Abordagens numéricas no estudo de localização de campos em branas

Abstract

This thesis presents the use of numerical analysis in the study of field localization in braneworld scenarios in five ans six dimensions. We discuss the importance of a model supporting massive states, which carry phenomenology implications. We use suitable numerical methods to attain the spectra and eigenfunctions for the gravitational, gauge and fermionic field in several braneworld models. The braneworld concept proposes to solve some of the most fundamental problems in Particle Physics and Cosmology such as the huge discrepancy between the Planck and electroweak scales, the darlk matter origin. tha cosmic acceleration and the value of the cosmological constant. In the braneworld hypothesis, our Universe is considered a hypersurface having the usual four space-time dimensions embedded in a bulk space with higher dimension. To guarantee that the fourdimensional laws of Physics is recovered in a dimensional reduction, the massless mode (also called zero-mode, eigenstates with zero energy), must be localized, i.e., finite. Moreover, the massive solutions, called Kaluza-Klein (KK) modes needs special attention. Such modes carry important phenomenological implications. For the gravitational field, for instance, the tower of KK massive states for the graviton implies in small correction in the Newton’s law at short distances. Only two models have exact solution to the correction: the Randall-Sundrum and Gherghetta-Shaposhnikov models, respectively in five and six dimensions. In the thick braneworld scenarios, whose brane has a richer internal structure, the calculation to the correction is not possible in a analytical way. the differential equations governing the massive modes in a Sturm-Liovulle problem has no analytical solution. We, therefore, presents the enforcement of numerical method to solve Sturm-Liouville problems in the context of braneworld models. Such approach allowed us to compute the correction in the Newton’s law in several thick braneworld models in five dimensions. The calculation of slight deviations in the gravitational potential may be used as a selection tool for braneworld scenarios match with future experimental measurements in high energy collisions.