Quark mass hierarchy and mixing via geometry of extra dimension with point interactions

TL;DR

This paper introduces a geometric extra-dimensional model with point interactions that naturally explains fermion generations, mass hierarchy, and mixing matrices by localizing chiral fermions and using boundary conditions.

Contribution

It presents a novel extra-dimensional setup with point interactions that simultaneously addresses fermion generations, mass hierarchy, and flavor mixing.

Findings

Three fermion generations emerge from a single 5D fermion.

Mass hierarchy is explained by a coordinate-dependent scalar VEV.

Flavor mixing matrices are constrained by the extra-dimensional geometry.

Abstract

We propose a new model which can naturally explain origins of fermion generations, quark mass hierarchy, and Cabibbo-Kobayashi-Maskawa matrix simultaneously from geometry of an extra dimension. We take the extra dimension to be an interval with point interactions, which are additional boundary points in the bulk space of the interval. Because of the Dirichlet boundary condition for fermion at the positions of point interactions, profiles of chiral fermion zero modes are split and localized, and then we can realize three generations from each five-dimensional Dirac fermion. Our model allows fermion flavor mixing but the form of non-diagonal elements of fermion mass matrices is found to be severely restricted due to geometry of the extra dimension. The Robin boundary condition for a scalar leads to an extra coordinate-dependent vacuum expectation value, which can naturally explain the fermion mass hierarchy.