The one-loop amplitude for six-gluon scattering

TL;DR

This paper computes the one-loop six-gluon scattering amplitude in QCD using a semi-numerical approach, enabling results for arbitrary momenta and helicities. It employs a color-decomposed framework with leading and subleading color structures and tensor-integral reductions, handling internal gluons, fermions, and scalars. By forming N=4 and N=1 SUSY multiplet contributions, the authors validate against analytic results and also present new numerical results for scalar loops. The work demonstrates the viability of semi-numerical methods for high-multiplicity amplitudes and suggests pathways to full NLO predictions for multi-jet processes.

Abstract

We present results for the six-gluon scattering amplitude at one-loop. Since our method is semi-numerical, it yields the result for arbitrary momenta and helicities of the external gluons. We evaluate the colour-ordered sub-amplitudes with gluons, fermions and scalars running in the internal loop. This is more than sufficient to give a complete description of six-gluon scattering at one-loop in QCD. Combination of these results into amplitudes with ${\cal{N}}=4$ and ${\cal{N}}=1$ multiplets of supersymmetric Yang-Mills or with a complex scalar in the internal loops allows comparison with analytic results in the literature. The numerical results for most of the helicity combinations with loops of complex scalars are new.