Investigation of a kind of neutrino mass matrix

Abstract

Abstract We carry out diagonalization of a kind of Majorana neutrino mass matrix M = M ν M ν † of which the real part and imaginary part are commutative. For the matrix M, it is shown in a model-independent way that δ = ±π/2, which implies the maximal strength of CP violation in neutrino oscillations and atmospherical mixing angle would be in the ranges, π/4 < θ 23 < 3π/4, or −3π/4 < θ 23 < −π/4. It is shown that the 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.