QCD multiplet bases with arbitrary parton ordering

TL;DR

This paper introduces a recursive algorithm to construct orthogonal multiplet bases for QCD color space with arbitrary parton order and Nc, enabling faster calculations of Wigner coefficients without explicit basis vectors.

Contribution

The authors develop a novel recursive method for constructing multiplet bases in QCD color space applicable to any parton order and Nc, improving computational efficiency.

Findings

Successfully constructed multiplet bases for various parton configurations.

Calculated Wigner 6j coefficients using the new bases.

Achieved significant speed-up in color structure calculations.

Abstract

We develop an algorithm for recursively constructing orthogonal multiplet bases for the color space of QCD, for any order of partons and any Nc. This recipe is then applied for explicitly constructing some of these bases. Using the bases, a corresponding set of Wigner 6j coefficients are calculated. The Wigner coefficients offer a method of using multiplet bases without resorting to the explicit expressions of the basis vectors, which lead to a significant speed-up compared to other methods of treating full color structure.