Spectrum in the presence of brane-localized mass on torus extra dimensions

TL;DR

This paper numerically evaluates the lightest mass eigenvalue in a six-dimensional torus compactification with brane-localized mass, revealing its sensitivity to cutoff scale and dependence on torus moduli, with implications for extra-dimensional models.

Contribution

It provides the first detailed numerical analysis of the lightest mass in 6D torus models with brane mass, including an approximate formula and cutoff dependence insights.

Findings

Lightest mass is sensitive to cutoff scale $\\Lambda$ even at high values.

Approximate expression for the lightest mass in the thin brane limit.

Lightest mass is much lighter than the compactification scale, even with large brane mass.

Abstract

The lightest mass eigenvalue of a six-dimensional theory compactified on a torus is numerically evaluated in the presence of the brane-localized mass term. The dependence on the cutoff scale $\Lambda$ is non-negligible even when $\Lambda$ is two orders of magnitude above the compactification scale, which indicates that the mass eigenvalue is sensitive to the size of the brane, in contrast to five-dimensional theories. We obtain an approximate expression of the lightest mass in the thin brane limit, which well fits the numerical calculations, and clarifies its dependence on the torus moduli parameter $\tau$. We find that the lightest mass is typically much lighter than the compactification scale by an order of magnitude even in the limit of a large brane mass.