Orthogonal multiplet bases in SU(Nc) color space

TL;DR

This paper introduces a systematic method to construct orthogonal, minimal color bases in SU(Nc) for QCD calculations, significantly reducing computational complexity for processes with multiple colored particles.

Contribution

It provides a general recipe for creating orthogonal, minimal multiplet bases in SU(Nc) color space applicable to any number of partons and Nc, improving efficiency in QCD computations.

Findings

Constructed multiplet bases for processes with up to 6 external colored partons.

Bases are orthogonal, minimal, and reduce the number of basis vectors needed.

Method is applicable for any Nc and arbitrary number of partons.

Abstract

We develop a general recipe for constructing orthogonal bases for the calculation of color structures appearing in QCD for any number of partons and arbitrary Nc. The bases are constructed using hermitian gluon projectors onto irreducible subspaces invariant under SU(Nc). Thus, each basis vector is associated with an irreducible representation of SU(Nc). The resulting multiplet bases are not only orthogonal, but also minimal for finite Nc. As a consequence, for calculations involving many colored particles, the number of basis vectors is reduced significantly compared to standard approaches employing overcomplete bases. We exemplify the method by constructing multiplet bases for all processes involving a total of 6 external colored partons.