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

A three-parameter (positive odd integer s, thickness factor λ, and asymmetry factor a) family of asymmetric thick brane solutions in five dimensions were constructed from a two-parameter (s and λ) 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≥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 Schrödinger 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.