Scattering Amplitudes and Conservative Binary Dynamics at $O(G^5)$ without Self-Force Truncation
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| Main Authors: | , , , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866911428525424640 |
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| author | Bern, Zvi Herrmann, Enrico Roiban, Radu Ruf, Michael S. Smirnov, Alexander V. Smith, Sid Zeng, Mao |
| author_facet | Bern, Zvi Herrmann, Enrico Roiban, Radu Ruf, Michael S. Smirnov, Alexander V. Smith, Sid Zeng, Mao |
| contents | We compute the complete potential-graviton contributions to the conservative radial action and scattering angle for two non-spinning bodies in general relativity, accurate through fifth order in Newton's constant and including second-order self-force (2SF) effects. The calculation is carried out in the scattering-amplitude framework, combining the double copy, effective field theory, and multi-loop integration techniques based on integration by parts and differential equations. To address a major computational bottleneck, we develop improved integration-by-parts algorithms that render calculations at this order tractable. The post-Minkowskian amplitude is presented as a series expansion, following the strategy used earlier in maximal supergravity. For the first self-force sector, which involves only polylogarithmic functions, we also provide a closed-form analytic expression. For the second self-force sector, as in earlier supergravity work, we find nontrivial cancellations among contributions related to integrals supported on Calabi-Yau geometry. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_23654 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Scattering Amplitudes and Conservative Binary Dynamics at $O(G^5)$ without Self-Force Truncation Bern, Zvi Herrmann, Enrico Roiban, Radu Ruf, Michael S. Smirnov, Alexander V. Smith, Sid Zeng, Mao High Energy Physics - Theory General Relativity and Quantum Cosmology High Energy Physics - Phenomenology We compute the complete potential-graviton contributions to the conservative radial action and scattering angle for two non-spinning bodies in general relativity, accurate through fifth order in Newton's constant and including second-order self-force (2SF) effects. The calculation is carried out in the scattering-amplitude framework, combining the double copy, effective field theory, and multi-loop integration techniques based on integration by parts and differential equations. To address a major computational bottleneck, we develop improved integration-by-parts algorithms that render calculations at this order tractable. The post-Minkowskian amplitude is presented as a series expansion, following the strategy used earlier in maximal supergravity. For the first self-force sector, which involves only polylogarithmic functions, we also provide a closed-form analytic expression. For the second self-force sector, as in earlier supergravity work, we find nontrivial cancellations among contributions related to integrals supported on Calabi-Yau geometry. |
| title | Scattering Amplitudes and Conservative Binary Dynamics at $O(G^5)$ without Self-Force Truncation |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2512.23654 |