The discrete family symmetry as a possible solution to the flavour problem

TL;DR

This paper explores extending the Standard Model with a discrete non-abelian family symmetry and an extra Higgs doublet to address fermion masses and mixing, emphasizing mathematical theorems and computational methods.

Contribution

It introduces a novel approach combining discrete non-abelian symmetries with additional Higgs fields to solve the flavor problem.

Findings

Mathematical theorems developed for symmetry analysis

Computational techniques applied to model predictions

Potential explanations for fermion mass hierarchies

Abstract

In order to explain the fermions masses and mixing parameters appearing in the lepton sector of the Standard Model, one proposes the extension of its symmetry. A discrete, non-abelian subgroup of $U(3)$ is added to the gauge group $SU(3)_{C}\times SU(2)_{L}\times U(1)_{Y}$ . Apart from that, one assumes the existence of one extra Higgs doublet. This article focuses mainly on the mathematical theorems and computational techniques which brought us to the results.