Spectrum structure of a fermion on Bloch branes with two scalar–fermion couplings

Abstract

It is known that the Bloch brane is generated by an odd scalar field ϕ and an even one χ. 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 and non-Yukawa coupling . The Yukawa coupling has been considered. In this paper, we consider both couplings between the fermion and the scalars with and , 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.