Hierarchies without symmetries from extra dimensions

Abstract

It is commonly thought that small couplings in a low-energy theory, such as those needed for the fermion mass hierarchy or proton stability, must originate from symmetries in a high-energy theory. We show that this expectation is violated in theories where the standard model fields are confined to a thick wall in extra dimensions, with the fermions ``stuck'' at different points in the wall. Couplings between them are then suppressed due to the exponentially small overlaps of their wave functions. This provides a framework for understanding both the fermion mass hierarchy and proton stability without imposing symmetries, but rather in terms of higher dimensional geography. A model independent prediction of this scenario is non-universal couplings of the standard model fermions to the ``Kaluza-Klein'' excitations of the gauge fields. This allows a measurement of the fermion locations in the extra dimensions at the CERN LHC or NLC if the wall thickness is close to the TeV scale.