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Higgs Mass Bounds Separate Models of Electroweak Symmetry Breaking

Vacuum stability implies a lower limit on the mass of the higgs boson in the Standard Model (SM). In contrast, an upper limit on the lightest higgs mass can be calculated in supersymmetric (susy) models. The main uncertainty in each limit is the value of the top mass, which may now be fixed by the recent CDF result. We study the possibility that these bounds do not overlap, and find that (i) a mass gap emerges at $m_t\sim 160$ GeV between the SM and the Minimal Susy Standard Model (MSSM); and between the SM and the Minimal plus Singlet Susy Model [(M+1)SSM] if the independent scalar self--coupling of the latter is perturbatively small or if the $\tanβ$ parameter is large; this gap widens with increasing $m_t$; (ii) there is no overlap between the SM and the MSSM bounds at even smaller values of $m_t$ for the $\tanβ$ value ($\sim 1$--2) preferred in Supersymmetric Grand Unified Theories. Thus, if the new top mass measurement remains valid, a measurement of the first higgs mass will serve to exclude either the SM or MSSM/(M+1)SSM higgs sectors. In addition, we discuss the upper bound on the lightest higgs mass in susy models with an extended higgs sector, and in models with a strongly interacting higgs sector. Finally, we comment on the discovery potential for the lightest higgses in these models.