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Classical gravitational scattering at O(G³) from Feynman diagrams

Cheung, Clifford and Solon, Mikhail P. (2020) Classical gravitational scattering at O(G³) from Feynman diagrams. Journal of High Energy Physics, 2020 (6). Art. No. 144. ISSN 1126-6708. doi:10.1007/JHEP06(2020)144.

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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.

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Additional Information:© 2020 The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. Article funded by SCOAP3. Received 09 May 2020; Accepted 05 June 2020; Published 23 June 2020. We thank Zvi Bern, Aneesh Manohar, Ira Rothstein, and Nabha Shah for helpful discussions. C.C. and M.P.S. are supported by the DOE under grant no. DE- SC0011632 and by the Walter Burke Institute for Theoretical Physics. The calculations here used the computer algebra system Mathematica [103] in combination with FeynCalc [104{106] and xAct [107].
Group:Walter Burke Institute for Theoretical Physics
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Department of Energy (DOE)DE-SC0011632
Walter Burke Institute for Theoretical Physics, CaltechUNSPECIFIED
Subject Keywords:Black Holes, Classical Theories of Gravity, Effective Field Theories, Scattering Amplitudes
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Issue or Number:6
Record Number:CaltechAUTHORS:20200408-134409453
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Official Citation:Cheung, C., Solon, M.P. Classical gravitational scattering at O(G3) from Feynman diagrams. J. High Energ. Phys. 2020, 144 (2020).
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:102408
Deposited By: Joy Painter
Deposited On:08 Apr 2020 20:55
Last Modified:16 Nov 2021 18:11

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