One-loop Singular Behaviour of QCD and SUSY QCD Amplitudes with Massive Partons

TL;DR

The paper addresses the structure of infrared and ultraviolet singularities at one loop in QCD and SUSY QCD when massive partons are present.It introduces a universal factorization formula, with an insertion operator ${\bf I}_m^{\rm RS}$ that captures all poles and mass-dependent logarithms, plus a finite, scheme-independent remainder.The authors relate these singular terms to generalized Altarelli–Parisi splitting functions via a quasi-collinear limit, and extend the formalism to SUSY QCD with appropriate beta-function and flavour coefficients.The framework provides a practical tool for validating and organizing one-loop computations and facilitates infrared cancellations in NLO calculations, including mass effects and regularization-scheme dependencies.

Abstract

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 epsilon-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.