In this paper, by presenting the potentials of Kaluza-Klein (KK) modes in the corresponding Schrödinger equations, we investigate the localization and resonances of gravity and fermion on the symmetric and asymmetric Bloch branes. We find that the localization properties of zero modes for gravity and fermion in the symmetric brane case are the same, whereas, for the asymmetric brane case, the fermion zero mode is localized on one of the sub-branes, while the gravity zero mode is localized on another sub-brane. The spectra of the gravity and the left-or right-handed fermion are composed of a bound zero mode and a series of gapless continuous massive KK modes.Among the continuous massive KK modes, we obtain some discrete gravity and fermion resonant (quasilocalized) KK states on the brane, which have a finite probability of escaping into the bulk.The KK states with lower resonant masses have a longer lifetime on the brane. And the number of the resonant KK states increases linearly with the width of the brane and the scalar-fermion coupling constant, but it decreases with the asymmetric factor β. The structure of the resonance spectrum is investigated in detail.

It is well known that the U (1) gauge vector field, with the standard fivedimensional (5D) action, cannot be localized on Randall-Sundrum-like braneworlds with an infinite extra dimension. In this paper, we propose a modified 5D action to localize U (1) gauge vector field on flat branes with an infinite or finite extra dimension. The localization method is realized by adding a dynamical mass term into the standard 5D action of the vector field, which is proportional to the 5D scalar curvature. It is shown that the vector zero mode is localizable if the 5D spacetime is (asymptotic) AdS 5 . Moreover, the massive tachyonic modes can be excluded.

It is known that a five-dimensional free vector field AM cannot be localized on Randall-Sundrum (RS)-like thick branes, namely, the thick branes embedded in asymptotic Anti-de Sitter (AdS) spacetime. In order to localize a vector field on the RS-like thick brane, an extra coupling term should be introduced. In this paper, we generalize the geometrical coupling mechanism by adding two mass terms (αRg M N AM AN + βR M N AM AN ) into the action. We decompose the fundamental vector field AM into three parts: transverse vector partµ, scalar parts φ and A5. Then, we find that the transverse vector partµ decouples from the scalar parts. In order to eliminate the tachyonic modes ofµ, the two coupling parameters α and β should satisfy a relation. Combining the restricted condition, we can get a combination parameter as γ = 3 2 ± √ 1 + 12α. Only if γ > 1/2, the zero mode ofµ can be localized on the RS-like thick brane. We also investigate the resonant character of the vector partµ for the general RS-like thick brane with the warp factor A(z) = − ln(1 + k 2 z 2 )/2 by choosing the relative probability method. The result shows that, only for γ > 3, the massive resonant Kaluza-Klein modes can exist. The number of resonant Kaluza-Klein states increases with the combination parameter γ, and the lifetime of the first resonant state can be long enough as the age of our universe. This indicates that the vector resonances might be considered as one of the candidates of dark matter. Combining the conditions of experimental observations, the constrain shows that the parameter k has a lower limit with k 10 −17 eV, the combination parameter γ should be greater than 57, and accordingly, the mass of the first resonant state should satisfy m1 10 −15 eV.