Dynamical generation of fermion mass hierarchy in an extra dimension

TL;DR

This paper introduces a novel mechanism in a five-dimensional model where fermion zero modes localize at boundaries, and their mass hierarchy emerges dynamically through scalar field VEVs and Casimir energy minimization.

Contribution

It presents a new dynamical approach to generate fermion mass hierarchies using extra-dimensional localization and Casimir energy effects.

Findings

Exponential fermion mass hierarchy achieved dynamically.

Localization of zero modes at boundaries controls mass differences.

Casimir energy minimization determines point interaction positions.

Abstract

We propose a new mechanism to produce a fermion mass hierarchy dynamically in a model with a singlet generation of fermions. A five dimensional gauge theory on an interval with point interactions (zero-width branes) takes responsibility for realizing three generations and each massless zero mode localizes at boundaries of the segments on the extra dimension. An extra-dimension coordinate-dependent vacuum expectation value of a scalar field makes large differences in overlap integrals of the localized zero modes and then an exponential fermion mass hierarchy can appear. The positions of the point interactions control the magnitude of the fermion mass hierarchy and are determined by the minimization condition of the Casimir energy. As a result of the minimization of the Casimir energy, an exponential mass hierarchy appears dynamically. We also discuss the stability of the extra dimension.