Abstract
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.
Highlights
Two important modern advances in understanding perturbative scattering amplitudes in quantum field theory have been the BCFW recursion relations and the formalism of the scattering equations
D Worldsheet formulas with double-forward limit scattering equations 77
Motivated by the loop-level BCFW recursion relation and the connection it suggests between the forward-limit terms and standard Feynman-like propagators, we investigate how local integrand expressions can arise from the worldsheet
Summary
Two important modern advances in understanding perturbative scattering amplitudes in quantum field theory have been the BCFW recursion relations and the formalism of the scattering equations. BCFW recursion that is suited to D-dimensional momentum space, describing the cancellation of spurious poles in simple examples with and without supersymmetry, and in non-planar theories; and (ii) present a new set of one-loop scattering equations that yields standard Feynman-type propagators, as opposed to more unorthodox representations of the loop integrand considered previously This new worldsheet approach is inspired by the BCFW story, but does not exhibit spurious poles in the same way.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
