Localization of Matters on Pure Geometrical Thick Branes

TL;DR

This paper investigates how various matter fields and gravitons can be localized on pure geometrical thick branes in a 5D Weyl integrable space, analyzing the spectrum of KK modes and conditions for localization.

Contribution

It provides a detailed analysis of matter field localization and KK spectra on pure geometrical thick branes in Weyl geometry, including conditions for massless mode localization.

Findings

Massless scalar modes are normalizable and localized.

Continuum KK spectrum exists for scalars and vectors with no mass gap.

Localized chiral fermions require specific Yukawa couplings.

Abstract

In the literatures, several types of thick smooth brane configurations in a pure geometric Weyl integrable 5-dimensional space time have been presented. The Weyl geometry is a non-Riemannian modification of 5-dimensional Kaluza--Klein (KK) theory. All these thick brane solutions preserve 4-dimensional Poincar\'e invariance, and some of them break $Z_2$--symmetry along the extra dimension. In this paper, we study localization of various matter fields on these pure geometrical thick branes, which also localize the graviton. We present the shape of the potential of the corresponding Schr$\mathrm{\ddot{o}}$dinger problem and obtain the lowest KK mode. It is showed that, for both spin 0 scalars and spin 1 vectors, there exists a continuum gapless spectrum of KK states with $m^2>0$. But only the massless mode of scalars is found to be normalizable on the brane. However, for the massless left or right chiral fermion localization, there must be some kind of Yukawa coupling. For a special coupling, there exist a series of discrete massive KK modes with $m^2 >0$. It is also showed that for a given coupling constant only one of the massless chiral modes is localized on the branes.