Complex factorization and recursion for one-loop amplitudes

Abstract

We consider the factorization of one-loop amplitudes at complex kinematic points. By determining the terms that are absent for real kinematics, we can construct a recursive ansatz for the purely rational pieces of one-loop amplitudes in massless theories. We illustrate this method by verifying the Bern et al. $n$-point ansatze for the single-minus one-loop amplitudes in Yang-Mills theory and by constructing the scalar contribution to the one-loop five-graviton maximal-helicity-violating scattering amplitude.