See-Saw Realization of the Texture Zeros in the Neutrino Mass Matrix

We study the see-saw realization of seven textures of the neutrino mass matrix, which were presented by Frampton, Glashow and Marfatia. Two of them ($\rm B_1$ and $\rm B_2$) are not realized in the see-saw mechanism without fine-tuning of parameters. We present some specific textures of the Dirac neutrino mass matrix and the right-handed Majorana neutrino one. In order to test these textures, we discuss the effect on the branching ratio of $\mu \to e \gamma$. We also study the $U(1)_X \times U(1)_{X'}$ flavor symmetry, in which $U(1)_X$ is anomalous and $U(1)_{X'}$ is non-anomolous, to reproduce texture zeros. We present examples of U(1) charges for two textures ($\rm A_1$ and $\rm A_2$) .