Neutrino phenomenology in the modular $S_3$ seesaw model

We have studied neutrino phenomenology in the supersymmetric type-I seesaw model endowed with the $\Gamma_2 \simeq S_3$ modular symmetry. We have identified different realizations of the $S_3$ modular symmetry, referred to as models A, B, C, and D. The 4 models are compatible with neutrino mass being inverted ordering (IO). Moreover, models A, B, and D can also accommodate normal ordering (NO) neutrino masses. We identify parameter space for each model compatible with neutrino oscillation at the 2-$\sigma$ level. We then proceed to study the neutrino phenomenology of each model. We find that the lightest neutrino mass can be as light as 0.64 meV in the case of NO in model A and 50 meV in the case of IO in model D. The smallest effective electron neutrino mass attainable in our analysis is 8.8 meV in the case of NO (model A), and 50 meV for IO (model D). Finally, we note that the effective Majorana mass can be as small as 0.33 meV in the case of NO (model A) and 22 meV for IO (model D).