Electromagnetic dipole operator effect on (B)over bar→Xsγ at partial derivative(αs2) -: art. no. 033014

The flavor-changing electromagnetic dipole operator O-7 gives the dominant contribution to the (B) over bar -> X(s)gamma 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 next-to-next-to-leading order QCD correction to Gamma(<(B)overbar >-> X(s)gamma)/Gamma((B) over bar -> X(u)e <(nu)over bar >). When both decay widths are normalized to m(b,R)(5) in the same renormalization scheme R, the calculated O(alpha(s)(2)) correction is sizable (similar to 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 Sxm(b)(<(MS)over bar >)(2)(m(b))/m(b,pole)(2), the calculated O(alpha(s)(2)) correction to S is at the level of 1% for both the complete and the NNA results.