Neutrino mass hierarchy from the discrete dark matter model

TL;DR

This paper proposes a model explaining the neutrino mass hierarchy by combining tree-level and one-loop mechanisms within a discrete dark matter framework, involving new particles and symmetries.

Contribution

It introduces a minimal discrete dark matter model with $A_4$ symmetry, new right-handed neutrinos, and scalar doublets to account for neutrino mass differences and mixing.

Findings

The model successfully reproduces neutrino mass hierarchy.

CP breaking is necessary to fit neutrino mixing angles.

Residual $ ext{Z}_2$ symmetry stabilizes dark matter.

Abstract

We explore a possible explanation for the hierarchy in scale between the atmospheric and solar neutrino mass differences ($\lvert \Delta m^{2}_{31} \rvert$, and $\Delta m^{2}_{21}$) through the presence of two distinct neutrino mass mechanisms from tree- and one-loop-level contributions. We demonstrate that the ingredients needed to explain this hierarchy are present in the minimal discrete dark matter model [arXiv:2301.10811]. This scenario is characterized by adding new RH neutrinos and scalar $SU(2)$ doublets to the Standard Model as triplet representations of an $A_4$ flavour 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. We show that CP breaking in the scalar potential is needed to fit the neutrino mixing angles.