学位論文

Observation of Higgs Boson with Di-photon
Events in Proton-Proton Collisions
陽子・陽子衝突を用いたヒッグス粒子の二光子事象の観測

平成 25 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 洋平

Observation of Higgs Boson with Di-photon Events inProton-Proton Collisions
Yohei YamaguchiContents
1 Introduction
1
1.1 Higgs mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1.1 Electroweak uniﬁcation . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.1.2 Electroweak symmetry breaking . . . . . . . . . . . . . . . . . . . . 4
1.1.3 Properties of the Standard Model Higgs boson . . . . . . . . . . . . 7
1.2 Higgs boson physics at the LHC . . . . . . . . . . . . . . . . . . . . . . . . 8
1.2.1 Production and decay of Higgs boson . . . . . . . . . . . . . . . . . 8
1.2.2 Feature of H → γγ events . . . . . . . . . . . . . . . . . . . . . . . 11
1.3 Thesis objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2 LHC and ATLAS detector
2.1 LHC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.1 Injection chain . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.2 LHC ring design . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.3 LHC operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 ATLAS detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.1 Concept of ATLAS detector . . . . . . . . . . . . . . . . . . . . . .
2.2.2 ATLAS coordinate system . . . . . . . . . . . . . . . . . . . . . . .
2.2.3 Magnet system . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.4 Inner detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.5 Calorimeter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.6 Muon spectrometer . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.7 Trigger system . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.8 Luminosity detector . . . . . . . . . . . . . . . . . . . . . . . . . .

17
17
17
17
19
20
20
20
22
23
27
34
37
38

3 Data set and Monte Carlo samples
3.1 Data set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Monte Carlo simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.1 Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.2 Corrections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

40
40
40
40
42

4 Photon reconstruction
4.1 Primary vertex selection for di-photon events . . . . . . . . . . . . . . . . .
4.1.1 Reconstruction of primary vertex candidates . . . . . . . . . . . . .
4.1.2 Primary vertex selection . . . . . . . . . . . . . . . . . . . . . . . .
4.1.3 Eﬃciency of primary vertex selection for di-photon events . . . . .
4.2 Photon trigger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

44
44
44
46
49
49

1

4.3 Photon reconstruction procedure . . . . . . . . . . . . . . . . . . . . . . .
4.4 Photon identiﬁcation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.5 Calibration of photon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.5.1 Calibration hits method . . . . . . . . . . . . . . . . . . . . . . . .
4.5.2 Energy correction in data . . . . . . . . . . . . . . . . . . . . . . .
4.6 Direction of photon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.7 Track isolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.8 Calorimeter isolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

51
52
55
55
58
60
61
62

5 Measurements of photon performance with Z → ℓℓγ
5.1 Event selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.1 Z + jet background . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2 Photon energy scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2.1 Correlation of energy scales between photons and electrons . . . . .
5.2.2 Systematic uncertainty . . . . . . . . . . . . . . . . . . . . . . . . .
5.2.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3 Photon identiﬁcation eﬃciency . . . . . . . . . . . . . . . . . . . . . . . . .
5.3.1 Other data-driven estimation measurements and combination . . .
5.4 Photon conversion fraction . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.5 Isolation eﬃciency estimation . . . . . . . . . . . . . . . . . . . . . . . . .

63
63
64
65
69
70
71
71
74
75
76

6 Event selection and categorization
6.1 Event selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2 Event categorization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2.1 Object selection . . . . . √. . . . . . . . . . . . . . . . . . . . . . . .
6.2.2 VH enriched categories ( √s = 8 TeV) . . . . . . . . . . . . . . . .
6.2.3 VBF enriched categories ( s = 7 and 8 TeV) . . . . . . . . . . . .
6.2.4 Untagged categories . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2.5 Di-photon mass distributions . . . . . . . . . . . . . . . . . . . . .

79
79
82
86
88
92
97
99

7 Signal and background modeling103
7.1 Signal modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
7.1.1 Signal probability density function . . . . . . . . . . . . . . . . . . 103
7.1.2 Signal yield . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
7.2 Background modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
7.2.1 Background composition . . . . . . . . . . . . . . . . . . . . . . . . 110
7.2.2 Fitting function for each event category . . . . . . . . . . . . . . . . 111
7.3 Systematic uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
7.3.1 Signal yield . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
7.3.2 Event migration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
7.3.3 Mass scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
7.3.4 Mass resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
8 Observation of a Higgs boson and measurement of its properties
122
8.1 Observation of a Higgs boson . . . . . . . . . . . . . . . . . . . . . . . . . 122
8.1.1 Statistical method . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
8.1.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
2

8.2 Coupling measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
8.2.1 Statistical method . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
8.2.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
8.3 Mass measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
8.3.1 Statistical method . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
8.3.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
8.4 Direct measurement of natural width . . . . . . . . . . . . . . . . . . . . . 136
8.4.1 Statistical method . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
8.4.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
9 Conclusion

141

A Luminosity determination
145
A.1 µvis measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
A.2 van der Meer scan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
B Electron reconstruction
147
B.1 Reconstruction procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
B.2 Identiﬁcation criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
B.2.1 Electron selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
C Muon reconstruction
149
C.1 Reconstruction procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
C.2 Muon selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
D Jet reconstruction
151
D.1 Reconstruction procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
D.2 Jet vertex fraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
D.3 Uncertainty of jet energy scale . . . . . . . . . . . . . . . . . . . . . . . . . 152
E Event migration summary

154

F Tables of nuisance parameters

159

3

Abstract
A search for the Standard Model Higgs boson with a di-photon ﬁnal state in proton-proton
collisions with the ATLAS detector at the Large Hadron Collider is presented. The data
sample used corresponds to integrated√luminosities of 4.8 fb−1 at center-of-mass energy√s = 7 TeV in 2011 and 20.3 fb−1 at s = 8 TeV in 2012. There is clear evidence forthe production of a Higgs boson in a two photon resonance with a measured mass of
126.8 ± 0.2(stat.) ± 0.7(syst.) GeV on background expectations with the signiﬁcance of
7.4 standard deviations. The Higgs mass, which is an input parameter of the Standard
Model, is measured with 0.6 % accuracy. The measurements of coupling property andnatural width of the Higgs boson are carried out. The measured signal strength (µ), which
is a cross section times branching fraction normalized to the Standard Model prediction,+0.25
is µ = 1.65 ± 0.24 (stat.)(sysy.). The upper limit on natural width of the Higgs−0.18
boson is set to be 1.8 GeV (95%CL). They are consistent with expectations of the Standard
Model Higgs boson.

Chapter 1
Introduction
The Standard Model of particle physics is a theory to describe elementary particles andtheir interactions. Developed in the early 1970s, the Standard Model has successfully
described precisely experimental results below an energy scale of the order of 100 GeV.
All the known matter is made up of elementary fermions called quarks and leptons.
These fermions exchange elementary particles called gauge bosons, which mediate one offundamental interactions. The Standard Model consists of six ﬂavors of quarks and six
ﬂavors of leptons with their corresponding antiparticles, as well as four gauge bosons andone Higgs boson which is the visible manifestation of a Higgs ﬁeld.
Before the Robert Brout, François Englert and Peter Higgs’s work, a theory including
massive bosons which carry interactions was not able to be constructed. However several
experiments veriﬁed the weak force is carried by massive boson. In 1964, they proposeda new theory which is called the Brout-Englert-Higgs (BEH) mechanism or simply Higgs
mechanism [1, 2, 3, 4, 5, 6]. According to their theory, Z and W bosons gain their mass
through electroweak symmetry breaking. The Higgs ﬁeld is introduced in order to breakthe symmetry spontaneously. In addition, the mass of fermions can also be generated by
the interactions with the Higgs ﬁeld. Thus the Higgs ﬁeld is considered as the origin ofmass for all massive elementary particles.
The observation of the Higgs boson conﬁrms the existence of the Higgs ﬁeld, hence itis crucial for the completion of the Standard Model. In addition, the precise measurementof Higgs boson properties represents critical tests of the Standard Model. However theboson was the last unobserved particle predicted by the Standard Model. In the last 50
years, many experiments, particularly at the LEP and Tevatron colliders, have searched
for the Higgs boson; no signiﬁcant signal was observed. A lower bound of 114.4 GeV has
been established at 95 % CL on the mass of the Higgs boson from searches at the LEP[7]. The results from experiments at the Tevatron have excluded the Higgs mass between
100 and 103, as well as between 147 and 180 GeV [8].
The Large Hadron Collider (LHC) at CERN
√enables us to search for new physics at theTeV energy scale. The center-of-mass energy ( s) of the LHC was 7 TeV during 2011, and
8 TeV during 2012 run. The instantaneous luminosity reached 7 × 1033 cm−2 s−1 in 2012.
Four main experiments are equipped with complex detectors which have been installed tocollect and analyze the corresponding collision data. The Higgs boson is studied at twoof them, ATLAS and CMS, which are general-purpose experiments.
In July 2012, CERN announced the discovery of a new boson at the LHC based on

1

combination results in di-photon (H → γγ), ZZ, W + W − , τ + τ − and bb̄ channels [9, 10].
The signiﬁcance was 5.9 standard deviations for the ATLAS experiment, while 5.8 for the
CMS
samplescorresponding to integrated luminosity up to 5.1 fb−1
√ experiment using data√
at s = 7 TeV and 5.8 fb−1 at s = 8 TeV. The nature of the new particle (couplings,
mass and spin) has been studied, and the results show that the new boson has a mass ofabout 125 GeV and is compatible with the Higgs boson predicted by the Standard Model.
The observation of the Higgs boson was conﬁrmed by the Tevatron experiments with alocal signiﬁcance of 3.0 standard deviations [8].
More precise measurements of the properties of this new boson are crucial to elucidate
the mass generation mechanism. The H → γγ channel has great advantages of theproperty measurement. In this thesis, a measurement on the boson in the di-photon
mode alone is presented with the full 2011 and 2012 data set. The coupling properties
and mass measurements are updated, a ﬁrst direct measurement of the natural width ispresented as well.

1.1

Higgs mechanism

The Standard Model describes three interactions, electromagnetic, weak and strong interactions, which are based on the gauge theory [11, 12, 13, 14]. The electromagnetic andweak interactions are sort of uniﬁed in a gauge theory based on the group SU (2) × U (1).
The Higgs ﬁeld is introduced to break the symmetry and generate masses of the weakgauge bosons. The mechanism of mass generation through the spontaneous breaking of
the gauge symmetry is called the Brout-Englert-Higgs mechanism (Higgs mechanism).
The Higgs boson is the visible manifestation of the Higgs ﬁeld.
In the Standard Model, the Higgs boson has neither spin, charge nor color charge.
Because there is no other elementary particle which does not have spin, the Higgs bosonis unique. The fermions, which are grouped into three generations, have spin of 1/2. Eachgeneration contains two quakes and two leptons. Thus there are six quarks (up, down,
charm, strange, top and bottom) and six leptons (electron, electron neutrino, muon, muon
neutrino, tau and tau neutrino). The Standard Model has spin-1 particles which carry theforces between these elementary particles. Photons mediate the electromagnetic force; themassive W + , W − and Z bosons carry the weak force; and eight gluons carry the strong
force.
Quantum electrodynamics Quantum electrodynamics (QED) describes the dynamics
of charged fermions and their electromagnetic interactions. The QED is an abelian gauge
theory with the symmetry group U (1)EM . The law of motion of a free fermion is givenby the Dirac equation for a spinor ψ:(iγ µ ∂µ − m) ψ|free = 0(1.1.1)

where γ µ (µ = 0, 1, 2 and 3) is the four Dirac gamma 4 × 4 matrices. The local gaugetransformation of ψ under U (1)EM writes:ψ → ψ ′ = e−χ(x) ψ2(1.1.2)

where χ is an arbitrary function of space-time coordinates. The requirement of local
gauge invariance has led us to introduce a photon ﬁeld Aµ , which is transformed as:
1
Aµ → A′µ = Aµ + ∂µ χewhere e is elementary charge. The Lagrangian of QED is deﬁned as:(1.1.3)

1
LQED = ψ̄ (iγ µ Dµ − m) ψ − Aµν Aµν(1.1.4)4
where ψ̄ = ψ † γ 0 , Aµν = ∂µ Aν − ∂ν Aµ and Dµ is a covariant derivative Dµ ≡ ∂µ − ieAµ .
The Lagrangian is invariant under the U (1)EM local gauge transformations of ﬁelds. TheAµ ﬁeld is the photon. Hence the Lagrangian has no mass term of Aµ .
Weak interaction The weak interaction only acts on left-handed fermions ψL . Thus
three W i bosons (i =1, 2, 3) of weak isospin triplet of SU (2)L , where the i-th W boson
couples to Pauli matrix τi , are introduced. Left-handed fermions have weak isospin 1/2(doublet) and the right-handed fermions have weak isospin 0 (singlet). For the ﬁrst
generation, this writes:
(
)
(
)
νL
uL
leptons :, (eR ) ,quarks :, (uR ) , (dR )
eL
dL
(
)
(
)
νL
uL
or
is written as ψL . The W + and W − bosons are formed as
eL
dL
)
1 (
(1.1.5)Wµ± = √ Wµ1 ∓ iWµ22
The local gauge transformation of ψL and Wµi under SU (2)L writes:
)
(
i i
′
τ χi (x) ψLψL → ψ L =exp
2
1
Wµi → Wµ′i = Wµi − ∂µ χi + ϵijk χj Wµkg(1.1.6)

where ϵijk , antisymmetric symbol, is the SU (2)L structure constant, and g is the weak√2

coupling constant. The g is expressed in Fermi’s constant GF : GF = 8m2g2 . In contrast,W
right-handed singlets do not rotate under SU (2)L because they have isospin 0. The
following covariant derivative is introduced:
Dµ = ∂µ − ig

τi i
W
2 µ

(1.1.7)

The Lagrangian for weak interaction writes:
1 i
LW = ψ̄L (iγ µ Dµ − m) ψL − Wµν
Wiµν(1.1.8)4i= ∂µ Wνi − ∂ν Wµi + igϵijk Wµj Wνk . The Lagrangian could include the mass terms
where Wµν)(of fermions (mψ̄ψ = m ψ̄L ψR + ψ̄R ψL ) and W bosons (m2W Wµ W µ ). However they are
not invariant under local gauge transformation. Therefore SU (2)L forbids the fermion
and boson mass terms, which are incompatible with experiment results. This is attributed
to the symmetry breaking of SU (2).
3

1.1.1

Electroweak uniﬁcation

In the Standard Model, the electromagnetic interaction and the weak interaction are uniﬁed under an SU (2)L × U (1)Y gauge group and referred to the electroweak interaction.
The corresponding gauge bosons are the three W i bosons which are introduced in theprevious subsection, and the B boson with weak hypercharge of U (1)Y . The corresponding gauge coupling constants for SU (1)Y and U (1)Y are given by g and g ′ , respectively.
These bosons and fermions are massless before symmetry breaking. The Z boson andphoton ﬁeld A are formed by mixing the W 3 and B bosons.
Similarly to QED, B boson couples both to left- and right-handed components ofthe fermion ﬁelds, respectively noted as ψL and ψR . The local gauge invariance underSU (2)L × U (1)Y is obtained by introducing two covariant derivatives:ii
DL µ =∂µ + gτi Wµi + g ′ Y Bµ
22i ′DR µ =∂µ + g Y Bµ2

(1.1.9)which are respectively applied to left-handed and right-handed fermions in the part ofLagrangian describing the electroweak interaction. Y is a hypercharge operator. The
Lagrangian writes:
1 i
1
LEW = iψ̄L γ µ DL µ ψL + iψ̄R γ µ DR µ ψR − Wµν
Wiµν − Bµν B µν
44(1.1.10)where Bµν = ∂µ Bν − ∂ν Bµ . The Lagrangian could include mass terms of bosons such as
m2W Wµ W µ . They are not invariant under the U (1) local transformations of ﬁelds. Sincecharge is conserved, U (1) symmetry is not broken unlike SU (2). Therefore a solution to
the mystery of the mass generation is needed. Hence the Higgs mechanism was proposed.

1.1.2

Electroweak symmetry breaking

A complex scalar ﬁeld ϕ of group SU (2)L , representing the Higgs ﬁeld, is introduced withfour real ﬁelds:
( + )
(
)
1
ϕ
ϕ1 + iϕ2
ϕ==√(1.1.11)ϕ0
2 ϕ3 + iϕ4Then they are added into the Lagrangian of the theory:1
1 iWiµν − Bµν B µν − V (ϕ)
L = (DL µ ϕ)† (DLµ ϕ) − Wµν
44(1.1.12)

where V (ϕ) is the potential of ϕ:()2
V (ϕ) = µ2ϕ ϕ† ϕ + λ ϕ† ϕ

(1.1.13)

The parameters of Eq.(1.1.13) are constrained by λ > 0 so that the ﬁeld is stable. The
Lagrangian is invariant under a local gauge transformation under SU (2)L :
)
(
i i
′
τi χ (x) ϕ(1.1.14)ϕ → ϕ = exp
2
4

Before symmetry breaking

A"er symmetry breaking

V( φ )V( φ )
Gauge transformaon

Gauge transforma!onIm(φ )Im(φ )Re( φ )Re( φ )

Figure 1.1.1: Illustration of the potential before and after the symmetry breaking ofSU (2).
The value of the ϕ at the vacuum is obtained when by minimizing V√(ϕ) (∂V /∂ϕ = 0).
√
In case −µ2ϕ > 0, the V (ϕ) has its minimum value at ϕ0 = v/ 2 = −µ2ϕ /2λ, while incase −µ2ϕ < 0, ϕ0 = 0 gives the minimum of V (ϕ). The v is called vacuum expectation
value. In the former case, the SU (2) symmetry is broken. It is appropriate to expand ϕnear its minimum:
)
)(
(
1
i ′i
0
ϕ = √ exp
τi χ (x)(1.1.15)v + h (x)22where h (x) represents the Higgs boson which is associated with the Higgs ﬁeld. There arethree freedoms for the rotation by χi . A local gauge transition chooses a speciﬁc rotation
angle as:
(
)
1
0
ϕ= √
(1.1.16)
2 v + h (x)then ϕ1 = ϕ2 = ϕ4 = 0 and ϕ3 = v + h (x). The symmetry vanishes by the choice ofthe speciﬁc gauge, that is the symmetry breaking of SU (2). Figure 1.1.1 illustrates thepotential before and after the symmetry breaking. Eq.(1.1.16) is substituted into the
Lagrangian:)2(1
gWµ1 − igWµ2∂µ h + i √ (v + h)L=
−gWµ3 + g ′ Bµ2 2(1.1.17)
1 i
1
µ2
λ
2
4
µν
µν
− Wµν Wi − Bµν B −(v + h) − (v + h)
4
4
2
4
(( )
( )2 )
22†
where | | corresponds to ( ) ( ). The Lagrangian has terms (g 2 v 2 /8) Wµ1 + Wµ2)2(
and (v 2 /8) gWµ3 − g ′ Bµ , which represent mass terms of W and Z bosons. Z boson and5photon ﬁeld A are formed by mixing W 3 and BA=
B cos θW + W 3 sin θW
Z = −B sin θW + W 3 cos θW(1.1.18)

where θW = arctan (g ′ /g) is the electroweak mixing angle, so called Weinberg angle. The
relations between e and g, g ′ are obtained.
e = g sin θW = g ′ cos θW(1.1.19)

From Eq.(1.1.5) and (1.1.18), the masses of W ± and Z are extracted.
mγ =mA = 0
v√ 2
mZ =
g + g ′22v
mW = g2(1.1.20)

Therefore the mass terms for the physical W ± and Z bosons naturally appear throughthe symmetry breaking of SU (2)L . The Aµ ﬁeld does not acquire mass, as no corresponding mass term is found in the Lagrangian. The relation between the Weinberg angle andWboson masses is also obtained: cos θW = m. There is also a term −µ2ϕ h2 = λv 2 h2 , hencemZ
the Higgs boson gains mass itself. The corresponding mass mH is:√√mH = −2µ2ϕ = 2λv(1.1.21)Since λ is a free parameter of the theory, the Higgs mass cannot be predicted within
the Standard Model. After the symmetry breaking, U (1)EM symmetry remain unbroken,
hence photon is massless. From the relation between v, mW and Fermi’s constant GF , thevacuum expectation value is calculated to be [15]:
v=

2mW
1
= √√
≃ 246.22 GeV
g
2GF(1.1.22)

Yukawa coupling As described above, fermion mass terms mψ̄ψ are not invariant
under SU (2)L local gauge transformation. Thus fermion also should be massless before
the symmetry breaking of SU (2)L , and has to have a mass after the breaking. In theStandard Model, the fermion mass is also generated with the Higgs mechanism. It is
possible to use the Higgs ﬁeld to deﬁne Yukawa couplings gf , where f represents a fermion,
into the Lagrangian. For down type fermions, the same ϕ is used. On the other hand forup type fermions, the charge conjugate of the Higgs doublet ϕc is used:( 0∗ )
ϕc∗(1.1.23)
ϕ = iτ2 ϕ =−ϕ+∗ϕc is equivalent to ϕ because they can be connected by a unitary transformation in caseof SU (2)L . Therefore for example for quarks, the following terms are added into the
Lagrangian:
)
]
(
)
] [
(
[
(1.1.24)
Lq = −gd ψ̄Ld ϕψRd + h.c. + −gu ψ̄Lu ϕc ψRu + h.c.
6these terms are gauge invariant before the symmetry breaking. After the breaking ofSU (2)L :
(
)
1
v+h
c
ϕ →√
0
2
(
)
(
)
1
1
h
h
− √ gu vūL uR 1 +(1.1.25)
Lq = − √ gd v d¯L dR 1 +v
v
2
2
In case of leptons, the following terms are added into the Lagrangian before the symmetry
breaking, since neutrinos are massless:and then[()]
Le = −ge ψ̄Le ϕψRe + h.c.

(1.1.26)

and then after the breaking of SU (2)L :)(1h
Le = − √ ge vēL eR 1 +v
2(1.1.27)

The mass of fermion is obtained:1
mf = √ gf v
2

1.1.3

(1.1.28)

Properties of the Standard Model Higgs boson

From the Lagrangian of the Standard Model, the vertex factors are obtained:
Hf f¯ : −i

mf
v

m2W
gµν
v
m2
HZZ : 2i Z gµνvm2
HHH : −3i Hv

HW W : 2i

m2W
gµν
v2
m2
HHZZ : 2i 2Z gµνvm2
HHHH : −3i 2Hv
HHW W : 2i

(1.1.29)

The Higgs couplings are therefore proportional to mf , m2W and m2Z . The Higgs boson also
couples to itself. From the vertex factors, decay widths are calculated of order one [16].
() Nc mH m2f
Γ H → f¯f =8πv 2(

Γ H → W +W

)
−

m3H
=
16πv 2m3H
Γ (H → ZZ) =32πv 2

√

√

(

m2
1−4 W
+ 12
m2H

m2
1−4 W
m2H

m2
1 − 4 2Z
mH

(
)3
m2f 2
1−4 2
mH

(

m2
1 − 4 2Z + 12
mH

7

(

(

(1.1.30)

m2W
m2H

m2Z
m2H

)2 )
(1.1.31))2 )(1.1.32)

α2 m3H ∑Γ (H → γγ) =Nc i e2i Fi
256π 3 v 2i2(1.1.33)

where the terms Nc i e2i Fi are summed for all charged particles, Nc is 1 for leptons andbosons as well as 3 for quarks, α is the ﬁne structure constant and ei is the electric charge
in units of e. The function expression of F depends on the spin of the particle:
F1 = 2 + 3τ + 3τ (2 − τ ) f (τ )F1/2 =−2τ (1 + (1 − τ ) f (τ ))F0 =τ (1 − τ f (τ ))(1.1.34)m2

where 1, 1/2, 0 corresponds to the spin, τ = 4 m2i and
H

(
(
))2
 sin−1 τ − 12
( ( √ ))f (τ ) =− 1 ln 1+√1−τ − iπ 241− 1−τ

if τ > 1(1.1.35)
if τ < 1

If the Higgs mass at 125 GeV is considered, the contributions of t/W loops are calculatedas:
Nc W e2W FW m =125 GeV =8.32
H(1.1.36)
Nc t e2t Ft m =125 GeV = − 1.84
H

1.2

Higgs boson physics at the LHC

1.2.1

Production and decay of Higgs boson

The dominant Higgs boson production processes in proton-proton collisions are gluongluon fusion (ggF), vector boson fusion (VBF), associated production with a W or Z
boson (VH ), or associated production with a pair of top quarks (tt̄H or simply, ttH ).
The leading-order Feynman diagrams for these four processes are represented in Figure
1.2.1. Since the vertex factors to the Higgs boson have mH dependence, the expectedcross sections for these four processes depend on the Higgs√ boson mass, as represented
in Figure 1.2.2 and 1.2.3, at a center-of-mass energy of s = 7 and 8 TeV, respectively.
They are provided by the LHC Higgs Cross Section Working Group [17, 18, 19].
The gluon-gluon fusion has the largest production cross section at the LHC. The
Higgs boson is produced by the annihilation of two gluons through a heavy quark loop.
The loop is dominated by the top quark due to the large Yukawa coupling to the Higgs
boson. The cross section of ggF production process is computed at next-to-next leading
order (NNLO) in QCD with electroweak√ corrections. At mH = 125 GeV, the ggF crosssection is σggF = 15.13 (19.27) pb at s = 7 (8) TeV, which corresponds to 87 % of
the Higgs production. Although the cross section is the largest, thee ggF events tend tohave low signal to background ratio because they do not have high pT particles in theﬁnal states except decay products of the Higgs boson. The vector boson fusion (VBF)
has the second largest cross section at the LHC. The VBF process is written with two
steps: q1 q2 → V V (∗) q1′ q2′ → Hq1′ q2′ . The quarks radiate electroweak bosons, which fuse
8

q
g

W=Z

t; b

H
H

W=Z
q

g

t

g

q

H

W=Z

q

g

H

t

pp →

s= 7 TeV

H (N

NLO

+NN

LL Q

10

CD

+N

LO

EW

)

pp →

1

pp
→

pp
→
ZH

(N

H

NL

O

pp

→

10

(N

NL

O

QC

D

ttH

(NNL

O QC

+N

QC
D
LO

(N

LO

-1

qqH

W

QC

D+N

LHC HIGGS XS WG 2010

σ(pp → H+X) [pb]Figure 1.2.1: Leading order Feynman diagrams of the four main SM Higgs boson production processes: gluon gluon fusion (ggF, top left), Vector Boson Fusion (VBF, top right),
associated production (VH, bottom left) and associated production with a pair of top
quarks (ttH, bottom right).

LO E

W)

+N

LO

EW

)

EW
)

D)

10-2
100

200

300

400 500

1000
MH [GeV]√Figure 1.2.2: Standard Model Higgs boson production cross sections at s = 7 GeV [19].
The cross sections provided by the LHC Higgs Cross Section Working Group [17, 18, 19]
are used, following the ATLAS recommendations.

9

pp →

s= 8 TeV
H (N

NLO

+NN

LL
Q

CD

10

+N

LO
E

LHC HIGGS XS WG 2012

σ(pp → H+X) [pb]

102

W)

pp →

1

10-1

qqH
(NNL
OQ
CD +
NLO
EW)
W
ZH
H
(N
(N
N
NL
LO
O
QC
QC
pp
D
→
D
+
ttH
+N
(N
LO NLO
LO
EW
EW
QC
)
)
D)

pp

→

pp

→

10-2
80 100

200

300

400

1000
MH [GeV]√Figure 1.2.3: Standard Model Higgs boson production cross sections at s = 8 GeV [19].
The cross sections provided by the LHC Higgs Cross Section Working Group [17, 18, 19]
are used, following the ATLAS recommendations.
together and produce the Higgs boson. At the leading order, it is a pure electroweak
interaction. With respect to q1 and q2 , the corresponding outgoing quarks q1′ , q2′ gain atypical transverse momentum around mV /2, where V denotes one of the weak bosons.
Then, these two quarks fragment and hadronize into high energy jets in the forward
and backward direction, respectively. The jets are characterized by a large separation in
rapidity and a large di-jet mass. The VBF cross section is computed at NLO in QCD
including electroweak and approximate NNLO QCD√ corrections. At mH = 125 GeV,
the VBF cross section is σVBF = 1.22 (1.58) pb at s = 7 (8) TeV. The VBF process
is responsible for about 7 % of the Higgs production. The VH processes are genericallycalled Higgs-strahlung, as the Higgs boson is radiated from an oﬀ-shell W ± or Z boson
from quark-antiquark annihilation. In the ﬁnal state, the presence of a weak boson isa distinguishing signature. The VH cross section is computed at NNLO in QCD and
NLO in electroweak corrections. At mH = 125 GeV,
√ the WH and ZH cross sections are
σW H = 0.58 (0.70) pb and σZH = 0.34 (0.42) pb at s = 7 (8) TeV, respectively. The VH
processes are responsible for about 5 % of the Higgs production. The ttH process is similar
to the gluon-gluon fusion process. The Higgs boson is produced by the annihilation of apair of top quarks as shown in Figure 1.2.1. The same order diagrams can be obtained
from the Higgs radiation oﬀ a top quarks. The top decays lead to high jet multiplicity
in the ﬁnal state including two b-jets, or leptons and transverse missing energy. The ttHcross section is computed√at NLO in QCD. At mH = 125 GeV, the ttH cross section is
σttH = 0.09 (0.13) pb at s = 7 (8) TeV. The ttH process is responsible for only 0.6 %of the Higgs production.
The Higgs boson can decay into di-photon via a loop. The dominant contributions are
top and W boson loops as shown in Eq.(1.1.33) and (1.1.36). The Feynman diagrams ofthe three processes involved in the H → γγ decay is shown in Figure 1.2.4. The branching
fractions, as a function of the Higgs boson mass, are represented in Figure 1.2.5. They also
are provided by the LHC Higgs Cross Section Working Group [17, 18, 19]. For H → γγ
branching fraction, all partial widths are calculated as accurately as possible. Then the
10

t; b
W

H

H

W
H

Figure 1.2.4: Leading-order Feynman diagrams of the three processes involved in the
H → γγ decay.
branching fraction is derived from the total width and the di-photon partial width. For
the diphoton partial width, NLO QCD correction and NLO electroweak correction areused. The H → γγ branching fraction is between 1.36 × 10−3 and 2.28 × 10−3 in the range
of mH ∈ [110, 150] GeV. The peak is at around mH = 125 GeV.
Figure 1.2.6 shows the total width of the Higgs boson as a function of the Higgs mass.
If mH is smaller than mW , the total decay width is smaller than 1 GeV. At mH = 125 GeV,
the width is expected to be 4 MeV. Table 1.2.1 summarizes the cross section, branching
fraction, expected number of signal events and total width for several Higgs mass.

1.2.2

Feature of H → γγ events

The signal di-photon decay mode has a clean signature, two high ET photons, therefore
the events can be surely triggered. Hence the eﬃciency of event reconstruction is large(∼ 0.4), and the number of reconstructed events is expected to be signiﬁcantly larger
than other channels even though the branching fraction of di-photon ﬁnal state is smaller
than many other decay modes. Because a trigger to the signal events does not needanything else but decay products of the Higgs boson, the ggF signal is a main channel inthe H → γγ analysis.
Because there is no missing particles in the Higgs decay particles, the Higgs mass canbe reconstructed by the invariant mass of the di-photon (mγγ ). The signal events make a
sharp peak at the Higgs mass on the smoothly falling background in the mγγ distribution.
The di-photon mass is calculated as:√
mγγ = 2E γ1 E γ2 (1 − cos ∆θ)(1.2.1)
where E γ1(2) is energy of a photon and ∆θ is opening angle of two photons. The background events are γ-γ, γ-jet and jet-jet events. In the γ-jet and jet-jet events, jets fakephotons. Because the LHC is the hadron collider, these events have large cross section.
Accordingly, the following three are crucial to discover the Higgs boson by the H → γγ
analysis:
11

bb
gg

ZZ

cc

10-2

1
WW

bb

10-1

ττ

gg

ZZ

cc

10-2

γγ

Zγ

γ γ Zγ

10-3

10-3
µµ

10-480

LHC HIGGS XS WG 2013

WWττ

Higgs BR + Total Uncert

10-1

LHC HIGGS XS WG 2013

Higgs BR + Total Uncert

1

100

µµ

120

140

160

180

10-4 90

200

200

300 400

MH [GeV]1000

MH [GeV]

(a)

(b)

103

LHC HIGGS XS WG 2010

ΓH [GeV]Figure 1.2.5: Standard Model Higgs boson decay branching ratios with mH between 80
and 200 GeV (a) and with a wider range (b) [19].

102
10
1
10-1

10-2
100

200

300

500

1000
MH [GeV]Figure 1.2.6: Total decay width of the Standard Model Higgs boson as a function of the
Higgs mass [19].

12mH
120 GeV 125 GeV 130 GeV√
Cross section at s = 7 TeV [pb]
ggF
16.43
15.13
13.98
VBF
1.279
1.222
1.168
WH
0.66170.57850.5059ZH
0.38080.33510.2957ttH
0.09758
0.08632
0.07660√
Cross section at s = 8 TeV [pb]
ggF
20.86
19.27
17.85
VBF
1.649
1.578
1.511
WH
0.80520.7046
0.6169ZH
0.47100.41530.3671ttH
0.14590.12930.1149Branching fraction
0.00223
0.00228
0.00224√
Expected number of signal events at √s = 7 TeV
203
191
173
Expected number of signal events at s = 8 TeV
1082
1022
929
Total width [MeV]
3.51
4.07
4.91
Table 1.2.1: Cross section of the Higgs boson production, branching fraction to diphoton,
the expected number of signal events and total width for mH = 120, 125 and 130 GeV.
1. Good mass resolution
2. High photon reconstruction eﬃciency
3. Strong photon-jet separation
At the ATLAS experiment, the energy of photons is measured with the electomagnetic(EM) calorimeter. The direction of photons is measured from the position of a primaryvertex where a Higgs boson is produced to the position of energy deposit in the EM
calorimeter. The primary vertex is determined by the inner tracker as well as the EM
calorimeter. The EM calorimeter is used for reconstruction and identiﬁcation of photons.
Thus the excellent performance of the EM calorimeter is essential for the H → γγ analysis.
Thanks to the great performance of the detector, many kinds of property of the Higgs
boson can be measured by the H → γγ analysis. The observed particle should be a bosonand its spin should not be 1 according to the Landau-Yang theorem [20]. The mass of the
new particle can be measured accurately in the H → γγ analysis because of the narrow
mass peak. In addition, the eﬃciencies of event reconstruction are high for all production
processes, the data accumulated in 2011 and 2012 allows to measure the signal yields foreach production process (ggF, VBF and VH ) except for ttH process which has small crosssection. Top-Higgs Yukawa coupling has large contributions to both production process
and decay process. Consequently, the observation of the particle with di-photon channel
provides a supporting evidence of the top-Higgs Yukawa coupling.
The Higgs mass is an input parameter of the Standard Model, hence it has to be
determined by experiments to complete the Standard Model. For example, the production cross section and decay branching ratio of the Higgs boson depend on the Higgs
mass. On the other hand, it is predicted in many beyond the Standard Model (BSM)
theories. Therefore the measurement of the Higgs mass constrains these theories. The
13

Figure 1.2.7: The Standard Model renormalization group evolution (RGE) of λ varying
the top mass M t, the Higgs mass Mh and the strong coupling αs [22].
Supersymmetry (SUSY) is one of the most popular extension of the Standard Model. In
SUSY models, Higgs mass is related to scalar top (stop) mass. For example, the simplest
SUSY extension of the Standard Model, the MSSM, predicts that the tree-level mass of
Higgs is smaller than the Z boson one [21]. The radiative corrections, however, make themass larger, and the largest contribution of the correction comes from stop which is asupersymmetric partner of top quark. In order to correct the Higgs mass up to about 126
GeV, either a contribution of stop mass or large mixing between left and right handedstop is required. The observation of the Higgs boson at∼ 126 GeV favors a heavy stop.
In the Standard Model, the Higgs potential is determined by the Higgs mass as shon in
Eq.(1.1.21). The Higgs potential reveals the stability of vacuum and the dynamics of thesymmetry breaking. They are signiﬁcant hints to BSM. The vacuum stability is studied
with a renormalization group equation (RGE) [22]. When the running of the quartic
Higgs coupling λ is calculated as a function of RGE scale, λ may drop to negative before
the Planck scale depending on the Higgs mass as shown in Figure 1.2.7. In case λ < 0,
the Higgs potential can go to negative inﬁnity as shown in Figure 1.2.8. In this case, thevacuum is not stable. If the vacuum is instable, the existence of new physics before thePlanck scale is proved because the Standard Model is not established at the energy scale.
However even if λ < 0, going to negative inﬁnity need a tunnel eﬀect. If the probabilityof the quantum tunneling is quite low, the vacuum does not go to the false vacuum.
This status is called metastable. According to NNLO analysis of the Standard Model
Higgs potential, the absolute vacuum stability requires the Higgs mass to be larger than
129.4 ± 1.8 GeV [22]. Therefore a precise measurement of mass of the Higgs boson canverify the vacuum stability. Figure 1.2.9 shows regions of absolute stability, metastability
and instability of the vacuum.
The Higgs coupling measurement is a test of the Standard Model. In general, if a new14

V( φ )Im(φ )Re( φ )

Figure 1.2.8: Illustration of the potential when λ < 0.

Figure 1.2.9: Regions of absolute stability, metastability and instability of the Standard
Model vacuum in the top mass and the Higgs mass plane [22].

15physics exists, the eﬀect of a new particle is signiﬁcant in a loop process. Thus couplings tomassless particles, such as gluons and photons, are good probes to study BSM because one
loop processes are leading order. In the H → γγ signal, loop contributions are signiﬁcantin both production and decay processes. The process of 2 gluons to Higgs, which has
the largest contribution to the production process as ggF, is sensitive to colored particles.
Furthermore, the decay of the Higgs boson into diphoton process allows to study a newparticle which has no color charge but electric charge. Thus the di-photon mode has thegreat advantages to BSM studies.
The H → γγ mode is one of the most important discovery channels, and has various
physics motivations.

1.3

Thesis objective

In this thesis, a search for the Higgs boson in the di-photon decay channel alone at the
ATLAS experiment is presented. The data used from proton-proton collisions is morethan doubled
from the observation√paper [9], corresponding integrated luminosities of 4.8√−1
fb at s = 7 and 20.3 fb−1 at s = 8 TeV. In July 2013, the ATLAS collaboration
published results indicating that the observed particle has no spin. Therefore the observed
particle is assumed to be a Higgs boson in this thesis.
This thesis is organized as follows. In the Chapter 2, outlines of the LHC and the
ATLAS detector are described. Because of the importance of the EM calorimeter for the
H → γγ analysis, this subdetector is focused in the chapter. The data set and Monte
Carlo simulation used in this analysis are given in the Chapter 3. The Chapter 4 describes
reconstruction of photons, as well as the primary vertex selection for di-photon eventswith the ATLAS detector. In the Chapter 5, the performance of the ATLAS detector for
identifying and measuring photons is described. In the Chapter 6, the event selection andcategorization of the H → γγ analysis in both 2011 and 2012 data sets are given. Several
event categories are introduced for study of VH process after the observation paper. In
the Chapter 7, the signal and background modeling is discussed including their systematic
uncertainties. The systematic uncertainties are estimated for the signal and backgroundmodels. The Chapter 8 presents statistical procedures and results of the search for the
Higgs boson in di-photon events. The signiﬁcance of observed excess of the Higgs boson
signal is amount to 7.4 standard deviations, which is accomplished by the di-photon mode
alone. Then measurements of the couplings, mass and width of the observed Higgs boson
are described. Finally in the Chapter 9, conclusion of this thesis is given.
As described in Section 1.2.2, high mass resolution, high photon reconstruction eﬃciency and great photon-jet separation are required. In order to satisfy these demands,
I have developed a photon-jet separation technique. This technique provides a strong
separation even in the extreme environment of high instantaneous luminosity. In addition, I have developed a data-driven technique to estimate the performance of the photon
reconstruction with the EM calorimeter. In the LHC, this is the only technique enabling
to obtain very high purity samples of genuine photons. I made a signiﬁcant contribution
on the estimation of the systematic uncertainties. For example, the uncertainty of thephoton identiﬁcation is reduced by considering the correlation between two photons.

16Chapter 2
LHC and ATLAS detector
2.1

LHC

The Large Hadron Collider (LHC) is a two-ring largest energy proton-proton collider withsuperconducting magnets at CERN (European Organization for Nuclear Search). It is
installed in the tunnel of 26.7 km of circumference located underground of about 100 m.

2.1.1

Injection chain

The LHC injecting system is a chain of accelerators that protons are accelerated to increasingly higher energies as shown in Figure 2.1.1. Each machine boosts the energy of abeam, before injecting the beam into the next machine in the chain. The LHC is the lastelement of the chain.
The proton source is a bottle of hydrogen gas. An electric ﬁeld breaks down thehydrogen into its constituent protons and electrons. The protons are accelerated andfocused by a radio frequency quadrupole, and then are sent to the linear accelerator(Linac2). The Linac2 accelerates the protons to the energy of 50 MeV with radio frequency
cavities. The beam is then injected into the Proton Synchrotron Booster (PSB), which isconstructed of synchrotron rings. The PSB contains four superimposed rings with a radiusof 25 meters, and pushes the protons to 1.4 GeV, followed by the Proton Synchrotron(PS). The PS is a synchrotron with a circumference of 628 m, which accelerates the beam
to 25 GeV. Protons are then sent to the Super Proton Synchrotron (SPS) where they areaccelerated to 450 GeV. The SPS, with a circumference of 7 km, is the second largest
machine in the accelerator complex at CERN. The protons are ﬁnally injected to the two
beam pipes of the LHC.

2.1.2

LHC ring design

The LHC ring is designed to collide protons
at the nominal energy of 7 TeV per beam, giv√
ing a total center-of-mass energy of s = 14 TeV. The design luminosity is 1034 cm−2 s−1 ,providing a beam bunch crossing rate of 40 MHz. The beam in one pipe circulates clockwise while the beam in the other pipe circulates anticlockwise. It takes 260 seconds to ﬁlleach LHC ring, and tens minutes for the protons to reach their maximum energy. Beams

17

Figure 2.1.1: The CERN accelerator complex [23].

18Design
2011
2012
Maximum proton energy [TeV]73.5
4
Number of bunches
2808
1380
1380
Bunch length (r.m.s) [cm]
7.55
5.5
4.5
Circumference of ring [m]26658.88
Frequency of bunch crossing [ns]2550
50
Number of interaction point
4
Injection energy [GeV]
450
Number of particles per bunch
1.15 × 1011 1.1 - 1.4 × 1011
1.5 × 1011
Crossing angle [µrad]300
β function at interaction point [m]0.55
1.0 - 1.5
0.6
Normalized emittance [µm]
3.75
2.4
2.4
−2 −1
34
33
Peak luminosity [cm s ]10< 3.65 × 10
< 7.73 × 1033
Table 2.1.1: LHC design and operation parameters [24, 25, 26, 27].
circulate for many hours inside the LHC beam pipes under normal operating conditions.
The design parameters of the LHC ring are summarized in Table 2.1.1.
The LHC ring includes 1232 super-conducting dipole magnets to bend the proton trajectory to the curvature radius of the LHC ring. Those dipoles produce the magnet ﬁeld of
8.33 T. A proton loses energy due to synchrotron radiation when in turns by the magnetic
ﬁeld. The energy loss per turn is 6.7 keV and is recovered by radio frequency cavities
located at one of the straight lines of the ring. Another main role of the radio frequency
cavities is to keep 2808 proton bunches tightly bunched to ensure high luminosity at theinteraction points (IPs). The LHC ring has 4 IPs in which experimental detectors are
installed; ATLAS, CMS, ALICE and LHCb. On upstream of each experiment, beams arefocused by using three superconducting quadrupole magnets. Proton beams are designed
to be focused into transverse radius of 16.7 µm at ATLAS and CMS.

2.1.3

LHC operation

The LHC operation started on September 2008 with 450 GeV proton beams. In 2010, thebeam energy is increased to 3.5 TeV√and delivered L = 48 pb−1 proton-proton collisiondata. In 2011, the LHC performed s = 7 TeV collisions. The peak luminosity was up
to L = 3.65 × 1033 cm−2 s−1 . Compared with the design parameters, the bunch spacing
was reduced to 50 ns, the number of bunches was up to 1380, as well as the β function
at IP (β ∗ ) was 1.5 or 1.0 m. The resulting transverse beam spot size is about 20 µm,
and longitudinal size is about 55 mm. The integrated luminosity delivered by the√ LHC
in 2011 is 5.46 fb−1 [28]. In 2012, the center-of-mass energy was increased to s = 8
TeV. With respect to 2011, the peak luminosity was up to L = 7.73 × 1033 cm−2 s−1 withhelped by decreasing β ∗ to 0.6 m and increasing protons per bunch higher than the design
value. The transverse beam spot size is about 15 µm, and longitudinal size is about 45
mm. The total integrated luminosity delivered in 2012 is 22.8 fb−1 . The LHC operation
parameters are summarized in Table 2.1.1. The data recorded in 2011 and 2012 is used
for analysis in this thesis.

19

2.2

ATLAS detector

2.2.1

Concept of ATLAS detector

The ATLAS (A Toroidal LHC ApparatuS) is a multi-purpose detector constructed at the
LHC. The main target physics of the ATLAS experiment is discovery for the Higgs bosonand new physics beyond the Standard Model, precise measurement for the electroweak
and top quark physics, as well as stringent test of QCD. The ATLAS is designed to adapt
to the extreme LHC running conditions of high instantaneous luminosity and depositedenergy. It covers nearly 4π around the IP and has a small dead time. Thus geometricaland timing acceptance of the ATLAS is very high. The ATLAS has a cylindrical geometry,
which surrounds the beam pipe. The center of the detector is at one of the IPs of the
LHC. The size of the ATLAS is 25 m × 44 m as diameter times length. The huge size
enables precise measurement of muon tracks.
The ATLAS detector consists of four major components: magnet system, inner detector, calorimeter and muon spectrometer. A schematic representation of the detector
and its subsystems is shown in Figure 2.2.1. The complete ATLAS detector is split intoa barrel part, where detector layers are in cylindrical layers around the beam axis, andtwo end-cap parts, where detector layers are located in transverse planes. Table 2.2.1
summarizes the dimensions of the detector. The magnet system for the ATLAS detector
is required to provide optimized magnetic ﬁeld conﬁguration for particle bending aroundthe sub-detectors. It consists of three subsystems:one central solenoid, one barrel toroid
and two endcap toroids. It is designed to minimize multiple-scattering eﬀects. The innerdetector identiﬁes charged particles, and enables precise measurement of their momenta
as well as the reconstruction of their tracks, and of primary and secondary vertices. The
calorimeter is divided into electromagnetic (EM) calorimeter and hadronic calorimeter.
They allow the identiﬁcation of electromagnetic (photon, electron) and hadronic particles
by a reconstruction of their shower shapes and measurement of their energies. The missing
transverse energy is also measured by the calorimeters. The muon spectrometer is locatedat the outermost of the detector. The identiﬁcation of muons and precise measurementof their momenta are performed by the muon spectrometer.
The trigger system is crucial components of the detector. It allows reducing the rateof selected events.

2.2.2

ATLAS coordinate system

The origin of the coordinate system is deﬁned to be the nominal proton-proton interaction
point. The z-axis is set to be the beam direction. The positive direction of z-axis isanticlockwise around the LHC ring. The x-y plane is transverse to the beam direction.
The x-axis is horizontal, while the y-axis is vertical. The positive x values point towards
the center of the ring, and the positive y values point upwards. The azimuthal angle
ϕ is√deﬁned around z-axis, the polar angle θ is the angle from the z-axis and R ≡ x2 + y 2
deﬁnes the polar radius. (E, px , py , pz ) is the four momentum of a particle. The rapidity
y is deﬁned as follows:
1 E + pz
(2.2.1)y ≡ ln2 E − pz

20

Figure 2.2.1: Overview of ATLAS detector [23].

Component
Barrel + endcap inner detector
Central solenoid magnet
Barrel EM calorimeter
Barrel hadronic calorimeter
Barrel toroid magnet
Barrel muon spectrometer
Endcap EM calorimeter
Endcap hadronic calorimeter
Endcap toroid magnet
Endcap muon spectrometer
Forward/backward calorimeter

outer radius [m] length [m]
1.15
6.8
1.32
5.3
2.25
6.42
4.25
12.2
10.05
25.3
11
26
2.25
0.63
2.25
2.25
5.35
5
11
2.8
integrated in endcap

η coverage|η| < 2.4
|η| < 1.4
|η| < 1.0
|η| < 1.4
1.4 < |η| < 3.2
1.5 < |η| < 3.2
1.1 < |η| < 2.8
3.1 < |η| < 4.9

Table 2.2.1: Dimensions of the ATLAS subsystem.

21

Muon spectro metermuon
photonelectron

Hadron calorimeter
EM calorimeter
Solenoid magnet
Inner detectorπ+-Figure 2.2.2: Illustration of barrel of ATLAS subdetectors.
√√
pT ≡ p2x + p2y deﬁnes the transverse momentum, and ET ≡ m2 + p2T is the transverse
energy. The pseudo-rapidity η is deﬁned as:()θη ≡ − ln tan(2.2.2)2
η → ∞ (−∞) when θ → 0 (π) and η = 0 when θ = π2 . The Eq.(2.2.2) is rewritten as
follows:
1 |⃗p| + pz
η = ln(2.2.3)2 |⃗p| − pz
for massless particles, y = η.

2.2.3

Magnet system

The ATLAS detector has the superconductive magnet system. The central solenoid provides an axial magnetic ﬁeld of 2 T for the inner detector. It is located inside the EM
calorimeter [31]. One of the advantages of the small solenoid in the EM calorimeter is acompact design. Another is reduction of the transverse spread of showers. The numberof radiation length of the solenoid is ∼ 0.66 radiation length (X0 ).
The barrel toroid consists of 8 ﬂat superconducting race-track coils. Two endcap
toroidal magnets, located inside the barrel toroid at both ends of the central solenoid.
Each coil of the barrel toroid has an axial length of 25.3 m and extends radially from 4.7
m to 10.05 m. The endcap toroids have a length of 5 m, an outer diameter of 10.7 m andan inner diameter of 1.65. The toroidal magnet ﬁelds enable to measure the momentum
for low-pT muon by bending for θ-direction. Magnetic ﬁeld made by the toroidal magnetic
system is not uniform in ϕ. The toroidal magnetic ﬁeld has not only ϕ component but
also z component. The peak of the magnetic ﬁeld provided by the toroids is 3.9 T by thebarrel toroid and 4.1 T by the endcap toroids. Figure 2.2.3 shows the three-dimensionalview of the magnet system.

22

Figure 2.2.3: Three-dimensional view of the ATLAS magnet system: the central solenoid,
the 8 coils of the barrel toroid and the 2 × 8 coils of the end-cap toroids [31].

2.2.4

Inner detector

The ATLAS Inner Detector (ID) [29, 30] is the innermost sub-detector. It is a tracking
detector providing excellent charge determination and particle momentum resolution capabilities. Primary and secondary vertices which include photon conversion vertices arealso reconstructed by the tracking. The ID also has particle identiﬁcation capabilities,
for example electron and photon separation as described its detail later. Immersed in
the solenoid magnetic ﬁeld, the ID consists of three sub-detectors: Pixel detector, Semiconductor Tracker (SCT) and Transition Radiation Tracker (TRT). Each of them have abarrel and two endcaps, one located on each side of the barrel as shown in Figure 2.2.4.
The total size of the ID is 2.1 m ×6.2 m as diameter times length. It covers |η| < 2.5 andfull azimuthal coverage. Figure 2.2.5 shows an over view of barrel ID. Material distribution
as a function of |η| is shown in Figure 2.2.6.
2.2.4.1

Pixel detector

The Pixel detector is the nearest detector to the beam-pipe with very high granularity followed by the SCT [30]. It consists of three barrel layers and three endcap disks,completing the |η| < 2.5 coverage. Table 2.2.2 summarizes the parameters of the Pixel
detector. The pixel size is 50 × 400 µm. The thickness of the Pixel detector is about 0.025
X0 per layer. The innermost layer is especially important for the separation between electrons and photons. Charge sharing between adjacentpixels improves spatial resolution√
better than the pixel intrinsic resolution (pitch/ 12). The typical position resolution of
the pixel detector is 10 µm in r − ϕ direction and 115 µm in z direction.
2.2.4.2

Semiconductor tracker

The Semiconductor Tracker (SCT) is the middle component of the ID, covering |η| < 2.5[30]. It consists in four layers in the barrel and nine disks in endcaps. An SCT module
consists of two pairs of single-sided silicon microstrip sensors glued back-to-back with a23

Figure 2.2.4: Cut-away view of the ATLAS Inner Detector [32].

Figure 2.2.5: Drawing showing the sensors and structural elements traversed by a charged
track of 10 GeV pT in the barrel inner detector (η = 0.3). The track traverses successively
the beryllium beam pipe, the three cylindrical silicon-pixel layers with individual sensor
elements of 50 × 400 µm2 , the four cylindrical double layers (one axial and one witha stereo angle of 40 mrad) of barrel silicon-microstrip sensors (SCT) of pitch 80 µm,
and approximately 36 axial straws of 4 mm diameter contained in the barrel transitionradiation tracker modules within their support structure [32].

240Radiation length (X )2.5
Services
TRT
SCT
Pixel
Beam-pipe

2
1.5
1
0.5
0
0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5
|η|

Figure 2.2.6: Material distribution (X0 ) at the exit of the ID envelope, including the services and thermal enclosures. The distribution is shown as a function of |η| and averaged
over ϕ. The breakdown indicates the contributions of external services and of individual
sub-detectors, including services in their active volume [32].

Barrel layer 1
Barrel layer 2
Barrel layer 3
Endcap disk 1
Endcap disk 2
Endcap disk 3

Radius [mm] Number of pixels
50.5
13.2 × 106
88.5
22.8 × 106
122.5
31.2 × 106|z| [mm] Number of pixels
495
2.2 × 106580
2.2 × 106650
2.2 × 106

Table 2.2.2: Parameters of the Pixel detector.

25

Layer 1
Layer 2
Layer 3Layer 4

Radius [mm] Length [mm] Rotation [deg]
299
1498
11.00
371
1498
11.00
443
1498
11.25
514
1498
11.25

Table 2.2.3: Parameters of the SCT in barrel.

Disk 1
Disk 2
Disk 3
Disk 4
Disk 5
Disk 6
Disk 7
Disk 8Disk 9|z| [mm]
853.8
934.0
1091.51299.91399.71771.42115.22505.02720.2

Inner R [mm]
337
270
270
270
270
270
337
408
439

Table 2.2.4: Parameters of the SCT in endcaps.
40 mrad stereo rotation angle around the geometrical center of the module. Table 2.2.3
and 2.2.4 summarize the parameters of the SCT. Each of the barrel strip is 126 mm longand the readout units are in 80 µm pitch. In the endcaps, the strips have an active
length between 55 and 120 mm, and the readout pitch has a width between 57 and 90µm depending on the modules. The average design thickness of the barrel SCT is 0.08
X0 , while that of the endcap SCT is 0.3 X0 .
2.2.4.3

Transition Radiation Tracker

The Transition Radiation Tracker (TRT) is the outermost sub-detector of the ID [30].
It is based on the use of straw detectors with diameter of 4 mm, which can operate at
the expected high rates due to their small diameter and the isolation of the sense wires
within individual gas volumes. Each straw is equipped with a 30 µm diameter gold-plated
tungsten wire. The straw tube volume is ﬁlled with the gas mixture of Xe : CO2 : O2 =70 : 27 : 3. A gas gain is 2.5×104 with the high voltage of 1530 V. The length of the straw
is 144 cm in barrel or 39 cm in endcaps. The TRT tubes cover the radius 563 < R < 1066
mm, as well as |z| < 712 mm in the barrel region where the tubes lie along z-direction.
On the other hand, in the endcap region where the straws point toward the R-direction,
straw planes are placed 644 < R < 1004 mm, as well as 848 < |z| < 2710 mm. Thus the
TRT covers |η| < 2. The thickness of the TRT is ∼ 0.3 X0 in barrel and ∼ 0.2 X0 in
endcap.
The TRT provides continuous tracking with many measurements in individual straw
tubes. Typically 36 tracking points are provided by the TRT. It uses not only ionization
but also transition radiation. The X-ray emission depends on the Lorentz boost of theparticle, and therefore on its mass. The output of the X-ray due to the transition radiation
is expected to be larger than ionization for high energy electrons, and hence electrons can
26

Figure 2.2.7: Cut-away view of the ATLAS calorimeter system [32].
be identiﬁed from heavier particles with the number of high-threshold hits in the TRT.
The expected charged pion rejection factor for electron identiﬁcation with using TRT
alone is about 10 for 20 < pT < 40 GeV.

2.2.5

Calorimeter

The calorimeter in ATLAS is composed of electromagnetic (EM) calorimeter and hadronic
calorimeter [33]. The EM calorimeter is designed for the reconstruction and identiﬁcationof photons and electrons, while the hadronic calorimeter is aimed at the identiﬁcation
and reconstruction of hadrons (protons, neutrons, pions, etc.). Both calorimeters∑ coverfull azimuthal angle. The missing and total transverse energies (ETmiss andET ) aremeasured with the calorimeters. They are sampling calorimeters. Therefore they consistof succession of dense material layers (absorber) and active material layers. The former
develops particle shower, while the latter produces an output signal proportional to thedeposit energy. Figure 2.2.7 shows the layout of the ATLAS calorimeter sub-detectors.
The EM calorimeter is constituted of a barrel part (|η| < 1.475) and two endcaps parts(1.375 < |η| < 3.2) of each side. It is located outside of the solenoid. The hadronic
calorimeter is placed outside of the EM calorimeter and is divided into a barrel (|η| < 1.), 2
extended barrels (0.8 < |η| < 1.7), 2 endcaps (1.5 < |η| < 3.2) and 2 forward calorimeters(3.1 < |η| < 4.9) which cover the region closest to the beam.
2.2.5.1

Electromagnetic calorimeter

The EM calorimeter uses liquid argon (LAr) as the active material, kept at a temperature of about 89 K by a cryostat [34]. LAr has natural response linearity, homogeneity,radiation tolerance and slow aging. The LAr ﬁlls the gaps between the sampling layersof absorbers made of lead. The gap between the absorbers are ∼ 4 mm. In the middle
of a gap, three planar layers of copper, which is 275 µm thick, are separated by insulator27η region Lead thickness [mm]0 < |η| < 0.8
1.5
0.8 < |η| < 1.4
1.1
1.4 < |η| < 2.5
1.7
2.5 < |η| < 3.2
2.2
Table 2.2.5: Lead thickness of the EM calorimeter.

Figure 2.2.8: Signal shape as produced in the detector (triangle), and after shaping (curvewith dots). The sampling points, every 25 ns, are shown in dots [34].
layers of kapton. The two outer layers distribute the high voltage of about 2000 V, while
the inner is the electrode that collects the signal. The absorbers are at ground voltage.
The lead thickness in the absorber plates has been optimized as a function of η in termsof the EM calorimeter performance of energy resolution. The thickness is summarized inTable 2.2.5.
In the EM calorimeters, LAr is ionized by secondary particles of the particle showers, resulting in electron-ion pairs drifting under the inﬂuence of an electric ﬁeld. The
ionization signal is collected from the electrodes by capacitive eﬀect. Since LAr has highionization density, great many electron-ion pairs are produced. Another merit of LAr is
the high mobility of the electrons in the LAr. Then the LAr has the small drift time andhence the great detector time response. The total integration of the charge is typically∼ 500 ns. The shape of a current pulse collected at the electrodes as a function of timeis triangular and it is shaped with a bipolar CR·(RC)2 ﬁlter as shown in Figure 2.2.8.
The EM calorimeter has an accordion geometry as shown in Figure 2.2.9. This geometry enables to achieve full coverage in ϕ because of absence of any cracks or deadmaterials. In addition, signal can be extracted fast at the rear or the front of electrodes.
In the barrel, the accordion waves are axial and run in ϕ, the folding angles of the waves
vary with radius in order to keep the gap constant (Figure 2.2.10). On the other hand in
the endcaps, the accordion waves are parallel to R-direction and run axially as shown in
Figure 2.2.11. Since the LAr gap increases with radius in the endcaps, the wave amplitude
and the folding angle of the absorbers and electrodes vary with radius. All these featuresof the accordion geometry lead to a very uniform performance in terms of linearity andresolution as a function of ϕ.
The LAr calorimeter is composed of three layers plus a presampler (Figure 2.2.9). The
1st layer has high granularity along η to identify electrons and photons, and to determine
28

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

00
m

m

4.3X0

15

1.7X0
∆ϕ=0.0245x36.8m 4mx
=147.3 4mm

ϕSquare cells in
Layer 2∆ϕ = 0.0245∆η = 0.025
m/8 =4∆η = 0 .69 mm.0031
Strip cells in Layer 1

37.5m

η

Figure 2.2.9: Sketch of a barrel module where the diﬀerent layers are clearly visible withthe ganging of electrodes in ϕ. The granularity in η and ϕ of the cells of each of the threelayers and of the trigger towers is also shown [32].

Figure 2.2.10: Perspective view of one half of the barrel cryostat [34].

29Figure 2.2.11: Perspective view of one endcap cryostat [34].
the direction of photons. The 2nd layer is long in R-direction (∼ 16 X0 ) and measures themost of energy deposit of electrons and photons. Because photons and electrons deposit
almost all of their energies before reaching to the 3rd layer, the 3rd layer is used for
identiﬁcation of electrons, photons and hadrons with using the ratio of energy deposits
between 2nd and 3rd layers. The presampler, which covers |η| < 1.8, is used to correct
for the energies of electrons and photons lost upstream of the calorimeter. It consists ofa LAr layer of thickness 1.1 cm (0.5 cm) in the barrel (end-cap) region. Thus it does nothave the accordion structure. The 1st and 2nd layer covers |η| < 3.2, the 3rd layer covers|η| < 2.5 and the coverage of the presampler is |η| < 1.8. Table 2.2.6 summarizes the
granularity of each layer. Figure 2.2.12 shows the material distribution of each layer asa function of |η|. The total thickness of the EM calorimeter is more than 22 X0 in thebarrel regions and more than 24 X0 in the endcap region. The layout of the layers with
η is shown in Figure 2.2.13.
The raw output of the calorimeter is longer than the bunch crossing. For making
rise time of the ionization signal fast and minimizing the impact of out-of-time pileup,
which refers to events from successive bunch crossings, the bipolar shaping is applied tothe output pulse. In addition, the output is ampliﬁed in order to suppress thermal noise
eﬀect. As Figure 2.2.10 and 2.2.11 show, the sensitive analog electronics are located on thedetector. Inside the cryostat, the calorimeter electrodes are grouped to form readout cells
and small coaxial cables bring the cell signals to the cold-to-warm cables. Front-end boards(FEB) are mounted near the cold-to-warm cables. The FEB receives the raw calorimetersignals and perform the analog processing, digitization and transmission oﬀ-detector of
the calorimeter signals. Each FEB processes up to 128 calorimeter channels. Figure
2.2.14 shows a block diagram indicating the main features of the FEB architecture. Fourchannel preampliﬁer matches accurately the cable impedance. The preampliﬁer outputs
are coupled into a four channel shaper, which splits each signal into three overlapping,linear gain scales in the ratio 1/10/100, and applies bipolar ﬁlter. The shape of output is30

LayerPresampler
Sampling 1
Sampling 2
Sampling 3

η region Granularity (η × ϕ)|η| < 1.52
0.025 × π/32
|η| < 1.4
0.025/8 × π/32
1.4 < |η| < 1.475
0.025 × π/128|η| < 1.4
0.025 × π/128
1.4 < |η| < 1.475
0.075 × π/128|η| < 1.35
0.05 × π/128
(a)

Layer
|η| region Granularity (η × ϕ)
Presampler
1.5 < |η| < 1.8
0.025 × π/32
Sampling 1 1.375 < |η| < 1.425
0.050 × π/32
1.425 < |η| < 1.5
0.025 × π/32
1.5 < |η| < 1.8
0.025/8 × π/32
1.8 < |η| < 2.0
0.025/6 × π/32
2.0 < |η| < 2.4
0.025/4 × π/32
2.4 < |η| < 2.5
0.025 × π/32
2.5 < |η| < 3.2
0.1 × π/32
Sampling 2 1.375 < |η| < 1.425
0.050 × π/128
1.425 < |η| < 2.5
0.025 × π/128
2.5 < |η| < 3.2
0.1 × π/32
Sampling 3
1.5 < |η| < 2.5
0.05 × π/128
(b)

X0

X0

Table 2.2.6: Granularity of the EM calorimeter (η × ϕ) in barrel (a) and in endcap (b).

40
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

(a)

1.6

1.8

2

2.2

2.4

2.6

2.8
3
3.2
Pseudorapidity(b)

Figure 2.2.12: Cumulative amounts of material, in units of radiation length X0 and as afunction of |η|, in front of and in the electromagnetic calorimeters. The two plots show,in contrast, separately for the barrel (a) and endcap (b), the thicknesses of each accordion
layer as well as the amount of material in front of the accordion [32].

31Figure 2.2.13: Layout of the signal layer for the four diﬀerent types of electrodes before
folding. The two top electrodes are for the barrel and the two bottom electrodes are forthe endcap inner (left) and outer (right) wheels. Dimensions are in millimeters. The
drawings are all at the same scale [32].
Detector
inputsShaperPreamp4

128
channelsT

Analogue
trigger sum

Σ

1
10
100
Σ

SCA

GSEL
M
U
X

144 cells

LSB

SMUX

12

ADC
OpAmp

GLINK
OTx
to ROD

Figure 2.2.14: Block diagram of the Front-end board architecture, depicting the data ﬂow
for four of the 128 channels [32].
shown in Figure 2.2.8.
The shaped signal are then sampled at the design LHC bunch crossing frequency of
40 MHz by four channel switched capacitor array (SCA). The SCA stores the analogue
signals during the L1 trigger latency in pipelines of 144 cells. For events accepted by theL1 trigger, only ﬁve sample points per channel and only one of the three gain scales areread out from the SCA. A gain selector chip (GSEL) is used to select the optimal readout
gain individually for each calorimeter channel. Two dual op-amp chips couple the SCA
outputs to 12-bit ADC which is used for digitization.
The electronics is calibrated cell-to-cell basis. Then an energy scale factor is applied
to all the cells. The linearity of the LAr calibrated response with energy has been demonstrated in the electron test beam [35]. For electrons with E > 20 GeV, the dispersion
from Erec /Ebeam = 1 is within ±0.1 %, where Erec is reconstructed energy and Ebeam isthe energy of test beam. Details on the energy calibration for photons as well as electrons
can be found in Section 4.5.
Since the intrinsic relative resolution of energy deposit in a layer E is proportional to
the number of drift charges N crossing the LAr gaps, it follows a Poisson ﬂuctuation law:
√
1
N
∆E
=
∝√
(2.2.4)E intrinsic
N
E
There are other eﬀects, which aﬀect the resolution. The thermal noise from electronics or
out-of-time pileup events can be parametrized by a relative resolution term proportional32

to 1/E because the noise is independent of energy deposit. In addition, impurities in LAr,
imperfection of detector geometry, temperature gradients, radiation damage, nonlinearities of response, or other sources, have an impact on the relative resolution. Finally, therelative resolution on the shower energy can be parametrized as:∆Eab= √ ⊕ ⊕cE
E E

(2.2.5)where the symbol ⊕ indicates that the two terms are added in quadrature, b is the noise
term√and c is called constant term. The resolution is estimated by test beam: a = 10.1±0.1% · GeV and c = 0.17 ± 0.04 % [35]. The parameter b is not estimated in the beam test
because this term does not have an impact under the condition of beam test. However,
the resolution can be worse due to the many sources such as pileup.
2.2.5.2

Hadronic calorimeter

The barrel and extended barrels of the hadronic calorimeter use tile scintillators which arebuilt from a succession of steel absorbers and doped plastic scintillators, while 2 endcaps
and 2 forward calorimeters use the LAr.
The scintillation light of the tile calorimeter is collected to the PMT through thewavelength shifting ﬁbers. Figure 2.2.15 shows the schematic drawing the tile calorimeter.
The central barrel is 5.8 m in length, 8.5 m in diameter. Each extended barrel is 2.6 m inlength, with inner (outer) radii of 2.28 m (4.5 m). The tile calorimeters are segmented into
three layers in the radial direction, and the cells granularity is between η × ϕ = 0.1 × 0.1(ﬁrst two layers) and η × ϕ = 0.1 × 0.2 (third layer). They cover |η| < 1.7. The expected
jet energy resolution with the tile calorimeter (E in GeV) is:
Tile

∆E
50 %
= √ ⊕ 3%
E expectedE(2.2.6)The hadronic endcap calorimeter is a copper and LAr sampling calorimeter. It covers
1.5 < |η| < 3.2, located behind the endcap EM calorimeters. It consists of two wheels ineach endcap: a front wheel and a rear wheel. The wheels are cylindrical with an outerradius of 2030 mm. The modules of the front wheels are made of copper plates of 25 mm
thick, while the rear wheels use copper plates of 50 mm thick. The gap between the plates
is 8.5 mm thick. The size of the readout cells is η × ϕ = 0.1 × 0.1 for 1.5 < |η| < 2.5and η × ϕ = 0.2 × 0.2 for 2.5 < |η| < 3.2. The expected jet energy resolution with thehadronic endcap calorimeter (E in GeV) is:
HCal Endcap∆E
E expected50 %= √ ⊕ 3%E

(2.2.7)

The forward calorimeter covers over 3.1 < |η| < 4.9. It consists of three modules. The
1st layer consists of copper plates stacked one behind the other. The 2nd and 3rd layers
use tungsten as a absorber. The granularity of the forward calorimeter is shown in the
Table 2.2.7. The expectation for the jet energy resolution with the forward calorimeter(E in GeV) is:
HCal Forward
100 %
∆E
= √
⊕ 10 %(2.2.8)
E expectedE
33

Photomultiplier

Wavelength-shifting fibre
Scintillator

Steel

Sourcetubes

Figure 2.2.15: Schematic drawing the tile calorimeter [32].
η region Granularity (η × ϕ)
3.15 < |η| < 4.30
0.1 × 0.1
3.10 < |η| < 3.15
4 times ﬁner
4.30 < |η| < 4.83
4 times ﬁner
2nd layer 3.24 < |η| < 4.50
3.3 × 4.2
3.20 < |η| < 3.24
4 times ﬁner
4.50 < |η| < 4.81
4 times ﬁner
3rd layer 3.32 < |η| < 4.60
5.4 × 4.7
3.29 < |η| < 3.32
4 times ﬁner
4.60 < |η| < 4.75
4 times ﬁner
Layer
1st layer

Table 2.2.7: Granularity of the forward calorimeter (η × ϕ).
The passage of hadrons in material is characterized by the interaction length λI , which
can be approximated roughly to:
λI ∼ 35 · A 3 g · cm−2
1(2.2.9)The material distribution of the ATLAS calorimeter as a function of λI is shown in
Figure 2.2.16. Because the integral interaction length in front of the hadronic calorimeter
is about 2 λI , the most of energy deposit of hadrons is measured with the hadronic
calorimeter which has a total thickness of about 11 λI .

2.2.6

Muon spectrometer

Muon spectrometer is the outermost part of the ATLAS detector. It is designed to detect
the charged particle which penetrates the calorimeter of the ATLAS, especially muons. It
consists of four detectors, Monitored Drift Tube (MDT), Cathode Strip Chamber (CSC),
Thin Gap Chamber (TGC) and Resistive Plate Chamber (RPC). Purpose of MDT and

34

Interaction lengths

20
18
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

4
4.5
5
Pseudorapidity

Figure 2.2.16: Cumulative amount of material, in units of interaction length, as a functionof |η|, in front of the electromagnetic calorimeters, in the electromagnetic calorimeters
themselves, in each hadronic compartment, and the total amount at the end of the active
calorimetry. Also shown for completeness is the total amount of material in front of theﬁrst active layer of the muon spectrometer (|η| < 3.0) [32].
CSC are precise tracking, meanwhile that of TGC and RPC are ﬁring triggers and providing the bunch-crossing identiﬁcation. Conceptual layout of the muon spectrometer isshown in Figure 2.2.17. The muon spectrometer covers |η| < 2.7.
2.2.6.1

Monitored drift tube

The Monitored drift tube (MDT) consists of many layers of drift tubes. The MDT covers|η| < 2.7 [32]. A diameter of the drift tube, which is made from aluminum, is 29.970 mm.
The tube encloses a Tungsten-Rhenium central conducting wire of 50 µm in radius. The
MDT volume is ﬁlled with a gas mixture of Ar : CO2 : H2 O = 93 :7: < 1000 pm. The
gas pressure is 3 bar and the gas gain is 2 × 104 . The wire is operated at a 3080 V electric
potential. When a muon traverses the tube, the gas is ionized and the potential gradientampliﬁes the ionization signal in the avalanche mode. The spatial resolution per tube of
80 µm, is obtained through the relation between the drift time and drift length of theionization electrons.
2.2.6.2

Cathode strip chamber

The safe operation of the MDT is limited about 150 Hz/cm2 . Then the Cathode strip
chamber (CSC) which is a multi-proportional chamber with radially-oriented wires isinstalled in the region which has the highest counting rate instead of the MDT [32]. The
safe operation limit of CSC is up to 1000 Hz/cm2 . The distance from interaction point to
CSC is about 7 m. Inner radius is 881 mm and outer radius is 2081 mm. Therefore the
CSC covers 2 < |η| < 2.7. Figure 2.2.18 shows the average expected single-plane counting
rates at 1034 cm−2 s−1 .
Anode wires are along radial direction applied high voltage of 1900 V. The diameterof the wires is 30 µm, while the wire pitch is 2.5 mm. Two cathodes are segmented tostrips. One cathode strips is orthogonal to the wires and the other is parallel. The anodecathode spacing is 2.5 mm. The chambers are ﬁlled with gas mixture of Ar : CO2 = 8035

Figure 2.2.17: Cut-away view of the ATLAS muon system [32].
: 20, and the gas gain is 6 × 104 . The position of a track is determined by interpolating
the induced charge of neighboring strips. The charge distribution in the anode allows
the measurement of the position in the bending plane with a 40 µm resolution, while thecharge distribution in the strips yields a 5 mm resolution on the position in the transverse
direction.
2.2.6.3

Thin gap chamber

The Thin gap chambers (TGC) is one of the trigger chambers located in endcaps[32]. It
is a multi-wire proportional chamber with distance of 1.4 mm between wire and cathodewhich is smaller than the distance of 1.8 mm between wire to wire. The gas mixture is
CO2 : n-C5 H12 = 55 : 45. High voltage around the wires and small distance between
wires leads to good time resolution. The TGC is robust against noise due to neutron
and photon background. The spatial resolution of the TGC is between 2 and 6 mm in
R-direction, as well as between 3 and 7 mm in ϕ-direction. The timing resolution is 4 ns.
2.2.6.4

Resistive plate chamber

The Resistive plate chamber (RPC) is located in the barrel and used for trigger system[32].
The RPC is not a wire chamber but a gaseous parallel electrode-plate detector. Is has
two resistive plates which are kept 2 mm apart with insulating spacer. The electric ﬁeldof 4.9 kV/mm is applied between the plates. The electric ﬁeld causes avalanche along
the track of particle towards anode. The RPC volume is ﬁlled with the gas mixture ofC2 H2 F4 : Iso - C4 H10 : SF6 = 94.7 : 5 : 0.3. The position resolution of the RPC is 10
mm in the z- and ϕ-direction. while the timing resolution is 1.5 ns.

36

End-cap
outer
muons

End-cap
middlemuons

Barrel RPC:
outer MDT:
muons

Barrel RPC:
middle MDT:
muons
Barrelinner MDT:
muons

8

10

12

7

9

10
MDT: 6

8

9

13

6

8

11

8

10

End-cap
inner
muons

End-cap toroid

11

MDT: 23
MDT: 40

Tile cal.

LAr cal.

{

MDT: 13
TGC: 17

MDT: 9{

MDT: 32
TGC: 32
MDT: 12

Tile cal.

LAr cal.

Inner det.
FCal

Disk

MDT: 103
TGC: 100

68{MDT:
TGC: 66

CSC: 347

Forwardshielding

Toroid shield.

Noseshield.
TASQUAD

Figure 2.2.18: Average expected single-plane counting rates in Hz/cm2 at 1034 cm−2 s−1
and for various regions in the muon spectrometer [32].
Characteristics
Bunch crossing rate
Interaction rate
ATLAS event size
L1 output rate (decision time)
L2 output rate (decision time)
EF output rate (decision time)
Data output

Value
20-40 MHz
1 GHz
1.5 MB
75 kHz (<2.5 µs)
5 kHz (40 ms)
400 Hz (1 s)
450 MB/s

Table 2.2.8: Typical ATLAS trigger characteristics.

2.2.7

Trigger system

Trigger system is a key component of the ATLAS detector. The trigger is aimed at
the online rejection of the huge background and the eﬃcient selection of processes ofinterest. The ATLAS trigger system is performed in three stages, Level 1 (L1), Level 2(L2) and Event Filter (EF) [36]. Together, the L2 and EF are usually called the HighLevel Trigger (HLT) [37]. Starting from L1, each level makes a decision if the event shouldbe passed or not to the next level, and eventually be saved for oﬄine analysis. L1 trigger
is implemented in the detector and works with the hardware. HLT is using computer andnetwork hardware. L1 is required to make a decision in less than 2.5 µs and to lessen thetrigger rate to about 75 kHz. Then, L2 uses the L1 seed, which is deﬁned as Region ofInterest (RoI). L2 is required to reduce the trigger rate to 5 kHz. Finally, the information
is passed to EF. EF uses the whole detector information and is required to reduce therate up to 400 Hz. The trigger characteristics are summarized in Table 2.2.8.
The L1 trigger looks for high transverse momentum (pT ) muons, photons, electrons,37

Calorimeters

Muon detectors

L1 trigger
Calorimeter triggers

EM



Jet

Muon trigger

Emiss
T

µ

ET

Central trigger
processor

Timing, trigger andcontrol distribution

Regionsof-Interest

Detector front-ends

L2 trigger

DAQ

Figure 2.2.19: Block diagram of the L1 trigger. The overall L1 accept decision is madeby the central trigger processor, taking input from calorimeter and muon trigger results.
The paths to the detector front-ends, L2 trigger, and data acquisition system are shown
from left to right in red, blue and black, respectively [32].
jets, taus decaying∑
into hadrons, large missing transverse energy (ETmiss ) and large totaltransverse energy ( ET ). The diagram of L1 trigger scheme is shown in the Figure 2.2.19.
Muon candidates are identiﬁed using trigger chambers in the RPC and TGC. Electrons,
photons, τ leptons, jets are identiﬁed by the calorimeters with reduced granularity. L1
trigger is made a decision at Central Trigger Processor (CTP). When an event is passed
in L1 trigger, the information for the positions of trigger objects are sent to L2 trigger as
RoI. Another important role of L1 is to identify a bunch crossing of interest.
The RoI builder receives the RoI information from the diﬀerent sources within the L1
trigger and merges them into the single data structure. L2 selection is seeded with RoIs.
Contrary to L1, L2 uses full granularity of the sub-detectors in the RoIs. It reconstructs
the objects quickly with using a cascade of algorithms of increasing complexity and hardened requirements, and rejects the event as soon as no objects are found to pass thecriteria in one of these algorithms. L2 is designed to perform to execute event selection
with an average throughout per farm node of about 300 Hz.
Seeded by L2, at the last stage of the trigger event selection, EF reconstructs the full
event. The EF reconstruction is almost the same as the one at oﬄine analysis. With adecision time between 1 and 4 s, EF is designed to reduce the trigger rate from about 3
kHz to a 300 Hz output, which is limited by data processing and storage capabilities.

2.2.8

Luminosity detector

The Beam Condition Monitor (BCM) detector consists of diamond sensors, which is
divided in 4 small components ∼ 1 cm2 and arranged around the beam pipe [38]. The
two BCMs are at |z| = 184 cm on each side of the interaction point. The BCM detects very
forward signals of inelastic proton-proton interactions around |η| = 4.2. The measured
38signals are used for the luminosity determination (Appendix A) and the average numberof inelastic interactions per bunch crossing µav .

39

Chapter 3
Data set and Monte Carlo samples
3.1

Data setThe√ at√ cumulative luminosity as a function of date is shown−1in Figure 3.1.1.−1 In 2011
s = 7 TeV, the integrated luminosity delivered is 5.48 fb , while 22.8 fb at s = 8
TeV in 2012 [28]. The delivered luminosity accounts for the luminosity delivered from thestart of stable beams until the LHC requests ATLAS to put the detector in a safe standby
mode to allow a beam dump or beam studies. The 93 % of the delivered luminosity wasrecorded with the ATLAS detector. The recorded luminosity reﬂects the DAQ ineﬃciency,
as well as the ineﬃciency of the so-called ”warm start”: when a stable beam ﬂag is raised,
the tracking detectors undergo a ramp of the high-voltage and, for the pixel system,turning on the preampliﬁers. Data collected during stable beam periods in which subdetectors were fully operational are√ used in the H → γγ analysis. The total integrated
luminosity√is 4.8 (20.3) fb−1 for s = 7 (8) TeV analysis. The diﬀerence between thevalue for s = 7 TeV analysis and that (4.57 fb−1 ) shown in the Figure 3.1.1 is due totheused in√ requirement of sub-detectors in data quality criteria. Since muons are not √s = 7 TeV analysis, data quality of the muon spectrometer is not required for s = 7
TeV data.

3.2

Monte Carlo simulation

3.2.1

SamplesMonte Carlo (MC) simulation samples are produced using the several event generators
and a GEANT4 [39] based detector simulation [40]. The energy deposited by particles in
the active detector material is converted into detector signals in the same format as thedetector read-out. The MC events are processed through the GEANT4-based detector
simulation and a trigger simulation and then are reconstructed with the same software as
for the real data. Samples of MC events are employed to model Higgs boson production
and compute signal selection eﬃciencies. Table 3.2.1 lists the event generators. Cross
section normalizations and other corrections (e.g. Higgs boson pT spectrum) are obtained
from calculations in Refs. [9, 17, 18, 19], [48]-[76]. Backgrounds are determined fromdata-driven estimates√√ and MC simulations.
PYTHIA6 (for s = 7 TeV samples) or PYTHIA8 (for s = 8 TeV samples) are used40

Total Integrated Luminosity fb-1

Total Integrated Luminosity fb-1

6
ATLAS

5
4
3

s = 7 TeV
LHC Delivered
ATLAS Recorded
Good for Physics

Total Delivered: 5.46 fb -1
Total Recorded: 5.08 fb -1
Good for Physics: 4.57 fb-1

2
1
0
1/3

1/5

1/7

25
ATLAS Preliminary

20

LHC Delivered
ATLAS Recorded
Good for Physics

15

Total Delivered: 22.8 fb -1
Total Recorded: 21.3 fb -1
Good for Physics: 20.3 fb-1

10
5
0
1/4

1/9
1/11
Day in 2011(a)s = 8 TeV

1/6

1/8

1/10
1/12
Day in 2012(b)

Figure 3.1.1: Cumulative luminosity versus time delivered to (green), recorded by ATLAS(yellow), and certiﬁed√ to be good quality data (blue) during stable beams and for protonproton collisions at s = 7 TeV in 2011 (a) and 8 TeV in 2012 (b) [28].

Process
ggF, VBF
WH, ZH, ttH
q q̄/gg → γγ
γ-jet
jet-jetGenerator
POWHEG [41, 42] + PYTHIAPYTHIASHERPA [43], DIPHOX [44], MADGRAPH [45]SHERPAPYTHIA

Table 3.2.1: Event generators used to model the signal and the main background processes.
“PYTHIA” indicates that PYTHIA6 [46] and PYTHIA8 [47] are used for the simulationsof 7 TeV and 8 TeV data, respectively.

41

Recorded Luminosity [pb-1/0.1]

180

ATLAS Online Luminosity

∫
∫

160

s = 8 TeV, Ldt = 21.7 fb-1, <µ> = 20.7

140

s = 7 TeV, Ldt = 5.2 fb-1, <µ> = 9.1

120
100
80
60
40
20
0
0

5

10

15

20

25

30

35

40

45

Mean Number of Interactions per Crossing

Figure 3.2.1: Distribution of the mean number of interactions per crossing for the 2011
and 2012 data [28].
to generate parton showers and their hadronization, and to simulate underlying events.
Alternatively, HERWIG [77] and JIMMY [78] are used. When PYTHIA6 or HERWIG
are used, PHOTOS [79, 80] is used to provide additional photon radiations from charged
leptons. The following parton distribution function (PDF) sets are used: CT10 [81] for
the POWHEG samples; CTEQ6L1 [82] for the PYTHIA8, MADGRAPH, HERWIG andSHERPA samples; and MRSTMCal [83] for the PYTHIA6 samples. Pileup events, which
are additional soft events overlaid hard interaction, are simulated in MC events by adding
additional inelastic proton-proton collisions. Events from successive bunch crossings arecalled out-of-time pileup, while events occur during the same bunch crossing as the hard
scattering are called in-time pileup.

3.2.2

Corrections

Corrections obtained from measurements in the data are applied to the simulation toaccount for small diﬀerences between data and simulation. The following corrections areapplied: The MC events are reweighted to match pileup condition in data as shown in Figure
3.2.1 The measurement of the average number of interactions µav is described inAppendix A.
 Beam spread is measured with vertices which are reconstructed with the inner detector. The MC events are reweighted such that the MC events have the same spreadas data. The beam spread before reweighting
is 65 mm and after reweighting is 55√(45) mm in simulation samples for s = 7 (8) TeV analysis.
 The shower shape variables of photons in the EM calorimeter in MC is rescaled with
Fudge factors obtained from the comparison between data and simulation to correct
for the diﬀerences [84]. The distributions of shower shape variables are checked in
Section 4.4. The values of Fudge factors are about 1 ± 0.01 depending on variables.
 The photon energies are smeared to account for diﬀerences in resolution between
data and simulation. The smearing has been derived from comparison of the Z → ee

42

peak in data and the MC events as described in Section 4.5.2. Energy or momentum
smearing is also applied to leptons and jets.
The following corrections are additionally applied to the MC events obtained from computing eﬀects which are not taken into account in the simulation.
 The signal gg → H → γγ process is interfered with gg → γγ background because
they have same ﬁnal state [85]. Then the ggF MC events are reweighted based on
the calculation of the interference. The reweighting factor, depending on the Higgs
mass and η of photons, is between 3.8 and 4.5 %.
√ In case of ggF, the MC events for s = 7 TeV analysis are reweighted in orderthat the distribution of the Higgs boson pT matches the one obtained from Hqt2.0
package [86], which is a program to compute√ the pT spectrum of the Standard
Model Higgs boson in hadron collisions. In s = 8 TeV MC, the pT distribution iscorrected with the Hqt2.0 at the stage the MC generation.

43

Chapter 4
Photon reconstruction
The photon reconstruction and identiﬁcation algorithms used in the ATLAS are designed
to achieve both a high eﬃciency for photons with transverse energies above 20 GeV anda high background rejection [87]. The background rejection is quite challenging becauseof the overwhelming majority of photons from neutral hadron decays (main contribution
is π 0 → γγ) or from radiative decays of other particles. Photons from a Higgs boson
are diﬀerent from fake photons due to the neutral hadrons because of the shape of theassociated EM showers and isolation from other particles. In addition, tracks associatedto the showers are used for separation of photons and electrons in order to reject Z → ee
background where electrons fake photons.

4.1

Primary vertex selection for di-photon events

The precise identiﬁcation of the primary vertex from a hard scattering process is crucial
for the H → γγ analysis because the position of the primary vertex is used to calculate
the photon direction,as well as to form jets. However, many inelastic proton-protoninteractions occur in a bunch crossing along the beam spot. A hard collision process ofinterest occurs at most once per beam crossing. The other vertices, called pileup vertex,
obscure the primary vertex. Accordingly, primary vertex candidates are reconstructedby using at least two charged tracks, and one vertex is selected as the primary vertex as
described later.
The beam spot size depends on beam condition such as the β function and the emittance at the interaction point. In 7 TeV runs, the transverse beam spot size σx ∼ σy ∼ 20
µm and the longitudinal beam spot size σz ∼ 55 mm on average. They are σx ∼ σy ∼ 15
µm and σz ∼ 45 mm on average in 8 TeV√ runs. The maximum number of such interactions per bunch crossing is 20 (40) in s = 7 (8) TeV data taking. Figure 4.1.1 shows
an event display under high pileup environment in 8 TeV run where a Z boson candidate
decays into two muons with 25 reconstructed vertices.

4.1.1

Reconstruction of primary vertex candidates

Primary vertex candidates are reconstructed with using tracks in the inner detector.
The tracks are required to be originated from a beam spot. An iterative vertex ﬁnding
algorithm is used [89, 90]:44

Figure 4.1.1: An event candidate of a di-muon decay of a Z boson with 25 reconstructedvertices in 8 TeV run. This event was recorded on April 15th 2012 [88].

45 A vertex seed is obtained from the global maximum in the distribution of the zpositions at the beam line of the reconstructed tracks.
 χ2 is evaluated for each track with the distance between a track and the seed, as
well as the uncertainty of the distance.
 The vertex position is determined using the seed and the tracks around it whichhave χ2 < 7σ.
 Tracks incompatible with the vertex by more than 7σ are used to seed a new vertex.
 This procedure is repeated until no unassociated tracks are left in the ever or no
additional vertex can be found.

The loose requirement χ2 < 7σ is intended to reduce the number of single vertices which
split into two due to the presence of outlying track measurements.

4.1.2

Primary vertex selection

After the reconstruction of vertices, one primary vertex is selected. If charged particles
with high pT are created in the primary vertex such as in Z → ll events, the primaryvertex ∑can be selected with the sum of squared momentum of∑track associated to thevertexp2T . In these events, the primary vertex has the largest
p2T in almost all cases.
However in di-photon events, a primary vertex may not have charged particle with highpT unless additional objects are generated like jets in VBF events. For eﬃcient primaryvertex selection, direction of energy clusters of photons in the EM calorimeter are used
as well as track information.
4.1.2.1

Calo pointing

Shower developments of photons in the EM calorimeter are reconstructed not only with
η − ϕ plane but also R or z direction because the calorimeter has three layers and thepresampler in R direction in barrel and z direction in endcap. The direction of a photon
can be determined with the 3-dimensional shower shape. This is the basic idea of calo
pointing. The material amount of the presampler is so small (0.08 to 0.15 X0 ) that shower
developments tend to start at the 1st layer. Then the presampler is not used for the calo
pointing. Also 3rd layer is not used since shower developments tend to end in the 2nd
layer and the uncertainty of shower shape in the 3rd layer deteriorates the resolution ofγ
the direction. Hence the pseudo-rapidity of photon ηcalo
and the primary vertex position
zcalo are extracted from the 1st and 2nd layers. Figure 4.1.2a illustrates calo pointing.
When the centroids of the energy deposit in the 1st and 2nd layers are reconstructed atγ(z1st , R1st ) and (z2nd , R2nd ) in z-R plane , ηcalo
and zcalo are calculated as:)(z2nd − z1stγ
−1ηcalo = sinhR2nd − R1st
(4.1.1)z1st R2nd − z2nd R1st
zcalo =
R2nd − R1st46

EM calorimeter

3rd
2nd

1st
pre-sampler
Inner detector

track
conversion vertex

Beamprimary vertex candidates(a)primary vertex candidates(b)

Figure 4.1.2: Illustration of calo pointing (a) and zHPV (b).
The resolution of zcalo is shown in Figure 4.1.3a. The distribution has a sharp peakaround 0 and a broad tail. A double Crystal-Ball which has a Gaussian core and powerlaw functions both in high tail and low tail describe the resolution distribution well andis used for ﬁt. The double Crystal-Ball is deﬁned as:
(
)−nR
)n R
(
)(
|αR |2nRnRx−x̄for αR ≤ x−x̄
exp
−
−
|α
|
+

R
2
|αR |
σCB
σCB

 |αR(|)(x−x̄)2
fCB (x) ≡ N × exp − 2σ2for − αL < x−x̄
≤ αR
σCB
CB

( )n L
)−nL
(
)(

2

nL
 nL
for x−x̄
exp − |α2L |− |αL | − x−x̄
≤ −αL
|αL |
|αL |
σCB
σCB
(4.1.2)where σCB is the width of a Gaussiancore
andrepresents
theresolution.
In
Figure4.1.3a,√σCB = 15 mm is estimated for s = 8 TeV analysis.
4.1.2.2

Conversion vertex

When a photon is converted to an electron-positron pair in the inner detector, a conversion
vertex where the electron pair is generated is reconstructed. The conversion vertex isused for the primary vertex selection. When a conversion vertex is reconstructed atγ(zconv , Rconv ) in z-R plane, the pseudo-rapidity of photon ηHPVand the primary vertex
position zHPV are calculated from the straight line between the conversion vertex andthe centroids of the energy deposit in the 1st layer of the EM calorimeter as illustratedγ
in Figure 4.1.2b. Therefore ηHPVand zHPV are obtained with exchanging (z2nd , R2nd ) to(zconv , Rconv ) in Eq.(4.1.1) as:)(
zconv − z1stγ
−1ηHPV = sinh
Rconv − R1st
(4.1.3)z1st Rconv − zconv R1stzHPV =
Rconv − R1st
47

10-2

Calo pointing
Unconverted photon
σcore = 15 mm

s = 8 TeV
ggF, mH = 125 GeV
Simulation

10-2

HPV
Converted photon
σcore = 0.093 mm

s = 8 TeV
ggF, mH = 125 GeV
Simulation

10-3

10-3

10-4

-200

-150

-100

-50

0

50

100

150

200

-2

-1.5

-1

-0.5

zcalo - ztruth [mm]

0

0.5

1

1.5

(a)

(b)

Figure 4.1.3: Comparison between the reconstructed primary vertex of the photon byusing the calo pointing (a) or the calo pointing + conversion vertex (b) and the truth
vertex. ztruth is true z position of the primary vertex
Figure 4.1.3b shows the resolution of zHPV . Compared with using only calo pointing, thehybrid method which uses both calo pointing and conversion vertex implements 1/100
better resolution. This is because the position resolution of the tracker is better than thatof energy cluster, as well as Rconv − R1st ≫ R2nd − R1st . Hence the hybrid method is used
for converted photons.
4.1.2.3

2

zHPV - ztruth [mm]Final primary vertex selection

In addition to calo pointing and conversion vertex, variables of tracks which associate toeach primary vertex candidates,√ as well as the beam spot position are also used for the
primary vertex selection for s = 8 TeV analysis. The primary vertex is ﬁnally identiﬁed
by combining those variables with a neural network based algorithm [91]. Four variables
are input parameters to the algorithm:
 The barycenter of the beam spot and zcalo or zHPV of the two photons. zcalo is used
for unconverted photons, while zHPV is used for converted photons.
∑ 2
 The sum of the squared momentum
pT of tracks associated with each reconstructed vertex∑
 The scalar sum of the momentum
pT of tracks associated with each reconstructedvertex The diﬀerence in azimuthal angle ∆ϕ between the direction deﬁned by the vector
sum of the tracks momenta and the di-photon system.

The neural network algorithm gives scores for each primary vertex candidate and thevertex with
∑ 2 vertex.
√ the highest score is selected as the primarypT of each primary
candidates
For s = 7 TeV analysis, a likelihood with∑vertex2
is used. The likelihood has signal and background templates of thepT . The primaryvertex is selected with combining the output of the likelihood and zcalo or zHPV .
48

Efficiency

Efficiency

1
0.9
0.8

1
0.9
0.8

0.7

0.7

0.6

0.6

0.5
0.4
0.3
0.2
0.1
0
0

0.5

Both unconverted
Neural Net
p2 maxT
Both converted
Neural Net
p2 max

0.4

∑
∑

10

∑

0.3
s=8 TeV
ggF, m = 125 GeV
H
0.3 mm efficiency

0.2

15

20

∑

0.1

T

5

s=8 TeV
ggF, mH = 125 GeV
0.3 mm efficiency
Both unconverted
Neural Net
p2 maxT
Both converted
Neural Net
p2 max

0
0

25

20

40

60

80

T

100 120 140 160 180 200
pγ γ [GeV]# of vertex

T

Figure 4.1.4: The eﬃciency of the primary vertex reconstruction as a function of the diphoton system transverse momentum pγγ
T (left), the number of primary vertices (right).

4.1.3

Eﬃciency of primary vertex selection for di-photon events

Although no threshold is applied to the primary vertex selection for the H → γγ analysis,
the eﬃciency of ﬁnding the primary vertex within 0.3 mm of the true one is used for a
performance
estimation. Figure 4.1.4 shows the eﬃciency in the H → γγ signal samples√
for s = 8 TeV analysis. The overall eﬃciency is 83 %. Converted photons have 10 %larger eﬃciency than unconverted ones because of using conversion vertex. The neuralnetwork based algorithm makes the primary vertex selection more robust against pileupand∑ 2then increases√the eﬃciency 20 % compared to selecting a vertex which has the highest
pT under the s = 8 TeV beam condition. The eﬃciency increases as the di-photon
system transverse momentum increases. This is because when the di-photon system isboosted,∑ 2 ∑ some jets are present in the opposite side then the tracks of the jets increasepT ,pT and ∆ϕ.
The vertex selection is studied in Z → ee decays to compare data and MC by removing
the electron ∑tracks from the events. These events emulate two unconverted photon events.
The highest p2T vertex before electron track removing is used as a reference point insteadof the true vertex.
∑ 2 Before removing the electron tracks, the primary vertex tends to havethe highest
pT due to the electrons from Z boson. In case selecting these vertices, theeﬃciency of ﬁnding the primary vertex within 0.3 mm of true one is about 97 %. We
demonstrate in Figure 4.1.5 that the shapes of eﬃciency curves are very similar as thatof H → γγ samples when both photons are not converted in front of the EM calorimeter(Figure 4.1.4). Although the eﬃciency is slightly low compared with
∑H2 →∑γγ samples
because of the diﬀerence of reference points, diﬀerent distributions of pT ,pT and ∆ϕ
between H → γγ and Z → ee events, Figure 4.1.5 demonstrates the data/MC agreement
very well.

4.2

Photon trigger

As described in Section 2.2.7, the ATLAS trigger system is subdivided in three levels: L1,
L2 and EF. For di-photon events in the H → γγ analysis, di-photon trigger chains are
used.

49

∫

s=8 TeV, Ldt=20.3 fb

0.8

Efficiency

Efficiency

1
0.9

-1

1
0.9
0.8

0.6

0.6

∫
0.3 mm efficiency

0.5

0.5

Neural Net, Data

0.4

0.4

Neural Net, Z→eep2 max, Data

0.3 mm efficiency

0.7

0.3
0.2
0.1
0
0

default∑

p2 max, Z→ee
T

Neural Net, Data
Neural Net, Z→ee
5

0.7

10

2

0.2

T
2

0.1

T

20

0
0

25

-1

∑
∑p max, Z→eedefault ∑p max, Z→ee

0.3

∑p max, Data∑p max, Z→ee

15

s=8 TeV, Ldt=20.3 fb

T
2

2

T

T

20

40

60

80

100 120 140 160 180 200
pee [GeV]# of vertex

T

Figure 4.1.5: The eﬃciency of the primary vertex reconstruction as a function of the diγγ
electron system transverse momentum∑ 2 pT (left), the number of primary vertices (right).
The reference point is the highest
pT vertex before electron track removing. The blackgraph shows∑the eﬃciency of ﬁnding the primary vertex within 0.3 mm of true one when
the highest
p2T vertex before the electron removing is selected.
The photon selection at L1 is based on energy deposit in the EM calorimeter. At L1,
granularity of the calorimeter is reduced to 0.1 × 0.1 in η × ϕ to manage high frequency.
In order to ﬁnd energy clusters, programmable thresholds are applied to the cells. 4 × 4
sliding window is used towards measuring a local energy maximum. If at least one cell inthe 2 × 2 core of the window has√larger energy deposit than the threshold, the information
1of the window is stored . For s = 8 TeV analysis, at least two clusters are required topass 12 GeV threshold and additionally one of them is required to pass higher thresholddepends on η.
From L2, full granularity data 0.025 × 0.025 in η × ϕ is used. L2 is seeded by the L1cluster position and builds 3 × 7 rectangular clusters of cells in the EM calorimeter The
shower shape variables are computed using the 1st and 2nd layer and the 1st layer of thehadron calorimeter. Then L2 imposes the following criteria:
 a lower cut on the transverse energy of the cluster.
 an upper cut on the energy leakage in the 1st layer of hadronic calorimeter.
 a lower cut on the fraction of energy deposit in the 1st layer.
 a lower cut on the lateral leakage (the ratio of the energy in the 2nd layer in the
3 × 7 cluster to the energy in a 7 × 7 cluster).
 a lower cut on the ratio of the diﬀerence between the energies of the two mostenergetic cells to the sum of these two energies.

EF trigger system uses the same tools as the oﬄine selection, but is only seeded by
L2 triggered clusters. Besides, any tracker information is not used for photon EF. Theenergies and shower shapes of photons are computed in the same as oﬄine analysis which1

The outer cells can be used for evaluation of isolation. The cells in the hadron calorimeter behindthe sliding window can be used for hadronic leakage measurement. But they are not used so far.

50

√is described in the following section. For s = 7 TeV analysis, two photon candidates
with ET > 20 GeV are required. On the other hand, E√T > 35 GeV and 25 GeV thresholds
are required to leading and sub-leading photons for s = 8 TeV analysis. The variablesof shower shape are as follow:
 the energy leakage in the 1st layer of hadronic calorimeter (Rhad1 ) (used in |η| < 0.8
and 1.37 < |η|).
 the energy leakage in the all hadronic calorimeter (Rhad ) (used in 0.8 < |η| < 1.37).
 the ratio of the energy in the 2nd layer in the 3 × 7 cluster to the energy in a 7 × 7cluster (Rη ).
√
(
)
∑
2
i E i ηi∑−i Ei

 the lateral width of the shower (w2 ) :∑Eη
∑i i ii Ei

2, where Ei is the energyand ηi is the pseudo-rapidity of cell i and the sum is calculated within a window of
3 × 5 cells.
The eﬃciency of the di-photon trigger for events fulﬁlling the ﬁnal event selection is
extracted from Bootstrap method, where the eﬃciency is determined with using samples√
which is selected by lower threshold trigger [92]. For the di-photon trigger used for s = 7
TeV analysis, a sample passing the 14 GeV ET L1 threshold is used. In the H → γγ
analysis, the photon candidates are required to pass the identiﬁcation criteria which is
described in the following section. Therefore in order to reject fake photon contamination,
the eﬃciency is measured
with respect to the identiﬁed photons.
The estimated eﬃciency√√
is 98.9 ± 0.2 % for s = 7 TeV data and 99.6 ± 0.1 % for s = 8 TeV data [93].

4.3

Photon reconstruction procedure

In the EM calorimeter, photons deposit energy in cells of the EM calorimeter. These cells
are clustered and used as a seed for reconstruction. There are three steps in the photon
reconstruction as follows [87].
Clustering The transverse energies in cells are summed in the η × ϕ = 0.075 × 0.125
window, which corresponds to 3 × 5 cells, as a function of the window position (η andϕ). A window with the local maximum transverse energy deposit with ET > 2.5 GeV isobtained as a seed.
Track matching Track information is used for photon/electron separation and photon
conversion reconstruction.
A Track with pT > 0.5 GeV is matched to a clustering window if the track and thecluster are generated from the same charged particle. For the track-to-cluster matching, a
track trajectory is extrapolated to the 2nd layer of the EM calorimeter. Thus ∆η and ∆ϕare calculated with the extrapolated point and the barycenter of a cluster. The track-tocluster matching requires ∆η < 0.05 and ∆ϕ < 0.05 on each side and ∆ϕ < 0.1 on the side
where the bremsstrahlung losses are expected during the track extrapolation. A cluster
which has no matched track is reconstructed as an unconverted photon candidate. On the51other hand, a photon which is converted to an electron-positron pair in the inner detector
is reconstructed as a converted photon. The converted photons are required to have atleast one matched track. However, because the energy deposit of electrons are clusteredand the clusters have matched tracks, separation of converted photons and electrons isneeded.
For converted photons, conversion vertices, where an electron-positron pair is produced, are reconstructed in the inner detector. Conversion vertices with two tracks arereconstructed by performing a constrained vertex ﬁt with using the track parameters of
the two participating electrons under the condition that the photon is a massless particle. If both of tracks are matched to window clusters, these objects are reconstructed
as double-track converted photons. By contrast, sometimes one of the two produced electron tracks failed to be reconstructed. This occurs when one of them is too soft to bereconstructed, or when the two tracks are too close to be distinguished. In this case, aconversion vertex with one electron track is reconstructed at a point of the ﬁrst measurement of the participating track. The conversion vertex is required to be out the innermost
layer of the Pixel detector. Consequently, in the same way as the double-track converted
photons, these objects are reconstructed as single-track converted photons if the track ismatched to a window cluster. When a cluster is not reconstructed unconverted photons
or converted photons, it is reconstructed as electrons. The track matching is illustrated
in Figure 4.3.1.
Re-clustering Finally re-clustering is applied to photon candidates. The clustering
window is centered on the energy barycenter deﬁned by the previous cluster. In the endcapof the EM calorimeter, the window size is ∆η × ∆ϕ = 0.125 × 0.125 which corresponds
to 5 × 5 cells. In the barrel of the EM calorimeter, 3 × 5 window is used for unconverted
photon candidates, while 3×7 for converted photon candidates because the magnetic ﬁeld
bents the conversion track trajectories in ϕ direction.

4.4

Photon identiﬁcation

Reconstructed photon candidates are contaminated with QCD jets. Genuine photons
have more localized energy deposit than jets. Therefore the jets are rejected by photon
identiﬁcation based on the shower shape in the calorimeter. The jets include less interactive particles than photons in the EM calorimeter, hence they have larger longitudinal
leakage to the hadronic calorimeter. Fake photons due to jets have wider shower shapethan photons because π 0 decays produce two photons and because other particles in thejets have energy deposits in the EM calorimeter. Figure XXX illustrates the diﬀerenceof shower shapes between photons and π 0 . The 1st layer of the EM calorimeter has theﬁne granularity in η (Table 2.2.6), and then the shower width in the 1st layer has strong
rejection power to π 0 decays. Based on these diﬀerences of shower shape, ten variables
are computed with energy cluster of photon candidates as shown in Table 4.4.1. The
variables of shower shape in MC are rescaled with Fudge factors to agree with those indata.
The distribution of the ten variables are shown in Figure 4.4.2 and 4.4.3 with using
Z + γ events. High purity photon sample in Z → llγ events is labeled as FSR, while fakephoton enriched sample is labeled as ISR. The photon purity in the ISR sample is 8.4 %52

Hadron calorimeter
EM calorimeter

Unconverted
photonElectronenergy deposit

Solenoid magnet
Inner detector(Pixel, SCT, TRT)
Beam
2-track
Converted
photon1-track
Converted
photonconversion vertex

Figure 4.3.1: Illustration of track matching.

3rd

2nd

1st
pre-sampler
π0

photonz

Figure 4.4.1: Illustration of diﬀerence of shower shapes between photons and π 0 .

53Category
Description
Hadronic leakage Ratio of ET in the ﬁrst sampling of the hadronic
calorimeter to ET of the EM cluster(used in |η| < 0.8 and 1.37 < |η|)Ratio of ET in all the hadronic calorimeter to ET of
the EM cluster (used in 0.8 < |η| < 1.37)
EM 2nd layer
Ratio in η of cell
7 × 7 cells√energies in( 3 × 7 versus
)
∑
∑
2
2
Eη
i Ei ηi∑
Lateral width:− ∑i Ei i i
Ei

Rhad

Ratio in ϕ of cell energies in 3 × 3 versus 3 × 7 cells
Showerwidth for three strips around maximum strip
√

Rϕ
ws3

i

EM 1st layer

i

∑3

2
max ) Eii (i−i
∑3
i Ei

Name
Rhad1

Rη
w2

(imax is the maximum strip index)

Total√ ∑ lateral2 shower width

wstot

) Ei
i (i−i∑ max
i Ei

Fraction of energy outside core of three central strips Fside
but within seven strips
Diﬀerence between the second largest energy of the∆Estrip and the the smallest energy of the strip between
the two leading strips
Ratio of energy diﬀerence between the ﬁrst andEratiothe second maximum to total energy
E1max −E2max
E1max +E2max

Table 4.4.1: Variables for photon identiﬁcation to reject fake photons due to π 0 → γγ.

54

Variable Unconverted photons Converted photons
Rhad1< 0.02 for ET < 80 GeV< 0.01825 for ET > 80 GeVRη> 0.92Rϕ> 0.93> 0.57w2< 0.011
wstot
< 3.0
< 2.8
ws3
< 0.67< 0.73Fside< 0.28< 0.33∆E< 0.18 GeV< 0.16 GeV
Eratio> 0.80> 0.85Table√ 4.4.2: Thresholds for shower shape variables used to identify photons in |η| < 0.6
for s = 8 TeV analysis.
√in s = 8 TeV data. The deﬁnitions of these samples are described in Section 5.1. The
shower variables in MC are rescaled with the Fudge factors obtained from the comparison
between data and MC. Before the correction, the shower depth in MC is narrower thanthat in data. After rescaling with the Fudge factors in MC, the photon shower shapes
in data and MC agree well. Compared with fake photons, genuine photons have narrow
width and√ small leakage from the EM calorimeter as expected.
For s = 7 TeV analysis, a neural net based identiﬁcation is used. The ten variables
are used as input parameters
to the neural net. The neural net is trained in single photon√
MC simulation. For s = 8 TeV, because the pileup condition is high, the neural net
based identiﬁcation
has large systematic uncertainty. Accordingly, cut based criteria are√used for s = 8 TeV. The cut thresholds are optimized in |η| bin, while no photon ET
dependence is introduced except for the hadronic leakage. Table 4.4.2 shows the thresholds
for the shower shape variables for photons in |η| < 0.6 as an example.

4.5

Calibration of photon

Energies of photons and electrons are measured by the EM calorimeter with the cluster
window. However particles deposit their energy not only in the active medium of the
EM calorimeter but also out of clusters as well as in dead material. These energy losses
are corrected in both data and MC with Calibration hits method. The remaining energy
diﬀerence between data and MC is corrected with comparison of Z line shapes.

4.5.1

Calibration hits method

This method is based on MC based studies of energy deposits in both the uninstrumented
and instrumented parts of the detector. It uses the cluster position and shower shapein the EM calorimeter. Through the correction, ﬁve corrections are applied: energy loss
in front of the calorimeter, sampling fraction, lateral and longitudinal leakage, as well as
energy modulation. The energy is reconstructed with the following formula:
E = Efront + EAcc × Fsampling × Flongitudinal × Flateral × Fmod
55

(4.5.1)

10
1

FSR Data
FSR MC w/o FF
FSR MC w FF

10
Genuine photons
Genuine photons

ISR Data

Fake photons
Fake photons

1

∫

10-3

10-4

10-4

0.05

0.1

0.15

FSR Data / MCFSR Data / MC

10-3

0.2

-1

s = 8 TeV, Ldt = 20.3 fb

10-1
10-2

0

Fake photons
Fake photons

∫

-1

10-2

2.5
2
1.5
1
0.5
-0.05

Genuine photons
Genuine photons

ISR Datas = 8 TeV, Ldt = 20.3 fb
10-1

FSR Data
FSR MC w/o FF
FSR MC w FF

2.5
2
1.5
1
0.5
-0.05

0

0.05

0.1

0.15

0.2

Rhad1

1

10-1

FSR Data
FSR MC w/o FF
FSR MC w FF

Genuine photons
Genuine photons

Rhad

Fake photons
Fake photons

1

ISR Data

FSR Data
FSR MC w/o FF
FSR MC w FF

Genuine photons
Genuine photons

Fake photons
Fake photons

ISR Data

∫

∫

10-1

-1

10-2

10-3

10-3

10-4

10-4

2.5
2
1.5
1
0.5
0.7

0.75

0.8

0.85

0.9

0.95

1

1.05

FSR Data / MCFSR Data / MC

10-2

1.1

-1

s = 8 TeV, Ldt = 20.3 fb

s = 8 TeV, Ldt = 20.3 fb

2.5
2
1.5
1
0.5
0.006

0.008

0.01

0.012

0.014

0.016

0.018

1

10-1

FSR Data
FSR MC w/o FF
FSR MC w FF

1
Genuine photons
Genuine photons

Fake photons
Fake photons

ISR Data

10

∫

0.02
w2

Rη

-1

-1

s = 8 TeV, Ldt = 20.3 fb

FSR Data
FSR MC w/o FF
FSR MC w FF

Genuine photons
Genuine photons

Fake photons
Fake photons

ISR Data∫-1

s = 8 TeV, Ldt = 20.3 fb
10

-2

10-2
10-3
10

-3

2.5
2
1.5
1
0.5
0.5

0.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

FSR Data / MCFSR Data / MC

10-4

1

2.5
2
1.5
1
0.5
0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9
w s3

Rφ

√
Figure 4.4.2: Shower shape variables for the photon identiﬁcation in s = 8 TeV data.
FF means rescaled with Fudge factors. In the ratio plots, FSR events in data and rescaled(pink) or not-rescaled (lightgreen) MC are compared.

56

1

FSR Data
FSR MC w/o FF
FSR MC w FF

Genuine photons
Genuine photons

Fake photons
Fake photons

ISR Data

10-2

10-2

10-3

10-3

10-4

10-4

1

2

3

4

Genuine photons
Genuine photons

Fake photons
Fake photons

5

6

∫

10-1

FSR Data / MCFSR Data / MC-1s = 8 TeV, Ldt = 20.3 fb

2.5
2
1.5
1
0.5
0

FSR Data
FSR MC w/o FF
FSR MC w FF
ISR Data

∫

10-1

1

7

2.5
2
1.5
1
0.5
0

-1

s = 8 TeV, Ldt = 20.3 fb

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

w tot

1

10-1

FSR Data
FSR MC w/o FF
FSR MC w FF

1
Genuine photons
Genuine photons

Fake photons
Fake photons

ISR Data

∫

1
Fside

10-1

-1

s = 8 TeV, Ldt = 20.3 fb

FSR Data
FSR MC w/o FF
FSR MC w FF

Genuine photons
Genuine photons

Fake photons
Fake photons

ISR Data∫-1

s = 8 TeV, Ldt = 20.3 fb

10-2
10-2
10

-3

10-3

2.5
2
1.5
1
0.5
0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

FSR Data / MCFSR Data / MC

10-4

2

∆ E [GeV]

10-4
2.5
2
1.5
1
0.5
0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1
EratioFigure 4.4.3: Shower shape variables for the photon identiﬁcation. FF means rescaledwith Fudge factors. In the ratio plots, FSR events in data and rescaled (pink) or notrescaled (light green) MC are compared.

57where Efront is the energy deposit in front the of the calorimeter, EAcc is sum of energies
in 1st, 2nd and 3rd layers, called Accordion energy because of their geometries, Fsampling iscorrection factor to the Accordion sampling fraction in the cluster, Flongitudinal is correction
factor for the longitudinal leakage, Flateral is factor of the lateral leakage correction, andFmod is energy correction depending on the impact point inside a cell.
Efront depends on the part of the cluster energy measured in the presampler (Eps ),EAcc and η. Efront is expressed as follows:2× c (EAcc , |η|)Efront = a (EAcc , |η|) + Eps × b (EAcc , |η|) + Eps(4.5.2)where a, b and c are parameters determined as a function of EAcc and |η|. For |η| > 1.8,
since this region is not covered with the presampler, Efront is parametrized as a functionof the shower longitudinal barycenter computed with the information given by the threelayers only.
Fsampling , Flonditudinal and Flateral are parametrized as a function of X and η, where X
is the longitudinal barycenter of the shower (Shower depth) deﬁned by:∑3
i=0 Ei Xi
X= ∑(4.5.3)3Eii=0where Ei is the energy deposit measured in the presampler (i = 0) and the three layers(i = 1, 2, 3), as well as Xi is the depth, expressed in radiation length, of the longitudinal
center of each component from the center of the ATLAS detector (R = 0). Xi is a functionof η.
The amount of the absorber material is modulated in ϕ and η depending on the position
inside a cell due to the accordion geometry. Consequently, EAcc is also modulated in ϕand η. The factor Fmod = Fmod (ϕ, η) corrects the modulation.
The energy correction with the Calibration hits method is applied in both data and
MC

4.5.2

Energy correction in data

After the MC based correction, the energies of photons and electrons in data are corrected
to match those in MC with using the invariant mass distributions of Z → ee peak. The
invariant mass of a reconstructed Z → ee is computed as:√
m12 = 2E1 E2 (1 − cos ∆θ12 )(4.5.4)
where E1 and E2 are the electron energies measured with the EM calorimeter, as well as∆θ12 is the opening angle of the two electrons measured by the ID. Residual miscalibrationin data to be corrected is parametrized by α:Erec = Etrue (1 + α)(4.5.5)where Erec and Etrue are the reconstructed and initial energies, respectively. α is estimatedin 34 η bins, without any ET bin. Neglecting second-order terms and supposing that theangle between the two electrons is perfectly known, the eﬀect on the di-electron invariant
mass is:()αi + αjtrue
rec1+(4.5.6)
mij = mij
2
58

Smearing factor

α

0.08
0.06

∫

s = 8 TeV, Ldt = 20.3 fb

-1

0.04
0.02
0

0.06
0.05

∫

s = 8 TeV, Ldt = 20.3 fb

-1

0.04
0.03

-0.02

0.02

-0.04
0.01

-0.06
-0.08
-2

-1

0

1

0

2

-2

-1

0

1

2

η

η

(a)

(b)

Figure 4.5.1: Estimated energy correction factor(a) and smearing factor (b) for
TeV analysis.

√

s=8

where mrec is the measured di-electron mass, mtrue is the invariant mass computed fromtrue energies and αi represents the α in a i-th η bin. Because the α values in two diﬀerent
η bins shift the invariant mass, the αi cannot be estimated individually. The following
unbinned likelihood is introduced in order to estimate the value of α :
( (
)−1 )
N
evt
∑
αi + αj− ln Lij mk 1 +− ln Ltot =(4.5.7)2kwhere Nevt is the total number of selected events and L (m) is the probability density
function (PDF) of the invariant mass m. The PDF is an expected Z boson line shapewhen electrons fall in i- and j-th η bins respectively. It is obtained from the MC simulation, which takes into account some impacts on the Z line shape: theoretical ones
like relativistic Breit-Wigner shape, γ ∗ contribution, Z − γ ∗ interference, parton density
function, and ﬁnal state radiation, as well as experimental ones like detector resolution,eﬀect of the bremsstrahlung. Thus the α of each η bin are estimated with the maximum
likelihood ﬁt. The PDF is computed with di-electron mass within [70, 110] GeV, and thelikelihood
ﬁt is performed in [80, 100] GeV. Figure 4.5.1a shows the estimated α values√
for s = 8 TeV analysis.
Thus the scale factor (1 + α)−1 is applied to energy in data:
E → E′ =Erec
1+α(4.5.8)Note that α is applied not only to electrons but also to photons.
As described in Section 3.2, the energy smearing for MC simulation is also derived
from comparison of the Z → ee peaks in data and MC. The smearing factor (β) is deﬁned
as:
E → E ′ = Erec × G(1, β)(4.5.9)where G(µ, σ) is a random number followed by a Gaussian function with mean µ andvariance σ 2 . The values of β are determined by the likelihood ﬁt in the same way as59

250 ×10

3

200

∫

s = 8 TeV, Ldt = 20.3 fb

Data
MC

-1

150
100
50
0
70

75

80

85

90

95

100

105

110

mee [GeV]

Figure 4.5.2: Invariant mass of di-electron (mee ). The selected electrons with opposite
charges are required to have pT >25, 20 GeV and |η| < 2.47.
√
energy scale. Figure 4.5.1b shows the estimated β values for s = 8 TeV analysis. Figure
4.5.2 shows the Z line shapes after applying the energy scale α to data as well as energy
smearing to MC. The shapes in data and MC agree very well.

4.6

Direction of photon

Photon direction is determined from the straight line between the barycenter of the energy
deposit in the 1st layer of the EM calorimeter and the primary vertex as described in
Section 4.1.
The direction determination of photons is crucial for the resolution of Higgs mass
because the opening angle of the two photons (∆θ) is used in the calculation of theirinvariant mass:√
mγγ = 2E γ1 E γ2 (1 − cos ∆θ)(4.6.1)
where E γ1(2) is the energy of a photon. The opening angle is calculated from the pseudorapidity η and the azimuthal angle ϕ of the photons. Eq.(4.6.1) is rewritten as follows:√
2E γ1 E γ2mγγ =[cosh (η γ1 − η γ2 ) − cos (ϕγ1 − ϕγ2 )](4.6.2)
cosh η γ1 cosh η γ2
where η γ1(2) and ϕγ1(2) are the pseudo-rapidity and the azimuthal angle of a photon. ηand ϕ are determined using the trajectories of the photons.
The resolution of η is determined by the determination of primary vertex selection.
When the barycenter of beam
√ spot is assumed as a primary vertex, the resolution ofprimary vertex is 45 mm in s = 8 TeV data. In this case, the degradation of the η
resolution of photons is 0.03, and then the mass resolution is degraded 1.5 % by the η
resolution. The mγγ resolution improves 23 % (19 %) when using the neural network∑
based algorithm ( p2T max) compared with using a barycenter of beam spot as shownin Figure 4.6.1.
60

0.16
0.14

Neural Net

s = 8 TeV
ggF, mH = 125 GeV

σ=1.49 GeV

0.12∑p max2

0.1

T

σ=1.54 GeV

0.08

beam spot

0.06

σ=1.91 GeV

0.04
0.02
0
110

115

120

125

130

135

140

mγ γ [GeV]

Figure 4.6.1: Distributions of the expected di-photon invariant mass for ggF signal events
as a function of the algorithm of the primary vertex selection.
Track momentum
Transverse impact parameter
Longitudinal impact parameter
Inner detector hit
B-layer
Self-track exclusionpT > 1 GeV
d0 < 1.5 mm
z0 sin θ < 15 mm
Si hits(Pixel + SCT) ≥ 9
B-layer hit (if expected)
Exclude conversion tracks of the photon

Table 4.7.1: Track selection for photon track isolation. z0 and θ are with respect toreconstructed primary vertex in di-photon events.

4.7

Track isolation

Trajectories of photons from a decay of a Higgs boson are well isolated from tracks ofcharged particles. In contrast, a fake photon in a jet can become distinct due to theexistence of charged particle tracks in the jet. This feature separates photons from fakephotons in jets. The degree of the isolation is measured with a variable track isolation. The
presence of pileup jets which are from pileup vertices decreases the separation power of the
track isolation. Accordingly, tracks used for calculation of the track isolation are required
to have small impact parameters so as to reject the inﬂuence of pileup jets. Accurate
measurement of the impact parameters needs precise determination of the primary vertex.
When any selections for impact parameters are not applied, the track isolation has looser
pileup robustness than the energy cluster based isolation in the EM calorimeter. Therefore
the primary vertex reconstruction is important for rejection of background events in whichjets fake photons. The deﬁnition of the track isolation is the scalar sum of pT of tracks thatpass the selection on Table 4.7.1 and within a cone around the photon. The selection is
optimized on MC to get best signal-background separation and pileup robustness. Because
one of the√advantages of the track isolation is pileup robustness, the track isolation is onlyused for s = 8 TeV analysis where pileup√ is high. The track isolation for photon is called
pTconeX where X is cone size (∆R = ∆η 2 + ∆ϕ2 ) times 100. For the H → γγ analysis
X = 20 is selected.

61

4.8

Calorimeter isolation

The calorimeter isolation uses energy clusters in the calorimeter. Not only charged objects
but also neutral objects are taken into account unlike the track isolation. Thus thecalorimeter isolation have stronger separation photons from fake photons than the track
isolation under low pileup condition.
The calorimeter isolation ETcone40 , is deﬁned as the scalar sum of transverse energyof clusters in a cone of ∆R = 0.4 except η × ϕ = 5 × 7 rectangular core centered on theobject.
Topological clustering Topological clustering is used for calculating the isolation. The
basic idea is extending a cluster to neighbor cells when the cells have signiﬁcant energy
deposit. More precisely, a cell that has Ecell > 4σnoise can be a seed of a cluster where
Ecell is the energy deposit in the cell and σcell is the noise of the cell. If a cell next to theedge of a cluster satisﬁes Ecell > 2σnoise , the cell is newly included in the cluster. This
operation is repeated until the cluster are unable to be extended further.
Leakage correction The lateral leakage to the core from the cone from the outside of
the core becomes larger as the energy of the photon candidates increases. This is corrected
as a function of η, ET and conversion status of the photon, which is deﬁned from MC
samples.
Pileup correction The performance of the calorimeter isolation is improved by subtracting the energies of pileup jets because only activities from a primary vertex contributeto photon-jet separation. The correction factor is computed from estimation of energy
density surround the cone.

62

Chapter 5
Measurements of photon
performance with Z → ℓℓγ
5.1

Event selection

The measurements of the photon performance of the ATLAS detector is crucial for the
H → γγ analysis. The Z → ℓℓγ process, where a Z boson decays into a pair of leptons (µor e) and one of the leptons emit a ﬁnal state radiation (FSR) photon, provides photon
candidates in data with a high purity. In this chapter, the estimation of photon energy
scale, photon identiﬁcation eﬃciency, isolation eﬃciency and conversion fraction with the
Z → ℓℓγ are described.
The mass of the Z boson can be reconstructed by not mℓℓ but mℓℓγ . On the other
hand, initial state radiation (ISR) jets can be removed by requirements for mℓℓγ and mℓℓ .
This feature strongly increases the purity of photons.
To select eeγ events single lepton triggers are used since they have higher eﬃciencies
than di-lepton triggers. This is because sub-leading leptons tend to have small pT due
to emitting√ hard FSR photons. For the Z → eeγ analysis, single electron triggers areused. For s = 7 TeV analysis, three diﬀerent single electron triggers are used one after
the other as the luminosity increase. The triggered electron is identiﬁed by requiring the
EM shower shape and track-cluster matching. The matched track is required to haveenough hits in the inner detector and have small transverse impact parameter (< 5 mm).
The triggered electron pT threshold is 20 GeV for lower luminosity run, while 22 GeV
q

`
`

q

Z= ?

`
Z= ?

q

`

q

Figure 5.1.1: Diagrams of Z + γ events: FSR (left) and ISR (right)
63

Lepton requirement

At least 2 opposite charged leptons passing the lepton
selection
Photon requirement
At least 1 photon passing the photon identiﬁcation
Photon isolation
ETcone40 < 4 GeV
Photon ET
ET > 15 GeV for leading photon
Photon pseudo-rapidity |η| < 1.37 or 1.56 < |η| < 2.37
Lepton pT
pT > 25/15 GeV for leading/sub-leading lepton
ISR rejection
45 < mℓℓ < 85 GeV
Z mass80 < mℓℓγ < 100 GeV
Overlap removal
Photon and its closest electron (muon) must have
∆R > 0.4 (0.2)
Table 5.1.1: Event selection for Z → ℓℓγ analysis.
√for higher luminosity run. For s = 8 TeV analysis, the pT threshold is increased to 24
GeV. In addition, track isolation is required to the triggered electron. On the other hand,in the Z → µµγ analysis, single muon triggers are used. The triggered muon is required
to have good√ track quality in the muon
√ spectrometers. The pT threshold of the muon
trigger for s = 7 TeV is 18 GeV. For s = 8 TeV analysis, two triggers are used in OR
condition. One requires isolation criteria to the muon and uses a pT threshold of 24 GeV.
The other does not require any isolation criteria but uses a 36 GeV pT threshold. Theoﬀ-line event selection is shown in Table 5.1.1. The reconstruction of electrons and muons
are described in Appendix B and C. Photons in the transition region between the barrel
and the endcap calorimeters (1.37 < |η| < 1.56) are removed because the transition region
has high fake rate of jet→photon. The events that have mll ∼ mZ are removed in order toreject initial state radiation (ISR) events (Z+ jets or Z+ ISR photons). In the Z → eeγ
channel, the wider ∆R is used for overlap removal with leptons than Z → µµγ. Thisis because electrons very close to photons increase the calorimeter isolation of photons.
The number of selected√ events is 3795 (16544) in Z → eeγ channel and 6452 (20877) in
Z → µµγ channel in s = 7 (8) TeV data.

5.1.1

Z + jet background

The main background of Z → ℓℓγ events is Z + jet events, where π 0 s in ISR jets fakephotons. Because the fake photons have diﬀerent energy scale compared with genuine
photons, Z + jet events have an impact on the measurement of photon scale. FSR events
are also contaminated by Z+ISR photon events. However since the Z+ISR photon events
have genuine photons, they only increase the high mass tail in mℓℓγ distributions and do
not aﬀect the photon scale measurement. Therefore Z + ISR photon events are treatedas signal.
The fraction of Z + jet events is estimated with comparing isolation distributions
between genuine photons and fake photons in an ISR control region. The control region
is deﬁned by the event selection same as FSR selection except the following requirements:
 the isolation cut to photons is removed
 the invariant mass cuts are modiﬁed to 80 < mℓℓ < 100 GeV and 105 < mℓℓγ GeV

64

mµµ [GeV]300∫

s=8 TeV, Ldt=20.3 fb
FSR region
ISR region

250

1200

-1

1000

200

800

150

600

100

400

50

200

0
0

50

100 150 200

250 300

0mµµγ [GeV]

Figure 5.1.2: FSR and ISR regions in mµµγ -mµµ plane in
criteria are required.
1800

∫

1600

s = 8 TeV, Ldt = 20.3 fb

1400

s = 8 TeV, Ldt = 20.3 fb

1200

Data
Genuine photon
Fake photon

800

800

-1

ISR Z(→ee)γ

1000

Data
Genuine photon
Fake photon

1000

∫

1400

-1

ISR Z(→µµ)γ1200√
s = 8 TeV data. Isolation

600

600
400

400

200

200
0
-10

-5

0

5

10

15

0
-10

20

ETcone40 [GeV]

-5

0

5

10

15

20

ETcone40 [GeV]

Figure5.1.3: Isolation distribution in the ISR control region after the template ﬁt in√
s = 8 TeV data.
Figure 5.1.2 shows FSR and ISR regions in mµµγ vs. mµµ plane. The normalization factors
for MC events are obtained from a template ﬁt with the calorimeter isolation distribution
in the control region in data as shown in Figure 5.1.3. The templates are obtained fromZ → ℓℓγ and Z+jet MC. From the ﬁt result, the purity of photons in the FSR region isestimated to be 99.6 %. Figure 5.1.4 shows mℓℓγ distributions. The ET and η distributionsof selected photons in Z → ℓℓγ events are shown in Figure 5.1.5.

5.2

Photon energy scale

The calibration obtained from Z → ee events is applied not only to electrons but also
to photons. The diﬀerences between electrons and photons on the energy calibration aretaken into account based only on the MC simulation. Then the energy calibration for
genuine photons with respect to the calibration for electrons is the remaining uncertainty.
A check of the photon energy calibration with pure photon samples is necessary to assure
65

104

3

10

∫

Z→µµγ

s = 8 TeV, Ldt = 20.3 fb

Data
Genuine photon
Fake photon

104

-1

103

102

102

10

10

1
60

70

80

90

100

110

120

Z→eeγ

∫

s = 8 TeV, Ldt = 20.3 fb

Data
Genuine photon
Fake photon

1
60

70

80

90

100

110

Figure 5.1.4: Three-body invariant mass mℓℓγ distribution in the FSR region in
TeV data.

∫s = 8 TeV, Ldt = 20.3 fb

102

120

meeγ [GeV]mµµγ [GeV]

103

-1

1000

-1

Data, Z→µµγ
MC, Z→µµγ
Data, Z→eeγ
MC, Z→eeγ

800

√

s=8

∫

Data, Z→µµγ
MC, Z→µµγ
Data, Z→eeγ
MC, Z→eeγ

s = 8 TeV, Ldt = 20.3 fb

-1

600
400

10
200
1
10

20

30

40

50

60

70

80

90

100

0
-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5
η

ET [GeV]Figure 5.1.5: ET and η distributions of selected photons in Z → ℓℓγ events in
TeV data.

66

√
s=8

the EM calorimeter performance for the H → γγ analysis. This section describes adata-driven measurement of photon energy scale with Z → ℓℓγ events.
A photon energy scale factor α is applied to photons in Z → ℓℓγ events in data after
applying all energy corrections as a probe to check that photons in data have the same
scale as MC.
′
Eγ,Data → Eγ,Data(α) =Eγ,Data1+αα is binned in η, ET and conversion status of photons. For
and conversion status binning are used.

(5.2.1)√s = 8 TeV analysis, η, ET 4 bins in η: |η| = {0, 0.6, 1.37, 1.56, 1.82, 2.37} without the crack region {1.37, 1.56}.
 3 bins in ET : ET = {15, 20, 30, 100} GeV.
 3 bins in conversion status: unconverted, 1-track converted and 2-track converted
photon√For s = 7 TeV analysis, only 2 conversion bins are used because of small statistics.
 2 bins in conversion status: unconverted and converted photon

After applying α in data, the three-body invariant mass is recalculated (mℓℓγ (α)) written
as the following equation shows:
[
(
(
)2 )]
mℓℓ
α
mℓℓγ → mℓℓγ (α) ≃ mℓℓγ 1 −1−(5.2.2)2mℓℓγ
where mℓℓ is the invariant mass of di-lepton in the FSR events. The distributions ofmℓℓγ (α) is compared to MC by changing theα value and the best value of α is estimatedsuch that data and MC agree well. If the best agreement of the distributions in data andMC is given by α = 0, the energy scale of photons is well calibrated by the electron energy
calibration. We have the following three methods for estimation of the best value of α.
Ratio method In this method, the peak positions of mℓℓγ in data and MC are measured
with Gaussian ﬁts. For diﬀerent value of α, the recomputed distribution is ﬁtted in data.
The ﬁt range is ±1.5σ around the peak, where σ denotes the deviation of the Gaussian.
non−rad) are also
In addition to mℓℓγ , the mℓℓ peak in non-radiative Z decay events (mℓℓﬁtted with a Gaussian in order to suppress an inﬂuence of lepton
uncertainty.
⟩⟨ scalenon−radare compared
After the Gaussian ﬁts to mℓℓγ and mℓℓ , the ratio ⟨mℓℓγ (α)⟩ / mℓℓbetween data and MC, where ⟨X⟩ is the peak position of X. When a value of α is applied
to data as Eq.(5.2.1) shows, the ratio is shifted as:
[
(
)2 )]
(
mℓℓγ (α)
mℓℓγ
αmℓℓ⟨ non−rad ⟩ → ⟨ non−rad ⟩ ≃ ⟨ non−rad ⟩ 1 −
1−
2
mℓℓγ
mℓℓ
mℓℓ
mℓℓ
mℓℓγ

(5.2.3)The best value of α is estimated such that the double-ratio R = 1 which is deﬁned as:
67

R

1.02
1.015
1.01
1.005
1
0.995
0.99
0.985
0.98

-0.04 -0.03 -0.02 -0.01

00.01 0.02 0.03 0.04
αFigure 5.2.1: Distribution of R. The best ﬁt value of α is estimated from the point at
R = 1.
⟨ non−rad ⟩⟨mℓℓγ (α)⟩Data / mℓℓ⟨ non−rad ⟩ DataR≡⟨mℓℓγ ⟩MC / mℓℓ
MC(5.2.4)⟨ non−rad ⟩Statistics error of α is calculated by propagating the errors of ⟨mℓℓγ ⟩ and mℓℓtoR. Figure 5.2.1 shows the distribution of R. The distribution R is obtained to be a
linear function of α, and the slope is ∼ 0.25. The slope is determined by (mℓℓ /mℓℓγ ) inEq.(5.2.3).
χ2 method In this method, the best value of α is estimated by minimizing χ2 which
represents the degree of agreement of mℓℓγ shapes between data and MC. One of the meritsof the χ2 method is that the best α can be estimated without assuming any function to
the invariant mass distribution. χ2 is calculated for each α by comparing the histogramsof mℓℓγ .
χ (α) ≡
2nbin∑
(NData, i (α) − NMC, i )222
σData,
i (α) + σMC, ii(5.2.5)where i is the bin label of the histogram, Ni is the number of events and σi is the error
in each bin. χ2 (α) is minimized by the best agreement of the distributions. When the
shape of the histograms are described by Gaussian, χ2 (α) follows parabola distribution.
But because the actual shapes are asymmetrical distributions due to some kinematic cuts,
asymmetric parabola well describes χ2 (α).
 (α−α2best )2 + χ2
α > αminmin(5.2.6)χ2 (α) = (α−ασRbest )2+ χ2min α ≤ αmin2σLwhere σR(L) corresponds to the statistical upper(lower) error of α and αbest is the best ﬁtvalue of α. The distribution of χ2 (α) is ﬁtted with the asymmetric parabola. All parameters in Eq.(5.2.6) are ﬂoating in the ﬁt. Figure 5.2.2 is an illustration of χ2 distribution.
E/p method for double-track converted photon When a photon is reconstructed
as a double-track converted photon, the sum of momentum of the two conversion tracks
68

χ2

250

200
σR

150

100

50
-0.06

-0.04

-0.02

0

0.02

0.04

0.06
α

Figure 5.2.2: Illustration of χ2 . The best ﬁt value of α is measured form the minimum point (χ2 (αbest ) = χ2min ). The upper error of α (σα ) is estimated the point whereχ2 (αbest + σα ) = χ2min + 1.
140

100

∫

100

∫

90

s = 8 TeV, Ldt = 20.3 fb

Z→µµγ
2-track converted photons

80

Z→eeγ
2-track converted photons

Data
Genuine photon
Fake photon

60

s = 8 TeV, Ldt = 20.3 fb

120

-1

80
60

70

-1

Data
Genuine photon
Fake photon

50
40
30

40

20
20
0
0

10
0.5

1

1.5

2

2.5

0
0

3

0.5

1

1.5

E/p

2

2.5

3
E/p

Figure 5.2.3: Distribution of E/p of double-track converted photons in√
s = 8 TeV data.

pγ ≡ |⃗pconv1 + p⃗conv2 | is equal to the energy of the converted photon Eγ . The pγ is a goodreference to the Eγ because the performance of the inner tracker is well studied [94]. A
distribution of Eγ /pγ has sharp Gaussian peak around 1, hence the energy scale of doubletrack converted photons can be estimated with Gaussian ﬁtting to the Eγ /pγ distribution.
The photon scale α in Eq.(5.2.1) is determined such that ⟨Eγ (α) /pγ ⟩Data = ⟨Eγ /pγ ⟩MC ,where ⟨Eγ /pγ ⟩ represents the mean of the Gaussian. The ﬁt range is −1.5σ to +1σ aroundthe peak, where σ is the deviation of the Gaussian. The distribution of E/p is shown in
Figure 5.2.3.

5.2.1

Correlation of energy scales between photons and electrons

Both electron and photon energies are measured with the EM calorimeter. Consequently,
the miscalibration should be correlated between electrons and photons. However, it isdiﬃcult to estimate the correlation coeﬃcient exactly. Accordingly, in Z → eeγ mode,
photons are assumed to be uncorrelated with electrons.
In case electrons and photons are fully correlated and have a common bias ∆ for their69

energies, the energies of electrons and photons are sifted as Ee → Ee (∆) = Ee (1 + ∆)and Eγ → Eγ (∆) = Eγ (1 + ∆). Hence the peak position of meeγ is shifted as:meeγ → mcorreeγ (∆) = meeγ (1 + ∆)(5.2.7)In this case, energy scale α is applied not only to photons but also to electrons:meeγ → mcorreeγ (α) =

meeγ
1+α

(5.2.8)From a requirement that α cancels the shift of meeγ by ∆, α = ∆ is obtained. On theother hand when they are uncorrelated and electrons have a bias ∆, meeγ is shifted as:
[
(
(
)2 )]
∆
m
ee
meeγ → muncorr(∆) ≃ meeγ 1 +1+∼ meeγ (1 + 0.75∆)(5.2.9)eeγ
2meeγ
In the last term, an approximation mee /meeγ ∼ 0.7 is used. Since energy scale α isapplied only to photons in this case, meeγ is shifted as Eq.(5.2.2). From a comparison
with Eq.(5.2.9), α ∼ 3∆ is obtained. Thus the best ﬁt value of α in uncorrelated model
is about three times larger than full correlated model. Therefore the uncorrelated model
is conservative.

5.2.2

Systematic uncertainty

5.2.2.1

Lepton energy scale

The peak position of mℓℓγ is sensitive to the uncertainty of lepton energy scale. If lepton energy
scale⟨⟩ is shifted by ∆, as Eℓ → Eℓ (∆) = Eℓ (1 + ∆), mℓℓγ and the ratiomℓℓγ / mnon−rad
are shifted as:ℓℓ[
mℓℓlγ → mℓℓγ (∆) ≃

mℓℓγ

∆
1+
2

(

(
1+

mℓℓ
mℓℓγ

)2 )]

[
(
(
)2 )]
mℓℓγ (∆)
mℓℓγ∆
mℓℓ⟨ non−rad ⟩ → ⟨ non−rad⟩ ≃ ⟨ non−rad ⟩ 1 −
1−
2
mℓℓγ
mℓℓ
mℓℓ
(∆)
mℓℓ

(5.2.10)mℓℓγ

Because mℓℓ /mℓℓγ ∼ 0.7 in the selected FSR events, Eq.(5.2.10) can be written approximately as:mℓℓγ (∆) ∼mℓℓγ (1 + 0.75∆)mℓℓγ
mℓℓγ (∆)(5.2.11)⟩ ∼ ⟨ non−rad⟩ (1 − 0.25∆)⟨ non−rad
(∆)
mℓℓ
mℓℓ
This is why the ratio can suppress the lepton scale uncertainty.
The systematic uncertainty on α due to the lepton scale uncertainty is evaluated withshifting lepton energies by their uncertainties. The error of muon scale is provided bycomparing the peak positions of Z resonance between data and MC. The electron scaleerrors are the uncertainty of energy correction using Z line shapes, the uncertainty ofthe material mapping in the inner detector and the presampler energy scale. The photon
energy scale uncertainties due to lepton scale are 0.1% for muons and 0.4% for electrons.
70Conversion Method
Unconverted Ratio
0.001
2
χ
0.001
Converted
Ratio -0.005
χ2
0.003

α
±0.003 (stat.) ±0.002 (syst.)±0.002 (stat.) ±0.003 (syst.)±0.005 (stat.) ±0.002 (syst.)±0.005 (stat.) ±0.005 (syst.)√
Table 5.2.1: Photon energy scale for s = 7 TeV data.

5.2.2.2

Z + jet contamination

The fraction of Z+jet background is determined by the signal and background samples
which is normalized with a template ﬁt as described in Section 5.1.1. The signal normalization factor can also be determined from very high purity mass region in the FSR
events (80 < mℓℓγ < 90 GeV) as in Figure 5.1.4. The diﬀerence of above two normalization factors, assumed as the uncertainty of the factor, is 11%. This is so small thatit does not inﬂuence on photon scale measurement. However, the uncertainty of energy
scale of fake photon have to be taken into account. The systematic error due to Z+jet
contamination is estimated to be < 4 × 10−4 by comparing photon energy scales between
only using genuine photons and adding fake photons in MC.
5.2.2.3

Electron ↔ photon confusion

Mismatching tracks to energy clusters in the EM calorimeter can cause electron ↔ photon
confusion. When one of the electrons from Z boson is confused with a FSR photon, mℓℓγ
is slightly shifted due to the diﬀerence of calibration between electrons and photons.
The impact of electron ↔ photon confusion is estimated with exchanging energy scales
between the electron that emit the photon and the emitted photon to be less than 10−4 .
The radiative electron is chosen by requiring smaller ∆R from the photon than the otheramong leading two electrons.

5.2.3

Results

The photon energy scale α is estimated by√the Ratio method, χ2 method and the E/pmethod.
√ The estimated photon scale α for s = 7 data set is shown in Table 5.2.1, while
α for s = 8 data set is shown in Figure 5.2.4 and 5.2.5. α is consistent with 0 in all bins.
Therefore photons are well calibrated. Table 5.2.2 and 5.2.3 summarize the systematic
uncertainties of α. The largest contribution comes from lepton scale uncertainties. The
total uncertainties are about 1 %. They are slightly larger than the uncertainties in the
MC based calibration. Therefore the estimated photon energy scales are not used for ﬁnal
results. Nevertheless this is very important cross check with the data-driven method.

5.3

Photon identiﬁcation eﬃciency

The shape of shower development of photons in the EM calorimeter is used for the photon
identiﬁcation in order to separate photons from jets as described in Section 4.4. The

71

Systematic uncertainty source
Electron scale Energy correction using Z line shape
Material mapping
Presampler energy scale
Linearity
Electron smearing
Z+jet
Electron ↔ photon confusion∆αRatio
2.9 × 10−3
3.0 × 10−3
7.4 × 10−4
3.8 × 10−4
2.5 × 10−3
1.0 × 10−4
< 10−4∆αχ2
1.8 × 10−2
3.2 × 10−3
9.7 × 10−4
6.1 × 10−4
6.6 × 10−4
3.5 × 10−4
< 10−4

Table 5.2.2: Systematic uncertainties of α in inclusive category of Z → eeγ channel.
∆αRatio denotes systematic uncertainty in Ration method, and ∆αχ2 is systematic uncertainty in χ2 method.
Systematic uncertainty source
Muon scale
Muon smearing
Z+jet∆αRatio
1.3 × 10−3
1.4 × 10−4
3.8 × 10−4

∆αχ2
6.2 × 10−3
1.1 × 10−4
1.8 × 10−4

0.05
0.04
0.03
0.02

α

α

Table 5.2.3: Systematic uncertainties of α in inclusive category of Z → µµγ channel.
∆αRatio denotes systematic uncertainty in Ration method, and ∆αχ2 is systematic uncertainty in χ2 method.

Unconverted photons∫

Ratio methods = 8 TeV, Ldt = 20.3 fb
χ2systematic uncertainty predicted in MC

0.05
0.04

-1

0.03
0.02

0.01

0.01

0

0

-0.01

-0.01

-0.02
0

1-track converted photons

-1

-0.02
0.2 0.4 0.6 0.81

1.2 1.4 1.6 1.8

2

2.2

0

0.2 0.4 0.6 0.81

1.2 1.4 1.6 1.8

|η|
α

∫

Ratio methods = 8 TeV, Ldt = 20.3 fb
χ2systematic uncertainty predicted in MC

2

2.2
|η|

0.1
0.08
0.06
0.04
0.02

2-track converted photons∫

Ratio methods = 8 TeV, Ldt = 20.3 fb
χ2E/p
systematic uncertainty predicted in MC

-1

0
-0.02
-0.04
-0.06
0

0.2 0.4 0.6 0.81

1.2 1.4 1.6 1.8

2

2.2
|η|

Figure 5.2.4: Photon scale extracted from Z → ℓℓγ events with |η| in72√
s = 8 TeV data.

0.04
0.03
0.02

α

α

0.05
Unconverted photons∫

Ratio methods = 8 TeV, Ldt = 20.3 fb
χ2systematic uncertainty predicted in MC

0.05
0.04

-1

0.03
0.02

0.01

0.01

0

0

-0.01

-0.01

-0.02
10

1-track converted photons

-1

-0.02
20

30

40

50

60

70

80

90

100

10

20

30

40

50

ET [GeV]α∫

Ratio methods = 8 TeV, Ldt = 20.3 fb
χ2systematic uncertainty predicted in MC

60

70

80

90

100

ET [GeV]

0.1
0.08
0.06
0.04
0.02

2-track converted photons∫

Ratio methods = 8 TeV, Ldt = 20.3 fb
χ2E/p
systematic uncertainty predicted in MC

-1

0
-0.02
-0.04
-0.06
10

20

30

40

50

60

70

80

90

100

ET [GeV]Figure 5.2.5: Photon scale extracted from Z → ℓℓγ events with ET in√s = 8 TeV data.

ten variables of photon shower shape used in the photon identiﬁcation are checked withZ → ℓℓγ events as shown in Figure 4.4.2 and 4.4.3.
The eﬃciency of the photon identiﬁcation is measured in data-driven methods [84].
One of them is relied on the use of photon sample selected from Z → ℓℓγ events. The
eﬃciency is deﬁned as the eﬃciency for reconstructed prompt photons to pass the identiﬁcation criteria in a given ET , η region.
ϵID (ET , η) ≡γ
NID(ET , η)γ
Nrec (ET , η)

(5.3.1)γγ
where NID
represents the number of identiﬁed photons and Nrec
is the number of reconstructed photons.
Z → ℓℓγ events are selected with the procedure described in Section 5.1 except thephoton identiﬁcation and isolation criteria for counting the denominator. Then the identiﬁcation criteria are applied and the numerator is counted. The photon purities areevaluated in both before and after the identiﬁcation requirement (ρrec and ρID ) with thetemplate ﬁt described in 5.1.1. Eq. 5.3.1 is rewritten as:

ϵID (ET , η) =Z→ℓℓγ
ρID (ET , η) NID(ET , η)Z→ℓℓγ
ρrec (ET , η) Nrec
(ET , η)(5.3.2)Z→ℓℓγ
where NID
is the number of selected events in the FSR region after applying theZ→ℓℓγ
is the number before applying the identiﬁcation criteria.
identiﬁcation criteria and Nrec

73

∈ID

∈ID

1

1

0.9

0.9

0.8

0.8

0.7

0.7

0.6
0.5
0.4
0

0.6

∫

s = 8 TeV, Ldt = 20.3 fb

Z→µµγ
Z→eeγ
10

20

-1

0.5

Converted photons
30

40

50

60

70

0.4
0

80

∫

s = 8 TeV, Ldt = 20.3 fb

Z→µµγ
Z→eeγ
10

Unconverted photons

20

30

40

50

60

70

1

0.9

0.9

0.8

0.8

0.7

0.7

0.6

0.6

0.5
0.4
0

∫

s = 8 TeV, Ldt = 20.3 fb

Z→µµγ
Z→eeγ
0.5

-1

0.5

Converted photons
1

1.5

2

80

ET [GeV]∈ID∈ID

ET [GeV]
1

-1

0.4
0

2.5

∫

s = 8 TeV, Ldt = 20.3 fb

Z→µµγ
Z→eeγ
0.5

-1

Unconverted photons
1

1.5

|η|

2

2.5
|η|

Figure 5.3.1: Eﬃciencies of photon identiﬁcation in√s = 8 TeV data.

Figure 5.3.1 shows the eﬃciencies of photon identiﬁcation. Both results in Z → eeγ
and µµγ modes agree very well. The shower shape variables of high ET photons havenarrower distributions than those of low ET photons because of better energy resolution
for high energy photons. Therefore higher ET photons have higher identiﬁcation eﬃciency.
If a photon is converted in front of the EM calorimeter, the photon has wider shower.
Hence the dependence of the eﬃciency on η comes from material traversed. However
because the thresholds for each shower variable are changed in |η|, the eﬃciency is not sostrongly correlated with the material traversed.

5.3.1

Other data-driven estimation measurements and combination

The eﬃciency of photon identiﬁcation is also estimated in Electron extrapolation andMatrix method. The diﬀerence of shower shapes between electrons and photons arestudied in MC. From the results, electrons in data, obtained from Z → ee events are
extrapolated to photons in the Electron extrapolation method. Therefore the photon
identiﬁcation eﬃciencies are estimated with using the extrapolated electrons. This method
provides a larger ET sample than the Z → ℓℓγ analysis. The main systematic uncertainty
in the Electron extrapolation method is the material uncertainty which have an impact on
the transform functions for the extrapolation. On the other hand, in the Matrix methodphoton candidates in data are selected using single photon triggers. In the collected
S
B
S++ Nfail+ Npass
sample, the observed numbers of photon candidates are expressed in Npass
74

B
Nfail
, where the superscripts S and B represent genuine photons and fake photons andthe subscripts pass and fail mean passing and failing the identiﬁcation criteria. Next,
the identiﬁcation criteria are applied to the photon candidates, and the number of events
TTwhich pass or fail the identiﬁcation criteria (Npass
or Nfail) are counted. They can be
expressed as:
T
S
B
Npass
=Npass+ Npass(5.3.3)TS
B
Nfail=Nfail+ Nfail

In addition, the number of events which pass or fail not only the identiﬁcation but also
TI
TI
) are counted. They can be expressed as:
isolation criteria (Npass
or Nfail
TI
S
B
Npass
=ϵSp Npass+ ϵB
p Npass(5.3.4)

TI
S
B
Nfail
=ϵSf Nfail+ ϵB
f NfailB
where ϵSp , ϵSf , ϵB
p and ϵf are the isolation eﬃciencies for signal and background candidatesBpassing or failing the identiﬁcation criteria. ϵB
p and ϵf are estimated from a data sample
enriched in fake photons. Besides, ϵSp and ϵSf are estimated from MC simulation. Then
S
S
B
B
Npass
, Nfail, Npassand Nfailare calculated using the counted numbers and the eﬃciencies.
NS

Therefore the eﬃciency of photon identiﬁcation is calculated as ϵID= N S pass
S . The main
pass +Nfailsystematic uncertainty is signal leakage into fake photon enriched sample.
Finally the eﬃciencies from the three measurements are combined and compared to
MC simulation as shown in Figure 5.3.2 and 5.3.3.

5.4

Photon conversion fraction

The conversion reconstruction is crucial for primary vertex selection since the selection
eﬃciency is increased by conversion tracks. In addition, it has an impact on photon
energy calibration because energy clustering in the EM calorimeter uses two diﬀerent
window sizes according to conversion status of photons.
Figure 5.4.1a shows the fractions of each photon conversion status with η. The fraction of converted photons increases in high η region where the material traversed is large.
The fraction of single-track converted photons is not proportional to that of double-track
converted photons. When a photon is converted at the more interior than the SCT,
the eﬃciency of double-track conversion reconstruction is higher than that of single-trackreconstruction because of a good separation of two conversion tracks (Figure 5.4.1b).
Therefore the fractions of double- and single-converted photons depend on material distribution along the radial direction.
The photon conversion fractions also depend on the photon ET as shown in Figure
5.4.2a. This is because a low ET converted photon has low pT conversion tracks, andthe eﬃciency of conversion track reconstruction decrease as the pT of the track decreases.
Figure 5.4.2b shows the pileup dependence on the conversion fractions. Even under thehigh pileup condition, the fractions keep ﬂat. The reconstruction of conversion vertex isrobust against pileup. The fractions in data and MC agree well in all the plots, .

75

εID

εID

1
0.9

0.9

0.8

s = 7 TeV
Data 2011
Corrected MC

0.6∫∫ L dt = 4.9 fb-1

Data 2011
Corrected MC

0.6

Converted γ
MC
data
εID
- εID

0

Converted γ

0.6 ≤ |η| < 1.37

0.5

-0.1

102

0.1
0
-0.1

30 40 50

2×102
ET [GeV]

102

20

εID

20

εID

s = 7 TeV

-1

L dt = 4.9 fb

102

0.1

ATLAS Preliminary

0.7|η| < 0.6

0.5
MC
data
εID
- εID

0.8

ATLAS Preliminary

0.7

1
0.9

30 40 50

2×102
ET [GeV]

102

1
0.9

0.8

0.8

ATLAS Preliminarys = 7 TeV

0.7
Data 2011
Corrected MC

0.6∫

ATLAS Preliminarys = 7 TeV

0.7
-1

1.52 ≤ |η| < 1.81

0.1

2

Data 2011
Corrected MC

0.6

Converted γ

0.5∫ L dt = 4.9 fb-1

L dt = 4.9 fb

10

0
-0.1

Converted γ

1.81 ≤ |η| < 2.37

0.5
MC
data
εID
- εID

MC
data
εID
- εID

1

102

0.1
0
-0.1

20

30 40 50

102

2×102
ET [GeV]20

30 40 50

102

2×102
ET [GeV]Figure 5.3.2: Comparisonof combined data-driven measurements of converted ϵID to MC√
predictions in s = 7 data [84].

5.5Isolation eﬃciency estimation

The isolation eﬃciency for di-photon events is estimated in H → γγ MC samples. The
systematic uncertainty of the eﬃciency is studied with comparing the eﬃciencies between
data and MC in Z → ee decays where an electron emulates a photon. The performanceof track isolation depends on the primary vertex selection eﬃciency. Hence several algorithms are used for the primary vertex selection in order to estimate the impact of
the eﬃciency of the primary vertex selection. Figure 5.5.1 shows the eﬃciency and theuncertainty predicted in H → γγ events. The error bars include systematic uncertainty
estimated with Z → ee events.

76

εID

εID

1
0.9

0.9

0.8

s = 7 TeV∫

Data 2011
Corrected MC

0.6

s = 7 TeV

∫ L dt = 4.9 fb-1-1

L dt = 4.9 fb

Unconverted γ

0.5|η| < 0.6

0.1

2

Data 2011
Corrected MC

0.6

10

0
-0.1

Unconverted γ

0.5

0.6 ≤ |η| < 1.37

0.1

2

10

0
-0.1

2×102
ET [GeV]102

30 40 50

20

εID

20

εID

ATLAS Preliminary

0.7

MC
data
εID
- εID

MC
data
εID
- εID

0.8

ATLAS Preliminary

0.7

1
0.9

2×102
ET [GeV]102

30 40 50

1
0.9

0.8

0.8

ATLAS Preliminarys = 7 TeV

0.7∫

Data 2011
Corrected MC

0.6

ATLAS Preliminarys = 7 TeV

0.7

∫ L dt = 4.9 fb-1-1

L dt = 4.9 fb

Data 2011
Corrected MC

0.6

Unconverted γ

0.5

1.52 ≤ |η| < 1.81

0.1

2

Unconverted γ

1.81 ≤ |η| < 2.37

0.5
MC
data
εID
- εID

MC
data
εID
- εID

1

10

0
-0.1

102

0.1
0
-0.1

20

2×102
ET [GeV]102

30 40 50

20

2×102
ET [GeV]102

30 40 50

Fraction of photon candidates

Figure 5.3.3: Comparisonof combined data-driven measurements of unconverted ϵID to√
MC predictions in s = 7 data [84].

900

1.4
1.2
1

Unconverted
1-track converted
2-track converted

800∫

s = 8 TeV, Ldt = 20.3 fb-1

1-track converted
2-track converted

700
600

0.8

500

0.6

400

∫

s = 8 TeV, Ldt = 20.3 fb

-1

300

0.4

200
0.2
0
-2.5

100
-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0
0

2.5

100

200

300

400

η

500

600

700

800

Conversion radius [cm]

(a)

(b)

Figure 5.4.1: Fraction of photon conversion status with η (a). The fraction in data isshown √
with markers, while that in MC is shown with line. Radius of conversion vertex(b) in s = 8 TeV data.

77

1.2
1

Unconverted
1-track converted
2-track converted∫

s = 8 TeV, Ldt = 20.3 fb

Fraction of photon candidates

Fraction of photon candidates

1.4
-1

0.8
0.6
0.4
0.2
0
10

1.4
1.2
1

Unconverted
1-track converted
2-track converted∫

s = 8 TeV, Ldt = 20.3 fb

-1

0.8
0.6
0.4
0.2

15

20

25

30

35

40

45

50

55

0

60

5

10

ET [GeV]

15

20

25

Number of primary vertex candidate

(a)

(b)

Isolation efficiency

Figure√ 5.4.2: The fraction of photon conversion status with photon ET (a) and pileup (b)in s = 8 TeV data. The fraction in data is shown with markers, while that in MC isshown with line.

1
0.9
0.8
0.7
0.6
s=8 TeV
mH=125 GeV

0.5
0.4
0

5

10

15

20

25

30

Number of primary vertex candidates

Figure 5.5.1: Isolation eﬃciency for di-photon in H → γγ MC samples. The error bars
include systematic uncertainty.

78

Chapter 6
Event selection and categorization
6.1

Event selection

Events√ recorded with di-photon triggers as described in Section 4.2 are used in the analysis.
For s = 7 TeV data analysis, the transverse energy (ET ) threshold is 20 GeV for leading(the√ highest ET ) and sub-leading (the second highest ET ) photons. The thresholds for
s = 8 TeV are 35 GeV and 25 GeV for leading photons and sub-leading photons,
respectively. The eﬃciencies of the triggers are about 99 % for events passing the following
ﬁnal event selection.
The oﬄine event selection is summarized in Table 6.1.1. Events are required to haveat least 2 photon candidates.
The two leading photons are√√ required to pass the neural net
identiﬁcation for s = 7 TeV or cut-based criteria for s = 8 TeV. The ET thresholds
are 40 GeV and 30 GeV for the leading and sub-leading photons. Both two photons need
to be within the ﬁducial calorimeter region |η| < 2.37 with excluding the transition region
between the barrel and the endcap calorimeters 1.37 < |η| < 1.56, where the reconstructed
eﬃciency is low, the energy resolution is worse and the fake rate of jet→photon is high.
After selecting the two leading photon candidates, the primary vertex is selected withusing the photons as described in Section 4.1. The track isolation is calculated with respect
to the primary vertex. The η of the photons are corrected with respect to the primaryvertex as well. The two photons are required to pass the track and calorimeter isolation
criteria in order to reject events having√fake photons. The calorimeter
isolation ETcone40 is√required to be smaller than 4 GeV for s = 7 TeV data. For s = 8 TeV, the requirementof < 2.6 GeV on the track isolation pTcone20 as well as < 6 GeV on the calorimeter isolation
are applied. Finally the events in a mass window 100 < mγγ < 160 GeV are selected. The
distributions of ET , η, ETcone40 and pTcone20 of the photon candidates are shown in Figure
6.1.1, 6.1.2, 6.1.3 and 6.1.4. The ET distributions in the signal MC have peaks at about
mH /2 as well as sharp cut-oﬀs at trigger thresholds. The η distributions in the signal
MC are centered compared to the observed data because the Higgs boson is tend to be
produced at rest due to the high mass. The observed data has larger transverse energy
deposit near the photon than signal MC because√√ of the fake photon contamination.
The number of selected events is 23788 in s = 7 data, 118893 in s = 8 TeV data.
The cut ﬂow for H → γγ selection is summarized in Table 6.1.2. Figure 6.1.5 and 6.1.6
show the observed mγγ distributions, as well as the expected signal distributions after the
event selection. Figure 6.1.7 shows an event display of a di-photon signal candidate. The79

√√
s = 7 TeV analysis
s = 8 TeV analysis
At least 2 reconstructed photons|η| < 1.37 or 1.56 < |η| < 2.37
ET > 40(30) GeV for the leading (sub-leading) photons
Neural net based
Cut based
ETcone40 < 4 GeV
ETcone40 < 6 GeV
pTcone20 < 2.6 GeV
100 < mγγ < 160 GeV

2 photons
Pseudo-rapidity
Transverse energy
Identiﬁcation
Calorimeter isolation
Track isolation
Mass window (only in data)

Table 6.1.1: Event selection for H → γγ analysis.

∫

0.04

s = 8 TeV, Ldt=20.3 fb
mH = 125 GeV
Signal MC
Data

0.035
0.03

0.03
0.025

0.02

0.02

0.015

0.015

0.01

0.01

0.005

0.005
20

40

60

80

100

120

s = 8 TeV, Ldt=20.3 fb
mH = 125 GeV
Signal MC
Data

0.035

0.025

0
0

∫

0.04

-1

0
0

140

20

40

60

80

leading E [GeV]

0.02

0.02

0.01

0.01

0.005

0.005
-1

0

1

2

3

4

s = 8 TeV, Ldt=20.3 fb
mH = 125 GeV
Signal MC
Data

0.025

0.015

-2

∫

-1

0.015

0
-3

√
s = 8 TeV data. The sum

0.03

∫

0.025

140
T

Figure 6.1.1: Distributions of ET of the selected photons inof histograms are normalized to 1.

s = 8 TeV, Ldt=20.3 fb
mH = 125 GeV
Signal MC
Data

120

sub-leading E [GeV]

T

0.03

100

-1

0
-3

5

-2

leading photon η

-1

0

1

2

3

4

-1

5

sub-leading photon ηFigure 6.1.2: Distributions of η of the selected photons inhistograms are normalized to 1.

80√
s = 8 TeV data. The sum of

∫

10-1

s = 8 TeV, Ldt=20.3 fb
mH = 125 GeV
Signal MC
Data

10-2

∫

10-1

-1

s = 8 TeV, Ldt=20.3 fb
mH = 125 GeV
Signal MC
Data

10-2

10-3

10-3

10-4

10-4

10-5

10-5

10-6

10-6
0

10

20

30

40

50

0

10

leading photon ETcone40 [GeV]∫1

s = 8 TeV, Ldt=20.3 fb
mH = 125 GeV
Signal MC
Data

10-1
10-2

10-4

10-5

10-5
20

50

∫

s = 8 TeV, Ldt=20.3 fb
mH = 125 GeV
Signal MC
Data

10-2

10-4

15

40

√
s = 8 TeV data. The

10-1

10-3

10

30

1

-1

10-3

5

20

sub-leading photon ETcone40 [GeV]

Figure 6.1.3: Distributions of ETcone40 of the selected photons insum of histograms are normalized to 1.

0

-1

25

0

5

leading photon pTcone20 [GeV]

10

15

20

-1

25

sub-leading photon pTcone20 [GeV]

Figure 6.1.4: Distributions of pTcone20 of the selected photons insum of histograms are normalized to 1.

81√
s = 8 TeV data. The√√s = 7 TeV
s = 8 TeV
Data
MC
Data
MC
100 %
100 %
Di-photon Trigger
6459127 69 % 25501602 67 %Photon reconstruction 1207197 54 % 11907820 51 %ET
437396 49 % 6550457 48 %Identiﬁcation
111699 45 %
675075 42 %Isolation
66058 41 %
311723 38 %mγγ
23788 41 %
118893 38 %√Table 6.1.2: Cut ﬂow for H → γγ selection. The MC
simulationfors = 7 TeV is ggF√
at mH = 120 GeV sample. The MC simulation for s = 8 TeV is ggF at mH = 125 GeV
sample. The statistical error of the MC simulation is < 0.1 %.
invariant mass of di-photon in this event is 126.9 GeV. This event contains not only two
photons but also two forward jets. The jet selection is described in Section 6.2.1. The
information of the event is matched to the feature of VBF process.

6.2

Event categorization

Events are separated into categories, which have diﬀerent signal-to-background ratios, for
the improvement of the sensitivity√ to the Higgs signal. The selected di-photon√ events are
divided into 10 categories for s = 7 TeV analysis and 14 categories for s = 8 TeV
analysis. There are two strategies in the event categorization;
1. The events are divided into categories which have good and bad mass resolutions
resulting in high and low signal-to-background ratios.
2. Some categories are designed to have high sensitivity to VBF and VH Higgs production processes.
Based on the ﬁrst strategy, η and conversion status are used for categorization. Unconverted photons have better energy resolution than converted photons since unconverted
photons do not loose the energy in the inner detector. When both photons are unconverted, the mass resolution is 1.8 GeV (r.m.s.), while 2.6 GeV (r.m.s) when both areconverted. Similarly photons in low η region have better energy resolution because theamount of material in this region is smaller than high η region. The mass resolution is 1.7
GeV (r.m.s) when both photons are in |η| < 0.6, and 2.7 GeV (r.m.s) when both are in
1.56 < |η| < 2.37. In addition, the signal to background ratio in the low η region is higher
than the high η region. Higgs pTt is the other parameter for categorization according tothe ﬁrst strategy, which is deﬁned as
pTt ≡

p⃗γγ
T ×

p⃗γ1
⃗γ2
T −p
T
γ2
p⃗γ1
−
p
⃗
T
T

(6.2.1)

where p⃗γγof) di-photon, p⃗γ1
⃗γ2
T is the transverse momentum
T and pT are the transverse mo( γ1γ2γ1γ2menta of the two photons, and p⃗T − p⃗T / p⃗T − p⃗T denotes the transverse thrust axis.
82Events / 1 GeV

800

∫

-1

s = 7 TeV, Ldt=4.8 fb
mH = 125 GeV
Signal MC x10
Data

700
600
500
400
300
200
100
0
100

110

120

130

140

150

160

mγ γ [GeV]

Events / 1 GeV√
Figure 6.1.5: mγγ distributions in s = 7 TeV data. The expected signal distributions(mH = 125 GeV) are shown in the pink histogram.

4000

∫

-1

s = 8 TeV, Ldt=20.3 fb
mH = 125 GeV
Signal MC x10
Data

3500
3000
2500
2000
1500
1000
500
0
100

110

120

130

140

150

160

mγ γ [GeV]√
Figure 6.1.6: mγγ distributions in s = 8 TeV data. The expected signal distributions(mH = 125 GeV) are shown in the pink histogram.

83

Figure 6.1.7: Event display of a VBF H → γγ candidate, √containing two converted
photons and two high-mass jets. The event was recorded at s = 8 TeV. The leading
photon has ET = 80.1 GeV and η = 1.01. The sub-leading photon has ET = 36.2 GeV
and η = −0.17. The measured di-photon mass is 126.9 GeV. The pT and pTt of the diphoton system are 44.3 GeV and 6.2 GeV, respectively. The leading jet has ET = 121.6
GeV and η = −2.90. The subleasing jet has ET = 82.8 GeV and η = 2.72. The measured
di-jet mass is 1.67 TeV. The ∆ϕ between the di-photon system and the system of thedi-jet is 2.90 [91].

pTt

pTγγ

pTγ1

pTγ2

Figure 6.2.1: sketch of pTt

84

∫

2200
2000
1800
1600
1400
1200

s = 8 TeV, Ldt=20.3 fbγγ

pT <8 GeV
γγ
8<pT <16 GeV
γγ
16<p <28 GeVT
γγ
28<p <54 GeVT
γγ
54<p GeV

1000
800
600
400
200
0
100

120

130

140

150

s = 8 TeV, Ldt=20.3 fb

160

-1

pTt <3 GeV
3<pTt <9 GeV
9<pTt <18 GeV
18<pTt <39 GeV
39<pTt GeV

1000
800

T

110

∫

2200
2000
1800
1600
1400
1200

-1

600
400
200
0
100

110

120

130

140

150

mγ γ [GeV]160

mγ γ [GeV]

ggF events efficiency [%]Figure 6.2.2: mγγ distributions in diﬀerent pTt and pγγ
T regions in data
100

s = 8 TeV
ggF, mH=125 GeV
pTt
γγ
pT

80
60
40
20
0
0

20

40

60

80

100

data sideband rejection [%]Figure 6.2.3: Separation of ggF signal events and backgrounds. The backgrounds are
emulated by data sideband (excluding mγγ ∈ [120, 130] GeV).
() ( γ1)γγ
Figure 6.2.1 illustrates the pTt . In case p⃗γ1⃗γ2
⃗T − p⃗γ2
T +p
T ⊥ p
T , pTt = pT . The meanvalue of pγγ
T in the signal MC is 45 GeV, while that in data contaminated by very intense
background is 31 GeV. The signal events have higher pγγ
T than the background events,
hence the pγγ
is
also
a
candidateofparametersforthecategorization.
With the categoTγγ
rization based on pT , mγγ distributions are distorted as shown in Figure 6.2.2. On theother hand, the pTt -based categorization does not distort mγγ , that is a good feature tomodel the background from data as mentioned in Section 7.2.
γγCompared with pγγ
T , pTt has the same discriminative power as the pT as shown in
Figure 7.2. The mean value of pTt in the signal MC is 30 GeV, while that in data is 19
GeV.
The second strategy requires additional objects associated to some kinds of Higgs
production processes. The signature of VBF process is the presence of forwards twojets. Hence two jets are required. In VH (= WH and ZH ) process, objects from thevector boson are tagged; leptons, jets and ETmiss . The distinct topologies provide better
discrimination against the background events. Taking the second strategy the sensitivity
to discovery can be increased. Moreover, the Higgs couplings can be measured for eachprocess due to the enhancement a particular production process.

85√s = 7 TeV

Event selection
At least 2 jets

Yes

No

400 < mjj GeV

Di-jet

2.8 < |ηjet1 - ηjet2|
2.6 < |φγγ - φjj|

Untagged 9 categories
Both converted ?

Unconverted : Converted|ηγ1| < 0.75 & |ηγ2| < 0.75 ?

Central : Rest, Transition

pTt > 60 GeV ?

High pTt : Low pTt

VBF enriched

Figure 6.2.4: Flowchart of the event categorization forevents are separated into 10 categories.

ggF enriched√s = 7 TeV analysis. Selected

The ordering of the categorization shown in√Figure 6.2.4 and 6.2.5 is applied, since thecategories are not completely orthogonal. For s = 7 TeV, the di-jet category is selected√
for VBF process and remaining events are divided into 9 categories for ggF. For s = 8
TeV analysis, VH enriched categories are selected before the ggF and VBF enrichedcategories. The object selection which is needed to deﬁne the categories is described in
the following section.

6.2.1

Object selection

6.2.1.1

Isolated electrons

Electrons are reconstructed by matching tracks in the inner detector to energy clusters in
the EM calorimeter as described in Appendix B. The energies of electrons are measured
with the EM calorimeter. They are corrected against energy losses in material in frontof the EM calorimeter, as well as lateral and longitudinal leakages. For MC, the electronenergy is smeared to match the observed mee resolution of the Z peak. The energy
scale of electrons in data is corrected based on the peak position of the Z peak. The
directions of electrons are measured with the inner detector. The curvature of electron
tracks may be changed by radiative energy losses due to bremsstrahlung. Accordingly, theparameters of tracks (ϕ, d0 ) are corrected with Gaussian Sum Fitter (GSF) [94] by which
the bremsstrahlung eﬀect is taken into account in the calculation of track parameters.
After all corrections, ET > 15 GeV and |η| < 2.47 are required. Electron identiﬁcation is
performed based on the shower shapes of the EM calorimeter and track quality. Electron
candidates are requires to be isolated from other tracks and from other clusters in thecalorimeter. The isolation parameters ETcone40 and pTcone20 are calculated in the same
way as photons. ETcone40 /ET < 0.2 and pTcone20 < 0.15 are required. Electron separationfrom the leading two photons is required to be ∆R > 0.4.

86√s = 8 TeV

Event selection
At least one muon

Yes

One-lepton
W( lν)H, Z( ll)No

At least one electronmeγ < 84 GeV or 94 GeV < meγ
Electron ID veto

miss

ET

/ σETmiss > 5

miss

ET

Electron ID vetosigniﬁcanceW( lν)H, Z( νν)At least 2 jets

60 < mjj < 100 GeV|ηjet1 - ηjet2| < 3.5

Low mass di-jet

pTt > 70 GeV

W( jj)H, Z( jj)|ηγγ - ηjj| < 1
0.77 < BDT response

Tight VBF

0.19 < BDT response

Loose VBF

Untagged 9 categories
Both converted ?

Unconverted : Converted|ηγ1| < 0.75 & |ηγ2| < 0.75 ?

Central : Rest, Transition

pTt > 60 GeV ?

High pTt : Low pTt

VH enriched

VBF enriched

Figure 6.2.5: Flowchart of the event categorization forevents are separated into 14 categories.

87

ggF enriched√
s = 8 TeV analysis. Selected6.2.1.2

Isolated muons

Tracks reconstructed in the muon spectrometer are muon candidates, which are required
to be |η| < 2.7. In the region covered by the inner detector (|η| < 2.5), muon candidates
are required to be reconstructed from tracks in the inner detector and the muon spectrometer. In the forward region (2.5 < |η| < 2.7), they are reconstructed from the muon
spectrometer alone as described in Appendix C. The momentum scale and resolution
corrections are derived from the Z → µµ candidates in data. A transverse momentum
pT > 10 GeV is required. Identiﬁcation criteria are based on track quality. The impact
parameters with respect to the primary vertex d0 and z0 are required to be |d0 | < 1 mm
and |z0 | < 10 mm. The isolation cuts pTcone20 /pT < 0.15 and ETcone40 /pT < 0.2 areapplied. Muon candidates must be separated from the photons and reconstructed jets by∆R > 0.4.
6.2.1.3

Jets

Jets are reconstructed with energy clusters in the hadronic and EM and calorimeters using
anti-kT algorithm [95] with a cone size R = 0.4 as described in Appendix D. Then pT > 25
GeV and |η| < 4.5 are required. The jet candidates are contaminated by low pT pileup
jets√especially in high η region. Accordingly, pT > 30 GeV is required in 2.4 < |η| < 4.5
for s = 8 TeV analysis. In addition, Jet Vertex Fraction (JVF)
cut is applied to reduce√
pileup jets (Appendix D). JVF > 0.5 (0.25) is required for s = 7 (8) TeV analysis.
6.2.1.4

Missing transverse energy (ETmiss )Missing transverse energy ETmiss is reconstructed by object-based algorithm. All photon,
electron and muon candidates and all jets after overlap removal, and all calorimeter clusters not associated to such objects are used for calculation of ETmiss . The last object iscalled CellOut. The other objects (photons, electrons, muons and jets) used are exactly
the same as objects deﬁned before. The ETmiss is deﬁned as:
ETmiss ≡ −∑photonp⃗photon+T∑electronp⃗electron
+
T

∑
muon

p⃗muon
+
T

∑
∑ jet
p⃗T +
p⃗CellOut
Tjet(6.2.2)

CellOut

The ETmiss signiﬁcance is deﬁned as the ratio between ETmiss and the resolution ofmiss
ET (ETmiss /σETmiss ) where σETmiss is the resolution. σETmiss can be parametrized as σETmiss =√∑∑k
ET , where
ET is a scalar sum of pT of all objects except muons. The factor k is
obtained from Z → µµ events, where no genuine ETmiss is expected. The resulting value
is k = 0.67 [GeV1/2 ] [96]. Due to the jet energy resolution, ETmiss can be overestimatedin multi-jet events. The ETmiss signiﬁcance allows higher rejection of the fake ETmiss events
than ETmiss . Therefore the ETmiss signiﬁcance is used for categorization instead of ETmiss .

6.2.2

√
VH enriched categories ( s = 8 TeV)

VH candidates are selected ﬁrst in the categorization for
Figure 6.2.5.

88√

s = 8 TeV data as shown inAt least one leptonmeγ < 84 and 94 < meγ
Electron ID veto

W (→ eν)H W (→ µν)H72.3 %
80.7 %
70.1 %
80.7 %
58.6 %
80.7 %W (→ τ ν)H
15.3 %
14.9 %
13.5 %

Table 6.2.1: Eﬃciency in the one-lepton category for W (→ ℓν)H events at mH = 125
GeV.
Z(→ ee)H Z(→ µµ)H Z(→ τ τ )H data (sideband)
At least one lepton
92.7 %
94.1 %
23.6 %
0.21 %
meγ < 84 and 94 < meγ
85.1 %
94.1 %
22.8 %
0.17 %
Electron ID veto70.3 %
94.1 %
22.1 %
0.12 %
Table 6.2.2: Eﬃciency of the one-lepton category forZ(→ ℓℓ)H events at mH = 125 GeV
and data sideband (excluding mγγ ∈ [120, 130] GeV) which emulate backgrounds.
6.2.2.1

One-lepton category

At least one electron or muon is required for lepton(s) from the leptonic decay of Z or
W boson. One of the considerable background in electron channel is Z → eeγ events
where one of the electrons fakes a photon. In case of the FSR (Z(→ eeγ)) events, meeγ =mZ ̸= mH , thus the FSR events are rejected by mass window cut (100 < mγγ < 160
GeV). On the other hand, the ISR events (Z(→ ee)γ) can be background because ofmee = mZ and meeγ > mZ . If an electron fakes a photon in an ISR Z(→ ee)γ event,meγ = mZ , where γ is one of the selected photons. In order to reject the ISR Z(→ ee)γ
background, meγ < 84 or 94 < meγ GeV are required. The ISR Z(→ ee)γ background isalso removed from the category by vetoing events if one of the selected two photons passes
the electron identiﬁcation (Electron ID veto). For muon channel, the rate that a muons
fakes photon is so small that no additional cut is needed. The dominant backgrounds
after the categorization are Z (→ ee) γ and γγ+fake lepton events.
The category selection eﬃciencies are summarized in Table 6.2.1 and 6.2.2. The eﬃciency is a fraction whose numerator is the number of events passing the event selection.
The pT , meγ and mµγ distributions when at least one lepton is required are shown in Figure
6.2.6. The data sideband, which is deﬁned by 100 < mγγ < 120 GeV or 130 < mγγ < 160
GeV, is used to check background contributions. In meγ distributions, Z peak from ISR
Zγ background is seen. This background is removed by meγ selection. Z peak is not seenin mµγ distributions because the µ → γ fake rate is quite lower than the e → γ fake rate.
6.2.2.2

ETmiss signiﬁcance category

In order to select W (→ ℓν)H and Z(→ νν)H events, the ETmiss signiﬁcance is used for the
event categorization: ETmiss /σETmiss > 5 is required. The electron ID veto is applied to reject
electroweak backgrounds particularly W (→ eν)γ background events where the electron
fakes a photon. ETmiss /σETmiss distribution in Z(→ νν)H and W (→ ℓν)H are shown in
Figure 6.2.7. The distributions of ggF and data sideband look similar in low ETmiss region
because no genuine ETmiss is expected in these events. After the event categorization, theelectroweak background dominates [91]. Table 6.2.3 shows the categorization eﬃciencies
in the VH events.
89

∫

50
40
30
20

∫

-1

s = 8 TeV, Ldt=20.3 fb
mH = 125 GeV
ggF x300
VBF x300
WH x300
ZH x300
ttH x300
data sideband-1

s = 8 TeV, Ldt=20.3 fb
mH = 125 GeV
ggF x300
VBF x300
WH x300
ZH x300
ttH x300
data sideband

60
50
40
30
20

10

10

0
0

50

100

150

200

250

300

0
0

50

100

150

200

45

∫

35
30
25
20
15

300

T

∫

30

-1

s = 8 TeV, Ldt=20.3 fb
mH = 125 GeV
ggF x300
VBF x300
WH x300
ZH x300
ttH x300
data sideband

40

250

pmuon [GeV]

Eelectron
[GeV]
T

-1

s = 8 TeV, Ldt=20.3 fb
mH = 125 GeV
ggF x300
VBF x300
WH x300
ZH x300
ttH x300
data sideband

25
20
15
10

10
5

5
0
0

50

100 150 200 250 300 350 400 450 500

0
0

50

100 150 200 250 300 350 400 450 500

meγ 1 [GeV]30∫

meγ 2 [GeV]

25
20
15
10

-1

s = 8 TeV, Ldt=20.3 fb
mH = 125 GeV
ggF x300
VBF x300
WH x300
ZH x300
ttH x300
data sideband

30
25
20
15
10

5
0
0

∫

-1

s = 8 TeV, Ldt=20.3 fb
mH = 125 GeV
ggF x300
VBF x300
WH x300
ZH x300
ttH x300
data sideband

550

100 150 200 250 300 350 400 450 500
mµγ 1 [GeV]

0
0

50

100 150 200 250 300 350 400 450 500mµγ 2 [GeV]

Figure 6.2.6: Distributions of lepton variables when at least one lepton is required after
event selection. The signal distributions are separately for diﬀerent production process.
The backgrounds are emulated by data sideband (excluding mγγ ∈ [120, 130] GeV).

90

W (→ eν)HW (→ µν)HW (→ τ ν)H

41.4 %
8.2 %7.2 %19.3 %
4.7 %4.7 %86.5 %
26.9 %
25.9 %

Category ordering
ETmiss /σETmiss > 5
Electron ID vetodata(sideband)
100 %99.9 %
46.0 %
0.07 %
43.8 %
0.06 %

Z(→ νν)H

Table 6.2.3: Eﬃciency of the ETmiss signiﬁcance category for W (→ ℓν)H and Z(→ νν)Hevents at mH = 125 GeV and data sideband (excluding mγγ ∈ [120, 130] GeV) whichemulate backgrounds. Before the ETmiss signiﬁcance categorization, the one-lepton categorization is performed. The eﬃciency from event selection to the one-lepton categorizationis shown in Category ordering.

∫-1

s = 8 TeV, Ldt=20.3 fb
mH = 125 GeV
ggF x300
VBF x300
WH x300
ZH x300
ttH x300
data sideband

104
103
102

103
102

-1

10

10

1
0

∫

s = 8 TeV, Ldt=20.3 fb
mH = 125 GeV
ggF x300
VBF x300
WH x300
ZH x300
ttH x300
data sideband

104

1
1

2

3

4

5

6

7

8

9

10

0

Emiss
T / σEmiss

20

40

60

80

100 120 140 160 180 200
Emiss
[GeV]
T

T

Figure 6.2.7: Distributions of MET variables after event selection. The signal distributions
are separately for diﬀerent production process. The backgrounds are emulated by data
sideband (excluding mγγ ∈ [120, 130] GeV).

91

Category ordering
At least 2 jets
60 < mjj < 100 GeV
η jet1 − η jet2 < 3.5
pTt > 70 GeV
η γγ − η jj < 1

W (→ hadrons)H Z(→ hadrons)H
100 %99.7 %
68.2 %
70.4 %
39.4 %
35.1 %
39.4 %
35.1 %
17.0 %
13.2 %
13.0 %
10.5 %

data (sideband)
99.8 %
16.7 %
3.6 %3.6 %0.55 %
0.23 %

Table 6.2.4: Eﬃciency of the low mass di-jet category for W (→ hadrons)H and Z(→
hadrons)H events at mH = 125 GeV and data sideband (excluding mγγ ∈ [120, 130]
GeV) which emulate backgrounds.
6.2.2.3

Low mass di-jet category

Events with hadronic decaying vector bosons are selected by requiring the presence of two
reconstructed jets. The main background in this category is QCD events (γγ+di-jet). In
order to separate the VH events from the QCD background, some additional cuts areapplied. The di-jet mass is required to reconstruct Z or W mass; 60 < mjj < 100 GeV.
In the γγ+di-jet backgrounds, t-channel which have large pseudo-rapidity gap largely
contributes. In contrast with the VH events, the di-jet is produced in decay of a vectorboson with momentum of ∼ 250 GeV in average. Hence the diﬀerence of η between
the jets from Z or W tend to be smaller than non-resonance γγ+di-jet backgrounds.
Thus η jet1 − η jet2 < 3.5 is required. When produced with a vector boson, the Higgs
boson can be boosted. This leads to a higher di-photon pTt . Therefore pTt > 70 GeV
is required. The diﬀerence between η of the di-photon system and the di-jet system( η γγ − η jj ) is small in the VH events as shown in Figure 6.2.8. The threshold is optimized
as η γγ − η jj < 1. The categorization eﬃciencies are summarized in Table 6.2.4. Figure
6.2.8 shows the distributions of variables for the low mass di-jet category when the dijet is selected. The mjj histograms in W H and ZH have W and Z peak as expected.
The distributions of mjj and pTt have peaks around 80 GeV. Their peak positions are
determined by kinematic selection criteria. The γγ+di-jet is the dominant backgroundafter the event categorization.

6.2.3

√
VBF enriched categories ( s = 7 and 8 TeV)

6.2.3.1

VBF category for√√
One category is deﬁned for VBF events for s = 7 TeV and two categories for s = 8
TeV. VBF process leads to forward two jets with large pseudo-rapidity gap ( η jet1 − η jet2 ).
The invariant mass of di-jet mjj is larger as the gap bigger as shown in Figure 6.2.9.
|ϕγγ − ϕjj | is used for the categorization because Higgs boson and the di-jet are back-toback in transverse plane. The main background is QCD events such as γγ+di-jet.
√s = 7 TeV analysis√
As shown in Figure 6.2.4, events for the VBF category is selected ﬁrst in s = 7 TeVγγjjanalysis. After two jets are selected, mjj > 400 GeV, η jet1 − η jet2 > 2.8 and |ϕ√ −ϕ |>
2.6 are required. Table 6.2.5 shows the selection eﬃciency for VBF events for s = 7 TeV

92

∫

103

102

∫

104

-1

s = 8 TeV, Ldt=20.3 fb
mH = 125 GeV
ggF x300
VBF x300
WH x300
ZH x300
ttH x300
data sideband-1

s = 8 TeV, Ldt=20.3 fb
mH = 125 GeV
ggF x300
VBF x300
WH x300
ZH x300
ttH x300
data sideband

103
102

10

10

1
1
0

50

100 150 200 250 300 350 400 450 500

050

100 150 200 250 300 350 400 450 500

pjet1 [GeV]
T
1000

∫

900

pjet2 [GeV]
T

800
700
600
500
400

∫

-1

s = 8 TeV, Ldt=20.3 fb
mH = 125 GeV
ggF x300
VBF x300
WH x300
ZH x300
ttH x300
data sideband

103

102

10

300

-1

s = 8 TeV, Ldt=20.3 fb
mH = 125 GeV
ggF x300
VBF x300
WH x300
ZH x300
ttH x300
data sideband

200
100
0
0

1
50

100 150 200 250 300 350 400 450 500

050

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

mjj [GeV]

∫

103

102

-1

s = 8 TeV, Ldt=20.3 fb
mH = 125 GeV
ggF x300
VBF x300
WH x300
ZH x300
ttH x300
data sideband

3

10

102

10

-10

∫

-1

s = 8 TeV, Ldt=20.3 fb
mH = 125 GeV
ggF x300
VBF x300
WH x300
ZH x300
ttH x300
data sideband

10

-5

0

5

10

15

20

-10

-5

0

5

10

15

20
ηγ γ -ηjjηjet1-ηjet2

Figure 6.2.8: Distributions of variables used for low mass di-jet category when di-jet
is required after event selection. The signal distributions are separately for diﬀerent
production process. The backgrounds are emulated by data sideband (excluding mγγ ∈[120, 130] GeV).

93

2000

mjj [GeV]

mjj [GeV]

2200
s = 8 TeV
VBF, mH = 125 TeV

1800

2200

1600

1400

1400

1200

1200

1000

1000

800

800

600

600

400

400

200

200
-6

-4

-2

0

2

4

6

0
-8

8

s = 8 TeV, Ldt=20.3 fb

1800

1600

0
-8

∫

2000

-6

-4

-2

η -η
jet1

0

2

4

6

-1

8

ηjet1-ηjet2

jet2

Figure 6.2.9: Correlation between η jet1 − η jet2 and mjj√in VBF events (left) and in data
sideband(excluding mγγ ∈ [120, 130] GeV) (right) for s = 8 TeV.
At least 2 jets
400 < mjj GeV
2.8 < η jet1 − η jet2
2.6 < |ϕγγ − ϕjj |VBF data (sideband)
56.7 %
12.2 %
32.0 %
0.92 %
31.1 %
0.63 %
28.9 %
0.37 %

Table 6.2.5: The categorization eﬃciency of the high mass di-jet category for VBF events
at mH = 125 GeV√ and data sideband (excluding mγγ ∈ [120, 130] GeV) which emulate
backgrounds for s = 7 TeV.
analysis. The distributions of the variables used for the high mass di-jet categorization
are shown in Figure 6.2.10.
6.2.3.2

VBF categories for√
s = 8 TeV analysis

A multivariate analysis is performed to deﬁned two VBF categories. Multivariate analysis
is suitable in case that discriminant variables are highly correlated with each other. In
VBF events, jets and photons kinetic quantities are correlated (e.g. correlation between
η jet1 − η jet2 and mjj as shown in Figure 6.2.9), hence the multivariate analysis can separate VBF events from backgrounds better than cut-based selection. Input variables are
required to have little correlation with mγγ in order to avoid bias from the mass of training
sample. Eight variables are used to build a boosted) tree (BDT) [97]: pTt , mjj ,( jet1decision
γγ
jj
jet1
jet2
⋆
γγ
jet2
jet1
jet2
/2 and the minimum ∆R, |ϕ − ϕ |, η , η , η ≡ η − η + ηη −ηγjbetween one of the photons and one of the two leading jets (∆Rmin). Some distributionsof the input variables are shown in Figure 6.2.11, while other distributions are alreadyshown in Figure 6.2.8.
The BDT is trained with MC samples. The input signal sample is a VBF sample
with mγγ = 125 GeV. The input background samples are di-photon sample generated
with SHERPA, while the photon-jet and the di-jet components are emulated by a control
region in data. The control region is deﬁned that one of the two photon candidates fails theisolation criteria. Each component is weighted according to the background composition
measured in data. The BDT responses are shown in Figure 6.2.12.
94

∫

102

10

1
0

-1

s = 7 TeV, Ldt=4.8 fb
mH = 125 GeV
ggF x1000
VBF x1000
WH x1000
ZH x1000
ttH x1000
data sideband

103

50

∫

102

10

100 150 200 250 300 350 400 450 500

1
0

50

100 150 200 250 300 350 400 450 500

pjet1 [GeV]

pjet2 [GeV]

T

1200
1000
800
600

∫

T

700

∫

-1

s = 7 TeV, Ldt=4.8 fb
mH = 125 GeV
ggF x1000
VBF x1000
WH x1000
ZH x1000
ttH x1000
data sideband

500
400
300
200

200

100
200 400 600 800 1000 1200 1400 1600 1800 2000

0
-10

-1

s = 7 TeV, Ldt=4.8 fb
mH = 125 GeV
ggF x1000
VBF x1000
WH x1000
ZH x1000
ttH x1000
data sideband

600

400

0
0

-1

s = 7 TeV, Ldt=4.8 fb
mH = 125 GeV
ggF x1000
VBF x1000
WH x1000
ZH x1000
ttH x1000
data sideband

103

-5

0

5

10

15

20
η -η
jet1

mjj [GeV]

jet2√
Figure 6.2.10: Distributions of variables used for high mass di-jet category for s = 7 TeV
when di-jet is required after event selection. The signal distributions are separately fordiﬀerent production process. The backgrounds are emulated by data sideband (excluding
mγγ ∈ [120, 130] GeV).

95

∫

102

-6

-1

-4

-2

0

2

4

6

8

10

∫

103

s = 8 TeV, Ldt=20.3 fb
mH = 125 GeV
ggF x300
VBF x300
WH x300
ZH x300
ttH x300
data sideband

103

102

12

-6

-1

s = 8 TeV, Ldt=20.3 fb
mH = 125 GeV
ggF x300
VBF x300
WH x300
ZH x300
ttH x300
data sideband

-4

-2

0

2

4

6

8

10

ηjet1

∫

104

-1

102

∫

103

s = 8 TeV, Ldt=20.3 fb
mH = 125 GeV
ggF x300
VBF x300
WH x300
ZH x300
ttH x300
data sideband

103

12
ηjet2

102

10

10

-1

s = 8 TeV, Ldt=20.3 fb
mH = 125 GeV
ggF x300
VBF x300
WH x300
ZH x300
ttH x300
data sideband

1

0

1

2

3

4

5

-10

γγ

|φ - φ |
1000

∫

900

-5

0

5

10

15

20
η*

jj

-1

s = 8 TeV, Ldt=20.3 fb
mH = 125 GeV
ggF x300
VBF x300
WH x300
ZH x300
ttH x300
data sideband

800
700
600
500
400
300
200
100
0
0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5
γj

∆Rmin

√
Figure 6.2.11: Distributions of variables used for high mass di-jet category for s = 8
TeV when di-jet is required after event selection. pTt , mjj and η jet1 − η jet2 distributions
are already shown in Figure 6.2.8. The signal distributions are separately for diﬀerent
production process. The backgrounds are emulated by data sideband (excluding mγγ ∈[120, 130] GeV).

96

Events (normalized to unity)

Data/Bkg Events (normalized to unity)

0.25

Data 2012 (sidebands)γγ
γ j + jγ + jj

H→γ γ

0.2
0.15

ATLAS Preliminary∫-1s = 8 TeV, Ldt = 20.7 fb

0.1
0.05
0
1.2
1
0.8
-1

0.25

VBF (m =125 GeV)H
ggF (m =125 GeV)ATLAS Preliminary∫s = 8 TeV, Ldt = 20.7 fb

0.2

-1

H

γ γ + γ j + jγ + jj

H→γ γ

0.15

0.1

0.05

-0.8 -0.6 -0.4 -0.2

0

0.2

0.4

0.6

0.8

0

-1

1

-0.8 -0.6 -0.4 -0.2

0

0.2

0.4

0.6

0.8

1

BDT Response

BDT Response

Figure 6.2.12: The output of the BDT for VBF categorization when applied to data
sideband (excluding mγγ ∈ [120, 130] GeV) and to the expected background (left). The
BDT output when applied to signal samples and the expected background, normalized tounity (right) [91].
Category ordering
At least 2 jets
0.19 < BDT response
0.77 < BDT response

VBF data (sideband)
99.6 %
99.5 %
59.9 %
16.5 %
31.4 %
0.49 %
21.5 %
0.17 %

Table 6.2.6: Eﬃciency of the high mass di-jet category for VBF events at mH = 125
GeV√ and data sideband (excluding mγγ ∈ [120, 130] GeV) which emulate backgrounds for
s = 8 TeV.
The two high mass di-jet categories are deﬁned for√s = 8 TeV analysis as: Tight VBF category: 0.77 < BDT response
 Loose VBF category: 0.19 < BDT response < 0.77

Table 6.2.6 shows the eﬃciency of the high mass di-jet categories.

6.2.4

Untagged categories

The remaining events are divided into nine categories for ggF events. No additional
objects are required but pTt , η and conversion status are used for categorization in thesecategories. When both photon candidates are unconverted photons, an event is called
unconverted, otherwise called converted. An event is called central when both photon
candidates are within |η| < 0.75, otherwise rest. The events are classiﬁed by whether the
events have pTt > 60 GeV (high pTt ), or not (low pTt ). The distribution of pTt is shownin Figure 6.2.13.
When a converted event has at least one photon candidate in1.3 < |η| < 1.75, the event
is categorized as converted transition. Because the energy resolution for converted photons
in this region is degraded due to large amount of material in front of the EM calorimeter,no pTt cut is applied to the converted transition events. Figure 6.2.14 illustrates η regions
for the untagged categories.
97

∫

-1

s = 8 TeV, Ldt=20.3 fb
mH = 125 GeV
ggF x300
VBF x300
WH x300
ZH x300
ttH x300
data sideband

105
104
103
102
10
1
0

50

100

150

200

250

300

pTt [GeV]ηγ2Figure 6.2.13: pTt distribution after event selection.

2

CentralTransition

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

0.5

1 1.5

2
ηγ 1

Figure 6.2.14: η regions for the untagged categories.

98Category
Unconverted central, low pTt
Unconverted central, high pTt
Unconverted rest, low pTt
Unconverted rest, high pTt
Converted central, low pTt
Converted central, high pTt
Converted rest, low pTt
Converted rest, high pTt
Converted transition

Fraction of ggF sample Fraction in data sideband
14.1 %
10.5 %
2.1 %1.2 %29.1 %
29.9 %
4.0 %
3.5 %
9.0 %
7.2 %
1.3 %
0.8 %
26.3 %
29.8 %
3.5 %3.4 %10.6 %
13.6 %

200

∫

-1

180

s = 7 TeV, Ldt = 4.8 fb

160

Unconverted central low pTt
Data
Signal + background

140
120

Events / 2 GeV

Events / 2 GeV

Table 6.2.7: Fraction of the untagged categories for ggF events at mH = 125 GeV.
900

-1

s = 8 TeV, Ldt = 20.3 fb

700

Unconverted central low pTt
Data
Signal + background

600
500

100

400

80

300

60
40

200

20

100

0
100

∫

800

110

120

130

140

150

160

mγ γ [GeV]

0
100

110

120

130

140

150

160

mγ γ [GeV]

Figure 6.2.15: Di-photon mass distributions in diﬀerent categories. The parameters of
the signal and the background models are best ﬁt values.
Table 6.2.7 summarizes the fraction of the untagged categories for ggF events in thenine untagged categories. The mass resolutions of each category are estimated in thefollowing chapter.

6.2.5

Di-photon mass distributions

Figure 6.2.15, 6.2.16, 6.2.17 and 6.2.18 show the observed invariant mass distributions foreach category with ﬁt results, which are explained in following chapters.

99

s = 7 TeV, Ldt = 4.8 fb

14

Events / 2 GeV

Events / 2 GeV

∫

16

-1

Unconverted central high pTt
Data
Signal + background

12
10

60

∫

s = 8 TeV, Ldt = 20.3 fb
50

Unconverted central high pTt
Data
Signal + background

40

8

30

6

20

-1

4
10

2
0
100

110

120

130

140

150

0
100

160

110

120

130

140

500

∫

450

s = 7 TeV, Ldt = 4.8 fb

400

-1

Unconverted rest low pTt
Data
Signal + background

350
300

150

160

mγ γ [GeV]
Events / 2 GeV

Events / 2 GeV

mγ γ [GeV]

250

3000

∫

s = 8 TeV, Ldt = 20.3 fb
2500

-1

Unconverted rest low pTt
Data
Signal + background

2000
1500

200
1000

150
100

500

50
0
100

110

120

130

140

150

0
100

160

110

120

130

140

∫

-1

50

s = 7 TeV, Ldt = 4.8 fb

40

Unconverted rest high pTt
Data
Signal + background

150

160

mγ γ [GeV]
Events / 2 GeV

Events / 2 GeV

mγ γ [GeV]

30

200

∫

180

s = 8 TeV, Ldt = 20.3 fb

160

Unconverted rest high pTt
Data
Signal + background

140
120

-1

100
80

20

60
40

10

20
0
100

110

120

130

140

150

0
100

160

110

120

130

140

∫

-1

120

s = 7 TeV, Ldt = 4.8 fb

100

Converted central low pTt
Data
Signal + background

80

160

600

∫

s = 8 TeV, Ldt = 20.3 fb
500-1Converted central low pTt
Data
Signal + background

400
300

60

200

40

100

20
0
100

150

mγ γ [GeV]
Events / 2 GeV

Events / 2 GeV

mγ γ [GeV]

110

120

130

140

150

160

mγ γ [GeV]

0
100

110

120

130

140

150

160

mγ γ [GeV]

Figure 6.2.16: Di-photon mass distributions in diﬀerent categories. The parameters of
the signal and the background models are best ﬁt values.

100

∫

s = 7 TeV, Ldt = 4.8 fb

14

Events / 2 GeV

Events / 2 GeV

16-1Converted central high pTt
Data
Signal + background

12
10

45

∫

40

s = 8 TeV, Ldt = 20.3 fb

35

Converted central high pTt
Data
Signal + background

30

-1

25
8

20

6

15

4

10

2

5

0
100

110

120

130

140

150

0
100

160

110

120

130

140

∫

500

s = 7 TeV, Ldt = 4.8 fb

400

Converted rest low pTt
Data
Signal + background

150

160

mγ γ [GeV]
Events / 2 GeV

Events / 2 GeV

mγ γ [GeV]

-1

2500

∫

s = 8 TeV, Ldt = 20.3 fb
2000

-1

Converted rest low pTt
Data
Signal + background

1500

300
1000

200

500

100
0
100

110

120

130

140

150

0
100

160

110

120

130

140

60

∫

s = 7 TeV, Ldt = 4.8 fb
50-1Converted rest high pTt
Data
Signal + background

40

150

160

mγ γ [GeV]
Events / 2 GeV

Events / 2 GeV

mγ γ [GeV]
180

∫

160

s = 8 TeV, Ldt = 20.3 fb

140

Converted rest high pTt
Data
Signal + background

120

-1

100
30

80

20

60
40

10
20
0
100

110

120

130

140

150

0
100

160

110

120

130

140

∫

250

s = 7 TeV, Ldt = 4.8 fb-1

Converted transition
Data
Signal + background

200

150

160

mγ γ [GeV]
Events / 2 GeV

Events / 2 GeV

mγ γ [GeV]

150

1000

∫

900

s = 8 TeV, Ldt = 20.3 fb

800

Converted transition
Data
Signal + background

700
600

-1

500
400

100

300
200

50

100
0
100

110

120

130

140

150

160

mγ γ [GeV]

0
100

110

120

130

140

150

160

mγ γ [GeV]

Figure 6.2.17: Di-photon mass distributions in diﬀerent categories. The parameters of
the signal and the background models are best ﬁt values.

101

∫

s = 7 TeV, Ldt = 4.8 fb

18

Events / 2 GeV

Events / 2 GeV

22
20

-1

Di-jetData
Signal + background

16
14

40

25
20

8

15

6

10

2
0
100

5
110

120

130

140

150

0
100

160

110

120

130

140

∫

30

s = 8 TeV, Ldt = 20.3 fb-1

Tight VBF
Data
Signal + background

25
20

30

10

10

5

5
130

140

150

0
100

160

110

120

130

140

∫

s = 8 TeV, Ldt = 20.3 fb

-1

miss
ET significance

12

Data
Signal + background

10
8
6
4
2
0
100

110

120

130

140

150

-1

150

160

mγ γ [GeV]
Events / 2 GeV

Events / 2 GeV

mγ γ [GeV]
14160

Low-mass di-jet
Data
Signal + background

20
15

120

∫

s = 8 TeV, Ldt = 20.3 fb
25

15

110

150

mγ γ [GeV]
Events / 2 GeV

Events / 2 GeV

mγ γ [GeV]

0
100

-1

Loose VBF
Data
Signal + background

30

12
10

4

∫

s = 8 TeV, Ldt = 20.3 fb

35

160

mγ γ [GeV]

24
22
20
18
16
14
12
10
8
6
4
2
0
100

∫

s = 8 TeV, Ldt = 20.3 fb-1

One lepton
Data
Signal + background

110

120

130

140

150

160

mγ γ [GeV]

Figure 6.2.18: Di-photon mass distributions in diﬀerent categories. The parameters of
the signal and the background models are best ﬁt values.

102Chapter 7
Signal and background modeling
The statistical procedure with a likelihood function is used to test the Standard Model
Higgs boson hypothesis and to measure couplings, mass and width. The likelihood function is constructed from probability density functions (PDF) of signal and backgroundcomponents with respect to mγγ . The modeling of the signal and background is describedin this chapter.

7.1

Signal modeling

The signal is modeled with MC-simulated events of the SM Higgs processes as describedin Sec 3.2. The yield and shape of the signal events are parametrized as a function of ahypothesized mH . The detector response is also modeled with GEANT4 program. Thus
the yield and the shape of the signal events are parametrized for a hypothesized mH . The
signal model is used for a likelihood which is described in Section 8.1.

7.1.1

Signal probability density function

The function of the PDF is the sum of a Crystal Ball function and a wider Gaussian
tail component. The parameters of the function are diﬀerent for each event category.
The Crystal Ball function has a Gaussian and a non-Gaussian low mass tail. The tail is
described by a power-law function. The Crystal Ball function is deﬁned by:()
exp − t2
)n2
(
)(
)−nCB
fCB (mγγ |mH ) = N (nCB
 nCB CB exp − |αCB |2− |αCB | − tt > −αCBt ≤ −αCB(7.1.1)−µCB, σCB is the sigma of the Gaussian part, µCB is the peak position
where t ≡ mγγσCBof the Gaussian , N is a normalization parameter and αCB and nCB parametrize the
non-Gaussian tail. Figure 7.1.1 illustrates the Crystal Ball function. The signal shapefunction fs is modeled by:()(mγγ − µGA )21
exp −(7.1.2)fs (mγγ |mH ) = cCB fCB (mγγ |mH ) + (1 − cCB ) √
2
2
2σGA
2πσGA
|αCB |

2103|αCB |

0.25
0.2
0.15

Crystal Ball
µ = 125
CB
σCB = 1.6
αCB = 1.3
nCB = 10
αCB x σCB

0.1
0.05
0
110

GaussianPower-law
115

120

125

130

135

Figure 7.1.1: Illustration of Crystal Ball function.
where cCB is the fraction of the Crystal Ball function. The σCB and σGA correspondto the mass resolution of the di-photon events. All event categories use the same signal
function form while parameters are determined category-by-category.
For the improvement of the accuracy of parameters, the ﬁt is performed with signalof all the mass points simultaneously under the assumption that the parameters have thefollowing dependence on mH :µCB (mH ) = mH + (µ0 + µ1 mH + µ2 m2H )σCB (mH ) = σ0 + σ1 mH + σ2 m2H αCB (mH ) = α0 + α1 mH
nCB (mH ) = 10
(7.1.3)


µ
(m
)
=
µ
(m
)

GA
H
CB
H



σ
(m
)
=
(k
+
k
mH ) σCB (mH )

GA
H
0
1


cCB (mH ) = c0 + c1 mH
where µi , σi , αi , n, ki and ci (i = 0, 1, ..) are ﬁtting parameters. nCB (mH ) is ﬁxed
to be 10 from a simulation study. Figure 7.1.2 shows results of the simultaneous ﬁt in
Unconverted central, low pTt category. The errors of the simultaneous ﬁt is so small
compared with other systematic uncertainties that the ﬁtting errors are not taken into
account as a systematic uncertainty.
Figure 7.1.3 compares the signal histograms√between Unconverted central, high pTt
category and Converted transition category in s = 8 TeV analysis at mH = 125 GeV.
The former category has the best mass resolution (σCB = 1.35 GeV), while the latterhas the widest shape (σCB = 2.25 GeV). Table 7.1.1 gives the parameters of the signal
functions for mH = 125 GeV. Their uncertainties are discussed in Section 7.3.3 and 7.3.4.

7.1.2

Signal yield

The diﬀerential cross section and branching ratio of the signal events are calculated insignal MC as described in Section 3.2. The signal eﬃciency is also computed in the MC
events based on GEANT4 program. The total eﬃciency depends on the eﬃciency ofphoton reconstruction described in Chapter 4 and estimated√to be 37.5 % at mH = 125
GeV. For this mass, the expected total signal yield is 80.8 in s = 7 TeV data and 355.5
104

450

s = 8 TeVσCB [GeV]

a.u.

500
Signal modeling
Unconverted central, low pTt

400
350

1.8
1.7
1.6

300
250

s = 8 TeV
Unconverted central, low pTt
Simultaneous fit
Individual fits

1.5

200
1.4

150
100

1.3

50
0
90

100

110

120

130

140

150

160

1.2

100

110

120

mγ γ [GeV]

130

140

150
mH [GeV](a)(b)

Figure 7.1.2: Simultaneous ﬁt to 11 signal MC samples with mH between 100 and 150
GeV in Unconverted central, low pTt category (a). Resulting σCB of simultaneous ﬁt andindividual ﬁts in Unconverted central, low pTt category. Band of σCB from simultaneousﬁt shows the error from the ﬁt (b).

0.16
0.14
0.12

mH = 125 GeV
Unconverted central, high pTt
Converted Transition

0.1
0.08
0.06
0.04
0.02
0
110 115 120 125 130 135 140 145 150 155 160
mγ γ [GeV]

Figure 7.1.3: mγγ histogramsin Unconverted central, high pTt category and Converted√
transition category in s = 8 TeV analysis at mH = 125 GeV.

105√
s = 7 TeV Inclusive
Unconverted central, low pTt
Unconverted central, high pTt
Unconverted rest, low pTt
Unconverted rest, high pTt
Converted central, low pTt
Converted central, high pTt
Converted rest, low pTt
Converted rest, high pTt
Converted transition
Di-jet√s = 8 TeV Inclusive
Unconverted central, low pTt
Unconverted central, high pTt
Unconverted rest, low pTt
Unconverted rest, high pTt
Converted central, low pTt
Converted central, high pTt
Converted rest, low pTt
Converted rest, high pTt
Converted transition
Loose VBF
Tight VBF
Low mass di-jet
ETmiss signiﬁcanceOne-lepton

µCB
124.6
124.7
124.7
124.6
124.7
124.5
124.6
124.5
124.6
124.4
124.6
124.6
124.7
124.8
124.6
124.7
124.5
124.7
124.4
124.6
124.5
124.7
124.7
124.7
124.7
124.6

σCB
1.61
1.43
1.35
1.56
1.41
1.62
1.46
1.78
1.60
2.25
1.50
1.76
1.49
1.39
1.72
1.67
1.67
1.53
2.00
1.85
2.50
1.69
1.62
1.60
1.72
1.73

αCB
1.3
2.3
2.5
1.7
1.8
1.6
1.7
1.3
1.4
0.9
1.3
1.5
2.1
1.9
1.9
2.2
1.5
1.8
1.5
1.6
1.3
1.6
1.6
1.6
1.6
1.5

nCB
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10

σGA
5.6
5.1
7.2
5.1
5.3
7.4
8.2
4.7
5.8
5.2
6.1
3.8
5.7
6.2
3.0
4.4
7.2
6.5
4.2
6.3
4.6
3.7
3.9
4.6
8.5
8.0

cCB
0.96
1.00
1.00
0.96
0.96
1.00
1.00
0.98
0.99
0.88
0.97
0.96
1.00
1.00
0.93
0.98
1.00
1.00
0.97
0.99
0.94
0.96
0.96
0.97
0.99
0.98

Table 7.1.1: The parameters of signal functions in the diﬀerent categories for mH = 125
GeV. The unit of µCB , σCB and σGA is GeV.

106

Observed

Inclusive
Unconverted central, low pTt
Unconverted central, high pTt
Unconverted rest, low pTt
Unconverted rest, high pTt
Converted central, low pTt
Converted central, high pTt
Converted rest, low pTt
Converted rest, high pTt
Converted transition
Di-jet

23788
2054
97
7129
444
1493
77
8313
501
3591
89

Expected
Signal Spurious
signal
80.8
7.3
10.7
2.0
1.5
0.2
22.0
2.2
2.8
0.5
6.8
1.6
1.0
2.7
21.4
4.6
2.8
0.5
9.1
3.2
2.2
0.4

Table 7.1.2: The number√ of events in data and the expected number of signal events for
mH = 126.5 GeV for s = 7 TeV analysis. Spurious signal represents the uncertainty ofthe signal yield due to background mismodeling, which Section 7.3.1.7 describes in detail.
√in s = 8 TeV data. The expected signal yield for each category depends not only on
the photon reconstruction eﬃciency but also on the probabilities of photon conversion
and reconstruction of additional objects used for event categorization. Table 7.1.2 and7.1.3 summarize the number of events observed in data and the expected number of signal
events for diﬀerent categories. The uncertainties are discussed in √Section 7.3.1 and 7.3.2.
Figure 7.1.4 and 7.1.5 shows the expected signal composition for s = 7 and 8 TeV.

7.2

Background modeling

The invariant mass distributions of the background for each category are parametrizedwith an analytic function. Diﬀerent functions are chosen for diﬀerent categories based onstudies with MC samples. The shape of the background are completely diﬀerent from thesignal; the signal events have a sharp resonance at the Higgs mass, while the background
events have monotonous shapes in the di-photon invariant mass distribution. This is oneof the largest advantages of the H → γγ analysis. Considered backgrounds are γ-γ, γ-jet,jet-jet, Drell-Yan and other electroweak background processes (Z + γ and W + γγ).
The main contribution to the γ-γ background is the q q̄, qg → γγX processes, namely
the Born and Bremsstrahlung. Another main γ-γ background is due to the gg → γγ,
referred to as the box contribution. Figure 7.2.1 shows their diagrams. The γ-jet andjet-jet background events have fake photons due to the presence of a leading π 0 resulting
from the fragmentation of a quark or a gluon. The diagrams of the γ-jet and jet-jet
backgrounds are shown in Figure 7.2.2 and 7.2.3. The ratio of cross sections of the γ-γ,
γ-jet and jet-jet is about 1 : 104 : 107 , where the photons and the jets are required to have
ET > 25 GeV and |η| < 2.5 and 80 < mγγ < 150 GeV [98].
Drell-Yan events contaminate the signal region when two electrons are misidentiﬁed
as photons due to failure in the track-to-cluster matching described in Section 4.3. The

107

Observed

Inclusive
Unconverted central, low pTt
Unconverted central, high pTt
Unconverted rest, low pTt
Unconverted rest, high pTt
Converted central, low pTt
Converted central, high pTt
Converted rest, low pTt
Converted rest, high pTt
Converted transition
Loose VBF
Tight VBF
Low mass di-jet
ETmiss signiﬁcanceOne-lepton

118893
10900
553
41236
2558
7109
363
38156
2360
14864
276
136
210
49
123

Expected
Signal Spurious
signal
355.5
12.0
46.6
4.6
7.1
0.8
97.1
11.4
14.4
2.0
29.8
2.4
4.6
0.8
88.0
8.0
12.9
1.1
36.1
9.1
4.8
1.1
7.3
0.3
3.0
0.6
1.1
0.1
2.6
0.3

Table 7.1.3: The number√ of events in data and the expected number of signal events for
mH = 126.5 GeV for s = 8 TeV analysis. Spurious signal represents the uncertainty ofthe signal yield due to background mismodeling, which Section 7.3.1.7 describes in detail.

Di-jetUntageds = 7 TeV

ggF

s = 7 TeV

VBF

WH

ZH

ttH

Di-jetttH
Conv. transition
Conv. rest high p

Tt

ZH
Conv. rest low p

Tt

Conv. central high p

Tt

WHConv. central low p

Tt

Unconv. rest high p

Tt

VBF

Unconv. rest low p

Tt

Unconv. central high p

Tt

ggF

Unconv. central low p

Tt

0

10

20

30

40

50

60 70 80 90 100
signal composition [%]

0

10

20

30

40

50

60 70 80 90 100
signal composition [%]Figure 7.1.4: The signal composition for each production process as a function of theevent category (left) The √signal composition for each event category as a function of thesignal process (right) for s = 7 TeV analysis at mH = 125 GeV.

108

High mass di-jet

Untageds = 8 TeVVH enrichggF

s = 8 TeV

VBF

WH

ZH

ttH

One lepton
miss

ttH

ET

significanceLow-mass di-jet
Tight VBF
ZH

Loose VBF
Conv. transition
Conv. rest high p
Tt

WHConv. rest low p

Tt

Conv. central high p

Tt

Conv. central low p

VBF

Tt

Unconv. rest high p

Tt

Unconv. rest low p

Tt

Unconv. central high p

ggF

Tt

Unconv. central low p

Tt

0

10

20

30

40

50

60 70 80 90 100
signal composition [%]

0

10

20

30

40

50

60 70 80 90 100
signal composition [%]Figure 7.1.5: The signal composition for each production process as a function of theevent category (left) The √signal composition for each event category as a function of thesignal process (right) for s = 8 TeV analysis at mH = 125 GeV.

q

g

q

q

q

q

g

g

Figure 7.2.1: Diagrams of the main γ-γ backgrounds: Born (left), Bremsstrahlung (middle) and Box (right)

q

g

q

g

g

g
q

q

q

g

q

g

Figure 7.2.2: Diagrams of γ-jet background (Leading-order)

109

Figure 7.2.3: Diagrams of jet-jet backgrounds (Leading-order)
high mass tail of the Drell-Yan peak in the mass window ([100, 160] GeV) is the source of
background. Because electrons have similar isolation distributions to photons as well as
shower shape, they have much higher fake rate to photons than jets. However since thecross section of Drell-Yan within the mass window is much smaller than γ-γ, γ-jet and jetjet, the expected fraction of Drell-Yan events is small. Other electroweak backgrounds,
such as Z + γ and W + γγ events, also have fake photons due to electrons and have
non-negligible contribution to the VH categories.

7.2.1

Background composition

In order to choose ﬁtting functions, the fraction of each background component is need tobe estimated. For Drell-Yan events, the misidentiﬁcation rate is extracted in data withusing Z → ee events reconstructed as di-electron and e−γ pairs. The fraction of Drell-Yan
events is estimated to be ∼ 1 % [93]. The Z + γ and the W + γγ samples are normalizedaccording to the cross section of the process. They have very small contributions except
in VH categories.
The fractions of γ-γ, γ-jet and jet-jet events are measured using several data-driven
techniques [99]. One of them is template ﬁt method [100]. In this method, templates ofisolation distributions of genuine photons and fake photons are formed for both leading
and sub-leading photons in data. The template of fake photons is obtained from photons
which fail the photon identiﬁcation criteria but pass certain relaxed identiﬁcation criteria.
The template of genuine photons is obtained by subtracting the fake photon templatefrom the isolation distribution of photon candidates which pass the identiﬁcation criteria.
For subtracting, the fake photon template is normalized such that the integrals of thetwo distributions are equal for bad isolation (high ETcone40 ) region. The template ﬁt is
performed to the leading photon and sub-leading photon simultaneously in each bin of thedi-photon invariant mass distribution relaxed isolation criteria. From the ﬁt result, thefractions of each background are estimated to be 80 ± 4 %, 19 ± 3 % and 1.8 ± 0.5 % for√+3%, 22 ± 2 % andthe γ-γ, the γ-jet and jet-jet events in s = 7 TeV data, while 75−2√2.6 ± 0.5 % in s = 8 TeV data. In this estimation, the signal events and the Drell-Yan

110

dN/dmγ γ [GeV-1]

900

ATLAS Preliminary

800

Data 2011
s = 7 TeV, ∫ Ldt = 4.9 fb-1

700

γ γ +DY dataγ j data
jj data

600

Statistical error

500

Total error

400
300
200
100
0
100

110

120

130

140

150

160

mγ γ [GeV]

Figure 7.2.4: Composition of the inclusive data sample as a function of mγγ , extracted
from the double two dimensional sideband method after the inclusive event selection. The
various components are stacked on top of each other. The error bars correspond to thestatistical uncertainties on each component separately. The gray bands show the overall
uncertainty on each component [99].
are included in the γ-γ fraction. However their contributions are so small. Figure√ 7.2.4
shows the di-photon sample composition as a function of the invariant mass at s = 7
TeV. The fractions are estimated in the inclusive category, and the results are applied to
all categories.
The results of background decomposition is used for ﬁt function choice, but not used
for likelihood ﬁt. Therefore the estimation of background decomposition does not aﬀect
ﬁnal physics results directly.

7.2.2

Fitting function for each event category

Fitting functions for each category are chosen to achieve a good compromise between thebias for signal yield due to the chosen parametrization and retaining the signiﬁcance ofobservation and measurement. Depending on the category, an exponential function, a
4th-order Bernstein polynomial or an exponential function of a 2nd-order polynomial isused as shown in Table 7.2.1. The 4th-order Bernstein polynomial and the exponentialfunction of a 2nd-order polynomial are deﬁned as:
4∑4!
miγγ (mγγmax − mγγ )4−i
i!
(4
−
i)!
i=0
)
(
Exp2nd (mγγ ) =N exp c1 mγγ + c2 m2γγ
Bern4 (mγγ ) =ai(7.2.1)

where Bern4 is a 4th-order Bernstein polynomial, Exp2nd is an exponential function of
2nd-order polynomial and coeﬃcients ai , c1 , c2 , N are ﬁtting parameters as well as mγγmax
is the maximum of mγγ (160 GeV). The coeﬃcient ai is constrained to be ai ≥ 0, hence
Bern4 a has non-negative value. If the background modeling is not perfect, when themγγ histogram of background processes are ﬁtted with signal + background model, thenon-zero signal is obtained from the ﬁt. This signal biases, called spurious signal, for eachcategory from the choice of background parametrization are estimated using MC samples
111

Category√√s = 7 TeV
s = 8 TeV
Inclusive
Unconverted central, low pTt
Unconverted central, high pTt
Unconverted rest, low pTt
Unconverted rest, high pTt
Converted central, low pTt
Converted central, high pTt
Converted rest, low pTt
Converted rest, high pTt
Converted transition
Loose VBF
Di-jetTight VBF—
Low mass di-jet—
ETmiss signiﬁcance—One-lepton

Function
4th-order Bernstein polynomial
Exponential of 2nd-order pol.
Exponential
4th-order Bernstein polynomial
Exponential
Exponential of 2nd-order pol.
Exponential
4th-order Bernstein polynomial
Exponential
Exponential of 2nd-order pol.
Exponential
Exponential
Exponential
Exponential
Exponential

Table 7.2.1: Functions for background events in the each event category.
normalized according to the studies in Section 7.2.1. The spurious signal is discussed in
Section 7.3.1.7.

7.3

Systematic uncertainties

Four diﬀerent groups of the systematic uncertainties are considered: signal yield, event
migration, mass scale and mass resolution. The ”signal yield” is the estimation of uncertainties on the amount of signal events observed. The ”event migration” is the uncertainty
on categorization, that is, uncertainties on the fraction of events being classiﬁed in different event categories. The ”mass scale” and ”mass resolution” are uncertainties on the
Higgs mass position and resolution, respectively.

7.3.1

Signal yield

Seven diﬀerent sources of the systematic uncertainty on signal yield are considered assummarized in Table 7.3.1. Each uncertainty is described below.
7.3.1.1

Luminosity

The uncertainty of luminosity is evaluated with the luminosity detector. The measurement method is described√in Appendix A. The estimated uncertainty
on the integrated√
luminosity is ±1.8 % for s = 7 TeV data and ±3.6 % for s = 8 TeV data.

112

Uncertainty
Luminosity
Trigger
Identiﬁcation
Isolation
Kinematics
Theory: cross section
Theory: branching fraction
Background modeling√√s = 7 TeV
s = 8 TeV
±1.8 %±3.6 %±1.0 %±0.5 %±8.4 %±2.4 %±0.4 %±1.0 %±0.3 %±0.3 %
Table 7.3.2
Table 7.3.3
+5.0
%
−4.9
Table 7.1.2
Table 7.1.3

Table 7.3.1: Systematic uncertainties on signal yield at mH = 125 GeV.

Uncertainty

Value

+7.1
% VBF: ±0.3 %WH : ±0.9 %
−7.8
+3.2
ZH : ±2.9 %
ttH :
%
−9.3
+7.6
+2.5
PDF +αS
ggF:% VBF:% WH : ±2.6 %
−7.1
−2.1
ZH : ±2.7 %ttH : ±8.4 %QCD scale for ggF + multi-jet
2 jet in di-jet category: ±20 %3 jet in di-jet category: ±15 %√Table 7.3.2: Systematic uncertainties on Higgs boson cross section for s = 7 TeV analysis
at mH = 125 GeV.
QCD scaleggF:

Uncertainty

Value
+7.2
QCD scaleggF:% VBF: ±0.2 %WH : ±1.0 %
−7.8
+3.8
ZH : ±3.1 %
ttH :
%
−9.3
+7.5
+2.6
PDF +αS
ggF:% VBF:% WH : ±2.3 %
−6.9
−2.8
ZH : ±2.5 %ttH : ±8.1 %QCD scale for ggF + multi-jet
2 jet in tight VBF category: ±20 %3 jet in tight VBF category: ±44 %2 jet in loose VBF category: ± 20 %3 jet in loose VBF category: ± 20 %2 jet in low mass di-jet category: ± 30 %√Table 7.3.3: Systematic uncertainties on Higgs boson cross section for s = 8 TeV analysis
at mH = 125 GeV.

113

7.3.1.2

Trigger eﬃciency

As described in Section 4.2, the di-photon trigger eﬃciency is measured by the Bootstrap
method. In order to estimate the bias of the method, the eﬃciency is also evaluated using
other measurements: data-driven study with high purity photons in Z → llγ events, aswell as MC simulation analysis with using H → γγ events and fake photon contaminating
events. The diﬀerence√of the results with respect to the results from the Bootstrap method
is ±1.0 (±0.5) % for s = 7 (8) TeV, and is considered as the systematic uncertainty ofthe di-photon trigger eﬃciency.
7.3.1.3

Photon identiﬁcation eﬃciency

The uncertainty of identiﬁcation eﬃciency per photon candidate is estimated in Section
5.3. For the H → γγ analysis, the multi-photon correlation are taken into account. Because some identiﬁcation uncertainties are correlated between two photons, the correlationcoeﬃcients are calculated as a function of η, ET and conversion status of two photons.
From the correlation coeﬃcients and the uncertainty per photon, the uncertainties of photon identiﬁcation eﬃciency is calculated event by event in the H → γγ signal samples.
Then the√ uncertainties are combined, and the total uncertainty is measured to be ±2.4
% for √
s = 8 TeV analysis.
For s = 7 TeV analysis, photons are assumed to be fully correlated. This is moreconservative model. The uncertainty is estimated to be ±8.4 %.
7.3.1.4

Isolation criteria eﬃciency

In Section 5.5, √the eﬃciency uncertainty of isolation
criteria for di-photon is measured to√be ±0.4 % for s = 7 TeV, and ±1.0 % for s = 8 TeV analysis.
7.3.1.5

Kinematic threshold eﬃciency

The energy scale uncertainty of photons causes signal yield uncertainty because the leading(sub-leading) photon candidates are required to pass 40 (30) GeV ET threshold. The
uncertainty is estimated to be ±0.3 %. This uncertainty is correlated with the mass scale
uncertainties which are described in Section 7.3.3.
7.3.1.6

Theoretical uncertainties for Higgs cross section and branching ratio

The theoretical uncertainties on the Higgs boson cross section for each production process,as well as branching ratio are taken from [17, 18] as summarized in Table 7.3.2 and 7.3.3.
The uncertainties on the cross section include PDF and missing higher order perturbative
QCD corrections. The αS uncertainty is added in quadrature to the PDF variation.
Hence PDF uncertainty is called PDF+αS . On the other hand, the uncertainty of QCD
renormalization and factorization is called QCD scale. These theoretical uncertainties
have the mH dependence. The typical value of the theoretical uncertainty is ±11 %.
For the ggF+2 jet as well as 3 jet cross section, the QCD perturbative uncertainties
are calculated separately.

114

7.3.1.7

Background modeling

The uncertainties on background modeling are sources of the signal yield uncertainty.
The bias on the signal yield is estimated for each event category by a likelihood ﬁt withsignal and background models to a simulated background only data set. The obtained
signal yield from the ﬁt is assumed as the signal yield bias. The signal bias due tobackground modeling is called spurious signal, and is estimated to be between ±4 and±23 % depending on event category.

7.3.2

Event migration

Some systematic uncertainties do not lead to the total signal yield uncertainty but lead tothe event migration uncertainties. Ten diﬀerent migration sources are taken into accountas described below. Appendix E summarizes the uncertainties.
7.3.2.1

Material mismodeling

The material mapping mismodeling causes bias on the fraction of converted photons. The
impact of the mismodeling is estimated with using signal MC samples with a special material conﬁguration, where the material amount is shifted by the geometry uncertainties.
The potential migration is −4 % for unconverted photon categories and +3.5 % for converted photon categories. The sign of the uncertainty is plus (minus) if the fraction of
the category is increased (decreased) when the material amount is increased.
7.3.2.2

Jet energy scale

The jet energy scale (JES) uncertainties lead to the event migration between categories
requiring jets and other categories. The potential migration is estimated by varying the
JES within their uncertainties [101]. The JES uncertainties are categorized into some
non-negligible independent uncertainties (called OﬀsetMu, Flavor Composition, Flavor
Response, Model 1, EtaCalib, Pileup and Close-By). They are described in Appendix D.3.
The estimated uncertainties are up to 12 % (11 %) for the tight (loose) VBF category,√
6.7 % for the low massdi-jetcategory
and
up
to
0.7
%
for
the
other
categories
ins=8√
TeV data, while in s = 7 TeV data, up to 15 % for di-jet category and up to 0.4 % for
the other categories.
7.3.2.3

Jet energy resolution

The jet energy resolution (JER) uncertainty aﬀects the event migration. The impact isfound to be up to 3.8 % (3.4 %) on the tight (loose) VBF category,
3.4 % on the low-mass√di-jet category, and up to 0.9 % on the other categories in s = 8 TeV data.
7.3.2.4

Jet vertex fraction

The diﬀerences of jet vertex fraction (JVF) eﬃciency between data and MC is estimatedfor pileup jets and jets from a hard process separately (see Appendix D). The uncertainties
are 0.3 (1.2) % in the loose VBF category for ggF (VBF), ans 2.3 (2.4) % in the low mass115

di-jet category for ggF (VBF). The uncertainties are only applied tobecause of high pileup condition.
7.3.2.5√
s = 8 TeV data

Higgs pT of gluon-gluon process

The Higgs pT uncertainty due to the modeling of the Higgs boson kinematic properties
is estimated from the HqT2.0 [86] as a function of the Higgs√ pT . The potential event
migration is evaluated from the Higgs pT uncertainty. For s = 8 TeV analysis, thepotential migration is 10.2 % on the high pTt categories, 10.4 % (8.5 %) on the tight(loose) VBF categories,√ 12.5 % on the low mass di-jet category and up to 4.0 % on theother categories. For s = 7 TeV analysis, the uncertainties are 12.5 % on the high pTt
categories, 9 % on the di-jet categories and 1.1 % on the other categories.
7.3.2.6

Underlying event

Underlying event is everything in single parton collisions except the hard process of interest [102]. The mismodeling of the underlying event in MC events leads to the migration
between di-jet events. For the systematic studies, special samples without multi-parton
interaction are used. From the comparison of the predicted fractions of the categories
between the default and the special sample√ events, up to 30 (13) % uncertainty for thedi-jet categories are assigned to ggF for s = 7 (8) TeV analysis.
To the other production√
process, the assigned uncertainties are up to 6 (4) % for s = 7 (8) TeV analysis.
7.3.2.7

Lepton eﬃciency

The lepton eﬃciency uncertainties aﬀects the number of signal events of the one-lepton
category. The uncertainties of lepton reconstruction, identiﬁcation, energy scale andenergy resolution are taken into account. The uncertainties of the event migration are
estimated to be up to 1 %.
7.3.2.8

ETmissThe uncertainties of ETmiss are estimated by propagating the ET uncertainties of input
objects (photons, electron, jets and cell out). The largest contribution comes from thecell-out term. The jet energy scale has the second largest contribution, and the uncertainty
of other objects are negligible. The potential event migration is estimated by varying theETmiss up and down by the uncertainty. In the ETmiss signiﬁcance category, the assigned
uncertainty is 66.4 % to ggF, 30.7 % to VBF and 1.2 % to VH.
7.3.2.9()η ⋆ = η γγ − η jet1 + η jet2 /2

The uncertainty of η ⋆ modeling aﬀects the eﬃciency of the di-jet categories. The uncertainty due to η ⋆ modeling is estimated by reweighting the jet distribution at MC generator
level to another generator distribution. The uncertainty of the event migration for thetight (loose) VBF category is 7.6 (6.2) %.

116

Z line shape Material |η| < 1.8 Material |η| > 1.8
0.30 %
0.30 %
0.30 %
0.30 %
0.30 %
0.50 %
0.10 %
0.30 %
0.50 %
0.10 %
0.30 %
0.10 %
0.30 %
0.10 %
0.30 %
0.20 %
0.10 %
0.30 %
0.20 %
0.10 %
0.40 %
0.60 %
0.30 %
0.30 %√
Table 7.3.4: Uncertainties on mass scale for s = 7 TeV.

Category
Unconverted central, low pTt
Unconverted central, high pTt
Unconverted rest, low pTt
Unconverted rest, high pTt
Converted central, low pTt
Converted central, high pTt
Converted rest, low pTt
Converted rest, high pTt
Converted transition
Di-jetCategory
Unconverted central, low pTt
Unconverted central, high pTt
Unconverted rest, low pTt
Unconverted rest, high pTt
Converted central, low pTt
Converted central, high pTt
Converted rest, low pTt
Converted rest, high pTt
Converted transition
Di-jetPresampler barrel Presampler endcap
0.10 %
0.10 %
0.20 %
0.30 %
0.10 %
0.10 %
0.10 %
0.10 %√
Table 7.3.5: Uncertainties on mass scale for s = 7 TeV.

7.3.2.10|ϕγγ − ϕjj |In the same way as η ⋆ , the uncertainty is estimated by reweighting the jet distribution.
The resulting uncertainty is 12.1 (8.5) % for the tight (loose) VBF categories.

7.3.3

Mass scale

Nine mass scale uncertainties aﬀect µCB of the signal PDF. The uncertainties are summarized in Table 7.3.4, 7.3.5, 7.3.6, 7.3.7 and 7.3.8.
7.3.3.1

Energy correction using Z line shape

As described in 4.5.2, the correction of photon energy in data is obtained from the Z → eeline shape. The uncertainty of the correction has one of the largest impacts on the massscale uncertainty, which is the range between 0.3% and 0.4% (see Table 7.3.4 and 7.3.6).
7.3.3.2

Material mapping

If mismodeling of the ATLAS detector material mapping exists in the MC samples, theenergies lost in front of the EM calorimeter are diﬀerent between data and MC. The impact
117

Z line shape Material |η| < 1.8 Material |η| > 1.8
0.30 %
0.26 %
0.31 %
0.26 %
0.35 %
0.47 %
0.10 %
0.35 %
0.49 %
0.08 %
0.31 %
0.19 %
0.31 %
0.20 %
0.35 %
0.31 %
0.09 %
0.35 %
0.39 %
0.11 %
0.38 %
0.71 %
0.07 %
0.33 %
0.41 %
0.07 %
0.33 %
0.38 %
0.03 %
0.33 %
0.43 %
0.06 %
0.34 %
0.39 %
0.05 %
0.34 %
0.40 %
0.07 %√
Table 7.3.6: Uncertainties on mass scale for s = 8 TeV.

Category
Unconverted central, low pTt
Unconverted central, high pTt
Unconverted rest, low pTt
Unconverted rest, high pTt
Converted central, low pTt
Converted central, high pTt
Converted rest, low pTt
Converted rest, high pTt
Converted transition
Loose VBF
Tight VBF
Low mass di-jet
ETmiss signiﬁcanceOne-lepton

Category
Unconverted central, low pTt
Unconverted central, high pTt
Unconverted rest, low pTt
Unconverted rest, high pTt
Converted central, low pTt
Converted central, high pTt
Converted rest, low pTt
Converted rest, high pTt
Converted transition
Loose VBF
Tight VBF
Low mass di-jet
ETmiss signiﬁcanceOne-lepton

Presampler barrel Presampler endcap
0.10 %
0.11 %
0.16 %
0.02 %
0.18 %
0.01 %
0.03 %
0.07 %
0.05 %
0.08 %
0.05 %
0.06 %
0.10 %
0.13 %
0.12 %
0.12 %
0.10 %√
Table 7.3.7: Uncertainties on mass scale for s = 8 TeV.

Uncertainty
Value
Conversion fraction
0.13 %
Lateral leakage, e/γ diﬀerence
0.10 %
Lateral leakage, energy dependence 0.02 %High/medium gain
0.15 %
Layer intercalibration
0.20 %
Primary vertex
0.03 %
Background model
0.10 %√
Table 7.3.8: Uncertainties on mass scale for s = 8 TeV. Listed uncertainties have thesame values in all categories.
118

of material mapping on mass scale uncertainty is estimated with special MC samples,named distorted sample, where the amount of material is shifted by the uncertainty.
Because the amount of material strongly depends on η, mass scale uncertainty due to thematerial mapping is divided into impacts from high η (|η| > 1.8) and low η (|η| < 1.8).
The estimated uncertainties are up to 0.7 %.
7.3.3.3

Presampler energy scale

The relative energy scale between the presampler and the accordion, which consists of the
1st, 2nd and 3rd layers in the EM calorimeter, aﬀects the energy scale because the presampler is used for the energy correction based on the Calibration hit method (Eq.(4.5.2)).
The energy scale in data is corrected with using Z line shape. Therefore the energies ofelectrons used for the correction are not aﬀected by the relative energy scale. However
the relative energy scale has an impact on photon energy scale. The impact is divided
into the barrel and endcap regions, and estimated to be up to 0.3 %.
7.3.3.4

Conversion fraction

The energy calibration for photons depends on photon conversion status. Consequently,
misreconstruction of photon conversion leads to the energy miscalibration. Because theconversion fraction relies on the material mapping in front of the EM calorimeter, theuncertainty of the fraction is estimated with using the distorted samples. From the results,
the mass scale uncertainty due to conversion fraction is estimated to be 0.13 %.
7.3.3.5

Energy leakage

The energy leakage is corrected in the MC based calibration. However, the shower widthis underestimated in the MC samples as shown in Section 4.4. Consequently, the lateralleakage correction has uncertainty. The diﬀerence of leakage between data and MC isstudied with Z → ee or Z → ℓℓγ events. The isolation variables are measured withvarious cone sizes, and from the results, the leakage is parametrized as a function ofradius from the cluster center. Then the uncertainty of leakage correction is estimatedfrom comparison between data and MC. The mass scale uncertainties due to the energy
leakage are estimated to be 0.1 % from the diﬀerence between the results from Z → eeand Z → ℓℓγ, and to be 0.02 % from energy dependence.
7.3.3.6

Energy scale diﬀerence between calorimeter gains

As described in Section 2.2.5.1, the shaper on the EM calorimeter front-end board has
three diﬀerent gains. The energy deposits of electrons for the energy calibration using Z
line shapes are ampliﬁed with the highest gain, while sometimes in H → γγ events, energy
deposits of photons are ampliﬁed with the medium gain because of their higher energy
deposits. Hence the miscalibration of the two gains causes the mass scale uncertainty.
The uncertainty is estimated to be 0.15 %.

119Unconverted central, low pTt
Unconverted central, high pTt
Unconverted rest, low pTt
Unconverted rest, high pTt
Converted central, low pTt
Converted central, high pTt
Converted rest, low pTt
Converted rest, high pTt
Converted transition
Others√√s = 7 TeV
s = 8 TeV
Smearing Pileup Smearing Pileup
18.9 %
21.6 %
23.2 %
23.3 %
19.3 %
13.4 % 3.0 %1.5 %27.2 %
19.6 %
21.8 %
14.4 %
21.0 %

Table 7.3.9: Uncertainties on mass resolution.
7.3.3.7

Layer inter-calibration

The relative energy scales in each layer of the EM calorimeter have an impact on theshower depth X, which is used for the MC based energy correction as described in Section
4.5.1. Therefore diﬀerence of the energy scales between data and MC lead bias for massscale. The ratio E1 /E2 is estimated with electrons in Z → ee and W → eν events,
where E1 and E2 are energy deposits in the 1st and 2nd layers, respectively. From themeasured diﬀerence of the relative scales between data and MC, the mass scale uncertainty
is estimated to be 0.20 %.
7.3.3.8

Primary vertex

The invariant mass is calculated with the energies, η and ϕ of the two photons, and photon
η is determined from the position of the primary vertex and the energy cluster position in
the EM calorimeter. Hence the systematic uncertainty of primary vertex determination istaken into account for the mass scale uncertainty. Several algorithms to select the primaryvertex are checked with Z → ee events in data and MC, and the impact of the primaryvertex determination on the mass scale uncertainty is estimated to be 0.03 %.
7.3.3.9

Background modeling

The choice of background function have an impact on the ﬁtted signal through the signal+ background likelihood ﬁt. Therefore the several functions are tested for backgroundmodel, and the diﬀerences of estimated mH are assumed as the systematic uncertainty.
The estimated mass scale systematic uncertainty is 0.1 %.

7.3.4

Mass resolution

The mass resolution is estimated as σCB or σGA in the signal PDF. The uncertainties ofmass resolution are summarized in Table 7.3.9.

120

7.3.4.1

Energy smearing

The MC energies are smeared such that the width of Z line shape in MC agrees with thatin data as described in Section 4.5.2. The uncertainty of the smearing is a main source ofthe mass resolution uncertainty. In addition, because the smearing factors are determinedwith using not photons but electrons, mismodeling of electron → photon extrapolation
has impact on the mass resolution uncertainty. They
√ are merged and estimated between
14.4
and
27.2
%
dependingonthecategoryfors = 8 TeV analysis, while 13.4 % for√s = 7 TeV analysis.
7.3.4.2

Pileup mismodeling

Since pileup events aﬀect the energy resolution of the EM calorimeter, the pileup mismodelingleads to mass resolution uncertainty. A 3.0 (1.5) % uncertainty is assigned for√s = 7 (8) TeV analysis by comparing high and low pileup condition simulation samples.

121Chapter 8
Observation of a Higgs boson andmeasurement of its properties
8.1

Observation of a Higgs boson

A likelihood is deﬁned by using the signal and background model. Then a maximum
likelihood ﬁt is performed. From the ﬁt results, the p-value for the background-only
hypothesis is calculated for discovery of the Higgs boson.

8.1.1

Statistical method

The statistical analysis in this thesis is based on an unbinned maximum likelihood usingmγγ distribution. A signal strength µ, which represents the observed scale of signal event
rate compared with the Standard Model prediction, is used as the hypothesized value fordiscovery of the Higgs boson. The µ is deﬁned as:µ≡σ · Br
σSM · BrSM

(8.1.1)

where σ · Br is the observed Higgs boson production cross section times decay branching
fraction to γγ ﬁnal state, and the subscript SM means the values are predicted by theStandard Model. The Higgs mass mH is the other hypothesized value and scanned from
110 GeV to 150 GeV.
8.1.1.1

Likelihood

The likelihood L includes the information of the numbers and mγγ shapes of signal andbackground events. It involves nuisance parameters which are not parameters of interest
but must be determined from the ﬁt. The nuisance parameters are associated to thesystematic uncertainties of the numbers and shapes. The L is constructed from Poissonand constraint factors; L = LP × Lθ , where LP and Lθ are the Poisson and constraint
factors, respectively. The Poisson factor is deﬁned by:122LP (µ, mH ) =

N
cat
∏

1

c

Nevt,c !

∏Nevt,cexp (−µsc − bc )(µsc fs,c (mγγ,ic |mH ) + bc fb,c (mγγ,ic ))ic(8.1.2)where Nevt is the number of events in the data set, Ncat is the number of the event
categories, s and b are the number of signal and background events, fs and fb are PDFs
of signal and background for hypothesized mH , the subscript c means the label of the event
category and the subscript i is the label of the event number. The constraint factors aredescribed as the product of Gaussian or asymmetric Gaussian functions which constrain
nuisance parameters.
∏∏Lθ =fGaus (θj )fasymGaus (θk )
j

(

k
2)
θj

1
fGaus (θj ) ≡ √ exp −
2
2π
( 2)

√
θ

θk < 0
exp
− 2k
2
σL,k
( σ2 θ2 )fasymGaus (θk ) ≡π (σL,k + σR,k ) exp − L,k2 k
θk > 02σ(8.1.3)R,kwhere θ is a nuisance parameter and σR(L) is the corresponding upper(lower) error. The
asymmetric Gaussian functions are used for the asymmetric uncertainties. The likelihood
L can be written as the product of LP and Lθ .
8.1.1.2

Nuisance parameter

The likelihood L has many nuisance parameters. The number of background events b istreated as a nuisance parameter which does not have any constraint. The parameters of
the background functions are also nuisance parameters which are not constrained. On theother hand, nuisance parameters of s and fs are constrained by Gaussian or asymmetric
Gaussian functions. The uncertainties of signal yield and event migration between event
categories aﬀect s, while the uncertainties of mass scale and resolution aﬀect fs . Allconstrained nuisance parameters and corresponding systematic uncertainties are listed inAppendix F.
Signal yield The uncertainties of signal yield (σyield1,c , σyield2,c , ...) are estimated in
Section 7.3.1. They are taken into account as scale factors, which are applied to thenumber of signal events. The scale factors are deﬁned with four diﬀerent ways:
(√
)
(
)
a
2
sc (θyieldl ) = exp
ln 1 + σyieldl,cθyieldl
(√
)
(
)
b
2
sc (θyieldl ) = exp
ln 1 + σL,yieldl,c θyieldl(8.1.4)()θ
scc (θyieldl ) = 1 + σL(R)yieldl,c yieldl
sdc (θyieldl ) = (1 + σyieldl,c θyieldl )123

where θyieldl is a nuisance parameter for the corresponding systematic uncertainty σyieldl,c .
These four formulas are diﬀerent but have similar mean and variance values. A nuisanceparameter θl does not have the label c because all categories have a common nuisanceparameter except spurious signal. Since the uncertainties due to the spurious signal are
not correlated among the event categories, diﬀerent nuisance parameters are used for
diﬀerent categories.
The choice of the formula depends on the type of uncertainties. For spurious signal,sdc (θyieldl ) is used. For the other yield uncertainties, the sc (θyieldl ) is restricted to positive
value. Therefore sac (θyieldl ), sbc (θyieldl ) or scc (θyieldl ) is used. Particularly when the uncertainty is symmetric, sac (θyieldl ) is used. On the other hand, because the uncertainties ofbranching ratio and cross section due to QCD scale have asymmetric values, sbc (θyieldl )is used. By contrast, scc (θyieldl ) is used for the cross section uncertainty due to PDF+αS
which also has asymmetric values. The QCD scale uncertainties have diﬀerent nuisanceparameters for diﬀerent production processes except WH and ZH. The PDF+αS uncertainties have two nuisance parameters. One is for ggF and ttH processes, while the otheris for VBF, WH and ZH processes.
Event migration The event migration (σmig1,c , σmig2,c , ...) are estimated in Section
7.3.2. Scale factors are deﬁned like the signal yield case:sc (θmigl ) = (1 + σmigl,c θmigl )(8.1.5)where θmigl is a nuisance parameter for the corresponding systematic uncertainty σmigl,c .
Theθmigl is constrained by a Gaussian. The number of signal in category c is written as
the product of sc (θyieldl ) and sc (θmigl′ ):∏∏sc = sc nominal
sc (θyieldl )sc (θmigl′ )(8.1.6)
l′

l

∑ cat
where sc nominal is the expected nominal signal yield. The total signal yield stot = N
sccis independent of σmigl.c because the total number of selected events cannot be changedby event migration.
Mass scale The uncertainties in the mass resolutions (σres1,c , σres2,c , ...) are estimatedin Section 7.3.4. The peak position of the signal PDF is scaled by the following factor:
mpeak,c (θpeakl ) = (1 + σpeakl,c θpeakl )(8.1.7)

where θpeakl corresponds to a nuisance parameter.
Mass resolution The mass resolution uncertainties (σresol1,c , σresol2,c , ...) are estimatedin Section 7.3.4. The corresponding nuisance parameter θresoll shifts the sigma of thecrystal ball and Gaussian function (σCB , σGA ) by following factors:
(√
)
(
)
2
ln 1 + σresoll,cθresoll(8.1.8)σCB(GA),c (θresoll ) = exp
The parameters of s, mpeak and σCB(GA) for each category are written by:124sc = sc0∏sc (θyieldl )lmpeak,c = mpeak,c0∏∏

sc (θmigl′ )l′mpeak,c (θpeakl )(8.1.9)l

σCB(GA),c = σCB(GA)c0∏

σCB(GA) (θresoll )lwhere sc0 , mpeak,c0 and σCB(GA)c0 are the nominal values.
8.1.1.3

Test statistic for µ ≥ 0

The discovery of Higgs boson is established by a frequentist signiﬁcance test using alikelihood ratio as a test statistic. The test statistic is deﬁned by:()
ˆ
L µ, mH , θ̂
−2 ln λ (µ, mH ) ≡ −2 ln L µ̂, m , θ̂µ̂ ≥ µ( H )qµ,mH ≡
(8.1.10)0µ̂ < µˆ
where θ is set of nuisance parameters, θ̂ are the values of θ that maximize L for the speciﬁed µ and mH , µ̂ and θ̂ are the maximum likelihood estimators (MLEs) that maximize
L with a given mH . Higher values of qµ,mH thus correspond to increasing incompatibility
between the data set and hypothesized µ and mH . Therefore qµ,mH = 0 for µ̂ < µ meansthat we only test if µ̂ is larger than µ, in other words, this is one-sided test for lower limit.
Nuisance parameters broaden the distribution of the test statistic as a function of µcompared with a test statistic that has no nuisance parameter, or a test statistic thathas ﬁxed parameters. This reﬂects the systematic uncertainties decrease the sensitivityof discovery. The level of incompatibility can be shown by p-value as shown Eq.(8.1.11).
∫ ∞
) ′
( ′
(8.1.11)|µ, mH dqµ,mpµ,mH =
f qµ,m
H
H
qµ,mH

( ′
)
′
where f qµ,m|µ, mH is the PDF of qµ,munder the assumption of µ and mH .
H
H
8.1.1.4

Asymptotic estimation

In order to ﬁnd the p-value which is deﬁned in Eq.(8.1.11), the PDF of qµ,mH is needed.
One method is to generate many
( ′ toy data) sets from the information of the target data set
then get the distribution f qµ,mH |µ, mH . Another method is asymptotic approximationthat can be used for the case of the following equation is established:)((µ − µ̂ (mH ))21(8.1.12)−2 ln λ (µ) =+O √σ 2 (mH )N
where µ̂ (mH ) follows a Gaussian function with a mean µ′ (mH ) and standard deviation
σ (mH (
) and N)denotes the size of data set. In case of the µ′ (mH ) = µ and if we neglect
1
the O (N )− 2 term in Eq.(8.1.12), the PDF is calculated by Wald [103] and Wilks [104].
( ′
)
)
( ′
) 1 ( ′
qµ,mH
1
1
exp −
f qµ,mH |µ, mH = δ qµ,mH + √ √ ′(8.1.13)222 2π qµ,mH
125then the p-value can be calculated as:
pµ,mH = 1 − Φ

(√
)
qµ,mH

(8.1.14)

where Φ is the cumulative distribution of the standard Gaussian.
For the discovery of the Higgs boson, a hypothesis µ = 0 is tested. This means we test
background-only hypothesis. If this hypothesis is rejected, we discover a new particle.
Therefore p0 (mH ) = p0,mH is used.
)(√
q0 (mH )(8.1.15)p0 (mH ) = 1 − Φ
where q0 (mH ) = q0,mH . Thus the signiﬁcance Z (mH ) for discovery can be written as:√
Z (mH ) = 1 − Φ−1 (1 − p0 ) = q0 (mH )(8.1.16)
where Φ−1 is the inverse of the Φ.
mH is scanned to seek signiﬁcantly small p0 (mH ), hence large Z (mH ) for the discoveryof the Higgs boson. If a standard Higgs boson has a mass m′H , the distribution of theobserved p0 -value has a narrow peak at m′H , and at the mass point, p0, obs = p0, exp is
expected, where p0, exp(obs) is an expected (observed) p0 -value. In addition, p0, obs = 1 is
expected except the surrounding the peak.
8.1.1.5

Asimov data set

The expected results are estimated with an Asimov data set which is generated from asignal and a background model for each mH . The signal model has the nominal signal
yield and shape for the speciﬁed mH . The parameters of the background functions are
given by ﬁtting to the observed data set with background-only model. Consequently, an
Asimov data set has the most probable mγγ distribution under the hypothesis of certain
mH and µ.
Even though the observed data set is unbinned, Asimov data set is binned. Accordingly, the binning of the Asimov data set have to be enough ﬁne. 1000 bins are used forthe mass window from 100 to 160 GeV. For generation of an Asimov data set for the Standard Model Higgs hypothesis, the observed data set is ﬁtted with signal + backgroundmodel with ﬁxing µ = 1.

8.1.2

Results

Figure 6.2.15, 6.2.16, 6.2.17 and 6.2.18 show the signal + background model after the
likelihood ﬁt. The best ﬁt value of the observed signal strength is µ̂ = 1.65 at mH = 125
GeV. The detail of coupling measurement is discussed in Section 8.2. Besides, the best ﬁtvalue of Higgs mass is m̂H = 126.8 GeV. The mass measurement is described in Section
8.3. The MLEs of the signal and the background models are also obtained. Figure
8.1.1 and 8.1.2 show the best ﬁt values and their uncertainties of constrained nuisanceparameters in the observed data set.
When the estimation of a systematic uncertainty is proper, an observed value of a corresponding constrained nuisance parameter is consistent with 0, as well as the uncertainty
is nominal value, that is 1. When an observed value is not consistent with the nominal
126

Trigger
Luminosity_8TeV
Luminosity_7TeV
Photon-ID
Isolation
QCDscale_ggH
QCDscale_qqH
QCDscale_VH
QCDscale_ttH
QCDscale_2jet-VBF
QCDscale_3jet-VBF
QCDscale_2jet-VH
Pdf_gg
Pdf_qqBr
Spurious-Signal_1
Spurious-Signal_2
Spurious-Signal_3
Spurious-Signal_4
Spurious-Signal_5
Spurious-Signal_6
Spurious-Signal_7
Spurious-Signal_8
Spurious-Signal_9
Spurious-Signal_10
Spurious-Signal_11
Spurious-Signal_12
Spurious-Signal_13
Spurious-Signal_14
Spurious-Signal_15
Spurious-Signal_16
Spurious-Signal_17
Spurious-Signal_18
Spurious-Signal_19
Spurious-Signal_20
Spurious-Signal_21
Spurious-Signal_22
Spurious-Signal_23
Spurious-Signal_24

Material
JES_Model1
JES_EtaIntCalib
JES_Rho
JES_FlavorC
JES_FlavorR
JES_Closeby
JER
Higgs-Pt
Soft-S
Soft_R
JVF
PS-UE
Dephoton-Eta
DeltaPhi_ggjj
Lepton-eff_El
Lepton-eff_Mu
JES_Pileup-Mu-2-1.5 -1-0.5 0 0.5 1 1.5 2-2-1.5 -1-0.5 0 0.5 1 1.5 2

θ

θ

(a)

(b)

Figure 8.1.1: The maximum likelihood estimators corresponding to the signal yield uncertainties (a) and the event migration uncertainties (b). Markers show the best ﬁt values,
while the bands show their errors. (See Appendix F)

127

ES_Method
ES_Mat-Low-Eta
ES_Mat-High-Eta
ES_PS-Barrel
ES_PS-Endcap
ES_Conv
ES_Leak
ES_Edep
ES_High-gain
ES_E1E2
ES_PV
ES_BG
Mres_Eresol
Mres_Pileup-2 -1.5 -1-0.5 0 0.5 1 1.5 2-2 -1.5 -1-0.5 0 0.5 1 1.5 2
θ

θ

(a)

(b)

Figure 8.1.2: The maximum likelihood estimators corresponding to the mass scale uncertainties (a) and the mass resolution uncertainties (b). Markers show the best ﬁt values,
while the bands show their errors. (See Appendix F)
value, the estimation of a corresponding systematic uncertainty has to be checked. In
addition, when the error of the observed value is signiﬁcantly smaller than the nominal
value, the corresponding observable is measured with better resolution than input uncertainty. In principle, a systematic uncertainty that has a constrained nuisance parameteris estimated from some control regions, and the estimation should have better sensitivity
to the uncertainty. Hence the signiﬁcantly small error suggests a mismeasurement. In the
Figure 8.1.2, the observed value corresponding to the energy resolution is −0.93 ± 0.74.
Therefore, the best ﬁt value of mass resolution is smaller than expected because the observed resonance is narrower than the expected. However the diﬀerence from the nominal
value is less than 1σ and not signiﬁcant.
Figure 8.1.3 shows the distributions of the likelihood ratio (−2 ln λ (µ, mH )) for theobserved and the expected data set. They are asymmetric distributions because µ̂ (mH )follows not a Gaussian function but a Poisson function when assuming only statisticalﬂuctuation. The diﬀerence of shapes between Gaussian and Poisson functions causes
the asymmetric distribution. Some systematic uncertainties with asymmetric errors contribute the asymmetry of the distribution of the likelihood ratio as well. Although the
distributions are asymmetric, Eq.(8.1.12) is established in both data sets1 . Therefore theasymptotic approximation can be used for both data sets. Thus p0 -value is calculated by
Eq.(8.1.15).
Figure 8.1.4 shows p0 -values for the observed and expected data sets. The energy
scale of photons is ﬁxed in this graph. The expected p0 -value is estimated for diﬀerent
hypothesized Higgs mass values with corresponding Asimov data sets. In the ﬁgure forthe expected p0 -value at a hypothesized Higgs mass m′H , an Asimov data set which is
generated from a signal model when m′H is hypothesized is used. Very large√ excess canbe seen at ∼ 125 GeV. The minimum observed p0 -value in combination of s = 7 TeV
1When a distribution of a likelihood ratio is asymmetric, the uncertainty of µ̂ has an asymmetric
uncertainty.

128

-2lnλ (µ)

10
9
8
7
6

∫
s=8 TeV, ∫ Ldt=20.3 fb-1

s=7 TeV, Ldt=4.8 fb

5
4
3

Expected
Observed
Hypothesized mH = 125 GeV

2
1
0
0

-1

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5
µ

Figure 8.1.3: The likelihood ratio (−2 ln λ (µ, mH )) distributions when mH = 125 GeV ishypothesized.
and√s = 8 TeV data sets is:
p0 (126.5 GeV) = 3.5 × 10−14(8.1.17)(the signiﬁcance Z (126.5 GeV) = 7.4σ), with the expected p0 -value at the mass is:−5pexp
0 (126.5 GeV) = 1.3 × 10

(8.1.18)(Z exp (126.5 GeV) = 4.1σ). The observed excess is larger than the expected by the Standard Model. The observed µ is larger than the expected, and the observed mass peak isnarrower. These two lead higher signal-to-background ratio, and then the larger excess.
The p0 -values is also calculated for the inclusive analysis as shown in Figure 8.1.4. The
expected and observed signiﬁcance at mH = 126.5 GeV is 2.9σ and 6.1σ, respectively.
These results give strong evidence of the discovery of a new particle. As discussed in
Chapter 1, the observed particle is a boson but is not spin-1 particle. By combining theresults from H → γγ, H → ZZ ∗ → 4ℓ and H → W W ∗ → ℓνℓν channels, the ATLAS
collaboration published a paper on evidence for the spin-0 nature of the observed boson in
July 2013 [105]. The spin-0 hypothesis was compared with spin-1 and spin-2 hypotheses.
The observed data was compatible with the spin-0 hypothesis. The hypotheses of spin1 and spin-2 were excluded at conﬁdence levels above 97.8 %. Considering together
with the boson having couplings with W and Z boson [9], the results from the ATLAS
experiment indicate that the boson is a Higgs boson. Hence a Higgs boson is observedwith di-photon events alone. The following sections describe the measurements of the
Higgs boson properties.

129p0-value

1
10-1
10-2
10-3
10-4
10-5
10-6
10-7
category
10-8
Expected
10-9
Observed
10-10
inclusive
10-11
Expected
10-12
Observed
10-13-14
10 110 115 120

1σ
2σ
3σ
4σ
5σ

∫
s=8 TeV, ∫ Ldt=20.3 fb

6σ-1

s=7 TeV, Ldt=4.8 fb

125

130

135

140

145

7σ

-1

150

mH [GeV]Figure 8.1.4: p0 -values of the observed and expected data set as a function of hypothesized
mH .

8.2

Coupling measurement

The Higgs coupling measurement is a crucial test for the Standard Model as described in
Section 1.2.2. Besides, since many BSM theories predict sizable deviation in the Higgs
coupling, precise measurement of each Higgs coupling is a probe of new physics. Because
the sensitivity to the direct coupling measurements is still limited by the data statistics,
the signal strength for total H → γγ process, or signal strengths for each production
process are measured in this chapter.

8.2.1

Statistical method

For Higgs coupling measurement, the same likelihood for observation is used. mH istreated as a free parameter. When assuming each Higgs production process has a common
signal strength, a signal strength µ is used as a parameter of interest. In this case, thefollowing test statistic is used:()
L µ, m̂H , θ̂qµ ≡ −2 ln λ (µ) = −2 ln ((8.2.1))
ˆ H , ˆθ̂L µ̂, m̂This is two-sided test unlike the test statistic for observation because both upper andlower errors are estimated in the coupling measurement. As Figure 8.1.3 shows, qµ is
described by:(µ − µ̂)2(8.2.2)qµ = −2 ln λ (µ) =2σL(R)Hence the asymptotic approximation is established. The best ﬁt value µ̂ is given by theminimum point of qµ , and the upper and lower errors (σL(R) ) are given by the points130qµ = 1. When a constrained nuisance parameter is ﬁxed to the MLE,
√ the estimated error′′2(σ ′ ) is reduced by a corresponding systematic error (σsyst): σ ′ = σ 2 − σsyst. When all
constrained nuisance parameters are ﬁxed, the statistical error σstat is estimated. The
total systematic error σsyst is calculated by:√2
2
σsyst = σtotal− σstat(8.2.3)

Because this is two-sided test, the p-value of µ is expressed with rewriting Eq.(8.1.4):((√ ))p µ = 2 1 − Φ qµ(8.2.4)

When assuming each process has each signal strength separately, three test statistics
for each signal strength (µggF+ttH , µVBF and µV H ) are deﬁned. In a test statistic for acoupling, other couplings are treated as free parameters.
()
L µggF+ttH , µ̂VBF , µ̂V H , m̂H , θ̂qµggF+ttH ≡ −2 ln λ (µggF+ttH ) = −2 ln ()
ˆVBF , µ̂
ˆV H , m̂ˆ H H , ˆθ̂L µ̂ggF+ttH , µ̂()
L µVBF , µ̂ggF+ttH , µ̂V H , m̂H , θ̂qµVBF ≡ −2 ln λ (µVBF )= −2 ln ()(8.2.5)ˆˆˆˆL µ̂VBF , µ̂ggF+ttH , µ̂V H , m̂H , θ̂()
L µV H , µ̂ggF+ttH , µ̂VBF , m̂H , θ̂qµVH ≡ −2 ln λ (µV H )= −2 ln ()ˆggF+ttH , µ̂ˆVBF , m̂ˆ H , ˆθ̂
L µ̂V H , µ̂
For the study of correlation between µVBF+V H and µggF+ttH , another test statistic withthe fraction of µVBF+V H and µggF+ttH is deﬁned:
qµVBF+V H /µggF+ttH ≡ −2 ln λ (µVBF+V H /µggF+ttH )()
L µVBF+V H /µggF+ttH , µ̂ggF+ttH , m̂H , θ̂
= −2 ln ()ˆggF+ttH , m̂
ˆ H , ˆθ̂
L µVBF+V H /µggF+ttH , µ̂

(8.2.6)

where µVBF = µV H = µVBF+V H is assumed.

8.2.2

Results

Figure 8.2.1a shows the distributions o f qµ for the observed data set. The µ̂ is measured
to be:+0.25µ̂ = 1.65 ± 0.24(stat.)(syst.)(8.2.7)−0.18
From comparison of qµ with ﬁxing some nuisance parameters, the impacts of each systematic uncertainty are estimated. The dominant systematic uncertainties are summarizedin Table 8.2.1. The QCD scale uncertainty for the cross section of the Higgs production
and the mass resolution uncertainty have the largest contributions to the systematic uncertainty on the µ measurement. The total systematic and statistical uncertainties are131

mH [GeV]qµ = -2 ln λ (µ)

1098w/ all NPs
Fix signal yield
No migration
Fix mass resolution
Fix mass scale
Fix all NPs

7
6
5
4

∫
s=8 TeV, ∫ Ldt=20.3 fb

3

127
126.5
126
125.5

-1

s=7 TeV, Ldt=4.8 fb

2
1
0
0.5

127.5

1

1.5

2

2.5

3

125

-1

3.5

124.5
0

4

w/ all NPs
Fix signal yield
No migration
Fix mass resolution
Fix mass scale
Fix all NPs
0.5∫
s=8 TeV, ∫ Ldt=20.3 fb-1

s=7 TeV, Ldt=4.8 fb

1

1.5

2

µ

-1

2.5
µ

(a)

(b)

Figure 8.2.1: Distribution of qµ for the observed data set with several conﬁgurations(a). The best ﬁt value of mH for each hypothesized µ (b). “w/ all NPs” means ﬁtusing all constrained nuisance parameters, that is nominal results. “Fix signal yield”,“No migration”, “Fix mass resolution” and “Fix mass scale” show distributions withﬁxing some constrained nuisance parameters at the best ﬁt values. Dashed line shows
distribution when all constrained nuisance parameters are ﬁxed.
approximately equal. Because mH is a free parameter to ﬁt, m̂H can be diﬀerent for
diﬀerent µ. Figure 8.2.1b shows the best ﬁt value of mH for each hypothesized µ. Theµ dependence on m̂H is 0.2 GeV per ∆µ = 1 due to the mass scale uncertainties. The
consistency with the Standard Model prediction is tested with p-value at µ = 1: p1 . From
Figure 8.2.1a, p1 = 1.1 % is obtained, which corresponds to 2.3σ. The measured signal
strength is consistent with the Standard Model with in 2.3σ.
Figure 8.2.2 shows the test statistics of µggF+ttH , µVBF , µV H and µVBF+V H /µggF+ttH .
Systematic Uncertainty
QCD scale
Mass resolution
Branching ratio
Luminosity
Identiﬁcation

∆µ
+0.15
−0.07
+0.11
−0.10
+0.08
−0.08
+0.06
−0.04
+0.05
−0.06

Table 8.2.1: Dominant systematic uncertainties on measurement of µ.

132

The best ﬁt values for each production process are:µ̂ggF+ttH =1.6 ± 0.3(stat.)+0.3(syst.)−0.2µ̂VBF =1.7 ± 0.8(stat.)+0.5(syst.)−0.4µ̂V H =1.8

(8.2.8)+1.5(stat.) ± 0.3(syst.)−1.3

The statistic uncertainties on µVBF and µV H are still large. The signal yield systematic
uncertainty dominates in µggF+ttH , while the event migration for µVBF and µV H . The
signal strength is larger than 1 for 3 diﬀerent production processes.
The signal strengths checks consistencies with the Standard Model on the productsof the production process (ggF, VBF, VH, ttH ) and the Higgs decay (H → γγ). Theirratios cancel the Higgs decay part and compare only production processes. The ratioµVBF+V H /µggF+ttH is measured to be :µVBF+V H /µggF+ttH = 1.1

+0.7
+0.3
(stat.)(syst.)−0.5−0.2(8.2.9)as shown in Figure 8.2.2. This is consistent with the Standard Model prediction(µVBF+V H /µggF+ttH = 1). It indicates that the observed large µ values for each process
could be larger due to the Higgs decay loop unless the cross section of all the production
processes. In this case, as described in Section 1.2.2, the candidates of new particles may
have no color charge but electromagnetic charge. Many models are proposed to enhance
the H → γγ rate: for example, charged scalar [106, 107], heavy fermion [108, 109] andheavy charged gauge boson [107]. In order to test these models, a combined analysis ofmany decay modes is critical. The increase of statistics is crucially important to improve
the signiﬁcance of the combined analysis. For example, the H → Zγ mode has similar
signature of the H → γγ mode. Therefore the signal strength in the the H → Zγ
mode has a similar dependence on new particles as the H → γγ mode. However some
BSM theories predict the diﬀerent deviations of signal strengths from the Standard Model
prediction between the two modes. Hence the comparison of the two modes is a test forsome BSM theories. The property measurement of the Higgs boson in the H → Zγ
analysis needs more statistics because the branching fraction is small as shown in Figure
1.2.5.

8.3

Mass measurement

The precise measurement of the Higgs mass is remarkably important to complete theStandard Model and to search BSM as described in Section 1.2.2. The H → γγ channel
has one of the highest precision of mass measurement.

8.3.1

Statistical method

A test statistic has a mH as the parameter of interest. µ is treated as a free parameter
for a likelihood ﬁt.
133

)

9

VBF

9
8

w/ all NPs
Fix signal yield
No migration
Fix mass resolution
Fix mass scale
Fix all NPs

7
6
5
4

∫
s=8 TeV, ∫ Ldt=20.3 fb

3

0

1

2

3

4

5

6

7
µ

w/ all NPs
Fix signal yield
No migration
Fix mass resolution
Fix mass scale
Fix all NPs

7
5
4

∫
s=8 TeV, ∫ Ldt=20.3 fb

3

s=7 TeV, Ldt=4.8 fb

1

8
6

-1

2
0

10

-2 ln λ (µ)

ggF+ttH-2 ln λ (µ10-1

s=7 TeV, Ldt=4.8 fb

2
-1

1
0

8

0

1

2

7
6
5

)

ggF+ttH

∫
∫

-1

/µ

w/ all NPs
s=7 TeV, Ldt=4.8 fb
Fix signal yield-1
No migration
s=8 TeV, Ldt=20.3 fb
Fix mass resolution
Fix mass scale
Fix all NPs

4

8
6
5
4
2

1

1
2

3

4

5

6

7

0

8
µ

w/ all NPs
Fix signal yield
No migration
Fix mass resolution
Fix mass scale
Fix all NPs

7

2

1

8
VBF

9

3

0

7

10

3

0

6

(b)

VBF+VH85µ-2 ln λ (µVH

-2 ln λ (µ )94

ggF+ttH

(a)
10

3

-1

∫
s=8 TeV, ∫ Ldt=20.3 fb-1

s=7 TeV, Ldt=4.8 fb

0

1

2

3

VH

(c)

4

5

6

7

µ

/µ

VBF+VH-1

8
ggF+ttH(d)

Figure 8.2.2: Distributions of test statistics for µggF+ttH (a), µVBF (b), µV H (c) andµVBF+V H /µggF+ttH (d) for the observed data set with several conﬁgurations. The meaningsof each line are the same as Figure 8.2.1.

134

µ

2.5

2

w/ all NPs
Fix mass scale
Fix all NPs

mH = 125 GeV

1.5

1
0.5
0
122

68% contour
95% contour
123

124

125

126

127

128

mH [GeV]Figure 8.3.1: −2 ln λ (µ, mH ) distribution in µ-mH plane for Asimov data set under the
hypothesized mH = 125 GeV. “w/ all NPs” means ﬁt using all constrained nuisanceparameters, that is nominal results. “Fix mass scale” shows distribution with ﬁxing
constrained nuisance parameters corresponding to mass scale uncertainties at the best ﬁtvalues. “Fix all NPs” shows distribution when all constrained nuisance parameters are
ﬁxed.
(
)
L mH , µ̂, θ̂
qmH ≡ −2 ln λ (mH ) = −2 ln ()ˆ ˆθ̂L m̂H , µ̂,(8.3.1)This is two-sided test. The best ﬁt value of mH (m̂H ) is given by qm̂H = 0. The error ofmH is obtained from the point qmH = 1.

8.3.2

Results

Figure 8.3.1 shows the distribution of −2 ln λ (µ, mH ) in µ-mH plane for an Asimov data
set when the Higgs mass is hypothesized mH = 125 GeV as well as the signal strength isµ = 1. The best ﬁt values of mH and µ agree with their hypothesized values. One of themerits of the H → γγ channel for the mass measurement is the low correlation between
the signal strength and the measured mass as this ﬁgure shows. The Higgs mass can bemeasured almost independently of the signal strength.
Figure 8.3.2 shows the distributions of qmH for the observed data set. The m̂H ismeasured to be:m̂H = 126.8 ± 0.2(stat.) ± 0.7(syst.) GeV(8.3.2)The statistical uncertainty is estimated in the same way as the measurement of µ. The
systematical uncertainty is calculated by comparing the total end the statistical error.
Substituting m̂H into Eq.(1.1.21), the Higgs potential parameters λ and µ2ϕ are estimated:
λ ≃0.133(8.3.3)µ2ϕ ≃ − (90 GeV)2
where v ≃ 246.22 GeV [15] is used. From the results, the stability of the vacuum isestimated to be metastability as shown in Figure 1.2.9. Therefore, the vacuum can fall135

H

-2 ln λ (m )

10
9
8
7
6
w/ all NPs
Fix mass scale
Fix all NPs

54∫
s=8 TeV, ∫ Ldt=20.3 fb

3-1

s=7 TeV, Ldt=4.8 fb

2
1
0

125

126

127

128

129

130

-1

131

mH [GeV]Figure 8.3.2: Distributions of qmH = −2 ln λ (mH ). “w/ all NPs” means ﬁt using all
constrained nuisance parameters, that is nominal results. “Fix mass scale” shows distributions with ﬁxing nuisance parameters corresponding to mass scale uncertainties at thebest ﬁt values. Dashed line shows distribution when all constrained nuisance parameters
are ﬁxed.
negative inﬁnity at the Planck scale, but the probability of the falling to wrong vacuum
is too low. The vacuum is not instable up to the Planck scale under the Standard Model,
and then the vacuum stability does not need a new physics.

8.4

Direct measurement of natural width

The natural width of Higgs boson is one of the most important properties especially forstudies of invisible decay and BSM. This section describes a direct measurement of thenatural width using the shape of mγγ peak. The natural width is predicted ∼ 4 MeV
in FWHM for mH ∼ 125 GeV by the Standard Model as described in Section 1.2.1. On
the other hand, the uncertainty of mass resolution is ∼ 100 MeV, thus the accuracy ofthis study does not reach the expected width. Consequently, this is a search for a large
deviation from the Standard Model. Some theories of BSM predict wider natural width,
hence this study can give a constraint on BSM without any hypothesis.

8.4.1

Statistical method

A measurement of the natural width of Higgs uses a likelihood that has the natural width(w) as a parameter of interest. µ and mH are used as free parameters. The signal shapeis changed by w. In the likelihood, the signal shape is changed to have the natural width
w by convoluting the nominal shape (Crystal Ball + Gaussian) with the Breit-Wigner136

function which has the width w. The Breit-Wigner function is deﬁned as:
fBW = N1m2γγ + w2 /4(8.4.1)

where N is a normalization factor. The signal function is convoluted after the event
selection. The signal MC samples have the Standard Model natural width (4 MeV formH ∼ 125 GeV) when they are generated. However the impact of the Standard Modelnatural width is negligible because of the uncertainty of the mass resolution of about 100
MeV.
8.4.1.1

Test statistic

In order to give an upper limit on the natural width, one-sided test is used. The test
statistic for one-sided test is therefore deﬁned as:−2 ln λ (w) = −2 ln L((w, µ̂, m̂H , θ̂)) (w > ŵ)ˆ m̂
ˆ H, ˆ
L ŵ, µ̂,θ̂qw ≡(8.4.2)0(w < ŵ)Because Breit-Wigner function which is used for the convolution cannot have negative
width, we have a physical boundary at w = 0. Due to the boundary, the asymptotic
approximation cannot be used. Therefore the p-value is measured by a toy MC study.
8.4.1.2

Toy MC study

In toy MC study, a number of pseudo-data sets are generated with signal and backgroundmodels.
1. The parameters in the likelihood are given from ﬁtting to the observed or expected
data sets for a ﬁxed tested value w = wtest . As a result, the maximum likelihood
estimators for each nuisance parameters (θ̂) are obtained.
2. In order to take errors of MLEs into account, the nuisance parameters that have constraints (e.g. luminosity and pTt uncertainty) are randomized as their constraints.
For example, a nuisance parameter θ that has a Gaussian constraint is given thebest ﬁt value θ̂ and the error σθ at the ﬁrst step. Then the parameter is randomized
with a Gaussian which mean is θ̂ and sigma is σθ .
3. Pseudo-data sets are generated with given parameters.
4. The generated pseudo-data sets are ﬁtted with a free width w and a ﬁxed test width
wtest , and then qwtest is obtained.
5. The second, third and fourth steps are repeated 1000 times.
6. The conﬁdence levels are estimated from the histogram of qwtest , i.e. p-value for wtest
is calculated as∫ ∞p (woe ) =F (qwtest |wtest ) dqwtest(8.4.3)
qwoe

where qwoe represents the observed or expected test statistic.
137

-2lnλ (w)10Asimov, w = 0 (SM predicted)
Asimov, w = 2 GeV
Asimov, w = 4 GeV

987mH = 125 GeV

6
5
4
3
2
1
0
0

2

4

6

8

10

12

14

16

18

20

w [GeV]

2.5
2

14
12
10

1.5
1

8
6

0.5

4
2

0
0

1

2

3

4

5

130

mH = 125 GeV
25

129

H

22
20
18
16

-2 ln λ (m , w)

mH = 125 GeV

mH [GeV]3-2 ln λ (µ, w)µ

Figure 8.4.1: Distributions of −2 ln λ (w) for Asimov data sets with several hypothesized
natural width.

128

20

127
126

15

125
124

10

123
122

5

121
120

6

1

2

3

4

5

w [GeV]

6

7

8

9

10

w [GeV](a)(b)

Figure 8.4.2: Correlation between w and µ̂ for expected data set (a). Correlation between
w and m̂H for expected data set (b). The expected data set is generated with w = 0 and
mH = 125 GeV.

8.4.2

Results

Figure 8.4.1 shows the distributions of −2 ln λ (w) for several Asimov data sets that have
hypothesized natural width w = 0, 2, 4 GeV. The Asimov data set with w = 0 corresponds
the standard expected data set. As expected, −2 ln λ (w) is minimum at the generated
width. The correlations between w and the best ﬁt values of the signal strength and the
Higgs mass of the standard expected data set are shown in Figure 8.4.2. The slope of µ̂
against w at w = 0 is 0.2 GeV−1 . This is because the likelihood is larger when the heightof signal shape is matched to the data. In contrast, the correlation between m̂H and w is
negligibly small.
Figure 8.4.3a compares −2 ln λ (w) between the observed and the standard expected
data sets. The maximum likelihood is given by w = 0 in both data sets. This is consistent
with the Standard Model prediction. Thus a large deviation from the Standard Model is
not observed. The observed data set has very sharp −2 ln λ (w) shape compared with the
expected data set. In order to investigate the cause, a special Asimov data set that has
138

-2lnλ (w)-2lnλ (w)10
Observed
Expected
mH = 125 GeV

9
8
7

10
9
8

6

6

5

5

4

4

∫
s=8 TeV, ∫ Ldt=20.3 fb

3

1
1

2

3

4

5

6

7

8

9

∫
s=8 TeV, ∫ Ldt=20.3 fb-1

s=7 TeV, Ldt=4.8 fb

2
-1

1
10

0
0

2

4

6

8

w [GeV](a)-1

Observed
Nominal expected
Expected, µ=1.5
Expected, µ=1.5, θresol=-1.8σ

3-1

s=7 TeV, Ldt=4.8 fb

200mH = 125 GeV

7

10

12

14

16

18

w [GeV](b)

Figure 8.4.3: Distributions of −2 ln λ (w) for the observed and expected data set (a).
Distributions of −2 ln λ (w) for special Asimov data sets that have the large signal strengthand the narrow mass resolution (b).
resol
µ = µ̂obs and a nuisance parameter of mass resolution θresol = θ̂obs
is generated, whereresolµ̂obs and θ̂obs are the best ﬁt values in the observed data set. Figure 8.4.3b shows thatthe special Asimov data set has very similar −2 ln λ (w) shape as the observed data set.
Hence the observed diﬀerence on the −2 ln λ (w) curves is due to the observation of thenarrow mass resonance with the large µ.
The upper limit on natural width in FWHM with 95 % CL is estimated to be:

w < 1.8 GeV (observed)(8.4.4)

w < 5.8 GeV (expected)(8.4.5)Figure 8.4.5 shows the PDF of qw obtained from pseudo-data sets for wtest = 1.8 GeV. The
p-value is then calculated from Eq.(8.4.3). The 1 − p-value corresponds to the conﬁdence
level. As described above, the observed large µ and the narrow mγγ peak make theupper limit for the observed data set small. The contribution of statistical uncertainty is
estimated by ﬁtting the pseudo-data sets with ﬁxing all constrained nuisance parameters
as shown in Figure 8.4.4. The resulting upper limit without systematic uncertainty is
w < 1.6 GeV (95 % CL) for observed data set. The contribution of the systematic
uncertainty is estimated by subtracting the contribution of the statistical uncertainty
from the total upper limit: w = 0.8 GeV.

139

-2lnλ (w)10w/ all NPs
Fix mass resolution
Fix all NPs

9
8
7
6
5
4

∫
s=8 TeV, ∫ Ldt=20.3 fb

3-1

s=7 TeV, Ldt=4.8 fb

2
1
0
0

0.5

1

1.5

2

2.5

3

3.5

-1

4

w [GeV]

Figure 8.4.4: Distributions of −2 ln λ (w) for the observed data set. “w/ all NPs” means ﬁtusing all constrained nuisance parameters, that is nominal results. “Fix mass resolution”
shows distributions with ﬁxing nuisance parameters corresponding to mass resolution
uncertainties at the best ﬁt values. Dashed line shows distribution when all constrained
nuisance parameters are ﬁxed.

w = 1.8 [GeV]
1 - p-value = 95 %∫s=8 TeV, ∫ Ldt=20.3 fb

102

-1

s=7 TeV, Ldt=4.8 fb

-1

10

1
0

1

2

3

4

5

6

7

8

9

10
qw

Figure 8.4.5: PDF of qw obtained from pseudo-data sets for wtest = 1.8 GeV. Red line
shows the observed qwtest . 1 − p-value is estimated to be 95 %.

140

Chapter 9
Conclusion
A search for the Standard Model Higgs boson in di-photon ﬁnal states is√performed using
data collected with the ATLAS detector √in proton-proton collisions at s = 7 TeV with−1
an integrated luminosity of 4.8 fb and s = 8 TeV with 20.3 fb−1 .
The Higgs ﬁeld gives mass to elementary particles through the gauge symmetry breaking of SU (2)L × U (1)Y into U (1)EM . The Higgs boson is the visible manifestation of
the Higgs ﬁeld, and couples with massive particles. The dominant production processes
in proton-proton collisions are gluon-gluon fusion, vector boson fusion, associated production with a W or Z boson, or associated production with a pair of top quarks. The
Higgs boson decays into di-photon via a t/W loop. Although the branching fraction ofdi-photon ﬁnal state is smaller than many other decay modes, the H → γγ mode hasa large signiﬁcance for the discovery of the Higgs boson because of the high eﬃciencyof event reconstruction, a sharp peak at the Higgs mass in the di-photon invariant mass
distribution.
The set of selection criteria of signal region for the H → γγ analysis removes fakephotons due to the presence of a leading π 0 resulting from the fragmentationof a quark√or a gluon. The selected√ events are divided into 10 categories for s = 7 TeV analysis
and 14 categories for s = 8 TeV analysis in order to improve the sensitivities for the
discovery and for the property measurement. The event categorization is performed suchthat diﬀerent categories have diﬀerent signiﬁcances and have large fractions of diﬀerent
production processes.
Clear evidence for a Higgs boson resonance is discovered with the signiﬁcance of 7.4σ
in the two photon invariant mass spectrum above background expectations. Then themeasurement of the Higgs boson properties is carried out. From all the measurement
results, this particle is consistent with the Standard Model Higgs boson.
The mass of the Higgs boson, which is an input parameter of the Standard Model, ismeasured with the signal peak shape. The mass is determined with 0.6 % accuracy:
mH = 126.8 ± 0.2(stat.) ± 0.7(syst.) GeV.
Under the Standard Model, the Higgs potential is determined by the Higgs mass:
λ ≃0.133µ2ϕ ≃ − (90 GeV)2
From the numbers of observed events in each category, the overall signal strength µ,141which denotes a cross section times branching fraction normalized to the Standard Model
prediction, is estimated to be:µ = 1.65 ± 0.24(stat.)+0.25(syst.).
−0.18

The√total cross section times branching fraction are predicted to be 38.4 fb and 49.0 fb
for s = 7 and 8 TeV, respectively, in the Standard Model. The signal strength for eachproduction process is:µggF+ttH =1.6 ± 0.3(stat.)+0.3(syst.)−0.2µVBF =1.7 ± 0.8(stat.)+0.5(syst.)−0.4µV H =1.8+1.5(stat.) ± 0.3(syst.) ,−1.3

where µggF+ttH is signal strength for gluon-gluon fusion and associated production with apair of top quarks, µVBF is for vector boson fusion and µV H is for associated production
with a W or Z boson. The fraction of µVBF+V H and µggF+ttH is estimated to be:µVBF+V H /µggF+ttH = 1.1

+0.7
+0.3
(stat.)(syst.).
−0.5−0.2

The results of signal strength measurement are summarized in Figure 9.0.1. The mostprobable values of the signal strengths are larger than 1, and are consistent in diﬀerent
production processes. The measured signal strength is estimated to be consistent with theStandard Model with in 2.3σ. However, if new particles make the signal strength larger,
they may have impacts on the decay loop. Many candidates are proposed to enhance
the H → γγ rate: charged scalar, heavy fermion and heavy charged gauge boson. The
signiﬁcance to test these models is increased by a combined analysis of many decay modes
and increase of statistics.

142

µggF+ttH/ µVBF+VH
µVH
Total
Stat.
Syst.

µVBF

∫
s = 8 TeV, ∫ Ldt = 20.3 fbµggF+ttH

s = 7 TeV, Ldt = 4.8 fb

µ
0

1

2

3

4

5

-1

-1

6

Signal strength (ratio)

Figure 9.0.1: Measured signal strengths for the diﬀerent production processes, overall
strength µ and the ratio of strength for the Yukawa coupling production and the gauge
coupling production µVBF+V H /µggF+ttH .
A search for deviation of the natural width of the Higgs boson from the Standard
Model prediction with the width of signal peak is presented. No signiﬁcant deviation isobserved, thus the upper limit on natural width of the Higgs boson is estimated. The
observed upper limit is estimated to be:
w < 1.8 GeV (95 % CL)
The discovery of the Higgs boson was a great achievement to complete the Standard
Model. The measurement of Higgs boson properties is a probe of new physics beyond theStandard Model. Further data will reveal the nature of the Higgs boson more precisely inorder to see whether the Standard Model is still valid or the physics beyond the Standard
Model can be found in a TeV energy scale. A new era of particle physics has started withthis discovery.

143

Acknowledgments
I would like to express my deepest appreciation to my supervisor, Prof. Sachio Komamiya. I thank him for introducing me to wonders of scientiﬁc research. I thank him
for encouraging me during this work.
I am really grateful to Prof. Junichi Tanaka. He has been teaching me all about
research at the ATLAS. I think I could not accomplish this study without his instruction,
help and encouragement.
I would like to warmly thanks Dr. Taiki Yamamura for his guidance and assistance,
and for giving me valuable insights into the Higgs search.
Staﬀ members of International Center for Elementary Particle Physics (ICEPP) in
the university of Tokyo, Prof. Tatsuo Kawamoto, Prof. Asai Shoji, Prof. Naoko Kanaya,
Prof. Yuji Enari, Prof. Koji Terashi , Prof. Shimpei Yamamoto, Prof. Yousuke Kataoka,
Dr. Tatsuya Masubuchi, Dr. Koji Nakamura, Dr. Takashi Yamanaka and Dr. Keita
Hanawa, they have been helping and teaching me very kindly and professionally. I would
like to express my gratitude to them. Prof. Enari gave me a lot helpful suggestions to
my thesis.
I deeply appreciate the conveners and collaborators of the H → γγ sub-working group.
The conveners of the group, Prof. Tanaka, Prof. Krisztian Peters, Dr. Kerstin Tackmann,
Dr. Nicolas Berger have been always taking care of my research. I also appreciate membersof the e/gamma working group. Dr. Maarten Boonekamp has been helping and teachingme greatly.
I am very grateful to my friends in the same period in the University of Tokyo. I
thank Mr. Yutaro Iiyama, Mr. Akira Miyazaki, Mr. Yuichi Sasaki, Mr. Shingo Kazama,
Mr. Keisuke Yoshihara for numerous advices and inspiring discussions.
I am very grateful to Mr. Jean-Jacques Bauswein, Prof. Kanaya, Mr. Iiyama forsupporting my life at CERN.
I want to express my sincere gratitude to past and present members of ICEPP and
Komamiya laboratory, Mr. Takashi Goto, Mr. Kaoru Tanaka, Ms. Aine Kobayashi, Ms.
Maya Okawa, Mr. Shingo Terao, Mr. Shingo Hisajima, Mr. Yuji Minegishi, Prof. Yoshio
Kamiya, Dr. Shinsuke Kawasaki, Dr. Shinya Sonoda, Dr. Masahiro Oroku, Dr. Go
Ichikawa, Ms. Jacqueline Yan, Mr. Yuto Minami, Ms. Misato Tani.
I would like to express my eternal gratitude to my family for their support.

144

Appendix A
Luminosity determination
The luminosity L delivered to the ATLAS detector is measured with the luminosity detectors described in Section 2.2.8 [38]. The luminosity can be converted to the average
number of inelastic interactions per bunch crossing µav .
For a storage ring, the luminosity can be expressed asL=µav nb fr
σinel(A.0.1)

where nb is the number of bunch pairs colliding per revolution, fr is the revolution frequency and σinel is the pp inelastic cross-section. The observed interaction rate per crossingµvis is used for the luminosity measurement instead of µav because µav cannot be measured
directly with the luminosity monitor. The luminosity can be written as
L=µvis nb fr
σvis(A.0.2)where σvis = ϵσinel is the visible cross-section for a particular detector, and similarlyµvis = ϵµav . nb and fr are determined by the LHC operating condition and µvis is anexperimentally observable quantity.

A.1µvis measurement√
For µvis measurement, several algorithms are used. Especially for s = 7 and 8 TeV
data, an EventOR algorithm is used. In the algorithm, the luminosity monitor counts abunch crossing when at least one hit is detected on either side of the detector. Since thevisible number of interactions per bunch can be described by a Poisson distribution withthe mean is µvis , the probability of observing at least one hit can be written as
1 − P (0|λ = µvis ) = 1 − exp (−µvis )Then when NOR events are counted during a number of bunch crossing NBC , µvis isestimated as)(
NOR(A.1.1)µvis = − ln 1 −NBC
For the estimation of µvis , the vertical pairs of BCM detectors are used. The basic
time unit for storing luminosity information is the Luminosity Block (LB). Then µvis isaveraged in every LB. The typical duration of each LB is one minute.
145

A.2

van der Meer scan

σvis in Eq.(A.0.2) can be measured with van der Meer (vdM ) scans.
In term of the colliding-beam parameters, L is deﬁned as∫
L = nb fr n1 n2 ρ1 (x, y) ρ2 (x, y) dxdy

(A.2.1)

where n1 and n2 are bunch populations and ρ1 (x, y) and ρ2 (x, y) are the normalized
densities in the transverse plane of beam 1 and 2 at the interaction point. n1(2) is measured
with current monitors at the LHC.
Under the assumption that√ ρ1(2) (x, y) is a 2-dimensional Gaussian and both beams
have the same sigma Σx(y) / 2, Eq.(A.2.1) can be rewritten as
)
(
∫
1
x2
y2
(x − δx )2 (y − δy )2
L = nb fr n1 n2
exp − 2 − 2 −−dxdy (A.2.2)
Σx Σy
Σ2x
Σ2y
(πΣx Σy )2where δx(y) is the horizontal (vertical) distance between 2 beams. In a vdM scan, the beam
are separated by steps of a known distance1 . Therefore δx(y) in Eq.(A.2.2) is scanned. Thus
Σx(y) is measured from the shape of L as a function of δx(y) .
In case of δx = δy = 0, Eq.(A.2.2) is described asL=n b fr n 1 n 22πΣx Σy(A.2.3)σvis is computed using Eq.(A.0.2) and (A.2.3):
σvis = µMAX
vis

2πΣx Σyn1 n2(A.2.4)

where µMAX
is µvis in case of δx = δy = 0, in other words the visible cross-section atvis
the peak of the vdM scan. This is the calibration of σvis . Because vdM scans cannot be
performed during nominal physics runs, the measured σvis is used for physics runs after
the scan.
L for physics runs are determined by substituting Eq.(A.2.4) and (A.1.1) to Eq.(A.0.2)
for each LB. Based on the assumption σinel = 71.5 mb [38], µav is also computed using
Eq.(A.0.1):
Lσinelµav =n b fr

1

The scale of the step is calibrated by the vertex reconstruction with the inner detector.

146

Appendix B
Electron reconstruction
B.1

Reconstruction procedure

Energy clusters in the EM calorimeter and tracks in the inner detector are used for electronreconstruction. The tracks are extrapolated to the calorimeter, and then the extrapolated
tracks are required to match the clusters. Direction of electrons is determined by using
tracks. In contrast, energy of electrons is measured with the EM calorimeter. The energyof electrons is corrected with the MVA calibration and Z → ee line shape correction.

B.2

Identiﬁcation criteria

In the same way as photons, shower shape is used for separation from jets. The criteria
are similar to but somewhat looser than those for photons. In addition, track parameters
are also used for the identiﬁcation: number of hits in the inner detector and transverse
impact parameter (< 5mm).

B.2.1

Electron selection

Track and calorimeter isolation variables are computed with the inner detector and the
EM calorimeter, respectively. The isolation criteria use the ratio of the isolation variables
to pT for relaxing the selection to high pT electron candidates which have originally highpurity. The longitudinal and transverse impact parameters with respect to the primaryvertex z0 and d0 are used as well as σd0 , which is the resolution of d0 for separation frompileup jets. The impact parameters are not used for the H → γγ analysis because of low
primary vertex reconstruction eﬃciency. The selection criteria are summarized in Table
B.2.1 and B.2.2.

147

Pass the identiﬁcation criteria
Transverse energy
Pseudo-rapidity
Longitudinal impact parameterTransverse impact parameter
Calorimeter isolation
Track isolation

pT > 10 GeV|η| < 2.47
|z0 | < 1.5 mm|d0 | /σd0 < 10
ETcone30 /pT < 0.18
pTcone20 /pT < 0.1

Table B.2.1: Electron Selection for Z → llγ analysis.

Pass the identiﬁcation criteria
Transverse energy
pT > 15 GeV
Pseudo-rapidity|η| < 2.47
Calorimeter isolation ETcone40 /pT < 0.2
Track isolation
pTcone20 /pT < 0.15
Table B.2.2: Electron Selection for H → γγ analysis.

148

Appendix C
Muon reconstruction
C.1

Reconstruction procedure

Tracks are reconstructed with the ID and the Muon spectrometer individually. Thenmuons are reconstructed from combined tracks between ID and the Muon spectrometer.
Direction of muons is determined by the tracks. In MC simulation, the momentum issmeared such that they have the same momentum resolution as observed data in Z → µµ
peak.

C.2

Muon selection

The impact parameters and isolation variables are used for separation from jets. Table
C.2.1 and C.2.2 summarize the muon selection.

Pass the identiﬁcation criteria
Transverse energy
pT > 10 GeV
Pseudo-rapidity|η| < 2.5
Longitudinal impact parameter|z0 | < 5 mm
Transverse impact parameter|d0 | < 1.5 mm
Calorimeter isolation
ET cone40 /pT < 0.25
Track isolation
pTcone20 /pT < 0.15
Table C.2.1: Muon Selection for Z → llγ analysis.
149

Pass the identiﬁcation criteria
Transverse energy
pT > 10 GeV
Pseudo-rapidity|η| < 2.7
Longitudinal impact parameter|z0 | < 10 mm
Transverse impact parameter|d0 | < 1 mm
Calorimeter isolation
ET cone40 /pT < 0.2
Track isolation
pTcone20 /pT < 0.15
Table C.2.2: Muon Selection for H → γγ analysis.

150Appendix D
Jet reconstruction
D.1

Reconstruction procedure

Jets are reconstructed from the energy clusters in the hadronic and hadronic calorimeter aswell as the EM calorimeter. The hadronic clusters are obtained by topological clustering:group of calorimeter cells topologically connected (η, ϕ and R direction). Then clusters are
merged with “anti-kT ” algorithm [95] if the distances are nearer than a certain threshold.
The distance dij between the i-th and j-th hadronic cluster is deﬁned as:()
11(yi − yj )2 + (ϕi − ϕj )2
dij = min,p2T i p2T j
R2
where pT i is transverse momentum, yi is rapidity, ϕi is azimuthal angle of i-th cluster,and R is cone size. The threshold dmin is deﬁned as:()
1
dmin = min dij , 2
pT i
If dij < dmin , the i-th cluster is merged with the j-th cluster by calculating vector sumof four-momenta of clusters. Then dmin of the new cluster object is evaluate for all theremaining clusters. This procedure is repeated until the all of the jet candidates are notremained. Then the merged cluster is assumed as a jet candidate.
After jet reconstruction, the energy is rescaled from EM scale to hadronic scale [110].
The calibration factor is obtained from MC simulation. The energy loss in the dead material is also corrected. The correction restores the calorimeter response of the reconstructed
jet to the true jet response

D.2

Jet vertex fraction

Event categorization in the H → γγ analysis requires jets from a primary vertex (Section
6.2). For eﬀective categorization, jets from a hard process are separated from pileup jets.
Jet Vertex Fraction (JVF), which is the sum of pT of all matched-tracks from a given
primary vertex candidate by total jet-matched track, measures the probability that a jet

151originated from a primary vertex. When track1 , track2 , ..., trackn in the jet are associatedto the primary vertex, while trackn+1 , trackn+2 , .., trackm are not, JVF is deﬁned as:∑n trackip
JVF ≡ ∑mi Ttrackj(D.2.1)pTj
If a jet is a pileup jet like, JVF is close to 0, whereas a jet coming from a primary vertex
has JVF close to 1. The separation of a hard process jet and a pileup jet by JVF depends
on the eﬃciency of the primary vertex selection.
The uncertainty of the JVF is estimated with Z+jet events, where Z boson decays
di-lepton. When the pT of Z boson and jet are well balanced and they are back-to-back,the jet is produced at the ISR. The jet is used for estimation of the JVF eﬃciency forhard process jets. On the other hand when the Z boson is at rest and the Z boson andjet are unbalanced, the jet is a pileup jet. Then the jet is used for estimation of JVF
performance for pileup jets.

D.3

Uncertainty of jet energy scale

Flavor response uncertainty The jet energy scale is derived for a particular admixture of light-quark and gluon jets. For a diﬀerent admixture, the jet energy scale
uncertainty could be diﬀerent. This uncertainty is estimated using MC with studying thediﬀerence between the gluon and light-quark jet response under various assumptions.
Flavor composition uncertainty The fraction of light-quark and gluon jets in samples for jet energy calibration in data could diﬀer from the fraction predicted by thesimulations, thus leading to a systematic shift in the jet energy scale.
OﬀsetMu uncertainty The pileup correction is applied based on MC-based studies.
The amount of transverse momentum generated by pileup in a jet is estimated in MC
simulation. The pileup oﬀset is subtracted from the reconstructed jet pT as a functionof the average number of inelastic interactions. The uncertainty of pileup correction isderived from the diﬀerence between data/MC using di-jet and γ+jet events.
Pileup uncertainty After the pileup correction as a function of the average numberof inelastic interactions, the remaining pileup inﬂuence is suppressed based on energy
depositions outside hard jets. The uncertainty is estimated from a potential mis-modelingof the sample dependence. The diﬀerence of the energy depositions outside hard jets
between data and MC is evaluated in di-jet, γ+jet and Z+jet events.
Model 1 uncertainty The energy calibration uncertainty is estimated from comparison
between MC generators (HERWIG and PYTHIA).
EtaCalib uncertainty The MC-based calibration is validated by a jet eta intercalibration. The validation is performed with physics processes in which the transverse
momenta of a Z boson or a photon are balancing to the transverse momentum of a jet.
The uncertainty on the jet energy scale correction is estimated with the intercalibration.
152

Close-By uncertainty The jet energy scale is determined with isolated jets that haveno other jet within a certain distance. Presence of any jets near-by could cause diﬀerencein jet response, and hence result in a JES systematic uncertainty.

153

Appendix E
Event migration summary

Unconverted central, low pTt
Unconverted central, high pTt
Unconverted rest, low pTt
Unconverted rest, high pTt
Converted central, low pTt
Converted central, high pTt
Converted rest, low pTt
Converted rest, high pTt
Converted transition
Di-jetMaterial Higgs pT−4.0 %
1.1 %−4.0 % −12.5 %−4.0 %
1.1 %−4.0 % −12.5 %+3.5 %
1.1 %+3.5 % −12.5 %+3.5 %
1.1 %+3.5 % −12.5 %+3.5 %
1.1 %−9.0 %

Underlying

VBF: 6.0 %the others: 30 %Table E.0.1:√ Migration uncertainties due to material mapping, Higgs pT and underlying
event for s = 7 TeV analysis.

154

Unconverted central, low pTt
Unconverted central, high pTt
Unconverted rest, low pTt
Unconverted rest, high pTt
Converted central, low pTt
Converted central, high pTt
Converted rest, low pTt
Converted rest, high pTt
Converted transition

Material−4.0 %−4.0 %−4.0 %−4.0 %+3.5 %+3.5 %+3.5 %+3.5 %+3.5 %

Loose VBF
Tight VBFJVF Higgs pT
1.3 %−10.2 %
1.3 %
−10.2 %
1.3 %
−10.2 %
1.3 %
−10.2 %
1.3 %ggF: −1.2 %−8.5 %
VBF: -0.3 %−10.4 %
ggF: −2.3 %VBF: −2.4 %Low mass di-jet
ETmiss signiﬁcanceOne-lepton

1.3 %Underlying

VBF: 3.9 %the others: 12.0 %VBF: 2.0 %the others: 8.8 %VBF: 3.3 %the others: 12.8 %−2.0 %−4.0 %

Table E.0.2: Migration√ uncertainties due to the material mapping, JVF, Higgs pT andunderlying event for s = 8 TeV analysis.

η⋆
Untagged
Loose VBF
ggF: 6.2 %Tight VBF
ggF: 7.6 %Low mass di-jet
ETmiss signiﬁcance|ϕγγ − ϕjj |Lepton (electron) Lepton (muon)

ggF: 8.5 %ggF: 12.1 %WH : 0.7 %ZH : 0.9 %ttH : 0.7 %One-lepton

WH 0.2 %:ZH : 0.3 %ttH : 0.2 %Table
E.0.3: Migration uncertainties due to η ⋆ , |ϕγγ − ϕjj | and lepton eﬃciencies for√
s = 8 TeV analysis.

155

ggF

VBF

VH /ttH

Low pTt
High pTt
ETmissLow pTt
High pTt
ETmissLow pTt
High pTt
ETmissJES
JES
JES
Close-By Model 1 EtaCalib-0.0 %-0.0 %-0.0 %
0.0 %
0.0 %
0.0 %
7.2 %
4.5 %
5.8 %
-0.0 %
0.0 %-0.0 %
0.0 %-0.0 %-0.0 %
10.5 %
6.2 %8.6 %-0.1 %-0.0 %-0.0 %
0.1 %0.0 %-0.0 %
0.5 %-0.2 %
0.3 %Table E.0.4: Migration uncertainties due to E√Tmiss uncertainties coming from JES uncertainties in the ETmiss signiﬁcance category for s = 8 TeV analysis.
JER

ggF

VBF

VH /ttH

Low pTt
High pTt
ETmissLow pTt
High pTt
ETmissLow pTt
High pTt
ETmissSoft
Soft
Scale Resolution-0.0 % -0.0 %-0.0 %
0.0 % -0.0 %-0.0 %
16.3 % 60.0 %21.1 %-0.0 % -0.0 %-0.0 %-0.0 % 0.0 %0.0 %11.0 % 22.4 %10.0 %-0.0 % -0.1 %0.0 %0.0 % 0.1 %-0.1 %-0.1 % 1.0 %0.2 %Table E.0.5: Migration uncertainties due to ETmiss uncertainties
coming from JER and√CellOut uncertainties in the ETmiss signiﬁcance category for s = 8 TeV analysis.

Low pTt
High pTt
Di-jet

ggF
VBF the others-0.0 % -0.7 %-0.0 %-0.1 % -1.1 %-0.0 %
5.4 % 2.1 %4.9 %Table E.0.6: Migration uncertainties due to JES OﬀsetMu uncertainty for
analysis.

Low pTt
High pTt
Di-jet√s = 7TeV

ggF
VBF the others-0.0 % -1.2 %-0.0 %-0.2 % -2.0 %-0.0 %
7.9 % 3.7 %
5.1 %

Table
E.0.7: Migration uncertainties due to JES Flavor Composition uncertainty for√s = 7 TeV analysis.
156

Low pTt
High pTt
Di-jet

ggF
VBF the others-0.0 % -0.6 %-0.0 %-0.1 % -1.0 %-0.0 %
3.5 % 1.9 %2.0 %Table E.0.8: Migration uncertainties due to JES Flavor Response uncertainty for
TeV analysis.

√

s=7

ggF
VBF the others
Low pTt-0.0 % -0.3 %0.0 %High pTt-0.2 % -0.4 %0.2 %Loose VBF
3.3 % 1.3 %-1.1 %
Tight VBF
3.1 % 1.9 %7.4 %Low mass di-jet 1.4 % 0.9 %-0.4 %
ETmiss signiﬁcance 0.0 % 0.0 %0.0 %One-lepton
0.0 % 0.0 %-0.1 %
Table E.0.9: Migration uncertainties due to JES Model 1 uncertainty for
analysis.

√s = 8 TeV

ggF
VBF the others
Low pTt-0.1 % -0.7 %-0.0 %High pTt-0.4 % -0.9 %0.1 %Loose VBF
6.8 % 2.6 %2.8 %Tight VBF
8.5 % 4.8 %11.4 %
Low mass di-jet 0.4 % -1.3 %-0.4 %
miss
ET signiﬁcance 0.0 % 0.0 %0.0 %One-lepton
0.0 % 0.0 %0.0 %Table E.0.10: Migration uncertainties due to JES EtaCalib uncertainty for
analysis.

√s = 8 TeV

ggF
VBF the others
Low pTt-0.0 % -0.2 %0.0 %High pTt-0.1 % -0.2 %-0.1 %
Loose VBF
1.6 % 0.8 %-2.0 %
Tight VBF
1.5 % 1.0 %7.3 %Low mass di-jet 1.2 % 0.3 %0.3 %ETmiss signiﬁcance 0.0 % 0.0 %0.0 %One-lepton
0.0 % 0.0 %-0.0 %
Table E.0.11: Migration uncertainties due to JES Pileup uncertainty for
analysis.

157√
s = 8 TeVggF
VBF the others
Low pTt-0.1 % -0.5 %-0.1 %High pTt-0.0 % -0.7 %0.3 %Loose VBF
6.5 % 2.3 %2.0 %Tight VBF
6.5 % 3.6 %9.1 %Low mass di-jet 2.9 % 1.1 %0.8 %ETmiss signiﬁcance 0.0 % 0.0 %0.0 %One-lepton
0.0 % 0.0 %-0.1 %
Table
E.0.12: Migration uncertainties due to JES Flavor Composition uncertainty for√s = 8 TeV analysis.
ggF
VBF the others
Low pTt-0.0 % -0.3 %-0.0 %High pTt-0.2 % -0.4 %-0.2 %
Loose VBF
3.4 % 1.2 %-1.2 %
Tight VBF
3.0 % 1.8 %8.7 %Low mass di-jet 1.8 % 0.8 %0.6 %ETmiss signiﬁcance 0.0 % 0.0 %0.0 %One-lepton
0.0 % 0.0 %-0.1 %
Table E.0.13: Migration uncertainties due to JES Flavor Response uncertainty for
TeV analysis.

√

s=8

ggF
VBF the others
Low pTt-0.0 % -0.2 %0.1 %High pTt-0.2 % -0.2 %-0.2 %
Loose VBF
1.4 % 0.8 %3.8 %Tight VBF
2.1 % 0.9 %-3.5 %
Low mass di-jet 2.6 % 1.4 %-0.7 %
ETmiss signiﬁcance 0.0 % 0.0 %0.0 %One-lepton
0.0 % 0.0 %-0.0 %
Table E.0.14: Migration uncertainties due to JES Close-By uncertainty for
analysis.

√s = 8 TeV

ggF
VBF the others
Low pTt-0.0 % 0.2 %0.0 %High pTt-0.3 % 0.2 %0.6 %Loose VBF
3.4 % -0.7 %1.2 %Tight VBF
3.8 % -1.3 %7.0 %Low mass di-jet 0.5 % 3.4 %-1.3 %
ETmiss signiﬁcance 0.0 % 0.0 %-0.0 %
One-lepton-0.9 % -0.5 %-0.1 %√
Table E.0.15: Migration uncertainties due to JER uncertainty for s = 8 TeV analysis.
158

Appendix F
Tables of nuisance parameters
Nuisance parameter
ES Method
ES Mat-Low-Eta
ES Mat-High-Eta
ES PS-Barrel
ES PS-Emdcap
ES Conv
ES Leak
ES Edep
ES High-gain
ES E1E2
ES PV
ES BG

Systematic uncertainty
Z line shape
Material |η| < 1.8
Material |η| > 1.8
Presampler barrel
Presampler endcap
Conversion fraction
Lateral leakage, e/γ diﬀerence
Lateral leakage, energy dependence
High/medium gain
Layer intercalibration
Primary vertex
Background model

Table F.0.1: Nuisance parameters for mass scale and corresponding systematic uncertainties.

Nuisance parameter
Mres Eresol
Mres Pileup

Systematic uncertainty
Energy smearing
Pileup mismodeling

Table F.0.2: Nuisance parameters for mass resolution and corresponding systematic uncertainties.

159

Nuisance parameter
Trigger
Luminosity 8TeV
Luminosity 7TeV
Photon-ID
Isolation
QCDscale ggH
QCDscale VBF
QCDscale VH
QCDscale ttH
QCDscale 2jet VBF
QCDscale 3jet VBF
QCDscale 2jet VH
Pdf ggPdf qqBr
Spurious Signal 1
Spurious Signal 2
Spurious Signal 3
Spurious Signal 4
Spurious Signal 5
Spurious Signal 6
Spurious Signal 7
Spurious Signal 8
Spurious Signal 9
Spurious Signal 10
Spurious Signal 11
Spurious Signal 12
Spurious Signal 13
Spurious Signal 14

Systematic uncertainty
trigger eﬃciency√
luminosity for √s = 8 TeV
luminosity for s = 7 TeV
identiﬁcation eﬃciency
isolation eﬃciency
QCD scale for ggF cross section
QCD scale for VBF cross section
QCD scale for WH and ZH cross sections
QCD scale for ttH cross section
QCD scale for ggF+2jet cross section in VBF enriched categories
QCD scale for ggF+3jet cross section in VBF enriched categories
QCD scale for ggF+2jet cross section in VH enriched categories
PDF+αS for ggF and ttH cross sections
PDF+αS for VBF and VH cross sections
branching fraction of Higgs to di-photon
spurioussignal in Unconverted central, low pTt category√
for s = 8 TeV
spurioussignal in Unconverted central, high pTt category√
for s = 8 TeV
spurioussignal in Unconverted rest, low pTt category√
for s = 8 TeV
spurioussignal in Unconverted rest, high pTt category√
for s = 8 TeV
spurioussignal in Converted central, low pTt category√
for s = 8 TeV
spurioussignal in Converted central, high pTt category√
for s = 8 TeV
spurioussignal in Converted rest, low pTt category√
for s = 8 TeV
spurioussignal in Converted rest, high pTt category√
for s = 8 TeV√
spurious signal in Converted transition categoryfors = 8 TeV√
spurious signal in loose VBF category for √ s = 8 TeV
spurious signal in tight VBF category for s =√8 TeV
spurious signal in low mass di-jet category for s√= 8 TeV
spurious signal in ETmiss signiﬁcance category√ for s = 8 TeV
spurious signal in one-lepton category for s = 8 TeV

Table F.0.3: Nuisance parameters for signal yield and corresponding systematic uncertainties.

160

Nuisance parameter
Spurious Signal 15
Spurious Signal 16
Spurious Signal 17
Spurious Signal 18
Spurious Signal 19
Spurious Signal 20
Spurious Signal 21
Spurious Signal 22
Spurious Signal 23
Spurious Signal 24

Systematic uncertainty
spurioussignal in Unconverted central, low pTt category√
for s = 7 TeV
spurioussignal in Unconverted central, high pTt category√
for s = 7 TeV
spurioussignal in Unconverted rest, low pTt category√
for s = 7 TeV
spurioussignal in Unconverted rest, high pTt category√
for s = 7 TeV
spurioussignal in Converted central, low pTt category√
for s = 7 TeV
spurioussignal in Converted central, high pTt category√
for s = 7 TeV
spurioussignal in Converted rest, low pTt category√
for s = 7 TeV
spurioussignal in Converted rest, high pTt category√
for s = 7 TeV√
spurious signal in Converted transition√ category for s = 7 TeV
spurious signal in di-jet category for s = 8 TeV

Table F.0.4: Nuisance parameters for signal yield and corresponding systematic uncertainties.

Nuisance parameter Systematic uncertainty
Material
Material mismodeling in front of the EM calorimeter
JES Pileup-Mu
Jet energy scale (OﬀsetMu)
JES FlavorC
Jet energy scale (Flavor Composition)
JES FlavorR
Jet energy scale (Flavor Response)
JES Model1
Jet energy scale (Model 1)
JES EtaIntCalib
Jet energy scale (EtaCalib)
JES Rho
Jet energy scale (Pileup)
JES Closeby
Jet energy scale (Close-By)
JER
Jet energy resolutionJVF
Jet vertex fraction eﬃciency
Higgs-Pt
Higgs pT
PS-UE
Underlying event
Electron eﬃciency
Lepton-eﬀ El
Lepton-eﬀ Mu
Muon eﬃciency
Soft-S
ETmiss uncertainty due to energy scale of cell out term
ETmiss uncertainty due to energy resolution of cell out termSoft R
Dephoton-Etaη⋆|ϕγγ − ϕjj |DeltaPhi ggjj
Table F.0.5: Nuisance parameters for event migration and corresponding systematic uncertainties.

161

Bibliography[1] F. Englert and R. Brout, Broken symmetry and the mass of gauge vector mesons,Phys. Rev. Lett. 13 (1964) 321.
[2] P. W. Higgs, Broken symmetries, massless particles and gauge ﬁelds, Phys. Lett. 12(1964) 132.
[3] P. W. Higgs, Broken symmetries and the masses of gauge bosons, Phys. Rev. Lett.
13 (1964) 508.
[4] G. S. Guralnik, C. R. Hagen, and T. W. B. Kibble, Global conservation laws andmassless particles, Phys. Rev. Lett. 13 (1964) 585.
[5] P. W. Higgs, Spontaneous symmetry breakdown without massless bosons, Phys. Rev.
145 (1966) 1156.
[6] T. W. B. Kibble, Symmetry breaking in non-Abelian gauge theories, Phys. Rev. 155(1967) 1554.
[7] LEP Working Group for Higgs boson searches, ALEPH, DELPHI, L3, OPAL Collaboration, R. Barate et al., Search for the standard model Higgs boson at LEP,
Phys.Lett. B565 (2003) 61–75, arXiv:hep-ex/0306033 [hep-ex].
[8] Tevatron New Physics, Higgs Working Group, CDF and D0 Collaboration, Updated
Combination of CDF and D0 Searches for Standard Model Higgs Boson Production
with up to 10.0 fb=1 of Data, arXiv:1207.0449 [hep-ex].
[9] ATLAS Collaboration, Observation of a new particle in the search for the Standard
Model Higgs boson with the ATLAS detector at the LHC, Phys. Lett. B 716 (2012)
1, arXiv:1207.7214 [hep-ex].
[10] CMS Collaboration, Observation of a new boson at a mass of 125 GeV with the CMS
experiment at the LHC, Phys. Lett. B 716 (2012) 30, arXiv:1207.7235 [hep-ex].
[11] S. L. Glashow, Partial-symmetries of weak interactions, Nucl. Phys. 22 no. 4, (1961)
579.
[12] S. Weinberg, A Model of Leptons, Phys. Rev. Lett. 19 (1967) 1264.
[13] A. Salam, Weak and electromagnetic interactions, in Elementary particle theory:
relativistic groups and analyticity, N. Svartholm, ed., p. 367. Almqvist & Wiksell,
1968. Proceedings of the eighth Nobel symposium.
162

[14] G. ’t Hooft and M. Veltman, Regularization and Renormalization of Gauge Fields,
Nucl. Phys. B44 (1972) 189.
[15] J. Beringer et al.(PDG), PR D86, 010001 (2012) and 2013 update for the 2014
edition (http://pdg.lbl.gov).
[16] John F. Gunion, Howard E. Haber, Gordon L. Kane, and Sally Dawson. The Higgs
Hunter’s. Guide. Front.Phys., 80:1–448, 2000.
[17] LHC Higgs Cross Section Working Group, Handbook of LHC Higgs Cross Sections:
1. Inclusive Observables, CERN-2011-002 (2011), arXiv:1101.0593 [hep-ph].
[18] LHC Higgs Cross Section Working Group, Handbook of LHC Higgs Cross Sections:
2. Diﬀerential Distributions, CERN-2012-002 (2012), arXiv:1201.3084 [hep-ph].
[19] LHC Higgs Cross Section Working Group, Handbook of LHC Higgs Cross Sections:3. Higgs Properties, CERN-2013-004 (2013), arXiv:1307.1347 [hep-ph].
[20] C. N. Yang, Selection Rules for the Dematerialization of a Particle Into Two Photons, Phys. Rev. 77 (1950) 242.
[21] M. E. Cabrera, J. A. Casas and R. R. de Austri, The health of SUSY after the Higgs
discovery and the XENON100 data, arXiv:1212.4821 [hep-ph].
[22] G. Degrassi, S. Vita, J. Elias-Mir, J. Espinosa, G. Giudice, G. Isidori, and A.
Strumia, Higgs mass and vacuum stability in the Standard Model at NNLO, Journalof High Energy Physics 2012 481 (2012) 1–33.
[23] CERN Document Server, http://cds.cern.ch/collection/Photos[24] The LHCStudy Group, LHC – The Large HadronCollider – Conceptual Design,
CERN/AC/95-05 (LHC) (1995).
[25] J. Wenninger et al., Operation of the LHC at high luminosity and high stored energy,
Proceedings of IPAC2012, New Orleans, Louisiana, USA.
[26] G. Arduini, Performance reach in the LHC for 2012, Proceedings of Chamonix 2012
workshop on LHC Performance, Geneva, Switzerland.
[27] M. Kuhn et al., LHC emittance preservation during the 2012 run, Proceedings ofthe 2012 Evian workshop on LHC beam operation, Geneva, Switzerland.
[28] ATLAS Experiment Public Results:
Luminosity Public Results,
https://twiki.cern.ch/twiki/bin/view/AtlasPublic/LuminosityPublicResults[29] ATLAS inner detector: Technical Design Report, 1. Technical Design Report ATLAS. CERN, Geneva, 1997.
[30] ATLAS inner detector: Technical Design Report, 2. Technical Design Report ATLAS. CERN, Geneva, 1997.

163

[31] ATLAS Magnet System:
magnet/gallery/images/

Illustrations, http://atlas-magnet.web.cern.ch/atlas-[32] The ATLAS Collaboration, The ATLAS Experiment at the CERN Large Hadron
Collider, JINST 3 (2008) S08003.
[33] ATLAS calorimeter performance: Technical Design Report. Technical Design Report
ATLAS. CERN, Geneva, 1996.
[34] ATLAS liquid argon calorimeter: Technical design report. Technical Design Report
ATLAS. CERN, Geneva, 1996.
[35] ATLAS Electromagnetic Barrel Calorimeter Collaboration, M. Aharrouche et al.,Energy linearity and resolution of the ATLAS electromagnetic barrel calorimeter inan electron test-beam, Nucl.Instrum.Meth. A568 (2006) 601–623.
[36] ATLAS level-1 trigger: Technical Design Report. Technical Design Report ATLAS.
CERN, Geneva, 1998.
[37] P. Jenni, M. Nessi, M. Nordberg, and K. Smith, ATLAS high-level trigger, dataacquisition and controls: Technical Design Report. Technical Design Report ATLAS.
CERN, Geneva, 2003.
[38] The√ ATLAS Collaboration, Improved luminosity determination in pp collisions at
s = 7 TeV using the ATLAS detector at the LHC, arXiv:1302.4393 [hep-ex].
[39] GEANT4 Collaboration, S. Agostinelli et al., GEANT4: A simulation toolkit , Nucl.
Inst. Meth. A506 (2003) 250–303.
[40] ATLAS Collaboration, The ATLAS simulation infrastructure, Eur. Phys. J. C 70
(2010) 823, arXiv:1005.4568 [physics.ins-det].
[41] S. Alioli, P. Nason, C. Oleari, and E. Re, NLO Higgs boson production via gluon
fusion matched with shower in POWHEG, JHEP 0904 (2009) 002.
[42] P. Nason and C. Oleari, NLO Higgs boson production via vector-boson fusion
matched with shower in POWHEG, JHEP 1002 (2010) 037.
[43] T. Gleisberg et al., Event generation with SHERPA 1.1, JHEP 0902 (2009) 007.
[44] T. Binoth, J. Guillet, E. Pilon, and M. Werlen, A full next-to-leading order study of
direct photon pair production in hadronic collisions, Eur. Phys. J C16 (2000) 311.
[45] J. Alwall, M. Herquet, F. Maltoni, O. Mattelaer, and T. Stelzer, MadGraph 5 :Going Beyond, JHEP 1106 (2011) 128, arXiv:1106.0522 [hep-ph].
[46] PT. Sjostrand, S. Mrenna, and P. Z. Skands, PYTHIA 6.4 Physics and Manual,
JHEP 0605 (2006) 026.
[47] T. Sjostrand, S. Mrenna, and P. Z. Skands, A Brief Introduction to PYTHIA 8.1,
Comput. Phys. Commun. 178 (2008) 852.
164

[48] H. Georgi, S. Glashow, M. Machacek, and D. V. Nanopoulos, Higgs bosons fromtwo gluon annihilation in proton proton collisions, Phys. Rev. Lett. 40 (1978) 692.
[49] A. Djouadi, M. Spira, and P. M. Zerwas, Production of Higgs bosons in proton
colliders: QCD corrections, Phys. Lett. B 264 (1991) 440.
[50] S. Dawson, Radiative corrections to Higgs boson production, Nucl. Phys. B359 (1991)
283.
[51] M. Spira, A. Djouadi, D. Graudenz, and P. M. Zerwas, Higgs boson production at
the LHC, Nucl. Phys. B453 (1995) 17.
[52] R. Harlander and W. B. Kilgore, Next-to-next-to-leading order Higgs production at
hadron colliders, Phys. Rev. Lett. 88 (2002) 201801.
[53] C. Anastasiou and K. Melnikov, Higgs boson production at hadron colliders in NNLO
QCD, Nucl. Phys. B646 (2002) 220.
[54] V. Ravindran, J. Smith, and W. L. van Neerven, NNLO corrections to the total
cross section for Higgs boson production in hadron hadron collisions, Nucl. Phys.
B665 (2003) 325.
[55] U. Aglietti, R. Bonciani, G. Degrassi, and A. Vicini, Two-loop light fermion contribution to Higgs production and decays, Phys. Lett. B 595 (2004) 432.
[56] S. Actis, G. Passarino, C. Sturm, and S. Uccirati, NLO electroweak corrections to
Higgs boson production at hadron colliders, Phys. Lett. B 670 (2008) 12.
[57] S. Catani, D. de Florian, M. Grazzini, and P. Nason, Soft-gluon re-summation for
Higgs boson production at hadron colliders, JHEP 0307 (2003) 028.
[58] D. √de Florian and M. Grazzini, Higgs production at the LHC: updated cross sections
at s = 8 TeV, arXiv:1206.4133 [hep-ph].
[59] C. Anastasiou, S. Buehler, F. Herzog, and A. Lazopoulos, Inclusive Higgs boson
cross-section for the LHC at 8 TeV, JHEP 1204 (2012) 004.
[60] J. Baglio and A. Djouadi, Higgs production at the lHC, JHEP 1103 (2011) 055.
[61] D. de Florian, G. Ferrera, M. Grazzini, and D. Tommasini, Transverse-momentum
resummation: Higgs boson production at the Tevatron and the LHC, JHEP 1111
(2011) 064.
[62] E. Bagnaschi, G. Degrassi, P. Slavich, and A. Vicini, Higgs production via gluon
fusion in the POWHEG approach in the SM and in the MSSM, JHEP 1202 (2012)88.
[63] R. Cahn and S. Dawson, Production of very massive Higgs bosons, Phys. Lett. B
136 (1984) 196, Erratum–ibid. B 138 (1984) 464.

165

[64] M. Ciccolini, A. Denner, and S. Dittmaier, Strong and electroweak corrections to
the production of Higgs+2jets via weak interactions at the LHC, Phys. Rev. Lett.
99 (2007) 161803.
[65] M. Ciccolini, A. Denner, and S. Dittmaier, Electroweak and QCD corrections to
Higgs production via vector-boson fusion at the LHC, Phys. Rev. D 77 (2008) 013002.
[66] K. Arnold, M. Bahr, G. Bozzi, F. Campanario, C. Englert, et al., VBFNLO: A parton level Monte Carlo for processes with electroweak bosons, Comput. Phys. Commun. 180 (2009) 1661.
[67] P. Bolzoni, F. Maltoni, S.-O. Moch, and M. Zaro, Higgs production via vector-boson
fusion at NNLO in QCD, Phys. Rev. Lett. 105 (2010) 011801.
[68] S. Glashow, D. V. Nanopoulos, and A. Yildiz, Associated production of Higgs bosons
and Z particles, Phys. Rev. D 18 (1978) 1724.
[69] T. Han and S. Willenbrock, QCD correction to the pp →WH and ZH total crosssections, Phys. Lett. B 273 (1991) 167.
[70] O. Brein, A. Djouadi, and R. Harlander, NNLO QCD corrections to the Higgsstrahlung processes at hadron colliders, Phys. Lett. B 579 (2004) 149.
[71] M. L. Ciccolini, S. Dittmaier, and M. Kramer, Electroweak radiative corrections
to associated WH and ZH production at hadron colliders, Phys. Rev. D 68 (2003)
073003.
[72] Z. Kunszt, Associated production of heavy Higgs boson with top quarks, Nucl. Phys.
B 247 (1984) 339.
[73] W. Beenakker et al., Higgs Radiation Oﬀ Top Quarks at the Tevatron and the LHC,
Phys. Rev. Lett. 87 (2001) 201805.
[74] W. Beenakker et al., NLO QCD corrections to t¯tH production in hadron collisions,
Nucl. Phys. B 653 (2003) 151.
[75] S. Dawson, L. H. Orr, L. Reina, and D. Wackeroth, Next-to-leading order QCD
corrections to pp → tt̄h at the CERN Large Hadron Collider, Phys. Rev. D 67
(2003) 071503.
[76] S. Dawson, C. Jackson, L. H. Orr, L. Reina, and D. Wackeroth, Associated Higgs
production with top quarks at the Large Hadron Collider: NLO QCD corrections,Phys. Rev. D 68 (2003) 034022.
[77] G. Corcella, I. Knowles, G. Marchesini, S. Moretti, K. Odagiri, et al., HERWIG 6:
An Event generator for hadron emission reactions with interfering gluons (including
supersymmetric processes), JHEP 0101 (2001) 010.
[78] J. M. Butterworth, J. R. Forshaw, and M. H. Seymour, Multiparton interactions inphotoproduction at HERA, Z. Phys. C 72 (1996) 637.

166

[79] P. Golonka and Z.Was, PHOTOS Monte Carlo: A Precision tool for QED corrections in Z and W decays, Eur. Phys. J. C 45 (2006) 97.
[80] N. Davidson, T. Przedzinski, and Z. Was, PHOTOS interface in C++: technicaland physics documentation, arXiv:1011.0937 [hep-ph].
[81] H.-L. Lai et al., New parton distributions for collider physics, Phys. Rev. D 82 (2010)
074024.
[82] P. M. Nadolsky et al., Implications of CTEQ global analysis for collider observables,
Phys. Rev. D 78 (2008) 013004.
[83] A. Sherstnev and R. S. Thorne, Parton distributions for the LHC, Eur. Phys. J C
55 (2009) 553, arXiv:0711.2473 [hep-ph].
[84] The ATLAS Collaboration, Measurements of the photon identiﬁcation eﬃciency
with the ATLAS detector using 4.9 fb−1 of pp collision data collected in 2011.
ATLAS-CONF-2012-123 (2012).
[85] Lance Dixon, M. Stewart Siu, Resonance-continuum interference in the di-photon
Higgs signal at the LHC, Phys. Rev. Lett. 90 (2003) 252001.
[86] D. de Florian, G. Ferrera, M. Grazzini, and D. Tommasini, Transverse-momentum
resummation: Higgs boson production at the Tevatron and the LHC, JHEP 1111
(2011) 064, arXiv:1109.2109 [hep-ph].
[87] ATLAS Collaboration, Expected photon performance in the ATLAS experiment,
ATLAS-PHYS-PUB-2011-007 (2011).
[88] ATLAS Stand-Alone Event Displays,
https://twiki.cern.ch/twiki/bin/view/AtlasPublic/EventDisplayStandAlone[89] ATLAS Collaboration,√ Performance of primary vertex reconstruction in protonproton collisions at s =7 TeV in the ATLAS experiment, ATLAS-CONF-2010-069(2010).
[90] ATLAS Collaboration, Performance of the ATLAS Inner Detector Track and Vertex
Reconstruction in the High Pile-Up LHC Environment, ATLAS-CONF-2012-042(2012).
[91] ATLAS collaboration, Measurements of the properties of the Higgs-like boson in thetwo photon decay channel with the ATLAS detector using 25 fb−1 of proton-proton
collision data, ATLAS-CONF-2013-012 (2013).
[92] The ATLAS Collaboration, Performance of the ATLAS Trigger System in 2010,
Eur. Phys. J. C72 938 (2012).
[93] ATLAS Collaboration, Observation of an excess of events in the search for the Standard Model Higgs boson in the gamma-gamma channel with the ATLAS detector,
ATLAS-CONF-2012-091 (2012).

167

[94] The ATLAS Collaboration, Improved electron reconstruction in ATLAS using
the Gaussian Sum Filter-based model for bremsstrahlung, ATLAS-CONF-2012-047(2012).
[95] M. Cacciari, G. P. Salam, and G. Soyez, The anti-kt jet clustering algorithm, JHEP
0804 (2008) 063.
[96] ATLAS collaboration, Performance of missing transverse
momentum reconstruction√in ATLAS with 2011 proton-proton collisions at s = 7 TeV, ATLAS-CONF-2012101 (2012).
[97] A. Hoecker, P. Speckmayer, J. Stelzer, J. Therhaag, E. von Toerne, and H. Voss,TMVA 4 (Toolkit for multivariate data analysis with ROOT) Users Guide. 2009.
[98] ATLAS Collaboration, Expected performance of the ATLAS experiment : detector,
trigger and physics, CERN Document Server.
[99] The ATLAS Collaboration, Search for the Standard Model
Higgs boson in the dipho√
ton decay channel with 4.9 fb−1 of ATLAS data at s = 7 TeV, ATLAS-CONF2011-161 (2011) .
[100] The ATLAS Collaboration,
Measurement of the isolated di-photon cross-section in√pp collisions at s = 7 TeV with the ATLAS detector, Phys. Rev. D85 (2012)
012003.
[101] The ATLAS Collaboration,√Jet energy measurement with the ATLAS detector inproton-proton collisions at s =7 TeV, arXiv:1112.6426 [hep-ex].
[102] ATLAS Collaboration, Summary of ATLAS Pythia 8 tunes, ATL-PHYS-PUB-2012003 (2012).
[103] A. Wald, Tests of Statistical Hypotheses Concerning Several Parameters When the
Number of Observations is Large, Transactions of the American Mathematical Society, Vol. 54, No. 3 (Nov., 1943), pp. 426-482.
[104] S.S. Wilks, The large-sample distribution of the likelihood ratio for testing composite
hypotheses, Ann. Math. Statist. 9 (1938) 60-2.
[105] ATLAS Collaboration, Evidence for the spin-0 nature of the Higgs boson using
ATLAS data, Phys.Lett. B726 (2013) 120-144.
[106] M. Carena, S. Gori, N. R. Shah, and C. E. M. Wagner, A 125 GeV SM-like Higgs
in the MSSM and the γγ rate, Journal of High Energy Physics, vol. 2012, no. 3,
article 014, 2012.
[107] M. Carena, I. Low and C.E.M Wagner, Implications of a modiﬁed Higgs to diphoton
decay width, JHEP 1208 (2012) 060.
[108] A. Joglekar, P. Schwaller and C.E.M. Wagner, Dark matter and enhanced Higgs to
di-photon rate from vector-like leptons, JHEP 12 (2012) 064.

168

[109] H. Davoudiasl, H.-S. Lee, and W. J. Marciano, Dark Side of Higgs Diphoton Decays
and Muon g-2, Phys.Rev. D86 (2012) 095009.
[110] ATLAS Collaboration,√ Jet energy scale and its sytematic uncertainty in protonproton collisions at s = 7 TeV with ATLAS 2010 data, tech. rep., CERN, 2011.
ATLAS-CONF-2011-032.
[111] The ATLAS Collaboration, Measurements of Higgs boson production and couplingsin diboson ﬁnal states with the ATLAS detector at the LHC, Phys. Lett. B 726(2013) 88.

169