The b->sgamma rate and Higgs boson limits in the Constrained Minimal Supersymmetric Model

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New NLO b->sgamma calculations have become available using resummed radiative corrections. Using these calculations we perform a global fit of the supergravity inspired constrained minimal supersymmetric model (CMSSM). We find that the resummed calculations show similar constraints as the LO calculations, namely that only with a relatively heavy supersymmetric mass spectrum of the order of 1 TeV the b-τYukawa unification and the b->sgamma rate can coexist in the large tanb scenario. The resummed b->sgamma calculations are found to reduce the renormalization scale uncertainty considerably. The low tanb scenario is excluded by the present Higgs limits from LEP II. The constraint from the Higgs limit in the m₀,m₁/₂ plane is severe, if the trilinear coupling A₀ at the GUT scale is fixed to zero, but is considerably reduced for A₀≤ -2m₀. The relatively heavy SUSY spectrum required by corresponds to a Higgs mass of mₕ=119± 1 (stop masses)± 2 (theory) ± 3 (top mass) GeV in the CMSSM.