Wigner 6j symbols with gluon lines: completing the set of 6j symbols required for color decomposition

Abstract

We construct a set of Wigner 6\U0001d457 symbols with gluon lines (adjoint representations) in closed form, expressed in terms of similar 6\U0001d457 symbols with quark lines (fundamental representations). Together with these Wigner 6\U0001d457 symbols with quark lines, this gives a set of 6\U0001d457 symbols sufficient for treating QCD color structure for any number of external particles, in or beyond perturbation theory. This facilitates a complete treatment of QCD color structure in terms of orthogonal multiplet bases, without the need of ever explicitly constructing the corresponding bases. We thereby open up for a completely representation theory based treatment of SU(N) color structure, with the potential of significantly speeding up the color structure treatment.