Maximal CP Violation in Flavor Neutrino Masses

TL;DR

This paper explores conditions under which the neutrino mass matrix exhibits maximal CP violation, deriving specific textures and analyzing their implications for Majorana CP violation and neutrino mixing angles.

Contribution

It introduces new constraints on neutrino mass matrix elements that lead to maximal CP violation and discusses specific textures including the case with maximal atmospheric mixing.

Findings

Derived textures of neutrino mass matrix with maximal CP violation.

Identified the dependence of Majorana CP violation on the phase of M_{ee}.

Proposed a simple solution with M_{ττ}=M_{μμ}* for maximal CP violation.

Abstract

Since flavor neutrino masses $M_{\mu\mu,\tau\tau,\mu\tau}$ can be expressed in terms of $M_{ee,e\mu,e\tau}$, mutual dependence among $M_{\mu\mu,\tau\tau,\mu\tau}$ is derived by imposing some constraints on $M_{ee,e\mu,e\tau}$. For appropriately imposed constraints on $M_{ee,e\mu,e\tau}$, we show a texture of neutrino mass matrix giving rise to maximal CP violation. When the atmospheric neutrino mixing is also maximal, we discuss various specific textures of neutrino mass matrices including the texture with $M_{\tau\tau}=M^\ast_{\mu\mu}$ derived as the simplest solution to the constraint of $M_{\tau\tau}-M_{\mu\mu}$=imaginary, which is required by the constraint of $M_{e\mu}\cos\theta_{23}-M_{e\tau}\sin\theta_{23}$=real for $\cos 2\theta_{23}=0$. It is found that Majorana CP violation depends on the phase of $M_{ee}$.