Analytical On-shell Calculation of Low Energy Higher Order Scattering

TL;DR

This paper introduces an analytical on-shell method for calculating one-loop electromagnetic and gravitational scattering, simplifying previous Feynman diagram approaches and enabling straightforward higher order computations.

Contribution

It presents a novel on-shell technique that simplifies the calculation of one-loop scattering amplitudes in electromagnetism and gravity, avoiding complex diagrammatic methods.

Findings

Reproduces known results using algebraic on-shell methods

Simplifies higher order gravitational scattering calculations

Eliminates need for ghost and triple-graviton considerations

Abstract

We demonstrate that the use of analytical on-shell methods involving calculation of the discontinuity across the t-channel cut associated with the exchange of a pair of massless particles (photons or gravitons) can be used to evaluate one-loop contributions to electromagnetic and gravitational scattering, with and without polarizability, reproducing via simple algebraic manipulations, results obtained previously, generally using Feynman diagram techniques. In the gravitational case the use of factorization permits a straightforward and algebraic calculation of higher order scattering without consideration of ghost contributions or of triple-graviton couplings, which made previous evaluations considerably more arduous.