Analytical On-shell Calculation of Higher Order Scattering: Massless Particles

We demonstrate that the use of on-shell methods involving calculation of the discontinuity across the t-channel cut associated with the exchange of a pair of massless particles can be used to evaluate loop contributions to the electromagnetic and gravitational scattering of both massive and massless particles. In the gravitational case the use of factorization permits a straightforward and algebraic calculation of higher order scattering results, which were obtained previously by considerably more arduous Feynman diagram techniques.