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The b → X s γ rate and Higgs boson limits in the Constrained Minimal Supersymmetric Model

New NLO b → X s γ calculations have become available using resummed radia-tive corrections. Using these calculations we perform a global fit of the supergravity inspired constrained minimal supersymmetric model. We find that the resummed calculations show similar constraints as the LO calculations, namely that only with a relatively heavy supersymmetric mass spectrum of O(1 TeV) the b−τ Yukawa unification and the b → X s γ rate can coexist in the large tan β scenario. The resummed b → X s γ calculations are found to reduce the renormalization scale uncertainty considerably. The low tan β scenario is excluded by the present Higgs limits from LEP II. The constraint from the Higgs limit in the m 0 , m 1/2 plane is severe, if the trili-near coupling A 0 at the GUT scale is fixed to zero, but is considerably reduced for A 0 ≤ −2m 0. The relatively heavy SUSY spectrum required by b → X s γ corresponds to a Higgs mass of m h = 119 ± 1 (stop masses) ± 2 (theory) ± 3 (top mass) GeV in the CMSSM.