Partial $A_4$ flavor symmetry of the leptonic 3HDM

TL;DR

This work analyzes a leptonic sector in a $3$Higgs-doublet model ($3$HDM) where all leptons and the three Higgs doublets form triplets under a finite flavor group $G$. By enforcing Dirac neutrinos and two independent flavor contractions ($n^l=n^ u=2$) and allowing free Higgs VEV alignments, a comprehensive scan for groups with order up to $600$ shows that $A_4$ uniquely yields viable lepton mixing via $U_{PMNS}$ while reproducing charged-lepton mass ratios; however, the absolute neutrino masses and the CP-violating phase do not match current data. The resulting mass matrices share a characteristic monomial form tied to the VEVs $v_i$, producing a fixed $M^l$ and $M^ u$ structure and a preserved normal mass ordering. The study highlights $A_4$ as the minimal flavorful symmetry capable of addressing both mixing and mass ordering in this Dirac-neutrino, $3$HDM context and points to CP-phase tension and avenues for refinement through extended representations or Majorana terms.

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.

Figures (2)

• Figure 1: Case $n^l = n^{\nu} = 2$. The blue (yellow) points are projections onto the $|v_2/v_1|-|v_3/v_1|$ plane from calculations of NO (IO) neutrino mass ratios consistent with experimental data. The black curve represents calculations of correct charged lepton mass ratios. The intersection of the latter curve and the blue area signifies the calculations of viable lepton masses. The red curve displays $|\lambda^l_2/\lambda^l_1|$ as function of $|v_2/v_1|$ from the calculations that produce the black curve.
• Figure 2: Case $n^l = n^{\nu} = 2$. Points projected onto the $|v_2/v_1|-|v_3/v_1|$ plane yielding PMNS mixing angles consistent with experimental data, satisfying $\chi^2 (\sin^2 \theta_{12}) + \chi^2 (\sin^2 \theta_{23}) + \chi^2 (\sin^2 \theta_{13}) < 3$.