Decomposing color structure into multiplet bases

TL;DR

This paper presents a method to decompose QCD color structures into orthogonal multiplet bases using group theory coefficients, simplifying calculations for complex gluon and quark-antiquark systems.

Contribution

It introduces a systematic approach to decompose color structures into multiplet bases and efficiently compute Wigner coefficients for practical QCD calculations.

Findings

Explicit calculation of all 6j coefficients up to six gluons and quark pairs.

Demonstration of the method's efficiency in reducing the number of coefficients needed.

Application potential for NLO QCD computations.

Abstract

We illustrate how QCD color structure elegantly can be decomposed into orthogonal multiplet bases corresponding to irreducible representations of SU(Nc) with the aid of Wigner 3j and 6j coefficients. We also show how to calculate the relevant 3j and 6j coefficients using multiplet bases and birdtrack techniques and argue that only a relatively small number of Wigner 3j and 6j coefficients are required. For up to six gluons plus quark-antiquark pairs we explicitly calculate all 6j coefficients required for up to NLO calculations.