Cyclic Mario Worlds -- Color-Decomposition for One-Loop QCD

TL;DR

This paper introduces a new color decomposition method for one-loop QCD amplitudes, generalizing existing tree-level decompositions, applicable to various quark flavors, gauge groups, and matter representations, with broad extensions.

Contribution

It proposes a minimal basis color decomposition for one-loop QCD amplitudes that is free of linear dependencies and universally applicable across different theories and extensions.

Findings

Decomposition applies to any number of quark flavors and gluons.

It is independent of gauge group and matter representation.

Results extend to higher-dimensional and supersymmetric QCD.

Abstract

We present a new color decomposition for QCD amplitudes at one-loop level as a generalization of the Del Duca-Dixon-Maltoni and Johansson-Ochirov decomposition at tree level. Starting from a minimal basis of planar primitive amplitudes we write down a color decomposition that is free of linear dependencies among appearing primitive amplitudes or color factors. The conjectured decomposition applies to any number of quark flavors and is independent of the choice of gauge group and matter representation. The results also hold for higher-dimensional or supersymmetric extensions of QCD. We provide expressions for any number of external quark-antiquark pairs and gluons.