Generating QCD amplitudes in the color-flow basis with MadGraph

TL;DR

This paper introduces a method to compute QCD amplitudes using off-shell recursive relations in the color-flow basis within MadGraph, enabling efficient calculations of multi-gluon and quark-gluon processes.

Contribution

It presents a novel implementation of color-flow basis calculations with recursive formulas in MadGraph for multi-gluon and quark-gluon amplitudes.

Findings

Successfully calculated up to 5-jet processes

Demonstrated recursive computation of multi-gluon amplitudes

Paves the way for more complex amplitude evaluations

Abstract

We propose to make use of the off-shell recursive relations with the color-flow decomposition in the calculation of QCD amplitudes on MadGraph. We introduce colored quarks and their interactions with nine gluons in the color-flow basis plus an Abelian gluon on MadGraph, such that it generates helicity amplitudes in the color-flow basis with off-shell recursive formulae for multi-gluon sub-amplitudes. We demonstrate calculations of up to 5-jet processes such as $gg\rightarrow 5g$, $u\bar{u}\rightarrow 5g$ and $uu\rightarrow uuggg$. Although our demonstration is limited, it paves the way to evaluate amplitudes with more quark lines and gluons with Madgraph.