Scattering Amplitudes and Conservative Binary Dynamics at O(G^{5}) without Self-Force Truncation.

Authors

Zvi Bern, Enrico Herrmann, Radu Roiban, Michael S Ruf, Alexander V Smirnov, Sid Smith, Mao Zeng

Published in

Physical review letters. Volume 137. Issue 2. Pages 021402. Jul 10, 2026.

Abstract

We compute the complete potential-graviton contributions to the conservative radial action and scattering angle for two nonspinning bodies in general relativity, accurate through fifth order in Newton's constant and including second-order self-force effects. The calculation is carried out in the scattering-amplitude framework, combining the double-copy, effective field theory, and multiloop integration techniques based on integration by parts and differential equations. To address a major computational bottleneck, we develop improved integration-by-parts algorithms that render calculations at this order tractable. The post-Minkowskian amplitude is presented as a series expansion, following the strategy used earlier in maximal supergravity. For the first self-force sector, which involves only polylogarithmic functions, we also provide a closed-form analytic expression. For the second self-force sector, as in earlier supergravity work, we find nontrivial cancellations among contributions related to integrals supported on Calabi-Yau geometry.

PMID:
42503098
Bibliographic data and abstract were imported from PubMed on 26 Jul 2026.

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