A Finite Group Analysis of the Quark Mass Matrices and Flavor Dynamics

We perform a finite group analysis on the quark mass matrices. We argue that the dominant terms should be proportional to class operators of the group and that symmetry breaking to split the mass spectrum and simultaneous diagonalizability to suppress flavor changing neutral currents can be accomplished at this point. The natural setting is a multi-scalar model and the scalar doublets can have masses of the weak scale without any parameter tuning. When we specialize to $S_3$ as the group of choice, we arrive at the results that the dominant mass terms are $\lhook$democratic$\rhook$ and that the ratios of light masses and the Cabbibo angle $\cong ({m_d\over m_s})^{1\over 2}$ are all given by group parameters in the breaking of $S_3$ to $S_2$. A large mass expansion is then performed and a generalized Wolfenstein parameterization is given. Further breaking by way of introducing heavy-light transitions in the down-type mass matrix is here related to the heavy-light Cabbibo-Kobayashi-Maskawa elements.