Neutrino Masses and Dark Matter Stability in 3HDMs with Minimal Non-Abelian Discrete Symmetries

Abstract

We present minimal three-Higgs-doublet models (3HDMs) based on global non-Abelian discrete symmetries that simultaneously explain neutrino masses and dark matter stability. A residual $Z_2$ parity from the spontaneous breaking of the new symmetry stabilizes the dark matter candidate, which runs in the loop generating neutrino masses at one loop alongside a tree-level type-I seesaw contribution. We identify $S_3$ and $D_4$ as the smallest non-Abelian groups realizing this framework and determine the minimal models in both cases that are consistent with current neutrino oscillation data. The resulting models conserve CP in both the Yukawa and scalar sectors.