Localization and mass spectra of fermions on symmetric and asymmetric thick branes

Abstract

A three-parameter (positive odd integer $s$, thickness factor $\ensuremath{\lambda}$, and asymmetry factor $a$) family of asymmetric thick brane solutions in five dimensions were constructed from a two-parameter ($s$ and $\ensuremath{\lambda}$) family of symmetric ones in by R. Guerrero, R. O. Rodriguez, and R. Torrealba in [Phys. Rev. D 72, 124012 (2005).]. The values $s=1$ and $s\ensuremath{\ge}3$ correspond to single branes and double branes, respectively. These branes have very rich inner structure. In this paper, by presenting the mass-independent potentials of Kaluza-Klein (KK) modes in the corresponding Schr\odinger equations, we investigate the localization and mass spectra of fermions on the symmetric and asymmetric thick branes in an anti-de Sitter background. In order to analyze the effect of gravity-fermion interaction (i.e., the effect of the inner structure of the branes) and scalar-fermion interaction to the spectrum of fermion KK modes, we consider three kinds of typical kink-fermion couplings. The spectra of left chiral fermions for these couplings consist of a bound zero mode and a series of gapless continuous massive KK modes, some discrete bound KK modes including zero mode (exist mass gaps), and a series of continuous massive KK modes, infinite discrete bound KK modes, respectively. The structures of the spectra are investigated in detail.