Cette thèse, conduite dans le contexte de la recherche du boson de Higgs, dernière pièce manquante du mécanisme de brisure de la symétrie électrofaible et qui est une des plus importantes recherches auprès des collisionneurs hadroniques actuels, traite de la phénoménologie de ce boson à la fois dans le Modèle Standard (SM) et dans son extension supersymétrique minimale (MSSM). Après un résumé de ce qui constitue le Modèle Standard dans une première partie, nous présenterons nos prédictions pour la section efficace inclusive de production du boson de Higgs dans ses principaux canaux de production auprès des deux collisionneurs hadroniques actuels que sont le Tevatron au Fermilab et le grand collisionneur de hadrons (LHC) au CERN, en commençant par le cas du Modèle Standard. Le principal résultat présenté est l'étude la plus exhaustive possible des différentes sources d'incertitudes théoriques qui pèsent sur le calcul : les incertitudes d'échelles vues comme une mesure de notre ignorance des termes d'ordre supérieur dans un calcul perturbatif à un ordre donné, les incertitudes reliées aux fonctions de distribution de partons dans le proton/l'anti--proton (PDF) ainsi que les incertitudes reliées à la valeur de la constante de couplage fort, et enfin les incertitudes provenant de l'utilisation d'une théorie effective qui simplifie le calcul des ordres supérieurs dans la section efficace de production. Dans un second temps nous étudierons les rapports de branchement de la désintégration du boson de Higgs en donnant ici aussi les incertitudes théoriques qui pèsent sur le calcul. Nous poursuivrons par la combinaison des sections efficaces de production avec le calcul portant sur la désintégration du boson de Higgs, pour un canal spécifique, montrant quelles en sont les conséquences intéressantes sur l'incertitude théorique totale. Ceci nous amènera à un résultat significatif de la thèse qui est la comparaison avec l'expérience et notamment les résultats des recherches du boson de Higgs au Tevatron. Nous irons ensuite au-delà du Modèle Standard dans une troisième partie où nous donnerons quelques ingrédients sur la supersymétrie et sa mise en application dans le MSSM où nous avons cinq bosons de Higgs, puis nous aborderons leur production et désintégration en se focalisant sur les deux canaux de production principaux par fusion de gluon et fusion de quarks $b$. Nous présenterons les résultats significatifs quant à la comparaison avec aussi bien le Tevatron que les résultats très récents d'ATLAS et CMS au LHC qui nous permettront d'analyser l'impact de ces incertitudes sur l'espace des paramètres du MSSM, sans oublier de mentionner quelques bruits de fond du signal des bosons de Higgs. Tout ceci va nous permettre de mettre en avant le deuxième résultat très important de la thèse, ouvrant une nouvelle voie de recherche pour le boson de Higgs standard au LHC. La dernière partie sera consacrée aux perspectives de ce travail et notamment donnera quelques résultats préliminaires dans le cadre d'une étude exclusive, d'un intérêt primordial pour les expérimentateurs. / This thesis has been conducted in the context of one of the utmost important searches at current hadron colliders, that is the search for the Higgs boson, the remnant of the electroweak symmetry breaking. We wish to study the phenomenology of the Higgs boson in both the Standard Model (SM) framework and its minimal Supersymmetric extension (MSSM). After a review of the Standard Model in a first part and of the key reasons and ingredients for the supersymmetry in general and the MSSM in particular in a third part, we will present the calculation of the inclusive production cross sections of the Higgs boson in the main channels at the two current hadron colliders that are the Fermilab Tevatron collider and the CERN Large Hadron Collider (LHC), starting by the SM case in the second part and presenting the MSSM results, where we have five Higgs bosons and focusing on the two main production channels that are the gluon gluon fusion and the bottom quarks fusion, in the fourth part. The main output of this calculation is the extensive study of the various theoretical uncertainties that affect the predictions: the scale uncertainties which probe our ignorance of the higher–order terms in a fixed order perturbative calculation, the parton distribution functions (PDF) uncertainties and its related uncertainties from the value of the strong coupling constant, and the uncertainties coming from the use of an effective field theory to simplify the hard calculation. We then move on to the study of the Higgs decay branching ratios which are also affected by diverse uncertainties. We will present the combination of the production cross sections and decay branching fractions in some specific cases which will show interesting consequences on the total theoretical uncertainties. We move on to present the results confronted to experiments and show that the theoretical uncertainties have a significant impact on the inferred limits either in the SM search for the Higgs boson or on the MSSM parameter space, including some assessments about SM backgrounds to the Higgs production and how they are affected by theoretical uncertainties. One significant result will also come out of the MSSM analysis and open a novel strategy search for the Standard Higgs boson at the LHC. We finally present in the last part some preliminary results of this study in the case of exclusive production which is of utmost interest for the experimentalists.

Covariant density functional theory (CDFT) is a modern theoretical tool for the description of nuclear structure physics. Here different physical properties of the ground and excited states in atomic nuclei have been investigated within the CDFT framework employing three major classes of the state-of-the-art covariant energy density functionals. The global performance of CEDFs for even-even nuclei are investigated and the systematic theoretical uncertainties are estimated within the set of four CEDFs in known regions of the nuclear chart and their propagation towards the neutron drip line. Large-scale axial relativistic Hartree-Bogoliubov (RHB) calculations are performed for even-even nuclei to calculate different ground state observabvles. The predictions for the two-neutron drip line are also compared in a systematic way with the non-relativistic results. CDFT has been applied for systematic study of extremely deformed, rotating N ∼ Z nuclei of the A ∼ 40 mass region. At spin zero such structures are located at high energies which prevents their experimental observation. The rotation acts as a tool to bring these exotic shapes down to the yrast line so that their observation could become possible with a future generation detectors such as GRETA or AGATA. The major physical observables of such structures, the underlying single-particle structure and the spins at which they become yrast or near yrast are defined. The search for the fingerprints of clusterization and molecular structures is performed and the configurations with such features are discussed. CDFT has been applied to study fission barriers of superheavy nuclei and related systematic theoretical uncertainties in the predictions of inner fission barrier heights in superheavy elements. Systematic uncertainties are substantial in superheavy elements and their behavior as a function of proton and neutron numbers contains a large random component. The benchmarking of the functionals to the experimental data on fission barriers in the actinides allows reduction of the systematic theoretical uncertainties for the inner fission barriers of unknown superheavy elements. However, even then they on average increase when moving away from the region where benchmarking has been performed.

Cette thèse de doctorat vise l’examen critique de certaines théories de champ moyen nucléaire phénoménologiques, en se focalisant sur la description fiable des niveaux de particules individuelles. L’approche suivie ici est nouvelle en ce sens que elle permet non seulement la prédiction des valeurs numériques obtenues avec ce formalisme, mais également une estimation des distributions de probabilités correspondant aux résultats expérimentaux. Nous introduisons le concept des ≪erreurs théoriques≫, visant estimer, dans un cadre mathématique bien établi, les incertitudes relatives aux modélisations théoriques. Il est également introduit une notion subjective de pouvoir prédictif des Hamiltoniens nucléaires, qui est analysé dans le contexte des spectres énergétiques de particules individuelles. Le concept mathématique du ≪Problème Inverse≫ est appliqué aux Hamiltoniens de champ moyen réalistes. Cette technique permet la prédiction de propriétés du système partir d’un nombre limité de données. Afin d'approfondir notre connaissance des Problèmes Inverses, nous focalisons notre attention sur un problème mathématique simple. Une fonction dépendant de quatre paramètres libres est introduite afin de reproduire des données ≪expérimentales≫. Nous étudions le comportement des paramètres ≪fittés≫, leur corrélation, ainsi que les erreurs associées. Cette étude nous aide comprendre la signification de la formulation correcte du problème en question. Il nous montre également l'importance d'inclure les erreurs expérimentales et théoriques dans la solution. / This thesis is a critical examination of phenomenological nuclear mean field theories, focusing on reliable description of levels of individual particles. The approach presented here is new in the sense that it not only allows to predict the numerical values obtained with this formalism, but also yields an estimate of the probability distributions corresponding to the experimental results. We introduce the concept of ‘theoretical errors’ to estimate uncertainties in theoreticalmodels. We also introduce a subjective notion of ‘Predictive Power’ of nuclear Hamiltonians, which is analyzed in the context of the energy spectra of individual particles. The mathematical concept of ‘Inverse Problem’ is applied to a realistic mean-field Hamiltonian. This technique allows to predict the properties of a system from a limited number of data. To deepen our understanding of Inverse Problems, we focus on a simple mathematical problem. A function dependent on four free parameters is introduced in order to reproduce ‘experimental’ data. We study the behavior of the ‘fitted’ parameters, their correlation and the associated errors. This study helps us understand the importance of the correct formulation of the problem. It also shows the importance of including theoretical and experimental errors in the solution.

Covariant density functional theory (CDFT) is a modern theoretical tool for the description of nuclear structure phenomena. Different physical observables of the ground and excited states in even-even nuclei have been studied within the CDFT framework employing three major classes of the state-of-the-art covariant energy density functionals. The global assessment of the accuracy of the description of the ground state properties and systematic theoretical uncertainties of atomic nuclei have been investigated. Large-scale axial relativistic Hartree-Bogoliubov (RHB) calculations are performed for all Z < 106 even-even nuclei between the two-proton and two-neutron drip lines. The sources of theoretical uncertainties in the prediction of the two-neutron drip line are analyzed in the framework of CDFT. We concentrate on single-particle and pairing properties as potential sources of these uncertainties. The major source of these uncertainties can be traced back to the differences in the underlying single-particle structure of the various CEDFs. A systematic search for axial octupole deformation in the actinides and superheavy nuclei with proton numbers Z = 88 - 126 and neutron numbers from two-proton drip line up to N = 210 has been performed in CDFT. The nuclei in the Z ~ 96, N ~ 196 region of octupole deformation have been investigated in detail and their systematic uncertainties have been quantified. The structure of superheavy nuclei has been reanalyzed with inclusion of quadrupole deformation. Theoretical uncertainties in the predictions of inner fission barrier heights in superheavy elements have been investigated in a systematic way. The correlations between global description of the ground state properties and nuclear matter properties have been studied. It was concluded that the strict enforcement of the constraints on the nuclear matter properties (NMP) defined in Ref. [1] will not necessary lead to the functionals with good description of ground state properties. The different aspects of the existence and stability of hyperheavy nuclei have been investigated. For the first time, we demonstrate the existence of three regions of spherical hyperheavy nuclei centered around (Z ~ 138, N ~ 230), (Z ~ 156, N ~ 310) and (Z ~ 174, N ~ 410) which are expected to be reasonably stable against spontaneous fission.

This thesis is a critical examination of phenomenological nuclear mean field theories, focusing on reliable description of levels of individual particles. The approach presented here is new in the sense that it not only allows to predict the numerical values obtained with this formalism, but also yields an estimate of the probability distributions corresponding to the experimental results. We introduce the concept of 'theoretical errors' to estimate uncertainties in theoreticalmodels. We also introduce a subjective notion of 'Predictive Power' of nuclear Hamiltonians, which is analyzed in the context of the energy spectra of individual particles. The mathematical concept of 'Inverse Problem' is applied to a realistic mean-field Hamiltonian. This technique allows to predict the properties of a system from a limited number of data. To deepen our understanding of Inverse Problems, we focus on a simple mathematical problem. A function dependent on four free parameters is introduced in order to reproduce 'experimental' data. We study the behavior of the 'fitted' parameters, their correlation and the associated errors. This study helps us understand the importance of the correct formulation of the problem. It also shows the importance of including theoretical and experimental errors in the solution.