Bootstrapping Six-Gluon QCD Amplitudes

TL;DR

This paper constructs the first explicit two-loop six-gluon scattering amplitude in QCD at the symbol level, revealing a simplified function space and new insights into amplitude structures.

Contribution

It introduces a symbol bootstrap method incorporating leading singularities, providing the first concrete characterization of two-loop six-gluon amplitudes in QCD.

Findings

Amplitude expressed with only 137 symbol letters, fewer than the full set.

Physical limits uniquely determine the amplitude at the symbol level.

New results on two-loop triple collinear and double soft limits.

Abstract

We present a symbol-level bootstrap construction of the planar, two-loop six-gluon scattering amplitude for the --++++ helicity configuration in QCD, focusing on the maximal weight pieces-the "most complicated terms" in the sense of Lipatov et al. Building on recent advances in the understanding of the relevant function space, we incorporate as a crucial new ingredient the complete set of leading singularities, obtained from an explicit analysis of on-shell diagrams. The resulting expressions are manifestly conformally invariant and clarify the structure of previous five-particle results. Combining this with the symbol bootstrap, we show that constraints from physical limits are sufficient to uniquely determine the answer. We thus obtain the first concrete characterization of two-loop six-gluon amplitudes at the symbol level and at highest weight. Remarkably, we find that the effective function space involves only 137 symbol letters, significantly fewer than the full set of 167 possible letters, suggesting a yet-unexplained underlying structure akin to that seen in maximally supersymmetric Yang-Mills theory. From the novel amplitude results we extract previously unknown symbol-level results describing two-loop triple collinear and double soft limits.