Form factor recursion relations at loop level

Abstract

Abstract We introduce a prescription to define form factor integrands at loop level in planar N = 4 $$ \mathcal{N}=4 $$ supersymmetric Yang-Mills theory. This relies on a periodic kinematic configuration that has been instrumental to describe form factors at strong coupling in terms of periodic Wilson loops. With this prescription, we are able to formulate loop-level recursion relations for planar form factor integrands, using a two-line (BCFW) and an all-line shift. We also point out important differences with the known recursion relations of integrands of planar loop amplitudes. We present a number of concrete one-loop examples to illustrate and validate our prescription for form factor integrands.

Keywords

• Scattering Amplitudes
• Supersymmetric Gauge Theory