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Peer-reviewedCC BYPhysical Review Letters

Conservative Black Hole Scattering at Fifth Post-Minkowskian and Second Self-Force Order

  • Anonymous1
  • Gustav Uhre Jakobsen1,2
  • Gustav Mogull1,2,3
  • Christoph Nega2,4
  • Jan Christoph Plefka1
  • Benjamin Sauer1
  • Johann Usovitsch1
4 affiliations
  1. 1Humboldt-Universität zu Berlin
  2. 2Max Planck Institut für Gravitationsphysik (Albert Einstein Institut)
  3. 3Queen Mary University of London
  4. 4Technische Universität München
Open at sourceDOICite

Abstract

Using the worldline quantum field theory formalism, we compute conservative contributions to the scattering angle and impulse for classical black hole scattering at fifth post-Minkowskian and second self-force order. This four-loop calculation involves nonplanar Feynman integrals and requires advanced integration-by-parts reduction, novel differential-equation strategies, and efficient boundary-integral algorithms to solve a system of hundreds of master integrals in four integral families on high-performance computing systems. The resulting function space includes multiple polylogarithms as well as iterated integrals with a K3 period, which generate a spurious velocity divergence at v/c=sqrt[8]/3, γ=3. This divergence is present in the potential region and must be canceled by contributions from the radiative memory region, while its dimensional-regularization pole should cancel against the radiative tail region. As the standard use of Feynman propagators fails to ensure this cancellation, we instead propose a "(γ-3)" conservative prescription that realizes both cancellations, leading to a physically sensible answer. All available low-velocity checks of our result against the post-Newtonian literature are satisfied.

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Cite

BibTeXRIS
BibTeX
@article{anonymous2026conservative,
  title = {{Conservative Black Hole Scattering at Fifth Post-Minkowskian and Second Self-Force Order}},
  author = {Anonymous and Gustav Uhre Jakobsen and Gustav Mogull and Christoph Nega and Jan Christoph Plefka and Benjamin Sauer and Johann Usovitsch},
  journal = {Physical Review Letters},
  year = {2026},
  month = jul,
  doi = {10.1103/4dvk-nglx},
  url = {https://doi.org/10.1103/4dvk-nglx},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - Conservative Black Hole Scattering at Fifth Post-Minkowskian and Second Self-Force Order
AU  - Anonymous
AU  - Gustav Uhre Jakobsen
AU  - Gustav Mogull
AU  - Christoph Nega
AU  - Jan Christoph Plefka
AU  - Benjamin Sauer
AU  - Johann Usovitsch
PY  - 2026
DA  - 2026/07/10
JO  - Physical Review Letters
DO  - 10.1103/4dvk-nglx
UR  - https://doi.org/10.1103/4dvk-nglx
AB  - Using the worldline quantum field theory formalism, we compute conservative contributions to the scattering angle and impulse for classical black hole scattering at fifth post-Minkowskian and second self-force order. This four-loop calculation involves nonplanar Feynman integrals and requires advanced integration-by-parts reduction, novel differential-equation strategies, and efficient boundary-integral algorithms to solve a system of hundreds of master integrals in four integral families on high-performance computing systems. The resulting function space includes multiple polylogarithms as well as iterated integrals with a K3 period, which generate a spurious velocity divergence at v/c=sqrt[8]/3, γ=3. This divergence is present in the potential region and must be canceled by contributions from the radiative memory region, while its dimensional-regularization pole should cancel against the radiative tail region. As the standard use of Feynman propagators fails to ensure this cancellation, we instead propose a "(γ-3)" conservative prescription that realizes both cancellations, leading to a physically sensible answer. All available low-velocity checks of our result against the post-Newtonian literature are satisfied.
SN  - 0031-9007
SN  - 1079-7114
SN  - 1092-0145
ER  -