Two-loop six gluon all plus helicity amplitude

TL;DR

This work targets the six-point all-plus helicity amplitude at two loops in QCD, a key but challenging NNLO calculation. The authors leverage IR factorization, unitarity cuts, and augmented recursion to reconstruct the amplitude from its singular structure, separating the two-loop result into a known IR part $A^{(1)}_n I^{(1)}_n$ and a finite remainder $F^{(2)}_n$, with $F^{(2)}_n = P^{(2)}_n + R^{(2)}_n$. They provide an explicit analytic expression for the rational remainder $R_6^{(2)}$, written as $R_6^{(2)} = \frac{i}{36} \sum_{i=1}^6 \frac{ G[i,i+1,i+2,i+3,i+4,i+5] }{ \langle12\rangle\langle23\rangle\langle34\rangle\langle45\rangle\langle56\rangle\langle61\rangle }$, with $G$ decomposed into $G_1+G_2+G_3+G_4+G_5$ to capture the full pole andphysical structure. The results are validated against known factorisation and symmetry properties, and the rational piece is shown to be computable by essentially one-loop–level techniques, providing a new analytic window into multi-loop amplitudes. This completes the first explicit analytic six-point two-loop QCD amplitude, offering a benchmark for future NNLO and multi-leg studies.

Abstract

We present an analytic expression for the six-point all-plus helicity amplitude in QCD at two-loops. We compute the rational terms in a compact analytic form organised by their singularity structure.