Classical gravitational scattering at $$ \mathcal{O} $$(G3) from Feynman diagrams

Clifford Cheung, Mikhail P. Solon
2020 Journal of High Energy Physics  
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
more » ... 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.
doi:10.1007/jhep06(2020)144 fatcat:fmj2gdjtibf7riwucnmlqtbmzi