Neutrino mass model with a modular $S_4$ symmetry

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 $195^{\circ }$.

Comments: 14 pages, 3 figures, 3 tables.; Modified model: Reanalyzed, appendix added; Modified model