Brane world: Disappearing massive matter

In a brane (domain wall) scenario with infinite extra dimensions and localized gravity, bulk fermions and scalars often have bound states with a zero four-dimensional mass. In this way, massless matter residing on the brane may be obtained. We consider what happens when one tries to introduce a small, but nonvanishing mass to these matter fields. We find that the discrete zero modes turn into quasilocalized states with a finite four-dimensional mass and finite width. The latter is due to tunneling of massive matter into extra dimensions. 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 four-dimensional scalar potential has, in fact, a power-law behavior at large distances.