A Generic Diagonalization of the 3X3 Neutrino Mass Matrix and Its Implications on the mu-tau Flavor Symmetry and Maximal CP Violation

TL;DR

This paper derives exact analytical relations for the neutrino mass matrix in a specific flavor basis, elucidating conditions for mu-tau symmetry and maximal CP violation, with implications for neutrino mass models and long-baseline experiments.

Contribution

It provides a generic diagonalization approach for the 3x3 neutrino mass matrix and establishes relations linking matrix elements to physical parameters, clarifying symmetry and CP violation conditions.

Findings

Conditions for mu-tau symmetry with theta_23 = pi/4

Conditions for maximal CP violation with delta = +/- pi/2

Invariance of these conditions under matter effects in long-baseline experiments

Abstract

In the flavor basis where the mass eigenstates of three charged leptons are identified with their flavor eigenstates, one may diagonalize a 3 X 3 Majorana neutrino mass matrix M_nu by means of the standard parametrization of the 3 X 3 neutrino mixing matrix V. In this treatment the unphysical phases of M_nu have to be carefully factored out, unless a special phase convention for neutrino fields is chosen so as to simplify M_nu to M'_nu without any unphysical phases. We choose this special flavor basis and establish some exact analytical relations between the matrix elements of M'_nu M'_nu^dag and seven physical parameters --- three neutrino masses (m_1, m_2, m_3), three flavor mixing angles (theta_12, theta_13, theta_23) and the Dirac CP-violating phase (delta). Such results allow us to derive the conditions for the mu-tau flavor symmetry with theta_23 = pi/4 and maximal CP violation with delta = +/- pi/2, which should be useful for discussing specific neutrino mass models. In particular, we show that theta_23 = pi/4 and delta = +/- pi/2 keep unchanged when constant matter effects are taken into account for a long-baseline neutrino oscillation experiment.