Weak-scale supersymmetry is one of the most favoured theories beyond the Standard Model of particle physics that elegantly solves various theoretical and observational problems in both particle physics and cosmology. In this thesis, I describe the theoretical foundations of supersymmetry, issues that it can address and concrete supersymmetric models that are widely used in phenomenological studies. I discuss how the predictions of supersymmetric models may be compared with observational data from both colliders and cosmology. I show why constraints on supersymmetric parameters by direct and indirect searches of particle dark matter are of particular interest in this respect. Gamma-ray observations of astrophysical sources, in particular dwarf spheroidal galaxies, by the Fermi satellite, and recording nuclear recoil events and energies by future ton-scale direct detection experiments are shown to provide powerful tools in searches for supersymmetric dark matter and estimating supersymmetric parameters. I discuss some major statistical issues in supersymmetric global fits to experimental data. In particular, I further demonstrate that existing advanced scanning techniques may fail in correctly mapping the statistical properties of the parameter spaces even for the simplest supersymmetric models. Complementary scanning methods based on Genetic Algorithms are proposed. / At the time of the doctoral defense, the following paper was unpublished and had a status as follows: Paper 4: Submitted.

Cette thèse présente la recherche de nouvelle physique avec un état final contenant un seul photon et de l'énergie transverse manquante. On recherche la matière sombre (ou noire) et la signature de particules supersymétriques. L'analyse des données collectées par le détecteur ATLAS au LHC, issues de collisions proton-proton dont l'énergie dans le centre de masse est de 8 TeV, est faite avec une luminosité intégrée de 20.3fb−1. L'accord entre les données mesurées et les prédictions du modèle standard permet d'établir une limite sur la section effi- cace de production mesurable. Cette limite est observée à la valeur de 3.64 fb à 95% de niveau de confiance.Dans cette thèse, la limite expérimentale obtenue est également interprétée comme une limite dans l'espace des paramètres de deux nouveaux modèles.Le premier est basé sur une théorie des champs effective qui s'inspire des résultats du satellite Fermi-LAT. Dans ce modèle, les particules de matière sombre se couplent aux pho- tons par une interaction de contact. Les limites sur l'échelle de masse effective sont établies et dépendent d'un postulat sur les constantes de couplage. Elles contraignent l'espace des paramètres qui est compatible avec les résultats de Fermi-LAT.Le second est un modèle supersymétrique simplifié décrivant la production de paires de squarks se désintégrant en un quark et un neutralino. Dans ce cas, le photon est émis soit dans l'état initial soit dans l'état final. De plus, le spectre en masse est compressé, i.e. que la différence de masse entre les squarks et les neutralinos est supposée petite. Les limites sont établies sur la section efficace de production. Ces limites montrent une exclusion sur la masse des squarks jusqu'à 250 GeV dans la région la plus compressée de l'espace des paramètres. Le photon pouvant être émis par le squark intermédiaire, cet état final pourrait permettre de déterminer la charge du squark.Enfin, une étude préliminaire prospective à l'énergie de collision de 13 TeV a égale- ment été menée. Elle montre qu'avec 5fb−1 de données seulement, les limites peuvent être améliorées de 10%. / This thesis presents the search for new physics in the final state containing a single photon and missing transverse momentum. The analysis is performed on 20.3fb−1 of proton-proton collisions data at a center-of-mass energy of 8 TeV collected by the ATLAS detector at the Large Hadron Collider. Given the good agreement of the data with the Standard Model pre- diction of such events, an upper limit to the visible cross section produced by new physics is derived. The observed limit at 95% confidence level is 3.64 fb.In this thesis, the results are also interpreted as limits in the parameter space of two new physics models. The first model is an effective field theory, inspired by Fermi-LAT results, in which dark matter particles couple to photons via a contact interaction vertex. Limits are set on the effective mass scale and depend on the postulated coupling constants. The limits set in this dark matter model provide an effective constraint in the parameter space of the theory compatible with the Fermi-LAT results. The second one is a simplified supersymmetric model describing squark pair production with their subsequent decay into a quark and a neutralino. The photon is emitted as initial or final state radiation and the spectrum is compressed, i.e. the mass difference between the squark and the neutralino is assumed to be small. Limits are set on the production cross-section; squark masses are excluded up to 250 GeV in the very compressed region. As the photon can be irradiated from the intermediate squark, this final state would eventually provide the possibility to probe the charge of the squark.A preliminary study has also been carried out to show the search sensitivity with 13 TeV data, which indicate that the limits presented in this thesis can already be improved by 10% with 5fb−1.

Le Modèle Standard, qui décrit les interactions entre les particules à l’échelle quantique, est une théorie imparfaite. Il possède plusieurs problèmes théoriques non-résolus et ne permet pas d’expliquer certaines observations astrophysiques comme celles de la matière noire et de l’asymétrie baryonique. Plusieurs théories, dites au-delà du Modèle Standard, ont été proposées afin de résoudre certains de ces problèmes, et une grande partie d’entre elles prévoient l’apparition de nouveaux phénomènes à haute énergie. L’objectif principal de cette thèse est de rechercher ces phénomènes dans les collisions proton-proton produites par le Large Hadron Collider à une énergie de centre de masse de 13 TeV. Une partie des travaux présentés dans cette thèse a en particulier été dédiée à la recherche de processus de production de quarks top de même signe, c’est-à-dire de même charge électrique, qui sont prédits par des modèles de supersymétrie à R-parité violée. Ces processus engendrent des évènements composés de leptons de même charge accompagnés de b-jets, lesquels ont l’avantage d’être faiblement contaminer par le bruit de fond provenant du Modèle Standard.Les travaux présentés dans cette thèse ont essentiellement porté sur deux analyses, chacune recherchant des phénomènes de nouvelle physique de nature différente dans les évènements composés de leptons de même charge dans les données enregistrées par le détecteur ATLAS. Une première analyse a porté sur la recherche de processus supersymétriques sur les données enregistrées en 2015 et en 2016 avec 36.1 fb$^{-1}$ de luminosité intégrée. Des signaux de production de quarks top de même signe ont été implémentés en se basant sur des processus supersymétriques violant la R-parité, et des régions de signal associées à ces processus ont été optimisées. Une deuxième analyse a porté sur la recherche de processus non-supersymétriques, dits exotiques, dans les données enregistrées en 2015 avec 3.2 fb$^{-1}$ de luminosité intégrée. Cette analyse a surtout été motivée par les résultats obtenus à 8 TeV, dans lesquels un modeste excès de nombre d’évènements par rapport aux prédictions du Modèle Standard a été observé dans deux régions de signal. Une partie des études relatives à cette analyse a été dédiée au développement et à la validation des méthodes d’estimation des différentes sources de bruit de fond.Aucune déviation par rapport aux prédictions du Modèle Standard n’a été observée dans chacune des régions de signal considérées dans les deux analyses. L’excès qui avait été observé dans les résultats obtenus à 8 TeV n’est donc pas confirmé. Des limites d’exclusion sur les modèles de nouvelle physique ont de plus été extraites à partir des résultats obtenus, en particulier sur les modèles de supersymétrie à R-parité violée utilisés pour produire les processus de production de quarks top de même signe. / The Standard Model, which describes the particle interactions at quantum level, is an imperfect theory. It has several theoretical problems and is unable to explain astrophysical observations like the dark matter and the baryonic asymmetry of the universe. Several beyond-standard models have been proposed to solve some of these issues, and predict new-physics phenomena at high energy. The aim of this thesis is to search for these phenomena in proton-proton collisions produced by the Large Hadron Collider at a center-of-mass energy of 13 TeV. Part of the studies presented in this thesis was dedicated to the search for production of same-sign top quarks based on R-parity violating supersymmetric models. These processes lead to a signature of same-sign leptons and b-jets, which have the advantage to be lowly contaminated by the Standard Model background.The studies presented in this thesis focused on two analyses, both searching for new-physics phenomena of different nature in same-sign leptons events in data recorded by the ATLAS detector. A first analysis focused on supersymmetric processes with data recorded in 2015 and in 2016 with 36.1 fb$^{-1}$ of integrated luminosity. Same-sign top quarks signals were implemented using R-parity violating supersymmetric processes, and signal regions associated to these processes were optimized. A second analysis focused on exotic (non-supersymmetric) processes with data recorded in 2015 with 3.2 fb$^{-1}$ of integrated luminosity. This analysis was motivated by a modest excess seen in two signal regions in the 8 TeV results. Several studies were focused on the development and the validation of background estimation methods.No deviations from the Standard Model predictions were observed the signal regions considered in both analyses. The 8 TeV excess is therefore not confirmed with the most recent data. Exclusion limits on new-physics models were extracted, in particular for the R-parity violating supersymmetric models that were used to produce the same-sign top quarks processes.

Le Modèle Standard Supersymétrique Minimal (MSSM), le plus étudié des modèles de Nouvelle Physique, contient un candidat à la matière noire : le neutralino. Un des mécanismes qui permet de réduire la densité relique de neutralino jusqu'à l'intervalle expérimental de WMAP et de Planck est la coannihilation entre le neutralino et le stop. Dans cette thèse nous étudions deux aspects différents liés à la prédiction de la densité relique dans la région de coannihilation neutralino-stop, ainsi qu'au calcul des sections efficaces d'annihilation et de coannihilation correspondantes. Nous présentons tout d'abord la matière noire en tant que WIMP ainsi que le Modèle Standard de la Physique des Particules, puis nous abordons le MSSM ainsi la phénoménologie de la densité relique de neutralino. Nous étudions ensuite la phénoménologie de la violation de saveur non minimale dans le secteur des squarks dans le contexte de la densité relique de neutralino. Nous considérons des termes violant la saveur dans le secteur des squarks up et down de chiralité droite et de troisième génération et montrons qu'ils peuvent avoir un impact important sur les sections efficaces d'annihilation et de coannihilation du neutralino, et en conséquence sur la densité relique. Finalement, nous nous intéressons à la possibilité d'améliorer la précision avec laquelle la densité relique est prédite, en calculant les sections efficaces d'annihilation et de coannihilation à l'ordre supérieur dans la théorie des perturbation. En se basant sur des travaux antérieurs qui ont montré que l'impact des corrections SUSY-QCD à une boucle pour l'annihilation de neutralino était supérieur à l'incertitude expérimentale, nous avons calculé de telles corrections dans le cas de la coannihilaiton neutralino-stop en bosons de jauge électrofaibles et bosons de Higgs. / The Minimal Supersymmetric Standard Model (MSSM), the most famous model of Physics beyond the Standard Model, provides a good dark matter candidate: the neutralino. One of the mechanisms which can reduce the predicted relic density of neutralino to the experimental range of WMAP and Planck is the coannihilation between the neutralino and the stop. In this thesis, we study two different aspects related to the prediction of the relic density in the neutralino-stop coannihilation region and the calculation of the corresponding annihilation and coannihilation cross sections. We first make short reviews of WIMP dark matter and the Standard Model of particle Physics, introduce the MSSM and discuss the phenomenology of neutralino relic density. We then study the phenomenology of Non Minimal Flavor Violation in the squark sector in the context of neutralino relic density. We consider flavor violating terms in the sectors of right handed third generation up and down squarks and show that they can have an important impact on the thermally averaged (co)annihilation cross section of the neutralino, and therefore on its relic density. Finally, we focus on the issue of improving the precision with which the relic density is calculated, by computing (co)annihilation cross sections at Next-to-Leading Order. Following earlier work in the calculation of one-loop SUSY-QCD corrections to the annihilation of neutralinos, which have shown that the impact of such corrections was larger than the experimental uncertainty, we have calculated similar corrections for the neutralino-stop coannihilation into electroweak gauge and Higgs bosons.

L'expérience CMS (Compact Muon Solenoid), construite sur l'anneau du LHC (Large Hadron Collider), enregistre des données provenant des collisions proton-proton depuis 2 ans. L'alignement entre toutes les couches du trajectographe, sous-détecteur de CMS permettant la reconstruction et la mesure de l'impulstion des particules chargées, est effectué à l'aide de traces de particules créées lors de la collision et des traces créées par le passage de muons d'origine cosmique à travers ce détecteur. La première partie de ce livre sera dédiée à la reconstruction des traces de ces muons lors des collisions. Une nouvelle méthode, appelée reconstruction cosmique régionale, a été développée et mise en place. L'efficacité de 69% et le taux de faux de l'ordre de 1% permettent l'utilisation de ces traces pour l'alignement. La deuxième partie, portant sur l'analyse des données de collision, s'intéressera à la recherche de particules prédites par un modèle d'extension du Modèle Standard, la Supersymétrie, dans un scénario particulier, le scénario du Stop Léger. Dans le cas d'un fort mélange dans la troisième génération de squarks, le stop, partenaire supersymétrique du quark top, peut être léger. Dans l'analyse effectuée au cours de cette thèse, nous nous sommes intéressés au cas au mstop < mtop. Dans le MSSM avec conservation de la R-parité, le gluino serait formé par paire et se désintégrerait en un squark stop et un quark top. Le stop se désintégrerait quant-à-lui en un quark c et un neutralino, particule supersymétrique la plus légère du modèle, stable et interagissant faiblement. Aucun excès par rapport aux prédictions du Modèle Standard n'a été relevé en utilisant les 40pb-1 de données enregistrées par CMS en 2010. Les limites obtenues à 95% de niveau de confiance permettent d'exclure des masses de stop jusqu'à 175 GeV pour des masses de gluinos allant jusqu'à 350 GeV et des faibles différences de masses entre le stop et le neutralino / The CMS experiment (Compact Muon Solenoid), built on the ring of the LHC (Large Hadron Collider), is recording data from proton-proton collisions for 2 years now. The alignment between all layers of the tracker, the sub-detector of CMS allowing the reconstruction and the measurement of the momentum of charged particles, is made by using tracks of particles created during collisions and tracks created by the passage of cosmic muons through this sub-detector. A first part of the presentation will be dedicated to the reconstruction of the tracks of these cosmic muons during collisions. A new method, called regional cosmic reconstruction, was developed and implemented. The 69 % efficiency and the fake rate around 1 % allow to use these tracks for the alignment. The second part, dedicated to the analysis of collision data, will concern the search of particles predicted by a model of extension of the Standard Model, the Supersymmetry, in a particular scenario, the light Stop scenario. In the case of a strong mixing in the third generation of squarks, the stop, supersymmetric partner of the top quark, could be light. In the analysis developped during this thesis, we were interested in the case where the mstop < mtop. In the MSSM with R-parity conservation, the gluino would be created by pair and would decay in a stop squark and a top quark. Stop would decays in a c quark and a neutralino, the lightest supereymmetric particle of the model, stable and interacting weakly. No excess with regards to Standard Model predictions was observed in 40pb-1 of data recorded by CMS in 2010. The limits obtained at 95 % confidence level allow to exclude masses of stop until 175 GeV for masses of gluinos going up to 350 GeV and low differences of masses between stop and neutralino

Centro Latino-Americano de Física / Os processos estocásticos com ruído branco multiplicativo são objeto de atenção constante em uma grande área da pesquisa científica. A variedade de prescrições possíveis para definir matematicamente estes processos oferece um obstáculo ao desenvolvimento de ferramentas gerais para seu tratamento. Na presente tese, estudamos propriedades de equilíbrio de processos markovianos com ruído branco multiplicativo. Para conseguirmos isto, definimos uma transformação de reversão temporal de tais processos levando em conta que a distribuição estacionária de probabilidade depende da prescrição. Deduzimos um formalismo funcional visando obter o funcional gerador das funções de correlação e resposta de um processo estocástico multiplicativo representado por uma equação de Langevin. Ao representar o processo estocástico neste formalismo (de Grassmann) funcional eludimos a necessidade de fixar uma prescrição particular. Neste contexto, analisamos as propriedades de equilíbrio e estudamos as simetrias ocultas do processo. Mostramos que, usando uma definição apropriada da distribuição de equilíbrio e considerando a transformação de reversão temporal adequada, as propriedades usuais de equilíbrio são satisfeitas para qualquer prescrição. Finalmente, apresentamos uma dedução detalhada da formulação supersimétrica covariante de um processo markoviano com ruído branco multiplicativo e estudamos algumas das relações impostas pelas funções de correlação através das identidades de Ward-Takahashi. / Multiplicativewhite-noise stochastic processes continuously attract the attention of a wide area of scientific research. The variety of prescriptions available to define it difficults the development of general tools for its characterization. In this thesis, we study equilibrium properties of Markovian multiplicative white-noise processes. For this, we define the time reversal transformation for this kind of processes, taking into account that the asymptotic stationary probability distribution depends on the prescription. We deduce a functional formalism to derive a generating functional for correlation and response functions of a multiplicative stochastic process represented by a Langevin equation. Representing the stochastic process in this functional (Grassmann) formalism, we avoid the necessity of fixing a particular prescription. In this framework, we analyze equilibrium properties and study hidden symmetries of the process. We show that, using a careful definition of equilibrium distribution and taking into account the appropriate time reversal transformation, usual equilibrium properties are satisfied for any prescription. Finally, we present a detailed deduction of a covariant supersymmetric formulation of a multiplicativeMarkovian white-noise process and study some of the constraints it imposes on correlation functions using Ward-Takahashi identities.

Submitted by Maike Costa (maiksebas@gmail.com) on 2016-03-15T12:00:51Z No. of bitstreams: 1 arquivototal.pdf: 537788 bytes, checksum: f4d2088488947fc0f778709eac62f92b (MD5) / Made available in DSpace on 2016-03-15T12:00:51Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 537788 bytes, checksum: f4d2088488947fc0f778709eac62f92b (MD5) Previous issue date: 2015-07-31 / Conselho Nacional de Pesquisa e Desenvolvimento Científico e Tecnológico - CNPq / Supersymmetry is a very useful tool for extending the Standard Model up to the grand unification scale, studying electoweak symmetry breaking and providing dark matter candidates. The presence of superpartners solves the problem of divergences, and changes the renormalization group equations in a way that allows gauge coupling unification. In a global supersymmetry the breaking scale is proportional to the vacuum energy, which makes it incompatible with the low value of the cosmological constant. Promoting SUSY to a local symmetry results in supergravity, which mandates existence of a spin-2 gravitational field, naturally integrates General Relativity and particle physics, and is required to adjust the potential and obtain a high breaking scale with low cosmological constant. This review work looks into models based on gravity-mediated supersymmetry breaking. These models allow a simpler hidden sector than their gauge-mediated or anomay-mediated counterparts. And the lightest supersymmetric particles, higgsino-like, could be detected once an electron-positron collider such as ILC is ready. / A supersimetria ´e uma ferramenta muito ´util para estender o Modelo Padr˜ao at´e a escala de grande unifica¸c˜ao, para estudar a quebra de simetria eletrofraca e prover candidatos a mat´eria escura. A presen¸ca dos superparceiros resolve o problema das divergˆencias, e altera as equa¸c˜oes do grupo de renormaliza¸c˜ao de modo a permitir a unifica¸c˜ao dos acoplamentos de gauge. A escala de quebra de uma supersimetria global ´e proporcional `a energia do v´acuo, o que a tornaria incompat´ıvel com o baixo valor da constante cosmol´ogica. A promo¸c˜ao de SUSY a uma simetria local resulta na supergravidade, que obriga a existˆencia do campo gravitacional com spin-2, integra naturalmente a Relatividade Geral e a f´ısica de part´ıculas, e ´e necess´aria para ajustar o potencial e obter alta escala de quebra com constante cosmol´ogica baixa. Este trabalho de revis˜ao aborda modelos baseados na quebra de supersimetria mediada por gravita¸c˜ao. Estes modelos aceitam um setor oculto mais simples que os modelos concorrentes mediados por gauge ou por anomalias. E as part´ıculas supersim´etricas mais leves, do tipo higgsino, podem ser detectadas quando um colisor el´etron-p´ositron como o ILC estiver pronto.

Submitted by Vasti Diniz (vastijpa@hotmail.com) on 2017-09-13T13:01:16Z No. of bitstreams: 1 arquivototal.pdf: 7899614 bytes, checksum: f001983854e55609b8ccfb1ce80578f2 (MD5) / Made available in DSpace on 2017-09-13T13:01:16Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 7899614 bytes, checksum: f001983854e55609b8ccfb1ce80578f2 (MD5) Previous issue date: 2015-02-27 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / One of the main problems that permeates the Particle Physics and Cosmology is the Dark Matter (DM), which makes up about 26% of the energy content of the Universe. The main evidence pointing to its existence provides us with important features, such as being neutral, stable (with lifetime over the age of the Universe), cold or warm, weakly interacting with Particle Physics Standard Model (SM) particles and sufficiently abundant. The SM does not provide a candidate who meets these characteristics and hence it is necessary to extend it. One of the most sophisticated extensions of the SM is the Supersymmetry, that in addition to solving the problem of DM, explains other unsolved puzzles that are present in SM, among them, the hierarchy and the unification of the gauge couplings. This model implies the inclusion of a new symmetry that puts bosons and fermions in equal footing. The minimal supersymmetric version of the SM is the Minimal Supersymmetric Standard Model (MSSM), whose viable candidate is the neutralino, which is a fermion composed of superpartners of neutral Higgs and gauge bosons. In this work, we performed the neutralino analysis as DM candidate in CMSSM or mSUGRA scenario, which contains 5 free parameters, M0, M1/2, tan , sign(μ) and A0, for two different analyzes. In the first one we varied the M0 and M1/2 parameters for three different values of tan while in the second and third one we varied all parameters except the sign(μ). In this study, we use some computational tools, including, SARAH, SPheno, SSP and Micromegas, in order to obtain DM Relic Abundance and DM scattering cross section in this scenario. We compared our results with the most recent experimental data, namely, we have used Planck satellite data for the relic abundance, LUX and XENON1T (prospect) for the spin-independent scattering cross section and XENON100 for the spin dependent one. We finally analyzed the implications concerning the viability of the MSSM under the light of the DM problem. / Um dos principais problemas que permeia a Física de Partículas e Cosmologia é a Matéria Escura (ME), que compõe cerca de 26% do conteúdo energético do Universo. As principais evidências que apontam para a sua existência nos fornecem importantes características, tais como, ser neutra, estável (com tempo de vida maior que a idade do Universo), fria ou morna, pouco interagente com partículas do Modelo Padrão de Física de Partículas (MP)e suficientemente abundante. O MP não fornece um candidato que supre estas características, sendo necessário estendê-lo. Uma das mais sofisticadas extensões do MP é a Supersimetria, que além de resolver o problema da ME, soluciona outros que estão presentes no MP, dentre eles, a hierarquia e a unificação dos acoplamentos de gauge. Tal modelo implica na inclusão de uma nova simetria que coloca bósons e férmions em pé de igualdade. A versão mínima supersimétrica do MP é o Modelo Padrão Supersimétrico Mínimo (MSSM), cujo candidato viável à ME é o neutralino, que se trata de um férmion composto pelos superparceiros dos bósons de gauge e Higgs neutros. Neste trabalho, fizemos uma análise do neutralino como candidato à ME no cenário CMSSM ou mSUGRA, que contém 5 parâmetros livres, M0, M1/2, tan , sinal(μ) e A0, para três análises distintas. Na primeira variamos apenas os parâmetros M0 e M1/2 para três valores distintos da tan e na segunda e terceira variamos todos os parâmetros com exceção do sinal(μ). Neste estudo, utilizamos algumas ferramentas computacionais, entre as quais, SARAH, SPheno, SSP e micrOMEGAs, no intuito de obter abundância e seção de choque de espalhamento de ME neste cenário. Obtidos os gráficos, comparamos com os resultados experimentais mais recentes, para a abundância utilizamos dados do satélite Planck, para a seção de choque de espalhamento independente de spin, o LUX e XENON1T (2017) e para dependente de spin, XENON100 e verificamos suas implicações na viabilidade do modelo.

Centro Latino-Americano de Física / Os processos estocásticos com ruído branco multiplicativo são objeto de atenção constante em uma grande área da pesquisa científica. A variedade de prescrições possíveis para definir matematicamente estes processos oferece um obstáculo ao desenvolvimento de ferramentas gerais para seu tratamento. Na presente tese, estudamos propriedades de equilíbrio de processos markovianos com ruído branco multiplicativo. Para conseguirmos isto, definimos uma transformação de reversão temporal de tais processos levando em conta que a distribuição estacionária de probabilidade depende da prescrição. Deduzimos um formalismo funcional visando obter o funcional gerador das funções de correlação e resposta de um processo estocástico multiplicativo representado por uma equação de Langevin. Ao representar o processo estocástico neste formalismo (de Grassmann) funcional eludimos a necessidade de fixar uma prescrição particular. Neste contexto, analisamos as propriedades de equilíbrio e estudamos as simetrias ocultas do processo. Mostramos que, usando uma definição apropriada da distribuição de equilíbrio e considerando a transformação de reversão temporal adequada, as propriedades usuais de equilíbrio são satisfeitas para qualquer prescrição. Finalmente, apresentamos uma dedução detalhada da formulação supersimétrica covariante de um processo markoviano com ruído branco multiplicativo e estudamos algumas das relações impostas pelas funções de correlação através das identidades de Ward-Takahashi. / Multiplicativewhite-noise stochastic processes continuously attract the attention of a wide area of scientific research. The variety of prescriptions available to define it difficults the development of general tools for its characterization. In this thesis, we study equilibrium properties of Markovian multiplicative white-noise processes. For this, we define the time reversal transformation for this kind of processes, taking into account that the asymptotic stationary probability distribution depends on the prescription. We deduce a functional formalism to derive a generating functional for correlation and response functions of a multiplicative stochastic process represented by a Langevin equation. Representing the stochastic process in this functional (Grassmann) formalism, we avoid the necessity of fixing a particular prescription. In this framework, we analyze equilibrium properties and study hidden symmetries of the process. We show that, using a careful definition of equilibrium distribution and taking into account the appropriate time reversal transformation, usual equilibrium properties are satisfied for any prescription. Finally, we present a detailed deduction of a covariant supersymmetric formulation of a multiplicativeMarkovian white-noise process and study some of the constraints it imposes on correlation functions using Ward-Takahashi identities.

Une très grande effervescence secoue le monde de la physique des particules depuis le lancement du grand collisionneur de hadrons (LHC) au CERN. Cette énorme machine capable de faire se collisionner des protons à des énergies égales à 14 TeV promet de lever le voile sur la physique régissant les interactions à ces échelles d’énergies. Ces résultats sont d’autant plus attendus que l’on a acquis la certitude que le Modèle Standard de la physique des particules est incomplet et devrait, en fait, être interprété comme la théorie effective d’une théorie plus fondamentale. Toutefois, depuis le lancement des expériences au LHC avec des énergies de 7 puis de 8 TeV aucun signe de nouvelle physique n’a été découvert. Par contre, un énorme bond en avant a été franchi avec la découverte d’une particule scalaire de masse égale à 125 GeV et dont les propriétés sont relativement proches de celles du boson de Higgs telles que prédites par le Modèle Standard. C’est dans ce contexte de forte émulation internationale que mon travail de thèse s’est inscrit. Dans un premier temps, nous avons voulu explorer la phénoménologie associée au secteur des neutralinos et charginos du modèle supersymétrique symétrique gauche-droit. Cette étude peut être motivée par plusieurs raisons notamment le fait que leur caractère supersymétrique apporte une solution au problème dit de la hiérarchie mais implique aussi l’unification des constantes de jauge ainsi que l’explication de la matière noire. L’introduction de la symétrie entre les fermions gauchers et les fermions droitiers permet, quant à elle, d’expliquer naturellement, via le mécanisme dit de la balançoire, la petitesse de la masse des neutrinos mais aussi de répondre à plusieurs autres questions non solubles dans le cadre du Modèle Standard. Nous concentrant uniquement sur le secteur des charginos et neutralinos les plus légers, nous avons montré que ces modèles peuvent être facilement mis en évidence dans les évènements multi-leptoniques en ce sens que les signatures qu’ils induisent sont tr`es différentes comparées à celles du Modèle Standard et de sa version supersymétrique.[...] / The field of high-energy physics has been living a very exciting period of its history with the Large Hadron Collider (LHC) at CERN collecting data. Indeed, this enormous machine able to collide protons at a center of mass energy of 14 TeV promises to unveil the mystery around the physics at such energy scales. From the physicists side, the expectations are very strong as it isnowadays a certitude that the Standard Model of particle physics is incomplete and should, in fact, be interpreted as the effective theory of a more fundamental one. Unfortunately, the 7 and 8 TeV runs of the LHC did not provide any sign of new physics yet but there has been at least one major discovery in 2010, namely the discovery of a scalar particle with a mass of 125 GeV and whichproperties are very close to those of the Standard Model Higgs boson. Since then, many questions have come up as we now want to understand if it really is the Standard Model Higgs boson or if it exhibits any deviations. It is in this peculiar context that my research work was carried. In a first project, we, my supervisors, our collaborator and I, have wanted to explore thephenomenology associated with the neutralinos and charginos sector of the left-right symmetric supersymmetric model. Such an analysis can be motivated by several reasons such as the fact that the supersymmetric nature of these models provides a natural explanation for the infamous hierarchy problem, implies the unification of the gauge coupling constants at very high energy and provides a natural candidate for dark matter. In addition to these nice features, the left-right symmetry introduces a natural framework for explaining the smallness of neutrino masses but also helps in addressing several other unresolved issues in the Standard Model framework. Only focusing on the lightest charginos and neutralinos decaying into one or more light leptons, we have shown in our study that these models can be easily discovered in multi-leptonic final states as theylead to signatures very different from those induced by the Standard Model or its supersymmetric version.[...]