Strategy for an Early Observation of the ZZ Diboson Production in the Four Lepton ﬁnal States at 10 Tev with the CMS Experiment at CERN

UNIVERSITA` DEGLI STUDI DI TORINO FACOLTA` DI SCIENZE MATEMATICHE, FISICHE E NATURALI

CORSO DI LAUREA MAGISTRALE IN FISICA DELLE INTERAZIONI FONDAMENTALI

Strategy for an early observation of the ZZ diboson production in the four lepton ﬁnal states at 10 TeV with the CMS experiment at CERN

Relatore Dott. Nicola Amapane

Co-Relatore Dott.ssa Chiara Mariotti

Candidato Laura Nervo

Anno Accademico 2008/2009

“You have not truly understood something until when you are not able to explain it to your grandmother.”

Albert Einstein

“The joy of physics isn’t in the results, but in the search itself”

Dennis Overbye

Alla mia famiglia, in particolare mia madre, che mi stimola e mi aiuta sempre nelle piccole e nelle grandi imprese quotidiane, e mio fratello, che mi ha guidato e supportato nel cammino della scienza . . .

♦

To my family, in particular my mother, who always encourages and helps me in the small and large-size daily businesses, and my brother, who advised to me and supported me moving down the road of science . . .

Contents

Contents vii

Introduction 1

1 The Standard Model Higgs boson3 1.1 Higgs boson mass...... 3 1.1.1 Theoretical constraints...... 3 1.1.2 Experimental constraints...... 4 1.2 Higgs boson search at the LHC...... 6 1.2.1 Higgs boson production...... 6 1.2.1.1 Gluon-gluon fusion...... 7 1.2.1.2 Vector boson fusion...... 8 1.2.1.3 Associated production...... 8 1.2.2 Higgs boson decay...... 8 1.2.2.1 Low mass region...... 9 1.2.2.2 Intermediate mass region...... 10 1.2.2.3 High mass region...... 10 1.2.2.4 Higgs boson total decay width...... 11 1.3 Electroweak measurements at LHC...... 12 1.3.1 Measurement of the W boson and the top quark masses...... 12 1.3.2 Measurement of the Z boson mass...... 14 1.3.3 Drell-Yan production of lepton pairs...... 15 1.3.4 The dibosons WW , WZ and ZZ ...... 16

2 The Large Hadron Collider 19 2.1 The Large Hadron Collider...... 19 2.1.1 Purpose of LHC...... 20 2.1.2 The accelerator...... 21 2.1.3 Phenomenology of proton-proton collisions...... 23

3 The CMS experiment 27 3.1 The Tracker...... 27 3.2 The Electromagnetic Calorimeter...... 29 3.3 The Hadronic Calorimeter...... 30 3.4 The magnet...... 31 3.5 The Muon System...... 33

vii viii Contents

√ 4 The H → ZZ(∗) → 4l channel at s = 10 TeV 35 4.1 Physics processes and their simulation...... 35 4.1.1 Signal: H → ZZ(∗) → 4l ...... 36 4.2 Backgrounds...... 37 4.2.1 qq¯ → ZZ(∗) → 4l ...... 37 4.2.2 gg → ZZ(∗) → 4l ...... 39 4.2.3 qq/gg¯ → Zb¯b → 4l ...... 40 4.2.4 qq/gg¯ → tt¯ → 4l ...... 42 4.2.5 Other backgrounds...... 43 4.3 Weights...... 43 4.3.1 Weights for ZZ as a function of m4l ...... 44 4.3.2 Weight for Z+jets...... 44 4.4 Trigger, skimming and pre-selection...... 45 4.4.1 The CMS trigger...... 45 4.4.2 Event skimming...... 46 4.4.3 Event preselection...... 47 4.4.4 Discriminating observables...... 51 4.4.4.1 Lepton isolation...... 52 4.4.4.2 Impact parameter...... 55 4.4.4.3 Kinematics...... 58 4.4.5 Baseline event selection and results...... 58 4.4.5.1 Baseline event selection...... 58 4.4.5.2 Analysis results with L = 1 fb−1: a simple counting experiment approach...... 61 √ 5 The ZZ(∗) → 4l analysis strategy at s = 10 TeV 67 5.1 Removing Zb¯b from Z+jets samples...... 68 5.2 The selection steps...... 69 5.2.1 Z and Z∗ boson invariant mass constraints...... 69 5.2.2 Cuts on the isolation and the 3D impact parameter significance...... 71 5.2.2.1 The new isolation definition...... 71 5.2.2.2 The impact parameter significance cut...... 74 5.2.3 The 2D cut ...... 77 rd 5.2.4 Cut on the pT of the 3 isolated lepton...... 78 th 5.2.5 Cut on the pT of the 4 isolated lepton...... 80 5.3 Results after the full selection...... 81 5.3.1 Combined significance for ZZ(∗) → 4l ...... 83

6 Control of Zb¯b and tt¯ backgrounds from data 85 6.1 Deﬁnition of the control region ...... 85 6.1.1 The 3µ1e channel...... 87 6.2 Fitting the mZ1 distribution...... 88

Conclusions 91

A Isolation algorithm 95 Contents ix

A.1 Electron isolation...... 95 A.2 Muon isolation...... 97

B Lepton reconstruction and identiﬁcation 99 B.1 Electrons...... 99 B.1.0.1 Electron reconstruction...... 99 B.1.0.2 Electron identiﬁcation...... 102 B.2 Muons...... 102 B.2.1 The “tracker muon” selection...... 104

C The Standard Model and the Higgs mechanism 107 C.1 The Standard Model of elementary particles...... 107 C.2 The electroweak theory...... 108 C.3 The Higgs mechanism...... 111 C.3.1 Vector boson masses and couplings...... 113 C.3.2 Fermion masses and couplings...... 114

List of Figures 116

List of Tables 121

Abbreviations 123

Symbols 125

Bibliography 127

Ringraziamenti 135

Introduction

The Standard Model (SM) of elementary particles is today one of the best theories of modern physics. It is a simple and comprehensive theory that explains the hundreds of known particles that compose matter with only six quarks and six leptons and their complex interactions with the exchange of three types of force carriers (more details in AppendixC).

The Standard Model is a succesful theory. Experiments have veriﬁed its predictions to incredible precision. But it does not explain everything. For example, gravity is not included in the Standard Model. While the SM provides a very good description of phenomena observed by experiments, it is still an incomplete theory. The problem is that the Standard Model cannot explain why some particles exist as they do. For example, even though physicists knew the masses of all the quarks except for the top quark for many years, they were simply unable to accurately predict the top quark’s mass without experimental evidence because the Standard Model cannot explain why a particle has a certain mass. Also, both the photon and the W boson are force carrier bosons: why is the photon massless and the W boson massive?

In the Standard Model, particle masses arise from a breakdown of the electroweak symmetry group SU(2)I ⊗ U(1)Y (see AppendixC for further details). The simplest way to realize such “spontaneous” ElectroWeak Symmetry Breaking (EWSB) is the so called Higgs mechanism, which gives rise in the SM to a massive scalar particle, the Higgs boson, never found experimentally so far. Both gauge bosons and fermions acquire mass by interacting with the Higgs boson.

Even if the Higgs boson has never been found experimentally, direct and indirect searches have been carried out at the Large Electron-Positron Collider (LEP-2): a fit of experimental data indicates ∼ 76 GeV/c2 as most probable value, with an upper bound of 157 GeV/c2 (95% C.L.). Direct searches have fixed a lower bound of 114.4 GeV/c2 (95% C.L.). At Tevatron experiments have demonstrated a robust Higgs boson program in their first 2 fb−1 of recorded data. Observed limits of the ratio σ95CL/σSM are 7.8 (1.4) at mH = 115 (160) GeV. All these experimental results suggest a low value for the Higgs boson mass. Theoretical considerations extend the Higgs boson discovery range up to ∼ 1 TeV/c2. Therefore, also high mass values must be taken into account.

1 2 Introduction

The search for the Higgs boson and for evidence of new Physics beyond the Standard Model are among the main goals of the Large Hadron Collider (LHC) at CERN and of the Compact Muon Solenoid (CMS) experiment in particular. The LHC is a proton-proton collider with a nominal energy of 14 TeV in the centre of mass and a nominal luminosity of 1034 cm−2s−1 and will allow the Higgs boson to be searched in the entire expected mass range.

The work presented in this thesis has been carried out within the Torino CMS group between October 2009 and April 2010. Its aim is to develop a study of the process ZZ(∗) → 4l, which is an irreducible background for the Higgs boson search in the channel H → ZZ(∗) → 4l. This is expected to be one of the most important channels for the discovery of a “heavy” Higgs boson at the LHC, because of its clear signature over the hadronic background and of the high branching

ratio of the H → ZZ decay for mH > 2MZ . Moreover, this channel is extremely important for the determination of the properties of the Higgs boson (e.g. spin, CP-parity, couplings to gauge bosons, etc.). Therefore, it is essential to test and improve all the event seleciton criteria for this process and to investigate the expected magnitude of the signal and the possibility to distinguish between the SM Higgs boson model and alternative scenarios in the ﬁrst years of data taking. This √ study is done at a center-of-mass energy ( s) of 10 TeV assuming a total integrated luminosity (L) of 1 fb−1.

A general introduction to the Standard Model Higgs boson production and search is given in Chap- ter1, with an overview of the electroweak measurements at LEP and at Tevatron and a summary of the main goals of the LHC experiments. The LHC accelerator is described in detail in Chapter2 and an overview of the CMS detector is presented in Chapter3. √ Chapter4 explains the analysis strategy for H → ZZ(∗) → 4l at s = 10 TeV. I contributed to the description of the background of H → ZZ(∗) → 4l, with the simulation of the Monte Carlo (MC) events for the process gg → ZZ(∗) → 4l. The last two chapters deal with my speciﬁc work on the ZZ production and decay into four lep- √ tons: the ZZ direct measurement at s = 10 TeV is presented in Chapter5, using exaclty the same analysis workﬂow of the Higgs boson analysis discussed in Chapter4. Finally, in Chapter6 a method to control Zb¯band tt¯backgrounds from data is proposed. Chapter 1

The Standard Model Higgs boson

The Standard Model (SM) and the Higgs mechanism are described in detail in AppendixC. Here there is a brief description of the SM Higgs boson from an experimental point of view. Starting from Section 1.1, a discussion about the SM Higgs boson mass is given with an indication of its theoretical and experimental constraints. In Section 1.2 the main Higgs boson production and decay processes are described, in order to determine the most promising channels to look at for the Higgs boson discovery. Finally, Section 1.3 presents constraints on SM parameters using published and preliminary precision electroweak results measured at the electron-positron colliders LEP and SLC. The results are compared with the precise electroweak measurements from other experiments, notably CDF and DØ at the Tevatron, and with the expected results at the LHC, which will improve the current experimental precision thanks to its large centre-of-mass energy and high luminosity.

1.1 Higgs boson mass

The Higgs boson mass is the only yet unknown free parameter of the SM. The Higgs boson in fact has never been observed experimentally and its mass cannot be predicted by the SM. It depends on the parameters v and λ (see AppendixC), but while the former can be estimated by its relation with the constant GF of Fermi’s theory, the latter is characteristic of the ﬁeld φ and cannot be determined other than measuring the Higgs boson mass itself. However, both theoretical and experimental constraints exist, including those from direct search at colliders, in particular LEP.

1.1.1 Theoretical constraints

Theoretical constraints to the Higgs boson mass value [1] can be found by imposing the energy scale Λ up to which the SM is valid, before the perturbation theory breaks down and non-SM phenomena 3 4 1. The Standard Model Higgs boson

emerge. The upper limit is obtained requiring that the running quartic coupling of Higgs boson potential λ remains ﬁnite up to the scale Λ (triviality). A lower limit is found instead by requiring that λ remains positive after the inclusion of radiative corrections, at least up to Λ: this implies that the Higgs boson potential is bounded from below, i.e. the minimum of such potential is an absolute minimum (vacuum stability). A looser constraint is found by requiring such minimum to be local, instead of absolute (metastability). These theoretical bounds on the Higgs boson mass as a function of Λ are shown in Figure 1.1.

Figure 1.1: Red line: triviality bound (for diﬀerent upper limits to λ); blue line: vacuum stability (or metastability) bound on the Higgs boson mass as a function of the new physics (or cut-oﬀ) scale Λ[1].

If the validity of the SM is assumed up to the Plank scale (Λ ∼ 1019 GeV), the allowed Higgs boson mass range is between 130 and 190 GeV, while for Λ ∼ 1 TeV the Higgs boson mass can be up to 700 GeV. On the basis of these results, therefore, future colliders should be designed for searches of the Higgs boson up to masses of ∼ 1 TeV. If the Higgs particle is not found in this mass range, then a more sophisticated explanation for the EWSB mechanism will be needed.

1.1.2 Experimental constraints

Bounds on the Higgs boson mass are also provided by measurements at LEP, SLC and Tevatron [2]. A lower bound has been ﬁxed at 114.4 GeV (95% C.L.) by direct searches [3]. Moreover, since the Higgs boson contributes to radiative corrections, many electroweak observables are logarithmically 1. The Standard Model Higgs boson 5

sensitive to mH and can thus be used to constraint its mass. All the precision electroweak measurements performed by the four LEP experiments and by SLD, CDF and DØ have been combined together and ﬁtted, assuming the SM as the correct theory and using the Higgs boson mass as free parameter. The result of this procedure is summarized in Figure 1.2. The solid curve is the result of the ﬁt, while the shaded band represents the theoretical uncertainty due to unknown higher order corrections.

Figure 1.2: ∆χ2 of the ﬁt to the electroweak precision measurements of LEP, SLC and Tevatron as a function of the Higgs boson mass (August 2009). The solid line represents the result of the ﬁt and the blue shaded band is the theoretical error from unknown higher-order corrections. The yellow area represents the region excluded by direct search.

The indirectly measured value of the Higgs boson mass, corresponding to the minimum of the curve, +33 is mH = 76−24 GeV (68% C.L. for the black line in Figure 1.2, thus not taking the theoretical uncertainty into account). An upper limit of 157 GeV can also be set as one-sided 95% C.L., including the theoretical uncertainty.

Such results are obviously model-dependent, as the loop corrections take into account only contributions from known physics. This result is thus well-grounded only within the SM theory and has to be conﬁrmed by the direct observation of the Higgs boson. 6 1. The Standard Model Higgs boson

1.2 Higgs boson search at the LHC

The experiments at the LHC will search for the Higgs boson within a mass range going from 100 GeV to about 1 TeV. While the Higgs boson mass is not predicted by the theory, its couplings to the fermions or bosons are predicted to be proportional to the corresponding particle masses, as in Equation C.23, Equation C.24 and Equation C.33. For this reason, the Higgs boson production and decay processes are dominated by channels involving the coupling of Higgs boson to heavy particles, mainly to W ± and Z bosons and to the third generation fermions. For what concerns the remaining gauge bosons, the Higgs boson does not couple to photons and gluons at tree level, but only by one-loop graphs where the main contribution is given by qq¯ loops for the gg → H channel and by W +W − and qq¯ loops for the γγ → H channel.

1.2.1 Higgs boson production

The main processes contributing to the Higgs boson production at a hadron collider [4] are represented by the Feynman diagrams shown in Figure 1.3. The corresponding cross sections for a √ centre of mass energy s = 14 TeV, the design LHC collision energy, are shown in Figure 1.4 on page7.

g q q

t W, Z

t H0 H0

t W, Z

g q’,q q’,q (a) (b) q H 0 g t¯

H0 W, Z t¯

q¯ W, Z g t (c) (d)

Figure 1.3: Higgs boson production mechanisms at tree level in proton-proton collisions: (a) gluon-gluon fusion; (b) VV fusion; (c) W and Z associated production (or Higgsstrahlung); (d) tt¯ associated production. 1. The Standard Model Higgs boson 7

σ(pp→H+X) [pb] 2 10 √s = 14 TeV

gg→H Mt = 175 GeV 10 CTEQ4M

→ -1 _ → qq Hqq 10 qq' HW

-2 10 _ _ gg,qq→Htt -3 10 _ _ → _ gg,qq Hbb qq→HZ -4 10 0 200 400 600 800 1000 [ ] MH GeV √ Figure 1.4: Higgs boson production cross sections at s = 14 TeV as a function of its mass.

1.2.1.1 Gluon-gluon fusion

The gg fusion [5] is the dominating mechanism for the Higgs boson production at the LHC over the whole Higgs boson mass spectrum at the nominal centre of mass energy, as shown in Figure 1.4. The gluon-gluon fusion process is shown in Figure 1.3(a), with a t-quark loop as the main contribution.

The cross section for the basic gluon to Higgs boson process is [6]:

2 2 2 Gµα (µ ) 3 X S√ R H σ(gg → H) = A1/2(τQ) (1.1) 288 2π 4 q

H 2 2 H where A1/2(τQ) with τQ = mH /4mq is a form factor normalized so that A1/2(τQ) → 4/3 for τQ → 0. The lowest order cross section has large corrections from higher order QCD diagrams. The increase in cross section from higher order diagrams is conventionally deﬁned as the K-factor:

σNLO KNLO = (1.2) σLO where LO (NLO) refers to leading (next-to-leading) order value.

In the limit of very heavy top quarks the NNLO QCD corrections have been recently calculated [7– 9], increasing the total cross section further by ∼ 20%. A full massive NNLO calculation is not available but the approximate NNLO results have been improved by a soft-gluon re-summation 8 1. The Standard Model Higgs boson

at the next-to-next-to-leading log (NNLL) level, which yields another increase of the total cross section by about 10% [10].

Electroweak corrections have been computed and turn out to be small [11–15]. The theoretical uncertainties of the total cross section can be estimated as 20% at NNLO due to the residual scale dependence, the uncertainties of the parton densities and due to neglected quark mass eﬀects.

The production of the Higgs boson through gluon fusion is sensitive to a fourth generation of quarks. Because the Higgs boson couples proportionally to the fermion mass, the presence of a fourth generation of very heavy quarks will more than double the cross section.

1.2.1.2 Vector boson fusion

The VV fusion process (Figure 1.3(b)) is the second contributor to Higgs boson production cross

section. It is about one order of magnitude lower than gg fusion for a large range of mH values. The two processes become comparable only for very high Higgs boson masses (O(1 TeV)). However, this channel is very interesting because of its clear experimental signature: the presence of two spectator jets with high invariant mass in the forward region provides a powerful tool to tag the signal events and discriminate the backgrounds, thus improving the signal to background ratio, despite the low cross section. Moreover, both leading order and next-to-leading order cross sections for this process are known with small uncertainties and the higher order QCD corrections are quite small [16].

1.2.1.3 Associated production

In the Higgsstrahlung process (Figure 1.3(c)), the Higgs boson is produced in association with a W ± or Z boson [17], which can be used to tag the event. The cross section for this process is several orders of magnitude lower than gg and VV fusion ones. The QCD corrections are quite large; the NLO cross-section is larger by a factor of 1.2 ÷ 1.4 with respect to LO.

The last process, illustrated in Figure 1.3(d), is the associated production of a Higgs boson with a tt¯ pair [18]. The cross section for this process is also lower by orders of magnitude lower than those of gg and VV fusion, but the presence of the tt¯ pair in the ﬁnal state can provide a good experimental signature. The higher order corrections increase the cross section of a factor of about 1.2.

1.2.2 Higgs boson decay

Fermion decay modes dominate the branching ratio (BR) in the low mass region (up to ∼150 GeV). In particular, the channel H → b¯b gives the largest contribution, since the b quark is the 1. The Standard Model Higgs boson 9 heaviest fermion available for the decay. When the decay channels into vector boson pairs open up, they quickly dominate. A peak in the H → W +W − decay is visible around 160 GeV, when the production of two on-shell W bosons becomes possible and the production of a real ZZ pair is still not allowed. At high masses (∼350 GeV), also tt¯ pairs can be produced. The branching ratios of the diﬀerent Higgs boson decay channels are shown in Figure 1.5 as a function of the Higgs boson mass. 1 _ bb WW BR(H) ZZ

-1 10 τ+τ− _ cc tt- gg -2 10

γγ Zγ

-3 10 50 100 200 500 1000 [ ] MH GeV

Figure 1.5: Branching ratios for diﬀerent Higgs boson decay channels as a function of the Higgs boson mass.

The most promising decay channels for the Higgs boson discovery do not only depend on the corresponding branching ratios, but also on the capability of experimentally detecting the signal while rejecting the backgrounds. Such channels are illustrated in the following, depending on the Higgs boson mass.

1.2.2.1 Low mass region

Though the branching ratio in this region is dominated by the Higgs boson decay into b¯b, the background constituted by the di-jet production makes it quite diﬃcult to use this channel for a Higgs boson discovery. Some results from this channel can be obtained when the Higgs boson is produced in association with a tt¯ or via Higgsstrahlung, since in this case the event has a clearer signature, despite its low cross section [19]. 10 1. The Standard Model Higgs boson

For mH < 130 GeV, instead, the channel H → γγ appears to be the most promising. In spite of its low branching ratio, the two high energy photons constitute a very clear signature, which suﬀers from the qq¯ → γγ and Z → e+e− backgrounds.

1.2.2.2 Intermediate mass region

For a Higgs boson mass value between 140 and 180 GeV, the Higgs boson decays into WW (∗) and ZZ(∗) open up and their branching ratios quickly increase, so the best channels in this mass region are H → WW (∗) → 2l2ν and H → ZZ(∗) → 4l.

The branching ratio of H → WW (∗) is higher, because of the higher coupling of the Higgs boson to charged currents with respect to neutral current. Moreover, this decay mode becomes particularly

important in the mass region between 2MW and 2MZ , where the Higgs boson can decay into two real W bosons (and not yet into two real Z): its branching ratio is ∼1. However, discovery in such channel is disfavoured because of the presence of the two neutrinos in the final state, which makes it impossible to reconstruct the Higgs boson mass. Such measurement can be performed instead when one W decays leptonically and the other one decays in two quarks. But, in this case, the final state suffers from a high hadronic background.

The decay H → ZZ(∗) → 4l, despite its lower branching ratio, oﬀers a very clear experimental signature and high signal to background ratio. Furthermore, it allows to reconstruct the Higgs boson mass with high precision. Therefore, this channel seems to be the best candidate for a Higgs boson discovery in this mass range.

1.2.2.3 High mass region

This region corresponds to Higgs boson mass values above the 2MZ threshold, where the Higgs boson can decay into a real ZZ pair. Though the H → ZZ width is still lower than H → WW one, a decay into four charged leptons (muons or electrons) is surely the “golden channel” for a high mass Higgs boson discovery.

The upper mass limit for detecting the Higgs boson in this decay channel is determined by the reduced production rate and the increased width of the Higgs boson. As an example, less than 200 2 (∗) Higgs particles with mH = 700 GeV/c will decay in the H → ZZ → 4l channel in a year at the LHC design luminosity, the large width will increase the diﬃculty to observe the mass peak.

In order to increase the sensitivity to a heavy Higgs boson production, decay channels with one

boson decaying into jets or neutrinos can be also considered. The decay channel H → WW → lνlqq, where q is a quark from the W decay, has a branching ratio just below 30%, yelding a rate some 50 times higher than the four lepton channel from H → ZZ decays. The decay channel 1. The Standard Model Higgs boson 11

¯ H → ZZ → llνl0 ν¯l0 which has a six times larger branching ratio than the four lepton channel could also be interesting.

1.2.2.4 Higgs boson total decay width

Below the 2MW threshold, the Higgs boson width is of the order of a MeV, then it rapidly increases,

but remains lower than 1 GeV up to mH ' 200 GeV: in the low mass range the measured width of the Higgs boson mass peak is dominated by the experimental resolution. The total width of the Higgs boson resonance, which is given by the sum over all possible decay channels, is shown in Figure 1.6 as a function of mH .

10 2 (H) [GeV] Γ

-1 10

-2 10

-3 10 2 3 10 10 MH [GeV]

Figure 1.6: Higgs boson total decay width as a function of its mass.

+ − In the high mass region (mH > 2MZ ), the total Higgs boson width is dominated by the W W and ZZ partial widths, which can be written as follows:

2 3 + − g mH √ 3 2 Γ(H → W W ) = 2 1 − xW 1 − xW + xW (1.3) 64π MW 4 2 3 g mH √ 3 2 Γ(H → ZZ) = 2 1 − xZ 1 − xZ + xZ (1.4) 128π MW 4 where 2 2 4MW 4MZ xW = 2 , xW = 2 mH mH

As the Higgs boson mass grows, xW , xZ → 0 and the leading term in Equation 1.3 and Equation 1.4 3 + − grows proportional to mH . Summing over the W W and ZZ channels, the Higgs boson width in 12 1. The Standard Model Higgs boson

the high mass region can be written as

3 m3 Γ(H → VV ) = H (1.5) 32π v2

From Equation 1.5, it results that ΓH ' mH for mH ' 1.4 TeV. When mH becomes larger than a TeV, therefore, it becomes experimentally very problematic to separate the Higgs boson resonance from the VV continuum. In addition, if the Higgs boson mass is above 1 TeV, the SM predictions violate unitarity. All these considerations suggest the TeV as a limit to the Higgs boson mass: the Higgs boson must be observed within the TeV scale, otherwise new physics must emerge.

1.3 Electroweak measurements at LHC

In 1973 Gargamelle discovered the neutral currents. In 1983 Ua1 discovered the W and Z bosons. From 1989 to 2000 LEP measured with very high precision the gauge bosons masses, the couplings between fermions and bosons and the triple coupling between bosons. The main goals of the two experiments ATLAS and CMS at LHC are:

K Understand the origin of particle masses, such as the electroweak spontaneous symmetry beaking of the SM Lagrangian (search the Higgs boson from 100 GeV to 1 TeV).

K Search new physics, especially if the Higgs boson is not found below 1 TeV.

K Improve the measurement precision of the electroweak variables (mtop, MW , sinθw, . . . ), in order to know more about the Higgs boson mass indirectly.

In the following, we shortly discuss the experimental challenges of some electroweak measurements performed in the past. The perspective of the ATLAS and CMS experiments in selected ﬁelds of electroweak physics, including W and top physics, Drell-Yan production of lepton pairs, and Triple Gauge Boson Couplings (TGCs), is presented. A more comprehensive discussion can be found elsewhere [20].

1.3.1 Measurement of the W boson and the top quark masses

The top quark mass measurement at Tevatron

The values of the top and Higgs boson masses enter in the prediction of the W mass through radiative corrections. Precise measurements of mtop and MW allow therefore to set limits on mH and, if the Higgs boson is found, they will allow stringent tests of the Standard Model (SM) or its extensions like the Minimal Supersymmetric Standard Model (MSSM). 1. The Standard Model Higgs boson 13

The most promising channel for the measurement of the top mass is tt¯ → W +W −b¯b with one leptonic and one hadronic W decay, where the hadronic part is used to reconstruct the top mass and the leptonic part to select the event. The main source of uncertainty will be the jet energy scale, which is aﬀected by the knowledge of fragmentation and gluon radiation and of the response of the detectors. The same sample of tt¯ events will provide a large number of hadronic W decays to be used for the calibration of the hadron calorimeters. The top subgroup of the Tevatron Electroweak Working Group combines sets of top quark mass measurements to obtain a world average value, using the best measurements in orthogonal decay channels from each collaboration [21]. All correlated and uncorrelated components in the uncertainties are properly taken into account. The resulting latest value of the top quark mass from Tevatron is:

mtop = 173.1 ± 1.3 GeV

2 The ﬁnal uncertainty on mtop is better than about 2 GeV/c . This will allow to constrain the Higgs boson mass to better than 30% but, in order not to become the dominant source of uncertainty, the W mass will have be measured with a precision of about 15 GeV/c2 [22].

The W boson mass measurement at LEP and CDF

Since the longitudinal component of the neutrino momentum cannot be measured in hadron col- T liders, the W mass is obtained from a ﬁt to the distribution of the W transverse mass MW : q T e ν MW = 2pT pT (1 − cosφeν) (1.6)

The main source of uncertainty is the lepton energy and momentum scale, which should be known with a precision of 0.02% to achieve the mentioned precision on MW . This is a challenging goal that at LHC could be reached thanks to the high statistics of Z → ll decays. Other sources of systematic uncertainty include the W pT spectrum, the W width and the proton structure functions. Since pile-up deteriorates the shape of the W transverse mass distribution, this measurement will probably be feasible only in the low luminosity mode. The LEP-2 combined values for the W mass and width [23], combined taking into account correlated systematics, are:

MW = 80.376 ± 0.033 GeV

ΓW = 2.196 ± 0.083 GeV

This is compared to the W mass value of MW = 80.361 ± 0.020, derived from all electroweak measurements without direct measurement. The W mass was measured also at Fermilab [24] from run II of the Tevatron 1.

1All the results are updated to August 2009. 14 1. The Standard Model Higgs boson

They measured:

MW = 80.420 ± 0.031 GeV

ΓW = 2.050 ± 0.058 GeV

The average value of the W boson mass and width from Tevatron and LEP-2 results is:

MW = 80.399 ± 0.023 GeV

ΓW = 2.098 ± 0.048 GeV

1.3.2 Measurement of the Z boson mass

The data accumulated by LEP and SLC in the 1990s are used to determine the Z boson parameters with high precision: its mass, its partial and total widths, and its couplings to fermion pairs. These results are compared to the predictions of the SM and found to be in agreement. From these measurements, the number of generations of fermions with a light neutrino is determined.

Moreover, for the first time, the experimental precision is sufficient to probe the predictions of the SM at the loop level, demonstrating not only that it is a good model at low energies but that as a quantum field theory it gives an adequate description of experimental observations up to much higher scales.

The mass and width of the Z boson, MZ and ΓZ , and its couplings to fermions, for example the ρ parameter and the eﬀective electroweak mixing angle for leptons, are precisely measured [25]:

MZ = 91.1875 ± 0.0021 GeV

ΓZ = 2.4952 ± 0.0023 GeV

ρl = 1.0050 ± 0.0010 2 lept sin θeff = 0.23153 ± 0.00016

The number of light neutrino species is determined to be 2.9840 ± 0.0082, in agreement with the three observed generations of fundamental fermions. The results are compared to the predictions of the SM. At the Z-pole, electroweak radiative corrections beyond the running of the QED and QCD coupling constants are observed with a significance of five standard deviations, and in agreement with the SM. Of the many Z-pole measurements, the forward-backward asymmetry in b-quark production shows the largest difference with respect to its SM expectation, at the level of 2.8 standard deviations.

Through radiative corrections evaluated in the framework of the SM, the Z-pole data are also +13 used to predict the mass of the top quark, mtop = 173−10 GeV, and the mass of the W boson, 1. The Standard Model Higgs boson 15

MW = 80.363 ± 0.032 GeV. These indirect constraints are compared to the direct measurements,

providing a stringent test of the SM. Using in addition the direct measurements of mtop and MW , the mass of the as yet unobserved SM Higgs boson is predicted with a relative uncertainty of about 50% and found to be less than 285 GeV at 95% conﬁdence level.

Z boson mass measurement at the LHC

The ATLAS and CMS detectors are designed to provide precise measurements of 14 TeV proton- proton collisions at the LHC. The Z boson at LHC is produced via Drell-Yan process and its theoretical cross-section is calculated at next-to-next-to-leading order. A total cross-section of 1.972 ± 0.019 nb of pp → Zγ → µµ is theoretically expected [26]. The study of the Z boson production and its properties provides not only a test of the standard model. A detailed study can constrain the parton density functions and is even sensitive to various exotic physics models. The large production cross-section and the detailed knowledge of the mass resonance curve of the Z boson from LEP experiments makes the decay of the Z boson to a standard physics process for the calibration of the ATLAS and CMS detector especially in the initial phase of LHC.

1.3.3 Drell-Yan production of lepton pairs

The Drell-Yan production of lepton pairs is a process with clean signature and low experimental backgrounds. The interesting quantities are the cross section and the forward-backward asymmetry, both functions of the rapidity y and of the invariant mass mll of the di-lepton system. The measurement of the cross section can provide evidence for new physics (new resonances, contact terms etc.) and probe electroweak radiative corrections up to 1.5 TeV.

The measurement of the forward-backward asymmetry AFB allows the determination of the ef- 2 lept fective electroweak mixing angle sin θeff . However, it requires the knowledge of the incoming quark and anti-quark direction, which in p − p colliders is diﬃcult to determine and is aﬀected 2 lept by the uncertainty on parton density functions. Improving the LEP+SLD accuracy on sin θeff is therefore a very ambitious goal.

The production of two weak bosons at the LHC will be one of the most important sources of SM backgrounds for ﬁnal states with multiple leptons. Ratios of inclusive cross sections for production of two weak bosons and Drell-Yan could be investigated and the corresponding theoretical errors evaluated at the LHC. For furthermore details see Reference [27]. 16 1. The Standard Model Higgs boson

1.3.4 The dibosons WW , WZ and ZZ

Only the charged Triple Guauge-boson Couplings (TGCs), such as WWZ and WWγ, are allowed in the SM at tree level. The existence of neutral TGCs, such as ZZγ and ZZZ, is forbidden in the SM. The presence of anomalous couplings would increase the cross sections and alter the production kinematics. Any deviations from the expected values would indicate the presence of new physics beyond the SM. √ At the Tevatron energy scale ( s = 1.96 TeV), the diboson production cross sections are expected to be small, according to the SM. The diboson production processes are sensitive to the TGC WW (Z/γ), and would be enhanced by the presence of nonstandard couplings Z(Z/γ)(Z/γ) (anomalous TGC, or aTGC). Therefore, measurements that deviate from the SM predicted cross sections would give an indication of new physics.

We summarize below the recent diboson measurements performed by the CDF collaboration at the √ Tevatron [28]. These results are complementary to LEP ones since pp¯ collisions at s = 1.96 TeV probe higher invariant masses, and also diﬀerent combinations of TGC, where new physics eﬀects might become more evident.

The diboson ﬁnal states with two heavy bosons decaying leptonically have small branching fractions. However the backgrounds for these states are very low, resulting in very clean signals, but with low event yields. Production of W boson pairs involves both W W γ and WWZ couplings. The signature of the WW signal in leptonic ﬁnal states is two isolated leptons with opposite charge and

large missing transverse energy (ET ) from the W neutrinos. After the selection cuts, the dominant backgrounds are from Drell-Yan and the W+jets where a jet fakes an isolated lepton.

Production of WZ involves the WWZ TGC. The study of WZ production allows a search to be performed independently for anomalous WWZ coupling independently of the W W γ coupling, in contrast to the WW production process. The WZ production was unaccessible at LEP and has been observed by CDF in October 2006, using 1.1 fb−1 of collected data. Improving the lepton selection by using all tracks and electromagnetic objects found in the detector was essential for the WZ observation. This selection improved the lepton acceptance by approximately 50%. CDF has an update to the first observation of WZ, using an integrated luminosity of L = 1.9 fb−1. The updated analysis uses a final state of 3 leptons (e or µ) and missing transverse energy. The dominant backgrounds are from Z + X, where X is a Z, γ or jet faking a lepton. Production of ZZ involves the aTGCs ZZγ and ZZZ. The ZZ final state has been observed at LEP and at Tevatron. CDF has a 3σ evidence for ZZ production, using the combination of two final states: the four charged leptons (e,µ) final state, with dominant background being the Z + X production, where X is a Z, γ or jet faking leptons; and two charged leptons plus two neutrinos final state, with the WW final state being the dominant background. WW /WZ separation is achieved using an event by event calculation of the matrix element probability. 1. The Standard Model Higgs boson 17

The measured cross sections for the processes described in this section are summarized in Table 1.1. All results are compatible with the SM predictions.

Process Measurement (pb) NLO (pb) R Ldt σ(pp¯ → WW ) 13.6 ± 2.3(stat) ± 1.6(sys) ± 1.2(lumi) 12.4 ± 0.8 825 pb−1 +1.3 −1 σ(pp¯ → WZ) 4.3−1.0(stat) ± 0.2(sys) ± 0.3(lumi) 3.7 ± 0.3 1.9 fb 1.1 fb−1 (llνν) σ(pp¯ → ZZ) 0.75+0.71(stat + sys) 1.4 ± 0.1 −0.54 1.4 fb−1 (4l)

Table 1.1: Cross section measurements for double vector boson production with leptonic ﬁnal states [28].

Diboson prodcution at the LHC

The study of mutiple gauge-boson production at the LHC provides a direct test of the non-Abelian structure of the SM at energy scales never reached before. The cross sections of diboson production at the LHC is 10 times or more higher than Tevatron. In the near future, the LHC will be the primary primary source of dibosons with the highest reach in invariant mass, where the new physics eﬀects might become evident, and high statistics. Further details about the diboson production at the LHC are given in [29].

The diboson production is also an important and irreducible background to the search of the SM Higgs boson and new physics such as SUSY. For further details about SUSY see References [30– 32]. Therefore, a detailed understanding of diboson production is needed in the ﬁrst phase of LHC data-taking before any new discovery can be made.

This thesis is devoted to this important channel, ZZ(∗) → 4l: the ZZ diboson production in a fully leptonic channel is a foundamental test of the SM, but also the irreducible background for the H → ZZ(∗) → 4l channel. Therefore its study will be an important step toward the discovery of the Higgs boson in the golden channel H → ZZ(∗) → 4l.

Chapter 2

The Large Hadron Collider

2.1 The Large Hadron Collider

The Large Hadron Collider (LHC) is the world’s largest and highest-energy particle accelerator, designed to collide opposing particle beams of either protons at an energy of 7 TeV per particle, or lead nuclei at an energy of 574 TeV per nucleus. It is expected that it will address the most fundamental questions of physics, hopefully allowing progress in understanding the deepest laws of nature. The LHC lies in a tunnel of 27 km in circumference, as much as 175 metres beneath the Franco-Swiss border near Geneva, Switzerland, as shown in Figure 2.1.

Figure 2.1: Scheme of the Large Hadron Collider site at CERN, near Geneva.

19 20 2. The Large Hadron Collider

The LHC was built by the European Organization for Nuclear Research (CERN). It is funded by and built in collaboration with over 10,000 scientists and engineers from over 100 countries as well as hundreds of universities and laboratories.

On 10 September 2008, the proton beams were successfully circulated in the main ring of the LHC for the first time. On 19 September 2008, the operations were halted due to a serious fault between two superconducting bending magnets. Repairing the resulting damage and installing additional safety features took over a year. On 20 November 2009 the proton beams were successfully circulated again and on 23 November 2009, the first proton-proton collisions were recorded, at the injection energy of 450 GeV per particle. On 18 December 2009 the LHC was shut down after its initial commissioning run, which achieved proton collision energies of 2.36 TeV, with multiple bunches of protons circulating for several hours and data from over one million proton-proton collected by the experiments. On 30 March 2010, the first planned collisions took place between two 3.5 TeV beams, which set a new world record for the highest energy man-made particle collisions. In 2012 it will be shut down for the upgrades necessary to bring it to its full design energy, and it will start up again in 2013.

2.1.1 Purpose of LHC

Physicists hope that the LHC will help answer the most fundamental questions in physics, questions concerning the basic laws governing the interactions and forces among the elementary objects, the deep structure of space and time, especially regarding the intersection of quantum mechanics and general relativity, where current theories and knowledge are unclear or break down altogether. These issues include, at least:

K Is the Higgs mechanism for generating elementary particle masses via electroweak symmetry breaking indeed realised in nature? It is anticipated that the collider will either demonstrate (or rule out) the existence of the elusive Higgs boson(s), completing (or refuting) the SM [33].

K Is supersymmetry (SUSY), an extension of the SM and Poincar´esymmetry, realised in nature, implying that all known particles have supersymmetric partners [34–36]? These may clear up the mystery of dark matter.

K Are there extra dimensions [37], as predicted by various models inspired by string theory, and can we detect them [38]? 2. The Large Hadron Collider 21

Other questions are:

K Are electromagnetism, the strong nuclear force and the weak nuclear force just different manifestations of a single unified force, as predicted by various Grand Unification Theories (GUT)?

K Why is gravity so many orders of magnitude weaker than the other three fundamental forces?

K Are there additional sources of quark ﬂavours, beyond those already predicted within the SM?

K Why are there apparent violations of the symmetry between matter and antimatter?

K What was the nature of the quark-gluon plasma in the early universe? This will be investigated with ion collisions by the ALICE experiment.

2.1.2 The accelerator

The LHC is the world’s largest and highest-energy particle accelerator [39]. The collider is contained in a circular tunnel, with a circumference of 27 km, at a depth ranging from 50 to 175 metres underground.

The 3.8-metre wide concrete-lined tunnel, constructed between 1983 and 1988, was formerly used to house the Large Electron-Positron Collider (Figure 2.2). It crosses the border between Switzerland and France at four points, with most of it in France. Surface buildings hold ancillary equipment such as compressors, ventilation equipment, control electronics and refrigeration plants.

Figure 2.2: The LHC tunnel

The collider tunnel contains two adjacent parallel beam pipes that intersect at four points, each containing a proton beam, which travel in opposite directions around the ring. Some 1,232 dipole magnets keep the beams on their circular path, while an additional 392 quadrupole magnets are 22 2. The Large Hadron Collider

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. In total, over 1,600 superconducting magnets are installed, with most weighing over 27 tonnes. Approximately 96 tonnes of liquid helium is needed to keep the magnets at their operating temperature of 1.9 K (−271.25◦C), making the LHC the largest cryogenic facility in the world at liquid helium temperature. Super- conducting quadrupole electromagnets are used to direct the beams to four intersection points, where interactions between accelerated protons will take place.

Once or twice a day, as the protons are accelerated from 450 GeV to 7 TeV, the ﬁeld of the superconducting dipole magnets will be increased from 0.54 to 8.3 Tesla (T). The protons will each have an energy of 7 TeV, giving a total collision energy of 14 TeV. At this energy the protons have a Lorentz factor of about 7,500 and move at about 99.9999991% of the speed of light. It will take less than 90 µs for a proton to travel once around the main ring - a speed of about 11,000 revolutions per second. Rather than continuous beams, the protons will be bunched together, into 2,808 bunches, so that interactions between the two beams will take place at discrete intervals never shorter than 25 ns apart. However it will be operated with fewer bunches when it is ﬁrst commissioned, giving it a bunch crossing interval of 75 ns.

Figure 2.3: The CERN accelerators complex

Prior to being injected into the main accelerator, the particles are prepared by a series of systems that successively increase their energy. The ﬁrst system is the linear particle accelerator LINAC 2 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. Finally the Super Proton Synchrotron (SPS) is used to further increase their energy to 450 GeV before they are at last 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 while collisions occur at the four intersection points. The scheme of the CERN accelerators complex is shown in Figure 2.3. 2. The Large Hadron Collider 23

The LHC physics program is mainly based on proton-proton collisions. However, shorter running periods, typically one month per year, with heavy-ion collisions are included in the program. While lighter ions are considered as well, the baseline scheme deals with lead ions. The lead ions will be ﬁrst accelerated by the linear accelerator LINAC 3, and the Low-Energy Ion Ring (LEIR) will be used as an ion storage and cooler unit. The ions then will be further accelerated by the PS and SPS before being injected into the LHC ring, where they will reach an energy of 2.76 TeV per nucleon (or 575 TeV per ion), higher than the energies reached by the Brookhaven’s Relativistic Heavy Ion Collider (RHIC). The aim of the heavy-ion program is to investigate quark-gluon plasma, which existed in the early universe.

2.1.3 Phenomenology of proton-proton collisions

√ At the nominal centre of mass energy, s = 14 TeV, the total inelastic proton-proton cross section 9 is σpp ' 80 mb, therefore an interaction rate of about 10 Hz is foreseen. These events include two classes of interactions:

K soft collisions: large distance collisions between two incoming protons, in which only a small momentum is transferred; particle scattering at large angle is thus suppressed and the

ﬁnal state particles have small transverse momentum, hpT i ' 500 MeV/c, so that most of them escape down the beam pipe;

K hard collisions: since protons are not elementary particles, occasionally collisions with high

transferred pT occur between two of their constituents (partons, i.e. quarks and gluons). These are the interesting physics events, where massive particles can be created. Hard interactions, however, have a rate of several orders of magnitude lower with respect to soft interactions (Figure 2.4 on page 24).

In the hard scattering interactions, the eﬀective centre of mass energy (i.e. centre of mass energy √ of the two interacting partons), sˆ, is therefore proportional to the fractional energies xa and xb carried by the two partons:

√ √ sˆ = xaxbs (2.1)

√ where s is the centre of mass energy of the proton beams. The momentum distributions of the partons inside the protons are called Parton Distribution Functions (PDFs). They are different for different partons and are functions of the exchanged four-momentum, Q2: for higher exchanged momenta, the contribution of gluons and sea quarks becomes higher with respect to valence quarks. PDFs are measured in Deep Inelastic Scattering (DIS) experiments and different models are available. In Figure 2.5 on page 25, the CTEQ4M PDFs [41] are shown for two different values of Q2. 24 2. The Large Hadron Collider

Figure 2.4: Cross sections and event rates of several processes as a function of the centre of mass energy of p − p collisions [40] 2. The Large Hadron Collider 25

Figure 2.5: CTEQ4M PDFs for Q2 = 20 GeV2 and Q2 = 104 GeV2.

The two interacting partons, therefore, have variable and unknown energy. This is a limitation for the event reconstruction: no initial state constraints are given on the longitudinal 1 component of particle momenta. Assuming that the transverse momenta of the interacting partons are negligible, in fact, the total transverse momentum of ﬁnal state particles must be zero: only the total and missing transverse energies can thus be evaluated.

Another important consequence is that the centre of mass of the interaction may be boosted along the beam direction. For this reason, it is necessary to use quantities which have invariance q 2 2 properties under boosts along this direction, such as the transverse momentum pT = px + py and the rapidity (y), which is deﬁned as

1 E + pz y = ln (2.2) 2 E − pz

Actually, the rapidity is not properly invariant, but additive under Lorentz boosts: distributions of kinematical variables given versus rapidity transform under boosts by the addition of a constant. Usually, anyway, this variable is replaced by pseudorapidity (η), which is a high energy approximation of rapidity. It is deﬁned as

θ η = − ln tan (2.3) 2 and only depends on the polar angle θ of the particle. Particles produced in soft collisions are mostly distributed at high rapidity. However, the soft interaction rate is so large that the residual tail at high pT is competitive with the hard interaction rate, and constitutes a background to high pT signal events.

1Longitudinal refers to the coordinate along the beam direction, while transverse refers to the plane orthogonal to the beams.

Chapter 3

The CMS experiment

Figure 3.1: The CMS detector

3.1 The Tracker

The CMS tracker [42] is a cylindrical detector of 5.5 m in length and 1.1 m in radius. It is equipped with silicon pixel detectors (66M channels) for the innermost part (for radii R < 15 cm and for |z| < 50 cm) and silicon strip detectors (2.8M channels) for the outer layers (R < 110 cm, |z| < 275 cm). The pixel detectors provide in general 2 or 3 hits per track, each with a three- dimensional precision of about 10 µm in the transverse plane (Rφ) and 15 µm in z. The strip detectors [43] can provide up to 14 hits per track, with a two-dimensional precision ranging from 10 µm to 60 µm in Rφ. Some of the silicon strip layers are double-sided to provide a longitudinal measurement with a similar accuracy. The inner barrel has four layers, the outer barrel has six layers. The inner endcap is made of three small disks on each side which close the inner barrel. The outer endcap is made of nine big disks on both sides of the Tracker. (See Figure 3.3) 27 28 3. The CMS Experiment

(a) (b)

Figure 3.2: (a) A spectacular view of the interior of one half of the Tracker Inner Barrel (TIB), unusually showing many of the silicon sensors. (b) A typical CMS Tracker Outer Barrel (TOB) double-sided rod, mounted on an assembly ﬁxture in the Lab C clean room. Three sets of silicon detectors are attached to the top side and three sets are attached to the bottom side of the carbon ﬁber support frame.

The tracker acceptance for a minimum of 5 collected hits extends up to pseudorapidities η of about |η| < 2.5. The eﬃciency for collecting 2 hits in the pixel detector drops from close to 100% at |η| ' 2.1 to below 70% at |η| ' 2.5 as shown in Figure 3.3.

Figure 3.3: r-z view of a quadrant of the silicon part of the Tracker. Positions in r (vertical axis) and z (horizontal axis) are in mm. Red lines represent single-sided modules, blue lines double-sided modules. 3. The CMS Experiment 29

The material thickness in the tracker volume, to be traversed by electrons and photons before reaching the ECAL, varies strongly with η. It amounts to about 0.35X0 at central pseudorapidities

(η = 0), increases to ' 1.4X0 towards the ECAL barrel/endcap transition, and falls back to about

0.8X0 at |η| = 2.5.

3.2 The Electromagnetic Calorimeter (ECAL)

Figure 3.4: The Electromagnetic Calorimeter Barrel (EB) supermodules of CMS

3 The CMS ECAL [44] is made of PbW04 crystals, a transparent material denser (8.3 g/cm ) than iron, with a radiation length X0 of 0.89 cm and a Moliere radius RM of 2.19 cm. The ECAL is < < < composed of a barrel covering |η| ∼ 1.48 and and two endcaps covering 1.48 ∼ |η| ∼ 3.0.

Figure 3.5: A trapezoidal and quasi-projective crystal of CMS ECAL

The barrel is made of 61200 trapezoidal and quasi-projective crystals of approximately 1 × RM in lateral size and about 25.8X0 in depth, shown in Figure 3.5. The inner radius of the barrel is 124 cm. Viewed from the nominal interaction vertex, the individual crystals appear tilted (oﬀ-pointing) by about 3◦ both in polar and azimuthal angles, and the granularity is about 30 3. The CMS Experiment

∆η × ∆φ = 0.0175 × 0.0175 rad. The barrel is divided in two halves, each made of 18 supermodules containing 1,700 crystals. Each supermodule is composed of four modules.

The endcaps consist of two detectors, a preshower device followed by PbW04 calorimetry. The preshower is made of silicon strips placed in a 19 cm sandwich of materials including approximately

2.3X0 of Pb absorber. The preshower covers inner radii from 45 cm to 123 cm, corresponding to the range 1.6 < |η| < 2.6. Each endcap calorimeter is made of 7324 rectangular and quasi-projective crystals of approximately 1.3 × RM in lateral size and about 24.7X0 in depth. The crystal front faces are aligned in the (x, y) plane but, as for the barrel, the crystal axes are oﬀ-pointing from the nominal vertex in the polar angle by approximately 3◦.

The CMS inner tracking and ECAL detectors are immersed in a 4 T magnetic ﬁeld parallel to the z axis.

3.3 The Hadronic Calorimeter (HCAL)

Figure 3.6: The Hadron Calorimeter of CMS is being installed in the solenoid.

The Hadron Calorimeter (HCAL) [45] measures the energy of “hadrons”, particles made of quarks and gluons (for example protons, neutrons, pions and kaons). Additionally it provides indirect measurement of the presence of non-interacting, uncharged particles such as neutrinos. Measuring these particles is important as they can tell us if new particles, such as the Higgs boson, or supersymmetric particles (much heavier versions of the standard particles we know) have been formed.

The HCAL is a sampling calorimeter, meaning it finds a particles position, energy and arrival time using alternating layers of “absorber” and fluorescent “scintillator” materials that produce a rapid light pulse when the particle passes through. Special optic fibres collect this light and feed it into 3. The CMS Experiment 31 readout boxes where photodetectors amplify the signal. When the amount of light in a given region is summed up over many layers of tiles in depth, called a “tower”, this total amount of light is a measure of a particles energy.

Figure 3.7: HCAL view in r-z plane

As the HCAL is massive and thick, ﬁtting it into “compact” CMS was a challenge, as the cascades of particles produced when a hadron hits the dense absorber material (known as showers) are large, and the minimum amount of material needed to contain and measure them is about one metre.

To accomplish this feat, the HCAL is organised into barrel (HB and HO), endcap (HE) and forward (HF) sections (See Figure 3.7). There are 36 barrel “wedges”, each weighing 26 tonnes. These form the last layer of the detector, inside the magnet coil whilst a few additional layers, the outer barrel (HO), sits outside the coil, ensuring no energy leaks out the back of the HB undetected. Similarly, 36 endcap wedges measure particle energies as they emerge through the ends of the solenoid magnet [46].

Finally, the two hadronic forward calorimeters (HF) [47] are positioned at either end of the CMS detector, to pick up the myriad of particles coming out of the collision region at shallow angles relative to the beam line. These receive the bulk of the particle energy contained in the collision so must be very resistant to radiation and use diﬀerent materials compared to the other parts of the HCAL.

3.4 The magnet

More coils give a stronger field, a stronger field gives more precise results, and with more precise results we can see more physics. But whilst getting the best magnetic field possible was the most 32 3. The CMS Experiment

important consideration in designing the detector, its size was also limited. For the sake of efficiency the magnet was built offsite and transported to CMS by road, which meant it physically could not be more than 7 metres in diameter, otherwise it would not fit through the streets on its way to Cessy.

The CMS magnet [48] is the central device around which the experiment is built, with a 4 Tesla magnetic ﬁeld that is 100,000 times stronger than that of the Earth.

Its job is to bend the paths of particles emerging from high-energy collisions in the LHC. The more momentum a particle has the less its path is curved by the magnetic ﬁeld, so tracing its path gives a measure of momentum. CMS began with the aim of having the strongest magnet possible because a higher strength ﬁeld bends paths more and, combined with high-precision position measurements in the tracker and muon detectors, this allows accurate measurement of the momentum of even high-energy particles.

Figure 3.8: The CMS superconducting magnet is being installed into the muon detection system

The CMS magnet is a “solenoid” - a magnet made of coils of wire that produce a uniform magnetic field when electricity flows through them. The CMS magnet is “superconducting”, allowing electricity to flow without resistance and creating a powerful magnetic field. In fact at ordinary temperatures the strongest possible magnet has only half the strength of the CMS solenoid 1.

The tracker and calorimeter detectors (ECAL, HCAL) fit snugly inside the magnet coil whilst the muon detectors are interleaved with a 12-sided iron structure that surrounds the magnet coils and contains and guides the field. Made up of three layers this “return yoke” reaches out 14 metres in diameter and also acts as a filter, allowing through only muons and weakly interacting particles

1The largest superconducting solenoid ever built (internal diameter 6 m, length 12.5 m) and the most powerful (central magnetic ﬁeld 4 T, stored energy 2.7 GJ). 3. The CMS Experiment 33 such as neutrinos through. The enormous magnet also provides most of the experiments structural support, and must be very strong itself to withstand the forces of its own magnetic ﬁeld.

3.5 The Muon System

As the name “Compact Muon Solenoid” suggests, detecting muons is one of CMS’s most important tasks. Muons are charged particles that are just like electrons and positrons, but are 200 times heavier. We expect them to be produced in the decay of a number of potential new particles; for instance, one of the clearest “signatures” of the Higgs boson is its decay into four muons.

Because muons can penetrate several metres of iron without interacting, unlike most particles they are not stopped by any of CMS’s calorimeters. Therefore, chambers to detect muons are placed at the very edge of the experiment where they are the only particles likely to register a signal.

Figure 3.9: Muon chambers wheels are prepared above the CMS pit [49]

A particle is measured by ﬁtting a curve to hits among the four muon stations, which sit outside the magnet coil and are interleaved with iron “return yoke” plates (shown in red below, for the barrel region). By tracking its position through the multiple layers of each station, combined with tracker measurements the detectors precisely trace a particles path. This gives a measurement of its momentum because we know that particles travelling with more momentum bend less in a magnetic ﬁeld. As a consequence, the CMS magnet is very powerful so we can bend the paths of even very high-energy muons and calculate their momenta. 34 3. The CMS Experiment

Figure 3.10: Muon track in the CMS detector

In total there are 1,400 muon chambers: 250 drift tubes (DTs) and 540 cathode strip chambers (CSCs) to track the particles positions and provide a trigger, while 610 resistive plate chambers (RPCs) form a redundant trigger system, which quickly decides to keep the acquired muon data or not. Because of the many layers of detector and diﬀerent specialities of each type, the system is naturally robust and able to ﬁlter out background noise.

DTs and RPCs are arranged in concentric cylinders around the beam line (“the barrel region”) whilst CSCs and RPCs, make up the “endcaps” disks that cover the ends of the barrel. Chapter 4

The H → ZZ(∗) → 4l channel at √ s = 10 TeV

One of the key channels for the discovery of the SM Higgs boson at LHC is the so called “golden” channel, H → ZZ(∗) → 4l. It is a very clean channel that allows a determination of the Higgs mass with very good resolution. Since the BR(H → ZZ(∗)) is not negligible from masses ranging between 115 GeV/c2 and 1 TeV, the Higgs boson mass can be measured in the entire mass range. The accessible ﬁnal states are 4µ, 4e and 2e2µ. The analysis described in this chapter is made at √ s = 10 TeV. This chapter is meant as an introduction to the discussion of the analysis strategy for the ZZ cross section measurement discussed in Chapter5.

4.1 Physics processes and their simulation

Signal and background datasets obtained with a detailed Monte Carlo simulation [50] of the detector response have been produced by using a perfectly aligned detector geometry. The samples have been subject to full reconstruction [51].

Producing generator level events is a two-step procedure which factorises the physics contents of the matrix element calculation from the parameters of the parton showering/fragmentation/underlying- event.

A large variety of Electroweak and QCD-induced SM processes, e.g. Z+jets and W+jets are simulated and used to measure the rate of some of the “signal-like events” as well as to provide various “control samples” in order to control efﬁciencies and systematics from “data”. The general multi-purpose Monte Carlo event generator PYTHIA [52] is used for several signal and background processes described in detail from Section 4.1.1 to Section 4.2.4, either to generate hard processes at leading order (LO), or just to model the showering and hadronization in cases where the hard

35 √ 36 4. The H → ZZ(∗) → 4l channel at s = 10 TeV

processes are generated at next-to-leading order (NLO). MadGraph Monte Carlo [53] event generator is also used to generate the amplitudes and events for the most important background processes. As for any parton level generators, events are then passed to PYTHIA which takes care of the parton showering by using a matching procedure of matrix elements to parton shower, and the hadronization.

All the signal and background processes are re-weigthed to NLO. The total cross section at the leading order of the signal and background processes takes into account the correction at next-

to-leading order: σNLO = σLO · Kfactor. (For further details see Section 4.3). In the case of Higgs boson production via the gluon fusion mechanisms the most recent NNLO calculation of cross-sections are included [54].

The signal and background processes considered are reported in Table 4.1. More details on the production of the corresponding samples are given from Section 4.1.1 to Section 4.2.4.

Process MC generator σNLO · BR GenFilter 2 H → ZZ → 4l (mH = 115 - 250 GeV/c ) PYTHIA 4-50 fb 68-78% qq¯ → ZZ → 4l MadGraph 255.15 fb 0.3165 Zb¯b → 2lb¯b MadGraph 93.3 pb 0.007 tt¯→ 2W b¯b MadGraph 410.1 pb 0.01091 gg → ZZ → 2l2l0 GG2ZZ 7.68 fb 0.25437 gg → ZZ → 4l GG2ZZ 3.84 fb 0.43753 W+jets MadGraph 40000 pb 1

QCD di-jets, (ˆpT = 15 − 3000 GeV/c) PYTHIA 0.008 fb - 1.45 mb 1

Z+jets, (ˆpT = 0 − 300 GeV/c) PYTHIA 0.2 - 6430 pb 1

Table 4.1: Monte Carlo simulation datasets used for signal and background processes; Z stands ∗ ∗ for Z, Z , γ ; l means e, µ, τ;p ˆT is the transverse momentum for 2 → 2 hard processes in the rest frame of the hard interaction.

4.1.1 Signal: H → ZZ(∗) → 4l

The Higgs boson samples are generated with PYTHIA 6.420 [52] (LO gluon and weak-boson fusion, gg → H and qq¯ → qqH¯ ). The Higgs boson is forced to decay to two Z-bosons, which are allowed to be off-shell, and both Z-bosons are forced to decay to two leptons, ZZ → ll (where l stands here for e, µ, and τ).

Events are then re-weighted by the total cross-section σ(pp → H) made of the gluon fusion contribution up to the NNLO taken from Reference [54] and the weak-boson contribution at the NLO computed in Reference [55]. √ 4. The H → ZZ(∗) → 4l channel at s = 10 TeV 37

Figure 4.1(a) shows the various production modes of the Higgs boson as a function of the Higgs boson mass mH and Figure 4.1(b) shows a comparison between the Higgs boson production cross √ √ section at s = 10 TeV and s = 14 TeV. The total cross section is scaled by the BR(H → ZZ(∗))· BR(Z → 2l)2, where BR(H → ZZ(∗)) was taken from Reference [55] and BR(Z → 2l) = 0.101 [56]. The branching ratio of the Higgs boson as a function of its mass is shown in Figure 1.5 on page9.

60 s = 10 TeV (fb) (pb)

gluon fusion (NNLO) 4l

H 50 2

10 vector boson fusion (NLO) → σ s = 14 TeV WH,ZH

ZZ* s = 10 TeV ttH 40 →

10 H σ 30

1 20

10-1 10

-2 10 120 140 160 180 200 220 240 120 140 160 180 200 220 240 2 2 mH (GeV/c ) mH (GeV/c )

(a) (b)

Figure√ 4.1: (a) The total cross-section for the Higgs boson production mechanisms at s = 10 TeV as a function of mH . In red the gluon gluon fusion, in blue the vector boson fusion, in green the associated production and in yellow the√ heavy quark associated production [57]. (b) The cross-section for H → 4l as a function of mH at s = 10 TeV as compared to 14 TeV [58].

A total of 20 Monte Carlo samples corresponding to different Higgs boson masses is used: from 115 to 205 GeV/c2 with a step of 5 GeV/c2 and an additional mass point of 250 GeV/c2. The analysis described below requires four leptons within the detector acceptance (|η| < 2.5) in the final state and with matching flavours and opposite signs: µ+µ−µ+µ−, e+e−e+e−, e+e−µ+µ−. So, we can have three different channels: 4µ, 4e and 2e2µ. Figure 4.2 shows the fraction of events with four such leptons in the detector acceptance at generator level. Events with one or both Z-bosons decay to τ +τ − are not considered. Although a few percent of such events will be reconstructed as four-lepton µ+µ−µ+µ−, e+e−e+e−, e+e−µ+µ− final states and will contribute to the off-peak tail in the m4l-distribution for the signal.

4.2 Backgrounds

4.2.1 qq¯ → ZZ(∗) → 4l

The qq¯ → ZZ(∗) → 4l sample is generated with the MadGraph [53] matrix element generator with q-quark taken as q = u, d, s, c or b. In Figure 4.3 the Feynman diagrams for qq¯ → ZZ(∗) → 4l at the leading order is shown. A ﬁltering √ 38 4. The H → ZZ(∗) → 4l channel at s = 10 TeV

100

60 H→ZZ*→2e2µ 50 Detector acceptance [%] H→ZZ*→4e 40 H→ZZ*→4µ 30

0 120 140 160 180 200 220 240 2 mH (GeV/c )

Figure 4.2: Fraction of events with four generated leptons in the detector acceptance in the ﬁnal states µ+µ−µ+µ−, e+e−e+e−, and e+e−µ+µ−. This is calculated with respect to all Higgs boson decays H → ZZ(∗), and Z-bosons decaying to ee and µµ.

procedure is applied at genetor level, by asking pT (l) > 3 GeV/c, |η(l)| < 3.0 and dR(η, φ) > 0.01 2 between two leptons. A cut mll > 5 GeV/c on the invariant mass of all possible pairs of same- ﬂavor opposite-sign di-leptons is also applied. These cuts are applied in order to ﬁnd an interesting kinematic region, in which the event can be reconstructed. Both t- and s-channel diagrams were included: the s-channel diagram, not available in PYTHIA, 2 gives a large peak at m4l = MZ . It contributes to about 10% for 120 < m4l < 180 GeV/c and can be safely neglected for higher 4l invariant masses. The interference between t- and s-channels is always found to be negligible. More details on the relative role of the s-channel can be found elsewhere [59].

Figure 4.3: Feynman diagram for qq → ZZ → 4l process at the tree level.

The MadGraph LO cross-section is 189.86 ± 0.22 fb. The MadGraph events are passed to PYTHIA 6.225 for showering and hadronization. A ﬁltering procedure is used at PYTHIA level, by requiring

at least 4 leptons (e, µ) with pT (e, µ) > 4 GeV/c and |η(e, µ)| < 2.7. The efﬁciency for that ﬁlter is about 31.6%. A sample of 1 million ZZ events was simulated corresponding to an integrated luminosity of about 11,100 fb−1. √ 4. The H → ZZ(∗) → 4l channel at s = 10 TeV 39

To account for contributions to all the NLO diagrams, events are re-weighted with a m4l-dependent K-factor:

σNLO K(m4l) = KNLO(m4l) + 0.2 ,KNLO = (4.1) σLO where 0.2 is the NNLO contribution of the gg → ZZ(∗) → 4l process [60]. The NLO K-factor

KNLO(m4l), obtained with MCFM [61], is shown in Figure 4.4. The average correction including the MCFM prediction for the qq¯ → ZZ(∗) is < K > = 1.35.

1.8 K factor 1.6

1.4

1.2 Range 30 GeV - 750 GeV

1 sigma NLO = 19.89 fb sigma LO = 14.73 fb 0.8 K factor = 1.3500

0.6 0 100 200 300 400 500 600 700 2 m4µ(GeV/c )

(∗) Figure 4.4: Mass-dependent Next-to-Leading-Order K-factor KNLO(m4l) for the ZZ → 4l process as evaluated with MCFM [61].

4.2.2 gg → ZZ(∗) → 4l

The gluon-induced ZZ background, although being a NNLO process compared to the ﬁrst order Z-pair production, amounts to a substantial fraction to the total irreducible background. A full NNLO calculation for the process qq¯ → ZZ(∗) taking into account these diagrams is not available. Therefore the contributions of these diagrams are estimated by using the dedicated tool GG2ZZ [54], (∗) 2 0 which computes the gg → ZZ cross section at LO, which is of order αs , compared to αs for the LO qq¯ → ZZ(∗). The hard scattering gg → ZZ(∗) → 4l events are then showered and hadronized using PYTHIA6. GG2ZZ provides the functionality to compute the cross-section after applying a cut on the mimimal generated invariant mass of the same-ﬂavour lepton pairs (which can be 2 interpreted as the Z/γ invariant mass) mll > 10 GeV/c .

GG2ZZ also provides the possibility to generate only non-same-flavour final state combinations; however for our study it was used also to estimate the same-flavour background. This is valid only

when m4l ≥ 2 mZ while below this threshold the relative amount of same-flavour events compared to non-same-flavour increases and the generator could not give the opportune rates for same-flavour final states. √ 40 4. The H → ZZ(∗) → 4l channel at s = 10 TeV ZZ

0.035 → qq LO 0.3 σ / [fb/GeV] ZZ 4l

0.03 →

gg 0.25 σ /dm

σ 0.025 d 0.2 0.02 0.15 0.015 0.1 0.01

0.005 0.05

0 0 0 50 100 150 200 250 300 350 400 450 500 0 50 100 150 200 250 300 350 400 450 500 m4l [GeV] m4l [GeV]

(a) (b)

Figure 4.5: (a) Differential cross-section for gg → ZZ(∗) as a function of the four lepton invariant mass for different flavour lepton pairs; (b) Ratio of gg → ZZ(∗) and qq¯ → ZZ(∗) (LO) as a function of the invariant mass of the four leptons system.

The total cross section is 4.425 ± 0.021 fb for events with different flavour lepton pairs in the final state. The differential cross-section as a function of the four lepton invariant mass for different flavour lepton pairs is reported in Figure 4.5(a). The ratio of gg → ZZ(∗) and qq¯ → ZZ(∗) (LO) is reported in Figure 4.5(b) and is found to saturate at about 20% at around m4l ≈ 2MZ . The gluon gluon fusion process contributes to the production of the ZZ diboson, as shown in Figure 4.6.

Figure 4.6: Feynman box diagram for gg → ZZ(∗) → 4l process.

Events are filtered at the level of PYTHIA as for the qq¯ → ZZ(∗), tt¯ and Zb¯b samples. The efficiency for that filter is about 44% (25%) for the events with same (different) flavour lepton pairs in the final state; about one million events for the two each of the two different set of samples are simulated.

4.2.3 qq/gg¯ → Zb¯b → 4l

The Zb¯b → 2lb¯b sample is generated by the MadGraph generator interfaced with PYTHIA. The included sub-processes are: qq/gg¯ → Zb¯b, where q can be any of the light quarks (u, d, s, c and b). √ 4. The H → ZZ(∗) → 4l channel at s = 10 TeV 41

The Z boson decays into 2e or 2µ and the b quark decays leptonically. In detail,

Z → l+l− b → lX l = e, µ (4.2)

The Zb¯b production is described by the Feynman diagrams shown in Figure 4.7. The b-quark decay is shown in Figure 4.8(a).

(a) (b)

(c)

Figure 4.7: (a) s-diagram and (b) t-diagram for the production of the Zb¯b state from qq¯ annihilation. (c) Diagram for the Zb¯b production from gg.

(a) (b)

Figure 4.8: (a) Decay of the b-quark. (b) Decay of the t-quark.

The corresponding MadGraph LO cross-section is 56.2 pb. To obtain the NLO cross-section, a

NLO K-factor using MCFM [61] is calculated: KNLO = 1.66 ± 0.03. A filtering procedure is used 2 at generator level, by asking pT (l) > 3 GeV/c, pT (b) > 5 GeV/c and m2l > 10 GeV/c . The efficiency for the PYTHIA filter (see Section 4.2.1) is about 7 × 10−3. A sample of about 1 milion Zb¯b events corresponding to an integrated luminosity of about 1,600 fb−1 is generated. √ 42 4. The H → ZZ(∗) → 4l channel at s = 10 TeV

4.2.4 qq/gg¯ → tt¯ → 4l

The tt¯ sample is simulated using the MadGraph event generator. The total NLO cross-section

σNLO(pp → tt¯) is 410 pb [62]. The t quark decays into W b with BR(t → W b) = 1. We then consider leptonic decays of the W boson and the b quark as shown in Figure 4.8(a). Some of the diagrams for the production of tt¯ are shown in Figure 4.9. The t-quark decay is shown in Figure 4.8(b).

(a) (b)

Figure 4.9: (a) s-diagram for the process qq¯ → tt¯. (b) t-diagram for the process gg → tt¯.

A matrix element to parton shower matching (MLM) procedure (the so-called KT -jet scheme) is used to avoid overlapping between phase-space descriptions given by matrix-element generators and the showering/hadronization handled by PYTHIA in multi-jets process simulation. 2 → 2 partonic hard scattering processes are manifested as jets of particles back to back in azimuth. These processes are described well by QCD predictions but there are some difﬁculties in explaining

the predictions of the cross sections at high pT and the behavior of the scaling laws. An addition

pT kick to the scattered partons needs to be introduced to explain the data. Since partons are conﬁned inside a hadron of ﬁnite dimension they have a certain amount of intrinsic motion. This

intrinsic motion gives rise to an effective transverse momentum vector KT of each of the two

colliding partons undergoing hard scattering in proton-proton collisions. Further details on KT can be found in [63, 64]. A ﬁltering procedure is applied at genetor level, by asking that the top pole mass is 170.9 GeV/c2

and pT (jet) > 20 GeV/c. After showering, but before hadronization and decays, the ﬁnal-state partons are clustered into jets and those are considered matched to the closest parton if the jet

measure, KT (parton, jet), is smaller than a cut-off, Qcut, set to 30 GeV/c for the tt¯ production; tipically the event is rejected unless each jet is matched to a parton. Only 30% of the generated events are able to survive to the MLM procedure.

To increase the statistics of events that could potentially survive the selection procedures the events are filtered at the PYTHIA level. The efficiency of the complete filtering procedure is of about 10−2, as reported in Table 4.1 at page 36. A sample of about 1 milion events corresponding to an integrated luminosity of more than 200 fb−1 is simulated. √ 4. The H → ZZ(∗) → 4l channel at s = 10 TeV 43

4.2.5 Other backgrounds

The other backgrounds considered are generated with PYTHIA. They are Z+jets, where the Z decays into two leptons and two jets which are misidentiﬁed as two leptons, QCD di-jets and W+jets [65].

4.3 Weights

In this analysis we weight every event in order to have L = 1 fb−1 with a factor computed as

skim wglobal = σtot · Km4l · filter · (4.3) Nskim with

√ σtot is MadGraph output LO cross section at s = 10 TeV

filter is the PYTHIA ﬁlter efﬁciency

Km4l is the K-factor, which depends on the m4l

skim is the skim efﬁciency

Nskim is the number of skim events processed

The skim selection is described in Section 4.4.2. The values of the cross section (σtot) of the main √ backgrounds at s = 10 TeV after the pre-selection cuts at generator level discussed in Section 4.2, the K-factor (Km4l), the generation ﬁlter efﬁciency (filter), the number of events after skim

(Nskim), the skim efﬁciency (skim) and the event weight (wglobal) for the three backgrounds ZZ, Zb¯b and tt¯ are listed in Table 4.2.

σtot [fb] Km4l filter skim Nskim wglobal ZZ 189.86 ± 0.22 1.35 0.3165 0.870 781721 0.0000898 Zb¯b 56200 1.66 0.007 0.642 682820 0.0006140 tt¯ 280900 1.46 0.01091 0.722 727618 0.0044398

Table 4.2: Weights for MC events for ZZ, Zb¯b and tt¯ at 10 TeV for 1 fb−1. √ 44 4. The H → ZZ(∗) → 4l channel at s = 10 TeV

4.3.1 Weights for ZZ as a function of m4l

For the ZZ background we weight each event with a correction factor depending on the invariant mass of the four leptons (corr(m4l)), so that we can take into account the NNLO contribution to the LO cross section. The value of the weight for ZZ for L = 1 fb−1 (see Equation 4.3) is

wglobal = 189 · 1.35 · 0.3165 · 0.870/781721 = 0.0000898 (4.4)

Then we compute a correction to the weight depending on the m4l as calculated in [61]:

  1.595 · (1 − exp((−0.007888) · m4l)) if m4l > 200   corr(m4l) = 9  X  par[i] · (m )i if m ≤ 200 and m > 30  4l 4l 4l i=0 with the par vector [61]:

par = (−0.494682, 0.300858, −0.017097, 0.000451, −6.46736 · 10−6, 5.34046 · 10−8, −2.53992 · 10−10, 6.4625 · 10−13, −6.81318 · 10−16) (4.5)

The weight becomes

0 w (m4l) = wglobal*(corr(m4l) / 1.35 + 0.2) (4.6) where 0.2 is the NNLO contribution from gg → ZZ(∗).

4.3.2 Weight for Z+jets

The Z+jets MC samples are treated differently, since they are generated in ten different Z pT 1 bins . As for the previous backgrounds, the global weight wglobal is computed with Equation 4.3, with filter = 1 and Km4l = 1. The formula becomes:

skim wglobal = σtot · (4.7) Nskim

The values of the weight for Z → µµ+jets are listed in Table 4.3 and for Z → ee+jets in Table 4.4. The cross sections are expressed in pb.

1 The pT bins are: 0-15, 5-20, 30-30, 30-50, 50-80, 80-120, 120-170, 170-230, 230-300, 300-Inﬁnite [GeV] √ 4. The H → ZZ(∗) → 4l channel at s = 10 TeV 45

pT bin σtot [pb] skim Nskim wglobal pT bin σtot [pb] skim Nskim wglobal

0 - 15 6430 0.006 1343 28.7267 0 - 15 6430 0.0045 1022 28.3121 15 - 20 230 0.02 4824 0.9535 15 - 20 230 0.017 3592 1.0885 20 - 30 211 0.04 6719 1.2561 20 - 30 211 0.037 7919 0.9858 30 - 50 142 0.09 14521 0.8801 30 - 50 142 0.084 15541 0.7675 50 - 80 56.8 0.16 17307 0.5251 50 - 80 56.8 0.15 15730 0.5416 80 - 120 18.8 0.22 45898 0.0901 80 - 120 18.8 0.212 22157 0.1798 120 - 170 5.4 0.27 29885 0.0487 120 - 170 5.4 0.269 28710 0.0505 170 - 230 1.55 0.33 35008 0.0146 170 - 230 1.55 0.316 33480 0.0146 230 - 300 0.45 0.36 38858 0.0041 230 - 300 0.45 0.346 36523 0.0042 300 - ∞ 0.2 0.40 44776 0.0017 300 - ∞ 0.2 0.377 40844 0.0018

Table 4.3: Weights for Z → µµ+jets MC Table 4.4: Weights for Z → ee+jets MC events at 10 TeV for 1 fb−1. events at 10 TeV for 1 fb−1.

4.4 Trigger, skimming and pre-selection

A ﬁrst selection is made online by the trigger system (Section 4.4.1), which has the aim to reduce the events rate, that could be otherwise too much elevated for being able to record it. Before the analysis, there are two steps of ofﬂine selections, called skimming and pre-selection. The aim of the skimming (Section 4.4.2) is to reduce the overall amount of data in order to preserve a manageable data volume. The main goal of the pre-selection (Section 4.4.3) is to eliminate QCD background events.

4.4.1 The CMS trigger

2 (∗) For Higgs boson masses mH above 100 GeV/c , the ZZ state is expected to be dominantly produced with a least one Z boson on the mass shell, which then decays into a pair of leptons each carrying a pT of about MZ /2. The triggering of the CMS detector [66] on the Higgs boson signal relies on the presence of one or two high pT leptons.

For the LHC start-up luminosity of L = 2 · 1030 cm−2s−1, the HLT conﬁguration foreseen in CMS

allows for single lepton pT thresholds well below 20 GeV/c. Hence a very high selection efﬁciency

is expected for the Higgs boson. The pT thresholds for the electron and muon trigger paths are reported, both for the L1 and for the HLT, in Table 4.5.

A global “OR” between different HLT sequences (trigger-paths) is chosen to maximize the signal detection efﬁciency. The triggers-paths taken into consideration are: single muon isolated, single muon (no isolation), double muon (no isolation), single electron isolated, single electron (relaxed √ 46 4. The H → ZZ(∗) → 4l channel at s = 10 TeV

Trigger Object HLT path name Level-1 th. [GeV/c] HLT th. [GeV/c] Isolated HLT IsoEle15 L1I 12 15 Single Relaxed HLT IsoEle18 L1R 15 18 e Isolated HLT DoubleIsoEle10 L1I 8.8 10.10 Double Relaxed HLT DoubleIsoEle12 L1R 10.10 12.12 Isolated HLT IsoMu11 7 11 Single µ Relaxed HLT Mu15 10 15 Double Relaxed HLT DoubleMu3 0.0 3.3

Table 4.5: pT thresholds for electron and muon trigger paths at Level-1 (L1) and at High Level Trigger (HLT). The “relaxed” lepton triggers imply loose isolation in the case of electron and no isolation requirements in the case of muons.

isolation), double electron isolated, double electron (relaxed isolation) and their combinations. The double muon isolated path is not used as it is essentially redundant with the corresponding non isolated path for what concerns signal selection. The expected trigger selection efﬁciency is determined for the purpose of this prospective analysis by applying the global “OR” of the HLT paths to Monte Carlo simulated event samples.

The HLT trigger efficiency, defined as the ratio between the number of events which pass the “OR” of the trigger selection specified in Table 4.5 and the input number of events is evaluated starting from the signal and background samples filtered in the way described in Section 4.1. The trigger efficiencies are reported in Table 4.6 for the H → 2e2µ, H → 4µ and H → 4e channels and for several selected values of the SM Higgs boson mass. A very high trigger efficiency is obtained for 2 the signal, with values above 98% for a Higgs boson mass mH above 115 GeV/c and reaching 2 close to 100% for mH above 200 GeV/c .

2 2 2 HLT (%) mH = 125 GeV/c mH = 150 GeV/c mH = 200 GeV/c 2e2µ 99.54 99.80 99.96 4µ 99.78 99.74 100.0 4e 99.29 99.59 99.91

Table 4.6: HLT efﬁciencies for signal samples of selected masses for the 2e2µ, 4µ and 4e channels.

4.4.2 Event skimming

A H → ZZ(∗) → 4l “skimming” common to all three channels is designed to select signal events with close to 100% efﬁciency, and reduce backgrounds signiﬁcantly from QCD, W+jets and Z+jets (e.g. events containing jets recoiling against a Drell-Yan production of lepton pairs). As said in Section 4.4, the aim of the skimming is to reduce the overall amount of data in order to have a more manageable data volume. √ 4. The H → ZZ(∗) → 4l channel at s = 10 TeV 47

The skimming is applied to the so-called “electron-” and “muon-primary data streams”. These data streams are built as a logical “OR” of the single and double electron and muon HLT paths respectively, representing an expected event rate of about 30 to 40 Hz [67], dominated by QCD.

The skimming selection required at least two leptons (e or µ) with pT > 10 GeV/c and one 32 33 −2 −1 additional lepton with pT > 5 GeV/c, intended for luminosities of about 10 ÷ 10 cm s [58]. Muon are asked to be “global”, i.e. reconstructed with a combined ﬁt of the hits in the muon spectrometer and the inner tracker.

Table 4.7 shows the overall skimming efficiency for the Higgs boson signal as a function of mH for the 4µ, 4e, and 2e2µ decay channels. For the H → 4µ (4e) (2e2µ) channel, the efficiency for the > > > 2 skimming step is ∼ 97% ( ∼ 88%) ( ∼ 94%) for mH ≥ 125 GeV/c . It was verified that none of the signal events that have been rejected by skimming would have passed the full event selection used for this analysis. The efficiencies of the skimming selection on the background samples used in this analysis are reported in Section 4.3.

4µ 115 125 150 165 180 200 skim(%) 96.4 97.6 98.7 99.2 99.5 99.4

4e 115 125 150 165 180 200 skim(%) 82.8 88.1 92.1 92.8 93.5 95.0

2e2µ 115 125 150 165 180 200 skim(%) 91.4 94.3 97.1 97.5 98.1 98.1

Table 4.7: Skimming efﬁciencies for signal samples of selected masses (mH ) for the 4µ, 4e and 2e2µ channels.

4.4.3 Event preselection

A set of pre-selection cuts is applied to suppress the contribution of “fake leptons”. The main objective is to bring the QCD multijets and Z/W+jet(s) contributions to a level comparable to or below the contribution of the three main backgrounds, tt¯, Zb¯b and ZZ. By reducing the number of extra (fake) leptons in signal events (coming e.g. from jets recoiling against the Higgs boson), the pre-selection also has the virtue of reducing the problem of the combinatorial ambiguities caused by the presence of more than 4 leptons. The choice of the 4 leptons truly belonging to the H → ZZ(∗) → 4l decay is thus postponed beyond the pre-selection step. √ 48 4. The H → ZZ(∗) → 4l channel at s = 10 TeV

The pre-selection of “signal-like” events consists of these requirements:

K At least two l+l− pairs of identified leptons with opposite charge and matching flavors. The e e electrons are required to satisfy pT > 5 GeV/c and |η | < 2.5, the muons are required to µ µ µ µ satisfy pT > 5 GeV/c in the barrel, pT > 3 GeV/c, P > 9 GeV/c and |η | < 2.4 in the endcaps. 2 K At least two different matching pairs with invariant mass ml+l− > 12 GeV/c . K At least one combination of two matching pairs with an invariant mass greater than 100 GeV/c2. K For all the channels at least 4 loose track-based isolated electron or muon candidates.

The requirement of two lepton pairs with opposite charge and matching flavours is a restriction beyond skimming motivated by the principal characteristics of signal event topologies. The identification of leptons is chosen to be loose (∼ 95% efficient on signal events) and brings additional rejection power against fake leptons. The cut on ml+l− protects against the contamination from low mass hadronic resonances. Requiring that at least one Higgs boson candidate built from the combination of 4 leptons in a given event fulfills an invariant mass of 100 GeV/c2 further suppresses unwanted events and brings a safe reduction of the phase space towards the signal phase space. The µIso and eIso variables are defined in Section 4.4.4.1. In the 4e channel, the electrons must satisfy a loose isolation requirement based on the presence of reconstructed tracker tracks around the electron. The variable is called eIsotrack and it is defined as the sum of the tracks’ pT divided P tracks e by the electron pT ( pT /pT ): this is required to be less than 0.7. The electrons identification algorithm is described in Section B.1.0.2. The efficiency of the isolation and electron identification cuts on signal and their effect on background reduction can be found in the Section “Electron identification” of Reference [58]. Imposing a loose track-based isolation is mandatory for the channels involving electrons, and useful in the case of the 4µ channel, to eliminate the remaining fake QCD. For the muon candidates, the µIso observable with a loose cut µIso < 60 is applied.

The main loss of signal events (e.g. 44% on the plateau for 4e) comes from the requirement of at least four basic reconstructed lepton objects within the detector acceptance. The residual loss (e.g. an additional 10% for 4e) comes from a combination of the requirements of matching pairs of identiﬁed leptons and of the loose lepton isolation. For the 4e channel, about half of this residual loss is caused by charge mis-identiﬁcation 2.

The suppression of the background rates obtained from the pre-selection steps is shown in Fig- ure 4.10. The background events, largely dominated at the ﬁrst steps by contributions involving multiple fake leptons (e.g. from light quark jets), are brought down to a level where tt¯ and Zb¯b become important. In particular the QCD multijets fake contribution is essentially eliminated after having imposed loose isolation.

2Electron reconstruction and identiﬁcation has been improved after completion of the present study. √ 4. The H → ZZ(∗) → 4l channel at s = 10 TeV 49

In the case where more than four identified leptons are found in a given event, the ambiguities have been resolved by building a single Higgs boson candidate from the pair of reconstructed vector bosons in the following way: the first Z is made of the lepton pair with matching lepton flavour and opposite charges and invariant mass the closest to the Z mass; the second Z is composed by the next pair involving the highest pT leptons among remaining leptons. This ambiguity resolving criteria will be applied when building masses for the final event selection. The invariant mass constructed with four leptons after pre-selection is shown in Figure 4.11.

11 11 10 10 -1 -1 QCD QCD 10 10 10 qq→ZZ→4l 10 qq→ZZ→4l → → H→ZZ*→ 4µ 9 H ZZ* 4e 9 10 → 10 Zbb→4l Zbb 4l 8 s = 10 TeV 8 s = 10 TeV 10 → 10 tt→4l tt 4l 7 Z+jets 107 Z+jets 10 W+jets 6 W+jets

6 #events/fb #events/fb 10 10 signal m =150 GeV signal m =150 GeV H H 5 105 10 4 104 10 3 103 10 2 102 10 10 10 1 1 10-1 10-1 -2 -2 10 HLT Skim 4µ with p/p m m loose isolation ( 10 HLT Skim 4e with p m m loose isolation (e) 2l > 12 GeV/c 4l>100 GeV/c 2l > 12 GeV/c 4l>100 GeV/c cuts cuts T T 2 2 2 2 µ)

(a) (b)

1011 -1 QCD 10 10 → → → → µ qq ZZ 4l 9 H ZZ* 2e2 10 Zbb→4l 8 s = 10 TeV 10 tt→4l 107 Z+jets 6 W+jets #events/fb 10 signal m =150 GeV H 105 104 103 102 10 1 10-1 -2 10 HLT Skim 2e & 2 m m loose isolation (e & µ with p/p 2l > 12 GeV/c 4l>100 GeV/c cuts 2 2 T µ)

(c)

Figure 4.10: Reduction of the QCD, Z/W+jet(s), tt¯, Zb¯b and ZZ backgrounds, and (∗) 2 H → ZZ → 4l signal at mH = 150 GeV/c , after the skimming and each pre-selection step in the (a) 4µ, (b) 2e2µ and (c) 4e channel. √ 50 4. The H → ZZ(∗) → 4l channel at s = 10 TeV ] ] 2 2 5 → → H→ZZ*→4µ H ZZ* 4e 18 After Preselection After Preselection Zbb Zbb qq→ZZ(*) 16 qq→ZZ(*) 4 tt tt 14 H130 H130 H150 H150 12 H200 3 H200 H250 H250 → 10 gg→ZZ(*) gg ZZ(*) Z+Jets Z+Jets /dm [fb/10 GeV/c /dm [fb/10 GeV/c 8 W+Jets 2 W+Jets σ σ QCD QCD d d 6

4 1

0 0 0 50 100 150 200 250 300 350 400 450 500 0 50 100 150 200 250 300 350 400 450 500 2 2 m4µ [GeV/c ] m4e [GeV/c ]

(a) (b) ] 2 H→ZZ*→2e2µ 14 After Preselection Zbb qq→ZZ(*) 12 tt H130 10 H150 H200 H250 8 gg→ZZ(*) Z+Jets

/dm [fb/10 GeV/c 6 W+Jets σ QCD d 4

0 0 50 100 150 200 250 300 350 400 450 500 2 m2e2µ [GeV/c ]

(c)

Figure 4.11: Invariant mass of the four lepton system after pre-selection in the (a) 4µ, (b) 2e2µ and (c) 4e channels for H → ZZ(∗) → 4l signal events and for the main backgrounds. √ 4. The H → ZZ(∗) → 4l channel at s = 10 TeV 51

Table 4.8 shows the expected mean number of events per 1 fb−1 in each of the three channels after the pre-selection, for three Higgs boson masses and for the remaining backgrounds. At this stage, the dominating backgrounds after pre-selection are the Z+jets and the tt¯ followed by Zb¯b.

4e 4µ 2e2µ (∗) 2 H → ZZ → 4l ( mH = 130 GeV/c ) 0.53 0.90 1.29 (∗) 2 H → ZZ → 4l ( mH = 150 GeV/c ) 0.96 1.61 2.33 (∗) 2 H → ZZ → 4l ( mH = 200 GeV/c ) 2.03 3.11 4.91 ZZ 8.43 10.8 17.9 Zb¯b 15.5 64.7 34.8 tt¯ 27.5 22.3 115.8 Z+jets 87.0 17.6 40.9 W+jets 3.00 0 3.0

Table 4.8: Summary of the number of events expected per L = 1 fb−1 after the pre-selection for the three H → ZZ(∗) → 4l channels, for three diﬀerent Higgs boson masses and the backgrounds.

All of these (and most notably the Z+jets) will be strongly reduced in the final selection by tighter isolation, vertexing requirements and kinematic cuts. A remarkable difference is observed between the relative number of expected tt¯background events when comparing the 2e2µ channel with other channels. This difference originates from pure combinatorics: there are many more ways to build 2e2µ final states (involving two misidentified primary leptons) than to build 4e or 4µ final states.

4.4.4 Discriminating observables

The trigger and skimming allowed for a drastic reduction of the event rate while preserving the highest possible Higgs boson signal detection eﬃciency. At this early stage the event sample was dominated by background contributions involving two or more “fake” leptons, such as contributions from QCD multi-jet and Z/W+jets, with fake leptons coming from gluon or light quark jets. This fake contribution has been considerably suppressed by the pre-selection which includes some loose lepton isolation requirements.

The event sample obtained following pre-selection is dominated by the tt¯ and Zb¯b backgrounds in the 4µ and 2e2µ channels whilst the Z+jetsfake rate remains the most important contribution in the 4e channel. The tt¯ background has a relatively large contribution in the 2e2µ channel, as shown in Figure 4.11 and in Table 4.8.

Hencefort, for the event selection, the focus is put on the reduction of the two remaining major reducible backgrounds: the tt¯ and Zb¯b with leptons coming from the decays of the b quarks. Such leptons are likely to be accompanied by hadronic products from the fragmentation and decay processes initiated in the b-quark jets. Moreover, because of the long lifetime of b-hadrons, they are likely to have a large impact parameter with respect to the primary vertex. Thus, lepton √ 52 4. The H → ZZ(∗) → 4l channel at s = 10 TeV

isolation and lepton impact parameter measurements should allow for a powerful rejection. While these characteristics might be suﬃcient to eliminate the leptons from heavily boosted b-quark jets in tt¯ events, the b-quark jets in Zb¯b events are in general less collimated in the detector and lead to leptons with a softer pT spectrum. In order to best preserve the signal detection eﬃciency while acting on low pT lepton candidates to suppress the Zb¯b background, the isolation criteria for the leptons from the pair at lowest ml+l− can be made pT dependent.

In the following section the main discriminating observables for the event selection are described. These are:

K isolation,

K impact parameter,

K two-lepton invariant masses,

K four-lepton invariant mass.

An optimal combination of these for a cut-based event selection will be discussed in Section 4.4.5.

4.4.4.1 Lepton isolation

The four leptons coming from the Higgs boson decay should appear isolated. This provides an excel- lent way to distinguish the signal from the reducible backgrounds, Zb¯b → 4l + X and tt¯→ 4l + X, where two leptons are produced inside the b-jets.

Muon Isolation. The degree of isolation of a muon can be quantiﬁed by considering the energy or momentum of the particles in a cone around the muon track. Among the several observables investigated, the one that showed the highest discriminating power, in terms of the best background rejection for a high signal acceptance, is µIso, deﬁned as

µIso = 2 · µIsotrack + 1.5 · µIsoECAL + µIsoHCAL (4.8)

The tracker based and calorimeter based isolation variables are defined in AppendixA. See Chapter “Lepton reconstruction, identification and isolation” of Reference [58] for the studies carried on the stability of the isolation observable. After having measured the degree of isolation of all the leptons, it has been found that the most effective way to define an event as “isolated”, is to consider either the least isolated lepton out of the four coming from two Z(Z∗)-candidates decays, or the two least isolated ones. In the case of the 4µ channel, it is found slightly better to consider the sum of the isolation observable µIso for the two least isolated muons. The distribution of µIso2least is shown in Figure 4.12(a) for the signal and for the main backgrounds. √ 4. The H → ZZ(∗) → 4l channel at s = 10 TeV 53

Although the improvement in background rejection power is small with respect to using only the least isolated muon and mostly compatible within statistical ﬂuctuations, but the choice of this variable makes sense given that both b and b quarks tend to decay semileptonically, yielding two muons that are likely to be non-isolated. The signal eﬃciency for a cut on µIso2least are shown

in Figure 4.12(b) as a function of the background efficiency. For a cut µIso2least < 30 the efficiency is 95%, while background efficiencies are 29% and 9% for Zb¯b and tt¯ respectively. Efficiencies are calculated with respect to events passing the pre-selection.

S 1.05

H→ZZ*→4µ ∈ 2 1 mH = 150 GeV/c signal 0.95 10-1 tt Zbb Zbb tt 0.9 working point 0.85

H→ZZ*→4µ 10-2 0.8 m = 150 GeV/c2 Fraction of events H 0.75

0.7

10-3 0.65

0.6 0 20 40 60 80 100 120 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 µIso [GeV] ∈ 2least B (a) (b)

Figure 4.12: (a) Distribution of the µIso2least variable for signal and for the main backgrounds for the 4µ channel. (b) Discriminating power of the µIso2least variable against tt¯ and Zb¯b backgrounds for the 4µ channel.

Electron Isolation. For electron isolation, tracker based and calorimetric based isolation variables are combined in the following way:

eIso = eIsotrack + eIsoHCAL (4.9)

Track based and calorimeter based isolation variables are deﬁned in AppendixA. As a ﬁnal discriminating observable a sum of the combined variables for two least isolated electrons, eIso2least is used. The distribution of this observable for signal and for the main backgrounds is shown in Fig- ure 4.13(a), while the rejection power against tt¯ and Zb¯b backgrounds is shown in Figure 4.13(b).

The signal efficiency for a cut eIso2least < 0.35 is 96%, while background efficiencies are 39% and 22% for Zb¯b and tt¯ respectively. Efficiencies are calculated with respect to events passing the pre-selection. √ 54 4. The H → ZZ(∗) → 4l channel at s = 10 TeV

S 1.05

H→ZZ*→4e ∈ 2 1 mH = 150 GeV/c 0.95 -1 Zbb 10 tt 0.9 working point 0.85 signal H→ZZ*→4e -2 tt 0.8 10 2 m = 150 GeV/c Fraction of events Zbb H 0.75

0.7

10-3 0.65

0.6 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9∈ 1 eIso 2least B

(a) (b)

Figure 4.13: (a) Distribution of the eIso2least variable for the sum of two least isolated electrons, for signal and for the main backgrounds for the 4e channel. (b) Discriminating power of the eIso2least variable against tt¯ and Zb¯b backgrounds for the 4e channel.

Isolation as a function of lepton pT . Another powerful selection criterion arises from observing the two-dimensional distribution of the isolation observable (from the least isolated or the sum of two least isolated leptons) versus the pT of the third or fourth lepton (sorted by decreasing order of pT ).

This is demonstrated here in the case of the 4µ channel. The µIso2least versus the pT of the 2 third muon pT,3 is shown in Figure 4.14, for a Higgs boson mass of 150 GeV/c and for the Zb¯b background. The signal and the background are well separated, so that the plane can be divided into two regions respectively dominated by the signal or the background. This conclusion has important consequences for the control of background systematics [58].

This separation can be expected, given that the leptons originating from the b-jets have usually

low pT , while those muons from Z (or W ) decays are more energetic. Therefore in Zb¯b (and tt¯)

events, unlike signal events, the third and fourth muons are usually characterized by low pT and larger values of the isolation variable. The cut illustrated in Figure 4.14 is used for all Higgs boson

masses in this analysis, but could possibly be made mH -dependent.

Two-dimensional cuts in eIso2least versus third and fourth electron pT is also used for the 4e analysis. In the case the 2e2µ final states, the two-dimensional cut is applied to the pair with matching flavours (opposite charges) with a reconstructed invariant mass least fitting the Z mass. √ 4. The H → ZZ(∗) → 4l channel at s = 10 TeV 55

60 1

[GeV] 2least 0.9

50 Iso e 2least 0.8 Zbb→ 4µ Zbb→ 4e Iso µ H→ZZ*→ 4µ 0.7 → → 40 H ZZ* 4e 0.6

30 0.5

0.4 20 0.3

0.2 10

0.1

0 0 0 10 20 30 40 50 60 70 80 90 100 0 10 20 30 40 50 60 70 80 90 100

Pt,3[GeV/c] Pt,3[GeV/c]

(a) (b)

Figure 4.14: Distribution of µIso2least and eIso2least versus pT of the third lepton for the Higgs boson mass of 150 GeV/c2 for H → 4µ (left) and H → 4e (right) and for the Zb¯b background. The signal and background regions are best separated by a slanted line of the form e(µ)Iso2least = A · pT,3 + B.

4.4.4.2 Impact parameter

Unlike the signal leptons, the leptons of at least one l+l− pair reconstructed in tt¯ and Zb¯b background events originate from a displaced secondary vertex because of the relatively long b-quark lifetime, and thus should be characterized by larger values of the impact parameter calculated with respect to the event Primary Vertex.

Leptons’ impact parameter can be thus used to build observables that can provide a significant background rejection while retaining the signal. Three different variables relying on the reconstructed impact parameter significance of the four leptons associated to a Higgs boson candidate have been developed.

The background discrimination power of the first two algorithms relies on the impact parameter significance (the impact parameter divided by its uncertainty) of the two leptons with the highest values of significance. A third algorithm, called geometrical discriminant algorithm, provides a single observable based on all the four leptons’ points of closest approach to the beamline. The latter method is based on minimizing the “spatial variance” formed by the 3-D points along each of the track trajectories: the standard deviation of this minimized region of convergence tests how close these tracks approach each other. Here follows detailed description of the first algorithm called “SIP3D”, used in this analysis. To know more on the other algorithms, see Section “Discriminating observables and baseline selection” of Reference [58]. √ 56 4. The H → ZZ(∗) → 4l channel at s = 10 TeV

The Impact parameter signiﬁcance algorithm (SIP3D) is based on the three-dimensional impact parameter signiﬁcance

IP3D SIP (3D) = (4.10) σIP3D

where IP3D is the lepton impact parameter calculated w.r.t the primary vertex and σIP3D is the associated uncertainty. After sorting the SIP (3D) of the four leptons in increasing order, the fourth (i.e. the worst), alone or possibly together with the third (i.e. the second worst), can be used to discriminate signal from background.

1.02 1 S ∈

1 H→ZZ*→4µ

2 Zbb: 3D-ip -1 mH = 150 GeV/c 10 --- Zbb 0.98 tt: 3D-ip --- tt working point: 3D-ip --- signal working point: 3D-ip Fraction of Events 0.96

10-2 0.94

0.92 -3 10 H→ZZ*→4mu 0.9 2 mH = 150 GeV/c

0.88 0 5 10 15 20 25 30 35 40 45 50 0.2 0.4 0.6 0.8 1 S (3D) ∈ IP B

(a) (b)

Figure 4.15: (a) Muon impact parameter signiﬁcance SIP (3D) distribution for the fourth/worst muon, for signal and for the main backgrounds; (b) Rejection power of SIP (3D) cuts on the fourth muon against tt¯ and Zb¯b backgrounds.

Considering for example the 4µ ﬁnal state, the SIP (3D) distribution for the fourth (i.e. worst) is shown in Figure 4.15(a) for signal and for the main backgrounds. The best criterion found th for this channel, when setting the signal eﬃciency at 99%, is to require SIP (3D)(4 µ) < 12. rd Slight improvements could be obtained requiring also SIP (3D)(3 µ) < 4. The rejection power of this combination of SIP (3D) cuts against main backgrounds, after pre-selection, is illustrated in Figure 4.15(b). The method shows the largest rejection power against tt¯ background.

Considering now the 4e ﬁnal state, the SIP (3D) distribution for the fourth/worst electron is shown in Figure 4.16(a) for signal and for the main backgrounds. The best criterion found for this channel, th when setting the signal eﬃciency at 99%, is to require SIP (3D)(4 e) < 5. The SIP (3D) for the third electron is required to be less than 4 to gain rejection power. The main background rejection

power of this SIP (3D) criterium, after pre-selection that includes electron identiﬁcation cuts and loose electron isolation cuts, is illustrated in Figure 4.16(b). √ 4. The H → ZZ(∗) → 4l channel at s = 10 TeV 57

1.02 S ∈

1 H→ZZ*→4e m = 150 GeV/c2 H Zbb: 3D-ip 10-1 --- Zbb 0.98 tt: 3D-ip --- tt working point: 3D-ip --- signal working point: 3D-ip Fraction of Events 0.96

10-2 0.94

0.92

H→ZZ*→4e -3 0.9 2 10 mH = 150 GeV/c

0.88 0 5 10 15 20 25 30 35 40 45 50 0.2 0.4 0.6 0.8 1 S (3D) ∈ IP B

(a) (b)

Figure 4.16: (a) Electron impact parameter signiﬁcance SIP (3D) distribution for the fourth/worst electron, for signal and for the main backgrounds; (b) Rejection power of SIP (3D) cuts on the fourth electron against tt¯ and Zb¯b backgrounds.

1.02 S ∈

0.98

0.96 H→ZZ*→4µ H→ZZ*→2e2µ 0.94 H→ZZ*→4e

0.92 2 mH = 150 GeV/c 0.9

0.88 0.2 0.4 0.6 0.8 1 ∈ B

Figure 4.17: Rejection power of SIP (3D) cuts against tt¯ background for the three ﬁnal states.

Compared to the four muon candidates, the rejection power (after pre-selection) is lower when the fourth lepton is an electron, as can be appreciated in Figure 4.17 for the 2e2µ mode as well. This can be explained either with a relatively larger contribution from fake electrons after pre-selection, and partly with a lower discriminating power when dealing with displaced vertices of true secondary electrons. Tightening the cut on the fourth electron with respect to the fourth muon allows only a partial recovery of background rejection power. √ 58 4. The H → ZZ(∗) → 4l channel at s = 10 TeV

4.4.4.3 Kinematics

Taking advantage of the likely presence of a real Z boson in the ﬁnal state, the selection can be further improved using kinematic requirements. As an example of the discrimination power of a cut on the invariant mass of lepton pairs, distribution of invariant mass is given in Figure 4.18 for the signal and for the main backgrounds. ] ] 2 2 H→ZZ*→2e2µ qq→ZZ(*) 2 H→ZZ*→2e2µ tt 4 After m cut qq→ZZ(*) After Preselection Zbb 1.8 Z Zbb 3.5 tt 1.6 H200 H150 H150 3 1.4

2.5 1.2 1 2 /dm [fb/2 GeV/c

/dm [fb/2 GeV/c 0.8 σ

1.5 σ d

d 0.6 1 0.4 0.5 0.2 0 0 0 20 40 60 80 100 120 140 0 20 40 60 80 100 120 140 2 2 mZ [GeV/c ] mZ* [GeV/c ] (a) (b)

Figure 4.18: (a) Invariant mass of the two leptons closest to the nominal Z mass for the signal and for the main backgrounds, in the 2e2µ channel. (b) Invariant mass of the two highest-pT remaining leptons, opposite charge and maching ﬂavour, in the 2e2µ channel.

4.4.5 Baseline event selection and results

4.4.5.1 Baseline event selection

The lepton isolation observables, the lepton impact parameter observables, the pT of each of the four

leptons, the two-lepton invariant masses and the four-lepton invariant mass m4l can be combined

to optimize the sensitivity to the Higgs boson as a function of the mass hypothesis mH , and for a given integrated luminosity. Such mass dependent cut-based analyses have been discussed in previous studies [68–70] in the context of measurements at L = 30 fb−1 at the LHC. For the start- up integrated luminosity of 1 fb−1 considered in this analysis, and given an improved suppression of the main background sources, it is found suﬃcient to consider a baseline cut-based selection,

leaving only a sliding window cut in the measured m4l spectrum to optimize the sensitivity for a

Higgs boson of given mass mH . This allows for a simple search procedure covering the mass range from ∼ 115 GeV/c2 to ∼ 250 GeV/c2. √ 4. The H → ZZ(∗) → 4l channel at s = 10 TeV 59

An optimal set of discriminating observables, each offering high background rejection power, are combined in a baseline selection. The baseline selection is designed to offer the best significance 2 for the observation of a Higgs boson with a mass around mH ' 150 GeV/c . Simple one-sided cuts are used for the lepton isolation and lepton impact parameter significance, and a low threshold is

imposed for the transverse momentum pT of the leptons. For the two-lepton invariant masses, only

loose cuts are chosen in order to minimize the dependence on mH and therefore obtain a simple

selection which is quasi-optimal for any mH hypothesis in the range considered in this analysis.

The cuts are optimized separately for the searches in the 4e, 4µ and 2e2µ channels. The set of baseline selection cuts for all three channels is given in Table 4.9.

4e 2e2µ 4µ

eIso2least < 0.35 eIso2least < 0.35 or µIso2least < 30 µIso2least < 30 3 3 eIso2least < 0.060 · pT − 0.9 µIso2least < 1.5 · pT − 15 4 4 eIso2least < 0.035 · pT − 0.2 e(µ)Iso2least vs pT : same as 4e/4µ µIso2least < 2.0 · pT − 10 th rd SIP (4 e) < 5 SIP (3 e) < 4 th rd SIP (4 µ) < 12 SIP (3 µ) < 4 e µ pT > 7 GeV/c pT > 5 GeV/c 2 mZ ∈ [50, 100] GeV/c 2 mZ∗ ∈ [20, 100] GeV/c

Table 4.9: Set of baseline selection cuts for all three channels.

The variables e(µ)Iso2least represent the sum of the isolation variable of the two least isolated electrons (muons) in 4e (4µ) channel or the sum of the isolation variable for the two leptons associated to the Z∗ in the 2e2µ channel. The four lepton reconstructed invariant mass spectrum after the baseline selection is shown in Fig- ure 4.19.

The tt¯background is completely eliminated. The Zb¯b background is considerably reduced and only survives towards low masses, with an event rate far below that of the ZZ continuum.

The SM Higgs boson signal expected for L = 1 fb−1 of integrated luminosity is superimposed for illustration in Figure 4.19 for various mass hypothesis. The signal is observed as a narrow peak. The average number of expected signal events is comparable or larger than that expected from the background in a narrow mass window centered on the signal. Thus, after the mH independent

baseline selection, a signal emerges above the background for any particular mH value, over the full mass range. √ 60 4. The H → ZZ(∗) → 4l channel at s = 10 TeV ] ] 2 2 3.5 H→ZZ*→4µ 3.5 H→ZZ*→4e After Selection After Selection → qq→ZZ(*) 3 qq ZZ(*) 3 → gg→ZZ(*) gg ZZ(*) Zbb Zbb 2.5 tt 2.5 tt Z+Jets Z+Jets W+Jets W+Jets 2 QCD 2 QCD H130 H130 H150 H150

1.5/dm [fb/10 GeV/c 1.5/dm [fb/10 GeV/c H200 H200 σ σ H250 H250 d d 1 1

0.5 0.5

0 0 0 50 100 150 200 250 300 350 400 450 500 0 50 100 150 200 250 300 350 400 450 500 2 2 m4e [GeV/c ] m4µ [GeV/c ]

(a) (b) ] 2 3.5 H→ZZ*→2e2µ After Selection → 3 qq ZZ(*) gg→ZZ(*) Zbb 2.5 tt Z+Jets W+Jets 2 QCD H130 H150

1.5/dm [fb/10 GeV/c H200

σ H250 d 1

0.5

0 0 50 100 150 200 250 300 350 400 450 500 2 m2e2µ [GeV/c ]

(c)

Figure 4.19: Four lepton reconstructed invariant mass spectrum after the baseline selection for (a) 4e, (b) 4µ and (c) 2e2µ. The spectrum should be interpreted as the average spectrum expected for an experiment with L = 1 fb−1. The 4l spectrum is composed mostly of the ZZ(∗) continuum and it receives an small contribution from Zb¯b. Superimposed here for illustration is the expectation from a Higgs boson signal for mass hypothesis of 130, 150, 200 and 250 GeV/c2. √ 4. The H → ZZ(∗) → 4l channel at s = 10 TeV 61

4.4.5.2 Analysis results with L = 1 fb−1: a simple counting experiment approach

In order to quantify the sensitivity of the experiment to the presence of a Higgs boson signal, a

simple counting experiment approach is used. For each possible mH hypothesis, the events are

counted in a reconstructed mass window m4l ± 2σm4l.

The reconstructed mass m4l, and hence the central value for the mass window, differs slightly (by less than about 0.5%) from the true Higgs boson mass (mH ), due to the pdf, the final state radiation and a reconstrution bias, as Figure 4.20(a) shows. For simplicity the width σm4l is nevertheless taken here from a Gaussian fit to the signal distribution for each given mH hypothesis. The mass window slides along the measured mass spectrum of Figure 4.19 to test the various possible mH hypothesis. The central value and the width of the sliding window used as a function of mH in each channel is illustrated in Figure 4.20(b).

260 red: 4e-channel

blue: 4 -channel

6 black: 2e2 -channel ( % ) 240

→ → µ σ ) H ZZ* 2e2 1 window 2 True H

4 L = 1 fb-1 2 σ window 220 | / m True H 2 -m

200 Reco H

|m 0

180 mass windowmass (GeV/c -2 4l

160

-4 Signalm

140

-6

120 140 160 180 200 220 240 120 120 140 160 180 200 220 240 260 mTrue (GeV/c2) H 2

Higgs boson mass m (GeV/c )

(a) (b)

Figure 4.20: (a) Diﬀerence between the reconstructed mass m4l and the true mass mH , and ±1 or ±2 σm4l mass window, as a function of mH in the 2e2µ channel. (b) Limits m4l ± 2σm4l of the mass window as a function of mH in the 4e, 4µ and 2e2µ channels.

−1 The number of expected signal and background events as a function of mH evaluated at L = 1 fb

in the m4l ± 2σm4l mass window are reported in Figure 4.21. The expected average number of

observed events (signal plus background, Ns+b) and the expected number of background events −1 (Nb) events evaluated at L = 1 fb in the m4l ± 2σm4l mass window for a selected set of mH masses are given in Table 4.10 on page 64 for the channels 4e, 4µ, and 2e2µ, as well as the total for the three channels lumped together.

The goal of a search is either to exclude the existence of a signal in its absence or to cinﬁrm the existence of a true signal, as strongly as possible, while holding the probabilities of falsely excluding a true signal or falsely discovering a non-existent signal at or below speciﬁed levels. √ 62 4. The H → ZZ(∗) → 4l channel at s = 10 TeV

CMS Preliminary

10 H→ZZ*→4l s = 10 TeV #events

signal at L = 1 fb1 10-1 bkg at L = 1 fb-1

140 160 180 200 220 240 2 mH (GeV/c )

Figure 4.21: Number of expected signal (red markers) and background (blue markers) events −1 for an integrated luminosity of 1 fb in the m4l ± 2σm4l mass window as a function of the Higgs boson mass hypothesis.

The analysis of search results could be formulated in terms of a hypothesis test; the null hypothesis

(H0) is that the signal is absent and the alternate hypothesis (H1) is that it exists. As a ﬁrst step the observables for testing the hypothesis are identiﬁed and in the simplest case the number of candidate events satisfying the full set of analysis criteria is chosen. The number of observed events in data surviving the full H → ZZ(∗) → 4l analysis is compared with the number of expected background events and the number of expected signal events from Standard Model-like Higgs.

Statistical estimators (or test-statistics), functions of the observables and the model parameters are used to probe the hypothesis and rules for exclusion or discovery need to be deﬁned. A typical estimator used in the searches at LEP and Tevatron is the likelihood ratio, which is the ratio of the probability densities for a given experimental result for two alternate hypothesis, deﬁned as the

L(s + b) Q = (4.11) L(b)

where, in case of a counting experiment, L(s + b)(L(b)) are the Poisson distributions with a mean

equal to the number of signal plus background events Ns+b (number of background events Nb). The probability distribution functions of the discriminating variable (the hypothetical Higgs mass) for the signal and background enter in the shape-based analysis not described here. Multiple toy Monte Carlo experiments are run to take into account the ﬂuctuation of the number of signal plus background events (or number of background events) according to the Posson distribution. The mean value of the likelihood ratio in a large number of toy Monte Carlo experiments is taken and bands corresponding to 1 or 2 σ of the Gaussian ﬁt to the distribution of those values are typically √ 4. The H → ZZ(∗) → 4l channel at s = 10 TeV 63 quoted. In the case of multiple channels the likelihood ratio is the product of the individual likelihood ratios for each channel.

The likelihood ratio can be thought of as a generalization of the change in χ2 for a fit to a distribution including signal plus background relative to a fit to a pure background distribution; in the high statistics limit the distribution of the log-likelihood ratio, −2lnQ, is in fact expected to converge toward a ∆χ2 distribution. The significance for the signal observation is estimated √ from the log-likelihood ratio as 2lnQ. The similarity of signal-over-background ratios between the three channels and strongly correlated overall systematic errors allow us to use lumped event counts as a good approximation for calculations. The fact that this does not lead to a loss of

performance is validated by comparing the results of two signiﬁcance estimators: ScL for the total

lumped event count and SL, the three-bin log-likelihood ratio estimator mentioned before. The typical relative diﬀerence is found to be less than 1%.

The significance for the signal observation is converted in an equivalent number of one-sided tail σ of a Gaussian distribution. The significance of an observation needs to be further de-rated by about 1σ unit to take into account the probability of a random fluctuation anywhere in the mass spectrum (the so-called look-elsewhere effect [69]).

In the absence of a signiﬁcant deviation from the background-only hypothesis, an upper limit on (∗) the H → ZZ → 4l cross-section σ in terms of the ratio r = σ/σSM with respect to the expected

cross section for a Standard Model Higgs σSM is set. Upper limits are computed from bayesian method [71] by using a ﬂat prior distribution on the signal cross-section, from a posteriori likelihood function for the ratio r. A limit at 1 means the Standard Model Higgs boson can be excluded at 95% CL.

The upper limit is computed by performing toy Monte Carlo experiments and by evaluating the upper limit every time. The mean of the distribution is then taken.

The treatment of the systematic uncertainties on the number of events is not considered in the following results. At the end, the eﬀect of including systematic errors was found rather small in the previous analysis results at 14 TeV reported in Reference [72].

The average expected number of observed events (signal plus background, Ns+b) and the expected −1 background events (Nb) evaluated at L = 1 fb in the m4l ± 2σm4l mass window for a set of mH masses is given in Table 4.10. The table shows the event counts for individual channels, 4e, 4µ, and 2e2µ, as well as the total for the three channels lumped together. √ 64 4. The H → ZZ(∗) → 4l channel at s = 10 TeV

2 4e 4µ 2e2µ total 4l mH [GeV/c ] Ns+b Nb Ns+b Nb Ns+b Nb Ns+b Nb 115 0.04 0.02 0.07 0.02 0.07 0.02 0.18 0.06 120 0.07 0.02 0.13 0.03 0.15 0.04 0.35 0.09 125 0.15 0.03 0.22 0.04 0.28 0.05 0.66 0.13 130 0.25 0.04 0.39 0.04 0.45 0.07 1.09 0.16 135 0.36 0.05 0.54 0.05 0.67 0.08 1.59 0.18 140 0.49 0.05 0.69 0.05 0.85 0.08 2.03 0.18 145 0.57 0.06 0.78 0.06 1.01 0.08 2.36 0.20 150 0.59 0.07 0.78 0.05 1.05 0.08 2.41 0.20 155 0.53 0.07 0.73 0.06 0.98 0.09 2.24 0.20 160 0.35 0.09 0.42 0.07 0.60 0.10 1.37 0.24 165 0.21 0.11 0.25 0.07 0.37 0.11 0.83 0.25 170 0.23 0.09 0.27 0.09 0.36 0.13 0.87 0.31 175 0.29 0.11 0.34 0.11 0.52 0.17 1.16 0.39 180 0.51 0.19 0.59 0.16 0.84 0.26 1.95 0.61 185 1.12 0.31 1.27 0.30 1.92 0.48 4.32 1.10 190 1.57 0.49 1.85 0.47 2.71 0.76 6.13 1.72 195 1.67 0.53 2.04 0.58 2.79 0.87 6.50 1.98 200 1.76 0.58 2.06 0.58 2.99 0.91 6.81 2.08 205 1.72 0.58 1.95 0.56 3.05 0.94 6.72 2.07 250 1.26 0.39 1.62 0.49 2.36 0.76 5.24 1.64

Table 4.10: Average expected number of observed (signal plus background) and expected back- −1 ground only events for diﬀerent Higgs boson masses at L = 1 fb . Events are counted in mH ±2σm windows around Higgs boson masses.

The expected mean signiﬁcance for the signal observation and the upper limit (UL) on r at 95%

C.L. are given in Table 4.11 for various mH hypothesis. The expected mean signiﬁcance for the signal observation in the 4e, 4µ and 2e2µ channels separately and their combination at L = 1 fb−1 is reported in Figure 4.22(a).

The expected mean significance for the signal observation at L = 1 fb−1 reaches values above two standard deviations (2σ) in a mass range from 135 to 155 GeV/c2 and above 185 GeV/c2. It overcomes 3σ for masses in vicinity of 150 GeV/c2 and 190-200 GeV/c2. Because of the look elesewhere effect the significance has to be derated by one unit but it is not unlikely that an integrated luminosity of 1 fb−1 will yield an observation of a mass peak with an overall significance above 2 σ.

The upper limit on r at 95% C.L. for the 4e, 4µ and 2e2µ channels separately and their combination at 1 fb−1 luminosity are represented in Figure 4.22(b). No Higgs mass hypothesis could be excluded at 95%C.L. in the range speciﬁed but the upper limit on r is coming close to the value of 1 needed for an exclusion at 95% C.L. √ 4. The H → ZZ(∗) → 4l channel at s = 10 TeV 65

2 3.5 10 → → SM → → H ZZ* 4l σ H ZZ* 4l / 3 s = 10 TeV s = 10 TeV Significance L = 1 fb -1 L = 1 fb -1

2.5 95% CL σ

2 r = 10 4e 4µ 1.5 2e2µ combination

1 4e 4µ µ 0.5 2e2 1 combination

0 120 140 160 180 200 220 240 260 120 140 160 180 200 220 240 260 2 2 Higgs mass (GeV/c ) Higgs mass (GeV/c )

(a) (b)

Figure 4.22: (a) Expected mean signiﬁcance for the signal observation for the 4e (green), 4µ (blue) and 2e2µ (magenta) channels, and their combination (black) at L = 1 fb−1. (b) The upper limit on r at 95% C.L. for the 4e (green), 4µ (blue) and 2e2µ (magenta) channels separately and their combination (black) at 1 fb−1 luminosity, at a center-of-mass energy of 10 TeV.

2 mH [GeV/c ] Ns Nb Signiﬁcance UL on r (95% C.L.) 115 0.12 0.06 0.34 24.8 120 0.26 0.09 0.57 12.2 125 0.54 0.12 0.95 4.3 130 0.93 0.16 1.41 1.6 135 1.39 0.18 1.87 1.2 140 1.84 0.18 2.33 1.3 145 2.16 0.20 2.60 1.1 150 2.22 0.20 2.65 1.1 155 2.04 0.20 2.47 1.2 160 1.13 0.24 1.49 1.6 165 0.58 0.25 0.90 4.3 170 0.56 0.31 0.85 4.5 175 0.77 0.39 1.00 2.3 180 1.34 0.61 1.35 1.4 185 3.22 1.10 2.24 1.2 190 4.42 1.72 2.49 1.1 195 4.52 1.98 2.43 1.1 200 4.74 2.07 2.49 1.1 205 4.65 2.07 2.46 1.1 250 3.60 1.64 2.14 1.2

Table 4.11: Number of expected signal and background events, average expected number of signal and background events, average expected signiﬁcance and upper limit on r at 95% C.L. for the combination of the 4e, 4µ and 2e2µ channels, for several Higgs boson masses at 1 fb−1 luminosity.

Chapter 5

The ZZ(∗) → 4l analysis strategy at √ s = 10 TeV

The early observation of the ZZ diboson production at LHC is an important step toward discovering the Higgs boson in the golden decay channel H → ZZ(∗) → 4l.

In addition, a number of Beyond-the-Standard Models predict possible enhancements in the ZZ production either via ZZ-decays of new particles or anomalous triple gauge vector boson couplings, which gives an additional motivation for this measurement.

With the same analysis flow of the H → ZZ(∗) → 4l, described in detail in Chapter4, we can directly measure the ZZ(∗) → 4l cross section with the very first data. The ZZ(∗) → 4l is the irreducible background of H → ZZ(∗) → 4l: 4l stands for 4µ, 4e and 2e2µ. In order to measure the ZZ(∗) → 4l cross section with the very first data and to understand them, the analysis should be as simple as possible. Therefore, a different analysis strategy is presented in this chapter. The goal is to simplify the isolation variable definition and to reduce the complexity of the analysis cuts. Firstly, Section 5.1 shows how the Zb¯b events have been removed from the Z+jets MC samples, avoiding the double counting of Zb¯b events. Starting from the pre-selection discussed in Section 4.4.3, a new set of selection cuts flow is described in Section 5.2. Finally, in Section 5.3 the new results are shown and compared to those obtained with the H → ZZ(∗) → 4l analysis discussed in Chapter4.

67 √ 68 5. The ZZ(∗) → 4l analysis strategy at s = 10 TeV

5.1 Removing Zb¯b from Z+jets samples

The Z+jets samples contain events in which the Z decays into 2e or 2µ and the two jets come from two quarks, which decay leptonically. The quarks q can be any of u, d, s, c and b. Since it is possible in some Z+jets events to have the same ﬁnal state of Zb¯b, we need to remove this double counting from Z+jets simulated samples. The jet-events are classiﬁed as uds, c and b; events containing jets with quarks as u , d , s or c are selected. In Table 5.1 and Table 5.2 the percentage of Zb¯b events removed from Z+jets samples is reported

for each Z pT bin. The percentage of the Zb¯b events removed is calculated as:

processed - selected % removed = · 100 processed where “processed” are all the Z+jets events, “selected” are the events without the b-quark.

pT bin processed selected removed % removed 0 - 15 1022 997 25 2,446 15 - 20 3592 3342 250 6,960 20 - 30 7919 7341 578 7,299 30 - 50 15541 14303 1238 7,966 50 - 80 15730 14485 1245 7,915 80 - 120 22157 20599 1558 7,032 120 - 170 28710 27060 1650 5,747 170 - 230 33480 31873 1607 4,800 230 - 300 36523 35156 1367 3,743 300 - Inf 40844 39773 1071 2,622

Table 5.1: Number of Zb¯b events removed from Z → ee+jets MC samples at 10 TeV.

pT bin processed selected removed % removed 0 - 15 1343 1295 48 3,574 15 - 20 4824 4474 350 7,255 20 - 30 6719 6279 440 6,549 30 - 50 14521 13392 1129 7,775 50 - 80 17307 15953 1354 7,823 80 - 120 45898 42637 3261 7,105 120 - 170 29885 28095 1790 5,990 170 - 230 35008 33330 1678 4,793 230 - 300 38858 37343 1515 3,899 300 - Inf 44776 43622 1154 2,577

Table 5.2: Number of Zb¯b events removed from Z → µµ+jets MC samples at 10 TeV. √ 5. The ZZ(∗) → 4l analysis strategy at s = 10 TeV 69

In Figure 5.1 the percentage of Zb¯b events removed from the Z+jets MC samples is shown as a function of the Z pT bin.

Figure 5.1: Percentage of Zb¯b events removed from Z+jets MC samples as a function of the Z pT bin.

5.2 The selection steps

The analysis described in this chapter is based on the same workflow of the H → ZZ(∗) → 4l analysis. However a different method is used starting from the pre-selection level, for which a new definition of the isolation variable is used and also the cuts applied are different and simpler. The distribution of the invariant mass of the four-lepton system (m4l) after the pre-selection for the three final states considered together is shown in Figure 5.2.1 on page 70.

5.2.1 Z and Z∗ boson invariant mass constraints

First of all, the two Z are requested to be on shell. The mass of the ﬁrst Z candidate has to be: 2 2 80 < MZ < 100 GeV/c and the second Z candidate: 70 < MZ < 110 GeV/c . Figure 5.3 shows

the invariant masses of the ﬁrst and second lepton pairs, labelled Z1 and the Z2 respectively, after the pre-selection cuts. √ 70 5. The ZZ(∗) → 4l analysis strategy at s = 10 TeV

m4l after pre-selection -1 14 4l ZZ* 4µ 4e 2e2µ total Zbb 12 tt ZZ 8.446 5.894 12.642 26,982 Zjet events for 1 fb 10 Zb¯b 17.915 3.352 7.858 29,125 ¯ 8 tt 26.323 8.476 42.729 77,528 Z+jets 4.964 49.272 55.207 109,443 6

4 Table 5.3: Events for the three ﬁnal states after the pre-selection cuts for 1 fb−1. 2 Figure 5.2: Invariant mass distribution of the 0 0 100 200 300 400 500 600 700 800 900 1000 four leptons (m4l) after the pre-selection cuts for m [GeV/c2] 4l the three ﬁnal states.

mZ1 after pre-selection mZ2 after pre-selection -1 -1 30 4l 5 4l ZZ* ZZ* 25 Zbb Zbb tt 4 tt events for 1 fb events for 1 fb Zjet Zjet 20

2 10

1 5

0 0 0 20 40 60 80 100 120 140 160 180 200 0 20 40 60 80 100 120 140 160 180 200 2 2 mZ1 [GeV/c ] mZ2 [GeV/c ]

(a) (b)

Figure 5.3: (a) Invariant mass distribution for the first lepton pair (mZ1) after the pre-selection cuts for the three final states combined together. (b) Invariant mass distribution for the second lepton pair (mZ2) after the pre-selection cuts for the sum of the three final states.

4µ 4e 2e2µ 2 [GeV/c ] ZZ Zbb tt ZZ Zbb tt ZZ Zbb tt

80 < mZ1 < 100 94 % 93 % 37 % 95 % 93 % 43 % 95 % 90 % 21 % 70 < mZ2 < 110 67 % 1.6 % 3.4 % 74 % 4.2 % 18.1 % 80 % 4.2 % 12.9 %

Table 5.4: Eﬃciencies for signal and backgrounds for the invariant mass cuts used for the three ﬁnal states. √ 5. The ZZ(∗) → 4l analysis strategy at s = 10 TeV 71

After the pre-selection cuts, these two additional selection cuts reduce the background to a level of few percent, as shown in Table 5.4. At this point the background eﬃciencies are still large: this is not a problem because it will be possible to remove almost all background after the full selection, without losing performance. Figure 5.2.1 shows the invariant mass distribution of the four leptons

(m4l) after invariant mass cuts for the three ﬁnal states considered together.

m4l after masses cuts -1 4µ 4e 2e2µ total 1.4 4l ZZ* Zbb 1.2 tt ZZ 4.815 3.650 8.584 17.049 Zjet events for 1 fb Zb¯b 0.182 0.085 0.201 0.468 1 tt¯ 0.266 0.293 0.662 1.221 0.8 Z+jets 0.008 2.178 2.721 4.907

0.6 Table 5.5: Events for the three ﬁnal states com- 0.4 bined together after invariant mass cuts for 1 fb−1.

0.2 Figure 5.4: Invariant mass distribution of the

0 four leptons (m4l) after cuts on the invariant 0 100 200 300 400 500 600 700 800 900 1000 2 ∗ m4l [GeV/c ] masses of the Z and Z candidates for the three ﬁnal states considered together.

5.2.2 Cuts on the isolation and the 3D impact parameter signiﬁcance

Following the H → ZZ(∗) → 4l analysis described in Chapter4, the cuts on the isolation variable and on the impact parameter signiﬁcance are now applied. The isolation variable of the least

(worst) isolated lepton, called Xlarge, is used to discriminate signal from background, instead of considering the sum of the isolation variable of the two least isolated leptons. The same is done with the impact parameter signiﬁcance SIP (3D) where only the value for the fourth lepton is chosen. This value will be called Slarge.

5.2.2.1 The new isolation deﬁnition

Let’s remember the deﬁnition of isolation used in Section 4.4.4.1 for the H → ZZ(∗) → 4l analysis:

X tracks e eIso = (eIsotrack + eIsoHCAL) , eIsotrack = pT /pT (5.1) X tracks µIso = 2 · µIsotrack + 1.5 · µIsoECAL + µIsoHCAL , µIsotrack = pT (5.2)

To simplify the variable definition and the complexity of the analysis cuts, we use few and simple cuts in order to not introduce correlations, which are difficult to cope with using the first data and to develop an analysis strategy that can be applied in the same way for all the 4l final states. √ 72 5. The ZZ(∗) → 4l analysis strategy at s = 10 TeV

For this purpose the new deﬁnition of isolation 1, which takes into account the track-based isolation variable only, both for e and µ, is:

P track eIso = µIso = pT = X (5.3)

(a) (b)

(c)

Figure 5.5: S vs B for diﬀerent values of the isolation cut for the three ﬁnal states: (a) 4µ, (b) 4e and (c) 2e2µ. In blue ZZ vs Zb¯b and in red ZZ vs tt¯. The chosen working point (?) is Xlarge < 12 GeV.

In Figure 5.5 the signal efficiency as a function of the background efficiency (S vs B) is shown for different values of the isolation cut for the three final states after the pre-selection cuts. In Table 5.6

1 The track-based isolation is not divided by the electron pT . Further details on the isolation algorithms can be found in AppendixA. √ 5. The ZZ(∗) → 4l analysis strategy at s = 10 TeV 73

S and B are shown, requiring for all three ﬁnal states: Xlarge < 12 GeV. Figure 5.6 shows the distribution of the isolation variable for the three ﬁnal states after the pre-selection cuts.

4µ 4e 2e2µ

ZZ Zbb tt ZZ Zbb tt ZZ Zbb tt 98 % 79 % 65 % 99 % 89 % 55 % 99 % 78 % 57 %

Table 5.6: Eﬃciencies for signal and backgrounds for the isolation cut used for the three ﬁnal states for Xlarge < 12 GeV

X after pre-selection large Xlarge after pre-selection -1 10 -1 ZZ* 4µ 4e Zbb tt ZZ* 1 Zjet 1 Zbb tt events for 1 fb events for 1 fb Zjet 10-1 10-1

10-2 10-2

10-3 10-3

10-4 0 5 10 15 20 25 30 0 5 10 15 20 25 30 35 40

Xlarge [GeV] Xlarge [GeV]

(a) (b)

Xlarge after pre-selection -1 ZZ* 10 µ Zbb 2e2 tt Zjet

1 events for 1 fb

10-1

10-2

10-3

10-4

0 5 10 15 20 25 30 35 40

Xlarge [GeV]

(c)

Figure 5.6: Distribution of the isolation variable Xlarge after the pre-selection cuts for the three ﬁnal states: (a) 4µ, (b) 4e and (c) 2e2µ. The vertical black line indicates the cut used. √ 74 5. The ZZ(∗) → 4l analysis strategy at s = 10 TeV

5.2.2.2 The impact parameter signiﬁcance cut

Instead of using both the third and the fourth leptons to cut on the impact parameter signiﬁcance

as described in Chapter4, only the largest impact parameter significance (S large) of the three lepton is used. In Figure 5.7 the signal efficiency as a function of the background efficiency (S vs B) is shown for different values of the impact parameter significance cut for the three final states after the pre-selection cuts. In Table 5.7 S and B are shown, requiring for all three final states: Slarge < 5.

(a) (b)

(c)

Figure 5.7: S vs B for different values of the impact parameter significance cut for the three final states: (a) 4µ, (b) 4e and (c) 2e2µ. In blue ZZ vs Zb¯b and in red ZZ vs tt¯. The chosen working point is Slarge < 5. √ 5. The ZZ(∗) → 4l analysis strategy at s = 10 TeV 75

4µ 4e 2e2µ

ZZ Zbb tt ZZ Zbb tt ZZ Zbb tt 96 % 19 % 14 % 96 % 48 % 37 % 97 % 29 % 22 %

Table 5.7: Efficiencies for signal and background for the impact parameter significance cut used for the three final states for Slarge < 5.

Figure 5.8 shows the distribution of the impact parameter signiﬁcance of the fourth lepton for the three ﬁnal states after the pre-selection cuts.

Slarge after pre-selection Slarge after pre-selection -1 -1 ZZ* 10 ZZ* 4µ Zbb 4e Zbb tt 1 tt Zjet 1 Zjet events for 1 fb events for 1 fb

10-1 10-1

10-2 10-2

-3 10 -3 10

10-4 10-4

0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40

Slarge Slarge

(a) (b)

Slarge after pre-selection -1 ZZ* 10 µ 2e2 Zbb tt Zjet 1 events for 1 fb

10-1

10-2

10-3

10-4

0 5 10 15 20 25 30 35 40

Slarge

(c)

Figure 5.8: Distribution of the impact parameter signiﬁcance Slarge after the pre-selection cuts for the three ﬁnal states: (a) 4µ, (b) 4e and (c) 2e2µ. The vertical black line indicates the cut used. √ 76 5. The ZZ(∗) → 4l analysis strategy at s = 10 TeV

The number of the remaining events after applying the kinematic cuts for signal and background is shown in Table 5.8, Table 5.9 and Table 5.10. X[0] is the worst isolated lepton, while X[1] is the second worst isolated lepton. S[0] is the fourth lepton with the biggest value of the impact parameter signiﬁcance. S[1] is the third lepton in increasing order of impact parameter signiﬁcance. A comparison between the analysis discussed in crefch:hzz and this one is shown in the following tables.

variable (H → ZZ(∗) → 4l)(ZZ(∗) → 4l) µIso X[0] + X[1] < 30 X[0] < 12 µSIP(3D) S[0] < 12, S[1] < 4 S[0] < 5 Background ZZ Zb¯b tt¯ Z+jets ZZ Zb¯b tt¯ Z+jets Events for 1 fb−1 4.735 0.028 0 0 4.749 0.027 0.004 0.004

Table 5.8: Remaining events after kinematic cuts for signal and background for 1 fb−1 for the 4µ ﬁnal state. On the left the results are relative to the H → ZZ(∗) → 4l analysis and on the right to the ZZ(∗) → 4l.

variable (H → ZZ(∗) → 4l)(ZZ(∗) → 4l) eIso X[0] + X[1] < 0.35 X[0] < 12 eSIP(3D) S[0] < 5, S[1] < 4 S[0] < 5 Background ZZ Zb¯b tt¯ Z+jets ZZ Zb¯b tt¯ Z+jets Events for 1 fb−1 3.469 0.003 0 - 3.490 0.016 0.013 0

Table 5.9: Remaining events after kinematic cuts for signal and background for 1 fb−1 for the 4e ﬁnal state.

variable (H → ZZ(∗) → 4l)(ZZ(∗) → 4l) µIso X[0] + X[1] < 30 X[0] < 12 eIso X[0] + X[1] < 0.35 µS (3D) S[0] < 12, S[1] < 4 IP S[0] < 5 eSIP(3D) S[0] < 5, S[1] < 4 Background ZZ Zb¯b tt¯ Z+jets ZZ Zb¯b tt¯ Z+jets Events for 1 fb−1 8.218 0.020 0.039 - 8.327 0.037 0.120 0.049

Table 5.10: Remaining events after kinematic cuts for signal and background for 1 fb−1 for the 2e2µ ﬁnal state.

Figure 5.9 shows the invariant mass distribution of the four lepton system (m4l) after kinematic cuts for the three ﬁnal states separetely (a)(b)(c), and combined together (d). √ 5. The ZZ(∗) → 4l analysis strategy at s = 10 TeV 77

m4l after kinematics cuts m4l after kinematics cuts -1 -1 0.2 0.14 4µ ZZ* 4e ZZ* 0.18 Zbb 0.12 Zbb 0.16 tt tt Zjet Zjet events for 1 fb events for 1 fb 0.14 0.1

0.12 0.08 0.1

0.06 0.08

0.06 0.04

0.04 0.02 0.02

0 0 0 100 200 300 400 500 600 700 800 900 1000 0 100 200 300 400 500 600 700 800 900 1000 2 2 m4l [GeV/c ] m4l [GeV/c ]

(a) (b)

m4l after kinematics cuts m4l after kinematics cuts -1 -1 0.35 0.6 2e2µ ZZ* 4l ZZ* 0.3 Zbb Zbb 0.5 tt tt Zjet Zjet events for 1 fb 0.25 events for 1 fb 0.4

0.2 0.3

0.15

0.2 0.1

0.1 0.05

0 0 0 100 200 300 400 500 600 700 800 900 1000 0 100 200 300 400 500 600 700 800 900 1000 2 2 m4l [GeV/c ] m4l [GeV/c ]

Figure 5.9: Invariant mass distribution of the four lepton system (m4l) after kinematic cuts for the three ﬁnal states: (a) 4µ, (b) 4e, (c) 2e2µ and (d) the three ﬁnal states combined together.

5.2.3 The 2D cut

After applying all the kinematic cuts, it is possible to suppress the background rates a little more by considering another powerful selection criterion: the two-dimensional distribution of the isolation variable (Xlarge) as a function of the pT of the third or fourth lepton (sorted by decreasing order of pT ). √ 78 5. The ZZ(∗) → 4l analysis strategy at s = 10 TeV

rd 5.2.4 Cut on the pT of the 3 isolated lepton

The distribution of Xlarge as a function of the pT of the third lepton pT,3 is shown in Figure 5.10, for the signal ZZ and the backgrounds: Zb¯b, tt¯, Z+jets.

(a) (b)

Figure 5.10: Distribution of Xlarge as a function of the pT of the third lepton for the three ﬁnal states: (a) µ, (b) 4e, (c) 2e2µ for muons and (d) 2e2µ for electrons.

The number of the surviving events after applying the ﬁrst 2-D cut (Xlarge vs pT,3) for signal and

background is shown in Table 5.11, Table 5.12 and Table 5.13. The m4l distribution after the ﬁrst 2-D cut for the three ﬁnal states combined together is shown in Figure 5.11. √ 5. The ZZ(∗) → 4l analysis strategy at s = 10 TeV 79

variable (H → ZZ(∗) → 4l)(ZZ(∗) → 4l)

µIso(pT,3) X[0] + X[1] < (1.5 · pT,3 − 15) X[0] < (0.37 · pT,3 − 3.7) Background ZZ Zb¯b tt¯ Z+jets ZZ Zb¯b tt¯ Z+jets Events for 1 fb−1 4.698 0.006 0 0 4.696 0.004 0 0

Table 5.11: Remaining events after the ﬁrst 2-D cut (Xlarge vs pT,3) for signal and backgrounds for 1 fb−1 in the 4µ ﬁnal state.

variable (H → ZZ(∗) → 4l)(ZZ(∗) → 4l)

eIso(pT,3) X[0] + X[1] < (0.006 · pT,3 − 0.9) X[0] < (0.14 · pT,3 − 1.1) Background ZZ Zb¯b tt¯ Z+jets ZZ Zb¯b tt¯ Z+jets Events for 1 fb−1 3.445 0.003 0 0 3.319 0.002 0 0

Table 5.12: Remaining events after the ﬁrst 2-D cut (Xlarge vs pT,3) for signal and backgrounds for 1 fb−1 in the 4e ﬁnal state.

variable (H → ZZ(∗) → 4l)(ZZ(∗) → 4l)

µIso(pT,3) X[0] + X[1] < (1.5 · pT,3 − 15) X[0] < (0.075 · pT,3 + 5.5) eIso(pT,3) X[0] + X[1] < (0.006 · pT,3 − 0.9) X[0] < (0.075 · pT,3 + 0.8) Background ZZ Zb¯b tt¯ Z+jets ZZ Zb¯b tt¯ Z+jets Events for 1 fb−1 8.153 0.011 0.036 0 8.062 0.006 0.031 0

Table 5.13: Remaining events after the ﬁrst 2-D cut (Xlarge vs pT,3) for signal and backgrounds for 1 fb−1 in the 2e2µ ﬁnal state.

m4l after the full selection

-1 0.6 4l ZZ* 0.5 Zbb tt Zjet events for 1 fb 0.4

0.3

0.2

0.1

0 0 100 200 300 400 500 600 700 800 900 1000 2 m4l [GeV/c ]

Figure 5.11: Invariant mass distribution of the four lepton system (m4l) after the ﬁrst 2-D cut (Xlarge vs pT,3) for signal and backgrounds for the three ﬁnal states combined together. √ 80 5. The ZZ(∗) → 4l analysis strategy at s = 10 TeV

th 5.2.5 Cut on the pT of the 4 isolated lepton

The distribution of Xlarge as a function of the pT of the fourth leptons pT,4 is shown in Figure 5.12, for ZZ and all the backgrounds.

(a) (b)

Figure 5.12: Distribution of Xlarge as a function of the pT of the fourth lepton for the three ﬁnal states: (a) µ, (b) 4e, (c) 2e2µ for muons and (d) 2e2µ for electrons.

The number of the remaining events after applying the second 2-D cut (Xlarge vs pT,4) for signal and background is shown in Table 5.14, Table 5.15 and Table 5.16. √ 5. The ZZ(∗) → 4l analysis strategy at s = 10 TeV 81

variable (H → ZZ(∗) → 4l)(ZZ(∗) → 4l)

µIso(pT,4) X[0] + X[1] < (2 · pT,4 − 10) X[0] < (1.5 · pT,4 − 7.5) Background ZZ Zb¯b tt¯ Z+jets ZZ Zb¯b tt¯ Z+jets Events for 1 fb−1 4.614 0.003 0 0 4.669 0.001 0 0

Table 5.14: Remaining events after the second 2-D cut (Xlarge vs pT,4) for signal and backgrounds for 1 fb−1 in the 4µ ﬁnal state.

variable (H → ZZ(∗) → 4l)(ZZ(∗) → 4l)

eIso(pT,4) X[0] + X[1] < (0.035 · pT,4 − 0.2) X[0] < (0.24 · pT,4 − 2.4) Background ZZ Zb¯b tt¯ Z+jets ZZ Zb¯b tt¯ Z+jets Events for 1 fb−1 3.413 0.003 0 0 3.234 0.002 0 0

Table 5.15: Remaining events after the second 2-D cut (Xlarge vs pT,4) for signal and backgrounds for 1 fb−1 in the 4e ﬁnal state.

variable (H → ZZ(∗) → 4l)(ZZ(∗) → 4l)

µIso(pT,4) X[0] + X[1] < (2 · pT,4 − 10) X[0] < (0.36 · pT,4 + 1.09) eIso(pT,4) X[0] + X[1] < (0.035 · pT,4 − 0.2) X[0] < (0.3 · pT,4 − 1) Background ZZ Zb¯b tt¯ Z+jets ZZ Zb¯b tt¯ Z+jets Events for 1 fb−1 8.043 0.009 0.027 0 8.011 0.005 0.027 0

Table 5.16: Remaining events after the second 2-D cut (Xlarge vs pT,4) for signal and backgrounds for 1 fb−1 in the 2e2µ ﬁnal state.

5.3 Results after the full selection

After applying the selection cuts described in this chapter, 16 ZZ events and 0.035 background events are expected for an integrated luminosity of 1 fb−1, as detailed in Table 5.17. The uncertainties on the number of the surviving events are computed as:

p σN = w ∗ Ntotal

Ntotal is the number of surviving events (not-weighted) after the full selection. w is the event weight calculated as in Equation 4.3:

σ ∗ filter ∗ K ∗ skim w = Nskim

Figure 5.13 shows the mZ1, mZ2 and m4l distributions after the second 2-D cut (Xlarge vs pT,4) for signal and backgrounds for the three ﬁnal states combined together. √ 82 5. The ZZ(∗) → 4l analysis strategy at s = 10 TeV

mZ1 after the full selection mZ2 after the full selection

-1 -1 4

9 ZZ* ZZ* 3.5 8 Zbb Zbb tt tt 3 7 Zjet Zjet events for 1 fb events for 1 fb

6 2.5

5 4l 2 4l

4 1.5 3 1 2

0.5 1

0 0 0 20 40 60 80 100 120 140 160 180 200 0 20 40 60 80 100 120 140 160 180 200 2 2 mZ1 [GeV/c ] mZ2 [GeV/c ]

(a) (b)

m4l after the full selection

-1 0.6 4l ZZ* 0.5 Zbb tt Zjet events for 1 fb 0.4

0.3

0.2

0.1

0 0 100 200 300 400 500 600 700 800 900 1000 2 m4l [GeV/c ]

(c)

Figure 5.13: Invariant mass distributions after the second 2-D cut (Xlarge vs pT,4) for signal and backgrounds for the three ﬁnal states combined together: (a) mZ1, (b) mZ2 and (c) m4l

4µ 4e 2e2µ Total ZZ 4.669 ± 0.025 3.234 ± 0.016 8.011 ± 0.026 15.914 ± 0.039 Zb¯b 0.0012 ± 0.0008 0.0025 ± 0.0012 0.0049 ± 0.0017 0.0086 ± 0.0022 tt¯ 0. ± 0.0044 0. ± 0.0044 0.0266 ± 0.0109 0.0266 ± 0.0126 Z+jets 0. 0. 0. 0.

Table 5.17: Number of background events after the full selection. √ 5. The ZZ(∗) → 4l analysis strategy at s = 10 TeV 83

5.3.1 Combined signiﬁcance for ZZ(∗) → 4l

Combining the three ﬁnal states together, an estimate of the minimal luminosity needed to “re- √ discover” the diboson ZZ production at LHC at s = 10 TeV can be obtained.

The likelihood ratio Q is estimated using Poisson distributions:

poisson(S + B,S + B) Q = (5.4) poisson(B,S + B) where S is the number of signal events, B is the number of the background events. The Poisson distribution is:

e−µ · µn poisson(µ, n) = (5.5) n! where µ is the mean of the distribution and n is the number of observed events. The likelihood ratio Q is computed separately for each channel, and a total likelihood is obtaind as the product:

Qtot = Q4µ · Q4e · Q2e2µ. The signiﬁcance S is deﬁned as:

p S = 2 · ln(Qtot) (5.6)

The systematic uncertainty on this measurement is estimated in exactly the same way as for the Higgs boson analysis (See Section “Systematic uncertainties” of Reference [58]). Figure 5.14 shows the signiﬁcance of the ZZ(∗) → 4l signal as a function of the integrated luminosity after the full selection.

significance (profile likelihood) 6 3σ : 49 pb-1

-1 4 5σ : 136 pb

0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 integrated luminosity (fb-1)

(∗) Figure 5.14: Signiﬁcance for ZZ → 4l √as a function of the integrated luminosity (L) collected at s = 10 TeV.

Chapter 6

Control of Zb¯b and tt¯ backgrounds from data

A contamination of Zb¯b and tt¯ events remains after the pre-selection, and a small amount of such events will survive the “baseline” selection cuts of Section 4.4.5 used for the final analysis. An appropriate strategy is therefore needed to control the contamination of these processes from data. The control of the Zb¯b and tt¯ event rate in the signal phase space profits from the strategy used at selection level to reject such process. This task is fulfilled by finding a kinematic region where the signal and backgrounds are well discriminated (control region). In this region the signal is removed and one can measure only the background. In this way the background can be estimated in the signal region, using the data.

6.1 Deﬁnition of the control region

√ In the Higgs boson analysis at s = 14 TeV the combination of the isolation of the two least isolated leptons with the pT of the third lepton was used to separate the background from the signal. The √ analysis presented in this thesis, which is done at s = 10 TeV, uses a diﬀerent method: the control region for measuring Zb¯b and tt¯ background is deﬁned by inverting and relaxing some simple cuts, which are described below.

K The invariant mass of any four lepton combinations (m4l) is requested to be larger than 100 GeV/c2, in order to suppress possible remaining QCD background. 2 K The mass of the oﬀ-mass shell Z boson (mZ2) is required to be less than 60 GeV/c in order to suppress the ZZ events. K The isolation value of the least isolated lepton (Xlarge) is requested to be larger than 5 GeV. K The largest impact parameter signiﬁcance of the lepton (Slarge) is requested to be larger than 4.

85 86 6. Control of Zb¯b and tt¯ backgrounds from data

After applying these cuts, the invariant mass of the on-mass shell Z boson (mZ1) is computed and two contributions can be easily disentangled: the Z mass peak of the Zb¯b and Z+jets events and the non-resonant tt¯ contribution. The ZZ events are fully suppressed.

The ﬁnal distribution of the invariant mass of the on-mass shell Z boson after the full selection for the three individual channels is shown in Figure 6.1.

mZ1 after selection mZ1 after selection -1 -1

10 ZZ* 10 ZZ* Zbb Zbb tt tt events for 1 fb events for 1 fb 8 Zjet 8 Zjet

6 6

4µ 4e 4 4

2 2

0 0 0 20 40 60 80 100 120 140 160 180 200 0 20 40 60 80 100 120 140 160 180 200 2 2 mZ1 [GeV/c ] mZ1 [GeV/c ]

(a) (b)

mZ1 after selection -1

25 ZZ* Zbb tt events for 1 fb 20 Zjet

2e2µ 10

0 0 20 40 60 80 100 120 140 160 180 200 2 mZ1 [GeV/c ]

(c)

Figure 6.1: mZ1 distribution after the full selection for the three channels: (a) 4µ, (b) 4e and (c) 2e2µ. The bin width is 4 GeV. 6. Control of Zb¯b and tt¯ backgrounds from data 87

The largest fraction of the selected Zb¯b events comes from the final state with four muons, due to the very small number of jets faking muons. The final state with four electrons has more Z+jets events than Zb¯b events 1. This channel will be not included in the fit, because the contribution of the Zb¯b background is very small (Table 6.1).

6.1.1 The 3µ1e channel

In order to increase the Zb¯b background statistics for a more precise measurement in an early stage of the experiment, the final state with three leptons of the same flavour and one lepton of a different flavour can be added to the four muons case. The final distribution of the invariant mass of the on-mass shell Z boson after the full selection for the 3µ1e channel is shown in Figure 6.2.

mZ1 after selection -1 20

18 ZZ* 16 Zbb tt events for 1 fb 14 Zjet

10 µ 8 3 1e

0 0 20 40 60 80 100 120 140 160 180 200 2 mZ1 [GeV/c ]

Figure 6.2: Distribution of the on-shell Z mass (mZ1) after the full selection for the 3µ1e channel. The bin width is 4 GeV.

4µ 4e 2e2µ 3µ1e total ZZ 0.018 0.064 0.100 0.059 0.257 Zb¯b 14.9 3.05 16.6 13.7 48.3 tt¯ 50.4 17.5 117.3 105.1 290.0 Z+jets 3.7 29.3 39.1 25.2 97.3

Table 6.1: Events in the control region after the full selection for 1 fb−1.

1Work is ongoing to improve electron reconstruction and identiﬁcation. It is expected that in a future reprocessing it will be possible to extend the study to the four electrons channel. 88 6. Control of Zb¯b and tt¯ backgrounds from data

6.2 Fitting the mZ1 distribution

By ﬁtting at the same time the tt¯ and the Zb¯b plus Z+jets contributions with a sum of one Crystal Ball and one Gaussian, the two contributions can thus be measured from the data themselves. The results of the ﬁt are shown in Figure 6.3.

mZ1 after selection mZ1 after selection -1 60 -1 20

18 ZZ* ZZ* 50 Zbb 16 Zbb tt tt events for 1 fb events for 1 fb 14 40 Zjet Zjet 12

30 10 µ µ µ 4 +2e2 +3 1e 8 3µ1e 20 6

4 10 2

0 0 0 20 40 60 80 100 120 140 160 180 200 0 20 40 60 80 100 120 140 160 180 200 2 2 mZ1 [GeV/c ] mZ1 [GeV/c ]

(a) (b)

Figure 6.3: Measured invariant mass of the on-mass shell Z candidate (mZ1) for the events in the control region, for the sum of the 4µ, 2e2µ and 3µ1e channels (a) and for the 3µ1e channel (b). The dashed line corresponds to the best ﬁt with a sum of one Crystal Ball and one Gaussian. The bin width is 4 GeV.

The number of events resulting from the best ﬁt with two gaussian is shown in Table 6.2.

4µ+2e2µ+3µ1e 3µ1e +19.4 +11.9 tt¯ 291.3−18.7 115.8−11.2

¯ +13.4 +7.2 Zbb + Zjet 93.7−12.3 27.2−6.3

Table 6.2: Events resulting from the best ﬁt to the mZ1 distribution after the full selection with 1 fb−1 of integrated luminosity.

The number of events resulting from the best ﬁt needs to normalized the background expected events in the segnal region. The number of background events measured from LHC data in the control region will be multiplied by the ratio of the expected background events in the segnal region taken from the MC and the background events in the control region from the MC.

SR SR NMC CR Ndata = CR · Ndata (6.1) NMC 6. Control of Zb¯b and tt¯ backgrounds from data 89 where SR is the segnal region and CR the control region.

The systematic uncertainty on the expected number of events in the mZ1 distribution can be estimated by performing many pseudo-experiments, while varying the number of initial expected events with a Poisson distribution. The estimated total error is ∼ 30%, taking into account also the uncertainty on the Z+jets contribution which has not been separated from the Zb¯b background yet. A similar strategy to control the Zb¯b and tt¯ backgrounds can be found in Reference [72].

Conclusions

The subject of this thesis is a study of the ZZ channel with the CMS experiment at the LHC. It is based on the H → ZZ(∗) → 4l analysis, described in Chapter4, focusing on the direct observation of ZZ production in the fully leptonic final states (Chapter5). This analysis is performed at √ s = 10 TeV for an integrated luminosity of 1 fb−1. The main goal is to develop a uniform strategy for all the three final states (4µ, 4e and 2e2µ) to be applied to the first LHC data. In particular, it is intended to be a basic study of the irreducible ZZ background of the Higgs “golden channel”, H → ZZ(∗) → 4l. Also, a simple method to control Zb¯b and tt¯ backgrounds of ZZ from data is presented (Chapter6). The ZZ analysis is focused on the first period of data-taking at the LHC, because it uses few simple cuts, thus avoiding correlations which would be difficult to understand with the first data. This work has been carried out using the official CMS software framework, CMSSW, and an advanced and powerful distributed computing tool, the Grid [73].

For what concerns my work on the direct observation of ZZ production, I developed an even simpler analysis, by simplifing the cuts and the isolation variable definition. The selection is made using only the track-based isolation criterion, instead of the isolation criteria definition used in Reference [58]. The analysis presented in this thesis allows a large fraction of ZZ(∗) → 4l events to be retained within the CMS detector acceptance, while suppressing the dominant backgrounds to essentially √ negligible level. At s = 10 TeV with 1 fb−1 of data, one should expect in total about 16 ZZ(∗) → 4l events, where 4l stands for the 4µ, 4e and 2e2µ final states, and 0.03 background events. Assuming that the present estimate of the background level is correct, a 3σ significance for √ the production of ZZ could be reached with only 49 pb−1 at s = 10 TeV expecting only 0.78 ZZ events, while 136 pb−1 are needed for a 5σ significance with 2.18 ZZ events. I presented this analysis at CERN in the CMS Higgs subgroup meetings [74] and in the CMS ElectroWeak Multiboson Group meetings [75].

In Chapter6, I present a study for a complete data-driven method used for the ZZ(∗) → 4l analysis, in order to derive the expected number of background and signal events at the same time. The method allows a separate estimate of the number of tt¯ and Zb¯b/Z+jets events.

91 92 Conclusions

The method consists in selecting the events by reverting and relaxing some simple cuts and ﬁtting

the mZ1 distribution with a sum of one Crystal Ball and one Gaussian. Finally, summing all the final states together, the best fit of the on-mass shell Z mass distribution, considering the sum of +19.4 +13.4 ¯ the 4µ, 2e2µ and 3µ1e final states, predicts 291.3 −18.7 tt¯ events and 93.7 −12.3 Zbb plus Z+jets events for 1 fb−1 luminosity. These are the total number of tt¯ and Zb¯b plus Z+jets events that can be used as a control sample. In the next reprocessing with an updated version of the CMS software, it will be possible to extend this study to the four electrons channel.

The software and computing tools I used for this study were a significant part of my work, in terms of learning time and development, testing and validation effort. In particular, I have contributed to the development of part of the Higgs software for the H → ZZ(∗) → 4l analysis. I have developed the code for the final state 3µ1e, in which two muons with opposite signs are originated by the Z decay and the other two leptons come from the b-quark decays. Adding this final state to the others, I could obtain a larger Zb¯b background control sample, improving the result of the fit of the on-shell mass Z peak. If we consider only the 3µ1e final state, the best fit of the on-mass shell +11.9 +7.2 ¯ −1 Z mass distribution predicts 115.8 −11.2 tt¯ events and 27.2 −6.3 Zbb plus Z+jets events for 1 fb luminosity.

On March 30th 2010, the Large Hadron Collider (LHC) at CERN has, for the ﬁrst time, collided two beams of 3.5 TeV protons, a new world energy record. The LHC experiments successfully detected these collisions, marking the beginning of the LHC physics programme. The data were quickly stored and processed by huge farms of computers at CERN before being delivered to collaborating particle physicists all over the world for further detailed analysis.

This is the moment all particle physicists around the world have been waiting for and preparing for many years. As soon as they have ”re-discovered” the known Standard Model particles, a necessary step prior to looking for new physics, the LHC experiments will start the systematic search for the Higgs boson, as well as for particles predicted by new theories such as Supersymmetry. A study of the known particles of the Standard Model is already started, to obtain a precise evaluation of the LHC detectors response and to measure accurately all possible backgrounds to new physics. We will have soon enough events for the observation of the ZZ(∗) → 4l process and then, hopefully, for H → ZZ(∗) → 4l. With the amount of data expected, the combined analysis of ATLAS and CMS will be able to explore a wide mass range, and there is a chance of discovery if the Higgs boson has a mass near 160 GeV/c2.

CERN will operate the LHC for 18-24 months with the objective of delivering enough data to the experiments to make signiﬁcant advances across a wide range of physics channels. Following this run, the LHC will be shutdown for routine maintenance, and to complete the repairs and consolidation work needed to reach the LHC design energy of 14 TeV. Conclusions 93

Two years of continuous running is a signiﬁcant task for both the LHC operators and the experiments. By starting with a long run and concentrating the preparations for 14 TeV collisions into a single shutdown, the overall running time over the next three years is maximized, recovering the delay of the LHC programme and giving the experiments the chance to make their mark.

Appendix A

Isolation algorithm

A.1 Electron isolation

Track based isolation:

p 2 2 An isolation cone of size Riso = ∆η + ∆φ is deﬁned around the electron direction. The tracks falling inside a narrower signal “internal veto cone” with size Rveto < Riso around the electron direction, as well as the candidate electron track itself are discarded for the calculation of the isolation observable. Within the isolation cone, the reconstructed tracks (excluding the ones belonging to pre-selected electron candidates) satisfying the loose quality requirements listed in Table A.1 and originating from the same vertex as the candidate electron are considered. Tracks from muons in the isolation cone of the electron are not considered for the computation of the isolation variable in order to avoid to discard events with a pair of close electron-muon, candidate signal for 2e2µ channel.

number of hits ≥ 10 [8, 9] [5, 7]

pT (GeV/c) > 1 > 1 > 1

d0 (cm) < 1 < 0.2 < 0.04

dz (cm) < 5 < 2 < 0.5

d0/σd0 – < 10 < 7

dz/σdz – < 10 < 7

Table A.1: The minimal track quality requirements for tracks considered in electron and muon isolation algorithms for diﬀerent track categories. The cut values are given for the lower pT threshold as well as for the longitudinal distance dz and the transverse distance d0, normalized or not

by their respective errors σdZ and σd0 . The distances are calculated at the track impact point (of closest approach to the z axis) with respect to the vertex.

95 96 A. Isolation algorithm

The quality requirements are designed to remove as many fake tracks as possible while preserving the highest possible efficiency for real tracks coming from the reconstructed primary vertex [76, 77]. They rely on a categorization of the tracks by the number of associated track hits, and make use of both transverse and longitudinal impact measurements. This is meant to better preserve the signal efficiency when compared to previous studies [70] where a single and more stringent cut, on the difference between the track longitudinal impact parameter and the z position of the primary vertex, was used for all tracks.

The isolation requirement is imposed on the transverse momentum sum of the considered tracks P tracks e divided by the electron transverse momentum, pT /pT , which is found to offer the best per- e formances in the pT range characteristic of the electrons from from Higgs boson decay, and for a wide range of possible Higgs boson masses. All parameters of the isolation, size of internal and external cones, and the lower pT threshold, have been optimized to provide the best tt¯ and Zb¯b rejection for a high signal efficiency. The values Riso = 0.25 and Rveto = 0.015, for tracks with P tracks e pT > 1 GeV/c are found as best working point when considering a pT /pT cut for a 4e signal efficiency in the range from 99 to 90% (see Section 4.4.3 on event pre-selection and Section 4.4.4 on discriminating observables for the analysis).

The distributions of track based isolation variable is shown in Figure A.1(a) for H → ZZ → 4e events and tt¯ events where leptons coming from b-jets are not isolated.

Calorimeter based isolation:

Isolated electrons are expected to have their superclusters in the ECAL surrounded by negligible additional deposits of energy, and to be accompanied by negligible energy deposits in the hadronic calorimeter (HCAL). The usage of the ECAL for electron isolation requires special care given the presence of internal bremsstrahlung (from fermions involved in the interaction process) and external bremsstrahlung (from ﬁnal state electrons traversing the tracker material) and the high probability of secondary photon conversion within the tracker volume.

As will be seen in Section 4.4.3, the QCD and Z+jets backgrounds can be largely suppressed at pre-selection with track based isolation observable alone. The baseline selection strategy deployed in this analysis and presented in Section 4.4.5 further succeeds in suppressing all remaining dis- tinguishable background sources, while maintaining a very high signal detection eﬃciency. The ECAL information for lepton isolation which could provide additional rejection power against fake leptons is not needed in this analysis and can be kept as a tool for sanity checks. One advantage is that the question of the eventual usage of internal bremsstrahlung recovery algorithms can be postponed to later stages (i.e. beyond pre-selection) of the analysis. Further studies for the usage of ECAL isolation in the H → 4l analysis are ongoing 1.

1New isolation algorithms exploiting the ECAL information have been made available recently in version 2 of the CMSSW software and are not used in this analysis. A. Isolation algorithm 97

The isolation using information from the HCAL is found to be a powerful tool in complement to track based isolation for the suppression of backgrounds involving “fake” primary electrons from p 2 2 QCD jets. Within the chosen track isolation cone of size Riso = ∆η + ∆φ = 0.25, all hadronic calorimeter towers satisfying ET > 0.5 GeV are considered. The hadronic isolation requirement is imposed on the transverse momentum sum of the considered HCAL towers divided by the electron transverse momentum.

The distributions of the calorimeter based isolation variable is reported in Figure A.1(b) for H → ZZ → 4e events and tt¯ events.

Both track based (eIsotrack) and HCAL based (eIsoHCAL) isolations are combined in a single isolation variable for ﬁnal analysis. Performance of this combination is described in Section 4.4.4.1.

Higgs Higgs

a.u. 1 a.u. 1

tt→4l tt→4l

10-1 10-1

10-2 10-2

10-3 10-3

-4 -4 10 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 10 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 Track isolation HCAL isolation

(a) (b)

Figure A.1: Track (a) and HCAL (b) isolation variable distributions for muons from H → ZZ → 4e events and tt¯ events.

A.2 Muon isolation

Similarly as in the case of electrons, an isolation cone is deﬁned in the η - φ space around the p 2 2 muon with cone radius Riso = ∆η + ∆φ . An inner cone is also deﬁned around the muon, in order to subtract the track (and energy deposits) of the muon itself from the overall amount. The sizes of both the isolation and the inner veto cones have been optimized for this analysis and the

values Riso = 0.3 and Rveto = 0.015 is found to provide the best working point for applications at pre-selection (see Section 4.4.3) and event analysis (see Section 4.4.4).

If two or more muons fall in the same isolation cone, the contributions of the extra muon(s) is subtracted. Electrons in the isolation cone of the muon are subtracted to keep events with close pair of electron-muon for 2e2µ analysis. 98 A. Isolation algorithm

Thresholds on the pT , on the radial and longitudinal impact parameters of the tracks and on the corresponding significancies have also been optimized. Their goal is to suppress fake tracks and they depend on the number of hits per track: a track is more likely to be a real one if it is made by a large number of track hits. Impact parameter selections are very effective especially against Zb¯b background. The efficiency of these cuts is estimated to be at the level of 98%. The sum of the deposits inside an isolation cone runs only over the tracks that survive these cuts.

Higgs Higgs 1

a.u. 1 a.u.

tt→4l tt→4l -1 10-1 10

-2 10-2 10

-3 10-3 10

-4 -4 10 0 10 20 30 40 50 10 0 5 10 15 20 25 30 Track isolation [GeV] ECAL isolation [GeV]

(a) (b)

Higgs

a.u. 1

tt→4l

10-1

10-2

10-3

-4 10 0 5 10 15 20 25 30 HCAL isolation [GeV]

(c)

Figure A.2: Track (a), ECAL (b) and HCAL (c) isolation variable distributions for muons from H → ZZ → 4µ events and tt¯.

The calorimeter-based observables refer to the ECAL (µIsoECAL) or to HCAL (µIsoHCAL) deposits in the cone around the muon track. An improvement of the isolation eﬃciency can be achieved by using α · µIsoECAL + µIsoHCAL, where α = 1.5 is found as optimal. The distributions of tracker- based and calorimenter-based isolation variables are shown in Figure A.2 for H → ZZ → 4µ events and tt¯ events where leptons coming form b-jets are not isolated. Both track based (µIsotrack) and calorimeter based isolations are combined in a single isolation variable for the ﬁnal muon selection. The performance of this combination is described in Section 4.4.4.1. Appendix B

Lepton reconstruction and identiﬁcation

B.1 Electrons

The standard collection of the “pixelMatchGsfElectrons” from the CMSSW reconstruction version 2.2.13 is used [51]. This incorporates improvements in the detailed steering of the reconstruction algorithm with respect to those used in the CMS Physics Technical Design Report [78], but the essential strategy described in [79] is maintained. However, a more realistic description of the tracker has been achieved, leading to a signiﬁcant increase in the material budget. The algorithm is brieﬂy described here for completeness.

B.1.0.1 Electron reconstruction

The reconstruction starts with the reconstruction of superclusters in the ECAL. A threshold of 1

GeV on the transverse energy ET is applied on a seed cluster to initiate supercluster building. In this procedure, clusters which lie within a φ road of extension up to 3 rad in both directions are then added in order to better collect bremsstrahlung. The ECAL supercluster is used to select trajectory seeds built from the combination of hits in the innermost tracker layers by inferring the hit position in the tracker layer from the measured supercluster energy and position. The seeding algorithm combines pixel and tracker endcap (TEC) layers so as to increase the efficiency in the forward region, where the pixel coverage is limited. The seed filtering is made by matching the supercluster with the tracker seed’s hit positions in the two corresponding layers, taking into account both e > charge hypotheses. The overall procedure was optimized for electrons down to pT ∼ 5 GeV/c. Starting from the tracker seed, a trajectory is created. The track building relies on the Bethe- Heitler modelling of the electron energy losses and a loose χ2 cut is used to efficiently collect

99 100 B. Lepton reconstruction and identiﬁcation

tracker hits up to the ECAL front face. A Gaussian Sum Filter (GSF) is applied for the forward and backward fits. The track momentum is taken from the most probable value of the mixture of the Gaussian distributions available for each hit position. This procedure allows to efficiently build electron tracks while maintaining good momentum resolution. The relative difference between the

momenta measured at both track ends, fbrem = (pin − pout)/pin is a measure of the fraction of the electron initial energy emitted via bremsstrahlung in the tracker [79].

The ﬁtted electron track together with the supercluster used to initiate the track are then associated to form an “electron object” if the following requirements are satisﬁed:

extrap. K |∆ηin| = |ηsc − ηin | < 0.02, where ηsc is the energy weighted position in η of the super- extrap. cluster and ηin is the η coordinate of the position of closest approach to the supercluster position, extrapolating from the innermost track position and direction

extrap. K |∆φin| = |φsc − φin | < 0.1, where ∆φin is a quantity similar as the preceeding one but in azimuthal coordinates

K max(Hi/E) < 0.1, where Hi is the energy deposited in the HCAL towers behind each sub- cluster i and E the energy of the electromagnetic supercluster

K ET > 4 GeV/c, where ET is the transverse energy of the electromagnetic supercluser

Compared to previous versions, a cut on Esc/pin, where Esc is the supercluster energy and pin the

track momentum at the innermost track position, is no longer requested. The pT cut has also been

slightly lowered and applied in supercluster ET rather than electron pT to account for threshold eﬀects. These requirements are designed to maintain high eﬃciency at the reconstruction stage while keeping the purity of the reconstructed object at a reasonable level.

Ambiguities in the cases where several GSF tracks are associated to the same supercluster or where two diﬀerent superclusters are associated with the same GSF track, and which occur with a

probability of 1-2% for electrons, are resolved by chosing the best Esc/pin matching.

e e The electron reconstruction efficiency is shown in Figure B.1 as a function of pT and η for the 2 electrons coming from Higgs boson events at mH = 150 GeV/c . It is computed by matching the generated electrons with the reconstructed ones, with a spatial ∆R(η, φ) requirement (<0.07). The e > efficiency steeply rises and reaches a plateau around 92% for pT ∼ 25 GeV/c. The efficiency is e < 94% for |η | ∼ 1.1 and decreases towards the edge of the tracker acceptance when approaching |ηe| ' 2.5. At |ηe| > 2, the efficiency loss is mainly due to the limited coverage of the entire tracker which extends up to |η| = 2.4. B. Lepton reconstruction and identification 101

1 1

0.9 0.9

0.8 0.8

0.7 0.7

0.6 0.6

0.5 0.5

0.4 0.4 Electron efficiency Electron efficiency 0.3 0.3

0.2 0.2 H→ZZ*→4e m =150 GeV/c2 H→ZZ*→4e m =150 GeV/c2 0.1 H 0.1 H

0 0 -3 -2 -1 0 1 2 3 0 10 20 30 40 50 60 70 80 90 100 ηe pe [GeV/c] T (a) (b)

2 e Figure B.1: Electron reconstruction eﬃciency for mH = 150 GeV/c : (a) as a function of pT ; (b) as a function of ηe.

After the preselection of the electron candidates, a charge mis-identification probability per electron candidate of about 1.5% is observed (e.g. for electrons from a Higgs boson signal). This is caused by a bremsstrahlung photon conversion close to the primary electron track and in the innermost layers of the silicon tracker. The inclusion of TEC layers in the seeding procedure increases the efficiency for conversions. The tighter electron identification requirements and impact matching to the interaction vertex that will be used for this analysis slightly diminish the probability that an event which could contribute to the signal efficiency is rejected by lepton charge requirements alone.

Studies have been performed and signiﬁcant improvement is obtained for the charge determination by combining several charge estimates but corresponding algorithm is only available from CMSSW 3 1 X onwards.

The fbrem, E/p and the number of the supercluster sub-clusters, sensitive to the amount of bremsstrahlung photons radiated along the electron trajectory and to the pattern of photon emis- sion and conversions, are used to classify electrons. Class-dependent electron energy measurement corrections are applied. The initial electron momentum direction is taken from the track. Depend- ing on the class and on the E/p range, the ECAL corrected supercluster energy or the tracker momentum or the weighted mean of both measurements is used to estimate the initial electron momentum. Weights are evaluated using class-dependant errors available for each reconstructed electron.

The purity is then increased by applying an electron identiﬁcation algorithm on electron candidates coming out of the reconstruction step. 102 B. Lepton reconstruction and identiﬁcation

B.1.0.2 Electron identiﬁcation

The final selection of electron candidates is performed using a cut-based approach with tighter requirements on electron identification observables. A standard CMSSW algorithm is used with cuts specifically tuned for the purpose of this analysis where the very highest electron reconstruction efficiency must be preserved, whilst providing a reduction of the background sources involving “fake” primary electrons.

The algorithm makes use of matching observables involving track parameters at both the outermost and the innermost track positions as well as shower shape observables. The electron classification is used to apply a different set of cuts for the different electron topologies. The following observables are used in the electron identification algorithm:

K |∆ηin|

K |∆φin|

K H/E

K Σ9/Σ25, where Σ9(25) is the sum of the 9(25) crystal energies centered on the hottest crystal of the seed cluster

K Eseed/pout, where Eseed is the seed cluster energy and pout the track momentum at the outermost track position

Figure B.2 presents the distributions of the electron identification observables H/E and of Eseed/pout 2 for electrons from the Higgs boson signal (mH = 150 GeV/c ) and fakes from the QCD background, after cuts on all other electron identification variables have been applied (so called “N-1 distributions”). The set of cut values for electron identification used in this analysis are listed in Table B.1. The electron candidates are organized in classes following the nomenclature introduced in Refer- ence [79].

The H/E distribution is shown for electrons in the golden class while the Eseed/pout is shown for electrons in the showering class. The discriminating power of these variables is clear. The threshold eﬀect visible at ∼ 0.5 in the Eseed/pout distribution for QCD events is due to the pixel match ﬁltering.

B.2 Muons

The description of the CMS Muon System, of the muon reconstruction and identiﬁcation and their performance can be found in references [80, 81]. B. Lepton reconstruction and identiﬁcation 103

Higgs (n-1) dist Higgs (n-1) dist

a.u. 1 a.u. 0.16 QCD (n-1) dist QCD (n-1) dist

0.14 QCD QCD 0.12 10-1 0.1

0.08 10-2 0.06

0.04 10-3 0.02

0 0 0.02 0.04 0.06 0.08 0.1 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 H/E Eseed/pout

(a) (b)

Figure B.2: N-1 distributions (see text) of electron identiﬁcation variables for the Higgs boson signal (plain-green histograms) and fakes from QCD background (solid-black lines): H/E for the seed out golden class (a) and ET /pT for the showering class (b). Distributions without any electron identiﬁcation cut are also shown for the background (dashed-red line).

golden bigbrem narrow showering H/E < 0.06 0.06 0.07 0.08 | ∆ηin| < 0.005 0.008 0.008 0.009 | ∆φin| < 0.02 0.06 0.06 0.08 Eseed/pout > 0.7-2.5 1.7 0.9-2.2 0.6 P P 9 / 25 > (barrel) 0.8 0.7 0.7 0.5 P P 9 / 25 > (endcaps) 0.8 0.8 0.8 0.5

Table B.1: Value of cuts on electron identiﬁcation variables for “loose” conﬁguration. The “golden”, “bigbrem”, “narrow” and “showering” categories follow the nomenclature introduced in Reference [79].

The reconstruction of the so-called “global muons” is done in two separate steps. First, so-called standalone muons are reconstructed inside the muon chambers (DT and CSC). Afterward, the standalone muons get extrapolated to the tracker and eventually combined with tracker hits. A combined global fit of tracker hits and standalone muon then results in a global muon. A standalone muon is reconstructed by first performing local reconstruction, joining hits within a single station into segments. Ambiguities are resolved by choosing the segment with the largest number of hits and the smallest χ2. The segment reconstruction is done separately in the rφ and rz projections. The final step is to combine these two projections into a 3D segment. Using a Kalman filter technique from the inside out, segments in the various stations of the muon systems then get combined into standalone muons, taking into account energy loss, multiple scattering and the non- uniformity of the magnetic field in the muon system. Finally, the standalone track gets extrapolated to the nominal interaction point and thus its parameters get further constrained. The standalone muon gets extrapolated to the outer surface of the tracker and tracker hits inside the region of 104 B. Lepton reconstruction and identification

interest are combined to form initial track trajectories. Moving from the inside out, all matching hits get added to this trajectory. In a ﬁnal step the trajectory that is most compatible with

the standalone muons gets selected. Global reconstruction improves the muons pT resolution by a factor of ∼ 10 compared to the standalone reconstruction. “Global muons” have been used, > presenting an eﬃciency above 97% over most of the η region and for pT ∼ 5 GeV/c.

In addition to “global muons” the possibility to use the muons identiﬁed considering all silicon tracker tracks and looking for compatible signatures in the muon system (segments), so-called

“tracker muons” [81], is investigated, expecially to recover signal events with low pT leptons at low Higgs boson mass.

In Figure B.3 the eﬃciency as a function of the muon transverse momentum pT in the muon system barrel and momentum p in the muon endcap is shown; the contribution of “tracker muons” is illustrated by a zoom of the eﬃciency at very low pT (p).

(a) (b)

Figure B.3: Global muon reconstruction eﬃciency as a function of pT for |η| < 1.1 (a) and p for 1.1 < |η| < 2.4 (b). The smaller graphs show the diﬀerences between global and tracker muons at very low (transverse) momentum.

B.2.1 The “tracker muon” selection

In the construction of a “tracker muon” the association between muon chamber segments and silicon tracker tracks is kept very loose by design so these objects should be used only with further requirements as described in Reference [82], in order to reduce the background due to decays in ﬂight and punch-through. B. Lepton reconstruction and identiﬁcation 105

Quality conditions on “tracker muons” are typically used to keep the rate of fake tracks low, and are based on the following variables:

K “arbitration”: the pattern recognition process which assigns each segment uniquely to a single tracker muon;

K “TM2DCompatibility”: a simple selection of muon candidates based on the calorimeter and segment-based compatibility values: a two-dimensional distribution of the calorimeter-based versus segment-based compatibility values for muon candidates is built.

K “TMOneStation”: to be used in conjunction with the “TMLastStation” algorithms to recover

eﬃciency at low pT in the central region by requiring a single matched segment. For |η| <

1.2, pT > 8 GeV/c a cut-based selection at low pT optimized for high eﬃciency would use “TMOneStationLoose” or “TMOneStationTight” variables;

K transverse impact parameter at the closest approach point (d0);

K longitudinal impact parameter at the closest approach point (dZ);

K χ2 of track;

K number of hits on the track.

Appendix C

The Standard Model and the Higgs mechanism

The fundamental components of matter and their interactions are nowadays best described by the SM, which is based upon two separate quantum ﬁeld theories, describing the electroweak interaction (Glashow-Weinberg-Salam model or GWS) and the strong interaction (QCD). In this chapter, a short overview of the SM (Section C.1) and of the electroweak theory (Section C.2) is given, focusing the attention on the EWSB, the Higgs mechanism and the Higgs boson (Section C.3).

In the following, natural units are used, so it will always be ~ = c = 1, unless clearly speciﬁed.

C.1 The Standard Model of elementary particles

The SM [83] describes the matter as composed by twelve elementary particles, the fermions, all having half-integer spin. The fermions can be divided into two main groups, leptons and quarks, whose classiﬁcation is given in Table C.1. Quarks are subject to both strong and electroweak interactions and do not exist as free states, but only as constituents of a wide class of particles, the hadrons, such as protons and neutrons. Leptons, instead, only interact by electromagnetic and weak forces.

Fermions 1st fam. 2nd fam. 3rd fam. Charge Interactions u c t +2/3 Quarks All d s b −1/3 e µ τ −1 Weak, E.M. Leptons νe νµ ντ 0 Weak

Table C.1: Classiﬁcation of the three families of fundamental fermions.

107 108 C. The Standard Model and the Higgs mechanism

In the SM, the interactions between particles are described in terms of the exchange of bosons, integer-spin particles which are carriers of the fundamental interactions. The main characteristics of bosons and corresponding interactions are summarized in Table C.2 (the gravitational interaction is not taken into account, as it is not relevant at the scales of mass and distance typical of the particle physics).

Force Electromagnetic Weak Strong Quantum Photon (γ) W ±, Z Gluons Mass [GeV] 0 80–90 0

Coupling 2 1 −5 −2 α(Q = 0) ≈ G ≈ 1.2 · 10 GeV αs(M ) ≈ 0.1 constant 137 F Z

Range [cm] ∞ 10−16 10−13

Table C.2: Fundamental interactions in particle physics and corresponding carriers.

As previously mentioned, the SM describes these interactions by means of two gauge theories: the QCD and the theory of the electroweak interaction (GWS model), which uniﬁes the electromagnetic and weak interactions. Since the present work deals with a purely electroweak decay, in the next sections only the latter theory will be described in some detail.

C.2 The electroweak theory

From a historical point of view, the starting point for the study of electroweak interactions is Fermi’s theory of muon decay [84], which is based on an eﬀective four-fermion Lagrangian 1:

4GF α 1 − γ5 1 − γ5 L = − √ ν¯µγ µeγ¯ α νe (C.1) 2 2 2

−5 −2 with GF ' 1.16639 × 10 GeV . Equation C.1 represents a “point like” interaction, with only one vertex and without any intermediate boson exchanged. It is usually referred to as V − A 1 interaction, being formed by a vectorial and an axial component. The term 2 (1 − γ5) that appears in it is the negative helicity projector. Only negative helicity (left-handed) component of fermions takes part to this interaction.

Fermi’s Lagrangian is not renormalizable and it results in a non-unitary S matrix. Both problems of renormalizability and unitarity can be overcome describing the weak interaction by a gauge theory, i.e. requiring its Lagrangian to be invariant under local transformations generated by the elements of some Lie group (gauge transformations). The speciﬁc group of local invariance (gauge

1The same formalism can also be used to treat β decays, starting from a Lagrangian similar to Equation C.1. C. The Standard Model and the Higgs mechanism 109 group) is to be determined by the phenomenological properties of the interaction and of the particles involved. In particular, the resulting Lagrangian must reduce to Equation C.1 in the low energy limit. A detailed derivation of this Lagrangian is not provided in this work, but the results are summarized in the following (for details about the GWS model, see [85][86][87]).

A gauge theory for weak interactions is conceived as an extension of the theory of electromagnetic interaction, the QED, which is based on the gauge group U(1)EM , associated to the conserved quantum number Q (electric charge). In this case, the condition of local invariance under the

U(1)EM group leads to the existence of a massless vector ﬁeld, the photon.

A theory reproducing both the electromagnetic and weak interaction phenomenology is achieved

by extending the gauge symmetry to the group SU(2)I ⊗ U(1)Y (in this sense, the weak and electromagnetic interactions are said to be uniﬁed). The generators of SU(2)I are the three components a 1 a a of the weak isospin operator, t = 2 τ , where τ are the Pauli matrices. The generator of U(1)Y is the weak hypercharge Y operator. The corresponding quantum numbers satisfy

Y Q = I3 + (C.2) 2

3 where I3 is the third component of the weak isospin (eigenvalue of t ).

Fermions can be divided in doublets of negative-helicity (left-handed) particles and singlets of positive-helicity (right-handed) particles, as follows:

! ! ν`,L uL LL = , `R ,QL = , uR , dR (C.3) `L dL

where ` = e, µ, τ, u = u, c, t and d = d, s, b. Neutrinos have no right component, as their mass is

≈ 0. In Table C.3, I3, Y and Q quantum numbers of all fermions are reported.

I3 YQ uL 1/2 1/3 2/3 dL −1/2 1/3 −1/3

uR, dR 0, 0 4/3, −2/3 2/3, −1/3 ν`,L 1/2 −1 0 `L −1/2 −1 −1

`R 0 −2 −1

Table C.3: Isospin (I3), hypercharge (Y ) and electric charge (Q) of all fermions.

As well as for QED, the requirement of local gauge invariance with respect to the SU(2)I ⊗ U(1)Y 1,2,3 group introduces now four massless vector fields (gauge fields), Wµ and Bµ, which couple to 0 fermions with two different coupling constants, g and g . Notice that Bµ does not represent the 110 C. The Standard Model and the Higgs mechanism

photon ﬁeld, because it arises from the U(1)Y group of hypercharge, instead of U(1)EM group of electric charge. The gauge-invariant Lagrangian for fermion ﬁelds can be written as follows:

µ a 1 0 µ 1 0 L = ΨLγ i∂µ + gtaWµ − 2 g YBµ ΨL + ψRγ i∂µ − 2 g YBµ ψR (C.4)

where ! ψ1 Ψ = L (C.5) L 2 ψL

and where ΨL and ψR are summed over all the possibilities in Equation C.3.

1,2,3 As already stated, Wµ and Bµ do not represent physical ﬁelds, which are given instead by linear combinations of the four mentioned ﬁelds: the charged bosons W + and W − correspond to2

r 1 W ± = (W 1 ∓ iW 2) (C.6) µ 2 µ µ while the neutral bosons γ and Z correspond to

3 Aµ = Bµ cos θW + Wµ sin θW (C.7) 3 Zµ = −Bµ sin θW + Wµ cos θW (C.8)

3 obtained by mixing the neutral ﬁelds Wµ and Bµ with a rotation deﬁned by the Weinberg angle

θW . In terms of the ﬁelds in Equation C.6 and Equation C.8, the interaction term between gauge ﬁelds and fermions, taken from the Lagrangian in Equation C.4, becomes

1 + (+)α − (−)α 1p 02 2 Z α EM α Lint = √ g(Jα W + Jα W ) + g + g Jα Z − eJα A (C.9) 2 2 2

where J EM is the electromagnetic current coupling to the photon ﬁeld, while J +, J − and J Z are the three weak isospin currents. It is found that

Z 3 2 EM Jα = Jα − 2 sin θW · Jα (C.10)

Aµ can then be identiﬁed with the photon ﬁeld and, requiring the coupling terms to be equal, one obtains

0 g sin θW = g cos θW = e (C.11)

which represents the electroweak unification. The GWS model thus predicts the existence of two charged gauge fields, which only couple to left-handed fermions, and two neutral gauge fields, which interact with both left- and right-handed components.

2 (−) (+) † In the following, a diﬀerent notation will be also used: Wµ = Wµ, Wµ = Wµ. C. The Standard Model and the Higgs mechanism 111

C.3 The Higgs mechanism

In order to correctly reproduce the phenomenology of weak interactions, both fermion and gauge boson ﬁelds must acquire mass, in agreement with experimental results. Up to this point, however, all particles are considered massless: in the electroweak Lagrangian, in fact, a mass term for the gauge bosons would violate gauge invariance 3, which is needed to ensure the renormalizability of the theory. Masses are thus introduced with the Higgs mechanism [88], which allows fermions and W ±, Z bosons to be massive, while keeping the photon massless. Such mechanism is accomplished by means of a doublet of complex scalar ﬁelds

! ! φ+ 1 φ1 + iφ2 φ = = √ (C.12) φ0 2 φ3 + iφ4 which is introduced in the electroweak Lagrangian within the term

µ † † LEWSB = (D φ) (Dµφ) + V (φ φ) (C.13)

a i 0 where Dµ = ∂µ −igtaWµ + 2 g YBµ is the covariant derivative. The Lagrangian in Equation C.13 is invariant under SU(2)I ⊗ U(1)Y transformations, since the kinetic part is written in terms of covariant derivatives and the potential V only depends on the product φ†φ. The φ ﬁeld is characterized by the following quantum numbers:

I3 YQ ! ! ! ! φ+ 1/2 1 1 φ0 −1/2 1 0

Writing the potential term as follows (see also Figure C.1)

V (φ†φ) = −µ2φ†φ − λ(φ†φ)2 (C.14)

with µ2 < 0 and λ > 0, it results to have a minimum for

1 µ2 v2 φ†φ = (φ2 + φ2 + φ2 + φ2) = − ≡ (C.15) 2 1 2 3 4 2λ 2

This minimum is not found for a single value of φ, but for a manifold of non-zero values. The choice of (φ+,φ0) corresponding to the ground state (i.e. the lowest energy state, or vacuum) is arbitrary and the chosen point is not invariant under rotations in the (φ+,φ0) plane: this is referred to as spontaneous symmetry breaking. If one chooses to ﬁx the ground state on the φ0 axis, the vacuum

3Explicit mass terms for fermions would not violate gauge invariance, but in the GWS model the Lagrangian is also required to preserve invariance under chirality transformations, and this is achieved only with massless fermions. 112 C. The Standard Model and the Higgs mechanism

expectation value of the φ ﬁeld is

! 1 0 µ2 hφi = √ , v2 = − (C.16) 2 v λ

Figure C.1: Shape of the Higgs boson potential of Equation C.14.

The φ ﬁeld can thus be rewritten in a generic gauge, in terms of its vacuum expectation value:

! 1 i φat 0 φ = √ e v a , a = 1, 2, 3 (C.17) 2 H + v where the three fields φa and the fourth φ4 = H + v are called Goldstone fields. Being scalar and massless, they introduce four new degrees of freedom, in addition to the six degrees due to the transverse polarizations of the massless vector bosons W ± and Z. The unitary gauge is fixed by the transformation ! ! 0 − i φat 1 0 1 0 φ = e v a φ = √ = √ (C.18) 2 H + v 2 φ4

The remaining ﬁeld, the Higgs boson ﬁeld, has now a zero expectation value.

Rewriting the Lagrangian in Equation C.13 with the φ ﬁeld in the unitary gauge, LEWSB results from the sum of three terms:

LEWSB = LH + LHW + LHZ (C.19) C. The Standard Model and the Higgs mechanism 113 where the three terms can be written as follows, using the approximation V ∼ µ2H2 + cost and neglecting higher order terms:

1 α 2 2 LH = ∂αH∂ H + µ H 2 1 2 2 †α 1 2 †α LHW = v g WαW + vg HWαW (C.20) 4 2 2 †α †α = mW WαW + gHW HWαW 1 2 2 02 α 1 2 02 α LHZ = v (g + g )ZαZ + v(g + g )HZαZ (C.21) 8 4 1 2 α 1 α = M ZαZ + gHZ HZαZ 2 Z 2

Equation C.20 and Equation C.21 now contain mass terms for W ± and Z: each of the three gauge bosons has acquired mass and an additional degree of freedom, corresponding to the longitudinal polarization. At the same time, three of the four Goldstone bosons have disappeared from the

Lagrangian LEWSB, thus preserving the total number of degrees of freedom: the degrees linked to the missing Goldstone bosons have become the longitudinal degrees of the vector bosons. Only the H scalar ﬁeld is still present and has acquired mass itself: it is the Higgs boson.

Summarizing, the Higgs mechanism is used to introduce the weak boson masses without explicitly breaking the gauge invariance and thus preserving the renormalizability of the theory. When a symmetry is “spontaneously” broken, in fact, it is not properly eliminated: it is rather “hidden” by the choice of the ground state. It can be shown that the minimum for the Higgs boson ﬁeld is still invariant for the U(1)EM group: the electromagnetic symmetry is therefore unbroken and the photon remains massless.

C.3.1 Vector boson masses and couplings

Equation C.20 and Equation C.21 show that the masses of vector bosons W ± and Z are related to the parameter v, characteristic of the EWSB, and to the electroweak coupling constants:

( 1 MW = 2 vg MW g p → = p = cos θW (C.22) 1 2 02 MZ 2 02 MZ = 2 v g + g g + g

Also the couplings of vector bosons to the Higgs boson can be obtained from Equation C.20

and Equation C.21 and are found to depend on the square of MW and MZ :

1 2 2 2 gHW = vg = M (C.23) 2 v W

1 2 02 2 2 gHZ = v(g + g ) = M (C.24) 2 v Z 114 C. The Standard Model and the Higgs mechanism

A relation between decay ratios of Higgs boson to a W pair and to a Z pair can be derived from Equation C.23 and Equation C.24:

2 + − ! 2 2 BR(H → W W ) gHW MW = 1 = 4 2 ∼ 3 (C.25) BR(H → ZZ) 2 gHZ MZ

Finally, the EWSB energy scale can be determined from the relation between the v parameter and the Fermi constant GF :

1 1 2 v = √ ' 246 GeV (C.26) 2GF

C.3.2 Fermion masses and couplings

The Higgs mechanism is also used to generate the fermion masses, by introducing in the SM

Lagrangian a SU(2)I ⊗ U(1)Y invariant term (called Yukawa term) that represents the interaction between the Higgs boson and the fermion ﬁelds. Since φ is an isodoublet, while the fermions are divided in left-handed doublet and right-handed singlet, the Yukawa terms (one for each fermion generation) must have the following expression for leptons:

† L` = −GH` · l`φ`R + `Rφ l` (C.27)

In the unitary gauge, the ﬁrst component of φ is zero, therefore a mass term will arise from the

Yukawa Lagrangian only for the second component of l`: this correctly reproduces the fact that neutrino is (approximately) massless.

GH` GH` L` = − √ v`` − √ H`` (C.28) 2 2

For what concerns the quark ﬁelds, the down quarks (d, s, b) are treated in the same way as leptons; up quarks (u, c, t), instead, must couple to the charge-conjugate of φ

3 4 ! c ∗ 1 φ − iφ φ = −iτ2φ = √ (C.29) 2 −φ1 + iφ4 which becomes in the unitary gauge

! 1 η + v φc = √ (C.30) 2 0 C. The Standard Model and the Higgs mechanism 115

The Yukawa Lagrangian will be therefore

c LY = −GH`LLφ`R − GHdQLφdR − GHuQLφ uR + h.c. (C.31)

From Equation C.28, the mass of a fermion (apart from neutrinos) and its coupling constant to the Higgs boson are found to be

GHf mf = √ v (C.32) 2

GHf mf gHf = √ = (C.33) 2 v

Being the GHf free parameters, the mass of the fermions cannot be predicted by the theory.

List of Figures

1.1 Red line: triviality bound (for different upper limits to λ); blue line: vacuum stability (or metastability) bound on the Higgs boson mass as a function of the new physics (or cut-off) scale Λ [1]...... 4 1.2 ∆χ2 of the fit to the electroweak precision measurements of LEP, SLC and Tevatron as a function of the Higgs boson mass (August 2009). The solid line represents the result of the fit and the blue shaded band is the theoretical error from unknown higher-order corrections. The yellow area represents the region excluded by direct search...... 5 1.3 Higgs boson production mechanisms at tree level in proton-proton collisions: (a) gluon-gluon fusion; (b) VV fusion; (c) W and Z associated production (or Hig- gsstrahlung); (d) tt¯ associated production...... 6 √ 1.4 Higgs boson production cross sections at s = 14 TeV as a function of its mass..7 1.5 Branching ratios for different Higgs boson decay channels as a function of the Higgs boson mass...... 9 1.6 Higgs boson total decay width as a function of its mass...... 11

2.1 Scheme of the Large Hadron Collider site at CERN, near Geneva...... 19 2.2 The LHC tunnel...... 21 2.3 The CERN accelerators complex...... 22 2.4 Cross sections and event rates of several processes as a function of the centre of mass energy of p − p collisions [40]...... 24 2.5 CTEQ4M PDFs for Q2 = 20 GeV2 and Q2 = 104 GeV2...... 25

3.1 The CMS detector...... 27 3.2 Tracker Inner Barrel view and Tracker Outer Barrel double-sided rod...... 28 3.3 r-z view of a quadrant of the silicon part of the Tracker...... 28 3.4 The Electromagnetic Calorimeter Barrel (EB) supermodules of CMS...... 29 3.5 A trapezoidal and quasi-projective crystal of CMS ECAL...... 29 3.6 The Hadron Calorimeter of CMS is being installed in the solenoid...... 30 3.7 HCAL view in r-z plane...... 31 3.8 The CMS superconducting magnet...... 32 3.9 Muon chambers wheels are prepared above the CMS pit...... 33 3.10 Muon track in the CMS detector...... 34

4.1 Total cross section for Higgs boson production as a function of its mass...... 37 4.2 Fraction of events with four generated leptons in the detector acceptance in the three ﬁnal states for the Higgs decay...... 38 4.3 Feynman diagram for qq → ZZ → 4l process at the tree level...... 38 4.4 Mass-dependent Next-to-Leading-Order K-factor...... 39

117 118 List of Figures

4.5 (a) Differential cross-section for gg → ZZ(∗) as a function of the four lepton invariant mass for different flavour lepton pairs; (b) Ratio of gg → ZZ(∗) and qq¯ → ZZ(∗) (LO) as a function of the invariant mass of the four leptons system...... 40 4.6 Feynman box diagram for gg → ZZ(∗) → 4l process...... 40 4.7 (a) s-diagram and (b) t-diagram for the production of the Zb¯b state from qq¯ annihilation. (c) Diagram for the Zb¯b production from gg...... 41 4.8 (a) Decay of the b-quark. (b) Decay of the t-quark...... 41 4.9 (a) s-diagram for the process qq¯ → tt¯. (b) t-diagram for the process gg → tt¯.... 42 2 4.10 Reduction of the backgrounds at mH = 150 GeV/c for each preselection step for the three channels...... 49 4.11 Invariant mass of the four lepton system after pre-selection in the (a) 4µ, (b) 2e2µ and (c) 4e channels for H → ZZ(∗) → 4l signal events and for the main backgrounds. 50 4.12 (a) Distribution of the µIso2least variable for signal and for the main backgrounds for the 4µ channel. (b) Discriminating power of the µIso2least variable against tt¯ and Zb¯b backgrounds for the 4µ channel...... 53 4.13 (a) Distribution of the eIso2least variable for the sum of two least isolated electrons, for signal and for the main backgrounds for the 4e channel. (b) Discriminating power of the eIso2least variable against tt¯ and Zb¯b backgrounds for the 4e channel..... 54 4.14 Distribution of µIso2least and eIso2least versus pT of the third lepton for the Higgs boson mass of 150 GeV/c2 for H → 4µ (left) and H → 4e (right) and for the Zb¯b background. The signal and background regions are best separated by a slanted line of the form e(µ)Iso2least = A · pT,3 + B...... 55 4.15 (a) Muon impact parameter significance SIP (3D) distribution for the fourth/worst muon, for signal and for the main backgrounds; (b) Rejection power of SIP (3D) cuts on the fourth muon against tt¯ and Zb¯b backgrounds...... 56 4.16 (a) Electron impact parameter significance SIP (3D) distribution for the fourth/worst electron, for signal and for the main backgrounds; (b) Rejection power of SIP (3D) cuts on the fourth electron against tt¯ and Zb¯b backgrounds...... 57 4.17 Rejection power of SIP (3D) cuts against tt¯ background for the three final states.. 57 4.18 (a) Invariant mass of the two leptons closest to the nominal Z mass for the signal and for the main backgrounds, in the 2e2µ channel. (b) Invariant mass of the two highest-pT remaining leptons, opposite charge and maching flavour, in the 2e2µ channel...... 58 4.19 Four lepton reconstructed invariant mass spectrum after the baseline selection for the three channels at L = 1 fb−1 ...... 60 4.20 (a) Difference between the reconstructed mass m4l and the true mass mH , and ±1 or ±2 σm4l mass window, as a function of mH in the 2e2µ channel. (b) Limits m4l ± 2σm4l of the mass window as a function of mH in the 4e, 4µ and 2e2µ channels. 61 4.21 Number of expected signal (red markers) and background (blue markers) events for −1 an integrated luminosity of 1 fb in the m4l ± 2σm4l mass window as a function of the Higgs boson mass hypothesis...... 62 4.22 (a) Expected mean significance for the signal observation for the 4e (green), 4µ (blue) and 2e2µ (magenta) channels, and their combination (black) at L = 1 fb−1. (b) The upper limit on r at 95% C.L. for the 4e (green), 4µ (blue) and 2e2µ (magenta) channels separately and their combination (black) at 1 fb−1 luminosity, at a center- of-mass energy of 10 TeV...... 65

5.1 Percentage of Zb¯b events removed from Z+jets MC samples as a function of the Z pT bin...... 69 List of Figures 119

5.2 Invariant mass distribution of the four leptons (m4l) after the pre-selection cuts for the three final states...... 70 5.3 Invariant mass distribution for mZ1 and mZ2 after the pre-selection cuts for all the three final states considered together...... 70 5.4 Invariant mass distribution of the four leptons (m4l) after cuts on the invariant masses of the Z and Z∗ candidates for the three final states considered together.. 71 5.5 S vs B for different values of the isolation cut for the three final states...... 72 5.6 Distribution of the isolation variable Xlarge after the pre-selection cuts for the three final states: (a) 4µ, (b) 4e and (c) 2e2µ ...... 73 5.7 S vs B for different values of the impact parameter significance cut for the three final states...... 74 5.8 Distribution of the impact parameter significance Slarge after the pre-selection cuts for the three final states: (a) 4µ, (b) 4e and (c) 2e2µ. The vertical black line indicates the cut used...... 75 5.9 Invariant mass distribution of the four lepton system (m4l) after kinematic cuts for the three final states: (a) 4µ, (b) 4e, (c) 2e2µ and (d) the three final states combined together...... 77 5.10 Distribution of Xlarge as a function of the pT of the third lepton for the three final states...... 78 5.11 Invariant mass distribution of the four lepton system after the Xlarge vs pT,3 cut for signal and backgrounds for the three final states combined together...... 79 5.12 Distribution of Xlarge as a function of the pT of the fourth lepton for the three final states: (a) µ, (b) 4e, (c) 2e2µ for muons and (d) 2e2µ for electrons...... 80 5.13 Invariant mass distributions after the second 2-D cut (Xlarge vs pT,4) for signal and backgrounds for the three final states combined together: (a) mZ1, (b) mZ2 and (c) m ...... 82 4l √ 5.14 Significance for ZZ(∗) → 4l as a function of L collected at s = 10 TeV...... 83

6.1 mZ1 distribution after the full selection for the three channels: (a) 4µ, (b) 4e and (c) 2e2µ. The bin width is 4 GeV...... 86 6.2 Distribution of the on-shell Z mass (mZ1) after the full selection for the 3µ1e channel. The bin width is 4 GeV...... 87 6.3 Measured invariant mass of the on-mass shell Z candidate (mZ1) for the events in the control region, for the sum of the 4µ, 2e2µ and 3µ1e channels (a) and for the 3µ1e channel (b). The dashed line corresponds to the best ﬁt with a sum of one Crystal Ball and one Gaussian. The bin width is 4 GeV...... 88

A.1 Track (a) and HCAL (b) isolation variable distributions for muons from H → ZZ → 4e events and tt¯ events...... 97 A.2 Track (a), ECAL (b) and HCAL (c) isolation variable distributions for muons from H → ZZ → 4µ events and tt¯...... 98

2 e B.1 Electron reconstruction efficiency for mH = 150 GeV/c : (a) as a function of pT ; (b) as a function of ηe...... 101 B.2 N-1 distributions (see text) of electron identification variables for the Higgs boson signal (plain-green histograms) and fakes from QCD background (solid-black lines): seed out H/E for the golden class (a) and ET /pT for the showering class (b). Distributions without any electron identification cut are also shown for the background (dashed- red line)...... 103 120 List of Figures

B.3 Global muon reconstruction eﬃciency as a function of pT for |η| < 1.1 (a) and p for 1.1 < |η| < 2.4 (b). The smaller graphs show the diﬀerences between global and tracker muons at very low (transverse) momentum...... 104

C.1 Shape of the Higgs boson potential of Equation C.14...... 112 List of Tables

1.1 Cross section measurements for double vector boson production with leptonic ﬁnal states [28]...... 17

4.1 Monte Carlo simulation samples used for signal and background processes..... 36 4.2 Weights for MC events for ZZ, Zb¯b and tt¯ at 10 TeV for 1 fb−1...... 43 4.3 Weights for Z → µµ+jets MC events at 10 TeV for 1 fb−1...... 45 4.4 Weights for Z → ee+jets MC events at 10 TeV for 1 fb−1...... 45 4.5 pT thresholds for electron and muon trigger paths at Level-1 (L1) and at High Level Trigger (HLT)...... 46 4.6 HLT efficiencies for signal samples for the 2e2µ, 4µ and 4e channels...... 46 4.7 Skimming efficiencies for signal samples of selected masses (mH ) for the 4µ, 4e and 2e2µ channels...... 47 4.8 Summary of the number of events expected per L = 1 fb−1 after the pre-selection for the three H → ZZ(∗) → 4l channels, for three different Higgs boson masses and the backgrounds...... 51 4.9 Set of baseline selection cuts for all three channels...... 59 4.10 Average expected number of observed (signal plus background) and expected background only events for different Higgs boson masses at L = 1 fb−1. Events are counted in mH ± 2σm windows around Higgs boson masses...... 64 4.11 Number of expected signal and background events, average expected number of signal and background events, average expected significance and upper limit on r at 95% C.L. for the combination of the 4e, 4µ and 2e2µ channels, for several Higgs boson masses at 1 fb−1 luminosity...... 65

5.1 Number of Zb¯b events removed from Z → ee+jets MC samples at 10 TeV...... 68 5.2 Number of Zb¯b events removed from Z → µµ+jets MC samples at 10 TeV..... 68 5.3 Events for the three final states after the pre-selection cuts for 1 fb−1...... 70 5.4 Efficiencies for signal and backgrounds for the invariant mass cuts used for the three final states...... 70 5.5 Events for the three final states combined together after invariant mass cuts for 1 fb−1...... 71 5.6 Efficiencies for signal and backgrounds for the isolation cut used for the three final states for Xlarge < 12 GeV...... 73 5.7 Efficiencies for signal and background for the impact parameter significance cut used for the three final states for Slarge < 5...... 75 5.8 Remaining events after kinematic cuts for signal and background for 1 fb−1 for the 4µ final state. On the left the results are relative to the H → ZZ(∗) → 4l analysis and on the right to the ZZ(∗) → 4l...... 76

121 122 List of Tables

5.9 Remaining events after kinematic cuts for signal and background for 1 fb−1 for the 4e final state...... 76 5.10 Remaining events after kinematic cuts for signal and background for 1 fb−1 for the 2e2µ final state...... 76 5.11 Remaining events after the first 2-D cut (Xlarge vs pT,3) for signal and backgrounds for 1 fb−1 in the 4µ final state...... 79 5.12 Remaining events after the first 2-D cut (Xlarge vs pT,3) for signal and backgrounds for 1 fb−1 in the 4e final state...... 79 5.13 Remaining events after the first 2-D cut (Xlarge vs pT,3) for signal and backgrounds for 1 fb−1 in the 2e2µ final state...... 79 5.14 Remaining events after the second 2-D cut (Xlarge vs pT,4) for signal and backgrounds for 1 fb−1 in the 4µ final state...... 81 5.15 Remaining events after the second 2-D cut (Xlarge vs pT,4) for signal and backgrounds for 1 fb−1 in the 4e final state...... 81 5.16 Remaining events after the second 2-D cut (Xlarge vs pT,4) for signal and backgrounds for 1 fb−1 in the 2e2µ final state...... 81 5.17 Number of background events after the full selection...... 82

6.1 Events in the control region after the full selection for 1 fb−1...... 87 6.2 Events resulting from the best ﬁt to the mZ1 distribution after the full selection with 1 fb−1 of integrated luminosity...... 88

A.1 The minimal track quality requirements for tracks considered in electron and muon isolation algorithms for diﬀerent track categories...... 95

B.1 Value of cuts on electron identiﬁcation variables for “loose” conﬁguration. The “golden”, “bigbrem”, “narrow” and “showering” categories follow the nomenclature introduced in Reference [79]...... 103

C.1 Classiﬁcation of the three families of fundamental fermions...... 107 C.2 Fundamental interactions in particle physics and corresponding carriers...... 108 C.3 Isospin (I3), hypercharge (Y ) and electric charge (Q) of all fermions...... 109 Abbreviations

SM Standard Model EWSB ElectroWeak Symmetry Breaking LEP Large Electron-Positron collider CL Confidence Level CERN 4 Centre Européenpour la Recherche Nucléaire CMS Compact Muon Solenoid LHC Large Hadron Collider MC Monte Carlo SLC Stanford Linear Collider CDF Collider Detector at Fermilab QCD Quantum ChromoDynamics LO Leading Order NLO Next Leading Order NNLO Next Next Leading Order NNLL Next Next Leading Log BR Branching Ratio ATLAS A Toroidal LHC ApparatuS TGC Triple Gauge boson Coupling MSSM Minimal Superymmetric Standard Model QED Quantum Electro-Dynamics SUSY SUper SYmmetry GUT Grand Unified Theory ALICE A Large Ion Collider Experiment LINAC LINear ACcelerator

4The European Organization for the Nuclear Research (Organisation Europ´eennepour la Recherche Nucl´eaire) known as CERN was established in 1954 and it has 20 European member states.

123 124 Abbreviations

PSB Proton Synchrotron Booster PS Proton Synchrotron SPS Super Proton Synchrotron LEIR Low-Energy Ion Ring RHIC Relativistic Heavy Ion Collider PDF Parton Distribution Function DIS Deep Inelastic Scattering TIB Tracker Inner Barrel TOB Tracker Outer Barrel ECAL Electromagnetic CALorimeter HCAL Hadron CALorimeter HB Hcal Barrel HO Hcal Outer barrel HE Hcal Endcap HF Hadron Forward calorimeters DT Drift Tube CSC Cathode Strip Chamber RPC Resistive Plate Chamber MCFM Monte Carlo for FeMtobarn processes L1 Level 1 trigger HLT High Level Trigger GSF Gaussian Sum Filter CRAB Cms Remote Analysis Builder TEC Tracker EndCap GWS Glashow-Weinberg-Salam model Symbols

symbol name unit √ s center of mass energy TeV λ scaling factor v vacuum expectation value of the Higgs scalar ﬁeld GeV Λ new physics (cut-oﬀ) scale GeV σ total cross section fb Γ partial decay width GeV/c2 2 lept sin θeff the effective weak interaction mixing angle y rapidity

AFB front-back asymmetry

ET transverse energy GeV √ sˆ effective center of mass energy TeV Q2 exchanged four-momentum in a 2 → 2 collision GeV2 η pseudorapidity

RM Molier radius cm

X0 radiation length cm

αs coupling strength of the Strong Interaction L integrated luminosity fb−1 φ angle R(η, φ) distance in the η − φ plane between two jets

SIP (3D) signiﬁcance of the 3D impact parameter

SL three-bin log-likelihood ratio signiﬁcance estimator

ScL signiﬁcance estimator for the total lumped event count Q likelihood ratio m invariant mass GeV/c2

125 126 Symbols

pT transverse momentum GeV/c

d0 transverse impact parameter at the closest approach point

dZ longitudinal impact parameter at the closest approach point

S signal efﬁciency

B background efﬁciency α coupling strength of the ElectroWeak Interaction

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[94] M. Spira and P.M. Zerwas. Electroweak Symmetry Breaking and Higgs Physics, volume 512, pages 161–225. Springer Berlin Heidelberg, May 1998. Ringraziamenti

Lavorare insieme alle persone del gruppo CMS di Torino `estata una bellissima ed intensa esperienza. Ringrazio tutte le persone del gruppo con cui ho lavorato e quelle invece con cui non ho potuto: entrambi mi hanno fatto capire l’importanza di avere un solido gruppo di persone su cui contare e da cui si pu`ocontinuamente imparare.

Vorrei ringraziare di cuore la Dott.ssa Chiara Mariotti che, nonostante fosse sempre molto impe- gnata, mi ha seguito fin dall’inizio (anche a distanza) e non ha mai smesso di supportarmi e di spronarmi ad affrontare nuove piccole “sfide” nel campo professionale, insegnandomi inoltre ad avere piùstima nelle mie capacità.Soprattutto non si èmai rifiutata di ripetermi le stesse cose più volte e, grazie ai suoi continui stimoli, ho potuto imparare moltissimo grazie alla sua disponibilità e alla sua simpatia.

Un grazie speciale al mio supervisore, Dott. Nicola Amapane, che, nonostante sia oberato di lavoro, ha trovato il tempo per aiutarmi nella stesura della tesi ed ha contribuito enormemente con molta precisione e attenzione alla sua correzione.

Un doveroso e particolarmente sentito ringraziamento va a Nicola De Filippis, per la disponibilitàe la pazienza nello spiegarmi ogni cosa. Mi èstato vicino e ha dato subito fiducia nelle mie capacità, accompagnandomi in quest’ultima fase del mio percorso di studi, con semplicitàe bontà.Grazie anche per avermi “illustrato” il suo codice e per avermi incoraggiato a modificarlo dicendomi: “Calma, una cosa alla volta e vedrai che si sistemeràtutto”.

Un ringraziamento in particolare alla Prof.ssa Alessandra Romero per avermi seguita professio- nalmente, provvedendo all’organizzazione della mia partecipazione alle attivitàdel gruppo CMS di Torino. Un grazie anche alle persone con piùesperienza del gruppo che hanno contribuito alla realizzazione di questa tesi, per avermi dato l’opportunitàdi andare in trasferta al CERN: tra questi Amedeo Staiano, Nadia Pastrone, Silvia Maselli, Ernesto Migliore, Marco Costa e tutti gli altri.

E poi un grazie altrettanto speciale ai “giovani” del gruppo, senza i quali avrei trascorso in uﬃcio intere giornate molto pi`unoiose: Alberto, per le piacevoli chiacchierate e risate, Giorgia, per essere

135 136 Ringraziamenti

stata compagna di ufficio fin dall’inizio, Marco, Matteo, Valentina per la loro simpatia e compagnia in ufficio; poi anche Cristina, Daniele e Roberto, per avermi ospitato piùvolte nella casa di Saint- Genis, Mario, per i suoi utili consigli sulla fisica e per avermi scorrazzato su e giùdal CERN, Gianluca, Riccardo, Sara, Susy e tutti gli amici di CMS del Building 40, per avermi accolto nel gruppo.

In cinque anni di università,ho incontrato moltissime persone, alcune delle quali mi hanno accom- pagnato e aiutato particolarmente: un grazie in particolare a Isa, Enri, Pier, Mirco, Cione, Davide, David, Marco, Jonida, Leo, Mimma, Linda, Ale, Fabri, Fede, Niccolò,Mario, Stefano, Alberto . . . e tutti quelli che ho scordato! A voi tutti un grande abbraccio e un grazie di cuore per essere stati al mio fianco in questi cinque anni e avermi sostenuto nei momenti difficili.

Special thanks go to Michael, for the fruitful and helpful corrections to this thesis. It was a pleasure to meet him and I hope to see him soon in Grenoble.

Ovviamente non possono mancare gli amici fuori dal mondo della ﬁsica, con i quali ho condiviso serate bellissime, momenti di svago ed esperienze indimenticabili. Un grazie quindi a Chiara, Karme, Roby, Luca, Ceci, Giorgia, Fra, Salva, e a tutti gli altri amici del gruppo OMG di Torino. Grazie anche a Valeria, Selene, Roby, Marco, Paola, Sara e alle mie compagne di squadra del Real Benny, con cui spero di poter ancora condivere la gioia e la mia passione per il calcio. Grazie anche ad Alessio e Corrado, che mi sono stati vicini in questi anni e hanno creduto in me ﬁn dall’inizio.

Inﬁne, ringrazio tutti i miei familiari e parenti. In particolare, abbraccio mia nonna, che nonostante i suoi problemi trova sempre il modo e il tempo di aiutarmi e di starmi vicina. E poi tutti gli zii e cugini, che vorranno festeggiare con me questo risultato, tra cui Maria Rosa e Angelo.