Addition of First Generation Leptons to the External Flux Model

TL;DR

This paper extends an extra-dimensional electroweak model by incorporating an external magnetic flux, adding first-generation leptons, and exploring the resulting rich mathematical physics.

Contribution

It introduces a theoretical framework for adding first-generation leptons to a flux-permeated extra-dimensional electroweak model, highlighting new phase effects.

Findings

Charged fields acquire additional phases due to external flux.

The model exhibits nontrivial periodicity and rich mathematical structure.

Extension to include leptons maintains key mass relations.

Abstract

In an extra dimensional EW model in M_4 X S_1 there is no distinction mathematically with the standard model analog as far as the degrees of freedom of the two models along with the masses and more importantly the mass ratio relation in the zero mode limit. In this paper we present a theoretical construct of the same geometry but with the addition of an external magnetic flux permeating the extra coordinate. This will give all of the charged fields in the model an additional phase with nontrivial periodicity. This rather important addition leads to very interesting and mathematically rich physics. Here we will present the generalized theory for the addition of first generation leptons to this theory.