Zee-Babu model in a non-holomorphic modular $A_4$ symmetry and modular stabilization

TL;DR

This paper develops a minimal Zee-Babu neutrino model with non-holomorphic modular $A_4$ symmetry, predicting normal hierarchy and specific CP phases, while also analyzing modulus stabilization and modular form expansions.

Contribution

It introduces a minimal Zee-Babu model with non-holomorphic modular $A_4$ symmetry, constraining parameters and providing analytical modular form expansions.

Findings

Only normal hierarchy is allowed.

Allowed parameter region near $ au=\omega$.

Predictions for CP phases and neutrinoless double beta decay.

Abstract

We study a Zee-Babu neutrino model in a non-holomorphic modular $A_4$ symmetry, and we construct a model so that there are minimum free parameters (two complex parameters). We find only the normal hierarchy is allowed. Moreover, the allowed region to satisfy the neutrino oscillation data is localized at nearby $\tau=\omega$. 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 square numerical analysis. We also study modulus stabilization within the framework of non-supersymmetric models. In the end, we compute the expansion of modular forms at nearby $\tau=\omega$ in the Appendix so that one can apply them for a model and understand its analytical structure.