Two-loop rainbow neutrino masses in a non-invertible symmetry

TL;DR

This paper introduces a two-loop neutrino mass model based on a non-invertible ${Z}_6$ symmetry, which naturally includes dark matter candidates and aligns with neutrino oscillation and other experimental constraints.

Contribution

It presents a novel two-loop rainbow neutrino mass model utilizing non-invertible symmetry, linking neutrino masses with dark matter stability and phenomenology.

Findings

Dark matter candidate is the lightest neutral fermion in the model.

The model accommodates neutrino oscillation data and experimental constraints.

The sum of neutrino masses differs between normal and inverted hierarchies.

Abstract

We propose two-loop rainbow type of the neutrino mass model via ${Z}_2$ gauging of ${Z}_6$ non-invertible symmetry in which we introduce three families of isospin doublet vector-like fermions, heavy right-handed neutrinos and isospin doublet and singlet bosons. All new fields, which have nonzero charges under the non-invertible symmetry, can be dark matter candidates, since the non-invertible symmetry possesses a remnant ${Z}_2$ symmetry that plays a role in assuring the stability of our dark matter candidate. Even though the non-invertible symmetry is dynamically broken at one-loop level, its violation does not affect our scenario. In this paper, we especially consider the lightest mode of the neutral components in the doublet vector-like fermions as our main dark matter candidate. The dark matter is potentially degenerated to the other two families of neutral fermions, since the mass difference is induced at one-loop level. Thus, we consider our dark matter candidate in rather simpler co-annihilation system among their particles. Considering all the constraints of neutrino oscillation data, lepton flavor violations, muon $g-2$ and the relic density of dark matter, we perform the numerical analysis and show some allowed regions for these phenomenology. Due to our dark matter nature, the sum of neutrino masses in case of normal hierarchy is larger than that in case of inverted hierarchy, which is opposite situation compared with typical active neutrino models.