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Propagators, BCFW recursion and new scattering equations at one loop.

Farrow, Joseph A. and Geyer, Yvonne and Lipstein, Arthur E. and Monteiro, Ricardo and Stark-Muchão, Ricardo (2020) 'Propagators, BCFW recursion and new scattering equations at one loop.', Journal of high energy physics., 2020 (10). 074.


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.

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Publisher 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.
Date accepted:15 September 2020
Date deposited:15 October 2020
Date of first online publication:12 October 2020
Date first made open access:15 October 2020

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