Bootstrapping Six-Gluon QCD Amplitudes

We present a symbol-level bootstrap construction of the planar, two-loop six-gluon scattering amplitude for the --++++ helicity configuration in quantum chromodynamics (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 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 determine the answer. We thus obtain the first concrete characterization of two-loop six-gluon amplitudes at 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.