Multiple soft radiation at one-loop order and the emission of a soft quark–antiquark pair

Abstract

AbstractWe consider the radiation of two or more soft partons in QCD hard-scattering at one-loop order. The corresponding scattering amplitude is singular, and the singular behaviour is controlled by a process-independent soft current. Using regularization in $$d=4 - 2\epsilon $$ d = 4 - 2 ϵ space-time dimensions, we explicitly evaluate the ultraviolet and infrared divergent ($$\epsilon $$ ϵ -pole) terms of the one-loop soft current for emission of an arbitrary number of soft partons in a generic hard-scattering process. Then we consider the specific case of soft quark–antiquark ($$q{{\bar{q}}}$$ q q ¯ ) emission and we compute the one-loop current by including the finite terms. We find that the one-loop soft-$$q{{\bar{q}}}$$ q q ¯ current exhibits a new type of transverse-momentum singularity, which has a quantum (absorptive) origin and a purely non-abelian character. At the squared amplitude (cross section) level, this transverse-momentum singularity produces contributions to multijet production processes in hadron collisions. The one-loop squared current also leads to charge asymmetry terms, which are a distinctive features of soft-$$q{{\bar{q}}}$$ q q ¯ radiation. We also extend these results to the cases of QED and mixed QCD$$\times $$ × QED radiative corrections for soft fermion–antifermion emission.