A method to explore flavor symmetries of the 3HDM and their implications on lepton masses and mixing

TL;DR

This paper introduces a computational method to identify and analyze flavor symmetry groups in the three-Higgs-doublet model, assessing their implications for lepton masses and mixing, and finds no exact match with experimental data among groups of order less than 1035.

Contribution

The paper develops a novel, computer-implemented approach to systematically explore flavor symmetry groups in the 3HDM and evaluate their phenomenological viability.

Findings

No discrete groups of order less than 1035 exactly reproduce lepton masses and mixing angles.

Several groups are found to be partially or approximately consistent with experimental data.

The method supports exploring various symmetry group hypotheses in the 3HDM.

Abstract

We present a method to identify symmetry groups of the Yukawa sector of the three-Higgs-doublet model and to determine the implication that the symmetry has on the lepton masses and mixing. The method can accommodate different hypotheses about the group representation assignments, and thus support the exploration of candidate symmetry groups. For one particular representation selection scheme we apply the computer-implemented method to scan all discrete groups of order less than 1035. It can be proven that none of these groups defines a flavor symmetry that implies masses and neutrino mixing angles consistent with the experimental lepton data, although several cases are found that are partially or approximately consistent.