Discrete dark matter mechanism as the source of neutrino mass scales

TL;DR

This paper proposes a minimal discrete dark matter mechanism involving $A_4$ flavor symmetry to explain the neutrino mass hierarchy and mixing angles, linking dark matter stability with neutrino phenomenology.

Contribution

It introduces a novel minimal model combining discrete dark matter stability with neutrino mass hierarchy using $A_4$ symmetry and CP violation in the scalar potential.

Findings

The model explains the atmospheric and solar neutrino mass splitting hierarchy.

Residual $ ext{Z}_2$ symmetry ensures dark matter stability.

CP violation in the scalar potential is necessary for correct neutrino mixing angles.

Abstract

The hierarchy in scale between atmospheric and solar neutrino mass splittings is investigated through two distinct neutrino mass mechanisms, from tree- and one-loop-level contributions. We demonstrate that the minimal discrete dark matter mechanism contains the ingredients for explaining this hierarchy. This scenario is characterized by adding new RH neutrinos and scalar $SU(2)$-doublets to the Standard Model as triplet representations of an $A_4$ flavor symmetry. The $A_4$ symmetry breaking, which occurs at the electroweak scale, leads to a residual $\mathbb{Z}_2$ symmetry responsible for the dark matter stability and dictates the neutrino phenomenology. Finally, we show that to reproduce the neutrino mixing angles correctly it is necessary to violate CP in the scalar potential.