Automating scattering amplitudes with chirality flow

TL;DR

The paper demonstrates that the chirality-flow formalism simplifies and accelerates the numerical evaluation of scattering amplitudes, notably reducing computation time for processes like $e^+ e^-$ to multiple photons.

Contribution

It introduces a novel application of the chirality-flow formalism to improve the efficiency of numerical amplitude calculations in particle physics.

Findings

Computation time reduced by about ten times for six photons.

Better scaling with the number of particles compared to standard methods.

More compact Lorentz structures and gauge choices contribute to performance gains.

Abstract

Recently we introduced the chirality-flow formalism, a method which builds on the spinor-helicity formalism and is inspired by the color-flow idea in QCD. With this formalism, Feynman rules and diagrams are simplified to the extent that it is often possible to immediately, by hand, write down a helicity amplitude given a Feynman diagram. In this paper we show that the method can also speed up numerical evaluation of scattering amplitudes by considering $e^+ e^-$ going to $n$ photons in a MadGraph-based tree-level implementation. We find that the computation time is reduced by roughly a factor ten for six photons, and that it scales better with the number of external particles than the default MadGraph5_aMC@NLO implementation. This performance gain is in part attributed to the more compact Lorentz structures involved, and in part due to a transparent choice of gauge reference vectors which reduces the number of Feynman diagrams considered.