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Orthogonal multiplet bases in SU(Nc) color space
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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.
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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