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

We discuss the structure of infrared and ultraviolet singularities in on-sh ell QCD and supersymmetric QCD amplitudes at one-loop order. Previous resul ts, valid for massless partons, are extended to the case of massive partons . Using dimensional regularization, we present a general factorization form ula that controls both the singular epsilon -poles and the logarithmic cont ributions that become singular for vanishing masses. We introduce generaliz ed Altarelli-Parisi splitting functions and discuss their relations with th e singular terms in the amplitudes. The dependence on the regularization sc heme is also considered. (C) 2001 Published by Elsevier Science B.V.