QCD-improved b->s gamma constraints on the minimal supergravity model

Recent advances in the QCD corrections to b-->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) less than or similar to Q<M(W), and (iii); calculations of O(alpha(s)) virtual and bremsstrahlung corrections to the b-->s gamma decay operators at scale Q similar to m(b). We assemble all these known results to gain an estimate of B(b-->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, 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.