Completing the NLO QCD calculation of B̄ → X s γ

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 mc/mb 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 B̄ → Xsγ 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[B̄ → Xsγ]Eγ>1.6 GeV = (3.57± 0.30)× 10−4.