Effective action of a self-interacting scalar field on brane

In extra dimensional theories, the four-dimensional field theory is reduced from a fundamental field theory in the bulk spacetime by integrating the extra dimensional part. In this paper we investigate the effective action of a self-interacting scalar field on a brane in the five-dimensional thick braneworld scenario. We consider two typical thick brane solutions and obtain the Poschl-Teller and harmonic potentials of the Kaluza-Klein (KK) modes, respectively. The analytical mass spectra and wave functions along extra dimension of the KK modes are obtained. Further, the effective coupling constant between different KK particles, cross section, and decay rate for some processes of the KK particles are related to the fundamental coupling in five dimensions and the new physics energy scale. Some interesting properties of these interactions are found with these calculations. The KK particles with higher mode have longer lifetime, and they almost do not interact with ordinary matter on the brane if their mode numbers are large enough. Thus, these KK particles with higher modes might be a candidate of dark matter.

Automated summary

In this paper, the effective action of a self-interacting scalar field on a brane in the five-dimensional thick braneworld scenario is investigated. The analytical mass spectra and wave functions of the Kaluza-Klein (KK) modes are obtained, and the effective coupling constant, cross section, and decay rate of the KK particles are related to the fundamental coupling in five dimensions and the new physics energy scale. It is found that KK particles with higher modes have longer lifetime and almost do not interact with ordinary matter on the brane if their mode numbers are large enough, making them potential candidates for dark matter.