New Color Decompositions for Gauge Amplitudes at Tree and Loop Level

TL;DR

This paper introduces new color decomposition methods for gluonic and quark-antiquark gauge amplitudes at tree and one-loop levels, providing proofs of their validity for arbitrary particle numbers.

Contribution

It presents novel color decompositions for gauge amplitudes at tree and one-loop levels, with rigorous proofs for their general applicability.

Findings

Color decomposition using structure constants is valid for any number of gluons.

New decompositions are established for one-loop pure gluon and quark-antiquark amplitudes.

Proofs confirm the decompositions' correctness for arbitrary particle counts.

Abstract

Recently, a color decomposition using structure constants was introduced for purely gluonic tree amplitudes, in a compact form involving only the linearly independent subamplitudes. We give two proofs that this decomposition holds for an arbitrary number of gluons. We also present and prove similar decompositions at one loop, both for pure gluon amplitudes and for amplitudes with an external quark-antiquark pair.