Brane world: disappearing massive matter

TL;DR

This paper investigates how introducing small masses to matter fields on a brane in extra-dimensional models causes zero modes to become quasi-localized with finite mass and width, due to tunneling into the extra dimension.

Contribution

It demonstrates that small mass perturbations turn zero modes into quasi-localized states with finite width, a phenomenon likely common in bulk field theories.

Findings

Zero modes become quasi-localized with finite mass and width.

Tunneling into the extra dimension causes the finite width.

Scalar potentials exhibit power-law behavior at large distances.

Abstract

In a brane (domain wall) scenario with an infinite extra dimension and localized gravity, bulk fermions and scalars often have bound states with zero 4-dimensional mass. In this way massless matter residing on the brane may be obtained. We consider what happens when one tries to introduce small, but non-vanishing mass to these matter fields. We find that the discrete zero modes turn into quasi-localized states with finite 4-dimensional mass and finite width. The latter is due to tunneling of massive matter into extra dimension. We argue that this phenomenon is generic to fields that can have bulk modes. We also point out that in theories meant to describe massive scalars, the 4-dimensional scalar potential has, in fact, power-law behavior at large distances.