UNIVERSITA DEGLI STUDI DI BARI Aldo Moro UNIVERSITA DEGLI STUDI DI BARI Aldo Moro FACOLTA DI SCIENZE MATEMATICHE FISICHE E NATURALI Dipartimento Interateneo di Fisica M. Merlin Tesi

UNIVERSITA DEGLI STUDI DI BARI

Aldo Moro

FACOLTA DI SCIENZE MATEMATICHE FISICHE E NATURALIDipartimento Interateneo di Fisica M. Merlin

Tesi di Laurea

SEARCH FOR A DOUBLY CHARGED HIGGS BOSON

IN LEPTONIC FINAL STATES

WITH THE CMS EXPERIMENT AT√s = 7 TeV

Relatori:Ch.mo Prof. Mauro de PalmaDott. Nicola De Filippis

Laureanda:Liliana Losurdo

Anno Accademico 2011-2012

To Mom and Dad,

my guardian angels.

”Se guardo il tuo cielo, opera delle tue dita,

la luna e le stelle che tu hai fissate,

che cosa e l’uomo perche te ne ricordi

e il figlio dell’uomo perche te ne curi?

Eppure l’hai fatto poco meno degli angeli,

di gloria e di onore lo hai coronato:

gli hai dato potere sulle opere delle tue mani,

tutto hai posto sotto i suoi piedi;

tutti i greggi e gli armenti,

tutte le bestie della campagna;

gli uccelli del cielo e i pesci del mare

che percorrono le vie del mare ...”

Salmo 8

Contents

Introduction 1

1 The Higgs Triplet Model 3

1.1 The Standard Model . . . . . . . . . . . . . . . . . . . . . . . 3

1.1.1 SM features . . . . . . . . . . . . . . . . . . . . . . . . 3

1.1.2 SM restrictions . . . . . . . . . . . . . . . . . . . . . . 4

1.2 Beyond the Standard Model . . . . . . . . . . . . . . . . . . . 6

1.2.1 Type-II Seesaw Mechanism . . . . . . . . . . . . . . . 7

1.2.2 Neutrino masses . . . . . . . . . . . . . . . . . . . . . . 10

1.3 The Higgs Triplet Model . . . . . . . . . . . . . . . . . . . . . 12

1.3.1 Constraint on the physical parameters . . . . . . . . . 13

1.3.2 General features of doubly charged Higgs decays . . . . 16

1.3.3 K-factor and QCD correction to the production

processes . . . . . . . . . . . . . . . . . . . . . . . . . . 22

1.4 Doubly charged scalars at the LHC . . . . . . . . . . . . . . . 24

2 The LHC Collider and the CMS Experiment 27

2.1 The Large Hadron Collider . . . . . . . . . . . . . . . . . . . . 27

2.1.1 LHC structure and features . . . . . . . . . . . . . . . 29

2.1.2 Experimental requirements . . . . . . . . . . . . . . . . 32

2.2 The Compact Muon Solenoid Detector . . . . . . . . . . . . . 33

2.2.1 Coordinate System . . . . . . . . . . . . . . . . . . . . 34

2.2.2 CMS structure . . . . . . . . . . . . . . . . . . . . . . 35

2.2.3 Inner Tracking System . . . . . . . . . . . . . . . . . . 36

2.2.4 Electromagnetic Calorimeter . . . . . . . . . . . . . . . 39

2.2.5 Hadron Calorimeter . . . . . . . . . . . . . . . . . . . . 43

i

2.2.6 Muon System . . . . . . . . . . . . . . . . . . . . . . . 45

2.2.7 Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

2.3 Physics Objects: Event Reconstruction . . . . . . . . . . . . . 49

2.3.1 Particle Flow . . . . . . . . . . . . . . . . . . . . . . . 49

2.3.2 Muons . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

2.3.3 Electrons . . . . . . . . . . . . . . . . . . . . . . . . . 57

2.3.4 Taus . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

3 Data Analysis 61

3.1 Trigger and Data samples . . . . . . . . . . . . . . . . . . . . 62

3.2 Simulation of events . . . . . . . . . . . . . . . . . . . . . . . 64

3.2.1 Event Generators . . . . . . . . . . . . . . . . . . . . . 65

3.2.2 MC samples . . . . . . . . . . . . . . . . . . . . . . . . 66

3.3 Lepton Reconstruction, Identification

and Isolation . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

3.3.1 Muon Reconstruction and Identification . . . . . . . . 71

3.3.2 Electron Reconstruction and Identification . . . . . . . 72

3.3.3 Muon Isolation . . . . . . . . . . . . . . . . . . . . . . 75

3.3.4 Electron Isolation . . . . . . . . . . . . . . . . . . . . . 76

3.3.5 Tau Reconstruction, Identification and Isolation . . . . 78

3.4 Event Selection . . . . . . . . . . . . . . . . . . . . . . . . . . 79

3.4.1 Preselection cuts . . . . . . . . . . . . . . . . . . . . . 80

3.4.2 Baseline Selection for four lepton final state . . . . . . 92

3.5 Selection efficiency . . . . . . . . . . . . . . . . . . . . . . . . 99

3.6 Systematic uncertainties . . . . . . . . . . . . . . . . . . . . . 102

4 Results and Statistical Interpretation 105

4.1 Final distributions . . . . . . . . . . . . . . . . . . . . . . . . 105

4.2 Statistical interpretation:

the CLs Method . . . . . . . . . . . . . . . . . . . . . . . . . . 111

4.3 Exclusion Limits . . . . . . . . . . . . . . . . . . . . . . . . . 114

Conclusions 121

Acknowledgements/Ringraziamenti 125

Bibliography 129

List of Figures

1.1 a) Diagram with a virtual fermion loop for the SM Higgs bo-

son; it is generated by corrections to the m2H that diverges

quadratically; b) Diagrams with an additional field f ; they

generate corrections to the m2H cancelling those of Diagram a). 5

1.2 Feynman diagrams of both pair and associated production. . . 17

1.3 Benchmark points for the type-II seesaw model. . . . . . . . . 20

1.4 Cross sections of the inclusive doubly charged Higgs boson

production (Eq. 1.31) as a function of mΦ±± . . . . . . . . . . . 21

1.5 Feynman graphs contributing to the production of doubly

charged Higgs boson at LHC. . . . . . . . . . . . . . . . . . . 25

2.1 The LHC accelerator complex. . . . . . . . . . . . . . . . . . . 28

2.2 View of the tunnel LHC machine. . . . . . . . . . . . . . . . . 29

2.3 Chain of LHC injection. . . . . . . . . . . . . . . . . . . . . . 31

2.4 The CMS coordinate system. . . . . . . . . . . . . . . . . . . 34

2.5 A perspective view of the CMS detector. . . . . . . . . . . . . 36

2.6 Longitudinal section view of one quadrant of the CMS detector. 37

2.7 The CMS pixel detector. . . . . . . . . . . . . . . . . . . . . . 38

2.8 Schematic cross section through the CMS tracker. . . . . . . . 39

2.9 Longitudinal view of part of the CMS ECAL showing the

ECAL barrel and a ECAL endcap, with the preshower in front. 40

2.10 Layout of the CMS ECAL showing the arrangement of crystal

moduls, supermodules and endcaps, with the preshower in front. 42

v

2.11 ECAL barrel energy resolution, σ(E)/E, as a function of elec-

tron energy as measured from a beam test. The points cor-

respond to events taken restricting the incident beam to a

narrow (4 × 4 mm2) region. The stochastic (S), noise (N),

and constant (C) terms are given. . . . . . . . . . . . . . . . . 43

2.12 Section view of the HCAL detector. . . . . . . . . . . . . . . . 44

2.13 Section view of the Muon System: DT, RPC and CSC. . . . . 46

2.14 Architecture of the Level-1 Trigger. . . . . . . . . . . . . . . . 47

2.15 Scheme of the Particle Flow algorithm. . . . . . . . . . . . . . 51

2.16 Scheme of tau decays into final states involving pions. . . . . . 59

3.1 Cross sections of doubly charged Higgs boson production as a

function of mΦ±± in the mass range between 130 and 700 GeV. 67

3.2 Representation of the isolation cone. The muon direction, es-

timated from the vertex, defines the cone axis. . . . . . . . . . 75

3.3 Representation of the strip of a footprint removal region in the

case of ECAL and HCAL isolation for electrons. . . . . . . . . 77

3.4 Distribution of the transverse momentum of the four muons

in the scenario BR (Φ±± → µ±µ±) = 100%, for signal events

with mΦ±± = 130 GeV (left) and mΦ±± = 300 GeV (right).

The leptons are ordered in pT . The samples correspond to an

integrated luminosity of L = 4.93 fb−1. . . . . . . . . . . . . . 81

3.5 Distribution of the transverse momentum of the four leptons

in the scenario BR (Φ±± → µ±µ±) = 100%, before (top) and

after (bottom) the pT cut on the two leptons with the highest

momentum (pT,1 > 20 and pT,2 > 10 GeV). The samples

correspond to an integrated luminosity of L = 4.93 fb−1. . . . 82


in the scenario BR (Φ±± → µ±τ±) = 100%, before (top) and





in the scenario BR (Φ±± → e±τ±) = 100%, before (top) and




3.8 Invariant mass distribution of the same sign dileptons in the

scenario BR (Φ±± → µ±µ±) = 100%, before (top) and after

(bottom) the mass cut (m(`±`±) > 12 GeV). The samples


3.9 Distribution of the lepton isolation variable in the scenario BR

(Φ±± → µ±µ±) = 100%, before (top) and after (bottom) the

cut (relIsoworst+relIsonexttoworst < 0.35). All of previous cuts

on lepton pT and same sign dilepton mass are also included.

The samples correspond to an integrated luminosity of L =

4.93 fb−1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

3.10 Distribution of the lepton isolation variable in the scenario BR

(Φ±± → e±τ±) = 100%, before (top) and after (bottom) the

cut (relIsoworst+relIsonexttoworst < 0.35). All of previous cuts

on lepton pT and same sign dilepton mass are also included.

The samples correspond to an integrated luminosity of L =

4.93 fb−1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

3.11 Distribution of the significance of the impact parameter in the

scenario BR (Φ±± → µ±µ±) = 100%, before (top) and after

(bottom) the cut on SIP` < 4. All of the preselection cuts

(see Table 3.7) are also applied. The samples correspond to

an integrated luminosity of L = 4.93 fb−1. . . . . . . . . . . . 89


scenario BR (Φ±± → µ±τ±) = 100%, before (top) and after





scenario BR (Φ±± → e±τ±) = 100%, before (top) and after




3.14 Acceptance (left) and Signal detection Efficiencies (right) from MC

in the scenario BR (Φ±± → µ±µ±) = 100%. The cuts applied at

each step are summarized in Tables 3.7 and 3.8. Each cut includes

the previous ones. . . . . . . . . . . . . . . . . . . . . . . . . . 99


in the scenario BR (Φ±± → e±e±) = 100%. The cuts applied at




in the scenario BR (Φ±± → e±µ±) = 100%. The cuts applied at




in the scenario BR (Φ±± → µ±τ±) = 100%. The cuts applied at




in the scenario BR (Φ±± → e±τ±) = 100%. The cuts applied at



4.1 Invariant mass distribution of Φ±± for BR = 100% to µµ chan-

nel, after full selection. The samples correspond to an inte-

grated luminosity of L = 4.93 fb−1. . . . . . . . . . . . . . . . 106

4.2 Invariant mass distribution of Φ±± for BR = 100% to ee chan-



4.3 Invariant mass distribution of Φ±± for BR = 100% to eµ chan-



4.4 Invariant mass distribution of Φ±± for BR = 100% to µτ chan-



4.5 Invariant mass distribution of Φ±± for BR = 100% to eτ chan-



4.6 (Left) An example of differential distribution of possible limits

on µ for the background-only hypothesis (s = 0, b = 1, no

systematic errors). (Right) c.d.f. of the plot on the left with

2.5%, 16%, 50%, 84% and 97% quantiles (horizontal lines)

defining the median expected limit as well as the ±1σ (68%)

and ±2σ (95%) bands for the expected value of µ for the

background-only hypothesis. . . . . . . . . . . . . . . . . . . . 114

4.7 Lower bound on Φ++ mass at 95% for BR = 100% to µµ channel.116

4.8 Lower bound on Φ++ mass at 95% for BR = 100% to ee channel.117

4.9 Lower bound on Φ++ mass at 95% for BR = 100% to eµ channel.118

4.10 Lower bound on Φ++ mass at 95% for BR = 100% to µτ channel.119

4.11 Lower bound on Φ++ mass at 95% for BR = 100% to eτ channel.120

List of Tables

1.1 Branching ratios of Φ++ to the various final states (τ means

a tau lepton before decay). . . . . . . . . . . . . . . . . . . . . 19

2.1 List of the nominal LHC parameters, with their values. . . . . 33

3.1 Triggers used for the analysis. . . . . . . . . . . . . . . . . . . 63

3.2 Collision datasets . . . . . . . . . . . . . . . . . . . . . . . . . 64

3.3 Main backgrounds. . . . . . . . . . . . . . . . . . . . . . . . . 68

3.4 Signal samples . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

3.5 Background samples . . . . . . . . . . . . . . . . . . . . . . . 70

3.6 Definition of cuts used in the electron identification for elec-

trons categories in the barrel (EB) and in the endcaps (EE).

Where a range is specified, the cuts are made ET -dependent

between EminT = 10 GeV and Emax

T = 40 GeV. . . . . . . . . . 74

3.7 Pre-selection criteria. . . . . . . . . . . . . . . . . . . . . . . . 92

3.8 Selection cuts applied in various four lepton final states. . . . . 93

3.9 Cut flow for 100% decay to muons with mass 130, 300 and 500

GeV. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

3.10 Cut flow for 100% decay to electrons with mass 130, 300 and

500 GeV. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

3.11 Cut flow for 100% decay to e-µ with mass 130, 300 and 500

GeV. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

3.12 Cut flow for 100% decay to µ-τ with mass 130, 300 and 500

GeV. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

3.13 Cut flow for 100% decay to e-τ with mass 130, 300 and 500

GeV. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

xi

3.14 Source of systematic uncertainties and impact on the full se-

lection efficiency. . . . . . . . . . . . . . . . . . . . . . . . . . 103

4.1 Summary of the 95% CL exclusion limits. . . . . . . . . . . . . 115

introduction

The Standard Model (SM) of particle physics is a relativistic quantum field

theory which gives a description of the behaviour of all known subatomic par-

ticles. It predicts the existence of a single scalar and neutral Higgs boson from

the spontaneous breaking mechanism of electroweak symmetry. Although the

SM has proven to be a very successful and precise theory describing the in-

teractions of fundamental particles, there are strong theoretical arguments

that lead us to think that the Standard Model is not the complete theory of

Nature.

Over the past twenty years, a large number of models has been developed

to extend the Standard Model in order to unify all fundamental interactions

and provide reasonable answers to the questions that remained unresolved

in it, like the CP violation, the exclusion of Gravity from the model, the

existence of only three generations of quarks and leptons and the neutrino

oscillations and their non-zero masses. These models, hereafter referred as

exotic models, theorize the existence of several charged and neutral Higgs

particles with different spin and parity.

This work deals with the search for a signal compatible with the pro-

duction of a doubly charged Higgs boson, Φ++, predicted in several exotic

models, in particular in the Higgs Triplet Model (HTM), with the CMS

experiment at LHC. Such model gives mass to neutrinos with the seesaw

mechanism and these masses are related to the Yukawa couplings of the lep-

tons. Thus, the Higgs boson discovery can be deduced by measuring the

fraction of its decay into leptons. The Φ++ can be produced at LHC both in

pair production process with another boson of the same type, but of opposite

charge, and in associated production process with a singlet, Φ+, giving rise to

a signature of four or three leptons (electrons, muons and taus), respectively,

1

coupled with the same sign for the reconstruction of the boson.

The purpose of this work is the development of analysis criteria for the

search for a signal compatible with the existence of the Φ++ with the data

collected by the experiment CMS during the 2011, in the case of pair pro-

duction processes.

The main background due to Standard Model processes are Z+jets, ZZ

and WZ events; they can be efficiently discriminated by the signal using

selection criteria based on the isolation, identification and transverse mo-

mentum of the leptons involved in the process.

In the first chapter we give an overview about the main features and

limitations of the Standard Model and the reasons why to go beyond it. We

then describe the seesaw mechanism that gives mass to neutrinos and the

exotic model that includes it. We summarize the previous searches for the

Φ++ at the LEP and Tevatron and then we describe the signatures of the

doubly charged Higgs production at LHC and the scenarios assumed for this

analysis.

In the second chapter we describe the LHC programme, the CMS ex-

periment, its main features, its operating logic and the performance of sub-

detector. The main reconstruction techniques involved for the analysis are

also described.

The third chapter presents the data analysis performed for this search,

by defining the selection criteria for the detection of the signatures and the

discrimination of the signal from the background, after an overview about

the main identification and isolation methods for electrons, muons and taus.

In the fourth chapter we discuss the results of the analysis. Finally we

calculate the lower limits in the different scenarios, by combining the four

lepton final state analysis with the three lepton final state analysis.

2

Chapter 1

The Higgs Triplet Model

1.1 The Standard Model

The Standard Model (SM) of particle physics is a theory which describes the

electromagnetic, weak and strong nuclear interactions of the subatomic parti-

cles. This model includes elementary particles of spin 12, known as fermions,

that are the matter particles, and particles of spin 1, known as gauge bosons,

that mediate the fundamental interactions.

1.1.1 SM features

The fermions of the Standard Model are classified according to how they

interact (or equivalently, by what type of charges they carry). There are six

quarks (up, down, charm, strange, top, bottom), and six leptons (electron,

electron neutrino, muon, muon neutrino, tau, tau neutrino). Pairs from each

classification are grouped together to form a generation, with corresponding

particles exhibiting similar physical behavior. The main property of the

quarks is that they carry color charge, and hence, interact via the strong

interaction. A phenomenon called color confinement results in quarks being

bound to each other, forming color-neutral composite particles (hadrons) con-

taining either a quark and an antiquark (mesons) or three quarks (baryons).

Quarks also carry electric charge and weak isospin. Hence, they interact with

other fermions both electromagnetically and via the weak interaction. The

remaining six fermions do not carry colour charge and are called leptons.

3

The three neutrinos are massless and do not carry electric charge either, so

they only interact with other particle by the weak force, which makes them

difficult to detect. However, by virtue of carrying an electric charge, the

electron, muon, and tau all interact also electromagnetically. In the SM,

the bosons are defined as force carriers that mediate the strong, weak, and

electromagnetic interactions. The different types of gauge bosons are: the

photons, that mediate the electromagnetic force between electrically charged

particles, the W+, the W−, and the Z gauge bosons that mediate the weak

interactions between particles of different flavors (all quarks and leptons),

and eight gluons that mediate the strong interactions between color charged

particles (the quarks).

The SM foresees the existence of a unique scalar and neutral Higgs particle

from the spontaneous electroweak symmetry breaking (EWSB) mechanism,

known as the Higgs mechanism [1]. The Higgs particle has spin 0, and for

that reason it is classified as a boson; it is the only fundamental particle

predicted by the Standard Model that has not yet been observed.

The Higgs mechanism plays a unique role in the Standard Model, by explai-

ning why the other elementary particles, except the photon and the gluon,

are massive. In particular, the Higgs mechanism would explain why the

photon has no mass, while the W and Z bosons are massive. The elementary

particle masses, and the differences between electromagnetism (mediated by

the photon) and the weak force (mediated by the W and Z bosons), are cri-

tical to many aspects of the structure of microscopic (and hence macroscopic)

matter.

1.1.2 SM restrictions

The Standard Model validity has been tested through a large number of mea-

surements. Nevertheless there are strong theoretical arguments which lead

one to think that the SM is not the ultimate theory describing the fundamen-

tal interactions. This theory in fact leaves many open questions. One of the

most serious structural problems is connected to the radiative corrections to

the Standard Model Higgs boson mass (problem of hierarchy). This problem

4

Figure 1.1: a) Diagram with a virtual fermion loop for the SM Higgs bo-son; it is generated by corrections to the m2

H that diverges quadratically; b)Diagrams with an additional field f ; they generate corrections to the m2

H

cancelling those of Diagram a).

is due to the existence of a hierarchy between the gauge boson masses and the

Plank scale (mP ≈ 1019 GeV)1, at which the gravitational interaction is of

comparable strength with the other forces. The radiative corrections are de-

rived from fermionic loops (see Fig.1.1) for which they diverge quadratically

and give a Higgs boson with a mass at least 30 orders of magnitude larger

than the values allowed by the experimental data. The conceptual structure

of the SM, indeed, is not able to explain the mass scale of vector bosons, fixed

by the Higgs mechanism at the Fermi scale m ∼ 1/√GF ∼ 250 GeV which

is about 1017 times smaller than Planck scale. This problem occurs when the

fundamental parameters (couplings or masses) of some Lagrangians are differ-

ent than the parameters measured by experiments. Therefore, a collection of

techniques used to treat divergences is introduced, and it is known as renor-

malization. Typically the renormalization parameters are connected to the

1Mass, energy and momentum are expressed in the natural units system, where c isset to a unitary adimensional constant and can thus be omitted, expressing all of thequantities in eV multiples.

5

fundamental parameters, but in some cases, it appears that there has been

a delicate cancellation between the fundamental quantities and the quan-

tum corrections to them. The hierarchy problem is related to the problems

of naturalness, or the fine-tuning problems. Studying the renormalization

in the hierarchy problem is difficult, because such quantum corrections are

usually power-law divergent. If the Standard Model was valid until the Plank

scale, the differences between the Fermi scale and the Plank scale could be

eliminated only by a not natural process of fine-tuning of the parameters.

Finally, the SM depends on a high number of free parameters: 19. Be-

sides the Higgs boson mass, they include the Weinberg angle, quark and

fermion masses, the Cabibbo-Kobayashi-Maskawa (CKM) matrix elements

and the CP violating phase. They have values known from experiment, but

their origin is unknown. Some theorists have tried to find relations between

different parameters, for example, between the masses of particles in diffe-

rent generations. Moreover, according to the Standard Model, the neutrinos

are massless particles. However, neutrino oscillation experiments have shown

that neutrinos do have mass. Mass terms for the neutrinos can be added to

the Standard Model by hand, but these lead to new theoretical problems (for

example, the mass terms need to be extraordinarily small). Therefore, re-

searchers postulate new theories that resolve the hierarchy problem without

fine-tuning [2].

1.2 Beyond the Standard Model

While in the Standard Model the quarks, the charged leptons and the

massive gauge bosons acquire masses via the Higgs mechanism, the non-zero

neutrino masses can be derived only by using an additional mechanism to

include them [3]. According this new mechanism, neutrinos have a mass

term like other fermions, referred as Dirac mass term, by mixing left-handed

and right-handed eigenstates: right-handed neutrinos appear with the same

masses as the observed left-handed neutrinos.

Moreover, neutrinos have no electromagnetic charge and no color charge: so

6

they could be also described as Majorana particles, i.e. particles that are their

own antiparticles. This fact would imply a non-conservation of the lepton

number (νi → νi); however measurements related with the observation of

the neutrino oscillations (νi → νj) already indicate some non-conservation

laws in the lepton numbers. The interesting feature of the Majorana mass

terms is that they do not mix left-handed and right-handed components of

a particle; therefore, a description of Majorana massive neutrinos does not

require the addition of right-handed neutrinos in the model. In this scenario,

a new model beyond the SM can be introduced.

1.2.1 Type-II Seesaw Mechanism

A strongly established signal of particle physics beyond the Standard

Model is the existence of non-zero neutrino masses. Therefore, in addition to

the electroweak symmetry breaking, a seesaw mechanism is required to give

mass2 to neutrinos.

The basic principle of the seesaw mechanism consists in introducing a corre-

spondence between some high-scale phenomenon and the low-scale observed

neutrino masses [5]. Four kinds of seesaw processes can be distinguished:

1. the type-I seesaw mechanism introduces right-handed neutrinos with

a Majorana mass of the order of the grand unification scale. The ad-

dition of Dirac mass terms mixing right-handed, that sets the new

physics scale Λ3, and left-handed neutrinos, provides a very small mass

to left-handed neutrinos. The higher the right-handed neutrino mass,

the lower the left-handed neutrino mass, hence the name of “seesaw”

mechanism;

2. the type-II seesaw mechanism adds an SU(2)L Higgs triplet ∆ to the

doublet of the Standard Model. This mixing between the doublet and

triplet, via a dimensional parameter µ, allows to obtain a relation v∆ ∼2Several extensions of the Standard Model suggest the addition of a scalar triplet little

Higgs models and left-right supersymmetric models for example [4].3The cut-off Λ is a parameter introduced in the renormalization theory to take into

account the divergences.

7

µv2/M2∆, where M∆ is the mass of the triplet. In this case the scale Λ

is replaced by M2∆/µ;

3. the type-III seesaw mechanism generates neutrino masses through ad-

dition at least two extra matter fields in the adjoint representation of

SU(2)L and with zero hypercharge. Therefore, the high scale Λ is re-

placed by the mass of the extra fermions in the adjoint representation;

4. the Hybrid seesaw mechanism, a combination of type-I and type-III, in

which one SM fermionic singlet and one fermion in the adjoint repre-

sentation of SU(2) are added. This mechanism has a very simple and

unique realization in the context of grand unified theories [6].

In this work, we assume that neutrinos may obtain masses via the mi-

nimal seesaw model of type-II, an extension of the scalar sector of SM, which

introduces some new physics at large scale. To the SU(2)L Higgs doublet of

the Standard Model

Φ =

(ϕ+

ϕ0

), (1.1)

with ϕ0 = 1√2

(ϕ+ v + iχ) and hypercharge YΦ = 1, it adds a SU(2)L Higgs

triplet ∆

∆ =

(∆+/√

2 ∆++

∆0 −∆+/√

2

), (1.2)

with ∆0 = 1√2

(δ + v∆ + iη) and hypercharge Y∆ = 2. Under a gauge tran-

sformation U , these fields transform as Φ→ U(x )Φ and ∆→ U(x )∆U(x )†.

While the general SM Lagrangian can be written as

LSM = Lf + Lg + LSMY + LH , (1.3)

where Lf is the fermionic propagation term, Lg is the gauge kinetic term,

LSMY is the Yukawa term in the SM, which provides masses to the fermions,

and LH is the Higgs term, that introduces the Higgs field h, the general

Seesaw Lagrangian can be written as

Lseesaw = Lf + Lg + LseesawY + LΦ,∆, (1.4)

8

where Lf and Lg are those appearing in the Standard Model Lagrangian,

LseesawY is the Yukawa term according to the seesaw mechanism, and LΦ,∆ is

the term corresponding to the propagation of the Higgs field. This last term

is given by

LΦ,∆ = (DµΦ)†(DµΦ) + Tr(Dµ∆)†(Dµ∆)− V (Φ,∆), (1.5)

where the covariant derivatives are written as:

DµΦ = ∂µΦ− ig1YΦ

2BµΦ− ig2

τa2Waµ Φ, (1.6)

Dµ∆ = ∂µ∆− ig1Y∆

2Bµ∆− ig2

[τa2Waµ ,∆

], (1.7)

and the scalar potential is written as:

V (Φ,∆) = − m2Φ†Φ +m2∆Tr(∆

†∆) +[µ(ΦT iτ2∆†Φ) + h.c.

]+ λ1(Φ†Φ)2 + λ2[(Tr(∆†∆)]2 + λ3Tr(∆

†∆)2

+ λ4(Φ†Φ)Tr(∆†∆) + λ5Φ†∆∆†Φ, (1.8)

where m and m∆ are mass parameters in the Standard Model and Seesaw

Lagrangian, respectively, µ is a mass parameter in common between the two

Lagrangians and λi (i = 1, 2, 3, 4) are dimensionless couplings [5], Tr is the

trace over 2 × 2 matrices and τ2 is the second Dirac-Pauli matrix4 . A priori,

both scalar fields Φ and ∆ can develop a non-zero vacuum expectation value

(VEV) of their neutral components5 :

〈Φ〉 =1√2

(0

v

)and 〈∆〉 =

1√2

(0

v∆

), (1.9)

where v and v∆ are Φ and ∆ vacuum expectation values, respectively.

4τ1 =

(0 11 0

); τ2 =

(0 −ii 0

); τ3 =

(1 00 −1

).

5An electrically charged field does not acquire any vacuum expectation value, becauseotherwise charge would be spontaneously broken.

9

Finally, the Yukawa Lagrangian LseesawY contains, in addition to the com-

plete SM Yukawa Lagrangian, a coupling term between the scalar triplet ∆

and the lepton doublets Li =

(νiL

`iL

):

LseesawY = LSMY + L∆,νY , (1.10)

with

L∆,νY = −YνLTC ⊗ iτ2∆L+ h.c.

= −Yij[νiLCνjL∆0 − 1√

2(νTiLC`jL + `TiLCνjL)∆+ − `TiLC`jL∆++

]+h.c., (1.11)

where C is the charge conjugation operator, and the symmetric complex

matrix Yν is the Yukawa coupling strenght (i, j = e, µ, τ). Due to the si-

multaneous presence of the Yukawa coupling Yν in Eq. 1.11 and the term

proportional to the µ parameter in Eq. 1.8, the leptonic number is explicitly

broken in this theory.

Therefore, considering the non-zero Higgs triplet VEV of neutral component

described in Eq. 1.9, this Yukawa Lagrangian gives rise to the Majorana

mass term for neutrinos, −12Mijν

TiLCνiL, whose mass matrix is related to the

Yukawa couplings through the following relation:

Mij = 2Yij〈∆0〉 =√

2Yijv∆ , (1.12)

which is the main relation for the type-II seesaw scenario [5][7].

1.2.2 Neutrino masses

Neutrino oscillation is a quantum mechanical phenomenon for which a neu-

trino created with a specific lepton flavour (electron, muon or tau) can later

be measured with a different flavour. The probability of measuring a par-

ticular flavour for a neutrino varies periodically as it propagates. This phe-

nomenon is of theoretical and experimental interest since observation of the

10

phenomenon implies that the neutrino has a non-zero mass, which is not part

of the original Standard Model of particle physics. The flavour change may

be due to a mismatch between neutrino flavour eigenstates (|νi〉, i = e, µ, τ)

and their mass eigenstates (|νk〉, k = 1, 2, 3). This implies that neutrinos have

several different mass eigenvalues, while the SM describes them as massless

particles.

Similarly to the quark flavour mixing and the CKM matrix of Standard

Model, the mass matrix Mij for three Dirac neutrinos is diagonalized by a

unitary matrix VPMNS (Pontecorvo-Maki-Nakagawa-Sakata) [8][9]. The 3 ×3 PMNS matrix is naturally composed of three rotations, involving three

mixing angles, called the Euler angles : θ12, θ13, θ23. If neutrino oscillations

happen to violate the CP symmetry, a phase factor δ (or Dirac phase) must

be added. Finally, since neutrinos are Majorana particles, two other phase

factors, α1 and α2 (or Majorana phases) can be added. Then the mixing

matrix V becomes

V = VPMNS × diag(1, eiα1/2, eiα2/2) , (1.13)

where −π ≤ α1, α2 < π. Since we can chose to work in the basis in which

the charged lepton mass matrix is diagonal, the neutrino mass matrix is

diagonalized by VPMNS. Using Eq.1.12, the couplings Yij can be written as:

Yij =Mij√2v∆

≡ 1√2v∆

[VPMNS diag(m1,m2e

iα1 ,m3eiα2) V T

PMNS

]ij. (1.14)

Here m1, m2 and m3 are the three masses eigenvalues of the neutrinos. Such

a description of neutrino sector involves a total of nine parameters: three

mixing angles, three potential phases, and three mass eigenvalues [3].

Neutrino oscillations are sensitive to the mixing angles (θij) and the Dirac

phase (δ), and the mass-squared differences, ∆m221(≡ m2

2−m21) and ∆m2

31(≡m2

3 −m21). Since the sign of ∆m2

31 is not determined at the present, distinct

patterns for the neutrino mass hierarchy are possible.

The case with ∆m231 > 0 is referred to as normal hierarchy (NH) where

m1 < m2 < m3, and the case with ∆m231 < 0 is known as inverted hierarchy

11

(IH) where m3 < m1 < m2. Denoting the lightest neutrino mass by m0, we

can write

m0 =

{m1 (NH)

m2 (IH). (1.15)

If m0 &√|∆m2

31| ' 0.05 eV, the neutrino mass spectrum is quasi-degenerate

(QD). However, information on the mass m0 and the Majorana phases cannot

be obtained from neutrino oscillation experiments. This is because the oscil-

lation probabilities are independent of these parameters, not only in vacuum

but also in matter [10].

1.3 The Higgs Triplet Model

In order to explain the non-zero neutrino masses, several scenarios have

been proposed, for which a source of lepton flavour violation (LFV) is in-

troduced with additional Majorana neutrinos, a triplet scalar field, or triplet

fermion fields. In particular, a simple model that contains a doubly charged

scalar boson is the ”Higgs Triplet Model” (HTM) [10]. This model is an ex-

tension of the Standard Model in which only the scalar sector is augmented

with a Higgs triplet.

Assuming that the triplet scalar field carries two units of lepton number,

the lepton number conservation is violated in a trilinear interaction among

the Higgs doublet field and the Higgs triplet field. Majorana masses for

neutrinos are then generated through the Yukawa interaction of the lepton

doublet and the triplet scalar field, given by Eq. 1.12. When the electroweak

symmetry is broken and the mass of the component fields of the triplet, given

by Eqs. 1.1 and 1.2, are at the TeV scale or less, there are seven physical

massive Higgs bosons

Φ++, Φ−−, Φ+, Φ−, Φ0(= Φ or A), H,

and the model can be tested by directly detecting them, such as the doubly

12

charged (Φ±±)6 , singly charged (Φ±) and the neutral scalar bosons (Φ0)7,

which is Φ or A with Φ to be the triplet-like CP even Higgs boson and A

to be the triplet-like CP odd Higgs boson. While these Higgs states are all

∆-like (triplet), the seventh boson H generated by the EWBS is the SM-like

(doublet) one.

In addition to the appearance of these charged scalar bosons, an attractive

prediction of the HTM is the relationship among the masses of the component

fields of the triplet scalar field:

m2Φ±± −m2

Φ± ' m2Φ± −m2

Φ0(≡ ξ),

where m2Φ±± , m2

Φ± and m2Φ0 are the masses of Φ±±, Φ± and Φ0, respectively.

The mass-squared differences ξ is determined by v (' 246 GeV), the VEV

of the doublet scalar field, as well as the Standard Model VEV, and a scalar

self-coupling constant [7].

1.3.1 Constraint on the physical parameters

Solving the Lagrangian is not a simple calculation because of its com-

plex structure, so we can proceed minimizing the scalar potential, given by

Eq. 1.8, to find the stable points around which a perturbative expansion can

be performed. This minimization (vacuum condition) implies non-zero values

for both v and v∆ and the two following constraints on the parameters [5]:

m2 =1

2

[−2v2λ1 − v2

∆(λ4 + λ5) + 2√

2µv∆

], (1.16)

m2∆ = M2

∆ −1

2

[2v2

∆(λ2 + λ3) + v2(λ4 + λ5)], (1.17)

with M2∆ ≡

µv2√

2v∆.

The mass of the doubly charged scalar bosons Φ±± ( that is ∆±± in the

6The doubly charged Higgs boson is denoted also with ∆ and H alternatively, becausein the literature also these two notations have been used. Our choice of Φ for the tripletcomponents avoids possible confusion with H+ in the MSSM.

7Singly charged or neutral boson appear in many models, e.g. from scalar doublets insupersymmetric models. Doubly charged scalars are more unusual.

13

Eq. 1.2) is calculated as

m2Φ±± = M2

∆ − v2∆λ3 −

v2

2λ5

' M2∆ −

v2

2λ5, (v2 � v2

∆). (1.18)

Mass eigenstates of the singly charged states, CP odd states and CP even

states are obtained by(ϕ±

∆±

)= R(β±)

(w±

Φ±

),

(χ

η

)= R(β0)

(z

A

),

(ϕ

δ

)= R(α)

(h

Φ

),

(1.19)

R(θ) ≡

(cos θ − sin θ

sin θ cos θ

), (1.20)

where w± and z are the Nambu-Goldstone bosons which are absorbed by the

longitudinal mode of W± and Z, respectively. The mixing angles β±, β0 and

α are expressed as

cos β± =v√

v2 + 2v2∆

,

cos β0 =v√

v2 + 4v2∆

,

tan 2α ' v∆

v

4M2∆ − 2v2(λ4 + λ5)

M2∆ − 2v2λ1

. (1.21)

The masses of the other bosons are calculated as

m2Φ± = M2

∆

(1 +

2v2∆

v2

)− 1

4

(v2 + 2v2

∆

)λ5, (1.22)

m2A = M2

∆

(1 +

4v2∆

v2

)'M2

∆, (1.23)

m2Φ 'M2

∆, (1.24)

m2H ' 2λ1v

2, (1.25)

14

for v2 � v2∆

8. We can note that Eq. 1.25 is valid as long as M2∆ > 2λ1v

2.

From above mass formulae, the mass-squared difference ξ is determined by

−v2

4λ5 [7].

The neutrino masses are generated through the Yukawa interaction, given by

Eq. 1.11 and the neutrino mass matrix is obtained as

Mij =√

2Yijv∆ = Yijµv2

M2∆

. (1.26)

By this equation, the Yukawa coupling constant Yij and the ∆ vacuum ex-

pectation value v∆ are related with each other.

This simple connection between the triplet Yukawa couplings and the pa-

rameters of the neutrino mass matrix (many of which are measurable) is

an important and attractive feature of the HTM. In contrast, Eq. 1.26 does

not hold in other models with a doubly charged scalar (e.g. the Left-Right

Symmetric Model [4] in which the couplings Yij are essentially arbitrary).

A perturbative Yij can be used to obtain realistic neutrino masses pro-

vided that v∆ & 1 eV. The presence of a non-zero v∆ gives rise to ρ 6= 1

at tree level, where ρ ≡ m2W

(m2Z cos2 θW )

. Therefore a limitation of the ratio9 v∆

v

is necessary in order to comply with the measurement of ρ ∼ 1: taking the

electroweak scale and v2 + v2∆ ≈ (246 GeV)2 conditions into account, this

results in:

v ≈ 246 GeV, v∆ . 1 GeV. (1.27)

The case where the leptonic decays of Φ±± are dominating is realized when

Yij are larger than the smallest Yukawa couplings in the SM (i.e., the electron

Yukawa coupling, Ye ∼ 10−6). So taking into account Eq. 1.12 one can write

v∆Yij . 10−10 GeV , (1.28)

8In the limit of v∆ → 0, Yukawa interactions and gauge interactions of H becomecompletely the same as those of the SM Higgs boson at the tree level. This is the reasonfor which it is called the SM-like Higgs boson and denoted as H.

9The Standard Model predicts a tree-level value ρ = 1, in perfect agreement withexperiments that give ρ = 1.0002+0.0024

−0.0009. After the introduction of v∆ 6= 0, defining

x = v∆

v , the constant writes: ρ = 1+2x2

1+4x2 . This is still in agreement with experimentalresults, given that x . 0.03.

15

and from Eq.1.26 it follows that in this scenario the upper limit becomes

v∆ . 1 MeV. (1.29)

Knowing that v∆

v. 0.03, the doubly charged Higgs boson mass scale depends

mainly on the scale of µ. Besides, the comparison of Eqs. 1.18 and 1.26

shows the seesaw mechanism at work: when the vacuum expectation value

v∆ gets small, the mass of the scalar triplet increases and the neutrino masses

decrease [10].

The differences between the masses of Φ±±, Φ±, Φ and A appear through

the quartic couplings in the Higgs potential. If one assume λiv∆ � µ (i = 1,

2, 3, 4) [11], then these masses are degenerate, and H takes the same mass

as the Standard Model Higgs boson:

m2Φ±± ≈ m2

Φ± ≈ m2Φ ≈ m2

A ≈µv2

√2v∆

; m2H ≈ 2λv2 . (1.30)

1.3.2 General features of doubly charged Higgs decays

A distinctive signal of the HTM would be the observation of a doubly

charged Higgs boson Φ±±, whose mass (mΦ±±) may be of the order of the

electroweak scale. If kinematically accessible, such particles may be produced

with sizeable rates at hadron colliders in the pair production process

qq → Φ++Φ−− → `+i `

+j `−k `−l ,

as well as in the associated production process

qq′ → Φ±±Φ∓ → `+i `

+j `−k νl ,

where Φ± is a singly charged Higgs boson in the same triplet representa-

tion. The Feynman diagrams of both production processes are shown in

Fig. 1.2. Direct searches for Φ±± have been performed both by LEP10 ex-

10LEP is the acronym of Large Electron-Positron, a circular collider that acceleratedelectrons and positrons located at CERN (Switzerland-France) since 1989. The necessityto build an e+e− collider in an energy range above 200 GeV was due to characterize with

16

Figure 1.2: Feynman diagrams of both pair and associated production.

periments (OPAL, DELPHI and L3) and Tevatron11 experiments (D0 and

CDF), assuming the production channel qq → Φ++Φ−− and the leptonic de-

cays Φ±± → `±i `±j (` = e, µ, τ), and mass limits in the range mΦ±± > 110-150

GeV have been obtained.

The summary of LEP searches for doubly charged Higgs boson is presented

below:

• OPAL searched for pair production into all 6 leptonic decay channels,

assuming both doubly charged Higgs particle to decay into the same

channel. The lower mass limit is set to 99 - 100.5 GeV, depending on

the channel [12];

• DELPHI searched for 4τ signature of the pair-production. The lower

mass limit is set to 97.3 GeV [13];

• L3 searched for the pair production into all 6 leptonic decay channels.

more accuracy the gauge bosons, provide additional contributions to the confirmationof Standard Model theory. The choice of leptonic accelerators allowed the compromisebetween very high energies and extreme precision. LEP consisted of four general purposedetector with a cylindrical geometry: ALEPH, DELPHI, OPAL, L3. It worked in twophases: LEPI (from 1989 to 1995) which allowed to reach centre-of mass energies in therange 89 GeV <

√s < 93 GeV, and LEPII (from 1996 to 2000) with centre-of-mass energies

up to 209 GeV. At the end of 2000, LEP was shut down and then dismantled in order tomake room in the tunnel for the construction of the Large Hadron Collider (LHC).

11The Tevatron is a circular hadronic accelerator in the United States (Chicago), at theFermi National Accelerator Laboratory (also known as Fermilab) that accelerated protonsand antiprotons with a centre-of-mass energy equal to 1.96 TeV. It worked in two runs:the first one was from 1992 to 1995, the second one was from 2001 to 2001. Its mainexperiments were CDF and D0. Tevatron ceased operations on 30 September, 2011, dueto budget cuts.

17

The lower mass limit is set to 95.5 - 100.2 GeV, depending on the

channel [14].

The summary of Tevatron searches for doubly charged Higgs boson is as

follows:

• D0 searched for:

– µ and τ final states. The lower limit is set 128 - 168 GeV for

various model options [15];

– 4µ signature of pair production. The lower limit is set to 150

GeV [16];

– 2µ final state. The lower limit is set to 118 GeV [17];

– µτ and ττ final states. The lower limits are set to 144 GeV and

128 GeV, respectively [15].

• CDF searched for:

– leptonic final states, setting limits between 190 GeV and 245

GeV12;

– µτ and eτ final states for pair production. The lower limits are

set to 114 GeV and 112 GeV, respectively [18];

– ee, µµ and eµ final states. The lower limits are set to 133 GeV,

135 GeV and 115 GeV, respectively [19].

The LHC13, using the above production mechanism, offers improved sensi-

tivity to mΦ±± . The production of doubly charged Higgs bosons at the LHC

can give rise to following distinctive signatures:

• three or four prompt isolated leptons in the final state;

• dilepton combination with the same charge;

12The results have not been published.13LHC is the acronym of Large Hadron Collider located at CERN. It is the world’s

largest and highest-energy particle accelerator. More details are in the next chapter.

18

• final states that are combinations of all possible leptons, due to flavour

non-conservation.

The search is designed to be fully inclusive allowing for all possible combina-

tions, called model independent search in which a 100% branching ratio (BR)

into each of the six channel (namely ee, µµ, ττ, eµ, eτ, µτ) is assumed. In ad-

dition to this model, the type-II seesaw model is tested in four benchmark

points (BP1-4) which are chosen according to the different characteristics of

the neutrino mass matrix structures; they describe the following neutrino

sector:

• BP1, in which a normal hierarchy is assumed, no CP violation, normal

neutrino mass ordering and the lowest neutrino mass to be vanishing;

• BP2, same as BP1, but with the assumption of an inverted hierarchy

of neutrino masses;

• BP3, same as BP1, but the lightest neutrino mass is assumed to be 0.2

eV, giving rise to a quasi-degenerate neutrino mass spectrum;

• BP4, in which all branching ratios are assumed to be equally 16.7%.

Such a model point is called degenerate case.

The branching ratios of benchmark points are summarized in Tab. 1.1 and

they are shown in Fig. 1.3.

Benchmark point ee eµ eτ µµ µτ ττ

BP1 0 0.01 0.01 0.30 0.38 0.30

BP2 0.50 0 0 0.125 0.25 0.125

BP3 0.34 0 0 0.33 0 0.33

BP4 1/6 1/6 1/6 1/6 1/6 1/6

Table 1.1: Branching ratios of Φ++ to the various final states (τ means a taulepton before decay).

19

Figure 1.3: Benchmark points for the type-II seesaw model.

Because of the proportionality between the Φ±± Yukawa coupling matrix

Yij and the light neutrino mass matrix Mij, given by Eq. 1.26, the branching

ratios Φ±± → `±i `±j measured at the LHC test the neutrino mass mechanism

directly. Thus, the LHC experiments are able to reconstruct unknown neu-

trino parameters such as the absolute neutrino mass scale, the mass hierarchy

and CP-violating phases that are not testable in neutrino oscillations.

An inclusive search for the doubly charged Higgs boson is performed with

the CMS experiments with data collected in 2011 at the collision energy of

7 TeV corresponding to an integrated luminosity of 4.93 fb−1. It is carried

out in events with four and three final state leptons of all flavours, searching

for a same sign dilepton invariant mass peak corresponding to a Φ±±, while

decaying in the same charged lepton pairs. The three (four) lepton signature

can include maximally one (two) tau hadronic decay that implies a missing

energy related to the neutrinos from the tau decay.

The decay channels Φ±± → `±i `±j and Φ± → `±i νj are the dominant ones if

v∆ . 10−4 GeV, and give rise to multi-lepton signatures. In the HTM, one

expects v∆ . 10−4 GeV if the triplet Yukawa coupling is larger the smallest

Yukawa coupling in the SM (i.e., the electron Yukawa coupling). Various

multi-lepton signatures can be originated from the production mechanism

qq → Φ++Φ−− and qq′ → Φ±±Φ∓. Assuming that the Φ±± and Φ± are

degenerate in mass, the cross section of the associated production exceeds

the one of the pair production.

The four-lepton signature (4`) only receives a contribution from qq →Φ++Φ−−. Although this 4` signature provides a very promising way to search

20

for Φ±±, it is not necessarily the channel which offers the best sensitivity for a

given integrated luminosity and mass mΦ±± . Special attention has been given

to the three-lepton channel, which also has relatively small SM backgrounds.

Significantly, the three-lepton signature is sensitive to the production mecha-

nism qq′ → Φ±±Φ∓ that contributes to the search for Φ±± [10]. Considering

the following inclusive single Φ±± cross section (σΦ±±)

σΦ±± = σ(qq, qq → Φ++Φ−−) + σ(qq′, qq → Φ++Φ−) + σ(qq′, qq → Φ−−Φ+) ,

(1.31)

the search at LHC is enhanced.

Figure 1.4: Cross sections of the inclusive doubly charged Higgs boson pro-duction (Eq. 1.31) as a function of mΦ±± .

While at the Tevatron

σ(qq′, qq → Φ++Φ−) = σ(qq′, qq → Φ−−Φ+) , (1.32)

at the LHC

σ(qq′, qq → Φ++Φ−) > σ(qq′, qq → Φ−−Φ+) . (1.33)

21

1.3.3 K-factor and QCD correction to the production

processes

For processes involving strongly interacting particles, as is the case for

the doubly charged Higgs boson, the leading order (LO) cross sections are

affected by large uncertainties arising from higher-order (HO) corrections. If

at least the next-to-leading order (NLO) QCD corrections to these processes

are included, the total cross sections can be defined properly. Besides, in this

way the renormalization scale µR, used to define the strong coupling constant,

and the factorization scale µF , used to perform the matching between the

perturbative calculation of the matrix elements and the non perturbative

part which resides in the parton distribution functions (PDFs)14, are fixed

and the generally non-negligible radiative corrections are taken into account.

The parameter, which quantifies the effects of higher-order QCD corrections,

is known as the K-factor. It is defined as the ratio of the cross section for

the process (or its distribution) at HO with the value of αs and the PDFs

evaluated also at HO, over the cross section (or distribution) at LO with αs

and the PDFs consistently also evaluated at LO. In most cases, the K-factor

is defined as the same ratio with the cross section calculated up to NLO

instead to HO, and it can written as [20]:

K =σNLO(qq → XX ′)

σLO(qq → XX ′). (1.34)

In the case of the doubly charged Higgs boson, where the dominant pro-

duction process at hadron colliders is qq → γ∗, Z∗ → Φ++Φ−−, the cross

section of this production mode only depends on the electroweak quan-

tum numbers and the mass of Φ++ states and not on further details of the

model. At both the Tevatron and the LHC, the hadronic cross section for its

pair production can be obtained from convoluting the partonic cross section

14A parton distribution function (PDF) is defined as the probability density for findinga particle with a certain longitudinal momentum fraction x at momentum transfer Q2.Because of the inherent non-perturbative effect in a QCD binding state, parton distributionfunctions cannot be obtained by perturbative QCD. Due to the limitations in presentlattice QCD calculations, the known parton distribution functions are instead obtained byusing experimental data.

22

σLO(q(q) → Φ++Φ−−) with the corresponding (anti)quark densities of the

(anti)protons:

σLO(p(p) → Φ++Φ−−) =

∫ 1

τ0

dτ∑q

dLq(q)

dτσLO(Q2 = τs) , (1.35)

where τ0 = 4m2Φ±±/s with mΦ±± being the lower mass bound of Φ±± and

s the total hadronic c.m. energy squared, Lq(q)denotes the q(q) partonic

luminosity and Q2 is the squared partonic c.m. energy.

The standard QCD corrections, with virtual gluon exchange, gluon emis-

sion and quark emission, modify the lowest order cross section in the following

way:

σ = σLO + ∆σq(q) + ∆σqg , (1.36)

with:

∆σq(q) =αs(µR)

π

∫ 1

τ0

dτ∑q

dLq(q)

dτ

∫ 1

τ0/τ

dzσLO(Q2 = τzs)ωq(q)(z)

∆σqg =αs(µR)

π

∫ 1

τ0

dτ∑q,q

dLqg

dτ

∫ 1

τ0/τ

dzσLO(Q2 = τzs)ωqg(z) (1.37)

where ωq(q)(z) and ωqg(z) are coefficient functions for quark and gluon emis-

sion, respectively, that depend on the probability of a quark emitting a quark

or a gluon, Pq(q)(z) and Pqg(z) [21].

Concerning the two production mechanisms studied at Tevatron and LHC

(see Eqs. 1.32 and 1.33), these have different QCD K-factors. Explicit cal-

culations for qq, qq → Φ++Φ−− give around K = 1.3 at the Tevatron and

K = 1.25 at the LHC, depending on mΦ±± . Actually, the K-factor for

qq′, qq → Φ±±Φ∓ is expected to be very similar (but not identical) to that for

qq, qq → Φ++Φ−−, with some dependence on the mass spitting mΦ±±−mΦ± .

Thus, since the scalar potential of the HTM gives mΦ±± ∼ mΦ± , the K-

factors are assumed to be equal [10].

23

1.4 Doubly charged scalars at the LHC

At the LHC the process

qq → Φ++Φ−− → `+`+`−`− (1.38)

provides a very spectacular signature, namely two like-sign lepton (` = e, µ)

pairs with the same invariant mass and no missing transverse momentum,

which has essentially no Standard Model background. The pair produc-

tion of the doubly charged scalar occurs by the Drell-Yan process qq →γ∗, Z∗ → Φ++Φ−−, with a subdominant contribution also from two-photon

fusion γγ → Φ++Φ−−. The cross section is not suppressed by any small

quantity (such as the Yukawa or triplet VEV) and depends only on the mass

mΦ++ .

The partial decay width for the decay Φ++ → `+i `

+j is given by

Γ(Φ++ → `+i `

+j ) =

1

4π(1 + δij)|Yij|2mΦ++ , (1.39)

with δij = 1 (0) for i = j (i 6= j). Hence, the rate is proportional to the

corresponding element of the neutrino mass matrix |Mij|2. Using Eqs. 1.26

and 1.34, the branching ratio can be expressed as

BRij ≡ BR (Φ++ → `+i `

+j ) ≡

Γ(Φ++ → `+i `

+j )∑

kl Γ(Φ++ → `+k `

+l )

=2

(1 + δij)

|Mij|2∑kl |Mkl|2

,

(1.40)

and therefore by Mij diagonalization and VPMNS unitarity:

∑kl

|Mkl|2 =3∑i=1

m2i =

{3m2

0 + ∆m221 + ∆m2

31 (NH)

3m20 + ∆m2

21 + 2|∆m231| (IH)

. (1.41)

Then, the BR of Φ++ → `+i `

+j depends on the six parameters of the neutrino

mixing matrix, V (see Eq. 1.13), the unknown mass of the lightest neutrino

(m0), the mass splittings of the neutrinos, and the ignorance of the neutrino

mass hierarchy.

In addition to the lepton channel the doubly charged Higgs can in princi-

24

Figure 1.5: Feynman graphs contributing to the production of doubly chargedHiggs boson at LHC.

ple decay also into the following two-body final states including singly charged

Higgs and/or the W :

Φ++ → W+W+, Φ++ → Φ+W+, Φ++ → Φ+Φ+, (1.42)

with the relative Feynman graphs shown in the Fig. 1.5. The last two decay

modes depend on the mass splitting within the triplet. We can assume in

the following that they are kinematically suppressed. The rate for the WW

mode is given by

Γ(Φ++ → W+W+) ≈v2

∆m3Φ++

2πv4, (1.43)

where we have used mΦ++ � mW for full expressions and a discussion of pos-

sibilities to observe this process at LHC. Hence, the branching ratio between

`+`+ and W+W+ decays depends on the relative magnitude of the triplet

Yukawas Yij and the VEV v∆. The requirement Γ(Φ++ → W+W+) �Γ(Φ++ → `+

i `+j ), together with the constraint from Eq. 1.28, implies:

v∆

v. 10−6

(100 GeV

mΦ++

)1/2

. (1.44)

The triplet VEV contributes to the ρ parameter at tree level as ρ ≈ 1 −2(v∆/v)2. The constraint from electroweak precision data ρ = 1.0002+0.0024

−0.0009

at 2σ translates into v∆/v < 0.02, which is satisfied by requiring Eq. 1.40.

It is known that the most stringent constraint on the Yukawa couplings Yij

25

comes from µ→ eee, a process which occurs at tree level via Eq. 1.11. The

branching ratio for this decay is given by:

BR(µ→ eee) =1

4G2F

|Y ∗eeYeµ|2

m4Φ++

≈ 20( mΦ++

100 GeV

)−4

|Y ∗eeYeµ|2 . (1.45)

Hence, the combination |Y ∗eeYeµ|2 . 2× 10−7( mΦ++

100 GeV

)2is constrained by the

experimental bound BR(µ → eee) < 10−12. Assuming that all Yij have

roughly the same order of magnitude, the range of Yukawa couplings can be

estimated as follows:

4× 10−7( mΦ++

100 GeV

)1/2

. Yij . 5× 10−4( mΦ++

100 GeV

), (1.46)

where the lower bound arises from Eq. 1.44 assuming the the bound, given

by Eq. 1.28, is saturated. We can see that several orders of magnitude are

available for Yukawa couplings. For Yij close to the lower bound of Eq. 1.41

the decay Φ±± → W±W± will become observable at LHC, whereas close to

the upper bound a signal in future searches for lepton flavour violation is

expected, where the details depend on the structure of the neutrino mass

matrix. The interval for the Yukawas from Eq. 1.41 implies a triplet VEV

roughly in the keV to MeV range [3][6][22].

26

Chapter 2

The LHC Collider and the

CMS Experiment

The European Organization for Nuclear Research, known as CERN , is an

international organization whose purpose is to operate the world’s largest

particle physics laboratory, which is placed in the immediate vicinity of

Geneva on the Franco-Swiss border. Founded in 1954, the organization has

twenty European member states.

Numerous experiments have been constructed at CERN by international col-

laborations for the purpose of high research. Most of the activities at CERN

are currently oriented to the operation of the Large Hadron Collider (LHC),

and the experiments along it.

2.1 The Large Hadron Collider

The LHC is the world’s largest and highest-energy particle accelerator. It is

located in a circular tunnel, with a circumference of 27 km, at a depth ranging

from 50 to 175 m underground, in the region between the Geneva airport and

the nearby Jura mountains. It is in the same tunnel previously occupied by

LEP which was closed in November 2000. CERN’s existing PS/SPS1 accele-

1The PS is the acronym of Proton Synchrotron, and the SPS means Super ProtonSynchrotron. They are particle accelerators of the synchrotron type at CERN. Startingin November 2009, the PS and SPS machines deliver protons and provide lead ion beamsfor the LHC.

27

Figure 2.1: The LHC accelerator complex.

rator complexes are used to pre-accelerate protons which will then be injected

into the LHC. Four interaction regions were equipped, and host four main

detectors: ALICE (A Large Ion Collider Experiment), ATLAS (A Toroidal

LHC ApparatuS), CMS (Compact Muon Solenoid), and LHCb (beauty) (see

Fig.2.1). Moreover, there are also TOTEM (TOTal Elastic and diffractive

cross section Measurementand) and LHCf (forward), that are smaller and are

designed for very specific research. The two experiments, ATLAS and CMS,

study Standard Model physics processes (electroweak processes, physics of

the top and bottom quarks, ...) and look for hints of physics beyond the

Standard Model. The main goal of them is the search for the Higgs boson,

and/or new particles expected in theories beyond the Standard Model.

28

Figure 2.2: View of the tunnel LHC machine.

2.1.1 LHC structure and features

The LHC [23] is designed for two kinds of collisions: collisions of protons,

and collisions of heavy ions. This section focuses on the case of proton colli-

sions.

The collider tunnel contains two adjacent parallel beam lines (or beam pipes)

that intersect at four points, each containing a proton beam, which travel in

opposite directions around the ring. Since the LHC is a proton accelerator

with a constrained circumference, its maximal energy per beam is related to

the strength of the dipole field which keeps the beam in orbit.

The nominal LHC beam energy of 7 TeV2 is made possible by a global magnet

system that uses a total of about 9600 magnets. Some 1232 dipole magnets

keep the beams on their circular path, while the 392 quadrupole magnets are

used to keep the beams focused, in order to maximize the chances of inte-

21 eV (electron volt) = 1.6× 10−19J

29

raction between the particles in the four intersection points, where the two

beams will cross. In total, over 1600 superconducting magnets are installed,

with most weighing over 27 ton each. Approximately 96 ton of liquid he-

lium is needed to keep the magnets, made of copper-clad niobium-titanium

operating at a temperature of 1.9 K (−271.25 ◦C). At that temperature,

when carrying a current of 11850 A the field of the superconducting dipole

magnets is increased from 0.54 to 8.33 T. Such a magnetic field is necessary

to bend the 7 TeV beams around the ring of the LHC. The curvilinear re-

gions are provided with radio-frequency cavities cooled to a temperature of

4.5 K. In these regions, electrical fields with a strength between 3 MVm−1

and 16 MVm−1 give the energy necessary to compensate for the energy loss

due to synchrotron radiation. Each proton beam has an energy of 7 TeV,

giving a total collision energy of 14 TeV (centre-of-mass energy). At this

energy the protons have a Lorentz factor of about 7500 and move at about

0.999999991 c, or about 3 metres per second slower than the speed of light (c).

Rather than continuous beams, the protons are accelerated into 2808 bunches,

so that interactions between the two beams, containing ∼ 1011 protons, take

place at discrete intervals never shorter than 25 nanoseconds (ns) (bunch

spacings). They provide a good time resolution (few ns), in order to di-

stinguish the events from two consecutive bunch crossing. For this reason, a

precise synchronization of all detector is requested. A bunch collision rate of

40 MHz is reached at LHC.

The LHC [24] is designed with two rings: two separate magnet fields

and vacuum chambers, in a twin-bore magnet design. The only common

sections are located at the insertion regions, equipped with the experimental

detectors. Before reaching at the LHC, the proton beams run across a chain

of acceleration (see Fig.2.3): it starts from a linear accelerator (LINAC) that

generates 50 MeV protons and injects them to the PSB3. There the protons

are accelerated to 1.4 GeV and injected into the PS, where they reach an

3The PSB is the acronym of Proton Synchrotron Booster, the first and smallest circularproton accelerator in the accelerator chain at the CERN Large Hadron Collider injectioncomplex. It was built in 1972, and contains four superimposed rings with a radius of 25meters. It receives protons from the linear accelerator Linac2 and accelerates them, toinjected them finally into the PS.

30

Figure 2.3: Chain of LHC injection.

energy of 26 GeV. In the following stage, the SPS accelerates the beams to

450 GeV before they are injected (over a period of 20 minutes) into the main

ring of LHC. Here the proton bunches are accumulated, accelerated (over a

period of 20 minutes) to their peak 7 TeV energy, and finally circulated for

10 to 24 hours while collisions occur at the four intersection points.

In addition to the centre-of-mass energy, provided by the accelerator,

another important quantity is the luminosity L4, which depends only on the

machine features, and carries out its construction.

In the general case of two colliding beams, the luminosity L is written as

follows:

L = fnbN1N2

A, (2.1)

where f is the revolution frequency, nb is the number of bunches per beam,

Ni is the number of particles in the bunches of each colliding beam, and A

4There are two kinds of luminosity: instantaneous luminosity and integrated luminosity.The instantaneous luminosity L is given by the relationship dN

dt = σL, where dNdt is the

event rate and σ is the cross section of the interaction. The integrated luminosity L isthe integral of the instantaneous luminosity over time, L =

∫Ldt. While the former

is measured in barn−1× second−1, the latter is measured in barn−1, where 1 barn =10−28cm2.

31

is the cross section of the beams. At LHC, the bunches are filled with an

identical number of protons, then we can write N1 = N2 = Nb.

The beam cross section is defined as:

A = 4πεnβ∗

γ, (2.2)

where εn is the normalized transverse beam emittance5 (with a design value

of 3.75 µm), β∗ is the beta function at collision point6, and γ is the Lorentz

relativistic factor. A further correction is required in Eq. 2.1 to account for

the geometric luminosity reduction factor, F , related to the fact that the two

beams cross at an angle at the interaction point:

L =fnbN

2b γ

4πεnβ?F. (2.3)

2.1.2 Experimental requirements

The nominal value for the luminosity, as well as the other parameters of

the LHC collider are summarized in Table 2.1. This value can be reached

with a number of bunches per beam nb = 2808 and a number of protons per

bunch Nb = 1.15 · 1011. As a high beam intensity could not be reached with

antiproton beams, a simple particle-antiparticle accelerator collider configu-

ration cannot be used at LHC.

The luminosity lifetime is an important parameter at LHC. Since the

intensities and emittances of the circulating and colliding beams degrade, the

luminosity tends to decay during a physics run. Under nominal conditions,

the LHC produces 109 inelastic collision events per second at a bunch crossing

rate of 40 MHz (i.e. a bunch crossing spacing of 25 ns), with approximately

20 collision events expected per bunch crossing. Though the very important

computing and storage facilities, events can only be recorded at a rate of

about 300 Hz. Therefore, an online selection system is necessary to determine

in a very small amount of time whether an event is worth being recorded.

5Emittance is a measure for the average spread of particles in the position-and-momentum phase space.

6It measures the beam focalization.

32

Cironference 26.659 kmCenter-of-mass energy (

√s) 14 TeV

Nominal Luminosity (L) 1034 cm−2s−1

Luminosity lifetime 15 hrs.Time between two bunch crossings 24.95 nsDistance between two bunches 7.48 mLongitudinal max. size of a bunch 7.55 cmNumber of bunches (nb) 2808Number of protons per bunch (Nb) 1.15× 1011

beta function at impact point (β?) 0.55 mTransverse RMS beam size at impact point (σ?) 16.7 µmDipole field at 7 TeV (B) 8.33 TDipole temperature (T) 1.9 K

Table 2.1: List of the nominal LHC parameters, with their values.

This system must be fast and very selective to reduce the event rate by

seven orders of magnitude. Finally, it must keep a very high efficiency on

interesting collision events.

A significant number of inelastic collisions, due to the large number of

protons per bunch, are expected to occur at each crossing, corresponding to

an average of 1000 particles per bunch crossing. In order to distinguish such

events from one another, a large number of detector channels are needed

because a high granularity is mandatory and a precise momentum measure-

ments is necessary.

Moreover, the detector must provide a fast response with a good time resolu-

tion, in order to distinguish the events from two consecutive bunch crossings.

This requires a precise synchronization of all detector channels. The limit

where two consecutive signals start to overlap is called out-of-time pile-up.

It affects the shape of the signal, which is typically a few bunch crossings,

and must be taken into account.

2.2 The Compact Muon Solenoid Detector

The CMS detector is one of the experiments currently running at the

LHC at CERN. The main purpose of the CMS experiment is to search for

the evidence of the Higgs boson and new physics. To achieve these goals,

the experiment was designed to provide extensive information in terms of

33

Figure 2.4: The CMS coordinate system.

particle identification with high spatial resolution.

2.2.1 Coordinate System

The system of coordinates used for the CMS detector is illustrated in

Fig. 2.4.

The detector [25] has a cylindrical shape around the beam axis (z axis). The

origin is centered at the nominal collision point inside the experiment: the x

axis points horizontally towards the center of the LHC, and the y axis points

vertically upwards, so the z longitudinal axis, horizontal and collinear to the

beam trajectory, points towards the Jura mountain.

In the transverse (x, y) plane, the azimuthal angle φ is measured from the

x axis and the radial coordinate is denoted r. The polar angle θ is measured

from the z axis. In experimental particle physics, the pseudorapidity η, de-

fined as η = − ln tan(θ/2), is used to describe the angle of a particle relative

to the beam axis. Hence, the direction of a particle trajectory at production

point is described by the coordinates (η, φ). The η coordinate is an important

variable because divides the subdetectors in two parts: the “barrel” and the

34

“endcaps”. The first one corresponds to the central, cylindrical region. The

last ones consist of the two discs at the extremities that close the detector

along the beam axis.

In an inelastic collision event between two partons coming from the pro-

tons, their energy is an unknown fraction of the proton energy, so the collision

energy is not fixed. However, the parton momentum, before the collision, is

expected to be longitudinal (along the beam axis): the transverse momen-

tum of each parton being negligible. Since the total transverse momentum

is conserved during an interaction, the transverse momentum of the collision

is expected to be negligible too.

A particle escaping the detection creates an unbalance in the total transverse

energy measurement, called missing transverse energy. If the detector is her-

metic, this missing transverse energy can be interpreted as the transverse

energy of the particles that the detector is not able to measure, such as

neutrinos.

2.2.2 CMS structure

The CMS [26] makes use of several subdetector systems (see Fig. 2.5)

to provide both spatial track location (precise measurement of particle mo-

mentum) and high resolution energy detection. The main subdetectors are

the two calorimeters and the tracking system. Electromagnetic particles are

stopped and measured in the first one; hadronic particles are measured in

both and stopped in the second one. In addition, an inner tracking de-

vice measures the trajectories of all charged particles, while an outer device

measures the charged particles that crossed both calorimeters, i.e. muons.

Finally, the tracking devices are submitted to a magnetic field that curve the

trajectories of charged particles.

In the design of the CMS detector, a particular attention is given to

muons: unlike other detectable particles, their energy can not be measured

by any of the calorimeters; this measurement only relies on the curvatures

of the tracks in the two tracking devices. The degree of curvature of the

trajectory of a particle decreases when its transverse momentum increases,

35

Figure 2.5: A perspective view of the CMS detector.

making the charge and pT measurements more difficult. So, a measurement

of the momentum is performed by analyzing the track bending under the

effect of the 3.8 T magnetic field provided by the superconducting solenoid

magnet which interleaves the detector systems. The flux is returned through

a 12500 ton iron yoke comprising 5 wheels and 2 endcaps, composed of three

discs each.

A longitudinal section view of the layout of the CMS detector is given in

Fig. 2.6, where the origin denotes the interaction point (IP), and the angle

specifications on the top and left are given in units of η.

2.2.3 Inner Tracking System

The CMS tracker [27] is a fundamental tool for the charge and momentum

measurements on charged particles. Surrounding the interaction point, it has

a length of 5.8 m and a diameter of 2.5 m, and covers a pseudorapidity range

of |η| < 2.5.

The CMS tracker is a full-silicon tracking system, made of a very resistant

36

Figure 2.6: Longitudinal section view of one quadrant of the CMS detector.

material to radiation, because of its position around the collision point. It

uses different technologies for achieving the requirements needed for vertex

identification7:

• requirements of high granularity and fast shaping;

• compactness allowing spatial measurements close to the interaction

point;

• necessity to operate in harsh environment, and requirement of high

reliability due to the extremely limited possibility to do maintenance

on the tracker itself.

The CMS silicon tracker is the most extended silicon tracker ever built for a

high energy physics experiment. However, it has some disadvantages:

1. an efficient cooling system is necessary because of the high power den-

sity of detector electronics;

7Besides the primary vertex, which corresponds to the IP of the spotted collision,secondary vertices can indicate another interaction that occurred during the same bunchcrossing (pile-up), or the late decay of a particle.

37

2. complications in the reconstruction of particles crossing the tracker

and loss of efficiency and precision, due to their interactions with high

amount of dense material.

The high number of particles crossing the tracker results in a high hit

density, which decreases when the distance to the center increases. So, the

granularity is dictated by the expected hit density of a given region.

The tracker is constituted by two different tracking subdetectors:

• a silicon pixel tracker;

• a silicon strip tracker;

Each of the detectors is then composed of different sections in order to ma-

ximize the η coverage, i.e. a barrel region covering the low pseudorapidity

region and two endcaps (see Fig. 2.7), one for each side, allowing high reso-

lution tracking of tracks with high pseudorapidity.

Figure 2.7: The CMS pixel detector.

The innermost part of the tracker is constituted by the pixel detector.

A schematic view of the different layers constituting the barrel and the two

endcaps is provided in Fig. 2.8, in which the schematic cross section through

38

the CMS tracker is illustrated. The pixel detector contains barrel and endcap

modules; the silicon strip detector contains two collections of barrel modules:

the Tracker Inner Barrel (TIB) and the Tracker Outer Barrel (TOB), and

two collections of endcap modules: the Tracker Inner Disc (TID) and the

Tracker EndCaps (TEC).

Figure 2.8: Schematic cross section through the CMS tracker.

The outermost part of the tracker is made of silicon strips; thicker silicon

sensors are used for this region. To prevent risks of thermal runaway, the

silicon tracker is coupled to a cooling system operating only at a temperature

below −10◦ C.

2.2.4 Electromagnetic Calorimeter

The Electromagnetic Calorimeter [28] (ECAL) was designed according

to the requirements of the search of the Higgs boson in two photons, H →γγ. It is the only subdetector to provide information about photons. For

a precise diphoton mass reconstruction, a very precise position and energy

measurement must be provided by the ECAL. The ECAL is also of primary

importance for the electron reconstruction in a Higgs boson analysis in a

39

multi-lepton final state. The combination of its information with the one

from the tracker ensures a very precise measurement of electron position and

momentum, and a significant background rejection. A good segmentation

is essential to distinguish the energy deposit shape of an electromagnetic

particle, from the one of a hadronic particle.

The CMS ECAL is a hermetic and homogeneous calorimeter, that covers

the pseudorapidity range of |η| < 3. It is made of 75848 lead tungstate

crystals, mounted in a barrel (|η| < 1.479) and two endcaps (1.479 < |η| <3). The crystals are followed by photodetectors that read and amplify their

scintillation. While in the barrel avalanche photodiodes (APDs) are used, in

the endcaps vacuum phototriodes (VPTs) are necessary to obtain a higher

resistivity to radiation.

The pion population is particularly important in the forward region, and

the decay π0 → γγ, with two photons very close to each others, is quite

difficult to distinguish from a single photon. For a better photon identifica-

tion, a preshower detector (with a thickness of 20 cm) is made of two parts

located at both ends of the tracker, in front of the ECAL endcaps, in the

pseudorapidity range 1.653 < |η| < 2.6 (see Fig. 2.9). Its absorber, made of

Figure 2.9: Longitudinal view of part of the CMS ECAL showing the ECALbarrel and a ECAL endcap, with the preshower in front.

40

lead radiators, causes electrons and muons to produce electromagnetic sho-

wers. Behind each radiator, two layers of silicon strip sensors are located,

with orthogonal orientation. These sensors measure the deposited energy

and the transverse shower profiles for better identification of electromagnetic

particles.

An electron or a photon emitted in the direction of the preshower deposits

5% of its energy in the preshower, and the rest in the ECAL endcap.

The choice of lead tungstate crystals is driven by some constraints as-

signed by the CMS detector design:

1. compactness of ECAL in order to include both calorimeters inside the

magnet;

2. good separability of electromagnetic showers due to the smallness of

Moliere radius8 (2.2 cm) of lead tungstate;

3. short time of scintillation decay of the crystal, necessary for the context

of LHC collision.

The ECAL barrel is made of 36 identical Supermodules, each covering

half the barrel length (−1.479 < η < 0 or 0 < η < 1.479), with a width

of 20 in φ. Each Supermodule is made of four Modules in the η direction

(see Fig. 2.10). The energy reconstruction is affected by the presence of

acceptance gaps, called cracks, between Modules. A larger crack is at η =

0 between Supermodules, and an even larger one marks the barrel-endcap

transition. Each ECAL endcap is made of two semi-circular plates called

Dees (Fig. 2.10). Small cracks are also present between the endcap Dees,

but they can be assumed negligible.

The energy loss is measured by comparing the energy measured in the

ECAL with the momentum measured in the tracker on electrons with lit-

8The Moliere radius Rµ is a characteristic constant of a material, giving the scale ofthe transverse dimension of the fully contained electromagnetic showers initiated by anincident high energy electron or photon. It is defined as the mean deflexion of an electronof critical energy after crossing a width 1X0, where X0 is defined as the radiation length,i.e. the average distance covered by an electron in a material through which it loose afraction of its energy equal to 1/e. A cylinder of radius Rµ contains on average 90% ofthe shower energy deposition.

41

Figure 2.10: Layout of the CMS ECAL showing the arrangement of crystalmoduls, supermodules and endcaps, with the preshower in front.

tle Bremsstrahlung, considering that the difference is due to energy loss in

cracks. In order to cancel these losses, a recovery method is applied for all

gaps, except at η = 0 and the barrel-endcap transition, where energy losses

are 5% and 10%, respectively.

The energy resolution has been measured on one barrel supermodule, using

incident electrons, during a beam test in 2004 [29]. It is made of a stochastic,

a noise and a constant contribution:(σ(E)

E

)2

=

(2.8%√E

)⊕(

0.12%

E

)2

+ (0.30%)2. (2.4)

and the result is shown in Fig. 2.11. A resolution higher than 1% is achieved

for electrons of energy higher than 15 GeV; for 40 GeV electrons it is of 0.6%.

42

Figure 2.11: ECAL barrel energy resolution, σ(E)/E, as a function of elec-tron energy as measured from a beam test. The points correspond to eventstaken restricting the incident beam to a narrow (4 × 4 mm2) region. Thestochastic (S), noise (N), and constant (C) terms are given.

2.2.5 Hadron Calorimeter

The CMS hadron calorimeter (HCAL) is located behind the tracker and the

ECAL as seen from the interaction point. It is designed to do measurements

about hadron jets and single hadrons. Hence, it has:

• to provide a sufficient containment to stop hadron showers;

• to have a wide extension in |η| for a precise description of the total

collision event, a reliable measurement of the missing transverse energy.

The HCAL measurement is very useful to distinguish electrons from hadron

jets. It is a sampling calorimeter, that is made of a barrel part (HB), cove-

ring the region with |η| < 1.3, and an endcap part (HE), complementing the

barrel coverage to |η| < 3.0. In order to enhance the HCAL performance, it

is completed by two other calorimeters: the outer calorimeter (HO), that im-

proves the efficiency of the barrel region, and the forward hadron calorimeter

(HF), that covers the region 3.0 < |η| < 5.0 (see Fig 2.12).

43

HF

HE

HB

HO

Figure 2.12: Section view of the HCAL detector.

The HB effective thickness increases with polar angle (θ) as 1/ sin θ. It

results in 10.6 λI at η = 1.3, where λI is the radiation lenght9. The HO

uses the solenoid coil as an additional absorber equal to 1.4/ sin θ interaction

lengths and is used to identify late starting showers and to measure the shower

energy deposited after HB. The material in the HCAL endcaps must cope

with the radiation, and handle high counting rates. Because of the magnetic

field, the absorber must be made from a non-magnetic material. Finally,

the HE has to fully contain hadronic showers. The calorimeter barrel energy

resolution (EB+HB+HO) has been measured on pions which energy varies

in a range of 3-500 GeV by test beams. It has been found to be:(σ(E)

E

)=

(84.7%√

E

)⊕ 7.4%. (2.5)

It can be observed that the energy resolution is dominated by the HCAL

contribution.

9Nuclear interaction length is defined as the mean path length in which the energy ofrelativistic charged hadrons is reduced by the factor of 1/e as they pass through matter.

44

2.2.6 Muon System

The outer detector of the CMS experiment is dedicated to the detection of

muons [30]. Its design allows to identify efficiently muons momenta from a

few GeV to a few TeV. The W and Z production in the Higgs decay requires

also to have a coverage of the large pseudorapidity interval.

The muon detector is made of a cylindrical barrel and two endcaps, and is

interleaved with the return yoke of the superconducting magnet. In this case

too, the barrel region is an easier case than the endcaps: less background,

a low muon rate and an uniform 3.8 T magnetic field, mostly contained in

the steel yoke. Three different detector technologies were used in the muon

detector:

• Drift Tubes (DT): used in the barrel region (|η| <1.3);

• Cathode Strip Chambers (CSC): used in the endcap region (0.9<

|η| < 2.4);

• Resistive Plate Chambers (RPC): used in both the barrel and endcap

region (|η| < 1.6).

The DTs chambers measure the muon coordinate in the (r, φ) bending plane

and are alternate with chambers providing a measurement in the z direction.

The presence of “cracks”, i.e. dead spots in efficiency between the chambers,

is the main problem of this design, solved by an offset of the drift cells bet-

ween neighbor chambers.

In CSCs the chambers are positioned perpendicular to the beam line and

provide a precision measurement in the (r, φ) bending plane, whereas the a-

node wires provide measurements of η and the beam crossing time of a muon.

Efficient tools are used to reject non-muon backgrounds and match hits to

those in the other stations and in the CMS inner tracker.

An additional system of RPCs is placed both in the barrel and endcap regions.

These are double-gap chambers, operated in avalanche mode to ensure good

operation at high rates. They produce a fast response with good time reso-

lution but coarser position resolution than the DTs or CSCs. They provide

45

an independent trigger system with good time resolution, and a reduction

of ambiguities in the track reconstruction due to multiple hits in a cham-

ber. Finally, the muon momentum resolution is optimized by a sophisticated

alignment system, that measures the positions of the muon detectors with

respect to each other and to the inner tracker.

Figure 2.13: Section view of the Muon System: DT, RPC and CSC.

2.2.7 Trigger

The trigger system is the first step of the physics event selection process

with the purpose to reduce the data of the 40 MHz event rate down to about

300 Hz, which is the maximum amount that can be stored for offline analysis.

Hence, it performs a fast selection of events likely to be interesting for physics

analysis, among the huge amount of events produced by LHC collisions. The

selection is divided in two steps called Level-1 Trigger (L1) and High-Level

46

Trigger (HLT).

Level-1 Trigger

The L1 Trigger is a hardware system made of largely programmable electro-

nics, that provides a first rate reduction to 100 kHz in a time range of 32 µs.

To satisfy this timing constraint, it considers coarse granularity objects from

the calorimeters and the muon system. No tracker information is used during

the L1 Trigger. During this time range, the event information is stored in

so-called pipelines.

The Fig. 2.14 shows the L1 Trigger architecture: it is divided in two

parallel trigger system, one corresponding to the calorimeters, the other to

the muon system. Each system is based on a local, a regional and a global

part, after which they are merged into a Global Trigger for the final L1

decision. Several categories of Level-1 Trigger candidates are created:

Figure 2.14: Architecture of the Level-1 Trigger.

47

• Muon, built in the Muon Trigger;

• Electron/Photon, (isolated and not-isolated, e/γ);

• Tau, built in the Regional Calorimeter Trigger;

• Jet, central and forward;

• Total Transverse Energy (ΣET ), Missing Transverse Energy (EmissT ),

Scalar Transverse Energy Sum of all Jets (above a given threshold,

HT ), built in the Global Calorimeter Trigger.

Local Triggers : on each subdetector, they create coarse granularity in-

formation. In the calorimeters, this information is a collection of Trigger

Primitives.

Regional Triggers : it collects local information in order to build L1 Trig-

ger candidates and combines the information of both calorimeters or muon

system and sends them to the Global Calorimeter Trigger or the Global Muon

Trigger, respectively.

Global Calorimeter Trigger and Global Muon Trigger : the former sorts

the L1 Trigger candidates to send the four most relevant ones of each category

to the Global Trigger; the latter collects and compares the candidates from

Regional Triggers, then it combines them into four Muon candidates and

sends them to the Global Trigger.

Global Trigger : it collects the candidates produced by the Global Calori-

meter Trigger and Global Muon Trigger, and compares them to the Level-1

Trigger Menu10. If the candidate collection satisfies at least one of the listed

triggers, the L1 Trigger decision is positive and the fine granularity event

information is sent to the High-Level Trigger. Some trigger rules are also

applied at that step, to prevent any memory overload.

High Level Trigger

The High Level Trigger builds candidates corresponding to all kinds of re-

constructed objects considered in the offline analysis. Its inner substructure

10The Level-1 Trigger Menu is a list of Level-1 enabled triggers.

48

consists of several steps of increasing complexity, starting at Level-2.

The L2 starts generally with the Level-1 Trigger information, and builds fine

granularity objects around the L1 candidates, using only information from

the calorimeters and muon system. The tracker information is used, when

necessary, in order to pass on the next level: Level-2.5.

The HLT sorts the selected events into several datasets with a little overlap

as possible, accepting an event that passes at least one of these trigger se-

lection, flagging it according to the passed selections and recording it in the

corresponding datasets.

2.3 Physics Objects: Event Reconstruction

The starting point for physics analyses in CMS is based on the recon-

struction of high-level physics objects which correspond to particles travel-

ling through the detector after collisions. In this section, we will describe the

different types of high-level objects and the algorithms used by CMS for the

identification and reconstruction of these objects.

The signal of a particle going through the material of the detectors is recorded

and reconstructed as individual points in space known as recHits. In order to

reconstruct a physical particle, the recHits are associated together to deter-

mine points on the particle trajectory. The characteristics of the trajectory

are then used to define its momentum, charge, and particle identification.

2.3.1 Particle Flow

Particle Flow (PF) [31] is an algorithm used to reconstruct the physics

objects. It handles all information obtained from all subdetectors and re-

constructs the events by identifying objects as muons, electrons, photons

(converted or not), charged hadrons and neutral hadrons. Then, the list of

object/particles is used to build jets (from which the quark and gluon ener-

gies and directions are inferred), to determine the missing transverse energy

EmissT (see Sec. 2.2.1), to reconstruct and identify taus from their decay pro-

ducts, to quantify charged lepton isolation with respect to other particles, to

49

tag b jets, etc.

The PF includes an iterative algorithm for the reconstruction of the tracks

in order to obtain a high tracking efficiency and a low fake rate. Since the

purpose of the iterative algorithm is to generate tracks, it analyzes the hits

from the position sensitive detectors, giving rise to a seed. The procedure to

form tracks consists of the following steps [32]:

1. Trajectory Seeding: the track reconstruction starts by using an e-

stimate trajectory state or set of hits that are compatible with the

assumed physics process, in particular in CMS it is assumed that they

are compatible with the beam spot to provide the initial vector. Addi-

tional requirements are that the seed direction undergoes certain crite-

ria, or that the hits have to be located in a certain geometric region of

the detector.

2. Trajectory Building: the track reconstruction proceeds in the direc-

tion specified by the seed to locate compatible hits on the subsequent

detector layers. An algorithm, called Kalman Filter 11 is used to find

and fit the track: the full knowledge of the track parameters at each

detector layer provides compatible measurements in the next detector

layer, forming combinatorial trees of track candidates.

3. Trajectory Cleaning: trajectory building produces a large number of

trajectories, many of which share a large fraction of their hits. This step

resolves ambiguities among the possible trajectories keeping a maxi-

mum number of track candidates.

4. Trajectory Smoothing: a backward fitting (smoothing) allows the use

of all covariance matrices to be applied to all the intermediate points

based on all measurements used so far. This step reduces constraints

on the vertex, which allows the reconstruction of secondary charged

particles originating from photon conversions and nuclear interactions

in the tracker material and from the decay of long-lived particles.

11The Kalman Filter is a mathematical method which produces estimates of the truevalues of measurements by predicting a value, estimating the uncertainty of the predictedvalue, and computing a weighted average of the predicted value and measured value.

50

Figure 2.15: Scheme of the Particle Flow algorithm.

Calorimeter Clustering

The Calorimeter Clustering [31] is an algorithm which allows

• to detect and measure the energy and direction of stable neutral par-

ticles such as photons and neutral hadrons;

• to separate these neutral particles from energy deposits from charged

hadrons;

• to reconstruct and identify electrons and all accompanying Bremsstra-

hlung photons;

• to help the energy measurement of charged hadrons for which the track

parameters were not determined accurately, which is the case for low-

quality, or high-pT tracks.

Therefore, a specific clustering algorithm has been developed for the Particle

Flow event reconstruction; its main purpose is a high detection efficiency even

for low-energy particles, and a separation of close energy deposits. The clu-

stering is performed separately in each subdetector. The algorithm consists

of three steps:

1. identification of “cluster seed” as local calorimeter-cell energy maxima

above a given energy;

51

2. increase of ”topological clusters” from the seeds by aggregating cells

with at least one side in common with a cell already in the cluster and

with an energy in excess of a given threshold;

3. generation of “Particle Flow clusters” as seeds from topological clusters.

Link algorithm

In general, a given particle is expected to generate several Particle Flow e-

lements in the CMS subdetectors [31]: one charged-particle track, and/or

several calorimeter clusters, and/or one muon track. In order to relate these

elements to each other, a link algorithm is used to fully reconstruct each

single particle and remove any possible double counting from different detec-

tors.

This particular algorithm is performed for each pair of elements in the event

and defines a distance between any two linked elements to quantify the qua-

lity of the link. Then, it produces blocks of elements linked directly or

indirectly. These blocks typically contain only one, two or three elements,

owing to the granularity of the CMS detectors. The independence of the

algorithm performance from the event complexity is due to the smallness of

the blocks. A link between a charged-particle track and a calorimeter cluster

occurs as follows: the track is extrapolated from its last measured hit in the

tracker firstly to the two layers of the PS (Silicon-Strip Pre-shower), then to

the ECAL and finally to the HCAL.

The first reconstructed particles are muons: tracks and clusters, that are

associated with segments in the muon chambers, are labeled as muons and

deleted from the list of objects that are not associated. Similarly, if the

tracks and the clusters are compatible with the topological characteristics of

an electron, the electron is detected. Then charged hadrons are identified.

After having assigned the HCAL cluster to a track, a comparison is made

between the energy of the cluster and the momentum of the track. If there

is compatibility between the two, a charged hadron with energy given by

the weighted average of the cluster energy and momentum of the track is

52

created. Conversely, if there is a difference between the energy of the cluster

and the momentum of the track, then the block is labeled as neutral hadron.

The same procedure is repeated if there are clusters of ECAL and HCAL

associated to a track. When the associations are completed, only ECAL and

HCAL clusters remain that are not related to each other neither to a track;

they are respectively associated with photons and neutral hadrons.

More details about muon, electron and tau reconstructions are in the next

subsections.

2.3.2 Muons

The reconstruction of muons is performed by combining tracking and

calorimeter information [32] that implies an increase in performance time of

the reconstruction procedure. Muon reconstruction requires a good detec-

tion of muons over the full acceptance of the CMS detector and over the very

high background rate expected at the LHC with full luminosity. The chain of

muon reconstruction occurs in the following three steps: Local Reconstruc-

tion, Standalone, Global and Tracker Muon Reconstruction.

Local Reconstruction

The first step of muon reconstruction uses hits in the muon detectors. There-

fore, during the Local Reconstruction, only information coming from the

DTs, CSCs and RPCs are used. The muon system has three functions: muon

identification, momentum measurement, and triggering over the entire kine-

matic range of the LHC. A high-field solenoidal magnet and its flux-return

yoke make allow for an excellent muon momentum resolution and trigger

capability.

The reconstruction starts from the identification of hits involved in the cros-

sing of the particle and proceeds by creating segments according techniques

which depend on the considered subdetector.

By using algorithms that provide the hit spatial resolution for the particle

from the drift time12, in the DTs, two hits from different layers are selected,

12There are two types of algorithms which make this time-position conversion: the first

53

starting from the most distant ones. The hit pair is accepted if the incidence

angle of the relative segment is compatible with a track that points toward

the vertex of the nominal interaction point. Then, the hits compatible with

this segment are sought in the other layers and the good segments are only

those for which we have nhits > 3 and χ2/ndof < 20. Hence, the two

orthogonal projections, (r, φ) and (r, z), are arranged in order to have the

tridimensional track. The low expected rate and the relatively low strength

of the local magnetic field, which is also relatively uniform, allow to use the

drift chambers as tracking detectors for the barrel muon system.

In the CSCs, the information from cathode strips and anode wires are

arranged. Since the charge given by the passing of a ionizing particle has a

distribution that involves 3-5 strips, the geometric center of this distribution

is considered to identify the most likely passing point of the particle. An

algorithm like that described for the DTs is used to build a track segment

in each CSC, starting from the two extreme hits in the first and in the last

layer.

In both the barrel and the endcaps, the RPCs are used as part of the

trigger. The RPC consists of two gas chambers in which an ionizing particle

develops an electron avalanche picked up a read out strip in contact with the

anode. Therefore, this subdetector is able to tag the time of an ionizing event

in a much shorter time than the 25 ns between two consecutive LHC bunch

crossings. Hence, a fast appropriate muon trigger device based on RPCs can

identify unambiguously the relevant bunch crossing to which a muon track

is associated even in the presence of the high rate and background expected

at the LHC. After collecting the strips, where a signal has been generated

(clustering), and created a sets of strips, a centre of gravity of the cluster in

the RPCs, namely the reconstructed hit, is established.

one works with a constant drift velocity; the second one works with a velocity depending onthe drift time, the magnetic field and the incidence angle relative to the normal directionof the cell.

54

Standalone Muon Reconstruction

The segments obtained from the local reconstruction are the starting points

for the track fit by the Kalman algorithm (see Subsec. 2.3.1) in the offline

reconstruction and the trajectory parameters estimated by the Level-1 Trig-

ger in the online.

The track reconstruction occurs in the following stages [33]:

1. Seed Generation, in which the clusters are combined in seeds. The seed

generation allows to identify good candidates in order to completely

reconstruct the track.

2. Pattern Recognition, in which the track reconstruction occurs by means

of the Kalman Filter, that starts from a seed and moves iteratively

updating the trajectory parameters at each step. The information pro-

vided by the seeds and by each layer of the outer subdetectors is com-

bined in order to improve the precision on the track parameters.

3. Ambiguity Resolution, which takes into account the possibility that

more than one track shares the same hits to avoid double counting of

tracks. This type of procedure is first applied to all tracks from the

same seed and then to all the reconstructed tracks.

4. Track Fitting, in which the track is refitted by a Kalman filter, starting

from the inner subdetectors. Once the hits are fitted and the fake tra-

jectory removed, the remaining tracks are extrapolated to the point of

closest approach to the beam line. The final fit of the track is achieved

by a constraint to the nominal IP in order to improve the pT resolution.

The resulting reconstructed track in the muon spectrometer is so called “stan-

dalone muon”.

Global Muon Reconstruction

In this stage, the trajectories given by the muon system are extended by

the tracker hits. The algorithm starts from a standalone muon and then

develops the trajectory in the outer detectors according to the equations

55

which describe the motion of a charged particle in a magnetic field and taking

into account the Coulomb multiple scattering and the loss of energy through

material.

While at low pT , the best momentum resolution for muons is obtained from

the silicon tracker, at higher pT the improvement of the muon momentum

resolution is obtained by combining the muon track from the silicon detector,

the so called “tracker track”, with the muon track from the muon system, the

standalone muon, into a “global muon”. The reconstruction of global muon

tracks begins after the complete reconstruction of the central tracker tracks

and the muon system tracks. The first step is to identify the silicon tracker

track to combine with the standalone muon track. This process of choosing

tracker tracks to be combined with standalone muon tracks is referred to as

track matching. The method of track matching proceeds in two steps:

1. definition of a region of interest that is rectangular in (η, φ) space, and

selection of a subset of tracker tracks located in this region of interest;

2. iteration over the subset of the tracker tracks and application of more

stringent spatial and momentum matching criteria to choose the best

tracker track to combine with the standalone muon.

Tracker Muon Reconstruction

The muon track reconstruction algorithm described in previous sections starts

from the muon system and combines standalone muon tracks with tracker

tracks. If in the muon detector the quality of muon track is high, this method

works well. However, in some cases the hit and segment information in the

muon system is minimal, and standalone muon reconstruction fails. Hence,

a complementary method is introduced to consider all silicon tracker tracks

and to identify them as muons by looking for compatible signatures in the

calorimeters and in the muon system. Muons identified with this approach

are called “tracker muons”.

The main purpose of this algorithm is to reconstruct and identify muons in

CMS starting from a silicon tracker track and then searching for a compatible

segments in the muon detectors. The energy deposition in the calorimeter

56

can also be used for muon identification. All relevant information are col-

lected and stored by the algorithm into a final “muon object”. No combined

(silicon-hits + muon-hits) track fit is performed. Thus, the momentum vector

of a tracker muon is the same as that of the silicon tracker track. However, if

a global muon is reconstructed using the same silicon tracker track, the global

muon fit is stored in the same muon object and the default momentum of

the muon in the object is taken from the global muon fit. At this stage of

reconstruction, it is still possible to retrieve the momentum of the silicon

tracker track fit through the reference to the silicon tracker track which is

stored in the muon object.

The final output from the algorithms is a muon physics object together with

a compatibility value indicating the probability of the track being a muon.

2.3.3 Electrons

The electron footprints can have a complex topology, involving Bremsstra-

hlung photons that may convert into electron-positron pairs; the final parti-

cles are spread in the φ direction by effect of the 3.8 T magnetic field.

The reconstruction of electrons in CMS [34] use algorithms developed in

order to ensure a good reconstruction efficiency and high precision for the

measurement of the energy and the direction at vertex. It starts by the recon-

struction of clusters seeded by hot cells in the ECAL, and uses them to form

clusters of clusters (superclusters) to further collect the energy radiated by

Bremsstrahlung in the tracker volume. Then, the superclusters are used to

select trajectory seeds built from the combination of hits from the innermost

tracker layers. A primary superclusters preselection is performed by using a

hadronic veto cut, given by the H/E ratio (H is the hadronic energy and E is

the supercluster energy) and applying a 4 GeV threshold on the supercluster

transverse energy.

The ECAL is the essential detector to estimate the electron energy from the

deposits issued by the electromagnetic showers that are produced by elec-

trons. However, a spread in φ of the energy deposit in the calorimeter is due

to the material before the ECAL which can trigger a Bremsstrahlung process,

57

and the high magnetic field of CMS. Hence, algorithms of superclusters are

considered in order to take into account these factors. The reconstruction of

electron seeds is carried out by two seeding algorithms, an ECAL driven and

a tracker driven, that are combined into a single collection, keeping track of

the seed provenance.

Then, the electron tracks are reconstructed from electron seeds by following a

fitting procedure that takes into account the effect of Bremsstrahlung energy

loss. The hits collected in this step are passed to a Gaussian Sum Filter

(GSF)13 for the final estimation of the track parameters.

Finally, the electron candidates are built from the tracks reconstructed by

the GSF and their associated superclusters. They undergo a loose prese-

lection to reduce the rate of jets faking electrons and a further selection to

reduce ambiguous electron candidates, that arise from the reconstruction of

conversion legs from photon(s) radiated by primary electrons.

2.3.4 Taus

Tau leptons decay into other leptons about 17% of the times, while the

rest of the decays is hadronic, mainly involving pions. The detection of tau is

complicated by its short average life. So the reconstruction and identification

of taus are only based on the detection of its decay products. QCD-jets,

in particular b-jets, can be reconstructed as fake τ -jets. Since the electron

reconstruction is complex task when the electrons do Bremsstrahlung, those

can fake also τ objects. In addition, a significant fraction of the τ and

associated neutrino momentum is not detected.

The main tau reconstruction and identification algorithm developed by

CMS group is the Hadron Plus Strips (HPS) algorithm [35]. It uses Particle

Flow technique, in which the information of all the CMS subdetectors are

combined to identify and reconstruct all particles produced in the collision

13The Gaussian Sum Filter is an algorithm for electron reconstruction in the CMStracker. It is used to improve the momentum resolution of electrons compared to thestandard Kalman filter, because the Bremsstrahlung energy loss distribution of electronspropagating in matter is highly non-Gaussian and the Kalman filter relies solely on Gaus-sian probability density functions. Hence, the GSF algorithm models the Bremsstrahlungenergy loss distribution by a Gaussian mixture rather than by a single Gaussian.

58

(photons, electrons, muons, charged and neutral hadrons). Neutrinos are not

considered. The resulting list of PF candidate objects is used to reconstruct

the PF jet object.

The HPS starts from a PF jet and searches for τ lepton decay products pro-

duced by any of the hadronic decay modes with one or three charged particles

and neutral pion(s) in the final state14. Since neutral pions are produced very

often in hadronic τ decays, one of the main task in reconstructing taus, that

decay hadronically, is determining the number of π0 produced in the decay.

The HPS combines the PF electromagnetic particles in the “strips”, taking

into account possible broadening of calorimeter deposits from photon conver-

sions. In order to reconstruct the hadronic tau decay products, the neutral

objects are then combined with existing charged hadrons.

When more than one hypothesis for a possible tau decay signature exists, the

hypothesis leading to the lowest ET sum of jet constituents not associated to

τ decay products is chosen.

Figure 2.16: Scheme of tau decays into final states involving pions.

14Tau decays can be classified into those that provide a single track (1-prong) and thosethat provide three tracks (3-prong). In the leptonic case, the decay contains a singlecharged lepton, giving a single track 1-prong. In the hadronic case, the charged pionseach provide a track. Because of the charge conservation, there must be an odd numberof charged pions in the final state which gives an odd number of tracks. Generally, thetau decays into a single charged pion (1-prong) and any number of neutral pions or threecharged pions (3-prong, π− + π+ + π±) and any number of neutral pions. It is possiblefor taus to give even five or seven tracks, but these are not very frequent and they areextremely hard to identify from background process, therefore tau physics generally focuseson 1 or 3-prong taus (see Fig. 2.16).

59

60

Chapter 3

Data Analysis

In this chapter we describe the analysis about the search of the doubly

charged Higgs boson in the channel Φ++Φ−− → `+`+`−`− (` = e, µ, τ) in

proton-proton (pp) collisions at√s = 7 TeV. The data correspond to an

integrated luminosity of L = 4.93 fb−1 collected by CMS experiment at the

LHC during 2011. The doubly charged Higgs boson mass range covered by

the analysis is [130; 500] GeV.

Due to the presence of four leptons in the final state, a high-performance

lepton reconstruction, identification and isolation, along with excellent lep-

ton energy-momentum measurements, is mandatory. A substantial reduction

of QCD-induced sources of misidentified (“fake”) leptons has been realized

by identifying isolated leptons coming from the event primary vertex.

High precision energy-momentum measurements allow to obtain a good re-

solution on the reconstructed mass m(`±`±), which is the most important

observable for the search of the doubly charged Higgs boson. We can note

that preserving the highest possible reconstruction efficiency and ensuring a

sufficient discrimination against hadronic jets are particularly challenging for

the reconstruction of leptons with low pT . In this range the combined infor-

mation from the tracker and the electromagnetic calorimeter (for electrons)

and from the tracker and the muon spectrometer (for muons) plays the most

important role for lepton reconstruction, identification and isolation.

61

3.1 Trigger and Data samples

The data used were officially validated for trigger selection and event recon-

struction during the 2011 running period. During the data taking periods,

the instantaneous luminosity, which is known with a precision of 2.2% [36],

varied over the range 1029−1033cm−2s−1. In the 2011, CMS collected a data

set corresponding to an integrated luminosity of L = 4.93± 0.11 fb−1.

The monitoring and certification of the quality of the CMS data consists of

a multi-step procedure, spanning from online data taking to the offline re-

processing of data recorded earlier. The quality assessment is based on both

visual inspection of data distributions by monitoring shift persons as well as

algorithmic tests of the distributions against references.

The Run Registry (RR) is the central workflow management tool used to

certify collected data, to keep track of the certification results and to expose

them to the whole CMS collaboration. It is regularly used for the creation of

official good-run list files in JSON format which are used as input to down-

stream selection of the data for re-processings and for physics analyses. The

JSON files used for this analysis are:

1. Cert-160404-163869_7TeV_May10ReReco_Collisions11_JSON.txt;

2. Cert-170249-172619_7TeV_ReReco5Aug_Collisions11_JSON_v3.txt;

3. Cert-160404-180252_7TeV_PromptReco_Collisions11_JSON.txt.

Events were required to pass double lepton (ee, eµ, µµ) High Level Trig-

ger (HLT) selection with a transverse momentum (pT ) threshold on each

lepton and additional selection criteria that changed during the data ta-

king according to the instantaneous luminosity and the available data taking

bandwidth. Given the high probability of jets to fake electrons, double elec-

tron events were selected with more complicated criteria based not only on

the transverse momentum of the electrons but also on their isolation and

identification.

For the 2011A data, the analysis relies on the so-called “DoubleElectron”,

62

“DoubleMuon” and “MuEG” PDs (Primary Datasets)1.

A detailed list of the trigger selection selection paths used for the 2011 data

is given in Table 3.1, in which the pT thresholds are pointed in the name.

DoubleElectron triggersHLT_Ele17_CaloIdL_CaloIsoVL_Ele8_CaloIdL_CaloIsoVL_v*

HLT_Ele17_CaloIdT_CaloIsoVL_TrkIdVL_TrkIsoVL_Ele8_CaloIdT_CaloIsoVL_TrkIdVL_TrkIsoVL_v*

DoubleMuon triggersHLT_DoubleMu7_v*

HLT_Mu13_Mu8_v*

HLT_Mu17_Mu8_v*

MuEG triggersHLT_Mu8_Ele17_CaloIdL_v*

HLT_Mu8_Ele17_CaloIdT_CaloIsoVL_v*

HLT_Mu17_Ele8_CaloIdL_v*

HLT_Mu17_Ele8_CaloIdT_CaloIsoVL_v*

Table 3.1: Triggers used for the analysis.

Some additional criteria on the reconstructed primary vertex are required

to select events from good collisions (discarding these from pile-up interac-

tions):

• the number of degrees of freedom > 4 for the vertex fit;

• the maximal distance of the nominal point of the pp collision along the

beam line |z(PV )| with respect to the center of CMS detector (z = 0)

is less than 24 cm;

• the maximal distance of the nominal point of the pp collision with

respect to the center of CMS detector in the transverse plane is less

than 2 cm.

1To enable the most effective access to CMS data, the data are first split into PrimaryDatasets (PDs) and then the events are filtered. The division into the Primary Datasetsis done based on the trigger decision. The PDs are structured and placed to make life aseasy as possible, e.g. to minimize the need of an average user to run on very large amountsof data.

63

In case of multiple primary vertex candidates, the one with the highest

value of the scalar sum of the total transverse momentum of the associated

tracks is selected.

Duplication of events in DoubleElectron, DoubleMuon and MuEG PDs

is avoided by selecting:

1. events in MuEG datasets that don’t fire the used double electron trig-

gers;

2. double muon events that don’t fire either the double electron or the

electron-muon cross triggers.

The Primary Datasets and the relevant run ranges for 2011 data are listed

in Table 3.2.

Dataset Run Range/Run2011A-May10ReReco-v1/AOD 160431 - 163869/Run2011A-PromptReco-v4/AOD 165088 - 167913/Run2011A-05Aug2011-v1/AOD 170826 - 172619/Run2011A-03Oct2011-v1/AOD 172620 - 173692/Run2011B-PromptReco-v1/AOD 175860 - 180252

Table 3.2: Collision datasets

3.2 Simulation of events

Signal and background datasets, used in the analysis, are obtained with

detailed Monte Carlo (MC) simulations by using programs to generate high

energy physics events. These events are sets of outgoing particles produced

in the interactions between two incoming particles. The target of the simu-

lations is to provide a representation of the event properties as accurate as

possible in a wide range of reactions, within and beyond the Standard Model.

In particular those where strong interactions play a basic role, and therefore

multi-hadronic final states are produced. These programs have to take into

account a combination of analytical results and various QCD based models.

64

3.2.1 Event Generators

PYTHIA [37] is a multipurpose MC event generator used for event ge-

neration in high energy physics. It is used for the simulation of signal and

background processes, either to generate a given hard process at leading or-

der, or for simulation of showering and hadronization in cases where the hard

processes are generated at the next-to-leading order. The event generation

is carried out in some steps by factorizing the process into a number of com-

ponents, each of which can be handled reasonably accurately. As a result,

a generated event should be in the form of “event”, with the same average

behaviour and the same fluctuations as for real data.

PYTHIA6 is a particular version of PYTHIA, that has been used in order to

generate events for several new processes of beyond the Standard Model

physics, such as the production of the doubly charged Higgs boson.

CalcHEP [38] is a package for automatic calculations of elementary par-

ticle decay and collision properties in the lowest order of perturbation theory

(the tree approximation). It is used to select a model of particle interaction

and to implement some changes in the model. The CalcHEP package consists

of two parts: the first one offers to the user the possibility to select a model

of the particle interaction and to implement some changes in the model,

by specifying incoming and outgoing particles, by generating Feynman dia-

grams, etc. The main tasks of the second part are related to the possibility

to modify physical parameters (incoming momenta, couplings, masses etc.)

involved in the process, selecting the scale parameter for evaluation of the

QCD coupling constant and partonic distribution functions, calculating par-

ticle widths and decay rates, by taking into account high order QCD loop

corrections and defining the kinematic scheme for the effective MC integra-

tion.

An other program used to generate events corresponding to different pre-

cesses, such as signal(s) and backgrounds, is MADGRAPH [39]. It allows to

simulate events at the parton, hadron and detector level directly from a web

interface, for processes in the Standard Model and in several physics scenarios

beyond the SM.

65

TAUOLA [40] is a Monte Carlo program dedicated to the generation of the

tau-lepton decays. This program includes more than twenty decay chan-

nels, including leptonic, semileptonic and meson modes. Complete QED

corrections are included in the leptonic decay channels, and for other decay

channels an interface is provided to Monte Carlo generators for approximate

simulation of the QED corrections. Tau leptons may be pre-generated with

any other event generator, for example with PYTHIA6, and then passed to the

TAUOLA package for detailed decay simulation.

POWHEG [41] generator has been used for the calculation at next-to-leading

order in QCD of s and t-channel single top production.

3.2.2 MC samples

Signal and background samples, used in the analysis, are obtained with a

detailed Monte Carlo simulations by using the previous generators and the

GEANT42 [42] program to simulate the detector response and the interac-

tions of the particles with the matter. All datasets were exposed to the full

reconstruction. The signal and background samples have been used for the

optimization of the event selection strategy prior to the analysis of the ex-

perimental data.

The doubly charged Higgs signal events in the pair production mode

(Φ++Φ−−) was simulated with PYTHIA6 and the TAUOLA generator interfaced

to PYTHIA for a correct treatment of the τ decay. Concerning the single pro-

duction mode (Φ±±Φ∓), the signal samples were generated using CalcHEP.

The Fig 3.1 shows the cross section of Φ±± in the both pair and associated

production as a function of mΦ±± . The signal processes were simulated in 14

2The GEANT4 is a program which describes the passage of elementary particlesthrough matter. It includes a complete range of functionality including tracking, geo-metry, physics models and hits. The physics processes offered cover a comprehensiverange, including electromagnetic, hadronic and optical processes, a large set of long-livedparticles, materials and elements, over a wide energy range. The principal applicationsof GEANT4 in high-energy physics are the tracking of particles through an experimentalsetup for simulation of detector response and the graphical representation of the setupand of the particle trajectories.

66

mass points: 130, 150, 170, 200, 225, 250, 275, 300, 325, 350, 375, 400, 450

and 500 GeV.

[GeV]±±ΦMass of 100 200 300 400 500 600 700

Cro

ss S

ectio

n [fb

]

-210

-110

1

10

210

310 Pair Production

Association Production

Total

CMS Preliminary 2011 -1 = 7 TeV L = 4.93 fbs

Figure 3.1: Cross sections of doubly charged Higgs boson production as afunction of mΦ±± in the mass range between 130 and 700 GeV.

The background samples include the 4` contributions from di-boson pro-

duction, as well as instrumental backgrounds. The main sources of back-

grounds contributions are the ZZ + jets production with Z → `+`−, the

WW + jets production with W± → `±ν`, the WZ + jets production and the

production of top quark pairs in the decay mode tt → WbWb → `+`−ννbb.

Processes where only one top quark appears in the final state are known

in the literature as single top processes. Their cross sections are smaller

than the tt pair cross section, due to their weak nature. The production of

dilepton events with ”a la Drell-Yan” mechanism, hereafter referred as Drell-

Yan events, also contribute to the background since a virtual photon or a Z

boson is generated, decaying in opposite charged leptons, together with one

or more additional jets. In all of these processes hadronic jets or secondary

67

leptons from heavy meson decays could be misidentified as primary leptons.

The V V+jets (sum of WW,WZ,ZZ + jets events) and the Drell-Yan events

from SM processes were generated using MADGRAPH , then passed to PYTHIA6

for the hadronization and the decay. Samples of tt+jets and single top, were

generated using POWHEG interfaced with PYTHIA6. All the other samples were

generated with PYTHIA6.

The main background processes are listed in the Table 3.3. In all cases the

background sources of events are reducible giving us effectively a background

free analysis.

The list of signal samples and the cross sections are shown in Table 3.4. The

background samples and the related cross sections used for this analysis are

listed in Table 3.5.

Process Signature Characteristics

ZZ + jets 4 leptons real leptons; irreducible

V V + jets 3-4 leptons real leptons, but easily reducible

Drell-Yan + jets 2 leptons + jets charge mis-id and possible fakes from jets;

reducible due to Z’s

tt+ jets 2 leptons + 2 b-jets soft leptons from b-jets

or b-jets faking τ -jets

W + jets 1 lepton + jets only one real lepton, but jets can fake leptons

Table 3.3: Main backgrounds.

3.3 Lepton Reconstruction, Identification

and Isolation

The reconstruction of the doubly charged Higgs boson in the decays in

three or four lepton final states requires high performance of the lepton recon-

struction, identification and isolation. An excellent lepton energy-momentum

measurements is also required.

A drastic reduction of QCD-induced sources of fake leptons is obtained from a

good identification of isolated leptons emerging from the primary vertex. An

68

Sam

ple

nam

eσ

inpb

/HPlusPlusHMinusMinusHTo4L_M-130_7TeV-pythia6/Fall11-PU_S6_START42_V14B-v1/AODSIM

0.1

4722


0.0

8307


0.0

49697


0.0

24996


0.0

147546


0.0

0907735


0.0

0582059


0.0

038862


0.0

0258755


0.0

0176115


0.0

0122651


0.0

0087369


0.0

00475443


0.0

00283502

/HPlusPlusHMinusHTo3L_M-130_7TeV-pythia6/Fall11-PU_S6_START42_V14B-v1/AODSIM

0.3

2025


0.1

795


0.1

0712


0.0

5375


0.0

32


0.0

1975


0.0

1275


0.0

0835


0.0

0563


0.0

0388


0.0

0263


0.0

0185


0.0

0096


0.0

00517

Tab

le3.

4:Sig

nal

sam

ple

s

69

Sam

ple

nam

eσ

inpb

/DYJetsToLL_M-10To50_TuneZ2_7TeV-madgraph/Fall11-PU_S6_START42_V14B-v1/AODSIM

12782.63/DYJetsToLL_TuneZ2_M-50_7TeV-madgraph-tauola/Fall11-PU_S6_START42_V14B-v1/AODSIM

3048/TTTo2L2Nu2B_7TeV-powheg-pythia6/Fall11-PU_S6_START42_V14B-v1/AODSIM

17.32/Tbar_TuneZ2_tW-channel-DR_7TeV-powheg-tauola/Fall11-PU_S6_START42_V14B-v1/AODSIM

7.87/Tbar_TuneZ2_t-channel_7TeV-powheg-tauola/Fall11-PU_S6_START42_V14B-v1/AODSIM

22.65/Tbar_TuneZ2_s-channel_7TeV-powheg-tauola/Fall11-PU_S6_START42_V14B-v1/AODSIM

1.44/T_TuneZ2_tW-channel-DR_7TeV-powheg-tauola/Fall11-PU_S6_START42_V14B-v1/AODSIM

7.87/T_TuneZ2_t-channel_7TeV-powheg-tauola/Fall11-PU_S6_START42_V14B-v1/AODSIM

41.92/T_TuneZ2_s-channel_7TeV-powheg-tauola/Fall11-PU_S6_START42_V14B-v1/AODSIM

3.19/WWJetsTo2L2Nu_TuneZ2_7TeV-madgraph-tauola/Fall11-PU_S6_START42_V14B-v1/AODSIM

4.526/WZJetsTo2L2Q_TuneZ2_7TeV-madgraph-tauola/Fall11-PU_S6_START42_V14B-v1/AODSIM

1.24/WZJetsTo3LNu_TuneZ2_7TeV-madgraph-tauola/Fall11-PU_S6_START42_V14B-v1/AODSIM

0.594/ZZJetsTo2L2Nu_TuneZ2_7TeV-madgraph-tauola/Fall11-PU_S6_START42_V14B-v1/AODSIM

0.161/ZZJetsTo2L2Q_TuneZ2_7TeV-madgraph-tauola/Fall11-PU_S6_START42_V14B-v1/AODSIM

0.56/ZZJetsTo4L_TuneZ2_7TeV-madgraph-tauola/Fall11-PU_S6_START42_V14B-v1/AODSIM

0.0807/WbbToLNu_TuneZ2_7TeV-madgraph-pythia6-tauola/Fall11-PU_S6_START42_V14B-v1/AODSIM

116.04

Tab

le3.5:

Back

ground

samples

70

accurate measurement of the Higgs boson mass is obtained from an accurate

measurement of the energy-momentum.

3.3.1 Muon Reconstruction and Identification

Muon candidates are reconstructed using two algorithms: the first matches

tracks in the silicon detector to segments in the muon chambers, while the

second performs a combined fit using hits in both the silicon tracker and the

muon system (see Sec. 2.3.2). Global muons are used for this analysis, di-

scarding candidates muons reconstructed only as tracker muons or standalone

muon.

Concerning the muon identification strategy, some definitions need to be

introduced in order to understand the kind of background muons we want to

reject for this analysis [43]:

• ”Fake Muon”: any muon passing whatever applied cuts that is recon-

structed in single pion or single kaon events. Thus, a muon from a

K → µ decay in flight is a fake muon.

• ”Fake Rate”: the ratio of fake muons to generated kaons and pions as

a function of the pT or η of the generated kaon or pion.

• ”Punch-Through”: a hadron which enters the calorimeter and produces

hits in the muon system. Most of the punch-through are due to kaons

and pions in the hadronic showers that decay in muons.

The global muon normalized-χ2 is used to reject both decays-in-flight and

punch-through. If χ2/ndof < 10, the muons are correctly identified with an

efficiency near to 1. Moreover, track quality cuts can be used to reject leftover

decays-in-flight. There are two other fundamental quantities to which these

cuts are applied:

1. the transverse impact parameter (d0) of the muon track with respect

to the reconstructed primary vertex;

2. the number of silicon tracker hits Nhits.

71

In this analysis, only muons with pT > 5 GeV and |η| < 2.4 are considered.

For the purpose of a tight muon identification, the muon is required to satisfy

some additional requirements:

• at least one muon chamber hit is included in the final track fit, matched

to muon segments in at least two muon stations;

• the corresponding tracker track must have Nhits > 10;

• a χ2/ndof of the global-muon track fit is required to be less than 10

for its discriminating power against decays-in-flight;

• |d0| < 2 mm, preserving the efficiency for muons from b- and c-quarks3.

3.3.2 Electron Reconstruction and Identification

In order to reject jets faking electrons and electrons resulting from con-

versions, the electron reconstruction uses a cut-based approach. It combines

the ECAL and tracker information. Electron candidates are reconstructed

from clusters of energy deposits in the ECAL, which are then matched to hits

in the silicon tracker. The standard CMS electron reconstruction algorithm,

described in Sec. 2.3.3, is used for this analysis.

The physics analysis of multi-electron final states requests a good identifica-

tion efficiency in order to enhance signal selection, in particular at low ET ,

where the Z and W background increases and the fake rate is much higher.

Efficient electron identification in CMS is quite different from identification

in many other experiments because of the large varying amount of material

in the tracker and the high magnetic field. However, thanks to a conve-

nient classification of electrons, it is possible to reach a good identification

efficiency of electrons.

Electrons are divided into categories [44]:

• brem electrons,

3A loose d0 cut is very efficient for prompt muons, coming from the primary vertex,and rejects a significant fraction of decays-in-flight. A too tight d0 cut, instead, rejectsmuons from bottom and charm decays, but too many prompt muons too.

72

• lowbrem electrons,

• badtrack electrons,

• crack electrons,

• pure tracker-driven electrons,

which are introduced to separate electrons with quite different measurement

characteristics and purity; all of them (except the last one) are split into

barrel and endcap, giving rise to nine categories. The technique that uses this

electron classification is called Cut-in-Category and it uses the following set

of variables in order to distinguish between real electrons and fake electrons:

• the H/E ratio of energy deposited in the HCAL directly behind the

ECAL cluster (H) and the energy of the electron supercluster (E);

• the energy-momentum matching variables E/pin, Eseed/pin and Eseed/

pout, where E is the supercluster energy, Eseed is the supercluster seed

energy, pin and pout are the electron track measured momentum at the

vertex and at the calorimeter, respectively;

• the geometrical matching variables ∆φin and ∆ηin, namely the diffe-

rences between the energy weighted position of the supercluster and

the position of closest approach to the supercluster position in φ and η

coordinates, respectively;

• the calorimeter shower shape variable, σiηiη.

In order to reject electrons from conversions, due to the material in front of

ECAL:

• the impact parameter d0 of the electron track computed with respect

to the reconstructed primary vertex;

• the number of “missing hits” which are the number of crossed layers

without compatible hits in the back-propagation of the track to the

beam line.

73

The algorithm gives as output a bit pattern for each electron candidate for

9 defined severity levels of cuts [45]. There is one bit for electron identifi-

cation, a second one for electron isolation, then one for conversion rejection

and the last one for impact parameter. The cut severity levels are called

VeryLoose, Loose, Medium, Tight, SuperTight, HyperTight1, HyperTight2,

HyperTight3 and HyperTight4. The names would give an indication of how

severe the cuts are for selecting dielectrons from Z. The cuts are optimized

to give the best signal to background ratio (s/b) for single electrons from W

and Z decays.

The cut severity level chosen for this analysis is Tight and its values for

each electron category are listed in Table 3.6, henceforward eID designates

electrons selected according to the technique and cuts just described.

|∆ηin| < |∆φin| < Eseed/pin < H/E < σiηiη <

[EminT -Emax

T ] [EminT -Emax

T ] [EminT -Emax

T ] [EminT -Emax

T ]

”brem” EB [8.92-9.23]×10−3 [0.063-0.069] 0.65 [0.171-0.222] [1.16-1.27]×10−2

”lowbrem” EB [3.96-3.77]×10−3 [0.153-0.233] 0.97 [0.049-0.052] [1.07-1.08]×10−2

”badtrack” EB [8.50-8.70]×10−3 [0.290-0.296] 0.91 [0.146-0.147] [1.08-1.13]×10−2

”crack” EB [13.4-13.9]×10−3 [0.077-0.086] 0.78 [0.364-0.357] [3.49-4.19]×10−2

”brem” EE [6.27-5.60]×10−3 [0.181-0.185] 0.37 [0.049-0.042] [2.89-2.81]×10−2

”lowbrem” EE [10.5-9.40]×10−3 [0.234-0.276] 0.70 [0.145-0.145] [3.08-3.02]×10−2

”badtrack” EE [11.2-10.7]×10−3 [0.342-0.334] 0.33 [0.429-0.326] [0.99-0.98]×10−2

”crack” EE [30.9-62.0]×10−3 [0.393-0.353] 0.97 [0.420-0.380] [3.37-4.28]×10−2

”pure

tracker-driven” [18.8-4.10]×10−3 [0.284-0.290] 0.59 [0.399-0.132] [4.40-2.98]×10−2

Table 3.6: Definition of cuts used in the electron identification for electronscategories in the barrel (EB) and in the endcaps (EE). Where a range isspecified, the cuts are made ET -dependent between Emin

T = 10 GeV andEmaxT = 40 GeV.

In addition, for this analysis, all electron candidates are required to have

pT > 15 GeV and |η| < 2.5; the first cut ensures high efficiency for the re-

construction while the second one corresponds to the geometrical acceptance

of the tracker detector.

74

3.3.3 Muon Isolation

An efficient rejection of QCD background, tt+jets and W+jets events can be

reached by using a muon isolation variable.

The isolation algorithm is based on the estimation of the total energy

deposited in a cone around the lepton, namely the isolation cone. The cone

is built around an axis (see Fig. 3.2), which overlaps the muon direction

pointing to the vertex. The value of opening angle, ∆R, is defined in the (η,

φ) space by the following equation

∆R =√

∆η2 + ∆φ2 , (3.1)

where ∆η and ∆φ are the pseudorapidity and azimuthal angle of the energy

deposit estimated respect to the cone axis. The ∆R opening angle has to

be lower than a certain value defined in the analysis; in this case, ∆R is less

than 0.3.

The contribution to the isolation variables come from the sum of the tran-

sverse momenta in the isolation cone around the lepton and the transverse

energies in the ECAL and HCAL calorimeters. The first contribution is

Figure 3.2: Representation of the isolation cone. The muon direction, esti-mated from the vertex, defines the cone axis.

75

defined as:

Isotrack =tracker∑

∆R

ptrackT . (3.2)

while the contribution from deposits in calorimeters is defined as:

Isoecal =ECAL∑

∆R

ET and Isohcal =HCAL∑

∆R

ET . (3.3)

When divided by pT , the isolation variable is defined as:

relIsoiso =Isotrack + Isoecal + Isohcal

pT, (3.4)

and we refer to it as relative isolation variable. The best performance in

terms of signal efficiency and background rejection are obtained by using the

relative isolation, as detailed in Ref. [46].

3.3.4 Electron Isolation

The isolation variables used to calculate electron isolation relying on the

information of the tracker, ECAL and HCAL are based on the sum on pT of

tracks and sum of ET depositions in cones in (η, φ) space around the lepton

and an inner veto region, called ”Jurassic” veto [45], to remove the electron

footprint coming from the path in φ due to Bremstrahlung.

Track Isolation

The sum of pT of tracks is made centered on the electron track at vertex and

it is calculated within a cone of radius

∆R =√

∆η2 + ∆φ2 < 0.3 , (3.5)

around the electron candidate direction. In the Eq. 3.5, ∆η and ∆φ are the

same variables defined in Eq. 3.1. The inner veto cone radius is set to 0.015

and the pT threshold cut on tracks is 1.0.

76

ECAL and HCAL Isolation

Electron isolation variables are summed in a cone centered on the the elec-

tron ECAL supercluster, with a footprint removal region consisting of a strip

of specified η width and an additional circular region (see Fig. 3.3). They

are computed using the ET from energy deposits in cells with geometrical

centroids situated within a cone of radius given by the Eq. 3.5, like for track

isolation. The cone axis is taken as the ECAL supercluster centroid viewed

from the electron vertex taken at (0, 0, 0). For electrons, the isolation va-

Figure 3.3: Representation of the strip of a footprint removal region in thecase of ECAL and HCAL isolation for electrons.

riables are given by Eqs. 3.2 and 3.3 and the relative isolation is given by

Eq. 3.4.

Isolation variables are among the most pile-up sensitive variables in this

analysis. An increase of the mean isolation values corresponds to an increase

of the mean energy deposited in the detector because of the pile-up. Thus,

the efficiency of a cut on isolation variables strongly depends on pile-up

conditions and a correction of the isolation variable is carried out to have a

good analysis with a reduced pile-up effects. The FastJet program [47],[48]

implements an algorithm used to estimate the mean pile-up contribution

within the isolation cone of a lepton, through the energy density (ρ) in the

event. The ρ variable is defined for each jet in a given event and the median

77

of the ρ distribution for each event is taken. The correction to the isolation

variable is given by: ∑Isocorrected =

∑Iso− ρ · A , (3.6)

where A is the area of the jet cone in the (η, φ) space. The ρ variable is

given in 1/(∆η∆φ) units; hence, A has the dimension of an angle. Rather

than computing a geometrical area, an effective area4 is considered, to avoid

dealing with different thresholds in the isolation and FastJet algorithms.

The values for the effective area have been computed in the context of the

H → ZZ → 4` analysis [49] and re-used in this analysis.

3.3.5 Tau Reconstruction, Identification and Isolation

In order to reconstruct tau leptons decaying hadronically, the HPS algo-

rithm [50], based on Particle Flow objects, is used. The main purpose is to

derive the number of pions produced in the decay (see Sec. 2.3.4).

The identification and isolation of τ leptons are carried out also by using the

HPS algorithm, in order to reduce the QCD background. The algorithm has a

modular design to facilitate building of higher analysis-specific discriminants

on top of these stable, well-measured results.

Reconstructed tau candidates are required to satisfy isolation criteria,

which are based on counting the number of charged hadrons and photons

above a certain ET threshold, not associated to the tau decay signature

within an isolation cone of size ∆R = 0.5. Three sets of ET thresholds

define “loose”, “medium” and “tight” working-points of the HPS algorithm.

The energy sum of the candidates in a solid cone of ∆R = 0.5 around the

reconstructed tau decay mode axis defines the isolation variable. Finally, pile-

up correction is applied by using three discriminators to which correspond

the three following HPS working-points:

1. Loose Isolation: no PF charged candidates with pT > 1.0 GeV and no

4Effective areas are defined as the ratio of the fit slope of the variable as a function ofthe number of reconstructed vertices Nvtx to the fit slope of ρ as a function of Nvtx.

78

PF gamma candidates with ET > 1.5 GeV;

2. Medium Isolation: no PF charged candidates with pT > 0.8 GeV and

no PF gamma candidates with ET > 0.8 GeV;

3. Tight Isolation: no PF charged candidates with pT > 0.5 GeV and no

PF gamma candidates with ET > 0.5 GeV.

For this analysis, the medium isolation is used and all taus candidates are

required to have pT > 15 GeV and |η| < 2.1.

The following additional requirements are imposed for τ -jets:

• discrimination of tau-jets against electrons and muons sharing the same

track, since these particles could fake 1-prong τ . The discriminators,

used in the analysis, are respectively

– HPSTAU discByMER (medium working-point)

– HPSTAU discByTMR (tight working-point)

• tau veto in the region 1.46 < |η| < 1.558, because of the reduced

ability to discriminate between electrons and hadrons in this portion

of the detector.

3.4 Event Selection

The analysis strategy can be divided in two steps, in addition to the

HLT trigger requirement and a basic selection of collision events described

previously.

A preliminary preselection is carried out in order to suppress most of the

QCD jet events with fake leptons. It is applied with the purpose also to keep

the events in the signal phase space.

Then, a baseline selection based on the kinematics of Φ±± production is

applied, so that the remaining background contributions can be reduced.

The production of the doubly charged Higgs boson at LHC (see Sec. 1.3.2)

can give rise to a distinctive multi-lepton signature: due to flavour non-

conservation, the final states can be combinations of all possible leptons.

79

Such different scenarios are analyzed separately in order to achieve the best

signal to background ratio. Additionally, final states are discriminated based

on the number of reconstructed τ -jets. The signal events include two pairs of

same sign leptons, hence six possible final states are looked for when searching

for the double charged Higgs in the BR=100% scenarios:

µ+µ+µ−µ−, e+e+e−e−, τ+τ+τ−τ−,

e+µ+e−µ−, µ+τ+µ−τ−, e+τ+e−τ−.

The leptonic decay of the taus in the final states including only taus are not

considered in this analysis; the final state with 4 hadronically decaying tau

is not relevant because the efficiency of the four hadronic tau reconstruc-

tion final state is too low to make the signal enhanced with respect to the

background.

3.4.1 Preselection cuts

The first condition set on the four final leptons concern the charge: two of

these leptons should be of the same charge, both coming from the same Φ±±

boson.

Then, some kinematical variables are studied to develop preselection cuts

for this analysis; the first important observable is the lepton pT . The pT

range of the leptons from the doubly charged Higgs decay depends on the

hypothesis made for the doubly charged Higgs mass, and can reach low values

down to 10-15 GeV for low Higgs masses. Anyway, since this analysis involves

at least two high pT leptons, we require that at least the two leptons with

the highest momentum in the event should have pT > 20 and 10 GeV,

respectively. This cut ensures that the background events for which the

leptons originate from the semi-leptonic b-decays (called non-prompt leptons)

are reduced as they tend to be less energetic. Moreover, it does not affect

the signal efficiency (see Sec. 3.5). The Fig. 3.4, where the distributions of

the four muons pT in the scenario BR (Φ±± → µ±µ±) = 100% are plotted in

the mΦ±± = 130 GeV (left) and mΦ±± = 300 GeV (right) hypotheses, shows

80

that in the highest mass hypothesis the pT spectrum is shifted towards higher

values of momentum because of the kinematics.

The same pT cuts are applied for the other scenarios with similar results; in

[GeV]T

Lepton p0 100 200 300 400 500 600 700

Eve

nts

/10

GeV

0

0.5

1

1.5

2

2.5

3

3.5

4CMS Preliminary 2011 -1 = 7 TeV, L = 4.93 fbs

) = 100%±µ±µ→±±ΦBR (

1µ

2µ

3µ

4µ

= 130 GeV±±Φ

for signal massT

HLT Selection: lepton p

[GeV]T

Lepton p0 100 200 300 400 500 600 700 800

Eve

nts

/10

GeV

0

0.01

0.02

0.03

0.04

0.05

0.06CMS Preliminary 2011 -1 = 7 TeV, L = 4.93 fbs

) = 100%±µ±µ→±±ΦBR (

1µ

2µ

3µ

4µ

= 300 GeV±±Φ

for signal massT

HLT Selection: lepton p

Figure 3.4: Distribution of the transverse momentum of the four muons in thescenario BR (Φ±± → µ±µ±) = 100%, for signal events with mΦ±± = 130 GeV(left) and mΦ±± = 300 GeV (right). The leptons are ordered in pT . Thesamples correspond to an integrated luminosity of L = 4.93 fb−1.

the final states where the taus are included, the distributions of the transverse

momentum are shifted towards lower values of pT because of the energy of

the neutrinos from the taus decay that is not detected (missing energy) and

does not contribute to the visible tau pT reconstructed by the detector.

The Figs. 3.5, 3.6, 3.7 show the distributions of the lepton pT for signal in

three different mass hypotheses (mΦ±± = 130, 300, 500 GeV), for background

and for data before and after the application of the pT cuts and by considering

different 100% BR scenarios.

The event number shown in the plots is rescaled to the integrated luminosity

of L = 4.93 fb−1 according to the cross section of the specific process.

The pairs of leptons with an invariant mass below 12 GeV are discarded in

order to suppress the background events coming from low mass b-resonances,

photon conversions and the low mass tail of the dilepton distribution for

signal and background that are generally not interesting for this analysis.

The Fig. 3.8 shows the mass distributions of the same sign dileptons for

81

Figure 3.5: Distribution of the transverse momentum of the four leptonsin the scenario BR (Φ±± → µ±µ±) = 100%, before (top) and after (bot-tom) the pT cut on the two leptons with the highest momentum (pT,1 >20 and pT,2 > 10 GeV). The samples correspond to an integrated luminosityof L = 4.93 fb−1.

82

Figure 3.6: Distribution of the transverse momentum of the four leptonsin the scenario BR (Φ±± → µ±τ±) = 100%, before (top) and after (bot-tom) the pT cut on the two leptons with the highest momentum (pT,1 >20 and pT,2 > 10 GeV). The samples correspond to an integrated luminosityof L = 4.93 fb−1.

83

Figure 3.7: Distribution of the transverse momentum of the four leptonsin the scenario BR (Φ±± → e±τ±) = 100%, before (top) and after (bot-tom) the pT cut on the two leptons with the highest momentum (pT,1 >20 and pT,2 > 10 GeV). The samples correspond to an integrated luminosityof L = 4.93 fb−1.

84

signal events generated with mass mΦ±± = 130, 300, 500 GeV, for background

events and for data before and after the cut on the mass, but anyway after

the previous cut on pT . In these plots, obtained for the BR (Φ±± → µ±µ±)

= 100% scenario, the signal has a tail on the left due to probably to the

events in which the doubly charged Higgs boson tends to be off mass shell

(top). This tail is reduced after the mass cut (bottom).

In addition to the kinematic selection criteria, the following requirements

on the relative isolation and the significance of the impact parameter (SIP`)5,

are used:

• the sum of the relative isolation of the two worst isolated leptons (e,µ)

is required to be (see Eq.3.4) less than 0.35;

• all reconstructed electrons and muons are required to have SIP` < 4

with respect to the primary vertex.

The cut on the relative isolation ensures an effective reduction of the

background contribution from QCD multi-jets and misidentified leptons. In

Figs. 3.9, 3.10, the distributions of lepton isolation variable for BR = 100%

to µµ channel and eτ channel are plotted before and after applying all the

cuts previously mentioned.

Leptons arising from b-quark decays have usually a sizable impact param-

eter due to their origin from a secondary vertex. A loose cut is applied on

the significance of the impact parameter SIP`, which ensures good signal effi-

ciency while removing some reducible background as we can see in Figs. 3.11,

3.12, 3.13. In these figures the relative distributions in the different scenarios

are shown at the HLT selection level (top) and after all of preselection cuts

(bottom).

It is worth to notice that the cuts on isolation and SIP` previously men-

tioned are only applied on muons and electrons, even in the final state inclu-

ding µτ and eτ same sign pairs; indeed tau can travel through the detector

and so a cut on the SIP` can affect the signal efficiency significantly; tau

5The significance of the impact parameter is a dimensionless quantity defined as SIP` =ρPV /σρPV

, where ρPV denotes the distance from primary vertex and σρPVits uncertainty.

85

Figure 3.8: Invariant mass distribution of the same sign dileptons in thescenario BR (Φ±± → µ±µ±) = 100%, before (top) and after (bottom) themass cut (m(`±`±) > 12 GeV). The samples correspond to an integratedluminosity of L = 4.93 fb−1.

86

Figure 3.9: Distribution of the lepton isolation variable in the scenarioBR (Φ±± → µ±µ±) = 100%, before (top) and after (bottom) the cut(relIsoworst + relIsonexttoworst < 0.35). All of previous cuts on lepton pTand same sign dilepton mass are also included. The samples correspond toan integrated luminosity of L = 4.93 fb−1.

87

Figure 3.10: Distribution of the lepton isolation variable in the scenario BR(Φ±± → e±τ±) = 100%, before (top) and after (bottom) the cut (relIsoworst+relIsonexttoworst < 0.35). All of previous cuts on lepton pT and same signdilepton mass are also included. The samples correspond to an integratedluminosity of L = 4.93 fb−1.

88

Figure 3.11: Distribution of the significance of the impact parameter in thescenario BR (Φ±± → µ±µ±) = 100%, before (top) and after (bottom) thecut on SIP` < 4. All of the preselection cuts (see Table 3.7) are also applied.The samples correspond to an integrated luminosity of L = 4.93 fb−1.

89

Figure 3.12: Distribution of the significance of the impact parameter in thescenario BR (Φ±± → µ±τ±) = 100%, before (top) and after (bottom) thecut on SIP` < 4. All of the preselection cuts (see Table 3.7) are also applied.The samples correspond to an integrated luminosity of L = 4.93 fb−1.

90

Figure 3.13: Distribution of the significance of the impact parameter in thescenario BR (Φ±± → e±τ±) = 100%, before (top) and after (bottom) thecut on SIP` < 4. All of the preselection cuts (see Table 3.7) are also applied.The samples correspond to an integrated luminosity of L = 4.93 fb−1.

91

isolation cuts are instead applied at the level of the identification criteria via

the HPS algorithm, as cited in Sec. 3.3.5.

Table 3.7 summarizes the preselection criteria used for this analysis.

Variable requirementLeading lepton pT > 20 GeVSecond lepton pT > 10 GeV

m(`±`±) > 12 GeVrelIsoworst + relIsonexttoworst < 0.35

SIP` < 4

Table 3.7: Pre-selection criteria.

3.4.2 Baseline Selection for four lepton final state

In this step of the analysis, we divide the remaining event sample into

two categories, based on the total number (three or four) of leptons in the

final state; the analysis is developed and tuned only the four lepton configu-

ration for a set of pre-determined mass hypotheses for the Φ++. In order to

discriminate signal from the remaining background after the preselection, we

use additional selection variables:

•∑pT : the sum of pT of all the leptons in the event;

• the veto on Z boson mass, defined as a cut on the min|m(`+`−)−m(Z)|over all possible opposite sign lepton pairs with the same flavour;

• the invariant mass of the same sign dilepton.

The cut on the sum of pT is performed in order to eliminate the remaining

tt events that involve light leptons.

The Z veto cut is applied only for the final states involving τ to suppress the

Drell-Yan events with leptons coming from the Z/γ decay.

Finally, the events are counted in a same sign dilepton mass window whose

size is different for each final state and each mass. This cut is applied in

order to discriminate the narrow signal from the ZZ background events.

92

The cuts on the sum pT and the mass window are optimized as a function of

the mass by maximizing the following statistical estimator for the significance

of an excess:

ScL =

√2[N0 ln

(1 +

s

b

)− s], (3.7)

where s is the expected number of signal events, b is the expected number of

background events and N0 is the number of observed events, which is assumed

to be N0 = s+ b for optimization purposes. The statistical estimator comes

from the asymptotic expression of significance Z =√

2 lnQ, where Q is

the likelihood ratio of Poisson distributions P (obs|s + b) and P (obs|b). The

estimator ScL applies in the case of a counting experiment without systematic

errors.

The selection criteria used for our analysis are summarized in Table 3.8.

Cut variable ee, eµ, µµ eτ , µτ∑pT > 0.6 ·mΦ±± + 130 GeV > mΦ±± + 100 GeV

or > 400 GeVZ veto none > 10 GeV

Mass window [0.9 ·mΦ±± ; 1.1 ·mΦ±± ] [mΦ±±/2; 1.1 ·mΦ±± ]

Table 3.8: Selection cuts applied in various four lepton final states.

In all of plots reported after cuts the background events ZZ → `+i `−i `

+j `−j

survive because they are very similar to a signal event Φ++Φ−− → `+i `

+j `−k `−l .

These backgrounds also have a higher cross section than the signal. However,

they can be distinguished from the signal by the presence of a resonance in

the same flavour opposite sign dilepton mass (Z → `+i `−i ) and not in the

same sign dilepton mass (Φ±± → `±i `±j ).

The event yields after each consecutive cut for four-lepton analysis have

been obtained for all of mass hypotheses in the five scenarios considered. The

Tables 3.9 - 3.13 report those only for masses of 130, 300 and 500 GeV. In all

cases the mass window for the particular final state has been applied. Each

cut reported in the tables includes the previous ones.

93

mΦ

++

Cu

tS

ingle

top

tt+jets

VV

+jets

Wbb

DY

+jets

Tota

lD

ata

Sig

nal

130

GeV

SIP`

0.0±

0.0

0.0±

0.0

0.2

2±

0.0

10.0±

0.0

0.0±

0.0

0.2

2±

0.0

10.0±

0.0

375.0

5±

2.9

8∑pT

0.0±

0.0

0.0±

0.0

0.1

5±

0.0

10.0±

0.0

0.0±

0.0

0.1

5±

0.0

10.0±

0.0

367.1

5±

2.9

8

300

GeV

SIP`

0.0±

0.0

0.0±

0.0

0.0

1±

0.0

00.0±

0.0

0.0±

0.0

0.0

1±

0.0

00.0±

0.0

11.0

1±

0.1

7∑pT

0.0±

0.0

0.0±

0.0

0.0

1±

0.0

00.0±

0.0

0.0±

0.0

0.0

1±

0.0

00.0±

0.0

11.0

0±

0.1

7

500

GeV

SIP`

0.0±

0.0

0.0±

0.0

0.0

0±

0.0

00.0±

0.0

0.0±

0.0

0.0±

0.0

00.0±

0.0

0.7

9±

0.0

2∑pT

0.0±

0.0

0.0±

0.0

0.0

0±

0.0

00.0±

0.0

0.0±

0.0

0.0±

0.0

00.0±

0.0

0.7

9±

0.0

2

Tab

le3.9:

Cut

flow

for100%

decay

tom

uon

sw

ithm

ass130,

300an

d500

GeV

.

94

mΦ

++

Cu

tS

ingle

top

tt+

jets

VV

+je

tsWbb

DY

+je

tsT

ota

lD

ata

Sig

nal

130

GeV

SIP`

0.0±

0.0

0.0±

0.0

0.2

0±

0.0

10.0±

0.0

0.0±

0.0

0.2

0±

0.0

10.0±

0.0

313.2

4±

2.9

6∑ p T

0.0±

0.0

0.0±

0.0

0.1

3±

0.0

10.0±

0.0

0.0±

0.0

0.1

3±

0.0

10.0±

0.0

308.2

2±

2.9

5

300

GeV

SIP`

0.0±

0.0

0.0±

0.0

0.0

3±

0.0

10.0±

0.0

0.0±

0.0

0.0

3±

0.0

10.0±

0.0

10.8

2±

0.1

7∑ p T

0.0±

0.0

0.0±

0.0

0.0

2±

0.0

10.0±

0.0

0.0±

0.0

0.0

2±

0.0

10.0±

0.0

10.8

2±

0.1

7

500

GeV

SIP`

0.0±

0.0

0.0±

0.0

0.0

0±

0.0

00.0±

0.0

0.0±

0.0

0.0

0±

0.0

00.0±

0.0

0.8

6±

0.0

2∑ p T

0.0±

0.0

0.0±

0.0

0.0

0±

0.0

00.0±

0.0

0.0±

0.0

0.0

0±

0.0

00.0±

0.0

0.8

6±

0.0

2

Tab

le3.

10:

Cut

flow

for

100%

dec

ayto

elec

tron

sw

ith

mas

s13

0,30

0an

d50

0G

eV.

95

mΦ

++

Cu

tS

ingle

top

tt+jets

VV

+jets

Wbb

DY

+jets

Tota

lD

ata

Sig

nal

130

GeV

SIP`

0.0±

0.0

0.0±

0.0

0.4

5±

0.0

20.0±

0.0

0.0±

0.0

0.4

5±

0.0

20.0±

0.0

347.3

6±

3.0

2∑pT

0.0±

0.0

0.0±

0.0

0.2

9±

0.0

10.0±

0.0

0.0±

0.0

0.2

9±

0.0

10.0±

0.0

340.9

3±

3.0

2

300

GeV

SIP`

0.0±

0.0

0.0±

0.0

0.0

2±

0.0

00.0±

0.0

0.0±

0.0

0.0

2±

0.0

00.0±

0.0

11.0

2±

0.1

8∑pT

0.0±

0.0

0.0±

0.0

0.0

2±

0.0

00.0±

0.0

0.0±

0.0

0.0

2±

0.0

00.0±

0.0

11.0

2±

0.1

8

500

GeV

SIP`

0.0±

0.0

0.0±

0.0

0.0

0±

0.0

00.0±

0.0

0.0±

0.0

0.0

0±

0.0

00.0±

0.0

0.8

3±

0.0

2∑pT

0.0±

0.0

0.0±

0.0

0.0

0±

0.0

00.0±

0.0

0.0±

0.0

0.0

0±

0.0

00.0±

0.0

0.8

3±

0.0

2

Tab

le3.11:

Cut

flow

for100%

decay

toe-µ

with

mass

130,300

and

500G

eV.

96

mΦ

++

Cu

tS

ingle

top

tt+

jets

VV

+je

tsWbb

DY

+je

tsT

ota

lD

ata

Sig

nal

130

GeV

SIP`

0.0±

0.0

0.0±

0.0

0.2

8±

0.0

70.0±

0.0

0.0±

0.0

0.2

8±

0.0

70.0±

0.0

7.4

2±

0.6

1∑ p T

0.0±

0.0

0.0±

0.0

0.0

3±

0.0

00.0±

0.0

0.0±

0.0

0.0

3±

0.0

00.0±

0.0

5.5

7±

0.5

3Z

vet

o0.0±

0.0

0.0±

0.0

0.0

3±

0.0

00.0±

0.0

0.0±

0.0

0.0

3±

0.0

00.0±

0.0

4.3

5±

0.4

7

300

GeV

SIP`4l-

10.0±

0.0

0.0±

0.0

0.0

7±

0.0

60.0±

0.0

0.0±

0.0

0.0

7±

0.0

60.0±

0.0

0.2

4±

0.0

4∑ p T

0.0±

0.0

0.0±

0.0

0.0

1±

0.0

00.0±

0.0

0.0±

0.0

0.0

1±

0.0

10.0±

0.0

0.2

4±

0.0

4Z

vet

o0.0±

0.0

0.0±

0.0

0.0

1±

0.0

00.0±

0.0

0.0±

0.0

0.0

1±

0.0

10.0±

0.0

0.2

0±

0.0

4

500

GeV

SIP`

0.0±

0.0

0.0±

0.0

0.0

0±

0.0

00.0±

0.0

0.0±

0.0

0.0

0±

0.0

00.0±

0.0

0.0

1±

0.0

0∑ p T

0.0±

0.0

0.0±

0.0

0.0

0±

0.0

00.0±

0.0

0.0±

0.0

0.0

0±

0.0

00.0±

0.0

0.0

1±

0.0

0Z

vet

o0.0±

0.0

0.0±

0.0

0.0

0±

0.0

00.0±

0.0

0.0±

0.0

0.0

0±

0.0

00.0±

0.0

0.0

1±

0.0

0

Tab

le3.

12:

Cut

flow

for

100%

dec

aytoµ

-τw

ith

mas

s13

0,30

0an

d50

0G

eV.

97

mΦ

++

Cu

tS

ingle

top

tt+jets

VV

+jets

Wbb

DY

+jets

Tota

lD

ata

Sig

nal

130

GeV

SIP`

0.0±

0.0

0.0

4±

0.0

30.2

9±

0.0

30.0±

0.0

0.0±

0.0

0.3

3±

0.0

415±

3.8

76.9

0±

0.6

0∑pT

0.0±

0.0

0.0±

0.0

0.0

3±

0.0

00.0±

0.0

0.0±

0.0

0.0

3±

0.0

00.0±

0.0

5.3

4±

0.4

8Z

veto

0.0±

0.0

0.0±

0.0

0.0

3±

0.0

00.0±

0.0

0.0±

0.0

0.0

3±

0.0

00.0±

0.0

4.4

6±

0.4

8

300

GeV

SIP`

0.0±

0.0

0.0

2±

0.0

20.0

3±

0.0

10.0±

0.0

0.0±

0.0

0.0

5±

0.0

21±

10.2

9±

0.0

4∑pT

0.0±

0.0

0.0±

0.0

0.0

1±

0.0

10.0±

0.0

0.0±

0.0

0.0

1±

0.0

10.0±

0.0

0.2

6±

0.0

4Z

veto

0.0±

0.0

0.0±

0.0

0.0

1±

0.0

10.0±

0.0

0.0±

0.0

0.0

1±

0.0

10.0±

0.0

0.2

6±

0.0

4

500

GeV

SIP`

0.0±

0.0

0.0±

0.0

0.0

0±

0.0

00.0±

0.0

0.0±

0.0

0.0

0±

0.0

00.0±

0.0

0.0

2±

0.0

0∑pT

0.0±

0.0

0.0±

0.0

0.0

0±

0.0

00.0±

0.0

0.0±

0.0

0.0

0±

0.0

00.0±

0.0

0.0

2±

0.0

0Z

veto

0.0±

0.0

0.0±

0.0

0.0

0±

0.0

00.0±

0.0

0.0±

0.0

0.0

0±

0.0

00.0±

0.0

0.0

2±

0.0

0

Tab

le3.13:

Cut

flow

for100%

decay

toe-τ

with

mass

130,300

and

500G

eV.

98

3.5 Selection efficiency

The Figs. 3.14, 3.15, 3.16, 3.17 and 3.18 show the acceptance (left), e-

stimated as the ratio between the number of reconstructed events and the

number of generated events, from MC signal in the five considered scena-

rios. In the Fig. 3.14, the acceptance assumes values between the 60% and

70%, due to the pseudorapidity range (|η| < 2.4) of the global muons that

we have considered. Also the electron acceptance (see Fig. 3.15) starts from

low values, but reaches higher ones than the previous scenario because of

a larger pseudorapidity range (|η| < 2.5). For the BR (Φ±± → e±µ±) =

100% scenario (see Fig. 3.16), this ratio is a wider range (60%-90%). The

acceptances plotted in the last two figures (3.17, 3.18), that include the taus,

are generally quite lower because of the lower tau hadronic reconstruction

efficiency if compared with electron and muon ones; this is also due the fact

that a significant fraction of the τ momentum escapes undetected with the

associated neutrino’s.

[GeV]±±ΦMass of 100 200 300 400 500

Acc

epta

nce

(MM

MM

)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9


) = 100%±µ±µ→±±ΦBR (

[GeV]±±ΦMass of 100 200 300 400 500

Sel

ectio

n E

ffici

ency

(M

MM

M)

0

0.2

0.4

0.6

0.8

1

) = 100%±µ±µ→±±ΦBR (>10 GeV

T2>20 GeV, p

T1p

)>12 GeV±l±m (l

relIso

SIP

T pΣ

Mass Window

CMS Preliminary 2011 -1 = 7 TeV, L = 4.93 fbs

Figure 3.14: Acceptance (left) and Signal detection Efficiencies (right) from MCin the scenario BR (Φ±± → µ±µ±) = 100%. The cuts applied at each step aresummarized in Tables 3.7 and 3.8. Each cut includes the previous ones.

On the right of these figures, the efficiencies for each of the selection and

for MC signal are shown for all the scenarios considered. They are estimated

99

[GeV]±±ΦMass of 100 200 300 400 500

Acc

epta

nce

(EE

EE

)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9


) = 100%±e±e→±±ΦBR (

[GeV]±±ΦMass of 100 200 300 400 500

Sel

ectio

n E

ffici

ency

(E

EE

E)

0

0.2

0.4

0.6

0.8

1

) = 100%±e±e→±±ΦBR (>10 GeV

T2>20 GeV, p

T1p

)>12 GeV±l±m (l

relIso

SIP

T pΣ

Mass Window


Figure 3.15: Acceptance (left) and Signal detection Efficiencies (right) from MCin the scenario BR (Φ±± → e±e±) = 100%. The cuts applied at each step aresummarized in Tables 3.7 and 3.8. Each cut includes the previous ones.

[GeV]±±ΦMass of 100 200 300 400 500

Acc

epta

nce

(EM

EM

)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9


) = 100%±µ±e→±±ΦBR (

[GeV]±±ΦMass of 100 200 300 400 500

Sel

ectio

n E

ffici

ency

(E

ME

M)

0

0.2

0.4

0.6

0.8

1

) = 100%±µ±e→±±ΦBR (>10 GeV

T2>20 GeV, p

T1p

)>12 GeV±l±m (l

relIso

SIP

T pΣ

Mass Window


Figure 3.16: Acceptance (left) and Signal detection Efficiencies (right) from MCin the scenario BR (Φ±± → e±µ±) = 100%. The cuts applied at each step aresummarized in Tables 3.7 and 3.8. Each cut includes the previous ones.

100

[GeV]±±ΦMass of

100 200 300 400 500

Acc

epta

nce

(MT

MT

)

0

0.005

0.01

0.015

0.02


) = 100%±τ±µ→±±ΦBR (

[GeV]±±ΦMass of 100 200 300 400 500

Sel

ectio

n E

ffici

ency

(M

TM

T)

0

0.2

0.4

0.6

0.8

1

) = 100%±τ±µ→±±ΦBR (>10 GeV

T2>20 GeV, p

T1p

)>12 GeV±l±m (lrelIsoSIP

T pΣ

Mass WindowZveto


Figure 3.17: Acceptance (left) and Signal detection Efficiencies (right) from MCin the scenario BR (Φ±± → µ±τ±) = 100%. The cuts applied at each step aresummarized in Tables 3.7 and 3.8. Each cut includes the previous ones.

[GeV]±±ΦMass of

100 200 300 400 500

Acc

epta

nce

(ET

ET

)

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035


) = 100%±τ±e→±±ΦBR (

[GeV]±±ΦMass of 100 200 300 400 500

Sel

ectio

n E

ffici

ency

(E

TE

T)

0

0.2

0.4

0.6

0.8

1

) = 100%±τ±e→±±ΦBR (>10 GeV

T2>20 GeV, p

T1p

)>12 GeV±l±m (lrelIsoSIP

T pΣ

Mass WindowZveto


Figure 3.18: Acceptance (left) and Signal detection Efficiencies (right) from MCin the scenario BR (Φ±± → e±τ±) = 100%. The cuts applied at each step aresummarized in Tables 3.7 and 3.8. Each cut includes the previous ones.

101

with respect to the acceptance. From the plots including only electrons and

muons, we can note that, after applying the cuts on the pT and same sign

dilepton mass, the efficiency is 100%, confirming the good choice of these two

kinematical cuts. From the plots including taus, the efficiencies are not flat

as a consequence of the rough tuning and the acceptance shown on the left

of the figures.

3.6 Systematic uncertainties

The impact on the selection efficiency of the uncertainties related to the

electron and muon identification and isolation algorithms and the relevant

misidentification rates, detailed in [45, 51, 52, 53, 54], are estimated to be less

than 2% by using a standard ‘tag-and-probe’ method [55] that relies on Z →`+`− decays to provide an unbiased and high-purity sample of leptons. A ‘tag’

lepton is required to satisfy stringent criteria on reconstruction, identification,

and isolation, while a ‘probe’ lepton is used to measure the efficiency of a

particular selection by using the Z mass constraint. The ratio of the overall

efficiencies as measured in data and simulated events is used as a correction

factor in the bins of pT and η for the efficiency determined through simulation,

and that is propagated to the final result.

The τhad reconstruction and identification efficiency via the HPS algo-

rithm is also derived from data and simulations, using the tag-and-probe

method with Z → τ+(→ µ+ + νµ + ντ )τ−(→ τhad + ντ ) events [52]. The

uncertainty of the measured efficiency of the τhad algorithms is 6% [52]. E-

stimation of the τhad energy-scale uncertainty is also performed with data in

the Z → ττ → µ+ τhad final state, and is found to be less than 3%. The τhad

charge misidentification rate is measured to be less than 3%.

The theoretical uncertainty in the signal cross section, which has been

calculated at NLO, is about 10-15%, and arises because of its sensitivity to

the renormalization scale and parton distribution functions [21].

The luminosity uncertainty is estimated to be 2.2% [36].

The systematic uncertainties are summarized in Table 3.14.

102

Lepton (e or µ) ID and isolation 2%τhad ID and isolation 6%τhad energy scale 3%τhad misid rate 3%

Trigger and primary vertex finding 1.5%Signal cross section 10-15%

Luminosity 2.2%Statistical uncertainty of signal samples 1-7%

Table 3.14: Source of systematic uncertainties and impact on the full selectionefficiency.

103

104

Chapter 4

Results and Statistical

Interpretation

In order to understand the results about a search of new particles or new

phenomena it is need to introduce the basic notions about the statistical

interpretation of them in terms of sensitivity to the exclusion or the discovery.

This sensitivity depends and can be compromised by some factors: a low

signal strength, the existence of a background comparable with the expected

signal and a bad experimental resolution.

4.1 Final distributions

The results of the analysis can be expressed in terms of invariant mass

distribution. They are shown in the Figs. 4.1, 4.2, 4.3, 4.4, 4.5 for each

scenario considered after applying all of cuts. The invariant mass distribu-

tions involving only light leptons (see Figs. 4.1, 4.2, 4.3) show a signal excess

for mΦ±± = 130 GeV compared to the background, but not any clustering

can be observed around the signal peak. Hence, this excess could be due

to statistical fluctuations. To understand the origin of this excess, more

data are required. We can observe that no event passes the full selection in

the invariant mass distribution of Φ±± for BR = 100% to µτ channel (see

Fig. 4.4). Moreover, we can note an obvious reduction of the background.

We find data and Monte Carlo simulations to be in reasonable agreement for

105

all final states. In fact, we observe only few events at low masses, consistent

with background expectations.

Figure 4.1: Invariant mass distribution of Φ±± for BR = 100% to µµ channel,after full selection. The samples correspond to an integrated luminosity ofL = 4.93 fb−1.

106

Figure 4.2: Invariant mass distribution of Φ±± for BR = 100% to ee channel,after full selection. The samples correspond to an integrated luminosity ofL = 4.93 fb−1.

107

Figure 4.3: Invariant mass distribution of Φ±± for BR = 100% to eµ channel,after full selection. The samples correspond to an integrated luminosity ofL = 4.93 fb−1.

108

Figure 4.4: Invariant mass distribution of Φ±± for BR = 100% to µτ channel,after full selection. The samples correspond to an integrated luminosity ofL = 4.93 fb−1.

109

Figure 4.5: Invariant mass distribution of Φ±± for BR = 100% to eτ channel,after full selection. The samples correspond to an integrated luminosity ofL = 4.93 fb−1.

110

4.2 Statistical interpretation:

the CLs Method

The concept of the Confidence Level (CLs) is related to the fact that,

while an experiment is performed, we are interesting to confirm a new theory

or to exclude it in equal measure. For each discovery, it is necessary to

consider the hypothesis that the model from which we start can also be

wrong. Experiments are designed to be sensitive to the parameter set for

each model in a way so that the confidence levels give meaningful information.

The goal of a search is to extract the greatest possible number of information

from the data in possession, despite not having an experimental evidence of

the validity of a theory. In the case of our search, it means to exclude as

effectively as possible the existence of Higgs boson in its absence and to

confirm its existence in its presence in a mass range in which the experiment

is sensible.

The CLs, or modified frequentist method [56], is used for calculations

of exclusion limits. The analysis of the results can be formulated in terms

of a hypothesis test. The null hypothesis (H0) is that the signal is absent

and the alternative hypothesis (H1) is that it exists. This method consists in

quantifying the degree (level) to which the hypotheses are favored or rejected

by an experimental observation. It can be divided in the following steps:

• to identify the observables in the experiment of which the search con-

sists (in our case the invariant mass of the reconstructed particle pairs

that we suppose coming from the Higgs decay);

• to define a test statistic (or function) of the observables and the model

parameters for both the background and the hypothetical signal;

• to set the ranges of the values for the test statistic in which the obser-

vations will lead to the acceptance or rejection of the null hypothesis.

In practice, this means to specify a confidence level for the exclusion, like in

our case, or for the discovery. A confidence limit for exclusion is defined as

the value of a population parameter (such as a particle mass or a production

111

rate) which is excluded at a specified confidence level; it is represented as a

percent value.

In order to define the method, we need to make a choice of the test stati-

stic and the treatment of the systematic uncertainties in the construction of

the test statistic and in generating data (toy Monte Carlo pseudo-data sets).

First of all, we take into account all independent sources of systematic un-

certainties, both theoretical and instrumental, and assign each of them its

own nuisance parameter θi, whose best estimate, prior data analysis, is θi.

When a nuisance parameter is taken to be distributed according to a normal

probability distribution function (p.d.f.), the effect of its variation on an ob-

servable O is propagated either as a Gaussian error, O = O0 · (1+σ ·θ) (used

only for observables that can take both positive and negative values), or as a

log-normal error, O = O0 ·κθ (used only for positive definite observables). In

this case, O0 is the observable value without error, and σ and κ characterize

the relative scale of the uncertainties [57].

In order to construct the test statistic, a likelihood function (L) is defined

as follows:

L(data|µ, θ) = Poisson(data|µ · s(θ) + b(θ)) · p(θ|θ) , (4.1)

where Poisson(data|µ · s(θ) + b(θ)) is the Poisson probability to observe

data, assuming that both the expected signal and background models, s(θ)

and b(θ), depend on some nuisance parameters θ. The free parameter µ is

the signal strength modifier, that is the ratio between the number of observed

events and the number of events expected by the model (process of normali-

zation). Thus, such a parameter µ takes into account how the cross section

of the Higgs boson varies with the collision energy and the decay mode, and

can be written by the σ/σmodel ratio.

The comparison between the data and the background-only (µ = 0) and

signal+background (µ) hypotheses is performed by the test statistic qµ, given

by the following likelihood ratio:

qµ = −2 lnL(data|µ, θµ)

L(data|µ, θ), (4.2)

112

where data can be the actual experimental observation or pseudo-data (toys).

Assuming the independence of the measurements, both the numerator and

the denominator are maximized according to the method of maximum like-

lihood [58]. In the numerator, µ remains fixed and only θ is allowed to float

and θµ denotes the value for which L reaches the maximum. In the denomi-

nator, both µ and θ are allowed to float and µ and θ denote the values for

which L reaches the maximum. The maximization of the likelihood func-

tion is equivalent to the minimization of the logarithmic function, so the

constructed variable qµ is distributed as a χ2 variable.

The two tail probabilities (p-value), associated with the actual observa-

tion, can be estimated under the signal+background hypothesis:

pµ = P(qµ ≥ qobsµ |µs(θobsµ + b(θobsµ ))

)=

∫ ∞qobsµ

f(qµ|µ, θobsµ )dqµ , (4.3)

and under the background-only hypothesis:

p0 = P(qµ ≥ qobsµ |b(θobsµ ))

)=

∫ ∞qobs0

f(qµ|0, θobs0 )dqµ , (4.4)

where qobsµ is the observed value of the test statistic, θobs0 and θobsµ are the values

of the nuisance parameters that best describe the experimentally observed

data (i.e. maximize L), f(qµ|0, θobs0 ) and f(qµ|µ, θobsµ ) are the qµ distributions,

corresponding to the two hypothesis, generated by toy Monte Carlo pseudo-

data sets.

Then, CLs(µ) is defined as the following ratio:

CLs(µ) =P(

qµ ≥ qobsµ |µs(θobs

µ + b(θobsµ ))

)P(

qµ ≥ qobsµ |b(θobs

µ ))) . (4.5)

If CLs ≤ α for µ = 1, we say that the Higgs boson of the model is excluded

at the (1 − α) confidence level. Since we are interesting to quote the 95%

confidence level upper limit on µ, we adjust µ until we reach CLs = 0.05, so

defining µ95%CL.

113

The most straightforward way for defining the expected median upper

limit and ±1σ and ±2σ bands for the background-only hypothesis is to

generate a large set of background-only pseudo-data and calculate CLs and

µ95%CL for each of them, as if they were real data (Fig. 4.6 (left)). Then, a

Figure 4.6: (Left) An example of differential distribution of possible limits onµ for the background-only hypothesis (s = 0, b = 1, no systematic errors).(Right) c.d.f. of the plot on the left with 2.5%, 16%, 50%, 84% and 97%quantiles (horizontal lines) defining the median expected limit as well asthe ±1σ (68%) and ±2σ (95%) bands for the expected value of µ for thebackground-only hypothesis.

cumulative probability distribution function (c.d.f.) of results can be built,

by starting the integration from the side corresponding to low event yields

(see Fig. 4.6 (right)). The point at which the c.d.f. crosses the quantile of

50% is the median expected value. The ±1σ (68%) and ±2σ (95%) bands

are defined by crossings of the 16% and 84% quantiles in the former case and

2.5% and 97.5% in the latter case.

In the Fig. 4.6 (right), the green and yellow bands are the ±1σ (68%) and

±2σ (95%) range in which the results are expected to fall in the background-

only hypothesis.

4.3 Exclusion Limits

A CLs method (see Sec. 4.2) is used to calculate an upper limit for the

Φ++ cross section at the 95% confidence level (CL) as a function of the Φ++

114

mass hypothesis; the exclusion limits have been calculated combining the

results of this analysis with those obtained by the three lepton final state

analysis. The systematic uncertainties summarized in Table 3.14 are taken

into account, too.

The results of the exclusion limit calculations are and reported in

Figs. 4.7, 4.8, 4.9, 4.10, 4.11, in which also the previous limit exclusion at

Tevatron are shown, except for the not studied eτ channel. The observed

limits are shown by the black line; the dashed line indicates the median

expected limit on µ for the background-only hypothesis, while the green

(yellow) bands indicate the range that are expected to contain 68% (95%) of

all observed limit excursions from the median.

The exclusion limits are calculated from the intersection between the ob-

served limits from the data and the median expected limit. Lower bounds on

the Φ++ mass are established of 459 GeV in the µµ channel, 444 GeV in the

ee channel, 453 GeV in the eµ channel, 375 GeV in the µτ channel, 373 GeV

in the eτ channel; so, we exclude the doubly charged Higgs boson in mass

range below these bounds, providing significantly more stringent constraints

than previously published limits. They are summarized in Table 4.1.

Benchmark point CMS 95% CL limit CMS combined 95% CL limit

for pair production only

BR (Φ++ → µ+µ+) = 100% 395 GeV 459 GeV

BR (Φ++ → e+e+) = 100% 382 GeV 444 GeV

BR (Φ++ → e+µ+) = 100% 391 GeV 453 GeV

BR (Φ++ → µ+τ+) = 100% 300 GeV 375 GeV

BR (Φ++ → e+τ+) = 100% 293 GeV 373 GeV

Table 4.1: Summary of the 95% CL exclusion limits.

115

Figure 4.7: Lower bound on Φ++ mass at 95% for BR = 100% to µµ channel.

116

Figure 4.8: Lower bound on Φ++ mass at 95% for BR = 100% to ee channel.

117

Figure 4.9: Lower bound on Φ++ mass at 95% for BR = 100% to eµ channel.

118

Figure 4.10: Lower bound on Φ++ mass at 95% for BR = 100% to µτ channel.

119

Figure 4.11: Lower bound on Φ++ mass at 95% for BR = 100% to eτ channel.

120

conclusions

A search for the doubly charged Higgs boson Φ++ has been conducted using

a data sample corresponding to an integrated luminosity of 4.93± 0.11 fb−1

collected by the CMS experiment at center-of-mass energy of 7 TeV.

The production of the doubly charged Higgs boson at LHC can give rise

to a distinctive multi-lepton signature: due to flavour non-conservation, the

final states can be combinations of all possible leptons, requiring that two of

these leptons should be of the same charge, both coming from the same Φ±±

boson.

Such different scenarios have been analyzed separately in order to achieve the

best signal to background ratio. Additionally, final states are discriminated

based on the number of reconstructed τ -jets. In this analysis, the Φ±± →τ±τ± final state is not included because the efficiency of the four hadronic

tau reconstruction final state is too low to make the signal enhanced with

respect to the background. The search has been performed only in the case

of pair production processes applying cuts on some observables relevant for

this analysis in order to reduce the background events.

The first observables on which we have been applied the cuts are kine-

matical variables. While the lepton pT cut has been used in order to reduce

the background events for which the leptons originate from the semi-leptonic

b-decays, tending to be less energetic, the cut on the same sign dilepton mass

has been applied in order to suppress the background events coming form low

mass b-resonances, photon conversions and the low mass tail of the dilepton

distribution for signal and background that are generally not interesting for

this analysis.

In addition to the kinematic selection criteria, some cuts on other obser-

vables are used for the selection: the cut on the sum of the relative isolation

121

of the two worst isolated leptons (e,µ) and the cut on the significance of

the impact parameter. The former ensures an effective reduction of the

background contribution from QCD multi-jets and misidentified leptons. The

latter is carried out to ensure that no leptons from secondary vertex are

selected by the analysis.

For a further signal discrimination against the background after preselec-

tion, we have used additional variables. The sum of pT of all the leptons in

the event has been used in order to eliminate the remaining tt events that

involve light leptons. The Z veto cut has been applied only for the final

states involving τ to suppress the Drell-Yan events with leptons coming from

the Z/γ decay. Finally, the events are counted in a same sign dilepton mass

window whose size is different for each final state and each mass in order to

reduce the ZZ background events as much as possible.

Then, we have obtained the event yields after each consecutive cut for

four lepton analysis for all of mass hypotheses in the five scenarios consi-

dered and the final results in terms of invariant mass distribution. We have

observed a reduction of the background events and the events that survive

are those coming from ZZ decay. We have also observed a signal excess for

mΦ±± = 130 GeV compared to the background in the invariant mass distri-

butions involving only light leptons without observing any clustering around

the signal peak. Hence, we can state that more data are required in order to

understand its origin and, in the present state, we can think only as due to

some statistical fluctuations.

Moreover, since we can observed only few events at low masses, consistent

with background expectations, we state that data and Monte Carlo simula-

tions are in reasonable agreement for all final states and a possible hint for

the existence of a double charged Higgs can be excluded.

The CLs method have been used to calculate an upper limit for the Φ++

cross section at the 95% confidence level (CL) as a function of the Φ++ mass

hypothesis.

No evidence for the existence of the Φ++ has been found. Lower bounds on

the Φ++ mass are established, of 459 GeV in the µµ channel, 444 GeV in the

ee channel, 453 GeV in the eµ channel, 375 GeV in the µτ channel, 373 GeV

122

in the eτ channel; so, we exclude the doubly charged Higgs boson in mass

range below these bounds, providing significantly more stringent constraints

than previously published limits.

123

124

Acknowledgements/

Ringraziamenti

Una o due volte nella vita puo capitare di trovarsi nel posto giusto al mo-

mento giusto: e cio che e capitato a me circa dieci mesi or sono! Ovviamente

i miei genitori avrebbero preferito che io finissi gli studi molto prima (e, ad

essere sinceri, anche io), magari in un periodo storico meno produttivo dal

punto di vista scientifico, ma cosı non e stato. Finalmente il bosone di Higgs

e uscito allo scoperto, forse per il caldo torrido di quest’ultima estate non

ancora conclusa (parafrasando una delle mie piu care amiche). La comunita

scientifica e comunque cauta: e chiaro che lı c’e qualcosa ma aspettiamo a

dire che e proprio la cara particella di Dio da tutti bramata!

Ed e proprio Dio che vorrei ringraziare prima di tutti, perche mi ha dato la

forza, la pazienza, l’equilibrio e la lucidita per affrontare e superare tutti gli

ostacoli lungo il mio cammino. Lo ringraziero sempre e comunque.

Subito dopo, il mio pensiero piu caro e il mio ringraziamento piu dovuto

vanno ai miei genitori meravigliosi, a cui ho voluto dedicare questo lavoro.

Li ringrazio perche senza di loro nulla di tutto questo sarebbe stato possibile,

e non mi riferisco solo al pagamento delle tasse! Sono i miei angeli custodi

(non e un caso che si chiamino Angela ed Angelo) e oggi voglio ricompensarli

di tutti i sacrifici, mettendo nero su bianco che voglio loro un mondo di bene!

Non posso tralasciare altre due persone molto importanti nella mia vita, che

mi hanno sopportato e amato: Patty e Gianni, la sorella e il fratello migliori

che io potessi mai avere. E Davide, “magabondo” come za’ Lili ma tanto

speciale e dolce, che fa impazzire d’amore il mio cuore ogni volta che mi

bacia e mi abbraccia.

125

Ringrazio i miei due relatori, il prof. de Palma e il dott. De Filippis,

i quali hanno creduto in me e mi hanno dato la possibilita di fare parte di

questo mondo. Li ringrazio per avermi formata, seguita, divertita e presa

in giro per i miei quaderni sempre pieni di appunti e per er Papaya, sempre

pronto a rimproverarmi per aver mandato in tilt la farm estone (a proposito,

che fine ha fatto? Ha saputo che hanno scoperto l’Higgs? Oppure e ancora

in giardino a tosare l’erba? Vabbe... gli mandero io un messaggio!), ma

soprattutto per avermi fatto comprendere appieno non quale lavoro voglio

fare, ma quale persona voglio essere.

Ringrazio Fritto, che sicuramente mi perdonera per averlo chiamato cosı,

in quest’ultimo periodo sempre molto vicino (e, secondo alcuni, anche un po’

troppo!). Mi mancheranno le sue visite in stanza dopo pranzo, le sue assurde

teorie riguardo... e i suoi modi di corteggiare le donzelle.

I want also to thank two terrible Indian guys, Gurpreet and Simran. In

these months, they have been very patient with me and my not perfect En-

glish. I will always remember the machine break at eleven thirty to meet

“some beautiful girls”, Gurpreet performance in Cellamare and Simran din-

ner in Genevra. They have been simply wonderful: I will have them in my

heart forever and I will miss them very much.

To Piet, the new entry of the group, for his sympathy in joking about my

little steps and his devotion in reading my thesis: thanks so much.

Al caro Mario per i suoi saggi consigli e le sue pungenti critiche: “Grazie

di tutto!”

E come posso non ringraziare il caro, fantastico, mitico Giacinto? E’ stato

favoloso nel darmi la precedenza quando disperata cercavo di sottomettere i

miei job che runnavano per giorni e giorni, intasando talvolta la farm di Bari

(essı, e un vizio che hanno dovuto sopportare in tanti, anche in Wisconsin!),

nel darmi consigli quando si bloccavano e nel progettare omicidi con con-

seguenti occultamenti di cadaveri nei sotterranei. Nessuna torta potra mai

ricompensare la sua infinita disponibilita.

Rivolgo un caro pensiero anche a tutti i professori e non del corridoio di

CMS e un po’ oltre: “Mi mancherete!”

A tutti i miei colleghi/amici di corso, che si sono avvicendati durante gli

126

anni: grazie per la compagnia, la comprensione, i consigli, le critiche, le gite,

le serate, le risate e i pianti!

Un grazie speciale alla mia grande amica Angela, alla quale voglio tantissimo

bene. Mi ha reso partecipe del suo mondo che con il tempo ho imparato ad

amare, mi ha sostenuto con tanto affetto anche quando la vita ci ha allon-

tanato, mi e stata accanto quando mi sono sentita persa.

E un grazie anche alla compagna di avventure/sventure degli ultimi tre anni,

Giorgia. Con lei ho condiviso gioie e dolori, sorrisi e lacrime, esami uni-

versitari e non. Alle ore passate insieme a studiare, a guardare telefilm, a

inventarci soprannomi per tutti, a cercare di risolvere gli indovinelli, i rebus

e i sudoku, ad analizzare i nostri status e a mandare a quel paese tutte le

persone che... se lo meritavano! E che dire della dolcissima Zoe e del bravis-

simo Colin? Solo che li ringrazio per il sostegno fisico-morale di questi anni:

provo per loro un grandissimo affetto e resteranno sempre nel mio cuore.

A tutti i miei amici di sempre che mi hanno vista cambiare e migliorare

(cosı mi hanno detto) durante il corso degli anni vorrei dire che finalmente

ho finito! Chiedo loro scusa se mi sono allontanata, soprattutto in questo pe-

riodo di tesi, ma ho continuato sempre a voler bene ad ognuno di loro: sono

stati sempre nei miei pensieri, sempre nel mio cuore e sempre lo saranno

nonostante tutto! A Rosanna, mia amica da trent’anni, che ha sempre cre-

duto in me. A Mario e a Maria Teresa, alla loro capacita di convincermi a

fare “un giro veloce a Bari”. A Valeria, che con la sua stravaganza e pazzia

mi ha spesso fatto passare i cinque minuti. A Terry e Vincenzo, e alle serate

passate con Picicco, intenti tutti e quattro a giocare ad Inkognito. A Maya,

dolce e gentile, sempre pronta ad incoraggiarmi. Ai piccoli Antonio e Mattia,

a Michele Los, a Michele Aff e a Maria Chiara. Al caro don Valentino, che

ha avuto cura della mia anima e della mia mente. E al dott. Fassoulis e al

dott. Sammarco, sempre disponibili a qualsiasi ora del giorno e della notte.

E, infine, ringrazio tutti quelli che mi hanno tradita, ferita, delusa, offesa,

ingannata: se oggi sono una persona migliore, lo devo anche a loro. FV!

127

128

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UNIVERSITA DEGLI STUDI DI BARI Aldo Moro UNIVERSITA DEGLI STUDI DI BARI Aldo Moro FACOLTA DI SCIENZE MATEMATICHE FISICHE E NATURALI Dipartimento Interateneo di Fisica M. Merlin Tesi