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B-->sγ Decay in Supersymmetric Theories

Recent advances in the calculation of the b → sγ decay branching ratio are presented in the context of supersymmetric theories. Theoretical accuracy increased by inclusion of the next-to-leading order QCD corrections makes it possible to significantly decrease scale dependence of the result. Comparison with the latest CLEO experimental results then allows to limit supersymmetric loop contributions to the process and consequently constrain the parameter space of supersymmetric extensions of the Standard Model. We discuss these constraints both in the minimal supergravity inspired model (SUGRA) and in the simplest gauge-mediated supersymmetry breaking model (GMSB) both of which are interesting from the point of view of the searches for supersymmetry at present and future colliders. Our analysis also includes the interesting region of large tan β relevant for models with Yukawa coupling unification. An important experimental check of SUSY models is provided by the measurement of the b → sγ decay rate. Weak scale SUSY particles contribute to the one loop decay amplitude and their presence can significantly modify the Standard Model (SM) result. The best experimental value available for the inclusive B → X s γ branching ratio as measured by the CLEO collaboration B(B → X s γ) = (2.32 ± 0.57 ± 0.35) × 10 −4 has to be compared to the next-to-leading order Standard Model prediction including non-perturbative corrections B(B → X s)γ = (3.38 ± 0.33)×10 −4 , see 1. SUSY contributions can correct the theoretical value in both directions and a requirement that the branching ratio remain restricted within the experimental 95% confidence level band 1 × 10 −4 < B(B → X s γ) < 4.2 × 10 −4 translates into constraints on the supersymmetric parameter space. All the next-to-leading order calculation ingredients for SUSY models are already available with the exception of the exact two-loop matching conditions between the full theory and the effective theory, which have been evaluated only for the SM contribution, the charged Higgs contribution and for some special cases of the chargino contribution. Here we adopt an approximate procedure effectively decoupling the heavy particles in the loop at different scales for the dominating SUSY contributions to approximate the exact matching conditions 2. In the minimal supersymmetric extension of the SM, the SUSY contribution involves the charged Higgs-top quark loop, chargino-squark loops, gluino-squark loops and neutralino-squark loops 3. The first two are most impor