On the Subleading-Soft Behaviour of QCD Amplitudes

TL;DR

The paper analyzes the subleading soft behavior of tree-level QCD amplitudes with single-gluon emission from quark–gluon configurations, showing that the subleading term is governed by universal differential operators tied to the emitter's total angular momentum. It derives these operators from both on-shell recursion (BCFW) and gauge invariance, demonstrating their equivalence and providing explicit spinor-helicity forms, e.g. $S_G^{(0)}$ and $S_G^{(1)}$, as well as fermionic analogues $S^{(0) ext{(} extlambda ext{)}}$ and $S^{(1) ext{(} extlambda ext{)}}$. The work first recalls subleading soft terms for pure YM amplitudes and then extends to quark–gluon amplitudes by studying soft-photon emission from the fermion line, yielding universal operators that are independent of emitter spin. Explicit NMHV six-point examples verify the predictions and illustrate the spinor-helicity machinery, reinforcing Low's theorem in the QCD context and highlighting the role of total angular momentum in subleading soft emissions.

Abstract

We elaborate on the radiative behaviour of tree-level scattering amplitudes in the soft regime. We show that the sub-leading soft term in single-gluon emission of quark-gluon amplitudes in QCD is controlled by differential operators, whose universal form can be derived from both on-shell recursion relation and gauge invariance, as it was shown to hold for graviton- and gluon-scattering.