La découverte d'une particule similaire au boson de Higgs, dernière pièce manquante du Modèle Standard (MS) de la physique des particules élémentaires, est en voie d'être confirmée par les expériences CMS et ATLAS du Large Hadron Collider du CERN. Cependant, il n'est pour le moment pas encore établit que les caractéristiques de la particule observée correspondent aux prédictions du MS. Cela, associé à d'autres observations (Matière Noire,...), motive l'analyse des extensions supersymétriques du MS comme le NMSSM. Nous étudions dans cette thèse la solution au problème de la hiérarchie des échelles d'énergie dans le NMSSM, lié aux divergences quadratiques de la masse du boson de Higgs, ainsi que la phénoménologie du NMSSM avec une brisure de la supersymétrie par interactions de jauge en tenant compte des dernières données du LHC. Enfin, nous détaillons les développements des codes de NMSSMTools effectués au cours de cette thèse~: l'introduction de Chaînes de Markov, le calcul du Fine Tuning, le calcul des cascades de désintégrations des partenaires supersymétriques en particules du MS et l'implémentation du NMSSM général. / The discovery of a particle similar to the Higgs boson predicted by the Standard Model (SM) of particle physics has been confirmed by the experiments CMS and ATLAS of the Large Hadron Collider at the CERN. However, it is not yet clear that the properties of this particle are those predicted by the SM. This, in addition with several other observations (Dark Matter,...), is a motivation for analysing supersymmetric extensions of the SM, as the NMSSM. We study in this thesis the solution of the Hierarchy problem in the NMSSM, linked with the quadratic divergences in the Higgs sector, and also the phenomenology of the NMSSM with gauge mediation supersymmetry breaking in the light of the latest data from the LHC. Finally, we present the developments made in the codes of the package NMSSMTools, featuring Monte Carlo Markov Chain methods, Fine Tuning calculus, the calculus of supersymmetric particle's cascade decays and the implementation of the general NMSSM.

In its first three years of operation, the Large Hadron Collider at CERN has already proved its worth as a discovery machine and reinvigorated the prospects for discovering new dynamics beyond the Standard Model. This thesis presents a range of experimental methods devised for discovery of supersymmetry, one of the most important extensions of the Standard Model being tested at the LHC. The first chapter discusses the concepts behind a set of transverse mass-bound variables, and explores connections between these variables and others in the literature. Not only are these variables important tools for mass measurement, should sparticles be seen at the LHC, they are also critical components of experimental searches. Accordingly, their performance has been compared in both mass measurement and search contexts, and the results are reported here. This is followed by the details of a search for hadronically-decaying squarks and gluinos, carried out on 4.7 fb−1 of data collected at 7 TeV in 2011 by the ATLAS detector. The search strategy is described, focusing on the implementation of a background estimation method using photon events to determine the background contamination due to invisible Z boson decays. The results of the search are then presented. Stringent limits are set on the production of squarks and gluinos in a variety of model scenarios.

Einstein's theory of general relativity has been the accepted theory of gravity for nearly a century but how well have we really tested it? The laws of gravity have been probed in our solar system to extremely high precision using several different tests and general relativity has passed each one with flying colours. Despite this, there are still some mysteries it cannot account for, one of which being the recently discovered acceleration of the universe and this has prompted a theoretical study of modified theories of gravity that can self-accelerate on large scales. Indeed, the next decade will be an exciting era where several satellites will probe the structure of gravity on cosmological scales and put these theoretical predictions to the test. Despite this, one must still worry about the behaviour of gravity on smaller scales and the vast majority of these theories are rendered cosmologically uninteresting when confronted with solar system tests of gravity. This has motivated the study of theories that differ from general relativity on large scales but include screening mechanisms which act to hide any modifications in our own solar system. This then presents the problem of being able to distinguish these theories from general relativity. In the last few years, astrophysical scales have emerged as a new and novel way of probing these theories. These scales encompass the mildly non-linear regime between galactic and cosmological scales where the astrophysical objects have not yet joined the Hubble flow. For this reason, the screening mechanism is active but not overly efficient and novel effects may be present. Furthermore, these tests do not require a large sample of galaxies and hence do not require dedicated surveys; instead they can piggyback on other experiments. This thesis explores a class of theories of screened modified gravity which are scalar-tensor theories where the field is conformally coupled to matter via the metric and includes chameleon and symmetron models as well as those that screen using the environment-dependent Damour-Polyakov effect. The thesis is split into two parts. The first is aimed at searching for new and novel astrophysical probes and using them to place new constraints on the model parameters. In particular, we derive the equations governing hydrodynamics in the presence of an external gravitational field that includes the modifications of general relativity. Using this, we derive the equations governing the equilibrium structure of stars and show that unscreened stars are brighter and hotter than their screened counterparts owing to the larger nuclear burning rate in the core needed to combat the additional inward force. These theories have the property that the laws of gravity are different in unscreened galaxies from our own. This means that the inferred distance to an unscreened galaxy using a stellar effect that depends on the law gravity will not agree with a measurement using a different method that is insensitive gravitational physics. We exploit this property by comparing the distances inferred using pulsating Cepheid variable stars, tip of the red giant branch stars and water masers to place new constraints on the model parameters that are three orders of magnitude stronger than those previously reported. Finally, we perturb the equations of modified gravity hydrodynamics to first order and derive the equations governing the oscillations of stars about their equilibrium structure. By solving these equations we show that unscreened stars are more stable to small perturbations than screened stars. Furthermore, we find that the oscillation period is far shorter than was previously estimated and this means that the current constraints can potentially be improved using previous data-sets. We discuss these new results in light of current and future astrophysical tests of modified gravity. The final part of this thesis is dedicated to the search for supersymmetric completions of modified theories of gravity. There have been recent investigations into the quantum stability of these models and there is evidence that they may suffer from quantum instabilities. Supersymmetric theories enjoy powerful non-renormalisation theories that may help to avoid these issues. For this reason, we construct a framework for embedding these models into global supersymmetry and investigate the new features this introduces. We show how supersymmetry is broken at a scale set by the ambient density and that, with the exception of no-scale models, supergravity corrections already constrain the model parameters to levels where it is not possible to probe the theories with astrophysics or laboratory experiments. Next, we construct a class of supersymmetric chameleon models and investigate their cosmology. In particular, we find that they are indistinguishable from the LCDM model at the background level but that they may show deviations in the cold dark matter power spectrum that can be probed using upcoming experiments. Finally, we introduce a novel mechanism where a cosmological constant in the form of a Fayet-Illiopoulos term can appear at late times and investigate the constraints this imposes on the model parameter space.

Cette thèse a été effectuée dans le cadre de la recherche de la supersymmetrie (SUSY) avec 20.3 fb^{-1} de collisions proton-proton délivrées par le LHC et collectées par le détecteur ATLAS à sqrt{s} = 8 TeV. Si SUSY est réalisée dans la nature, des squarks (partenaires des quarks) et des gluinos (partenaires des gluons) devraient être produits à cette énergie, et on attend à ce qu'ils se désintègrent en états finaux sans electron ni muon, plusieurs jets et de l'énergie transverse manquante (due à la production de la particule SUSY la plus légère (LSP) qui traverse le détecteur sans être observée). La première partie de cette thèse consiste à définir deux régions de validation utilisées dans la procédure finale de fit visant à évaluer le bruit de fond provenant des bosons W et des top quarks qui se désintègrent en leptons tau. A partir de ce fait, et comme on n'a observé aucun excès, on dérive des limites sur les masses des particules dans des modèles simplifiés ou dans des modèles SUSY avec peu de paramètres. Une limite d'exclusion à 95% de niveau de confiance sur la masse des gluinos a été déterminée à 1330 GeV pour le modèle simplifié avec un gluino et un neutralino sans masse. Dans le cadre de mSUGRA/CMSSM avec tan beta = 30, A_0 = -2m_0 et mu > 0, les squarks et gluinos sont exclus pour des masses inférieures à 1700 GeV. L'ajout d'un véto sur les évènements avec les leptons tau est aussi explorée et l'impact sur l'exclusion a été évaluée.Le deuxième partie de cette thèse a été effectuée dans le cadre du modèle phénoménologique minimal supersymmétrique (pMSSM) où l'interprétation des résultats de l'analyse 0-lepton mentionnée ci-dessus, ainsi que les résultats d'autres analyses d'ATLAS, a été menée à bien. Le choix des paramètres et de leur domaine d'exploration a été faite sur la base de résultats non-SUSY comme les désintégrations rares des mésons B, la masse de boson de Higgs, les limites de recherche directe de la matière noire et la limite sur la densité de matière noire de l'Univers. La contribution de cette thèse commence par la validation de la sélection des évènements au niveau truth et reconstruit. Comme cette analyse est la plus contraignante dans le pMSSM, cette validation est faite avec une attention particulière. Les contraintes obtenues avec toutes les analyses sur les masses des différentes particules SUSY sont décrites, en particulier pour les squarks, gluinos et neutralinos. Les résultats sont discutés pour les types des LSP différents: bino, wino et Higgsino. Enfin, les résultats de l'analyse 0-lepton seule sont décrits et expliqués, à la fois pour les masses des sparticules et pour les valeurs des paramètres du pMSSM, puisque l'analyse 0-lepton est la seule qui permet de mettre des limites en se basant sur une procédure statistique bien définie. / This thesis has been performed in the context of the search for supersymmetry (SUSY) with the 20.3 fb^{-1} of LHC proton-proton collision data collected with the ATLAS detector at $sqrt{s}$ = 8 TeV. If SUSY is present in nature, squarks (partners of quarks) and gluinos (partners of gluons) are expected to be produced copiously at this energy, leading to events which main signature is no electron nor muon, a large number of jets and missing transverse energy (from the production of the lightest supersymmetric particle (LSP) leaving the detector unseen) denoted the 0-lepton analysis. The first part of the work presented in this thesis concentrates on the definition of Validation Regions used in the final fitting procedure to better assess the background coming from W-boson and top quark decays to tau leptons. From this fit, and since no excess has been observed, upper limits on various supersymmetric particles production have been derived within simplified models or SUSY models with low number of parameters. The exclusion limits at the 95% confidence level on the mass of the gluino has been set to 1330 GeV for a simplified model incorporating only a gluino and the (massless) lightest neutralino. In the mSUGRA/CMSSM models with $tanbeta=30$, $A_0=-2m_0$ and $mu>0$, squarks and gluinos of equal mass have been excluded for masses below 1700 GeV. A possible addition of a veto on the events containing tau leptons was also explored by assessing its impact on the exclusion reach of the analysis.The second part of this thesis has been done under the 19 parameters phenomenological Minimal Supersymmetric Standard Model (pMSSM) interpretation which not only uses the results of the above mentioned 0-lepton analysis but also other ATLAS searches results. The choice of the parameters and their range of exploration has been done on the basis of non-SUSY experimental results such as the rare B-decays, the mass of the SM Higgs boson, the limits from direct DM searches and the upper limit on the cold dark matter energy density of the Universe. The contribution of this thesis starts with the validation of the event selection at the truth and reconstructed levels. Knowing that this is the most constraining ATLAS analysis in the pMSSM parameter space, those checks have been performed with particular care. The constraints obtained with all the analyses on the various sparticle masses are described afterwards, concentrating on squarks, gluinos and neutralinos. The results are discussed for the different natures of the LSP: bino, wino and higgsino. Finally the 0-lepton-only results are described and further explained, first on sparticle mass planes and later on the pMSSM parameters, since only the 0-lepton analysis leads to a well defined statistical procedure that allows to derive properly all those results.

Supersymmetry is an attractive extension of the Standard Model (SM) of particle physics. The minimal supersymmetric extension (MSSM) provides gauge coupling unification, a dark matter candidate particle and can explain the breaking of the electroweak symmetry dynamically. However, it suffers from the little hierarchy and the mu-problem. Non-minimal supersymmetric extensions of the SM with a larger particle content or a higher symmetry can evade the problems of the MSSM. Such models may be well-motivated by Grand Unified Theories (GUTs) and can provide a rich new phenomenology with an extended Higgs sector, exotic particles, additional interactions and a close connection to String Theory. Interesting examples are the Next-to Minimal Supersymmetric Standard Model (NMSSM), which is motivated by the mu-problem, and the Exceptional Supersymmetric Standard Model (E6SSM), which is inspired by E6 GUTs. For phenomenological investigations of supersymmetric (SUSY) models the pole mass spectrum must be calculated from the fundamental model parameters. This task, however, is non-trivial as the spectrum must be consistent with measured low-energy observables (fine-structure constant, Z boson pole mass, muon decay etc.) as well as electroweak symmetry breaking and potential universality conditions on the soft supersymmetry breaking parameters at the GUT scale. Programs, which calculate the SUSY mass spectrum consistent with constraints of this kind are called spectrum generators. In this thesis four different contributions to the prediction of mass spectra and model parameters in non-minimal SUSY models are presented. (i) One-loop matching corrections of the E6SSM gauge and Yukawa couplings to the SM are calculated to increase the precision of the mass spectrum prediction in the constrained E6SSM. (ii) The beta-functions of vacuum expectation values (VEVs) are calculated in a general and supersymmetric gauge theory at the one- and two-loop level. The results enable an accurate calculation of the renormalization group running of the VEVs in non-minimal SUSY models. (iii) An NMSSM extension of Softsusy, a spectrum generator for the MSSM, is implemented. It represents a precise alternative to the already existing spectrum generator NMSPEC. (iv) FlexibleSUSY is presented, a general framework which creates a fast, modular and precise spectrum generator for any user-defined SUSY model. It represents a generalization of the hand-written SUSY spectrum generators and allows the study of a large variety of new SUSY models easily with high precision.

Uncertainties in radiative effects of the quarks in -background in the form of final state radiation (FSR) are significant when it comes to reducing all forms of systematics that can arise from measuring the jets energy. Analysis on FSR is in general conducted on different simulated samples where one has included the radiative effect using algorithms such as PYTHIA[29]. The hypothesis is that through the re-weighting of the -background nominal sample one could add a better representation of the FSR effect. Finding a simple way to include a better description of FSR would not only save time in the simulation process but it would also be a way to reduce the systematic errors originating from limited MC statistics. Due to statistical effects coming from the simulations one cannot use the basic approach to define the effect of FSR as simply the difference between nominal and FSR. Two methods are tested to estimate the FSR effects; the first method uses a set of efficiency factors to represent the signal regions, the second method is to add a weight to the events of the nominal sample. The first method show positive results, especially in SR2, compared to a basic analysis, with an uncertainty of the FSR effect of: SR1:±29% SR2: ±51% SR3: ±37%. While a basic analysis gave an uncertainty of ±42%, ±122% and 36%. The second method shows positive signs where the re-weighted sample moves closer to the behaviour of the FSR sample. However, both methods are based on insufficient amount of statistics to draw any absolute conclusions.

The Large Hadron Collider (LHC) located at the European Organization for Nuclear Research (CERN) is the most powerful particle accelerator in the world in terms of collision energy and luminosity. This thesis presents a search for supersymmetric particles in proton-proton collision data recorded by the ATLAS experiment. A search for direct production of chargino and slepton pairs in a final state characterised by the presence of two leptons and missing transverse momentum is presented. This analysis is done using L = 20 fb-1 proton-proton collisions at √s = 8 TeV collected in 2012. No significant excess over background is observed. Exclusion limits at 95% confidence level on chargino, neutralino and slepton production are set. In 2011-12 the LHC was providing collisions every 50 ns. This puts very strong requirements on the energy measurement in presence of energy deposits from different collisions in the same read-out window and in the same calorimeter channel (pile-up). A quality factor computed offline for each collision and for each channel in the ATLAS Tile Calorimeter (TileCal) is studied. It is shown that the quality factor can be used to select channels that need a special treatment to account for large energy deposition from pile-up. Efficient criteria to detect pile-up in TileCal channels are proposed.

The introduction of supersymmetry has led to great progress in the study of quantum field theories. Notably, with supersymmetry, properties of a quantum field theory can be computed with higher precision than what would otherwise be possible. In this project, we investigate supersymmetry in the context of quantum mechanics. In particular, we show how the Witten index is insensitive to the details of the supersymmetric quantum mechanical system, making it a robust quantity when considering variations in the system’s parameters. Explicit calculations of the supersymmetric ground states are carried out to identify what determines the Witten index. The concept of superpotential is introduced and we relate Morse theory to the Witten index by identifying the superpotential as a Morse function. Moreover, we consider supersymmetric quantum mechanics on compact orientable Riemann manifolds. We show how the structure of supersymmetric quantum mechanics has a close connection to topological properties of the target manifolds. Specifically, the Witten index is shown to be the Euler characteristic, a topological invariant.

research submitted to the Faculty of Science, University of the Witwatersrand, in ful llment for the degree of Master of Science in Physics / Supersymmetry plays a main role in all current thinking about superstring theory. Indeed, many remarkable properties of string theory have been explained using supersymmetry as a tool. In this dissertation, we review the basics formulation of supersymmetric quantum mechanics starting with introducing the concepts of supercharges and superalgebra. We show that, if there is a supersymmetric state, it is the zero-energy ground state. If such a state exists, the supersymmetry is unbroken otherwise it is broken. So far, there has been no unbroken supersymmetry observed in nature, and if nature is described by supersymmetry, it must be broken. In fact, supersymmetry may be broken spontaneously at any order of perturbation theory, or dynamically due to non-perturbative e ects. The goal of this dissertation is to study the methods of supersymmetry breaking. For this purpose, a special attention is given to discuss the normalization of the ground state of the supersymmetric harmonic oscillator. Then we explain that perturbation theory gives us incorrect results for both the ground state wave function as well as the energy spectrum and it fails to give an explanation to the supersymmetry breaking. Later in the dissertation, a review of the uses of instantons in quantum mechanics is given. In particular, instantons are used to compute the tunneling e ects within the path integral approach to quantum mechanics. As a result, we give evidence that the instantons, which are a non-perturbative e ect in quantum mechanics and can not be seen in perturbation theory, leads to calculate the corrections to the ground state energy and provides a possible explanation for the supersymmetry breaking. / E.K. 2019

Symmetry plays a crucial role in exploring the laws of nature. By exploiting some of the underlying analogies between the mathematical formalism of quantum mechanics and that of electrodynamics, in this dissertation we show that optics can provide a fertile ground for studying, observing, and utilizing some of the peculiar symmetries that are currently out of reach in other areas of physics. In particular, in this work, we investigate two important classes of symmetries, parity-time symmetry (PT) and supersymmetry (SUSY), within the context of classical optics. The presence of PT symmetry can lead to entirely real spectra in non-Hermitian systems. In optics, PT-symmetric structures involving balanced regions of gain and loss exhibit intriguing properties which are otherwise unattainable in traditional Hermitian systems. We show that selective PT symmetry breaking offers a new method for achieving single mode operation in laser cavities. Other interesting phenomena also arise in connection with PT periodic structures. Along these lines, we introduce a new class of optical lattices, the so called mesh lattices. Such arrays provide an ideal platform for observing a range of PT-related phenomena. We show that defect sates and solitons exist in such periodic environments exhibiting unusual behavior. We also investigate the scattering properties of PT-symmetric particles and we show that such structures can deflect light in a controllable manner. In the second part of this dissertation, we introduce the concept of supersymmetric optics. In this regard, we show that any optical structure can be paired with a superpartner with similar guided wave and scattering properties. As a result, the guided mode spectra of these optical waveguide systems can be judiciously engineered so as to realize new families of mode filters and mode division multiplexers and demultiplexers. We also present the first experimental demonstration of light dynamics in SUSY ladders of photonic lattices. In addition a new type of transformation optics based on supersymmetry is also explored. Finally, using the SUSY formalism in non-Hermitian settings, we identify more general families of complex optical potentials with real spectra.