A Model for the Quark Mass and Flavor Mixing Matrices Based on Discrete Chiral Symmetry as the Origin of Families

We construct a model for the quark mass and flavor mixing matrices, based on the hypothesis that the flavor weak eigenstates in the three families are distinguished by a spontaneously broken discrete $Z_6$ chiral symmetry. In a leading partially symmetric approximation, the model accommodates the family mass spectra, with a CKM matrix that is exactly unity. Adding small asymmetries in first order perturbation theory gives a CKM matrix with the correct qualitative structure, with $s_{23}/s_{12}$ and $s_{13}/s_{12}$ naturally of order $M_s/M_b$.