Systematic Uncertainties on the Top Quark Background in the 1 Jet Channel of the ATLAS H → WW Analysis of the Higgs Boson at the LHC.

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Systematic Uncertainties on the Top Quark Background in the 1 Jet Channel of the ATLAS H → WW Analysis of the

Higgs Boson at the LHC.

WILLIAM SKÖLD

Master of Science Thesis Supervisor: Jonas Strandberg Examiner: Bengt Lund-Jensen

TRITA-FYS 2013:26 ISSN 0280-316X ISRN KTH/FYS/–13:26–SE

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iii

Abstract

The Large Hadron Collider (LHC) is the worlds largest proton-proton collider experiment, located at CERN in Switzerland. Two of the main detector experiments are ATLAS and CMS. This thesis presents the cut-based analysis of the Higgs boson H → W W^∗→ ``νν decay mode, using 20.7 fb⁻¹of collected data at a center of mass energy of√

s = 8 TeV at ATLAS. The analysis shows a 3.8 standard deviation excess of events, consistent with a Higgs boson of mH = 125 GeV. The signal strength at this mass is µ = 1.01 ± 0.31, where both systematic and statistic uncertainties are accounted for.

Estimations of the top quark systematic uncertainty is also presented. The system- atics come from the extrapolation of events from the top control region to the signal region. Two sources are taken into account in the analysis: event generator and parton showering algorithms. The analysis is performed for the 1-jet channel of H → W W . The estimate is obtained by using alternative Monte Carlo samples for the top background. Each sample varies one of the systematic sources to determine its effect. For the combined `` channel, the two sources amount to a total of 2.9% systematic error.

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iv

Sammanfattning

LHC (the Large Hadron Collider) är världens största proton-proton accelerator.

Den är byggd vid CERN i Schweiz, och två av dess huvudsakliga detektorer är ATLAS och CMS. Den här avhandlingen sammanfattar den nominella analysen av higgsboso- nen i sönderfallskanalen H → W W^∗→ ``νν vid ATLAS. Analysen använder den fulla datamängden på 20.7 fb⁻¹, vid kollisionsenergin√

s = 8 TeV. Resultaten visar ett sig- nalöverskott på 3.8 standardavvikelser, något som stämmer överens med en higgsboson vid mH = 125 GeV. Signalstyrkan vid den här massan är µ = 1.01 ± 0.31, där både statistiska och systematiska fel är inräknade.

En uppskattning har också gjorts av den systematiska osäkerheten på toppkvarks- bakgrunden. Denna osäkerhet kommer från extrapolationen av kollisioner i kontroll- regionen till signalregionen. Två systematiska felkällor är medtagna i beräkningen:

event-generator och hadroniseringsalgoritmer. Analysen är för de H → W W kollision- er som innehåller en jet i sluttillståndet. Uppskattningen är gjord genom att byta ut Monte Carlo simuleringarna mot alternativa simuleringar. Vid varje byte varieras en källa för systematiska fel för att uppskatta dess effekt. Den kombinerade `` analysen ger ett slutgiltigt systematiskt fel på 2.9% från de två felkällorna.

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Introduction

Humans have always had a fundamental desire to explain the world around them. Elemen- tary particle physics focuses on the basic interactions of matter on the smallest of scale.

Complex macroscopic systems are stripped down to find the basic rules that explain matter and govern its interactions in our universe. These basic rules are summarized in what we call the Standard Model. This model explains how matter is built from a relatively small number of independent fundamental particles, like for example the electron. It also explains how these particles interact with each other through the electromagnetic, the weak and the strong force. The model does not however incorporate the gravitational force, which is several orders of magnitude weaker than the others.

The theoretical framework of particle physics is quantum field theory [1]. Here particles are explained as excitations of an underlying quantum field that permeates the universe.

These fields are specific to each type of particle and there is no way of distinguishing the properties of different excitations if they belong to the same underlying field. The fields are independent of each other and they communicate only through exchange of force quanta – excitations of the different force fields. Each force couples to a specific property of another particle. In the case of the electromagnetic force we have the electric charge, while the strong force couples to color charge. It was eventually discovered that the underlying fields of the electromagnetic and the weak forces are in fact mixed with each other, and the two forces were thus combined to form the electroweak force.

The Standard Model has been able to account for many of our experimental observations, but it could not explain why the particles that mediate the weak force were massive. A solution to this problem came in the 1960s by Peter Higgs among others and is named the Higgs mechanism [2]. It predicts a breaking of the electroweak symmetry via a scalar field with a non-zero vacuum expectation value. This scalar field and its connected Higgs boson would introduce mass terms to the weak bosons as they interact with the vacuum of the Higgs field. The masses given by this theory agrees with measurements, but the underlying Higgs particle could not be found.

Since then, one of the major goals with experimental particle physics has been to find this missing piece of the puzzle. One attempt is done at the particle accelerator LHC in CERN, which collides high energy protons against each other. In July 2012 they announced that they had discovered a new particle with a mass of around 125 GeV that is consistent with the long searched for Higgs particle [3, 4]. This thesis will give a short theoretical introduction of the Standard Model and the Higgs mechanism, but will mainly focus on the experimental part of improving the significance of the Higgs boson signal in one of its decay modes. Throughout the thesis, the constants c and ¯h will be set to unity.

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viii INTRODUCTION

Author’s Contribution

The Higgs boson analysis described in this thesis is a collaborative work performed by the H → W W group at the ATLAS experiment. The study of systematic uncertainties described in Chapter 5 is however carried out solely by the author. The Figures that are connected to the analysis are all provided by CERN, except for the Feynman diagrams, which are produced by the author.

In addition to this document, the author has gained a lot of knowledge during the process of making this thesis. Firstly, a general insight to the world of cutting-edge research and scientific methodology. Secondly, the author also has learned the software analysis framework (HWWAnalysisCode) that is used to perform the H → W W analysis. This provides the possibility to recreate the event distributions seen in the analysis figures, which are identical to what ATLAS presented at the Moriond conference in 2013. The number of expected events for each background is also obtained using the same framework.

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Chapter 1

The Standard Model

The Standard Model (SM) of particle physics is an attempt to summarize our understanding of how particles interact on a fundamental scale. It includes the fermions, that constitute the matter in our universe, and the bosons, that govern the interactions between particles [5, 1].

The theory has been tested experimentally to great success, and the modern formulation was completed in the 1970s as experimentalists confirmed the existence of quarks.

Since particle physics treats objects on a very small scale, the theory to describe them must have roots in quantum mechanics. But the particles are generally moving at speeds close to c, so it is necessary to also incorporate the theory of special relativity. When taking both of these into account, particle physics ends up on the theoretical foundations of quantum field theory (QFT). Here particles are introduced as fields that span the universe.

The field is initially in its vacuum state and no particles exist. If energy is transferred to it, the field can be excited – much like the different energy states of a harmonic oscillator. It is these excitations that are interpreted as particles. This way particles can be created and annihilated, something that cannot be done in quantum mechanics alone. But in particle physics the number of particles does not need to be conserved. What is important is the conservation of energy and quantum numbers such as spin and charge.

Different types of particles are members of different fields, and they exist independently of each other. They interact through exchange of force quanta, and so the force is determined by the couplings to the different force fields. To every particle there also exist an antiparticle. They are connected by inverting their charges. Here charge refer not only to the electromagnetic charge, but the charges of all the different forces (see Section 1.2).

An antiparticle is denoted by the particle letter with a bar above, for example ¯p for the antiproton. Some particles, like the photon, is its own antiparticle.

Since its first formulation, the SM has made several predictions such as the existence of the neutral current of weak interactions and the top quark. But even though the theory can explain a wide variety of experimental observations, it is not the complete picture of our universe. The concepts of dark matter and neutrino oscillations are not included, and nor is the gravitational force. The last thing in the model that was proven experimentally was the existence of the Higgs boson, the particle that is responsible for the mass of fundamental particles. The origin of this particle is discussed separately in this chapter.

1.1 Matter

The fundamental constituents of matter are the fermions – particles with non-integer spin.

These particles obey Fermi-Dirac statistics and are subjects to the Pauli exclusion principle, 1

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2 CHAPTER 1. THE STANDARD MODEL

saying that two identical fermions cannot occupy the same quantum state [5]. Matter can be divided further into leptons and quarks, and each of these are divided into three different generations. The different generations hold particles of quite similar properties, but with a separation in mass. The first generation of particles are the lightest ones, and it is these particles that are the most common in our universe (see Table 1.1). The reason for this is a rule of thumb: if a particle can decay – it will. Nature seem to search for the lowest energy state and if a decay is allowed, a large mass difference makes this process happen faster.

1.1.1 Quarks

Quarks (denoted by q) are characterized by their fractional electric charge and their property of having color. They can be either red (r), green (g) or blue (b), while antiquarks have anticolor. This is however not a color in the usual sense. It is just the quantum number that makes quarks couple to the strong force. Its only similarity with color is that when they are all added together, the result is something neutral, or white. This is closely related to the concept of quark confinement – quarks cannot exist as free particles. Instead they are found as bound states of either two (q¯q) or three (qqq/¯q¯q¯q) quarks that together form a color neutral combination (that incidentally also has an integer electric charge). These combinations form the so-called hadrons. Protons (duu) and neutrons (ddu) are the two most common examples. More exotic hadrons exist, but these usually involve the second and third generations of quarks, and thus decay with time.

The hadrons are divided into groups depending on the amount of quarks they have. The ones with three quarks are called baryons and form a fermionic state. The lighter mesons consist of two quarks and form bosons¹, like for example the pion π⁻ (d¯u). Each quark has a so-called baryon number B assigned to it: quarks have 1/3 and antiquarks have −1/3.

Thus all mesons have B = 0, while baryons and antibaryons have B = ±1. Particles not composed of quarks all have zero baryon number. The baryon number is conserved in all interactions. So if a neutron decays and B is conserved, the only lighter particle available is the proton. The mass difference here is however quite small, so the lifetime of a neutron is long.

1.1.2 Leptons

Leptons (denoted by ` and ν) is the other group of fermions. They are also divided into three different generations, with two particles in each – one negatively charged and one neutral known as a neutrino. The most well-known lepton is the electron. Each generation of leptons are given a lepton number L` much like the baryon numbers of quarks. In each interaction, the lepton numbers of each generation must be conserved. In the case of the first generation, both the electron and its neutrino has Le = 1, while their antiparticles have the opposite sign.

When it comes to the interactions of leptons, they can in general interact through the electromagnetic and the weak forces. But it is only the charged leptons that couple to the photon of electromagnetism. The neutrinos can only interact weakly, and since this force is weak, neutrinos tend not to interact much. They are created mainly in the β decay of a nucleus and in the fusion processes of the sun, and can easily pass through earth without interacting at all. In detector experiments, they are thus shown as imbalances in the energy and momentum conservation equations.

1Fundamentally, the word boson does not refer to the property of mediating force. The categorization just refers to the particles spin, and what statistical distribution it follows.

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1.2. FORCES 3

Fermions (spin 1/2)

Leptons Quarks

Generation Flavor Charge Mass Flavor Charge Mass

First e(electron) −1 0.511 d(down) −1/3 4.8

ν_e (e neutrino) 0 0 u(up) 2/3 2.3

Second µ(muon) −1 106 s(strange) −1/3 95

ν_µ (µ neutrino) 0 0 c(charm) 2/3 1280

Third τ (tau) −1 1777 b(bottom) −1/3 4180

ντ (τ neutrino) 0 0 t(top) 2/3 174000

Table 1.1: Masses are given in MeV and charge in units of the proton charge [6].

Gauge Bosons (spin 1)

Force Mediator Charge Mass Lifetime

Electromagnetic γ (photon) 0 0 ∞

Strong g (8 gluons) 0 0 ∞

Weak W^± (charged) ±1 80 3 × 10⁻²⁵

Z⁰(neutral) 0 91 3 × 10⁻²⁵ Table 1.2: Masses are given in GeV, lifetime in seconds, and charge in units of the proton charge [6].

1.2 Forces

There are four known forces in our universe: the electromagnetic (EM), the weak, the strong and the gravitational force. Of these, the three first are accounted for by the SM. This thesis will briefly describe these three forces. The unification of the two first into the electroweak force is later brought up together with the mass mechanism in Section 1.3.

Quantum field theory uses the Lagrangian formalism to solve the equations of motion for particles. All three force fields arise out of a so-called gauge theory. This theory describes the set of local transformations that leave the Lagrangian invariant. Since the Lagrangian determines the motions, these transformations form the set of redundant degrees of freedom of the system. Together the transformations form a group, and it is on this gauge group that the theory of a force field is based. The quantizations of such fields form spin 1 bosons that mediate the different forces (see Table 1.2). It is the amount of degrees of freedom (or generators) that determine the number of gauge bosons connected to a force. The concept of gauge theory was first used in Maxwell’s classical theory of electromagnetism, where a function can be added to the field potentials without changing the fields themselves.

1.2.1 Gauge Theory as Applied to QED

The theory that describes the electromagnetic force is called quantum electrodynamics (QED). Since it has the simplest gauge group structure, this force will be described in more detail here than the others. This is done to give a description of how the forces arise out of

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symmetries through gauge theory. The Lagrangian of a non-interacting Dirac electron ψ of mass m is given by

LDirac= ¯ψ(iγ^µ∂_µ− m)ψ (1.1)

where γ^µ are the Dirac matrices. Note that there is no interaction of the electron with a force field – that is, no term containing both the electron field and a force field. Naturally, an electron should interact with the electromagnetic field, so this cannot be the complete picture.

Gauge theory is used to find the missing interaction part. QED is based on the symmetry group U(1). This group consist of all the rotations of complex phase e^iθof a field, and it has only one group generator, or one degree of freedom. It is clear that a global change of phase in the field does not affect the Lagrangian above, the same way as shifting the universe one meter to the right does not change our physics. But the gauge theory should be of a local transformation, and the phase shift should thus be allowed to vary over spacetime as θ= θ(x^µ). If this local transformation is scaled to the electric charge as e^−ieθ(x^µ⁾ and put into Equation 1.1, the derivative creates a new term.

LDirac → LDirac+ (e ¯ψγ^µψ)∂µθ(x) (1.2) Since the goal is to have a Lagrangian that is locally gauge invariant under U(1), an extra term is added to counteract this. The new Lagrangian then becomes

L= LDirac+ Lint= ¯ψ(iγ^µ∂_µ− m)ψ − (e ¯ψγ^µψ)Aµ (1.3) where Aµ is a new field that also transforms under the gauge transformation as²

A_µ→ A_µ+ ∂µθ(x) (1.4)

To conclude what just happened: The Lagrangian was demanded to be invariant under a local U(1) transformation. As a consequence, a new field was forced to be added to counteract the extra term that came from the derivative. This new field couples to the electron as Lint in Equation 1.3, and is nothing else than the normal four-potential of electromagnetism. Thus this extra term gives the couplings of electrons to photons and its connection to the electric charge −e. This interaction term can also be included in a so- called Covariant Derivative Dµ. That way the derivative of the transformed field transform the same way as the field itself.

Dµ≡ ∂µ+ ieAµ(x), Dµψ → e^−ieθ(x)Dµψ (1.5) The final Lagrangian of QED is given by adding the part from the EM field itself:

LQED= ¯ψ(iγ^µDµ− m)ψ −1

4F^µνFµν (1.6)

where Fµν = ∂µAν− ∂νAµ is the electromagnetic field tensor. This Lagrangian is invariant as both the fermion field ψ and the gauge field Aµsimultaneously are transformed as above.

It can easily be shown that also Fµν is invariant under this U(1) gauge.

The theory of electrodynamics have had several very accurate predictions of experimental results and have thus provided a good theoretical foundation for the other forces. All of them are based on the same type of gauge theory, but with other local symmetries. What makes the theory of the other forces more complex is the fact that their gauge group is

2Compare this to the gauge transformation of classical electrodynamics.

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1.2. FORCES 5

non-Abelian. While QED arose from the multiplications of a complex phase, the two other forces have symmetry groups involving complex matrices.

1.2.2 The Weak Force

The weak interactions are a bit special in the sense that they only couples to left-handed particles. The property of handedness of a particle is called chirality and they can be transformed into each other by the parity operator P , whereby all space vectors change sign. This means that the physics of weak interactions does not look the same in a mirror.

The gauge theory of weak force is based on the SU(2) gauge group³. What governs the weak force is the so-called weak isospin, intrinsic properties whose operators Tⁱare rescaled versions of the three 2×2 Pauli matices σⁱ. All fermions have weak isospin, but the concepts will here only be applied to the leptons. The problem with parity violation is due to the fact that there are no right-handed neutrinos. The chirality states of the electron generation consists of one doublet and one singlet:

νe

e

!

L

e

R (1.7)

What the weak force does is to do a local symmetry rotation of the isodoublet, and thus converting an electron into its neutrino. This is why the weak force cannot act on right- handed particles. Much like there are three independent Pauli matrices, there are three degrees of freedom in the gauge theory of the weak force, and thus three gauge fields. Of the three isospin operators, only T¹and T² rotate the isodoublet. A linear combination of their corresponding gauge fields form the well known W^±bosons that constitute the charged weak current. The third gauge boson, connected to the T³generator, does not however form the Z⁰ boson. Instead it forms the W⁰ boson, a close relative. This only makes up for a part of the neutral weak current. The missing part is found once the electromagnetic and weak forces are unified, as will be demonstrated in Section 1.3. Another thing that makes the weak force different is that it is the only force with massive gauge bosons. Taking the normal approach of gauge theory, the resulting fields must be those of massless particles.

This is however explained by the addition of a Higgs boson. The high mass is the reason why the weak force has a very short range. For a mediating boson to be exchanged, energy must be borrowed from the vacuum. It is quite fundamental that energy should be conserved, but due to Heisenberg’s principle this violation is possible during a very short time, under which the bosons cannot travel too far.

1.2.3 The Strong Force

The strong force couples to the color charge of quarks, and is the theory of quantum chromodynamics (QCD). It is the force that binds the quarks together in hadrons, and the force mediator is the massless gluon. The idea of strong interactions is the same as for the weak force’s rotations of weak isodoublets. But instead it describes rotations in a space of colors. Since there are three colors, the rotations are members of the SU(3) group. There are eight group generators in the form of the 3 × 3 equivalents of the Pauli matrices, and these are the representations of gluons. Gluons carry the strong charge themselves – they have one color and one anticolor.

3SU (N ) is the group of Special Unitary N × N matrices. The word special refers to the property of having determinant 1, and a matrix is unitary when its transposed conjugate is the same as its inverse. The group can thus be thought of as rigid rotations in a complex N -dimensional space.

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q

¯ q

q

¯ q^′ q^′

¯ q

Figure 1.1: The potential build-up of energy when quarks are separated eventually gets high enough to create new quark pairs from the gluon field.

In a pure combinatoric approach one might expect there to be a total of nine gluons, since there are three colors and three anticolors. But the group has only eight degrees of freedom, and one of these nine gluons are in fact a linear superposition of other gluons.

Since the force carriers themselves have color, they are also subject to the strong force.

Thus by self-interactions, a gluon can be emitted from another gluon. This property is the reason why the strength of the force increase as a function of interaction distance. At small separations of quarks, the QCD coupling goes down, and thus quarks in a proton do not feel the force as much. This is called asymptotic freedom. This odd behavior can be contrasted to the r⁻² behavior of the photon, which do not carry electric charge and thus cannot interact with itself.

Since the potential is increased when two quarks are separated, the quarks are confined to colorless bound states. If two quarks are separated, the potential energy build-up is even- tually enough to create q¯q pairs from the gluon field. This process is called hadronization (see Figure 1.1). If there is a large amount of energy, this can happen repeatedly to create a shower of newly created hadrons, known as a jet.

1.3 The Mass Mechanism

Now all forces in nature had their own theory, based on gauge invariance. But there were still some questions unanswered, especially concerning the weak force. The theory of weak SU(2) invariance produces three independent fields, and predicted the existence of a neutral weak current. But when this was experimentally verified, its coupling strength was found to be smaller than the theoretical predictions.

To explain this, the electromagnetic and weak interactions are combined [7] under the gauge group SU(2) × U(1). The idea is that the neutral generator T³of the weak force is mixed with a new U(1) field. This new field is given the property of weak hypercharge Y . The well-known electric charge Q is then constructed as a mixture of T³ and Y as:

Q= T³+1

2Y (1.8)

The whole U(1) theory is redone with Y as the fundamental charge, and the emerging boson field is called B. But this field is not what is observed. It mixes with the weak W⁰

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1.3. THE MASS MECHANISM 7

Figure 1.2: This is a summary of the particles in the Standard Model and their interactions with each other.

boson and forms our known Z⁰ and γ:

Z⁰ γ

!

= cos θw −sin θw

sin θw cos θw

! W⁰ B

!

(1.9) The theory gives us a weak mixing angle, that determines how much the forces are mixed to give the strength of the electromagnetic force and the weak neutral current that we measure. Thus QED and weak interactions are merged together into a SU(2)L× U(1)Y

electroweak gauge theory. Hidden by a mix of these lies the usual electromagnetic U(1)em

gauge group.

By this unification, it was possible to explain the coupling strength of the Z⁰boson. But an even bigger problem existed. When creating these gauge theories, the resulting gauge fields are demanded to be massless to keep Lorentz invariance. But in the case of the weak force, experiments prove that this is not true at all. The masses are in fact quite large, lying at mZ = 91 GeV and mW = 80 GeV.

The solution to the problem is given by spontaneous symmetry breaking and the mass mechanism⁴ [8]. This mechanism starts by introducing a new scalar field with a non-zero vacuum expectation value into the electroweak theory. Then the field would be a complex SU(2) doublet of the form:

φ= φ₁+ iφ2

φ3+ iφ4

!

(1.10) For an easier example, the principles will here instead be applied to a U(1) theory, with a complex field of the form φ = φ1+ iφ2. Consider this quite special Lagrangian:

L= T − U =1

2(Dµφ)^∗(D^µφ) +1

2µ²(φ^∗φ) −1

4λ²(φ^∗φ)² (1.11) Here the first term is recognized as the kinetic energy of the field, while the two latter terms form the famous ”mexican hat” potential (see Figure 1.3). The covariant derivative

4Also referred to as the Higgs mechanism. But since there are many more names involved in the discovery of this theory, it will here be referred to in a more neutral way.

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Figure 1.3: The potential shape of a field φ = φ1+ iφ2 with a non-zero vacuum expectation value.

D_µ = ∂µ+ iqAµ assures that the lagrangian is gauge invariant under local U(1) transfor- mations, and contains the electromagnetic field Aµ. From the figure it is easy to see that the vacuum state of the field φ is not zero. The φ = 0 state is unstable, and thus inevitably falls down to a lower energy state. The energy minimum is given by a circle at the bottom of the potential. But the lower states does not (locally) seem to have the radial symmetry that existed before. This symmetry has been hidden by the choice of a particular ground state. This is what is called a spontaneously broken symmetry. Any given universe is in one particular ground state. A collection of them would show that the symmetry still exists, but any given ground states hides it.

The ground state is determined by |φ| = µ/λ ≡ v and can be given any phase. By the help of U(1) gauge transformations it is possible to transform the ground states into each other. One can thus choose to work with the real valued state where φ1 = v and φ₂= 0. This state is taken to be our universe. It is necessary to translate the Lagrangian to a shifted field η = φ − v to get the physics of the ground state. After inserting η into Equation 1.11 the result is:

L=1

2(Dµη)^∗(D^µη) − µ²η²

+q²µ² 2λ² AµA^µ + q²µ

λ A_µA^µη − λµη³−λ² 4 η⁴

+ µ⁴

4λ²

(1.12)

The first row is the Lagrangian of the now massive η field, while the second row shows a quadratic term in Aµ representing the newly acquired mass of the electromagnetic field.

Inside the curly brackets there are terms containing three or more fields. These represent fundamental interaction vertices in Feynman diagrams. The final term is just a constant, and does not affect the physics of the Lagrangian. Equation 1.12 is still gauge invariant under U(1) transformations. Here it is written in a particular gauge in which the complex scalar field has a real valued ground state, and this is done to be able to interpret the physics easier.

Finally it has been shown how the use of local gauge invariance and spontaneous symmetry breaking of a field with a non-zero vacuum expectation value leads to a mass of the

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1.3. THE MASS MECHANISM 9

gauge field. In this case, the photon gained a mass. One important thing to notice is that the mass comes from interactions with the vacuum state of η. There is no need for the photon to interact with its excitations to gain mass. In the case of the Higgs boson, the theory is applied to the complex SU(2) doublet seen in Equation 1.10. Thus the weak vector bosons are given mass instead, and the η used above describes the Higgs boson. In order to keep the photon massless, this field is also assigned a hypercharge Y = 1/2. Thus φtransforms as

φ → eîαâ^Tâeîβ/2φ (1.13)

If one now performs a gauge transformation on the ground state⁵with

α¹= α²= 0, α³= β, φ= 0

v

!

(1.14) it is easy to see that φ remains invariant. Incidentally, this transformation is exactly the subgroup of SU(2) × U(1) that makes up the electromagnetic field U(1)em (compare this to Equation 1.8). This invariance leads to the zero mass of the photon.

This mechanism also describes how fermions gain mass through so-called Yukawa couplings to the Higgs field. By adding such a coupling and following the steps of symmetry breaking and expanding the lagrangian in a suitable vacuum state, one gets a mass term for a fermion f as

m_f = λfv (1.15)

where v is the vacuum expectation value of the Higgs field. But this theory introduces the dimensionless parameter λf which is not fixed by the theory.

The theory of this mass mechanism is the only part of the Standard Model that is yet to be experimentally confirmed. The theory has been known for 50 years and remains the only pretty way of giving masses to the weak gauge bosons. But in 2012 ATLAS and CMS both reported the discovery of a new particle at a mass of 125 GeV consistent with the predictions of the Standard Model Higgs boson [3, 4]. Now the analysis continues to better determine its properties.

5This ground state can be chosen by gauge transformations, in the same way as with the SU (2) singlet field.

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Chapter 2

The LHC and the ATLAS Detector

To probe the world of fundamental particles and their behavior, energy is required. This energy has to be enough to create the particles that an experiment is set out to study.

Historically, the only place where these high energetic particles could be found was in cos- mic rays and radioactive decay. Today experiments are performed in particle accelerators.

One of these experiments is the Large Hadron Collider (LHC) which is built by CERN in Switzerland. It is the largest accelerator ever built, and one of its main purposes is to search for the long lost Higgs boson and thereby find the last piece of the Standard Model.

2.1 The Large Hadron Collider

The European Organization of Nuclear Research, known as CERN, is operating the worlds largest particle accelerator LHC [9] outside of Geneva in Switzerland. The accelerator was finished in 2008 and replaced the previous lepton accelerator LEP. Since a project of this size consumes a large budget, the accelerator ring was built to fit into the already existing tunnels of LEP. These tunnels lie on average 100 m below ground and has a total circumference of 27 km. The accelerator is a synchrotron that accelerates protons in opposite directions along the beam pipe. The accelerator is built to operate at the enormous center of mass energy√

s= 14 TeV, an energy that is several times higher than any previous experiment¹. To get an idea of how much energy this is, it is comparable with the energy of a flying mosquito [10]. This does not sound much, but it is concentrated into one single subatomic particle and there are 10¹¹ protons traveling together in a bunch, so it makes up for a lot of kinetic energy. This high energy requires strong magnetic fields to bend the particle tracks, and a 7 TeV proton would require a 8.33 T field to stay on track. To reach these strengths, superconducting magnets are used. These magnets operate at below 2 K by the help a cryogenic system of liquid Helium. But it is not only a high energy that is needed in these experiments. Another important factor is the beam luminosity, that determines the collisions per second in the detectors. The LHC is built for the high peak luminosity of L= 10³⁴ cm⁻²s⁻¹. All these high precision technologies make the LHC a wonder among engineering systems.

Hadron colliders are usually the choice when searching for new physics, but they have one inherent issue. When hadrons are accelerated, it is well known what the hadron energy is. But one can never know the energy stored in the separate quarks. And since the collisions at these energies are between the quarks and the gluons, the total energy in a collision cannot be determined more than as a stochastic sample of an energy distribution.

1The second largest accelerator, the Tevatron, reached a maximum center of mass energy of 2 TeV.

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12 CHAPTER 2. THE LHC AND THE ATLAS DETECTOR

Figure 2.1: Layout of the LHC accelerator, including the injection chain and the four main experiments.

There is thus no way of a priori knowing the rest frame of a collision. The only thing that is known is that the collision is at rest in the plane transverse to the beam axis.

The LHC is built mainly for the use of protons, sent in opposite directions at equal energies. But the underground tunnels where the accelerator is built are too small to fit two separate accelerators. The two beams thus have to be fit into one single accelerator tube. This tube separates the two beams everywhere except at four points, where the detector systems are built and the protons collide. The fact that both beams have the same electric charge makes it necessary to have opposite magnetic fields to direct the beams around the accelerator. Another way of solving this would be to use antiprotons in one of the directions. But it is much cheaper to use protons, and at these energies the particle type does not matter much.

The four main experiments of the LHC are located where the opposing beams coincide (see Figure 2.1). There are two large general purpose detectors: ATLAS [11] and CMS [12].

Their job is to identify all the different kinds of reactions that can occur when the protons collide. They investigate a wide variety of physics, including the Higgs boson and signs of dark matter. The ATLAS detector is discussed in more detail below, since it is used for the analysis of this thesis. The two slightly smaller detectors are LHCb [13] and ALICE [14].

The former studies the b quark and the CP -violation to get a better understanding of the abundance of matter over antimatter in our universe, while ALICE do not study proton collisions at all. Instead it operates when the LHC collides lead ions. In these collisions enormous temperatures are reached, and the hadrons melt into a quark-gluon plasma. This is then analyzed to get a better understanding of our early universe and of the big bang.

2.1.1 Acceleration Process

At its full potential of 7 TeV, the protons move almost at the speed of light. In the lab frame, light only outruns the protons by 3 m/s. But to get to those speeds, a separate acceleration system is needed before the protons are injected into the LHC. This system

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2.1. THE LARGE HADRON COLLIDER 13

consist of four pre-accelerators in a chain: Linac2 – Proton Synchrotron Booster (PSB) – Proton Synchrotron (PS) – Super Proton Synchrotron (SPS), as seen in Figure 2.1.

The protons are first accelerated by the linear accelerator to 50 MeV and fed into the chain of synchrotrons. Here they are boosted to 1.4 GeV, 25 GeV and 450 GeV respectively before being injected into the main accelerator [15]. The LHC is this way filled up with bunches of protons before the last acceleration process initiates and the particles gain their final energy.

Once the proton beams are operating at full energy, they have a certain lifetime. The main factor is the luminosity decay due to collisions at the intersection points. Other factors are loss of beam quality and mean free paths in the beam pipe vacuum. When the luminosity is low enough, the acceleration process starts over to gain an overall higher integrated luminosity and thus better statistics.

2.1.2 LHC Subsystems

There are a lot of systems that work together to make an accelerator like the LHC possible [9]. To get the high energies necessary, radio-frequency (RF) cavities are used to accelerate the protons. A high vacuum must be achieved so that the beam can move freely inside the beam pipes, and strong magnets are used to shape and direct the beam. The magnetic fields used require a very large current, so they must be superconducting. Thus a cryogenic cooling system of liquid Helium is incorporated. Here follow a brief description of these systems.

• RF System

The acceleration is performed by using the electric parts of a photon field. A wave guide that holds a standing wave of 400 MHz radio-frequency photons is placed in the beam pipe. The field phase is controlled so that the proton bunches pass as the field strength is at its maximum. This system automatically dampens any longitudinal injection errors since the field phase varies in time. When the protons are injected, they already travel close to the speed of light, so during the whole acceleration process the RF cavity frequency only change by 1 kHz in order to make sure that the EM phase is the same when the protons come back to the cavity.

• Magnets

The proton beams are manipulated using magnetic fields. The fields are produced by superconducting NbTi dipole and quadrupole magnets along the tracks at the LHC.

The dipole magnets produce a uniform transverse field to bend the proton tracks.

Each dipole bends the tracks by 5.1 mrad. It is the field strength of over 8 T in these magnets that is the limiting factor of the total energy attainable. The quadrupole magnets are used to focus the beam. This is necessary since the proton charges make the beam divergent with time.

• Vacuum

Vacuum systems are used for two things in the LHC. It is used to insulate the cryogenic system and to ensure a long lifetime of the proton beam. The criteria of the beam vacuum is very strict to ensure a lifetime of 100 hours – up to 10⁻⁹ Pa at the interaction points.

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• Cryogenics

Installed along the beam pipe is the cryogenic system. It is filled with superfluid He- lium to cool the magnets to well below the critical temperature. The nominal value for the magnetic fields are produced by currents up to 12 kA, and to have a sufficient temperature margin the magnets are cooled down to 1.9 K. To keep the temperatures low, efficient beam operation is required, since beam losses are absorbed by the beam pipe as heat.

Day in 2012

26/03 31/05 06/08 11/10 17/12

]-1 Total Integrated Luminosity [fb

0 5 10 15 20 25

30 ATLAS Online Luminosity^s^{= 8 TeV} LHC Delivered

ATLAS Recorded Total Delivered: 23.3 fb-1

Total Recorded: 21.7 fb-1

Figure 2.2: Integrated luminosity during 2012.

2.1.3 Performance

The most important parameter of the LHC is the number of events detected by the experiments. This number is proportional to the luminosity integrated over time as

Ne= Lσe (2.1)

where σe is the cross section of a particular type of event. The only way of gaining large statistics for rare events is thus to have a high integrated luminosity L. This is achieved at the LHC by its high beam intensity. But there is a limiting factor in the detector systems, something that is known as pile-up. This is the number of proton interactions in one bunch crossing, and this should not get too large in order to separate different events from each other. If too many events occur close to each other, the tracks of individual particles cannot be categorized into unique events. There is also a limitation in the calorimeter response time to separate events in time. Using the nominal beam parameters, the expected amount of pile-up is estimated to be around 23 [16].

In Figure 2.2 the integrated luminosity is shown as delivered by the LHC and recorded by the ATLAS experiment. The difference between the two is due to the fact that the detector has a measured 95% efficiency at recording data. Table 2.1 also shows some beam parameters at their designed values and the once used in the 2012 physics run. At the end

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2.2. THE ATLAS DETECTOR 15

2012 Nominal

CM Energy [TeV] 8 14

Gamma factor 4260 7460

Luminosity [cm⁻²s⁻¹] 7 × 10³³ 10³⁴

Amount of bunches 1380 2808

Bunch spacing [ns] 50 25

Protons per bunch 1.4 × 10¹¹ 1.15 × 10¹¹ Table 2.1: LHC beam parameters. [18]

Figure 2.3: The ATLAS detector.

of 2012 years data collection, the accelerator was shut down for maintenance and will start again in 2015 at a center of mass energy close to the nominal of 14 TeV [17].

2.2 The ATLAS Detector

The ATLAS (A Toroidal LHC ApparatuS) detector is one of two general purpose detectors of the LHC, and is the largest of the two. It spans 25 m in diameter, is 44 m long and weights 7000 tonnes, as seen in Figure 2.3. It is designed to account for any expected new physics at the new energy scales that LHC provides, with the Higgs boson production as a benchmark for the performance of the detector subsystems. It thus has to be able to reconstruct the vast majority of different particles that are created in an event. At a Higgs mass of 125 GeV, the expected natural width is only a few MeV, so the observed width is defined by the detector resolutions. The detector thus has to be able to make precise measurements of particle tracks, charge, mass, momentum and energy in order to get the desired precision. In addition to this, there are many other requirements on a detector at the LHC. The high fluxes makes it essential to have radiation resistant materials and a fast read-out time to reduce eventual overlap between events. The detector is therefore divided into subsystems that specializes on different types of measurements.

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ATLAS has a cylindrical shape centered around the beam axis, including two end-cap detectors at either side. This makes interactions rotationally invariant around the beam pipe. Its design is optimized to minimize the probability of not detecting particles by removing dead angles and inactive material. Closest to the beam pipe is the inner detector (ID), which is used to trace charged particles as they move away from their creation point.

Outside of this lies the calorimetric system that is responsible for determining the total energy of particles. In the outer layers are the muon spectrometer, which is implemented to take advantage of the large penetration depth of muons. The detector is embedded in a magnetic field that bend the tracks of charged particles to give information about their charge and momentum. The subsystems of ATLAS will be covered in more detail below.

2.2.1 Coordinate System

Because of the detector symmetry, cylindric coordinates (θ, φ) are used with the beam pipe as the axis of symmetry. But due to the fact that collisions are head on and the average center of mass frame is at θ = π/2, one often incorporates the so-called pseudorapidity, defined as

η= − ln

tan θ

2

(2.2) This way, a typical reaction would be uniformly distributed in φ and have an expectation value of hηi = 0. The shape of η is antisymmetric around this value, and large positive or negative values correspond to angles close to the beam axis. At η = 2.44, the corresponging polar angle is θ = 10^◦. Any reference to a cone is defined in these variables as in Equa- tion 2.3. The reason for defining η as above is that it is an approximation of the relativistic quantity rapidity when β → 1. This is desirable since differences between two rapidities are Lorentz invariant under boosts in the beam direction [19].

∆R=p

∆η²+ ∆φ² (2.3)

Since the quarks carry a probabilistic fraction of the proton momentum one can never know the exact center of mass frame of a collision. But the transverse momentum distribution of the quarks is much smaller. Therefore, the conservation of momenta is a helpful tool only in the transverse plane of the interactions. Variables such as transverse momenta pT and transverse energy ET are thus defined as projections onto the plane η = 0. The reason for this is to have a way of detecting neutrinos. Since they do not interact, they can only be seen indirectly as an unbalance in the vectorial addition of particle momenta in an event. This quantity is called the ET^missand is important to the study of Higgs in one of its decay modes, as will be seen in Chapter 4.

2.2.2 The Inner Detector

The inner detector of ATLAS is used to track the particles as they are created. It lies within a solenoid magnet of 2 T in order to bend the particle tracks and measure the momentum and the charge of particles as they pass. Since the particles bend very little if they have a large momentum, this method has less uncertainty for particles with low momentum. To track particles is also important to reconstruct event vertices. Since there is a large pile-up of events in one bunch crossing, the origins of different collisions has to be separated. It is also important to find secondary vertices, arising from semi-stable particle decays. This is for example used to identify the creation of a τ lepton that soon decays into lower mass

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Figure 2.4: The ATLAS Inner Detector.

leptons. It is also important for the so-called b-tagging of jets. Jets containing a b quark often contain a hadron of longer lifetime. Since top quarks almost always decay into a W and a b quark, this tagging is important to identify and reduce the top background, as will be seen later in Chapter 4.

To track charged particles, an ionizing material is used. These are often either gaseous chambers or semiconductor detectors. Free charges are then collected by an applied voltage to record a hit. The inner detector is divided into three components: the pixel detector, the semiconductor tracker (SCT) and the transition radiation tracker (TRT), as seen in Figure 2.4. Together they cover the range |η| < 2.5 and track approximately 1000 particles every 25 ns. The pixel detector lies closest to the beam pipe and has the highest resolution of the three. It is divided into three layers of silicon semiconductor pixels. There are around 80.4 million pixels, each covering 50 × 400 µm² in a cylindrical pattern. Around the pixel detector lies the SCT. This is also a semiconductor detector, divided into eight layers of silicon strip detectors. It operates in a similar manner as the pixel detector. Since the particle flux is lower in the SCT, the resolution does not need to be as high, so there are 6.3 million read-out channels. Furthest from the beam pipe is the TRT. It consists of a collection of gas-filled tubes with diameters of 4 mm. In the middle of each tube is the anode wire that records the hits. The ”straws” are placed parallel to the beam axis, and thus only give information in the R − φ plane. The TRT has the lowest resolution of the inner detector, but this is compensated by around 35 detector hits per traversing particle². Thus it contribute significantly to momentum measurements. All three components of the inner detector also have end-cap regions that are placed perpendicular to the beam pipe, used to track particles at high η.

2.2.3 The Calorimeters

The calorimeters of ATLAS are used to measure the total energy of a particle. This is done by stopping them and collecting the released energy. Since different particles interact in different ways, there are two calorimeter subsystems: the electromagnetic calorimeter

2This can be compared to the semiconductor detectors, which only give one hit per layer.

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Figure 2.5: The ATLAS Calorimeters.

(ECAL) and the hadronic calorimeter (HCAL), seen in Figure 2.5. The first collects the energy of electrons and photons, while the latter absorbs hadronic showers after they passed the ECAL. The calorimeters also detect neutral particles, something that is not done in the ID. A forward calorimeter (FCAL) lets the calorimetric system cover the whole range of

|η| <4.9. The ECAL is placed just outside of the ID. It detects particles by EM interactions, and is thick enough to collect the full energy of electrons and photons. Hadronic particles penetrate this calorimeter with most of its energy intact. They are instead stopped by the HCAL which is placed outside the ECAL. This calorimeter is designed to collect the full energy of strongly interacting particles. Since the full energy of particles can be measured at high precision over a wide η range, it is possible to get a good measurement of ET^miss.

Both calorimeters are built as layered structures with alternating passive and active layers. The passive layers are made of absorption materials to create particle showers, while the active layers collect the emitted energy and transmits it to a read-out channel. The ECAL uses lead as absorber and liguid argon (LAr) as the active material. The layers are structured with an accordion geometry, giving complete φ symmetry. Any hit induce the LAr to ionize and a potential drives the charges to the anode, where they are read out as a current. The ECAL is divided into the central barrel region, and two end-caps at higher

|η|. Right outside the solenoid magnet of the ID is a pre-sampler to correct for any energy lost before reaching the calorimeter.

The HCAL uses different technologies at different |η| to detect hadronic showers. The central region uses steel as absorber and scintillating tiles as the active material. Scintillation light is then fed through fibers to photomultiplier tubes where they are read out. Two hadronic end-caps lie just outside of the ECAL end-caps and are Cu-LAr calorimeters. The region 3.1 < |η| < 4.9 is covered by the forward calorimeter. It is divided into three layers where the first is dedicated to electromagnetic showers and the two others measure hadronic ones. The active material is LAr and the absorber material is copper in the first layer and tungsten for the hadronic sections.

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Figure 2.6: The ATLAS Muon System.

2.2.4 The Muon Spectrometer

Muons are the most penetrating particle that is detected at ATLAS. The muon spectrometer is thus placed on the outside of the detector, where other particles are already likely to be absorbed. The muon momentum is measured by bending magnets and high precision tracking chambers. Together with the ID, the charge and momentum of muons can be accurately measured.

There are three toroid magnets in the muon system. The main one is placed around the calorimeter barrel and two end-cap toroids are placed at each side of the main magnet.

Their geometry ensures an optimal bending power for the traversing muons. Each toroid is constructed from eight coils assembled radially around the beam pipe. The end-cap regions provide a magnetic field of 1 T, while the central toroid provides 0.5 T.

In order to measure the muon momentum at high precision, four subsystems are incorporated into the muon spectrometer (see Figure 2.6). The precision tracking is done by the monitored drift tubes (MDTs) and cathode strip chambers (CSCs), while the resistive plate chambers (RPCs) and thin gap chambers (TGCs) are used for triggers. The MDTs are gas filled tubes arranged in plates around the detector. In the middle of each tube there is an anode wire that collects the ionization as muons pass. Each muon will on average produce a signal in 20 different tubes. The CSCs are multi-wire proportional chambers with anode and cathode wires running perpendicular to each other. This structure allows for precise η − φmeasurements of the muon tracks. The barrel part of the triggering system is done by the RPCs, while the end-cap triggering is done by the TGCs. Both these systems consist of two plates separated by a layer of gas that ionize when a muon pass. In addition to the triggering of muons, they also provide extra coordinates to the tracking system.

2.2.5 Particle Identification

The identification of different particles is done by all the subsystems of ATLAS. As seen in Figure 2.7, different particles leave different footprints in the detector. Photons have no

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Figure 2.7: How different particles interact at ATLAS.

charge, so they remain unseen in the ID and deposit all their energy by showering in the ECAL. Electrons shower in a similar way in the ECAL, but since they are charged they also leave a track in the ID. The solenoid magnet makes it possible to distinguish between positive and negative charged electrons. The muon is characterized by traversing the whole detector, and its charge is measured by the help of the detector magnets. Hadronic particles will interact mostly with the HCAL, and charged particles will leave tracks in the ID, making it possible to distinguish between for example protons and neutrons. Neutrinos escape the detector without interacting at all. But they are indirectly identified as missing energy in the momentum conservation. Jets are formed from the hadronization of quarks, and they are identified using clustering algorithms that group detected particles that lie close to each other.

2.2.6 The Triggering System

The bunch crossing rate at a luminosity of 10³⁴cm⁻²s⁻¹ is around 20 MHz. But the data storage rate capacity at ATLAS is limited to around 200 bunch crossings per second. This means that there has to be an efficient way of rejecting events that are not interesting for observing new physics, such as events with low momentum transfer. This is done by the so-called triggering system, which is divided into three separate parts. The first level (L1) is hardware based and reduces the rate down to around 75 kHz. The second trigger L2 is software based and reduces it further to the order of 1 kHz, while the third layer is the event filter (EF) that is able to bring the final event rate down to the desirable 200 Hz.

At the first level, only a subset of the total detector information is used to make a quick decision in less than 2.5 µm to see if an event is worth keeping. At the preceding layers, more refined decisions are made using more precise algorithms and selection criteria. The final decision is made offline by the EF and takes around four seconds per event. The final event consist of approximately 1.3 MB of data.

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Chapter 3

Searching for the Higgs Boson

One of the main tasks of the LHC was to determine whether or not the predicted Higgs boson exists. There were two experiments exploring this question: ATLAS and CMS. In the field of particle physics, there is a methodological problem. To explore the physics, the experiments are required to be performed on a very large scale. The LHC is the biggest experiment of particle physics ever built, and no other accelerator has been able to detect a signal that is consistent with the Higgs particle. This means that a scientific discovery cannot be independently confirmed by someone outside of the LHC – something that is important when performing science. This is solved by the fact that there are two experiments at CERN, both investigating the same hypothesis: Does a Standard Model Higgs particle exist?

The two detectors ATLAS and CMS are as independent as they can be. Unavoidably they share the same beam of protons, but except that, they are kept apart. The detector hardware has been constructed independently by different teams of engineers, and the software analysis is done completely separate. There are no results of either detector team that is known by the other before a publication of their results. Thus, any potential experimental bias is contained within just one of the two experiments.

3.1 Finding a New Particle

The Standard Model gives us the capability to calculate the cross section to create a new particle. This calculation involves summing up the contributions from each Feynman dia- gram that describe a possible creation process. New particles of interest are unstable and quickly decay after having been produced. The signature in a detector is therefore determined by the final state particles. The particle of interest is referred to as signal, while the creation of already known processes leading to the same final state are background events.

A new particle would show itself as an excess of events over this background. With Monte Carlo simulations, it is possible to account for the background events, and thus see if there is a signal excess of events somewhere.

At the event such an excess is found, statistical methods is used to quantify its significance. Since the world of particle physics is based on probabilities, an excess could in principle be just statistical fluctuations. To be sure this is not the case, a five σ (standard deviations) excess is required to claim the discovery of a new particle. This means that the probability of the results to have occurred by chance is extremely small. The measure of deviation must be related to some alternative hypothesis. When the rates of a new particle is studied, this alternative would be that there exist no new particle. As a measure of this

21

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22 CHAPTER 3. SEARCHING FOR THE HIGGS BOSON

Figure 3.1: The local p-value (with respect to a background-only hypothesis) as as function mH. The results are obtained at ATLAS at the discovery of a new particle.

The expected significance is calculated from a SM Higgs model.

probability, a p-value is defined as the probability to obtain an outcome equally or less compatible with a hypothesis than the observed data.

In the case of the Higgs boson, the Standard Model does not fix the mass of the particle. In the search of this boson, one had to consider the rates given at different masses. Theoretical considerations gave an upper limit on the mass of mH <1 TeV, with an expected mass of between 115 GeV and 260 GeV [20]. In July 2012, both ATLAS and CMS published results of a newfound particle consistent with the Standard Model Higgs boson. The significances gained at ATLAS can be seen in Figure 3.1 as a function of different Higgs masses. The largest significance of 5.9 standard deviations is ob- served at mH = 126.0 ± 0.4 (stat.) ± 0.4 (syst.) GeV [3], while CMS reported a mass of mH= 125.3 ± 0.4 (stat.) ± 0.5 (syst.) GeV [4].

It is clear that this is a new particle not seen before, but it is not possible to say that it is the Higgs boson just by looking at the rates. It could very well be another particle, not yet explained by some theory. It is thus necessary to look at the different properties before one can say that it is the Higgs boson that is found.

3.2 The Creation and Decays of the Higgs Boson

To know how to look for a SM Higgs particle, it is essential to know how it is created and how it decays [20]. The different creation modes gives an expected signal rate for its production, and the decay modes say what type of events are potential signal events. In the hostile environment of the LHC collisions, the total cross sections is over 100 mb and it requires much knowledge to successfully remove enough background events to gain a reasonable concentration of signal events.

The Higgs boson couples to different particles with a strength proportional to their mass.

Thus the Feynman diagrams containing electrons and light quarks does not contribute much.

The main interactions involve top quarks and the weak vector bosons. There are three main

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3.2. THE CREATION AND DECAYS OF THE HIGGS BOSON 23

[GeV]

MH

80 100 200 300 400 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 3.2: The cross section for the different Higgs boson creation processes. The values are calculated for 8 TeV at the LHC as a function of the Higgs boson mass.

The values of interest are located at mH = 125 GeV.

g g

Q H

(a) ggF

V^∗ V^∗

q q

q H q

(b) VBF

V^∗

q

¯ q

H V

(c) W H/ZH Figure 3.3: The three dominant Higgs boson production mechanisms at the LHC:

ggF (gg → H), VBF (qq → V^∗V^∗→ qq + H) and W H/ZH (q ¯q → V + H).

creation mechanisms for the Higgs boson: gluon-gluon fusion (ggF), weak vector boson fusion (VBF) and the Higgs-strahlung process (W H/ZH). Their Feynman diagrams can be seen in Figure 3.3. The ggF process is possible due to the loop of a heavy quark. Otherwise this could not happen, since gluons are massless and do not interact with the Higgs boson.

It is always possible to draw higher order Feynman diagrams, and they contribute directly to the cross section, so it is never possible to account for all of them. This makes QFT a perturbation theory with expansions of the different production diagrams. In Figure 3.2 the cross sections are calculated at best at next-to-next-to-leading-order (NNLO).

The SM predicts a Higgs particle with spin-0, a so-called scalar particle. There is no other known particle with this property – all other particles have either spin-1 or spin-1/2.

Because of this, the Higgs boson is allowed to decay into a final state of two photons (again,

Systematic Uncertainties on the Top Quark Background in the 1 Jet Channel of the ATLAS H → WW Analysis of the Higgs Boson at the LHC.