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Propagators, BCFW recursion and new scattering equations at one loop

Farrow, Joseph A.; Geyer, Yvonne; Lipstein, Arthur E.; Monteiro, Ricardo; Stark-Muchão, Ricardo

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Yvonne Geyer

Ricardo Monteiro

Ricardo Stark-Muchão


We investigate how loop-level propagators arise from tree level via a forward-limit procedure in two modern approaches to scattering amplitudes, namely the BCFW recursion relations and the scattering equations formalism. In the first part of the paper, we revisit the BCFW construction of one-loop integrands in momentum space, using a convenient parametrisation of the D-dimensional loop momentum. We work out explicit examples with and without supersymmetry, and discuss the non-planar case in both gauge theory and gravity. In the second part of the paper, we study an alternative approach to one-loop integrands, where these are written as worldsheet formulas based on new one-loop scattering equations. These equations, which are inspired by BCFW, lead to standard Feynman-type propagators, instead of the ‘linear’-type loop-level propagators that first arose from the formalism of ambitwistor strings. We exploit the analogies between the two approaches, and present a proof of an all-multiplicity worldsheet formula using the BCFW recursion.


Farrow, J. A., Geyer, Y., Lipstein, A. E., Monteiro, R., & Stark-Muchão, R. (2020). Propagators, BCFW recursion and new scattering equations at one loop. Journal of High Energy Physics, 2020(10), Article 74.

Journal Article Type Article
Acceptance Date Sep 15, 2020
Online Publication Date Oct 12, 2020
Publication Date 2020-10
Deposit Date Oct 14, 2020
Publicly Available Date Oct 15, 2020
Journal Journal of High Energy Physics
Print ISSN 1126-6708
Publisher Scuola Internazionale Superiore di Studi Avanzati (SISSA)
Peer Reviewed Peer Reviewed
Volume 2020
Issue 10
Article Number 74


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Copyright Statement
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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