UNIVERSITA' DEGLI STUDI DI MILANO BICOCCA acoltàF di Scienze Matematiche Fisiche … UNIVERSITA'...
Transcript of UNIVERSITA' DEGLI STUDI DI MILANO BICOCCA acoltàF di Scienze Matematiche Fisiche … UNIVERSITA'...
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UNIVERSITA' DEGLI STUDI DI MILANO BICOCCA
Facoltà di Scienze Matematiche Fisiche e Naturali
Corso di Laurea in Fisica
Search of the standard model Higgs decay into two photons:
photon energy reconstruction, calibration and resolution
Relatore Prof. Tommaso Tabarelli de Fatis
Correlatore Dott. Alessio Ghezzi
Tesi di Laurea Magistrale di
Badder Marzocchi
Matricola 709790
Anno Accademico 2011-2012
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Contents
1 Executive Summary 5
2 The standard model of electroweak interactions 8
2.1 Theoretical introduction . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.1.1 Non-interacting �elds . . . . . . . . . . . . . . . . . . . . . . . 9
2.1.2 Interacting �elds and gauge invariance principle . . . . . . . . 10
2.1.3 The Higgs mechanism . . . . . . . . . . . . . . . . . . . . . . 13
2.2 Higgs boson searches . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.2.1 Theoretical constraints on the Higgs mass . . . . . . . . . . . 16
2.2.2 Experimental constraints on the Higgs mass . . . . . . . . . . 17
2.2.3 Higgs boson production and decay modes . . . . . . . . . . . . 21
3 CMS Experiment 24
3.1 The Large Hadron Collider . . . . . . . . . . . . . . . . . . . . . . . . 24
3.2 CMS Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.2.1 Tracker System . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.2.2 ECAL Calorimeter . . . . . . . . . . . . . . . . . . . . . . . . 28
3.2.3 HCAL Calorimeter . . . . . . . . . . . . . . . . . . . . . . . . 30
3.2.4 Muon System . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4 Monitoring System 34
4.1 Experimental Apparatus . . . . . . . . . . . . . . . . . . . . . . . . . 34
4.2 Light collection in PbWO4 . . . . . . . . . . . . . . . . . . . . . . . . 37
4.3 Test Beam Measurements . . . . . . . . . . . . . . . . . . . . . . . . 41
5 ECAL Calibration and Stability Studies 45
5.1 Electrons and photons reconstruction . . . . . . . . . . . . . . . . . . 46
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CONTENTS 3
5.2 ECAL energy reconstruction . . . . . . . . . . . . . . . . . . . . . . . 48
5.3 Calibration Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
5.3.1 φ-symmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
5.3.2 π0/η-calibration . . . . . . . . . . . . . . . . . . . . . . . . . . 51
5.4 ECAL calibration with electrons and positrons from Z0 and W± decays 52
5.4.1 Event Selection . . . . . . . . . . . . . . . . . . . . . . . . . . 53
5.4.2 Template Fit . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
5.4.3 Supercluster Energy Correction . . . . . . . . . . . . . . . . . 56
5.4.4 Pile up corrections . . . . . . . . . . . . . . . . . . . . . . . . 56
5.4.5 Intercalibration constants . . . . . . . . . . . . . . . . . . . . 57
5.4.6 ECAL Stability . . . . . . . . . . . . . . . . . . . . . . . . . . 58
6 In situ α Measurements 61
6.1 General procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
6.2 Measurements from stability plots . . . . . . . . . . . . . . . . . . . . 62
6.2.1 Barrel Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
6.2.2 Endcaps results . . . . . . . . . . . . . . . . . . . . . . . . . . 64
6.3 Measurements from Z0-peak . . . . . . . . . . . . . . . . . . . . . . . 69
7 Search of the channel H → γγ 787.1 Photon reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . 78
7.2 Photon energy reconstruction . . . . . . . . . . . . . . . . . . . . . . 79
7.2.1 Supercluster energy correction . . . . . . . . . . . . . . . . . . 79
7.2.2 Resolving data and simulations discrepancies . . . . . . . . . . 80
7.3 Diphoton vertex identi�cation . . . . . . . . . . . . . . . . . . . . . . 81
7.4 Photon identi�cation MVA . . . . . . . . . . . . . . . . . . . . . . . . 83
7.4.1 List Of Input Variables . . . . . . . . . . . . . . . . . . . . . . 83
7.4.2 BDT Output and Photon Identi�cation Performance . . . . . 84
7.5 Dijet Tag for VBF Selection . . . . . . . . . . . . . . . . . . . . . . . 84
7.6 Diphoton mass resolution and kinematics MVA . . . . . . . . . . . . 85
7.6.1 Validation of the Signal Model using Z → e+e− . . . . . . . . 867.7 Statistical analysis using the diphoton mass shape . . . . . . . . . . . 87
7.7.1 Background Modelling . . . . . . . . . . . . . . . . . . . . . . 88
7.7.2 Signal Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
7.8 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
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CONTENTS 4
8 Energy Scales Studies 95
8.1 Z0 energy scales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
8.2 Higgs Mass systematic uncertainties . . . . . . . . . . . . . . . . . . . 97
8.3 Higgs Search Final Results . . . . . . . . . . . . . . . . . . . . . . . . 101
9 Conclusions 105
10 Acknowledgements 106
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Chapter 1
Executive Summary
The CMS experiment is a general purpose experiment at the Large Hadron
Collider (LHC). One of the main CMS goals is the search for the Higgs boson.
A search for standard model (SM) Higgs boson is fundamental as it is the only
missing particle, which explains how it and all the other SM particles gain mass.
Among possible Higgs decays, the decay H → γγ is the main channel for the Higgsdiscovery at masses about or below 140 GeV/c2. This channel has a clear signature,
consisting of a peak in the two photons invariant mass distribution, a small intrinsic
width but also a small branching ratio and a sizeable irreducible background. For
these reasons, a detector with an excellent energy and position resolution is needed.
The Electromagnetic Calorimeter (ECAL) of the CMS experiment was designed to
provide excellent energy resolution. It is an homogeneous and compact detector,
composed by lead tungstate (PbWO4) crystals. During the data taking, in situ
control of the uniformity and stability of response is a great challenge, as it a�ects
the resolution which in�uences the sensitivity of the H→ γγ search. Other featureslike response linearity are important in order to perform precise measurements of
the mass or other Higgs boson properties, once discovered.
The choice of PbWO4 crystals was driven by their radiation tolerance and their fast
light emission. Although the good radiation tolerance, The LHC high luminosity (of
order 1034cm−2s−1) a�ects the transparency of PbWO4 crystals, with variations that
impact on the ECAL resolution. Most of this thesis is dedicated to the study of the
transparency variations of the ECAL crystals in the context of resolution studies.
In CMS a monitoring system is used to correct for crystals transparency variations,
based on the injection of laser light in the crystals. An approximate empirical
relation between the relative scintillation signal induced by energy deposits in the
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CHAPTER 1. EXECUTIVE SUMMARY 6
crystals (S/S0) and the relative monitoring laser signal (R/R0) is:
S
S0=
(R
R0
)αwhere α is believed to be an universal parameter, according to the test beam results.
The aim of this thesis is to verify this ansatz in the LHC radiation conditions and to
study the impact of the approximation of the above equation upon the resolution.
The above formula is strictly valid only in the limit of small transparency losses
while at large losses α is a function of the loss itself. As an additional complication,
in the endcaps the quantum e�ciency of the photodetectors also decreases as the ac-
cumulated dose increases. The monitoring system cannot disentangle transparency
losses and photodetectors response losses, this e�ect also results into an e�ective α
with time and transparency variation dependence. For these reasons also the above
features are studied.
Two methods are exploited in order to check ECAL stability and extract its contri-
bution to the ECAL resolution. One compares the energy (E) measured by ECAL
to the momentum (p) measured by the tracker, for isolated electrons/positrons from
the W decay. From the variations of E/p ratio versus the transparency changes, an
average α value is measured. An alternative procedure based on electrons from Z
decays is performed on the endcaps. This later method maximizes the likelihood of
the invariant mass distribution of the two electrons in order to extract the best α
value which optimizes the resolution. In both cases the resolution on the invariant
mass of the electrons pair from Z → ee is used to gauge the improvement in theenergy resolution.
The measurements from the barrel events con�rmed the test beam results, since in
the barrel there are small transparency changes (3%) because of the small absorbed
doses. On the other hand, in the endcaps the average transparency loss is about
15%, and reaches a maximum of the 50% in the forward regions of the calorimeter,
the extracted α value is about 25% lower than the value measured at test beams.
Moreover, even in spite of the high radiation dose, a constant value of α, with no
dependence on time or transparency losses, is su�cient to minimize the resolution.
The optimization of the transparency corrections, combined with the progressive
improvement of the intercalibration of the response among the di�erent channels,
led to a substantial improvement of the mass resolution from 2.40 to 2.06 GeV/c2, in
the search region for the H→ γγ decay (115-140 GeV/c2), enabling CMS to discoverit, at a mass of about 125 GeV/c2 and with a signal strength of 1.6±0.4 compared
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CHAPTER 1. EXECUTIVE SUMMARY 7
to the expected SM Higgs production.
The �nal part of this thesis is dedicated to the description of the CMS H → γγanalysis, the Higgs boson discovery and the systematic uncertainties of the mass
measurements. The latter are related to the knowledge of the calibration of the
CMS response to photons. The Zee mass peak provides the calibration point closest
to the Higgs mass. MC is used to extrapolate this calibration from electrons to pho-
tons and from the Z mass (91.18 GeV/c2) to the Higgs mass (about 125 GeV/c2).
Any di�erential non-linearity between data and MC in the response to electrons or
photons, chie�y induced by the impact of the material upstream of ECAL, would
impact on the knowledge of the mass scale at the Higgs mass. These e�ects have
been studied through the variation of the E/p ratio as a function of the electron
energy and other, bremsstrahlung-sensitive variables. From this, a systematic error
on the Higgs mass of 0.5% is estimated, is comparable to the current statistical
error, yielding mH = 125.2±0.4stat±0.5syst GeV/c2.
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Chapter 2
The standard model of electroweak
interactions
The Higgs Boson is an elementary particle which was proposed at the beginning
of the 1960s in order to explain in a very simple way how all the massive particles
gain the mass. The mechanism by which the Higgs boson itself and all the other
particles gain mass is called Higgs mechanism. This theory is based on the particle
physics Standard Model (SM) [1].
2.1 Theoretical introduction
in order to describe the observed phenomena, four forces are believed to be
enough and fundamental, i.e. directly associated with matter properties. The forces
are: Electromagnetic, Strong, Weak and Gravitational Force. The Standard Model
explains how to describe a particle and how it can interact with another one, through
one of the fundamental forces. Unfortunately, by now we are not able to ascribe in
the Standard Model the gravitational force.
The background of the SM is the relativistic Quantum Field Theory, so that a quan-
tum �eld is associated to each particle. Basing on their spin, all particles are split
into two groups: fermions and bosons. Fermions have half-integer spin and follow
the Fermi-Dirac statistics. On the other hand, bosons have integer spin, follow Bose-
Einstein statistics and can be seen as the intermediates of the interaction forces.
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CHAPTER 2. THE STANDARDMODEL OF ELECTROWEAK INTERACTIONS9
1st family 2nd family 3rd family Q
Leptons νe (∼ 0) νµ (∼ 0) ντ (∼ 0) 0e (511 KeV/c2) µ (105.7 MeV/c2) τ (1.777 GeV/c2) -1
Quarks u (1.7-3.1 MeV/c2) c (1.29+0.05−0.11GeV/c2) t (172.9+1.1−1.1GeV/c
2) 1/3
d (4.1-5.7 MeV/c2) s (100+30−20MeV/c2) b (4.19+0.18−0.01GeV/c
2) -2/3
Table 2.1: Spin-1/2 fermions
Mass (GeV/c2) Q
Photon (γ) 0 0
Gluon (g) 0 0
W 80.385 ± 0.015 ±1Z0 91.188 ± 0.002 0
Table 2.2: Spin-1 bosons
As shown in Table 2.1, the matter is composed by two types of spin-1/2 con-
stituents: leptons and quarks. Besides the masses and the electromagnetic charges,
quarks and leptons di�er for the colour charges (r, b, g, r̄, b̄ and ḡ).
Because of the colour charge quarks can create bound states: mesons (qq̄) and
baryons (qqq).
Table 2.2 shows all the spin-1 particles (forces intermediates). Note that gluons, the
Strong force intermediates, have also colour charges.
The last particle in this theory is the Higgs Boson; it is a massive, chargeless, spin-0
particle.
2.1.1 Non-interacting �elds
By means of a variational principle it is possible to derive the equations of motion
from the Lagrangian density for each non-interacting and interacting particle. For
free particles we have:
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CHAPTER 2. THE STANDARDMODEL OF ELECTROWEAK INTERACTIONS10
Spin-0 complex �eld φ:
L = 12
(∂µφ)†∂µφ+m2
2φ†φ −→ (∂µ∂µ +m2)φ = 0
Spin-1/2 �eld ψ (bispinor):
L = ψ̄(i/∂ −m)ψ −→ (−i/∂ +m)ψ = 0 (2.1)
Spin-1 �eld Aµ: after de�ning Fµν = ∂µAν-∂νAµ
L = −14F µνFµν +
m2
2AµAµ −→ (∂µ∂µ +m2)Aν = 0
The SM is based on the group of symmetries SUC(3) × SUL(2) × UY (1). SUC(3)is related to the colour charges, each quark can be seen to be a triplet under this
symmetry, whereas each lepton is a colourless singlet. As gluons carry colour they
can interact with each other giving rise to other terms in the Lagrangian that we
don't �nd in the electromagnetic one. On the other hand, SUL(2) is related to the
chirality. If we consider the Dirac bispinor we can separate it: ψ = ψR + ψL, where
ψR and ψL are the eigenstate of chirality, γ5. If we consider the Dirac representation:
ψL =1− γ5
2ψ
ψR =1 + γ5
2ψ
Note that right bispinors and left bispinors interact in di�erent ways. Given the
SU(2) symmetry it is possible to identify the couples of same family left-handed
fermions as isospin doublets. On the other hand, right-handed fermions are isospin
singlets.
The last symmetry, UY (1) is related to the weak hypercharge.
2.1.2 Interacting �elds and gauge invariance principle
Consider a Dirac �eld ψ and the local gauge transformation eigα(x):
ψ → eigα(x)ψ
ψ̄ → e−igα(x)ψ̄
∂µψ → eigα(x)(∂µψ + igψ∂µα(x))
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CHAPTER 2. THE STANDARDMODEL OF ELECTROWEAK INTERACTIONS11
∂µψ̄ → e−igα(x)(∂µψ̄ − igψ̄∂µα(x))
Under these transformations the Lagrangian of Equation 2.1 is not invariant. Intro-
ducing a gauge �eld it is possible to recover the gauge invariance. Aµ is a gauge �eld
and under gauge transformations becomes A′µ = Aµ - ∂µα(x). Due to this property it
is possible to replace each ∂µ with the covariant derivative, such that Dµψ ≡ ∂µψ +igAµψ. Adding the Aµ kinetic term, we arrive to the complete invariant Lagrangian:
L = ψ̄(i /D −m)ψ − 14F µνFµν = ψ̄(i/∂ −m)ψ −
1
4F µνFµν − gψ̄ /Aψ
The �rst term is the free electron Lagrangian, the second is the photon kinetic term
and the third is the interaction between photon and electron term. Thus, by means
of gauge invariance principle we introduce gauge bosons (forces intermediates) and
their interactions with the fermions.
In a more general way, considering a non-Abelian gauge group, with transformation
U and a �eld φ :
φ → Uφ
φ† → φ†U†
Fµν → UFµνU†
Aµ = Aaµta
Fµν = Faµνt
a = [∂µAaν - ∂νA
aµ + iA
bµA
cνf
abc]ta
Dµφ ≡ ∂µφ + iAaµtaφ
(Dµφ)† ≡ ∂µφ† - iAaµtaφ†
where ta are the group generators and fabc ≡ [tb,tc] are the structure constants.Now we can apply invariance under SU(2) × U(1) to SM. U(1) has one generator (aconstant) and SU(2) has three generators (a representation are the Pauli matrices
σi), therefore we can introduce four gauge �elds Wµi and B
µ (i = 1, 2, 3). The
covariant derivative becomes:
Dµ = ∂µ + igσi2W µi + ig
′Y
2Bµ
As already said, under the SU(2) symmetry we have left-handed isospin doublets:
L =
(νl
l
)L
or L =
(qu
qd
)L
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CHAPTER 2. THE STANDARDMODEL OF ELECTROWEAK INTERACTIONS12
whereas the right-handed fermions are singlet. For sake of simplicity consider only
the electron family and de�ne:
τ± =σ1 ± iσ2
2
W±µ =W µ2 ± iW
µ1√
2
and τ 3 = σ3, the interacting Lagrangian L̄γµDµL can be divided in two parts, one
in charged current and the other in neutral current:
LCC =g√2
[L̄ /W
+τ+L+ L̄ /W
−τ−L
]
LNC =g
2
[L̄ /W
3τ 3L
]+g′
2
[YνL ν̄L /BνL + YeL ēL /BeL + YνR ν̄R /BνR + YeR ēR /BeR
](2.2)
It is possible to condensate the NC Lagrangian, de�ning:
Ψ =
νL
eL
νR
eR
, T3 =
1/2
−1/20
0
, Y =YνL
YeLYνR
YeR
where T3 is the third component of the isospin and Y is the hypercharge. The
Lagrangian of Equation 2.2 becomes:
LNC = gΨ̄ /W3µT3Ψ +
g′
2Ψ̄ /BYΨ
In order to give physical meaning to Wµ3 and Bµ �elds it is necessary to introduce
the Weinberg angle and the following relations:(Bµ
W µ3
)=
(cos θW − sin θWsin θW cos θW
)(Aµ
Zµ
)(2.3)
Q ≡ T3 +Y
2
e = g sin θW = g′ cos θW
gV ≡ T3 − 2Q sin2 θW
gA ≡ T3
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CHAPTER 2. THE STANDARDMODEL OF ELECTROWEAK INTERACTIONS13
T T3 Y Q
νlL12
12
-1 0
lL12
-12
-1 -1
νlR 0 0 0 0
lR 0 0 -2 -1
T T3 Y Q
qupL12
12
13
23
qdownL12
-12
13
-13
qupR 0 043
23
qdownR 0 0 -23
-13
Table 2.3: Left: leptons quantum numbers; Right: quarks quantum numbers
where Aµ and Zµ are respectively the photon and the Z0 boson �elds and e is the
positron charge in natural units. Finally the interaction Lagrangians become:
LA = eQΨ̄ /AΨ (2.4)
LZ =e
2 sin θW cos θWΨ̄/Z(gV − gAγ5)Ψ (2.5)
We can generalize to all the leptons and quarks families, Table 2.3 shows all the
values of isospin, hypercharge and electron charge. Note that since νR has all the
quantum numbers equal to zero it doesn't interact.
The complete Lagrangian will also feature the gauge bosons kinetics terms. It can
be demonstrated that they are gauge invariant.
The mass terms:
m2WW+µW−µ +
1
2m2ZZ
µZµ +∑f
mf (ψ̄RψL + ψ̄LψR)
cannot be put in the Lagrangian because they are not gauge invariant. Maintaining
the gauge invariance, a way to give mass to these particles is the Higgs Mechanism.
2.1.3 The Higgs mechanism
Consider a complex scalar �eld φ, a vector �eld Aµ and the Lagrangian:
L = Dµφ∗Dµφ− µ2|φ|2 − λ|φ|4 −1
4F µνFµν
with Dµφ = [∂µ + iqAµ]φ and V(x) ≡ µ2|φ(x)|2 + λ|φ(x)|4.Because φ is a complex �eld it can be decomposed in two �elds φ1 and φ2. Indeed,
the potential V(x) has very di�erent physical meanings depending on µ2 and λ signs.
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CHAPTER 2. THE STANDARDMODEL OF ELECTROWEAK INTERACTIONS14
In order to be inferiorly limited the potential must have λ positive. If µ2 > 0 the
potential has only one minimum in zero, it becomes the Klein-Gordon potential with
an extra auto-interaction term and µ2 can be interpreted as the square mass of the
particle. On the other hand, if µ2 < 0 V(x) has a maximum in zero and minima in φ
=√−µ22λeiθ; thus, it is not possible to use the perturbation theory in φ = 0. Figure
2.1 shows the potential for µ2 < 0. We can expand the �eld on the minima-circle,
Figure 2.1: Higgs boson potential if µ2 < 0
choosing one minimum and breaking the θ-symmetry of the potential (Spontaneous
Symmetry Breaking). Fixing one minimum, v, and expanding:
φ(x) =1√2
[v + h(x) + iη(x)]
Inserting this expansion in the Lagrangian:
L = 12∂µh∂µh(x)+
1
2∂µη(x)∂µη(x)−
1
4F µνFµν−
1
2(2λv2)h(x)2+vqAµ(x)∂µη(x)+interaction terms
This Lagrangian is inconsistent since we begin with φ and Aµ, thus with 4 degrees
of freedom, and after the spontaneous symmetry breaking, we arrive to 5 degrees of
freedom: a massless real scalar �eld η(x) (Goldstone boson), a massive real scalar
�eld h(x) and a massive vector �elds Aµ(x). By means of the invariance under U(1),
it is possible to perform a gauge transformation which eliminates the non physical
�eld, η(x) = 0.
L = 12∂µh(x)∂µh(x)−
1
4F µνFµν−
1
2(2λv2)h2(x)+
1
2(qv)2Aµ(x)A
µ(x)+ interaction terms
Now there are one massive vector �eld Aµ(x) with mass qv and a massive scalar
�eld h(x) with mass√
2λv2, therefore 4 degrees of freedom.
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CHAPTER 2. THE STANDARDMODEL OF ELECTROWEAK INTERACTIONS15
Applying this mechanism to SM, it is necessary to introduce an Higgs doublet Φ(x)
which transforms in the following manner under gauge transformation:
Φ =
(φa(x)
φb(x)
) U(1): Φ → eig′Y/2f(x)Φ
SU(2): Φ → eigτiωi(x)/2Φ
DµΦ = [∂µ + ig2τiW
µi + ig
′ Y2Bµ]Φ
Since we do not want to give mass to the photon, the UEM(1) symmetry cannot be
broken. So, from the relation Q =Y
2+ T3, we have two possibilities:
1. Y = 1: Φ upper component has charge 1 and the lower one chargeless;
2. Y = -1: Φ upper component has charge 0 and the lower charge -1;
A way to give mass to the leptons is to introduce the Yukawa interactions:
LY K = −gl[Ψ̄LΨlRΦ + Φ†Ψ̄lRΨL]− gνl [Ψ̄LΨνlRΦ̃ + Φ̃
†Ψ̄νlRΨL]
where Φ̃ ≡ -i[Φ†τ2]T . Note that this Lagrangian is invariant under SU(2)× U(1).The total Lagrangian to apply the Spontaneous Symmetry Breaking mechanism is:
L = [DµΦ]†[DµΦ]− µ2Φ†Φ− λ[Φ†Φ]2−
−gl[Ψ̄LΨlRΦ + Φ†Ψ̄lRΨL]− gνl [Ψ̄LΨνlRΦ̃ + Φ̃
†Ψ̄νlRΨL]+
+i[Ψ̄L /DΨL + Ψ̄lR/DΨlR + Ψ̄
νlR/DΨνlR ]−
−14BµνBµν −
1
4W µνi Wiµν (2.6)
Now, if λ > 0 and µ2 < 0, < 0|Φ|0 > 6= 0, it is possible to expand Φ near theminimum v as:
Φ(x) =1√2
(η1(x) + iη2(x)
v + h(x) + iη3(x)
)where η1(x), η2(x) and η3(x) are Goldstone bosons. After the expansion, all the
SU(2)×U(1) symmetry but UEM(1) is broken. As previously done, it is possible tocancel all the Goldstone bosons performing gauge transformation, taking to:
Φ(x) =1√2
(0
v + h(x)
)
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CHAPTER 2. THE STANDARDMODEL OF ELECTROWEAK INTERACTIONS16
Inserting this in the Lagrangian of Equation 2.6 and achieving the transformation of
Equation 2.3, interactions terms between Higgs Boson, fermions and gauge bosons
appear, as well as the desired mass terms, where:
m2γ = 0 ;
m2l =glv√
2
m2νl =gνlv√
2
m2W =g2v2
4;
m2Z =v2(g2 + g′2)
4;
m2H = 2λv2 ;
2.2 Higgs boson searches
Here there are some details about the current constraints on the Higgs boson
mass , driven both by theoretical assumptions [2] and direct experimental searches.
2.2.1 Theoretical constraints on the Higgs mass
A �rst upper constraint is found considering the weak boson scattering process
WW → WW: mH . 720 GeV/c2. Bounds on the Higgs mass can also be set asa function of a cut-o� energy scale Λ, up to which we assume the validity of the
Standard Model (i.e. the scale up to which no new interactions and particles are
expected). These bounds are derived from the renormalization group equation for
the Higgs quartic coupling λ, which describes the evolution of the parameter with
energy. In a simpli�ed theory with only scalars, the evolution of λ is given by:
λ(Q) =λ(Q0)
1− 3λ(Q0)4π2
logQ2/Q20
If we consider the SM as an e�ective theory, a scale after which it leaves the pertur-
bative domain, Q0 ≡ v and λ(v) ≡ m2H/2v2, the mass upper limit becomes:
m2H <8π2v2
3 log Λ2/v2
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CHAPTER 2. THE STANDARDMODEL OF ELECTROWEAK INTERACTIONS17
In Figure 2.2 the Higgs mass constraints as a function of the cut-o� scale are shown,
also top-loops are considered, therefore the theoretical limit depends on top mass.
As it can be seen, this plot suggests that if the Standard Model validity extends up
Figure 2.2: Upper and lower theoretical limits on the Higgs mass as a function of
the energy scale Λ up to which the Standard Model is assumed to hold. The shaded
area indicates the theoretical uncertainties in the calculation of the bounds. Here
the values mt = 175 GeV/c2 and αS = 0.118 have been used.
to the scale of Grand Uni�cation Theories (ΛGUT 1016 GeV), the Higgs boson mass
has to lie roughly in the 150 - 180 GeV/c2 range. Conversely, for a Higgs particle
lighter than 150 or heavier than 180 GeV/c2 , new Physics is expected to exist at
an energy scale inferior to ΛGUT .
2.2.2 Experimental constraints on the Higgs mass
In order to obtain the most stringent constraint on the mass of the SM Higgs
boson, most of the electroweak measurements are used as input to perform a global
�t [3]. The �t consists in a χ2 minimization, where the χ2 is calculated comparing
the measured values of 18 di�erent variables and their errors with their predictions
calculated within the framework of the Standard Model as a function of �ve input
-
CHAPTER 2. THE STANDARDMODEL OF ELECTROWEAK INTERACTIONS18
parameters (∆α5had(m2Z), αD(m
2Z), mZ , mt , mH ). This analysis procedure tests
quantitatively how well the Standard Model is able to describe the complete set of
measurements with just one value for each of the �ve input parameters. Moreover,
the �t yields a best value expected for the only unknown parameter mH . The result
of the �t is reported in Figure 1.4, where the ∆χ2(mH) = χ2max(mH) - χ
2min(mH)
curve is shown. From the result of the �t it is clear that electroweak measurements
seem to favour a light Higgs, with the one-sided 95% C.L. upper limit on mH being:
mH < 161GeV/c2
The �rst direct search for the Higgs boson was carried out at the LEP accelerator
Figure 2.3: Global �t of all precision electroweak measurements. Left: The black
continuous line shows ∆χ2(mH) = χ2max(mH) - χ
2min(mH). The shaded cyan area
represents the associated theoretical error due to missing higher-order corrections.
The yellow shaded area corresponds to the 95% C.L. exclusion limit mH > 114.4
GeV/c2 (LEP-II, 2003) and mH ∈ [158, 175] GeV/c2 (Tevatron, 2010). Right: Com-parison of all the 18 measurements with their SM expectations calculated for the
�ve input parameters values in the minimum of the global χ2 of the �t.
at CERN [4]. Data from e+e− collisions at a center-of-mass energy up to 209 GeV
were used to look for hints of the particle. The main production mechanism at a
e+e− collider was the so-called Higgs-strahlung, where a Higgs boson is radiated by
-
CHAPTER 2. THE STANDARDMODEL OF ELECTROWEAK INTERACTIONS19
a virtual Z0 boson. As shown in Figure 2.4, no signi�cant excess of events with a
Higgs-compatible topology were found, thus allowing to set a lower bound on the
Higgs boson mass at 95% con�dence level:
mH > 114.4GeV/c2
The search for the Standard Model Higgs particle continued at Tevatron [5], a pp̄
Figure 2.4: Observed and expected behaviour of the test statistics −2logQ as afunction of the Higgs mass. The test statistics Q is de�ned as the ratio between the
signal plus background likelihood and the background only likelihood. The result
is the combination of the data collected by the four LEP experiments. Green and
yellow shaded bands represent the 68% and 95% probability C.L. The observed trend
in data (solid black line) is compatible with a background-only hypothesis (dashed
blue line) up to 114.4 GeV/c2 . Picture from [4].
collider with a center-of-mass energy of√s = 1.96 TeV which ended its operation
in 2011. Also in this case, the main production mechanism consists in Higgs boson
production in association with a vector boson (W or Z). As shown in Figure 2.5, the
SM Higgs boson particle exclusions are:
mH /∈ [147 , 179]GeV/c2
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CHAPTER 2. THE STANDARDMODEL OF ELECTROWEAK INTERACTIONS20
mH /∈ [147 , 179]GeV/c2
The quest for the Higgs boson started at the LHC already in 2010, by the end
Figure 2.5: Observed and expected (median, for the background-only hypothesis)
95% C.L. upper limits on the ratios to the SM cross section, as a function of the
Higgs boson mass for the combined CDF and D∅ analyses. The limits are expressedas a multiple of the SM prediction for test masses for which both experiments have
performed dedicated searches in di�erent channels. The bands indicate the 68% and
95% probability regions where the limits can �uctuate, in the absence of signal. The
limits displayed in this �gure are obtained with the Bayesian calculation. Picture
from [5].
of the 2011 CMS and ATLAS experiments gave more stringent limits on the Higgs
mass, by means of di�erent decay channels: H → τ+τ−, H → γγ, H → W+W−
and H → ZZ. Finally on the 4th of July, thanks to the combined results of all thecollaborations and all the decay channels, CMS and ATLAS experiments declared
the discovery. Chapters 7 and 8 feature a detailed description of the CMS H → γγanalysis and the �nal results.
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CHAPTER 2. THE STANDARDMODEL OF ELECTROWEAK INTERACTIONS21
2.2.3 Higgs boson production and decay modes
The SM Higgs boson production cross-section at a pp hadron collider of center-of-
mass energy√s = 7 TeV [6] is shown in Figure 2.6. In Figure 2.7 the corresponding
leading-order Feynman diagrams are drawn.
The gluon fusion (gg → H) is the dominating Higgs production process over the
Figure 2.6: Higgs production cross-sections at√s = 7 TeV as a function of the Higgs
mass for the di�erent production mechanisms. From top to bottom, sorted for their
relevance: gluon fusion (blue), VBF (red), associate production with a W/Z boson
(green/grey), tt̄ associated production (violet). NNLO QCD corrections as well as
NLO EKW corrections are taken into account. Picture from [6].
entire mass range accessible at the LHC. It proceeds with a heavy quark triangle
loop, as shown in Figure 2.7. Because of the Higgs couplings to fermions, the t-quark
loop is the most important.
The second largest production mechanism of the Higgs boson is by means of vector
boson fusion (VBF,qq → qqH). In this process Higgs boson is originated from thefusion of two weak bosons radiated o� the incoming quarks. Their hadronization
produces two forward jets of high invariant mass which can be used to tag the event
and di�erentiate it from backgrounds.
In the Higgs-strahlung (qq̄′ → WH, qq̄ → ZH) and tt̄ associated production
-
CHAPTER 2. THE STANDARDMODEL OF ELECTROWEAK INTERACTIONS22
Figure 2.7: Feynman diagrams for the most important LO production processes of
the SM Higgs boson:(a) gluon fusion, (b) vector boson fusion, (c) Higgs-strahlung,
(d) tt̄ associated production.
(gg, qq̄ → tt̄H) processes the Higgs is produced in association with a W/Z boson ora pair of t quarks. In both cases, their decay products can be used to tag the event.
Depending on the Higgs mass, di�erent decay channels can be exploited to detect the
particle. The Higgs total decay width and its di�erent decay branching ratios depend
on the Higgs couplings to the vector bosons and to the fermions in the Standard
Model Lagrangian of Equation 2.6. Due to the dependance of Higgs couplings on
the particle masses, the Higgs tends to decay into the heaviest particles which are
kinematically allowed. Figure 2.8a shows the Higgs decay branching ratios including
also NLO QCD and EWK corrections. Light-fermion decay modes contribute only
in the low mass region (up to ∼ 150 GeV/c2 ). Once the decay into a pair of weakboson is possible, it quickly dominates. The Higgs boson does not couple to photons
and gluons at tree level, but such couplings can arise via fermion loops and they
give a contribution in the low mass region. The total width, given by the sum over
all the possible decay channels, is shown in Figure 2.8b. It quickly increases with
the Higgs mass due to the opening of new channels.
-
CHAPTER 2. THE STANDARDMODEL OF ELECTROWEAK INTERACTIONS23
The decay H → γγ is the main channel for the discovery of the Higgs boson at
Figure 2.8: Left: Decay branching ratios of the SM Higgs boson in the di�erent
channels versus its mass.Right: Total decay width (in GeV) of the SM Higgs boson
with respect to its mass. Pictures from [6].
masses of about 140 GeV/c2 or below. The study of this decay channel is described
in more details in Chapter 7.
Due to its very clean signature with 4 isolated leptons in the �nal state, H → ZZ(∗)
→ l+l−l+l− is considered the golden-plated mode for the discovery of the Higgsboson in the mass region between 130 and 500 GeV/c2, apart for the small region
around mH ' 160 GeV/c2. The backgrounds to this channel are ZZ(∗) , tt̄ and Zbb̄productions, which can be suppressed in an e�cient way by some requirements on
the lepton isolation, transverse momentum and invariant mass and by requirements
on the event vertex.
In the mass region mH ' 160 GeV/c2, the Higgs branching ratio into WW is close toone. This makes H→WW(∗) → lνllνl the discovery channel in this mass range. Thesignature is two charged leptons and missing energy. Since the mass peak can not
be reconstructed due to the neutrinos in the �nal state, the search strategy is based
on event counting, for which an accurate knowledge of all the possible backgrounds
is needed. The main backgrounds are electroweak WW, tt̄ and W+jets productions.
-
Chapter 3
CMS Experiment
The study of the decay H → γγ in the CMS experiment is performed throughECAL detector. CMS (Compact Muon Solenoid) is one of the four main experi-
ments placed along the LHC ring.
3.1 The Large Hadron Collider
The Large Hadron Collider (LHC) is a 27 km long proton collider installed 100
m underneath the ground level in the tunnel previously built for the LEP e+e− ac-
celerator. The choice to reach on regime cernter-of-mass energies of 14 TeV, forces
to have a magnetic �eld of ∼ 8.3 T, 1232 super-conducting dipole magnets at atemperature of 1.9 K by means of super-�uid Helium.
Figure 3.1 shows all the acceleration steps the particles have to ful�l to reach 14 TeV
energies. First of all, each colliding bunch is formed in the Proton Synchrotron (PS)
at an energy of 26 GeV, accelerated to 450 GeV by the Super Proton Synchrotron
(SPS) and then injected in the LHC. Here 8 radio-frequency resonant cavities os-
cillating at 400 MHz accelerate the bunches to their �nal energy with �kicks� of 0.5
MeV per turn.
LHC is designed to reach luminosity of 1034cm−2s−1. To reach thi luminosity, up to
2808 bunches per beam, with about 1.1×1010 protons each will be collided every 25ns. Up to 2012, collisions have been delivered with a frequency of 20 MHz instead
of 40 MHz and the maximal reached energy is 8 TeV in the center of mass.
On the LHC ring four main experiments are located: CMS [7] and ATLAS [8]
(general purpose experiments), LHCb [9](dedicated to CP violation and b-physics
24
-
CHAPTER 3. CMS EXPERIMENT 25
studies) and ALICE [10] (devoted to heavy ions collisions).
Figure 3.1: LHC injection scheme.
3.2 CMS Detector
CMS is a multi-purpose experiment, thus it is composed by detectors for charged
particles momentum measurements, for calorimetry and for muon detection proper-
ties measurement. All the detectors but the muon chamber are inside a magnetic
solenoid with a length of 13 m and an internal diameter of 6 m. The internal mag-
netic �eld is about 3.8 T in order to have good muons momentum resolution and to
need less tracker thickness, therefore it is compact. The solenoid requires a return
yoke, which is made of iron and can host four concentric muon detectors (muon
stations).
In a typical proton-proton collision, the fractions xa and xb of the parent proton
momentum carried by the interacting partons are in general di�erent, and the rest
frame of the hard collision is boosted along the beam line with respect to the labo-
ratory frame. Because of the unknown energy balance along the beam-line, proton
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CHAPTER 3. CMS EXPERIMENT 26
collisions are usually studied in a convenient coordinate frame where the coordinates
are (r,η,φ), where r is the radial distance from the pipe (z-axis), φ is the azimuthal
angle in the transverse plane and η ≡ − log tan θ2. These quantities are chosen as r,
φ and ∆η are invariant under z-axis boost. Figures 3.2 and 3.3 show pictorial views
of the CMS experiment subdetectors.
Figure 3.2: Pictorial view of the CMS detector.
3.2.1 Tracker System
The inner CMS tracking system [11] is designed to provide a precise and e�cient
measurement of the trajectories and the momentum of charged particles as well as
a precise reconstruction of secondary vertexes. It surrounds the interaction point
and has a length of 5.8 m and a diameter of 2.5 m. Giving the high luminosity
and the large number of created particles in each collision, a detector technology
featuring high granularity and fast response is required. Since intense particle �ux
will also cause severe radiation damage, the main challenge in the design of the
tracking system was then to develop detector components able to operate in this
harsh environment for an expected lifetime of ten years. All of these requirements
-
CHAPTER 3. CMS EXPERIMENT 27
Figure 3.3: A slice of CMS: the picture shows the sub-detector sequence. Paths of
di�erent particles are also drawn.
led to design a detector tecnology entirely based on silicon.
The CMS tracker is composed of a pixel detector with three barrel layers at radii
Figure 3.4: Schematic cross section through the CMS tracker. Each line represents
a detector module.
between 4.4 cm and 10.2 cm and a silicon strip tracker with 10 barrel detection layers
extending outwards to a radius of 1.1 m. Each system is completed by endcaps which
-
CHAPTER 3. CMS EXPERIMENT 28
consist of 2 disks in the pixel detector and 3 plus 9 disks in the strip tracker on each
side of the barrel, extending the acceptance of the tracker up to a pseudorapidity of
2.5. A schematic view of the tracker is in Figure 3.4.
In the pixel detector, the estimated resolution on the single hit is of 10 µm for the
(r,φ) coordinate and 15 µm for z in the barrel, while it is of 15 µm and 20 µm
respectively in the endcaps. For the silicon strip detector, the expected resolutions
grow to ∼ 50 µm in (r,φ) and ∼ 500 µm along the z coordinate.
3.2.2 ECAL Calorimeter
The CMS electromagnetic calorimeter (ECAL) [12] plays an essential role in the
search for the Higgs boson by measuring, with high precision, the energy of photons
arising in the H → γγ channel and of electrons from the H → ZZ and H → W+W−
decay chains. Resolution issues and H → γγ will be described in more detail inChapter 5 and 6. Here there is a brie�y description of the detector.
In order to reach the high energy resolution these physics channels require, a ho-
mogeneous, scintillating crystal calorimeter has been chosen. The nearly 83000 lead
tungstate (PbWO4 ) crystal shape is that of a truncated pyramid, with a front face
cross section of about 22×22 mm2 (∆η×∆φ = 0.0174×0.0174◦ ) and a length of 230mm (which corresponds to 25.8 radiation length X0 ). Thanks to the PbWO4 short
radiation length (X0 = 0.89 cm) and the small Molière radius (rM = 21.9 mm), most
of an electron or photon energy can be collected within a small matrix of crystals.
As shown in Figure 3.5, ECAL crystals are divided into the two main parts of the
calorimeter:
Barrel (EB): it is made of 61200 crystals and comes in the shape of a cylinder,
with an inner radius of 1.290 m. It covers a pseudorapidity range of 0 < |η|
< 1.479 and its granularity is 360-fold in φ and 2×85-fold in η. EB crystalsare grouped in arrays of 5×2 elements, called sub-modules. There are 17di�erent crystal shapes along η, one for each sub-module. Sub-modules are
then arranged in a module, in the number of 40/50 and, eventually, 4 modules
are assembled to create a super-module (SM). On the whole there are therefore
36 supermodules, 18 for each side of the interaction point. Supermodules in
EB are mounted in a quasi-projective geometry to avoid cracks aligned with
particle trajectories, so that the crystal axes are tilted of 3◦ in both the φ and
η projections.
-
CHAPTER 3. CMS EXPERIMENT 29
Figure 3.5: Schematic ECAL composition
Two endcaps (EE): they cover the pseudorapidity range 1.479 < |η| < 3.0 and
consist of identically shaped crystals, grouped into carbon-�ber structures of
5×5 elements, called supercrystals. Each endcap is divided into 2 halves, orDees, holding 3662 crystals each;
In addition, a preshower (ES) is placed in front of EE crystals with the aim of iden-
tifying neutral pions in the endcaps and improving the position determination of
electrons and photons. The preshower is a sampling calorimeter with two layers:
passive lead radiators, that initiate electromagnetic showers, and active silicon strip
sensors placed after each radiator, that measure the deposited energy and the trans-
verse shower pro�les.
Lead Tungstate has been chosen for the crystals as the scintillating material as its
characteristics make it suitable for operation at LHC, in particular its very fast
emission, 80% of a crystal scintillation light is emitted within 25 ns, and its great
resilience to irradiation. The relatively low light yield of ' 30 γ/ MeV makes itnecessary to use intrinsic high-gain photodetectors, capable of operating in high
magnetic �elds. Avalanche PhotoDiodes (APDs) are used for barrel crystals and
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CHAPTER 3. CMS EXPERIMENT 30
Vacuum PhotoTriodes (VPTs) are used for endcaps crystals.
Although radiation resilient, crystals lose transparency because of irradiation. This
leads to wrong energy measurements. This aspect is crucial for resolution studies
and the crystals transparency evolution is constantly measured through a monitor-
ing system. Chapter 4 is completely dedicated to describe it and understand how
to correct transparency losses.
3.2.3 HCAL Calorimeter
The goal of the hadronic calorimeter (HCAL) [13] is to measure the energy and
the direction of hadronic jets as well as the missing transverse energy. HCAL is
a sampling calorimeter and HCAL barrel is radially restricted between the outer
extent of the electromagnetic calorimeter (r = 1.77 m) and the inner extent of the
magnet coil (r = 2.95 m). Because of this constraint on radiation absorbing material,
an outer hadronic calorimeter is placed outside the solenoid. Furthermore, Beyond
|η| = 3, the forward hadron calorimeters are placed at 11.2 m from the interaction
point and extend the pseudorapidity coverage down to |η| = 5.2. A schematic view
of HCAL location in CMS is shown in Figure 3.6.
The central calorimeter is divided into a barrel part (HB, 0 < |η| < 1.3) and two end-
caps (HE,1.3 < |η| < 3), with a transverse granularity of ∆η ×∆φ = 0.087×0.087◦
and ∆η × ∆φ '0.17×0.17◦ respectively. The 3.7 mm thick active layers of plasticscintillators are interleaved with 5 to 8 cm thick brass absorbers. Wavelength-shifter
are used to bring out the scintillation light and read the signal. The HB e�ective
thickness increases with polar angle θ as 1/sin θ, resulting in a total absorber thick-
ness spanning from 5.82 interaction length (λI) at 90◦ to 10.6 λI at the end of the
barrel. In the endcaps, the total length of the calorimeter is about 10 interaction
lengths.
As in the central pseudorapidity region the combined stopping power of EB plus
HB does not provide su�cient containment for hadron showers, hadron calorimeter
is extended outside the solenoid with an additional absorber equal to 1.4/sin θ in-
teraction lengths (HO).
The forward calorimeter (HF) experiences unprecedented particle �uxes, thus the
design of the HF calorimeter was guided by the necessity to survive in this environ-
ment, preferably for at least a decade (10 MGy of absorbed dose are expected at |η|
= 5 after ten years of LHC operation). The calorimeter consists of a steel absorber
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CHAPTER 3. CMS EXPERIMENT 31
structure composed of 5 mm thick grooved plates. Quartz �bers are inserted in these
grooves and constitute the calorimeter active medium, detecting energy emitted by
particles via Cherenkov radiation.
According to the test-beam results, the expected energy resolution for single pions
interacting in the central part of the calorimeter is:
σEE
=94%√E⊕ 4.5%
Figure 3.6: Schematic HCAL composition
3.2.4 Muon System
The CMS muon system [14] provides full geometric coverage for muon measure-
ment up to |η| = 2.4. The detectors are embedded in the magnet return yoke, so that
muon momentum and charge measurements can also exploit the strong magnetic re-
turn �eld. This is particularly important for muons with transverse momentum in
the TeV range, for which the complementary tracker measurements degrade.
CMS muon spectrometer is composed of a barrel part (|η| < 1.2) and a forward
region (0.9 < |η| < 2.4). The barrel consists of �ve wheels, in which drift-tube (DT)
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CHAPTER 3. CMS EXPERIMENT 32
detectors and resistive-plate chambers (RPC) are placed in concentric muon stations
around the beam line. The total radius is between about 4 and 7 m. In the forward
region cathode-strip chambers (CSC) and RPC are mounted perpendicular to the
beam line in overlapping rings on the endcaps. In Figure 3.7 an (r,z) view is given
of the di�erent parts of a quarter of the CMS muon system.
The CMS muon system uses three types of gaseous detectors. The choice of detec-
Figure 3.7: Schematic Muon System composition
tor technologies has been driven by the need for fast triggers, excellent resolution,
coverage of a very large total surface and operation in dense radiation environments.
The drift tubes (DT): they are located in the barrel part, where the muon rate
is expected to be low. Each station is designed to measure muon positions
with about 1 mrad resolution in φ;
The cathode strip chambers (CSC): they are used in the endcap regions, where
the magnetic �eld is very intense (up to several Tesla) and very inhomogeneous.
The resistive plate chambers (RPC): the position resolution from the RPCs is
poorer than for the DTs and CSCs, but the collection of charges on the strips
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CHAPTER 3. CMS EXPERIMENT 33
is very fast. Therefore these chambers are used mainly for trigger purposes
and for an unambiguous identi�cation of the bunch crossing.
-
Chapter 4
Monitoring System
The choice of PbWO4 is based on the crystal's high density and its radiation
hardness; note that the scintillation mechanism is not a�ected by irradiation. How-
ever, the optical transmission at the scintillation wavelengths is a�ected by the
production of colour centers under ionizing radiation. On the other hand, sponta-
neous annealing of the colour centers occurs at room temperature. This leads to a
transmission recovery, which is evident when the crystals are not irradiated, such as
during machine-�ll gaps. During time, light transmission results into an equilibrium
between the rates of colour centers production and their annealing. Crystals pro-
duced for ECAL are optimized to reduce the relative variations in light transmission
during an LHC collision running period (luminosity of 1034 cm−2s−1) to less than 6%
for barrel crystals (dose rates of 0.15 Gy/h) and less than 20% [15] for the endcpas
at |η| = 2.5 (dose rates of 1.9 Gy/h). Uncertainties in the relative measurement ofthe optical transmission, from crystal to crystal, contribute directly to the energy
resolution. The energy resolution and uniform response of the calorimeter are criti-
cal to the discovery of the Higgs boson via its decay into two photons. In situ light
transmission measurements are performed through a laser monitoring system which
is based on injecting light in the crystal when the crystal is not irradiated.
4.1 Experimental Apparatus
The major components of the laser monitoring system are shown in Figure 4.1
[15]. Laser light is produced at a source at the principle wavelength of 440 nm
(blue), near the Y-doped PbWO4 scintillation emission peak, or at 796 nm (near
34
-
CHAPTER 4. MONITORING SYSTEM 35
infra-red). The monitoring light source consists of three laser systems (two "active"
and one "spare") each equipped with diagnostics. The IR source is weakly sensitive
to colour center production thus is used as a cross-check of gain variations.
Figure 4.1: Monitoring system
The laser light pulses are directed to individual crystals via a multi-level optical-
�ber distribution system: (a) a �ber-optic switch at the source directs the pulses
to a calorimeter element. Altogether the elements are 88: 72 Super-Module halves
and 16 quarter Dees. The second level is composed by (b) a primary optical-�ber
-
CHAPTER 4. MONITORING SYSTEM 36
distribution system which transports the pulses over a distance of 95-130 m to each
calorimeter element mounted in CMS, and �nally (c) a two-level distribution sys-
tem mounted on the detector sends the pulses to the individual crystals. The total
attenuation of the light distribution system is measured to be 69 dB.
The basic operations for barrel geometry is the following: laser pulses transported
via an optical �ber are injected at a �xed position at the crystal's front face, the
injected light is collected, as for scintillation light from an electromagnetic shower,
with the pair of APDs glued to the crystal's rear face. Although the optical light
path is di�erent from that taken by shower scintillation photons, this design guaran-
tees that the light transmission is measured in the interest region. The underlying
principle is similar for ECAL endcaps; however, laser light is injected at a corner of
each endcap crystal's rear face, and the light is collected (as for scintillation) via a
VPT glued on the crystal's rear face.
In order not to interfere with ECAL performance during physics collisions at LHC,
the laser pulses are injected during 3.17 µs gaps foreseen every 88.924 µs in the LHC
beam structure. The laser monitoring system independently measures the injected
light for each pulse distributed to a group of typically 200 crystals, using pairs of
radiation-hard PN photodiodes. The crystal optical transmission corrections are
made using the ratio of the crystal's APD (VPT for the endcaps) response normal-
ized by the associated group's PN response. The system is foreseen to continuously
cycle over the calorimeter elements, giving a transparency measurement every 20-40
min.
The laser source speci�cations and its environmental requirements are listed below:
Operation duty cycle: 100% during LHC data taking periods;
Two operating wavelengths: 440 nm (blue) and 796 nm (near IR);
Spectral contamination: < 10−3;
Pulse energy (Epulse): 1 mJ at the source for a dynamic range up to an equiv-
alent deposition of 1.3 TeV in a crystal with 69 dB attenuation in the distri-
bution system;
Pulse width Γpulse: < 40 ns FWHM to match the ECAL readout;
Pulse rate: ∼ 100 Hz;
Temperature stabilization: ± 0.5 ◦C;
-
CHAPTER 4. MONITORING SYSTEM 37
Figure 4.2: Multiple wavelength light source
Figure 4.3: ECAL barrel tertiary (L1) 240-�ber fan-out
4.2 Light collection in PbWO4
The light collection mechanism is very complex and it is out of this thesis scope
to explain it in detail. However, in a very simple way it is possible to �nd a relation
between the shower energy (S) and the injected laser energy (R). The naive demon-
stration begins considering the average light optical path (Λ) and the average light
-
CHAPTER 4. MONITORING SYSTEM 38
attenuation coe�cient (λ), which is directly related to the light transmission. If we
consider a shower, with initial energy S0, which goes through the crystal, the �nal
energy S measured from the crystal electronics is:
S = S0 e−ΛSλS
with the same idea, if we consider the injected light, with initial energy R0 (it is
measured by the PN):
R = R0 e−ΛRλR
this gives:
S
S0=
(R
R0
)ΛSλRλSΛR
=
(R
R0
)α(4.1)
Thus the laser correction to apply to �nal energy S is:
LC =
(R
R0
)−α(4.2)
The quantities S, R and R0 are experimentally measured, what is necessary to know
is the parameter α.
In order to understand the dependences of the α parameter, consider a more com-
plex model [16]. The scintillation signal Si for a single channel i can be factorize
approximately as:
Si = E0i
ˆNi(~x)Ci(t, ~x, λ)Pi(t, T, ~x, λ)Gi(V, t, T, λ)dλd~x
E0i (GeV) is the total energy deposited by the particle in the crystal.
Ni(~x) is the relative distribution of the energy along the crystal. It is nor-
malized to one and depends on the particle type, its energy, its angle and its
impact position with respect to the crystal front face.
Ci(t, ~x, λ) represents the transmission of the crystal in the normal conditions,
that is when the light is emitted by scintillation along the trajectories of the
particles. It combines the geometrical acceptance and the light attenuation.
Pi(t, T, ~x, λ) is the spectrum of the scintillation light. It is a number of photons
per unit of deposited energy and per unit of wavelength (nm).
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CHAPTER 4. MONITORING SYSTEM 39
Gi(V, t, T, λ) is the product of the quantum e�ciency �Q of the APD (or VPT)
and the gain M:
Gi(V, t, T, λ) = �Q(t, λ)M(V, t, T, λ)
In a system where ageing and other secondary modi�cations are under control, the
only terms a�ected by the irradiation are Ci and Gi.
The light injection signal, per crystal, expressed in number of e− at the preampli�er
input, can be expressed as:
Ri = ai(tm, λl)Li(tm, λl)Bi(tm, λl)Gi(V, tm, T, λl)
ai(tm, λl) is a parameter describing the relative light transmission of the �bers.
Li(tm, λl) is the number of photons arriving on the monitoring PN diodes. It is
de�ned as the signal arriving to the PN (in e− units) divided by PN's quantum
e�ciency.
Bi(tm, λl) is the transmission of the monitoring light through the crystal.
where t and λ indices denote that the monitoring is performed with only one wave-
length and at �xed time per crystal. Through a system una�ected by irradiation
and ageing e�ects, the monitoring measures Bi and Gi.
In order to make some approximations, consider the ratio S/E0 (for sake of simplicity
the i index is erased):
S
E0=
R
aL
ˆN(~x)
C(t, ~x, λ)
B(tm, λl)P (t, T, ~x, λ)
G(V, t, T, λ)
G(V, tm, T, λl)dλd~x (4.3)
Considering a stable system, a, L, N and P are not a�ected by irradiation, and they
can be estimated with some models. With this assumption, the termG(V, t, T, λ)
G(V, tm, T, λl)becomes almost equal to one. Finally, the only term a�ected by the irradiation isC(t, ~x, λ)
B(tm, λl).
For the barrel, where light is injected at the front, B(tm, λl) is related to the atten-
uation length Λ(t, z, λ) through the following approximate formula:
B(t, λ) = B0e−r1
´ L0
dzΛ(t,z,λ)
1− ke−2r2´ L0
dzΛ(t,z,λ)
B0 includes the geometrical acceptance and optical couplings. L is the crystal to-
tal length. The denominator represents possible return path for the light with a
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CHAPTER 4. MONITORING SYSTEM 40
magnitude given by the re�ection coe�cient k. The coe�cients r1 and r2 take into
account the fact that the injection light do not propagate along the z axis, but with
di�erent trajectories due to the numerical aperture of the �bers. With almost the
same approximation C(t, z, λ) can be related to Λ(t, z, λ), in this approximation
the light travels along the z-axis and modi�cations in the trajectory are taken into
account by coe�cients similar to r1 and r2, thus:
C(t, z, λ) =Ω1(z)e
−s1´ L0
dzΛ(t,z,λ) + Ω2(z)e
−s2´ L0
dzΛ(t,z,λ) · e−s3
´ z0
dz′Λ(t,z′,λ)
1− k′e−2s4´ L0
dzΛ(t,z,λ)
where Ω1(z) and Ω2(z) are the geometrical acceptance for the scintillation light
emitted at z respectively towards the photodetector or towards the front crystal
face.
Finally, from Equation 4.3, with some degrees of approximation, we have:
S
S0'(R
R0
) ρ̄−ρmρm
+1+η
(4.4)
where:
ρ̄ ' (s1 + 2k′s4) γ(λ̄)
ρm ' (r1 + 2kr2) γ(λm)
λm and λ̄ correspond respectively to the monitoring wavelength and to the scintilla-
tion emission peak and η is a corrective of the order of ±0.1 to ±0.5. Consider thedefects density b and the attenuation coe�cients before irradiation, γ0:
1
Λ≡ γ(λ)b+ γ0
In the limit for little transparency losses Equation 4.4 becomes the more simple
Equation 4.1. Since this is an approximation, in cases where there are big trans-
parency losses (as in the endcaps) some modi�cations are applied when these features
are measured, like dividing samples in η-zones so that the overall R/R0 range does
not vary too much or like assuming a directly dependence of α on the transparency
losses.
Another important feature is that in the endcaps the absorbed radiation dose is
much higher than in the barrel; for this reason, in the endcaps Vacuum PhotoTri-
odes are used as photodetectors. Although their high radiation resilience, during
the LHC running their response can deteriorate, leading to a wrong R/R0 measure-
ment. ECAL cannot monitor also these losses, the net e�ect is a reduction on the
-
CHAPTER 4. MONITORING SYSTEM 41
e�ective α value. Because of the non-predictability of the VPT losses α parameter
can also varying over time. One of the aims of this thesis is to perform an in situ
measurement of α and to understand its dependences.
4.3 Test Beam Measurements
The stability of the �nal laser monitoring system was evaluated in test-beam runs
at CERN on partially equipped Super-Modules (SM) in 2003 and on fully equipped
SMs in 2004 [15]. The CERN SPS H4 secondary test-beam facility supplying elec-
tron beams from 20 to 250 GeV/c was used. Any one of the SM's crystals can be
irradiated at the test facility using an automated rotating scanning table shown in
Figure 4.4. The setup is designed to reproduce the incident geometry for photons
produced at the LHC interaction point.
The stabilities of two operating parameters are critical to the performance of the
Figure 4.4: Super Module mounted on automated scanning table in CERN H4
electron test beam.
SM at the test beam: temperature and high voltage. A large e�ort has gone into
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CHAPTER 4. MONITORING SYSTEM 42
designing an 18 ◦C cooling system that can maintain the mean temperature spread
below 0.05 ◦C. About the voltage supply, a CAEN prototype of the �nal system HV
supply was used for the tests, providing dispersion within speci�cations of less than
±720 mV at 500 V.The laser light signal from each crystal's pair of APD is shaped and digitized at
the 40 MHz LHC clock rate (10 samples recorded, sampling rate every 25 ns). The
normalized laser response APD/PN of each channel is obtained by dividing its APD
maximum amplitude by the commonly shared PN maximum amplitude on an event
by event basis. Afterword, an average of the 1200 events for the laser run is com-
puted.
First, the stability of the light calibration system was veri�ed for each group of 200
crystals using the relative stability of the associated pair of reference PN photodi-
odes. The results, shown in Figure 4.5(Left), demonstrate that the system achieves
an RMS spread of 0.0074% over this period. Next, the stability of the response
to injected laser light at 440 nm (blue) was veri�ed for a group of non-irradiated
crystals using the normalized laser response APD/PN determined for each laser run.
Figure 4.5(Right) shows that a stability of 0.068% has been achieved.
Single-crystal relative responses to both 120 GeV electrons, S/S0 (measured in
Figure 4.5: Left: Relative stability between pair of reference PN photodiodes mon-
itoring 200 crystals (SM 10 module 3) measured in autumn 2004 at the CERN
test-beam facility. RMS spread over 7.5 day's operation (104 laser runs) is 0.74
×10−4. Right: Stability of crystal transmission measurements at 440 nm (blue)over 11.5 day's operation (136 laser runs) at CERN test-beam facility is 6.76 ×10−4
RMS for a module of 200 non-irradiated crystals (SM 10 module 3).
low-intensity electron runs), and to injected laser light from the monitoring system,
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CHAPTER 4. MONITORING SYSTEM 43
R/R0 (measured in alternated laser runs), are plotted during an irradiation run at
0.15 Gy/h. Measurements were taken both during the irradiation phase ending at
15 h and during the subsequent recovery phase, as shown in Figure 4.6 (Left).
It was also veri�ed with excellent agreement the relation between S and R, as shown
in Figure 4.6 (Right), and the α value extracted from the �t was 1.6. Actually, crys-
tals were grown in two di�erent facilities, one in China (SIC crystals) and the other
in Russia (BTCP crystals). After all the test beams the measured α of barrel crys-
tals is 1.52, as the α of the encaps BTCP crystals, whereas the measured α of the
endcaps SIC crystals is 1.00. The overall α dispersion is 6% in the barrel and ∼15%in the endcaps. This dispersion is proportional to the response dispersion, thus di-
rectly a�ects it. It is striking that barrel and endcaps BTCP crystals from the test
beam measurements have the same α value. Because of the possible photodetectors
response loss, di�erent values are expected from in situ measurements with 2011
and 2012 data samples.
Finally, also a measure of the intercalibration constants (crystal by crystal relative
energy scales) is performed , the results are intercalibration spread of about 1-2% for
the barrel, about 5% for the endcaps. This measure gives a limit to the contribution
of the calibration onto the ECAL �nal resolution, as a worsening of the conditions is
expected during LHC runs. In the next Chapter a detailed description of the ECAL
calibration is presented.
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CHAPTER 4. MONITORING SYSTEM 44
Figure 4.6: Irradiation with 120 GeV electrons and recovery for a single PbWO4
crystal (SM10): (Left) upper curve shows APD response to laser injection at 440
nm (blue laser) and lower curve shows response to 120 GeV electrons; (Right) plots
the signal response S/S0 against the laser response R/R0 for the same data, where
the line shows the �t for α = 1.6.
-
Chapter 5
ECAL Calibration and Stability
Studies
The H → γγ decay channel provides a clean �nal-state topology with a masspeak that can be reconstructed with high precision. In the mass range 110 < mH <
150 GeV, the γγ �nal state is one of the most promising channels for Higgs searches
at the LHC. As in this mass range the intrinsic Higgs width varies between 2.82
and 17.3 MeV, ECAL was designed to provide excellent energy resolution in order
to maintain the advantage of such a narrow width. The parametrization of ECAL
resolution is [17]:σEE
=A√E⊕ BE⊕ C (5.1)
where A ' 2.8% is the stochastic contribution and B ' 12% is the noise term. Ifelectrons or photons have energy Ee,γ & 50 GeV these terms are negligible and the
resolution is dominated by the constant term C. The CMS target is to reach C '0.55%. This term depends on the non-uniformity of the longitudinal light collection,
the energy leakage from the rear face of the crystals, instabilities in the operation
of ECAL and the intercalibration constants accuracy. Figure 5.1(Left) shows the
di�erent contributions to ECAL resolution.
The e�ect of the whole calibration procedures on the discovery of the Higgs boson
is shown in Figure 5.1(Right). It shows that the whole calibration procedures will
improve the sensitivity upon SM Higgs at least of 25% for a Higgs mass range from
110 to 140 Gev/c2.
45
-
CHAPTER 5. ECAL CALIBRATION AND STABILITY STUDIES 46
Figure 5.1: Left: Contributions to ECAL resolution. Right: Comparison of 95% CL
exclusion limits on the cross section relative to the expected SM cross section in the
asymptotic CLS approximation, with di�erent ECAL calibration scenarios.
5.1 Electrons and photons reconstruction
ECAL detector is apt to the detection of electrons and photons. When a photon
or an electron strikes the detector it creates showers through the crystals. The energy
of these showers is deposited in crystals matrices. On average the electrons/photons
leave 94% of their total energy in a 3×3 crystals matrix and 97% of their totalenergy in a 5×5 crystals matrix. The energy reconstruction is complicated by thefact that electrons and photons can interact with the tracker, the former by means
of bremsstrahlung and the latter by means of conversion. Furthermore the magnetic
�eld causes an energy deposition spread along φ.
In general a shower is a local maximum of deposited energy in one crystal (seed),
surrounded by other smaller deposits. For this reason, the reconstruction begins
with the search of these crystals and continues to adjacent ones. Two di�erent type
of algorithms are used in ECAL in order to cluster the shower deposits [18]: hybrid
algorithm and island algorithm.
Hybrid algorithm: it is based on the barrel φ-η geometry and it begins from
the knowledge of the lateral shower shape along η, then it moves along φ in
order to perform a shower complete scan. Arrays of 1×3 crystals are created ofwhich the center has the same η of the seed. If the central crystal has greater
energy than the lateral ones the arrays are extend to 1×5 crystals. These
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CHAPTER 5. ECAL CALIBRATION AND STABILITY STUDIES 47
arrays are combined giving rise to clusters and then clusters are combined
in order to form superclusters. A schematic description of this algorithm is
shown in Figure 5.2.
Island algorithm: it seeks for the seed, sorts them by decreasing energy and
discards those which are adjacent to ones with greater energy. Beginning from
the seed the algorithm moves in η and φ directions until it �nds a deposit with
energy greater than threshold energy. Threshold energy has to be chosen in
order to cut minimum bias and low noise pile-up and to maintain an optimal
resolution. A schematic description of the island algorithm is shown in Figure
5.3.
About the measurement of a shower position, it is calculated as:
x =
∑i xiwi∑wi
where the sum is performed over supercluster crystals and wi is a correction weight
which takes into account the fact that the crystal axis varies with the crystal depth
(tilted-geometry) and that the energy density decreases exponentially with the dis-
tance from shower axis.
Figure 5.2: Schematic description of the hybrid algorithm
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CHAPTER 5. ECAL CALIBRATION AND STABILITY STUDIES 48
Figure 5.3: Schematic description of the island algorithm
5.2 ECAL energy reconstruction
The ECAL energy is given by [17]:
EECALe,γ (GeV ) = Fe,γ(ET , η) ·G ·∑
i ∈ cluster
Si(t) ci Ai (5.2)
where:
Ai: the energy deposited in each ECAL crystal, it is digitized by a sampling
ADC. In each channel the result is ten samples separated by 25 ns. The
amplitude Ai of the signal in channel i is then reconstructed using a linear
combination of these samples, i.e. Ai =∑10
j=1wjsij , where sij is the sample
value in ADC counts and wj is a weight.
ci: the intercalibration coe�cient, it takes into account crystal-to-crystal vari-
ations in the response by equalizing the di�erent crystal responses and nor-
malizing them to an arbitrary reference value.
Si(t): the monitoring correction factor to each crystal signal amplitude.
∑i: since the ECAL crystals are approximately one Molière radius in trans-
verse size, high energy electromagnetic showers spread over a few crystals.
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CHAPTER 5. ECAL CALIBRATION AND STABILITY STUDIES 49
Note that the presence of material in front of the electromagnetic calorimeter
(corresponding to 1 - 2 X0 ) causes conversion of photons and bremsstrahlung
from electrons and positrons. Furthermore, as already said, the strong mag-
netic �eld of the experiment tends to spread this radiated energy in φ. The
ECAL clustering algorithms are also designed to recover this energy. Thus,
The sum∑
i is over ECAL crystals that are associated by the clustering algo-
rithm.
G: the global ECAL energy scale that converts ADC counts into GeV. It is
determined separately for the barrel and the endcaps from resonances such as
J/Ψ → e+e− and Z → e+e−
Fe,γ(ET , η): small energy corrections are necessary to correct for residual clus-
ter non-containment e�ects, shower leakage and bremsstrahlung losses which
depends on the type of the particle, its momentum, direction and impact point
position.
5.3 Calibration Methods
Calibration is fundamental in order to take under control all the systematics
which a�ect ECAL energy measurements. The aim is the resolution constant term
thus every uncontrolled issue, like wrong laser correction, wrong crystal intercal-
ibration or wrong ECAL energy scales measurements, e�ects dramatically ECAL
resolution. For this reason all the term in Equation 5.2 are continuously checked
and corrected.
In the context of ECAL calibration isolated electrons/positrons from W→ eν, elec-trons and positrons from Z → e+e− and γs from π0/η → γγ have proven to begood events to verify ECAL response stability and uniformity and to provide set of
intercalibration coe�cients. In the next sections there are detailed descriptions of
this method [17], in general:
φ-symmetry: it is used to extract intercalibration constant. A derived method
is used to measure crystal by crystal the α parameter.
π0/η: they are used to extract intercalibration constants, measure the energy
scales and verify ECAL time stability.
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CHAPTER 5. ECAL CALIBRATION AND STABILITY STUDIES 50
Z0: they are used to measure ECAL scales, extract α parameter, calculate
intercalibration constants and to verify possible resolution improvements.
W±: they are used to verify ECAL stability, measure α parameter and extract
intercalibration constants.
5.3.1 φ-symmetry
The φ-symmetry method is based on the expectation that for a large sample
of minimum bias events the total deposited transverse energy (ET ) should be the
same for all the crystals in a ring, at �xed pseudorapidity. Intercalibration in φ is
performed by comparing the total transverse energy (∑ET ) deposited in one crystal
with the mean of the total∑ET collected by crystals at the same absolute value of
η. Therefore, for each ring in φ the average of 360 inter-calibration constants ci is
equal to the unity by construction.
In the determination of the transverse energy sum, only deposits with energies be-
tween lower and upper thresholds are considered. The former is applied to remove
the noise contribution and it is derived by studying the noise spectrum in randomly
triggered events. The latter is applied to avoid a possible bias from very high ET
deposits (e.g. from electrons originating from W± or Z0 decays). The lower thresh-
old, in the barrel, has a �xed value in energy of 250 MeV, thus the corresponding
lower ET cut is therefore 250 MeV/cosh η. In the endcaps, channels are arranged
so that VPTs with lower gain are located at higher pseudorapidity; therefore, the
equivalent noise distribution varies with pseudorapidity and the lower threshold is
parametrized accordingly. The upper ET threshold is set to be 1 GeV above the
lower threshold in both the barrel and the encaps.
The ECAL geometry itself is not uniform in azimuth and the material budget be-
tween the calorimeter and the interaction point is not perfectly homogeneous. For
this reason, to crystals receiving less irradiation higher intercalibration constants are
assigned and vice versa. In the absence of asymmetries, a �at distribution within
statistical �uctuations would be expected. Instead, as shown in Figure 5.4, sev-
eral features are observed. This leads to use adhoc correction in order to take into
account these discrepancies.
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CHAPTER 5. ECAL CALIBRATION AND STABILITY STUDIES 51
Figure 5.4: Average di�erence from unity of the inter-calibration constants derived
with the φ-symmetry method for data (solid circles) and simulation (histogram) in
the crystal η index range [1, 25]
5.3.2 π0/η-calibration
In order to take advantage of the high rate of π0 decays, a specialized data-
taking stream has been developed. To be considered in the combinatorial selection
of di-photon pairs, in EB a photon candidate is required to have a transverse energy
above 0.8 GeV. The π0 candidates are then selected by requiring their transverse
energy to be above 1.6 GeV. The π0 → γγ candidate should also be isolated fromother signi�cant energy deposits in the unpacked region of ECAL. In addition, the
π0 candidates are required to have an invariant mass below 0.25 GeV/c2.
A separate calibration stream has been implemented to select η → γγ decays. Thesame selection and reconstruction methods are used except that the cut of the pho-
ton pair transverse energy is tightened to ET > 3 GeV. In addition, a veto cut is
applied to reject photons coming from di-photon candidates within the 3σ window
around the �tted π0 peak. In the EE same methods are used to select π0 or η events.
The method to extract the intercalibration constants is similar to that used for the
φ-symmetry, the results are shown in Figure 5.5.
The absolute scale of the ECAL, the G factor, can also be measured by means
of π0/η. Given the di�erent calibration level of the EB and EE, it is desirable to
extract the energy scale independently for each subdetector. Furthermore, as a cross
check the scale is determined separately for each half of the barrel (on either side of
η = 0), and for each of the two endcaps. The energy scale is derived by measuring
-
CHAPTER 5. ECAL CALIBRATION AND STABILITY STUDIES 52
Figure 5.5: Left: Distribution of the inter-calibration constants in the central EB
region |crystal η index| ≤ 45. Right: Inter-calibration precision as a function ofη-index. The expected precision estimated from simulation studies is also shown.
the ratio of the position of the reconstructed invariant mass peak between data and
Monte Carlo. Assuming perfect simulation of the material in front of ECAL and
alignment of the detector, this ratio provides the correction to be applied to the
ECAL scale.
In order to verify the time stability, data are divided in temporal interval, for each
interval the distribution of corrected π0-mass normalize to theoretical π0-mass is
extracted. For each distribution we expect it to be peaked at 1, if everything works
correctly. Through this method, it's possible to give a diagnosis of stability problem.
A similar stability method by means of isolated electrons/positrons from W decays
is described in more details in the next Section.
5.4 ECAL calibration with electrons and positrons
from Z0 and W± decays
In this section, the calibration with electrons from W → eν and Z0 → e+e− isdescribed. This method is described in a more detailed way because it is related to
the study of α parameter. The analysis technique relies on the comparison between
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CHAPTER 5. ECAL CALIBRATION AND STABILITY STUDIES 53
the electron energy as measured by the ECAL supercluster Esc and the tracker
momentum ptk [19].
5.4.1 Event Selection
The event selection for isolated electrons is based on the necessity of suppressing
all background sources for which the Esc /ptk distribution is broader than for real
electrons. The following requirements are applied:
Exactly one electron with pT > 30 GeV/c and satisfying the o�ine electron
identi�cation criteria;
The sum of the tracker, ECAL, and HCAL deposits in a cone of size ∆R =√(∆η)2 + (∆φ)2 = 0.03 around the electron track divided by the electron pT
is required to be smaller than 0.04 (0.03) for electrons in the ECAL barrel
(endcaps);
EmissT > 25 GeV and mT > 50 GeV/c2. These cuts are applied in order to kill
most of the contamination of fake electrons from QCD events.
The opening angle ∆φ between the electron and the ET direction in the trans-
verse plane, is required to be greater than π/2. This cut further reduce the
QCD contamination by a factor of about two, being its distribution nearly �at
in ∆φ.
In Figure 5.6 the Esc/ptk Monte Carlo distributions and Monte Carlo signal contri-
bution for background and desired events are shown.
Also Z0 decays electrons/positrons have an important role in this analysis. Given
the practically negligible level of QCD contamination in di-electron �nal states, the
selections applied to save Z → e+e− events are looser. In particular, the followingrequirements are applied:
Exactly two electrons with pminT > 12 GeV/c, pmaxT > 20 GeV/c and satisfying
o�ine electron identi�cation criteria;
Combined relative isolation smaller than 0.07 (0.06) for electrons in the barrel
(endcaps);
EmissT < 40 GeV;
60 < mee < 120 GeV/c2, since the electrons must come from Z0 resonance.
-
CHAPTER 5. ECAL CALIBRATION AND STABILITY STUDIES 54
Figure 5.6: Left: Esc/ptk distribution for W → eνe events, QCD fake electronsand all other electroweak background sources summed together (mainly Z+jets and
tt̄) as expected from the Monte Carlo simulation (the QCD shape is data driven).
Each histogram is normalized to unity area so to allow a shape comparison of the
di�erent event topologies. Right: the data vs. Monte Carlo comparison for the
ESC/ptk distribution is shown for the �rst 211 pb−1 of data collected in 2011. As
can be noticed, the contamination from non W → eνe events is kept at a negligiblelevel.
5.4.2 Template Fit
The ratio of the measured supercluster (sc) energy of an electron and the mo-
mentum measured in the tracker (tk) has been used to monitor the stability and
uniformity of the ECAL response. Assuming that the measurement of the electron
momentum is stable in time and uniform, the analysis gives an unbiased answer on
the electron energy measurement.
We are interested in relative variations of the response. On the other hand, the
absolute response is �xed in ECAL via the invariant mass of di-electron/di-photon
resonances. The analysis therefore relies on the construction of a reference distribu-
tion T , "the template", describing the Esc /ptk observable at a given time, position
or laser correction. This distribution is then scaled to �t subsets of data, properly
partitioned in order to measure the response relative to the reference.
To avoid biases related to the imperfect description of the data by the simulation,
-
CHAPTER 5. ECAL CALIBRATION AND STABILITY STUDIES 55
the reference distribution has been in general derived from data themselves. Monte
Carlo samples have been sometimes used for cross checks. In formulae:
f(x; k) = N · k (T ∗R)(kx) (5.3)
where N is a normalization factor, k is the dilatation factor and x = Esc /ptk.
Note that 1/k is what we need to perform the ECAL stability measurements, it
can be interpreted as the energy scale of the subset relative to the template. If´ +∞0
T (x)dx = 1, f is naturally normalized to the number of the events of the
subset and k is the only parameter �oated in the �t. R is a properly normalized
resolution distribution. In general, R is a Dirac's delta function.
The shape of the Esc /ptk distribution can vary with varying datasets and selections.
It is thus important that the template is built using a consistent set of selection.
This has been measured by monitoring the χ2 of the best-�ts. Since the energy and
the momentum resolution are noticeably di�erent in barrel and endcaps regions, and
strongly η dependent, the analysis has been typically split in ECAL barrel (EB) and
ECAL endcaps (EE). Figure 5.7 shows some �t examples.
Figure 5.7: Examples of Esc /ptk distributions in (Left) ECAL barrel and (Right)
ECAL endcaps with the best-�t reference distribution superimposed (line). In this
examples, the reference distribution is sampled from a calibrated set of data and
�tted to a subset of the same data before calibration (red) and after calibration
(green).
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CHAPTER 5. ECAL CALIBRATION AND STABILITY STUDIES 56
5.4.3 Supercluster Energy Correction
In order to take into account systematics, Supercluster energy is corrected through
a factor, F ′e,γ which is an improvement of the Fe,γ of Equation 5.2. This factor is
calculated by means of a MVA. The input variables are:
1. Shower topology variables;
2. Isolation Variables;
3. ρ (rho), the median energy density per solid angle;
4. Supercluster η, the η of the supercluster corresponding to the reconstructed
photon;
The improvement that this correction gives is related to the pile up, it will be
described in more detail in the next Section.
5.4.4 Pile up corrections
The beam conditions have varied throughout the run. The number of pile-up
(PU) interactions per beam crossing has increased from a few units at an instanta-
neous luminosity L = 1032 cm−2s−1 at the beginning of the 2011 run, to about 15
at L = 5·1033 cm−2s−1 at the end of the 2011 run. The probability that depositsin ECAL generated by particles other than the isolated electron randomly overlap
with the electron shower increases with the number of PU interactions. This a�ects
the