CP violation in neutrino mixing with $\delta = -\pi/2$ in $A_4$ Type-II seesaw model

TL;DR

This paper explores a neutrino mass model with $A_4$ symmetry that predicts specific CP violation and mixing angles, and examines how breaking a certain symmetry affects these predictions, providing testable scenarios for future experiments.

Contribution

It introduces a class of $A_4$ symmetric Type-II seesaw models with a specific symmetry that predicts fixed CP phase and mixing angles, and analyzes the impact of symmetry breaking on these predictions.

Findings

Model predicts $ heta_{23} = rac{\pi}{4}$ and $\delta = -rac{\pi}{2}$ under GLS symmetry.

Breaking GLS with complex Yukawa couplings modifies $ heta_{23}$ and $\delta$, allowing deviations from initial predictions.

Future experiments can test the effects of GLS breaking on neutrino mixing parameters.

Abstract

We study a class of models for neutrino mass matrix in Type-II seesaw with $A_4$ family symmetry. The resulting neutrino mass matrix can be naturally made to respect a $\mu-\tau$ exchange plus CP conjugate symmetry (GLS) with the CP violating phase $\delta$ and the mixing angle $\theta_{23}$ predicted to be $\pm\pi/2$ and $\pi/4$, respectively. When GLS is explicitly broken by complex Yukawa couplings, the model predictions for $\delta$ and $\theta_{23}$ can be significantly modified. Should future experiments will indeed determine $\theta_{23}$ and $\delta_{CP}$ away from the GLS limit values, one then had to consider models with broken GLS. We study several simple scenarios to show how the modifications arise when GLS is broken and how future experiments can test this class of models.