Lepton models from non-holomorphic $A^{\prime}_{5}$ modular flavor symmetry

Abstract

In the framework of non-holomorphic modular invariance approach, we have systematically constructed all minimal lepton models based on the non-holomorphic $A^{\prime}_{5}$ modular symmetry from a bottom-up approach. In these models, the Yukawa couplings are described by polyharmonic Maaß forms of integer weights at level $N=5$. Under the assumption of Majorana neutrinos, both the Weinberg operator and the type-I seesaw mechanism are considered for neutrino mass generation. All minimal models are found to be based on generalized CP (gCP) symmetry, and each of them depends on five real dimensionless parameters and two overall scales. Through comprehensive numerical scanning, we obtain 6 (4) phenomenologically viable Weinberg operator models and 94 (76) phenomenologically viable seesaw models for normal (inverted) ordering neutrino masses. For each viable model, we present predictions for key neutrino properties, such as lepton masses, CP violation phases, mixing angles, effective Majorana mass for neutrinoless double beta decay and the kinematical mass in beta decay. Furthermore, we provide detailed numerical analysis for two representative models to illustrate our results.