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Wigner 6j symbols with gluon lines: completing the set of 6j symbols required for color decomposition
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We construct a set of Wigner 6j symbols with gluon lines (adjoint representations) in closed form, expressed in terms of similar 6j symbols with quark lines (fundamental representations). Together with Wigner 6j symbols with quark lines, this gives a set of 6j 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.
Forward citations
Cited by 2 Pith papers
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An $N$-independent tensor decomposition for SU($N$)
A new column-based Littlewood-Richardson algorithm decomposes products of SU(N) representations labeled by Young diagram pairs, valid simultaneously for all N.
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All-gluon amplitudes with off-shell recursion in multiplet bases
A new off-shell recursion in orthogonal multiplet bases computes all-gluon tree-level color-summed squared amplitudes with estimated O(17^n) complexity, beating the factorial scaling of trace and color-flow bases.
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