A general quartic potential invariant under a group G and containing any number of scalar fields in arbitrary representations is shown to have a mass spectrum at the symmetrybreaking global minimum satisfying ΣA^MA²vA²<~2λ(ΣA^vA²)², where vA is the vacuum expectation value of the Ath mass eigenfield with any singlet removed. For SU(2) {} U(1) with arbitrary Higgs particles this guarantees that the lightest neutral scalar boson will satisfy Mₘᵢₙ²<~λ√2GF=λ(350 GeV)² where λ is a particular quartic coupling constant.
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Langacker et al. (1984) studied this question.
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