Quark-Lepton Mass Matrices with $U(1)\times Z_2 \times Z_2'$ Flavor Symmetry

Abstract

The U(1) flavor symmetry explains the large mixing of neutrinos while it leads to the unique texture for the quark mass matrices. It is remarked that U(1) symmetric mass matrices have the phenomenological defects. In the quark sector, the mixing $V_{ub}$ is predicted to be large compared with the expected value $\l^4$ at the GUT scale. In the lepton sector, U(1) charges, which give a large mixing in the neutrino sector, also lead to the large one in the charged lepton sector. In the viewpoint of the flavor symmetry, this is an unpleasant feature because the neutrino mass hierarchy is determined only by unknown coefficients of ${\cal O}(1)$, and the near-maximal flavor mixing is not guaranteed in the case of both large angle rotations. These defects disappear by introducing additional discrete symmetries $Z_2\times Z_2'$. The $U(1)\times Z_2\times Z_2'$ quark-lepton mass matrices are presented by taking account of the recent data of atmospheric neutrinos and solar neutrinos.