Localização da ação de milicargas e escala universal de massa para campos bosônicos através do acoplamento geométrico

Abstract

In this thesis we study how geometrical coupling can be used to localize a model with kinetic gauge mixing, and also generate an universal mass scale for bosonic fields. The kinetic mixing is a theory for millicharged particles, proposed by Holdom in 1985, and that has been object of study in the LHC. We propose a geometrical coupling between the gauge fields, the Ricci scalar and the Ricci tensor. We show that it is possible to localize such a model by regarding specific values for the coupling constants. We find the solutions for the two gauge fields, and discuss the localization for scalar components that appears naturally in the process. We show that not necessarily the gauge and scalar fields are localized simultaneously. Also, we find an universal mass scale for all $p-$ forms in multi-brane worlds models. It is a known fact that this model provides an ultralight mode for the fields. However, to get this, the Lagrangians considered in the literature are not covariant. In order to solve this, we propose a covariant version, with the geometrical coupling, to multi-localize $q- $form fields. As a consequence of the covariance, we show that all the $q$-form fields have an ultralight mode with the same mass that the gravitational one. That way we show that there is an universal mass scale for the ultralight modes of the bosonic fields. This suggests that a new physics must emerge, for all theses fields, at the same scale. After that, we revisit the results that consider a crystal manyfold background in the Randall-Sundrum scenary (RS), and add the discussion related to geometrical couplings in such a configuration. The wave functions of fields trapped in the crystal are Bloch-like waves, and their behavior is very similar to electrons inside a lattice, just like in the Kronig-Penney model (KP). We compute the mass dispersion relations for those fields with and without a dilaton coupling. It leads to new results for the band gap structure of these fields. In the case of the Kalb-Ramond field, and with the correct dispersion relation, there is no gap between the mass bands. Also, always that the field is coupled with the dilaton, its first mass mode decreases. When the generalization to the $q-$form is done, we show that it is not possible to suppress or generate mass for the fields by controlling the dilaton coupling, differently of what is showed in the literature.