Higgs potential in S3 invariant model for quark/lepton mass and mixing

We analyzed the S-3 invariant Higgs potential with S-3 singlet and doublet Higgs. We obtained a relation (vertical bar v(1)vertical bar/vertical bar v(2)vertical bar)(2) = - sin2 phi(2)/sin2 phi(1) from this S-3 invariant Higgs potential, where v(1), v(2) and phi(1), phi(2) are vacuum expectation values and phases of S-3 doublet Higgs, respectively. This relation could be satisfied exactly by the results vertical bar v(1)vertical bar/vertical bar v(2)vertical bar =0.207, phi(1) = -74.9 degrees, and phi(2) = 0.74 degrees obtained from our previous work analyzing the quark/lepton mass and mixing in the S-3 invariant Yukawa interaction. Furthermore, the relation v(S) similar to v(D) = root vertical bar v(1)vertical bar(2) + vertical bar v(2)vertical bar(2) = 174 GeV is obtained, and then the coupling strength of the Higgs to the top quark gH(S)(tt) = m(t)/v(S) is altered by a factor root 2 from thestandard value. Introducing the S-3 doublet Higgs, flavor changing neutral currents are produced at tree level. The predicted branching ratios for rare decays mu(-)-> e(-) e(+) e(-), K-L(0) -> mu(+) mu(-), etc., induced by the flavor changing neutral currents, are sufficiently below the present experimental upper bounds.