Propagators, BCFW Recursion and New Scattering Equations at One Loop

Understand

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.