Measurement of the Higgs Boson Mass in Decays into Four Leptons

Physik-Department

Masterarbeit

Measurement of the Higgs Boson Mass in Decays into Four Leptons

with the ATLAS Detector

von

Rainer Röhrig

München

Dezember 2014

Erstgutachter (Themensteller): Priv.-Doz. Dr. H. Kroha

only supported by declared resources.

Ich versichere, dass ich diese Masterarbeit selbstständig verfasst und nur die angegebenen Quellen und Hilfsmittel verwendet habe.

München, 22. Dezember 2014

Unterschrift

This master thesis presents a measurement of the mass of the observed Higgs boson candidate in the decay channel H

ZZ

`

`

`

`

, with `, `

= e or µ. The result is based on the full 2011 and 2012 proton- proton collision dataset recorded with the ATLAS detector at the Large Hadron Collider, corresponding to an integrated luminosity of 4.5 fb

and 20.3 fb

at a center-of-mass energy of

s = 7 TeV and 8 TeV,

respectively. The mass is measured to be m

= 124.58

(stat)

0.06 (syst) GeV using an analytical parametrization of the expected mass

distribution on an event-by-event basis.

Abstract

. . . . vii

Contents

. . . . ix

1 Introduction

. . . . 1

2 The Higgs Boson in the Standard Model

. . . . 3

2.1 The Standard Model of Particle Physics . . . . 3

2.1.1 The Gauge Interactions of the Standard Model . . . . 4

2.2 The Higgs Mechanism . . . . 7

2.3 Constraints on the Higgs Boson Mass . . . . 9

2.3.1 Theoretical Constraints on the Higgs Boson Mass . . . . 9

2.3.2 Experimental Constraints on the Higgs Boson Mass . . . . 11

3 Higgs Boson Production and Decay at the LHC

. . . . 13

3.1 Proton–Proton Collisions . . . . 13

3.2 Standard Model Higgs Boson Production at the LHC . . . . 14

3.3 Standard Model Higgs Boson Decays . . . . 18

3.3.1 The Width of the Higgs Boson in the Standard Model . . . . 18

3.4 Status of the Higgs Boson Measurements at the LHC . . . . 20

4 The ATLAS Experiment at the LHC

. . . . 27

4.1 The Large Hadron Collider . . . . 27

4.2 The ATLAS Detector . . . . 30

4.2.1 The ATLAS Coordinate System . . . . 32

4.2.2 The Inner Detector . . . . 33

4.2.3 The Calorimeters . . . . 33

4.2.4 The Muon Spectrometer . . . . 35

4.2.5 The Trigger System . . . . 36

5 Electron and Muon Identification

. . . . 39

5.1 Electron Identification and Reconstruction . . . . 39

5.2 Muon Identification and Reconstruction . . . . 40

Contents

5.4 Lepton Energy-Momentum Scale Uncertainties and Resolution . . . . . 43

6 The Standard Model Higgs Boson Decay

H

ZZ

4` . . . . 49

6.1 Motivation . . . . 49

6.2 Signal and Background Processes . . . . 49

6.3 Data and Monte Carlo Samples . . . . 50

6.4 Signal Selection . . . . 52

6.4.1 Multivariate Discriminant . . . . 54

6.4.2 Final State Radiation Correction . . . . 55

6.4.3 Z Mass Constraint . . . . 58

6.5 Results of the Event Selection . . . . 60

6.6 Higgs Mass Measurement . . . . 65

7 Optimized Measurement of the Higgs Boson Mass

. . . . 71

7.1 Introduction . . . . 71

7.2 Lepton Energy Resolution Functions . . . . 71

7.2.1 Muon Resolution Function . . . . 72

7.2.2 Electron Energy Resolution Function . . . . 75

7.3 Higgs Boson Mass Measurement with Event-by-Event Mass Errors and Z Mass Constraint . . . . 77

7.3.1 Distribution of the True Four-Lepton Invariant Mass for Higgs Boson Decays . . . . 77

7.3.2 Distribution of the True Four-Lepton Invariant Mass for Background Processes . . . . 79

7.3.3 Event-by-Event Higgs Mass Distribution Function . . . . 79

7.3.4 Likelihood Function for the m

Determination . . . . 81

7.4 Validation of the New Mass Measurement Method with Simulated Data 81 7.5 Results for LHC Run 1 Data . . . . 84

8 Summary

. . . . 87

Appendices

. . . . 89

A Event Displays

. . . . 91

B Candidate Events

. . . . 95

Bibliography

. . . . 99

x

Introduction

The Standard Model, developed in the 1960s and 1970s, has stood up for 30 years as the theory of particle physics, and has been successfully tested in numerous high- precision experiments. While many people believe that the Standard Model is not the final description of particle physics, it is an excellent effective description of the phenomena observed at low energies. The last missing piece has for a long time been the Higgs boson which is predicted by the Standard Model as a consequence of the Brout-Englert-Higgs mechanism.

The search for the Standard Model Higgs boson was one of the most important goals of the physics program at the Large Hadron Collider (LHC) at CERN [1]. On 4 of July 2012, the ATLAS and CMS experiments at the LHC reported the observation of a new boson with a mass around 125 GeV [2, 3]. Measurements of its spin and CP quantum numbers and of its coupling properties to other particles show good compatibility with the predictions of the Standard Model [4, 5].

In the Standard Model, the mass of the Higgs boson is a free parameter. The pre- cision measurement of the Higgs boson mass is crucial for the precise prediction of electroweak observables and of the production and decay properties of the Higgs boson and therefore for further tests of the Standard Model. The decay channels H

ZZ

4` and H

γγ are the main discovery channels of the Higgs boson.

Since they provide a clear signature in the detector and a high signal sensitivity with a narrow resonance in the invariant mass distribution of the final state particles.

These decay channels allow for the measurement of the Higgs boson mass, because the kinematics of the final state particles can be fully reconstructed with the ATLAS detector.

The main topic of this thesis is the precise measurement of the Higgs boson mass

in the decay channel H

ZZ

4`, where the final state leptons are electrons or

muons. The excellent mass resolution in this channel is due to the high energy and

momentum resolution of the ATLAS detector for electrons and muons. The Higgs

boson mass is determined by fitting the measured four-lepton invariant mass in the

H

ZZ

4` decay channel with an analytical function by taking event-by-event

mass errors and the Z mass constraint into account.

The Higgs Boson in the Standard Model

2.1 The Standard Model of Particle Physics

The Standard Model (SM) [6, 7] of particle physics provides a description of all in- teractions between subatomic particles, with the exception of gravity. At the present stage of knowledge, the smallest units of matter are leptons and quarks, which are spin

1/2 fermions.

The three fundamental interactions of the SM between those fermions, namely the electromagnetic, the weak and the strong interaction, are mediated by spin-1 gauge bosons and can be described by a non-Abelian gauge field theory (Yang-Mills the- ory) [8]. Where the field themselves are charge carrier and interact directly with each other. The principle of local gauge invariance is universal for all SM interactions. The symmetry group of the SM is a direct product of three simplest special unitary Lie groups:

SU (3)

SU (2)

U (1)

. (2.1)

The SU (3)

gauge group of the strong interaction is generated by eight colour charge

operators and the corresponding field quanta, G

(a = 1, ..., 8), are eight coloured

massless spin

1 gluons. The quantum theory of the strong interaction is called quan-

tum chromodynamics (QCD) [9]. The strong interaction is responsible for the binding

of particles carrying colour charges, such as quarks and gluons in hadrons. The quarks

and gluons are confined [10,11] in colour-singlet bound states of either quark-antiquark

pairs (mesons) or triplets of quarks (baryons). The electromagnetic and weak inter-

actions are unified to the electroweak gauge theory, with the SU (2)

U (1)

gauge

group. Three spin-1 particles, W

(i = 1, 2, 3), are associated with the weak isospin

group SU (2)

, and one particle, B

, with the weak hypercharge group U (1)

. The

massless photon γ, mediating the electromagnetic interaction, and the W

and Z

boson, mediating the charged flavour changing and parity violating weak interactions,

respectively, are mixtures of the W

and B

fields (see Section 2.1.1). The quan-

tum electrodynamics (QED) [12–17] is the theory of the electromagnetic interactions.

Chapter 2 The Higgs Boson in the Standard Model

the Glashow-Salam-Weinberg theory (GWS) [18–21]. While the weak interaction is responsible for radioactive β

decay processes, the electromagnetic force acts on electrically charged particles.

The SU (2)

U (1)

symmetry is spontaneously broken by the Higgs mechanism which generates the masses of the weak gauge bosons and of the fermions (see Sec- tion 2.2).

Throughout this thesis natural units, c = ¯ h = 1, are used.

2.1.1 The Gauge Interactions of the Standard Model

The local gauge symmetry of the SM determines the electroweak and the strong interaction via minimal gauge invariant couplings of the gauge fields to the matter fields. The structure of the gauge fields and coupling terms is outlined below.

The Matter Fields

The leptons and quarks form three generations of left-handed weak isospin doublets right-handed singlets, ψ

=

ψ, of the fundamental representation of the SU (2)

group and couple differently to the weak gauge bosons. γ

is the product of the four Dirac matrices, γ

= iγ

γ

γ

γ

. Distinction of the left-handed and right-handed multiplets can be effected by introducing a new quantum number of the weak isospin, with three generators I

(i = 1, 2, 3). The third component of the weak isospin is used to distinguish between left-handed, I

=

, and right-handed fermions, I

= 0. The weak hypercharge, Y

, of the U (1)

group is related to the electric charge by the Gell-Mann–Nishijima relation [22, 23]

Y

= 2(Q

I

). (2.2)

Table 2.1 summarises the electroweak multiplets and quantum numbers of the SM fermions. In the fundamental representation of the SU (3)

symmetry group, the quarks appear in three colour triplet states,

q =





q

q

q





(2.3)

with q = u, d, s, c, b, t and the three colour number r, g and b. The leptons do not undergo the strong interactions, as leptons carry no colour quantum number and forming a colour singlet under SU (3)

.

4

Table 2.1:Summary of the electroweak multiplets. The weak quark eigenstatesd⁰,s⁰ and b⁰ results from CKM mixing of the mass eigenstates [24, 25].Qis the electric charge,I3 the third component of the weak isospin andYW the weak hypercharge .

Name

Q [e] I

Y

Fermions Leptons

ν

e

L

ν

µ

L

ν

τ

L

0 +1/2

1

−

1

1/2

1

e

µ

τ

1 0

2

Quarks

u d

L

c s

L

t b

L

+2/3 +1/2 +1/3

−

1/3

1/2 +1/3

u

c

t

+2/3 0 +4/3

d

s

b

1/3 0

2/3

The Gauge Fields

The symmetry group of a gauge field theory determines the properties of the in- teraction. The electroweak symmetry group SU (2)

U (1)

has four generators

I

= σ

2 , (2.4)

where σ

(i = 1, 2, 3) are the 2

2 Pauli matrices in the fundamental representation, and the hypercharge operator. The gauge vector fields W

of the SU(2)

symmetry group form a weak isospin triplet. B

is the gauge field of the U (1)

group and forms an isospin singlet.

The SU (3)

symmetry group is non-Abelian, like SU (2)

, and has eight generators T

= λ

2 , (2.5)

where λ

(a = 1, ..., 8) are the 3

3 Gell-Mann matrices in the fundamental repre- sentation. The corresponding gauge fields are eight gluon fields, G

, which couple to all coloured particles including themselves.

The field strength tensors of the strong and electroweak gauge fields, are given by G

= ∂

G

∂

G

+ g

f

G

G

,

W

= ∂

W

∂

W

+ g

W

W

and (2.6)

Chapter 2 The Higgs Boson in the Standard Model

where g

and g

are the gauge coupling constants and f

and

are the structure constants of the SU (3)

and SU (2)

groups, respectively.

Lagrangian of the Standard Model

The ordinary derivative is replaced by the covariant derivative for left- and right- handed fermion fields and is defined as

D

= (∂

ig

T

G

ig

I

W

ig

Y

2 B

) and D

= (∂

ig

T

G

ig

Y

2 B

),

(2.7)

to preserve the local gauge invariance, where g

is the gauge coupling constant of the U (1)

group. The Lagrangian of the SM without the Higgs sector takes the form

LSM

=

1

4 G

G

1

4 W

W

1

4 B

B

+ + i ψ ¯

γ

D

ψ

+ i ψ ¯

γ

D

ψ

.

(2.8) The insertion of Eq. (2.6) and (2.7) into Eq. (2.8) defines the interactions between matter and gauge fields and the self-interactions of the non-Abelian gauge fields.

Writing the SU (2)

term of the covariant derivative in Eq. (2.7)

−

ig

I

W

=

ig

W

W

+ W

W

W

φ

W

, (2.9)

explicitly in the fundamental representation leads to the physical weak gauge fields W

= 1

√

2 (W

iW

), (2.10)

mediating the weak charged current interaction. The electrically neutral gauge fields, W

and B

, mixes to

A

Z

=

cos θ

sin θ

−

sin θ

cos θ

B

W

. (2.11)

to give the weak neutral current mediating gauge field Z

and the electromagnetic field A

.

The mixing angle θ

, the so-called Weinberg angle, is determined by the two coupling constants g

and g

accordingly to the relations

sin θ

= g

g

+ g

or cos θ

= g

p

g

+ g

.

(2.12)

6

The Weinberg angle is chosen in such a way that the coupling of the neutrino to the photon field is zero.

At this point the masses of the weak gauge bosons and of the fermions are still missing in the Lagrangian of Eq. (2.8). Explicit gauge boson mass terms would violate the local weak gauge invariance and fermion mass terms the global SU (2)

gauge invariance. Fermion mass terms in the Lagrangian takes the form

m ψψ. Since ¯ the left-handed fermions form weak isospin doublets and the right-handed fermions form weak isospin singlets, they transform differently under SU (2)

transformations.

Introducing masses without violating these symmetries will be the topic of the next section.

2.2 The Higgs Mechanism

The Higgs mechanism [26–28] introduces masses of the weak gauge bosons and of the leptons and quarks by adding a complex scalar field Φ to the SM Lagrangian.

This approach has been proposed by P.W. Higgs, F. Englert, R. Brout and by G.S.

Guralnik, C.R. Hagen and T.W.B. Kibble [26–28] and is nowadays also called Brout- Englert–Higgs (BEH) mechanism. This mechanism gives additional longitudinal po- larisation degrees of freedom to the weak gauge bosons. In the minimal version of the Higgs mechanism, one scalar SU (2)

doublet

Φ = φ

φ

= 1

√

2

φ

+ iφ

φ

+ iφ

, (2.13)

with four degrees of freedom is introduced. The Lagrangian of the scalar field

= (D

Φ)

(D

Φ)

V (Φ) (2.14) consists of the kinematic term with the covariant derivative of the electroweak theory,

D

= (∂

ig

I

W

ig

Y

2 B

), (2.15)

and of the Higgs potential,

V (Φ) = µ

Φ

Φ + λ(Φ

Φ)

, (2.16) where the µ is the mass parameter and λ the self-coupling constant. Unitarity requires that the constants µ

and λ be real and vacuum stability demands that λ be positive.

If µ

> 0, the scalar potential has its minimum at

Φ

= 0, preserving the symmetries of the Lagrangian. However, if µ

< 0, the scalar field acquires a vacuum expectation value v,

µ

v

Chapter 2 The Higgs Boson in the Standard Model

in an infinite set of degenerated ground states.

As the U (1)

symmetry of the electromagnetic interaction must remain unbroken, because of the massless photon, the non–zero vacuum expectation value, v =

q−µ² λ

, of the scalar field is chosen for the neutral component of the scalar field,

Φ

= 1

√

2 0

v

. (2.18)

The choice of this particular ground state breaks the SU (2)

U (1)

symmetry spon- taneously, while the electromagnetic gauge symmetry U (1)

remains as a symmetry of the ground state. Field excitations from the ground state can be parametrized as

Φ

= 1

√

2

0 v + H(x)

, (2.19)

where H(x) is a massive scalar field, the so-called Higgs field, corresponding to the Higgs boson H. Mass terms of the weak gauge bosons and of the Higgs boson are generated by inserting the scalar field of Eq. (2.19) into the scalar Lagrangian of Eq.

(2.14) and rewriting in

= 1

2 ∂

H∂

H + g

(2vH + H

)

4 (W

W

+ 1 2 cos

θ

Z

Z

) + m

2 (W

W

+ W

W

) + m

2 Z

Z

−

m

2 H

λvH

λ v H

,

(2.20)

after spontaneously symmetry breaking. The masses of the weak gauge bosons and of the Higgs boson in Eq. (2.20) are given by the relations

m

= gv 2 , m

= m

cos θ

and m

= v

2λ.

(2.21)

The fermion masses are generated by the Higgs mechanism by introducing Yukawa couplings of the fermions to the scalar field Φ [29, 30], of the form

Lf

=

λ

( ¯ ψ

Φψ

+ ¯ ψ

Φψ ¯

), (2.22) where ψ

and ψ

represent the left-handed doublets and right-handed singlets under SU (2)

. Hence, the Lagrangian of the first fermion generation has the form

Lf

=

λ

(¯ ν, ¯ e)

Φe

λ

(¯ u, d) ¯

Φd

λ

(¯ u, d) ¯

Φu ¯

+ h.c., (2.23)

8

where λ

denotes the Yukawa coupling constant of the fermion f to the Higgs field Φ and Φ = ¯ iI

Φ. The fermion masses m

after spontaneously symmetry breaking are

m

= λ

√

v

2 , (2.24)

proportional to their Yukawa coupling constants λ

. The Fermi coupling constant G

, which can be measured precisely in muon decays [31], is related to the vacuum expectation value via the relation

v = (

2G

)

= 246 GeV. (2.25) The Higgs mechanism is essential for introducing the masses of the weak gauge bosons and of the fermions without violating the SU (2)

U (1)

gauge symmetry of the Lagrangian and keeping the theory re-normalisable. The Higgs boson mass is a free parameter in the SM. The precise determination is important as the Higgs boson mass determines production and decay rates of the Higgs boson.

2.3 Constraints on the Higgs Boson Mass

The Higgs boson mass, m

, is a free parameter in the SM. Constraints on its value follow from the requirements of unitarity of scattering amplitudes, for instance of longitudinally polarised massive gauge bosons, and from vacuum stability. They depend on the energy scale Λ up to which the SM is supposed to be valid [32]. Λ indicates the scale at which perturbation theory breaks down and new physics beyond the SM should appear. Furthermore, limits on the Higgs boson mass are obtained in the SM by electroweak precision measurements and direct searches at colliders.

2.3.1 Theoretical Constraints on the Higgs Boson Mass

The Higgs boson mass, m

, is constrained by requiring self-consistency of the elec- troweak theory. The limits depend on the validity scale Λ, of the SM where new physics should appear. The highest energy scale, above which quantum gravitational effects need to be taken into account is the Planck mass, M

= 2.4

10

GeV [33].

Unitarity Condition

The scattering amplitude of longitudinally polarised W bosons, W

W

W

W

, diverges quadratically with increasing centre-of-mass energy in perturbation theory.

At an energy of Λ

1.2 TeV, unitary is violated which is enforced by including the

Higgs boson exchange in the scattering process with a mass m

less 780 GeV [34].

Chapter 2 The Higgs Boson in the Standard Model

Vacuum Stability Condition

The Higgs self-coupling λ depends on the energy of the interaction process. Contri- butions from Higgs boson loops to the re-normalisation of the self-coupling drive λ to infinity as energy increases while it approaches zero with decreasing energy. Top quark loops to the Higgs self-interaction drive λ, in the potential V (Φ) in Eq. (2.16), to negative values reaching the vacuum to be unstable without a lower bound on V (Φ).

Therefore, the self-coupling is required to be positive for vacuum stability and finite for perturbativity of the theory, i.e. 0 < λ(Q

) <

for momentum transfer of Q < Λ.

This requirement lead to upper and lower bounds on the Higgs boson mass depending on the top quark mass.

Figure 2.1: The (perturbativity) uppper bound (forλ=πor2πas examples) and (vacuum stability) lower bound on the Standard Model Higgs boson mass as a function of the energy scale Λ up to which the SM is assumed to be valid [32]. The absolute vacuum stability bound (green) and the less restrictive finite–temperature (blue) and zero–temperature (red) metastability bounds are shown with their1σuncertainty bands due to the uncertainties in the top quark mass and in the coupling constantαS=g3²/(4π)of the strong interaction.

Theoretical uncertainties in these bounds are not included. The grey shaded bands show the mass regions excluded by the LEP [35] and Tevatron [36] experiments.

The theoretical Higgs mass constraints are summarised in Figure 2.1 as a function of the validity scale Λ of the SM. The pair of blue lines for λ = π and 2π indicates

10

the perturbativity upper bound. There are three different lower vacuum stability bounds shown, in the green, blue and red bands. The green band corresponds to a strictly stable vacuum while the other two are metastable vacua, with, however, a lifetime longer than the age of the universe. The vacuum decay can take place either via thermal fluctuations (below the blue band) or via zero–temperature quantum fluctuations (below the red band).

In summary, considering that no new physics beyond the SM exists up to the Planck scale the Higgs boson mass is constrained by these theoretical arguments to the range 130 GeV < m

< 175 GeV. (2.26) Assuming a value of the cut-off scale of Λ

1 TeV, the limits are relaxed to

50 GeV < m

< 780 GeV. (2.27) 2.3.2 Experimental Constraints on the Higgs Boson Mass

Limits on the Higgs boson mass come also from electroweak precision measurements, compared to higher order calculations in perturbativity theory of electroweak observ- ables which depend on the Higgs boson mass via Higgs loop corrections. From the high precision measurements at high energy electron-positron colliders at an Λ above the Z resonance, the Stanford Linear Collider (SLC) and the Large Electron Positron collider (LEP), the Higgs boson mass can be constrained by performing a χ

-fit of the SM predictions to the data. In Figure 2.2 the χ

-function is shown with minimum at the preferred value of the Higgs boson mass of m

= 89

GeV indicated by the blue line. The one-sided 95% CL upper limit on m

is 158 GeV.

The four LEP experiments ALEPH, OPAL, L3 and DELPHI performed direct searches for the Higgs boson. The results of these experiments allow also for an exclusion of the SM Higgs boson at masses below 114.4 GeV at 95% CL [35]. The combined results of the two Tevatron experiments D0 and CDF using p¯ p collisions at a center-of-mass energy of 1.96 TeV exclude the mass region 147 GeV < m

< 180 GeV at 95%

CL [38]. The two excluded regions are depicted in Figure 2.2, where the left yellow

band corresponds to the LEP and the right one to the Tevatron exclusion region.

Chapter 2 The Higgs Boson in the Standard Model

Figure 2.2: ∆χ² ≡ χ² −χ²_min of the global fit of the SM predictions for electroweak observables to precision measurements as a function of the Higgs boson massmH [37]. The blue band correspond to the theoretical error due to missing higher order corrections. The yellow vertical bands show the 95% CL exclusion limit onmH from the direct searches at LEP (left) [35] and Tevatron (right) [38].

12

Higgs Boson Production and Decay at the LHC

3.1 Proton–Proton Collisions

The calculation of production cross sections at pp colliders has to take into account that protons are composite particles consisting of quarks and gluons. The scattering processes at a high energy hadron collider are categorized as either soft or hard depending on the momentum transfer, Q

. The production of the Higgs boson is a hard process and can be predicted by using perturbation theory, while soft processes are affected by non-pertubative QCD effects. The hard scattering process of quarks or gluons is often accompanied by soft interactions like initial and final state radiation of gluons and interactions of the proton remnants which lead to additional final state particles referred to as the underlying event. Also additional parton-parton interactions can occur.

A hadronic interaction is illustrated in Figure 3.1, where two protons A and B collide and only two partons a and b participate in the hard scattering process. The inclusive production cross section of the Higgs boson H with additional hadronic particles X in pp scattering is given by

σ

=

dx

dx

f

(x

, µ

)f

(x

, µ

)ˆ σ

(µ

, µ

), (3.1)

where the renormalization scale for the QCD running coupling, µ

, is usually chosen

to be on the order of Q

and µ

is the factorization scale which separates short form

long range interactions at which hadrons formed from quarks and gluons. The Q

dependence of the parton distribution functions (PDFs) in Eq. (3.1), f

(x

, Q

)

and f

(x

, Q

), described by the DGLAP evolution equations [39, 40], are the

probability density functions for the momentum fraction x

of a parton a (b) in the

proton A (B) in a process with momentum transfer Q

. The total cross section for a

process AB

HX can be calculated by using short range perturbative calculations

for the parton cross section σ ˆ

(µ

, µ

) and convolving with the PDFs. This

Chapter 3 Higgs Boson Production and Decay at the LHC

The predictions for SM production cross sections at pp and p p ¯ colliders depending on the center-of-mass energy are shown in Figure 3.2 at next-to-leading pertubation theory.

Figure 3.1: Structure of a hard scattering process between two hadrons [42].

3.2 Standard Model Higgs Boson Production at the LHC

The SM Higgs boson production processes at the LHC are dominated by heavy particles, which couple strongly to the Higgs boson like the massive W and Z bosons or the top quark, as illustrated by the Feynman diagrams in Figure 3.3. The predicted cross sections are shown in Figure 3.4 as a function of the Higgs boson mass at a center-of-mass energy of

s = 8 TeV. Table 3.3 shows the production cross sections for a Higgs boson with a mass of 125 GeV at center-of-mass energies of

s = 7 TeV and 8 TeV.

The dominant production process over the entire Higgs boson mass range is gluon fusion (see Figure 3.3(a)), where the Higgs boson is produced via an intermediate top quark loop. Although in principle all quark flavours contribute to the loop process the top quark dominates by far because the Higgs boson coupling to the top quark is about 35 times stronger than to the next lighter quark, the bottom quark.

The cross section for vector boson fusion (V BF ) is an order of magnitude smaller than the one for gluon fusion (ggF ). Nevertheless, the vector boson fusion process (see in Figure 3.3(b)) allows for an efficient suppression of background due to two high-energy forward jets which are produced in association with the Higgs boson and provide a good experimental signature. The Higgs production modes in association with a vector boson (V H with V = W or Z) or with a top quark pair (t ¯ tH) (see Figures 3.3(c) and 3.3(d)) have significantly lower cross sections than the V BF process, but provide signatures for discriminating H

b ¯ b decays from the large background.

14

0.1 1 10 10^-7

10^-6 10^-5 10^-4 10^-3 10^-2 10^-1 10⁰ 10¹ 10² 10³ 10⁴ 10⁵ 10⁶ 10⁷ 10⁸ 10⁹

10^-7 10^-6 10^-5 10^-4 10^-3 10^-2 10^-1 10⁰ 10¹ 10² 10³ 10⁴ 10⁵ 10⁶ 10⁷ 10⁸ 10⁹

WJS2009

σjet(E

T

jet > 100 GeV) σjet(E

T

jet > √s/20)

σjet(E

T

jet > √s/4) σHiggs(M

H=120 GeV) 200 GeV

LHC Tevatron

e v e n ts / s e c f o r L = 1 0

c m

s

σtot

proton - (anti)proton cross sections

σW

σZ

σt

500 GeV

σ (

n b

√

s (TeV)

Figure 3.2:Standard Model cross sections as a function of the center-of-mass energy [42].

Chapter 3 Higgs Boson Production and Decay at the LHC

The production cross sections fall rapidly with increasing Higgs boson mass but increase with increasing center-of-mass energy as shown in Figure 3.2.

g

g

t H

(a)

q

q

q

q W/Z H W/Z

(b)

q q

W/Z H

W/Z (c)

g

g

H t

t t t

(d)

Figure 3.3: Tree-level Feynman diagrams for the dominant production modes of the SM Higgs boson inppcollisions at the LHC: (a) the gluon fusion process (ggF), (b) vector boson fusion (V BF), (c) associated production with a W or Z boson (V H) and (d) associated production with a top quark pairs (ttH).¯

16

[GeV]

MH

80 100 200 300 1000

H+X) [pb] →(pp σ

10-2

10-1

1 10 102

= 8 TeV s

LHC HIGGS XS WG 2012

H (NNLO+NNLL QCD + NLO EW) pp →

qqH (NNLO QCD + NLO EW) pp →

WH (NNLO QCD + NLO EW) pp →

ZH (NNLO QCD +NLO EW) pp →

ttH (NLO QCD) pp →

Figure 3.4: The SM Higgs boson production cross sections in proton-proton collisions at the LHC of a center-of-mass energy of√s= 8 TeVreached in 2012 as a function of the Higgs boson mass [43].

Table 3.1:The dominant Higgs boson production cross sections at the two center-of-mass energies of the LHC in 2011 and 2012 for a Higgs boson mass of125 GeV [43] and their branching ratios.

√

s = 7 TeV

s = 8 TeV

Production Cross section Cross section Fraction of total

mechanism [pb] [pb] [%]

pp

H 15.13

19.27

87.2

pp

qqH 1.222

1.578

7.1

pp

W H 1.5785

0.7046

3.2

pp

ZH 0.3351

0.4153

1.9

pp

t ¯ tH 0.08632

0.1293

0.6

Chapter 3 Higgs Boson Production and Decay at the LHC

3.3 Standard Model Higgs Boson Decays

The properties of the Standard Model Higgs boson, such as the production cross sections, the decay rates to fermions and gauge bosons, and the total decay width, are completely determined once the Higgs boson mass, m

, is known. The Higgs couplings to fermions and weak gauge bosons are directly proportional to the masses of the particles such that the Higgs boson decays predominantly into the heaviest ones allowed by phase space. Figure 3.5 shows the decay branching ratios of the SM Higgs boson as a function of its mass. For a Higgs boson mass of 125 GeV the decays into pairs of b quarks, gauge bosons and τ leptons are the most frequent ones.

The sensitivity of the Higgs boson search in a particular decay channel depends not only on the branching ratio but also on the final state signature and the amount of background. Decays with strongly interacting decay products, such as b and c quarks, gluons or hadronic decays of W and Z bosons, are less sensitive than decays into final states with leptons because of the large hadronic background especially at a hadron collider.

The tree-level Feynman diagrams for the Higgs boson decays are shown in Figure 3.6.

Since the photon is massless there is no direct coupling to the Higgs boson. However, the decay into a photon pair (see Figure 3.6(a)) is possible through loop processes with either fermions or weak gauge bosons in the loop. The predicted decay branching ratio of the decay H

ZZ

4` (with ` = e, µ), studied in this thesis, is (0.125

0.005)

10

[43] at a Higgs boson mass of 125 GeV.

3.3.1 The Width of the Higgs Boson in the Standard Model

The total width, Γ

, of the Higgs boson is shown in Figure 3.7 as a function of its mass. Up to a Higgs boson mass of 150 GeV, the decay width is very narrow, Γ(m

)

10 MeV. In this mass region the width cannot be measured directly at the LHC. For higher Higgs masses, the Higgs resonance becomes broad enough to be resolved experimentally. After opening up the phase space for the production of real and virtual gauge bosons, the width quickly increases reaching a value of about 1 GeV at the ZZ threshold.

The partial width of the Higgs decay in to one on-shell and one off-shell Z boson is given by

Γ(H

ZZ

) = 3G

m

δ

16π

m

R(x) (3.2)

with δ

=

sin

θ

+

sin

θ

, R(x) = 3(1

8x + 20x

)

(4x

1)

arccos

3x

1 2x

−

1

x

2x (2

13x + 47x

)

−

3

2 (1

6x + 4x

) log x,

(3.3)

18

[GeV]

MH

80 100 120 140 160 180 200

Higgs BR + Total Uncert

10-4

10-3

10-2

10-1

1

LHC HIGGS XS WG 2013

b b

τ τ

µ µ c c

gg

γ

γ Zγ

WW

ZZ

Figure 3.5:The decay branching ratios of the SM Higgs boson as a function of the Higgs boson mass [43].

H t, W

γ

γ (a)

H

W/Z

W/Z (b)

H

f

f¯ (c)

Chapter 3 Higgs Boson Production and Decay at the LHC

where x = m

/m

[44]. The decay width for a Higgs boson mass of 125 GeV is approximately 4 MeV.

[GeV]

MH

100 200 300 1000

[GeV]HΓ

10-2

10-1

1 10 102

103

LHC HIGGS XS WG 2010

500

Figure 3.7: The width of the Higgs boson as a function of its mass [43].

3.4 Status of the Higgs Boson Measurements at the LHC

The ATLAS and CMS experiments at the LHC independently reported in July 2012 the discovery of a new boson with a mass of about 125.5 GeV and properties compatible with the expectations of the SM [2, 3]. The results of the two experiments are in agreement. In the following only the ATLAS results are summarized.

The Higgs boson searches by the ATLAS experiment were performed with pp collision data sets recorded at a center–of–mass energy of

s = 7 TeV in 2011 corresponding to an integrated luminosity of 4.8 fb

and at

s = 8 TeV in 2012 corresponding to 20.7 fb

. Decays of the Higgs boson to γγ, ZZ

and W

W

[45] were considered in the searches. The combined 95% CL exclusion limits on the production of the SM Higgs boson, expressed in terms of the signal strength parameter µ =

SM·BR_SM

, are shown in Figure 3.8 as a function of the Higgs boson mass, m

. The mass regions excluded at 95% CL are 111 to 122 GeV and 131 to 559 GeV.

An excess of events was first observed in the decay channels H

ZZ

4`, H

γγ and H

W W

in the mass region around m

= 126 GeV. The observed p

values for the background-only hypothesis from the combination of the channels are shown as a function of m

in Figure 3.9. A resonance of a new boson was discovered by ATLAS

20

with significance of almost 10 σ at a mass of m

= 126.0

0.4 (stat)

0.4 (sys) GeV.

The average signal strength parameter µ had a value of 1.30

0.15 (stat)

(sys) at m

= 125.5 GeV [46], consistent with the SM hypothesis of µ = 1.

The discovery of the Higgs boson relied on the di-bosonic decay modes, H

γγ, ZZ

and W

W

. In order to establish the mass generation for fermions as implemented in the SM by Yukawa couplings, it is of fundamental importance to verify the direct coupling of the Higgs boson to fermions and it is proportionality to the mass of the fermion (see Section 2.2) to identify the boson as the SM Higgs boson. The most promising Higgs decay channels to fermions are the decays into tau leptons, H

τ

τ

, and to bottom quarks, H

b ¯ b, because of their high branching ratios (see Figure 3.5). The search for the decays to a pair of b quarks requires restriction to Higgs boson production in association with vector bosons V H and to t ¯ t pairs ,t ¯ tH, to provide a trigger signal and to separate the high hadronic background from the signal which is still a challenge. The ATLAS experiment has observed an excess of events above the expected background in the process pp

V H

V b ¯ b with a significance of 1.4 σ [47].

In addition, an excess of events in the decay channel H

τ

τ

has been found by ATLAS with a significance of 4.5 σ [48]. This result provides evidence for the direct coupling of the Higgs boson to fermions.

[GeV]

m

200 300 400 500

µ 9 5 % C L L im it o n

10-1

1

10 ± 1σ

σ

± 2

Observed Bkg. Expected

ATLAS 2011 - 2012

Ldt = 4.6-4.8 fb-1

∫

= 7 TeV:

s

Ldt = 5.8-5.9 fb-1

∫

= 8 TeV:

s

Limits CL

110 150

Figure 3.8:The observed (solid line) and expected (dashed line with1σand2σuncertainty bands) 95% CL limit on the signal strengthµ= _σSM^σ·BR_·BRSM as a function of the Higgs boson mass,mH, from combined measurements ofH →γγ/ZZ/W W decays [2].

Chapter 3 Higgs Boson Production and Decay at the LHC

[GeV]

mH

115 120 125 130 135

0p

10-24

10-21

10-18

10-15

10-12

10-9

10-6

10-3

1 103

106

109

Observed SM expected ATLAS Preliminary

Ldt = 13-20.7 fb-1

∫

= 8 TeV, s

Ldt = 4.6-4.8 fb-1

∫

= 7 TeV, s

σ 0σ 2

σ 4

σ 6

σ 8

σ 10

Figure 3.9:The local probabilityp0for the background-only hypothesis and the correspond- ing signal significance as a function of the Higgs boson mass for the combined decay channels H →γγ/ZZ/W W [49].

The Mass and Signal Strength of the Higgs Boson

The mass of the Higgs boson has been measured to be

m

= 125.5

0.2(stat)

(sys) GeV (3.4) using the two channels with the best mass resolution, H

γγ and H

ZZ

4` [50]. This mass is used for the determination of the signal strength µ of the Higgs production and decay modes. The combination of the three di-boson decay channels [51] gives an average signal strength of

µ = 1.33

0.14(stat)

0.15(sys). (3.5) By including the two decay channels into fermions, H

τ

τ

and H

b ¯ b, an average signal strength of

µ = 1.30

0.12(stat)

(sys), (3.6) is measured which is in good agreement of the SM expectation of 1. The results of the signal strength measurements are shown in Figure 3.10.

22

µ ) Signal strength (

-0.5 0 0.5 1 1.5 2

ATLAS Prelim.

Ldt = 4.6-4.8 fb-1

∫

= 7 TeV s

Ldt = 20.3 fb-1

∫

= 8 TeV s

= 125.5 GeV mH

0.28 -

0.33

= 1.57+

µ γ γ

→ H

0.12 -

0.17 +

0.18 -

0.24 +

0.22 -

0.23 +

0.35 -

0.40

= 1.44+

µ

→ 4l ZZ*

→ H

0.10 -

0.17 +

0.13 -

0.20 +

0.32 -

0.35 +

0.29 -

0.32

= 1.00+

µ→ lνlν WW*

→ H

0.08 -

0.16 +

0.19 -

0.24 +

0.21 -

0.21 +

0.20 -

0.21

= 1.35+

, ZZ*, WW*µ γ

γ

→ H

Combined

0.11 -

0.13 +

0.14 -

0.16 +

0.14 -

0.14 +

0.6 -

0.7

= 0.2+

µ b

→ b W,Z H

<0.1

±0.4

±0.5

0.4 -

0.5

= 1.4+

µ

(8 TeV data only)

τ τ

→ H

0.1 -

0.2 +

0.3 -

0.4 +

0.3 -

0.3 +

0.32 -

0.36

= 1.09+

τ µ τ , b

→b H

Combined

0.04 -

0.08 +

0.21 -

0.27 +

0.24 -

0.24 +

0.17 -

0.18

= 1.30+

µ

Combined

0.08 -

0.10 +

0.11 -

0.14 +

0.12 -

0.12 +

Total uncertainty µ

σ on

± 1

(stat.) σ

theory

)

sys inc.

(

σ

(theory) σ

Figure 3.10: The measured production signal strengths of the Higgs boson with mass mH= 125.5 GeV[46].

Chapter 3 Higgs Boson Production and Decay at the LHC

The Spin and Parity of the Higgs Boson

The measurements of the spin and parity of the newly discovered boson are important for the verification if it is the SM Higgs boson which has spin 0 and even parity (J

= 0

). The observation of the decay H

γγ excludes the possibility of spin 1 as the decay of a massive spin-1 particle into a pair of identical massless spin-1 particles is forbidden [52, 53].

The most sensitive Higgs boson decay channel for the spin and parity measurement is the decay into four leptons. The angular distributions of the final state particles depend on the spin and parity quantum numbers. The decay channels H

γγ and H

W W can also be used for spin and parity measurement. The SM J

= 0

hypothesis has been tested against alternative spin-parity hypotheses, J

= 0

, 1

, 1

or 2

. The J

= 2

hypothesis is based on a graviton model [54]. The observed and expected confidence levels of exclusion of the different spin and parity hypotheses are summarised in Figure 3.11. The 0

, 1

, 1

and 2

hypotheses are excluded at 97.8, 99.97, 99.7 and 99.9% CL, respectively. The SM prediction of J

= 0

is strongly favoured compared to the alternative scenarios [4, 55].

All measurements show good agreement with the SM predictions and the results of the ATLAS and CMS experiments are well compatible with each other.

24

= 0

J

J

= 1

J

= 1

J

= 2

ATLAS

→ 4l ZZ*

→ H

Ldt = 4.6 fb-1

∫

= 7 TeV s

Ldt = 20.7 fb-1

∫

= 8 TeV s

γ γ

→ H

Ldt = 20.7 fb-1

∫

= 8 TeV s

ν νe µ ν/ µ ν

→ e WW*

→ H

Ldt = 20.7 fb-1

∫

= 8 TeV s

σ 1

σ 2

σ 3

σ 4

Data

expected CLs

= 0 +

assuming J P σ

± 1

) alt P ( JsCL

10-6

10-5

10-4

10-3

10-2

10-1

1

Figure 3.11:Observed (black) and expected (blue) confidence levels of excluded alternative spin-parity hypotheses from the combinedH →γγ,H →ZZ^∗ →4`and H →W W^∗lνlν channels [55]. The CL_S is the confidence level of the signal-only hypothesis derived from the ratio of the probability density functions of the hypotheses of interest.

The ATLAS Experiment at the LHC

4.1 The Large Hadron Collider

The LHC at CERN started operation in the year 2009. The LHC is a proton or heavy ion storage ring with 26.7 km circumference located up to 170 m below ground. It is used to accelerate protons or heavy ions and collide them. These proton beams circulate in opposite directions in two vacuum beam pipes which are surrounded by superconducting dipole magnets. The superconducting magnets bend the two beams in a magnetic field of 8.33 T strength which limits the available center-of-mass energy to 14 TeV.

A schematic overview of the LHC and the accelerator chain is shown in Figure 4.1. The interaction regions where the beams cross and the particles are brought to collision are allocated to the four main experiments ATLAS, CMS, ALICE and LHCb. Two of them, the multipurpose and high luminosity detectors ATLAS and CMS, have been designed for the search for the Higgs boson, while ALICE is optimized to study heavy ion collisions and LHCb is a specialized B-physics experiment and for new physics beyond the SM.

Luminosity

The number of events N of a particular process per second generated in LHC collisions depend on the cross section σ(

s) of the process and the instantaneous luminosity, L, of the accelerator and is given by

N = L

σ(

s). (4.1)

Cross sections of important SM processes as a function of the center-of-mass energy and the corresponding event rates for a luminosity of L = 10

cm

s

are shown in Figure 3.2. The machine luminosity depends on the beam parameters such as the number of particles per bunch N

, the number of bunches per beam n

, the relativistic gamma factor γ

, the circulation frequency f

, the geometric luminosity reduction factor F which is due to the crossing angle at the interaction point, the

∗

Chapter 4 The ATLAS Experiment at the LHC

Figure 4.1: The CERN accelerator complex [56]. The protons, produced by ionizing hydro- gen, and first accelerated in LINAC 2 followed by the BOOSTER. Afterwards, the protons are further accelerated by the Proton Synchrotron (PS) and the Super Proton Synchrotron (SPS) before they are injected into the LHC were they reach their final collision energy. The ATLAS experiment is one of the of four major experiments at the LHC together with CMS, LHCb and ALICE, at the LHC.

28