Radiative lepton seesaw model in a non-invertible fusion rule and gauged $B-L$ symmetry

TL;DR

This paper introduces a novel radiative lepton seesaw model utilizing a ${f Z}_3$ Tambara-Yamagami fusion rule and gauged $B-L$ symmetry, addressing neutrino masses, dark matter relic density, and lepton flavor violations.

Contribution

It presents a new model combining a non-invertible fusion rule with gauged $B-L$ symmetry to explain neutrino masses and dark matter within a unified framework.

Findings

Successfully fits neutrino oscillation data

Achieves correct dark matter relic density

Predicts observable lepton flavor violation signals

Abstract

We propose a radiative lepton seesaw model with the ${\mathbb Z}_3$ Tambara-Yamagami fusion rule and gauged $B-L$ symmetry. The heavier right-handed neutral fermions ($N_R$) simultaneously contribute to the masses of charged-leptons and neutrinos, and three families of $N_R$ are necessary in realizing realistic mass matrices. On the other hand, we introduce a gauged $B-L$ symmetry to preserve the lepton seesaw mechanism. As a result, this gauged symmetry not only assures the three families of $N_R$ from view point of chiral gauge anomaly cancellation, but also provides a dominant annihilation cross section via Higgs portal in order to explain the correct relic density of dark matter. Finally, we show several numerical results satisfying the neutrino oscillation data, lepton flavor violations, muon $g-2$, and relic density of dark matter.