Multi-particle processes in QCD without Feynman diagrams

A way to efficiently compute helicity amplitudes for arbitrary tree-level scattering processes in QCD is presented. The scattering amplitude is evaluated recursively through a set of Dyson–Schwinger equations. The computational cost of this algorithm grows asymptotically as 3n3n, where nn is the number of particles involved in the process, compared to n!n! in the traditional Feynman graphs approach. Unitary gauge is used and mass effects are available as well. Additionally, the color and helicity structures are appropriately transformed so the usual summation is replaced by the Monte Carlo techniques.