On a Covariant Determination of Mass Scales in Warped Backgrounds

TL;DR

This paper introduces a covariant method for determining masses in warped extra-dimensional models, ensuring coordinate independence and providing new insights into mass scales and hierarchy preservation in the Randall-Sundrum scenario.

Contribution

It presents a novel covariant approach to mass determination in brane models, clarifying the relationship between fundamental scales and observed mass spectra.

Findings

Masses are inversely proportional to proper distances, not exponentially suppressed.

Hierarchy between gravitational and weak forces is maintained despite non-exponentiated masses.

Kaluza-Klein mass spacings vary across branes, but mass ratios remain consistent.

Abstract

We propose a method of determining masses in brane scenarios which is independent of coordinate transformations. We apply our method to the scenario of Randall and Sundrum (RS) with two branes, which provides a solution to the hierarchy problem. The core of our proposal is the use of covariant equations and expressing all coordinate quantities in terms of invariant distances. In the RS model we find that massive brane fields propagate proper distances inversely proportional to masses that are not exponentially suppressed. The hierarchy between the gravitational and weak interactions is nevertheless preserved on the visible brane due to suppression of gravitational interactions on that brane. The towers of Kaluza-Klein states for bulk fields are observed to have different spacings on different branes when all masses are measured in units of the fundamental scale. Ratios of masses on each brane are the same in our covariant and the standard interpretations. Since masses of brane fields are not exponentiated, the fundamental scale of higher-dimensional gravity must be of the order of the weak scale.