Efficient Calculation of Crossing Symmetric BCJ Tree Numerators

Abstract

In this paper, we propose an improved method for directly calculating double-copy-compatible tree numerators in (super-)Yang-Mills and Yang-Mills-scalar theories. Our new scheme gets rid of any explicit dependence on reference orderings, restoring a form of crossing symmetry to the numerators. This in turn improves the computational efficiency of the algorithm, allowing us to go well beyond the number of external particles accessible with the reference order based methods. Motivated by a parallel study of one-loop BCJ numerators from forward limits, we explore the generalization to include a pair of fermions. To improve the accessiblity of the new algorithm, we provide a Mathematica package that implements the numerator construction. The structure of the computation also provides for a straightforward introduction of minimally-coupled massive particles potentially useful for future computations in both classical and quantum gravity.

arXiv comment27+7 pages; 3 labeled figures; v2: published version

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• Covariant Color-Kinematics Duality
• Kinematic Hopf Algebra for BCJ Numerators in Heavy-Mass Effective Field Theory and Yang-Mills Theory
• Off-Shell Color-Kinematics Duality for Chern-Simons
• Celestial double copy from the worldsheet
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• Classical Limit of Higher-Spin String Amplitudes
• 10D Super-Yang-Mills Scattering Amplitudes From Its Pure Spinor Action
• Loop amplitudes monodromy relations and color-kinematics duality
• Perfecting one-loop BCJ numerators in SYM and supergravity
• Scattering of Gravitons and Spinning Massive States from Compact Numerators
• Effective Field Theories and Cosmological Scattering Equations
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• First Look at Quartic-in-Spin Binary Dynamics at Third Post-Minkowskian Order
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• One-loop amplitudes in Einstein-Yang-Mills from forward limits
• Universal expansions of scattering amplitudes for gravitons, gluons and Goldstone particles
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• One-loop Bern-Carrasco-Johansson Numerators on Quadratic Propagators from the Worldsheet
• Covariant color-kinematics duality, Hopf algebras and permutohedra
• Higher-order tails and RG flows due to scattering of gravitational radiation from binary inspirals
• Color-Kinematic Numerators for Fermion Compton Amplitudes
• Next-to-MHV Yang-Mills kinematic algebra
• New relations for tree-level form factors and scattering amplitudes
• $D$-Dimensional Modular Assembly of Higher-Derivative Four-Point Contact Amplitudes Involving Fermions
• Color-Kinematics Relation from the Feynman Diagram Perspective