Classical gravitational scattering at O $$ \mathcal{O} $$ (G 3) from Feynman diagrams

• Main Authors: Clifford Cheung, Mikhail P. Solon
• Format: Article
• Language: English
• Published: SpringerOpen 2020-06-01
• Series: Journal of High Energy Physics
• Subjects: Black Holes; Classical Theories of Gravity; Effective Field Theories; Scattering Amplitudes
• Online Access: http://link.springer.com/article/10.1007/JHEP06(2020)144

Abstract We perform a Feynman diagram calculation of the two-loop scattering amplitude for gravitationally interacting massive particles in the classical limit. Conveniently, we are able to sidestep the most taxing diagrams by exploiting the test-particle limit in which the system is fully characterized by a particle propagating in a Schwarzschild spacetime. We assume a general choice of graviton field basis and gauge fixing that contains as a subset the well-known deDonder gauge and its various cousins. As a highly nontrivial consistency check, all gauge parameters evaporate from the final answer. Moreover, our result exactly matches that of Bern et al. [39], here verified up to sixth post-Newtonian order while also reproducing the same unique velocity resummation at third post-Minkowksian order.