CP phase from Higgs's boundary condition

TL;DR

This paper introduces a novel mechanism where a non-trivial Higgs boundary condition in extra dimensions generates a CP phase, explaining fermion generations, mass hierarchy, and CKM matrix structure.

Contribution

It presents a new approach using twisted boundary conditions in extra dimensions to produce a CP phase from the Higgs vacuum expectation value.

Findings

Successfully generates a CP phase from boundary conditions

Explains fermion mass hierarchy and generations

Reproduces CKM matrix structure with CP phase

Abstract

We propose a new mechanism to generate a CP phase originating from a non-trivial Higgs vacuum expectation value in an extra dimension. A twisted boundary condition for the Higgs doublet can produce an extra dimensional coordinate-dependent vacuum expectation value containing a CP phase degree of freedom. With this mechanism, we construct a phenomenological model on S^{1} which can simultaneously and naturally explain the origins of the fermion generations, the quark mass hierarchy and the structure of the Cabibbo-Kobayashi-Maskawa matrix with the CP phase.