The hierarchical three-body problem at O G 2 $$ \mathcal{O}\left({G}^2\right) $$
Abstract Employing techniques from scattering amplitudes and effective field theory, we model the dynamics of hierarchical triples, which are three-body systems composed of two bodies separated by a distance r and a third body a distance ρ away, with r ≪ ρ. We apply the method of regions to systemat...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2025-01-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP01(2025)186 |
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| author | Mikhail P. Solon Anna M. Wolz |
| author_facet | Mikhail P. Solon Anna M. Wolz |
| author_sort | Mikhail P. Solon |
| collection | DOAJ |
| description | Abstract Employing techniques from scattering amplitudes and effective field theory, we model the dynamics of hierarchical triples, which are three-body systems composed of two bodies separated by a distance r and a third body a distance ρ away, with r ≪ ρ. We apply the method of regions to systematically expand in the small ratio r/ρ and illustrate this approach for evaluating Fourier transform integrals, which have been the bottleneck for deriving complete results in position space. In the limit where the distant third body is much heavier than the other two, we derive new analytic results in position space for the three-body conservative potential at O G 2 $$ \mathcal{O}\left({G}^2\right) $$ and at leading and next-to-leading order in r/ρ. We also derive new results for arbitrary masses in the rest frame of the distant particle. Our results are exact in velocity, and can be used in analyses involving both bound and unbound hierarchical triples in astrophysical systems. |
| format | Article |
| id | doaj-art-e58d522f0aa94689b0c90e20b9885ee4 |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-e58d522f0aa94689b0c90e20b9885ee42025-02-09T12:08:21ZengSpringerOpenJournal of High Energy Physics1029-84792025-01-012025113010.1007/JHEP01(2025)186The hierarchical three-body problem at O G 2 $$ \mathcal{O}\left({G}^2\right) $$Mikhail P. Solon0Anna M. Wolz1Mani L. Bhaumik Institute for Theoretical Physics, Department of Physics and Astronomy, University of California Los AngelesMani L. Bhaumik Institute for Theoretical Physics, Department of Physics and Astronomy, University of California Los AngelesAbstract Employing techniques from scattering amplitudes and effective field theory, we model the dynamics of hierarchical triples, which are three-body systems composed of two bodies separated by a distance r and a third body a distance ρ away, with r ≪ ρ. We apply the method of regions to systematically expand in the small ratio r/ρ and illustrate this approach for evaluating Fourier transform integrals, which have been the bottleneck for deriving complete results in position space. In the limit where the distant third body is much heavier than the other two, we derive new analytic results in position space for the three-body conservative potential at O G 2 $$ \mathcal{O}\left({G}^2\right) $$ and at leading and next-to-leading order in r/ρ. We also derive new results for arbitrary masses in the rest frame of the distant particle. Our results are exact in velocity, and can be used in analyses involving both bound and unbound hierarchical triples in astrophysical systems.https://doi.org/10.1007/JHEP01(2025)186Black HolesEffective Field TheoriesScattering AmplitudesClassical Theories of Gravity |
| spellingShingle | Mikhail P. Solon Anna M. Wolz The hierarchical three-body problem at O G 2 $$ \mathcal{O}\left({G}^2\right) $$ Journal of High Energy Physics Black Holes Effective Field Theories Scattering Amplitudes Classical Theories of Gravity |
| title | The hierarchical three-body problem at O G 2 $$ \mathcal{O}\left({G}^2\right) $$ |
| title_full | The hierarchical three-body problem at O G 2 $$ \mathcal{O}\left({G}^2\right) $$ |
| title_fullStr | The hierarchical three-body problem at O G 2 $$ \mathcal{O}\left({G}^2\right) $$ |
| title_full_unstemmed | The hierarchical three-body problem at O G 2 $$ \mathcal{O}\left({G}^2\right) $$ |
| title_short | The hierarchical three-body problem at O G 2 $$ \mathcal{O}\left({G}^2\right) $$ |
| title_sort | hierarchical three body problem at o g 2 mathcal o left g 2 right |
| topic | Black Holes Effective Field Theories Scattering Amplitudes Classical Theories of Gravity |
| url | https://doi.org/10.1007/JHEP01(2025)186 |
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