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Nonlocal-in-time tail effects in gravitational scattering to fifth post-Minkowskian and tenth self-force orders

Christoph Dlapa1,*, Gregor Kälin2,†, Zhengwen Liu3,‡, and Rafael A. Porto4,§

  • *Contact author: christoph.dlapa@desy.de
  • †Contact author: kaeling@phys.ethz.ch
  • ‡Contact author: zhengwen.liu@seu.edu.cn
  • §Contact author: rafael.porto@desy.de
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Phys. Rev. D 114, 024029 – Published 10 July, 2026

DOI: https://doi.org/10.1103/wkp4-vy6g

Abstract

Using the worldline effective field theory formalism, we derive the nonlocal-in-time conservative contributions arising from tail effects in gravitational scattering to the fifth post-Minkowskian (5PM) and tenth self-force (10SF) orders. The result features multiple polylogarithms of up to weight 3. This challenging computation relies on state-of-the-art integration techniques, including a novel integration-by-parts algorithm: the “Sparse Integral Reducer” (). We find perfect agreement in the overlap with all existing literature through the sixth post-Newtonian order. The results presented here provide a key ingredient for isolating the local-in-time component of the conservative two-body dynamics of binary inspirals at the 5PM order.

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Local-in-Time Conservative Binary Dynamics at Fifth Post-Minkowskian and First Self-Force Orders

Christoph Dlapa, Gregor Kälin, Zhengwen Liu, and Rafael A. Porto
Phys. Rev. Lett. 135, 251401 (2025)

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Phys. Rev. D 114, 024029– Published 10 July, 2026
  • Received 4 May 2026
  • Accepted 3 June 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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