Efficient Calculation of Crossing Symmetric BCJ Tree Numerators


Authors: Alex Edison and Fei Teng

Preprint number: UUITP-12/20

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 an upcoming 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 com-
putations in both classical and quantum gravity.