No description available.

No description available.

The main purpose of this thesis is to study quantum-electrodynamics (QED) in the presence of external background fields. We address this purpose by computing the Delbrück scattering amplitudes in the low-energy limit, the low-energy N-photon amplitudes in the presence of a constant field, the low-energy four-photon amplitudes in the presence of a constant magnetic field, the forward Compton scattering amplitudes in a constant magnetic field and the one-loop vertex correction in an arbitrary plane-wave field. In most cases, except for the vertex correction, we employ the worldline formalism to perform all calculations simultaneously for both scalar and spinor QED. We utilize the previously obtained result of the off-shell four-photon amplitude with two low- energy photons to calculate the circularly polarized amplitudes for the leading-order contributions to Delbrück scattering, assuming that the incoming and outgoing photons have low-energy. We compute the one-loop N-photon amplitudes in a constant background field considering off- shell low-energy photons in various field configurations. Assuming parallel magnetic and electric components of the background field enables us to obtain compact representations for these amplitudes involving only simple algebra and a single global proper-time integral with trigonometric integrands. Similarly, assuming a constant crossed field, we derive compact expressions for these amplitudes, represented by a single proper-time integral. The outcome of this integral, for fixed parameters, takes the form of a factorial function. The latter case is further refined by employing the spinor helicity formalism, where the helicity components are expressed solely in terms of Bernoulli numbers and spinor products. Moreover, for an arbitrary constant field, we obtain another representation of these amplitudes as series expansions in the external field. As an application, we compute the one-loop four-photon amplitudes in the presence of a pure magnetic field for off-shell low-energy photons. Using these results, we calculate the polarized amplitudes for linear and circular polarizations in two distinct scenarios: when the magnetic field is coplanar with the scattering plane and when it is orthogonal to it. We study the polarization flip of a photon scattered by an off-shell particle in the presence of a magnetic field. Specifically, we compute the Compton scattering amplitudes in a magnetic background field for off-shell massive particles and on-shell photons under the assumption that the scattering occurs in the forward direction, aligned along the same axis as the magnetic field. Additionally, we consider the polarization of the external photons to be perpendicular to each other. We apply the operator technique within the Furry picture (Volkov states) to compute the general expression of the one-loop vertex correction in an arbitrary plane-wave background field for the case of two on-shell external electrons and an off-shell external photon. We show that the ultraviolet divergence can be renormalized exactly as in vacuum while the infrared divergence is avoided by introducing a finite photon mass. This calculation completes the study of QED in a plane-wave background field at one-loop order. In most cases, except for the Delbrück scattering amplitudes, we perform non-perturbative calculations, given that the external background fields are taken into account exactly.

Les calculs de précision dans les théories de jauge jouent un rôle très important pour l’étude de la physique du Modèle Standard et au-delà dans les super-collisionneurs de particules comme le LHC, TeVatron et ILC. Par conséquent, il est extrêmement important de fournir des outils du calcul d’amplitudes à une boucle stables, rapides, efficaces et hautement automatisés. Cette thèse a pour but de développer la bibliothèque d’intégrales Golem95. Cette bibliothèque est un programme écrit en Fortran95, qui contient tous les ingrédients nécessaires pour calculer une intégrale scalaire ou tensorielle à une boucle avec jusqu’à six pattes externes. Golem95 utilise une méthode traditionnelle de réduction (réduction à la Golem) qui réduit les facteurs de forme en des intégrales de base redondantes qui peuvent être scalaires (sans paramètres de Feynman au numérateur) ou tensorielles (avec des paramètres de Feynman au numérateur); ce formalisme permet d’éviter les problèmes de l’instabilité numérique engendrés par des singularités factices dues à l’annulation des déterminants de Gram. En plus, cette bibliothèque peut être interfacée avec des programmes du calcul automatique basés sur les méthodes d’unitarité comme GoSam par exemple. Les versions antérieures de Golem95 ont été conçues pour le calcul des amplitudes sans masses internes. Le but de ce travail de thèse est de généraliser cette bibliothèque pour les configurations les plus générales (les masses complexes sont incluses), et de fournir un calcul numériquement stable dans les régions problématique en donnant une représentation intégrale unidimensionnelle stable pour chaque intégrale de base de Golem95. / Higher order corrections in gauge theories play a crucial role in studying physics within the standard model and beyond at TeV colliders, like LHC, TeVatron and ILC. Therefore, it is of extreme importance to provide tools for next-to-leading order amplitude computation which are fast, stable, efficient and highly automatized. This thesis aims at developing the library of integrals Golem95. This library is a program written in Fortran95, it contains all the necessary ingredients to calculate any one-loop scalar or tensorial integral with up to six external legs. Golem95 uses the traditional reduction method (Golem reduction) to reduce the form factors into redundant basic integrals, which can be scalar (without Feynman parameters in the numerator) or tensorial (with Feynman parameter in the numerator); this formalism allows us to avoid the problems of numerical instabilities generated by the spurious singularities induced by the vanishing of the Gram determinants. In addition, this library can be interfaced with automatic programs of NLO calculation based on the unitarity inspired reduction methods as GoSam for example. Earlierversions of Golem95 were designed for the calculation of amplitudes without internal masses. The purpose of this thesis is to extend this library for more general configurations (complex masses are supported); and to provide numerically stable calculation in the problematic regions (det(G) → 0), by providing a stable one-dimensional integral representation for each Golem95 basic integral.

To learn more about the structure of hadrons we study form factors. In the semi-leptonic decay Ω- → Ξ0W- two types of form factors arise namely the vector and axial-vector transition form factors. We focus on the vector transition form factors at next-to-next-to-leading order in the power counting of chiral perturbation theory and study their quark mass dependence. They are related to the scattering amplitude for the transition and therefore we have to calculate Feynman diagrams. Next-to-next-to-leading order Feynman diagrams translate to 1-loop diagrams and at this order there is a substantial amount of them. This study is a feasibility study and therefore we limit this study to diagrams containing the low-energy constants HA and hA from the leading order chiral Lagrangian. There are 5 such diagrams, three with two propagators in the loop (bubble diagrams) and two with three propagators in the loop (triangle diagrams). We derive explicit expressions for all 5 diagrams. To calculate these diagrams numerically we use Mathematica and FeynCalc. We provide numerical results for the three bubble diagrams but not the triangle diagrams due to the long computing time for these diagrams. Therefore, we show that performing form factor calculations at NNLO seems feasible but there needs to be more investment into figuring out the coding aspects regarding the triangle diagrams.