Discrete Flavor Symmetries and Mass Matrix Textures

We show how introducing discrete Abelian flavor symmetries can produce texture zeros in the fermion mass matrices, while preserving the correct relationships with the low-energy data on quark and lepton masses. We outline a procedure for defining texture zeros as suppressed entries in Yukawa matrices. These texture zeros can account for the coexistence of the observed large mixing in atmospheric neutrino oscillations with a hierarchy in the neutrino masses, and offer the possibility of alignment of the quark and squark mass matrices, and thus giving a solution to the supersymmetric flavor problem. A requirement that the flavor symmetry commutes with the SU(5) grand unified group can be used to explain the lepton mass hierarchies as well as the neutrino parameters, including the large mixing observed in the atmospheric neutrino data. We present one such model that yields a large atmospheric neutrino mixing angle, as well as a solar neutrino mixing angle of order $\lambda \simeq 0.22$.