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The flavor-changing electromagnetic dipole operator O_7 gives the dominantcontribution to the B -> Xs gamma decay rate. We calculate two-loop QCDcorrections to its matrix element together with the correspondingbremsstrahlung contributions. The optical theorem is applied, and the relevantimaginary parts of three-loop diagrams are computed following the lines of ourrecent t -> Xb W calculation. The complete result allows us to test thevalidity of the naive non-abelianization (NNA) approximation that has beenpreviously applied to estimate the NNLO QCD correction to Gamma(B -> Xsgamma)/Gamma(B -> Xu e nu). When both decay widths are normalized to m^5_{b,R}in the same renormalization scheme R, the calculated O(alpha_s^2) correction issizeable (~ 6%), and the NNA estimate is about 1/3 too large. On the otherhand, when the ratio of the decay widths is written asS*(m_b(m_b)/m_{b,pole})^2, the calculated O(alpha_s^2) correction to S is atthe level of 1% for both the complete and the NNA results.Comment: Corrected pi^2 terms in the description of intermediate steps in  Section II. Final results unchange

physical review. d. particles, fields, gravitation, and cosmology/physical review. d, particles, fields, gravitation, and cosmology

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Electromagnetic dipole operator effect onB¯→XsγatO(αs…