Mass Spectrum of Fermion on Bloch Branes with New Scalar-fermion Coupling

In order to localize a left- or right-handed fermion zero mode on a thick brane, one usually introduces the Yukawa coupling $\eta \bar{\Psi} F(\chi) \Psi$ between a bulk fermion and the background scalar field $\chi$. However, the Yukawa coupling will do not work if the background scalar is an even function of the extra dimension. Recently, Ref. [Phy. Rev. \textbf{D} 89 (2014) 086001] has presented a new scalar-fermion coupling form $\lambda \bar \Psi \Gamma^M \partial_M F(\chi) \gamma^5 \Psi$ in order to deal with this problem. In this paper, we investigate the localization and mass spectrum of fermion on the Bloch brane by using the new scalar-fermion coupling with $F(\chi)=\chi^n$. It is found that the effective potentials have rich structure and may be volcano-like, finite square well-like, and infinite potentials, which depend on the parameter $n$. As a result, there may appear some resonant KK fermions, finite or infinite numbers of bound KK fermions.