QCD-improvedb→sγconstraints on the minimal supergravity model

Recent advances in the QCD corrections to $b\to s\gamma$ decay in the MSSM include (i) evaluation of the relevant operators, Wilson coefficients, and anomalous dimension matrix elements for the various MSSM effective theories valid at scales beyond ${Q=M}_W,$ (ii) calculations of most of the needed anomalous dimension matrix elements to next-to-leading order for scales $m_b\lesssim Q<\mathrm{}{M}_W,$ and (iii) calculations of $O\left({\alpha }_s\right)$ virtual and bremsstrahlung corrections to the $b\to s\gamma$ decay operators at scale $Q\sim m_b.$ We assemble all these known results to gain an estimate of $B(b\to s\gamma )$ for the parameter space of the minimal supergravity model (MSUGRA). We find a much reduced scale dependence of our result compared to usual leading-log evaluations. Comparison with the latest CLEO results yields stringent constraints on parameter space. Much of MSUGRA parameter space is ruled out for $\mu <0\mathrm{}$, especially for large $\tan \beta$. We compare these results with other constraints from cosmology and nonstandard vacua. Also, we compare with expectations for discovering MSUGRA at CERN LEP 2, the Fermilab Tevatron, and the CERN LHC.