# Trimaximal Neutrino Mixing from Modular A4 Invariance with Residual Symmetries

## TL;DR

This paper develops models of lepton masses and mixing based on modular A4 symmetry, predicting trimaximal neutrino mixing and correlations among neutrino oscillation parameters, CP phases, and mass scale.

## Contribution

It introduces new models with residual symmetries in modular A4 framework that successfully describe lepton masses and predict specific neutrino parameter correlations.

## Key findings

- Models predict trimaximal neutrino mixing matrix.
- Models determine the absolute neutrino mass scale.
- Predictions include CP violation phases and parameter correlations.

## Abstract

We construct phenomenologically viable models of lepton masses and mixing based on modular $A_4$ invariance broken to residual symmetries $\mathbb{Z}^{T}_3$ or $\mathbb{Z}^{ST}_3$ and $\mathbb{Z}^S_2$ respectively in the charged lepton and neutrino sectors. In these models the neutrino mixing matrix is of trimaximal mixing form. In addition to successfully describing the charged lepton masses, neutrino mass-squared differences and the atmospheric and reactor neutrino mixing angles $\theta_{23}$ and $\theta_{13}$, these models predict the values of the lightest neutrino mass (i.e., the absolute neutrino mass scale), of the Dirac and Majorana CP violation(CPV) phases, as well as the existence of specific correlations between i) the values of the solar neutrino mixing angle $\theta_{12}$ and the angle $\theta_{13}$ (which determines $\theta_{12}$), ii) the values of the Dirac CPV phase $\delta$ and of the angles $\theta_{23}$ and $\theta_{13}$, iii) the sum of the neutrino masses and $\theta_{23}$, and iv) between the two Majorana phases.