Radiative neutrino mass models from non-invertible selection rules

TL;DR

This paper introduces a novel approach to radiative neutrino mass models using non-invertible fusion algebra selection rules, which naturally explain tiny neutrino masses and dark matter stability.

Contribution

It applies non-invertible fusion algebra rules to neutrino models, providing a natural explanation for neutrino masses and dark matter stability without additional assumptions.

Findings

Non-invertible selection rules operate at tree level.

Radiative corrections generate tiny neutrino masses.

Remnant symmetry stabilizes dark matter.

Abstract

We apply non-invertible selection rules coming from a fusion algebra to radiative neutrino mass models where fields are labeled by the elements in the algebra. Since non-invertible selection rules only hold at tree level, radiative corrections naturally explain the origin of tiny neutrino masses. Furthermore, a remnant symmetry of the fusion algebra protects the stability of dark matter, which is conventionally imposed in radiative neutrino models. We also find that interesting neutrino mass textures are realized by assigning fields to family-dependent elements in the algebra.