Hybrid Textures of Neutrinos

We present numerical and comprehensive analyses of the sixty hybrid textures of neutrinos, which have an equality of matrix elements and one zero. These textures are possibly derived from the discrete symmetry. Only six textures among sixty ones are excluded by the present experimental data. Since there are many textures which give similar predictions, the textures are classified based on the numerical results. The neutrinoless double beta decay is also examined in these textures. Our results suggest that there remain still rich structures of the neutrino mass matrix in the phenomenological point of view.Comment: 19 pages, 9 figures; analytical discussions added, table and reference adde

Geometrical characterization of textures consisting of two or three discrete colorings

Geometrical characterization for discretized contrast textures is realized by computing the Gaussian and mean curvatures relative to the central pixel of a clique and four neighboring pixels, these four neighbors either being first or second order neighbors. Practical formulae for computing these curvatures are presented. Curvatures based on the central pixel depend upon the brightness configuration of the clique pixels. Therefore the cliques are classified into classes by configuration of pixel contrast or coloring. To look at the textures formed by geometrically classified cliques, we create several textures using overlapping tiling of cliques belonging to a single curvature class. Several examples of hyperbolic textures, consisting of repeated hyperbolic cliques surrounded by non-hyperbolic cliques, are presented with the nonhyperbolic textures. We also introduce a system of 81 rotationally and brightness shift invariant geo-cliques that have shared curvatures and show that histograms of these 81 geo-cliques seem to be able to distinguish isotrigon textures

Birefringent Electroweak Textures

The behaviour of electromagnetic waves propagating through an electroweak homilia string network is examined. This string network is topologically stable as a cosmic texture, and is characterized by the spatial variation of the isospin rotation of the Higgs field. As a consequence the photon field couples to the intermediate vector bosons, producing a finite range electromagnetic field. It is found that the propagation speed of the photon depends on its polarization vector, whence an homilia string network acts as a birefringent medium. We estimate the birefringent scale for this texture and show that it depends on the frequency of the electromagnetic wave and the length scale of the homilia string network.Comment: 10 page

Zeros of the inverted neutrino mass matrix

I investigate viable textures with two texture zeros for the inverted neutrino mass matrix, and present the predictions of those textures for the neutrino masses and for lepton mixing. By using an Abelian symmetry and one or two heavy scalar singlets, I construct realizations of those textures in the context of seesaw models.Comment: 7 pages, LaTe