Lepton masses and mixing in a three-Higgs doublet model

TL;DR

This paper investigates discrete non-Abelian flavor symmetries within a three-Higgs doublet model to understand lepton masses and mixing, finding some groups approximate experimental data but none fully predict it.

Contribution

It systematically searches for discrete flavor symmetries in 3HDM that relate lepton masses and mixing angles, identifying specific groups compatible with observations.

Findings

$ ext{Delta}(96)$ fits neutrino data best

$S_4$ approximates Dirac neutrino mixing

No group fully predicts lepton data

Abstract

In the three-Higgs doublet model (3HDM) frame, we search for discrete flavour symmetries that give relations among the lepton masses and their mixing angles. We explore discreet non-Abelian groups of order less than 1035, treating neutrinos as Majorana or Dirac particles. Despite the free dynamic parameters available in the model, none of the groups fully predicts the lepton data. However, some of the scanned groups provide either the correct neutrino masses and mixing angles or the correct masses of the charged leptons. $\Delta(96)$ is the smallest group compatible with the experimental data of neutrino masses and PMNS mixing. $S_4$ is an approximate symmetry of Dirac neutrino mixing, with parameters staying about $3\sigma$ apart from the measured $\theta_{12}$, $\theta_{23}$, $\theta_{13}$.