Quark/lepton mass and mixing in S_3 invariant model and CP-violation of neutrino

Understand

Weak bases of flavors (u, c), (d,s), (e, \mu), (\nu_e,\nu_\mu) are assumed as the S_3 doublet and t, b, \tau, {\nu_\tau} are the S_3 singlet and further there are assumed S_3 doublet Higgs (H_1, H_2) and S_3 singlet Higgs H_S.

• We suggest an S_3 invariant model in which the Yukawa interactions constructed from these S_3 doublets and singlets are S_3 invariant.
• In this model, we can explain the quark sector mass hierarchy, quark mixing V_{CKM} and measure of CP violation naturally.
• In the leptonic sector, neutrino masses are assumed to be constructed through the see-saw mechanism from the Majorana mass.