Effective action of a self-interacting scalar field on brane

TL;DR

This paper analyzes the effective action of a self-interacting scalar field on a brane within a five-dimensional thick braneworld, deriving mass spectra, wave functions, and interaction properties of Kaluza-Klein modes, with implications for dark matter.

Contribution

It provides analytical solutions for KK mode spectra and interactions in a thick brane scenario, linking higher-dimensional physics to observable phenomena.

Findings

Higher KK modes have longer lifetimes.

Higher KK modes interact weakly with ordinary matter.

Higher KK modes could be dark matter candidates.

Abstract

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 P\"{o}schl-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.