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We construct a class of renormalizable models for lepton mixing that generate predictions given in terms of the charged-lepton mass ratios. We show that one of those models leads, when one takes into account the known experimental values, to almost maximal CP-breaking phases and to almost maximal neutrinoless double-beta decay. We study in detail the scalar potential of the models, especially the bounds imposed by unitarity on the values of the quartic couplings.
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A model independent analysis of the leptonic Dirac CP-violating phase ({delta}) is presented. The analysis uses the experimentally determined values of the mixing angles in the lepton mixing matrix in order to explore the allowed values for {delta} and possible general forms for the charged lepton mixing matrix. This is done under two general assumptions: 1) that the mixing matrix in the neutrino sector is the so-called tribimaximal matrix and hence the non zero value for {theta}13 arises due to the mixing matrix in the charged lepton sector and 2) the charged lepton mixing matrix is parametrized in terms of three angles and one phase. It is found that any value of {delta} is still consistent with the data and that, considering the assumptions above, regardless of the value for {delta}, the 1-3 mixing angle in the charged lepton sector is small but non zero and the 2-3 mixing angle can take values in only two possible small ranges around 0 and {pi}/2 respectively.
After the successful determination of the reactor neutrino mixing angle theta_13 ~ 0.16 eq 0, a new feature suggested by the current neutrino oscillation data is a sizeable deviation of the atmospheric neutrino mixing angle theta_23 from pi/4. Using the fact that the neutrino mixing matrix U = U_e^dagger U_ u, where U_e and U_ u result from the diagonalisation of the charged lepton and neutrino mass matrices, and assuming that U_ u has a i) bimaximal (BM), ii) tri-bimaximal (TBM) form, or else iii) corresponds to the conservation of the lepton charge L = L_e - L_mu - L_tau (LC), we investigate quantitatively what are the minimal forms of U_e, in terms of angles and phases it contains, that can provide the requisite corrections to U_ u so that theta_13, theta_23 and the solar neutrino mixing angle theta_12 have values compatible with the current data. Two possible orderings of the 12 and the 23 rotations in U_e, standard and inverse, are considered. The results we obtain depend strongly on the type of ordering. In the case of standard ordering, in particular, the Dirac CP violation phase delta, present in U, is predicted to have a value in a narrow interval around i) delta ~ pi in the BM (or LC) case, ii) delta ~ 3pi/2 or pi/2 in the TBM case, the CP conserving values delta = 0, pi, 2pi being excluded in the TBM case at more than 4sigma. In the addendum we discuss the implications of the latest 2013 data.
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.
We present a general framework for models in which the lepton mixing matrix is the product of the maximal mixing matrix U_omega times a matrix constrained by a well-defined Z_2 symmetry. Our framework relies on neither supersymmetry nor non-renormalizable Lagrangians nor higher dimensions; it relies instead on the double seesaw mechanism and on the soft breaking of symmetries. The framework may be used to construct models for virtually all the lepton mixing matrices of the type mentioned above which have been proposed in the literature.
We show how the two physically-distinct sources of CP-asymmetry relevant to scenarios of leptogenesis: (i) resonant mixing and (ii) oscillations between different flavours can be unambiguously identified within the Kadanoff-Baym formalism. These contributions are isolated by analyzing the spectral structure of the non-equilibrium propagators without relying on the definition of particle number densities. The mixing source is associated with the usual mass shells, whereas the oscillation source is identified with a third intermediate shell. In addition, we identify terms lying on the oscillation shell that can be interpreted as the destructive interference between mixing and oscillation. We confirm that identical shell structure is obtained in both the Heisenberg- and interaction-picture realizations of the Kadanoff-Baym formalism. In so doing, we illustrate the self-consistency and complementarity of these two approaches. The interaction-picture approach in particular has the advantage that it may be used to analyze all forms of mass spectra from quasi-degenerate through to hierarchical.
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