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

Abstract. New NLO $b \to X_s \gamma$ calculations have become available using resummed radiative 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 $\mathcal{O}$(1 TeV) the b–$\tau$ Yukawa unification and the $b \to X_s \gamma$ rate can coexist in the large $\tan\beta$ scenario. The resummed $b \to X_s \gamma$ calculations are found to reduce the renormalization scale uncertainty considerably. The low $\tan\beta$ 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 trilinear coupling $A_0$ 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 $b \to X_s \gamma$ corresponds to a Higgs mass of $m_h=119\pm1 \mbox{(stop masses)} \pm2 ({\mathrm{theory}}) \pm3 \mbox{(top mass)}$ GeV in the CMSSM.