Search for Stop Using the ATLAS Detector and Performance Analysis of the Tile Calorimeter with Muons from W Decays

(1)

Search for Stop Using the ATLAS Detector and Performance Analysis

of the Tile Calorimeter with Muons from W Decays

Licentiate thesis

Stefio Yosse Andrean

Department of Physics

Stockholm University

(2)

(3)

Abstract

This thesis presents a search for the supersymmetric partner of the top quark in the final state with one lepton. The search focuses especially in the region of the parameter space where the 2-body decay dominates. The analysis is performed using LHC full Run 2 data at√s=13 TeV as recorded by the ATLAS detector. No significant excess above the backgrounds is observed, and 95% confidence level exclusion limits are calculated in the stop-neutralino mass plane. Stops are excluded up to 1200 GeV in the low neutralino mass scenario of below 400 GeV.

The Tile Calorimeter is part of the ATLAS calorimeter system whose main task is to measure the energy of hadrons. A performance study is conducted on the Tile Calorimeter using muons from W boson decay originating from proton-proton collisions. Each calorimeter cell response is measure in data and compared with detector simulation. The azimuthal cell response uni-formity is also investigated using a likelihood method. Overall, a good data to detector simu-lation agreement and azimuthal uniformity is observed which shows well-calibrated cells and uniform responses among the calorimeter modules.

(4)

(5)

Sammanfattning

I detta arbete söker vi efter den supersymmetriska partnern till toppkvarken, den så kallade "stoppkvarken". Stoppkvarken kan teoretiskt sönderfalla till olika sluttillstånd. Sökningen som presenteras här fokuserar på stoppkvarkens tvåkroppssönderfall, till en toppkvark och en så kallad neutralino. Inom supersymmetri är neutralinon en möjligen stabil partikel och kandidat till att utgöra den mörka materian.

Vi analyserar all tillgänglig data från ATLAS-experimentet vid LHC run-2. Inget statistiskt säkerställt överskott observeras i det betraktade sluttillståndet. Vi härleder därmed nya ex-perimentella gränser på stoppkvarkens massa. Stoppkvarkar med en massa upp till 1200 GeV uteslutas bl.a. i scenarier där neutralinon väger mindre än 400 GeV.

ATLAS Tile Calorimeter är en viktig del av ATLAS-detektorn som används av ATLAS för att mäta hadronskurar. I detta arbete använder vi myoner som produceras i sönderfall av W-bosoner för att studera kalorimeterns respons och kalibrering. Metoden är tillräckligt noggrann för att kunna identifiera enstaka kanaler med avvikande respons och visar jämn respons över hela kalorimetern.

(6)

(7)

Acknowledgements

I would first and foremost like to thank my supervisor Christophe Clement for his continuous support throughout my study and the making of this thesis. Christophe, thank you for the discussions and conversations both on physics and fiction. I have learned a lot from you. I would also like to thank my co-supervisor Sara Strandberg for the support she has given during my study.

Thanks to the stop-1lepton analysis team and the Tile community whom I have been working closely with in the past two years. The work documented here is the product from all our labor rather than mine alone.

Thanks to Chad Finley for reading and reviewing the draft of this thesis. I appreciate your feedback which has very much improved the quality of the thesis.

To my wife Angela who has made the past difficult times survivable, I wouldn’t have made it this far without you.

Finally to friends within and outside the field who have made this journey much more fun, cheers!

(8)

(9)

Preface

The ancient Greek philosopher Democritus initiated the idea that everything is composed of smaller indivisible matter called “atoms”. The implication of this seemingly simple idea is ex-tensive: one can understand everything in nature by understanding the smallest objects. Since then, the pursuit of describing Nature in a simple and elegant way at the most fundamental level has been the driving force of physics.

Particle physics is a field of science at the forefront of this pursuit. Particle physicists describe the universe in the picture of fundamental particles and the interactions between them. In this picture, the current best description of the universe is comprised in a collective theory called the Standard Model of particle physics.

The Standard Model has superb predictive power. It had predicted phenomena long before its detection and is able to predict known processes down to incredible precision. Yet, it is not perfect. As later described in this thesis, there are questions it cannot answer, and we need the answers if we ever hope to fully understand the universe. To investigate these questions, we need to stress-test the Standard Model, find where it fails to work and fill the blank.

The Large Hadron Collider (LHC) is built for this very reason. It collides particles to create particle interactions which can be matched against the Standard Model in a statistical manner. This thesis contains my work in ATLAS – a particle detector in the LHC – in analyzing the LHC collision data as part of the collective effort to refine the Standard Model.

About this thesis

Part I includes both theoretical and experimental overview that are meant to provide basic understanding to be used throughout the thesis. Chapter1 starts with the description of the Standard Model, the particle content and the interactions, followed by its shortcomings and theories that try to fix them. Supersymmetry is introduced in Chapter 2 where the hierar-chy problem is explained and how supersymmetry can solve it. Chapter3and4describe the experimental setup: the LHC and ATLAS, respectively. Due to the interest in the particular sub-detector as part of the thesis work, Chapter5is reserved for a more detailed description of the ATLAS Tile Calorimeter.

(10)

CHAPTER 0. PREFACE state. Chapter 6 explains the specific signal model targeted by the analysis along with the backgrounds. Chapter7describes all the variables that are used as a selection of the signal re-gions. The signal regions themselves are defined in Chapter8which also details the optimiza-tion algorithm that is performed on the signal regions. The background estimaoptimiza-tion strategy is described in Chapter9. It also features a study on single top interference which is strongly observed in this search. All considered systematic uncertainties and how to calculate them are explained in Chapter10. Chapter11discusses the fit procedure as part of the statistical analysis of the search. And finally, the results and conclusion are summarized in Chapter12.

PartIIIis dedicated to the performance analysis of the ATLAS Tile Calorimeter. Two aspects of the performance are investigated in this work, namely cell response agreement between data and Monte Carlo, and the azimuthal cell response uniformity. Chapter 13 describes the motivation, datasets, event selections, and the analysis method. The results and conclusions are summarized in Chapter14.

The work in this thesis is directly related to the following paper which is attached to the thesis:

• PAPER: ATLAS Collaboration. “Search for new phenomena with top quark pairs in fi-nal states with one lepton, jets, and missing transverse momentum in pp collisions at √

s = 13 TeV with the ATLAS detector”. [1]

Additional papers and scientific reports which are related to this work but are not attached to the thesis:

• INTERNAL NOTE: Keisuke Yoshihara et al. “Search for new phenomena with top quark pairs in final states with one lepton, jets, and missing transverse momentum using 140 fb−1 of√s =13 TeV data with ATLAS” Tech. rep. ATL-COM-PHYS-2018-1413. [2]

• PAPER: ATLAS Collaboration. “Operation and Performance of the ATLAS Tile Calorime-ter in LHC Run-2”. In preparation.

• INTERNAL NOTE: S.Y. Andrean, C. Clement, and P. Klimek. “Performance study of the ATLAS Tile Calorimeter using isolated muon events from W →µνin Full-Run2 collision data”. In preparation.

Author’s contribution

Since the beginning of my PhD study I had been involved in the analysis work of the stop search in one lepton channel. I was responsible for the development of signal regions that target 2-body decay topology, which includes the optimization of the signal regions, designing control and validation regions, estimating systematic uncertainties, and performing all the fits. For the optimization work, I created a software package that automates the optimization algorithm. The optimization software is also used for the development of the signal region targeting dark matter in the same analysis and various sensitivity studies in other signal regions. As one of the main analyzers, I also contributed to the ATLAS Internal Note that supports the paper. The paper is now public in preprint and was submited to Journal of High Energy Physics. This work is featured in PartIIof this thesis.

(11)

As part of the ATLAS authorship qualification task, I conduct the performance analysis of the Tile Calorimeter using collision muons from W boson decays. The work starts with preparing the data derivation framework, so called TCAL1 derivation, so that the datasets produced con-tain all the necessary observables. Once the framework is ready, I initiate the batch production of the full Run 2 data and the appropriate Monte Carlo simulations in the TCAL1 format. I also set up and execute all analysis code where all the calculations take place. The analysis is still developing and its final output will be part of the Tile Calorimeter Run 2 performance paper in which I also contribute as a co-editor. This work is featured in PartIIIof this thesis.

(12)

(13)

10 Systematic Uncertainties 67 10.1 Experimental uncertainties. . . 67 10.2 Theoretical uncertainties . . . 68 10.2.1 Signal. . . 68 10.2.2 Dileptonic t¯t . . . 70 10.2.3 W+jets . . . 70 10.2.4 Single top . . . 70 10.2.5 t¯tV . . . 71 11 Fit Procedure 75 11.1 Background-only fit. . . 75 11.2 Discovery fit . . . 76 11.3 Exclusion fit . . . 76

12 Results and Conclusion 79 12.1 Background-only and discovery fit result . . . 79

12.2 Exclusion fit result . . . 80

(15)

III Performance of the ATLAS Tile Calorimeter 83

13 Event Samples and Methods 85

13.1 Datasets . . . 85

13.2 Event Selection . . . 87

13.3 Methods . . . 92

13.3.1 Definition of cell response with respect to simulation . . . 92

13.3.2 Definition of azimuthal cell response uniformity . . . 93

14 Results and conclusions 95 14.1 Cell response with respect to simulation . . . 95

14.2 Azimuthal cell response uniformity . . . 99

14.3 Conclusion . . . 105

Attached paper 115

Search for new phenomena with top quark pairs in final states with one lepton, jets, and

missing transverse momentum in pp collisions at √s = 13 TeV with the ATLAS

(16)

(17)

Part I

(18)

(19)

1

The Standard Model of Particle Physics

The Standard Model (SM) of particle physics is the current best description of the universe at the most fundamental level. It is the base of understanding for every elementary particle physics experiments and a predictive framework for calculations of high energy particle inter-actions in the cosmos and the early universe. In the following section, the particle content of the Standard Model and the interaction between the particles is explored. The Standard Model, however, is not a complete picture due to its inability to explain some phenomena. Later, we will briefly explore some of the Standard Model shortcomings and some theories prepared to mitigate them.

1.1 Particle content of the Standard Model

When you go to a bookstore, you see series of bookshelves containing the vast range of the lit-erary world. From books of science, law, culinary, to fiction. All these litlit-erary complexities can be broken down into smaller and simpler elements. Chapters into paragraphs, paragraphs into sentences, sentences into words, and eventually words into the 26 letters of the latin alphabet. These letters – the elementary particles of literature – follow simple rules of phonetics which govern how they sound when they are put together. Yet from this simple rule, more complex elements (words) and rules (grammar) can be constructed, which eventually leads to an infinite range of meaning: from Shakespeare to a manual on how to build a rocket ship.

The physical world acts much like the literary world. Complex structures that we encounter everyday are built by smaller and simpler things that follow a set of simple rules. On the most fundamental level, the rule is called the Standard Model of Particle Physics which governs how the elementary particles interact with each other. Figure 1.1 shows all the known fun-damental particles, classified into different categories by their properties. These properties are called quantum numbers which include spin, electric charge, and color charge. These quantum numbers become the identity of elementary particles, each carrying a unique set of quantum numbers. It is important to note that for each particle listed in Figure1.1, there is an anti-particle with identical quantum numbers except for an opposite charge sign1_.

1_{Neutrally charged particles are their own anti-particles, with the exception of neutrinos. It is still unclear}

(20)

CHAPTER 1. THE STANDARD MODEL OF PARTICLE PHYSICS

Figure 1.1:Diagram of the particle content of the Standard Model of particle physics [3].

The fermions –1_/2-integer spin particles – are classified by whether they carry a color charge

or not. Those which carry a color charge are called quarks and those which do not are called leptons. Together, quarks and leptons make up for the building blocks of all complex matter of the universe. Particles that carry color charge interact with the strong interaction.

Quarks come in six flavors: up u, down d, charm c, strange s, top t, and bottom b. The up, charm, and top carry+2₃ electric charge, and they are referred to as the “up-type” quarks. Sim-ilarly, the down, strange, and bottom quarks are referred to as the “down-type” quarks with −1

3 electric charge. Quarks of the same type have the same properties except for mass. There

are three types of color charge that each quark can carry, cleverly named after the primary col-ors: red, green, and blue. Due to the fact that gluons – mediator of the strong force – also carry a color charge, no isolated color-charged particles can be observed in nature. This phenomenon is called color confinement. Consequently, quarks can only be observed in a color-neutral state called hadrons. A hadron can be a quark-antiquark pair (meson), or a combination of three quarks (baryon). Due to this phenomenon, every color charged particle created in particle col-lisions is hadronized to create a bound state, and would split and further hadronize if it has sufficient energy. In the detector frame, this looks like a cone-shaped particle shower called jet.

Unlike quarks, leptons do not carry the color charge which means that they do not interact with the strong force. The electron e – the first elementary particle to be discovered – is the particle responsible for much of chemistry. Just like the up quark, the electron has two heavier siblings: muon µ, and tau τ; possessing the same properties except for the mass. Electrons, muons, and taus carry −1 electric charge and therefore can interact electromagnetically. Alongside these three electrically charged leptons, there are the electrically neutral neutrinos ν: electron neu-trino νe, muon neutrino νµ, and tau neutrino ντ. The existence of neutrinos was first hinted

by careful measurement of neutron beta decay whose energy of the final products is always somewhat less than the initial energy. In 1930, Wolfgang Pauli postulated the neutrino as the

(21)

1.2. BEYOND STANDARD MODEL invisible particle that carries away this missing energy2. Looking for missing energy (or mo-mentum) is still the main method for detecting neutrinos in particle detectors today.

The vector bosons – spin one particles – take up the role of force mediators. Each of them is assigned one fundamental force to mediate. The gluon mediates the strong force, the photon mediates the electromagnetic force, and the Z and W bosons mediate the weak force. One might notice that the Standard Model is lacking a boson for gravity. In order for gravity to operate inside the framework of the Standard Model, it requires a boson to mediate it just like the other three forces, and thus the graviton has been postulated but yet to be discovered. Due to how much weaker gravity is compared to the other fundamental forces, the lack of gravity in the theory does not have any experimentally detectable consequences for particle physics experiments.

Before going further, it is important to acknowledge that electroweak bosons discussed previ-ously: W±, Z, and photon, are actually combinations of three isospin gauge bosons: W1, W2,

and W3, and a hypercharge gauge boson: B. However, preserving gauge invariance, there is no

way for the isospin and hypercharge bosons to combine and produce massive W±, Z bosons as observed in experiments. Something was missing.

Robert Brout, François Englert and Peter Higgs proposed in the 60’s that there exists a scalar field with a non-zero vacuum expectation value that permeates the whole universe [4,5]. This field gives rise to four additional bosons, technically called the Goldstone bosons. Two of those combine with W1 and W2 to make W+ and W−, and one combines with W3 and B to make

the Z boson. The leftover combination of W3 and B which does not merge with any

Gold-stone boson becomes the massless photon. These bosons mixing, called the Brout-Englert-Higgs (BEH) mechanism, consequentially breaks the electroweak symmetry, splitting apart electroweak force into the electromagnetic and the weak force. The fourth and remaining Gold-stone boson is what is known as the Higgs boson. The discovery of the Higgs boson in 2012 [6, 7] became the hallmark discovery in fundamental physics of the early 21st century.

The Standard Model is known to be the most successful theory at describing the universe at the most fundamental level and at impeccable precision. Figure1.2demonstrates the incredible precision of the Standard Model at predicting the cross sections of processes that are produced at proton-proton collisions in LHC at different center of mass energies√s = 7, 8, and 13 TeV.

1.2 Beyond Standard Model

Despite the triumph of the Standard Model at describing known processes, there are still big questions which the Standard Model is unable to answer. Many theories are prepared to an-swer these questions. These theories, called Beyond Standard Model (BSM), are subjects of experimental searches in the field of particle physics. Several of these are discussed briefly in the following subsections.

2_{It was later realized that it was actually the anti-neutrinos that take part in neutron beta decays}

(22)

CHAPTER 1. THE STANDARD MODEL OF PARTICLE PHYSICS R Ldt [fb−1_] Reference WWZ WWW t¯tZ t¯tW ts−chan ZZ WZ Wt H WW tt−chan t¯t Z W pp σ = 0.55 ± 0.14 + 0.15 − 0.13 pb (data) Sherpa 2.2.2 (theory) 79.8 PLB 798 (2019) 134913 σ = 0.65 + 0.16 − 0.15 + 0.16 − 0.14 pb (data) Sherpa 2.2.2 (theory) 79.8 PLB 798 (2019) 134913 σ = 176 + 52 − 48 ± 24 fb (data)

HELAC-NLO (theory) 20.3 JHEP 11, 172 (2015)

σ = 950 ± 80 ± 100 fb (data)

Madgraph5 + aMCNLO (theory) 36.1 PRD 99, 072009 (2019)

σ = 369 + 86 − 79 ± 44 fb (data)

MCFM (theory) 20.3 JHEP 11, 172 (2015)

σ = 870 ± 130 ± 140 fb (data)

Madgraph5 + aMCNLO (theory) 36.1 PRD 99, 072009 (2019)

σ = 4.8 ± 0.8 + 1.6 − 1.3 pb (data)

NLO+NNL (theory) 20.3 PLB 756, 228-246 (2016)

σ = 6.7 ± 0.7 + 0.5 − 0.4 pb (data)

NNLO (theory) 4.6 JHEP 03, 128 (2013)PLB 735 (2014) 311

σ = 7.3 ± 0.4 + 0.4 − 0.3 pb (data)

NNLO (theory) 20.3 JHEP 01, 099 (2017)

σ = 17.3 ± 0.6 ± 0.8 pb (data)

Matrix (NNLO) & Sherpa (NLO) (theory) 36.1 PRD 97 (2018) 032005

σ = 19 + 1.4 − 1.3 ± 1 pb (data)

MATRIX (NNLO) (theory) 4.6 EPJC 72, 2173 (2012)PLB 761 (2016) 179

σ = 24.3 ± 0.6 ± 0.9 pb (data)

MATRIX (NNLO) (theory) 20.3 PRD 93, 092004 (2016)PLB 761 (2016) 179

σ = 51 ± 0.8 ± 2.3 pb (data)

MATRIX (NNLO) (theory) 36.1 EPJC 79, 535 (2019)PLB 761 (2016) 179

σ = 16.8 ± 2.9 ± 3.9 pb (data)

NLO+NLL (theory) 2.0 PLB 716, 142-159 (2012)

σ = 23 ± 1.3 + 3.4 − 3.7 pb (data)

NLO+NLL (theory) 20.3 JHEP 01, 064 (2016)

σ = 94 ± 10 + 28 − 23 pb (data)

NLO+NNLL (theory) 3.2 JHEP 01 (2018) 63

σ = 22.1 + 6.7 − 5.3 + 3.3 − 2.7 pb (data)

LHC-HXSWG YR4 (theory) 4.5 EPJC 76, 6 (2016)

σ = 27.7 ± 3 + 2.3 − 1.9 pb (data)

LHC-HXSWG YR4 (theory) 20.3 EPJC 76, 6 (2016)

σ = 61.7 ± 2.8 + 4.3 − 3.6 pb (data) LHC-HXSWG YR4 (theory) 79.8 PRD 101 (2020) 012002 σ = 51.9 ± 2 ± 4.4 pb (data) NNLO (theory) 4.6 PRD 87, 112001 (2013)PRL 113, 212001 (2014) σ = 68.2 ± 1.2 ± 4.6 pb (data) NNLO (theory) 20.3 PLB 763, 114 (2016) σ = 130.04 ± 1.7 ± 10.6 pb (data)

NNLO (theory) 36.1 EPJC 79, 884 (2019)

σ = 68 ± 2 ± 8 pb (data)

NLO+NLL (theory) 4.6 PRD 90, 112006 (2014)

σ = 89.6 ± 1.7 + 7.2 − 6.4 pb (data)

NLO+NLL (theory) 20.3 EPJC 77, 531 (2017)

σ = 247 ± 6 ± 46 pb (data)

NLO+NLL (theory) 3.2 JHEP 04 (2017) 086

σ = 182.9 ± 3.1 ± 6.4 pb (data)

top++ NNLO+NNLL (theory) 4.6 EPJC 74, 3109 (2014)

σ = 242.9 ± 1.7 ± 8.6 pb (data)

top++ NNLO+NNLL (theory) 20.2 EPJC 74, 3109 (2014)

σ = 826.4 ± 3.6 ± 19.6 pb (data)

top++ NNLO+NNLL (theory) 36.1 arXiv: 1910.08819

σ = 29.53 ± 0.03 ± 0.77 nb (data)

DYNNLO+CT14 NNLO (theory) 4.6 JHEP 02 (2017) 117

σ = 34.24 ± 0.03 ± 0.92 nb (data)

σ = 58.43 ± 0.03 ± 1.66 nb (data)

σ = 98.71 ± 0.028 ± 2.191 nb (data)

DYNNLO + CT14NNLO (theory) 4.6 EPJC 77, 367 (2017)

σ = 112.69 ± 3.1 nb (data)

DYNNLO + CT14NNLO (theory) 20.2 EPJC 79, 760 (2019)

σ = 190.1 ± 0.2 ± 6.4 nb (data)

DYNNLO + CT14NNLO (theory) 0.081 PLB 759 (2016) 601

σ = 95.35 ± 0.38 ± 1.3 mb (data) COMPETE HPR1R2 (theory) 8×10−8 NPB 889, 486 (2014) σ = 96.07 ± 0.18 ± 0.91 mb (data) COMPETE HPR1R2 (theory) 50×10−8 PLB 761 (2016) 158 10−4 ₁₀−3 ₁₀−2 ₁₀−1 ₁ ₁₀1 ₁₀2 ₁₀3 ₁₀4 ₁₀5 ₁₀6 ₁₀11

σ

[pb]

0.5 1.0 1.5 2.0

data/theory

Status: May 2020 ATLAS Preliminary Run 1,2 √s= 7,8,13TeV Theory LHC pp√s = 13 TeV Data stat stat ⊕ syst LHC pp√s = 8 TeV Data stat stat ⊕ syst LHC pp√s = 7 TeV Data stat stat ⊕ syst

Standard Model Total Production Cross Section Measurements

Figure 1.2: Cross section measurements of several Standard Model processes compared to the

theoretical predictions at different center of mass energies√s = 7, 8, and 13 TeV. Taken from Ref. [8].

1.2.1 Gravity

As mentioned briefly before, the lack of a boson mediator for gravity is one of the most obvious shortcomings of the Standard Model. Despite the familiar presence of gravity in daily life and its important role in the scheme of cosmology, the working of gravity in the Standard Model remains a mystery, therefore putting gravity in the realm of BSM. It is not even clear how the graviton – the postulated spin-2 boson for gravity – can work in the Standard Model. Introducing the graviton into the SM breaks the renormalizability of the theory, causing it to lose its predictive power [9].

Another puzzling aspect of gravity is its apparent weakness. Gravity is 10−25 times weaker compared to the weak force. One possible explanation for this arbitrary weakness of gravity is that there is an extra dimension of spacetime in which gravity gets diluted, and its small mag-nitude that we observe is only a fraction that gets projected to our 4-dimensional spacetime. In the Randall-Sundrum model [10], the SM fields can propagate through the extra dimension and manifest into Kaluza-Klein excited particles whose decay is detectable in the ordinary four dimensions. However, no signature of the excited particles has ever been observed in the LHC.

(23)

1.2. BEYOND STANDARD MODEL

1.2.2 Origin of neutrino masses

From observations of flavor oscillations of solar and atmospheric neutrinos, we know that neu-trinos must have non-zero rest mass [11,12]. The Cosmic Microwave Background (CMB) data collected by the Planck satellite provide the most stringent upper limit on the sum of the three neutrino masses_{∑ m}νat 0.09 eV [13]. However, it is unclear how neutrinos can gain their mass.

The BEH mechanism which gives the massive SM particles their mass requires change of he-licity in the interaction with the Higgs particle. Since right-handed neutrinos have never been observed, neutrinos cannot interact with Higgs particle, and therefore must gain their mass from other mechanism.

1.2.3 Dark matter

Throughout the cosmos, astrophysical objects move around each other to form bigger struc-tures: planets orbit a star to form a solar system, stars orbit a galactic center to form a galaxy, galaxies orbit each other to form a galaxy cluster. For the structure to remain intact, there must be sufficient gravitational pull in the system to balance the centrifugal push from the rotation. Fritz Zwicky in 1933 found that the measured mass of the Coma galaxy cluster inferred from its luminous matter was not enough to keep the cluster from disintegrating [14]. Zwicky then coined the term “dark matter” to stand for the missing material that must be present to hold the galaxy cluster together.

It was later found that dark matter also exists within galaxies. Kepler’s third law states that the orbital velocity of objects declines with the distance from their orbital center assumming most of the mass of the system are located near the orbital center. In the 60’s, Vera Rubin and Kent Ford discovered that most stars within M31 galaxy move at roughly the same veloc-ity regardless of the distance from the galactic center, as shown by Figure1.3, which violates Kepler’s third law [15]. This hints at the existence of substantial amount of unobserved matter distributed in a spherical halo encasing the galaxy, further proving the existence of dark matter.

As demonstrated by the two mentioned observations, the existence of dark matter is inferred only from a deficit of gravitational pull to fit the observations. Dark matter itself has never been observed directly and its properties as a particle remain unknown. Search for dark matter is one of the most active fields in the quest for BSM. In the next chapter, we will see how super-symmetry can answer the questions of dark matter while also solving the hierarchy problem – another fundamental issue of the Standard Model.

(24)

CHAPTER 1. THE STANDARD MODEL OF PARTICLE PHYSICS

Figure 1.3: First observation of a constant rotation curve by Vera Rubin and Kent Ford using

measurements of stars within M31 galaxy [15].

(25)

2

Supersymmetry

One way to understand supersymmetry, or SUSY for short, is to first understand the problem that motivates it. The hierarchy problem is introduced as a consequence of mass renormaliza-tion in SM and how SUSY comes as a solurenormaliza-tion. Then, the SUSY breaking in the context of the Minimum Supersymmetric Standard Model (MSSM) is briefly introduced followed by the mass eigenstates that come from it. The conservation of R-parity which keeps SUSY from allowing proton decays is also introduced. More specific models, in particular the phenomenological MSSM (pMSSM) and the simplified models, are explained in which some constraints are used to suppress the vast number of MSSM’s parameters down to a more experimentally workable level.

2.1 Higgs mass renormalization and the hierarchy problem

Quantum field theory, which lays the foundation of the Standard Model, is a pertubative theory. This means that a physical property like mass is calculable in quantum field theory by orders of approximation. Consider the potential Lagrangian term of a massive fermion ψ coupled to the Higgs field H:

L = −mbare_f ψψ¯ − (λ_fψ¯LHψR+h.c.) (2.1)

where the first term is the mass term of the particle generated by the Higgs mechanism, and the second term is the interaction term between the fermion and the Higgs field. From these two Lagrangian terms, one can construct Feynman diagrams that contribute to the mass of the fermion. Below are the tree level diagram and the first order radiative correction:

f

+

H

f

These two diagrams contribute to the zeroeth and first order expansion of the observed fermion mass mf [16]: mf =mbaref +mbaref 3λ2_f 32π2log( Λ2 m2_f) (2.2)

(26)

CHAPTER 2. SUPERSYMMETRY cut-off limit to avoid infinity in the integration leading to Equation2.2, which implies that the approximation of quantum field theory – or rather the Standard Model – can only work up to that momentum scale. If there is no new physics to be expected up to the Planck scale ∼ 1019 GeV, then the Planck scale can be used as Λ. Note that even in the presence of exceedingly huge Planck scale in the equation, the logarithm suppresses it so that mbare

f is still in the same

order of magnitude as mf.

The same, however, cannot be said for the mass of the Higgs boson. Just like the mass of fermions, the observed mass of the Higgs boson mH is estimated by means of expansion from

the bare mass mbare_H :

m2_H = (mbare_H )2+∆m2_H (2.3)

where∆m2_H is the total correction of the Higgs mass squared coming from fermion and boson loops. Since the Higgs boson coupling is proportional to the mass, the top quark loop domi-nates the correction term. Consider the first loop correction to the Higgs mass from a top quark loop:

t

H H

which yields a mass correction of

∆m2

H = −

|λ_f|2

8π2 Λ

2 _(2.4)

Taking Λ to the Planck scale gives the top loop correction term an extremely large negative value. Couple this with the fact that the Higgs mass was observed to be around 126 GeV, the bare mass of the Higgs needs not only to be extremely large to cancel out the correction, but also tuned with an incredible precision. This seemingly fine-tuned value of the Higgs mass is what is known as the fine tuning. The problem is also known as the hierarchy problem from the fact that the correction is much bigger than the original quantity.

2.2 SUSY as a solution to the hierarchy problem

Suppose that there are two boson partners for every fermion in the SM1, where partner here is defined as a particle with identical quantum numbers as its counterpart, except for the spin. Then, for the top quark, there would be two boson partners ˜t1,2, each contributes to the

correc-tion of the Higgs mass coming from the following boson loop,

˜t

H

1_{It is one partner for every gauge eigenstate of the SM. Partners of the same flavor then mix to make two mass}

eigenstates. See Section2.5for details.

(27)

2.3. SUSY NOTATIONS The two bosons ˜t1,2would yield a total correction of

∆m2

H =

λs

8π2Λ

2 _(2.5)

The sign difference between the negative fermion contribution in Equation2.4and the positive boson loop correction in Equation2.5arises from the fermion and boson spin statistics. Putting this term into the total mass correction suppresses the top quark contribution and elegantly removes the necessity for fine tuning.

Notice that this solution only works if λs ≈ |λf|2to achieve appreciable cancelation. Knowing

that the Higgs boson coupling to a particle is proportional to the particle’s mass, it follows that the mass of the partner particle needs to be the same order of magnitude as the SM particle for supersymmetry to be an effective solution to the hierarchy problem.

2.3 SUSY notations

Here, and for the rest of the thesis, we consider only the Minimal Supersymmetric Standard Model (MSSM) [17] which minimally extends the Standard Model into SUSY by adding ex-actly one SUSY partner to every SM gauge eigenstate. Table2.1lists the SM gauge eigenstates and their SUSY partners. The bosonic SUSY partners of fermions gain an additional ’s’ at the beginning of their SM particle names; for example, the superpartner for the top quark is called stop. The fermionic SUSY partners for SM bosons are given an ’ino’ at the end of their SM particle names; e.g. gluino for gluon. The SUSY particles are denoted with a ’tilde’ above their letters.

Table 2.1: The SM particles and their SUSY partners and spin. Only the first generation of

(s)fermions are shown, but the notation applies also to all three generations.

SM particles Spin SUSY partners Spin

uL, uR 1/2 u˜L, ˜uR 0 dL, dR 1/2 d˜L, ˜dR 0 eL, eR 1/2 ˜eL, ˜eR 0 νe 1/2 ˜νe 0 W1, W2, W3 1 W˜ ±, ˜W0 1/2 B 1 B˜ 1_/₂ g 1 ˜g 1_/2

2.4 SUSY breaking

If Nature was perfectly supersymmetric, SUSY particles would have the same mass as their SM counterparts and the hierarchy problem would be nicely solved with no extra parameters to the theory. However, that cannot be true because if there were SUSY particles with the same masses as their SM counterpart, they would have been found. Then, it becomes an empirical fact that SUSY, if it exists, must be broken.

(28)

CHAPTER 2. SUPERSYMMETRY To break SUSY, additional terms must be added to the SUSY Langrangian. However, these terms must not reintroduce quadratic divergences that they intend to remove. Thus, they are called the ’soft’ SUSY breaking terms. The soft breaking terms assumes that there is a SUSY breaking sector existing at a high energy scale. The SUSY breaking is then mediated to the observable sector and the soft breaking terms appear as a result. This shows that MSSM is a mere effective theory that is only valid below a certain energy scale, and the soft breaking terms only represent the unknown finer details of the SUSY breaking sector [17].

Many models are proposed to explain the aforementioned SUSY breaking and its mediation to the electroweak scale. The three most common models are called gravity-mediated, gauge-mediated, and anomaly-mediated supersymmetry breaking [18]. Regardless of the lack of con-sensus on which one may be true, the Lagrangian of the observable sector will gain additional terms from the SUSY breaking which determine the amount by which supersymmetry is bro-ken. These terms contain masses and couplings which govern flavor mixing and may also allow new sources of CP violation. In total, this amounts to more than 100 additional parame-ters to the Standard Model.

2.5 The mass eigenstates

After SUSY is broken, states with the same quantum numbers mix. For example, the left- and right-handed stop ˜tL, ˜tRmix to form mass eigenstates ˜t1and ˜t2, where ˜t1 is the lightest of the

two. Similar mixing applies to other squarks and charged sleptons. The mixing for the third generation squarks can be larger than other generations due to the large Yukawa coupling.

The Higgs sector requires additional complexity. The Higgs sector in SUSY needs to be ex-tended because two complex Higgs doublets, shown in Equation 2.6 below, are required to give mass to all fermions in a way that is consistent with supersymmetry.

h_d = h 0 d h−_d , hu=h + u h0 u (2.6)

The two doublets mix to give eight mass eigenstates, three of which are absorbed by the Higgs mechanism to give mass to the W±and Z boson. This yields five physical fields: a pseudoscalar A, a lighter scalar h, a heavier scalar H, and two charged fields H±.

Each of the gauge eigenstates in the doublets has its own SUSY partner, called the Higgsinos: ˜h0

d, ˜h0u, ˜h−d, ˜h+u. The neutral Higgsinos ˜h0d, ˜h0umix with the neutral gauginos ˜W0, ˜B to form four

mass eigenstates called the neutralinos ˜χ0₁, ˜χ0₂, ˜χ0₃, ˜χ0₄, ordered in increasing mass. Similarly, the charged Higgsinos ˜h−_d, ˜h+_u mix with the charged gauginos ˜W± to give the charginos ˜χ₁±, ˜χ±₂. Table 2.2summarizes the gauge eigenstates and the corresponding mass eigenstates of SUSY particles in MSSM.

(29)

2.6. R-PARITY AND THE PROTON DECAY

Table 2.2: The gauge eigenstates and the corresponding mass eigenstates of SUSY particles in

MSSM. Only the first generation of (s)fermions is shown, but the notation applies also to all three generations.

Gauge eigenstates Mass eigenstates

Up-type squarks u˜Lu˜R u˜1u˜2

Down-type squarks d˜Ld˜R d˜1d˜2

Charged sleptons ˜eL ˜eR ˜e1 ˜e2

Sneutrinos ˜νe ˜νe

Neutralinos B˜0_W_˜ 0 _˜h0

d ˜h0u χ˜01χ˜02χ˜03χ˜04

Charginos W˜ ± ˜h−_d ˜h_u+ χ˜±₁ χ˜₂±

Gluino ˜g ˜g

2.6 R-parity and the proton decay

A potential risk of introducing a set of new particles is that they may allow interactions that have never been observed. With the existence of SUSY particles, an anti-down squark can mediate a proton decaying into a positron and a pion, as shown in the diagram in Figure2.2. However, proton has never been observed to decay. Current experiments have constrained the proton lifetime to be longer than 1034seconds [19].

u d u e+ ¯ u u ¯˜ d p π0

Figure 2.2: Feynman diagram for a proton decay mediated by a squark, a process that is

al-lowed by SUSY without R-parity conservation.

To avoid this contradiction with data, proton decay is prevented in SUSY by introducing a new discrete symmetry called R-parity RP, defined as

RP = (−1)3(B−L)+2S (2.7)

where B is baryon number, L is lepton number, and S is the spin. Following this definition, all SM particles have RP = 1 and all SUSY particles have RP = −1. Hence, in models where

R-parity is conserved, the proton decay is not allowed. R-R-parity conservation leads to profound phenomenological implications on SUSY signatures in collider experiments:

• SUSY particles can only be produced in pairs,

• SUSY particles must decay into SM particles plus an odd number (usually one) of lighter SUSY particles,

• The lightest SUSY particle (LSP) – unable to decay to a heavier SUSY particle – must be stable.

(30)

CHAPTER 2. SUPERSYMMETRY The LSP has a very small cross sections in interacting with SM particles due to the suppression by high SUSY mass scale [20]. Being stable and not very interactive, the LSP provide a candi-date for dark matter if it is electrically neutral and does not interact via the strong interaction. SUSY could thus solve both the hierarchy problem and the existence of dark matter.

2.7 Phenomenological MSSM and simplified models

The soft SUSY breaking terms in MSSM contain 105 extra free parameters, of which there is no theoretical insight whatsoever on their magnitudes [21]. This extremely high number of parameters makes the phase space enormously large for any experimental search. Therefore the MSSM needs to be further constrained by some justifiable assumptions in order to come up with a model that is testable in experiments.

The phenomenological MSSM (pMSSM) is one such model where the MSSM is constrained using the following assumptions which are motivated from experimental observations [22]:

• No new source of CP-violation.

• No flavor changing neutral currents.

• Degenerate mass of first and second generation of sfermions.

After applying these assumptions to MSSM, the 105 parameters are reduced to 19 parameters.

Even after putting all these constraints, 19 parameters still represent a vast parameter space to explore. To further optimize the search for SUSY signatures, the so called simplified models [23] are developed. The principle of a simplified model is to isolate minimal particle content that is required to produce a given SUSY signature. In a simplified model, only the mass of two SUSY particles (1 sparticle plus the LSP) of interest are set to be free parameters while the mass of other SUSY particles are fixed at values where they cannot participate in the decay chain of the two SUSY particles of interest.

Note that the simplified models, with all their additional assumptions, cannot hope to cover the full parameter space of the pMSSM. In Ref. [24], it is evaluated that 40% of points that are excluded in ATLAS pMSSM study [25] are not covered by the simplified models. However, simplified models provide the means for an early detection of SUSY signature if it is produced in a collider.

Since the correction from the top quark loop is the main source of the quadrative divergence, as discussed in Section2.1, the correction from stop is expected to be the main cancellation of the divergence. This makes the stop to be of particular interest to the hierarchy problem. Signatures of stop-neutralino simplified models have been tested using proton-proton collisions at the LHC by ATLAS. No evidence of such signature has been observed. The ATLAS summary on stop searches using 36 fb−1 LHC data at √s = 13 TeV is shown in Figure2.3. PartIIof this thesis discusses an updated version of this search using full Run 2 data of 139 fb−1 in one lepton final state.

(31)

2.8. GAUGE UNIFICATION AS FURTHER MOTIVATION FOR SUSY

Figure 2.3:The 95% CL exclusion limits on the ˜t1and ˜χ0₁mass plane derived from ATLAS data

by combining multiple stop decay channels using 36.1 fb−1 of Run 2 data [26,27, 28, 29, 30] with the exclusion from Run 1 [31] also shown for reference.

2.8 Gauge unification as further motivation for SUSY

In addition to providing a dark matter candidate while elegantly solving the hierarchy prob-lem, SUSY has another reason that adds to its appeal: it also provides a pathway to unify three of the fundamental forces of the SM.

The gauge bosons that mediate the fundamental forces are gauge fields of a corresponding local symmetry group. These symmetry groups, called SU(3), SU(2), and U(1), have coupling constants α3, α2, α1 that govern the strength of the interactions. Due to the divergence from

gauge boson propagator, the coupling constants can be expressed as effective values that are dependent on the energy scale of the interaction Q [32]:

1 α_i(Q2) = 1 α_i(µ2)− bi 2π log Q2 µ2 (2.8)

where i = 1, 2, 3 and αi(µ2) is the coupling constants as measured at energy scale µ. The

coefficient bi determines how the coupling runs with the energy scale and depends on the

particle content of the symmetry groups. The three running coupling constants are thought to be unified at some high energy scale which gives the first hint of gauge unification, called the Grand Unified Theory (GUT).

It turns out the SM alone is not enough to realize GUT. The coupling constants cannot be unified at any energy scale under the SM scenario, as shown by Figure2.4 (left) [33]. However, it is remarkable that the additional particles introduced by MSSM modify the coefficient biin such

(32)

CHAPTER 2. SUPERSYMMETRY a way that that the coupling constants meet as demonstrated in the Figure2.4(right). This is achieved assuming that the SUSY masses are in the order of 1 TeV, which can be seen in the plot where the SUSY particles start being effective at around the SUSY mass scale (log Q[GeV] ≈ 3). Realizing GUT is very appealing as it is a step towards the Theory of Everything where gravity is unified with the rest of the fundamental forces.

Figure 2.4: The inverse coupling constants as a function of log energy scale Q [GeV] in the

SM (left), and MSSM SUSY (right). Unification is obtained in the MSSM case where the SUSY particles contribute after the assumed SUSY mass scale of around 1 TeV (log Q[GeV] ≈ 3). Taken from Ref. [33]

(33)

3

The Large Hadron Collider

The Large Hadron Collider (LHC) [34] is a 27 kilometer double accelerator ring tunnel that is used to accelerate protons and heavy ions to high energy and smash them at predetermined locations. Constructed 100 meters below ground at the border of France and Switzerland, the LHC is the most powerful particle accelerator ever built.

Due to its design specifics, the LHC is unable to accelerate particles from zero velocity and therefore must be supported by a series of smaller accelerators. The diagram of CERN’s inter-connected accelerators including the LHC is shown in Figure 3.1. The protons are created by stripping away the electrons from hydrogen gas before they start their journey at Linear Accel-erator 2 (LINAC2). At the end of LINAC2 is where the Proton Synchrotron Booster starts where the protons are further accelerated. When the protons reach the desired energy of 1.4 GeV, they are injected into the Proton Synchroton (PS) which takes the proton energy to 25 GeV and passes them to the Super Proton Synchrotron (SPS). The SPS becomes the final staging phase before the hadrons are sent to the LHC at the energy of 450 GeV.

When the stream of protons from SPS enters the LHC, it is split into the two opposite directions: clockwise and anti-clockwise, thus the need for the double-ring structure of the LHC. The two beams meet at four different points where the particles collide at center-of-mass energy √s of 13 TeV. At each of these four colliding points, four major particle detectors were built, each specialized to study a particular type of physics. LHCb (LHC beauty) [36] is dedicated to study the decay of b quarks which can be a gateway to answer matter-antimatter imbalance in the universe. ALICE (A Large Ion Collider Experiment) [37] is a detector specifically designed to study the strong interaction by probing the quark-gluon plasma created by heavy ion collisions. ATLAS (A Toroidal LHC Apparatus) [38] and CMS (Compact Muon Solenoid) [39] are general-purpose detectors whose design philosophy is to detect and record every particle produced in particle collisions.

The Lorentz force, shown in Equation 3.1, demonstrates the basic principle on how the LHC guides and accelerates protons. The Lorentz force~F acting on a charged particle is a vector sum of the electric force and magnetic force:

~_F₌_q~_E₊_q_~_v_{× ~}_B _(3.1)

where~v is the velocity vector of the particle,~E and~B are the electric and magnetic field imposed on the particle. The electric force supplies linear acceleration to the particle, while the magnetic

(34)

CHAPTER 3. THE LARGE HADRON COLLIDER

Figure 3.1:Diagram of CERN’s accelerator complex [35].

force steers the particle along the curve of the tunnel. The counter-circulating beam design of the LHC requires two magnetic fields of different direction, one for each beam. This is reflected in the design of the dipole magnet as seen in Figure 3.2. The dipole magnet of the LHC is capable of generating 8.3 Tesla of magnetic fields, but operates at 7.7 Tesla for √s = 13 TeV collisions1.

The Radiofrequency (RF) cavities generate the electric force that drives the acceleration of the protons. Installed at one point of the LHC, there are a total of 16 RF cavities, 8 for each beam. Neighboring cavities drive a time-varying electromagnetic field in opposite directions. Travel-ling protons that arrive at the cavity when their velocity vector has the same direction as the electric field are accelerated, while the protons at the region with opposite direction of electric field (at the neighboting cavities) are decelerated. This causes the protons to be bunched up at the spaces between the cavities. This process is repeated for every revolution around the accelerator ring with the proton bunches gaining energy from the push of the electric field each time they pass the RF cavities.

Collisions occur when the bunches are made to cross paths at the collision points. The

acceler-1_{For comparison, a magnet used in a typical MRI machine is 1.5 Tesla strong.}

(35)

Figure 3.2:Cross section of the LHC dipole magnet [40].

ator’s ability to collide protons is measured in luminosity, as formulated by

L= f bn1n2 4πσxσy

(3.2)

where f is the revolution frequency, b is the number of bunches in each beam, niis the number

of particles in one bunch of beam i, and σx,y is the size of the beam in the transverse plane2of

the bunches. The typical values for these parameters are given in Table3.1[41,42], which gives the LHC design luminosity of about 1034cm−2s−1.

Table 3.1:Typical parameter values of the LHC beam at the design luminosity of 1034cm−2s−1.

Parameter Value

Revolution frequency f [MHz] 40

Number of bunches in one beam b 2556

Number of particles per bunch n1, n2[1011] 1.15

Transverse beam size σx, σy[mm] 0.04

The number of events for a given physics process produced by the collisions is the product of the luminosity integrated over the accelerator running time with the probability of said events happening – the cross section σ – as shown in Equation3.3below.

N=

Z

L dt×σ (3.3)

2_{Refers to the detector’s coordinate system discussed in Section}_4.1 19

(36)

CHAPTER 3. THE LARGE HADRON COLLIDER The formula nicely connects the experimental and theoretical aspect of high energy physics: with N number of events observed in a certain accelerator of luminosity L run over time t, the cross section σ can be calculated and matched against the theoretical prediction.

The first operational period of the LHC, called Run 1, started from 2010 until 2013. The center-of-mass energy was at 7 TeV and increased to 8 TeV in 2012. Following Run 1, the LHC was turned off in Long Shutdown 1 for several upgrades including preparations for another in-crease in center-of-mass energy. The LHC was then restarted for Run 2 in 2015 running with the new collision energy of 13 TeV until it was turned off again in 2018. Since then, the LHC is in the state of Long Shutdown 2 until 2021 for scheduled maintenance and upgrade works to prepare for High Luminosity LHC (HL-LHC) that will increase the luminosity by a factor of 10 [43].

(37)

4

The ATLAS Detector

As a general-purpose detector, ATLAS aims to measure and record all long-lived particles that come out of particle collisions. To do this, ATLAS is designed to encapsulate nearly 4π stera-dians solid angle around the collision point, making sure all long-lived particles coming out of the collisions pass through the detector. The 25 m tall and 44 m long cylinder-shaped detector is an assembly of concentric layers of subdetectors, each specialized in detecting certain types of particles. Figure 4.1shows a model of the ATLAS detector, and Figure 4.2shows how dif-ferent particles interact with each layer of the detector which determine how the particles are identified.

(38)

CHAPTER 4. THE ATLAS DETECTOR

Figure 4.2:Illustration of the cross-section of the ATLAS detector showing how different

parti-cles interact with each layer of the detector [45].

4.1 The Coordinate System

To understand the position and direction of relevant objects relative to the detector, it is im-portant to agree on a practical coordinate system. With the geometrical center of the detector as the point of origin, ATLAS uses a right-handed cartesian coordinate system with the posi-tive x-axis pointing to the center of the LHC ring, the posiposi-tive y-axis pointing upward, and the positive z-axis pointing along the beam line. The proton-proton collisions the LHC occur in a volume close to the origin of this coordinate system.

As particles move away from the collision point, in most cases spherical coordinates are use-ful to describe the direction in which particles are travelling relative to the origin. Both the cartesian and spherical coordinate systems are visualized in Figure4.3with φ and θ being the azimuthal angle and the polar angle of the spherical system, respectively.

One useful coordinate that is commonly used is called rapidity y, defined as

y≡ 1 2ln(

E+pz

E−pz

) (4.1)

where E is the energy of the particle and pz is the longitudinal momentum along the beam

axis. Rapidity is used to describe the forwardness of a particle’s trajectory relative to the beam

(39)

4.2. INNER DETECTOR x y z ATLAS LHC φ θ

Figure 4.3:The coordinate system used in the ATLAS experiment. The red arrow is an arbitrary

vector to show the azimuthal angle φ and polar angle θ of the spherical coordinate. The image is adapted from Ref. [46].

line. Rapidity is often preferred over θ to describe forwardness because differences in rapidity are invariant under Lorentz boost along the z-axis and particle production rate is independent of rapidity. One can construct the distance between two particle vectors in the φ-y plane as ∆Ry =

p

∆ φ2 ₊ _{∆ y}2_.

An approximation to rapidity can be made by substituting the energy E by the modulus of three-momentum|~p|. This simplification is called pseudorapidity η, defined as

η≡ 1 2ln( |~p| +pz |~p| −pz ) = −ln(tanθ 2) (4.2)

Notice that at high energy limit, or in the case of massless particles, rapidity and pseudorapid-ity are the same. Similarly, the distance of two particle vectors in the φ-η plane is defined as ∆R=p∆φ2₊∆η2_.

Momentum of a particle is often expressed in its projection to the transverse (xy) plane for several reasons. Head-on particle collisions always start with purely longitudinal momenta, therefore the transverse momenta of final state particles comes purely from particle interac-tions during the collision. The modulus of the transverse momentum of an outgoing particle, denoted pT, is then often used to describe the momentum transfer of the interaction. The

con-servation of momentum states that the momentum of any final state particle has to be cancelled out by opposing momenta of other final state particles. Since the momenta of all outgoing par-ticles must sum up to zero, the missing transverse momentum after summing all detectable transverse momenta can be attributed to invisible particles, such as neutrinos.

4.2 Inner Detector

The Inner Detector (ID), shown in Figure 4.4, tracks any charged particles coming out from the collision before they reach the calorimeters. With the track information, one can trace the point of origin of the tracks by looking for their intersections, called vertices. A primary vertex is the point where two protons interacted. As noted before, in LHC the protons are collided in bunches which means there is more than one primary vertex per event. Given the high luminosity of the LHC, there are up to∼40 primary vertices per bunch crossing. The primary vertex which has the highest ∑ p2_T of the tracks is labelled the hard scatter primary vertex.

(40)

CHAPTER 4. THE ATLAS DETECTOR Any tracks and subsequent objects that are not associated with a hard scatter primary vertex are called pile-up. Most analyses are mainly interested in objects originated from hard scatter primary vertices, therefore pile-up is usually removed in a process called pile-up suppression.

The ID is subjected to 2 T magnetic field parallel to the beam axis generated by a superconduct-ing solenoid magnet. Under the influence of the magnetic field, any charged particle bends its trajectory in the transverse plane; and following Equation3.1, the momentum can be derived from the radius of the curvature. Since the measurement depends on the bending radius, the relative momentum resolution σpT/pTgets worse with increasing transverse momentum of the particle, which is given by1

σpT pT

=3.4·10−4GeV−1pT[GeV] ⊕0.015 (4.3)

Being in the innermost volume of the detector closest to the interaction point, the ID is re-quired to have the greatest spatial resolution of all the ATLAS subdetectors to perform its task. To achieve this, the ID is further divided into three complementary sub-detectors: the Pixel De-tector (PD), the Semiconductor Tracker (SCT), and the Transition Radiation Tracker (TRT). In general these sub-detectors are structurally divided into the barrel and the end-cap side; with the barrel covering a more central part of the detector (low|η|), while the end-cap covers the more forward side of the detector (high|η|).

Figure 4.4:The ATLAS Inner Detector [47].

The Pixel Detector[48]– is the innermost part of ATLAS closest to the beam pipe. To cope with

high multiplicity particles coming out of the collision, the PD is built out of 80 million pixels, each the size of 50×400 µm2and resolution of 14×115 µm2. In the barrel region (|η| < 1.7), the PD consists of four layers of pixel sensors at radii of 33 mm, 50.5 mm, 88.5 mm, and 122.5 mm from the beam axis. The layer closest to the beam, called Insertable B-Layer (IBL), is a more

1_⊕_{is quadratic sum.}

(41)

4.3. CALORIMETERS recent addition to the PD added during Long Shutdown 1. It has smaller pixel size compared to the original layers at 50×250 µm. In the end-cap region (1.7< |η| <2.5), the PD is shaped like disks and are located at|z|= 495, 580, and 650 mm. This design allows the PD to provide at least three points on a charged track emerging from the collision. The PD is the main tool for reconstructing primary and secondary vertex.

The Semiconductor Tracker[49] – is located at higher radii between 275 mm and 560 mm. It

consists of silicon microstrip detectors distributed among four cylindrical layers in the barrel and nine discs in each of the two end-caps. There are 8448 rectangular sensors in the SCT barrel and 6944 wedge-shaped sensors in the SCT end-caps. The SCT provides tracking information on the radii-θ plane that complements the tracking from TRT.

The Transition Radiation Tracker [50] – consists of 370,000 cylindrical drift tubes (or straws).

Each straw is a cathode-anode system where the surface of the straw acts as an cathode and a wire running inside it acts as a anode. The straws are filled with a gas mixture of xenon (70%), CO2 (27%), and O2 [51]2. Charged particles passing a straw ionize the gas, leaving a

trail of electrons that will drift towards the anode and read out as electrical signal. Due to the orientations of the stacked straws parallel to the beam axis, TRT can only read radii-φ information of the particle hits. But for the same reason, it provides a large number of points to the track reconstruction that, when combined with the information from the SCT, improves the spatial and momentum resolution of the charged particles. The spaces between the straws are filled with polymer fibres to enhance transition radiation that are emitted by relativistic particles as they pass through different materials. This effect is stronger for an electron than a pion of the same momentum due to its lighter mass which can be used to discriminate electrons from charged pions.

4.3 Calorimeters

Outside the Inner Detector, the ATLAS calorimeter system [53] is installed to measure the en-ergy of outgoing charged particles. It is made of about a hundred thousand active granular cells to achieve the needed spatial reconstruction. Measurement in the calorimeter is disrup-tive, meaning the measured particles are fully absorbed and are no longer available for further measurements. Based on the particle’s interaction with matter, the calorimeter is divided into two parts: electromagnetic (EM) and hadronic calorimeter, with the first located at inner radii. Photons and electrons are stopped and their energy and direction are measured by the elec-tromagnetic calorimeter, while hadrons start showering in the EM calorimeter and end their course in the hadronic calorimeter.

The ATLAS calorimeter system is an integrated system of multiple calorimeters that are based on different technologies to suit varying physics processes and radiation environments. Fig-ure4.5shows the calorimeters that make up the ATLAS calorimeter system: the Liquid Argon (LAr) Electromagnetic Calorimeter, the Tile Hadronic Calorimeter (TileCal), the LAr Electro-magnetic End-cap (EMEC), the LAr Hadronic End-cap (HEC), and the LAr Forward Calorime-ter (FCal).

2_{In 2012, leaks were found in the TRT tubes. To avoid losing the expensive xenon gas, the gas mixture in high}

leak rates module is replaced with an argon-based gas mixture[52]

(42)

CHAPTER 4. THE ATLAS DETECTOR

Figure 4.5:The ATLAS calorimeter system. [53].

4.3.1 Electromagnetic calorimeter

Electromagnetic calorimetry relies on two physics processes: Bremsstrahlung (e → eγ), and pair production (γ→ee). Electrons or photons that pass through the calorimeter will undergo a cascade of both processes creating an electromagnetic shower. This shower of particles is then collected and converted into readable signal that is proportional to the initial energy. The rate of these interactions can be characteristically described by a term called radiation length X0.

It is defined as the distance travelled by an electron through a material over which its energy will be reduced in average by a factor of 1/e via radiation3. The radiation length for a given material can be calculated following the formula [54]

X0 =

716.4 g cm−2A

Z(Z+1)ln(287/√Z) (4.4)

where A and Z are mass and atomic number of the material. To maximize the development of the showers, the radiation length needs to be small and thus the stopping material is required to be heavy (high Z).

The ATLAS electromagnetic calorimeter is a sampling calorimeter, using alternating layers of absorber and active material. An absorber is a high Z material that is placed on the path of travelling particles to maximize the development of the electromagnetic showers. The charged particles in the shower ionize the active material whose ions and electrons are then collected into electrical signal. In ATLAS electromagnetic calorimeter, liquid argon is used as active material and a combination of lead, tungsten, and copper as absorber. Cryostat systems are installed to keep the argon in liquid state at 88 K. The absorber plates are shaped like an accor-dion, as shown in Figure4.6, to give a seamless structure in the φ direction and to maximize

3_{In 1 X}

0a photon has∼7/9 probability to undergo pair production.

(43)

4.3. CALORIMETERS the uniformity of material volume that particles pass through.

The ATLAS LAr EM calorimeter’s relative energy resolution is given by

σE

E ≈

10%

pE[GeV]⊕0.7% (4.5)

which shows that the resolution gets better with increase of energy E.

Figure 4.6: A cut view of the accordion geometry of absorber plates of the ATLAS barrel

elec-tromagnetic calorimeter [53].

4.3.2 Hadronic calorimeter

The hadronic calorimeter mainly follows the same techniques as the electromagnetic calorime-ter described previously, only that the hadronic calorimecalorime-ter deals more with hadronic showers rather than electromagnetic ones. Hadronic showers are more complex compared to electro-magnetic showers due to the larger number of interactions and particles involved in them.

Hadronic interaction with a nucleus can be described by two distinct interactions: elastic (h+ N → h+N) and inelastic (h+N → X) interaction. At high energy (E> 1 GeV), the inelastic interaction dominates the total cross section. The interaction length λ, defined as the mean distance travelled by a hadronic particle before experiencing an inelastic nuclear interaction, can be calculated by

λ= A·Mu

NA·σ·ρ (4.6)

where A is the mass number of the target material, σ is the inelastic nuclear cross section, ρ is

(44)

CHAPTER 4. THE ATLAS DETECTOR the target mass density, NAis the Avogadro number, and Muis the molar mass constant which

is equal to 1 gram/mol. For example in the Tile Calorimeter, the interaction length for pions and protons are λπ = 251 mm and λp = 207 mm, respectively [55]. To make the hadronic

calorimeter structure even more compact than it would otherwise be, the ATLAS hadronic calorimeter is designed to be a sampling calorimeter of which layers of dense absorbers are placed to further shorten the interaction length.

At every inelastic nuclear interaction point, the incoming hadron strongly interacts with the medium creating pions, protons, and neutrons. These secondary hadrons then interact further inelastically with the medium creating more particles and losing energy until their energy falls below pion production threshold ∼ 2mπ ∼ 270 MeV. Neutral mesons like π0 and η that are

produced in the shower decay into two photons which yields an electromagnetic shower.

Some interactions can cause energy loss that are invisible to the calorimeter. Examples of these processes are nuclear excitation when the nuclei in the target medium absorbs a neutron, spal-lation by knocking a nucleon out of a nucleus, nuclear recoil, and production of muons and neutrinos that escape which are invisible to the calorimeter. The energy loss from these sources must be compensated in average by calibrating the energy readings of the calorimeter.

The ATLAS hadronic calorimeter system is divided into two hadronic calorimeters based on its location. The Tile Calorimeter (TileCal) is placed in the central region of the detector|η| <1.7, while the LAr hadronic end-cap is located at the forward and backward region|η| >1.7. Since one of the analyses in this thesis directly relates to the Tile Calorimeter, it will be discussed more deeply in Chapter5.

4.4 Muon Spectrometer

The Muon Spectrometer (MS) is located at the outermost radius of ATLAS, and it is installed there specifically to measure one flavour of particle that escapes all the inner sub-detectors: the muons. Taking up the most volume of ATLAS, the MS tracks the trajectory and measures the momentum of muons passing through it.

Just like in the Inner Detector, muon trajectories need to be bent for the measuremement of their momentum, therefore the Muon Spectrometer incorporates magnetic fields produced by toroidal magnets which give ATLAS its name. In the barrel chamber, eight toroidal magnets – Barrel Toroids (BT) – are installed radially and symmetrically around the beam axis, each pro-duces magnetic field that extends over the inner and outer tracking stations. In each end-cap, there are also eight toroidal magnets – End-Cap Toroids (ECT) – installed with 22.5◦azimuthal rotation relative to the BT to provide radial overlap. Coils that makes up BT and ECT carry 20 kA of current generating up to 2 T magnetic fields.

The Muon Spectrometer is formed out of four types of chambers: two with precise spatial measurement in the bending plane for precise momentum determination – Monitored Drift Tube chambers (MDT), Cathode Strip Chambers (CSC) – and two fast chambers for trigger-ing and coarse position measurement perpendicular to the bendtrigger-ing direction – Resistive Plate Chambers (RPC), and Thin Gap Chambers (TGC). Due to the high radiation and high particle multiplicity environment of the forward region, different technologies are used in the barrel and end-cap part of the spectrometer.

(45)

4.4. MUON SPECTROMETER Figure4.7shows the overall layout of the ATLAS Muon Spectrometer system, and Figure4.8 shows the detailed position and coverage of each tracking chamber in a quadrant view. It is designed to ensure that muons produced at the interaction point pass through three stations of chambers. Multiple hits from each chamber are then transformed into a segment. This information is then used to calculate the sagitta of the arc which is then translated into the particle’s momentum. The barrel chambers are positioned at radii ∼ 5, 7.5, and 9.5 m; and cover the pseudorapidity range |η| < 1.0. The end-cap chambers extend the pseudorapidity range with the coverage of 1.0< |η| <2.7.

Figure 4.7:The ATLAS Muon Spectrometer [56].

2 4 6 8 10 12 m 0 0 Radiation shield MDT chambers End-cap toroid

Barrel toroid coil

Thin gap chambers

Cathode strip chambers

Resistive plate chambers

14 16 18

20 12 10 8 6 4 2m

Figure 4.8: Quadrant view of the ATLAS Muon Spectrometer detailing each detector elements

dimension and coverage. [56].

Search for Stop Using the ATLAS Detector and Performance Analysis of the Tile Calorimeter with Muons from W Decays