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Accepted · first revision · record

Title: Local color-kinematics duality for one-loop pure Yang-Mills amplitudes
Plain: Even at one loop it is unclear whether gluon amplitudes of ordinary Yang-Mills theory, with no supersymmetry, can be put in the special form using simple polynomial numerators.
Precise: Determine for which multiplicities n the one-loop n-gluon amplitude of pure Yang-Mills admits BCJ numerators that are local (polynomial in momenta and polarization vectors) and valid in arbitrary spacetime dimension D. An answer is the set of n for which such numerators exist, with constructions and obstructions, and a statement of whether dimension-specific (for example 4D) numerators escape any obstruction.
Settled by: Explicit local numerators for all n, or a verified obstruction at a specific n.
Kind: well-posed
Answer type: classification
References: (empty)
Literature status: partially-resolved
Status note: A September 2026 preprint (Sung, arXiv:2609.10693) reports that no dimension-independent, parity-even polynomial numerators multilinear in polarizations exist at $n = 6$; unrefereed and not independently checked; dimension-specific numerators are not excluded.
Posed since: (empty)