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In the flavor basis where the mass eigenstates of three charged leptons areidentified with their flavor eigenstates, one may diagonalize a 3 X 3 Majorananeutrino mass matrix M_nu by means of the standard parametrization of the 3 X 3neutrino mixing matrix V. In this treatment the unphysical phases of M_nu haveto be carefully factored out, unless a special phase convention for neutrinofields 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 analyticalrelations between the matrix elements of M'_nu M'_nu^dag and seven physicalparameters --- three neutrino masses (m_1, m_2, m_3), three flavor mixingangles (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 symmetrywith theta_23 = pi/4 and maximal CP violation with delta = +/- pi/2, whichshould be useful for discussing specific neutrino mass models. In particular,we show that theta_23 = pi/4 and delta = +/- pi/2 keep unchanged when constantmatter effects are taken into account for a long-baseline neutrino oscillationexperiment.

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