Spectrum Structure of Fermion on Bloch Branes with Two Scalar-fermion Couplings

TL;DR

This paper explores how fermions can be localized on Bloch branes using two types of scalar-fermion couplings, revealing complex potential structures and a spectrum of bound and resonant Kaluza-Klein modes, including novel features with combined couplings.

Contribution

It introduces a combined scalar-fermion coupling framework and analyzes the resulting rich fermion spectrum on Bloch branes, highlighting new spectral features.

Findings

Left-handed fermion zero mode can be localized under certain conditions.

Effective potentials exhibit diverse structures, including volcano-like and square well-like.

Spectrum includes both resonant and bound Kaluza-Klein fermions, with novel coexistence of localized massive modes.

Abstract

It is known that the Bloch brane is generated by an odd scalar field $\phi$ and an even one $\chi$. In order to localize a bulk fermion on the Bloch brane, the coupling between the fermion and scalars should be introduced. { There are two localization mechanisms in the literature, the Yukawa coupling $-\eta \bar{\Psi} F_1(\phi,\chi) \Psi$ and non-Yukawa coupling $\lambda \bar \Psi \Gamma^M \partial_M F_2(\phi,\chi) \gamma^5 \Psi $. The Yukawa coupling has been considered.} In this paper, we consider { both couplings between the fermion and the scalars with $F_1=\chi^m\phi^{2p+1}$ and $F_2=\chi^n\phi^{2q}$}, and investigate the localization and spectrum structure of the fermion on the Bloch brane. { It is found that the} left-handed fermion zero mode can be localized on the Bloch brane under some conditions, and the effective potentials have { rich} structure and may be volcano-like, finite square well-like, and infinite potentials. As a result, the spectrum { consists of} a series of resonant Kaluza-Klein fermions, finite or infinite numbers of bound Kaluza-Klein fermions. { Especially, we find a new feature of the introduction of both couplings: the spectrum for the case of finite square well-like potentials contains discrete quasi-localized and localized massive KK modes simultaneously.