BCJ duality and the double copy in the soft limit

TL;DR

The paper tests the BCJ duality and the double-copy construction in the soft (IR) limit by analyzing one- and two-loop infrared divergences in massless QCD and their gravity counterparts. It shows that gravity IR divergences, known to be one-loop exact, are reproduced by double-copying the QCD IR structure, providing all-order evidence for the double-copy conjecture in a non-supersymmetric setting. The analysis highlights that many IR singularities disappear under the double copy and clarifies how subleading IR terms relate to the hard scattering. These results strengthen the link between gauge and gravity amplitudes and illuminate how the dipole structure in QCD interacts with the gravitational counterpart.

Abstract

We examine the structure of infrared singularities in QCD and quantum General Relativity, from the point of view of the recently conjectured double copy property which relates scattering amplitudes in non-Abelian gauge theories with gravitational counterparts. We show that IR divergences in both theories are consistent with the double copy procedure, to all orders in perturbation theory, thus providing all loop-level evidence for the conjecture. We further comment on the relevance, or otherwise, to the so-called dipole formula, a conjecture for the complete structure of IR singularities in QCD.

Figures (10)

• Figure 1: Illustration of three graphs related by BCJ transformations, where the grey boxes denote the rest of the amplitude.
• Figure 2: Four point scattering, where all momenta are taken to be outgoing.
• Figure 3: Set of all box graphs at one-loop order, where we depict the basis momenta entering the numerator for each graph.
• Figure 4: Set of all triangle graphs at one-loop order, where we depict the basis momenta entering the numerator for each graph.
• Figure 5: Set of all bubble graphs at one-loop order, where we show the choice of internal basis momentum for each graph. All external momenta are labelled as in graph (b9).