$A_4$ and CP symmetry and a model with maximal CP violation

TL;DR

This paper explores a novel $A_4$ and CP symmetry framework that predicts maximal CP violation and specific lepton mixing angles, providing a concrete model consistent with observed lepton masses and mixing parameters.

Contribution

It introduces a new CP symmetry compatible with $A_4$, analyzes resulting mixing patterns, and constructs a model achieving observed lepton properties with maximal CP violation.

Findings

Predicts maximal atmospheric mixing angle and Dirac CP phase.

Reproduces charged lepton mass hierarchy and correct reactor angle.

Establishes a correlation between mixing angles $ ext{sin}^2 heta_{12} ext{cos}^2 heta_{13}=1/3$.

Abstract

We study a second CP symmetry compatible with the $A_4$ flavor group, which interchanges the representations $\mathbf{1}'$ and $\mathbf{1}"$. We analyze the lepton mixing patterns arising from the $A_4$ and CP symmetry broken to residual subgroups $Z_3$ and $Z_2\times CP$ in the charged lepton and neutrino sectors respectively. One phenomenologically viable mixing pattern is found, and it predicts maximal atmospheric mixing angle as well as maximal Dirac CP phase, trivial Majorana phase and the correlation $\sin^2\theta_{12}\cos^2\theta_{13}=1/3$. We construct a concrete model based on the $A_4$ and CP symmetry, the above interesting mixing pattern is achieved, the observed charged lepton mass hierarchy is reproduced, and the reactor mixing angle $\theta_{13}$ is of the correct order.