Higgs potential in S3 invariant model for quark/lepton mass and mixing
Abstract
We analyzed the S3 invariant Higgs potential with S3 singlet and doublet Higgs. We obtained a relation (|v1|/|v2|)2=-sin2phi2/sin2phi1 from this S3 invariant Higgs potential, where v1, v2 and phi1, phi2 are vacuum pectation values and phases of S3 doublet Higgs, respectively. This relation could be satisfied exactly by the results |v1|/ |v2|=0.207, phi1=-74.9deg and phi2=0.74deg obtained from the previous our work analyzing the quark/lepton mass and mixing in S3 invariant Yukawa interaction. Furthermore, the relation vS ~ vD=sqrt|v1|2+|v2|2=174GeV is obtained and then the coupling strength of Higgs to top quark gHStt=mt/vS is altered as by a factor sqrt2 from the standard value. Introduced the S3 doublet Higgs, FCNC are produced in tree level. Predicted branching ratios for rare decays mu- to e-e+e-, K0L to mu+μ- etc., induced by the FCNC are sufficiently below the present experimental upper bounds.