Asymmetry and Minimality of Quark Mass Matrices

Abstract

We systematically investigate general forms of mass matrices for three-generation up and down quarks, including asymmetrical ones in generation space. Viable zero matrix elements are explored which are compatible with the current observation of masses and mixing angles, and also with the recent measurement of CP violation in the B-meson system. The simplest form with the maximal number of vanishing matrix elements is found to be almost consistent with the experimental data, but has a scratch that one of the mixing angle is slightly large. At the next-to-minimal level, it is found with a help of leptonic generation mixing that only six patterns of mass matrices well describe the experimental data. These sets of mass textures predict all the properties of quarks, including the CP violation, as well as the large (charged) lepton mixing, which may be appropriate for the atmospheric neutrino in grand unification scheme.