Effects of the variation of mass on fermion localization and resonances on thick branes

TL;DR

This paper studies how varying the mass parameter affects fermion localization and resonances on thick branes generated by a scalar field, revealing critical behavior and changes in fermionic modes.

Contribution

It introduces a toy model with a specific scalar potential to analyze the impact of mass variation on brane solutions and fermion resonances, including the discovery of a critical mass value.

Findings

Existence of a critical mass parameter where scalar solutions become double kinks

Number of fermion bound states increases with mass parameter

Resonant fermion states grow as the mass parameter increases

Abstract

A few years ago, Campos investigated the critical phenomena of thick branes in warped spacetimes [Phys. Rev. Lett. {\bf 88} (2002) 141602]. Inspired by his work, we consider a toy model of thick branes generated by a real scalar field with the potential $V(\phi)=a\phi^2-b\phi^4+c\phi^6$, and investigate the variation of the mass parameter $a$ on the branes as well as the localization and resonances of fermions. An interesting result is found: there is a critical value for the mass parameter $a$, and when the critical value of $a$ is reached the solution of the background scalar field is not unique and has the shape of a double kink. This happens in both cases with and without gravity. It is also shown that the numbers of the bound Kaluza-Klein modes of fermions on the gravity-free brane and the resonant states of fermions on the brane with gravity increase with the value of $a$.