Neutrino mass model with a modular $S_4$ symmetry

TL;DR

This paper introduces a predictive neutrino mass model based on a modular $S_4$ symmetry, utilizing radiative seesaw mechanisms and modular weights to explain neutrino properties and dark matter stability.

Contribution

It presents a novel neutrino mass model with modular $S_4$ symmetry, incorporating radiative seesaw and modular weights to predict neutrino parameters and dark matter stability.

Findings

Predictive neutrino mass matrices in the normal hierarchy.

Numerical analysis matching observed neutrino mixing and phases.

Sample points demonstrating minimal $chi^2$ and best-fit CP phase.

Abstract

We propose a predictive lepton model under a modular $S_4$ symmetry, where the neutrino mass matrix arises from a radiative seesaw at one-loop level. The tree-level mass matrix is forbidden by well-assigned modular weights, which also play an important role in stabilizing dark matter candidate due to a remnant $Z_2$ symmetry even after breaking the modular symmetry. Supposing three families of the Majorana neutrinos, right-handed charged-leptons and left-handed charged-leptons to be embedded respectively into singlet, doublet, and triplet under $S_4$, we obtain the predictive mass matrices in the normal hierarchy. Then, we show our numerical results such as phases, mixings, and neutrino masses, applying $\chi^2$ analysis. We also demonstrate two sample points, imposing on minimizing $\chi^2$ and best fit value of $\delta_{CP}^\ell$ of $195^\circ$.