Testing a method for determining the Higgs boson linewidth by using off shell Higgs boson-contributions in the gg→H→ZZ channel

Testing a method for determining the Higgs

boson linewidth by using off shell Higgs

boson-contributions in the g g → H → ZZ

channel

FACULTY OF SCIENCE, VU & FACULTY OF SCIENCE, UVA

REPORT BACHELOR PROJECTPHYSICS ANDASTRONOMY(15 EC)

CONDUCTED BETWEEN20-03-2020AND04-07-2020

July 4, 2020 Author: Liselotte Dijkema 12018880 Supervisor: dr. Hella Snoek Second Examiner: prof. dr. Patrick Decowski

Contents

1 Introduction 5

2 The Large Hadron Collider (LHC) 7

2.1 The ATLAS detector . . . 7

2.1.1 Main components . . . 8

3 Standard Model of the elementary particles 10 3.1 The Higgs boson . . . 11

3.1.1 Higgs production . . . 12

3.1.2 Invariant mass distribution . . . 13

3.1.3 Interference . . . 13

3.1.4 Higgs linewidth . . . 15

4 Using off peak Higgs boson events to determine its linewidth 18 4.1 On and off peak cross sections . . . 18

4.2 Introduction of scaling factorξ. . . 19

4.3 Influence of scaling factorξon invariant mass distribution . . . 19

4.4 Determining linewidth of unknown data set . . . 20

5 Conclusion 25

Abstract

The Standard Model provides a prediction of the Higgs boson linewidth, namely ∼ 4 MeV. In this thesis, it is shown that we can only measure a resolution in the order of 1 GeV. Thus, due to the limitedATLASdetector resolution, the Standard Model value can not be confirmed experimentally. It is important to know whether the predicted Standard Model value is correct, since it could indicate new physics if theory does not match experiments. This thesis tests a method presented by Caola and Melnikov (2013) [1], which is based on constraining the Higgs boson linewidth by using off shell Higgs boson-contributions in the g g → H → ZZ production and decay channel. In this method, the Higgs boson spectrum is divided into an on and off peak region from which a relation can be obtained where the ratio between the off and on peak cross sections only depend on the Higgs boson linewidth ΓH. A scaling factor ξ that makes

the simulated on peak cross section agree with the Standard Model value is introduced. By adjusting ξ4 for each value ofΓH, this ratio can be obtained. Four data sets were generated

using Monte Carlo simulations from [2] in whichΓHhad a value of 1, 2, 3 or 4 ×ΓSM_H . The data

was used to precisely determine the relation between the off and on peak cross section ratio and the Higgs boson linewidth, yielding σo f f

σon = 4.57 + 0.09

ΓH

ΓSM H

. With this relation, the linewidth of a data set with an unknown value could be determined, yielding a value ofΓ_H= 1.63±0.64×ΓSM_H .

Popular Summary (in Dutch)

In deeltjesfysica beschrijft het Standaard Model een theorie waarin alle eigenschappen van de elementaire deeltjes en hun interacties beschreven staan. In 2012 werd het Higgs boson ontdekt opCERNin deLHCdeeltjesversneller door deATLASenCMS detectoren. Het bestaan van het Higgs boson was reeds voorspeld door het Standaard Model, echter ontbrak het exper-imentele bewijs nog. Sindsdien is er veel onderzoek gedaan naar de eigenschappen van het Higgs boson. Een vraag waar wetenschappers tegenwoordig nog geen antwoord op hebben, is wat de breedte van het Higgs boson is. De breedte van een deeltje kan ons iets vertellen over de levensduur van het deeltje, aangezien ze schalen als elkaars inverse. Het Standaard Model voorspelt een breedte van ongeveer 4 MeV. Echter, door de beperkte resolutie van de

ATLAS en CMS detectoren is deze experimenteel niet te bepalen. Er moet dus een andere

methode gebruikt worden om de breedte van het Higgs boson te bepalen. In deze scriptie is een reeds bestaande methode getest, waarin gebruik werd gemaakt van verschillende ges-imuleerde breedtes. Deze breedtes werden geschaald met een factorξ4, welke gebruikt werd om de gesimuleerde werkzame doorsnede in het gebied rond de Higgs massa overeen te laten komen met de waarde die voorspeld is door het Standaard Model. Door dezeξ4 aan te passen

voor elke waarde van de Higgs boson lijnbreedte, kon een relatie worden afgeleid tussen de verschillende breedtes. Vervolgens kon met behulp van deze relatie de breedte van een data set met een onbekende waarde bepaald worden.

Introduction

TheATLAS and CMS detectors confirmed the existence of the Higgs boson in 2012[3][4]. This

particle could explain why and how other particles acquire their mass, since it produces an energy field which transfers mass to particles that cross it. Since the detection of the Higgs boson, a lot has been learnt about it. For example, the Higgs boson mass region and its spin parity are known[1]. However, some questions still remain unanswered. Due to the limited resolution of theATLASandCMSdetectors, the precise linewidth of the Higgs boson can not be confirmed to be in agreement with the Standard Model value of ∼ 4 MeV. Since the linewidth of a particle can tell us something about its average lifetime, it is considered to be of importance. If the linewidth does not agree with the Standard Model value, it could indicate that there exist other, still unknown particles. If, for example, we measure a linewidth that is larger than predicted by the Standard Model, the Higgs boson might decay to particles we do not yet know of that make its linewidth wider, and thus making it decay faster[5].

The production of two Z-bosons after Higgs decay, as well as interference between the g g → H → ZZ and gg → ZZ channels, cause for off peak Higgs-related ZZ-events in the Higgs bo-son distribution. Caolo and Melnikov (2013) have described a method in [1] in which these Z Z-events can be used to put a constraint on the Higgs boson linewidth. They found a method that makes a measurement possible that is independent of a certain scaling factorξ, which keeps the on peak cross section constant when altering the linewidth. This results in the off peak cross section being linearly dependent onξ4. When the ratio of the off and on peak cross section is calculated, a relation only dependent on the Higgs boson linewidthΓHcan be

estab-lished.

In this thesis, this method for constraining the Higgs boson linewidth is tested. In chapter two, technical details on theLHCand ATLASdetector are given, as well as an overview of the main components of the ATLAS detector. In chapter three, the Standard Model and the role

of the Higgs boson are explained. We will dive further into Higgs boson properties, such as the production and decay channels, invariant mass, quantum interference and linewidth. In chapter four, the previously described method is tested. First, a detailed description of the used scaling factor is given. The importance of the scaling factor is shown as well. Then, four data sets with linewidth values of 1, 2, 3 or 4 ×ΓSM

H are used to extract a relation between the on

and off peak cross sections and the linewidth of the Higgs boson,ΓH. Finally, the linewidth of

a data set with an unknown value is determined with the use of the derived relation. Monte Carlo generated simulations from [2] are used throughout this thesis instead of real data.

The Large Hadron Collider (

LHC

)

The Large Hadron Collider (LHC), located in CERN, Geneva, is the largest particle accelera-tor in the world. The LHC consists of a ring with a total circumference of 27 km. Inside the ring, two relativistic particle beams, usually two protons, are traveling in opposite direction in two different ultrahigh-vacuum beam pipes. The energies of the beams have values up to 8 TeV, with their speed approaching the speed of light. The particles are accelerated by 1232 dipole magnets and 392 quadrupole magnets. The dipole magnets bend the beams, while the quadrupole magnets focus the beam[6]. Two two particle beams collide up to a billion times per second[7]. These collisions are used to study possible new physical phenomena. TheLHC

houses four different detectors: ATLAS, CMS, ALICE and LHCb. At each detector location, the particle beams are set to collide.

TheATLAS experiment is a general-purpose experiment, which tries to understand the

funda-mental building blocks of matter. Its major aims and working is discussed in detail in section 2.1. The Complete Muon Solenoid (CMS) detector is also a general-purpose detector and has its scientific goals set to, amongst others, finding and studying the Higgs boson and search-ing for new particles. As its name already suggests, theCMSdetector is constructed around a solenoid magnet that can bend the trajectories of the particles[8]. A Large Ion Collider Experi-ment, orALICE, is an experiment that aims to study extreme nuclear systems, like quark-gluon plasma[9]. The Large Hadron Collider beauty (LHCb) detector aims to study the "beauty (or b)

quark", in order to find out more about the difference between matter and antimatter[10].

2.1

The ATLAS detector

TheATLASexperiment, which is an abbreviation for ’A ToroidalLHCApparatus’, is one of the

four major experiments conducted at theLHC. Like theCMS experiment, its goal can best be described by trying to understand the fundamental components of matter as far as theLHC

Figure 2.1: A schematic overview of the main components of the ATLAS detector (Figure modified from[13]).

enables this research. More specifically, theATLASexperiment tries to explore a wide range of high-energy particle physics, from searching for dark matter and extra dimensions to studying the Higgs boson[11].

2.1.1 Main components

The concept of theATLASexperiment was first excogitated in the 1980s. On the 29th of Novem-ber 2009, the first data was obtained. The detector itself consists of four main sub-detectors. In figure 2.1, the main components and the detector itself are shown. The Magnet System gives rise to a magnetic field for the inner tracker by the use of a Central Solenoid (CS). The Central

Solenoid is surrounded by three large-air-core toroids, which provide the muon spectrometer with a magnetic field. Two end-cap toroids (ECT) placed inside a Barrel Toroid (BT) are located at the outer ends of the detector[12]. The purpose of the Magnet System is to bend the particles in order to measure their momenta[11].

As its name suggests, the Inner Detector, or Tracking Detector, tracks the particles inside the detector. Due to the magnetic field created by the Magnet System, the direction and degree of curvature of the particles in the detector is used to determine the particles’ momenta. The

Figure 2.2: A cross section of the components of theATLASdetector (Figure modified from[14]).

Calorimeters detect the energy of particles going through. Incoming particles are absorbed, in such a way that all energy is lost[11]. In the ATLAS detector, an inner Electromagnetic Calorimeter (EC) as well as an outer Hadronic Calorimeter (HC) are used. Both calorimeters

cover a distinct pseudo-rapidity region[12], in a way that the Electromagnetic Calorimeter can detect the energy of electrons and photons, and the Hadronic Calorimeters that of quarks or particles built from quarks (e.g. protons)[11]. The only particles that pass through the Calorimeters are muons and neutrinos. This is why a fourth component was needed. The Muon Spectrometer can measure the momentum of muons by bending their paths. Neutrinos are can simply be regarded as missing energy. In figure 2.2, a cross section of the components of the detectors is presented.

Standard Model of the elementary

par-ticles

The Standard Model of elementary particles is a theory that describes the elementary particles and the way they interact with each other. The three forces that are described within the Standard Model are the electromagnetic, strong and weak forces. There are two classes of particles within the Standard Model: fermions and bosons. Fermions are half-integer spin particles and consist of six types of quarks (up, down, charm, strange, top and bottom) and three types of leptons (electron, muon and tau), along with their corresponding anti-particles and neutrinos. Fermions have to obey Pauli’s exclusion principle, which states that two similar fermions cannot occupy the same quantum mechanical state at the same time. Bosons are integer spin particles that mediate the interactions between fermions. Particles that classify as bosons are photons, gluons, Z-bosons, W-bosons and the Higgs boson[15][16]. An overview of the elementary particles in the Standard Model is presented in figure 3.1.

3.1

The Higgs boson

It is generally known that most elementary particles in the Standard Model have mass. How-ever, the reason why has long been unknown. The Standard Model does not describe a mech-anism that can explain the acquiring of mass by these particles, without breaking the elec-troweak symmetry. Due to symmetry requirements, the W and Z gauge bosons should have zero mass. This, however, is not the case. In 1964, three research groups independently sub-mitted papers that came up with a theory that could explain the reason that particles have mass[17]. They each proposed the idea of a scalar field that gives particles mass. The main idea behind the theory is that the scalar field would have a non-zero value in its ground state, which makes it possible for the field to break electroweak symmetry[18][19]. This scalar field has been given the name "Higgs field" after Peter Higgs, one of the researchers that came up with the theory. The carrier of the Higgs field is the Higgs boson.

The mass of the Higgs boson can not be predicted by the Standard Model, so the only way to determine it is experimentally. In July 2012, theATLASandCMSdetectors atCERNannounced that they both independently observed a particle that has the same properties as the predicted Higgs boson would have, with a mass of 126.0 ± 0.4 GeV[3] and 125.3 ± 0.4 GeV[4] respectively. Both research groups conducted searches at p_{s = 7 and} p_{s = 8 TeV and focused on decay} channels H → ZZ∗_{→ 4l, H →γγ, H → WW}∗_{→ eνeµνµ, H →τ}+_τ−_{and H → b ¯b. Both detectors}

achieve the highest sensitivity for the H → ZZ∗→ 4l decay mode[3][4]. In this thesis, we will focus on this decay as well. The Feynman diagram for this decay is shown in figure 3.2.

Figure 3.2: Higgs decay through Z Z∗ _{to four leptons. The four final leptons can either be 4µ, 4e, or} 2µ2e.

3.1.1 Higgs production

Higgs production can occur in many ways. The Feynman diagrams of the four main production channels atLHCare displayed in figure 3.3. In this thesis, we will focus on Higgs production

through gluon-gluon fusion (ggF), which is the most dominant production channel atLHCwith a cross section of 15.0 ± 1.6 pb (atps = 7 TeV) and 19.2 ± 2.0 pb (atps = 8 TeV)[20].

Figure 3.3: The four main Higgs production channels atLHC. Figure a) shows the most dominant production channel atLHC. A Higgs boson is produced by gluon-gluon fusion through a virtual

top-quark loop. b) shows the second most dominant production channel at LCH. In Vector Boson Fusion (VBF), a quark and an anti-quark radiate two W- or Z-bosons, which then combine to make a Higgs boson. In c), a quark and an anti-quark annihilate to form a W- or Z-boson, which then emits a Higgs boson. This is the third most dominant production channel atLHC. d) the least likely production channel to occur atLHCis the top quark fusion, where two gluons decay into a top and anti-top quark. A quark from the first gluon and an anti-quark from the second then fuse to create a Higgs boson.

The total Higgs channel we will focus on in this thesis is displayed in figure 3.4a. Another, very similar channel that yields the same initial and final states as the Higgs channel is shown in figure 3.4b. This channel is called the continuum and can be regarded as a continuous background. In section 3.1.3, we will go deeper into the properties of the continuum channel.

(a) (b)

Figure 3.4: a) Higgs mediated channel: the most dominant Higgs production and decay channel atLHC

that we will focus on in this thesis. b) continuum channel, where two gluons fuse into two Z-bosons through a quark loop. The Z-bosons then decay into four leptons. The two Z-bosons are thus created without the mediation of a Higgs boson, but they yield the same final product. In the region where the Higgs mass is defined, the Higgs-mediated channel can be up to 47 times higher, while around 180 GeV, where the two Z-bosons are formed, the continuum channel can contribute up to 103 times more (calculated from figure 3.5 in section 3.1.2).

3.1.2 Invariant mass distribution

The invariant mass of a particle is its mass before it decays. The invariant mass can be calcu-lated by using the energies and momenta of the decay products and is the same in all reference frames[21]. Since we can only measure the energies and momenta of the decay products of the Higgs boson, namely the four leptons M_4l, the obtained signal is a distribution of the invari-ant mass. The invariinvari-ant mass distribution of the Higgs-mediated and continuum channels are shown in figure 3.5. Data sets from Monte Carlo-simulations[2] have been used, simulating either the Higgs-mediated or the continuum channel. In both simulations, the detector reso-lution and reconstruction efficiencies have been accounted for. When we measure a the signal of the Higgs-mediated channel that is shown in 3.4a, the distribution around the Higgs boson resonance of ∼ 126 GeV will peak. In the continuum channel, the two Z-bosons form at ∼ 180 GeV, after which the distribution falls off.

3.1.3 Interference

Since the Higgs channel and continuum channel that are displayed in figure 3.4 have the same initial and final states (two gluons and four leptons, respectively), and the two different paths from the initial to the final state cause a phase difference, the two channels can interfere with each other. Because we measure at one specific location, we can only see if the interference happens constructively or destructively, opposed to seeing a wave form.

addi-Figure 3.5: The invariant mass distribution of the Higgs mediated (black) and continuum (green) chan-nels, logarithmic scale. The Higgs boson resonance can be observed around 126 GeV. Events observed at higher invariant masses result from the creation of two Z-bosons and the top quark mass loop. In the continuum channel, the two Z-bosons form at ∼ 180 GeV. Thereafter, the distribution falls off.

tion to the previously used data to create figure 3.5, another simulation has been done in which both the Higgs mediated and continuum channels were simulated simultaneously. Again, the detector resolution and reconstruction efficiencies have been accounted for. In the last men-tioned data set, it is expected for interference to take place. Now, if we add the cross sections of the Higgs-mediated and continuum channels that were simulated separately, we can see the effect interference has on the total Higgs boson channel since there can be no interference in this naive addition. In figure 3.6, the channel in which interference occurs and the naive ad-dition are added to figure 3.5. It can be observed that the naive adad-dition yields a higher cross section, implying that the interference is destructive. We can calculate this quantitatively by summing over the cross sections. Interference has the highest impact above 300 GeV, as can be observed from the increased difference between the naive addition and the data in which interference occurs in figure 3.6. This is the range in which the heavy top quark loop that is shown in figure 3.4a is produced. If we compare the part of the distribution in the tail above 300 GeV from the data with interference with the naive addition, we find that the summation of the cross sections yield 0.146 ± 0.002 pb and 0.197 ± 0.002 pb respectively, which means that the interference must indeed be destructive.

Figure 3.6: The effect of interference on the g g (→ H) → ZZ → 4l cross section, logarithmic scale. In black and green, the Higgs-mediated respectively continuum channels are shown. The red markers show a naive addition of the cross sections of the Higgs-mediated channel to the continuum channel. The two channels were simulated separately. This means that no interference can occur. In blue, the amplitudes of the Higgs-mediated and continuum channels are added to each other in the simulation before squaring. This means that interference terms are important in the process. We can view the difference between the red and blue graphs as the effect interference has on the processes. Here, the interference occurs destructively.

3.1.4 Higgs linewidth

The linewidth (Γ), or lineshape, of a particle is the distribution of the invariant mass of the particle’s end product. This distribution arises from the quantum mechanical uncertainty in the particle’s mass. The linewidth of a particle can tell us something about its lifetime (τ), since the two are related by

Γ ∝1

τ. (3.1)

For the Higgs channel that we study in this thesis, the end products observed in the ATLAS -detector are the four leptons. In figure 3.7a, the distribution of the invariant mass of the four leptons is shown with perfect detector resolution. The data has again been generated with the

gg2VV-package from [2]. Around 126 GeV, a resonance can be observed. This resonance is the

linewidth of the Higgs boson. The data points are fit to a Breit-Wigner distribution, which is a distribution function that describes the linewidth of a particle. The Breit-Wigner distribution

is given by

σ(E) = 2 p

2MΓγ

πpM2_+γ¡(E2_{− M}2₎2_{+ M}2_Γ2¢, (3.2) with_σ the cross section, M the mass of the resonance,Γ the linewidth, E the center-of-mass energy of the resonance andγ=pM2_(M2_+Γ2_{). The fit gives a linewidth value of 4.43 ± 0.04}

MeV at a mass of 126.000 ± 0.002 GeV.

(a) (b)

Figure 3.7: a) the linewidth of the Higgs boson, when detector resolution has not been accounted for. The data has been fit to a Breit-Wigner distribution function. A resonance can be observed at 126.000±0.002 GeV. b) the linewidth of the Z-boson, again when the detector resolution was not accounted for. The data has been fit to a Breit-Wigner distribution function as well. A resonance can be observed at 91.23 ± 0.01 GeV.

One can also determine the linewidth of the Z-boson in the same way as was done for the Higgs boson. The result is shown in figure 3.7b. The Breit-Wigner fit gives a linewidth of 2.54 ± 0.02 GeV at a mass of 91.23 ± 0.01 GeV.

Next, instead of studying an ideal detector, a data set has been considered in which the detector resolution and reconstruction efficiencies have been simulated. In figure 3.8, the distribution is shown. This time, since we are not dealing with an ideal simulation, a Breit-Wigner fit will not suffice. A Gaussian fit has to be used instead. As can be seen in the figure, the Higgs linewidth cannot be observed anymore. Thus, a method that does not rely on measuring the Higgs boson linewidth directly is needed to confirm the predicted Standard Model linewidth. In the next section, a possible method first proposed in [1] that uses on and off shell contributions is tested.

Figure 3.8: The linewidth of the Higgs boson, when detector resolution and reconstruction efficiencies have been taken into account. The data has been fit to a Gaussian distribution function, with mean 126.06 ± 0.01 GeV and σ = 1.342 ± 0.007 GeV.

Using off peak Higgs boson events to

determine its linewidth

In chapter 3, we concluded that theATLASdetector resolution is not precise enough to measure the Higgs linewidth directly. In this section, an alternative method to determine the Higgs linewidth is proposed, after it was first presented in [1].

4.1

On and off peak cross sections

The production cross section for the process i → H → f is given by

σ_i→H→f ∼ g2_ig2_f

ΓH

, (4.1)

with gi, f the Higgs boson couplings to respectively the initial and final states and ΓH the

linewidth of the Higgs boson. The range in which the Higgs mass is defined is called the on peak section. The region outside the on peak section is called the off peak section. According to [1], the production cross section can be written as a function of the invariant mass of the final four leptons, M4l: d_{σp p→H→ZZ} dM2_4l ∼ g2_{g gH}g2_{H Z Z} (M_4l2 _{− m}2_H)2_{+ m}2 HΓ 2 H . (4.2)

In the on peak region, M2_4l− m2_H→ mHΓH, and in the off peak region, M_4l2 >> m2_H, since the

Z Z-events dominate the concerning region. We can use this to simplify both equations and integrate them, in order to obtain a relation for both the on and off peak cross sections:

σo f f ∼ cgZ (4.3)

σon∼

cgZ

ΓH

where c_{gZ= g}2_{g gH}g2_{H Z Z}, the product of the squared coupling constants. We see that the equa-tion for the on peak cross secequa-tion becomes equaequa-tion 4.1. We can use these equaequa-tions obtain a relation that is only dependent on the Higgs boson linewidth. When taking the ratios of the on and off peak cross sections, we are left with

σo f f

σon ∼

cgZΓH

c_gZ ∼ΓH (4.5) This equation depends only linearly onΓH.

4.2

Introduction of scaling factor

ξ

Due to uncertainties in gg gH and gH Z Z, there can be certain scaling factors present which we

also measure when conducting experiments on the cross sections. Each of the coupling con-stants may include such a scaling factor, which we will callξfrom now on. This scaling factor

ξcauses the whole cross section to shift either up or down. Because the value ofξhas not yet been determined, we need to find a way to eliminateξfrom any calculation done on the Higgs boson linewidth.

In [1], a method has been suggested that makes use of the relation between the on and off peak cross sections where_ξis accounted for. _ξhas been chosen in such a way that the measured on peak cross section σmeasured_on remains equal to its Standard Model value σSM_on . By looking at equation 4.4, we can see that keeping the on peak cross section fixed would require both the coupling constants g and the Higgs boson linewidthΓHto be scaled withξ, so that g ∼ξgSMor

cgZ∼ξ4cSM_gZ andΓH∼ξ4ΓSM_H . If we now go back to equations 4.3 and 4.4, we see that addition

of _ξwould make the on peak cross section independent of_ξ, while the off peak cross section depends on linearly onξ4, withσo f f ∼ξ4. If we look at the ratio between the on and off peak

cross section in equation 4.5, we see that

σo f f σon ∼ ξ4_cSM gZξ 4_ΓSM H ξ4_cSM gZ ∼cgZΓH cgZ ∼ΓH , (4.6)

to obtain the same equation as in equation 4.5. We have thus found a way to determineΓ_H from the on and off peak cross sections, without having to know the value ofξ4.

4.3

Influence of scaling factor

ξ

on invariant mass distribution

In order to compare the influence of different scaling factors on the Higgs boson linewidth, data samples have been generated by using Monte-Carlo simulations from [2] with different

Higgs boson linewidths and scaling factors. In figure 4.1, four figures of the M_4l-invariant mass distribution are shown in which the effect of adding a scaling factor is visualised. 1G or 3G meansΓH= 1×ΓSM_H orΓH= 3×ΓSM_H , respectively, and 1S or 3S meansξ4= 1 respectivelyξ4= 3.

In figure 4.1a, the on shell region for a Higgs-mediated production channel is presented, while 4.1b shows the on shell region for the production channel in which interference can occur. In both figures, scaling withξ4_{= 3 stretches out the linewidth when}ΓHremains constant, while

scaling the linewidth withΓ_{H= 3 ×}ΓSM_H results in shrinking the linewidth. WhenΓ_His scaled and the scaling factor is applied as well, it can be seen that the distribution is comparable to the distribution in which ΓH= 1 ×ΓSM_H and ξ4= 1, which is in line with the expectation.

Figures 4.1c and 4.1d show the off shell region for both a Higgs-mediated production channel as a production channel with interference. A shift upwards can be observed whenξ4 is equal to 3 instead of 1, while scaling the linewidth does not affect the off shell region.

4.4

Determining linewidth of unknown data set

Data sets have been generated in which the Standard Model linewidth value for the Higgs boson has been multiplied 1, 2, 3 and 4 times, thus creating a shorter expected lifetime for the Higgs boson. Again, Monte Carlo simulations from [2] were used. The total off peak cross section for each data set has been determined by summing over the cross sections in the region above 180 GeV. This region has been chosen to be the off peak region, since the two Z-bosons are both created at ∼ 90 GeV (see section 3.1.4 and figure 3.6), resulting in a peak at 180 GeV. As mentioned before in section 3.1.3, the highest contribution of the interference occurs around ∼ 300 GeV, so taking 180 GeV as lower limit covers both sources of Higgs-related ZZ-events in the off peak. The region of the total on peak cross section is set to be from 120 − 132 GeV, since it can be seen in figure 3.8 that the Higgs resonance is defined within those boundaries.

In figure 4.2, the on peak invariant mass distribution for the four different linewidths is shown. The addition of a scaling factor causes the on peak cross section to remain the same for all linewidths. The off peak invariant mass distribution for the four different linewidths is shown in figure 4.3. Since the off peak region depends on a scaling factorξ4, the off peak cross section has higher values at larger linewidths.

Now we are left to determine the ratio of the off and on peak cross sections. The result is displayed in figure 4.4. According to equation 4.5, a linear fit should be applied. The fit yields

σo f f

σon = 4.57 ± 0.04 + 0.09 ± 0.01

ΓH

ΓSM H

, so the off and off peak cross section ratio is related toΓ_Hby

σo f f σon = 4.57 + 0.09 ΓH ΓSM H . (4.7)

With the obtained result in equation 4.7, we can determine the linewidth of a data set with an unknown linewidth in terms of its Standard Model value. With the off and on peak cross section ratio determined, we can use the fit result to determineΓHin terms ofΓSM_H . A data set

in which the number of events was measured has been generated and the linewidth at which it was generated has not been communicated beforehand. The number of events N is given by

N = Lσ Z

dt, (4.8)

with L the luminosity, which is the number of events measured within a certain time and area, in pb−1s−1,σthe cross section in pb and dt the time interval in s in which the measurement takes place. Since both the time interval dt and the luminosity L remain the same in each single measurement, they are also the same for the on and off peak cross section of that mea-surement. Thus, N_{o f f} Non = L_{σo f f}R dt LσonR dt = σo f f σon . (4.9)

This means that we can still use equation 4.5 to determine the ratio of the on and off peak cross sections. The off and on peak cross sections were thus calculated, after which the linewidthΓH

could be determined with the help of the obtained fit parameters. The unknown linewidth was calculated to beΓH= 1.63 ± 0.64 ×ΓSM_H . In figure 4.5, the result has been added to figure 4.4.

The linewidth of the data set with unknown value has been set atΓH= 1.5×ΓSM_H . Although the

determined value ofΓH= 1.63 ± 0.64 ×ΓSM_H lies within this region, the error margin of 39% is

significant. The uncertainty in the obtained linewidth has several causes. Firstly, the obtained results are all derived from Monte Carlo-generated simulations[2]. These simulations carry a certain error, which is visible in the final results. In addition, an estimation for the on and off peak cross section has been made, by stating that M_4l2 _−m2_{H→ m}HΓHin the on peak region and

M2_4l>> m2_Hin the off peak region. This estimation might be plausible, but not exact. Also, the on and off peak regions have been assumed to be located at 120-132 GeV respectively 180-1000 GeV, however the argument could be made to enlarge or shrink this region for more precision.

Figure 4.1: Visualisation of the effect of adjusting scaling factorξ4 and the Higgs boson linewidth ΓH, with G and S being the Standard Model linewidth of the Higgs bosonΓSM_H and scaling factorξ4, respectively. a) shows the on shell region for a Higgs-mediated production channel, while b) shows the on shell region for the production channel in which interference occurs. The distributions are stretch out whenξ4is set to 3, while the distributions are shrunk whenΓHis equal to 3×ΓSM_H . When bothξ4= 3 and ΓH= 3 ×ΓSM_H , the distribution is again comparable to the one whereξ4= 1 andΓH= 1 ×ΓSM_H . Figures c) and d) show the off shell region for both a Higgs-mediated production channel as the production channel in which interference occurs, from 140 to 800 GeV. Figure d) is plotted on logarithmic scale. The difference between the off peak cross sections is due to the difference chosen scaling factor: the distributions in whichξ4

= 3 are scaled up by a factor 3. As can be expected, altering the linewidth does not affect the off peak region.

Figure 4.2: The on peak invariant mass distribution for linewidthsΓH= 1, 2, 3 and 4 ×ΓSM_H . Because of the addition of a scaling factor, the on peak cross section is the same for all linewidths.

Figure 4.3: The off peak invariant mass distribution for linewidthsΓH= 1, 2, 3 and 4 ×ΓSM_H , logarithmic scale. Linewidths with a higher value will have a higher value for the cross section, because of the off peak’s dependence on the scaling factor.

Figure 4.4: The ratio of the off and on peak cross sections. A linear fit has been applied, yielding σo f f σon4.57 ± 0.04 + 0.09 ± 0.01 ΓH ΓSM H .

Figure 4.5: The ratio between the on and off peak cross sections, with the value of the unknown linewidthΓH= 1.63 ± 0.64 ×ΓSM_H added to the figure. The fit from figure 4.4 has remained the same.

Conclusion

We tested a method proposed in [1] for determining the Higgs boson linewidth that is indepen-dent of a scaling factorξand the luminosity. On and off peak Higgs boson contributions were used to establish a relation between the ratio between the two and the Higgs boson linewidth. The relation found has form

σo f f σon = 4.57 + 0.09 ΓH ΓSM H . (5.1)

Thereafter, a data set with an unknown value was generated. The linewidth was determined by using the above equation, yielding a linewidth ofΓ_{H= 1.63 ± 0.64 ×}ΓSM_H . The linewidth was set to beΓH= 1.5 ×ΓSM_H , which lies within the error margins of the found linewidth. The main

uncertainties come from the simulations and assumptions made on the on the on and off peak cross section regions.

Future experiments could include more data sets with different linewidths in order to provide for a more accurate relation. In addition, instead of using simulated data, real data from the

ATLASandCMSdetectors could be used to allow for more accurate and real-life data. On top of

that, other decay and production channels that take place in theLHCcould be used to conduct similar experiments with, since although the g g → H → ZZ channel is the most dominant one, there are many others that can help us understand the Higgs boson better.

Context

In this thesis, only simulations were used to mimic an ideal scenario. More interesting of course, is to look at real data from theCMSandATLASdetectors, since background channels in real experiments make the analyses much more complex. TheATLASgroup presented in [22] in 2018 that they had constrained the Higgs boson linewidth to an upper limit of 14.4 (15.2) MeV, using the method that was also used in this thesis. In 2019, theCMSgroup presented in [23]

Higgs boson linewidth of 3.2±2.8

±2.2 MeV. The error margins are still within the Standard Model

value. In the analysis of the CMSgroup, the results of production and decay channels besides g g → H → ZZz → 4l were combined to provide for a more accurate result. Both research groups are still conducting experiments to constrain the Higgs boson linewidth even further.

Acknowledgements

I would like to thank my supervisor, dr. Hella Snoek, for guiding me through this process. Her expertise and patience made me really confident in conducting this research. She put a lot of time and effort into making this project possible under the current circumstances which made us work from home, and I really appreciate her for doing that.

Popular scientific summary

Testing a method for determining the Higgs boson linewidth

Since the first introduction of the possible existence of a particle that could give mass to par-ticles in the 1960s by Peter Higgs, particle physicists have tried to reveal the mysteries sur-rounding this particle. In 2012, theATLASand CMSdetectors independently discovered a par-ticle that obeyed all the properties of the theorized parpar-ticle. The Higgs parpar-ticle was officially found. Still a lot of properties remain unknown up until today, among other the Higgs boson linewidth - a property that can tell us something about a particle’s average lifetime before it decays into other particles. The Standard Model predicts a value of ∼ 4 MeV, but bothATLAS

and CMS have a detector resolution that is not precise enough to measure it. Other methods thus have to be used in order to confirm the Higgs boson linewidth. In this thesis, a method first proposed by Caola and Melnikov (2013) is tested to put a constraint on the Higgs boson linewidth. Off peak Higgs boson contributions in the g g → H → ZZ channel are used to es-tablish a relation between the particle’s on and off peak cross section and the Higgs boson linewidth. This is possible by adding a scaling factorξthat scales the linewidth and coupling constants in such a way that the on peak cross section remains constant when the linewidth is altered. Four data sets with a different linewidth in terms of the Standard Model value, namely 1, 2, 3 and 4 times the Standard Model value, were Monte Carlo-generated. A relation ofσo f f

σon = 4.57+0.09

ΓH

ΓSM H

was obtained. Then, the linewidth of a data set with an unknown value could be determined, yielding a value ofΓH= 1.63 ± 0.64 ×ΓSM_H .

Figure 6.1: The g g → H → ZZ Higgs production and decay channel. The Higgs boson is created by two gluons that, through a top quark loop, form the Higgs boson. The Higgs boson then decays into two Z-bosons, which decay into two lepton pairs.

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