CP violation in neutrino mixing with $δ= -π/2$ in $A_4$ Type-II seesaw model

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.