cluster∆η between the cluster position in the strip layer and the extrapmatchingolated track (∆η < 0.01)
tight selection (includes medium)
Track-cluster∆ϕ between the cluster position in the middle layer and the exmatching
trapolated track (∆ϕ < 0.02)
Ratio of the cluster energy to the track momentum
Tighter ∆η requirement (|∆η| < 0.005)
Track quality
Tighter transverse impact parameter requirement (|d0 | < 1 mm)
TRT
Total number of hits in the TRT
Ratio of the number of high-threshold hits to the total number ofhits in the TRT
Conversions
Number of hits in the b-layer (≥ 1)
Veto electron candidates matched to reconstructed photon conversions

Rhad1
Rhad
Reta
wη2

wstot

Erationpixel
nSi
d0
∆η

∆ϕ
E/p
∆η
d0
nTRT
fHT
nBL

Table B.1: Deﬁnition of variables used for loose, medium and tight electron identiﬁcation cutsdeﬁnition of each category is summarised in Table B.1. The three categories are expected to be powerful jet
rejections as 500, 5000 and 50000 for loose, medium and tight, respectively, based on the MC study.

B.1.3

Electron Energy Scale

The energy scale in EM calorimeter (EM scale) is derived from beam test measurement. The total uncertaintyof this energy scale is 3%, and the most of uncertainty comes from LAr absolute temperature normalisation in
the test beam cryostat.
The energy calibration for electrons is divided into three steps [56, 57]:
1. The raw signal from each cell as ADC counts is converted into a deposit energy using the electroniccalibration in the EM calorimeter.
2. MC-based calibration corrects the cluster energy with an energy loss due to absorption in dead materials
and leakage outside of the cluster.

101

3. The in-situ calibration by using Z → ee decays, alternatively W → eν and J/ψ → ee events, determines
the energy scale.
In this section, only the EM scale calibration by using the in-situ measurement is described.
The miscalibration is parameterized by using residual calibration constants αi (i is given by each ∆η × ∆ϕregion) and the αi is deﬁned as
E mean = E true (1 + αi ) ,(B.1.1)

where E true is the true electron energy, E mean is the measured electron energy after the MC-based energy
scale correction. The αi is estimated by ﬁtting the Z mass peak of MC to that of data on an invariant mass
distribution to shift the calibration constant αi in each ∆η×∆ϕ region. The αi estimation uses the log-likelihood
function as following
N events [− ln L =

ij
∑ ∑

i,j

(
− ln Lij

mk
1+

k=1

αi +αj2)],(B.1.2)where the indices i and j denote the regions with one of electrons from Z → ee decaying in region i and the othereventsin region j, Nijis the total number of selected Z decays, mk is the measured dielectrons invariant mass.
The Lij is the probability density function quantifying the compatibility with the line-shape of Z invariant mass
distribution in MC simulation. The calibration constants are given by minimizing the − ln L in each region.
The considered uncertainties contributing to the calibration constant are (1) Additional materials in frontof the calorimeter which is not accounted for in MC-based calibration (∼2%); (2) low ET electrons due todiﬀerence of calibration constant between using the Z events and J/ψ events (1% with ET ≤10 GeV electron
decreasing linearly to 0% for ET =20 GeV); (3) pre-sampler detector energy scale whose uncertainty is measured
by comparing the electron energy extracted from W → eν events in data with that of MC simulation (0-1.4%).
The other uncertainties are extremely small (0-0.5%).
The calibration constants as a function of ET in 0 < |η| < 0.6 and 1.52 < |η| < 1.8 are shown in Figure B.1.

B.1.4

Electron Energy Resolution

The electron energy resolution can be describedσEab= √ ⊕ ⊕ c,
E
E
E

(B.1.3)

0.05
0.04
0.03

Z →ee dataJ/ ψ→ee data
W →eν data
Uncertainty band

ATLAS Data 2010
s=7 TeV, ∫ Ldt ≈40 pb-1

ααwhere a, b and c are the sampling term, noise term and constant term, respectively. The resolutions are estimatedby using the Z → ee events and comparing data with MC samples. We can assume that the sampling term aregood modeling within a 10% uncertainty in simulation, and the contribution from noise term is negligible in high

0.05
0.04
0.03

0.02

0.02

0.01

0.01

0

0

-0.01

-0.01

-0.02

-0.02

-0.03

-0.03

-0.04
-0.05
0

0<| η |<0.6-0.04

1.52<| η |<1.8

10

-0.05
0

50

20

30

40

50

60

70
E [GeV]Z →ee dataJ/ ψ→ee data
W →eν data
Uncertainty band

ATLAS Data 2010
s=7 TeV, ∫ Ldt ≈40 pb-1

100

150
E [GeV]

Figure B.1: Correction factors of the electron energy scale as a function of ET in Z → ee and J/ψ → ee events.

102

energy scale. Moreover, the constant term can be cancel out at ﬁrst order of those terms. These assumptions
can indicate a formula
v [
u
(
)2
(
)2 ]
u
σ
σ
t
cdata = 2 ·−+ c2MC ,(B.1.4)mZ datamZ MC
where mZ is Z mass calculated in the dielectrons events, σ is the Gaussian component of the experimental
resolution and cdata(MC) is eﬀective constant term of data (MC). The resolutions σdata(MC) are estimated byﬁtting the invariant mass distribution of data and simulation in the 80-100 GeV by Breit-Wigner convolved witha Crystal Ball function. In the ﬁt, the Breit-Wigner width is ﬁxed to measured Z width and the experimental
resolution is determined by the Crystal Ball function. Figure B.2 shows the ﬁtting results with Z mass peak
both data and MC in barrel and end-cap region. The value of cMC used in the MC simulation is 0.5%, thus the
cdata is calculated 1-3% by using the Equation B.1.4 and results in Figure B.2. The systematic uncertainty is
estimated 0.4-1.5% in an assumption that the sampling term increases by 10% in simulation. The contribution
from discrepancy of the constant term between data and MC compensates for electron energy in the MC
simulation.

B.1.5

Electron Scale Factors

In order to ensure the electron distribution on MC, we estimate the eﬃciencies both data and MC and the
distributions of MC samples are corrected for the discrepancy of the eﬃciencies. The total eﬃciency ϵ and thecorrection factor (or scale factor) ϵsf areϵϵsf= ϵevent · ϵreco · ϵid · ϵtrig · ϵiso ,
ϵdata
=
,
ϵMC

(B.1.5)(B.1.6)1000
900 ATLAS Data 2010,

Events / GeV

Events / GeV

where ϵevent is the eﬃciency of pre-selection cuts e.g. noise suppression. The ϵreco is reconstruction eﬃciency
that algorithm ﬁnds both an EM cluster and a charged track, and the objects are reconstructed to an electron.
The ϵid , ϵtrig and ϵiso are the identiﬁcation eﬃciency relative to the reconstructed electrons, the trigger eﬃciency
with respect to all reconstructed and identiﬁed electron, and the isolation eﬃciency relative to the identiﬁed
electrons, respectively. The ϵdata and ϵMC are total eﬃciencies of data and MC, respectively.
These eﬃciencies are estimated by using the Z → ee, W → eν and J/ψ → ee events and the scale factor
is estimated in each ∆ET × ∆η region. In order to obtain the clean and unbiased sample of electrons, thescale factor is measured by using a tag-and-probe method [58] [59]. This method assumes the events lying on
the Z (or J/ψ) mass window are coming from Z (or J/ψ) decay, thus both electrons can be regarded as trueelectrons. In the case, the one of them so-called “tagged electron” satisﬁes the tight criteria and isolation, theother electron so-called “probe electron” is used to measure the eﬃciency after the background subtraction.
The tagged electron for the Z → ee and J/ψ → ee events is deﬁned:

s=7 TeV, ∫Ldt ≈40 pb-1
|η|<1.37800 σdata=1.62±0.09 GeV
700 σMC =1.45±0.02 GeV

Data

600

Fit

500

Z →ee MC

140 ATLAS Data 2010,

s=7 TeV, ∫Ldt ≈40 pb-1
1.52<|η|<2.47

120 σdata=1.99±0.22 GeV
100

σMC =1.63±0.06 GeV

Data
Fit
Z →ee MC

80

400

60

300

40

200
20

100
0
70

75

80

85

90

95

100

105

110

mee [GeV]

0
70

75

80

85

90

95

100

105

110

mee [GeV]

Figure B.2: Distributions of invariant mass and correction factor of the electron energy resolution as a functionof η in Z → ee and J/ψ → ee events.

103• The tagged electron matches the corresponding trigger object.
• The tagged electron satisﬁes the tight selection criteria.
• The tagged electron is required to have ET > 20 GeV.
On the other hand the probe electron is basically deﬁned:• The charge of probe electron is opposite to tagged electron for the Z → ee and J/ψ → ee events.
• The ET of probe electron is ET > 15 GeV for Z → ee and W → eν events, ET > 4 GeV for J/ψ → ee
events.
The other deﬁnitions corresponding to each eﬃciency measurement are applied to the probe electrons. The
trigger eﬃciency are measured by taking the ratio of the number of probe electrons matching the trigger object
in ∆R < 0.15 to total number of probe electrons. In the identiﬁcation eﬃciency, the probe electrons which
consist of a EM calorimeter cluster and matching track are checked to passing the medium or tight selection
criteria.
The background estimation for the eﬃciency measurement is ﬁtted by exponential, Landau function anddistribution of same sign sample in the side-band of Z or J/ψ peaks. The signal events are modeled either
by a Breit-Wigner distribution convolved with a parameterization of the low mass tail, by a Crystal Ballfunction, or by a template obtained from MC simulation. The background subtraction becomes a dominantsource of a systematic uncertainty. The uncertainties of each eﬃciency are estimated by varying the backgroundsubtraction, for example the signal window and the electron deﬁnition.
Figure B.3 shows the identiﬁcation eﬃciency of each selection criteria and Figure B.4 shows the scale factorof tight electrons except the trigger eﬃciency. The MC distributions are corrected by these scale factors.

B.2

Muon

B.2.1

Muon Reconstruction

Track Reconstruction in Inner Detectors
A inner detector tracks are reconstructed by using NEWT algorithm [60]. This algorithm covers the twosequences; (1) inside-out track reconstruction; and (2) outside-in tracking. A kink track reconstruction is also
deployed common tracking tool, but is not particular to an approach of this algorithm.

1Electron identification efficiency

Electron identification efficiency• Inside-out sequence

0.9
0.8
0.7
0.6
ATLAS Preliminary

0.5

Simulation

0.4

Loose
Medium
Tight

0.3
0.2
0.1
0

1
0.9
0.8
0.7
0.6
0.5
0.4
0.3

ATLAS Preliminary
Simulation
Loose
Medium
Tight

0.2
0.1

10

20

30

40

50

60

70

80

90

100

0
0

0.5

1

1.5

2

2.5
|η|

ET [GeV]Figure B.3: Eﬃciency of the electron identiﬁcation as a function of ET and η for the loose, medium and tightin Z → ee channel.

104

1. Global track seeding
The primary inner detector pattern recognition starts with seeding in the inner silicon tracker (Pixeland SCT) and ﬁnds hits toward the outer border of the inner detector. The track seed is created as
three-dimensional representation and a window search through the direction of track seed is applied.
Hits on the inner detector elements within the windows are collected and judged whether these hits
are added to the track candidate by using a simpliﬁed Kalman ﬁltering.
2. Ambiguity solving
In order to reject the fake tracks, the track candidates are scored with respect to the disposal of hitsin Pixel and SCT. In general, each hit associated with the track leads to a better score value to favor
fully reconstructed track rather than small segments. Currently, a hit-pattern based scoring and amaximum likelihood approach are available.
3. TRT track extension
The track (segment) is extended from the silicon detectors into the outer TRT. The track passing theambiguity solving is used as an input to ﬁnd compatible sets of TRT measurements that is further
processed as candidate of extension. The silicon-only track is not modiﬁed, then the association of
the TRT hits is a pure extension. Two concrete implementations of the track extension tool exist:– The standard implementation follows a classical approach starting to ﬁnd hits through track
extrapolation.
– A second implementation is based on an extension of the standard Kalman ﬁlter formalism• Outside-in sequence
The tracks coming from secondary vertices or photon conversions may not be reconstructed by insideout sequence due to lack of silicon hits. In outside-in sequence, track segments are identiﬁed by using
a standard Hough transform mechanism which is an extraction technique, while a dedicated association
tool prevents hits that have already been assigned to tracks in the inside-out procedure to be used again.
The TRT segments are followed back into the silicon detectors.

Figure B.4: Value and uncertainty of scale factor and the uncertainty for the electrons as functions of ET andη.

105Track Reconstruction in Muon Spectrometer
1. Identiﬁcation of region of activity (ROA) in the muon system through the muon trigger systems (RPC/TGC).
The regions of activity (ROA) deﬁned the size as roughly ∆η × ∆ϕ = 0.4 × 0.4 are required at least one
hit in RPC and TGC. The ROA becomes a seed for the muon segments and tracks.
2. Reconstruction of the local segments in each muon station in these ROA.
A straight track segment is formed by combining with the hits in multi-layers of the same MDT station.
The pair of hits in two multi-layers is required and points to the interaction point loosely to suppress
background hits. A track segment is validated by requiring its quality factor χ2 to be small suﬃciently.
The deﬁnition of quality factor χ2 is described in Equation B.2.1.
3. Combination of segments of diﬀerent muon stations to form muon track candidates using three-dimensional
tracking in the magnetic ﬁeld.
Tracks are seeded from the segments with a ﬁrst estimation of the momentum deduced from the positionand direction of the segment. These segments are extrapolated to the other stations with its relaxedmomentum. If some matching segments exist, the extrapolated tracks are ﬁtted to perform more accurate
estimation of the momentum. In the ﬁtting procedure, only one segment is kept per crossed station anda candidate track has at least two segments.
4. Global track ﬁt of the muon track candidates through the full detector systems using individual hit
information.
The global ﬁt is performed with starting from the best ﬁtting tracks by using raw information (i.e. TDC
values) to suppress the δ-rays, gamma and neutron background. The procedure estimates the likelihoodof the candidate tracks and selects more good tracks among all hits a priori belonging to the track fromthe bad track which are too far from the reconstructed path of the muon. Finally, the ﬁt including matteris performed by using Kalman ﬁlter method.
Muon Track Reconstruction
The muon reconstruction employs three diﬀerent algorithm, Muonboy, MuTag and STACO, as follow [61]. This
analysis employs the STACO muons and MuTag muons.
1. Standalone reconstruction (Muonboy)
The muon candidates are reconstructed by using the segments and tracks in only the muon spectrometer.
These standalone tracks are extrapolated to the primary vertex.
2. Tagged muon (MuTag)
The Tagged muons are reconstructed by the hit information in the inner detector and matching witha segment (not track) in the muon spectrometer to ensure the muon candidate. This reconstruction isprepared for the low pT muons since these muons lost most of their energy in the calorimeters and theirtrajectories in the muon spectrometer are diﬃcult to reconstruct. This algorithm runs after the STACO.
3. Combined reconstruction (STACO)
The candidate tracks are combined with a inner track and a muon spectrometer track. The combined
track is estimated as follow. Suppose i-th measured hit position mi , the error ei of the position and theposition on the ﬁtting track Mp⃗ to minimize the distance between the hit position and the ﬁtting track
whose vector is p⃗. The likelihood parameter p⃗ is evaluated by the function,
χ2 (⃗
p) =

2
∑ (mi − Mi (⃗
p))

e2i

i

.

(B.2.1)

If the p⃗0 minimizing χ2 at χ20 is deﬁned, the χ2 can be described around the minimum of χ2Tχ2 (⃗p) = χ20 + (⃗p0 − p⃗) W0 (⃗p0 − p⃗) ,(B.2.2)where the weight W0 serves to evaluate the errors and correlations of the p⃗0 . Now the likelihood functionof the ﬁtting track estimated by the inner detector and muon spectrometer is
χ2 (⃗
p) =

ID
2
∑
(mi − Mi (⃗
p))
i

e2i

+

MS
2
∑
(mj − Mj (⃗
p))
j

106

e2j

.

(B.2.3)

This function can be written as()2 ( MS )2 ( ID
)T
(
) (
)T
(
)
χ2 (⃗
p) = χID+ χ0+ p⃗0 − p⃗ W ID p⃗ID
⃗ + p⃗MS⃗ W MS p⃗MS
⃗ .
0
0 −p
0 −p
0 −p

(B.2.4)The combined track satisﬁes the below equations,
( ID
)
MS MS
W + W MS p⃗0 = W ID p⃗ID
p⃗0 ,
0 +W

(B.2.5)

W0

= W

ID

+W

MS

.

(B.2.6)Then,
χ20( match )2χ( ID )2 ( MS )2 ( match )2
χ0
+ χ0
+ χ
,
(
)
)
)
( ID
T
−1
−1 −1 ( IDp⃗0 − p⃗MS
W ID + W MS
= p⃗0 − p⃗MS
00=(B.2.7)(B.2.8)The track of combined muon is reconstructed by minimizing the χmatch .

B.2.2

Muon Momentum Resolution

The muon momentum resolution measurement is estimated by applying the Z mass ﬁtting. The dimuonsinvariant mass distribution is obtained from the muon momentum estimated by the inner detector (ID) and themuon spectrometer (MS), separately. The Z mass shape line is ﬁtted by the double Gaussian function modelingthe detector resolution as follow( 2)
x − x̄2x2
1+C,(B.2.9)f (x) = A 2 + B
22x(x2 − x̄2 ) + σx2 x̄2(x2 − x̄2 ) + σx2 x̄20.14

σ(M)/M

σ(M)/M

where x indicates the reconstructed dimuons invariant mass mµµ , the A, B, C and σx are ﬁxed parameters
determined from the MC dimuons invariant mass distribution. The only ﬁtted parameter is x̄ and this results
are shown in Figure B.5 for the inner detector and the muon spectrometer separately. The discrepancy between
data and MC in Figure B.5 becomes the correction factor and the factors are applied to the muon momentum
on simulation.

ATLAS Preliminary
0.12
0.1
0.08

∫ L = 40 pb , s = 7 TeV-1

0.14 ATLAS Preliminary∫ L = 40 pb , s = 7 TeV
-1

0.12

ID parameters

MS parameters

0.1
Data

0.08

Simulation

Data
Simulation

0.06

0.06

0.04

0.04

0.02

0.02

0
-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5

η0-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5

η

Figure B.5: The muon momentum resolution as a function of η for the inner detector (left) and muon spectrometer (right).

107

B.2.3

Muon Reconstruction Eﬃciency and Scale Factor

The muon reconstruction eﬃciency and isolation eﬃciency are estimated by using the tag-and-probe method
and Z events as well as the electrons in Section B.1.5 [62]. The events lie in the Z mass window (|mZ − mµµ | <10∑GeV) and the tagged muons are selected from combined muons and required for pT > 20 GeV and isolation( tracks pID
T /pT < 0.2, ∆R < 0.4). The inner track muons are employed for probe muons and the muonssatisfy the pT > 20 GeV and coming from the same vertex to tagged muons. The J/ψ events are ﬁtted by
Gaussian function and the background are described by second-order polynomial function. These functions are
estimated by using a χ2 ﬁt simultaneously. The probe muons are required the combined or segment tagged
muon reconstructed by the STACO muon algorithm.
The systematic uncertainties are derived from the both signal and background shape given by ﬁt functions.
The results [63] for low pT muons are obtained from the J/ψ events and shown in the bottom two plots in
Figure B.6 and scale factors are shown in Table B.2. The trigger eﬃciency is also shown in Figure B.7 [64].

B.3

Jet

B.3.1

Jet Reconstruction

The jets are reconstructed by so-called “anti-kT ” jet algorithm. As the input seeds, the topological clusters are
created event by event.
Topological Cluster

Efficiency

Efficiency

The topological clusters (topocluster) are generated through three steps to suppress the noise [44].

1
0.95
0.9

1
0.95
0.9
0.85

0.85

ATLAS Preliminary

0.8

Autumn reprocessing, 2010 data

∫

1.04
1.02
1
0.98
0.96
20

MC
data

-1

Ldt = 40 pb , chain 1

30

40

50

60

70

80

Autumn reprocessing, 2010 data

0.75

∫

0.7

SF

SF

0.75

ATLAS Preliminary

0.8

90
100
p [GeV]

MC
data

-1

Ldt = 40 pb , chain 1

1.05
1
0.95
-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5
η

1.2

ATLAS Preliminary

Efficiency

Efficiency

Tp > 3 GeV

0.1 <|η|<1.1

1
0.8

1.2

ATLAS Preliminary1
0.8

s= 7 TeV∫ Ldt = 3.1 pb

-1

0.6

0.6

CB+ST MC Chain 1

0.4

0.4

p > 6 GeVT

CB+ST Data Chain 1
CB MC Chain 1

0.2

0.2

∫ Ldt = 3.1 pb
0

CB Data Chain 1

0
0

2

4

6

8

s= 7 TeV
CB+ST MC Chain 1
CB+ST Data Chain 1

-1

10

12
p [GeV]

-3

T

-2

-1

0

1

2

3
q×η

Figure B.6: Eﬃciencies and correction scale factor of the muon as a function of pT (top-left) and η (top-right)
for the high pT muon and eﬃciencies of the low pT muon as a function of pT (bottom-left) and η (bottom-right)
in Z → µµ and J/ψ → µµ events.

108

|η|

Algorithm
Combined Muon

Inner Track + Segment Muon

scale factor

0.0-0.1

1.022 ± 0.084 (stat.) +0.025−0.042 (syst.)

0.1-1.1

0.973 ± 0.018 (stat.) +0.022−0.001 (syst.)

1.1-1.3

0.909 ± 0.050 (stat.) +0.025−0.007 (syst.)

1.3-2.0

0.951 ± 0.023 (stat.) +0.037−0.075 (syst.)

2.0-2.5

0.976 ± 0.056 (stat.) +0.040−0.013 (syst.)

0.0-0.1

0.958 ± 0.155 (stat.) +0.009−0.019 (syst.)

0.1-1.1

0.989 ± 0.017 (stat.) +0.015−0.001 (syst.)

1.1-1.3

1.024 ± 0.046 (stat.) +0.015−0.020 (syst.)

1.3-2.0

0.970 ± 0.024 (stat.) +0.036−0.066 (syst.)

2.0-2.5

0.976 ± 0.050 (stat.) +0.040−0.013 (syst.)

Table B.2: Scale factors for the eﬃciency with respect to the combined muon and the inner track plus segment
muon for |η| < 2.5 and pT > 6 GeV.

1. The topological cluster algorithm ﬁnds the |Ecell | > 4σcell cell as a seed, where σcell is the RMS of energy
distribution of random events in each calorimeter cell (typically σcell ∼ 40 MeV).
2. Neighbor cells of the seed are added if the cell satisﬁes |Ecell | > 2σcell until no nearest-neighbor cell has|Ecell | > 2σcell .

Efficiency

1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
1.05
1
0.95

ATLAS Preliminary
Data 2011 s = 7 TeV|ηµ| < 1.05
mu18 medium outside-in
Data
MC

Data/MC

Data/MC

Efficiency

3. Finally all nearest-neighbor cells surrounding the cluster are added to the cluster. These three steps are
executed to direction of 3D (r, η, ϕ). In case the cluster energy is negative, the jet algorithm rejects suchclusters.

10

20

30

40

50 60 70 80

102
pT [GeV]

1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
1.05
1
0.95

ATLAS Preliminary
Data 2011 s = 7 TeV|ηµ| > 1.05
mu18 medium outside-in
Data
MC

10

20

30

40

50 60 70 80

102
pT [GeV]Figure B.7: Trigger eﬃciencies and scale factors of the muon as a function of pT in barrel region (left) andend-cap region (right).

109

Anti kT jet algorithm
The jet algorithm estimates the distance between clusters and merges if the distances are nearer than a certain
threshold [45] [46]. The distance dij between the i-th and j-th jet cluster is calculated by() 2
2p
2p ∆ij= min kTi
, kTj
R2
2p
= kTi

dij
diB

(B.3.1)(B.3.2)where kT , ∆ij are the transverse momentum of the topocluster and distance ∆2ij = (ηi − ηj )2 + (ϕi − ϕj )2 ,respectively. The cluster is merged until diB < dij . The topocluster reconstruction is illustrated in Figure B.8.
ATLAS usually employs the R = 0.4 and p = -1 called ”anti-kT ” jet algorithm.

B.3.2

Jet Energy Scale Uncertainty

The jet response in a calorimeter is smaller than that of electron and photon with the same energy because thesome of hadronic interaction, for example the nuclear excitation and slow neutrons, are invisible. Typical valueof the ratio of energy deposit of hadron in calorimeter to that of electron is e/h ∼ 1.3. In oﬀ-line reconstruction,
the visible cluster energies are calculated by using the EM scale and the jet energy in the EM scale is factoredby the jet energy scale (JES). The jet energy scale is estimated by comparing the energy
deposit⟩ of the truth⟨⟨ EM+JES⟩
truth
particle with that of the reconstructed particle ⟨R⟩ = Ecalo/Etruth or ⟨R⟩ = pjet
/pon the MCT
T
simulations [65]. Figure B.9 show the average of jet energy scale correction as a function of jet transverse
momentum pT and pseudo-rapidity, respectively.
The ratio ⟨R⟩ is included the uncertainties derived from several eﬀects, for example the dead material notconsidering on the simulations and modeling of calorimeter response with single particle. These contributions
are concluded as follows
1. The each source of uncertainty is calculated in each pjet
T and η bin.

phi

Cluster0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 2 3 0 0 0
0 0 2 4 5 3 0 0
0 0 3 7 4 3 0 0
0 0 1 4 2 1 0 0

0 0 0 0 0 2 0 0 0 0
0 1 0 0 1 0 0 0 0
0 1 2 2 1
0 1 3 2 0
0 0 2 1 0
0 0 0

Not Clus
ter etaFigure B.8: Schematic of the algorithm of topological cluster.

110

2. The deviations ∆JES is estimated from ⟨Rvar ⟩ of each source and the nominal ratio ⟨Rnom ⟩ as follows⟨⟩
Rvar (pjet, |η|)T⟨⟩∆JES (pjet(B.3.3)
T , |η|) = 1 −Rnom (pjet
T , |η|)3. The largest ∆JES is selected from the jet energy (E) or jet transverse momentum (pT )
(
)
jet
pT
jet
E
∆JES (pjet
,
|η|)
=
max
∆
,
|η|),
∆
(p
,
|η|)
(p
JES
T
JES T
T

(B.3.4)

4. Estimate the total uncertainties to add the all contributions.
This jet energy scale uncertainty is validated by the in-situ techniques like these• Direct transverse momentum balance between a jet and a photon (∼ 1.5% uncertainty) [66].
miss(∼ 1% uncertainty) [66].
• Photon balance using the missing transverse momentum ET• Balance between a high pT jet recoiling against one or more lower pT jets (∼ 4% uncertainty) [67].
• Comparison of jet calorimeter energy to the momentum carried by tracks associated to a jet (∼ 3%
uncertainty) [68].
The total jet energy scale uncertainty in barrel region (0.3 < |η| < 0.8) shows the left of Figure B.10 and theright of B.10 shows the uncertainty in the end-cap region.

B.3.3

b-tag algorithm

The jets derived from the b-quark have the second vertex because the average of ﬂight length of b-hadron isabout ℓ ∼ 500 µm. There are some b-tagging algorithm, this analysis uses “JetFitterCombNN” algorithm [69]which is combined with the “JetFitter” algorithm and “IP3D” algorithm by using artiﬁcial neural network
techniques with Monte Carlo simulated training samples and additional variables describing the topology of the
decay chain. The IP3D algorithm is based on the likelihood ratio between the transverse impact parameterd0 /σd0 and longitudinal impact parameter z0 /σz0 . The feature of JetFitter algorithm is assuming the c-hadrons
decay on the b-hadron ﬂight direction and looking for the both b-hadron and c-hadron decay points.
The JetFitter algorithm needs the jet information (the position of b-hadron and c-hadron decay), vertex
information (mass and energy fraction reconstructed by tracks). The variables of jet information are introduced
as follows,2

Jet response at EM scale

Average JES correctiond⃗ = (xPV , yPV , zPV , ϕ, θ, d1 , d2 , · · · , dN )0.3 < |η| < 0.8
2.1 < |η| < 2.8
3.6 < |η| < 4.4

ATLAS Preliminary

1.8
1.6
1.4

(B.3.5)

1 ATLAS Preliminary
Barrel0.9

Barrel-Endcap
Transition

20 30

2

10

2×10

2

3

0.6

10

0

2×10
p jet
[GeV]
T
3

FCal

0.7

0.4

Anti-k t R = 0.6, EM+JES

1

HEC-FCal
Transition

0.8

0.5

1.2

HEC

E = 30 GeV
E = 60 GeV
E = 110 GeV

Anti-k t R = 0.6, EM+JES

0.5

1

1.5

2

2.5

3

E = 400 GeV
E = 2000 GeV

3.5

4

4.5
Jet |η |det

Figure B.9: Average of jet energy scale correction as a function of calibrated jet pT in three η region (left)
and simulated jet energy response at the electromagnetic energy scale as a function of EM+JES calibrated jet
energy and η.

111

where (xPV , yPV , zPV ) is position at a primary vertex, ϕ, θ are direction of the track and di are distance from theprimary vertex to the intersection between the di -th track and b-hadron ﬂight axis. This d⃗ and these vertices
have following variables• Massthe invariant mass of all charged particle tracks associating with the decay chain.
• Energy Fraction
the fraction of energy of these particles divided by the sum of the energies of all charged particles matchedto the jet.
• Flight length signiﬁcance d/σ(d)the weighted average position divided by their errors of the displaced vertices.
The category of decay topology is deﬁned to avoid the correlation between the ﬂavors by the following.
1. Number of vertices with at least two tracks.
2. Total number of tracks at these vertices.
3. Number of additional single track vertices on the b-hadron ﬂight axis.
The likelihood function is formed by these variables as follow∑
Lb,c,l =coef f · P DFcategory (mass) · P DFcategory (EnergyFraction) · P DFcategory (d/σ(d))(B.3.6)category

The three diﬀerent ﬂavors (b, c and light ﬂavor) are parameterized separately. The coeﬃcient coef f is estimatedby using the JetFitter variable d⃗ in a given ﬂavor and each PDF has been already predicted by MC which isshown in Figure B.13.
Finally the likelihood ratio of IP3D and JetFitter are multiplied and the b-tag weight is estimated by applying
the neural network results. Figure B.11 (right) shows a distribution of the output of the JetFitterCombNN
algorithm for observed data and simulated data. In this analysis, the operating point at 1.8 is applied where
the b-tagging eﬃciency is about 60%. Figure B.12 show the rejection power for the light and charm ﬂavor jets,
and the 60% of b-tagging eﬃciency indicates ∼ 500 and ∼ 7 rejection power for light ﬂavour and charm jets,
respectively.

B.3.4

b-tagging Eﬃciency and Scale Factor

0.12

Fractional JES systematic uncertainty

Fractional JES systematic uncertainty

The b-tagging eﬃciency is estimated by two method, “prelT method” and “System8 method”.
The prel
T is deﬁned as the muon momentum transverse to the direction combined with muon and jet. The
templates prel
T distribution of light-ﬂavour jets, c-jets and b-jets before and after b-tagging by using MC are

Anti-k t R =0.6, EM+JES, 0.3 ≤ | η | < 0.8, Data 2010 + Monte Carlo QCD jets

0.1

ALPGEN + Herwig + Jimmy

0.08

JES calibration non-closure
Single particle (calorimeter)
Total JES uncertainty

0.06

Noise Thresholds
PYTHIA Perugia2010
Additional dead material

ATLAS Preliminary

0.04
0.02
0
30 40

102

2×102

2×10
p jet [GeV]

3

10

3

0.12
Anti-k t R=0.6, EM+JES, 2.1 ≤ | η | < 2.8, Data 2010 + Monte Carlo QCD jets

0.1

ALPGEN + Herwig + Jimmy

0.08

Intercalibration

0.06

ATLAS Preliminary

0.04
0.02
0
30 40

T

Noise Thresholds
PYTHIA Perugia2010
Additional dead material
Total JES uncertainty

JES calibration non-closure
Single particle (calorimeter)

102

2×102

3

10
p jet [GeV]T

Figure B.10: Distributions of the jet energy scale uncertainties as a function of jet pT in barrel region (0.3
< |η| < 0.8) and end-cap region (2,1 < |η| < 2.8).

112

prepared and ﬁtted to data to obtain the fraction of each quark component. Figure B.14 shows prel
T distribution
before and after b-tagging. The b-tagging eﬃciency ϵdata
is deﬁned as
b
ϵdata
=
b

fbtag · N tag· C,
fb · N(B.3.7)tagwhere fb and fbtag are the fractions of b-jets before and after b-tagging to prelareT samples and N and N
the total number of jets and the number of b-tagged jets in those samples. The factor C is a correction factor
for the eﬃciency for the biases coming from diﬀerence of modeling between data and MC. The scale factor forb-tagging eﬃciency is measured as ϵSF = ϵdata/ϵMCbb
The System8 method uses three uncorrelated selection criteria and estimates the b-jet and non b-jet eﬃciencies, and the number of real b-jets and non b-jets in the samples to pass each of three selection criteria. The
three selection criteria are• The lifetime tagging criteria• The muon prelT ≤ 700 MeV• An opposite-jet with pT > 10 GeV, |η| < 2.5 and π − |∆ϕjj | < 1 where ∆ϕjj is azimuth diﬀerence between
selection jet and opposite side jet. The opposite jet is required for the b-tagging by the secondary vertex
with L/σ(L) > 1.
The eight equations are described as follows
=
=
=
=
=
=
=
=

nb
pb
ϵLT
b nb
α6 ϵLT
b pb
T
ϵM
nb
b
T
α5 ϵM
pb
b
LT M T
α1 ϵb ϵb nbMT
α7 α6 α5 ϵLT
pb
b ϵb

+
+
+
+
+
+
+
+

Number of jets / 0.32

n
p
nLT
pLT
nM T
pM T
nLT,M T
pLT,M T

ncl ,
pcl ,
ϵLT
cl ncl ,α4 ϵLTcl pcl ,TϵM
cl ncl ,T
α3 ϵ Mcl pcl ,LT M T
α2 ϵcl ϵcl ncl ,MT
α8 α4 α3 ϵLTcl ϵcl pcl .

108(B.3.8)

Untuned simulation & jet flavor fractions∫ Ldt = 330pb

ATLAS Preliminary

-1

107

Pythia Dijet MC : light jets
Pythia Dijet MC : c jets
Pythia Dijet MC : b jets
data 2011106

High-performance tagger:
IP3D+JetFitter

105
104
103
102

Primary Vertex(xPV ; yPV ; zPV )di

B ight axis(; )data/MC ratio

Tra k i
1.3
1.2
1.1
1
0.9
0.8
0.7

-6

-4

-2

0

2

-6

-4

-2

0

2

4

6

8

IP3D+JetFitter weight4
6
8
IP3D+JetFitter weight

Figure B.11: Schematic of the relation between the primary vertex and secondary vertex about b-jets (left)and distribution of b-tagged jets as a function of operating point of combination of IP3D and JetFitterComb
algorithms

113

In these equations, the superscript LT and M T mean the lifetime tagging and soft muon tagging, respectively.
The n and p are the number of events of the sample with applied or without applied opposite-jet correction.
The b and cl mean b-jet and non-b ﬂavour jet (c, s, d, u, g), respectively. The correction factor αi are
α1
α3
α5
α7

=
=
=
=

T,n
ϵLT,M
b
M T,p
ϵcl
/
T,p
ϵM
/
b
T,p
ϵLT,M
b

T,n
/ (ϵLT,n
ϵM
),
b
b
M T,n
ϵcl
,
T,n
ϵM
,
b
T,p
/ (ϵLT,n
ϵM
),
b
b

α2
α4
α6
α8

=
=
=
=

T,n
T,n
ϵLT,M
/ (ϵLT,n
ϵM
),
cl
cl
cl
LT,p
LT,n
ϵcl
/ ϵcl ,ϵLT,p/ ϵLT,n,bbLT,M T,pT,pϵcl/ (ϵLT,p
ϵM
).
cl
cl

(B.3.9)The b-tagging eﬃciency and light ﬂavor eﬃciency are estimated by resolving these equations. For the eﬃciency,
the source of systematic uncertainties are considered as modeling of b- and c-production, b-Hadron direction
modeling, b-quark fragmentation and so on. The combined eﬃciency of prel
T method with system8 method are
estimated by applying the maximum likelihood method in each jet pT bin. The likelihood function is expressed
as follows(())
1 syst1
2 syst2
λ×(B.3.10)
L = L′ κ1 |κ̂ 1 + ∆κsyst+ ∆κsyst
λ, ∆κstat
1
1
1
(
(
)
syst1 syst1
syst2 syst2 )′statL κ2 |κ̂ 1 + ∆κ2
λ
+ ∆κ2
λ
, ∆κ1
×
(B.3.11)( syst1)( syst2)′′L λ|0, 1 × L λ|0, 1 ,
(B.3.12)
where the κ̂ is the combined b-tagging scale factor when each measurement of κi corresponds i = 1 to the prelTmethod and i = 2 to System8 method, the ∆κ means the width of uncertainties and λ expresses the how muchstandard deviations the systematic uncertainties are shifting. The (λsyst |0, 1) term are constrained to the factor
of uncertainties between zero to one. The scale factors estimated by this method are shown in Figure B.15.

Missing Transverse Energy ETmiss

B.4

Because the energy and the momentum are preserved in the transverse plane, the unbalance of energy in thismissplane indicates the total energy of invisible objects [70]. The missing transverse energy ET
consists of four
components as follows

105
ATLAS Preliminary

c-jet rejection

Light jet rejection• Electron
Reconstructed electrons satisfy pT > 10 GeV and medium selection criteria.

MV1
JetFitterCombNN

104

JetFitterCombNNc
IP3D+SV1

103
ATLAS Preliminary

MV1
JetFitterCombNN
JetFitterCombNNc

2

10

IP3D+SV1

3

10

SV0

SV0

102
10
10

tt simulation, s=7 TeV

tt simulation, s=7 TeV

p >15 GeV, |ηjet |<2.5

p >15 GeV, |ηjet |<2.5

jet

jet

T

1
0.3

0.4

0.5

0.6

T

0.7

1
0.3

0.8 0.9
1b-jet efficiency

0.4

0.5

0.6

0.7

0.8 0.9
1b-jet efficiency

Figure B.12: Light ﬂavour jet rejection (left) and c-hadron jet rejection as a function of the b-tag eﬃciency forthe each b-tag algorithm based on tt̄ MC samples.

114• MuonSTACO muon applied the isolation cut satisfy the out of ∆R > 0.3 cone with selected jets.
• Jet
Jet seeded the topocluster jet and applied size parameter ∆R = 0.4 AntiKtTopo algorithm with calibrationby the EM+JES scale. The transverse momentum is larger than pT > 20 GeV.
• Cell Out
The Cell Out term is formed from all topocluster in the calorimeter not to belong to the any other objects.
This energy scale is calibrated by the EM scale.
miss
The ETis calculated by below formulas

ExmissEymiss
miss
ET

) ∑
∑
∑
Excalo,µ −pµx −Exjet −
ExCellOut
(
)
∑
∑
∑
∑
∑
= −
Eye −
Eycalo,µ −pµy −Eyjet −
EyCellOut√()(Exmiss ) + Eymiss .
=

= −

∑

Exe −

(∑

(B.4.1)(B.4.2)(B.4.3)calo,µIn these formulas, the energy deposit terms of muon in calorimeter Ex,yare depended on the qualiﬁcationof the muon. When its muon is isolated with jets i.e. the angular distance ∆R(µ, jets) is further than 0.3,
the energy deposit in the calorimeters is used to calculate the muon momentum, then the Excalo,µ term is not
added. On the other hand overlapped muon with jets ∆R(µ, jets) < 0.3 can not resolved the energy deposit㻹㼍㼟㼟㻱㼚㼑㼞㼓㼥 㻲㼞㼍㼏㼠㼕㼛㼚

0.03

ATLAS

0.025

0.006

2 Tracks
3 or more Tracks

0.02

0.007

0.005
0.004

ATLAS

ATLAS

0.045

1 single Track
0.04

2 single Tracks
2 Tracks

0.035

no Vertex

3 Tracks

0.03

1 or more Vertices

4 or more Tracks

0.025

0.015

0.02

0.003
0.01

0.015

0.002

0.01

㼎㻙㼖㼑㼠㼟

0.005
00

0.001
1

2

3

4
5
Mass [GeV]

00

0.005
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Energy fraction

00

5

10
15
20
25
30
Weighted flight length significance

0.009

ATLAS

0.04

0.03

2 Tracks

0.007

3 or more Tracks

0.006

0.025

㼏㻙㼖㼑㼠㼟

ATLAS
0.008

0.035

0.005

1 single Track

0.07

2 Tracks

0.06

3 Tracks

0.004

0.04

0.015

0.003

0.03

0.01

0.002

0.02

0.005

0.001
1

2

3

4
5
Mass [GeV]

00

ATLAS

0.012
0.01

2 Tracks

0.05

3 or more Tracks

5

10
15
20
25
30
Weighted flight length significance

0.1

ATLAS

1 single Track
2 single Tracks

0.08

3 Tracks

no Vertex

4 or more Tracks

1 or more Vertices

0.06

0.006

0.03

0.04
0.004

0.02

㼘㼕㼓㼔㼠㻙㼖㼑㼠㼟

ATLAS

00

2 Tracks
0.008

0.04

0.02

0.002

0.01
00

1 or more Vertices

0.01
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Energy fraction

0.07
0.06

no Vertex

0.05

4 or more Tracks

0.02

00

ATLAS

0.08

2 single Tracks

1

2

3

4
5
Mass [GeV]00

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Energy fraction

00

5

10
15
20
25
30
Weighted flight length significanceFigure B.13: Probability density function (PDF) of the parameters to identify the b-jet, c-jet and light ﬂavor
jet.

115

derived from the muon with the jet cluster, therefore the muon momentum is calculated as after energy loss
missand Excalo,µ term is add to the ET. If there are signiﬁcant diﬀerence between the only muon spectrometermeasurement and the combined measurement with inner detector and muon spectrometer, the muon energy
loss in calorimeters is parameterized and subtracted from Excalo,µ .
missFigure B.16 shows the ET
distributions in the W → eν events (left) and W → µν events (right). The
miss
MC predictions are in good agreement with data in these plots. Figure B.17 (left) shows the expected ET
linearity of the W →() eν and W → µν events on MC. The linearity is deﬁned as the mean value of the ratio
miss,True
miss,True
miss
miss
ET
− ET
/ET
. The mean value is expected to be zero, but the bias in low ET
is estimated
miss
miss
about 5% and the ﬁnite resolution of the ET
measurement deviate the reconstructed ET
from zero.
miss
The ET resolution is estimated by using the minimum bias and Z → ℓℓ events since these dijets andmissdileptons events are expected for the ET
to be zero. In this estimation, the distributions of Exmiss and ∑Eymissare ﬁtted by the Gaussian function in each the summation of energy deposit√of∑each calorimeter cell
ET
E
since
the
resolution
isbin and the standard deviations of Gaussianfunctionisexamined
σ
=
k
·
T
∑
∑
approximated stochastic as a function of
ET . TheET is calculated as follows

∑

ET =

N
cell
∑

Ei sin θi ,(B.4.4)i=1

where the Ei and θi are the energy deposit and polar angle∑ for each calorimeter cell, respectively. Figure B.18
(right) shows the ﬁtted results of the resolution in eachET bin for each sample. The MC predictions arereasonably agreement with data.

B.4.1

Systematic Uncertainties

miss
The ETis contributed from the systematic uncertainties derived from any objects.

The contributions fromthe energy scale uncertainty or the energy resolution uncertainty of objects propagate to the components of
miss
ET
.
miss
The major sources of own ET
uncertainties are the cell out term and the pile-up (soft jet) term. Thesesources originate from the inaccuracies in the description of the detector material, the choice of shower modeland the model for the underlying event in the simulation.
Cell Out Term

ATLAS Preliminary

0.08

Data

0.07

∫ L=5 fb-1b-jetsc-jetslight-flavour jets

0.06

arbitrary units

arbitrary units

miss
The energy scale uncertainty of the ET
cell out term is estimated by using two methods; (1) based on MC
simulation and; (2) the track momentum measurement instead of topocluster energy measurement.
In the uncertainty measurement based on simulation, some alternative MC samples which are changed to thedescription with dead material, the choice of shower model and the model of underlying events. The systematic

0.05

ATLAS Preliminary

0.06

Data

∫ L=5 fb-1b-jetsc-jetslight-flavour jets

0.05
0.04

0.04

0.03

no tag

0.03

MV170

0.02

0.02

0.01

0.01
0
0

0.07

500

1000

1500

2000

2500
prel
[MeV]
T

0

500

1000

1500

2000

2500
prel
[MeV]
T

Figure B.14: Examples of template ﬁt to the prel
T distributions in data before (left) and after (right) b-tagging
by applying the multivariate method at 70% eﬃciency.

116

uncertainty of modeling in simulation comes from the quadrature of the deviations with distribution between
missthe alternative samples and nominal sample. This method leads the 2.6% uncertainty for the ET
cell outterm.
In the track momentum measurement, the all selected tracks satisfy the track qualities and are extrapolated
to the second layer of the electromagnetic calorimeter to match the topocluster. The track momentum sum iscompared with the matching topocluster energy and a shift of the energy scale is ﬁtted to a function depending
with the momentum. The function is described as following()
b
1±a× 1+(B.4.5)pT
The a is obtained by comparing the ratio of topocluster energy to track momentum E/p in observed data andMC simulation. The value in the forward region, where tracks can not be used to validate the energy scale,is estimated from the transverse momentum balance between the one jet in the central region and one jet inforward region. The coeﬃcient b addresses the possible change in the clustering eﬃciency and scale in a nonisolated environment. The results are obtained as a = 3(10)% for |η| < (>) 3.2 and b = 1.2 GeV in data andMC simulation.
miss,CellOut
The ET
uncertainty is evaluated to shift the topocluster energies up and down by using the Equation
miss,CellOut
B.4.5. The fraction of ET
uncertainty is evaluated from:∆CellOut+ + ∆CellOut−
miss,CellOut
2 · ET,(B.4.6)

where
miss,CellOut
miss,CellOut+∆CellOut+ = ET
− ET,

(B.4.7)

miss,CellOut−
miss,CellOut∆CellOut− = ET
− ET.

(B.4.8)

miss,CellOut+
miss,CellOut−
miss,CellOut
The ETand ET
correspond to Equation B.4.5. The value of fractional ET
uncertainty is approximately 13%.

Pile-up Calibration
miss
The ET
resolution in the presence of pile-up is degraded by three main eﬀects.

Scale factor• Because of the higher activity in the detector, the energy deposit in the calorimeters increases. This causes
the sampling term to grow accordingly.

1.8
1.6

system8prel
T
combination∫

L = 5 fb

80

100

ATLAS Preliminary
JetFitterCombNN60

-1

1.4
1.2
1
0.8
0.6
0.4
20

40

60

120

140

160

180
200
Jet p [GeV]T

Figure B.15: Examples of template ﬁt for the prel
T distributions before (left) and after (right) b-tagging byapplying the multivariate method at 70% eﬃciency.

117• The noise level in the calorimeter cells increases.
• More energy is lost because the calorimeters can not start to take data at appropriate timing.
To reduce this pile-up eﬀects, the oﬀ-set subtraction is applied to the topocluster. The oﬀ-set value is estimatedby using the depth of the topocluster and the vertex multiplicity as function of the pseudo-rapidity in themissminimum bias events, and the ET
is recomputed from oﬀ-set subtracted topoclusters. The shift of energy
scale is regarded as systematic uncertainty and the value is estimated about 3%. The systematic uncertainties
missof each component with ET
are shown in Figure B.19 in W → eν and W → µν channel. The total uncertainty
misswith ETis estimated 1%-7% for both W → eν and W → µν events.

B.5

Luminosity Measurements

The luminosity as functions of time and µ which is an average number of inelastic interactions per bunch crossing
are obtained by several detectors and multiple algorithm independently [48]. The luminosity L is described byusing the inelastic cross section σinel and the rate of inelastic collisions Rinel as following,
Rinel
.
σinel

L=

(B.5.1)

For a storage ring, operating at a revolution frequency fr and bunch pairs colliding per revolution nb , thisexpression can be rewritten by using the average number of inelastic interactions per bunch crossing µ asL=

µnb fr.
σinel(B.5.2)The total inelastic cross section σvis and the observed interaction rate per crossing µvis can be expressing byusing eﬃciency ϵ of a particular detector and algorithms as σvis = ϵσinel and µvis = ϵµinel , then the luminosity
can be expressed as
L=µvis nb fr.
σvis(B.5.3)104∫ Ldt=36 pb-1

Events / 2 GeV

Events / 2 GeV

Here the luminosity in arbitrary unit Rx (δ) is introduced. The value is measured during a horizontal scan at
the time the two beams are separated by the distance δ and δ = 0 represents the case of zero beam separation.
Deﬁning the parameter Σx as∫
Rx (δ)dδ1
Σx = √(B.5.4)2π Rx (0)ATLAS
Data 2010
MC W → eν
MC W → τνMC ttbar
MC WW
MC Z → ee
MC WZ

s = 7 TeV

103
102

102

1
150

200

Data 2010
MC W → µν
MC W → τν
MC Z → µµ
MC ttbar
MC WW
MC WZ

10

1
100

ATLAS

3

10

50

-1

s = 7 TeV

100

∫ Ldt=36 pb

104

250

[GeV]
Emiss
T

0

50

100

150

200

250

[GeV]
Emiss
T

miss
Figure B.16: ET
distributions both data and MC predications with the W → eν events (left) and W → µν
events (right). The MC samples are normalized by entries of data and the theoretical cross section. [70]118and similarly for Σy . The luminosity can be rewritten asL=nb fr n1 n22πΣx Σy(B.5.5)where n1 and n2 are the bunch populations (number of protons per bunch) in beam 1 and beam 2. The Σx andΣy are measured by using van der M err (vdM ) scan. This method scans to cross the two beams along the x
and y directions and estimates the beam width from the number of interaction events. In order to calibrate theluminosity measurement, the visible interaction rate per bunch crossing µMAX
which is observed at the peak ofvis
the scan curve as applied by a particular algorithm
σvis = µMAX
vis

2πΣx Σyn1 n2(B.5.6)is used.
For the µvis measurement four event count algorithms are performed as “EventOR”, “EventAND”, “EventA”
and “EventC”. The LUCID and BCM detectors are placed in the forward (labeled “A”) and backward (labeled“C”) direction from the interaction point as symmetry. For event counting algorithms, a threshold is applied tothe analogue signal output from each readout channel, and every channel with a response above this thresholdis counted as containing “hit”. The EventOR algorithm reports the mean number of hits per bunch crossing
detected by at least one hit in either A side or C side. Assuming that the number of interactions in a bunch
crossing can be detected by a Poisson distribution, the probability of observing an OR event can be computed
as
NOR
NBC

PEventOR (µORvis ) =

(B.5.7)
OR= 1 − eµvis(B.5.8)where NOR is the number of events satisfying the event-selection criteria of the OR algorithm and NBC is thetotal number of bunch crossing in a given time interval. The µOR
vis is calculated by using the number NOR andtotal number of bunch crossing NBC ,
(
)
NOR
=
−
ln
1
−
µOR
when µvis ≪ 1.
(B.5.9)vis
NBC
In the case of an EventAND algorithm the probability of observing at least one hit on both side of the detectors
is expressed as
PEventAND (µANDvis ) =

< (ET

miss

- ET

miss,True) / ET

miss,True

>

=

NAND
NBC

(B.5.10)

OR
AND
AND
OR
AND
AND
1 − 2e−1+(σvis /σvis )µvis /2 + e−(σvis /σvis )µvis(B.5.11)

0.2
0.15
0.1

MC W→ eνATLAS

MC W→ µ ν

Simulations = 7 TeV

0.05
0
-0.05
-0.1
-0.15
-0.2
25

30

35

40

45

50

55

60

65

70

miss,True
ET

[GeV]

miss,True
miss
Figure B.17: ET
linearity in W → eν and W → µν MC events as a function of ET. [70]

119

16

Emiss
,EmissResolution [GeV]
x
y

Emiss
,EmissResolution [GeV]xyThis relationship can not be inverted analytically to determine µAND
as a function of NAND /NBC thus avisnumerical inversion is performed instead.
In the luminosity measurement the largest source of systematic uncertainty is the bunch population. Eachbeam is also monitored by two DC current transformers (DCCT) which are high accuracy devices but not haveany ability to separate individual bunch populations. The uncertainty derived from this device is measured as
3.0%. In addition the uncertainty coming from calibration to σvis are considered and the value is measured as
1.6%. The total uncertainty of the luminosity of 3.7% is assigned for this analysis.

ATLAS
14

Data 201012∫Ldt=36 pb

10

s = 7 TeV

-1

8
6

MinBias: fit 0.45 Σ ET

4

QCD di-jets: fit 0.51 Σ ET

0
0

200

300

400

500

600

12

Simulations = 7 TeV

108MC MinBias: fit 0.48 Σ ET
MC QCD: fit 0.50 Σ ET
MC Z→ ee: fit 0.42 Σ ET
MC Z→ µµ: fit 0.42 Σ ET
MC W→ eν: fit 0.47 Σ ET
MC W→ µν: fit 0.47 Σ ET

62

Z→ µµ: fit 0.44 Σ ET

100

ATLAS
14

4

Z→ ee: fit 0.42 Σ ET

2

16

0
0

700

Σ ET(event) [GeV]

100

200

300

400

500

600

700

Σ ET(event) [GeV]

miss
Figure B.18: ET
resolution of both observed data (left) and MC simulation (right) as a function of the totaltransverse energy in the event calculated by summing the pT of muons and the total transverse
energy in the√
misscalorimeter. The resolution of the two ET
components is ﬁtted with a function of σ = k ΣET and the ﬁtted
values of the parameter k, expressed in GeV1/2 . [70]120

miss,CellOutET
miss, softjets
ETmiss, jetsETmiss,eET

Simulation
W→ eν
s = 7 TeV

0.15

miss,term

0.2

uncertainty

ATLAS

Fractional ET

uncertainty
miss,term

Fractional ET

0.25

0.1
0.05
0
0

50

100

150

200

250

0.25
ATLAS

s = 7 TeV

0.15
0.1
0.05
0
0

300

miss,CellOutET
miss, softjets
ETmiss, jetsETmiss,µET

Simulation
W→ µν

0.2

50

100

Σ Eterm
[GeV]
T

150

200

250

300

Σ Eterm
[GeV]
T

0.25
ATLAS Preliminary

0.2
LHC fill: 1783

0.15

vis

1

µ /(n n2) [BC-1 (1011 p)-2 ]

miss
term
Figure B.19: Fractional systematic uncertainty on diﬀerent ET
terms as a function of respective ΣETin
W → eν events (left) and W → µν events (right).

0.1

0.05

data-fit
σ data0
3
2
1
Horizontal
Beam Separation [mm]
0
-1
-2
-3
-0.2

-0.1

0

0.1

0.2

Horizontal Beam Separation [mm]Figure B.20: Speciﬁc interaction rate versus nominal beam separation for the EventOR algorithm of BCM(horizon) in the x plain at May 15th 2011. The residual deviation of the data from the Gaussian plus constantterm ﬁt, assuming statistical error only, is shown in the bottom panel.

121

Appendix C

Simultaneous Fit
C.1

Profiling Likelihood Method

The distributions of background and signal include the uncertainties, thus these distributions can not be determined uniformly. This analysis estimates the most probable distributions by using a likelihood method [71].
The likelihood function L consists of two parameters, signal strength µ and nuisance parameter θ. If each binof a histogram is distributed by Poisson probability, the likelihood function is composed of the product of the
Poisson probability between all bins as following
L(µ, θ) =Nn∏(µsi + bi ) i
i=1

ni !

e−(µsi +bi )(C.1.1)

where si , bi and ni are entries of predicted signal, background and observed data in i-th bin, respectively. Thenthe expectation value of the sum of the signal and background ni is
E [ni ] = µsi + bi

(C.1.2)in the histogram n = (n1 , n2 , · · · , nN ).
To test a hypothesized value of µ and θ, the proﬁle likelihood ratio described below is consideredλ(µ) =

ˆL(µ, θ̂)L(µ̂, θ̂)

(C.1.3)where the µ̂ and θ̂ in the denominator are values maximizing L so-called “maximum-likelihood (ML) estimator”.
ˆˆIn the numerator the θ̂ is a value maximizing the L at an arbitrary µ thus the θ̂ is depending on µ. It is convenient
to introduce the tµ so-called “test statistics” as followingtµ = −2 ln λ(µ)(C.1.4)and the probability density function is calculated by this tµ .
For the method, it is possible that the signal strength µ̂ is obtained as negative value, however the signal
process should contribute as the positive. Therefore this likelihood function is switched by the µ̂ and alternative
test statistics q̃µ are provided as followingˆ
L(µ,θ̂(µ))
(µ̂ < 0) ,
 −2 ln{ˆL(0,θ̂(0))−2 ln λ̃(µ)(µ̂ ≤ µ)ˆ
(C.1.5)q̃µ ==θ̂(µ))(0 ≤ µ̂ ≤ µ) ,−2 ln L(µ,0(µ̂ > µ)L(µ̂,θ̂(µ̂))
0(µ̂ > µ) .
The probability density function (pdf) of q̃µ is described as f (q̃µ |µ′ ) at signal strength µ′ . When we discuss
whether discovery or exclusion for the searching model, we can conclude to compare the observed data with thea hypothesis including signal events (signal-plus-background hypothesis) H1 or null hypothesis (backgroundonly hypothesis) H0 by using the pdf as f (q̃µ |µ). If the test statistics of the observed data q̃µ,obs is farther
122

from the f (q̃µ |0) distribution of H0 , the background-only hypothesis H0 can be excluded, in other word we canconclude to discover a new particle. On the other hand, for the exclusion with a signal model we compare theobserved data with the signal-plus-background hypothesis H1 . If there are discrepancy between observed dataand signal-plus-background hypothesis, we can conclude that the signal model can be excluded.
In order to estimate the discrepancy, the p-value is introduced as∫ ∞pµ =f (q̃µ |µ) dq̃µ .
(C.1.6)q̃µ,obs

In practice, the p-value of 0.05 (corresponding to 95% CL (conﬁdence level) or 1.64σ) for the exclusion thresholdis often used meanwhile for the discovery p0 is 2.87 × 10−7 (corresponding to 99.99998% CL or 5σ).

C.2

Asymptotic approach

The proﬁle likelihood method takes long times to search the ML estimators µ̂ and θ̂ or 95% CL signal strengthˆµ95%CL by scanning µ and θ̂, thus the asymptotic formula is applied [72]. The distribution of proﬁle likelihood
ratio are approximated by the χ2 distribution as following2√(µ − µ̂)+ O(1/ N ).
(C.2.1)2σ√
The large number of sample entries can neglect the O(1/ N ) term. The standard deviation σ of µ̂ is obtained
from the covariance matrix of the estimator Vij = cov[θ̂i , θ̂j ] composed√ of signal strength and all nuisanceparameters. In the large sample limit, the bias of ML estimators O(1/ N ) are negligible therefore the inverseof the covariance matrix can be described as][ 2∂ ln L−1
Vij = −E.
(C.2.2)∂θi ∂θj−2 ln λ(µ) =The θi represent both µ and all nuisance parameters θ (θ0 = µ and σ 2 = V00 ). In the case, the pdf of test
statistic qµ = −2 ln λ(µ) is approximated to be a non-central chi-square distribution for one degree of freedom,
{
[
]
[
]}
√ )2
√ )2
1
1 (√
1 (√
1
f (qµ ; Λ) = √ √exp −qµ + Λ
+ exp −
qµ + Λ
,(C.2.3)2 qµ 2π22where the non-centrality parameter Λ is2Λ=(µ − µ̂).
σ2(C.2.4)The uncertainties of each parameter can be calculated by the covariance matrix. The formula is described as
∑
−1
∆θi =
F T (θi , θj )Ṽjk
F (θi , θk )(C.2.5)
j,k

=

i
∑

−1
∆θj Vjk∆θk(C.2.6)j,k−1
where Ṽjk
is the inverse of the submatrix obtained from restricting the full covariance matrix to the parametersof interest.
In order to estimate the σ, Asimov data set which evaluates the estimators for all parameters is introduced.
To simplify the notation is deﬁned as following

νi = µ′ si + bi .

(C.2.7)The ln L becomes zero at ML estimators θ̂j , then the derivatives of ln L satisﬁes
)
N (
∂νi
∂ ln L ∑ ni
=
−1
=0
∂θj
ν
∂θ
i
j
i=1
123

(C.2.8)

q

2
1.8
1.6
1.4
q

1.2
1
0.8
0.6
0.4
0.2

q

0
0

0.5

1

1.5

2

2.5

3

Figure C.1: Example of qµ (left) and the distributions both f (q̃µ |µ = 0) and f (q̃µ |µ = 1) (right) [71].
In the Asimov data set ni,A are equal to the expectation valueni,A = E [ni ] νi = µ′ si (θ) + bi (θ),(C.2.9)and the “Asimov likelihood” LA and corresponding proﬁle likelihood ratio λA are given
λA (µ) =ˆLA (µ, θ̂)LA (µ̂, θ̂)=ˆLA (µ, θ̂).
LA (µ′ , θ)

(C.2.10)

Because the Asimov data set corresponding to a signal strength µ′ gives µ′ = µ̂, then
−2 ln λA (µ) ≈(µ − µ′ )=Λ
σ2(C.2.11)

is obtained from Equation C.2.1. By using the equation, the variance σ 2 is obtained as following(µ − µ′ )
qµ,A

2

2
=
σA

(C.2.12)

where qµ,A = −2 ln λA (µ).
For ﬁnding the median exclusion, signiﬁcance for the hypothesis µ assuming that there is no signal, µ′ = 0
is substituted into Equation C.2.12
2
σA
=

µ2
,
qµ,A

(C.2.13)

2
σA
=

µ′2
.
q0,A

(C.2.14)and discovery case µ = 0 is tested

C.3

Experimental Sensitivity

The experimental sensitivity is estimated from the discrepancy of pdf f (q̃µ |µ) between the background-only
hypothesis and the signal-plus-background hypothesis. Figure C.1 (left) shows an example of the distributionsof q̃µ . The values of q̃0 and q̃1 are obtained from the proﬁle likelihood function scanned with the signal strengthµ. The toy pseudo-experiment or asymptotic method give the pdf of the f (q̃µ |0) and f (q̃µ |1). Figure C.1 (right)
shows a example of the pdf f (q̃µ |0) and f (q̃µ |1). The observed conﬁdence level of the signal-plus-background124

hypothesis CLs+b and the background-only hypothesis CLb are given as∫ ∞f (q̃µ |µ = 1) dq̃µ ,CLs+b = 1 − pµ = 1 −CLb=

1 − pb =∫ ∞(C.3.1)q̃µ,obsf (q̃µ |µ = 0) dq̃µ .

(C.3.2)q̃µ,obs

On the other hand, the expected conﬁdence level are given to replace the q̃µ,obs to the median[qµ |µ=1] andmedian[qµ |µ=0] for the exclusion and discovery, respectively. In this analysis the CLs is introduced to suppress
the statistical ﬂuctuation
CLs =

CLs+b
.
1 − CLb(C.3.3)

If CLs > 0.95, the signal point is regarded as exclusion. On the other hand, if CLb > 1 − 2.87 × 10−7 , then thesignal point is regarded as discovery.
The error band of ±N σ for the expected limit of signal strength are estimated as follow[]
bandN σ = µ′ + σ Φ−1 (1 − α) ± N(C.3.4)
where Φ is the cumulative distribution of the standard Gaussian, (1 − α) is a conﬁdence level, respectively. The
standard deviation σ is given by the Asimov data set.

C.4

Fit Configuration

C.4.1

Fit Parameters

The main background normalizations and the signal yields are estimated by applying the simultaneous ﬁt thatmeans the same proﬁling value for each parameter is implemented in the all control regions and signal regions.
The two type of ﬁt parameters are provided as following. The proﬁling likelihood method are applied to theboth parameters and these are calculated by using the pdf.
• Free parameters
The normalization of signal component and main backgrounds are ﬁtted by using free scales without any
constrains.
• Nuisance parameterAll systematic and statistic uncertainties are inputted as the nuisance parameters. Each nuisance parameter is performed to the distribution or weight by applying the ±1σ uncertainty. The likelihood function
proﬁles the most probable value of each free parameter within the ±1σ bandwidth of nuisance parameters.
The nuisance parameters are constrained by using the covariance matrix in Equation C.2.6.

Figure C.2: Distributions both f (q̃µ |µ = 0) and f (q̃µ |µ = 1) and relation to the median[qµ |µ = 0] (left) andmedian[qµ |µ = 0]-1σ (right) [71]. The ±1, ±2σ band of the expected limit estimated these distributions.

125• Probability Density Function (pdf)
Both free and nuisance parameters are estimated the probability density function (pdf) of the proﬁlelikelihood ratio q̃µ in each bin of all histograms of the control regions and signal regions, respectively.
The optimal values and errors of both the free parameters and nuisance parameters are determined simultaneously by calculating the likelihood function to ﬁt to data in both the control regions and signal regions andthe covariance matrix.

C.4.2

Fit Conﬁgurations

To conclude whether the searching model exists or not, the background-only model and the signal-plusbackground model are compared with the observed data. The three type conﬁgurations are prepared to discusssuch issues as below• Background-only ﬁt
This conﬁguration assumes that the distributions in both the control regions and signal regions consist of
background-only components. Then the normalizations of only background are ﬁtted simultaneously todata in the regions on the condition that the any signal contributions do not exist everywhere.
• Discovery ﬁt
The discovery ﬁt is applied to the background-only hypothesis and the observed data, and estimate thediscrepancy between the hypothesis and data as the conﬁdence level of background-only hypothesis CLb .
This conﬁguration inputs a dummy signal event into the signal regions and ﬁt it to data, although thebackground-only hypothesis is ﬁtted to data in the control regions and the normalizations of backgrounds
are determined in the control regions. In this case, the dummy signal events in signal regions are independently scaled by compensating the discrepancy between data and background-only hypothesis, then
the normalization of dummy signal is equivalent with the signal cross section.
• Exclusion ﬁt
In case that the estimation of the discrepancy between the signal-plus-background hypothesis and theobserved data is signiﬁcant, we can conclude the signal model is excluded. This conﬁguration compares
the signal-plus-background hypothesis with observed data. The conﬁdence level of the hypothesis CLs are
estimated by scanning the signal strength µ in 20 steps between ±4σ from the most probable value of µ̂.
The upper limit for signal strength µ′ is determined as the p-value fall below 5%.

C.4.3

Fit Options

The background distribution is determined by calculating the most probable value within the nuisance parameters. There are some kind of the ﬁt method which determine the width of nuisance parameter. In this analysis,
the width of nuisance parameters are determined by taking the diﬀerence of distributions where ±1σ uncertainties are applied. The width is inputted into the ﬁt as a probable density function and the ﬁt is executed within
the width. These ﬁtting options are described below• overallSys
The overallSys inputs the nuisance parameters into the distribution uniformly. The option scales the
background distribution by using α to be ﬁtted to data within the width which is determined by nuisanceparameters. The α is the global scale factor in units of the width. Therefore this option vary thenormalization of distribution but the shape of distribution does not change. The nuisance parameter isconstrained by the covariance matrix as γ · σ where γ is coeﬃcient of nuisance parameter and σ is the
input nuisance parameter. Figure C.3 shows the histograms before and after ﬁtting.
• HistoSys
The HistoSys inputs the nuisance parameter into each bin in distribution. Therefore the widths of nuisanceparameters are diﬀerent bin by bin. The background distribution is ﬁtted within the widths to minimize
the likelihood function as well as overallSys. The HistoSys calculate the α as scale factor in units of thewidth. The distribution after ﬁt is varying because of diﬀerence of widths. The nuisance parameters areconstrained as γ · σ by taking the covariance matrix as well as overallSys. Figure C.3 also shows thehistograms before and after ﬁtting.

126

[ events ][ events ]14
before fitting : median
before fitting : ± 1σ

12after fitting : α ± γ σ

1014before fitting : median

8

6

6

4

4

2

2
1

2

3

4

after fitting : α ± γ σ

10

8

0
0

before fitting : ± 1σ

12

0
0

5

1

2

3

4

5

Figure C.3: Example of the overallSys (left) and HistoSys (right) options. The dashed lines show the distribution
and uncertainty. The overallSys gives all histogram bins the same space to ﬁt uniformly while the HistoSys
gives each histogram bin the corresponding space to ﬁt.
• normHistoSys
The normHistoSys option is the same operation as the HistoSys except the normalization. This option
keeps the normalization but changes the shape.
• MCStatError
This option calculates a Poisson statistical uncertainty derived from the MC statistic. This uncertainty isapplied independently to the each bin and does not eﬀect to shift the content of histogram but multiply
to the uncertainty of each bin as (α ± γ) · σ.

C.5

Closure Test

The analysis employs HistFitter tool provided from ATLAS SUSY one lepton analysis group. This tool calculates
the likelihood function and the covariance matrix by inputting the systematic uncertainties and the interesting
parameters. In this section, this tool would be conﬁrmed whether the ﬁtting results are correct or not by using
pseudo-data. The pseudo-data are generated to the same as the background MC samples including W+jets,
Z+jets, tt̄, single-top and dibosons MC samples. In addition the pseudo-data samples are added the signal
samples where numbers of the events are multiplied by ×0.1, ×0.2, ×0.5, ×0, ×1, ×2, ×5 and ×10, respectively.
The signal-plus-background distribution are ﬁtted to that of pseudo-data and conﬁrmed that the ﬁtting results
show the signal strengths as 0.1, 0.2, 0.5, 0, 1, 2, 5 and 10, respectively. In order to make the simple condition,
only statistical uncertainty is applied to each bin. The ﬁtting results are shown in Figure C.5 and Table C.2.
These results show the sample corresponding with each signal strength is ﬁtted by its signal strength. Therefore
ﬁtting results obtained from this tool are valid.
It is afraid that the signal strength is constrained by ﬁtting in the control regions. Therefore the signal
yield is conﬁrmed in low statistic region for the signal model. The ﬁt result at mg̃ = 665 GeV and mLSP = 585
GeV for the simpliﬁed SUSY g̃-g̃ pair production in both W +jets and tt̄ control regions and signal region isshown in Figure C.6. The background events are constrained strictly due to large statistic in the control regions
while the statistical uncertainty becomes large for signal events. Therefore the signal strength is determined
to compensate for the discrepancy between observed data and background estimation in the signal regions. In
the signal point the signal yield is small, thus the ﬁgures show the signal contribution is visible though theuncertainty is large. According to the results, the signal strength can be ﬁtted properly by HistFitter tool.

127

(=Background-only)

Total Background

80

40

30

30

20

20

10

10

0

0
2

Data / Exp

40

2
1
0.5

100

0.6
0.7
Arbitary unit

Pseudo-Data

90(=Background-only)

Total Background80

EventsData / Exp
Events

50

0.4

0
0.1

40

30

30

20

20

10

10

0

0
2

Data / Exp

40

2
1
0.5

120

0.6
0.7
Arbitary unit

Pseudo-Data(=Background-only)

Total Background

100

0.4

0.5

(=Background-only)

Total Background
SignalW+jets & Z+jets
tt
single top & dibosons

1
0
0.1

0.2

0.3

0.4

0.5

120

(=Background+Signal× 2)

Total Background100

SignalW+jets & Z+jets

W+jets & Z+jets

80

tt

tt
single top & diboson

60

60

40

40

20

20

0
2

0
2

Data / SM

Data / Exp

single top & dibosons

1
0
0.1

0.2

0.3

0.4

0.5

0.6
0.7
Arbitary unit

Pseudo-Data

Signal80

0.6
0.7
Arbitary unit

Pseudo-Data

60
50

0.4

0.3

70

single top & dibosons

0.3

0.2

80

tt

0.2

single top & dibosons

1

50

0
0.1

tt

90

W+jets & Z+jets

60

W+jets & Z+jets

100

Signal70

Signal60

single top & dibosons

0.3

Total Background

70

tt

0.2

(=Background-only)

80

50

0
0.1

Pseudo-Data

90

W+jets & Z+jets

60

Data / Exp

100

Signal70

EventsEventsPseudo-Data

90

EventsEvents

100

0.6
0.7
Arbitary unit

1
0
0.1

0.2

0.3

0.4

0.5

0.6
0.7
miss
ET / meff

Figure C.4: Results of closure test with the HistFitter before ﬁtting (left) and after ﬁtting (right). The pseudodata including ×0 (top), ×1 (middle) and ×2 (bottom) of signal events are ﬁtted by the background samples
and signal samples.

128

(=Background+Signal× 1)

Total Background60

EventsEventsPseudo-Data70

SignalPseudo-Data

70(=Background+Signal× 1)

60

SignalTotal Background

W+jets & Z+jets

50

W+jets & Z+jets

50

tt

tt
single top & diboson

40

30

30

20

20

10

10

0
2

0
2

Data / SM

40

1
0
0.1

0.2

0.3

0.4

0.5

0.6
0.7
Arbitrary unit

Pseudo-Data(=Background+Signal× 1/2)

70

Total Background60

EventsEventsData / SMsingle top & diboson

Signal

1
0
0.1

0.2

0.3

0.4

0.5

Pseudo-Data

70(=Background+Signal× 1/2)

60

SignalTotal Background

W+jets & Z+jets

50

W+jets & Z+jets

50

tt

tt
single top & diboson

40

30

30

20

20

10

10

0
2

0
2

Data / SM

40

1
0.2

0.3

0.4

0.5

0.6
0.7
Arbitrary unit

Pseudo-Data(=Background+Signal× 1/5)

70

Total Background60

EventsEventsData / SMsingle top & diboson00.1

Signal

1
0
0.1

0.2

0.3

0.4

0.5

Pseudo-Data(=Background+Signal× 1/5)

60

SignalTotal Background

W+jets & Z+jets

50

tt

tt
single top & diboson

40

40

30

30

20

20

10

10

0
2

0
2

Data / SM

Data / SMsingle top & diboson

1
0
0.1

0.2

0.3

0.4

0.5

0.6
0.7
Arbitrary unit

70

W+jets & Z+jets

50

0.6
0.7
Arbitrary unit

0.6
0.7
Arbitrary unit

1
0
0.1

0.2

0.3

0.4

0.5

0.6
0.7
Arbitrary unit

Figure C.5: Results of closure test with the HistFitter before ﬁtting (left) and after ﬁtting (right). The pseudodata including signal events are ﬁtted by the background samples plus ×1 (top), ×5 (middle) and ×10 (bottom)
signal events.

129

-1

1800

SUSY Simplified Model (~g~g)
mg~=665GeV, mLSP=585GeV

1400
1200
1000
800
600

1000
800
600

Data / SM

0
2

2
1
7

8

Data 2011 ( s=7 TeV)
Standard Model∫ Ldt = 4.7 fb

-1

800

9
10
Number of jets

SUSY Simplified Model (~g~g)
mg~=665GeV, mLSP=585GeV

EventsData / SM

200

0

6

W+jets & Z+jets Np0
W+jets & Z+jets Np1
W+jets & Z+jets Np2
W+jets & Z+jets Np3
W+jets & Z+jets Np4
W+jets & Z+jets Np5
tt Np0tt Np1
tt Np2
tt Np3
tt Np4
tt Np5
single top & diboson
multijets (data estimate)

700
600
500
400
300
200

1
0
3

Data / SM∫ Ldt = 4.7 fb-1

12

SUSY Simplified Model (~g~g)
mg~=665GeV, mLSP=585GeV

W+jets & Z+jets Np2
W+jets & Z+jets Np3
W+jets & Z+jets Np4

10

6
4

1
0
3

8

∫ Ldt = 4.7 fb

Data / SM
0.6
0.7
miss
ET / meff

910
Number of jets

Data 2011 ( s=7 TeV)
Standard Model
SUSY Simplified Model (~g~g)
mg~=665GeV, mLSP=585GeV

W+jets & Z+jets Np2
W+jets & Z+jets Np3
W+jets & Z+jets Np4
tt Np0tt Np1
tt Np2
tt Np3
tt Np4
tt Np5
single top & diboson
multijets (data estimate)

4

1
0.5

7

6

0
2

0.4

6

8

0
2

0.3

5

12

2

0.2

4

-1

2

0
0.1

SUSY Simplified Model (~g~g)
mg~=665GeV, mLSP=585GeV

W+jets & Z+jets Np0
W+jets & Z+jets Np1
W+jets & Z+jets Np2
W+jets & Z+jets Np3
W+jets & Z+jets Np4
W+jets & Z+jets Np5
tt Np0tt Np1
tt Np2
tt Np3
tt Np4
tt Np5
single top & diboson
multijets (data estimate)10

tt Np0tt Np1
tt Np2
tt Np3
tt Np4
tt Np5
single top & diboson
multijets (data estimate)

8

Data / SM

Data 2011 ( s=7 TeV)
Standard Model

-1

200

9
10
Number of jets

910
Number of jets

Data 2011 ( s=7 TeV)
Standard Model∫ Ldt = 4.7 fb

300

EventsData / SM
Events

8

8

400

1
7

7

500

0
2

6

6

600

0
2

5

5

700

100

4

4

800

100

0
3

W+jets & Z+jets Np0
W+jets & Z+jets Np1
W+jets & Z+jets Np2
W+jets & Z+jets Np3
W+jets & Z+jets Np4
W+jets & Z+jets Np5
tt Np0tt Np1
tt Np2
tt Np3
tt Np4
tt Np5
single top & diboson
multijets (data estimate)

1200

400

5

SUSY Simplified Model (~g~g)
mg~=665GeV, mLSP=585GeV

1400

200

4

-1

1600

400

0
3

Data 2011 ( s=7 TeV)
Standard Model∫ Ldt = 4.7 fb

1800

W+jets & Z+jets Np0
W+jets & Z+jets Np1
W+jets & Z+jets Np2
W+jets & Z+jets Np3
W+jets & Z+jets Np4
W+jets & Z+jets Np5
tt Np0tt Np1
tt Np2
tt Np3
tt Np4
tt Np5
single top & diboson
multijets (data estimate)

1600

EventsEventsEventsData 2011 ( s=7 TeV)
Standard Model∫ Ldt = 4.7 fb

2000

1
0
0.1

0.2

0.3

0.4

0.5

0.6
0.7
miss
ET / meff

Figure C.6: Simultaneous ﬁt results in HistFitter before ﬁtting (left) and after ﬁtting (right). Used signal model
is simpliﬁed SUSY model at mg̃ = 665 GeV, mLSP = 585 GeV.

130

×0

signal strength
signalW+jets & Z+jets
tt̄
single top & dibosons

×1

×2

×5

× 10

−3

1.00 ± 0.33
1.00 ± 0.03
1.00 ± 0.02
1.00 ± 0.09

2.00 ± 0.43
1,00 ± 0.03
1.00 ± 0.02
1.00 ± 0.06

5.01 ± 0.69
1.00 ± 0.03
1,00 ± 0.02
1,00 ± 0.09

10.00 ± 1.03
1.00 ± 0.03
1.00 ± 0.02
1.00 ± 0.09

× 0.1

× 0.2

× 0.5

× 1.0

0.09 ± 0.42
1.00 ± 0.02
1.00 ± 0.02
1.00 ± 0.06

0.20 ± 1.22
1.00 ± 0.03
1.00 ± 0.02
1.00 ± 0.09

0.48 ± 3.03
1,00 ± 0.03
1.00 ± 0.02
1.00 ± 0.09

1.00 ± 10.1
1.00 ± 0.03
1,00 ± 0.02
1,00 ± 0.09

(0.03 ± 897)×10
1.00 ± 0.02
1.00 ± 0.02
1.00 ± 0.06

signal strength
signalW+jets & Z+jets
tt̄
single top & dibosons

Table C.1: Results of the closure test in HistFitter tool.
normalizations
signal (mg̃ = 665 GeV, mLSP = 585 GeV)
W+jets & Z+jets Np0
W+jets & Z+jets Np1
W+jets & Z+jets Np2
W+jets & Z+jets Np3
W+jets & Z+jets Np4
W+jets & Z+jets Np5
single top & dibosons

0.61 ± 1.03
1.0
1.0
1.21 ± 0.13
0.80 ± 0.11
0.98 ± 0.07
0.76 ± 0.22
1.00 ± 0.06

tt̄ Np0tt̄ Np1
tt̄ Np2tt̄ Np3tt̄ Np4
tt̄ Np50.69 ± 0.24
1.11 ± 0.07
1.00 ± 0.09
0.94 ± 0.06
0.94 ± 0.06
0.94 ± 0.06

Table C.2: Fit results of HistFitter tool by using simpliﬁed SUSY model at mg̃ = 665 GeV, mLSP = 585 GeV.

C.6

Signal-Strength-Only Fit Results

Until 2011 summer results, the background events are normalized in only the control regions, not simultaneous ﬁt
in both control regions and signal regions. In the old method, background are corrected by the normalizations inTable 7.3, but shape corrections and signal contributions to the control regions and signal regions are neglected.
The exclusion regions for simpliﬁed SUSY model and UED model after applying the old method are shownin Figure C.7.

131∼0, x=1/2~∼0χ
g~
g → qqqqWWχ

Minimal Universal Extra Dimension

1 1

ΛR

mLSP [GeV]1000∫ L dt = 4.71 fb , s=7 TeV
-1

900
800

40

Hard and Soft Lepton Combined

Hard and Soft Lepton Combined

Observed limit (± 1 σtheory)

30

Observed limit (± 1 σtheory)

25

Observed limit (± 1 σtheory)

Sinal Strength only Fit

700

Sinal Strength only Fit

Observed limit (± 1 σtheory)600∫ L dt = 4.71 fb , s=7 TeV-1

35

Simultaneous Fit

Simultaneous Fit

20
500
15

400
300

10

200

5

100

300

400

500

600

700

800

900

1000

1100 1200m~g [GeV]

600

650

700

750

800

850

900
950
1/R [GeV]

Figure C.7: 95% CLs exclusion limits for simpliﬁed SUSY model (left) and UED model (right) by using signal
strength only ﬁt.

132

MSUGRA/CMSSM: tanβ = 10, A = 0, µ>0= 4.71 fb , s=7 TeV∫SoftLdtLepton
ChannelExpected limit (± 1 σexp )Observed limit (± 1 σtheory)
LEP2 ∼
χ~ (140g
0 GeV)±MSUGRA/CMSSM: tanβ = 10, A = 0, µ>00= 4.71 fb , s=7 TeV∫HardLdtLepton
Channel

600

Stau LSP

Observed limit (± 1 σtheory)~ (140g
0 GeV)

0
00

0
00

V)

Ge

V)

Ge

300

V)
Ge

V)
Ge

1000

1500

700

2000

2500

100

3000
3500
m0 [GeV]

500

1500

2000

2500

3000
3500
m0 [GeV]0= 4.71 fb , s=7 TeV∫HardLdtand
Soft Lepton Combined

Expected limit (± 1 σexp )

-1

600

1000

MSUGRA/CMSSM: tanβ = 10, A = 0, µ>0

Observed limit (± 1 σtheory)~ (14g00 GeV)40~q (1m1/2 [GeV]

500~
g (600 GeV)

00

00

200

~q (6

~
g (600 GeV)

~q (6

100

negmasssq~
g (1000 GeV)

~q (1

~q (1

400

300

200

1

Non-convergent RGE

negmasssq~
g (1000 GeV)±No EW SB

Non-convergent RGE

400

LEP2 ∼
χ

Stau LSP

)
eV

500

No EW SB

Expected limit (± 1 σexp )

-1

1

)
eV

500

700

0G
40
~q (1

600

m1/2 [GeV]

0

-1

0G
40
~q (1

m1/2 [GeV]

700

±
1

Stau LSP

eV

0G

No EW SB)

500

LEP2 ∼
χ

Non-convergent RGE
~q (1

400

negmasssq~
g (1000 GeV)

0G

00
)

eV

300
~
g (600 GeV)

~q (6
00

200

V)

Ge

100

500

1000

1500

2000

2500

3000
3500
m0 [GeV]Figure C.8: Exclusion limits at 95% CL with the MSUGRA in the soft lepton channel (top-left), hard lepton
channel (top-right) and combined result (bottom), respectively.

C.7

Exclusion Region for SUSY models

In following sections, the exclusion region at 95% CLs upper limit for MSUGRA, simpliﬁed SUSY models
containing squark pair productions and gluino pair production with ﬁxing mLSP at 60 GeV are shown.

MSUGRA exclusion region
The excluded regions for the MSUGRA are shown in Figure C.8. The red solid line and dashed line show theobserved exclusion limit with the nominal and the ±1σ theoretical cross section, respectively. The blue dashedline and yellow band show the nominal and ±1σ exclusion limit, respectively. The exclusion region of the hardand soft lepton channel combined reaches the m0 ∼ 3000 GeV and m1/2 ∼ 580 GeV. These results correspondwith mg̃ ∼ 800 GeV and mq̃ ∼ 1200 GeV.

133

∼0, m∼0 = 60 GeV~∼0χg~
g → qqqqWWχ
χ
1
1

χ
g

0.8
0.7
0.6

1

-1

χ

1

∫ Ldt = 4.71 fb , s=7 TeVSoft Lepton Channel
Expected limit (± 1 σexp )0.5

Observed limit (± 1 σtheory)

1

0.6

1 1

0.9

χ

χ
g

0.7

1

χ

0.8

χ

0.9

X = ( m∼± - m∼0 ) / ( m~ - m∼0 )1 1

1

X = ( m∼± - m∼0 ) / ( m~ - m∼0 )∼0, m∼0 = 60 GeV~∼0χg~
g → qqqqWWχχ
1

Hard Lepton Channel
Expected limit (± 1 σexp )Observed limit (± 1 σtheory)

0.4

0.3

0.3

0.2

0.2

400

-1

0.5

0.4

0.1

∫ Ldt = 4.71 fb , s=7 TeV

0.1
500

600

700

800

900

1000
1100
m~g [GeV]

400

500

600

700

800

900

1000
1100
m~g [GeV]

1 1

χ

0.7
0.6

1

1

χ

0.8

χ

0.9

g

1

X = ( m∼± - m∼0 ) / ( m~ - m∼0 )∼0, m∼0 = 60 GeV~∼0χg~
g → qqqqWWχ
χ
1

0.5

∫ Ldt = 4.71 fb , s=7 TeV-1Hard and Soft Lepton Combined
Expected limit (± 1 σexp )Observed limit (± 1 σtheory)

0.4
0.3
0.2
0.1
400

500

600

700

800

900

1000
1100
m~g [GeV]

Figure C.9: Exclusion limits at 95% CL with the simpliﬁed model gluino pair production with X = (mg̃ −mχ̃± )/(mg̃ − mLSP ) samples ﬁxing the LSP mass at 60 GeV for the soft lepton channel (top-left), hard lepton
1channel (top-right) and combined results (bottom), respectively.

Simpliﬁed SUSY model (g̃-g̃ Pair Production with ﬁxing at mLSP = 60 GeV)
The simpliﬁed model is considered for varying the chargino mass and the LSP mass is ﬁxed at 60 GeV. The soft
lepton channel is sensitive to the small X(= [mχ̃± − mχ̃01 ]/[mg̃ − mχ̃01 ]) region since the mass diﬀerence between
1chargino and neutralino are small. The exclusion limit for the signal samples are shown in Figure C.9. The
soft lepton channel contributes little to exclude the signals since the exclusion limit for the hard lepton channel
extend to large mg̃ region. In the combined result, the exclusion limit reaches the mg̃ ∼ 740 GeV at small X
region and mg̃ ∼ 860 GeV at large X region.

134

~
∼0χ
∼0, x=1/2
q~
q → qqWW χ
1 1

mLSP [GeV]mLSP [GeV]900∫ L dt = 4.71 fb , s=7 TeV-1800

Soft Lepton Channel
Expected limit (±1 σexp)

700

900

~
∼0χ
∼0, x=1/2
q~
q → qqWW χ
1 1∫ L dt = 4.71 fb , s=7 TeV-1800

Hard Lepton Channel
Expected limit (±1 σexp)

700

Observed limit (±1 σtheory)

600

Observed limit (±1 σtheory)600

All limits at 95% CL s

500

500

400

400

300

300

200

200

300

400

500

mLSP [GeV]

100

600

900

700

800

900

1000 1100m~q [GeV]100

All limits at 95% CL s

300

400

500

600

700

800

900

1000 1100m~q [GeV]~∼0χ
∼0, x=1/2
q~
q → qqWW χ
1 1∫ L dt = 4.71 fb , s=7 TeV-1800

Hard and Soft Lepton Combined
Expected limit (±1 σexp)

700

Observed limit (±1 σtheory)600

All limits at 95% CL s

500
400
300
200
100

300

400

500

600

700

800

900

1000 1100m~q [GeV]

Figure C.10: Exclusion limits at 95% CL with the simpliﬁed model squark pair production with X = (mχ̃± −1mχ̃01 )/(mq̃ − mχ̃01 ) = 1/2 samples for the soft lepton channel (top-left), hard lepton channel (top-right) andcombined results (bottom), respectively.

Simpliﬁed SUSY model (q̃-q̃ Pair Production)
The cross sections of q̃-q̃ pair production are smaller than that of g̃-g̃ pair production due to parton distributionfunction. The signal sensitivity in diagonal region for the squark production are larger than the hard lepton
channel as well as gluino production. Figure C.10 shows the exclusion limit at 95% CL on the mq̃ -mLSP plane
and the limit reaches to mq̃ ∼ 320 GeV in such region.

135∼0, m∼0 = 60 GeV~∼0χq~
q → qqWWχ
χ
1
1

χ
q

χ

1

0.7
0.6

1

0.5

∫ Ldt = 4.71 fb , s=7 TeV

0.4

Expected limit (± 1 σexp )

300

400

500

600

-1

700

Hard Lepton Channel
Expected limit (± 1 σexp )0.2

Observed limit (± 1 σtheory)

0.1∫ Ldt = 4.71 fb , s=7 TeV

0.3

Soft Lepton Channel

0.2

0.5
0.4

-1

0.3

200

0.8

1

0.6

1 1

0.9

χ

χ
q

0.7

1

χ

0.8

χ

0.9

X = ( m∼± - m∼0 ) / ( m~ - m∼0 )1 1

1

X = ( m∼± - m∼0 ) / ( m~ - m∼0 )∼0, m∼0 = 60 GeV~∼0χq~
q → qqWWχχ
1

Observed limit (± 1 σtheory)

0.1

800
m~q [GeV]

200

300

400

500

600

700

800
m~q [GeV]

1 1

χ

0.7
0.6

1

1

χ

0.8

χ

0.9

q

1

X = ( m∼± - m∼0 ) / ( m~ - m∼0 )∼0, m∼0 = 60 GeV~∼0χq~
q → qqWWχχ1

0.5∫ Ldt = 4.71 fb , s=7 TeV

0.4

-1

0.3

Hard and Soft Lepton Combined
Expected limit (± 1 σexp )0.2

Observed limit (± 1 σtheory)

0.1
200

300

400

500

600

700

800
m~q [GeV]

Figure C.11: Exclusion limits at 95% CL with the simpliﬁed model squark pair production with X = (mχ̃± −1mχ̃01 )/(mq̃ − mχ̃01 ) samples ﬁxing the LSP mass at 60 GeV for the soft lepton channel (top-left), hard lepton
channel (top-right) and combined results (bottom), respectively.

Simpliﬁed SUSY model (q̃-q̃ Pair Production with ﬁxing at mLSP = 60 GeV)
The exclusion limits for q̃-q̃ production with ﬁxing the LSP mass at 60 GeV are shown in Figure C.11. The
contribution from the soft lepton channel is shown at small X region around mq̃ ∼ 350 GeV. The exclusion
limit reaches to mq̃ ∼ 540 GeV in large X region and mq̃ ∼ 340 GeV in small X for combined result.

136

Appendix D

Electromagnetic Scale Calibration in
Tile Calorimeter
D.1

Introduction

In the summer and autumn of 2004, the combined ATLAS test beam (CTB) took place at CERN beam lineof SPS [73]. This was the ﬁrst time all the detectors in ATLAS were tested together and many of the systems
were ﬁnal production versions. The level-1 trigger, combining signals from the calorimeter and muon system
has also been tested during the test beam.
Our purpose on this analysis is to validate the EM scale by calculating the energy depositions of single muon
par unit length (i.e. dE/dℓ) and comparing the values to the MC predictions with the tile calorimeter. We also
validate the layer inter-calibration. The EM scale validation were already performed by using the cosmic raymuons in 2008, 2009 and 2010 [74]. These results show
• upper limits on the average non uniformity of the response of the cells within a layer that was estimatedto be about 2%.
• the response of the third longitudinal layer of the barrel diﬀers from the ones of ﬁrst and second barrel
layer by about 4 and 3 sigma respectively.
• the diﬀerences between the energy scales of each layer obtained using muons and the value set at test
beams using electrons was found to range between -3% and +1%.
• the stability of the Tile calorimeter response to cosmic rays in the years 2008, 2009 and 2010 was estimatedto be at the level of 1% in the long barrel layer.
The cosmic-ray muons are not projective and a reconstruction of the path in each cell is necessary to
determine dE/dℓ. Their momentum ranges between 10 GeV and 30 GeV. The CTB muons are projective andmonochromatic. They have been used to cross-check the results obtained using cosmic-rays.

D.2

Experimental Setup

D.2.1

CTB setup

The H8 beam line provided hadrons, electrons, muons with energies from 1 up to 350 GeV for the combined
ATLAS test beam. The H8 beam was created by extracting a up to 400 GeV/c proton beam from the Super
Proton Synchrotron. Typical intensity of this primary beam are a few 1012 protons per burst. The secondary
beam created from a Beryllium target and had energies from 10 to 350 GeV. A secondary ﬁlter target, 8 or 16
mm of lead or 1000mm Polyethylene, plus absorber, air or lead, can be placed in the beam to produce a tertiary
beam of “pure” electrons (lead plus air) or pions (Polyethylene plus air).
In this combined ATLAS test beam, several detectors, for example the Scintillators (S1, S2, S3 in FigureD.3), the Beam Chambers (BC0, BC1, BC2 in Figure D.3), Cherenkov Counters were installed on the beamline to obtain beam information. The beam line consisted of a number of magnets, quadrapole and dipoles, forfocusing and bending the particles in order to select the required momentum by controlling the magnet currents.

137

LAr barrel electromagnetic
calorimeter

Pixel
SCT

Figure D.1: Schematic view of the test beam table setup.
η
0.25
0.35
0.45
0.55
0.65

ηmin
0.10
0.19
0.30
0.39
0.39

ηmax
0.41
0.50
0.61
0.70
0.85

TRT

Tile
calorimeter

Figure D.2: Photo of the test beam setup.
ϕmin

ϕmax

0.8836

0.9818

Table D.1: Deﬁnition of calorimeter window

D.2.2

The Tile calorimeter

The ATLAS Tile Calorimeter (TileCal) is the central hadronic calorimeter for the ATLAS detector at the
LHC [75]. Within the ATLAS detector, the tile calorimeter is located outside the liquid Argon calorimeter
between the Liquid Argon electromagnetic calorimeter and the muon system. The detector is divided into
three main sections, a central long barrel (LB) and two smaller extended barrels (EB) on each side. Each tile
calorimeter barrel has three segmented radial sampling layers. The inner most layer is referred to as the A
layer, the middle layer is the BC (or just B in the EB) and the outer most layer is the D layer. For the A andBC layers, the segmentation in ∆η is 0.1. The D layer is larger and each cell spans a range of ∆η = 0.2. Eachbarrel consists of 64 wedges evenly spaced around. The granularity is 0.1. In this study, only a part of the LB
and three wedges with the ϕ direction is used. The reach in terms of pseudo-rapidity η for the LB is from 0.0
to 1.0. Its construction consists of alternating steel and scintillator tiles orientated transversely with respect tothe beam direction. A tile calorimeter cell consists of many steel absorber plates with scintillator sandwichedin between. On the two sides of each scintillating tile, wavelength shifting has been installed that shifts theultraviolet light produced by the scintillator down to the visible light spectrum before delivering the light to a
photomultiplier tube (PMT). The majority of cells are read out by two PMTs for redundancy.

D.3

Reconstruction and Event Selection

D.3.1

Reconstruction

We measure the energy depositions of muons in the tile calorimeter cells with given η and ϕ values. This window
size is deﬁned in Table D.1. The following criteria are used to reconstruct the energy depositions in the tile
calorimeter.
• Select the cell in |E| > 1σnoise , where E and σnoise are the energy depositions in each cell and the electronicnoise, respectively.
• Sum up the cell energies within a given calorimeter window in η (see the Table 1).

138

Figure D.3: Schematic outline of the beam line instrumentation, and also of the ATLAS sub-detector elements.
In this test beam, the scintillators (S1, S2, S3) and beam chambers (BC0, BC1, BC2) were installed. The beamenergy were determined by bending at dipole magnets. The muons ﬁred the muon trigger.

139

D.3.2

Event Selection

For calculating dE/dℓ of minimum ionizing muons, we apply the following selection criteria to the CTB data.
1. Require physics trigger.
2. Require signal from the muon tag scintillator (SMT). The SMT was placed downstream after the ﬁrst
beam dump and its dimensions is 40×40×2.0 cm3 (see Figure D.3).
3. Remove the pile up events.
We remove the events in which the scintillator show high activities, since the pile-up events
cause large energy deposition in the scintillators. Figure D.4 shows the distribution of energy
deposition in the S3 scintillator. We apply 5% truncation to these energy distribution in the
scintillators to cut pile up events.
4. Reject events in which muons point away from the center of beam.
By using beam chamber information, we reject the events in which muons point away from thecenter of beam. Applying this event selection is used the most downstream beam chamber BC2
since we can consider that the position in this beam chamber is near to the hit position on thetile calorimeter surface. Figure D.5 shows the hit distribution of beam muons in the BC2. This
beam proﬁle indicates that the muon hit position were spread to positive x direction by thebending magnet. We then apply 5% truncation to the hit distribution of this beam chamber(BC2).
5. Reject events other than MIP events.
We remove the events in which the tile calorimeter show high activities, since the multi-scattering
events cause large energy deposition in the tile calorimeter. We then apply 1% truncation to
the energy distribution in each layer of the tile calorimeter.

D.3.3

The Monte Carlo simulation

We generate the simulation events to compare with the CTB data as follows,• The CTB was taken place in the beam energy equal to 20GeV, 50 GeV and 100 GeV, η equal to 0.25,
0.35, 0.45, 0.55 and 0.65. Then, in simulation, 10,000 single muon events are generated for each η andbeam energies.
• We assume that the eﬀects from the inner detector is negligible, muons are generated on the inner-surfaceof the Liquid Argon calorimeter (radius = 1400 mm) and injected into the center of a cell reproducing
the experimental situation.
• The beam proﬁle is emulated by smearing along η-direction uniformly between -25 mm and 25 mm frombeam center (see Figure 5).
We consider that the detector geometry has been not changed but the reconstruction algorithm has been changed
from the CTB setup. Then, the MC samples are generated using;• Athena software release version 16.2.1.5• ATLAS geometry version ATLAS-GEO-16-00-00• signal reconstruction used the digitization algorithm which was used in the then CTB setup at 2004

140

102
5% trunremoved10

1
0

50 100 150 200 250 300 350 400 450 500
S3r

Figure D.4: Distribution of the energy deposition in the S3 in ADC channel units. The higher energy deposition
events rejected by applying 5% truncation. The remaining events (MIP-like events) and the rejected ones arein blue and red, respectively.

102

5% trunremoved10

1-50 -40 -30 -20 -10

0

10

20

30

40

50

X [mm]

Figure D.5: Distribution of the x-coordinate of the impact point of the muon in the BC2 chamber. The events
far from beam core are rejected by applying 5% truncation. The remaining events (beam core events) andrejected events are in blue and red, respectively.

141

Data
MC

0.1

0.2

events/0.1/entries

LB-A

events/0.1/entries

events/0.1/entries

0.15

LB-BC

Data

0.15

MC

0.15
LB-D

Data
MC

0.1

0.1
0.05

0.05

0.05

0
0

2

4
6
dE/dl [ MeV/mm ]

0
0

2

4
6
dE/dl [ MeV/mm ]

0
0

2

4
6
dE/dl [ MeV/mm ]Figure D.6: The distribution of dE/dℓ obtained in the LB-A, LB-BC, and LB-D layers using muons withenergy equal to 20 GeV and η equal to 0.25. The data and MC events are shown by ﬁlled circles and solid lines,
respectively. The distributions are normalized to one.

D.4

Results

D.4.1

dE/dℓ distributions

The Figure D.6 shows the dE/dℓ distributions in each layer in the case of muon beams with η = 0.25 and energy= 20 GeV. The path length ℓ is given by ℓ = r cosh(η), where the r is the radius of each cell (r = 300 mm in
LB-A, 840 mm in LB-BC and 380 mm in LB-D, respectively). We estimate the truncated mean ⟨dE/dℓ⟩ byapplying the 1% truncation to these distributions. After that, we apply the constant ﬁt to the distribution oftruncated mean as a function of η.

D.4.2

Data/MC ratios

In Figure D.7, each top ﬁgure shows the dE/dℓ distributions for data and MC events in each η. Each bottom
ﬁgure shows the ratios of dE/dℓ between data and MC events in each η. These ﬁgures are ﬁtted by the constantparameter function since the ratios of (dE/dℓ)data /(dE/dℓ)M C must be constant against η. However, we observe
the large ﬂuctuations in the distributions of ratios in some layers and beam energies. Table D.2 summarizes theresulting ⟨dE/dℓ⟩ of data and MC events, and ratios between them. The reduced χ2 and χ2 -probabilities arealso reported. The ﬁtting results produce bad χ2 probabilities, especially at beam energy equal to 50 GeV and
LB-D. These bad χ2 probabilities indicate that the systematic eﬀects of the measured points are larger than
the statistical ﬂuctuations.
First, we check whether these ratio distributions have η-dependence. We assume that the better χ2 probability are given when we use the events in more center of beam if there is not η-dependence, since the ﬂuctuation

Beam Energy
20 GeV

50 GeV

100 GeV

Layer
LB-A
LB-BC
LB-D
LB-A
LB-BC
LB-D
LB-A
LB-BC
LB-D

dE/dℓ [GeV/m]
Data
1.288±0.009
1.327±0.006
1.381±0.008
1.357±0.010
1.416±0.008
1.463±0.009
1.496±0.009
1.557±0.007
1.591±0.008

dE/dℓ [GeV/m]
MC1.333±0.002
1.375±0.002
1.362±0.002
1.414±0.003
1.473±0.003
1.463±0.003
1.520±0.004
1.598±0.004
1.566±0.004

Ratio
0.966±0.007
0.966±0.005
1.014±0.006
0.958±0.007
0.962±0.006
1.001±0.006
0.983±0.006
0.970±0.005
1.017±0.006

χ2 / NDF
5.18 / 4
11.49 / 45.36 / 4
11.56 / 415.42 / 422.84 / 49.78 / 4
2.19 / 49.81 / 4

Probability
26.9%
2.2%
25.2%
2.1%
0.4%
0.01%
4.4%
70.1%
4.3%

Table D.2: Results obtained applying a constant ﬁt to the experimental and simulated ⟨dE/dℓ⟩ distribution as
a function of η. The results of the ratios are also reported. The last column shows the χ2 probability of theselast ﬁts. Only statistical uncertainties are shown in this table.

142

dE/dl [ MeV/mm ]

1.6
MC

DATA

LB-A

1.5

c 2 / ndfχ4.908 / 4

χc2 / ndf

Prob
p0

0.2968Probp0

1.288 ±
ｱ 0.009208

6.104 / 40.1915
ｱ 0.002455
1.333 ±

1.4
1.3
1.2
c 2 / ndfχ

Data / MC

1.1

Prob
p0

1.05
1
0.95
0.9
0.2

dE/dl [ MeV/mm ]5.182 / 4
0.26910.9665 ±ｱ 0.00714

0.3

0.4

0.5

0.6

0.7
Eta

1.6
MC

DATA

LB-BC

1.5

c 2 / ndfχ

14.08 / 4

c2 / ndf
χ

Prob
p0

0.007046Prob
p0

1.375 ±
ｱ 0.001857

cχ2 / ndfProb
p0

11.49 / 4
0.02157
0.9665 ±ｱ 0.004853

1.327 ±
ｱ 0.00639

5.333 / 40.25481.4
1.3
1.2
Data / MC

1.1
1.05
1
0.95

dE/dl [ MeV/mm ]

0.9
0.2

0.3

0.4

0.5

0.6

0.7
Eta

1.6
MC

DATA

LB-D

1.5

c 2 / ndfχ9.428 / 4

c2 / ndf
χ

Prob
p0

0.05126Prob
p0

1.381 ±
ｱ 0.007872

7.741 / 4
0.10151.362 ±
ｱ 0.002277

1.4
1.3
1.2
cχ 2 / ndf
5.361 / 4Prob0.2523p0
1.014 ±
ｱ 0.006032

Data / MC

1.1
1.05
1
0.95
0.9
0.2

0.3

0.4

0.5

0.6

0.7
Eta

Figure D.7: Each top distribution shows the mean of dE/dℓ distribution in each η obtained using the CTB
data (red points) and the MC samples (blue points) in LB-A, LB-BC, and LB-D, respectively. Each bottom
distribution shows ratios between the mean of dE/dℓ distribution in the data and the mean of dE/dℓ distribution
in the MC samples in the LB-A, LB-BC, and LB-D, respectively.

143

not applied IP
IP < 2σIP < 1σRatio
1.001±0.006
1.013±0.007
1.009±0.010

χ2 /NDF
22.84 /4
17.82 /4
12.98 /4

Probability
0.01%
0.13%
1.1%

Table D.3: Fitting results of the ratios of the dE/dℓ between the data and the MC samples in each η point withthe energy equal to 50 GeV and the LB-D layer.

with the path length become small. Then, for selecting the events in center of beam, we categorize the events
based on the impact point on the tile calorimeter which are calculated to extrapolate track by using the beamchamber information. We check whether the ﬁtting results make improve when we select events more centerof beam. Table D.3 shows these results. In this table, the“not apply IP” means these values are estimated byusing the distributions of ratios applied only the selection criteria. The “IP < 2σ” and the “IP < 1σ” meanthese values are obtained by using the distributions of ratios in the events applied the selection criteria andwithin 2σ and 1σ of the impact point distributions, respectively. Figure D.8 shows the distributions of theratios of dE/dℓ between the data and the MC samples by using the beam core events. These results show thatthe η-dependence does not have a signiﬁcant eﬀect on the dE/dℓ measurement and the χ2 probabilities gives abad value even if we select the more beam core events. Therefore, we conclude that the ratio distributions havelarger ﬂuctuations than the η-dependence in this region.

D.4.3

Non uniformity of cell responses

Since the ﬁtting results show the bad ﬁtting probabilities, we introduce the “non-uniformity” term which accounts for the diﬀerence of cell responses, for example optical contact between the scintillators in the calorimeterand the PMTs. We assume that this diﬀerence causes the large ﬂuctuations of dE/dℓ in data since the cell response is uniform in the MC samples. We measure the ratios between the data and the MC samples by applying
maximum likelihood method with the parameters of non-uniformity sℓ and the mean of ratio distribution µℓ .
We assume that the data/MC ratios follow Gaussian distributions with respect to the mean of the ratio, themaximum likelihood function is given as:

(
)2 
5
ℓ
ℓ
∏
1
1
R −µ

√
√ c
L=
(D.4.1)
exp −ℓ2 + sℓ2 ) 2π2(σσcℓ2 + sℓ2cc=1
where Rcℓ and σcℓ are the mean and the statistical errors of data/MC ratios, respectively. We use Rcℓ and σcℓ , andﬁnd values producing a maximum of L. These results are summarized in Table D.4 and Figure D.9. In LB-BC
and E=20GeV, LB-BC and E=100GeV, the ŝℓ are not able to be derived since the ﬁtting can not converge due
to statistical ﬂuctuations.

Beam Energy
20 GeV

50 GeV

100 GeV

Layer
LB-A
LB-BC
LB-D
LB-A
LB-BC
LB-D
LB-A
LB-BC
LB-D

CTB
µ̂ℓ
ŝℓ
0.966±0.007 0.012±0.007
0.970±0.008- (*)
1.014±0.006 0.003±0.018
0.962±0.012 0.019±0.010
0.965±0.011 0.020±0.010
1.001±0.013 0.026±0.011
0.983±0.005 0.014±0.009
0.970±0.005- (*)
1.015±0.009 0.014±0.008

Cosmicµ̂ℓŝℓ0.968±0.003 0.028±0.003
0.974±0.002 0.020±0.002
1.005±0.003 0.024±0.003

Table D.4: Fitting results of mean of dE/dℓ (µ̂ℓ ) and the ﬂuctuation derived from the non uniformities incell (ŝℓ ), respectively. The cosmic results are also shown. These results are obtained by using the maximum
likelihood function. The (*) means that the minimum value of L can not be calculated since the ﬁt does notconverge due to statistical ﬂuctuations.

144

Figure D.8: Each top plot is the distribution of dE/dℓ as a function of η obtained using the CTB data (redpoints) and the MC samples (blue points). Each bottom plot is the distribution of ratios of dE/dℓ between thedata and the MC samples. All ﬁgures are in LB-BC and E = 50 GeV. The upper ﬁgure shows the results applied
only truncation to the hit position distribution. The center ﬁgure shows results applied truncation to the hit
position and required the events within two sigma of the distribution of the impact point. The lower ﬁgureshows results applied truncation to the hit position and required the events within one sigma of the distributionof the impact point.
145

1.2
LB-A

1.15

Data / MC

1.1
1.05
1
0.95
0.9
0.85
0.8
0.2

0.3

0.4

0.5

0.6

0.7
Eta

1.2
1.15

LB-BC

Data / MC

1.1
1.05
1
0.95
0.9
0.85
0.8
0.2

0.3

0.4

0.5

0.6

0.7
Eta

1.2
LB-D

1.15

Data / MC

1.1
1.05
1
0.95
0.9
0.85
0.8
0.2

0.3

0.4

0.5

0.6

0.7
Eta

Figure D.9: The distribution of ratios between the data and the MC samples and ﬁtting results obtained
applying the Maximum Likelihood Method for the LB-A, LB=BC and LB-D layers , respectively. The beamenergy is equal to 20 GeV.

D.4.4

Systematic uncertainties

We consider the followings as systematic uncertainties which aﬀect the dE/dℓ measurements.
• Pile up• Response uniformity in cell
• Pion contamination
Pile up
When we estimate the uncertainties of the pile up, we change the cut value of truncation from 1% to 10%.
Figure D.10 show the results of ﬁtting to the ratio distributions of dE/dℓ by using the maximum likelihood
method in each value of truncation. In addition, the results for each layer and each truncation value in theenergy equal to 20 GeV are shown in Table D.5. We quote an uncertainty by taking maximum µ̂ℓ diﬀerence
between truncation value. The eﬀect of pile up is estimated to be less than 0.6%, and is smaller than thestatistical ﬂuctuations.
Response uniformity in cellIf the response diﬀers from point by point in one cell, the diﬀerence of cell response aﬀects the measurement ofenergy depositions in layer. We separated three regions in beam by using beam chamber information as Figure
D.12, and estimate this uncertainty by maximum µ̂ℓ diﬀerence between each beam region. This results are
showed in Figure D.13. The systematic uncertainty of response uniformity a cell is estimated to be less than
1.4%, and is smaller than the statistical ﬂuctuations.
146

Truncation

0%
1%
5%

102

10 %

10

1
0

200

400

600

800
ADC [ch]Figure D.10: Distribution of energy deposition in S3 and the region
separated by the truncation at 10%, 5%, and 1%, respectively.

Pion contamination
We check eﬀect of energy ﬂuctuation caused by pion decay in ﬂight by using a toy MC simulation. The
ﬂuctuation of muon energy is estimated to be less than 0.2%. This uncertainty is negligible against the statisticaluncertainty in this CTB data. However we must discuss this contaminations with the beam experts because
this MC condition may have some diﬀerence from the CTB condition.
Summary of systematic uncertainties
We estimate the systematic uncertainties of 1)pile up, 2)response of a cell and 3)pion contamination. As for theﬁrst two item, we do not quote any numbers because the systematic eﬀects are not visible due to the limited
statistics. Then, we are planing to estimate the systematic uncertainties by using MC samples now. In addition,
we have to consider the other sources of systematic uncertainties, for example the beam momentum spread andtruncation of the dE/dℓ.

D.5

Conclusion

We compared the CTB data with the MC events by measuring dE/dℓ. The results show 1)the ﬂuctuations
derived from non uniformity of the cell response are about 2%, 2)the response of the LB-D in the tile calorimeteris diﬀerent from that of the LB-A and LB-BC layer by about 4%. We quote systematic uncertainties tentatively,
but these are need to be revised using MC samples to compensate for statistical shortage. In addition, we haveto estimate any other systematic uncertainties e.g. the beam momentum spread and the eﬀect of truncation ofdE/dℓ. These results are consistent with those of the cosmic-ray analysis [73].

LB-A
LB-BC
LB-D

Data/MC
10% truncation
0.966±0.006
0.969±0.007
1.013±0.010

Data/MC
5% truncation
0.966±0.007
0.966±0.004
1.014±0.006

Data/MC
1% truncation
0.972±0.007
0.967±0.005
1.017±0.006

sys.(%)
0.6%
0.3%
0.3%

Table D.5: Fitting results by using the maximum likelihood method to distributions of ratio of dE/dℓ between
the CTB data and the MC samples applied truncation at 10%, 5% and 1% to each distribution of scintillator.
The diﬀerence of the ﬁtting results are estimated as the eﬀects of systematic uncertainties derived from the pile
up events.

147

1.1
LB-A

Data / MC

1.05
1
0.95
0.9
0.2

0.3

0.4

0.5

0.6

0.7
Eta

1.1
LB-BC

Data / MC

1.05
1
0.95
0.9
0.2

0.3

0.4

0.5

0.6

0.7
Eta

1.1
LB-D

Data / MC

1.05
1
0.95
0.9
0.2

0.3

0.4

0.5

0.6

0.7
Eta

Figure D.11: Fitting results of ratio distributions by using maximum likelihood method in each truncation cut.
The top ﬁgure shows the results in the LB-A, the middle ﬁgure shows in the LB-BC and the bottom ﬁgureshows in the LB-D, respectively. The red points correspond to the results in the 10% truncation, the green
points correspond to the 5% truncation and the blue points correspond to the 1% truncation, respectively.

LB-A
LB-BC
LB-D

Data/MCLeft in beam
0.993±0.019
0.970±0.018
1.010±0.016

Data/MC
Center in beam
0.956±0.008
0.972±0.009
1.012±0.007

Data/MC
Right in beam
0.985±0.014
0.957±0.008
1.026±0.015

sys.(%)
1.4%
1.4%
1%

Table D.6: Fitting results by applying the maximum likelihood method to the data/MC distribution. We
separate the beam into three region to be same number of events in each region. The diﬀerence of the ﬁtting
results are estimated as the eﬀects of systematic uncertainties derived from the diﬀerence of response in a cell.

148

102

10

1
-40

-20

0

20

40
x [mm]

Figure D.12: Distribution of the hit position in BC2 and the region separated
to be the same number of events in each region. We estimate the systematic
uncertainties derived from the diﬀerence of response in a cell.

149

1.1
LB-A

Data / MC

1.05
1
0.95
0.9
0.2

0.3

0.4

0.5

0.6

0.7
Eta

1.1
LB-BC

Data / MC

1.05
1
0.95
0.9
0.2

0.3

0.4

0.5

0.6

0.7
Eta

1.2
LB-D

Data / MC

1.1
1
0.9
0.8
0.2

0.3

0.4

0.5

0.6

0.7
Eta

Figure D.13: Fitting results of ratio distributions by using maximum likelihood method in each region of hit
position in BC2. The top ﬁgure shows the results in the LB-A, the middle ﬁgure shows in the LB-BC and thebottom ﬁgure shows in the LB-D, respectively. The red points correspond to the results in the left region in the
beam position along beam line, the green points correspond to the center region, and the blue points correspondto the right region, respectively.

150

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