Revisiting the double-soft asymptotics of one-loop amplitudes in massless QCD

Abstract

We evaluate the one-loop soft current for the emission of two soft gluons or a soft quark-anti-quark pair in massless Quantum Chromodynamics. The results are exact in dimensional regularisation up to a single Feynman integral. Two terms of the Taylor series of the latter integral as a function of $\epsilon \equiv (4-d)/2$ with $d$ the dimension of spacetime are available from a recent calculation of one-loop triple-collinear splitting functions. Our formulae are necessary for the construction of a subtraction scheme for the evaluation of next-to-next-to-next-to-leading order cross sections in massless QCD.