Hierarchies without Symmetries from Extra Dimensions

TL;DR

This paper proposes a geometric mechanism in extra dimensions where fermion mass hierarchies and proton stability arise from wave function overlaps, eliminating the need for symmetries and predicting non-universal gauge couplings.

Contribution

It introduces a framework where fermion hierarchies and stability are explained by extra-dimensional geography rather than symmetries, with testable predictions at colliders.

Findings

Wave function overlaps suppress couplings exponentially.

Fermion mass hierarchy and proton stability explained without symmetries.

Non-universal couplings to Kaluza-Klein gauge modes predicted.

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 LHC or NLC if the wall thickness is close to the TeV scale.