Physical degrees of freedom in stabilized brane world models

TL;DR

This paper analyzes the physical degrees of freedom in stabilized brane world models with a Goldberger-Wise scalar, deriving the effective four-dimensional theory and exploring the mass spectrum of gravitons and scalars.

Contribution

It provides a detailed construction of the second variation Lagrangian, gauge invariance analysis, and an effective 4D Lagrangian for stabilized brane models, including mass spectra.

Findings

Graviton masses can be a few TeV for certain backgrounds.

Radion mass is around 100 GeV.

Coupling of the radion to matter is similar to unstabilized models.

Abstract

We consider brane world models with interbrane separation stabilized by the Goldberger-Wise scalar field. For arbitrary background, or vacuum configurations of the gravitational and scalar fields in such models, we construct the second variation Lagrangian, study its gauge invariance, find the corresponding equations of motion and decouple them in a suitable gauge. We also derive an effective four-dimensional Lagrangian for such models, which describes the massless graviton, a tower of massive gravitons and a tower of massive scalars. It is shown that for a special choice of the background solution the masses of the graviton excitations may be of the order of a few TeV, the radion mass of the order of 100 GeV, the inverse size of the extra dimension being tens of GeV. In this case the coupling of the radion to matter on the negative tension brane is approximately the same as in the unstabilized model with the same values of the fundamental five-dimensional energy scale and the interbrane distance.