This thesis focuses on form factors in superconformal theories, in particular maximally supersymmetric Yang-Mills (MSYM) and ABJM. Scattering amplitudes in these theories have a wealth of special properties and significant amount of insight has been developed for these along with the modern techniques to calculate them. In this thesis, it is presented that form factors have very similar properties to scattering amplitudes and the techniques for scattering amplitudes can be successfully applied to form factors. After a review of the methods employed, the results for tree-level and multi-loop form factors of protected operators are derived. In four dimensions, it is shown that the tree-level form factors can be computed using MHV diagrams BCFWrelations by augmenting the set of vertices with elementary form factors. Tree and loop-level MHV and non-MHV form factors of protected operators in the stress-tensor multiplet of MSYM are computed as examples. A solution to the BCFW recursion relations for form factors is derived in terms of a diagrammatic representation. Supersymmetric multiplets of form factors of protected operators are constructed. In three dimensions, Sudakov form factor of a protected biscalar operator is computed in ABJM theory. This form factor captures the IR divergences of the scattering amplitudes. It is found that this form factor can be written in terms of a single, non-planar Feynman integral which is maximally transcendental. Additionally, the sub-leading colour corrections to the one-loop four-particle amplitude in ABJM is derived using unitarity cuts. Finally a basis of two-loo pure master integrals for the Sudakov form factor topology is constructed from a principle that relies on certain unitarity cuts.

The study of scattering amplitudes in the maximally supersymmetric Yang-Mills theory (N = 4 SYM) is a thriving field of research. Since the reformulation of perturbative gauge theory as a twistor string theory by Witten, this area has witnessed a flurry of activity, leading to the discovery of a multitude of novel techniques, such as recursion relations and MHV diagrams, collectively referred to as on-shell methods. In parallel, many previously hidden properties and rich mathematical structures have been found, a powerful example of such being the dual superconformal symmetry. It is natural to ask whether this understanding can be extended to phenomenologically relevant theories as well as other quantities. The goal of the present work is to apply the modern on-shell methods to calculations of form factors, with particular focus on those which are relevant for describing Higgs production in QCD from the point of view of an effective field theory. Specifically, our analysis will be carried out in supersymmetric gauge theories at two-loop level and will consist of several steps. We focus first on operators in the SU(2j3) closed subsector of N = 4 SYM, in particular two non-protected, dimension-three operators. We then move on to consider the trilinear operator Tr(F3) and a related descendant of the Konishi operator which contains Tr(F3), also in N =4 SYM. Finally, we concentrate on two-loop form factors of these two operators in theories with less-than-maximal supersymmetry. The result of our investigation shows an emergence of a small number of universal building blocks, ultimately related to the two-loop form factor of a trilinear half-BPS operator. This finding suggests that the most complicated, maximally transcendental part of Higgs plus multi-gluon amplitudes in QCD can be equivalently computed in a remarkably simple way by considering form factors of half-BPS operators in N =4 SYM.

In the design of all marine craft the prediction of a vessel??s resistance characteristics is a major consideration. The accurate prediction of resistance is particularly important in the design of modern high-speed vessels where the primary contractual obligation placed upon the builder is the vessel??s achievable speed. Investigation was made of the methods of Doctors and Day, whereby the traditional Michell wave-resistance theory, published in 1898, is improved on through a better understanding of the hydrodynamics of transom sterns and the application of statistically determined form factors. One of the difficulties with the Michell theory is how to account for the hollow that forms behind a transom stern, a feature prevalent in high-speed vessels. A common approach in the numerical prediction of wave resistance for transom-stern vessels is to discretize the hollow as a geometrically-smooth addition to the vessel. Therefore, of great importance in accurate prediction of wave resistance is the hydrodynamics of, and in particular, the length and depth of the hollow formed behind the transom stern. Accordingly, a systematic series of transom-stern models were tank tested at various drafts and speeds in order to determine experimentally the length and depth of the hollow as a function of vessel speed, draft and beam. From the experimental data, algorithms for the determination of the length and depth of the transom hollow, have been developed and utilised in the discretization of the transom hollow for prediction of resistance using the Michell wave- resistance theory. Application of the developed hollow algorithms produced significant improvements in correlation of the experimental and theoretical predictions of total resistance, particularly in the lower Froude range. In addition to the transom-hollow investigation, form factors were obtained using least-squares regression of existing experimental data. The form factors were based on the major geometric parameters of the models used. In the research presented here, the method was applied to a large range of published resistance data for high-speed displacement vessels. Considerable improvement in correlation, between theoretical and experimental predictions of total resistance, was obtained by incorporating the calculated form-factors into the total resistance formulation.

In the design of all marine craft the prediction of a vessel??s resistance characteristics is a major consideration. The accurate prediction of resistance is particularly important in the design of modern high-speed vessels where the primary contractual obligation placed upon the builder is the vessel??s achievable speed. Investigation was made of the methods of Doctors and Day, whereby the traditional Michell wave-resistance theory, published in 1898, is improved on through a better understanding of the hydrodynamics of transom sterns and the application of statistically determined form factors. One of the difficulties with the Michell theory is how to account for the hollow that forms behind a transom stern, a feature prevalent in high-speed vessels. A common approach in the numerical prediction of wave resistance for transom-stern vessels is to discretize the hollow as a geometrically-smooth addition to the vessel. Therefore, of great importance in accurate prediction of wave resistance is the hydrodynamics of, and in particular, the length and depth of the hollow formed behind the transom stern. Accordingly, a systematic series of transom-stern models were tank tested at various drafts and speeds in order to determine experimentally the length and depth of the hollow as a function of vessel speed, draft and beam. From the experimental data, algorithms for the determination of the length and depth of the transom hollow, have been developed and utilised in the discretization of the transom hollow for prediction of resistance using the Michell wave- resistance theory. Application of the developed hollow algorithms produced significant improvements in correlation of the experimental and theoretical predictions of total resistance, particularly in the lower Froude range. In addition to the transom-hollow investigation, form factors were obtained using least-squares regression of existing experimental data. The form factors were based on the major geometric parameters of the models used. In the research presented here, the method was applied to a large range of published resistance data for high-speed displacement vessels. Considerable improvement in correlation, between theoretical and experimental predictions of total resistance, was obtained by incorporating the calculated form-factors into the total resistance formulation.

No description available.

We introduce and examine the analytic properties of the three electromagnetic transition form factors of the Sigma*-Lambda hyperon transition. In the first part of the thesis, we discuss the interaction Lagrangian for the hyperons at hand. We calculate the decay rate of the Dalitz decay  Sigma* Lambda -> e+e- in the one-photon approximation in terms of the form factors, as well as the differential cross section of the scattering e+e- -> Sigma*bar Lambda in the one-photon approximation. In the second part of the thesis, we build up the machinery for calculation of the form factors using dispersion relations, performing an analytic continuation from the timelike, q2 > 0, to the spacelike, q2 < 0, region of the virtual photon invariant mass q2. Due to an anomalous cut in the triangle diagram arising from a two-pion saturation of the photon-hyperon vertex, there is an additional term in the dispersive integral. We use the scalar three-point function as a model for the examination of the dispersive approach with the anomalous cut. The one-loop diagram is calculated both directly and using dispersion relations. After comparison of the two methods, they are found to coincide when the anomalous contribution is added to the dispersive integral in the case of the octet Sigma exchange. By examination of the branch points of the logarithm in the discontinuity, we deduce the structure of the Riemann surface of the unitarity cut and present trajectories of the branch points. The result of our analysis of the analytic structure yields a correct dispersive relation for the electromagnetic transition form factors. This opens the way for the calculation of these form factors in the low-energy region for both space- and timelike q2. As an outlook, we present preliminary calculations for the hyperon-pion scattering amplitude using the unitarity and the anomalous contribution in a once-subtracted dispersion relation. Finally we present the corresponding preliminary unsubtracted dispersive calculations for the form factors.

Pour réduire la consommation énergétique des bâtiments, les systèmes de chauffage agissant par rayonnement semblent particulièrement intéressants puisqu'ils ne nécessitent pas de chauffer l'air de la pièce pour que leur action soit perçue (moins d'énergie dépensée et moins de déperditions) et qu'jls permettent une meilleure réactivité au mode de vie des utilisateurs. De plus, des expériences réalisées au MIT ont montré que nous préférons un air frais et des murs chauds plutôt que le contraire, ce qui milite en paveur du chauffage par rayonnement. L'objectif de ce travail est de développer un outil permettant de paire le lien entre le rayonnement échangé entre un occupant et son environnement et le confort qu'il exprime vis-a- vis de celui-ci. L'étude des transferts radiatifs dans l'habitat peut se ramener a la résolution de l'équation des radiosités. Celle-ci nécessite l'évaluation de couplages géométriques entre les éléments de la scène appelés facteurs de forme. Leur obtention est particulièrement ardue, notamment lorsqu'il s'agit de tenir compte d'éventuelles obstructions. Une comparaison des méthodes numériques disponibles pour cela est proposée. Outre l'évaluation de ces facteurs, le système a résoudre est très lourd, puisque chaque surface interagit, le plus souvent, avec toutes les autres et que le nombre de nœuds mis en jeu dans la description d'une scène complexe est important. Nous présentons une méthode de résolution qui raffine le maillage d'une scène tout en construisant simultanément une représentation a différentes échelles des facteurs de forme entre ses éléments, dans le but de ne pas calculer tous les échanges a la résolution la plus fine. Elle permet ainsi de réduire considérablement le temps de calcul et rend son utilisation possible en bureau d'étude.une fois que les transferts radiatifs entre un individu, la source de chauffage et différents éléments de l'environnement sont connus, le modèle de confort de Fanger est mis en oeuvre pour déterminer si les configurations envisagées sont confortables ou non, au regard des normes en vigueur dans le bâtiment. Ainsi, nous avons pu déterminer quels types d'appareils de chauffage sont les plus susceptibles d'apporter du confort, dans diverses situations, et sans accroitre la puissance consommée. / In order to reduce building's energy consumption, radiant heater seems particularly attractives because they didn't require to heat the air of the room to be perceived (less energy spent and less losses), and because they provide a better reactivity to users life rythmes. Moreover, experiences of the MIT showed that we prefer a fresh ai with warm wall rather than the opposite. The goal of the work is to develop a tool to study the link between the radiant energy exchange by an occupant with his environment and the thermal comfort express under some hypothesis, radiative beat transfers can be idealized by the radiosity equation. This one needs the evaluation of geometrics couplings between the elements of the scene called form factors or view factors. It's generally hard to get them, especially when there are obstructions. A comparison of existing numerical methods is proposed. beyond the evaluation of those factors, the algebraic system is heavy to solve because each surface interact, usually, with all the others and because the number of nodes required for the description of a complexe scene is important. We present a resolution method which refine the mesh of the scene while constructing a multi scale representation of form factors between its elements, in order to don't have to compute all the transfers at the finest resolution. This drastically reduce the computation time and allow to use this method in a industrial development process.When the radiative transfers between the occupant, heaters and differents elements of the environment are known, the thermal comfort model of fanger is used to determine if the considered env!ronments are confortable or not, according to international standards. This way, we could find which type of heaters are the most subject to provide thermal comfort without increasing energy consumption.

No description available.

No description available.

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.