Dirac one-loop seesaw in a non-invertible fusion rule

TL;DR

This paper introduces a radiative Dirac neutrino mass model stabilized by a non-invertible fusion rule from a gauged symmetry, explaining neutrino masses, mixings, and dark matter while remaining consistent with experimental bounds.

Contribution

It presents a novel minimal framework using non-invertible fusion rules to connect neutrino physics and dark matter in a radiative model.

Findings

Neutrino masses and mixings match current oscillation data.

Dark matter candidate is a bosonic singlet with correct relic density.

Lepton flavor violation and magnetic moments are within experimental bounds.

Abstract

We propose a radiative Dirac neutrino mass model stabilized by a non-invertible fusion rule originating from a $Z_3 \times Z_3'$ gauging. The imposed symmetry forbids tree-level Yukawa couplings and ensures that neutrino masses are generated only at the one-loop level through the exchange of exotic fermions and inert scalars. This minimal framework simultaneously accommodates neutrino masses and mixings consistent with current oscillation data, while providing a viable dark matter candidate. We analyze lepton flavor violating processes and lepton anomalous magnetic moments, finding that all contributions remain well below present experimental bounds. In the dark matter sector, the bosonic singlet emerges as a promising candidate with relic density compatible with cosmological observations, whereas the fermionic option is strongly disfavored due to suppressed annihilation cross sections. Our study demonstrates that non-invertible fusion rules can serve as a powerful organizing principle for constructing minimal and phenomenologically consistent extensions of the Standard Model, linking neutrino physics and dark matter within a unified radiative framework.