estimation of fake lepton backgrounds in the higgs to ww...
TRANSCRIPT
Estimation of fake lepton backgrounds in the Higgs to
WW analysis in ATLAS
Author:Eleni - Myrto Asimakopoulou
Department of PhysicsRoyal Institute of Technology (KTH)
Supervisors:Edvin Sidebo
Bengt Lund - JensenJonas Strandberg
19 oktober 2016
Typeset in LATEX
TRITA-FYS 2016:66ISSN 0280-316XISRN KTH/FYS/–16:66–SE©Asimakopoulou Eleni-Myrto, 2016
Abstract
The discovery of the Higgs boson by the ATLAS and CMS collaborations in 2012 broughta long awaited confirmation of the Standard Model (SM), and paved the way for furtherstudies. Run-II explores new energy regimes at
√s = 13 TeV and aims to carry out
precision measurements for further SM validations. Direct observation of the Higgs bosonparticle in individual decay channels is of particular interest.
The H → WW ? → `ν`ν decay constitutes a good candidate for observation withthe corresponding signal being composed of two opposite-sign leptons (e or µ) and twoneutrinos (identified as an imbalance in the transverse momentum conservation in theevent).
The quality of the analysis is directly dependent on how accurately the signature ofthe Higgs boson final states can be distinguished from background. Background processesthat produce the same leptonic plus missing transverse energy signature in the detector,but do not naturally contain two leptons from W or Z bosons and neutrinos, are labeledas “fakes” and their presence needs to be accounted for.
The thesis focuses on the W+Jet(s) background to the analysis. The process can bewrongly considered as signal when the W decays leptonically and the jet is misidentifiedas a lepton. The number of fakes for the process is estimated from the observed yields ina set control region in data. The calculation is carried out in a presumably W+Jet(s) richcontrol region and is extrapolated with a dedicated fake factor to the signal region. Thecalculation of the fake factor is done in Z+Jet(s) samples (data and MC). The resultsare compared to fake factor calculations in W+Jet(s) MC samples.
Sammanfattning
I juli 2012 rapporterade ATLAS och CMS upptackten av en ny boson. Denna partikelhar visats vara Higgsbosonen, den saknade pusselbiten i partikelfysikens standardmodell.Under andra korperioden 2015-2018 av Large Hadron Collider, vid energi
√s = 13 TeV,
fortsatter studierna av denna boson, nu med fokus pa noggrannare matningar och ob-servationer i olika sonderfallskanaler. Det ar sarskilt intressant att mata Higgspartikelnsolika kopplingskonstanter, men ocksa att leta efter ytterligare, tyngre Higgspartiklar.
For matning av kopplingskonstanterna ar sonderfallskanalen H → WW ? → `ν`νviktig. Detta tack vare Higgsbosonens relativt hoga sannolikhet att sonderfalla till tvaW -bosoner samt mojligheten att urskilja signal i det rena sluttillstandet med tva leptonermed olika smak (elektron och myon) och motsatt laddning samt en obalans i rorelsemangdi det transversella planet pa grund av neutrinerna. Fokus for denna avhandling ar studienav Higgsbosonen via denna kanal och specifikt pa den bakgrund i analysen orsakad av pro-cesser med en W -boson tillsammans med en eller flera jets. Sadana processer kan produ-cera en signallik signatur da en jet, en kollimerad strale av hadroner, felaktigt identifierassom en lepton i detektorn. Denna missidentifikation ar ovanlig, men da tvarsnittet for jet-produktion vid LHC ar hogt blir denna process en icke forsumbar bakgrund. Bakgrundenuppskattas med en datadriven metod dar antalet registrerade handelser i en W+Jet(s)-rik kontrollregion extrapoleras till signalregionen. Extrapoleringen gors med en sarskildfaktor som mats i ett separat dataprov med lite eller ingen signal, samt berikat medfelaktigt identifierade jets. Extrapoleringsfaktorn mats med fordel i ett prov berikat medZ-bosoner for att efterlikna W+Jet(s)-processen. Denna avhandling presenterar en forstasadan matning med data fran 2015 och 2016 motsvarande 5.8 fb−1 insamlat av ATLAS-experimentet. Resultaten jamfors med forutsagelser fran Monte Carlo-simuleringar forW+Jet(s) och Z+Jet(s). Inom statistiska osakerheter ar alla tre faktorerna kompatibla.
Contents
1 Introduction 31.1 Outline of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.2 Author’s Contribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2 Theoretical Background 52.1 The Standard Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1.1 The Building Blocks . . . . . . . . . . . . . . . . . . . . . . . . . 62.1.2 The Fundamental Forces . . . . . . . . . . . . . . . . . . . . . . . 72.1.3 Symmetries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.1.4 Rise of the Higgs mechanism . . . . . . . . . . . . . . . . . . . . . 102.1.5 Spontaneous Symmetry Breaking in the SM . . . . . . . . . . . . 11
3 The Large Hadron Collider and the ATLAS Detector 123.1 Elementary Particles and Particle accelerators . . . . . . . . . . . . . . . 12
3.1.1 Beam Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123.1.2 Luminosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.2 LHC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133.3 The ATLAS Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.3.1 Detector Complex . . . . . . . . . . . . . . . . . . . . . . . . . . . 153.3.2 Magnets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233.3.3 Trigger System and Data Acquisition . . . . . . . . . . . . . . . . 243.3.4 Data Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . 253.3.5 Particle Identification . . . . . . . . . . . . . . . . . . . . . . . . . 26
4 The Higgs Boson at the LHC 294.1 Production in proton-proton collisions . . . . . . . . . . . . . . . . . . . 294.2 Decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
5 The H → WW ? → `ν`ν analysis 335.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335.2 Data and Simulated Samples . . . . . . . . . . . . . . . . . . . . . . . . . 345.3 Event Signature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345.4 Background Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355.5 Event Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
5.5.1 Pre-selection Cuts . . . . . . . . . . . . . . . . . . . . . . . . . . . 375.5.2 Jet Multiplicity Cuts . . . . . . . . . . . . . . . . . . . . . . . . . 385.5.3 Topological Cuts . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
5.6 Statistical procedure and results . . . . . . . . . . . . . . . . . . . . . . . 38
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6 W+Jet(s) Fakes Background Estimation 406.1 The W+Jet(s) background process . . . . . . . . . . . . . . . . . . . . . 406.2 W+Jet(s) Fakes Estimation Strategy . . . . . . . . . . . . . . . . . . . . 416.3 W+Jet(s) Control Region . . . . . . . . . . . . . . . . . . . . . . . . . . 426.4 Fake Factor estimation in Z+Jet(s) data samples . . . . . . . . . . . . . 43
6.4.1 Fake Factor estimation in W+Jet(s) MC and Z+Jet(s) MC samples 48
7 Summary and Conclusions 50
Acknowledgments 51
Appendix A 56
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Chapter 1
Introduction
The Standard Model (SM) of particle physics encapsulates the best understanding of ourtime regarding the building blocks and the fundamental forces of nature. The model wasdeveloped in the early 1970s and has succeeded in explaining most of the experimentalresults as well as predicting a wide variety of phenomena. Over time and through manyexperiments, the SM has become established as a well-tested physics theory.
The theory has managed to successfully describe the electromagnetic, weak and strongforces in the framework of quantum field theory. In order to keep the structure of thegauge interactions at high energy untouched, the SM requires for the symmetry of the sys-tem to be broken. The Brout–Englert–Higgs (BEH) mechanism [1] proposed a quantumfield (BEH field) that would cause spontaneous symmetry breaking during interactionsin lower energy scales. The simplest manifestation of the mechanism, is the existence ofa boson (Higgs boson1) [2,3], resulting from the excitation of the field, and its discoverywould serve as proof for the proposed mechanism.
In 2012, ATLAS and CMS, observed a boson with a mass of 125 GeV [4,5], that agreedwith the theoretical predictions of the SM for the Higgs boson [6,7]. This discovery addedthe last missing piece of the SM that had remained to be proven.
Post discovery, new studies have started. In Run-II, new energy regimes will beaccessible and studies on precision measurements for further SM validations are one ofthe main parts on the agenda. Direct observations of the Higgs boson in individual decaychannels are of particular interest as means of studying how the Higgs couples to differentparticles.
The H → WW ? → `ν`ν decay channel is a very good candidate for observation andan extended amount of work has been focused on this analysis. The corresponding signalis composed of two opposite-sign (OS) leptons (e or µ) and two neutrinos (identified asan imbalance in the transverse momentum in the event). The quality of the analysisis directly dependent on how accurately the signature of the Higgs’ final states can bedistinguished from background processes. Background processes that do not naturallycontain two leptons from W s, Zs or which don’t have neutrinos, but produce the samesignature in the detector, are labeled as fakes. Fakes need to be properly accounted forin order to ensure that the analysis is carried out on real Higgs events.
1For the rest of the thesis the Higgs boson will also be simply referred to as the Higgs.
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1.1 Outline of the Thesis
The present work has as its main objective the estimation of the contribution of theW+Jet(s) process as background to the H → WW ? analysis. The process can be wronglyconsidered as signal when a W decays leptonically (matching half of the Higgs signal)and the jet is misidentified as a prompt lepton in the detector.
The number of fakes from the process is estimated from the observed yields in aselected control region in data. The calculation is carried out in a selected, presumablyW+Jet(s) rich control region (CR) and is extrapolated with a dedicated fake factor (FF)to the signal region (SR). The calculation of the FF is done in Z+Jet(s) samples (data andMC) and are compared to FF calculations in W+Jet(s) MC samples. The final resultsare compared to the respective results that were obtained during the Run-I analysis.
The thesis is outlined as follows. In the following chapter, Chapter 2, a short the-oretical overview of the Standard Model is provided to bring the presented work intocontext. Subsequently, in Chapter 3, the ATLAS detector experimental apparatus andthe particle detection and identification process are discussed. Chapter 4, concerns theHiggs boson production mechanisms in proton-proton collisions and its decay channels.Chapter 5 provides an overview of the H → WW ? → `ν`ν analysis carried out by theATLAS group. Chapter 6 contains the author’s contribution to the analysis. The methodfor fake factor estimation is outlined, followed by the presentation of the results. Finally,Chapter 7, is an overview of the overall work along with the obtained conclusions.
1.2 Author’s Contribution
The H → WW ? analysis work described in this thesis is a collaborative work performedby the HWW working group of the ATLAS experiment at CERN. The author has beeninvolved in the estimation of fake lepton contamination in the H → WW ? → `ν`νchannel of the analysis, specifically from jets originating from the W+Jet(s) backgroundprocess. The Fake Factor method has been used on Z+Jet(s) data samples for the firsttime in the Run-II analysis. Chapter 6 summarizes the applied methodology and containsthe results produced by the author.
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Chapter 2
Theoretical Background
The discussion of the analysis that was carried out in the thesis presupposes a generaltheoretical background. A brief overview of the particle content of the SM and thefundamental interactions will be given, along with other some concepts which form thetheoretical background to the work presented in this thesis. For more in depth referenceson the discussed subjects, the reader is referred to more specialized textbooks such as“Introduction to elementary particles” by D. J. Griffiths [8], “Particle Physics” by B. R.Martin and G. Shaw [9] and “Quarks and Leptons: An Introductory Course in ModernParticle Physics” by F. Halzen and A. D. Martin [10].
2.1 The Standard Model
The physical world can be described in the context of quantum field theories (QFT),which provide a framework to explain its building blocks, called fundamental particles,and the four fundamental forces that govern their interactions. Particles are consideredas results of excitations of quantized fields, with each field being correlated to a spe-cific particle. The interactions among the particles are realized with exchanges of forcecarriers, which are considered to be quantized excitation of force fields.
The SM is an example of such a quantum field theory. In the SM, matter is com-posed of fermions, while the interactions among them (strong nuclear, electromagnetic,weak nuclear and gravitational) are realized with the exchange of bosons. Fermions arecharacterized by half-integer spin values and obey the Fermi-Dirac statistics1. They aredivided in quarks and leptons, with each type being further grouped in generations. TheSM has succeeded in describing in a QFT formulation three out of the four known forces,the strong, electromagnetic and weak, but not gravity. The carriers of each force com-pose the mentioned bosons, the photon is the mediator of the electromagnetic force, theW± and Z0 the mediators of the weak and finally the gluons are the mediators of thestrong force. Bosons are characterized by integer spin values and obey the Bose-Einsteinstatistics2. In principle, gravity is also believed to potentially be a quantized theory and
1Fermi-Dirac statistics describes the distribution of particles over energy states in systems consistingof many identical particles that obey the Pauli exclusion principle. Pauli’s principle states that twoidentical particles cannot occupy the same quantum state simultaneously.
2Bose-Einstein statistics determines how a collection of non-interacting indistinguishable particles,that are not subject to the Pauli principle, may occupy a set of available discrete energy states, atthermodynamic equilibrium.
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it is speculated that it would have a mediator of spin-2 called graviton [11].The fundamental forces can be mathematically expressed by a Lagrangian subject
to the gauge symmetry group U(1) × SU(2) × SU(3) (see Sec. 2.1.3). U(1) is the gaugegroup that refers to the electromagnetic force, SU(2) to the weak force and SU(3) to thestrong force.
The SM theory also predicts the existence of a Higgs field, mediated by a spin-0particle called the Higgs boson. The Higgs field and the Higgs boson will be furtherdiscussed in Sec. 4.
2.1.1 The Building Blocks
In the SM all matter is composed of elementary particles often referred to as Fermions.These particles are distinguished into two types; quarks and leptons. Each type consists ofsix particles, which are grouped in “generations”. Fermions are characterized by variousintrinsic properties such as electric charge, mass and spin that refer to all types (Tab.2.1)and certain other properties that are type-dependent. All fermions have their respectiveantiparticles, which are characterized from the same mass and spin but have oppositevalues for the rest of the quantum numbers.
Quarks
The three quark generations are grouped in flavors as: “up” and “down”, “charm” and“strange”, and finally, “top” and “bottom (beauty)” quarks, constituting the first, secondand third generation respectively. The ordering in three generations is based on theirmass.
Aside from electric charge, mass and spin, quarks are assigned a baryon number (B)and are associated with a quark number, separately for each flavor. Furthermore, quarksare characterized by a quantum number called color charge.
The baryon number is a strictly conserved quantum number that is associated to asystem. It is defined as
B =1
3(nq − nq), (2.1)
where nq is the number of quarks, and nq is the number of anti-quarks.Each quark flavor is assigned a quark number. The quantum number is conserved
in all electromagnetic and strong interactions, for each flavor separately, but it can beviolated in weak interactions.
Shortly after the existence of quarks was first proposed, it was considered necessaryto introduce the color charge. The need came about in order to explain how quarks thatoccupied identical quantum states, could coexist in composite formations, seeminglyviolating the Pauli exclusion principle. The introduction of the color charge extendedthe quantum numbers that compose a state, lifting this infringement. Hadrons3 wereallowed to exist in those states when a certain combination of color charge was achievedfrom the involved quarks and gluons, the so-called “colorless” combination. The colorcharge has three values: red, green and blue and their respective anti-values (anti-red,anti-green, anti-blue). Based on these values, the colorless combination is achieved eitherby combining three quarks with different colors (qqq), baryons, or one quark and one
3Hadrons are the composite formations made of quarks and gluons
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anti-quark (qq), mesons. The restriction of colorless formation imposes the need forcolor-charged particles (i.e. quarks and gluons) to combine among themselves, creatingthe hadrons. Quarks therefore cannot be isolated singularly; a phenomenon known asconfinement, and their masses can only be inferred indirectly.
Leptons
The lepton family is composed from three flavors, the electron (e), the muon (µ), thetau (τ) and their corresponding neutrinos (νe, νµ, ντ ). Each combination of lepton andneutrino (for example, electron - electron neutrino) share the same flavor.
The electron, muon and tau are electrically charged and have a sizable mass, whereasneutrinos are electrically neutral and have almost zero mass.
Similarly to quarks, each lepton flavor is characterized by a parameter called leptonnumber (L). L is defined to be 1 for leptons and −1 for their corresponding antiparticles.
Type Particle Electric charge Spin Mass
Fermions
Quar
ks
u (up) 2/3 1/2 2.3+0.7−0.5 MeV
d (down) −1/3 1/2 4.8+0.5−0.3 MeV
c (charm) 2/3 1/2 1.275(25) GeVs (strange) −1/3 1/2 95(5) MeVt (top) 2/3 1/2 173.21(71) GeVb (bottom) −1/3 1/2 4.18(3) GeV
Lep
tons
e (electron) −1 1/2 0.511 MeVνe (e neutrino) 0 1/2 < 2 eVµ (muon) −1 1/2 106 MeVνµ (µ neutrino) 0 1/2 < 2 eVτ (tau) −1 1/2 1776.82(16) GeVντ (τ neutrino) 0 1/2 < 2 eV
Bosons
γ (photon) 0 1 0W± ±1 1 80.385(15) GeVZ0 0 1 91.1876(21) GeVg (gluon) 0 1 0H (Higgs) 0 0 125.7(4) GeV
Table 2.1: Table of the SM elementary particles. The presented values are taken from ParticleData Group Listings.
2.1.2 The Fundamental Forces
The forces in nature are considered to be of four types: Gravitational, Electromagnetic,Weak nuclear and Strong nuclear.
They differ in many respects as they interact with different properties of particles, haveuniquely assigned mediators as well as different ranges and strengths. Their generalizedproperties are summarized in Tab. 2.2.
In the context of QFT, each force has its own force carrier that transfers energybetween the interacting particles. Namely, the force carrier types are the photon (elec-
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tromagnetic force), the W± and Z0 bosons (weak force) and the gluon (strong force).Each of them is further characterized by their range and strength. The range of any forceis directly related to its force carrier and is defined as:
R =~
M · c(2.2)
where M is the mass of the mediator. The strength of a force exerted in an interactionis quantified with a number called coupling constant, or gauge coupling parameter. Thisdimensionless quantity determines the relative strength of interactions between particles.The coupling parameter does not remain constant with respect to the energy of theinteracting particles, a phenomenon known as “running”.
Strong Force
As the name indicates, the strong force has the highest relative strength (coupling con-stant) among the forces in the femtometer scale. Its mediators, the gluons, are masslessand electrically neutral particles. They have zero spin and are color charged. The in-teraction couples to color charge, hence it occurs among quarks, antiquarks, and othergluons.
While quarks can have three types of color charge, gluons are mixtures of color andanti-color, such as red and anti-green. Depending on their color charge, they can changethe color of a quark. The compact formation of quarks and gluons however must remaincolorless.
The strong force is described by quantum chromodynamics (QCD), which is a gaugetheory with an SU(3) symmetry. The possible independent gluon formations that arisefrom the theory are 8 (octet).
Two noteworthy properties of the strong force are confinement and asymptotic free-dom. These two properties are linked to the running of the strong coupling constantwith energy. At small inter-particle distances, the strong force becomes asymptoticallyweaker and strongly interacting particles are moving freely. This phenomenon is knownas asymptotic freedom. At large distances however, the exerted force becomes strongerprohibiting their separation from one another. When quarks attempt to separate, a fluxtube of gluons is formed, preventing them to do so. The energy density of the gluon fluxtube increases as the distance between the quarks increases, eventually leading to theformation of a new quark pair (qq). Color charged particles cannot therefore be isolated,but can only exist in confined formations (i.e. hadrons). This behavior of the strongforce causes it to have short range, despite the fact that its force carrier is massless.
The strength of the strong force at large distances (order of fm) can lead to theformation of jets. When an object containing color charge fragments, each fragmentcarries away some of the color charge. In order to obey confinement, these fragmentscreate other colored objects around them to create a colorless formation. These objectscompose a jet.
Electromagnetic Force
The electromagnetic (EM) force has the second highest relative strength. Its mediatoris the photon, a massless, electrically neutral, spin-1 boson particle. It only couples toelectromagnetically charged particles (i.e. it has no self-coupling). Like the strong force,
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the EM coupling parameter is dependent on energy, but not in the same way. The EMforce is stronger at small distances and grows weaker with distance.
Given that the mediator of the EM force is the photon, which is massless, the rangeof the force is infinite, even though its strength is fading.
Weak Force
The weak force is the weakest of the three forces. It is mediated by the W± and Z0
bosons. The W± are electrically (one positively and one negatively) charged particles,with mass of 80 GeV and spin-1, while Z0 is electrically neutral, with mass of 91 GeVand spin-1.
The weak interaction affects all the fermions, and the coupling is dependent on aquantum number called weak isospin (T3). All fermions are assigned a T3 value: u, c andt quarks have T3 = +1/2, while d, s, and b quarks have T3 = −1/2. Similarly, e, µ andτ have T3 = −1/2, while νe, νµ and ντ have T3 = +1/2. The weak isospin is an additivequantity, conserved in all interactions.
The weak interaction is quite unique as it is the only of the forces that changes theflavor of quarks (i.e. changing one type of quark into another), violates the C, P, T andCP symmetries (see Sec. 2.1.3) and has massive force carrier particles. The high mass ofits mediators makes the range of the force quite small, of the order of 10−17 m to 10−16 m.
Gravitational Force
Gravity has not been successfully described as part of a field theory yet. Its respectiveforce carrier is hypothesized to be a massless, electrically neutral, spin-2 boson calledgraviton that will interact with particles that have mass-energy.
At the scales of interest for particle studies (order of TeV), gravity is extremely weakcompared to the other forces and has negligible effect in the studies. In that regard, theSM provides a suitable framework for high energy particle studies.
Force Couples to: Mediator Group Range
Strong color gluon (g) SU(3) ∼10−15 mElectromagnetic electric charge photon (γ) U(1) infiniteWeak weak isospin W±, Z0 SU(2) 10−17 m to 10−16 mGravity mass - energy [graviton] [undefined] infinite
Table 2.2: Table of the SM fundamental forces’ general properties.
2.1.3 Symmetries
One of the underlining laws of nature is the search for the most energetically favorablestate. One of the manifestations of this principle is that any localized particle of finitemass should be unstable, since the decay into several smaller particles leads to higherenergy distribution and hence higher entropy. If a theoretically possible decay does notoccur, it should be prevented from a conservation law, or in mathematical formulation,the symmetry of the system under a group transformation.
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In general, transformations may be continuous or discrete, and give rise to corre-sponding types of symmetries. The fact that symmetries are linked to conservation lawsis stated in Noether’s theorem [12]: “every differentiable symmetry of the action of aphysical system has a corresponding conservation law”. An example is time translationsymmetries, which implies the conservation of energy in the system.
The SM has three related natural near-symmetries, which state that the physicalsystem of the universe is indistinguishable from one where:
• Every particle is replaced with its antiparticle. (C-symmetry or charge symmetry);
• Everything appears as if reflected in a mirror. (P-symmetry or parity symmetry);
• The direction of time is reversed. (T-symmetry or time symmetry).
The characterization of these symmetries as “near-symmetries” is attributed as eachof them is broken in the present-day universe. However, the SM predicts that the com-bination of the three (that is, the simultaneous application of all three transformations)must be a symmetry, called CPT symmetry.
Mathematically, symmetry operations are described by groups. Continuous symme-tries can be described by Lie groups, while discrete symmetries are described by finitegroups. Without going into details, the mathematical representation of the SM QFT isgiven by a Lagrangian, based on the group symmetry4: SU(3) × SU(2) × U(1). Each ofthe groups determines the symmetries of the involved forces in the model: SU(3) refers tothe symmetries of the strong force (gives rise to 8 particles: gluons), SU(2) refers to thesymmetries of the weak force (3 particles: W±, Z0) and U(1) refers to the electromagneticforce (1 particle: photon).
2.1.4 Rise of the Higgs mechanism
In the 1970s a breakthrough came about with the realization that the weak and elec-tromagnetic force could be considered as manifestations of one unified force, called theelectroweak force.
The mathematical formulation of the unification was accomplished with the SU(2)× U(1) group. The associated equations describe correctly the electroweak force and itscorresponding force-carrying particles (the photon, and the W and Z bosons), but thetheory predicts that the particles are massless. This is satisfied for the electromagneticforce, since the photon is massless, but the W± and Z0 bosons are known to be massive.
A solution to this problem came with the introduction of the Brout–Englert–Higgsmechanism (BEH). The mechanism is based on the postulate that in order to generatemasses, the gauge symmetry needs to be broken in some way. It predicts the existenceof a field (BEH or Higgs field5) that permeates all space. The proposed field has apotential that is symmetric under rotations in φ space, but its minimum does not occurat < φ >= 0. The value of the field at < φ >= 0 is known as the vacuum expectationvalue (VEV), denoted as u, and it has been calculated to be: u = 246 GeV. The form
4In mathematics, U(n) (or else, the unitary group of degree n) denotes a group of n×n unitarymatrices, with the group operation of matrix multiplication. SU(n) (the special unitary group of degreen), is a subgroup of U(n) and refers to the Lie group of n×n unitary matrices with determinant 1.
5Through out this thesis the terms BEH and Higgs fields will be used interchangeably.
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Figure 2.1: Higgs potential in the SM, also known as the “mexican hat”. Figure from: [13].
of the Higg’s field potential (Fig. 2.1) implies a degeneracy in ground states. Once aparticular ground state has been chosen, the SM gauge symmetry gets spontaneouslybroken.
2.1.5 Spontaneous Symmetry Breaking in the SM
Spontaneous symmetry breaking (SSB) is the process of symmetry breaking in a physicalsystem, where the underlying laws are invariant under a symmetry transformation, butthe system as a whole changes. The system starts from a symmetrical state and ends upin an asymmetrical state. The Lagrangian of the system still obeys certain symmetries,but the lowest-energy solutions do not exhibit that symmetry. After SSB, there areseveral “ground states” that could all potentially be occupied, i.e. the ground statesare degenerate, and the symmetry that the system satisfies manifests itself in relationsbetween the ground states.
The Higgs mechanism is specifically the spontaneous symmetry breaking of gaugesymmetries, meaning that it does not refer to a symmetry of the physical states; but asymmetry of the description of a physical state.
The Higgs field requires the choice of a particular ground state, which causes theSU(2) × U(1) symmetry to get spontaneously broken to the electromagnetic subgroupU(1), which by construction still remains a true symmetry of the vacuum. Accordingto the Goldstone theorem, the SSB mechanism results in massless excitations knownas Goldstone bosons [14]. Three massless Goldstone bosons are generated, which areabsorbed to give masses to the W and Z gauge bosons. The remaining component of thecomplex doublet becomes the Higgs boson – a new fundamental scalar particle.
The mechanism of electroweak symmetry breaking (EWSB) succeeds in providinga general framework to keep the structure of the gauge interactions untouched at highenergy and still generate the observed masses of the W and Z gauge bosons.
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Chapter 3
The Large Hadron Collider and theATLAS Detector
The present chapter focuses on the experimental equipment used for this study, includinga discussion on the study principles for elementary particles, how they are applied at theLarge Hadron Collider (LHC) [15] in Geneva and, finally, how ATLAS [16] (one of thegeneral purpose detectors at the LHC) is structured for the purpose of identifying andstudying the particles. A short overview of particle identification will also be given,providing the background to the discussion on hadronic jet misidentification as leptons,given in Ch. 6, which is of main interest to this thesis.
3.1 Elementary Particles and Particle accelerators
The need to understand nature has been the major driving force for human evolution.The study of elementary particles is no exception. Over time specialized techniques forsuch research have been implemented and used.
One of the most highly used experimental approaches for the study of elementaryand composite particles are particle accelerators ; machines that accelerate particles ina controlled environment at high speeds, and smash them together (“beam collider”accelerators) or on targets (“fixed target” accelerators). Collider accelerators pose specialinterest for high energy studies and will be discussed more extensively here. The physicsreach of a particle collider is dependent on the levels of achieved energy and luminosity,two concepts that are discussed below.
3.1.1 Beam Energy
Assuming two beams of equal mass particles, each accelerated to a high energy E, theenergy available for creation of new particles in the collision of the two beams is equalto the center-of -mass energy (COM),
√s, which is:√s = 2 · E (3.1)
The higher the COM energy of the collision, the more new exotic high mass particlesmay be created. The particle accelerator facility that presently has the highest COMenergy is the Large Hadron Collider (LHC) at CERN, which during the ongoing Run-IIdelivers proton-proton collisions at an energy of 13 TeV.
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3.1.2 Luminosity
Analysis studies are dependent on the amount of available data. For the case of particleaccelerators this quantity is called the luminosity.
Luminosity (L) is the proportionality factor between the rate of detected events (i.e.particle interactions that have been captured and recorded from a detector) per unit timeand the cross section σ1:
dN
dt= L · σ (3.2)
It has the dimensions of events per time per area (cm−2s−1 in SI units or b−1s−1 in non-SIunits) and is dependent on the particle beam parameters (beam width, particle flow rate,etc.).
Of related interest is also the so called integrated luminosity (Lint), which is theintegral of the luminosity with respect to time:
Lint =
∫L dt. (3.3)
At the LHC, during Run-I (2009-2013), the total integrated luminosity recorder atthe ATLAS collision point for
√s = 8 TeV proton collisions was 25 fb−1. Currently, the
LHC is in the middle of Run-II, operating at√s = 13 TeV proton-proton collision energy
and up until present the achieved total integrated luminosity is about 35 fb−1 at thisenergy. While the Run-II data taking is on-going at the time of writing, the data usedin this thesis corresponds to an integrated luminosity of 5.807 fb−1.
3.2 LHC
The Large Hadron Collider (LHC) is a superconducting hadron accelerator and colliderinstalled in a 27 km circumference underground tunnel (with 4 m cross section diameter),located at CERN2.
The purpose of the LHC is to study the elementary constituents of matter and theirinteractions by creating high energy collisions in a controlled environment and furtheron detecting and analyzing their products.
The collider tunnel contains two adjacent parallel beamlines (or beam pipes) thatintersect at four points, each containing a beam that travel in opposite directions aroundthe ring. The beams are kept in a circular path by a total of 1,232 dipole magnets, while392 additional quadrupole magnets keep the beams focused, maximizing the chances ofparticle interactions at the designated intersection points. The magnets are supercon-ducting and superfluid helium-4 is used to ensure proper operating temperatures (at1.9 K).
The beams are typically proton-proton or lead-lead. Currently, the achieved COMenergy for proton-proton beams is 13 TeV. In reality the beam is consists of bunchesof protons, with each bunch containing about 100 billion particles. Each bunch getssqueezed down (using magnetics lenses) to 16×16 µm section at an interaction point,
1The cross-section is an effective area expressing the intrinsic likelihood that a scattering event willtake place when an incident beam strikes a target object.
2European Organization for Nuclear Research, one of the world’s largest centres for scientific research,located at the borders between Switzerland and France
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Figure 3.1: Schematic overview of the CERN accelerator complex. Image credit CERN.
where collisions take place. In August of 2016, the number of proton bunches was in-creased to 2220 per beam, with each bunch being introduced in the ring at 25 ns intervals.Future plans aim to further increase this number, as not all 25 ns separated bunches arefilled.
The acceleration of the particles is done in stages that successively increase theirenergy. For protons, the process begins by stripping hydrogen atoms of their electronswith an electric field. After their extraction, the protons are inserted into the firstaccelerator of the chain, Linac 2, reaching a final energy of 50 MeV. The beam is theninjected into the Proton Synchrotron Booster (PSB), reaching 1.4 GeV, followed by theProton Synchrotron (PS), where an acceleration to 25 GeV is achieved. Protons are thensent to the Super Proton Synchrotron (SPS) where they are accelerated to 450 GeV.Finally, the particles are transferred to the two beam pipes of the LHC. In the mainring the protons reach their maximum energy of 6.5 TeV. A schematic overview of theaccelerator complex can be seen in Fig. 3.1.
The two beams are collided in four designated points along the LHC, each constitutinga separate experiment. At the point where the two beams cross, a large number ofcollisions take place that may lead to the creation of new particles. The produced particlesare often rather massive and decay shortly after their formation. This means that theydo not travel far enough in order to be detected. Their existence however can be inferredby detecting more stable particles produced in their decays. Detectors have been builtaround the four intersection points in order to detect these final products. The analysesthat are carried out on the gathered data are aiming to reverse-engineer the observed
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events in order to identify the type of particles that were initially created. The higherthe COM of the collision, the more probable it is to create new, more massive particlesthat have not been detected before.
The four largest experiments located around the LHC ring are ALICE [17], ATLAS[16], CMS [18], and LHCb [19]. The largest of these experiments are ATLAS and CMS.They constitute general-purpose detectors, built for investigating the largest range ofphysics possible. They have independent designs and their analyses are carried outseparately from one another. This way cross-confirmation of any new discoveries can bemade. ALICE and LHCb, have detectors specialized for focusing on specific phenomena,such as quark-gluon plasma and particle-antiparticle oscillation studies.
3.3 The ATLAS Detector
The abbreviation ATLAS stands for A Toroidal LHC ApparatuS and is a detector de-signed to address a wide range of physics studies. Its design is described in detail inRef. [16].
General purpose studies need detectors that take full advantage of the unprecedentedenergy available at the LHC and have the ability to reconstruct of a wide range of particles(leptons, jets, missing transverse energy, b quarks, etc). Particle identification, coverage,tracking performance and hermeticity are essential qualities for this purpose. To fulfillthese requirement, at the extremely high energies present at the LHC, a rather massivedetector construction is needed.
ATLAS meets these requirements with a cylindrical structure, measuring 44 m inlength and 25 m in diameter. It is composed of separate subsystems, each designed to besensitive to the signatures of different traversing particles, in order to achieve the mostwholesome picture of particle detection possible.
The gathered information for the particles that go through the detector are based ontheir interactions with each layer. The detector has been designed so that particles ofdifferent type, energy and traveling direction will produce different types of signatures,based on which it is possible to reconstruct them. A schematic overview of ATLAS canbe seen in Fig. 3.2. Each of its layers are discussed in Sec. 3.3.1.
3.3.1 Detector Complex
Before discussing the detectors that compose ATLAS, it is important to define a coor-dinate system. The origin of the coordinate system is defined at the beam interactionpoint. In cartesian coordinates, the x axis is defined to be pointing in the direction to-wards the center of the LHC, the y axis upwards and the z axis along the beam direction.An important plane of reference, is the transverse plane, defined by θ = 90deg, where θ isthe angle of a track relative to the beam axis. It is used in all particle physics analysesdue to momentum conservation in this plane.
A very useful parameter is pseudorapidity, η, which is defined as:
η = − ln
(tan
(θ
2
)). (3.4)
A track transverse to the beam axis (θ = 90◦) is denoted by η = 0, while a parallel track
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Figure 3.2: Computer generated cut-away view of the ATLAS detector showing its variouscomponents. Image credit: ATLAS collaboration.
(θ = 0◦) by η = ∞. It is preferred over the polar angle θ due to its Lorentz invarianceunder boosts, and it is used to express the area-coverage capabilities of the detectors.
For cases where the particles are traveling close to the speed of light (light particlessuch as electrons and muons at the LHC, for example), the pseudorapidity converges tothe definition of rapidity:
y =1
2ln
(E + pzE − pz
), (3.5)
where pz is the longitudinal momentum of the particle. In those cases, pseudorapidity ispreferred over rapidity since it can be simple measured based on the polar angle θ. η iscommonly used along the cylindrical coordinate r and φ. η and φ describe the directionof a particle after its emission from an interaction vertex based on the angular separationbetween particles:
∆R =√
(∆φ)2 + (∆η)2 (3.6)
The overall structure (Fig. 3.2) is composed of concentric cylinders around the inter-action point. The apparatus can be divided in:
• three Detector systems:
– the Inner Detector, composed of the Pixel Detector, the Semi-ConductorTracker (SCT) and the Transition Radiation Tracker (TRT),
– the Calorimeters (electromagnetic and hadronic),
– the Muon spectrometer, and
• the Magnet system, composed of solenoid and toroidal parts.
A short overview of the purpose and technical characteristics of each part will follow.
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(a) (b)
Figure 3.3: Overview of the ATLAS inner detector. (a) is showing a general cut view of thesubsystems, while (b) their radial placement. Image credit: ATLAS collaboration.
Inner Detector
The Inner Detector (ID) starts a few centimeters from the proton beam axis (about3 cm) extending to a final radius of 1.2 m, and has a length of 6.2 m along the beam pipe.All traversing charged particles are expected to interact with the detector providingmeasurements regarding their trajectories and properties.
The interactions of the particles with the detector material causes ionization tracesat discrete points that are used to reconstruct their paths. A solenoid magnet surroundsthe ID and produces a 2 T axial magnetic field, causing the tracks of the charged particlesto bend. The bending direction can be used to determine the particle’s charge, while theamount of curvature depends on the particle’s momentum. The coordinates of the track’sorigin can also be used to determine from which interaction the particles emanated andto identify particles from secondary decays.
The Inner detector is composed of the Pixel Detector, the Semi-Conductor Tracker(SCT) and the Transition Radiation Tracker (TRT) (Fig. 3.3).
The innermost part is the Pixel Detector (Fig. 3.4). Due to its proximity to theinteraction point of the beams, its design has been largely driven by the immense flowof particles that it is being subjected to. The pixel technology is well-suited for thatpurpose.
It is composed of four concentric layers, the Insertable B-Layer (IBL) and three barrellayers, centered around the beam axis. The mean radii of the parts are: 33.25 mm,50.5 mm, 88.5 mm and 122.5 mm respectively. Two end-caps with three discs each, arealso part of the assembly, forming a three-hit system up to pseudo-rapidities of |η| < 2.5.
The IBL, was inserted for Run-II. The necessity for the addition came from the higherluminosity levels during Run-II, which introduced the danger of significant radiationdamage in the inner layers of the detector. This could result in tracking efficiency losesand it was considered beneficial to introduce an additional measurement closer to theinteraction point to increase the tracking efficiency.
Each of the layers is made out of module units, composed of silicon pads as thedetecting material, readout chips and other electronic components. In the IBL, thereare 12 million silicon pads. It consists of 14 staves, each loaded with silicon sensorsbump-bonded to FE-I4 front-end chips [20, 21]. The FE-I4 carry pixel cells with typical
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Figure 3.4: Schematic view of the ATLAS 4-Layer Pixel Detector for Run-II. Image creditATLAS collaboration.
dimensions of 50 × 250 µm. In the other three layers of the pixel detector, the siliconpads are connected to 16 front-end (FE-I3) integrated circuits [22]. Due to the smallsize of the modules, the electronics are mounted directly on top of the silicon sensingelements. The Pixel Detector is composed by 1744 modules in total, each consistingof a 16.4 × 60.4 mm2 planar n-in-n silicon sensor tile, 250 µm thick, with 47232 pixels(size of 50 × 400 µm). They are mounted on carbon fiber local supports (staves), witha cooling system around them to ensure the operation of the system at temperaturesbelow 0 ◦C. The cooling system is used to limit radiation damage effects. One mainadvantage of the pixelated silicon tracker is its position resolution performance. Its smallpixel dimensions, give high point resolution for the impact parameter using a singlemeasurement plane. Furthermore, its high granularity results in low occupancy of thepixel system, optimizing the pattern recognition with a small number of measurementplanes, thus facilitating critical vertex identification.
The Semi-Conductor Tracker (SCT) is the middle component of the inner detector.The detector is consisted of 4088 modules of silicon-strip detectors in total, arranged infour concentric barrels and two endcaps of nine disks each. The barrels carry 2112 of thedetector units (Fig. 3.5), while the disks carry the remaining 1976.
The SCT is similar in concept and function to the Pixel Detector but with long, narrowstrips rather than small pixels. The strip format achieved measurements of particles overa larger area. The accuracy of the SCT is comparable to that of the Pixel Detector by theuse of stereo-angle along the strips and a total of eight precise measurements gatheredfor each track. These characteristics make the SCT the most critical part of the innerdetector for basic tracking in the plane perpendicular to the beam. It is composed offour double layers of silicon strips, it has 6.3 million readout channels and a total area of61 m2. Specifically, each silicon detector has a typical size of 6.36 × 6.40 cm2 with 780readout strips of 80 µm pitch.
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Figure 3.5: Schematic representation ofthe SCT module. Image credit CERN.
Figure 3.6: Schematic representation ofthe TRT module. Image credit ATLAS collab-oration.
The outermost part of the Inner Detector is the Transition Radiation Tracker (TRT).It is a combination of a straw tracker and a transition radiation detector. The detectingelements are drift tubes or straws (about 298,000 in total), each 4 mm in diameter andup to 144 cm long. Each straw is filled with gas that becomes ionized when a chargedparticle passes through (Fig. 3.6). The electrons are collected through a fine wire byapplying a -1.5 kV bias to the tubes and there produce a signal. By monitoring whichwires have a signal, it is possible to infer the path of charged particles. The achievedposition resolution is of the order of 200 µm. The precision is lower than in the other twoparts (Pixel and SCT), but its large volume imposed cost effective requirements for itsconstruction.
Aside from the path of the charged particles, it is desirable to estimate whether thetracks belong to light (electrons, positrons) or heavier particles (pions). The space be-tween the straws is filled with materials of varying refraction indices. The interaction ofthe particles with these materials causes relativistic charged particles to produce transi-tion radiation and leave much stronger signals in some straws. The effect is dependenton the mass of the particles and can be used as a first “tag” for their nature.
Calorimeters
The Calorimeters follow after the Inner Detector and the solenoidal magnet that sur-rounds it. They are of two types, the electromagnetic calorimeter and the hadroncalorimeter. As their names suggest they target different types of particles and theirconstruction differs accordingly.
The purpose of the calorimeters is to measure the energy of the entering particlesby absorption. The calorimeters are constructed out of a dense absorbing material,i.e. a material suitable to fully absorb incident particles, and an active material, whichproduces an output signal proportional to the deposited energy. While traveling throughthe material, the charged particles interact with it, losing energy and creating particleshowers. By altering periodically the absorbing and active materials in each calorimeterit is possible to get a sample of the shower shape and use it for determining the energyof the original particle. The intrinsic relative resolution of calorimeters improves withenergy, making them a perfect match for studies of high energy particles like the ones
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produced at the LHC.The electromagnetic (EM) calorimeter absorbs energy from particles that interact
electromagnetically, i.e. charged particles and photons. Photons and electrons are ex-pected to lose all their energy in this part, while charged hadrons and muons will passthrough depositing a limited amount of energy. Neutrinos are electrically neutral andare not expected to interact at all. The EM calorimeter has very high precision for theabsorbed energy measurements as well as the location of the energy deposition.
The main part of the ATLAS EM calorimeter is a lead–liquid argon (LAr) samplingdetector with accordion-shaped electrodes and lead absorber plates over its full coverage.The structure is divided into a Barrel part and two End-Caps, while a Forward Calorime-ter (FCAL) is also placed in the forward region of the ATLAS setup. Each End-Cap isdivided into two coaxial wheels: an outer wheel and an inner wheel covering, respectively,1.375 < |η| < 2.5 and 2.5 < |η| < 3.2 (Fig. 3.7). The structure is placed inside cryostatsfor cooling to ensure its proper function.
Figure 3.7: Schematic representation of the Atlas Calorimeters. Image credit ATLAS collab-oration.
In the range |η| < 1.8, the calorimeter is preceded by a presampler to recover theenergy loss that occurs in materials such as the cryostat, the superconducting coil, theinner detector, etc..
The signals produced from the hits in the calorimeter, are amplified on front-endboards with warm preamplifiers located just outside of the cryostat. The signals areshaped and stored in analog pipelines, waiting for a level-1 trigger signal (see Sec. 3.3.3)in order to digitize and send the data to off-detector electronics via optic fibers for furthertreatment.
The EM Calorimeter system is surrounded by the Hadron calorimeter (HCAL). Thiscalorimeter absorbs energy from hadrons, i.e. particles that interact via the strong in-teraction, that pass through the EM calorimeter. Due to the nature of their interaction,there are larger fluctuations in the produced scintillation or ionization signal, result-
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Figure 3.8: Picture of the EM LArcalorimeter. Image credit ATLAS collabora-tion.
Figure 3.9: Schematic view of an EMcalorimeter barrel module and detailed view ofthe accordion structure. Image credit ATLAScollaboration.
ing in worse resolution compared to the EM calorimeter. Furthermore, hadrons do notexperience radiation losses when traveling through the HCAL (unlike electrons and pho-tons in the EM calorimeter), making their expected shower size longer. The hadroniccalorimeter has to contain the showers, meaning that it has to be bigger in size than theEM calorimeter. Due to its larger size, many of its components have been chosen in acost-effective manor.
The hadronic calorimeter can be divided into three parts: the Tile Calorimeter, theEnd-Cap and a Forward Calorimeter.
The Tile calorimeter is the main part of the hadron calorimeter and is located outsidethe EM calorimeter in radius. It is 8 m in diameter and covers 12 meter along the beamaxis. The absorbing material is iron, while scintillating tiles are chosen as the activematerial. Both sides of the tiles are read by wavelength shifting fibers into two separatephotomultipliers. The Tile calorimeter is split in a Barrel and two Extended Barrel parts.
The Hadronic End-Cap (HEC) is a LAr sampling calorimeter and provides hadroniccoverage for 1.5 < |η| < 3.2. It uses parallel Cu plate absorbers, orthogonal to thebeam axis and consists of two consecutive wheels with absorber plate thickness of 25 mmand 50 mm, respectively. The 8 mm LAr gaps are divided into four 2 mm gaps coupledcapacitantly into one readout unit, limiting ion build-up3.
As mentioned, a separate set of electromagnetic and hadronic calorimeters is built inthe forward region of the ATLAS structure. The EM Forward Calorimeter (EM FCAL)covers the region 3.1 < |η| < 4.9. It consists of copper rods parallel to the beam axis,inside an outer tube with a 250 µm liquid argon gap in between. The matrix in which therods and tubes are inserted is also made of copper. In this case the reading of the signal isdone directly on the rods. The tiny gap thickness aims to prevent the ion build-up effect.The hadronic calorimeter in the far-forward section is contained within the forward EMcalorimeter’s cryostat and it is of similar design to the EM FCAL, but based on tungstenas absorber material.
The design energy resolutions for each LAr sub-detector are listed in Tab. 3.1.
3The passage of high energy charged particles through argon causes ionization. The liberated electronsdrift quickly in the electric field, while positive ions move slower. In the high rate environment of theLHC, the rate of ionization is large enough that positive ions accumulate and distort the electric field,causing degradation of the signal. This effect is known as build-up.
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Figure 3.10: Schematic view of a Tile Calorimeter module with the iron absorbers, the scin-tillating tiles, the optical fibers and the photomultipliers. Image credit ATLAS collaboration.
LAr sub-detector Resolution(σEE
)
EM Barrel 10%√E⊕ 0.7%
EM End-Cap 10%√E⊕ 0.7%
HEC 50%√E⊕ 3%
EM FCAL 100%√E⊕ 10%
Table 3.1: Design energy resolutions for each LAr Calorimeters in ATLAS. Values fromRef. [23].
Muon Spectrometer
The muon spectrometer surrounds the calorimeter and, as the name suggests, its purposeis to detect muons. The muons are expected to be the only particles to be reaching thispart of the detector having undergone only small energy losses. All other particles willhave been absorbed in one of the previous layers (except from neutrinos that will notinteract in any part of the detector).
The spectrometer measures the trajectories of the muons so as to determine theirdirection, electric charge and momentum. Its function can be considered as similar to thatof the inner detector, measuring muon momenta based on the curvature of their track.The magnetic field configuration is however different as three large superconducting air-core toroids are used for bending the muon tracks. Its spatial precision is lower than thatof the Inner Detector and it has a much larger volume. It has been designed to measurehigh energy muons at high precision, independently from the ID.
The muon spectrometer is composed of two types of trigger detectors, the ResistivePlate Chambers (RPC) in the barrel region and the Thin Gap Chambers (TGC) in theEnd-Cap region. At the same time, Monitored Drift Tube (MDT) chambers are usedfor precision tracking and momentum measurement for both barrel and End-Cap, exceptclose to the beampipe for the innermost layer of the End-Cap, where Cathode Strip
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Figure 3.11: Cut-away view of the ATLAS muon detector. Image credit ATLAS collaboration.
Chambers (CSC) are placed.The MDT detection elements are made of thousands (in total) of metal tubes equipped
with a central wire and filled with gas. When a muon passes through the tubes, it willinteract, leaving a trail of electrically charged ions and electrons which drift to the sideand center of the tube. By measuring the time it takes to drift from the starting pointto the collection point, it is possible to determine the position of the interacting muon.
The muon spectrometer is optimized to provide momentum measurements with arelative resolution better than 3% over a wide transverse momentum range and 10% attransverse momentum values of 1 TeV [24].
3.3.2 Magnets
ATLAS has two large superconducting magnet systems incorporated. They are used tobend the paths of charged particles in order to determine their momenta and sign ofcharge.
When a charged particle enters a magnetic field it experiences a Lorentz force thatcauses it to bend its path. The track appearing in the detector is curved with the directionof curvature being dependent on the particle’s sign of charge. The amount of curvatureis dependent on the momentum of the particle; the tracks of high-momentum particleswill only curve slightly from their original path, while low-momentum particles’ trackscurve significantly.
The magnet systems are of two types: solenoidal and toroidal.The solenoid magnet is located around the Inner Detector, producing a magnetic
field of 2 T. The strength of the magnetic field causes even very energetic particles tocurve enough so that their momentum can be determined. It contributes to very highprecision due to its nearly uniform direction and strength. The strength of the magnetalso imposes a threshold for particles of very low momentum (<400 MeV), which are notrelevant to the studies. Their tracks bend to the point of circular motion and do not
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Period: year Bunch spacing√s Peak luminosity Peak number of collisions per bunch
Run-I: 2012 50 ns 8 TeV 8× 1033 cm−2s−1 40 (at 8× 1033 cm−2s−1)Run-II: 2015-2018 25 ns 13 TeV 1.4× 1034 cm−2s−1 ? 48 (at 1.4× 1034 cm−2s−1)
Table 3.2: The LHC running conditions during Run-I and Run-II. ? denotes the record peakluminosity value observed in 2016.
travel to any further parts of the detector.The toroidal magnet is placed outside of the calorimeters and within the muon spec-
trometer. It is composed of eight very large air-core superconducting barrel loops andtwo end-cap air toroidal magnets. Its magnetic field varies in an octagonal pattern, withan average intensity of 0.5 T [25]. The structure extends to an area 26 m long and 20 min diameter.
3.3.3 Trigger System and Data Acquisition
Each bunch crossing that takes place in the center of the detector results in a numberof collisions4. The crossings occur 40.000 times per second, leading to a vast amountof data. It is impossible to record all of them, but even if it were, the amount of timerequired for their analysis would be counter productive as it would not be likely thatthey all would reveal new phenomena.
A “trigger” is therefore needed, a mechanism that will select the potentially interestingevents and reduce the original rate to just some hundred events per second. Those eventscan be read out and stored for subsequent analysis.
The trigger system needs to be extremely fast due to the small time window betweeneach proton collision; 40 million collisions per second equals to 25 ns between each eventin the detector. For efficiency, data are stored in pipelines that can retain and processinformation from many interactions at the same time. To avoid mixing up signals fromtwo different events, the detectors must have very good time resolution and the signalsfrom each of the numerous electronic channels must be synchronized, so that they canall be identified as being from the same event.
The ATLAS triggering system consists of two levels: a hardware Level-1 (L1) anda software-based high-level trigger (HLT). This two-stage system is an upgrade of aprevious three-stage trigger system used during Run-I. The Run-II running conditions(Tab. 3.2) at the LHC were expected to be challenging to the old trigger system due tohigher rates (5 times higher than Run-I), larger peak number of interactions per bunchcrossing and narrower bunch spacing (i.e. spacing between proton beam collisions).
The Run-II two-level trigger system reduces the original 40 MHz bunch-crossing rate(“event rate”) to 100 kHz at L1 (first stage) and to an average recording rate of 1 kHz atthe HLT (second stage).
At L1, fast custom-made electronics find regions of interest (RoI) using the calorimeterand muon data with coarse information within a latency of 2.5 µs, which includes the
4The mean number of interactions per crossing is calculated from the instantaneous per bunch lu-minosity as µ = Lbunch · σinel./fr where Lbunch is the per bunch instantaneous luminosity, σinel. is theinelastic cross section (80 mb for 13 TeV collisions), and fr is the LHC revolution frequency. Presently,µ ' 40.
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trigger decision time. It should be noted that about 1 µs of this time is occupied bycable-propagation delays. It consists of the L1 calorimeter trigger system (L1Calo), theL1 muon trigger system (L1Muon), the L1 topological trigger modules (L1Topo) and theCentral Trigger Processors (CTP). L1 searches for high transverse momentum leptons,photons, jets and large missing and total transverse energy. The ROI’s are regions in ηand φ coordinates, where interesting features have been identified. They are used by thesubsequent trigger as starting point for more refined trigger algorithms.
The High Level Trigger (HLT) is implemented in software that is executed on a farmof about 2300 rack-mounted computing nodes [26]. The algorithms have access to datafrom all ATLAS sub-detectors. The speed-optimized algorithm execution uses all thedetector information inside the ROIs defined from L1, which accounts for about 2% ofthe total event. Approved events by the L2 are sent to the Event Filter farm. The HLTprocessing time is typically 1 s to 2 s.
The decision for accepting an event is based on trigger menus. A trigger menu is a setof event characteristics (e.g. regarding Emiss
T ) that are driven by the physics priorities ofATLAS and depend on the achieved luminosity. Events that have passed the selectioncriteria are tagged on basis of the results of the HLT and sorted into data streams (Debugstreams, Physics streams, Express streams and Calibration streams). Physics streamscontain events that are relevant for data analysis.
Normally, an HLT-accepted event is classified into one or more data streams and theentire event data is written to disk in its raw form awaiting offline reconstruction. ForRun-II, a new data stream type, (“data scouting stream”), has been added in which onlycollections of the physics objects reconstructed by the trigger are written to disk. Someof the most frequent triggers are prescaled, meaning that a specified fraction of randomlychosen events are kept, thus effectively reducing the corresponding rate. The new datastream type by definition keep only a fraction of event data, enabling the use of high-ratetriggers in an unprescaled configuration.
3.3.4 Data Preparation
Events that have successfully passed the Triggering system, are further stored and an-alyzed. Even with use of the triggering system, the amount of raw data remains quitelarge, which makes it challenging to distribute it to a worldwide collaboration. To tacklethis problem, two stages of data preparation are imposed, the Event Summary Data(ESD) and the Analysis Object Data (AOD).
The ESD contains the detailed output of the detector reconstruction and is producedfrom raw data. It contains sufficient information to allow particle identification, track re-fitting, jet calibration etc. thus allowing for the rapid tuning of reconstruction algorithmsand calibrations. Its average size is about 2 MB per event.
The next stage is the Analysis Object Data (AOD), which is a summary of thereconstructed event, and contains sufficient information for common analyses. Severaltailor–made streams of AOD’s are foreseen for different types of analysis needs. It isproduced from the ESD and has an average size of 300 kB per event.
Further on, in a centralized data-reduction framework (Derivation Framework), thefiles are read and subsequently fixes, corrections, and preliminary selections, driven bythe needs of groups’ analyses, are applied on them. Finally, physics related selections andpotentially more detailed information are added to the files, depending on the analysis.
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The results are stored in output files, referred to as DAODs.
3.3.5 Particle Identification
Using the data provided from the detector subsystems (Sec. 3.3.1) it is possible to identifythe particles that were detected, from their distinctive signatures (Fig. 3.12, Tab. 3.3) andreconstruct the recorded events. The only particles that have sufficiently long lifetimes totravel through the detector are: photons, electrons, muons, some hadrons and neutrinos.
Photon candidates leave energy deposition at the EM calorimeter but no signature inthe inner detector as they electrically neutral.
Electron candidates are clusters of energy deposited in the electromagnetic calorime-ter, associated with tracks at the inner detector. The identification is based on criteriathat require the longitudinal and transverse shower profiles to match the ones expectedfrom electromagnetic showers, the track and cluster positions to match in η and φ, andsignals of transition radiation in the TRT. A likelihood-based method that allows theinclusion of discriminating variables is used along the selection-based method for betterresults.
Muon candidates are identified by matching a reconstructed inner detector track witha reconstructed muon spectrometer track.
Hadrons, like protons and neutrons, deposit their most of their energy in the Hadroniccalorimeter, and the signal will match signatures on the inner detector and energy clustersin the EM calorimeter. The total energy of hadrons is calculated based on the depositedenergy in the two calorimeters: ETot = EEMCal + EHCal.
Neutrinos go through the detector without being detected. High-momentum neutrinoshowever are identified from observed momentum imbalance in the transverse plane. Thereconstruction of the “missing” transverse momentum is calculated as the negative vectorsum of the momentum of all identified particles.
Jets are reconstructed by combining signatures from the calorimeters and the ID.Algorithms are used to combine the signatures in order to define the jets. As a reference,the two main classes of jet algorithms in use are cone algorithms and sequential clusteringalgorithms [27], with the standard being the Anti-kT algorithm. An illustration of howjet reconstruction algorithms define jets can be seen in Fig. 3.13.
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Figure 3.12: Schematic overview of how different particle types are expected tointeract in each section of the ATLAS detector. The continuous tracks indicate theinteraction of a particle with the detector. Dashed tracks on the other hand areinvisible to the detector. The spread of a track signifies the generation of a particleshower in the detector. Image credit ATLAS collaboration.
Particle Inner Detector EM Calorimeter Hadronic Calorimeter Muon Spectrometer
γ — — —
e — —
µ
n — —
p —
ν — — — —
Table 3.3: Correlation of detector signatures with the corresponding particle type.Each particle is identified from its interactions while traveling through the detector.Checkmarks refer to the interaction of a particle with a detector part, while dashedlines denote the lack of any interaction.
27
Figure 3.13: Illustration of jet reconstruction algorithm.
28
Chapter 4
The Higgs Boson at the LHC
In 2012 the CMS and ATLAS groups discovered the Higgs boson [4, 5]; validating thepredictions of the electroweak theory and completing the SM framework puzzle. TheHiggs particle arises from the Brout–Englert–Higgs mechanism and is theorized to bethe carrier of the Higgs field, which is responsible for the masses of the known particles.The coupling of the Higgs to the various massive particles is proportional to their masses.
The newly found fundamental particle was compatible with the gauge-boson cou-plings of the SM Higgs boson and had the expected even-parity and zero-spin (0+) char-acteristics [28, 29]. Measurements of its mass yielded a value of approximately 125 GeV,consistent with the mass of the SM Higgs boson provided by a global fit to electroweakmeasurements [6, 7]. The identification of the Higgs was done with use of the theorizedfinal state products after its decay: ZZ? , γγ, and WW ? (the decay mechanisms will bediscussed in Sec. 4.2).
The discovery paved the way for further, more detailed and specified studies of theHiggs. By determining the mass of the particle, it was possible to calculate the Higgs’production mechanisms cross sections and also scale all future Higgs analyses respectively.All Higgs studies are carried out through its decay products, due to its brief lifetime(about 1.56× 10−22 s)1. There are numerous possible decay channels and separate studiesare carried out for each of them.
4.1 Production in proton-proton collisions
The Higgs bosons can be formed in a number of ways, yet the probability of its productionin any collision is expected to be very small. A main part of the general Higgs bosonstudy are its production channels.
The probability of producing the Higgs is dependent on the cross sections of its variousproduction channels. The calculation of these cross sections is complicated due to thenon-fundamental character of the proton (it is composed of more elementary components,i.e. quarks and gluons). Specifically, they need to be done at parton level2 and thenextrapolated to the proton level with the use of parton distribution functions.
1In the SM, the total decay width of a Higgs boson with a mass of 125 GeV is predicted to be4.21× 10−3 GeV [30]. The mean lifetime is given by τ = ~
Γ2In the parton model, hadrons are composed of a number of point-like constituents, namely quarks
and gluons, termed partons
29
The cross section of each production channel depends on the mass of the Higgs boson.Before the Higgs discovery its mass was kept as a variable in the calculations. The crosssection values for the different production channels as a function of the Higgs mass can beseen in Fig. 4.1. After the discovery of the Higgs at a mass of 125 GeV the cross sectionsof the production channels were determined, with the most dominant ones being: gluonfusion (ggF), vector-boson fusion (VBF) and vector-Higgs fusion (VF).
Figure 4.1: The cross sections for the main Higgs production channels as a function of itsmass. The represented values correspond to the discovered boson at mH = 125 GeV. Figurefrom Ref. [31].
For the present work, the production mechanisms that are considered relevant aregluon fusion and vector-boson fusion (Fig. 4.2). In gluon fusion two gluons fuse to forma Higgs through a quark loop (typically a top quark), while in vector-boson fusion thereare two quarks initially present that each radiates a vector boson, on- or off-shell, whichannihilate to a Higgs boson.
The cross sections of the ggF and VBF production channels of the Higgs boson atthe LHC are presented in Tab. 4.1.
t H
g
g
(a) gluon-gluon fusion (ggF)
H
p
p′
p
W/Z
W/Z
p′
(b) vector-boson fusion (VBF)
Figure 4.2: Productions mechanisms of interest for the Higgs boson.
30
Process σ (pb)
pp(ggF) → H 19.52pp(VBF) → H 1.578
Table 4.1: The main production channels of the Higgs boson at the LHC, with the corre-sponding cross sections, for a Higgs mass of 125 GeV. The uncertainties are omitted.
(a) (b)
Figure 4.3: Branching fractions of the different Higgs decay modes (a) and total decay widthof the Higgs boson (b) as function of its mass. Figures from Ref. [31]
4.2 Decay
Due to the proportionality of the coupling strength of the Higgs to the respective massof the particle it interacts with, the most probable decay paths are the ones consistingof the heaviest possible particles. The main requirements for the decay products are tosatisfy the zero-spin and neutral-charge character of the Higgs and conserve the totalenergy during the decay. Before determining the mass of the Higgs, the probability ofeach decay channel was calculated as a function of the Higgs mass (Fig. 4.3).
The decay can occur either fermionically or bosonically and the probability of eachdecay channel depends, as mentioned, on the mass of the decay products, but also onthe type of coupling between them and the Higgs. In fact, the observed cross sections ofeach channel can be used to study how the Higgs couples with the SM particles.
At a mass of 125 GeV, the most probable channel, that would also satisfy the neutralcharge character of the Higgs, is the bb. Theoretically the corresponding branching ratiois expected to be 56.1% but this channel has not been experimentally measured yet. Nextwould be the ττ channel. The expected branching ratio of this channel however is muchlower, at 6%.
For the massive boson channel, the most likely possibility is for the Higgs to decayinto a pair of W bosons, which happens with a branching ratio of 23.1%. The W bosonscan subsequently decay either into a quark and an antiquark or into a charged lepton
31
and a neutrino. From the two channels, the quark channel has a higher branching ratio,but the leptonic one is easier to study, as discussed in Ch. 5.
The other massive-boson decay channel is to a Z-boson pair. The Z bosons willthereon decay to same flavor leptons which are easily identified in the detector, providinga clear signal for the Higgs. The relative branching ratio of this decay however is only2.9%.
Finally, the Higgs can decay into massless gauge bosons (i.e., gluons or photons)through intermediate loops of virtual heavy quarks (top or bottom) or massive gaugebosons. The most common one of these processes is the decay into a pair of gluonsthrough a loop of virtual heavy quarks and occurs with a branching ratio of approximately8.5%. The decay into a pair of photons is more rare, ∼ 0.5%, and is mediated by a loopof W bosons or heavy quarks.
The most prominent decay channels for the study of Higgs (in highest probabilityranking) are summarized in Tab.4.2.
Decay Channel Branching Ratio Rel. Uncertainty
H → bb 5.77 · 10−1 +3.2%+3.3%
H → WW ? 2.15 · 10−1 +4.3%+4.2%
H → τ+τ− 6.32 · 10−2 +5.7%+5.7%
H → ZZ? 2.64 · 10−2 +4.3%+4.1%
H → γγ 2.28 · 10−3 +5.0%+4.9%
Table 4.2: Most probable Higgs decay channels for a mass of 125 GeV. Values from Ref. [32].
32
Chapter 5
The H → WW ?→ `ν`ν analysis
As previously mentioned, after the discovery of the Higgs boson, the research interestfocused on studies regarding the particle’s properties. Direct observation of the Higgsin individual decay channels could provide validations of the SM predictions. The H →WW ? decay channel (second in cross section ranking) constitutes a very good candidatefor observation, with the final state `ν`ν being the best channel for Higgs studies. In thepresent chapter the motivation for these studies will be discussed and an overview of theRun-I analysis will be presented.
Run-II is scheduled to stretch until 2018. The corresponding analysis with 13 TeVdata is ongoing.
5.1 Motivation
The direct observation of the Higgs boson in individual decay channels could provideessential confirmations of the SM predictions. As mentioned in Sec. 4.2, the H → bbchannel is the most probable to occur, but it has not been experimentally observed yet.The H → WW ? channel however, which is second in cross section ranking, constitutes avery good candidate for observation.
In the decay the Higgs mass (mH = 125 GeV), prohibits the formation of two realW bosons (mW = 80 GeV > mH
2), meaning that one of the W bosons has to be virtual,
denoted as W ?. The W bosons are short-lived and their presence can be inferred fromthe observation of their decay products. They can decay both leptonically (to a leptonand a neutrino) or hadronically. The sum of all hadronic branching ratios of the W hasbeen experimentally measured to be Bh = (67.60 ± 0.27)%, while the average leptonicbranching ratio is: B`+ν` = (10.80± 0.09)%, where ` indicates each type of lepton (e, µand τ), not sum over them [33].
The W → `ν decay channel of the W , where ` is an electron or muon1, constitutes thebest channel for Higgs studies despite its lower branching ratio, due to its high purity.It is easier to identify leptonic decay products (a lepton and the missing transversemomentum that would signify the neutrino), than the hadronic decay products as itis challenging to distinguish them from background. Nonetheless, the leptonic decaystill has identification difficulties since the neutrino can never be directly measured,
1The decay to a τ -lepton decay is not considered as the particle decays hadronically, making in hardto reconstruct.
33
prohibiting the full reconstruction of the decay. An example is the inability to reconstructthe invariant mass for the decay. An alternative variable is defined for this purpose, calledtransverse mass, mT :
mT =√
(E``T + Emiss
T )2 − |p``T − EmissT |2
where E``T =
√|p``T |2 +m2
``. p``T is the vector sum of the two leptons’ momenta in thetransverse plane, while m`` is the invariant mass of the di-lepton system. Emiss
T andEmissT are the vector and scalar missing energy in the transverse plane (i.e. the amount
of energy missing to conserve total energy in the decay).The inability to fully reconstruct the decay through this channel, prohibits its use
for accurate mass measurements. It is however an important channel for probing thecouplings between the Higgs boson and the weak bosons, as well as the Higgs’ properties.Nevertheless, searches for this decay produced the first direct limits on the mass of theHiggs boson at a proton-proton collider.
5.2 Data and Simulated Samples
The analysis of H → WW ? → `ν`ν is carried out with the use of both experimental dataand simulated samples.
As the H → WW ? → `ν`ν signature is not unique, it is important to estimatethe number of expected events due to background processes. These processes are esti-mated using samples produced with computer simulations with so-called Monte Carlo(MC) event generators2. There is a number of different generators, some of which aregeneral-purpose like the HERWIG [34], PYTHIA [35] and SHERPA [36] generator fami-lies and provide fully exclusive modeling of high-energy collisions, while others are somespecialized, an example is MadGraph [37] which is specialized on Z+Jet(s).
5.3 Event Signature
The H → WW ? → `ν`ν decay channel is identified from the identification of twoopposite-charge (OS) leptons (originating from the two W bosons) and missing transversemomentum (from the neutrinos).
The anatomy of the Higgs events can be exploited to partly suppress backgroundprocesses. The Higgs final states are affected by its production mode. The ggF mecha-nism can in some cases generate extra jets from radiation during the production, whilethe VBF mechanism always produces two highly energetic forward jets in opposite di-rections [38]. Furthermore, the Higgs decay is constrained from spin conservation laws.Since the Higgs is a spin-0 particle, the produced W bosons (spin-1 particles) shouldhave opposite spins. The W bosons will only couple to left-handed neutrinos (momen-tum anti-parallel to spin) and right-handed anti-neutrinos (momentum parallel to spin).As the total spin must be conserved, the lepton (spin-1/2) and the neutrino (spin-1/2)spin orientations must be aligned. This restriction affects the direction of the leptonsin the transverse plane of the detector. An illustration of the products’ direction in the
2Event generators, like MC, are software libraries that randomly generate simulated events.
34
Figure 5.1: Illustration of the H →WW ? → `ν`ν decay channel in the reference frame of theHiggs and the W . The small arrows indicate the particles’ directions of motion, while the largedouble arrows indicate their spin projections. The spin-0 Higgs boson decays to W bosons withopposite spins, and the spin-1 W bosons decay into charged leptons with aligned spins. Thefinal state leptons travel with a small opening angle with respect to the laboratory referenceframe, due to chirality requirements in the W decay. Figure adapted from Ref. [39]
reference frames of Higgs and W can be seen in Fig. 5.1. In the laboratory frame thedirections of the final state leptons are expected to travel in the same direction, withonly a small opening angle between them.
5.4 Background Processes
A number of background processes can produce signatures in the detector that are similarto that of the signal process. The most relevant background processes for this study aresummarized in Tab. 5.1. In the cases where a background process produces the sameOS leptonic and missing transverse energy signature, but does not naturally contain twoleptons from W or Z bosons, or has any neutrinos, it is labeled as fake. The quality ofthe Higgs analysis is directly dependent on the accuracy of the background estimates, asthe complete isolation of the signal is not possible.
In the SM WW process, a WW pair is created from a Higgs unrelated process. Thesubsequent leptonic decay of the pair generates the same signature as the signal events.The main difference between the SM WW production and the Higgs WW production,is the leptons’ propagation direction. The SM WW final state leptons are not boundfrom the Higgs spin-0 conservation and are not expected to have a preferable propaga-tion direction. The Higgs WW leptons however are expected to propagate in the samedirection. This background process can be suppressed with use of topological cuts (seeSec. 5.5), which constrain the opening angle between the two leptons.
Top-quark associated processes can also enter the signal region. Specifically, theproduction of tt pairs constitutes a background as the top quarks almost always decayto a W and a b quark. If the W decays leptonically and the b quark is not identified,the detected signature would imitate the one from signal events. Top-quark backgroundprocesses are in general associated with b-quarks. b-quarks are characterized by a longlifetime that allows them to travel in the detector before decaying (roughly a fraction ofa millimeter), resulting in the detection of a second-vertex in the event. The detection ofsuch a vertex (a process called “b-tagging”), distinguishes the top background from realHiggs events.
35
Name Process Features
WW WW IrreducibleTop quarks
tt tt→ WbWb Unidentified b-quarks
t{ tW Unidentified b-quark
tb, tqb q or b misidentified as leptons;unidentified b-quarks
Misidentified leptonsWj W + Jet(s) j misidentified as `jj Multijet Production jj misidentified as ``;
misidentified neutrinosOther dibosons
VV
{ Wγ γ misidentified as eWγ?,WZ,ZZ → ```` Unidentified leptonsZZ → ``νν IrreducibleZγ γ misidentified as e;
unidentified leptonsDrell-Yan (DY)ee/µµ Z/γ? → eeµµ Misidentified neutrinosττ Z/γ? → ττ → `νν`νν Irreducible
Table 5.1: List of background processes for the H →WW ? analysis. Irreducible backgroundshave the same final state; other backgrounds are shown with the features that lead to this finalstate. The highlighted process (W+Jet(s)) is the main focus of the presented thesis. Tablefrom Ref. [39].
Di-bosons, other than WW can also enter the Higgs signal region. Some cases areWγ, WZ, ZZ, etc. As an example, the Wγ background enters the signal region whenthe W boson decays leptonically and the photon converts into a ee+ pair in the detectormaterial.
The Drell-Yan (DY) process is the decay of a photon or Z boson to an oppositely-charged pair of leptons. The photon or Z-boson are created from the annihilation of aquark and an antiquark. When the lepton pair is electrons or muons, the signature ofthe process is very similar to half of the Higgs signature. Some of the DY events arereconstructed with significant missing transverse momentum, matching the whole Higgssignal, however requirements on missing transverse energy in the event suppresses mostof the DY background.
An important background contribution can arise from the misidentification of objectsas leptons. In those case, a produced object (either a non-prompt lepton from the decayof a hadron containing a heavy quark, or a jet) is reconstructed as a lepton candidate.As the signature in the detector imitates the Higgs signal, but the process itself doesnot naturally contain a lepton, these processes belong to the category of “fakes”. Thepresent work focuses on studying the contribution of fakes from theW+Jet(s) backgroundprocess, when a jet is misidentified as a lepton. A detailed description of that analysis isgiven in Sec. 6.
36
The contribution of each background processes varies depending on the Higgs signaldefinition. Based on their signatures, the most sensitive signal region (i.e. a set ofrequirements that Higgs events are expected to fulfill) for the analysis is considered to bethe ggF Higgs production channel, with final decay to differently flavored leptons (eµ)and no jet generation.
5.5 Event Selection
The event selection process aims for maximal number of signal events and minimumbackground. This is achieved by applying a series of cuts on different variables to thedata. The cuts are of three types: pre-selection cuts, jet multiplicity cuts and topologicalcuts.
5.5.1 Pre-selection Cuts
The pre-selection cuts are the first to be applied and select events containing the objectsexpected from the H → WW ? → `ν`ν signal process. The events are required to containexactly two isolated leptons, with opposite charge.
Furthermore, additional requirements regarding momentum and invariant mass areimposed to minimize background contributions. The two identified leptons must havemomenta above a certain threshold; the transverse momentum of the leading lepton, p`1T ,should be above 22 GeV (p`1T ≥ 22 GeV), while of the subleading leptons, p`2T , shouldbe above 10 GeV (p`2T ≥ 10 GeV). The differentiation on the applied thresholds is donebecause one of the W bosons in the Higgs decay will be virtual, hence its decay productsare expected to have less momentum. The invariant mass of the two leptons is alsorequired to surpass a set threshold in order to suppress background from virtual photonsand low mass resonances: m`` ≥ 10 GeV for same-flavor leptons and m`` ≥ 12 GeV fordifferent-flavor leptons. Same-flavor lepton events that fulfill all the above requirementscould also be a result of a Z boson decay, Z → ``. To suppress this background theinvariant mass of the observed leptons is required to deviate significantly from the Zboson mass (mZ = 91 GeV): |m`` −mZ | ≥ 15 GeV.
Finally, a threshold on missing transverse energy, EmissT , is imposed regarding its di-
rection with respect to identified leptons or jets in the event. This cut is aiming to reducebackground contribution from DY and the di-boson processes, with the introduction ofthe Emiss
T,rel. parameter:
EmissT,rel. =
{EmissT · sin(∆φ), ∆φ < π
2
EmissT , otherwise
where ∆φ is the relative azimuthal angle between the identified object and the missingtransverse energy. As mentioned in Sec. 5.3, the neutrino (identified in the studies as thedetected Emiss
T ) is not expected to be traveling in the same direction as the leptons. EmissT,rel.
has to satisfy EmissT,rel. ≥ 20 GeV for different-flavor and Emiss
T,rel. ≥ 40 GeV for same-flavorlepton events.
37
5.5.2 Jet Multiplicity Cuts
Depending on the number of jets found in the event, different background processesbecome important in the signal region. Different branches are defined based on theobserved jet-multiplicity: Njet = 0, Njet = 1, and Njet ≥ 2.
The Njet = 0 branch, where no jets are detected, is the most prominent branch inthe ggF Higgs analysis, since it suppresses the top-background process. In that branchhowever, the DY process becomes significant, but its contamination to the Higgs signalevents can be reduced by focusing only on different-flavor leptons and requiring P ``
T ≥30 GeV.
5.5.3 Topological Cuts
The final set of cuts aims to further reduce background in the analysis with main focuson the the SM WW process. The most important topological cuts are applied on: ∆φ``(the opening angle between the two charged leptons in the transverse plane), ∆φ``−Emiss
T
(the opening angle between the di-lepton system and the missing transverse energy inthe event) and m`` (the invariant mass for the two leptons). For the zero-jet case thatconcerns this analysis, the cut values are: ∆φ`` < π/2, ∆φ``−Emiss
T> π/2 and m`` <
55 GeV.
5.6 Statistical procedure and results
The statistical treatment of data is as important as their experimental collection, as theorganization of the data is essential to ensure that appropriate conclusions are drawnfrom their analysis.
For the H → WW ? analyis the statistical treatment is carried out through a likelihoodratio test. Based on the hypotheses of having no signal and having a SM Higgs boson, alikelihood function is used to measure the probability to obtain the observed data.
The likelihood function is defined based on the signal strength (µ) parameter and aset of nuisance parameters θ3, L(µ, θ). µ parametrizes the Higgs boson cross section andis defined as
µ =σdataH
σSMH.
The SM Higgs cross section, σSMH , is calculated for a Higgs boson mass mH = 125 GeV.µ ranges from 0 to 1, with µ = 0 corresponding to no signal (where only background isobserved) and µ = 1 corresponding to the SM prediction for a Higgs boson with mH =125 GeV. The parameter is allowed to float to obtain the best fit to data. The likelihoodfunction is different depending on the lepton flavor channel of the H → WW ? → `ν`νanalysis.
During Run-I the data were collected with the ATLAS detector during proton-protoncollisions at center of mass energies
√s = 7 and 8 TeV. The combined Higgs signal
strength µ and all signal region categories from the Run-I Analysis [39], is:
µ = 1.09+0.23−0.21
3In statistics, a nuisance parameter is any parameter which is not of immediate interest but whichmust be accounted for in the analysis of those parameters which are of interest.
38
(a) (b)
Figure 5.2: (a) Best-fit signal strength µ as a function of mH . The observed values are shownas a solid line with points where µ is evaluated. The expected values for mH = 125.36 GeVare shown as a solid line without points. The dashed and shaded (solid) bands represent theone standard deviation uncertainties for the observed (expected) values. (b) Observed signalstrength µ as a function of mH as evaluated by the likelihood fit. The shaded areas representthe one, two, and three standard deviation contours with respect to the best-fit values mH andµ. Figures from Ref. [39]
showing an agreement with the SM Higgs boson hypothesis. The best-fit signal strengthµ as a function of mH are shown in Fig. 5.2.
39
Chapter 6
W+Jet(s) Fakes BackgroundEstimation
A challenging source of background are processes that enter the signal region as fakes. Inthe case of the W+Jet(s) background, the fake is originating from the misidentificationof a jet as a lepton. The fake rate of jets in ATLAS is quite small, but the large jetproduction cross sections make their contribution non-negligible.
In the present chapter the so-called fake factor estimation for jet misidentificationas leptons (electrons and muons) will be presented. The estimations have been carriedout with data from
√s = 13 TeV collisions as part of the on-going work with the Run-II
analysis. The same analysis strategy for H → WW ? → `ν`ν as the one presented inCh. 5 for Run-I is used.
6.1 The W+Jet(s) background process
The most relevant background processes to the Higgs analysis have been summarized inTab. 5.1. The present thesis focuses on the W+Jet(s) processes, where a W boson iscreated, through a Higgs-unrelated process, in association with a jet. If the W decaysleptonically and the jet is misidentified as a lepton from its detector signature the processenters the signal region, as it resembles the two-lepton plus missing transverse energyHiggs signature.
Before addressing the suppression of this particular background process from the sig-nal region, one needs to examine how big of a contribution is to be expected and whetherit poses a significant problem. In ATLAS, the jet suppression is at the level of 10−5; onlyjets in the tails of the detector response are misidentified as leptons. Despite the smalllepton fake rates however, a significant level of background from misidentification can bepresent due to the large production cross section of jets at the LHC.
The estimate of misidentification background is not expected to be accurately modeledby Monte Carlo simulations, as a thorough theoretical prediction would require accuratesimulations of the misidentified particles along with a precise model of the misidentifica-tion rate [40]. As mentioned, jet misidentification occurs at small rates making it difficultto model it theoretically and one has to make data-driven estimations.
40
6.2 W+Jet(s) Fakes Estimation Strategy
The fundamental idea of the fake factor method is to select a control sample of eventsenriched in the background being estimated (also referred to as control region, CR), andthen use an extrapolation factor to relate these events to the background in the signalregion (SR). The method is data-driven provided the control sample is selected in data,and the extrapolation factor is measured with data. The extrapolation is done in particleidentification space (given that the background process can enter the signal region dueto particle misidentification).
To collect background events more efficiently, the particle selection of the SR is re-placed in the CR with a particle selection for which the misidentification occurs moreoften. The CR is defined to be the same as the SR, apart from some parameters thatare required to be loosened compared to the full particle selection in the SR. Specifically,the CR consists of two-lepton events, where one of the leptons satisfies all signal samplecriteria (these lepton candidates are denoted as “identified” or “ID”), while the otherfails to meet these criteria but instead satisfies a less restrictive set of requirements (de-noted as “anti-identified” or “Anti-ID”). The selection requirements that distinguish theID and Anti-ID leptons are orthogonal to one another.
The extrapolation factor, denoted “fake factor” (FF), relates background misidentifiedwith this criteria, to background misidentified as passing the full particle selection of thesignal region. It is measured in a data set with no, or very few, Higgs boson events andthen applied to the Higgs boson candidate data. This is done under the assumption thatthe fake factor is independent of overall event kinematics.
The main concept of the FF method can be summarized in the following relation:
NW+Jetid+id = FF x NW+Jet
id+Anti−id. (6.1)
NW+Jetid+id refers to the W+Jet(s) events that enter the signal region. NW+Jet
id+Anti−id, arethe number of W+Jet(s) events where one of the lepton signatures satisfies all signallepton criteria and the other fails them, but satisfies a looser set of requirements instead.NW+Jetid+Anti−id is estimated in the CR. The linearity of the extrapolation is an assumption,
based on the definition of the CR; given that the CR is only slightly varied from the SRit can be assumed that a first order polynomial extrapolation (i.e. linear) is a reasonableapproximation.
In the H → WW ? → `ν`ν analysis, the final states of interest contain electrons andmuons. The W+Jet(s) background can arise from misidentification of the jet as eitheran electron or a muon. Since the criteria for identifying a particle as an electron or amuon are different, the FF for jet misidentification as an electron or a muon are expectedto be distinct and separate calculations have to be carried out.
For the Run-II analysis, the extrapolation factor has so far been estimated in di-jet samples. This thesis focuses on estimating the factor in Z+Jet(s) samples instead.The merits of this method lie in the similarity of the jet composition compared to theW+Jet(s) events and also the possibility to fully reconstruct the Z boson in order to tagthe jets. The method is limited however from the low statistics of the Run-II dataset.
41
electron muon
ID Anti-ID ID Anti-ID
pT > 15 GeV pT > 15 GeVη < 2.47 excluding 1.37 < η < 1.52 η < 2.45
|z0 sin(θ)| < 0.5 mm |z0 sin(θ)| < 0.5 mmPass LHTight if pT < 25 GeV
Pass LHLoosePass Quality Tight if pT < 25 GeV
Pass LHMedium if pT > 25 GeV Pass Quality Medium if pT > 25 GeV|d0|σ(d0)
< 5|d0|σ(d0)
< 3|d0|σ(d0)
< 6
Pass Gradient isolation Veto against identified electron Pass Gradient Isolation Veto against identified muon
Table 6.1: Requirements for fully ID and Anti-ID electrons (left) and muons (right).
6.3 W+Jet(s) Control Region
The CR, as already mentioned, is defined to be rich in W+Jet(s) events, i.e. about 85%to 90% of the events should be coming from this process [39], and have no overlappingwith the Higgs SR. This is required in order to ensure that no actual Higgs events will beconsidered as fakes and lost when the subtraction of the W+Jet(s) process takes place.Real lepton events must also be removed from the region as only fake signatures shouldbe studied.
The ID and Anti-ID definition for the CR particle selection is based on identificationand isolation criteria. The selection requirements for electrons and muons regardingthese parameters vary with respect to transverse momentum (pT ) and pseudorapidity(η), hence the calculations of the FF are binned with respect to these variables as wellas lepton flavor. The criteria for a lepton candidate to be considered as ID or Anti-IDare based on: d0 significance, z0 sin(θ), isolation gradient, muon quality and electronlikelihood [41]. A summary of the requirements is presented in Tab. 6.1.
The parameters d0 significance and z0 sin(θ) are related to how well a primary leptonis reconstructed in the detector. The reconstructed lepton tracks should be compatiblewith the primary vertex (i.e. place of initial p-p of collision). The two parametersquantify the relative deviation of the tracks from the primary vertex. z0 sin(θ) quantifiesthe deviation with respect to the longitudinal plane, while d0 to the transverse (Fig. 6.1).
Figure 6.1: Definitions of the d0, z0 sin(θ) track reconstruction parameters. PV denotes theprimary vertex of the proton-proton collision.
Isolation refers to the amount of tracks and calorimeter energy deposition in thevicinity of the lepton. Specifically, the selection is based on the so-called “gradientisolation” which incorporates an η dependency of the parameter.
Electrons are further characterized based on a multi-variate likelihood parameter.The likelihood is built from different shower property variables, track quality measuresand variables concerning relations between the track and the EM clusters. Depending on
42
Figure 6.2: Example of CR definition based on lepton isolation requirements. For theW+Jet(s) process, the real lepton originating from the W will pass the ID requirements. Thejet will in some cases pass all ID requirements (entering the signal region), while in some casesit will only pass the looser requirements.
the likelihood value, the electrons are characterized (in order of increasing lepton purity)as loose, medium and tight.
Similarly to electron identification, there are loose, medium, tight and high-pT selectioncriteria for muons. The distinction is based on the way muons are reconstructed withinformation from the different detector subsystems (mainly muon spectrometer and innerdetector).
The specific “cut” definition for the distinction between identified and anti-identifiedleptons is not fixed, but is selected so as to optimize the analysis. A tight definitioncan limit the statistics, while with a broad one the objects that enter the CR may notindicate similar characteristics of the SR objects. An illustration of the CR definitionbased on the isolation parameter can be seen in Fig. 6.2. The real lepton of the W+Jet(s)process will pass the ID requirements. The jet will in some cases pass all ID requirements(entering the signal region), while in some cases it will only pass the looser requirements.
6.4 Fake Factor estimation in Z+Jet(s) data samples
The extrapolation factor serves the purpose of transferring the obtained estimate of thenumber of W+Jet(s) events in the CR to the SR.
In the present work the determination of the fake factor is carried out with Z+Jet(s)events, in contrast to the di-jet sample approach that has been used so far in Run-II.The positive attributes of this sample are both the possibility to fully reconstruct the Ztrack (from its same-flavor final state leptons) and the similarities in jet composition be-tween Z+Jet(s) and W+Jet(s) events. The two jet compositions can be observed in therespective Feynman diagrams of the two processes (as pictured in Fig. 6.3). Monte Carlosimulations support the view that the two compositions are identical in a first-order ap-
43
potential fake `
q
g
W
Jet
`±
ν`
(a) W+Jet(s)
potential fake `
q Z
Jet
`±
`∓
(b) Z+Jet(s)
Figure 6.3: Feynman diagrams of the W+Jet(s) and Z+Jet(s) processes. The two processesshare a similar jet composition. Monte Carlo simulations (see text) motivate the assumptionthat the two composition can be considered identical in a first order approximation for fakefactors calculations regarding lepton misidentification from jets.
proximation. In the Run-I analysis [39] calculations with alpgen+pythia6, alpgen+herwigand powheg+pythia8 generators, resulted in correction factors and uncertainties veryclose to unity:
0.99± 0.20 for Anti-ID electrons,1.00± 0.22 for Anti-ID muons
The calculation of the FF in the Z+Jet(s) samples is carried out in a dedicated CR.The same flavor, oppositely charged leptons that compose the Z boson final states areused as “tags” for the search of additional leptons in the same event (specifically, muonsand electrons)1. The additional reconstructed leptons in the event may be originatingeither from the Z+Jet(s) process (jet misidentification) or from background processes.
The main background comes from the di-boson, V-γ and ττ process. The di-boson,V −γ processes produce real leptons and need to be subtracted from the Z+Jet(s)sample.The presence of real leptons is not desirable as one wants to solely study fake leptons.With MC simulations the real lepton contamination from the processes are estimatedand subtracted from data. The ττ process has a much smaller contribution in the regionof study. It does not introduce any concerns on the further on analysis as it also producesfake leptons. It is estimated that this process only contributes to a minor degree, andtherefore it will not be addressed independently; all fake leptons will be considered tohave originated from the Z+Jet(s) process.
After the real-lepton removal, the remaining additional leptons in the event are con-sidered as fakes originating from jets. The fake factor is then computed by separatingthe anti-identified and identified categories and computing their ratio in bins of pT andη.
Event and Object Selection
To carry out the analysis on fake leptons a series of cuts is applied to the data (Tab. 6.2).The first three cuts appearing in the table are of general nature: (i) the event needs tohave passed the triggering stage, (ii) the two main leptons of the event (`l, `sl) shouldpass a first filtering on isolation requirements, (iii) there should be no jets in the event,
1Only e and µ are considered for the Higgs decay study, since as already mentioned, the τ is unstabledue to its high mass.
44
as the focus is on no-jet ggf production of the Higgs. These cuts set a basis of generalrequirements for more specialized cuts to follow.
Cutflow
Event is triggeredLeptons (`l, `sl) fulfill isolation requirementsNJets = 0
P `lT ≥ 25/22 GeV for e/µ and P `sl
T ≥ 15 GeV`l and `sl are: ID with m`l`sl ≥ 12/10 GeV for SF/DF`l, `sl are: SF & OS with m`l`sl within Z-boson mass-window
Additional lepton (`add) present∆R`add−`l ≥ 0.1 and ∆R`add−`sl ≥ 0.1
EmissT ≤ 30 GeV ? and m
`add−EmissT
T ≤ 50 GeV ?
Table 6.2: Sequential cuts applied on events for the fake factor estimation. `add, `l and `slrefer to the additional, leading and subleading leptons respectively. ∆R`add−`l and ∆R`add−`sl
refer to the angular separation of the additional lepton from the leading or subleading leptonrespectively. ∆R has been defined in Eq. 3.6. After the last selection cut, ID and Anti-IDrequirements are applied on the additional fakable lepton to finally compute the fake factor.
The leading and subleading leptons are required to fulfill the specific momentumrequirements that correspond to their flavor as well as a set transverse mass threshold(discussed in Sec. 5). Furthermore, they need to pass ID requirements and a total massabove 12 GeV if they are same flavor or 10 GeV if they are of different flavor. In order tosatisfy the Z boson final state criteria, the leptons must have same flavor (SF), oppositecharge (OS) and a transverse mass within an acceptable range from the Z boson mass.
An additional lepton should be present in the event. This is the presumed fakelepton originating from the jet. Cuts on ∆R of the additional lepton direction and theleading/subleading leptons are used to ensure that the additional lepton is not result ofthe Bremsstrahlung effect2 or wrongly identifying a single lepton as two leptons.
The EmissT and m
`addEmissT
T cuts (denoted with ? in the table) were imposed after theempirical observation that events with additional leptons were observed above certainvalues of the respective variables. It was considered beneficial for the study to includethese cuts as means of increasing the signal to background ratio in the analysis.
A final cut on ID and Anti-ID requirements is applied to the additional leptons. Thefake factor is calculated based on the number of events that fulfill each set of requirementswith use of Eq. 6.1. The series of cuts is done separately for the different flavors of theadditional lepton (e or µ) resulting in different FF estimations for each flavor.
The pT and η distributions of the additional leptons in the events that pass ID orAnti-ID requirements are presented in Fig. 6.4 and 6.5 respectively. The data is shown inblack data points, the colored histograms show the expected contribution from processeswith real leptons. Their contributions are subtracted from data before the calculation ofthe FF.
2Bremsstrahlung is electromagnetic radiation produced by the deceleration of a charged particle whendeflected by another charged particle, typically an electron.
45
(a) Additional ID electron pT distribution (b) Additional Anti-ID electron pT distribution
(c) Additional ID muon pT distribution (d) Additional Anti-ID muon pT distribution
Figure 6.4: pT distribution for additional leptons in the event that pass ID ((a) electrons, (c)muons) or Anti-ID ((b) electrons, (d) muons) requirements. The estimation is carried out in Z+ Jet data samples. The lepton is identified as the object recoiling off a Z boson, where theZ boson is tagged by requiring two isolated opposite-sign, same-flavour leptons (electrons ormuons). The black data points represent data, while the dominant background processes (di-boson, V-γ and ττ) can be seen in the colored histograms. Their contributions are subtractedfrom data for the calculation of the FF. The subplots are showing the ratio between the dataand the MC backgrounds. The yellow band denotes the statistical uncertainty on the MCsimulations.
Results
The results of the FF calculation for both electrons and muons, with respect to theirmomentum and pseudorapidity can be seen in Fig. 6.6 and 6.7.
46
(a) Additional ID electron η distribution (b) Additional Anti-ID electron η distribution
(c) Additional ID muon η distribution (d) Additional Anti-ID muon η distribution
Figure 6.5: η distribution for additional leptons in the event that pass ID ((a) electrons, (c)muons) or Anti-ID ((b) electrons, (d) muons) requirements. The estimation is carried out in Z+ Jet data samples. The lepton is identified as the object recoiling off a Z boson, where theZ boson is tagged by requiring two isolated opposite-sign, same-flavour leptons (electrons ormuons). The black data points represent data, while the dominant background processes (di-boson, V-γ and ττ) can be seen in the colored histograms. Their contributions are subtractedfrom data for the calculation of the FF. The subplots are showing the ratio between the dataand the MC backgrounds. The yellow band denotes the statistical uncertainty on the MCsimulations.
Furthermore, a cutflow, showing the number of events satisfying each cut level canbe seen in the table provided in Appendix A.
The estimated FF are of the order of 4 % to 19 % (2 % to 24 %) for electrons (muons).The larger values for muons do not imply a higher misidentification rate for muons
47
(a) electron FF distribution as a function of η (b) muon FF distribution as a function of η
Figure 6.6: Fake Factor η distribution estimated in Z + Jet data samples, for electrons (a)and muons (b)
(a) electron FF distribution as a function of pT (b) muon FF distribution as a function of pT
Figure 6.7: Fake Factor pT distribution estimated in Z + Jet data samples for electrons (a)and muons (b). A different binning for muons is used due to poor statistics.
compared to electrons but are a result of having a more statistically limited sample formuons. Poor statistics lead also to the choice of different binning for muons.
6.4.1 Fake Factor estimation in W+Jet(s) MC and Z+Jet(s)MC samples
FF calculations were also carried out with W+Jet(s) MC samples, aiming to comparethe distributions of the FF from the two samples, W+Jet(s) and Z+Jet(s). For a morecomplete picture, the FFs were also calculated for Z+Jet(s) MC samples.
The cut definition for each sample is done based on the theoretically expected numberof events. For W+Jet(s), the analysis requires that both the leading and subleadingleptons have momenta higher than 15 GeV (P `l
T > 15 GeV and P `slT > 15 GeV). Both
the leading and subleading lepton can be the fake lepton. Depending on which leptonsignature is originating from the W (real lepton), ID and Anti-ID cut requirements areapplied on the other lepton (fake lepton) for the estimation of the FF.
The FF calculation from Z+Jet(s) MC samples is done in a similar fashion. In the MCZ+Jet(s) sample, the leading and subleading leptons are identified and the additional
48
(a) electron FF distribution over pT (b) muon FF distribution over pT
Figure 6.8: Fake Factor pT distribution estimated for electrons(a) and muons (b).The FakeFactors have been estimated in Z + Jet data (black), Z + Jet MC (red) and W + Jet MC(blue) samples. A different binning for muons is used due to poor statistics.
(a) electron FF distribution over η (b) muon FF distribution over η
Figure 6.9: Fake Factor η distribution estimated for electrons(a) and muons (b).The FakeFactors have been estimated in Z + Jet data (black), Z + Jet MC (red) and W + Jet MC(blue) samples.
lepton is assigned as the fake. ID and Anti-ID requirements are applied on the fakeleptons for the FF estimation.
Results
The FF have been calculated in Z+Jet(s) data, Z+Jet(s) MC and W+Jet(s) MC samplesfor jet misidentification as electrons and muons. In Fig. 6.8 and 6.9 the distributions of allFF estimations with regard to transverse momentum and pseudorapidity are presented.
The distributions behave similarly. The similarities between the FF calculations fromall three samples reinforces the argument that the FF calculations in Z+Jet(s) samplescan be used for the W+Jet(s) samples. It is important to stress however that the factorsare subject to large statistical uncertainties.
49
Chapter 7
Summary and Conclusions
This thesis concerns the estimation of fake lepton backgrounds in the H → WW ? → `ν`νanalysis in ATLAS. Background processes can produce signatures in the detector thatare similar to that of the Higgs decay, hindering the analysis. The complete isolation ofthe signal is not possible and background estimates need to be carried out. An importantbackground contribution can arise from the misidentification of an object. The presentwork focuses on studying the contribution of fakes from the W+Jet(s) process whichenters as background when a jet is misidentified as a lepton (electron or muon).
The study of jet misidentification is carried out with the data-driven Fake Factormethod, which selects a control sample of events enriched in the W+Jet(s) backgroundand then uses an extrapolation factor to relate these events to the background in theHiggs signal region. Relying on data rather than MC is motivated by the fact thatmisidentification is a rare process not expected to be accurately predicted by simula-tion. The author has been involved in the first estimation of the fake factor in Run-IIZ+Jet(s) data samples. The fake factors are measured in bins of transverse momentumand pseudorapidity of the misidentified object. The results are compared to calculationof the fake factor in Z+Jet(s) and W+Jet(s) MC samples.
Within statistical uncertainties, the fake factors agree in all three samples. Additionalstatistics over the course of Run-II are expected to reduce uncertainties, allowing for moreconclusive statements.
50
Acknowledgments
First of all I would like to express my deepest gratitude to my supervisors Jonas Strand-berg and Bengt Lund-Jensen for having given me the opportunity to do my master’sdegree project at KTH. It enabled me to become actively better in my field and openedthe way for new experiences.
Furthermore, I wish to warmly thank Edvin Sidebo for his unlimited patience andclose guidance during this project. For allowing me to become his shadow and sharingall bits of wisdom. Words do not begin to cover my appreciation!
Many thanks to Giulia Ripellino for her useful comments and, most importantly, herinspiration and to Alex Kastanas for his much appreciated help.
I wish to express once again my gratitude to my family; for their unlimited love andsupport throughout the years. All that I have achieved is thanks to you! Finally, I wantto thank Lefteris for his patience, love and understanding during the dark times of thethesis writing. Thank you!
51
List of Figures
2.1 Higgs potential in the SM, also known as the “mexican hat”. Figurefrom: [13]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.1 Schematic overview of the CERN accelerator complex. Image credit CERN. 143.2 Computer generated cut-away view of the ATLAS detector showing its
various components. Image credit: ATLAS collaboration. . . . . . . . . . 163.3 Overview of the ATLAS inner detector. (a) is showing a general cut view
of the subsystems, while (b) their radial placement. Image credit: ATLAScollaboration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.4 Schematic view of the ATLAS 4-Layer Pixel Detector for Run-II. Imagecredit ATLAS collaboration. . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.5 Schematic representation ofthe SCT module. Image credit CERN. . . . . . . . . . . . . . . . . . . . 19
3.6 Schematic representation ofthe TRT module. Image credit ATLAS collaboration. . . . . . . . . . . . 19
3.7 Schematic representation of the Atlas Calorimeters. Image credit ATLAScollaboration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.8 Picture of the EM LArcalorimeter. Image credit ATLAS collaboration. . . . . . . . . . . . . . . 21
3.9 Schematic view of an EM calorimeter barrel module and detailed view ofthe accordion structure. Image credit ATLAS collaboration. . . . . . . . 21
3.10 Schematic view of a Tile Calorimeter module with the iron absorbers, thescintillating tiles, the optical fibers and the photomultipliers. Image creditATLAS collaboration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.11 Cut-away view of the ATLAS muon detector. Image credit ATLAS col-laboration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.12 Schematic overview of how different particle types are expected to interactin each section of the ATLAS detector. The continuous tracks indicate theinteraction of a particle with the detector. Dashed tracks on the other handare invisible to the detector. The spread of a track signifies the generationof a particle shower in the detector. Image credit ATLAS collaboration. . 27
3.13 Illustration of jet reconstruction algorithm. . . . . . . . . . . . . . . . . . 28
4.1 The cross sections for the main Higgs production channels as a functionof its mass. The represented values correspond to the discovered boson atmH = 125 GeV. Figure from Ref. [31]. . . . . . . . . . . . . . . . . . . . 30
4.2 Productions mechanisms of interest for the Higgs boson. . . . . . . . . . 30
52
4.3 Branching fractions of the different Higgs decay modes (a) and total decaywidth of the Higgs boson (b) as function of its mass. Figures from Ref. [31] 31
5.1 Illustration of the H → WW ? → `ν`ν decay channel in the reference frameof the Higgs and the W . The small arrows indicate the particles’ directionsof motion, while the large double arrows indicate their spin projections.The spin-0 Higgs boson decays to W bosons with opposite spins, andthe spin-1 W bosons decay into charged leptons with aligned spins. Thefinal state leptons travel with a small opening angle with respect to thelaboratory reference frame, due to chirality requirements in the W decay.Figure adapted from Ref. [39] . . . . . . . . . . . . . . . . . . . . . . . . 35
5.2 (a) Best-fit signal strength µ as a function of mH . The observed values areshown as a solid line with points where µ is evaluated. The expected valuesfor mH = 125.36 GeV are shown as a solid line without points. The dashedand shaded (solid) bands represent the one standard deviation uncertain-ties for the observed (expected) values. (b) Observed signal strength µas a function of mH as evaluated by the likelihood fit. The shaded areasrepresent the one, two, and three standard deviation contours with respectto the best-fit values mH and µ. Figures from Ref. [39] . . . . . . . . . . 39
6.1 Definitions of the d0, z0 sin(θ) track reconstruction parameters. PV de-notes the primary vertex of the proton-proton collision. . . . . . . . . . . 42
6.2 Example of CR definition based on lepton isolation requirements. Forthe W+Jet(s) process, the real lepton originating from the W will passthe ID requirements. The jet will in some cases pass all ID requirements(entering the signal region), while in some cases it will only pass the looserrequirements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
6.3 Feynman diagrams of the W+Jet(s) and Z+Jet(s) processes. The twoprocesses share a similar jet composition. Monte Carlo simulations (seetext) motivate the assumption that the two composition can be consid-ered identical in a first order approximation for fake factors calculationsregarding lepton misidentification from jets. . . . . . . . . . . . . . . . . 44
6.4 pT distribution for additional leptons in the event that pass ID ((a) elec-trons, (c) muons) or Anti-ID ((b) electrons, (d) muons) requirements. Theestimation is carried out in Z + Jet data samples. The lepton is identifiedas the object recoiling off a Z boson, where the Z boson is tagged by requir-ing two isolated opposite-sign, same-flavour leptons (electrons or muons).The black data points represent data, while the dominant background pro-cesses (di-boson, V-γ and ττ) can be seen in the colored histograms. Theircontributions are subtracted from data for the calculation of the FF. Thesubplots are showing the ratio between the data and the MC backgrounds.The yellow band denotes the statistical uncertainty on the MC simulations. 46
53
6.5 η distribution for additional leptons in the event that pass ID ((a) elec-trons, (c) muons) or Anti-ID ((b) electrons, (d) muons) requirements. Theestimation is carried out in Z + Jet data samples. The lepton is identifiedas the object recoiling off a Z boson, where the Z boson is tagged by requir-ing two isolated opposite-sign, same-flavour leptons (electrons or muons).The black data points represent data, while the dominant background pro-cesses (di-boson, V-γ and ττ) can be seen in the colored histograms. Theircontributions are subtracted from data for the calculation of the FF. Thesubplots are showing the ratio between the data and the MC backgrounds.The yellow band denotes the statistical uncertainty on the MC simulations. 47
6.6 Fake Factor η distribution estimated in Z + Jet data samples, for electrons(a) and muons (b) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
6.7 Fake Factor pT distribution estimated in Z + Jet data samples for electrons(a) and muons (b). A different binning for muons is used due to poorstatistics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
6.8 Fake Factor pT distribution estimated for electrons(a) and muons (b).TheFake Factors have been estimated in Z + Jet data (black), Z + Jet MC(red) and W + Jet MC (blue) samples. A different binning for muons isused due to poor statistics. . . . . . . . . . . . . . . . . . . . . . . . . . . 49
6.9 Fake Factor η distribution estimated for electrons(a) and muons (b).TheFake Factors have been estimated in Z + Jet data (black), Z + Jet MC(red) and W + Jet MC (blue) samples. . . . . . . . . . . . . . . . . . . . 49
54
List of Tables
2.1 Table of the SM elementary particles. The presented values are taken fromParticle Data Group Listings. . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 Table of the SM fundamental forces’ general properties. . . . . . . . . . . 9
3.1 Design energy resolutions for each LAr Calorimeters in ATLAS. Valuesfrom Ref. [23]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.2 The LHC running conditions during Run-I and Run-II. ? denotes therecord peak luminosity value observed in 2016. . . . . . . . . . . . . . . . 24
3.3 Correlation of detector signatures with the corresponding particle type.Each particle is identified from its interactions while traveling through thedetector. Checkmarks refer to the interaction of a particle with a detectorpart, while dashed lines denote the lack of any interaction. . . . . . . . . 27
4.1 The main production channels of the Higgs boson at the LHC, with thecorresponding cross sections, for a Higgs mass of 125 GeV. The uncertain-ties are omitted. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4.2 Most probable Higgs decay channels for a mass of 125 GeV. Values fromRef. [32]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
5.1 List of background processes for the H → WW ? analysis. Irreduciblebackgrounds have the same final state; other backgrounds are shown withthe features that lead to this final state. The highlighted process (W+Jet(s))is the main focus of the presented thesis. Table from Ref. [39]. . . . . . . 36
6.1 Requirements for fully ID and Anti-ID electrons (left) and muons (right). 426.2 Sequential cuts applied on events for the fake factor estimation. `add, `l
and `sl refer to the additional, leading and subleading leptons respectively.∆R`add−`l and ∆R`add−`sl refer to the angular separation of the additionallepton from the leading or subleading lepton respectively. ∆R has beendefined in Eq. 3.6. After the last selection cut, ID and Anti-ID require-ments are applied on the additional fakable lepton to finally compute thefake factor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
7.1 Cutflow applied on Z+Jet(s) samples for the selection of additional leptons(e or µ) that fulfill ID and AntiID requirements. Based on the number ofobjects that pass these requirements, the FF for jet misidentification aselectrons and muons are calculated. . . . . . . . . . . . . . . . . . . . . . 56
55
Appendix A - Cutflows
√s
=13TeV
,L
=5.
81fb−
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WW
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ttS
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jets
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265
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525
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523
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5±
0.54
322.
73±
11.1
326
4.16±
25.5
52.
79±
0.87
07.
48±
0.73
1349.9
1±
28.4
810
87Z
vali
dat
ion
regi
on0.
26±
0.13
352.
79±
4.62
94.2
0±
1.55
4.86±
0.33
284.
74±
10.3
325
1.34±
25.3
50.
29±
0.21
05.
24±
0.57
993.
73±
27.8
177
6L
ead
Lep
ton
isID
0.26±
0.13
352.
79±
4.62
94.2
0±
1.55
4.86±
0.33
284.
74±
10.3
325
1.34±
25.3
50.
29±
0.21
05.
24±
0.57
993.
73±
27.8
177
6S
ub
lead
Lep
ton
isID
0.26±
0.13
352.
23±
4.62
94.0
0±
1.55
4.86±
0.33
284.
74±
10.3
324
8.28±
25.1
60.
29±
0.21
05.
18±
0.56
989.
85±
27.6
477
2M
ET≤
30G
eV0.
04±
0.04
109.
85±
3.47
12.9
3±
0.58
0.53±
0.11
165.
61±
8.02
143.
37±
18.2
60.
29±
0.21
01.
90±
0.34
434.
50±
20.2
534
2
mµadd−MET
T≤
50G
eV0.
04±
0.04
77.3
8±
3.26
10.9
3±
0.53
0.40±
0.09
152.
45±
7.78
138.
00±
18.0
80.
29±
0.21
01.
59±
0.31
381.
07±
19.9
630
3µadd
isA
nti
ID0
72.4
7±
3.22
10.0
3±
0.51
0.35±
0.09
121.
76±
7.13
104.
07±
15.5
80.
16±
0.16
01.
30±
0.29
310.
15±
17.4
423
5µadd
isID
057.2
6±
3.02
1.85±
0.22
0.02±
0.02
22.9
7±
3.32
18.4
3±
5.25
00
0.26±
0.13
100.
79±
6.91
83
AdditionalElectrons
Oth
erE
lect
ron
sP
rese
nt
3.88±
0.51
666.
89±
5.97
675.
23±
4.16
35.2
7±
0.88
1061.4
1±
21.5
614
25.3
7±
58.3
17.
85±
1.40
7.08±
4.10
1373.1
1±
9.14
5256.0
9±
63.4
136
32pL
ead`
T>
25/2
2G
eVfo
re/
m3.
88±
0.51
666.
89±
5.97
675.
23±
4.16
35.2
7±
0.88
1061.4
1±
21.5
614
25.3
7±
58.3
17.
85±
1.40
7.08±
4.10
1373.1
1±
9.14
5256.0
9±
63.4
136
32pS
ublead`
T>
15G
eV3.
88±
0.51
666.
89±
5.97
675.
23±
4.16
35.2
7±
0.88
1061.4
1±
21.5
614
25.3
7±
58.3
17.
85±
1.40
7.08±
4.10
1373.1
1±
9.14
5256.0
9±
63.4
136
32T
ight
Lep
ton
s3.
16±
0.46
577.
32±
5.29
552.
04±
3.76
29.1
2±
0.80
1031.8
1±
21.1
610
42.8
4±
49.3
84.
65±
1.08
7.08±
4.10
1035.4
6±
7.87
4283.4
9±
54.8
630
12O
SL
epto
ns
3.16±
0.46
474.
74±
4.89
539.
22±
3.72
28.5
3±
0.79
961.
45±
20.0
910
42.8
4±
49.3
84.
48±
1.06
4.82±
3.41
1002.1
7±
7.75
4061.4
0±
54.3
528
14M
``>
12/1
0G
eV3.
16±
0.46
473.
08±
4.88
536.
94±
3.71
28.4
8±
0.79
954.
24±
19.9
910
41.4
4±
49.3
84.
48±
1.06
4.82±
3.41
1000.1
5±
7.75
4046.7
8±
54.3
028
00Z
vali
dat
ion
regi
on1.
25±
0.29
357.
51±
4.30
187.
18±
2.19
10.1
0±
0.47
822.
25±
18.3
997
9.10±
48.6
60
064
0.36±
6.20
2997.7
5±
52.6
120
14L
ead
Lep
ton
isID
1.25±
0.29
357.
51±
4.30
187.
18±
2.19
10.1
0±
0.47
822.
25±
18.3
997
9.10±
48.6
60
064
0.36±
6.20
2997.7
5±
52.6
120
14S
ub
lead
Lep
ton
isID
1.25±
0.29
355.
11±
4.28
185.
90±
2.18
9.99±
0.47
822.
25±
18.3
996
4.67±
48.3
00
063
5.74±
6.17
2974.9
1±
52.2
719
99M
ET≤
30G
eV0.
30±
0.14
126.
50±
2.92
25.4
2±
0.81
1.52±
0.18
510.
87±
14.6
360
2.95±
39.7
20
042
7.18±
5.07
1694.7
4±
42.7
411
00
me a
dd−MET
T≤
50G
eV0.
23±
0.12
95.3
4±
2.66
23.3
1±
0.77
1.41±
0.18
485.
44±
14.2
858
1.80±
39.5
10
039
0.71±
4.91
1578.2
4±
42.3
910
15me a
dd
isA
nti
ID0.
04±
0.04
25.0
5±
1.60
19.8
3±
0.71
1.19±
0.16
370.
68±
12.3
047
9.20±
36.9
10
033
1.66±
4.51
1227.6
5±
39.2
174
1me a
dd
isID
0.14±
0.10
62.7
9±
1.87
1.62±
0.20
0.07±
0.04
47.3
7±
5.47
48.8
9±
10.6
40
033.4
1±
1.43
194.
29±
12.1
914
5
Table 7.1: Cutflow applied on Z+Jet(s) samples for the selection of additional leptons (e orµ) that fulfill ID and AntiID requirements. Based on the number of objects that pass theserequirements, the FF for jet misidentification as electrons and muons are calculated.
56
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