universita' degli studi di milano bicocca acoltàf di scienze matematiche fisiche … universita'...

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

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

2

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

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

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

5

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

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.

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.

8

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:


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))


∂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


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


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.


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.


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)

)


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


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


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


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


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.


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


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.


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


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


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


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.


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


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


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)


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


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


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;


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


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).


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


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


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


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,


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.


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


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


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.


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.


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.


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


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


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.


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,


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).


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

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