Toward a NNLO calculation of the anti-B ---> X(s) gamma decay rate with a cut on photon energy: I. Two-loop result for the soft function

Abstract The complete two-loop expression for the jet function J ( p 2 , μ ) of soft-collinear effective theory is presented, including non-logarithmic terms. Combined with our previous calculation of the soft function S ( ω , μ ) , this result provides the basis for a calculation of the effect of a photon-energy cut in the measurement of the B ¯ → X s γ decay rate at next-to-next-to-leading order in renormalization-group improved perturbation theory. The jet function is also relevant to the resummation of Sudakov logarithms in other hard QCD processes.