Zee–Babu model in a Nonholomorphic Modular A 4 Symmetry and Modular Stabilization

Abstract We study a Zee–Babu neutrino model in a nonholomorphic modular $A_4$ symmetry, and we construct a model so that there are minimum free parameters (two complex parameters for the neutrino sector). We find that only the normal hierarchy is allowed. Moreover, the allowed region to satisfy the neutrino oscillation data is localized near $\tau =\omega$. The small absolute deviation plays a crucial role in fitting two mixings of $s^2_{23}$ and $s^2_{12}$. In addition, we obtain several predictions on Majorana and Dirac CP phases and neutrinoless double beta decay, as shown in our chi squared numerical analysis. We also discuss modulus stabilization within the framework of nonsupersymmetric models. Finally, we compute the expansion of modular forms near $\tau =\omega$ in the appendix so that one can apply them to a model and understand its analytical structure.