Higgs Potential in Minimal S3 Invariant Extension of the Standard Model
Abstract
Minimal S3 invariant Higgs potential with real soft S3 breaking masses is investigated. It is required that without having a problem with triviality, all physical Higgs bosons, except one neutral one, become heavy ~O(10) TeV in order to sufficiently suppress flavor changing neutral currents. There exist three nonequivalent soft mass terms that can be characterized according to their discrete symmetries, and the one which breaks S3 completely. The S2' invariant vacuum expectation values (VEVs) of the Higgs fields are the most economic VEVs in the sense that the freedom of VEVs can be completely absorbed into the Yukawa couplings so that it is possible to derive, without referring to the details of the VEVs, the most general form for the fermion mass matrices in minimal S3 extension of the standard model. We find that except for the completely broken case of the soft terms, the S2' invariant VEVs are unique VEVs that satisfy the requirement of heavy Higgs bosons. It is found that they also correspond to a local minimum in the completely broken case.
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