The electromagnetic dipole operator effect on B - Xs gamma at O(alpha_s^2).pdf

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The electromagnetic dipole operator effect on B - Xs gamma at O(alpha_s^2).pdf

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The electromagnetic dipole operator effect on B - Xs gamma at O(alpha_s^2)

a r X i v : h e p - p h / 0 5 0 6 0 5 5 v 1 6 J u n 2 0 0 5 Alberta Thy 01-05 UVIC-THY-05-01 IFT-12/2005 The electromagnetic dipole operator effect on B? → X s γ at O(α2 s ) I. Blokland1,2, A. Czarnecki1, M. Misiak3, M. S?lusarczyk1,4, and F. Tkachov5 1) Department of Physics, University of Alberta, Edmonton, AB T6G 2J1, Canada 2) Department of Physics and Astronomy, University of Victoria, Victoria, BC V8P 5C2, Canada 3) Institute of Theoretical Physics, Warsaw University, 00-681 Warszawa, Poland 4) Institute of Physics, Jagiellonian University, 30-059 Krako?w, Poland 5) Institute for Nuclear Research, Russian Academy of Sciences, Moscow, 117312, Russian Federation The flavor-changing electromagnetic dipole operator O7 gives the dominant contribution to the B? → Xsγ decay rate. We calculate two-loop QCD corrections to its matrix element together with the corresponding bremsstrahlung contributions. The optical theorem is applied, and the relevant imaginary parts of three-loop diagrams are computed following the lines of our recent t → XbW calculation. The complete result allows us to test the validity of the naive non-abelianization (NNA) approximation that has been previously applied to estimate the NNLO QCD correction to Γ(B? → Xsγ)/Γ(B? → Xueν?). When both decay widths are normalized to m 5 b,R in the same renormalization scheme R, the calculated O(α2s) correction is sizeable (～ 6%), and the NNA estimate is about 1/3 too large. On the other hand, when the ratio of the decay widths is written as S × m2 b,MS (mb)/m 2 b,pole, the calculated O(α 2 s) correction to S is at the level of 1% for both the complete and the NNA results. PACS numbers: 13.40.Hq,14.65.Fy,12.38.Bx I. INTRODUCTION The radiative decay b → sγ occurs only through quantum loop effects, similarly to the muon anomalous magnetic moment (gμ? 2) or radiative hyperon decays [1]. The largest contribution by far to (gμ? 2) is due to electromagnetic interactions. In contrast, the flavor-changing hyperon