A generic diagonalization of the 3×3 neutrino mass matrix and its implications on the μ-τ flavor symmetry and maximal CP violation

In the flavor basis where the mass eigenstates of three charged leptons are identified with their flavor eigenstates, one may diagonalize a 3×3 Majorana neutrino mass matrix Mν by means of the standard parametrization of the 3×3 neutrino mixing matrix V. In this treatment the unphysical phases of Mν have to be carefully factored out, unless a special phase convention for neutrino fields is chosen so as to simplify Mν to Mν′ without any unphysical phases. We choose this special flavor basis and establish some exact analytical relations between the matrix elements of Mν′Mν′† and seven physical parameters - three neutrino masses (m1, m2, m3), three flavor mixing angles (θ12, θ13, θ23) and the Dirac CP-violating phase (δ). Such results allow us to derive the conditions for the μ-τ flavor symmetry with θ23=π/4 and maximal CP violation with δ=±π/2, which should be useful for discussing specific neutrino mass models. In particular, we show that θ23=π/4 and δ=±π/2 keep unchanged when constant matter effects are taken into account for a long-baseline neutrino oscillation experiment.