The Flavor Symmetry

Assuming that the lepton, quark and Higgs fields belong to the three-dimensional reducible representation of the permutation group S₃, we suggest a minimal S₃ invariant extension of the standard model. We find that in the leptonic sector, the exact S₃ × Z₂ symmetry, which allows 6 real independent parameters, is consistent with experimental data and predicts the bi-maximal mixing of the left-handed neutrinos and that the third neutrino is the lightest neutrino. Z₂ is anomaly-free, but it forbids CP-violations in the leptonic, as well as in the hadronic sector. Therefore, the origin of CP-violations can be identified with the breaking of the Z₂ symmetry, which may be understood in a more fundamental theory. With the exact S₃ only, there are 10 real independent parameters and one independent phase, on which the Cabibbo-Kobayashi-Maskawa mixing matrix V_CKM depends. A set of values of these parameters that are consistent with experimental observations is given.