Completing the NLO QCD calculation of B̄→Xsγ Original Research Article

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.