Kinematic Hopf algebra for amplitudes and form factors

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 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.

5 pages+appendices

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Cited by in corpus (8)

• One-loop Gravitational Bremsstrahlung and Waveforms from a Heavy-Mass Effective Field Theory
• Tree-level amplitudes from the pure spinor superstring
• Classical Spin Gravitational Compton Scattering
• Gauge independent kinematic algebra of self-dual Yang-Mills theory
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• Double copy for tree-level form factors. Part II. Generalizations and special topics
• Color-Kinematic Numerators for Fermion Compton Amplitudes
• Algebraic Consistency and Explicit Construction of One-Loop BCJ Numerators of Yang-Mills and Related Theories