Unitarity constraints on trimaximal mixing

TL;DR

This paper explores the constraints on neutrino mixing matrices when the middle column is trimaximal, revealing how unitarity and CP violation interplay and identifying conditions for maximal CP violation.

Contribution

It provides a detailed analysis of unitarity constraints on trimaximal neutrino mixing, highlighting the relationship between mixing angles and CP violation, and characterizing the parameter space.

Findings

Maximal CP violation occurs at maximal 2-3 mixing.

The mixing matrix has four independent parameters, reducing to one in CP conservation.

Constraints link deviations from maximal mixing to CP violation levels.

Abstract

When the neutrino mass eigenstate $\nu_2$ is trimaximally mixed, the mixing matrix is called trimaximal. The middle column of trimaximal mixing matrix is identical to tri-bimaximal mixing and the other two columns are subject to unitarity constraints. This corresponds to a mixing matrix with four independent parameters in the most general case. Apart from the two Majorana phases, the mixing matrix has only one free parameter in the CP conserving limit. Trimaximality results into interesting interplay between mixing angles and CP violation. A notion of maximal CP violation naturally emerges here: CP violation is maximal for maximal 2-3 mixing. Similarly, there is a natural constraint on the deviation from maximal 2-3 mixing which takes its maximal value in the CP conserving limit.