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

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 $L^{\prime }$ 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 $L^{\prime }$ 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.

Comments: 18 pages, 9 figures