Investigation of a kind of neutrino mass matrix

TL;DR

This paper analyzes a specific Majorana neutrino mass matrix, showing it predicts maximal CP violation and constrains mixing angles, with a minimal parameter set, independent of specific models.

Contribution

It provides a model-independent analysis of a special neutrino mass matrix, deriving predictions for CP violation and mixing angles with a minimal parameter set.

Findings

Maximal CP violation with δ = ±π/2.

Atmospheric mixing angle range: π/4 to 3π/4.

Only one free parameter remains after using experimental data.

Abstract

We carry out diagonalization of a kind of Majorana neutrino mass matrix $M=M_\nu M_\nu^\dagger$ of which Real part and Imaginary part are commutative. For the kind of matrix M, it is shown in a model-independent way that $\delta = \pm\pi/2$ which implies the maximal strength of CP violation in neutrino oscillations and atmospherical mixing angle would be in the ranges, $\pi/4 < \theta_{23} < 3\pi/4$, or $-3\pi/4<\theta_{23} < - \pi/4$. It is shown that the kind of Hermitian Majorana neutrino mass matrix M has only five real parameters and furthermore, only one free real parameter (A or D) if using the measured values of three mixing angles and mass squared differences as inputs.