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Register a new userCorrelations and textures in the neutrino mass matrix
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The recent enormous improvement of our knowledge of the neutrino oscillation parameters has motivated us to reinvestigate the allowed ranges of the elements of the neutrino mass matrix in the basis where the charged-lepton mass mass matrix is diagonal. Moreover, we have studied the correlations of the elements of the neutrino mass matrix. The result of this analysis is useful for finding textures in the neutrino mass matrix and, therefore, for model building in the lepton sector. As an example, we present two textures of the neutrino mass matrix which have only two parameters and fit very well all current experimental data on the neutrino parameters.
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In view of the latest T2K and MINOS neutrino oscillation data which hint at a relatively large theta_13, we perform a systematic study of the Majorana neutrino mass matrix M_nu with two independent texture zeros. We show that three neutrino masses (m_1, m_2, m_3) and three CP-violating phases (delta, rho, sigma) can fully be determined from two neutrino mass-squared differences (delta m^2, Delta m^2) and three flavor mixing angles (theta_12, theta_23, theta_13). We find that seven patterns of M_nu (i.e., A_{1,2}, B_{1,2,3,4} and C) are compatible with current experimental data at the 3-sigma level, but the parameter space of each pattern is more strictly constrained than before. We demonstrate that the texture zeros of M_nu are stable against the one-loop quantum corrections, and there exists a permutation symmetry between Patterns A_1 and A_2, B_1 and B_2 or B_3 and B_4. Phenomenological implications of M_nu on the neutrinoless double-beta decay and leptonic CP violation are discussed, and a realization of those texture zeros by means of the Z_n flavor symmetries is illustrated.
We discuss the viability of the $mu$--$tau$ interchange symmetry imposed on the neutrino mass matrix in the flavor space. Whereas the exact symmetry is shown to lead to textures of completely degenerate spectrum which is incompatible with the neutrino oscillation data, introducing small perturbations into the preceding textures, inserted in a minimal way, lead however to four deformed textures representing an approximate $mu$--$tau$ symmetry. We motivate the form of these `minimal textures, which disentangle the effects of the perturbations, and present some concrete realizations assuming exact $mu$--$tau$ at the Lagrangian level but at the expense of adding new symmetries and matter fields. We find that all these deformed textures are capable to accommodate the experimental data, and in all types of neutrino mass hierarchies, in particular the non-vanishing value for the smallest mixing angle.
Experimental data on the neutrino mixing and masses strongly suggest an underlying approximate symmetry of the relevant Yukawa superpotential terms. Intensive phenomenological explorations during the last decade indicate that permutation symmetries such as S_4, A_4 and their subgroups, under certain assumptions and vacuum alignments, predict neutrino mass textures compatible with such data. Motivated by these findings, in the present work we analyse the neutrino properties in F-theory GUT models derived in the framework of the maximal underlying E_8 symmetry in the elliptic fibration. More specifically, we consider local F-SU(5) GUT models and study in detail spectral cover geometries with monodromies associated to the finite symmetries S_4, A_4 and their transitive subgroups, including the dihedral group D_4 and Z_2 X Z_2. We discuss various issues that emerge in the implementation of S_4, A_4 neutrino models in the F-theory context and suggest how these can be resolved. Realistic models are presented for the case of monodromies based on their transitive subgroups. We exemplify this procedure with a detailed analysis performed for the case of Z_2 X Z_2 model.
Using the residual symmetry approach, we propose a complex extension of the scaling ansatz on $M_ u$ which allows a nonzero mass for each of the three light neutrinos as well as a nonvanishing $theta_{13}$. Leptonic Dirac CP violation must be maximal while atmospheric neutrino mixing need not to be exactly maximal. Each of the two Majorana phases, to be probed by the search for $0 u betabeta$ decay, has to be zero or $pi$ and a normal neutrino mass hierarchy is allowed.
Neutrino mass sum rules have recently gained again more attention as a powerful tool to discriminate and test various flavour models in the near future. A related question which was not yet discussed fully satisfactorily was the origin of these sum rules and if they are related to any residual or accidental symmetry. We will address this open issue here systematically and find previous statements confirmed. Namely, that the sum rules are not related to any enhanced symmetry of the Lagrangian after family symmetry breaking but that they are simply the result of a reduction of free parameters due to skillful model building.
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