Lepton masses and mixing in a two-Higgs-doublet model

TL;DR

This paper investigates whether finite non-abelian flavor symmetries within a two-Higgs-doublet model can explain lepton masses and mixing, finding no suitable symmetry groups up to order 1025.

Contribution

The study systematically searches for finite subgroups of U3 that could explain lepton properties in 2HDM, concluding none fit the observed data.

Findings

No finite subgroup up to order 1025 reproduces lepton masses and mixing.

The flavor symmetry approach in 2HDM does not resolve lepton flavor structure.

Systematic computational analysis rules out candidate groups.

Abstract

Within the framework of the two-Higgs Doublet Model (2HDM), we attempt to find some discrete, non-abelian flavour symmetry which could provide an explanation for the masses and mixing matrix elements of leptons. Unlike the Standard Model, currently there is no need for the flavour symmetry to be broken. With the GAP program we investigate all finite subgroups of the U3 group up to the order of 1025. Up to such an order there is no group for which it is possible to select free model parameters in order to match the masses of charged leptons, masses of neutrinos, and the Pontecorvo-Maki-Nakagawa-Sakata mixing matrix elements in a satisfactory manner.