KK-mode contribution to the crossover scale for the brane-induced force

TL;DR

This paper investigates how KK modes influence the crossover scale in a 5D scalar model with a domain-wall background, revealing that warping effects keep the scale finite and affect parameter hierarchies.

Contribution

It demonstrates that KK modes contribute to the crossover scale in a warped 5D model, relaxing parameter hierarchies needed for phenomenological viability.

Findings

KK modes contribute to the crossover scale $r_c$.

Warping effects keep $r_c$ finite despite infinite KK modes.

Inclusion of KK modes relaxes hierarchy constraints.

Abstract

We discuss contributions of the KK modes to the crossover length scale $r_{\rm c}$ for the brane-induced force when the brane is given by a solitonic background field. We work in a 5D scalar model with a domain-wall background that mimics the DGP model. In spite of the infinite number of the KK modes, the crossover scale remains finite due to the warping effect on the ambient space of the domain wall. The inclusion of the KK modes relaxes the hierarchy among the model parameters that is required to realize a phenomenologically viable size of $r_{\rm c}$. We also discuss whether a nontrivial dilaton background enlarges $r_{\rm c}$ or not.