Generalized geometrical coupling for vector field localization on thick brane in asymptotic anti-de Sitter spacetime

It is known that a five-dimensional free vector field A(M) cannot be localized on Randall-Sundrum (RS)-like thick branes-namely, the thick branes embedded in asymptotic anti-dc Sitter spacetime. To localize a vector field on the RS-like thick brave, an extra coupling term should be introduced. We generalize the geometrical coupling mechanism by adding two mass terms (alpha Rg(MN)A(M)A(N) + beta R(MN)A(M)A(N)) to the action. We decompose the fundamental vector field A(M) into three parts: transverse vector part (A) over cap mu, and scalar parts phi and A(5). Then we find that the transverse vector part (A) over cap mu decouples from the scalar parts. To eliminate the tachyonic modes of (A) over cap mu, the two coupling parameters alpha and beta should satisfy a relation. Combining the restricted condition, we can get a combination parameter as gamma = 3/2 +/- root 1 + 12 alpha. Only if gamma > 1/2 can the zero mode of (A) over cap mu be localized on the RS-like thick brane. We also investigate the resonant character of the vector part (A) over cap mu for a general RS-like thick brane with a warp factor A(z) = -ln(1 + k(2)z(2))/2 by choosing the relative probability method. The results show that the massive resonant Kaluza-Klein modes can exist only for gamma > 3. The number of resonant Kaluza-Klein states increases with the combination parameter gamma, and the lifetime of the first resonant state can be as long as our Universe's. This indicates that the vector resonances might be considered one of the candidates of dark matter. Combining the conditions of experimental observations, the constraint shows that the parameter k has a lower limit with k greater than or similar to 10(-17) eV, the combination parameter gamma should be greater than 57, and, accordingly, the mass of the first resonant state should satisfy m(1) greater than or similar to 10(-15) eV.