Flavor Mass and Mixing and S_3 Symmetry -- An S_3 Invariant Model Reasonable to All --

Abstract

We assume that weak bases of flavors (u, c)_{L,R}, (d,s)_{L,R}, (e, \mu) _{L,R}, (\nu_e, \nu_\mu)_{L,R} are the S_3 doublet and t_{L,R}, b_{L,R}, \tau_{L,R}, {\nu_\tau}_{L,R} are the S_3 singlet and further there are S_3 doublet Higgs (H_D^1, H_D^2) and S_3 singlet Higgs H_S. We suggest an S_3 invariant Yukawa interaction, in which masses caused from the interaction of S_3 singlet flavors and Higgs is very large and masses caused from interactions of S_3 doublet flavors and Higgs are very small, and the vacuum expectation value <|H_D^1|>_0 is rather small compared to the <|H_D^2|>_0. In this model, we can explain the quark sector mass hierarchy, flavor mixing V_{CKM} and measure of CP violation naturally. The leptonic sector mass hierarchy and flavor mixing described by V_{MNS} having one-maximal and one-large mixing character can also be explained naturally with no other symmetry restriction. In our model, an origin of Cabibbo angle is the ratio \lambda=<|H_D^1|>_0 /<|H_D^2|>_0 and an origin of CP violation is the phase of H_D^1.