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

الأصل · EN

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 Mₙu by means of the standard parametrization of the 3 X 3 neutrino mixing matrix V. In this treatment the unphysical phases of Mₙu have to be carefully factored out, unless a special phase convention for neutrino fields is chosen so as to simplify Mₙu 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'ₙuᵈag and seven physical parameters --- three neutrino masses (m₁, m₂, m₃), three flavor mixing angles (theta₁2, theta₁3, theta₂3) and the Dirac CP-violating phase (delta). Such results allow us to derive the conditions for the mu-tau flavor symmetry with theta₂3 = 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 theta₂3 = pi/4 and delta = +/- pi/2 keep unchanged when constant matter effects are taken into account for a long-baseline neutrino oscillation experiment.