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  • Letter
  • Open Access

Kinematic Hopf algebra for amplitudes and form factors

Gang Chen1,*, Guanda Lin1,2,†, and Congkao Wen1,‡

  • 1Centre for Theoretical Physics, Department of Physics and Astronomy, Queen Mary University of London, Mile End Road, London E1 4NS, United Kingdom
  • 2CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China

  • *g.chen@qmul.ac.uk
  • †linguandak@pku.edu.cn
  • ‡c.wen@qmul.ac.uk
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Phys. Rev. D 107, L081701 – Published 19 April, 2023

DOI: https://doi.org/10.1103/PhysRevD.107.L081701

Abstract

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 biadjoint scalars. The algebraic generators of the algebra contain two parts: the first part is simply the flavor factor of the biadjoint scalars, and the second part that maps to nontrivial kinematic structures of the BCJ numerators obeys extended quasishuffle 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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Outline

Information

Phys. Rev. D 107, L081701– Published 19 April, 2023
  • Received 30 August 2022
  • Accepted 28 March 2023
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