Non-holomorphic modular $A_{5}$ symmetry for lepton masses and mixing

TL;DR

This paper systematically explores lepton mass and mixing models based on non-holomorphic $A_{5}$ modular symmetry, identifying models consistent with experimental data with and without generalized CP symmetry, and provides detailed numerical analyses.

Contribution

It offers the first comprehensive classification of lepton models with non-holomorphic $A_{5}$ modular symmetry, including the effects of generalized CP symmetry, and performs detailed numerical studies of selected models.

Findings

21 Weinberg operator models fit data without gCP symmetry.

174 seesaw models fit data without gCP symmetry.

Imposing gCP reduces free parameters and narrows viable models.

Abstract

We perform a comprehensive bottom-up study of all the simplest lepton models based on non-holomorphic $A_{5}$ modular flavor symmetry, in which neutrinos are assumed to be Majorana particles and their masses are generated by the Weinberg operator or the type I seesaw mechanism. In the case that the generalized CP (gCP) symmetry is not considered, we find that 21 Weinberg operator models and 174 seesaw models can accommodate the experimental data in lepton sector, and all of them depend on six dimensionless free parameters and two overall scales. If gCP symmetry compatible with $A_{5}$ modular symmetry is imposed, one more free parameter would be reduced. Then only 4 of the 21 Weinberg operator models and 100 of the 174 seesaw models agree with the experimental data on lepton masses and mixing parameters. Furthermore, we perform a detailed numerical analysis for two example models for illustration.