Soft-gluon factorization and multi-gluon amplitude

Abstract

The infrared analysis of perturbative QCD starts from the formula of factorization of the soft-gluon radiation, which has the form of a semi-classical non-abelian current. This formula has been proved within the framework of the old-fashioned perturbation theory but no general proof is available in the more familiar framework of the Feynman-diagram technique. In this paper we present a proof of the factorization formula in Feynman-diagram perturbative amplitudes. This derivation provides further insight into the infrared structure of the theory and in particular into the role of coherence of colour charges. We also discuss the spin- and colour-averaged squared amplitude for the multi-gluon soft emission. We present a new derivation of the planar contribution and show that the first non-planar correction does not contain a leading singularity.