Partial \(A_4\) Flavor Symmetry of the Leptonic 3HDM

When the Higgs doublets in the three-Higgs-doublet model (3HDM) transform as a flavor triplet under the \(A_4\) group, the resulting lepton mass matrices reproduce the experimentally observed neutrino mixing angles with arbitrary precision, while simultaneously maintaining the correct mass ordering of both charged and neutral leptons, where the latter are Dirac neutrinos with a normal mass hierarchy. Imposing the \(A_4\) symmetry also allows for agreement between the calculated and observed lepton masses for Higgs vacuum configurations that differ from those required to fit \(U_{\mathrm {PMNS}}\). Among all discrete groups of order less than or equal to 600, no contraction other than the one associated with \(A_4\) leads to a better agreement with experimental data, and the solution structure presented here is unique within the set of groups investigated. Abstract Published by the Jagiellonian University 2026 authors