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New NLO b->sgamma calculations have become available using resummed radiativecorrections. Using these calculations we perform a global fit of thesupergravity inspired constrained minimal supersymmetric model (CMSSM). We findthat the resummed calculations show similar constraints as the LO calculations,namely that only with a relatively heavy supersymmetric mass spectrum of theorder of 1 TeV the b-\tau Yukawa unification and the b->sgamma rate can coexistin the large tanb scenario. The resummed b->sgamma calculations are found toreduce the renormalization scale uncertainty considerably. The low tanbscenario is excluded by the present Higgs limits from LEP II. The constraintfrom the Higgs limit in the $m_0,m_{1/2}$ plane is severe, if the trilinearcoupling A_0 at the GUT scale is fixed to zero, but is considerably reduced for$A_0\le -2m_0$. The relatively heavy SUSY spectrum required by \besgcorresponds to a Higgs mass of $m_h=119\pm 1~ (stop masses)}\pm2~(theory)~\pm~3 (top mass) GeV $ in the CMSSM.Comment: latex + 7 eps figs, 14 pages, final version to be published in EPJ

The $b \to X_s \gamma$ rate and Higgs boson limits in the constrained minimal supersymmetric model