Investigation of a kind of neutrino mass matrix

Abstract

We carry out diagonalization of a kind of Majorana neutrino mass matrix $M=M_{\nu }{M}_{\nu }^{†}$ 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.

14 pages