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Second-Order Self-Force Potential-Region Binary Dynamics at O(G5) in Supergravity

Zvi Bern1, Enrico Herrmann1, Radu Roiban2,3, Michael S. Ruf4, Alexander V. Smirnov5,6, Vladimir A. Smirnov6,7, and Mao Zeng8

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Phys. Rev. Lett. 136, 081401 – Published 24 February, 2026

DOI: https://doi.org/10.1103/jmby-htz9

Abstract

We compute the potential-graviton contributions to the conservative scattering angle of two nonspinning bodies in maximal supergravity at fifth order in Newton’s constant, including second-order self-force effects. Our goal is to tackle the challenging integrals arising at this order in Einstein gravity, but within the technically simpler framework of supergravity. The calculation employs the scattering-amplitude framework, effective field theory, and multiloop integration techniques based on integration by parts and differential equations. The final result is expressed as a series expansion around the static limit, thereby avoiding the explicit evaluation of intricate special functions. This series solution for the master integrals applies, as well, to the corresponding computation in general relativity. Remarkably, we observe nontrivial cancellations among contributions associated with Calabi-Yau integrals, alongside a distinct contribution governed by a Heun differential equation.

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Phys. Rev. Lett. 136, 081401– Published 24 February, 2026
  • Received 23 October 2025
  • Accepted 27 January 2026
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