One-loop singular behaviour of QCD and SUSY QCD amplitudes with massive partons

We discuss the structure of infrared and ultraviolet singularities in on-shell QCD and supersymmetric QCD amplitudes at one-loop order. Previous results, valid for massless partons, are extended to the case of massive partons. Using dimensional regularization, we present a general factorization formula that controls both the singular ϵ-poles and the logarithmic contributions that become singular for vanishing masses. We introduce generalized Altarelli–Parisi splitting functions and discuss their relations with the singular terms in the amplitudes. The dependence on the regularization scheme is also considered.