Partial $A_4$ flavor symmetry of the leptonic 3HDM

Abstract

When the Higgs doublets in the 3HDM transform as a flavor triplet of the $A_4$ group, the lepton mass matrices accommodate the experimental neutrino mixing angles at arbitrary precision while maintaining the correct mass ordering of the charged and neutral leptons, the latter being Dirac neutrinos in the normal spectrum. Under $A_4$ symmetry, also agreement of the lepton masses with experimental data is obtained for Higgs vacua differing from those for fitting $U_{\text{PMNS}}$. For groups of order equal or less than 600 no contractions different from the one found for $A_4$ yield better agreement with experimental data, and the solution structure presented is unique within the set of groups studied.