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In this paper, we investigate thick branes with a nonminimally coupled background scalar field, whose solution is a single-kink or a double-kink. The effects of the nonminimal coupling constant on the structure of the thick branes and the localization of gravity, fermions, scalars, and vectors are discussed. It is shown that each brane will split into two sub-branes as increasing the nonminimal coupling constant. By investigating the tensor perturbation equations of gravity and the general covariant Dirac equation of fermions, we find that both the gravity zero mode and left-chiral fermion zero mode are localized at the center of the single-kink branes and localized between the two sub-branes generated by the double kink, which indicates that the constant does not effect the localization of these zero modes. However, the zero mode of scalars is localized on each sub-brane (for both single-kink and double-kink branes) when is larger than its critical value ₀. The effects of the nonminimal coupling constant on the resonances of gravity and fermions with finite lifetime on the branes are also discussed.
Guo et al. (Mon,) studied this question.