Completing the NLO QCD calculation of [formula omitted

Abstract

We evaluate two-loop b→ sγ matrix elements of all the four-quark operators containing no derivatives. Contrary to previous calculations, no expansion in the mass ratio m c / m b is performed, and all the possible Dirac and flavor structures are included. Consequently, we are able to provide the last item in the NLO analysis of B ̄ →X sγ that has been missing so far, namely the two-loop matrix elements of the QCD-penguin operators. Due to smallness of the Wilson coefficients of those operators in the Standard Model, their effect on the branching ratio is small: a reduction by roughly 1%. We find BR[ B ̄ →X sγ] E γ>1.6 GeV =(3.57±0.30)×10 −4 .