exclusive search for a fermiophobic higgs at · pdf fileexclusive search for a fermiophobic...

Exclusive search for a

Fermiophobic Higgs at CMS

Cristiano Fanelli

Matr. 695354

Dipartimento di Fisica

La Sapienza

A thesis submitted for the degree of

MSc, Laurea Specialistica

A.A. 2010/2011

Advisors: Prof. Daniele Del Re, Prof. Shahram Rahatlou

Abstract

This dissertation deals with the exclusive search for a fermiophobic Higgs

decaying into two photons recorded by CMS detector exploiting the pecu-

liar topologies of vector boson fusion and Higgs-strahlung mechanisms of

production, in particular selecting the jets involved in the related Feynman

diagrams. Assuming fermiophobia, i.e. Higgs doesn’t couple to fermions at

tree-level, this resolves in an enhancement of the Higgs B.R. in two pho-

tons, making this channel really promising especially for low mass Higgs.

We discuss the Monte Carlo samples generated for this analysis and the

characteristics of CMS detector, in particular the electromagnetic calorime-

ter. Then the discussion is focused on the strategy of the analysis and

the obtained results. A 95% confidence level upper limit on the produc-

tion cross-section of fermiophobic Higgs with 2010 data at CMS is finally

presented. In conclusion, this analysis proves that the exclusive search is

promising.

Contents

List of Figures v

List of Tables ix

Glossary xi

1 Introduction 1

2 Fermiophobic Higgs in 2HDM 3

2.1 The structure of 2HDM . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.2 The fermiophobic limit . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.2.1 Neutral Higgses couplings to fermions in 2HDM type I . . . . . . 9

2.3 Fermiophobic branching ratios and cross sections . . . . . . . . . . . . . 10

2.3.1 Branching ratio of fermiophobic Higgs . . . . . . . . . . . . . . . 10

2.3.2 Charged scalar Higgs loops . . . . . . . . . . . . . . . . . . . . . 11

2.3.3 Production cross sections at LHC . . . . . . . . . . . . . . . . . . 11

2.3.4 Irreducible background for Higgs decay into γγ . . . . . . . . . . 16

2.3.5 MC Samples for preliminary studies . . . . . . . . . . . . . . . . 17

3 The Large Hadron Collider and CMS Experiment 19

3.1 The Compact Muon Solenoid detector . . . . . . . . . . . . . . . . . . . 22

3.2 The inner tracking system . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.3 The Electromagnetic Calorimeter (ECAL) . . . . . . . . . . . . . . . . . 28

3.3.1 The PbWO4 crystals . . . . . . . . . . . . . . . . . . . . . . . . 29

3.3.2 The ECAL Barrel . . . . . . . . . . . . . . . . . . . . . . . . . . 30

3.3.3 The ECAL Endcaps . . . . . . . . . . . . . . . . . . . . . . . . . 32

3.3.4 The ECAL energy resolution . . . . . . . . . . . . . . . . . . . . 33

i

CONTENTS

3.4 The Hadronic Calorimeter . . . . . . . . . . . . . . . . . . . . . . . . . . 33

3.5 The Muon Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3.6 The CMS Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

4 Photon and Jet Reconstruction 43

4.1 Photon reconstruction in ECAL . . . . . . . . . . . . . . . . . . . . . . . 44

4.1.1 Energy corrections . . . . . . . . . . . . . . . . . . . . . . . . . . 46

4.1.2 Determination of shower position . . . . . . . . . . . . . . . . . . 47

4.2 Definition of Isolation Criteria . . . . . . . . . . . . . . . . . . . . . . . . 47

4.2.1 Tracks Isolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

4.2.2 Electromagnetic Isolation . . . . . . . . . . . . . . . . . . . . . . 48

4.2.3 Hadronic Isolation . . . . . . . . . . . . . . . . . . . . . . . . . . 48

4.2.4 Cluster Shape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

4.3 Photon Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

4.4 Particle Flow Jets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

5 Analysis Method and Optimization 55

5.1 MC Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

5.1.1 Signal Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

5.1.2 Background Samples . . . . . . . . . . . . . . . . . . . . . . . . . 58

5.2 Selection Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

5.2.1 Photons selection variables . . . . . . . . . . . . . . . . . . . . . 63

5.2.2 Jets selection variables . . . . . . . . . . . . . . . . . . . . . . . . 64

5.2.3 Zeppenfeld . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

5.3 Optimization of Selection Criteria . . . . . . . . . . . . . . . . . . . . . 68

5.4 Signal and Background Efficiency . . . . . . . . . . . . . . . . . . . . . . 72

5.4.1 VBF: Yields and Efficiencies . . . . . . . . . . . . . . . . . . . . 72

5.4.2 HSTRA: Yields and Efficiencies . . . . . . . . . . . . . . . . . . . 77

6 Results 83

6.1 Upper Limit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

6.2 Estimate for Exclusion Potential on Simulation . . . . . . . . . . . . . . 85

6.3 Data-MC Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

6.4 Control Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

ii

CONTENTS

6.5 Systematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

6.5.1 Signal Detector Efficiency . . . . . . . . . . . . . . . . . . . . . . 97

6.5.2 Background Uncertainties . . . . . . . . . . . . . . . . . . . . . . 99

6.5.3 Luminosity Uncertainties . . . . . . . . . . . . . . . . . . . . . . 100

6.5.4 Theoretical Uncertainties . . . . . . . . . . . . . . . . . . . . . . 101

6.6 Observed Upper Limit on Cross Section . . . . . . . . . . . . . . . . . . 103

7 Conclusions 105

A Fermiophobic Higgs production induced by gluon fusion 107

References 113

iii

CONTENTS

iv

List of Figures

2.1 Higgs coupling to fermions at tree-level . . . . . . . . . . . . . . . . . . . 10

2.2 Loop of top in H → γγ . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.3 The main loops responsible for fermiophobic decay into γγ . . . . . . . . 11

2.4 SM and fermiophobic BR’s . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.5 Charged Higgs loops . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.6 Fermiophobic Higgs coupling to charged Higgses . . . . . . . . . . . . . 13

2.7 SM Higgs production at LHC . . . . . . . . . . . . . . . . . . . . . . . . 14

2.8 SM Higgs cross sections . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.9 Transverse momentum of SM Higgs . . . . . . . . . . . . . . . . . . . . . 15

2.10 Irreducible background for γγ . . . . . . . . . . . . . . . . . . . . . . . . 16

2.11 Example of reducible background to diphoton search . . . . . . . . . . . 16

2.12 Photons transverse momentum distributions . . . . . . . . . . . . . . . . 17

2.13 Photons pseudorapidity distributions . . . . . . . . . . . . . . . . . . . . 17

3.2 View of the four LHC experiments . . . . . . . . . . . . . . . . . . . . . 21

3.3 CMS experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.4 CMS slice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.5 Pseudorapidity η . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.6 Layout of the tracker system . . . . . . . . . . . . . . . . . . . . . . . . 26

3.7 Si-Modules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.8 Tracker pT resolution and efficiency . . . . . . . . . . . . . . . . . . . . . 27

3.9 Material budget . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.10 ECAL layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.11 ECAL quarter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.12 Stages of an ECAL supermodule assembly . . . . . . . . . . . . . . . . . 32

v

LIST OF FIGURES

3.13 ECAL resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

3.14 HCAL longitudinal view . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.15 Longitudinal and transverse section of muon detector . . . . . . . . . . . 38

3.16 DT chamber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

3.17 Muon detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

4.1 View of supercluster reconstruction . . . . . . . . . . . . . . . . . . . . . 45

4.2 Hybrid algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

4.3 N − 1 (ECAL) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

4.4 N − 1 (HCAL) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

4.5 N − 1 (Track Iso) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

4.6 Particle Flow Jet response . . . . . . . . . . . . . . . . . . . . . . . . . . 54

5.1 sketch of VBF and HSTRA topologies . . . . . . . . . . . . . . . . . . . 56

5.2 MADGRAPH - qq → γγ and qq → γγg . . . . . . . . . . . . . . . . . . 59

5.3 MADGRAPH - qg → γγq and qq → γγqq . . . . . . . . . . . . . . . . . 60

5.4 MADGRAPH - qq → γγgg and qg → γγqg . . . . . . . . . . . . . . . . 61

5.5 MC Signal and Background shapes . . . . . . . . . . . . . . . . . . . . . 63

5.6 Transverse momentum distributions of the two highest pT photons of the

event . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

5.7 Transverse momentum distributions of the two highest pT jets of the event 65

5.8 Di-jet invariant mass spectrum . . . . . . . . . . . . . . . . . . . . . . . 65

5.9 Difference in pseudorapidity of the two jets . . . . . . . . . . . . . . . . 66

5.10 Zeppenfeld variable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

5.11 step-1 optimization: (VBF) . . . . . . . . . . . . . . . . . . . . . . . . . 69

5.12 VBF and HSTRA step-2 optimization . . . . . . . . . . . . . . . . . . . 70

5.13 VBF mγγ after cut1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

5.14 VBF mγγ after cut2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

5.15 VBF mγγ after cut3 and after cut4 . . . . . . . . . . . . . . . . . . . . . 76

5.16 VBF mγγ after cut5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

5.17 HSTRA mγγ after cut1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79


5.19 HSTRA mγγ after cut3 and after cut4 . . . . . . . . . . . . . . . . . . . 81


vi

LIST OF FIGURES

6.1 Estimated upper limit on VBF and HSTRA with 1 fb−1 . . . . . . . . . 86

6.2 VBF and HSTRA significance . . . . . . . . . . . . . . . . . . . . . . . . 87

6.3 VBF variables (data-MC) . . . . . . . . . . . . . . . . . . . . . . . . . . 88

6.4 VBF di-photon spectrum (data-MC) . . . . . . . . . . . . . . . . . . . . 89

6.5 HSTRA variables (data-MC) . . . . . . . . . . . . . . . . . . . . . . . . 90

6.6 HSTRA di-photon spectrum (data-MC) . . . . . . . . . . . . . . . . . . 91

6.7 VBF variables Control Sample . . . . . . . . . . . . . . . . . . . . . . . 93

6.8 VBF di-photon spectrum Control Sample . . . . . . . . . . . . . . . . . 94

6.9 HSTRA variables Control Sample . . . . . . . . . . . . . . . . . . . . . . 95

6.10 HSTRA di-photon spectrum Control Sample . . . . . . . . . . . . . . . 96

6.11 Efficiency vs number of vertices . . . . . . . . . . . . . . . . . . . . . . . 98

6.12 CMS Exclusive Search: preliminary upper limit on cross section . . . . . 103

7.1 DØ preliminary results (2011) from inclusive analysis . . . . . . . . . . 106

7.2 CMS estimated U.L. of VBF and HSTRA . . . . . . . . . . . . . . . . . 106

A.1 A possible Fermiophobic Higgs production via gluon fusion . . . . . . . 107

A.2 1-loop Mixing of Higgs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

A.3 Double real emission in gluon fusion . . . . . . . . . . . . . . . . . . . . 112

vii

LIST OF FIGURES

viii

List of Tables

2.1 2HDM I and II: couplings to fermions . . . . . . . . . . . . . . . . . . . 9

2.2 Fermiophobic BR and cross-sections . . . . . . . . . . . . . . . . . . . . 15

3.1 Summary of designed LHC characteristics. . . . . . . . . . . . . . . . . . 22

4.1 Parameters used in the Hybrid algorithm. . . . . . . . . . . . . . . . . . 46

4.2 Photon identification thresholds . . . . . . . . . . . . . . . . . . . . . . . 51

5.1 Main characteristics of the signal MC samples: σ, εMC , Leq . . . . . . . 57

5.2 Main characteristics of the bkg MC samples: σ, εMC , Leq . . . . . . . . 62

5.3 VBF and HSTRA optimization: step-1 and step-2 summary . . . . . . . 71

5.4 Absolute Efficiencies after each cut (VBF) . . . . . . . . . . . . . . . . . 73

5.5 Events after each cut (VBF) . . . . . . . . . . . . . . . . . . . . . . . . . 73

5.6 Absolute Efficiencies after each cut (HSTRA) . . . . . . . . . . . . . . . 78

5.7 Events after each cut (HSTRA) . . . . . . . . . . . . . . . . . . . . . . . 78

6.1 Systematic uncertainties on background . . . . . . . . . . . . . . . . . . 99

6.2 Estimates of main systematic uncertainties . . . . . . . . . . . . . . . . 100

6.3 VBF and HSTRA theoretical uncertainties . . . . . . . . . . . . . . . . 102

ix

GLOSSARY

x

Glossary

2HDM two Higgs doublets model; the sim-

plest extension of SM which provides

two neutral scalar Higgses.

bkg Background

BR Branching Ratio

CMS Compact Muon Solenoid; one of the

two large general-purpose particle

physics detectors built in the Large

Hadron Collider (LHC) at CERN.

CS Control Sample

fpho fermiophobic; of a particle which

doesn’t couple at tree-level with

fermions.

GGF gluon-fusion; the main mechanism of

production of SM Higgs, not allowed

under the hypothesis of fermiopho-

bia.

HSTRA Higgs-strahlung; the second main

mechanism of production of a fermio-

phobic Higgs.

LHC Large Hadron Collider; proton-

proton collider at CERN.

MC Monte Carlo

phID Photon Identification

s.s.b. spontaneous symmetry breaking;

mechanism through which is possible

to provide a gauge invariant theory

with massive particles.

SM Standard Model

UL Upper Limit

V.E.V. Vacuum Expectation Value

VBF vector boson fusion; the main mecha-

nism of production of a fermiophobic

Higgs.

xi

GLOSSARY

xii

1

Introduction

The search for a standard model (SM) Higgs boson decaying into two photons is chal-

lenging because of the very small branching ratio. In the SM, a Higgs boson with

nominal mass of 120 GeV, has a B.R.(H → γγ) ≈ 0.23% (see Fig. 2.4). Nevertheless,

some theoretical models beyond the SM enhance this branching fraction ([1, 2, 3]) of an

order of magnitude. For instance, in the two Higgs-doublet model (2HDM) framework

(Chap. 2), it is possible to imagine a scenario with the presence of a fermiophobic Higgs

boson (hf ), which is assumed to have zero coupling to fermions at tree-level. For such

a Higgs the γγ branching ratio is enhanced of a factor 10, as reported in Tab. 2.2 and

in Fig. 2.4. This hypothesis has been already investigated at LEP [4] and Tevatron

[5]. The main Higgs production mechanism in the SM is gluon fusion (see Fig. 2.7

top left), which is suppressed when allowing fermiophobia because of the top quark

loop. The fermiophobic scenario leaves therefore the vector boson fusion (VBF, Fig.

2.7 top right) and Higgs-strahlung (HSTRA, Fig. 2.7 bottom left) as the only relevant

production mechanisms of a fermiophobic Higgs. In this dissertation, respecting the

general prescription of all previous fermiophobic Higgs analyses (see [6]), we assume to

have the coupling strength of the fermiophobic Higgs to the gauge vector bosons equal

to that of SM. Recently, at Tevatron the DØ collaboration excluded the Fermiophobic

Higgs with a mass Mhf < 112 GeV, which is currently the best limit [7].

The outline of this work is the following:

• In Chapter 2 we briefly discuss the 2HDM focusing on the “type I” framework:

only the heavier of the two Higgs couples to fermions in the Yukawa Lagrangian,

while the other Higgs is fermiophobic.

1

1. INTRODUCTION

• In Chapter 3 we report a short description of LHC, with particular emphasis on

CMS experiment.

• Chapter 4 is dedicated to the reconstruction of photons and jets, the main in-

gredients of this analysis, which aims to detect events with two photons and two

jets in the final state. The two photons are produced in the Higgs decay. The

two jets arise in VBF from the hadronization of the partons (Fig. 2.7 top right),

whereas in HSTRA from the vector boson (W or Z) decay (Fig. 2.7 bottom left).

• In Chapter 5 we describe the analysis strategy and the optimization of selection

criteria for the two separated exclusive mechanisms VBF and HSTRA.

• In Chapter 6 we present the results and the expected 95% confidence level (CL)

upper limit assuming 1 fb−1 of collected data. With this estimated luminosity, it

is possible to predict the exclusion region of parameters characterizing the bench-

mark model. In this chapter we present also the data-Monte Carlo comparison

of the main variables of this analysis, with nowadays luminosity.

• In the final Chapter we summarize the main empirical and theoretical conclusions

of this dissertation.

2

2

Fermiophobic Higgs in 2HDM

The decay of the Higgs in two photons is one of the most important discovery channels

at the Large Hadron Collider (LHC), and it is certainly the golden mode at low masses,

where the decay channels into heavy gauge bosons are closed.

The Standard Model (SM) [8] requires the breaking of the SU(2) x U(1) symmetry.

This is achieved in an elegant way by introducing a complex scalar doublet with a non-

zero vacuum expectation value (VEV): a neutral scalar is thus predicted, the Higgs

boson (φ0) [9]. Since so far no such a scalar boson was found, this inspired physicists

to enlarge the Higgs sector of SM, opening a world of possibilities, and, among these,

Multi-Higgs-doublet models (MHDM) have been explored [10].

In this case, the minimal choice consists in extending the SM with an additional SU(2)

x U(1) Higgs doublet [1], thus obtaining the so-called “Two Higgs Doublet Model”

(2HDM). This approach is also motivated by the large ratio between top and bottom

quarks masses, mt/mb ≈ 43. In the SM, both quark masses derive from the same Higgs

doublet, and this does imply a non natural hierarchy between their Yukawa couplings.

In the 2HDM two neutral Higgs bosons (h0, H0) arise, with different branching

ratios from those of SM Higgs (φ0). As we will see in the next section, 2HDM keeps most

of the characteristics of the SM but, at the same time, opens a wider phenomenology,

including besides the two neutral Higgses also two charged scalars, a pseudoscalar and

the possibility of CP-violation.

The minimal supersymmetric standard model (MSSM) is also based on two Higgs

doublets [11] hypothesis. But, contrary to the SM and MSSM, 2HDM may be realized in

the “Type I” scenario, with very weak couplings between scalars and fermions, allowing

3

2. FERMIOPHOBIC HIGGS IN 2HDM

fermiophobia for one of the Higgses (e.g. h0) . The only way to detect such a Higgs is

through its decays into vector bosons, in particular the γγ signature.

The major constraints to be observed in 2HDM are essentially two [1].

The first, is the experimental fact that:

ρ ≡m2W

m2Z · cos2 θW

≈ 1. (2.1)

This property is observed by any version of the SM with any number of Higgs doublets

through the general formula:

ρ ≡m2W

m2Z · cos2 θW

=

∑T,Y

[4T (T + 1)− Y 2

](|VT,Y |) 2cT,Y∑

T,Y 2Y 2| (|VT,Y |) 2(2.2)

where VT,Y = 〈φ(T, Y )〉 defines the VEV of each neutral Higgs field, and T and Y

specify the total SU(2)L isospin and hypercharge of the Higgs representation to which

it belongs. The coefficients above are:

cT,Y =

1, (T, Y ) ∈ complex representation12 , (T, Y = 0) ∈ real representation

(2.3)

The second major constraint comes from the almost null presence of flavor-changing

neutral currents (FCNC’s). A theorem of Glashow and Weinberg [12] states that tree

level FCNC’s mediated by Higgs bosons will be absent if all fermions of a given electric

charge, couple to no more than one Higgs doublet. This is true by construction in the

2HDM type I, where only one doublet couples to fermions.

The two Higgses version of the Standard Model we are going to introduce is attrac-

tive beacuse:

• It is a minimal extension of SM which adds new phenomena.

• It adds the fewest new arbitrary parameters.

• It satisfies theoretical constraints and the absence of tree-level FCNC’s.

2.1 The structure of 2HDM

The 2HDM contains two Higgs doublets, Φ1 and Φ2 with the same quantum numbers,

and hypercharge Y1 = Y2 = 1. We introduce the most general 2HDM potential which

4


spontaneously breaks SU(2)L x U(1)Y down to U(1)EM [1]:

V (Φ1,Φ2) = λ1

(Φ†1Φ1 − v2

1

)2 + λ2

(Φ†2Φ2 − v2

2

)2

+λ3

[(Φ†1Φ1 − v2

1

)+(

Φ†2Φ2 − v22

)]2

+λ4

[(Φ†1Φ1

)(Φ†2Φ2

)−(

Φ†1Φ2

)(Φ†2Φ1

)]+λ5

[Re(

Φ†1Φ2

)− v1v2cosξ

]2

+λ6

[Im(

Φ†1Φ2

)− v1v2sinξ

]2

(2.4)

The λi are all real parameters by hermiticity. This potential is subject to gauge in-

variance and to a discrete symmetry Z2, i.e. for Φ1 → −Φ1 or Φ2 → −Φ2, which is

only softly violated. This technical constraint provides FCNC’s not too large1. For

this thesis, we assume, according to MSSM, no FCNC’s at tree level and no explicit

or spontaneous CP violation, by setting ξ=0. With these assumptions, if all the λi are

non negative, we can easily choose a minimum of the potential as:

〈Φ1〉 =

(0v1

), 〈Φ2〉 =

(0v2

)(2.5)

With this choice, we break SU(2)LxU(1)Y down to U(1)EM . We write each complex

doublet Φi in form of deviations from the relative VEV:

Φ1(x) =

(φ+

1v1+h1(x)+ig1(x)√

2

),Φ2(x) =

(φ+

2v2+h2(x)+ig2(x)√

2

)(2.6)

Each doublet has Yi = 1 and 4 d.o.f., the upper charged component being a complex

scalar field.

According to Gell-Mann Nishijima formula Q(φ+i ) = +1 while Q(hi(x)) = 0.

By substituting (2.6) in the general potential (2.4), a subset of mass squared terms

arise, which can be arranged into a mass potential [13]:

V mass =(φ+

1 φ+2

)Mφ±

(φ−1φ−2

)+ (h1h2)Mh

(h1

h2

)+ (g1g2)Mg

(g1

g2

)(2.7)

where φ−i =(φ+i

) ∗.1we can choose a Higgs fermion coupling which avoids tree-level FCNC’s; the effect of soft violation

of the discrete symmetry would be to radiatively generate FCNC’s, arranged to be small enough

according to experimental results.

5


The two physical Higgs scalars related to the real (CP even) sector, are mixed by

the following mass-squared matrix:

Mh =

(4v2

1 (λ1 + λ3) + v22λ5 (4λ3 + λ5) v1v2

(4λ3 + λ5) v1v2 4v22 (λ2 + λ3) + v2

1λ5

)(2.8)

After diagonalization of (2.8), we obtain the mass eigenvalues (2.9) and the relative

eigenstates (2.10):

m2H0,h0 =

1

2

[(Mh)11 + (Mh)22 ±

√((Mh)11 − (Mh)22) 2 + 4 (Mh)2

12

](2.9)

(H0

h0

)=√

2Rα

((h1 − v1)(h2 − v2)

)(2.10)

where Rα is:

Rα =

(cosα sinα−sinα cosα

)(2.11)

From (2.9), we clearly see that m0H>m

0h. The mixing angle α can be evaluated by the

formulas:

sin(2α) =2 (Mh)12√

((Mh)11 − (Mh)22) 2 + 4 (Mh)212

cos(2α) =(Mh)11 − (Mh)22√

((Mh)11 − (Mh)22) 2 + 4 (Mh)212

(2.12)

Similarly, diagonalizing the other mass-squared matrices we get the sets of eigenstates:

(G±

H±

)= Rβ

(φ±1φ±2

)(2.13)

(G0

A0

)= Rβ

(g1

g2

)(2.14)

both expressed in terms of the rotation matrix:

Rβ =

(cosβ sinβ−sinβ cosβ

)(2.15)

where β is a fundamental parameter, that can be expressed in terms of the V.E.V.’s :

tanβ = v2/v1, with 0< β < π/2 (2.16)

6


Thus, the spectrum consists of two CP-even Higgs scalars (H0, h0), one CP-odd

scalar (A0), two charged Higgs bosons (H±) and three Goldstone bosons (G±, G0)1.

For completeness we report the squared-mass eigenvalues of (H±) and (A0):

m2H± = λ4

(v2

1 + v22

)(2.17)

m2A0 = λ6

(v2

1 + v22

)(2.18)

We note that v21 + v2

2 is fixed by the W mass, m2W = g2

(v2

1 + v22

)/2.

Then, the total Lagrangian for the Higgs sector can be sketched in the form:

LH =∑i=1,2

(DµΦi)† (DµΦi)− V (Φ1,Φ2) + LY . (2.19)

We can summarize (2.19) in three main parts:

• The first term is the kinetic one, and provides the masses of vector bosons after

spontaneous symmetry breaking (s.s.b.). From this sector it is possible to derive

how Higgses couple to vector bosons in 2HDM and how these couplings differ

from the SM one; this can be done in terms of α (2.12) and β (2.16) previously

introduced:

gh0VV

gφ0VV= sin(β − α)

gH0VV

gφ0VV= cos(β − α)

(2.20)

• The second term is the general potential already discussed, crucial for giving the

proper masses to Higgses.

• The last term instead, represents the Yukawa Lagrangian, which describes the

interaction between Higgs and fermions and provides masses to fermions after

s.s.b. .

There are many models concerning the Yukawa sector that have been widely studied

by theorists. The main ones are:

1the Goldstone bosons become the longitudinal part of the Z0 and W± when gauged away.

7


• Type I - Only Φ2 couples to fermions and give mass to all particles (quarks and

leptons). Only one doublet couples to the fermions, and we choose Φ2 as we will

motivate in Sec. 2.3 dedicated to the fermiophobic limit.

Ltype IY = −

(aij

leptLiΦ2dlepR,j + bijupQiΦ

C2 uR,j + cij

downQiΦ2dR,j + h.c.)

(2.21)

• Type II - Φ1 couples to down-type quarks and leptons while Φ2 couples only to

up-type quarks and neutrinos.

Ltype IIY = −

(aij

leptLiΦ1dlepR,j + bijupQiΦ

C2 uR,j + cij

downQiΦ1dR,j + h.c.)

(2.22)

• Type III - It allows each Higgs doublet coupling to up and down quarks, and

leptons

Ltype IIIY =

(−aij

1,leptLiΦ1dlepR,j + bij1,upQiΦ

C1 uR,j + cij

1,downQiΦ1dR,j

+aij2,leptLiΦ2d

lepR,j + bij2,upQiΦ

C2 uR,j + cij

2,downQiΦ2dR,j + h.c) (2.23)

For the purpose of this thesis we can generally assume that SM φ0 and h0 possess

a very similar phenomenology [2]. In the next section we are going to highlight the

existence of a fermiophobic Higgs, possible in the 2HDM Type I.

2.2 The fermiophobic limit

Fermiophobia may arise in the Type I framework of 2HDM. This model consists in

letting just one Higgs doublet to be coupled to fermions [1, 2]. Only in this case, we

can get the other Higgs with very suppressed or zero coupling to fermions. We will

consider the particular case in which the lightest CP-even Higgs scalar (h0) has turned

off couplings to fermions at tree level, while we require the second doublet Φ2(x) coupled

to fermions. We then consider the limit of α approaching π2 : we get a fermiophobic

Higgs (hf ) with enhanced branching ratios into bosons (e.g. the γγ signature, at low

mass). This choice is clear if we look at (2.10).

8

2.2 The fermiophobic limit

2.2.1 Neutral Higgses couplings to fermions in 2HDM type I

If we take in consideration the 2HDM type I Yukawa Lagrangian of Eq. (2.21), the

Higgses couplings to fermions can be explicitly written as functions of cosα, sinα, and

tanβ [1, 14, 15].

LtypeIY ∝ − g

2m2W sinβ

(DMDD + UMUU

)·(H0sinα+ h0cosα

)+ ... (2.24)

where MU and MD are diagonal positive quark matrices for charge 23 and −1

3 quarks

respectively. It can be demonstrated [16] that the lighter Higgs couples to all fermions

(quarks and leptons) like:

h0ff ∼ cosα/sinβ (2.25)

We want now to show the essential differences between Type I and Type II Higgs

couplings to fermions. In Tab. 2.0(a) we show which doublet couples to which fermions,

whereas in Tab. 2.0(b) we report the effective couplings of h0 to fermions in terms of

the main parameters of 2HDM.

(a) Doublet coupling to fermions

Type I Type II

u(up-type quarks) 2 2

d(down-type quarks) 2 1

l(charged leptons) 2 1

(b) Light Higgs (h0) couplings to

fermions relative to those for the

minimal SM Higgs boson (φ0)

Type I Type II

huu cosαsinβ

cosαsinβ

hdd cosαsinβ − sinα

cosβ

hll cosαsinβ − sinα

cosβ

Table 2.1: 2HDM I and II: couplings to fermions

By these considerations, fermiophobia arises in Type I when α approaches π2 as

sketched in Fig. 2.1.

9


Figure 2.1: Higgs coupling to fermions at tree-level

2.3 Fermiophobic branching ratios and cross sections

Several fermiophobic models are possible, and the Working Group chose to use the

HDECAY branching ratios (see Sec. 2.3.1) as benchmark [6, 17], and SM production

rates (see Sec. 2.3.3).

In the SM, the Higgs decays in γγ with very small branching ratio, about 0.2% for

a Higgs with mass of 130 GeV. However, in the case of a fermiophobic Higgs boson

(hf ), this branching ratio is almost an order of magnitude larger. At the end of this

section, Tab. 2.2 shows the HDECAY values of cross-sections and B.R. into γγ of the

fermiophobic Higgs, as functions of its mass.

2.3.1 Branching ratio of fermiophobic Higgs

A fermiophobic Higgs cannot couple to fermions, therefore the tree-level SM diagram

responsible for the Higgs decay into γγ through a triangular loop of top-quarks has to

be suppressed (Fig. 2.2).

Figure 2.2: Higgs in γγ by loop of quarks is suppressed in the fermiophobic case

In the fermiophobic model, it is generally assumed that the di-photon Higgs decay

is mediated solely by W boson loops [2], with a SM coupling to vector bosons, although

in the 2HDM a factor of sin(β − α) must be included as reported in Eq. 2.20 (this

factor becomes − cos(β) in the fermiophobic case).

10


Thus, the main diagrams contributing to fermiophobic Higgs decay into γγ concern

charged W, either through a triangular loop or through a seagull diagram, as shown in

Fig. 2.3.

Figure 2.3: The main loops responsible for fermiophobic decay into γγ

Fig. 2.4 shows a comparison between SM and fermiophobic Higgs branching ratios,

as functions of the Higgs mass.

2.3.2 Charged scalar Higgs loops

Diagram with charged Higgs loops may give important contribution to fermiophobic

Higgs decay into γγ. The lower level diagrams are reported in Fig. 2.5.

In the low mass region it has been shown [18] that such contributions can cause

either large suppressions, or moderate enhancements (25% correction) of BR(hf → γγ).

The knowledge of hfH+H− coupling, reported as a function of tanβ (Fig. 2.6), is an

important issue to be taken into account, if we want to implement loops involving

charged Higgses. We won’t consider those diagrams anyway, and we will keep following

the HDECAY conventions throughout this work.

2.3.3 Production cross sections at LHC

Fig. 2.7 shows the Feynman diagrams of all the SM Higgs mechanisms of production

at Large Hadron Collider (LHC, proton-proton collider). Their cross-sections at√s =

7 TeV are reported in Fig. 2.8, as a function of the Higgs mass. As we can see in

the figure, the main mechanism in hadronic collisions is the gluon fusion (GGF), which

involves a loop of top quarks.

If the Higgs does not couple to fermions, GGF is not allowed, and the Higgs boson

is produced through vector boson fusion (VBF) or Higgs-strahlung (HSTRA). These

two topologies have been searched for in this work, and in the following we propose the

results obtained with two dedicated exclusive analyses. In both mechanisms the Higgs

11


Figure 2.4: SM (up) and fermiophobic (down) Higgs BR’s as functions of Higgs mass

12


Figure 2.5: Charged Higgs loops - Fermiophobic Higgs may decay into γγ through

charged Higgs loops

Figure 2.6: Fermiophobic Higgs coupling to charged Higgses - Fermiophobic

2HDM hfH+H− coupling, normalized by mW , as a function of tanβ [18]

13


Figure 2.7: SM Higgs production at LHC - Feynman diagrams of the main mecha-

nisms of production of SM Higgs at LHC

Figure 2.8: SM Higgs cross sections - Cross-sections of the main mechanisms of

production of the SM Higgs at LHC, at√s =7 TeV

14


couples to vector bosons by Eq. (2.20) for 2HDM.

A distinctive feature of these two mechanisms is the fact that the Higgs boson is pro-

duced with large transverse momentum (pT ), as reported in Fig. 2.9, and this can

result in signal photons with high pγT spectra (see Sec. 2.3.4).

Figure 2.9: Transverse momentum of SM Higgs - Overlaid shapes (in arbitrary

units) of transverse momentum pT of SM Higgs produced via gluon fusion, vector boson

fusion and Higgs-strahlung.

Tab. 2.2 summarizes the HDECAY values for BR(hf → γγ) and the production

rates through VBF and HSTRA.

Mass(GeV/c2) BR(hf → γγ) V BF : σ(pb)×BR W/Z-hf : σ(pb)×BR90 0.41 0.74 1.05

100 0.18 0.29 0.32

110 0.062 0.089 0.083

120 0.028 0.037 0.028

130 0.019 0.023 0.015

140 0.0061 0.0066 0.0037

150 0.0020 0.0020 0.0009

Table 2.2: Fermiophobic B.R. and cross sections of main mechanisms of production (VBF,

HSTRA)

15


2.3.4 Irreducible background for Higgs decay into γγ

Irreducible background arises from direct production of diphoton events in SM. The

main diagrams responsible for irreducible background are Born and Box (see Fig. 2.10).

They are irreducible because any signal selection selects also these events.

Figure 2.10: Irreducible background for γγ - main diagrams contributing to irre-

ducible background for γγ channel; (left) Born diagram (right) Box diagram.

Diagrams such as γ+jet (jet mis-identified as photon) and di-jet (two jets with

misidentified photons) can instead be considered reducible background (see Fig. 2.11).

Figure 2.11: Example of reducible background to diphoton search - main re-

ducible background, known as γ+jet. In the figure above the jet hadronizes into a pion,

which decays into two close photons, detected as one fake photon.

This sources of background can be cured by implementing in the analysis selective

criteria for a proper identification of real photons. A description of photon identification

techinques implemented in this thesis is reported in Sec. 4.3. As we can see from

Monte Carlo, signal photons have harder spectra in pT than background photons (see

Fig. 2.12), and a more central distribution in pseudorapidity (η) (see Fig. 2.13): those

characteristics indicate the cuts to apply in order to select signal candidate events.

16


Figure 2.12: Overlaid shapes (in arbitrary units) of pT MC distributions, for the first

highest pT photon (left) and second highest pT photon (right), from Higgs decay (signal:

VBF, GGF, HSTRA) or irreducible background (Born and Box)

Figure 2.13: Overlaid shapes (in arbitrary units) of η MC distributions, for the highest

pT photon (left) and second highest pT photon (right), from Higgs decay (signal: VBF,

GGF, HSTRA) or irreducible background (Born and Box)

2.3.5 MC Samples for preliminary studies

The MC samples used for preliminary studies have been produced with PYTHIA gen-

erator (see also [19] for details). They can be summarized as signal samples (gluon

fusion, vector boson fusion (VBF) and Higgs-strahlung (HSTRA) for a 120 GeV mass

Higgs) and background samples (Born, Box).

17


18

3

The Large Hadron Collider and

CMS Experiment

The Large Hadron Collider (LHC) is a circular hadron collider designed to accelerate

protons at the energy of 7 TeV per beam (14 TeV in the center of mass) and ions (Pb)

at the energy of 2.76 TeV per nucleon in the center of mass. At the present time LHC

works at 7 TeV in the center of mass. Up to now, the LHC is the highest and biggest

energy hadron collider ever constructed.

LHC needs a very large radius tunnel in which particle beams circulate, in order

to get such high energies. It is installed in the LEP (Large Electron-Positron Collider,

shut down in 2000) tunnel situated 100 meters underground between the French and

Swiss territory in the Geneva area (Fig. 3.1). The tunnel is 27 km long.

Before the injection in the LHC the particles are prepared by a series of injective

systems that successively accelerate them: the first system is the linear particle ac-

celerator LINAC2, generating 50 MeV protons, which feeds the Proton Synchrotron

Booster (PSB). There the protons are accelerated to 1.4 GeV and injected into the

Proton Synchrotron (PS), where they are accelerated to 26 GeV. Thus the Super Pro-

ton Synchrotron (SPS) is used to further increase their energy to 450 GeV before they

are finally injected (over a period of 20 minutes) into the main ring. 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 (Fig. 3.2).

The LHC is structured in octants, hosting superconducting magnets that operate

at a temperature of 1.9 K (−271.25C), making the LHC the largest cryogenic facility

19

3. THE LARGE HADRON COLLIDER AND CMS EXPERIMENT

Figure 3.1: - View of the LHC location.

in the world at liquid helium temperature. More specifically, 1232 dipole magnets keep

the beams on their circular path, while an additional 392 quadrupole magnets are used

to keep the beams focused, in order to maximize the chances of interaction between

the particles in the four intersection points, where the two beams will cross.

The experimental caverns are located in these four points where the two beam pipes

intersect to produce collisions. Four experiments are installed there (see Fig.3.2), with

different designs and aims: ALICE (A Large Ion Collider Experiment) studies quark-

gluon plasma in heavy ion collisions, LHCb (Large Hadron Collider beauty experiment)

for the study of the CP violation in heavy flavor quarks physics (b-quark), ATLAS (A

Toroidal Light Hadron Collider Apparatus) and CMS (Compact Muon Solenoid), which

are two general purpose experiments.

The protons in the accelerator are inserted in bunches. Up to 2800 bunches of 1010

protons can be inserted in the machine, so that interactions between the two beams

will take place at nominal discrete intervals of 25 ns. The design luminosity of the

LHC is 1034 × cm−2s−1, providing a bunch collision rate of 40 MHz. The main LHC

characteristics are reported in Tab. 3.1.

20

Figure 3.2: Protons (ions) acceleration and injection system to the LHC: LINAC2, PSB,

PS, SPS and LHC (top); view of the four LHC experiments and LHC layout (bottom)

21


(a) LHC

lenght 27 km

center mass energy 14 TeV

luminosity 1034cm−2s−1

bunches 2800

protons per bunch 1010

collision rate 40 MHz

(b) MAGNETS

number 1600

working temperature 1.9 K

magnetc field 8 T

Table 3.1: Summary of designed LHC characteristics.

3.1 The Compact Muon Solenoid detector

The Compact Muon Solenoid (CMS) experiment is one of the two large general purpose

particle physics detectors built on the proton-proton LHC at CERN. Approximately

3,600 people from 183 scientific institutes, representing 38 countries, form the CMS

collaboration. It is located in an underground cavern at Cessy in France, just across

the border from Geneva.

The CMS experiment (shown in Fig. 3.3) is made of a large superconducting

solenoid producing a magnetic field of 4T and containing a full silicon tracker for mo-

mentum measurements and charged particles tracks reconstruction, a precise crystal

electromagnetic calorimeter (ECAL) and a hadron calorimeter (HCAL). Muon cham-

bers are embedded in the iron return yoke of the magnet, thus forming a compact

muonic system.

Large bending power is needed to measure precisely the momentum of high-energy

charged particles since the momentum resolution improves with a stronger magnetic

field: the relative uncertainty on the momentum measurement is δpp ∝

pB [20] . This

forces a choice of superconducting technology for the magnets. The CMS magnet is a

superconducting solenoid providing a 3.8 T magnetic field at the interaction point. The

tracker system, ECAL and HCAL are hosted within the magnet. The magnet return

yoke of the barrel has 12-fold rotational symmetry and consists of three sections along

22

3.1 The Compact Muon Solenoid detector

the z-axis; each is split into 4 layers (holding the muon chambers in the gaps). Most

of the iron volume is saturated or nearly saturated, and the field in the yoke is around

1.8 T. The overall experiment measures 21.6 m in lenght, 14.6 m in height and weighs

12500 t.

Figure 3.3: CMS experiment - Overall view of the detector.

As reported in Fig. 3.4, the combined information from the different subdetectors

allows to distinguish the final stable particles produced in the collision.

We will describe briefly all the subdetectors, focusing on the ECAL and HCAL,

which allow us to detect photons and jets respectively. Our aim is indeed to reconstruct

the invariant mass of the two-photons from Higgs decay, and complete the topology of

the final state with the two jets arising from VBF or HSTRA diagrams. We remember

that each photon developes in an electromagnetic shower that is almost completely

contained in the ECAL crystal length. Thus, almost no signals are released in the

HCAL and in the muon chambers from these showers. This helps to define appropriate

observables used in the photon identification (see Sec. 4.3).

At the design luminosity, a mean of about 20 inelastic collisions will be superim-

posed on the event of interest: resulting effects of pile-up can be reduced by using

high-granularity detectors with good time resolution, resulting in low occupancy. The

millions of electronic channels need of course a very good synchronization.

The coordinate system has the origin centered at the nominal collision point inside

the experiment, the y-axis pointing vertically upward, and the x-axis pointing radi-

23


Figure 3.4: CMS slice - Sketch demonstrating the particle-identification chances in the

CMS experiment: a muon originating from the vertex is deflected in the central solenoidal

magnet; the counter-bending of the muon is detectable in the outer magnetic spectrometer.

ally toward the center of the LHC. Thus, the z-axis points along the beam direction

according to the write-hand rule. In the x-y plane, transverse to the beam direction,

we measure the azimuthal angle φ, and the radial coordinate denoted by r. The polar

angle θ is measured with respect to the z-axis. Pseudorapidity (see Fig. 3.5) is defined

as:

η = −log(tanθ

2). (3.1)

Figure 3.5: Pseudorapidity η - Values of η as a function of polar angle θ.

Eq. (3.1) results to be an useful quantity, since at high energies is a good approxi-

24

3.2 The inner tracking system

mation of the rapidity of a particle, defined as:

y =1

2log

(E + pLE − pL

)(3.2)

where the subscript L means longitudinal.

According to these definitions, the transverse momentum and energy, denoted by

pT and ET respectively, are computed from the x and y components. The imbalance of

energy measured in the transverse plane is called missing transverse energy and denoted

by 6ET .

In the following set of relations, momentum components are expressed in terms of

the introduced variables η, φ, pT :

px =pT cosφ,

py =pT sinφ,

pz =pT sinh η,

p =pT cosh η,

tan θ =1

sinh η.

(3.3)

We are now going to describe the subdetectors of CMS, and, particularly, we will

stress on ECAL and HCAL, fundamental for the work of this thesis.


The silicon tracker [21] is the innermost part of the CMS detector. At design lumi-

nosity, about 1000 tracks per event are expected, therefore high detector granularity is

required. The tracker system reconstructs the tracks of charged particles and provides

a very precise measurement of particle momentum. Because of the high intense flux of

charged particle expected at the LHC design luminosity, speed and radiation hardness

are necessary for the tracker. The minimum material budget is required also, in order

to keep, as low as possible, phenomena like multiple scattering, photon conversion and

bremsstrahlung emission.

The CMS Tracker is a cylindrical device of 5.4 m in length and 2.4 m in diameter,

immersed in a solenoidal magnetic field. A description of the CMS Silicon Strip Tracker

(SST) can be found in [22].

25


The innermost region (4.4 cm < r < 10.2 cm and for |z| < 50 cm) is occupied by a

3 silicon pixel layers detector, whereas the remaining volume is instrumented by using

silicon microstrip modules organized in 10 cylindrical layers and 12 disks as sketched

in Fig. 3.6, corresponding to more than 200 m2 of active area. Altogether, the inner

tracking system consists of 66 millions pixel channels and 9.6 millions silicon strips.

This part of CMS is the world’s largest silicon detector.

Figure 3.6: Layout of the tracker system - The Tracker consists of 10 barrel layers and

two times nine end cap layers inside a volume of about 5.4 m length and 2.4 m diameter.

Legend: Silicon Strip Tracker (SST); Tracker Inner Barrel (TIB); Tracker Inner Disks

(TID); Tracker Endcaps (TEC)

We can identify 3 regions:

• the innermost region, nearby the interaction vertex, where the flux of particles

is intense; here pixel detectors are used. The dimensions of each pixel is around

100×150 µm2, with an occupancy of 10−4 per pixel, per each beams collision;

• the intermediate region, at 20 < r < 55 cm, where the flux is enough low to

allow the usage of microstrips with mimimum dimensions of 10 cm ×80 µm, thus

obtaining an occupancy of about 0.2−0.3 per beam crossing.

• the outmost region, at r > 55 cm, where the flux decreases such that is possible

to use larger silicon strips, with cells of maximum dimension of 25 cm × 180 µm,

in order to maintain an occupancy about 10−2.

26


A visualization of the Si-Modules of the CMS Tracker is reported in Fig.3.7.

Figure 3.7: Si-Modules - View of Si-Modules inside CMS Tracker

For high pT track (100 GeV) the pT resolution is about 1−2% in the central region

and a bit worse in the endcaps. At this pT values, the multiple scattering contribution

is about 20 − 30% and it increases for lower transverse momentum. The efficiency is

above 99% in most of the acceptance. There is a small drop at high η due to the lack

of coverage of the pixels (see Fig. 3.8).

Figure 3.8: Tracker pT resolution and efficiency - Performance of CMS Tracker:

resolution and reconstruction efficiency for single muon

The silicon pixels provide precision measurements of 10µm in the transverse plane

(x−y), and of e 20 µm for the z-coordinate. The microstrips provide a resolution which

27


depends on the thickness of the cell, but anyway better than 55 µm in the transverse

plane [23].

The material thickness in the tracker crossed by electrons and photons before reach-

ing the ECAL depends on η (see Fig. 3.9). It goes from about 0.35 radiation length

(X0) at central (η = 0), increasing towards the ECAL barrel-endcap transition, and

then falling back. The simulation of the material budget in front of ECAL is of great

importance for the estimation of the photon conversion (photons interacting with the

tracker material producing an electron-positron pair) for photon analyses as lost signal.

Figure 3.9: Material budget - Material budget distribution in the CMS tracker, in

radiation length units, as a function of pseudorapidity η.

3.3 The Electromagnetic Calorimeter (ECAL)

One of the driving criteria in the design of the electromagnetic calorimeter (ECAL) [24]

was the capability to detect the decay into two photons from the Higgs boson decay.

In the range of Higgs mass sensitive to the γγ signature, the Higgs intrinsic width

Γ is small, therefore to have a good experimental resolution becomes fundamental

in order to minimize the uncertainty on the Higgs mass measurement. The Higgs

decay into two photons has thus been the landmark in optimizing the CMS ECAL

realization. The experimental difficulties embodied in the γγ channel have driven the

CMS collaboration towards the choice of an electromagnetic calorimeter with excellent

28


energy resolution, and fine granularity. For all these reasons it has been chosen a

hermetic and homogeneous crystal calorimeter. ECAL consists of 61200 crystals of

stolzite, i.e. lead tungstate (PbWO4), in the barrel region, and is closed by 7324 crystals

in each endcap. ECAL measures, with high precision, electromagnetic particles, and,

combined with the measurements of the Hadronic Calorimeter, it also contributes to

the energy reconstruction of hadronic jets.

In the next subsections we will describe in more detail the principal properties of

the Electromagnetic Calorimeter of CMS.

3.3.1 The PbWO4 crystals

The stolzite PbWO4 has been chosen for the realization of ECAL, being a transparent

scintillating material, compact, endowed with fast response, and radiation hardness.

Its essential properties, basically are:

• the short radiation length (X0 = 0.89 cm), which allows the construction of a

compact calorimeter: with 23 cm long crystals, we obtain 25.8 X0, assuring a

good longitudinal containment of electromagnetic showers even at high energies;

• the small Moliere radius (RM = 2.19 cm) allows an efficacious transversal con-

tainment, and at the same time a fine granularity;

• the scintillation decay time of these crystals is of the same order of magnitude

as the LHC bunch crossing time; about 80% of the light is emitted in 25 ns, and

with such a fast response, most of the light can be collected before the next beam

crossing, thus reducing pile up effects;

• its robustness to radiation allows the stolzite crystals to be used for several

decades of LHC activity at high luminosity. By doping PbWO4 with Nb (nio-

bium), it has been obtained the best transmission spectrum, and, at the same

time, the best robustness to radiation.

On the contrary, the PbWO4 presents some problematic aspects:

• the low light yield (about 100 photons per MeV);

• the dependency of the amount of emitted light on the crystal temperature.

29


The first problem is essentially due to part of the energy absorbed by the crystal

dissipated in form of thermal emissions through the crystal lattice. In order to com-

pensate this loss of energy, the lead tungstate crystals are coupled to photodetectors

with a high gain amplification system: Avalanche Photo-Diodes (APDs) [25] developed

by Hamamatsu for CMS are used in the Barrel, which is characterized by a higher

magnetic field, while vacuum phototriodes (VPTs) [26] are used in the Endcaps be-

cause insensitive to the high hadron flux. The choice of this kind of amplifiers has been

motivated by their good quantum efficiency, for wavelengths belonging to the emission

region of PbWO4, by their insensitivity to the presence of the magnetic field, and,

finally, by their compactness.

The second problem is somehow related to thermal dissipation of the absorbed

energy, and, in order to ensure a constant response of the detector, it is mandatory to

keep stable its temperature, and this motivated the construction of a hydraulic cooling

system able to keep a working temperature of (18 ± 0.05) C.

The CMS ECAL is a hermetic calorimeter with a cylindrical structure, consisting

in a central part (barrel) placed between the tracker and the hadron calorimeter and

closed by two endcaps. A preshower detector is placed in front of the endcap crystals,

and provides informations on the transverse development of the shower. The ECAL

layout is shown in Fig. 3.10, while in Fig. 3.11 we sketch a quarter of the calorimeter.

3.3.2 The ECAL Barrel

The ECAL Barrel covers the region η < 1.479. The barrel is made of 61200 trapezoidal

crystals of about 23 cm (25.8 X0) in length and approximately 1 Moliere Radius (RM )

in lateral size, measuring 22× 22 mm2 in the frontal extremity, while 26 × 26 mm2 in

the opposite extremity, corresponding to a granularity of 360 crystals in φ and of (2 ×85) in η. The barrel inner radius is of 124 cm.

The crystals are placed in a quasi-projective geometry, such that, the individual

crystals appear tilted (off-pointing) by about 3 both in polar (η) and azimuthal angles

(φ), with respect to the nominal interaction vertex.

Each crystal, with the two APD (avalanche photodiode) attached to its final ex-

tremity, constitutes a subunit.

The mechanical design is based on modularity and on the use of high-strength, low-Z

materials, where alveolar submodules (Fig. 3.12, left) of 2×5 fiberglass cells containing

30


Figure 3.10: ECAL layout - Schematic view of ECAL layout

Figure 3.11: ECAL quarter - Schematic view of ECAL layout

31


individual crystals (each with two APD (avalanche photodiode) attached to its final

extremity) are the smallest subunits in the barrel. Such submodules are assembled into

modules (Fig. 3.12, centre). Supermodules (Fig. 3.12, right) consist of four modules,

held by a U-shaped spine at the outer ECAL radius, and contain 1700 crystals.

Figure 3.12: Stages of an ECAL supermodule assembly - left: Alveolar submodule;

centre: Complete module; right: supermodule

The barrel part consists of 36 supermodules.

3.3.3 The ECAL Endcaps

The endcaps consist of two detectors, a preshower device followed by a PbW04 calorime-

ter (see Fig. 3.11).

The preshower is employed in the range 1.653 < |η| < 2.6: it is a annulus shape

sampling calorimeter, with inner radius of 45.7 cm and outer radius of 1,23 m. It

consists of two layers, made of silicon strips placed in a 19 cm sandwich of materials

including about 2.3 X0 of Pb absorber. Electromagnetic showers are produced when

electrons or photons penetrate the Pb layers (2 and 1 X0 respectively); the silicon

strips between the Pb layers, measure the deposited energy and the lateral profile of

the showers.

The principal aim of the preshower is to distinguish photons from pions (π0). The

latter, decays (at rest in τ ≈ 10−16s) in two close photons at high energy, and thus

difficult to be discriminated. It also helps to distinguish electrons from other minimum

ionizing particles (MIP), and, due to its granularity higher than endcaps, contributes

to detect with major precision electrons and photons positions.

Each endcap calorimeter is made of 7324 rectangular and quasi-projective crystals

of approximately 1.3 RM in lateral size and about 24.7 X0 in depth. The crystal front

32

3.4 The Hadronic Calorimeter

faces are aligned in the transverse plane (x, y), but, as in the barrel case, the crystal

axes are off-pointing from the nominal vertex in the polar angle by 3.

The endcaps are placed at a longitudinal distance of 3144 mm from the interaction

point. They are made of identical crystals, of lenght of 220 mm (about 24.7X0), with

front face of 28 × 28 mm2, and outer face of 30 × 30 mm2 . The crystals are gathered

in mechanical units, formed by 5× 5 crystals, called super-crystals (SC).

At value of η larger than 2.5, the radiation level is high and precision measurements

are almost impossible. The crystals closest to the beams are used only for measuring

the transverse energy of the event, and together with the hadronic calorimeter, in order

to reconstruct jets.

3.3.4 The ECAL energy resolution

The energy resolution of the CMS ECAL can be parametrized as follows:

(σ(E)

E

)2

=

(S√E

)2

⊕(N

E

)2

⊕ C2 (3.4)

In equation (3.4), S is a stochastic term, N represents the noise, and C is a constant

term. S depends on event to event fluctuations in lateral shower containment, photo-

statistics and photodetector gain; N represents the noise term, which depends on the

level of electronic noise and event pile-up; the constant term C depends mainly on

intercalibration, temperature, high voltage stability, non-uniformity of the longitudinal

light collection, leakage of energy from the rear face of the crystal, and finally on

geometrical imperfections. At high energies the constant term dominates the resolution.

The mean values of the stochastic and constant term in the barrel have been measured

in test beam [27]: S = 2.8%, N = 124 MeV and C = 0.3% (see Fig. 3.13).


The Hadronic Calorimeter (HCAL) [28] is built to measure the energies and directions

of particles in hadronic jets. It plays an essential role in the identification and mea-

surement of quarks, gluons, and neutrinos by measuring the energy and direction of

jets and, in conjunction with ECAL, of missing transverse energy flow (6ET ) in events.

33


Figure 3.13: ECAL resolution - Fit of ECAL resolution as a function of energy in 18

different 3x3 arrays of crystals.

Missing energy forms a crucial signature of new particles, like the supersymmetric part-

ners of quarks and gluons. For good 6ET resolution, two fundemantal requirements are

therefore necessary: good hermeticity and good transverse granularity.

Moreover, it is required a good energetic resolution and adequate longitudinal con-

tainment of hadronic cascades. The HCAL provides then good segmentation, and

angular coverage up to |η| <5. The design of HCAL is strongly influenced by the

choice of the magnet parameters since most of the CMS calorimetry is located inside

the magnet coil and surrounds the ECAL system. Hence, the HCAL design maxi-

mizes material inside the magnet coil in terms of interaction lengths (λI). Brass has

been chosen as absorber material as it has a rather short λI , is easy to machine and

is non-magnetic. The tile/fibre technology represents an ideal choice for keeping to a

minimum the amount of space devoted to the active medium.

The HCAL has been assembled with essentially neither dead areas in φ nor un-

instrumented cracks. It is basically composed of four subdetectors (see Fig. 3.14):

• the Barrel Hadronic Calorimeter (HB), which is placed inside the magnetic coil,

covers the central region |η| < 1.3;

34


Figure 3.14: HCAL longitudinal view - HCAL composition: HB, HO, HE, HF; it

totally covers up to |η| < 5.

• the Endcap Hadronic Calorimeter (HE), which is also inside the magnetic coil, is

made of two endcaps extending the angular coverage to the region 1.3 < |η| < 3;

• the Outer Hadronic Calorimeter (HO, or Tail-Catcher), which is placed in the

barrel region, outside the magnetic coil is necessary to enhance the depth of the

calorimeter in terms of nuclear interaction length λI ;

• the Forward Hadronic Calorimeter (HF), which consists of two units placed out-

side the magnetic coil, at ±11 m from the interaction point along the beams

direction, covers the region 3 < |η| < 5.

The HB is constructed with two half-barrels each of 4.3 meter length. HB has an

energy resolution for single pions of approximately 120%/√E.

The HE consists of two large structures, situated at each end of the barrel detector

and within the region of high magnetic field. HE has a minimum depth of 10 λI .

HB and HE are sampling calorimeters with 50 mm thick copper absorber plates

which are interleaved with 4 mm thick scintillator sheets. Copper has been chosen as

absorber material because of its density. The central cylindrical structure (HB+HE)

35


consists of 2593 trigger towers, without longitudinal segmentation. This central part

has a granularity ∆φ × ∆η of 0.087 × 0.087, corresponding to ECAL trigger towers

granularity.

The central calorimeter has a depth of about 7 λI , not enough thick to contain longi-

tudinally the hadronic cascades. For this reason, in order to increase the calorimeter

depth in the barrel region, additional scintillation layers (a tail catcher, HO) have been

added just outside the magnetic coil. HO is made of two scintillator layers, with the

same granularity as HB; the total depth in the central region (HB+HO) is thus ex-

tended to about 11.8 λI , with an improvement in both linearity and energy resolution.

The signal is readout through wavelength-shift fibres and hybrid photodiodes (HPD).

The high η calorimeters (HF), placed in high radiation dose environment, can’t be

constructed with conventional scintillator and waveshifter materials. Therefore HF con-

sist of sampling calorimeters made of steel absorber plates (steel suffers less activation

under irradiation than copper) with embedded radiation hard quartz fibers. Hadronic

showers are thus sampled at various depths by radiation-resistant quartz fibers, of se-

lected λI , which are inserted into the absorber plates.

The energy of jets is measured from the fast Cherenkov light signals produced, as they

pass through the quartz fibers. This Cerenkov light results principally from the elec-

tromagnetic component of showers, providing excellent directional information for jet

reconstruction. Fiber optics convey the light to photomultipliers, placed in radiation

shielded zones.

The fibers can have two lenghts: the longest start from the frontal face of the

calorimeter, and the shortest after 22 cm. In this way the electromagnetic component

of the cascade, deposited in the initial part of the calorimeter, can be evaluated by

subtraction. This high-η part of HCAL consists of 1728 trigger towers, with ∆φ×∆η

of 0.175× 0.175.

The energy resolution of the ECAL-HCAL combined system has been evaluated by

a combined test beam with high energy pions [29] and it is given by:

σ(E)

E=

84.7%√E⊕ 7.4% (3.5)

36

3.5 The Muon Detector


The CMS muon system [30] is dedicated to the triggering and identification of muons;

in conjunction with the tracker, provides an accurate momentum measurement of high

pT muons. Detecting muons is one of the most important tasks for the Compact Muon

Solenoid. Muons are the only charged particles able to pass across the calorimeters

without being absorbed. Therefore, chambers to detect muons are placed outside the

magnetic coil of CMS, embedded in the return yoke, to fully exploit the 1.8 T return

flux; there muons can be the only particles likely to register a signal.

Many interesting processes are characterized by muon in the final state; the most

stringent requirements for the muon detector perfomances come from the likely “sig-

nature” of the Higgs Boson decaying into four muons: H → ZZ → 4µ.

The muon system covers the pseudorapidity region up to |η| < 2.4 (see Fig. 3.15).

It consists of a barrel and two endcaps, the latter using different technologies respect

to the former. If we look at Fig. 3.15, we see that it is made from four muon stations,

both in the barrel and endcaps, interleaved with iron “return yoke” plates: a particle

is measured by fitting a curve to hits among the four muon stations.

The system is characterized by three independent subsystems (Fig. 3.15 (up)):

• Drift Tubes (DT), chosen for the barrel region, where the occupancy is rather low

(< 10 Hz/cm2), the magnetic field uniform and the hadron flux moderate;

• Cathode Strip Chambers (CSC), used in the endcaps, where the occupancy is

higher (> 100 Hz/cm2);

• Resistive Plate Chambers (RPC), both in the barrel and in the endcaps.

The muon system, outside the magnet, in addition to the usual radial geometry, is

divided also in planes orthogonal to the beam-line: it is composed of 5 wheels for the

barrel, and 3 wheels for the two endcaps. The drift chambers belong to the central

wheels. Each wheel is subdivided into 12 sectors (see Fig. 3.15 (down)), each hosting 4

or 5 chambers, depending on the sector. In total we have 250 drift chambers, equivalent

to 195000 DT channels. DTs and RPCs are arranged in concentric cylinders around

the beam line (“the barrel region”) whiles CSCs and RPCs, form the “endcaps” disks

that cover the ends of the barrel.

37


Figure 3.15: Longitudinal one quarter (up) and transversal (down) view of muon detector

38


The barrel muon system consists of four stations interleaved with iron return yoke

plates of the magnet. Each chamber consists of 3 detector layers, called Super Layer

(SL): these subunits are made up of four planes with parallel wires. Thus, each DT

chamber, on average 2 m × 2.5 m in size, consists of 12 aluminium planes of 60 drift

tubes. Chambers are filled with a gas mixture of Ar(85%) and CO2(15%).

In each chamber two super-layers have anode wires parallel to the beam axis, and

one has perpendicular wires. Thus, each chamber can provide two measurements along

the r−φ coordinate and one measurement along z (see Fig.3.16). The position resolution

is about 100 µm in both r−φ and z. In the outermost station, MB 4, each DT chamber

Figure 3.16: DT chamber - Layout of a DT chamber inside a muon barrel station.

has only two SLs that measure the r − φ coordinate.

For the endcaps, Cathode Strip Chambers have been chosen, in order to have precise

measurement even with strong magnetic field, and high particles multiplicity. CSCs are

multi-wire proportional chambers with segmented cathodes. Each chamber can provide

both hit position coordinates. Chambers are filled with a gas mixture of Ar(40%),

CO2(50%), CF4(10%). The chamber spatial resolution is about 80-85 µm. They are

assembled in six-layers modules.

In addition, both in the barrel and in the endcaps, Resistive Plate Chambers have

been used for trigger purposes. RPCs are made of parallel bakelite planes, with a bulk

resistivity of 1010÷1011 Ωcm. They operate in avalanche mode. These chambers have

limited spatial resolution, but they have excellent timing performances (3 ns). They

39


make for a fast trigger system able to identify muons with high efficiency. There are 6

stations of them in the barrel, and 4 in the endcaps.

The muon tracks reconstruction efficiency is better than 90% for muons up to 100

GeV, while charge assignment is 99% correct.

The muon momentum resolution when combining the inner tracker and muon de-

tector measurements is reported in Fig. 3.17 for both barrel and endcaps.

Figure 3.17: Muon detector - The muon momentum resolution as a function of mo-

mentum using the muon system, the inner tracker, or both (“full system”); (left) Barrel:

|η| < 0.2; (right) Endcap: 1.8 < |η| < 2.0.

To summarize, we have a total of 1400 muon chambers:

• 250 drift tubes (DTs) plus 540 cathode strip chambers (CSCs) are used to track

the positions of particles;

• 610 resistive plate chambers (RPCs) make for a trigger system, deciding to keep

or not the acquired muon data.

The described system is robust and able to filter out bkg noise.

40

3.6 The CMS Trigger

3.6 The CMS Trigger

Combining the number of interactions per beam-crossing, with the LHC crossing fre-

quency, and the physical cross sections at LHC center of mass energy, it is necessary to

reduce the number of informations that CMS should register to the interesting events

only. This is pursued by a system of integrated circuits which operates simple choices

and that is called the CMS trigger [31, 32].

The trigger system consists of two main steps: a Level-1 Trigger (L1) and a High

Level Trigger (HLT):

• The L1 consists of custom-designed, largely-programmable electronics, which do

simple choices.

• The HLT is a software system implemented in a filter farm of about one thou-

sand commercial processors. It requires photons with transverse energy above a

threshold, and use some loose isolation criteria.

An event with two candidate photons has to pass the trigger requirements for being

registered. The rate reduction capability is designed to be a factor of 107 for the

combined L1 and HLT. Considering photons produced by the decay of 120 GeV/c2

mass Higgs, it has been shown [32] that they satisfy the trigger-L1 requirements with

efficiency larger than 99%, whereas, for HLT, it has been obtained the 88% of them.

Our analysis will make use of much more selective cuts than HLT, concerning thresh-

olds on energies, transverse momenta and isolation criteria. Therefore, HLT inefficien-

cies can be considered negligible for this analysis.

41


42

4

Photon and Jet Reconstruction

VBF and HSTRA topologies are characterized by the presence of 2 jets in addition

to 2 signal photons. Higgs is measured through the di-photon invariant mass, whose

formula is:

Mγγ =√

2E1E2(1− cos∆ξ) (4.1)

where E1,2 stands for the two photon energies, and ∆ξ is their relative angle.

As we can see from Eq. (4.1), the width of the Higgs depends on detector resolution,

the intrinsic width being negligible. Therefore it is necessary to have good energetic

and angular resolutions on photons to perform this measurement.

Since the VBF and HSTRA final states are characterized by 2 jets, it becomes

crucial to have a good resolution on jets and to use a proper scale, in order to obtain

a good signal efficiency, and to reject combinatorial background.

In this chapter we will discuss the main techniques of reconstruction and identifi-

cation of photons and jets. In Sec. 4.1 we discuss the photon reconstruction, in Sec.

4.2 the isolation criteria, in Sec. 4.3 the photon identification, and finally in Sec. 4.4

the jet reconstruction.

43

4. PHOTON AND JET RECONSTRUCTION

4.1 Photon reconstruction in ECAL

A good photon candidate is an energetic deposit in ECAL, since photons showers

deposit all their energies inside crystals. Since the deposit can involve more crystals,

many algorithms have been developed in order to measure the correct deposited energy.

As we saw in chapter 3, the transversal dimension of crystals has been chosen equal

to Moliere radius of PWO, such that for a photon incident on the frontal face of a

crystal, the 90% of its energy is contained inside this radius. A collection of adjacent

ECAL crystals which is used to reconstruct the energy and the direction of a particle

is commonly referred as “cluster”. There are several algorithms of clustering [33] used

in the CMSSW framework. We will discuss the one used in ECAL Barrel at CMS.

Usually the general strategy of all these algorithms starts from finding the local

maximum in energy surrounded by other energetic deposits. The crystal in which is

found to be deposited the most of the energy is called the “seed”. There are different

methodologies for including all the nearby crystals, in the attempt to recover the entire

energy of the shower with the caveat of not including the deposits belonging to other

particles than photons or to the detector noise.

It has been measured that 94% of the energy of a single incident photon is con-

tained in 3 × 3 cluster and 97% in 5 × 5 cluster. It has been proved that summing

the energy measured in such fixed dimensional matrices gives the best reconstruction

performance for unconverted photons. Because of the presence of material in front of

the calorimeter, photons could convert in couples (e+e−), while electrons may radiate

photons via bremsstrahlung process. Furthermore, the deposits can be found in a more

extended region of ECAL than what expected from a single shower. Because of the

magnetic field, indeed, the energy reaching the calorimeter is spread along φ. For all

these reasons, dynamic cluster algorithms have been necessary in order to retrieve the

largest fraction of energy of the incident photon. In the following, we briefly describe

the dynamic super-clustering algorithm employed in CMS.

Hybrid Algorithm in Barrel

The Hybrid algorithm is a dedicated superclustering algorithm for ECAL Barrel. For

instance, we need to sum the contribution of several clusters which form a “superclus-

ter”, either when an electron in the tracker irradiates bremsstrahlung photons with

44

4.1 Photon reconstruction in ECAL

consequent several deposits in ECAL, or when a photon converts into a e+e− pair,

resulting in two rather distant deposits. Hybrid has been realized for such cases. A

schematic view of supercluster formation is shown in Fig. 4.1.

Figure 4.1: View of supercluster reconstruction - An electron which irradiates

bremsstrahlung photons forms in ECAL a sequence of energetic clusters. The Hybrid is

realized to collect these deposits.

The Hybrid algorithm is based on the observation that, at high energies, a charged

particle is bent almost only in the φ−direction, basically keeping constant its η value.

The Hybrid thus searches for clusters covering a wider φ region than η, exploiting the

knowledge of the lateral shower shape in the η direction, whilst dynamically looking

for distinct energetic deposits in the φ direction.

Figure 4.2: Hybrid algorithm - Basic principles of Hybrid algorithm.

The algorithm method is sketched in Fig. 4.2. First of all a “seed” crystal with

ET > EhybrT is found; then, from the seed, 1φ×3η crystal dominoes are considered, whose

45


central crystal is aligned in η with the seed crystal. If, considering the above defined

domino, its central crystal energy exceeds a certain threshold Ewing, then another

domino, 1φ×5η large, it has to be used. This method is iterated Nstep times, along the

two φ directions from the starting seed, and, this scanning ends when dominoes with

E < Ethr are removed, with the consequent possible formation of several disconnected

clusters. Then, all the clusters with some domino with energy E < Eseed are suppressed.

Finally, all the remaining clusters connected along the φ−direction, are grouped in a

unique “supercluster”. The parameters of the standard reconstruction procedure are

listed in Table 4.1.

EhybrT 1 GeV

Nstep 10

Ewing 1 GeV

Ethr 0.1 GeV

Eseed 0.35 GeV

Table 4.1: Parameters used in the Hybrid algorithm.

4.1.1 Energy corrections

Ideally, we can reconstruct the total energy of a photon by just summing up the energies

from all the crystals that form a cluster (or supercluster). Nevertheless, we have to

consider other sources of variation in the energy depending on the energetic scale and

eventually on the pseudorapidity in ECAL:

• the energy scale corrections depend on the ECAL residual non-linearities, i.e. the

not full containment of the shower and light collection effects of the crystals. The

overall effect is known as variation of local containment;

• the η−dependance is due to the presence of material to be crossed in the detector,

which is maximum in the Barrel-Endcap junctions. This of course entails a energy

fraction lost by electrons via bremsstrahlung and, for photons, the possibility to

convert into e+e− pairs.

These effects on the reconstructed energy can be estimated with high accuracy and

simple corrections, and, it has been demonstrated [34] that they can be parametrized

46

4.2 Definition of Isolation Criteria

by means of a corrective function explicitly depending on the “seed” cluster number of

crystals.

4.1.2 Determination of shower position

The shower position can be estimated as the energy weighted mean position of the

crystals in the cluster. Since the energy follows an exponential decrease with the lateral

distance from the shower core, we can measure the cluster position as a weighted mean

evaluated with the logarithm of the crystal energy [35] as follows:

x =

∑i xi ·Wi∑iWi

(4.2)

where xi is the position of the ith crystal and Wi is the logarithmic weight defined as:

Wi = max

[W0 + log

(Ei∑j Ej

); 0

](4.3)

The parameter W0 represents the smallest fraction of energy for a crystal allowed to

contribute to the position measurement. After optimization studies, its default value

has been determined to be 4.2, which corresponds to consider only those crystals con-

taining >1.5% of the cluster energy. Finally, the position of a supercluster is evaluated

by another energy-weighted mean, this time of its component clusters positions.


The photon candidate direction is characterized by the pseudorapidity ηγ and the az-

imuthal angle φγ . We introduce the variable ∆R, which represents a conical surface

around the direction of the photon, inside which we will ask for no “activity” in order

to define isolated photons:

∆R =√

(η − ηγ)2 + (φ− φγ)2 (4.4)

The detector activity is defined by any variable able to describe the presence of

other particles besides the photon candidate. The choice of the cone aperture and the

threshold value of the variable, can be found through an optimization (for example of

the significance 6.6).

47


4.2.1 Tracks Isolation

Photons produced by Higgs decay don’t leave any track in the detector, being neutral

particles, and are not produced in association with charged particles. We will therefore

search for photons with no reconstructed tracks around its direction of motion. Most

common variables which account for tracks isolation are essentially the sum of all the

transverse momenta of tracks belonging to the cone ∆R∗, and also the number of tracks

inside the cone (Ntracks):

pISOT =∑

∆R<∆R∗

pT |track (4.5)

This variable can be normalized to the photon momentum, pT (γ). Again, the value

of ∆R∗ can be obtained by an optimization procedure, for both the first and second

photon in pT . We shall use the defined variable pISOT , by keeping only those events

with pISOT less than a certain threshold, above which we are confident it is background

activity.

4.2.2 Electromagnetic Isolation

We can make the further request that the energetic deposit of the photon, is not

accompanied by additional deposits, in order to reduce the “jet-contamination”. The

following variables are considered:

EISOT =∑

∆R<∆R∗

ET |basic cluster (4.6)

This variables can be normalized to the photon energy. The sum is conducted over

all the basic clusters inside the ∆R∗ cone around the photon position in ECAL. The

sum doesn’t include basic clusters belonging to the considered photon supercluster.

The value of ∆R∗ can be obtained by an optimization procedure, for both the first and

second photon in pT .

4.2.3 Hadronic Isolation

The other requirement a signal photon candidate must satisfy is the hadronic isolation,

i.e. HCAL must not register activity around the direction of the photon. This is done

48


in order to maximize the rejection of events in which the deposit in ECAL is caused by

a particle inside a hadronic jet. Different variables have been studied, among these:

• HISOT : the sum of HCAL ET around the photon candidate in an annular region

of given inner and outer radii. A signal photon candidate is indeed produced

isolated, and thus we require no registered activity in HCAL around its direction

1.

• H/E, which relates the energy deposits in HCAL towers to the photon energy

measured in ECAL, inside a cone of radius ∆R∗:

H/E =∑

∆R<∆R∗

H|HCAL tower

E(γ)(4.7)

4.2.4 Cluster Shape

The shape of the energetic deposit left by a particle can be exploited too, adding other

informations on the photon candidate, and thus making the photon identification more

complete. The main purpose is to discriminate hadrons, such as neutral pions (π0),

which decay into two photons with a mean lifetime at rest of 10−16s. The π0 production

inside jets is really abundant, and the angle between the two photons from the pion

decay is approximatively inversely proportional to the pion energy, therefore the two

deposits will be likely overlaid, forming an unique electromagnetic cluster in ECAL.

By studying the spatial distribution moments of the electromagnetic deposit, it has

been possible to distinguish photons from neutral pions [36]. This spatial distribution

can be described by a symmetric matrix of covariance (S):

S =

(Sηη SηφSηφ Sφφ

)(4.8)

The elements of 4.8 are defined according to:

Sµν =N∑i=1

Wi (µi− < µ >) (νi− < ν >) µ, ν = η, φ (4.9)

1inside inner radius

49


with the sum made over the N crystals of the considered cluster, whereas Wi is de-

fined by eq.(4.3), and is used for the weighted means like < µ >=∑N

i=1Wi · µi. By

diagonalizing S, we can get the eigenvalues:

Smaj,min =Sηη + Sφφ ±

√(Sηη − Sφφ)2 + 4S2

ηφ

2(4.10)

An alternative definition of Smaj,min can be given by considering the 2nd moments

of the energetic distributions:

Smaj =

∑Ni=1Wi · (dMIN

i )2∑Ni=1Wi

Smin =

∑Ni=1Wi · (dMAJ

i )2∑Ni=1Wi

(4.11)

where dMIN(MAX) is the distance between the center of ith crystal and the minor

(major) axis. The length of the major axis, is an index of the cluster shape asymmetry.

The photons produced by a π0 decay, which are usually distant enough from each other,

form “stretched” clusters compared to single photon clusters. The length of the minor

axis, instead, for pure electromagnetic deposits, is about the Moliere radius of PWO.

For hadronic particle deposits, nevertheless, the minor axis length is rather arbitrary.

The minor axis is a sort of index of the electromagnetic nature of the deposits.

4.3 Photon Identification

The photon Identification is based on the criteria provided by the “egamma” group at

CMS [37]. We considered only superclusters in regions in η covered by the tracking

detectors (η ≤ 2.5), and we exclude the region between the barrel and the endcaps (|η| >1.4442 and |η| < 1.566); The photon identification and isolation essential features are:

• the hadronic to electromagnetic energy ratio: H/E < 0.05 to reject jets with a

substantial hadronic component.

• ECAL isolation: EISOT is evaluated around the photon candidate in an annular

region of inner radius ∆R = 0.06 and outer radius 0.4.

50

4.3 Photon Identification

• HCAL isolation: we calculate HISOT around the photon candidate in an annular

region of inner radius ∆R = 0.15 and outer radius 0.4.

• Tracker isolation: pISOT is the scalar sum of pT of tracks consistent with the

primary vertex in a hollow cone around the photon candidate in an annular region

of inner radius ∆R = 0.04 and outer radius 0.4.

• we consider Sηη (4.9), the ηη element of the ηφ covariance matrix.

In Tab. 4.2, we report the “tight” and the “loose” thresholds of the photon identi-

fication variables.

“tight” phID “loose” phID

pT (γ) > 20 > 20

Tracker Iso < 2.0 < 3.5

ECAL Iso < 4.2 < 4.2

HCAL Iso < 2.2 < 2.2

H/E < 0.05 < 0.05

Sηη|EB < 0.013 < 1000

Sηη|EE < 0.030 < 1000

Table 4.2: Threshold values for “EG” phID - Energies and momenta are expressed

in GeV. The “tight” selection is applied to VBF and HSTRA exclusive analyses. The

“loose” selection is used for CS (see Sec. 6.4.)

In Fig. 4.3, 4.4 and 4.5, we show the N−1 plots for each of the described variables,

after having applied all the cuts in the selection except for the cut on the plotted

variable [37]. These plots are produced with the first 74 nb−1 of integrated luminosity

of 2010. From the data-MC comparison we can see the agreement is quite good for the

above mentioned isolation variables.

51


Figure 4.3: N − 1 (ECAL) - ECAL isolation distribution for data and MC, shown for

barrel (right) and endcap (left). The Monte Carlo results are normalized separately for

each plot to the number of entries in the data histogram.

Figure 4.4: N − 1 (HCAL) - HCAL isolation distribution for data and MC, shown

for barrel (right) and endcap (left). The Monte Carlo results are normalized separately for


Figure 4.5: N − 1 (Track Iso) - Track isolation distribution for data and MC, shown

for barrel (right) and endcap (left). The Monte Carlo results are normalized separately for


52

4.4 Particle Flow Jets

4.4 Particle Flow Jets

Our analysis aims to look at events with two photons and two jets in the final state.

The jet energy calibration and resolution is fundamental and can be a leading source

of systematic uncertainty for an analysis involving jets in the final state. Four jets

reconstruction methods exist at CMS, which provide the inputs to the jet clustering

algorithm: calorimeter jets, Jet-Plus-Track (JPT) jets, Particle-Flow (PF) jets, and

track jets (see [38]). We used PF Jets, since the jet momentum and spatial resolutions

are expected to be improved with respect to calorimeter jets as the use of the tracking

detectors and of the excellent granularity of the ECAL allows to resolve and precisely

measure charged hadrons and photons inside jets, which constitute ≈ 90% of the jet

energy. The PF method identifies and reconstructs all particles in the event, combining

the informations from all sub-detectors, prior to the jet clustering. For instance, charged

hadrons, are reconstructed from tracks in the central tracker, while photons and neutral

hadrons are reconstructed from energy clusters in ECAL and HCAL. PFlow jets are

finally reconstructed from the resulting list of particles. In particular, PF Jets are

reconstructed using the Anti-kT clustering algorithm (with size parameter R = 0.5),

which is a sequential recombination algorithm that gives conical jets [39].

Since the response to a particle level jet is smaller than unity and is a function of

the jet pT , a method to evaluate the absolute jet energy correction has been developed.

This correction removes these variations, making the response uniform to unity at all

values of jet transverse momentum. In order to determine this, γ+jet events have been

studied, where the idealized topology consists in a jet recoiling against a photon with

exactly compensating transverse momenta. Figure 4.6 (top) shows the jet response

obtained from γ+jet events, using the PF method. Jet pT resolutions are estimated

by dijet asymmetry method, which exploits momentum conservation in the transverse

plane of dijet system and is based exclusively on the measured kinematics of the dijet

events. We call the matched reference generator jet pTREF . The obtained jet pT

resolutions are shown in Figure 4.6 (bottom). Current physics analyses in CMS use

5% jet energy calibration (JEC) uncertainty for PFlow jets, with the additional 2%

uncertainty per unit rapidity. Supported by current limited statistics, these seem to be

conservative estimates. The 10% uncertainty is used for evaluation of the systematic

errors due to the jet resolutions effects.

53


Figure 4.6: (top) Particle Flow Jet response - Response < pT /pTγ > versus pT

γ in

data and MC for PFlow jets. MC truth response is also shown. Data/MC ratio and the

one-parameter linear fit function is shown at the bottom of the plots, together with ± 5%

and ±10% lines. [38]; (bottom) Particle Flow Jet resolution - PFlow jet resolution for

0 ≤ |η| < 1.4 determined with the asymmetry method from QCD simulation and compared

with the result from data using the same procedure. [38].

54

5

Analysis Method and

Optimization

Generally, hf → γγ decay can be studied with both inclusive and exclusive approaches.

The inclusive approach selects the two most energetic photons of the event, with a

tighter requirement on Higgs transverse momentum. This method guarantees high

statistics, with the drawback of a large background. The exclusive search can instead

distinguish gluon gluon fusion, vector boson fusion and Higgs-strahlung requiring 2 jets

in addition to 2 photons in the event. This approach is cleaner than the inclusive one,

but it has lower efficiency. In previous works at LEP and Tevatron only the inclusive

approach has been pursued. Each of the four experiments at the LEP collider at

CERN place 95% confidence level (C.L.) lower limits on the fermiophobic Higgs mass

(the most stringent being 105.5 GeV/c2), and a combination of this results obtains

a 95% C.L. limit of 109.7 GeV/c2 [40]. Recently, at Tevatron, the DØ collaboration

excluded the Fermiophobic Higgs with a mass Mhf < 112 GeV/c2, which is currently

the best limit [7]. As described in Chap. 2, the main mechanisms of production for a

fermiophobic Higgs are vector boson fusion (VBF) and Higgs-strahlung (HSTRA). An

exclusive search is dedicated to both.

In the VBF case (see Fig. 2.7 top-right), the typical topology can be sketched as in

Fig. 5.1 (left), where we have two high pT central photons and two back to back jets at

high pseudorapidity values. The two jets are induced by the incoming quarks (usually

called “tagging jets”), which scatter at high energy and enter the active volume of CMS

in the high rapidity regions (for a detailed study of VBF jets see [41]). Therefore, in the

55

5. ANALYSIS METHOD AND OPTIMIZATION

Figure 5.1: sketch of VBF and HSTRA − (left) VBF topology (back to back jets);

(right) HSTRA topology (central jets produced by W or Z decay)

VBF exclusive search, in addition to two high pT photons we require two back to back

jets at high η: this guarantees a very clean signature, a better signal to background

(S/B) ratio, but at the same time a lower signal efficiency compared to that of inclusive

search. In the HSTRA scenario (see Fig. 2.7 bottom-left), whose topology is sketched

in Fig. 5.1 (right), the two jets are mainly central; in the final state we require 2 photons

and 2 jets, the former produced by Higgs decay the latter produced by the associated

gauge vector boson (W or Z) decay, whose invariant mass constrains the di-jet system.

This mechanism appears promising for having a cross section of the same order of VBF

for low Higgs mass.

Since the two exclusive analyses (VBF and HSTRA) share the same final state

2γ + 2j, it has been possible to use the same discriminating variables, with ad hoc

threshold for each case. This will be discussed in Sec. 5.2. It is important to remark

that VBF and HSTRA have been optimized separately to maximize the CMS potential

of discovery. The optimization procedure is described in Sec. 5.3, and is based on

the minimization of the upper limit to cross section considering the LHC short-term

scenario of 1 fb−1 of integrated luminosity.

5.1 MC Samples

Monte Carlo simulation plays a key role in modern high energy physics experiments,

simulating collision dynamics and the detector response to particles in the final state.

The generation step makes use of the main different theoretical MC generators. In

this analysis we use PYTHIA, POWHEG, MADGRAPH [42]. The simulation step is

56

5.1 MC Samples

performed using a full simulation of the CMS detector based on GEANT4 [43, 44].

In order to estimate the expected number of events in a given integrated luminosity

(Lint), the MC sample must contain a large number of simulated events, corresponding

at least to the same order of magnitude of the analyzed data. Therefore we calculate

the equivalent integrated luminosity (Leq) of the sample:

Leq =N

σ · ε(5.1)

where N is the number of events generated and simulated for that sample, σ is the

process cross-section and ε is the MC filter efficiency. In this section we describe the

main characteristics of MC samples used in this analysis.

5.1.1 Signal Samples

Vector boson fusion is realized with PYTHIA 6 [19] , which calculates cross sections

and perform quark showering and hadronization (see VBF diagram in Fig. 2.7 (top

right)). This production is processed with POWHEG [45], which is the acronym of

Positive Weight Hardest Emission Generator, a method to interface NLO calculations

with Parton Shower (NLO+PS). An important advantage of POWHEG is the complete

separation of the hardest radiation generation and the subsequent shower. This method

is demonstrated to be a viable tool for NLO jet physics, a really important characteristic

to be guaranteed in the VBF analysis, where we have in the final state two photons

and two jets.

Higgs-strahlung production (Fig. 2.7 (bottom left)) is realized by PYTHIA 6 [19],

making use of the Probability Distribution (“ProbDist”) method [19]. The reported

cross section is the sum of Higgs-strahlung with a W and with a Z associated to the

Higgs.

The main characteristic of the signal MC samples are summarized in Tab. 5.1.

MC sample σ[pb] εMC σ · εMC [pb] Leq[fb−1]

VBF 1.269 1 1.269 3.0×103

HSTRA 1.016 1 1.016 2.8×103

Table 5.1: Main characteristics of the signal MC samples − σ: cross section; εMC :

Filter efficiency; σ · εMC : Effective cross section; Leq: Equivalent integrated luminosity

57


5.1.2 Background Samples

• “QCD events with γγ”:

The Box diagram is one of the main sources of irreducible background (see Fig.

2.10 (right)). Partons producing the box-diagram possess transverse momenta

in the range 25÷250 GeV/c. The MC sample has been produced by PYTHIA 6

[19].

• “γ + j events”:

This reducible background has been produced by PYTHIA 6: a jet can hadronize

into a pion decaying into two close photons, detected as one fake photon, as

reported in Fig. 2.11.

• “γγ + jets events”:

Many diagrams are reproduced by this MC sample. First of all, it covers the

irreducible background of Born diagram (Fig. 2.10 (left)). This sample is realized

with the generator MADGRAPH [42, 46], which reproduces diphoton + X, whose

main types of diagrams are:

1. Irreducible background such as diagrams of type “Born” (see Fig. 2.10

(left)).

2. Diagrams of type “prompt and bremsstrahlung”, which means 1 photon from

the hard interaction and 1 photon from final state radiation (FSR).

Both these types of diagrams can be accompanied by up to 2 “explicit” jets,

meaning with this in the matrix element:

qq → γγ (see Fig. 5.2 (left));

qq → γγg (see Fig. 5.2 (right));

qg → γγq (see Fig. 5.3 (left)); 1

qq → γγqq (see Fig. 5.3 (right));

qq → γγgg (see Fig. 5.4 (left));

qg → γγqg (see Fig. 5.4 (right)).

58

5.1 MC Samples

Figure 5.2: MADGRAPH - (left) qq → γγ (right) qq → γγg

• “QCD events”

Signal selection is contaminated by a background stemming mainly from QCD

di-jets, in which at least one of the jets has been revealed as a well-isolated single

electromagnetic (EM) cluster and it is misidentified as a photon. The cluster

is caused mainly by energetic (single or multiple) π0,±, η,K0s and K± mesons

decaying into photons in the final state. As in general it is not possible to suppress

completely all the background events, the fraction of the remaining events has

to be evaluated. In order to generate a sufficiently large sample of QCD di-jets

in a pT range which is representative of the background for a di-photon selection

in a reasonable time, a generator-level preselection algorithm is needed to enrich

the QCD sample with photons. Thus, the more realistic QCD background MC

sample available for the hf → γγ study is represented by the QCD Double Electro

Magnetic Enriched (QCDDoubleEMEnriched) sample. The specific filter before

1This is an example of “1 prompt + 1 brem” photons, which is also included in PYTHIA γ + jet

samples described above, and that it has been vetoed in PYTHIA, to avoid double-counting.

59


Figure 5.3: MADGRAPH - (left) qg → γγq (right) qq → γγqq

60

5.1 MC Samples

Figure 5.4: MADGRAPH - (left) qq → γγgg (right) qg → γγqg

61


the simulation requires the presence in the event of at least two particles that

can produce an energy deposit in the ECAL sufficient to mimic a photon (“fake

photon”) or a real photon in final state. Given the difference in cross-section,

QCD events have been produced separately for two bins in pT of the partons

(30÷40 and 40÷∞ GeV/c).

The main characteristic of the background samples are summarized in Tab. 5.2.

MC sample σ[pb] εMC σ · εMC [pb] Leq[fb−1]

Box 12.37 1 12.37 63

γ + jet 77100 0.0064 493.4 2.4

γγ + jets 134 1 134 8.0

QCD pT 30÷40 4.18·107 0.00023 9610 0.37

QCD pT 40÷∞ 1.87 ·107 0.00216 40390 0.52

Table 5.2: Main characteristics of the bkg MC samples − σ: cross section; εMC :

Filter efficiency; σ · εMC : Effective cross section; Leq: Equivalent integrated luminosity

5.2 Selection Criteria

In this section we describe the kinematic variables used to discriminate signal (S) events

from background (B) events. In the following we discuss the flow of the selection.

We require the presence of at least two jets, and we select the 2 jets with highest

transverse momentum. In the VBF case, this corresponds to take the “tagging” jets.

In the HSTRA case, this criterion selects the two jets produced by W or Z decay.

We then take advantage of VBF and HSTRA topologies and kinematics, i.e. the

discriminating variables based on the two jets of the event. For a detailed study of their

discriminating power go to Sec. 5.2.2, where the main differences are spotted for the

two channels (e.g. VBF: large ∆ηj1j2 and large di-jet invariant mass Mj1j2 , HSTRA:

small ∆ηj1j2 and Mj1j2 ∼MW (Z)).

Finally we optimize the requirements on each variable to get a better sensitiv-

ity of the signal. The optimization is based on minimizing the upper limit on cross

sections[47], as described in section 5.3.

62


We use the invariant mass spectrum mγγ to measure signal yield (S) and estimate

background (B). S is estimated counting the number of events inside a signal window

of 5 GeV/c2 centered around the Higgs nominal mass value. Signal distribution is

influenced by instrumental effects and leakage of the photon energies (see Fig. 5.5(left)).

With regard to B, its distribution is assumed flat after all cuts are applied (see Fig.

5.5). Therefore B is obtained by integrating the sidebands events contained in the

window 100-150 GeV, normalizing the result to the width of signal window.

Figure 5.5: MC Signal and Background shapes − (left) Signal (VBF and HSTRA)

is distributed asymmetrically around the nominal mass value. We choose the window 117-

122 GeV to estimate the signal yield. (right) With all cuts applied, background is flat.

This allows to estimate the background contribution by integrating in the whole window

100-150 GeV, and dividing by 10 (to normalize to the 5 GeV signal window width)

In what follows we describe the variables to select photons and jets.

5.2.1 Photons selection variables

Fig. 5.6 shows the transverse momentum distributions of the two highest pT photons

of the event. We see that signal is always distributed at higher values than background,

for both photons. This suggests to look at events with high pT photons for both VBF

and HSTRA channels, since their spectra are quite similar.

63


Figure 5.6: Transverse momentum distributions of the two highest pT photons

of the event − (left) 1st highest pT photon; (right) 2nd highest pT photon. VBF and

HSTRA are distributed at high values compared to background.

5.2.2 Jets selection variables

In this section we describe the discriminating variables involving the two highest pT jets

of the event: they essentially are the transverse momenta (pj1T , pj2T ), the di-jet invariant

mass (Mj1j2), and the difference in pseudorapidity (∆ηj1j2).

Looking at pj1T and pj2T normalized distributions of Fig. 5.7, we notice that signal

(VBF and HSTRA) is expected to have a harder spectrum than background. This

suggests to look at events with two high pT photons and with the further requirement

of two high pT jets.

The other variable concerning the jets kinematics is the invariant mass of the two

(Mj1j2). For VBF analysis, the typical choice is to select very large di-jet invariant

mass events [41]. Indeed, being the jets mostly back to back, the angle between them

is ideally π, and this maximises the di-jet invariant mass formula. Since the tagging

jets are very energetic at√s =7 TeV in LHC, it is legitimate to expect large Mj1j2

values for VBF events (see Fig. 5.8 (left)). With regard to the HSTRA channel instead,

the diagram requires the presence of a W or Z boson. We then select all the events

with two jets forming an invariant mass Mj1j2 with values cosnistent with the W or Z

boson mass (see Fig. 5.8 (right) for a close-up of the window comprising the W and Z

resonances in the di-jet invariant mass spectrum).

64


Figure 5.7: Transverse momentum distributions of the two highest pT jets of

the event − (left) 1st highest pT jet; (right) 2nd highest pT jet. VBF and HSTRA are

distributed at high values compared to background.

Figure 5.8: Di-jet invariant mass spectrum − The invariant mass distributions of

the two highest pT jets of the event for different samples. The distributions are normalized

to unity. (left) Plot in the window (0-1500) GeV: the VBF spectrum is distributed at high

values of Mj1j2 ; (right) Close-up of the window (40-130) GeV: for HSTRA, the associated

production of W or Z is highlighted in the low-mass region of Mj1j2 .

65


Figure 5.9: Difference in pseudorapidity of the two jets(top) − VBF is character-

ized by a large difference in η between the two jets. VBF have two back to back jets, both

at high η with consequent large |∆ηj1j2 | values. For HSTRA we have a complementary

situation: the two jets possess similar η, and ∆ηj1j2 is centrally distributed around zero.

Nevertheless this variable is still discriminating, since it is much more central and peaked

than background; for HSTRA channel, we select events with |∆ηj1j2 | less than a certain

threshold.

Another discriminating variable is the difference in pseudorapidity of the two jets

(∆ηj1j2). The VBF topology implies two forward jets at high η, back to back: this

means large ∆ηj1j2 . In Fig. 5.9, we clearly see how VBF signal is characterized by high

values of this variable. As far as HSTRA is concerned, ∆ηj1j2 spectrum behaves com-

plementarily compared to VBF. We can envision the two jets being produced around

the direction of the vector boson, at close η values; their difference is therefore small

and ∆ηj1j2 is distributed in the central region with 0 as mean value, as shown in Fig.

5.9.

5.2.3 Zeppenfeld

It is possible to build variables which exploit both photons and jets characteristics.

The Zeppenfeld variable, for instance, is largely used to describe the topology of VBF

events [48]: it consists, for a given physical observable, in its η re-scaled to the two

66


Figure 5.10: Zeppenfeld variable(bottom) − The Zeppenfeld variable has been defined

by photons and jets η, as shown in Eq. (5.2). The signal distribution is central, and the

physical interpretation of this behaviour is that the Higgs lays in the pseudorapidity space

among the two back to back jets, according to VBF topology. For HSTRA, the Higgs takes

η values close to those of W or Z, therefore Zeppenfeld is distributed around zero.

tagging jet candidates frame of reference, and is generally expressed as:

Z = η|obs −η(j1) + η(j2)

2(5.2)

where the subscript “obs” indicates any meaningful observable. In this analysis we use

η|obs = η(γ1 + γ2), where clearly it coincides with the Higgs candidate pseudorapidity.

For VBF, as shown in Fig. 5.10, the Zeppenfeld normalized distribution is peaked

and central, and differs significantly from background: the Higgs is indeed distributed

in the η-space among the two back to back jets. We notice also that the Zeppenfeld

distribution of HSTRA is very similar to the VBF case: in fact the HSTRA Higgs has a

pseudorapidity close to that of W or Z (and is rotated of an angle φ ∼ π with respect to

the associated vector boson). Hence, the way to cut on the Zeppenfeld is the same for

both analyses: given a certain threshold, we select only those events with |Z| ≤ Zthr.

67


5.3 Optimization of Selection Criteria

This section deals with the optimization of selection criteria to provide the minimum

upper limit on cross section. The set of cuts consists of:

1. pγ1T > pγ1T |thr pγ2T > pγ2T |thr

2. pj1T > pj1T |thr pj2T > pj2T |thr

3. |∆ηj1j2 | > |∆ηj1j2 |thr (VBF), |∆ηj1j2 | < |∆ηj1j2 |thr (HSTRA)

4. |Z| < |Z|thr,

5. Mj1j2 > Mj1j2 |thr (VBF), |Mj1j2 − 85.| < Mj1j2 |thr (HSTRA)

where we reported, when necessary, the differences for the two cases. The subscript

“thr” stands for threshold. We choose to optimize the upper limit (UL) on the cross-

section, by finding the set of cuts for which the UL is minimised. The concept of

upper limit will be discussed in detail in Chap. 6. Briefly, the definition of UL can be

enunciated as follows: given an ensemble of experiments, an UL with confidence level

α is the value for which a fraction α of experiments gives a result smaller than UL.

We use an upper limit calculator which evaluates the UL on cross section (pb) for our

analysis [47]. In the following we describe the optimization method, which basically

consists of two steps:

1. The initial point (“seed”) from which the optimization starts, consists in a certain

set of cuts whose thresholds have been chosen “at first glance”. We optimize the

UL by varying the cuts one by one, by keeping constant all the thresholds except

that of the variable involved in the optimization. For each cut, many different

threshold values are tested. The threshold value which is found to minimize the

UL is kept fixed at next iteration, when we optimize the following cut. When

this procedure is completed, we have got a set of cuts, which is the “new seed”

for the second step.

2. In order to make a finer optimization, we start from the “new seed”, and then we

look at all the possible combinations of cuts obtainable by moving each threshold

from its step-1 value. A matrix of input values (around the “new seed” thresholds)

is provided to the program of optimization.

68


If a smaller UL is found after step-2 we consider the corresponding set of cuts as the

optimal set, otherwise we take the final set from step-1 procedure.

Let’s take VBF for instance. The set : 55-30-30-20-2.5-2.5-250 is the starting “seed”

of the step-1 optimization; then the algorithm proceeds as follows:

X-30-30-20-2.5-2.5-250

pγ1T new-X-20-15-2.5-1.5-300...

...

pγ1T new-pγ2T new-pj1T new-pj2T new- |∆ηj1j2 |new- |Z|new-Mj1j2new

where X each time is a given array of values to be tested. We have 7 cuts to optimize,

therefore 7 iterations. In Fig. 5.11 we report the UL’s found after each iteration of

step-1 optimization.

Figure 5.11: step-1 optimization: (VBF) - : − The resulting UL’s obtained with

step-1 procedure. Each UL corresponds to one single variable optimization.

Step-1 leads to the set of cuts 60-25-25-20-2.5-1.8-250, which is the “new seed” for

step-2 optimization. Step-2 performs another scanning to minimize the UL, by varying

the cuts “all together”: each threshold can assume N values which scan the range

around step-1 output value. We get a total of N7 sets of cuts to test, considering all

the possible combinations. In order to have a nice visualization of the procedure which

controls the most important quantities of the analysis, for each combination of cuts, we

69


Figure 5.12: step-2 optimization for VBF (top) and HSTRA (bottom) - Testing

more than 2000 set of cuts. The “seed” is obtained by step-1 procedure. For each set, signal

efficiency (Seff ), background rejection (Brej), and upper limit (UL) are drawn.

(left) 3D-visualization: x: Seff , y: Brej , z: UL − (right) 2D plot: x: Seff , y: Brej .

The “star” indicates the minimum point, corresponding to the final “optimal” set of cuts.

VBF final set: 55-25-30-20-3.5-2.0-400, UL: 0.0395 pb;

HSTRA: final set:60-25-35-20-2.5-1.5-30, UL: 0.0999 pb.

70


can calculate the Upper Limit (UL), the signal efficiency (Seff ), and the background

rejection (Brej). Each combination of cuts results in a point in the 3D space of Seff -

Brej-UL. We get an Upper Limit surface and the optimization corresponds, in this

representation, to find the minimum of the surface, as in Fig. 5.12. The final optimized

set of cuts for VBF analysis obtained after step-2 is 55-25-30-20-3.5-2.0-400 (and the

corresponding UL is σ =0.0395 pb): this set will be used in the following.

The “step-1 seed”, “the step-2 seed” and the final optimized set of cuts with the

corresponding UL, are summarized in Tab. 5.3 for both VBF and HSTRA.

Analysis step-1 seed step-2 seed final set UL(pb)

VBF 55-30-30-20-2.5-2.5-250 60-25-25-20-2.5-1.8-250 55-25-30-20-3.5-2.0-400 0.0395

HSTRA 65-35-40-30-3.0-2.0-30 60-30-35-25-2.8-1.8-25 60-25-35-20-2.5-1.5-30 0.0999

Table 5.3: VBF and HSTRA optimization− summary of step-1 and step-2 optimiza-

tion based on UL minimization, separately conducted for VBF and HSTRA. For more

details, see Sec. 5.3.

71


5.4 Signal and Background Efficiency

In this section we want to show the signal efficiency and the background rejection power

after each cut. We use the optimized set of cuts found in Sec. 5.3. We add the cuts in

cascade, one after the other. In the following we show:

• the normalized distributions of the variables in cascade;

• the mγγ distribution after having applied the selection criteria in cascade.

Final tables summarize the efficiencies and the number of selected events after each cut

for every MC sample.

5.4.1 VBF: Yields and Efficiencies

As discussed in Sec. 5.3, we impose the optimized cuts for VBF:

1. cut1 : pγ1T >55 GeV/c & pγ2T >25 GeV/c

2. cut2 : cut1 & pj1T >30 GeV/c & pj2T >20 GeV/c,

3. cut3 : cut2 & |∆ηj1j2 | > 3.5,

4. cut4 : cut3 & |Z| < 2.0,

5. cut5 : cut4 & Mj1j2 > 400 GeV/c2

The normalized distributions of the variables and the di-photon invariant mass

spectrum are shown for each cut in cascade (see Fig. 5.13 after cut1, Fig. 5.14 after

cut2, Fig. 5.15 after cut3 (top) and cut4 (bottom), and Fig. 5.16 after cut5). For every

MC sample we report in Tab. 5.4 and 5.5 respectively the efficiencies and the number

of selected events after each cut.

72


MC sample after cut1(%) after cut2(%) after cut3(%) after cut4(%) after cut5(%)

VBF 37.7±8.1 27.9±7.5 17.1±6.3 14.8±5.9 12.1±5.5

box 2.33±0.14 0.15±0.03 0.04±0.02 0.03±0.01 0.010±0.009

γγ + jets 1.02±0.03 0.23±0.01 0.012±0.003 0.005±0.002 0.002±0.001

γ + j 0.332±0.008 0.048±0.003 0.006±0.001 0.0024±0.0007 0.0009±0.0004

qcd(pT40) (201±7)·10−5 (91±5)·10−5 (12±2)·10−5 (5±1)·10−5 (19±7)·10−6

qcd(pT30−40) (28±5)·10−5 (8±3)·10−5 (3±2)·10−5 0 0

Table 5.4: Absolute Efficiencies after each cut (VBF) − the mass window for

signal is (117-122) GeV while background samples are estimated in the window (100-150)

GeV; Efficiencies are expressed in %. The standard deviations of efficiencies are estimated

assuming the MC events being binomially distributed; under this hypothesis the following

formula holds: σ[ε] =√

ε(1−ε)N where ε is the efficiency and N the total number of events

of a particular MC sample.

MC sample after cut1 after cut2 after cut3 after cut4 after cut5

VBF 13.4 9.9 6.1 5.3 4.3

box 28.8 1.85 0.51 0.36 0.12

γγ + jets 137.0 30.6 1.67 0.74 0.30

γ + j 164.1 23.5 2.75 1.18 0.46

qcd(pT40) 81.4 36.8 4.77 2.10 0.76

qcd(pT30−40) 2.72 0.82 0.27 0 0

Table 5.5: Events after each cut (VBF) − Expected numbers after each cut at 1

fb−1 in the signal window (117-122) GeV.

73


Figure 5.13: mγγ after cut1 − (top) distributions of pγ1T and pγ2T . The two photons

forming the invariant mass have to pass before the “tight” Photon ID criteria; (bottom)

mγγ invariant mass spectrum is drawn adding the cuts pγ1T >55 GeV/c and pγ2T >25 GeV/c

(cut1).

74


Figure 5.14: mγγ after cut2 − (top) distributions of pj1T and pj2T after cuts on pT of

photons (cut1); (bottom) mγγ invariant mass spectrum is drawn adding the cuts pj1T >30

GeV/c, pj2T >20 GeV/c (cut2).

75


Figure 5.15: mγγ after cut3 (top), and after cut4 (bottom) − (top left) ∆η dis-

tribution after cuts on pT of photons and jets (cut2); (top right) mγγ (bottom) spectrum

adding the cut |∆η| >3.5 (cut3); (bottom left) Z distribution after cut3; (bottom right)

mγγ spectrum adding the cut Z <2.0 (cut4);

76


Figure 5.16: mγγ after cut5 − (left) Mjj distribution after cuts on pT of photons and

jets, ∆η and Z (cut4); (right) mγγ diphoton mass spectrum adding the cut Mjj >400

GeV/c2 (cut5).

5.4.2 HSTRA: Yields and Efficiencies

As discussed in Sec. 5.3, we impose the optimized set of cuts for HSTRA:

1. cut1 : pγ1T >60 GeV/c & pγ2T >25 GeV/c

2. cut2 : cut1 & pj1T >35 GeV/c & pj2T >20 GeV/c,

3. cut3 : cut2 & |∆ηj1j2 | < 2.5,

4. cut4 : cut3 & |Z| < 1.5,

5. cut5 : cut4 & |Mj1j2 − 85| < 30 GeV/c2

The normalized distributions of the variables and the di-photon invariant mass

spectrum are shown for each cut in cascade (see Fig. 5.17 after cut1, Fig. 5.18 after

cut2, Fig. 5.19 after cut3 (top) and cut4 (bottom), and Fig. 5.20 after cut5). For every

MC sample we report in Tab. 5.6 and 5.7 respectively the efficiencies and the number

of selected events after each cut.

77


MC sample after cut1(%) after cut2(%) after cut3(%) after cut4(%) after cut5(%)

HSTRA 25.9±8.2 15.8±6.8 14.8±6.7 12.2±6.2 9.2±5.4

box 1.60±0.11 0.095±0.028 0.050±0.020 0.020±0.012 0.013±0.010

γγ + jets 0.792±0.024 0.181±0.012 0.1524±0.0107 0.0905±0.0082 0.0429±0.0057

γ + j 0.2480±0.0071 0.0392±0.0028 0.0285±0.0024 0.0147±0.0017 0.0078±0.0013

qcd(pT40) (155±6.2)·10−5 (73.1±4.3)·10−5 (55.2±3.7)·10−5 (21.2±2.3)·10−5 (5.2±1.1)·10−5

qcd(pT30−40) (17.0±4.2)·10−5 (2.8±1.7)·10−5 (2.8±1.7)·10−5 0 0

Table 5.6: Absolute Efficiencies after each cut (HSTRA)− the mass window for

signal is (117-122) GeV while background samples are estimated in the window (100-150)

GeV; Efficiencies are expressed in %. The standard deviations of efficiencies are estimated

assuming the MC events being binomially distributed; under this hypothesis the following

formula holds: σ[ε] =√

ε(1−ε)N where ε is the efficiency and N the total number of events

of a particular MC sample.

MC sample after cut1 after cut2 after cut3 after cut4 after cut5

HSTRA 7.4 5.2 4.2 3.5 2.6

box 19.4 1.17 0.62 0.24 0.17

γγ + jets 106.2 24.3 20.4 12.1 5.75

γ + j 122.4 19.3 14.0 7.28 3.85

qcd(pT40) 62.9 29.5 22.3 8.58 2.10

qcd(pT30−40) 1.63 0.27 0.27 0 0

Table 5.7: Events after each cut (HSTRA) − Expected numbers after each cut at 1

fb−1 in the signal window (117-122) GeV.

78


Figure 5.17: mγγ after cut1 − (top) distributions of pγ1T and pγ2T . The two photons

forming the invariant mass have to pass before the “tight” Photon ID criteria; (bottom)

mγγ invariant mass spectrum is drawn adding the cuts pγ1T >60 GeV/c and pγ2T >25 GeV/c

(cut1).

79


Figure 5.18: mγγ after cut2 − (top) distributions of pj1T and pj2T after cuts on pT of

photons (cut1); (bottom) mγγ invariant mass spectrum is drawn adding the cuts pj1T >35

GeV/c, pj2T >20 GeV/c (cut2).

80


Figure 5.19: mγγ after cut3 (top), and after cut4 (bottom) − (top left) ∆η distri-

bution after cuts on pT of photons and jets (cut2); (top right) mγγ spectrum adding the

cut |∆η| <2.5 (cut3); (bottom left) Z distribution after cut3; (bottom right) mγγ spectrum

adding the cut Z <1.5 (cut4).

81


Figure 5.20: mγγ after cut5 − (left) Mjj distribution after cuts on pT of photons and

jets, ∆η and Z (cut4); (right) mγγ diphoton mass spectrum adding the cut |Mjj − 85| <30

GeV/c2 (cut5).

82

6

Results

This chapter is devoted to describe the results obtained in this analysis using the final

optimized set of cuts discussed in Sec 5.3. Its architecture is organized as follows:

• Sec. 6.1 is dedicated to describe the methodology followed to calculate the upper

limit on cross-sections.

• Sec. 6.2 shows the CMS exclusion potential with an estimated integrated lumi-

nosity of 1 fb−1.

• Sec. 6.3 is dedicated to results from data with 2011 integrated luminosity (Lint =

233 pb−1).

• Sec. 6.4 describes the control sample used for data, whereas Sec. 6.5 deals with

the main systematics that affect the analysis.

• In Sec. 6.6 a limit on the fermiophobic Higgs cross-section is extracted from data.

83

6. RESULTS

6.1 Upper Limit

There are several methods to calculate an upper limit on σ for a given confidence level.

The CMS upper limit Calculator refers to the Bayesian approach, assuming a flat prior

distribution. The Limit σCL can be evaluated from [49]:

CL =

∫ σCL0 p(S(σ) +B|N)dσ∫∞0 p(S(σ) +B|N)dσ

(6.1)

The probability density function can be calculated directly from Bayes’ theorem

[50]:

p(S(σ) +B|N) =p(N |S(σ) +B) · P (S(σ) +B)

P (N)(6.2)

where P stands for prior, N is the number of observed events statistically compatible

with the expected average number of background (B) events, and number of signal (S)

events is given by S = ε · L · σ. The routine “RooStatsCl95” [51], which is part of the

package of the standard procedures for statistical inference in CMS physics analyses,

estimates observed upper limits on the process cross section in a counting experiment,

and the corresponding median expected limit with 1- and 2-standard deviation quantile

bands. The routine addresses the task of a Bayesian evaluation of limits for a one-bin

counting experiment with systematic uncertainties on luminosity and efficiency for the

signal and a global uncertainty on the expected background. The observable is the

measured number of events. The upper limit corresponds to one-sided 95%, and is

evaluated as a function of the observed number of events in a hypothetical experiment.

As reported in [52], the likelihood in Bayes’ theorem (6.2) can be written as:

p(N |S(σ) +B) = p(N |µ(σ,L, ε, B, νS , νB)) =µNe−µ

N !· p(νS |δS) · p(νB|δB) (6.3)

where νS , νB are nuisance parameters with mean 1, used to incorporate the combined

systematic uncertainties, and δS =√

(∆LL

)2 + (∆εε )2 and δB = ∆B

B . A flat prior is

used in Bayes’ theorem (6.2). We remark that in this work we keep the two channels

(VBF,HSTRA) separated in order to maximize the exclusion potential.

84

6.2 Estimate for Exclusion Potential on Simulation

6.2 Estimate for Exclusion Potential on Simulation

In this section we use Monte Carlo simulations to investigate the exclusion potential

that can be reached with a short-term scenario of 1 fb−1 of integrated luminosity. For

both exclusive analyses, an upper limit on cross-section has been estimated at each

mass point (see Fig. 6.1). The simulation predicts that with 1 fb−1 CMS can exclude

a fermiophobic Higgs up to 116 GeV by VBF exclusive analysis, while up to 106 GeV

by HSTRA.

As discussed in Chap. 5, we have followed the HDECAY prescriptions, which

indicate to use SM cross-sections in the analysis of a fermiophobic Higgs. As discussed

in Chap. 2, for Two Higgs-Doublet Models the proper coupling to bosons is described

by Eq.(2.20). Therefore, benchmarking 2HDM against SM, both VBF and HSTRA

cross-sections have to scale of a factor 11+tan2 β

. Thus the 2HDM production of a

fermiophobic Higgs decaying in two photons can be re-written as:

σ2HDMfpho =

σSM ·B.R.(hf → γγ)

1 + tan2 β(6.4)

As shown in Eq. (2.16), in 2HDM’s tanβ can not be equal to 0, because it is the

ratio of the two neutral Higgs V.E.V.’s. The fermiophobic Higgs production is now a

function of Mhf and tanβ, and, as a consequence, its exclusion is a function of these

two parameters. Hence, the possible region of exclusion with 1 fb−1 in the parameters

space (Mhf , tanβ) is obtained when the following inequality holds:

σSM ·B.R.(hf → γγ)

1 + tan2 β> σUL (6.5)

In Fig. 6.1 (bottom) is shown the prediction with 1 fb−1 on the excluded regions

in the parameter space (Mhf , tanβ) respectively for VBF (left) and HSTRA (right).

In this section, for completeness, we also give a rough estimate of the discovery

potential of the analysis. To do that we use the significance for tanβ =0 (SM cross-

sections as in HDECAY), at 1 fb−1. Assuming the background statistical fluctuations

of the number of events being Poisson-distributed, then the signal significance ς can be

defined as:

ς =S√B

(6.6)

Fig. 6.2 shows significance vs mass for VBF (left) and HSTRA (right) respectively.

85

6. RESULTS

Figure 6.1: U.L. of VBF(top left) - HSTRA(top right) - Upper limit to fermiophobic

cross-section vs mhf: when the theoretical cross-section exceeds the upper limit, evidence

of fermiophobic Higgs at 1 fb−1 at the indicated mass is possible with a 95% confidence

level; Fermiophobic Higgs exclusion in the plane tanβ vs Mhffor VBF(bottom

left) and HSTRA(bottom right) - Excluded region in the 2HDM type I scenario at 1

fb−1: the theoretical cross section scales as 11+tan2 β because of eq. (2.20)

86

6.3 Data-MC Comparison

Figure 6.2: Significance of VBF(left) - HSTRA(right)


Before calculating the UL on data we verified that data and Monte Carlo distributions of

the main variables of the analyses were consistent. The available integrated luminosity

is 233 pb−1. The comparison is made applying the optimized cuts of Sec. 5.3 in the

entire invariant mass window. Plots of VBF and HSTRA variables are reported in Fig.

6.3 and 6.5 respectively, with 233 pb−1 of integrated luminosity. From those plots we

notice for both analyses a good data-MC agreement of the main variables distributions;

this results in an encouraging projection at 1 fb−1. The di-photon invariant mass

spectrum for each cut in cascade is shown in Fig. 6.4 and 6.6 for VBF and HSTRA

respectively, with 2010 luminosity (33 pb−1). The observed upper limit on cross-section

with 33 pb−1, calculated separately for the two channels, is discussed in Sec. 6.6.

87

6. RESULTS

Figure 6.3: VBF variables (data-MC): (top) pTj1,j2 after pγ1T >55 pγ2T >25 (cut1);

(middle) ∆ηjj and Z(γ, γ, j, j) adding pj1T >30 pj2T >20 (cut2); (bottom) Mjj after cut2

(left), and adding |∆η| >3.5 |Z| < 2.0 (cut4) (right). Lint = 233 pb−1.

88


Figure 6.4: VBF di-photon spectrum (data-MC): mγγ after pγ1T >55 pγ2T >25 (cut1),

adding the cut pj1T >30 pj2T >20 (cut2), adding |∆η| >3.5 (cut3), adding |Z| < 2.0 (cut4),

and after Mjj >400 (cut5), with Lint = 33 pb−1.

89

6. RESULTS

Figure 6.5: HSTRA variables (data-MC): (top) pTj1,j2 after pγ1T >60 pγ2T >25 (cut1);

(middle) ∆ηjj and Z(γ, γ, j, j) after pj1T >35 pj2T >20 (cut2); (bottom) ∆ηjj (left) and Mjj

(right) N-1 plots. Lint = 233 pb−1.

90


Figure 6.6: HSTRA di-photon spectrum (data-MC): mγγ after pγ1T >60 pγ2T >25

(cut1), adding the cut pj1T >35 pj2T >20 (cut2), adding |∆η| <2.5 (cut3), adding |Z| < 1.5

(cut4), and finally adding |Mjj − 85| <30 (cut5), with Lint = 33 pb−1.

91

6. RESULTS

6.4 Control Samples

Data-driven control samples (CS) are introduced for the estimation of the background

events. The requirements that a control sample must satisfy are essentially three:

1. CS statistics must be larger than data.

2. CS has to be uncorrelated with the reference signal.

3. The shapes of the main variables of the analysis must be reproduced by the CS.

We want to use the CS to estimate the shape of the di-photon invariant mass

spectrum, and to check if the jet related distributions are under control. The CS

selection criteria must be suitable to select a kinematics very similar to background.

To achieve this we require at least one of the two photon candidates to pass tight cuts,

whereas the other must satisfy a much looser photon identification but must fail the

tight photon identification used in the analysis (see Tab. 4.2), in order to be completely

uncorrelated. This CS is suitable for backgrounds with one fake photon, but it is not

a good CS for Born and Box with two real photons (see Sec. 2.3.4).

We report the CS plots of the VBF and HSTRA variables (see Fig. 6.8, Fig. 6.7

and Fig. 6.10, Fig. 6.9 respectively). As for the data-MC comparison plots, here too

we notice a nice agreement between data and CS distributions of the main variables of

the analyses, especially jet variables are predicted with good precision.

92

6.4 Control Samples

Figure 6.7: VBF variables Control Sample: (top) pTj1,j2 after cut on pT of photons

(cut1); (middle) ∆ηjj and Z(γ, γ, j, j) adding the cut on pT of jets (cut2); (bottom) Mjj

after cut2 and after adding the cut on ∆η and Zeppenfeld (cut4). Lint = 233 pb−1.

93

6. RESULTS

Figure 6.8: VBF di-photon spectrum Control Sample: mγγ CS after cut on pT of

photons (cut1), adding the cut on pT of jets (cut2), adding the cut on ∆η (cut3), adding

the cut on Zeppenfeld variable (cut4), with Lint = 33 pb−1.

94

6.4 Control Samples

Figure 6.9: HSTRA variables Control Sample: (top) pTj1,j2 after cut on pT of

photons (cut1); (middle) ∆ηjj and Z(γ, γ, j, j) adding the cut on pT of jets (cut2); (bottom)

∆ηjj (left) and Mjj (right) N-1 plots. Lint = 233 pb−1.

95

6. RESULTS

Figure 6.10: HSTRA di-photon spectrum Control Sample: mγγ after cut on pT

of photons (cut1), adding cut on pT of jets (cut2), adding cut on ∆η (cut3), adding cut on

Z (cut4), and adding the cut on |Mjj − 85| (cut5), with Lint = 33 pb−1.

96

6.5 Systematics

6.5 Systematics

Several systematics affect the determination of the 2HDM type I fermiophobic Higgs

cross section upper limit:

1. signal detector efficiency: trigger, photon identification, photon scale and resolu-

tion, jet reconstruction;

2. background shape;

3. luminosity;

4. theoretical uncertainties.

In the following subsections we give a description of the listed sources of systematic

uncertainties. The final Tab. 6.2 is a summary of the main systematics of the analysis

reported in this section.

6.5.1 Signal Detector Efficiency

• Trigger Uncertainties

The photon Level 1 and HLT trigger efficiencies have been measured from data

[53]. A conservative estimate of the systematic uncertainty due to trigger photon

efficiency is 2%, considering our selection criteria in the analysis.

• Photon Identification Uncertainties

The identification of photons in events with large pile-up is made difficult because

of the differences in isolation with respect to the case with no pile-up [54]. With

LHC current setup, the average number of primary vertices is around 5. In

particular, the efficiency has been measured with the Tag and Probe method,

selecting the electrons from Z decay. The Tag consists of a well identified electron

with transverse momentum peT > 30 GeV, while the Probes are all reconstructed

photons with pT > 25 GeV. The systematic uncertainty on efficiency due to

photon identification is estimated to be 4%, considering both ECAL endcap and

barrel (see Fig. 6.11).

97

6. RESULTS

Figure 6.11: Efficiency vs number of vertices - (left) Barrel; (right) EndCap; for

more details see Sec. 6.5.

• Photon Scale and Resolution Uncertainties

The ECAL energy scale is tuned in-situ both in the ECAL Barrel and Endcap.

The scale is affected by the crystal transparency loss. The tuning of the ECAL

energy scale has been performed with Z → e + e− data collected by CMS ex-

periment at√s = 7 TeV [55]. Actual knowledge of systematic uncertainty on

efficiency due to photon scale and resolution is 2%.

• Jet Systematics

Jets are composite objects observed in the CMS detector. The calorimeter re-

sponse to particles is not linear and it is not straightforward to translate the

measured jet energy to the true particle or parton energy. The purpose of the jet

energy corrections (JEC) is to associate the measured jet energy to the energy of

the final state particle jet [56]. We estimate the systematic error due to jet scale

considering a 4% correction on jet scale. The calculated values are reported in

Tab. 6.2 (top) and (bottom) for VBF and HSTRA analyses respectively.

98

6.5 Systematics

6.5.2 Background Uncertainties

When extracting the upper limit, we made the assumption of a flat background after

all cuts have been applied. The systematics on this assumption are evaluated using the

mγγ shape from the CS.

We take the total window (100-150) GeV, inside which we open a signal window

(s.w.) around the nominal mass point (mγγ - 3, mγγ + 2) GeV, with the complementary

regions forming the sidebands (s.b.).

For each mass hypothesis we evaluate from the CS the following numbers:

• Bs.w.cs : it corresponds to the number of CS events in the signal window.

• Bs.b.cs : it corresponds to the number of CS events in the sidebands.

• R1 = 1/9 , R2 = Bs.w.cs /Bs.b.

cs : it is a ratio used to calculate the number of

background events (1: flat assumption, 2: from CS). 1

The amount of background events in the signal box is then estimated by doing:

B1,2s.w.data = Bs.b.

data ·R1,2 (6.7)

where Bs.b.data is the number of data-events integrated in the sidebands.

In Tab. 6.1 we report the systematic errors inferred by the method described above,

for both VBF and HSTRA, having applied the final set of cuts of the two analyses.

mass [GeV] errsyst (VBF) errsyst (HSTRA)

100 (180) 43.4

105 22.7 58.6

110 17.4 50.7

115 (280) 12.5

120 28.0 42.1

130 25.0 20.1

140 17.4 11.1

Table 6.1: Systematic Uncertainties on Background − The uncertainties are ex-

pressed in %, and are estimated considering the final set of cut of the two analyses.

1for mγγ =100 GeV we considered the total window (95-150), with R1 = 1/10

99

6. RESULTS

6.5.3 Luminosity Uncertainties

Luminosity L measurement is used to monitor the LHC performance in real time and

provides an overall normalization necessary for cross section measurements. To esti-

mate the uncertainty propagated on cross section due to the uncertainty on luminosity

measurements the following relation has to be taken:

σ ∝ 1/L (6.8)

The systematic error on the luminosity normalization is estimated to be 11% [57].

With more luminosity the uncertainty is expected to decrease to 5%, which is the

designed precision of the absolute scale of the luminosity at CMS, which can be achieved

after 1 fb−1 of collected data.

mH [GeV] 100 105 110 120 130 140

Trigger (%) 2

ph ID (%) 4

ph Scale & Reco (%) 2

jet Scale (%) 4.1 4.5 4.6 4.6 4.5 4.2

Signal Eff (%) 6.4 6.7 6.7 6.7 6.7 6.5

Bkg (%) 180 22.7 17.4 28.0 25.0 17.4

L (%) 11

mH [GeV] 100 105 110 115 120 130 140

Trigger (%) 2

ph ID (%) 4

ph Scale & Reco (%) 2

jet Scale (%) 2.6 2.1 2.4 2.2 2.1 2.1 1.8

Signal Eff (%) 5.5 5.3 5.5 5.4 5.3 5.3 5.2

Bkg (%) 43.4 58.6 50.7 12.5 42.1 20.1 11.1

L (%) 11

Table 6.2: VBF (top) and HSTRA (bottom) estimates of main systematic

uncertainties − The main sources of systematic uncertainties for signal detector efficiency

(Signal Eff ) derive from trigger, photon identification, photon scale and reconstruction,

jet scale; each contribution is reported in table. Uncertainty on background (Bkg) is

estimated by the procedure described in Sec. 6.5.2 with 233 pb−1, while uncertainty on

(2010) luminosity is discussed in 6.5.3.

100

6.5 Systematics

6.5.4 Theoretical Uncertainties

We summarize the theoretical uncertainties on signal and background as:

• the fermiophobic Higgs cross-section and B.R.: since we follow HDECAY

prescriptions, we must consider the uncertainties related to the branching ratio

into di-photon, and the uncertainties associated to the SM cross-sections of VBF

and HSTRA. At present time there is no work dedicated to quantify the theo-

retical uncertainties on the fermiophobic Higgs branching ratios. With regard to

cross sections instead, the sum of scale and Parton Density Function uncertainties

for SM Higgs are reported in Tab. 6.3 (see [58]).

• 1-loop level diagrams: in 2HDM type I, the coupling of fermiophobic Higgs to

fermions is put to zero as a renormalisation condition, by taking the mixing angle

α = π/2 exactly. Fermiophobia holds only at tree-level. Indeed, even though

α = π/2, Higgs to ff can be generated at one loop. Moreover the mixing dia-

gram mediated by either H± or W± loop is always possible and this contributes

to break exact fermiophobia too. In appendix A we try to estimate the effect

of 1-loop mixing diagram neglecting other 1-loop corrections. The mixing dia-

gram is interesting because can allow gluon fusion as an indirect production of a

fermiophobic Higgs.

• the effect of neglecting higher order corrections to the coupling constants in

the matrix element calculation of the physics process;

• the parton showering, which describes the QCD radiation of outgoing partons

from the hard processes;

• the fragmentation model, which describes the hadronization using phenomeno-

logical models tuned with experimental data;

• the description of the Parton Density Functions (PDF) used to model the

proton structure in the p - p collision.

101

6. RESULTS

mH [GeV] σ[pb] errsyst(%) errsyst(%)

100 1.546 2.6 -2.4

105 1.472 2.5 -2.4

110 1.398 2.8 -2.3

115 1.332 2.5 -2.3

120 1.269 2.8 -2.5

130 1.154 2.8 -2.3

140 1.052 2.8 -2.2

150 0.9617 2.9 -2.2

160 0.8787 2.9 -2.3

mH [GeV] σHW [pb] errsyst(%) errsyst(%) σHZ [pb] errsyst(%) errsyst(%)

100 1.186 4.0 -3.9 0.6313 4.5 -4.6

105 1.018 3.8 -4.3 0.5449 5.0 -5.3

110 0.8754 4.1 -4.5 0.4721 5.3 -5.3

115 0.7546 4.3 -4.7 0.4107 5.5 -5.4

120 0.6561 3.8 -4.1 0.3598 5.0 -4.7

130 0.5008 3.8 -4.3 0.2778 5.2 -5.1

140 0.3857 4.0 -4.0 0.2172 5.2 -5.3

150 0.3001 3.7 -4.1 0.1713 5.4 -5.2

160 0.2291 4.3 -4.5 0.1334 6.0 -5.7

Table 6.3: VBF (top) and HSTRA (bottom) theoretical uncertainties on cross-

sections

102

6.6 Observed Upper Limit on Cross Section

6.6 Observed Upper Limit on Cross Section

We finally report our preliminary plots of the observed upper limit on cross sections,

obtained with 2010 data. These are shown in Fig. 6.12 for the vector boson fusion

(left) and Higgs-strahlung (right) exclusive analyses. The two upper limits for VBF

and HSTRA will be combined when we will get more integrated luminosity.

Figure 6.12: CMS Exclusive Search: preliminary upper limit on cross section -

Observed and expected (with CL bands) upper limit on cross-section obtained with VBF

(left) and HSTRA (right) exclusive analyses, with 2010 data corresponding to an integrated

luminosity L =33 pb−1.

103

6. RESULTS

104

7

Conclusions

Theoretical models with enhanced production of Higgs decaying into bosons, in par-

ticular in the di-photon final state, have been largely developed and have recently

received a renewed large interest from experimentalists. These models, which are con-

cerned with a fermiophobic Higgs, possess a relatively high cross section and a large

branching ratio. The detector of Compact Muon Solenoid (CMS) experiment, with

the excellent performance of its electromagnetic calorimeter (ECAL), allows for very

precise measurement of high energy photons in the final state. The inclusive study of

a fermiophobic Higgs decaying in two photons becomes really attractive at low Higgs

mass. Fig. 7.1 shows the inclusive analysis of DØ collaboration, which sets the limit

of 112 GeV on fermiophobic Higgs mass.

In this analysis we have followed a different strategy, using the exclusive signatures

provided by the two main production mechanisms of a fermiophobic Higgs: vector boson

fusion (VBF) and Higgs-strahlung (HSTRA). The advantage of this choice consists in

a larger background rejection.

Fig 7.2 shows that with 3 fb−1, which is the statistics CMS is expected to collect

in 2011, this analysis is already competitive.

In conclusion, the preliminary results reported in this work demonstrate that exclu-

sive analyses dedicated to VBF and HSTRA represent viable approaches to be pursued

for a potential fermiophobic Higgs discovery.

105

7. CONCLUSIONS

Figure 7.1: DØ preliminary results (2011) from inclusive analysis - (left) di-

photon invariant mass, (right) 95% C.L. upper limits on σ ×BR as a function of Fermio-

phobic Higgs mass. The observed limit is shown as a solid black line while the expected

limit under the background-only hypothesis is shown as a dashed red line. The green and

yellow areas correspond to the 1 and 2 standard deviations (s.d.) around the expected

limit. [7]

Figure 7.2: CMS estimated U.L. of VBF(top left)-HSTRA(top right) with 3 fb−1

- Estimated upper limit on fermiophobic cross-section with 3 fb−1 at CMS: it will be

possible to exclude the model up to 127 GeV. For comparison, current exclusion limit on

fermiophobic Higgs obtained by DØ is reported.

106

Appendix A

Fermiophobic Higgs production

induced by gluon fusion

In this appendix we try to provide an estimate of the 1-loop mixing term contribu-

tion to fermiophobia. As we largely discussed throughout this thesis, the basic idea

of fermiophobia is that the fermiophobic Higgs of 2HDM cannot couple at tree level

with fermions, and this is done by turning off the coupling to fermions of the lightest

Higgs, by imposing the mixing angle in the neutral Higgs sector to be exactly π2 . Thus,

gluon fusion, can’t be considered under ‘fermiophobic prescription’ as a direct mech-

anism to produce the fermiophobic Higgs. Nevertheless diagrams involving the other

(fermiophilic) Higgs and other bosons such as in [59] have already been studied for the

production of a light fermiophobic Higgs via gluon fusion; let’s consider for instance

the inclusive production gg → hf +X → γγ +X, such as in Fig. A.1 .

Figure A.1: A possible Fermiophobic Higgs production via gluon fusion - This

diagram involves both neutral Higgses. The heavier Higgs can couple to top-loop allowing

for gluon fusion to be an indirect fermiophobic Higgs mechanism of production [59]

Gluon fusion as known is the main SM Higgs mechanism of production in LHC (at

107

A. FERMIOPHOBIC HIGGS PRODUCTION INDUCED BY GLUONFUSION

7 TeV the cross section of a SM Higgs of mass 120 GeV is σgluon =17 pb, while σV BF

and σHSTRA are both about 1 pb). A still open question is therefore to investigate

what happens for a mixing angle “close” to π2 .

It is certainly worth doing at tree-level, i.e. seeing how large gg to H can be as

one goes away from α = π/2, using the tree-level mass matrix. The interesting thing

will be to see which value of α maximises gg to H×BR(h→ γγ), and how large it

can be relative to VBF or HSTRA, just by opening the possibility of “approximate

tree-level fermiophobia”. Heuristically, one could preserve the enhancement of the

fermiophobic Higgs branching fraction to γγ (e.g. for a Mh = 120 GeV BR(hf → γγ)=

0.03 compared to BR(HSM → γγ) = 0.002), with hopefully getting also the benefits

from the larger gluon-gluon fusion cross-section. Moreover, as one approaches α = π/2

(and so the tree-level Hff couplings are becoming very small) one should also start to

worry about the one-loop Hff vertex, and the consequent mixing diagram (see Fig.

A.2) but this should ideally be done in a consistent framework (one-loop mass matrix,

one-loop decay widths). Only a dedicated study can confirm if the pure fermiophobic

scenario is more relevant than the “approximate tree-level” fermiophobia in terms of

Higgs production. Anyway, the “pure” fermiophobic scenario1 holds only at tree-level;

in this appendix we try to formulate a very simple analytical approach to evaluate

the contribution of the 1-loop term mixing diagram of Fig. A.2 ([60]) in the case of a

fermiophobic Higgs at tree-level.

We follow the general 2HDM potential which spontaneously breaks SU(2)L x U(1)Y

down to U(1)EM (2.4). If we consider α ∼ π2 , and take into account the mixing di-

agram A.2, we could re-write the Higgs mass matrix including the terms which al-

lows the mixing, i.e. the couplings to charged Higgs or charged gauge boson (e.g.

HH+H− × H+H−hf ). Wrt the sketched diagram gg → H → blob → h → γγ both

fermiophobic and fermiophilic Higgses could contribute at propagator level with same

coupling strenght. Let’s call the “blob” coupling ε. The Branching Ratio of fermio-

phobic Higgs into γγ should be normalized to the new total fermiophobic Higgs width,

which includes also the main decays of the fermiophilic. In first approximation, we

can assume that the fermiophilic decays exclusively in bb (e.g. if mh=120 GeV/c2 and

mh < mH < 250GeV). The 1-loop mixed fermiophobic Higgs (h∗), can now decay via

1i.e. the Higgs doesn’t couple to fermions at tree level but it could at 1-loop level, then α ∼ π/2

108

Figure A.2: 1-loop Mixing of Higgs - The fermiophobic Higgs couples to the heavier

neutral Higgs through a loop of charged Higgses or of W bosons. The heavier neutral Higgs

is produced by gluon fusion.

mixing to fermions too at next orders. Thus, the branching fraction of the fermiopho-

bic Higgs into γγ should be re-weighted by the total width which has now to account

for the squared amplitude of the mixing diagram, hence for the dominant fermiophilic

decay 1:

BR(h∗ → γγ) =BR(h → γγ)

1 + ε2

Λ2 × [BR(H → bb) + ...]× ΓHtotΓhtot

(A.1)

where Λ is a constant dimensional parameter corresponding to a squared mass. For a

fermiophobic Higgs of 120 GeV/c2, we could also reach BR(h → γγ) = 0.03, whereas

[BR(H → bb) + ...] can also be considered ≈ 1.

We keep assuming 120≤ mh < mH ≤ 250, then the ratioΓHtotΓhtot∈ (1 − 102), if (h,H)

total widths are comparable with those of SM Higgs.

The B.R. reported in Eq. (A.1), could be estimated considering charged scalar loop

contributions (Charged Higgs loop), as done in [18].

The “blob” enters the matrix adding to its off-diagonal elements. Therefore we

may rewrite the neutral Higgs sector mass matrix (Eq. 2.8), considering the case of

1With h∗ we indicate the fermiophobic Higgs recalculated considering the 1-loop mixing.

109


fermiophobia at tree level ((4λ3 + λ5) v1v2 ≈ 0) as:

Mh∗ =

(4v2

1 (λ1 + λ3) + v22λ5 ε

ε 4v22 (λ2 + λ3) + v2

1λ5

)(A.2)

To get a feel of this mixing, one can proceed again by diagonalizing the matrix

above A.2, in order to estimate the rotational angle of the mass eigenstates; by simple

algebra we obtain:

tan(2α∗) = 2ε

M22 −M11(A.3)

where Mij is the element (i, j) of the matrix expressed in Eq. (2.8). If all the λi are

non negative, the following inequality must be satisfied in order to have ε > 0 :

ε =M11 −M22

2· δ > 0 (A.4)

where we used δ2(≥ 0) to quantify the 1-loop angular deviation from the fermiophobic

scenario: tan(2α∗) = tan(π− δ) = − tan(δ) = −δ, by a Taylor expansion. In the previ-

ous formula we required M11 > M22. Thus the mixing parameter ε can be expressed in

terms of the deviation from fermiophobic scenario. Coming back to Eq. (A.1), we can

now write the new B.R. in γγ in terms of the angular deviation from fermiophobia:

BR(h∗ → γγ)(δ) =BR(h → γγ)

1 + 1Λ2

((M11−M22)

2 · δ)2× ΓHtot

Γhtot

(A.5)

The next step is to express the rate of gg → h → γγ production, i.e. σ(gg → h∗) ×

BR(h∗ → γγ). We recall here that the gluon-gluon cross section is:

σ(gg → H) =8π2 · ΓH→ggN2gmH

δ(s−m2H) (A.6)

where Ng = 8 is the number of different gluons and s = x1x2s is the squared energy of

the gluon pair. To get the full cross section the gluon cross section must be integrated

with the structure functions of the gluons (and then get in LHC σ(pp→ H) via gluon

110

fusion). We won’t do this for simplicity. The mixing allows the fermiophobic Higgs to

be produced via gluon fusion, therefore we can write:

Γ(h∗ → gg) ≈ ε2

Λ2· Γ(H → gg) (A.7)

The substitution of (A.7) in (A.6) gives:

σ(gg → h∗) =8π2 · 1

Λ2

((M11−M22)

2 · δ)2

ΓH→gg

N2gm∗H

δ(s−m∗H2) (A.8)

Now we have all the ingredients to measure the gluon-gluon fusion production.

We finally use Eq. (A.5) for the B.R., to estimate the fermiophobic Higgs into γγ

production as a function of the small mixing angle δ:

σ(gg → h∗)×BR(h∗ → γγ) =

8π2 · 1Λ2

((M11−M22)

2 · δ)2

ΓH→gg

N2gm∗H

δ(s−m∗H2)

× BR(h→ γγ)

1 + 1Λ2

(M11−M22

2 · δ)2 × ΓHtot

Γhtot

(A.9)

In this framework we can make the further assumption that the new mass eigenvalues

mH∗,h∗ don’t differ too much from the initial mH,h. We can use this to calculate the

mass eigenvalues (see (2.9)):

m2H∗,h∗ =

1

2

[M11 +M22 ±

√(M11 −M22)2 + 4ε2

]=

1

2

[M11 +M22 ± (M11 −M22)

√1 + 4

ε2

(M11 −M22)2

] (A.10)

Now, assuming ε(M11−M22)2

1, which is consistent with Eq. (A.4), we can parametrize

the mass eigenvalues in terms of the mixing angle:

m2H∗,h∗ =

M11 + ε2

(M11−M22)2

M22 − ε2

(M11−M22)2

(A.11)

By means of Eq. (A.11), the fermiophobic Higgs production induced by gluon

fusion through 1-loop mixing diagram represented by Eq. (A.9) can be expressed as a

111


function of the parameters MH∗,h∗ and δ, the former being the observed masses of the

two neutral Higgses, the latter the 1-loop mixing angle.

A theoretical study dedicated to approximate fermiophobia is necessary to under-

stand the potential contribution of gluon fusion to a low mass Higgs production. In this

new scenario, the analysis strategies discussed in this work on fermiophobia could be

still worth for channels involving gluon fusion. For example, the VBF approach could

be applied to diagrams such as in Fig. A.3, whereas HSTRA techniques could be used

for diagrams such as the one reported in Fig. A.1.

Figure A.3: Double real emission in gluon fusion - Double real emission of gluons

in gluon fusion [61]. This diagram could be enhanced under the hypothesis of approximate

fermiophobia, and can be similar to vector boson fusion topology.

112

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Declaration

I herewith declare that I have produced this paper without the prohibited

assistance of third parties and without making use of aids other than those

specified; notions taken over directly or indirectly from other sources have

been identified as such. This paper has not previously been presented in

identical or similar form to any examination board.

The thesis work was conducted from April 2010 to June 2011 under the

supervision of Professors D. Del Re and S. Rahatlou.

Rome, June 6, 2011

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