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Kinematic Hopf algebra for amplitudes and form factors

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arxiv 2208.05519 v2 pith:5TIUKYUA submitted 2022-08-10 hep-th

Gang Chen , Guanda Lin , Congkao Wen This is my paper · ORCID
classification hep-th
keywords algebrakinematicnumeratorsamplitudesfactorsformscalarsbi-adjoint
verification ladder T0 review T1 audit T2 compute T3 formal
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We propose a kinematic algebra for the Bern-Carrasco-Johansson (BCJ) numerators of tree-level amplitudes and form factors in Yang-Mills theory coupled with bi-adjoint scalars. The algebraic generators of the algebra contain two parts: the first part is simply the flavour factor of the bi-adjoint scalars, and the second part that maps to non-trivial kinematic structures of the BCJ numerators obeys extended quasi-shuffle fusion products. The underlying kinematic algebra allows us to present closed forms for the BCJ numerators with any number of gluons and two or more scalars for both on-shell amplitudes and form factors that involve an off-shell operator. The BCJ numerators constructed in this way are manifestly gauge invariant and obey many novel relations that are inherited from the kinematic algebra.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Gleaning gravitational amplitudes -- a double copy for canceling dilatons

    hep-th 2025-01 conditional novelty 7.0 of 10

    An asymmetric double copy with a ghost-like sqrt-dilaton cancels dilaton contaminations in tree-level GR amplitudes with massive scalars up to six points, leaving a residual bubble ambiguity at one loop.

  2. Off-shell double copy theories in BV

    hep-th 2025-06 conditional novelty 6.0 of 10

    A BV-formalism construction gives off-shell double-copy actions for Chern-Simons, BF, and 2D Yang-Mills theories, with Kodaira-Spencer and Kähler gravity as natural examples.

  3. HEFT Numerators from Kinematic Algebra

    hep-th 2025-01 conditional novelty 6.0 of 10

    The heavy-mass effective field theory kinematic numerators are derived as the field theory limit of nested commutators of string vertex operators, reproducing and extending earlier fusion-rule results.

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