Color Decompositions of the Two Loop Amplitudes of Yang-Mills theory

TL;DR

This paper analyzes the color structure of two-loop gluon amplitudes in Yang-Mills theory, comparing trace basis and structure constant approaches to understand relations among partial amplitudes.

Contribution

It systematically explores the color decomposition of two-loop amplitudes, providing new insights into relations between different color formalisms.

Findings

Identifies relations between trace basis and structure constant formalisms.

Provides a systematic framework for color decomposition at two loops.

Enhances understanding of color structures in Yang-Mills amplitudes.

Abstract

The color structure of two-loop gluon amplitudes is examined both from a color trace basis expansion and an alternative based upon structure constants. We use use this as a vehicle for systemising relations between the partial amplitudes of the color trace formalism.