Brane world: disappearing massive matter

TL;DR

In a brane-world scenario with an infinite extra dimension and localized gravity, bulk fields with zero-mode localization do not acquire true 4D masses when a small bulk mass is introduced; instead, they form metastable quasi-localized states with a complex mass $m=m_0-i\Gamma$, reflecting leakage into the bulk. The scalar sector exhibits a brane-only resonance with $m_0$ and width $\Gamma$, plus a light bulk-mode contribution that produces a power-law long-range potential on the brane, $V(r) \sim 1/r^{7}$, at large distances. The fermion sector shows parameter-dependent width suppression, including regimes where the width is exponentially small, allowing long-lived 4D-like massive fermions. Overall, the work demonstrates a generic mechanism by which brane-localized matter with bulk modes can acquire metastable masses and leak into the extra dimension, with measurable implications for long-distance interactions.

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.