Phenomenological study on supersymmetry searches at the LHC, through stau pairs electroweak production with an initial state radiation jet

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UNIVERSIDAD DE LOS

A

NDES

B

ACHELOR

T

HESIS

Phenomenological Study on

SuperSymmetry Searches at the LHC,

through Stau Pairs Electroweak Production

with an Initial State Radiation Jet

Author:

Juan David Godoy _{Carlos Andrés Flórez P}Supervisor:H.D.

A thesis submitted in fulfilment of the requirements for the degree of Bachelor

in the

High Energy Physics Research Group Department of Physics

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Declaration of Authorship

I, Juan David Godoy, declare that this thesis titled, “Phenomenological Study on Su-perSymmetry Searches at the LHC, through Stau Pairs Electroweak Production with an Initial State Radiation Jet” and the work presented in it are my own. I confirm that:

• This work was done wholly or mainly while in candidature for a research degree at this University.

• Where any part of this thesis has previously been submitted for a degree or any other qualification at this University or any other institution, this has been clearly stated.

• Where I have consulted the published work of others, this is always clearly at-tributed.

• Where I have quoted from the work of others, the source is always given. With the exception of such quotations, this thesis is entirely my own work.

• I have acknowledged all main sources of help.

• Where the thesis is based on work done by myself jointly with others, I have made clear exactly what was done by others and what I have contributed myself.

Signed:

Date:

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“Simplicity is the highest goal, achievable when you have overcome all difficulties. After one has played a vast quantity of notes and more notes, it is simplicity that emerges as the crowning reward of art.”

Frédéric Chopin

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UNIVERSIDAD DE LOS ANDES

Abstract

Faculty of Science Department of Physics

Bachelor

Phenomenological Study on SuperSymmetry Searches at the LHC, through Stau Pairs Electroweak Production with an Initial State Radiation Jet

by Juan David Godoy

Searching for supersymmetry in compressed mass spectra scenarios has become a major challenge in experimental particle physics. Search channels that have been succesful at other ranges of masses lack of sensitivity for this situation. The small dif-ferences in mass between SUSY particles and standard model particles at compressed mass spectra prevent to have a significant discrimination between signal and back-ground events.

This project proposes a new search channel that might be helpful to boost the miss-ing transverse energy in the generation of SUSY events to extract signal from back-ground events in hypothetical compressed mass spectra scenarios. This channel is the production of stau pairs with an initial state radiation jet that boost the missing trans-verse energy from the undetected neutralinos. Three samples of the proposed signal were generated and compared with the main backgrounds for this type of events (W and jets production and Drell Yann process).

The analysis showed that the best discrimination between signal and background is achieved when the difference in the azimuthal angle between the initial state radiation jet and the tau with the highest transverse momentum is chosen in the selection criteria. The optimal result is obtained when only the events with a value less than 1.3 in this angle are taken into account for the statistical analysis. After applying the selection of events, there seems to be a a good potential for extraction of signal events from the unwanted backgrounds.

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Acknowledgements

This project would not have been possible without the continous help and guidance of my project advisor Carlos Andrés Flórez. His patience and teachings were priceless. His advices trascend the academical background and serve as a role model for future professional challenges.

Thanks to the doctoral researcher Manuel Alejandro Segura, who eased the progress of this project by helping with the improvement of the necessary scripts and codes for the proposed analysis. Together with the students Luis Alfredo Bravo and Andrés Fe-lipe García, Manuel also produced some of the background samples used for this thesis.

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List of Figures

2.1 Neutron and Proton internal structure. . . 8

2.2 Combined measurement of the Higgs Boson mass in pp collisions at_√ s=7 and 8 TeV with the ATLAS and CMS experiments [14]. . . 9

2.3 Feynmann Diagram of a Coulomb repulsion of identical particles. . . 9

2.4 Feynmann Diagram of an electron-positron scattering. . . 10

2.5 Composition of the universe [15]. . . 11

2.6 History of relic density. [16] . . . 12

2.7 Sector map of the LHC [18] . . . 14

2.8 Proton beam path through the LHC [18] . . . 14

2.9 Arrangement of calorimeters used for energy measurements [18] . . . . 15

2.10 Spherical coordinate system.. . . 16

2.11 Published limits for SUSY searches in color sector at the CMS through_t˜_t˜ production. [7]. . . 18

2.12 Published limits for SUSY searches in color sector at the CMS through ˜ g˜gproduction. [7] . . . 19

2.13 Published limits by CMS for SUSY searches using electroweak channels [9].. . . 20

2.14 Cross section for SUSY particles production using different channels [22]. . . . 21

2.15 Limits published by CMS for SUSY searches using electroweak channels. [8] . . . 21

2.16 Limits for SUSY particles masses consistent with cosmological observa-tions [10].. . . 22

2.17 Diagram of the production of a pair of staus with an ISR jet. . . 23

2.18 Feynmann Diagram of a Drell-Yan process. . . 24

2.19 Feynmann Diagram ofW +jetsproduction. . . 25

4.1 η(τ) after applying the initial cuts: N(e) = 0, N(µ) = 0, N(τ) = 1, N(jet) = 1andpT(τ)>10GeV . . . 32

4.2 η(jet) after applying the initial cuts: N(e) = 0, N(µ) = 0, N(τ) = 1, N(jet) = 1andpT(τ)>10GeV . . . 32

4.3 Φ(jet) after applying the initial cuts: N(e) = 0, N(µ) = 0, N(τ) = 1, N(jet) = 1andpT(τ)>10GeV . . . 33

4.4 Φ(τ) after applying the initial cuts: N(e) = 0, N(µ) = 0, N(τ) = 1, N(jet) = 1andpT(τ)>10GeV . . . 33

4.5 pT(jet) after applying the initial cuts: N(e) = 0,N(µ) = 0, N(τ) = 1, N(jet) = 1andpT(τ)>10GeV . . . 34

4.6 pT(τ) after applying the initial cuts: N(e) = 0, N(µ) = 0, N(τ) = 1, N(jet) = 1andpT(τ)>10GeV . . . 34

4.7 MET after applying the initial cuts: N(e) = 0, N(µ) = 0, N(τ) = 1, N(jet) = 1andpT(τ)>10GeV . . . 35

4.8 ∆φ(jet, M ET) after applying the initial cuts: N(e) = 0, N(µ) = 0, N(τ) = 1,N(jet) = 1andpT(τ)>10GeV . . . 35

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4.9 ∆φ(τ, jet)after applying the initial cuts:N(e) = 0,N(µ) = 0,N(τ) = 1,

N(jet) = 1andpT(τ)>10GeV . . . 36

4.10 MT(τ, M ET)after applying the initial cuts:N(e) = 0,N(µ) = 0,N(τ) = 1,N(jet) = 1andpT(τ)>10GeV . . . 36

4.11 Effective mass after applying the initial cuts: N(e) = 0, N(µ) = 0, N(τ) = 1,N(jet) = 1andpT(τ)>10GeV . . . 37

4.12 Significance of signal 1 when a cut in∆φ(τ, jet)is applied (∆φ(τ, jet)< ∆φ(τ, jet)max.). . . 38

4.15 Significance of signal 1 when a cut inM ET is applied (M ET > M ETmin). 39 4.16 Significance of signal 2 when a cut inM ET is applied (M ET > M ETmin). 40 4.17 Significance of signal 3 when a cut inM ET is applied (M ET > M ETmin). 40 4.18 Significance of signal 1 when a cut inMT(τ, M ET)is applied (MT(τ, M ET)> MT(τ, M ET)min). . . 41

4.19 Significance of signal 2 when a cut inMT(τ, M ET)is applied (MT(τ, M ET)> MT(τ, M ET)min). . . 41

4.20 Significance of signal 3 when a cut inMT(τ, M ET)is applied (MT(τ, M ET)> MT(τ, M ET)min). . . 42

4.21 MT(τ, M ET)after applying the optimal cut in∆φ(τ, jet) . . . 45

4.22 MET after applying the optimal cut in∆φ(τ, jet) . . . 45

4.23 ∆φ(jet, M ET)after applying the optimal cut in∆φ(τ, jet) . . . 46

A.1 Significance of signal 1 when a cut in∆φ(jet, M ET)is applied (∆φ(jet, M ET)> ∆φ(jet, M ET)max.) . . . 49

A.2 Significance of signal 2 when a cut in∆φ(jet, M ET)is applied (∆φ(jet, M ET)> ∆φ(jet, M ET)max). . . 50

A.3 Significance of signal 3 when a cut in∆φ(jet, M ET)is applied (∆φ(jet, M ET)> ∆φ(jet, M ET)max). . . 50

A.4 MT(τ, M ET)after applying the optimal cut in∆φ(jet, M ET) . . . 51

A.5 MET after applying the optimal cut in∆φ(jet, M ET) . . . 51

A.6 Effective mass after applying the optimal cut in∆φ(jet, M ET) . . . 52

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List of Tables

2.1 Magnitude of the 4 Fundamental interactions in nature. . . 6

2.2 Mediators of the fundamental interactions explained by the SM [3]. . . . 6

2.3 Leptons flavor, mass and electric charge. . . 7

2.4 Quarks flavor mass and electric charge. . . 7

2.5 Supersymmetryc Particles in the MSSM [17]. . . 13

3.1 Signal samples produced. . . 27

3.2 Background samples produced. . . 27

4.1 Table of expected rate of events of signal for the optimal cut in∆φ(τ, jet). 42 4.2 Table of expected rate of events of background for the optimal cut in ∆φ(τ, jet). . . 43

4.3 Table of expected rate of events of signal for the optimal cut inM ET. . . 43

4.4 Table of expected rate of events of background for the optimal cut inM ET. 43 4.5 Table of expected rate of events of signal for the optimal cut inMT. . . . 44

4.6 Table of expected rate of events of background for the optimal cut inMT. 44

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List of Abbreviations

SM StandardModel

LHC LargeHadronCollider

CMS CompactMuonSolenoid

ATLAS A ToroidalLHCApparatuS

DM DarkMatter

SUSY SUperSYmmetry

VBF VectorBosonFusion

ISR InitialStateRadiation

MET MissingTransverseEnergy

MC MonteCarlo

MSSM MinimalSuperSymmetricStandardModel

QCD QuantumChromoDynamics

WIMP WeaklyInteractiveMassiveParticle

ALICE A LargeIonColliderExperiment

PSB ProtonSynchrotronBooster

PS ProtonSynchrotron

SPS SuperProtonSynchrotron

MG MadGraph

CERN ConseilEuropéen pour laRechercheNucléaire

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Dedicated to my aunt Carmenza Tolosa for her excentrical

teachings.. . .

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Chapter 1

Introduction

This chapter summarizes the motivation and objectives proposed for the development of this thesis project.

1.1 Problem

The Standard Model (SM) summarizes the scientific knowledge regarding fundamental particles and their interactions. In this model, matter is formed by fermions and inter-actions are mediated by bosons. Fermions are half-integer spin particles, which obey the Pauli’s exclusion principle. These particles are characterized by the Fermi-Dirac statistics [1]. On the other hand, bosons are integer spin particles that do not obey the Pauli’s exclusion principle and whose behavior is described by the Bose-Einstein statis-tics [1].

In the SM fermions are considered fundamental particles (without internal struc-ture) and are classified in to two smaller groups: quarks and leptons. Quarks are par-ticles with an intrinsic fractional electric charge, with respect to the charge of the elec-tron, and a color charge (associated charge in strong interactions). Leptons are particles electrically charged but without color charge. Each of these two groups of particles is composed by six different particles, which are classified in three different generations according to their mass[2].

The SM includes three out of the four existing fundamental interactions: the strong Interaction, which keeps quarks together and it is mediated by a group of bosons known as gluons; the weak Interaction, which is responsible of radioactive processes and whose mediators are theZ0,W+ andW−bosons; and the electromagnetic inter-action, mediated by the photonγ[3].

In the SM, particles get their mass due to their interaction with the Higgs field, which is believed to permeate the whole space-time. The Higgs boson is the quantum of the Higgs field and it was discovered in 2012, at the Large Hadron Collider (LHC) by the CMS and ATLAS collaborations [4,5].

Although the SM has been successful explaining the behavior of known particles, there are still many unanswered questions left, for which SM is not sufficient. The SM does not have a candidate particle for dark matter (DM), neither incorporates the gravitational interaction, nor explains the asymmetry observed between matter and antimatter in the universe, neither accounts for the difference in many order of mag-nitudes within the fundamental interactions, among others. In order to answer these

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2 Chapter 1. Introduction

questions, some new models have been proposed. These models include the SM postu-lates but extend the parameters of it, to find mechanisms that could explain the physics phenomena yet to be understood. Supersymmetric models (SUSY) have been, for some decades, a special interest focus in the scientific community. These models propose the existence of new particles, known as “superpartners”, which incorporate new degrees of freedom to the model, providing possible answers to the open questions in the SM.

SUSY searches have been, together with the search for the Higgs boson, one of the most important topics in the physics program at the LHC[6]. Until now, SUSY have not been observed at the LHC, which have made the scientific community question the ex-istence of these hypothetical particles. However, although many maximum likelihood limits have been traced, excluding the existence of SUSY in various mass ranges, most of these limits correspond to the color sector [7,8,9]. A large area of the SUSY phase-space, specially in the electroweak sector, has not yet been probed at the LHC due to limited experimental sensitivity. One example of these areas are the compressed-mass-spectra scenarios, where the masses of the superpartners are predicted to be close to the known SM particles, which makes their experimental detection very difficult[10].

Several phenomenological studies have proposed diverse experimental techniques to identify SUSY particles from the SM ones, in compressed-mass-spectra scenarios. Techniques such as Mono-jet [7,8] and Vector Boson Fusion (VBF)[6] are being imple-mented at the LHC.

It is proposed for this project to develop a phenomenological study about the pos-sible production of stau-pairs, superpartners of the tau lepton (τ) in the SM, in associa-tion with an initial state radiaassocia-tion jet (ISR jet). Each stau (anti-stau)(˜τ)(τ˜∗) is expected to decay into aτ(τ¯) and a neutralino one (χ1₀). Theχ˜1₀is the DM candidate in SUSY models where R-parity is conserved. The concept of R-parity is related with the conservation of leptonic and barionic numbers in the decay of SUSY particles (PR = (−1)3B+L+2s). Theχ˜1₀ is predicted to only have weak and gravitational interactions. Nevertheless, at the quantum level, the gravitational interaction with other particles is negligible with respect to the weak interactions. As the neutralino only interacts weakly, it cannot be observed directly by the LHC. However, it can be observed indirectly as missing trans-verse energy (MET).

When the stau pair decays, the two stau may have exactly opposite direction, so that the resulting taus and neutralinos might also have opposite directions. In this sce-nario, it would be impossible to detect the neutralinos, because the vector sum of their momentum would be zero, giving no MET. On the other hand, if the event is required to have an ISR jet, this jet might give a boost to the system, changing the direction of the taus and the neutralinos. Therefore, the total momentum of the neutralinos will not cancel, which gives a unique opportunity to detect these elusive particles indirectly.

1.2 Objectives

1.2.1 General Objective

To carry out the first steps of a phenomenological study to determine THE experimental sensitivity of SUSY searches at the LHC, through stau-pair production channels, with

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Chapter 1. Introduction 3

an associated Initial state radiation jet.

1.2.2 Specific Objectives

• Produce signal and background events through Monte Carlo (MC) simulations.

• To write a C++ code, in order to analyze the data obtained from the computational simulations.

• Perform the study of the kinematic and topological variables that could help to distinguish the hypothetical signals from the SM background.

• Find the optimal points for the variables that give the best separation between the signal and the background, using a figure of merit (significance).

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Chapter 2

Theoretical Framework

This chapter summarizes the physical and technical knowledge necessary for the de-velopment of this project. It includes a review of the standard model (SM) and the minimal supersymmetric standard model (MSSM). Some relationships between cos-mological observations and particle physics are also introduced. Regarding the pro-posed study, this chapter presents the expected background for the signal under study and reviews the particle processes involved. Finally, it gives a brief description about the software necessary to simulate the events needed for the analysis.

2.1 Key Concepts

2.1.1 Standard Model

The standard model is the ensemble which gathers known particles that conform mat-ter and its fundamental inmat-teractions. It includes the theory of electroweak inmat-teractions and Quantum Chromodynamics (QCD) interactions. Charge and energy are conserved in the SM [3]. It is the result of more than five hundred years of advancements in physics [2].

The standard model is a gauge theory, which means the Lagrangian remains invari-ant under certain group of transformations. These transformations define a gauge field, which is associated with fundamental interactions [3]. It has well-defined calculation rules and agrees well with the experimental measurements. In fact, the SM has been build upon both, theoretical predictions and experimental measurements. However, there are still phenomena that can not be explained by the SM [2].

Fundamental Interactions

The SM explains three out of four fundamental interactions, and it does not include gravity. These forces are the electromagnetic, the weak and the strong interactions. Particles with no neutral electric charge have electromagnetic interactions. The strong force is responsible of holding nuclei together and the weak interaction is responsible of some radioactive decays, such as beta decay [11].

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6 Chapter 2. Theoretical Framework

TABLE2.1: Magnitude of the 4 Fundamental interactions in nature.

Force Strength Theory Mediator

Strong 10 Chromodinamics Gluon

Electromagnetic 10−2 Electrodynamics Photon Weak 10−13 Flavordynamics W andZ

Gravity 10−42 Geometrodynamics Graviton

These interactions differ substantially in magnitude. Table2.1shows the strength, in orders of magnitude, of the known fundamental interactions [11]. As shown in ta-ble2.1, the gravitational force is the weakest of all the fundamental interactions. Since gravity is more than 25 orders of magnitude lower than other interactions, it has no visible effect at low range observations.

Each interaction has a gauge field associated with it. When this field is quan-tized, the quantum eigenstate obtained corresponds to a particle in the standard model. Specifically, a particle with integer spin, called boson. In the SM, bosons are the medi-ators of the fundamental interactions [3]. The photon, with spin one, is the quantum of the 4-vector electromagnetic field. The called vector bosonsZ0, W+ andW− mediate the weak interaction. Finally, there are eight types of bosons mediating the strong in-teraction, which are called gluons [2].

TABLE 2.2: Mediators of the fundamental interactions explained by the SM [3].

Name Notation Charge Mass

Vector Boson Z0 0 91.187 GeV Vector Boson W+ +1 80.33 GeV Vector Boson W− -1 80.33 GeV

Photon γ 0 0

Gluon g_ab 0 0

Whenever there is an interaction, there is a constant that determine the magnitude of the interaction, referred to as coupling constant. As an example, the charge of the particles involved in an electromagnetic interaction is the coupling constant in such interaction [2]. Some bosons have coupling constants associated so that they may in-teract with fermions and with other bosons. For example, W bosons have charge, so they interact through electromagnetic fields with themselves and with fermions. The coupling constant for the strong force is known as the color charge, which has associ-ated different types: red, free and blue. The word color in this case is not used literally, it describes an extra quantum number that experimental results have shown is needed in strong interactions [2].. Some characteristics of these particles are described in table 2.2.

In table 2.2, the sub-indexes “a” and “b” for the gluon indicate the color charge they carry. Gluons couple with quarks and other gluons according to the charge color they carry and the charge color of quarks. Each type of gluon annihilates a quark and changes it for other. The blue-antired gluon for example, annihilates the red quark and creates a blue quark. It is logic to think that there should be nine gluons as there are nine possible combinations for “a” and “b”. However, there are only eight independent

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Chapter 2. Theoretical Framework 7

states for Gluons as there are no coupled states for gluons, which are neutral. They are called the color octet [2,3].

Particles

According to the Standard Model, all matter is made out of two types of particles: leptons and quarks. Each of them has a corresponding antiparticle. Particles and an-tiparticles have equal masses, but they have exactly opposite electric and color charges. Leptons and Quarks have integer spin, so they follow Pauli’s exclusion principle [2]. These particles interact with and through the mediators described before. Following, some properties of fermions are described [12]:

TABLE2.3: Leptons flavor, mass and electric charge.

Name Notation Charge Mass

Electron neutrino νe 0 <7x10−9 GeV

Electron e− -1 .000511 GeV

Muon neutrino νµ 0 <0.0003 GeV

Muon γ -1 0.106 GeV

Tau neutrino ντ 0 <0.03

Tau τ -1 1.7771 GeV

There are six types of leptons (called flavors). As table2.3shows, their masses have different order of magnitude. Leptons do not have color charge so they can not inter-act through the strong force. The strong force is necessary to make nuclei. This is the reason that nuclei do not have electrons in their composition [3]. Particles are classified also in three generations according to their mass. Electron and electron neutrino are the first generation, muon and its neutrino the second one and finally tau and tau neutrino are called the third generation of leptons [2].

As it is seen also in table 2.3, neutrinos do not have electric charge. Hence, they are not affected neither by the electromagnetif force nor by the strong force (as they are leptons) [2]. Detecting neutrinos is a hard task because they only interact weakly due to weak force and gravity. Neutrinos were indirectly discovered because, as it will be explained, detectors can not interact with the detectors used today.

TABLE2.4: Quarks flavor mass and electric charge.

Name Notation Charge Mass

Up u +2₃ 0.005 GeV

Down d -1₃ 0.01 GeV

Strange s +2₃ 1.5 GeV

Charm c -1₃ 0.2 GeV

Top t +2₃ 180 GeV

Bottom b -1₃ 4.7 GeV

There are also six flavors of quarks (table2.4) [12]. They are classified in three gen-erations too. Up and Down quarks correspond to the first generation, the charm and

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strange quarks conform the second generation and the top and bottom the third gen-eration [3]. Quarks interact strongly due to the color charge. Gluons hold together quarks and create bounded states of three quarks such as neutrons and protons. These bounded states are stable and are color neutral [2].

As a matter of example, protons are made of two up quarks and a down quark. Neutrons, on the other hand, are made of two down quarks and one up quark. Each of the quarks must be of different color (see figure2.1). It is not known which of them is blue, which red or which green. In fact, their colors are changing constantly due to the intervention of gluons, but nevertheless they still remain neutral. As down quarks are more massive than up quarks, the neutron is more massive and tends to decay easily, becoming unstable [2].

FIGURE2.1: Neutron and Proton internal structure.

Higgs Mechanism

Gauge theories usually lead to symmetries in Lagrangians which are hard to interpret physically. In the SM, particles acquire mass through a spontaneous symmetry break-ing mechanism in the lagrangian, which gives rise to a new term that can be associated to mass. This process is known as the Higgs Mechanism [13]. This mechanism is the explanation of how particles acquire mass. Unfortunately, it doesn’t permit to calculate the mass of particles, but it is still shown that the magnitude of these masses is propor-tional to the intensity of the interaction with the Higgs field [2]. Theoretically, the Higgs boson is the quantum of the Higgs field. This boson has spin zero and a neutral electric charge [3].

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FIGURE 2.2: Combined measurement of the Higgs Boson mass in pp collisions at√s=7 and 8 TeV with the ATLAS and CMS experiments [14].

In July 2012, the CMS and ATLAS collaborations announced the discovery of the Higgs boson, which confirmed the existence of its field in the Universe [4,5]. Figure 2.2 shows the measurements of the mass of the discovered particle by the different channels used by CMS and ATLAS in the LHC. The reported mean value of the mass is 125.1 GeV [14].

Feynmann Diagrams

Feynmann diagrams are an important tool used by theorists to understand particle interactions. These diagrams involve basic concepts of quantum mechanics and are intuitive. In Feynmann diagrams, particles are represented by lines and every interac-tion is represented by a vertex. The lines touching each vertex account for the particles involved in the interaction [2].

FIGURE 2.3: Feynmann Diagram of a Coulomb repulsion of identical particles.

As an example, in figure2.3, electrons are represented by arrows and the photon is represented by a curved line. The diagram has two vertices. One of them corresponds to an electron emitting a photon and the other one to an electron receiving a photon.

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So, in this diagram, two electrons are sharing a photon which is, indeed, a Coulomb interaction [2,3].

FIGURE2.4: Feynmann Diagram of an electron-positron scattering.

A practical way to understand Feynmann diagrams is obtained by tracing an hori-zontal line which represents the flux of time, aswell as a vertical line which corresponds to space. Following the time line in figure2.4, there are, initially, a positron and an elec-tron (elecelec-trons are represented by arrows that follow the direction of the time line and positrons by lines that point in the opposite direction). As time flows, these particles interact (this interaction is represented by the only vertex in the diagram) and scatter anhilating each other, creating a photon.

When solving problems, initial and final states are usually known. Feynmann dia-grams are used to calculate the probability for a process to occur, given its initial and final states. To calculate the probability of a process, all posible feynmann diagrams consistent with this process should be taken into account, summing the probabilities of all possible interactons. However, some Feynmann diagrams are too complicated and lead to hard calculations. This is not a problem when these contributions are small and can be ignored [2].

Limitations

The SM has not yet been contradicted by any experimental observations. Thus, this model is widely accepted by the scientific community. However, there are some ques-tions that remain unanswered by the SM. To begin with, the standard model does not predict the masses of quarks and leptons. These are constants determined experimen-tally. In fact, the SM has over 20 arbitrary constants determined experimentally to agree with the theory [2]. Another limitation is the inability of the SM to explain grav-ity. There have been some efforts to unify gravity with the SM through the possible existence of the graviton, which is a hypothetical boson that would mediate the grav-itational interaction. However, there is no evidence yet for such particle [3]. The SM does not give any explanation for assymetry in the quantity of matter and anti-matter in the universe. It also fails to explain the difference in magnitude of the fundamental interactions (hierarchy problem) [3]. Finally, one last limitation of the SM is that it does not provide a candidate particle for Dark Matter (DM), which is believed to exist due to

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all of the indirect cosmological evidence, though it has not yet been found. In fact, the SM only explains 4.6% of the composition of the universe (see figure2.5) [15]. There is still much to investigate and understand [16].

FIGURE2.5: Composition of the universe [15].

2.1.2 Dark Matter

The observations of our Galaxy, the Milky Way, shows that the velocity of rotation of the galaxy tends to be constant, no matter the radius. According to these, and follow-ing the keplerian relationship, one find that this can only be explained if there is much more mass than the one seen in gases and stars in the observable universe. Moreover, the observation of clusters of galaxies in the universe have shown that the velocities measured can not be explained only by the existance of the baryonic mass. Therefore, it has been theoretically proposed that there should be a form of matter which is not visible. This is known as the dark matter (DM) [16].

There is strong evidence that dark matter is neutral and interacts very weakly with baryons. It has been seen during the merge of galaxy clusters that the two halos of dark matter merge easily with each other, while the baryonic mass shocks. Besides, DM has almost none or none interaction with photons. Otherwise, it would change the spectra of quasars as they would get dimmed by this interaction. These properties make im-possible for any of the particles in the Standard Model to be the formers of Dark Matter. Although neutrinos are neutral, they are discarted because the mean spacing of neutri-nos is not congruent with the observations made for the density of DM consistent with the cosmological observations [16].

Relic Density

Several extensions of the SM increase the quantity of fundamental particles. Some of these proposed particles only interact weakly, they are called Weakly Interactive Mas-sive Particles (WIMPs). As their properties are consistent with cosmological observa-tions, WIMPs are postulated as DM candidates in many of the SM extensions such as

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SUSY or models considering extra dimensions [16,17].

Assuming that WIMPs production is thermal (temperature dependent); moments after the big bang, WIMPs must have been in equilibrium as they were able to anhilate and create themselves continuously. However, there must have been a time where the temperature was so small that they were not able to keep shocking. The remaining WIMPs are a relic population that still exists today [16]. As Figure2.6shows, the relic density depends on the cross section of WIMPs formation as it affects the probability for WIMPs continuous creation and anihilation. Since the cross section depends on the mass of the particle, if the WIMP is detected and its mass is measured, cosmology and particle physics would converge in this single number, as long as the data are consis-tent.

FIGURE2.6: History of relic density. [16]

2.1.3 Supersymmetry

Supersymmetry is a new proposed theory to solve some of the limitations of the Stan-dard Model. It enhances the amount of elementary particles. It states that fermions can act as mediators of the fundamental interactions and that bosons can form matter [17]. One of the most studied models of supersymmetry is the Minimal Supersymmet-ric Standard Model (MSSM), which has the least quantity of particles posible. In the MSSM, each fermion has one bosonic superpartner and each boson has a fermionic su-perpartner. In this model, R-parity is conserved [17].

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Particles in the MSSM

The MSSM is the supersymmetryc model with the least amount of particles possible that is plausible according to experimental observations, being congruent with the SM. In the initial formulation of the MSSM, there was nothing to prevent the decay of the proton, which had a predicted lifetime ofτp ∼6×10−13s. However, the proton is stable in the Standard Model. To solve this incongruence, a new quantum number conserva-tion is proposed for the model, this number is called the R-Parity. All SM particles have even R-Parity (R= 1) and all SUSY particles have odd R-Parity (R=−1) [17] .

TABLE2.5: Supersymmetryc Particles in the MSSM [17]

Name Notation Spin R-parity

Selectron ˜e− 0 -1

Smuon µ˜− 0 -1

Stau τ˜− 0 -1

Selectron-neutrino ν˜e 0 -1 Smuon-neutrino ν˜µ 0 -1

Stau-neutrino ν˜τ 0 -1

Wino W˜ 1₂ -1

Bino B˜ 1₂ -1

Gluino ˜g 1₂ -1

Higgsinos ˜hu,˜hd 1₂ -1

Table2.5shows the particles in the MSSM model. As it shows, there is a supersym-metryc particle for each particle in the SM. However, there are some observations to be made. First, to be consistent, the MSSM must have at least two Higgs doublet chiral fields. Otherwise, the model has some gauge anomalies. This is the reason for the two higgsinos in table 2.5. In the MSSM model, there are three types ofW boson: one of them is neutral (W3_{) and is the supertpartner of the photon; the two others are charged} and are the superparticles of theW+andW−bosons [17].

In the MSSM model, the Wino, Bino and Higgsinos can make mixtures to form par-ticles called Neutralinos and Charginos. As its name suggests, neutralinos are neutral particles, they are the linear combinations of the neutral wino, the bino and the hig-gsinos. There are four neutralinos possible. The lightest neutralino (χ0

1) is actually the lightest supersymmetric particle(LSP). If R-Parity is conserved, this particle turns out to be stable. As this particle is weakly interactive (WIMP), it is a natural candidate for DM composition. The mixture of charged SUSY fermions are called charginos [17].

2.1.4 Large Hadron Collider(LHC)

The LHC is the largest collider created until now. It is placed in the fields of thePays de Gex, at the border between Switzerland and France. It is located 100 m under the soil and forms a circumference of 27 km of perimeter. Its construction lasted 20 years. The LHC is formed by two rings divided in 8 sectors, called octants. The proton bunches collide at different points of the ring, where particle detectors are located, reaching an energy of collision of 13 TeV at the center of momentum. Such high energies allowed

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scientists to find the Higgs Boson in 2013 [18].

FIGURE2.7: Sector map of the LHC [18]

As figure2.1.4shows, the LHC has eight sectors. Two octants are reserved for clean-ing, letting the proton beam to accelerate without interruptions. One of the regions is used for dumping the beam after its joruney through the ring. There are four regions with different detectors to study the collisions (CMS, Atlas, LHCb and ALICE). To ac-celerate the beams, superconducting magnets are positionated along the ring.

FIGURE2.8: Proton beam path through the LHC [18]

The LHC uses protom beams that are accelerated in opposite directions in two dif-ferent rings. Figure2.8shows the path taken by the beam in the LHC. The protons are prepared using hydrogen gas (at full beam loading, about 2 ng of gas are consumed by the LHC daily). The gas is accelerated through a linear accelerator (LINEAC 2) to about

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a third the speed of light in order to strip the electrons in the hydrogen gas and accel-erate the remaining protons. These protons are sent through the Proton Synchrotron Booster (PSB) to the Proton Synchrotron (PS). The PS is an accelerator of 200 m long, which increases the kinetical energy of the protons. Then, the protons are injected to the Super Proton Synchrotron (SPS), which has a perimeter of 2.25 km, acquiring even more energy. By this time, the protons have acquired a speed of nearly 9/10 the speed of light. Finally, the beam is passed to the LHC and is accelerated to the speed of 0.999999991 times the speed of light [18].

Detectors and Important Concepts

The two main detectors at the LHC are CMS (Compact Muon Solenoid) and ATLAS (A Toroidal LHC ApparatuS). Once collisions are induced, these detectors are responsible of the detection and identification of the particles generated after the collision. To iden-tify particles electrically charged, these detectors use magnets. Hence, the trajectory of the particle will change according to its electromagnetic properties and momentum. Particles with very high momentum will have almost straight trajectories, while low momentum ones will follow curved lines [18].

FIGURE 2.9: Arrangement of calorimeters used for energy measure-ments [18]

To measure the energy of the particles produced after the collision, highly sensitive calorimeters are used. As every particle has different properties and interact differently with materials, different types of calorimeters are used in a nested arrengement. Fig-ure2.9shows this arrangement and how different types of particles interact with the detector.

Some basic concepts about detector studies are introduced now, necessary for the comprehension of this project:

• Cross sectionσ

The cross section is an effective area which is directly related with the probabil-ity of a certain interaction to occur. Processes that have a bigger cross section are more likely to happen than those with small ones. It can be understood as the size

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of the target that certain beam must hit for a given process to occur. The standard unit used to measure the cross section is the barn (1barn= 10−24cm2). The cross section is usually notated with the greek letter sigma (σ).

• Luminosity

Luminosity is a quantity that indicates how many collisions may occur per unit of time. This number shows how many particles may be squeezed within the detector’s area. It is not precisely the collision rate because not all particles inside a collider actually collide. This value deppends on the technology of the collider. Luminosity is an important feature for the discrimination of the signal from the noise generated by disrupting backgrounds [11].

The rate of reactions for a certain process(N˙) is directly related to luminosity (L) by the cross section of the respective process (σ):

˙

N =Lσ (2.1)

• Coordinate system

FIGURE2.10: Spherical coordinate system.

Detectors are able to measure the position of the particles produced in a collision. The coordinate system used to measure the position of particles in a collision is the spherical one. In figure2.10, theyaxis correspond to the axis parallel to the movement of the beam of particles before the collision. When they collide, the azimuthal angleφand the angleθdescribe the deviation of the multiple beams generated due to the collision.

• Pseudorapidityη

The pseudorapidity is a function of angleθ(see figure2.10) [11]. It is called psu-dorapidity because it is an approximation to the definition of rapidity in special

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relativity [3]. This function is used instead of the angle θbecause it has a bet-ter behaviour for statistical analysis [11] as a difference∆ηis Lorentz invariant, while a difference∆θis not. The equation2.2gives the value ofη.

η=−ln(tan(θ

2))) (2.2)

• Missing Transverse Energy MET

In the collision of protons at the LHC, the vectorial sum of the momenta of parti-cles at the centre of the collision should be zero, as identical partiparti-cles move with the same velocity in opposite directions. However, not all particles emerging after the collision are detected. The missing momenta needed to balance the vectorial sum to zero, is referred as missing momenta or missing energy.

Since many of the most interesting events are recorded by the detector in the plane transverse to the beam direction, the missing energy in this region of the fiducial volume is of special interest. Therefore, the Missing Transverse Energy (MET) is an interesting variable commonly used by experimentalist at collider experiments. [11]. MET is a critical variable for particle studies. It is very impor-tant that the accelerator is hermetic. Otherwise, energy measurements would be erroneous as some particles would get lost.

Among the particles that can not be detected by calorimeters is the neutralino (χ0₁). Thus, it is impossible to confirm its existance by direct observation at the calorimeters. Nevertheless, MET is a helpful variable to approach these searches and has potential to extract clean signals of SUSY events from unwanted back-grounds with low MET.

• Transverse mass (MT)

In every collider, an unknown part of the energy of the collision escapes down the beam pipe. Hence, the momentum of invisible particles can only be constrained to the direction transverse to the beam of particles. The transverse mass is a vari-able used by hadron collider experimentalists to constrain the mass M of a heavy particle that decays into a pair of lighter particles, with the particularity that one of them is invisible (it does not interact with the detectors) [19].

In our case of study, the heavy particle is the stau (τ˜), which decays in a tau (τ) and a neutralino (χ0₁) (an invisible particle). The mass of the stau constrained to the transverse direction is then found by equation2.3. Here, the MET corresponds to the energy associated to the neutralino. The transverse mass gives a lower bound for the total mass M of the stau whereM < Mt.

Mt=

q

2Pt(τ)6E(1−cos∆φ(τ,6E)) (2.3)

• Effective mass Mef f The effective mass is a variable which is widely used in

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decay into jets, leptons and MET [20]. As staus may decay in the mentioned species, this variable seems to have potential for the proposed analysis.

Mef f =

q

Pt(τ)2+Pt(jet)2+6E2 (2.4)

SUSY searches

SUSY searches at the LHC are divided in two different approaches.

• Color sector searches

Color sector searches are characterized by the hypothetical production of heavy SUSY particles which decay into DM particles. The channels of these searches involve a high multiplicity of particles and jets. These searches usually have a large MET due to the production of neutrinos in the process. Besides, if SUSY ex-ists, the neutralinos created would contribute more to the MET produced in these types of interactions.

stop mass [GeV]

100 200 300 400 500 600 700 800

LSP mass [GeV]

0 100 200 300 400 500 600 700 W = m 1 0 χ∼ - m t ~ m t = m 1 0 χ∼ - m t ~ m

= 8 TeV

s

CMS

1 0

χ∼

/ c

1 0

χ∼

t

→

t

~

production,

t

~

-t

~

-1 SUS-13-023 0-lep (2 body decays) 18.9 fb

-1 SUS-13-011 1-lep (2 and 3 body decays) 19.5 fb

-1 SUS-14-015 1,2-lep (2 and 3 body decays) 19.5 fb

-1 SUS-14-011 0-lep (Razor) + 1-lep (MVA) 19.5 fb

-1 SUS-14-011 0,1,2-lep (Razor) 19.3 fb

-1 ) 19.7 fb 1 0 χ∼ c → t ~ SUS-14-001 Monojet (

Observed Expected t = m 1 0 χ∼ - m t ~ m

FIGURE2.11: Published limits for SUSY searches in color sector at the CMS through˜t˜tproduction. [7]

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gluino mass [GeV]

600 800 1000 1200 1400 1600

LSP mass [GeV]

0 100 200 300 400 500 600 700 800 900 1000

m(gluino) - m(LSP) = 2 m(top)

= 8 TeV

s

CMS

1 0

χ∼

t

→

g

~

production,

g

~

-g

~

-1 ) 19.5 fb T +H T E SUS-13-012 0-lep (

-1 6) 19.3 fb

≥

jets SUS-13-007 1-lep (n

-1 SUS-13-013 2-lep (SS+b) 19.5 fb

-1 SUS-14-010 3-lep (3l+b) 19.5 fb

-1 SUS-14-010 2-lep(OS) 19.5 fb

-1 SUS-14-010 0+1+2(SS,OS)+>2-lep 19.5 fb Observed

Expected

FIGURE2.12: Published limits for SUSY searches in color sector at the CMS through˜gg˜production. [7]

In order to analyze the collected data in the different analyzes carried out at AT-LAS and CMS, an statistical likelihood test is performed. The test is used to de-termine the probability that a certain group of data acquired is consistent with a signal of interest, given an expected rate of background events. The likelihood is commonly expressed with a 95% confidence level [21]. Figures2.11and2.12 correspond to SUSY searches using two different channels by CMS collaboration. The solid lines represent the observed limits, while the long dashed lines corre-spond to the expected limits. In some cases, the minus one sigma deviation with respect to the mean value is also presented as a fine dashed line.

Color sector searches have two limitations. First, SUSY colored particles migh be too heavy to be produced by the LHC. This would make impossible to detect SUSY using the actual technology. Besides, as color searches involve heavier par-ticles, it requires very energetic collisions. This produces a high multiplicity of particles and large values of MET, involving a high rate of backgorund events.

• Electroweak sector searches

Electroweak sector searches consist in the direct production of noncolored SUSY particles (such as slepton pairs or charginos and neutralinos) which might also include production of neutralinos. These searches are characterized by weak in-teractions and small cross sections. Only few particles are produced compared to color sector searches and the MET is smaller.

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neutralino mass = chargino mass [GeV]

100 200 300 400 500 600 700 800

LSP mass [GeV]

0 100 200 300 400 500 600 700 800 900 1 0 χ∼ = m 1 ± χ ∼ m Z +m 1 0 χ∼ = m 1 ± χ ∼ m H +m 1 0 χ∼ = m 1 ± χ ∼ m

ICHEP 2014

= 8 TeV

s

CMS Preliminary

production

1 ±

χ∼

-2 0

χ∼

) 1 0 χ∼ )(W 1 0 χ∼ (H → 1 ± χ∼ 2 0 χ∼ ) 1 0 χ∼ )(W 1 0 χ∼ (Z → 1 ± χ∼ 2 0 χ∼ ) )=0.5 -l + l , BF( L l ~ ( 1 ± χ∼ 2 0 χ∼ ) )=1 -l + l , BF( L l ~ ( 1 -χ∼ 1 + χ∼ ) τ ν∼ τ∼ ( 1 ± χ∼ 2 0 χ∼ ) )=1 -l + l , BF( R l ~ ( 1 ± χ∼ 2 0 χ∼ -1

SUS-13-006 19.5 fb

-1

SUS-14-002 19.5 fb

Observed Expected 1 0 χ∼ = m 1 ± χ ∼ m

FIGURE2.13: Published limits by CMS for SUSY searches using electroweak channels [9].

Figure 2.13 shows the limits published by CMS for SUSY searches using elec-troweak channels. The area under the lines in the figure shows the region where SUSY has already been discarded by the use of different search channels [8,9]. A large region of possible masses for the neutralino and chargino has already been analyzed by the two types of searches. The search for SUSY is becoming more challenging as the regions left outside the limits are harder to analyze.

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WG σ LPCC SUSY

https://twiki.cern.ch/twiki/bin/view/LHCPhysics/SUSYCrossSections arXiv:1206.2892

SUSY sparticle mass [GeV]

200 400 600 800 1000 1200 1400 1600

SUSY) [pb]

→

(pp

σ

NLO(-NLL)

₁₀-4

-3 10 -2 10 -1 10 1 10

g

~

g

~

L,R u,d,s,c q=

*

q

~

q

~

*

t

~

t

~

-χ∼

+

χ∼

0

χ∼

±

χ∼

-l

~

+

l

~

8 T eV L H C d at a -1

#events in 20 fb

10 2 10 3 10 4 10 5 10

FIGURE 2.14: Cross section for SUSY particles production using different channels [22].

If, as mentioned in color searches section, the mass of SUSY colored particles is too heavy to be produced at the LHC, electroweak channels would be the only way (unless a bigger collider is built) to find SUSY. Figure2.14shows that cross sections for electroweak searches are smaller than color searches ones. However, electroweak searches have less backgrounds, needing less luminosity.

[GeV]

0 2 χ∼

=m

± 1 χ∼

m

100 150 200 250 300 350

[GeV]

₀ ₁

χ∼

m

0 50 100 150 200 250

[fb]

σ

9

5 %

C

L

u

p

e

r

lim

it

o

n

10 2 10 3 10 4 10 -1

= 9.2 fb

int

= 8 TeV, L s

CMS Preliminary

95% C.L. CLs NLO Exclusions theory σ 1 ± l Observed 3 theory σ 1 ± l Expected 3 0 2 χ∼ ± 1 χ∼ → pp τ ν τ∼ → ± 1 χ∼ τ τ∼ → 0 2 χ∼ 0 1 χ∼ + 0.5m ± 1 χ∼ = 0.5m l ~ m

FIGURE2.15: Limits published by CMS for SUSY searches using electroweak channels. [8]

Some of the hardest scenarios to tackle in SUSY searches are compressed ones. Compressed scenarios are possible situations where the mass of SUSY particles is similar compared to each other. Figure 2.15shows that compressed area (the area where the mass of the neutralino is similar to the mass of the chargino) is not yet discarded. The experiments made until today have low sensitivity at this

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scenarios.

FIGURE 2.16: Limits for SUSY particles masses consistent with cosmological observations [10].

A final remark to be made is that compressed scenarios seem to be likely. Figure 2.16shows the area for different values of neutralino and chargino masses that are congruent with cosmologic observations regarding Dark Matter. As the fig-ure shows, the mass of stau is similar to the mass of the neutralino, the difference vary between 20 GeV to 55 GeV, depending on the mass of the neutralino [10].

2.1.5 Stau pair production with Initial State Radiation (ISR) jet

A new idea to tackle compressed scenarios is the analysis of the production of staus with an ISR jet. An ISR jet is the radiation emitted by quarks before the interaction when they collide [11].

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FIGURE2.17: Diagram of the production of a pair of staus with an ISR jet.

Figure2.17shows a basic diagram of the production of stau pairs with an ISR jet. Staus decay into a neutrlino and a tau. This idea might be a powerful tool to search for DM particles at compressed mass scenarios, because the ISR jet makes a boost which increases the MET in the process. To ilustrate better this phenomena, it is useful to pose the momentum conservation analysis.

When there is no ISR in the production of staus, the sum of momentum is given by:

0 =−→p(τ+) +−→p(τ−) +→−p(χ0₁1) +−→p(χ0₁2) (2.5) Equation 2.5 shows the total sum of momentum for staus production. For com-pressed scenarios, the taus produced have low momentum then the equation is simpli-fied to:

−−→p(χ0₁1) =−→p(χ0₁2) (2.6) From equation 2.6, it is deduced that the neutralinos produced move in exactly opposite directions. This means no MET will be detected. This is the reason why com-pressed scenarios are so hard to tackle. However, in the presence of an ISR jet, the sum of momentum is given by:

0 =−→p(τ+) +→−p(τ−) +−→p(χ0₁1) +−→p(χ₁02) +−→p(jet) (2.7) Equation2.7is reduced when the taus produced have low moentum (characteristic of compressed scenarios).

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−−→p(χ0₁1) =−→p(χ0₁2) +−→p(jet) (2.8) In equation2.8, the ISR jet plays the role of a booster. Whenever this jet is present, neutralinos will not be produced with exactly opposite momentum. This channel is able to produce large MET, easing DM detection in compressed scenarios.

Possible Backgrounds for the signal

Backgrounds are the possible SM processes which may be taken falsely as SUSY events. These signals must be discriminated from the original signal with as much efficiency as possible. The main backgrounds for the staus production with an ISR jet process are described below.

• Drell-Yan process

In a Drell-Yan process, a quark from one hadron and an antiquark of other hadron annihilate each other and create a virtual photon (a virtual state is the name for the states that would be impossible clasically but are real due to quantum be-haviour). The virtual photon decays then into a pair of leptons (such as a tau and an antitau) [23].

FIGURE2.18: Feynmann Diagram of a Drell-Yan process.

Figure2.18shows a Feynmann Diagram of a Drell Yan process. When the leptons generated in the process decay, they usually form pions and neutrinos [12]. When these particles interact with the detectors, the neutrinos formed are detected as a signal of MET. These signal could be confused with the hypothetical neutralinos generated due to SUSY events.

• W+jets production

W bosons may decay into a tau lepton and a neutrino [12]. As neutrinos are a source for MET, they might be confused with neutralinos. Thus, W productions are a background for SUSY searches using stau pair productions. Moreover, when the W boson is produced with radiation jets, these could be confused with the ISR jet for the channel proposed in this project. In figure2.19, the particles radiated are gluons. As it is seen, W boson decay in a lepton (which could be a tau) and a neutrino.

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FIGURE2.19: Feynmann Diagram ofW+jetsproduction.

2.2 Software

In this section are described all the softwares necessary for the development of this thesis project.

2.2.1 Madgraph

Madgraph(MG) is a software package able to simulate particle collision events. It ap-plies the Montecarlo method to the SM. Madgraph has the capacity to predict possible particle decays, given the initial particles that collide. Some other hypothetical mod-els, such as MSSM may be also be taken into account by MG [24]. Other functions of Madgraph include the calculus of Cross Sections and graphing of Feynmann Diagrams.

Madgraph take as an input the collision parameters, such as the particles involved, energy of the collision at the center of mass, possible final states and associated radia-tion jets [24]. The user must specify the number of events required. Madgraph is able to restrict the events generated to cuts required by the user. The output of Madgraph is a file with LHE format.

2.2.2 Pythia

Another important software for the generation of high enery physics events is Pythia. Pythia is responsible for the simulation of hadronization events, which can lead to ISR jets [25]. Pythia take the LHE file produced from MadGraph as an input and produces an output with HEP format.

Hadronization

Hadronization is a physical phenomenum occurred when two quarks are separated considerably due to high energy collisions. When they separate, the energy of the sys-tem tend to increase due to strong force. This energy increase creates a quark antiquark couple at vacuum. This is an iterative process able to form jets with high momentum [23].

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2.2.3 Delphes

Delphes is a software package, written in C++, that emulates the signal produced by detectors when interacting with particles. Delphes takes into account the effects of magnetic fields, the calormiters granularity and resolution of the detectors [26]. In other words, this software permits to control technical uncertainties and errors due to interaction with detectors.

Delphes take an HEP file as an input. This file is the output from Pythia. The out-put of Delphes is an ntuple with the jets and leptons properties (Pt, η, φandM ET) that would be registered by detectors [26]. The ntuple is writen in root format.

2.2.4 ROOT

ROOT is a framework designed by CERN. It is written in C++. However, it is easily integrated with Python and R. The main functionalities of ROOT are big data process-ing, statistical analysis, visualization and storage [27]. ROOT read ntuples with root format.

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Chapter 3

Methodology

This chapter presents the methodology used to achieve the proposed objectives. It de-scribes briefly the steps for the production of signal and background samples and the parameters used. The main concepts of the data analysis followed with the data ac-quired are reviewed. This chapter also introduces the important concepts of efficiency and significance.

3.1 Signal Production

The signal samples were produced using MadGrapgh5_aMC@NLO v2.2. As the main purpose of this project is to analyze compressed scenarios, the samples produced be-long to the compressed mass spectra.

TABLE3.1: Signal samples produced.

Label χ0₁mass τ˜−mass χ±mass Cross Section Number of events Signal 1 150 GeV 175 GeV 200 GeV 10 fb 1000000 Signal 2 150 GeV 185 GeV 200 GeV 10 fb 1000000 Signal 3 150 GeV 195 GeV 200 GeV 10 fb 1000000

Table 3.1 shows the samples produced. The three samples correspond to highly compressed scenarios. The mass difference betweenχ0₁and˜τ is 25 GeV, 35 GeV and 45 GeV for the signals generated. The cross sections were calculated by MadGraph and one million events were produced for each signal.

3.2 Background Production

To produce the background samples, the same version of MadGrap was used.

TABLE3.2: Background samples produced.

Background process Cross Section Number of events

W and jets production 1641000 fb 17000000 Drell Yan process 709000 fb 10000000

Table 3.2 shows the number of events and the cross sections of the background samples created. The samples produced are constrained to have at least one jet with

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28 Chapter 3. Methodology

transverse momentum higher than 100 GeV. This was done to diminish the cross sec-tion of these processes to make the background samples more comparable to the signal samples, as the last ones have comparatively a small cross section.

3.3 Data Analysis

This section explains the statistical analysis followed to determine the optimal cuts and significance of the proposed channel for SUSY searches.

3.3.1 Variable cuts and efficiency

To discriminate Signal and Background samples, it is necessary to select the proper events from the ntuples generated. Only the events that can uniquely be explained by SUSY should be considered. The difficulty rellies on the fact that some SUSY events may also be explained as background events that are congruent with the SM (thus they can not be identified as SUSY) [21]. The “cutting” procedure is the most common methodology to discriminate signal from background. It consist on the discard of the events according to the data produced by delphes [21]. The cuts applied in this project will be discused deeply in chapter 4.

Two type of errors can be made when applying a set of selection criteria. Either a background event can be selected as signal event (this is known as error type I) or a signal event can be discarded as a background event (this is known as error type II). A quantity known as efficiency is introduced to quantify these errors for a given selection criterion (cut) [21]. This quantity is given by equation3.1. The valueN is the number of events after the cut andN0is the number of events before the cut.

δ= N

N0

(3.1)

When equation3.1 is applied to signal events it quantifies errors type I (discard a SUSY event). On the other hand, if it is applied to background events, it quantifies errors type II (choose a background event as a SUSY event). A perfect cut is obttained when the efficiency of the signal is 1 and the efficiency of the backgorund is 0. How-ever, this result is impossible because the signal and the background are statistically correlated [21].

3.3.2 Significance Analysis

The significance analysis is made to optimize the cuts. In general, signal events want to be maximized and background events minimized. However, as these quantities are related, they can not be directly optimized. Then, a new function calledsignificance

is introduced to make an optimization [21,11]. In equation3.2,λcorresponds to sig-nificance, S is the rate of events of signal after applying the cuts and B is the rate of background events after applying the cuts. The values of S and B may be found using

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Chapter 3. Methodology 29

dimensional analysis which gives equations number3.3 and3.4, where L is the lumi-nosity,δthe efficiency andσthe cross section.

λ= √ S

S+B (3.2)

S =Lδ(signal)σ(signal) (3.3)

B =Lδ(background)σ(background) (3.4) The significance gives the number of standard deviations that the signal number of events is away from zero. This number should be as large as possible. Different values of the variables chosen to make the cuts are tested to find the maximum significance. The value which gives the maximum significance is the limit for the cut [21].

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Chapter 4

Results and Analysis

In this section, the preliminary results of the study of the event selection criteria to discriminate signal from background are presented. The initial steps included the im-plementation in the code of graphs of kinematical and topological variables, in order to determine a possible set of distributions that could help reduce the contamination from SM processes, such asW +jetsand Drell-yan + jets. Kinematical variables such as the transverse momentum (pT) of the tau candidates, the highestpT jet in the event, and theηandφdistributions of the taus and jets, were plotted. Also, topological variables such as theM ET, the∆φ(jet, M ET),∆φ(τ, M ET), theMT(τ, M ET)and the effective mass, were implemented in the code.

To determine the important variables that could give a separation between the sig-nal and the background, the graphs of the various kinematical and topological distri-butions were normalized to the area under the curve, that is to say, normalized to unity. The normalization to unity allows to probe the charactestics of a distribution regardless of the cross section of the process, which for backgrounds might be several orders of magnitude higher with respect to those for SUSY events.

To ease the search of variables that may discriminate the signal from the back-grounds, some preliminary cuts were applied such that the data were actually coherent with the channel proposed. Only the events with exactly one tau and an ISR jet were taken into account. Events with two taus could also be analyzed. The events with electrons and muons were discarded as none electrons or muons are produced in the proposed channel. Finally, only taus with apT above 10 GeV were selected, since ex-perimentally the erroneous identification rate of taus to QCD jets is high for very low momentum candidates.

Figures 4.1 to 4.6 show some overlaid kinematical variables with the mentioned initial cuts applied, normalized to unity, of three signal points and the two main back-grounds. Note there is no significant separation between signal and background for any of these variables.

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32 Chapter 4. Results and Analysis

η(τ

)

) 1 τ ( η 3

− −2 −1 0 1 2 3

a.u./ 0.125 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045

0.05 _χ∼±_{) = 200 GeV}

) = 175 GeV, m(

τ∼

) =150 GeV, m(

1 0

χ∼

m(

) = 200 GeV

±

χ∼

) = 185 GeV, m(

τ∼

) =150 GeV, m(

1 0

χ∼

m(

) = 200 GeV

±

χ∼

) = 195 GeV, m(

τ∼

) =150 GeV, m(

1 0 χ∼ m( BG1: W+jets BG2: Drell-Yan

FIGURE4.1: η(τ)after applying the initial cuts: N(e) = 0,N(µ) = 0,

N(τ) = 1,N(jet) = 1andpT(τ)>10GeV

η

(jet)

(jet) η

5

− −4 −3 −2 −1 0 1 2 3 4 5

a.u./ 0.2 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

) = 200 GeV

±

χ∼

) = 175 GeV, m(

τ∼

) =150 GeV, m(

1 0

χ∼

m(

) = 200 GeV

±

χ∼

) = 185 GeV, m(

τ∼

) =150 GeV, m(

1 0

χ∼

m(

) = 200 GeV

±

χ∼

) = 195 GeV, m(

τ∼

) =150 GeV, m(

FIGURE4.2: η(jet)after applying the initial cuts: N(e) = 0,N(µ) = 0,

(53)

Chapter 4. Results and Analysis 33

φ(jet)

(jet) φ

3

− −2 −1 0 1 2 3

a.u./ 0.1 0 0.005 0.01 0.015 0.02

0.025 _χ∼±_{) = 200 GeV}

) = 175 GeV, m(

τ∼

) =150 GeV, m(

1 0

χ∼

m(

) = 200 GeV

±

χ∼

) = 185 GeV, m(

τ∼

) =150 GeV, m(

1 0

χ∼

m(

) = 200 GeV

±

χ∼

) = 195 GeV, m(

τ∼

) =150 GeV, m(

FIGURE4.3: Φ(jet)after applying the initial cuts:N(e) = 0,N(µ) = 0,

N(τ) = 1,N(jet) = 1andpT(τ)>10GeV

φ(τ

)

) 1 τ ( φ 3

− −2 −1 0 1 2 3

a.u./ 0.2 0 0.01 0.02 0.03 0.04 0.05 0.06

) = 200 GeV

±

χ∼

) = 175 GeV, m(

τ∼

) =150 GeV, m(

1 0

χ∼

m(

) = 200 GeV

±

χ∼

) = 185 GeV, m(

τ∼

) =150 GeV, m(

1 0

χ∼

m(

) = 200 GeV

±

χ∼

) = 195 GeV, m(

τ∼

) =150 GeV, m(

FIGURE4.4: Φ(τ)after applying the initial cuts: N(e) = 0,N(µ) = 0,

Phenomenological study on supersymmetry searches at the LHC, through stau pairs electroweak production with an initial state radiation jet

UNIVERSIDAD DE LOS

A

NDES

B

T

Phenomenological Study on

SuperSymmetry Searches at the LHC,

through Stau Pairs Electroweak Production

with an Initial State Radiation Jet

Declaration of Authorship

Abstract

Acknowledgements

Contents

List of Figures

List of Tables

List of Abbreviations

Dedicated to my aunt Carmenza Tolosa for her excentrical

teachings.. . .

Chapter 1

Introduction

1.1

Problem

1.2

Objectives

Chapter 2

Theoretical Framework

2.1

Key Concepts

= 8 TeV

s

CMS

χ∼

/ c

χ∼

t

→

t

~

production,

t

~

-t

~

= 8 TeV

s

CMS

χ∼

t

t

→

g

~

production,

g

~

-g

~

ICHEP 2014

= 8 TeV

s

CMS Preliminary

production

χ∼

χ∼

SUSY sparticle mass [GeV]

SUSY) [pb]

→

(pp

σ

NLO(-NLL)

g

~

g

~

*

q

~

q

~