Dissolving N=4 loop amplitudes into QCD tree amplitudes

TL;DR

The paper leverages infrared consistency of one-loop amplitudes in N=4 Yang-Mills to derive a compact analytic formula for a tree-level NNMHV eight-gluon amplitude in QCD, marking the first such result. By combining IR constraints with modern box-coefficient techniques (quadruple cuts), it demonstrates that tree-level amplitudes can be efficiently reconstructed from a small set of one-loop building blocks, revealing structures simpler than those exposed by current twistor-space approaches. The eight-gluon amplitude A_8 is shown to admit an unexpectedly concise expression, with extensive cancellations reducing the number of necessary terms, and the result passes nontrivial checks against CSW diagrams and known limits. This work suggests a broader utility of IR-based methods for deriving compact tree-level amplitudes in gauge theories and hints at deeper underlying simplicity in Yang-Mills scattering.

Abstract

We use the infrared consistency of one-loop amplitudes in N=4 Yang-Mills theory to derive a compact analytic formula for a tree-level NNMHV gluon scattering amplitude in QCD, the first such formula known. We argue that the IR conditions, coupled with recent advances in calculating one-loop box coefficients, can give a new tool for computing tree-level amplitudes in general. Our calculation suggests that many amplitudes have a structure which is even simpler than that revealed so far by current twistor-space constructions.