Vacuum stability and metastability imply lower limits on the mass of the Higgs boson in the standard model (SM). In contrast, we present an improved calculation of the lightest Higgs boson mass in supersymmetric (SUSY) models, by summing to all orders in perturbation theory the leading and next-to-leading logarithms with a renormalization group equation technique, and by including finite two-loop QCD corrections. We believe our result to be the most accurate available in the literature. The mass calculation leads to an upper bound on the Higgs boson mass when the SUSY-breaking scale is sensibly restricted to ≲1 TeV. In particular, our improvements to the SUSY Higgs boson mass calculation lower the minimal SUSY standard model (MSSM) upper limit by about 10 GeV. We study the possibility that these SM and MSSM bounds do not overlap, in which case a single Higgs boson mass measurement will distinguish between the two models. We find the following: (i) A gap emerges between the SM Higgs boson and the lightest MSSM Higgs boson at ∼120 GeV for $m_t\sim 175$ GeV and ${\alpha }_s\left(M_Z^2\right)=0.118\mathrm{}$, and for $m_t\sim 180$ GeV and more generous values ∼(0.130) of ${\alpha }_s$, and between the SM and the minimal plus singlet SUSY model [$\mathrm{}(M+1\mathrm{})\mathrm{}\mathrm{SSM}$] Higgs bosons if the independent scalar self-coupling of the latter is perturbatively small or if the $tan\beta$ parameter is small; these mass gaps widen with increasing $m_t$; (ii) the mass gap emerges with $m_t$ 10 GeV lighter if only vacuum stability and not metastability is imposed; (iii) restricting $tan\beta$ to the values (∼1-2) preferred in supersymmetric grand unified theories, the lightest MSSM Higgs boson mass upper bound is reduced by at least 10 GeV (which implies no overlap between the SM and the MSSM bounds at even smaller values of $m_t$); for $m_t\sim 175$ GeV, the bound is $m_h\lesssim 110$ GeV. Thus, a measurement of the first Higgs boson mass will serve to exclude either the MSSM or ($\mathrm{}(M+1\mathrm{})\mathrm{}\mathrm{SSM}$ Higgs sectors or the SM Higgs sector. In addition, we discuss the upper bound on the lightest Higgs boson mass in SUSY models with an extended Higgs sector. Finally, we comment on the discovery potential for the lightest Higgs bosons in these models.

• Received 5 December 1995

DOI:https://doi.org/10.1103/PhysRevD.54.5855