# Towards a next-to-leading logarithmic result in $B to X_s gamma$

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SLAC-PUB-7267ITP-SB-96-46hep-ph/9608449August 1996Towards a next-to-leading logarithmic result in B → X s γa CHRISTOPH GREUB Stanford Linear Accelerator Center, Stanford University, Stanford, California 94309, USA TOBIAS HURTH Institute for Theoretical Physics, SUNY at Stony Brook, Stony Brook, New York 11794-3840, USA The calculation of the O (αs ) virtual corrections to the matrix element of the in-clusive decay b → sγis reported. These contributions drastically reduce the large renormalization scale dependence of the leading logarithmic calculation. Com-bining these results with the preliminary result for the Wilson coeﬃcient C 7(m b ) calculated recently by Chetyrkin, Misiak, and M¨u nz, we estimate the branching ratio to be BR (B → X s γ) =(3. 25±0. 50) ×10− 4. 1Introduction Rare B meson decays are particularly sensitive to physics beyond the standard model (SM).In order to extract the eﬀects of possible new physics, precise experimental and theoretical work on these decays is required. The inclusive mode B → X s γcan be systematically analyzed with help

of the expansion in inverse powers of the (heavy)b -quark mass, m b . At the leading order in such an expansion, the inclusive decay rate is given by the perturbatively calculable free quark decay rate. As the power corrections start at the 1/m2b level only, we neglect these contributions in this talk and model the decay rate Γ(B → X s γ) by the quark level decay width Γ(b → sγ), including perturbative QCD corrections.

The earlier SM computations of the branching ratio for B → X s γpresented e.g. in refs. 1, 2, 3, 4are in full agreement with the CLEO measurement 5BR (B → X s γ) =(2. 32±0. 67) ×10− 4. There are large uncertainties, however, in both

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