Three-loop induced neutrino mass model in a non-invertible symmetry

TL;DR

This paper introduces a novel three-loop neutrino mass model utilizing a non-invertible symmetry, which naturally suppresses tree-level neutrino masses and incorporates dark matter candidates, with detailed numerical analysis of phenomenological constraints.

Contribution

It presents a new three-loop neutrino mass generation mechanism based on a non-invertible symmetry, extending the Ma model with vector-like fermions and singlet bosons, and explores its phenomenological viability.

Findings

Successfully satisfies lepton flavor violation constraints

Explains muon g-2 anomaly within the model

Identifies viable dark matter candidates

Abstract

We propose a new type of radiatively induced neutrino masses at three-loop level based on the Ma model, introducing a non-invertible symmetry in the class under a ${\mathbb Z_2}$ gauging of ${\mathbb Z_6}$ symmetry and adding three isospin doublet vector-like fermions $L'$ and singlet boson $S_0$. Under this symmetry, the Yukawa interactions directly related to the neutrino masses are not allowed at tree-level. However it is allowed at one-loop level due to $L'$ and $S_0$ as well as $\eta$, which is no longer invariant under this symmetry. Therefore, the symmetry is dynamically broken. Intriguingly, $\eta$ plays important roles in contributing to both the radiative matrices $y^\eta$ and $m_\nu$. After constructing our model, we show some numerical analyses to satisfy the lepton flavor violations, muon anomalous magnetic dipole moment, and a boson dark matter candidate $S_0$ or $\eta_R$ for the cases of normal hierarchy and inverted hierarchy. Then, we demonstrate allowed space for our input parameters.