Efficient Calculation of Crossing Symmetric BCJ Tree Numerators

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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.