Phenomenology of Inverse Seesaw Using $S_3$ Modular Symmetry

Abstract

Describing neutrino masses using the inverse seesaw mechanism with discrete flavor symmetry imposed through modular forms provides a testable framework at TeV scales with fewer parameters. However, $S_3$, the smallest modular group, remains relatively underexplored. In this work, we construct the minimal supersymmetric inverse seesaw model based on the modular $S_3$ flavor symmetry. In our model, the light neutrino mass matrix depends on 6 real parameters: the complex modulus, an overall scale for light neutrino mass, a real ratio and a complex ratio of Yukawa coupling. Thanks to its minimality, our model offers various definite predictions: the lightest neutrino is massless, the neutrino masses are inverted ordering, the sum of the three light neutrino masses (${\sum }_i{m}_i$) is 100 meV, the effective mass for the end point of the beta decay spectrum is 50 meV, the effective mass for neutrinoless double beta decay ($m_{ee}$) is in the range $38-58$ meV. In particular, the predicted values for ${\sum }_i{m}_i$ and $m_{ee}$ from our model are within reach of the next generation experiments. Our model also predicts radiative lepton flavor violating decays $\ell \to {\ell }^{\prime }\gamma$ which are compatible with experimental constraints.

Comments: 20 pages, 4 figures. V2: added references