Conservative Black Hole Scattering at Fifth Post-Minkowskian and Second Self-Force Order
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arXiv
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| Autori principali: | , , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917243416215552 |
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| author | Driesse, Mathias Jakobsen, Gustav Uhre Mogull, Gustav Nega, Christoph Plefka, Jan Sauer, Benjamin Usovitsch, Johann |
| author_facet | Driesse, Mathias Jakobsen, Gustav Uhre Mogull, Gustav Nega, Christoph Plefka, Jan Sauer, Benjamin Usovitsch, Johann |
| contents | Using the worldline quantum field theory formalism, we compute the conservative scattering angle and impulse for classical black hole scattering at fifth post-Minkowskian (5PM) order by providing the second self-force (2SF) contributions. This four-loop calculation involves non-planar 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 $v/c=\sqrt{8}/3$. This divergence is present in the potential region and must be canceled by contributions from the radiative memory region, while its dimensional-regularisation pole should cancel against the radiative tail region. We find that the standard use of Feynman propagators to access the conservative sector fails to ensure this cancellation. We propose a conservative propagator prescription which realises both cancellations leading to a physically sensible answer. All available low-velocity checks of our result against the post-Newtonian literature are satisfied. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_16256 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Conservative Black Hole Scattering at Fifth Post-Minkowskian and Second Self-Force Order Driesse, Mathias Jakobsen, Gustav Uhre Mogull, Gustav Nega, Christoph Plefka, Jan Sauer, Benjamin Usovitsch, Johann High Energy Physics - Theory General Relativity and Quantum Cosmology High Energy Physics - Phenomenology Using the worldline quantum field theory formalism, we compute the conservative scattering angle and impulse for classical black hole scattering at fifth post-Minkowskian (5PM) order by providing the second self-force (2SF) contributions. This four-loop calculation involves non-planar 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 $v/c=\sqrt{8}/3$. This divergence is present in the potential region and must be canceled by contributions from the radiative memory region, while its dimensional-regularisation pole should cancel against the radiative tail region. We find that the standard use of Feynman propagators to access the conservative sector fails to ensure this cancellation. We propose a conservative propagator prescription which realises both cancellations leading to a physically sensible answer. All available low-velocity checks of our result against the post-Newtonian literature are satisfied. |
| title | Conservative Black Hole Scattering at Fifth Post-Minkowskian and Second Self-Force Order |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2601.16256 |