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

TL;DR

This paper derives exact one-loop soft current formulas for gluon and quark-antiquark pair emissions in massless QCD, crucial for NN3LO cross section calculations, with results expressed up to a single Feynman integral.

Contribution

It provides new exact formulas for one-loop soft currents in massless QCD, incorporating recent triple-collinear splitting function results, aiding higher-order cross section computations.

Findings

Exact one-loop soft current formulas derived.

Results expressed up to a single Feynman integral.

Formulas are essential for NN3LO subtraction schemes.

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.