Color decomposition of multi-quark one-loop QCD amplitudes

TL;DR

This paper introduces a combinatorial method for decomposing multi-quark one-loop QCD amplitudes into primitive amplitudes, simplifying calculations by avoiding linear system inversions.

Contribution

It presents a new shuffle relation-based approach for color decomposition that yields closed-form formulas for arbitrary multi-quark amplitudes.

Findings

Provides a systematic combinatorial decomposition method

Derives closed formulas without linear system inversion

Applicable to arbitrary numbers of quarks and gluons

Abstract

In this talk we discuss the color decomposition of tree-level and one-loop QCD amplitudes with arbitrary numbers of quarks and gluons. We present a method for the decomposition of partial amplitudes into primitive amplitudes, which is based on shuffle relations and is purely combinatorial. Closed formulae are derived, which do not require the inversion of a system of linear equations.