A Generic Diagonalization of the 3X3 Neutrino Mass Matrix and Its Implications on the mu-tau 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 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.

Relating the neutrino mixing angles to a lepton mass hierarchy

We propose two phenomenological scenarios of lepton mass matrices and show that either of them can exactly give rise to tan^2theta_{13} = m_e/(m_e + 2m_mu), tan^2theta_{23} = m_mu/(m_e + m_mu) and tan^2theta_{12} = (m_e m_2 + 2m_mu m_1)/(m_e m_1 + 2m_mu m_2) in the standard parametrization of lepton flavor mixing. The third relation, together with current experimental data, predicts a normal but weak hierarchy for the neutrino mass spectrum. We also obtain theta_{13} approx 2.8^circ for the smallest neutrino mixing angle and J approx 1.1% for the Jarlskog invariant of leptonic CP violation, which will soon be tested in the long-baseline reactor and accelerator neutrino oscillation experiments. A seesaw realization of both scenarios is briefly discussed.

Deviations from Tri-bimaximal Neutrino Mixing in Type-II Seesaw and Leptogenesis

Current experimental data allow the zero value for one neutrino mass, either m_1 = 0 or m_3 = 0. This observation implies that a realistic neutrino mass texture can be established by starting from the limit (a) m_1 = m_2 = 0 and m_3 eq 0 or (b) m_1 = m_2 eq 0 and m_3 = 0. In both cases, we may introduce a particular perturbation which ensures the resultant neutrino mixing matrix to be the tri-bimaximal mixing pattern or its viable variations with all entries being formed from small integers and their square roots. We find that it is natural to incorporate this kind of neutrino mass matrix in the minimal Type-II seesaw model with only one heavy right-handed Majorana neutrino N in addition to the SU(2)_L Higgs triplet Delta_L. We show that it is possible to account for the cosmological baryon number asymmetry in the m_3 =0 case via thermal leptogenesis, in which the one-loop vertex correction to N decays is mediated by Delta_L and the CP-violating asymmetry of N decays is attributed to the electron flavor.