Localization and quasilocalization of spin-$1/2$ fermion field on two-field thick braneworld

TL;DR

This paper investigates how spin-1/2 fermions can be localized or quasi-localized on a thick braneworld generated by two scalar fields, considering different couplings, and finds conditions for trapping massless and massive fermions.

Contribution

It introduces a model with two scalar fields and analyzes fermion localization using two types of couplings, providing new insights into trapping fermions on thick braneworlds.

Findings

Left-chiral zero mode can be localized on the brane.

Massive fermion modes can be localized or quasilocalized.

Massless and massive fermions with finite or infinite lifetime can be realized.

Abstract

Localization of a spin-$1/2$ fermion on the braneworld is an important and interesting problem. It is well known that a five-dimensional free massless fermion $\Psi$ minimally coupled to gravity cannot be localized on the Randall-Sundrum braneworld. In order to trap such a fermion, the coupling between the fermion and bulk scalar fields should be introduced. In this paper, localization and quasilocalization of a bulk fermion on the thick braneworld generated by two scalar fields (a kink scalar $\phi$ and a dilaton scalar $\pi$) are investigated. Two types of couplings between the fermion and two scalars are considered. One coupling is the usual Yukawa coupling $-\eta\bar{\Psi}\phi\Psi$ between the fermion and kink scalar, another one is $\lambda\bar{\Psi}\Gamma^{M}\partial_{M}\pi\gamma^{5}\Psi$ between the fermion and dilaton scalar. The left-chiral fermion zero mode can be localized on the brane, and both the left- and right-chiral fermion massive Kaluza-Klein modes may be localized or quasilocalized. Hence the four-dimensional massless left-chiral fermion and massive Dirac fermions, whose lifetime is infinite or finite, can be obtained on the brane.