Spinning black hole scattering at O $$ \mathcal{O} $$ (G 3 S 2): Casimir terms, radial action and hidden symmetry
Abstract We resolve subtleties in calculating the post-Minksowskian dynamics of binary systems, as a spin expansion, from massive scattering amplitudes of fixed finite spin. In particular, the apparently ambiguous spin Casimir terms can be fully determined from the gradient of the spin-diagonal part...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2025-03-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP03(2025)126 |
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| author | Dogan Akpinar Fernando Febres Cordero Manfred Kraus Michael S. Ruf Mao Zeng |
| author_facet | Dogan Akpinar Fernando Febres Cordero Manfred Kraus Michael S. Ruf Mao Zeng |
| author_sort | Dogan Akpinar |
| collection | DOAJ |
| description | Abstract We resolve subtleties in calculating the post-Minksowskian dynamics of binary systems, as a spin expansion, from massive scattering amplitudes of fixed finite spin. In particular, the apparently ambiguous spin Casimir terms can be fully determined from the gradient of the spin-diagonal part of the amplitudes with respect to S 2 = −s(s+1)ħ 2, using an interpolation between massive amplitudes with different spin representations. From two-loop amplitudes of spin-0 and spin-1 particles minimally coupled to gravity, we extract the spin Casimir terms in the conservative scattering angle between a spinless and a spinning black hole at O $$ \mathcal{O} $$ (G 3 S 2), finding agreement with known results in the literature. This completes an earlier study [Phys. Rev. Lett. 130 (2023), 021601] that calculated the non-Casimir terms from amplitudes. We also illustrate our methods using a model of spinning bodies in electrodynamics, finding agreement between scattering amplitude predictions and classical predictions in a root-Kerr electromagnetic background up to O $$ \mathcal{O} $$ (α 3 S 2). For both gravity and electrodynamics, the finite part of the amplitude coincides with the two-body radial action in the aligned spin limit, generalizing the amplitude-action relation beyond the spinless case. Surprisingly, the two-loop amplitude displays a hidden spin-shift symmetry in the probe limit, which was previously observed at one loop. We conjecture that the symmetry holds to all orders in the coupling constant and is a consequence of integrability of Kerr orbits in the probe limit at the first few orders in spin. |
| format | Article |
| id | doaj-art-cb689da04ea04075a640eb2d0de9262f |
| institution | DOAJ |
| issn | 1029-8479 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | SpringerOpen |
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| series | Journal of High Energy Physics |
| spelling | doaj-art-cb689da04ea04075a640eb2d0de9262f2025-08-20T03:06:48ZengSpringerOpenJournal of High Energy Physics1029-84792025-03-012025314510.1007/JHEP03(2025)126Spinning black hole scattering at O $$ \mathcal{O} $$ (G 3 S 2): Casimir terms, radial action and hidden symmetryDogan Akpinar0Fernando Febres Cordero1Manfred Kraus2Michael S. Ruf3Mao Zeng4Higgs Centre for Theoretical Physics, University of EdinburghPhysics Department, Florida State UniversityDepartamento de Física Teórica, Instituto de Física, Universidad Nacional Autónoma de MéxicoMani L. Bhaumik Institute for Theoretical Physics, University of California at Los AngelesHiggs Centre for Theoretical Physics, University of EdinburghAbstract We resolve subtleties in calculating the post-Minksowskian dynamics of binary systems, as a spin expansion, from massive scattering amplitudes of fixed finite spin. In particular, the apparently ambiguous spin Casimir terms can be fully determined from the gradient of the spin-diagonal part of the amplitudes with respect to S 2 = −s(s+1)ħ 2, using an interpolation between massive amplitudes with different spin representations. From two-loop amplitudes of spin-0 and spin-1 particles minimally coupled to gravity, we extract the spin Casimir terms in the conservative scattering angle between a spinless and a spinning black hole at O $$ \mathcal{O} $$ (G 3 S 2), finding agreement with known results in the literature. This completes an earlier study [Phys. Rev. Lett. 130 (2023), 021601] that calculated the non-Casimir terms from amplitudes. We also illustrate our methods using a model of spinning bodies in electrodynamics, finding agreement between scattering amplitude predictions and classical predictions in a root-Kerr electromagnetic background up to O $$ \mathcal{O} $$ (α 3 S 2). For both gravity and electrodynamics, the finite part of the amplitude coincides with the two-body radial action in the aligned spin limit, generalizing the amplitude-action relation beyond the spinless case. Surprisingly, the two-loop amplitude displays a hidden spin-shift symmetry in the probe limit, which was previously observed at one loop. We conjecture that the symmetry holds to all orders in the coupling constant and is a consequence of integrability of Kerr orbits in the probe limit at the first few orders in spin.https://doi.org/10.1007/JHEP03(2025)126Scattering AmplitudesClassical Theories of Gravity |
| spellingShingle | Dogan Akpinar Fernando Febres Cordero Manfred Kraus Michael S. Ruf Mao Zeng Spinning black hole scattering at O $$ \mathcal{O} $$ (G 3 S 2): Casimir terms, radial action and hidden symmetry Journal of High Energy Physics Scattering Amplitudes Classical Theories of Gravity |
| title | Spinning black hole scattering at O $$ \mathcal{O} $$ (G 3 S 2): Casimir terms, radial action and hidden symmetry |
| title_full | Spinning black hole scattering at O $$ \mathcal{O} $$ (G 3 S 2): Casimir terms, radial action and hidden symmetry |
| title_fullStr | Spinning black hole scattering at O $$ \mathcal{O} $$ (G 3 S 2): Casimir terms, radial action and hidden symmetry |
| title_full_unstemmed | Spinning black hole scattering at O $$ \mathcal{O} $$ (G 3 S 2): Casimir terms, radial action and hidden symmetry |
| title_short | Spinning black hole scattering at O $$ \mathcal{O} $$ (G 3 S 2): Casimir terms, radial action and hidden symmetry |
| title_sort | spinning black hole scattering at o mathcal o g 3 s 2 casimir terms radial action and hidden symmetry |
| topic | Scattering Amplitudes Classical Theories of Gravity |
| url | https://doi.org/10.1007/JHEP03(2025)126 |
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