Efficient calculation of crossing symmetric BCJ tree numerators

Abstract

In this paper, we develop 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 accessibility 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.

Celestial double copy from the worldsheet

“…The fact that CHY numerators produce BCJ-satisfying numerators was already shown in the orginal work[28] (see also[66,67] for explicit constructions).…”

Loop amplitudes monodromy relations and color-kinematics duality

“…Over the past few years a related approach based on ambitwistor string theory has emerged, see, e.g., [21][22][23][24][25][26][27] (various other recent worldsheet approaches to color-kinematics duality include [28][29][30][31][32][33][34][35][36][37]), which gives a handle on the problem of constructing BCJ numerators, at a cost of introducing linearized propagators which need to be transformed into quadratic ones using non-trivial partial fraction identities. Despite many successes of this research direction, our goal here is to obtain Feynman diagrams directly from worldsheet degenerations, which at present is understood most appropriately in the case of string theory.…”

Scattering of gravitons and spinning massive states from compact numerators

“…An important result of refs. [72,73] was the extension of the above diagrammatic rules for spinors. We treat these cases through the same diagrams by exchanging the polarization vectors with spinors and the gluon field strength tensor coming from the baseline by the following spinor replacement…”

“…Another prerequisite is the introduction of fermions in the scattering equations by refs. [72,73], where non-integer spins are included by modifying an algorithm developed in refs. [74,75].…”

“…Ref. [72] presented an improved method by constructing crossing symmetric numerators and thereby directly reducing the computation to (n − 1)! diagrams.…”