Second-order self-force potential-region binary dynamics at $O(G^5)$ in supergravity

Zvi Bern; Enrico Herrmann; Radu Roiban; Michael S. Ruf; Alexander V. Smirnov; Vladimir A. Smirnov; Mao Zeng

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arXiv · 2509.17412

Second-order self-force potential-region binary dynamics at $O(G^5)$ in supergravity

Zvi Bern·Enrico Herrmann·Radu Roiban·Michael S. Ruf·Alexander V. Smirnov·Vladimir A. Smirnov·Mao Zeng

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Abstract

We compute the potential-graviton contributions to the conservative scattering angle of two non-spinning 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 multi-loop 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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Zvi Bern, Enrico Herrmann, Radu Roiban, Michael S. Ruf, Alexander V. Smirnov, Vladimir A. Smirnov, Mao Zeng. 2026-01-19. Second-order self-force potential-region binary dynamics at $O(G^5)$ in supergravity. https://arxiv.org/abs/2509.17412

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