Calabi-Yau periods for black hole scattering in classical general relativity
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866914836102774784 |
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| author | Klemm, Albrecht Nega, Christoph Sauer, Benjamin Plefka, Jan |
| author_facet | Klemm, Albrecht Nega, Christoph Sauer, Benjamin Plefka, Jan |
| contents | The high-precision description of black hole scattering in classical general relativity using the post-Minkowskian (PM) expansion requires the evaluation of single-scale Feynman integrals at increasing loop orders. Up to 4PM, the scattering angle and the impulse are expressible in terms of polylogarithmic functions and Calabi-Yau (CY) two-fold periods. As in QFT, periods of higher dimensional CY n-folds are expected at higher PM order. We find at 5PM in the dissipative leading order self-force sector (5PM-1SF) that the only non-polylogarithmic functions are the K3 periods encountered before and the ones of a new hypergeometric CY three-fold. In the 5PM-2SF sector further CY two- and three-fold periods appear. Griffiths transversality of the CY period motives allows to transform the differential equations for the master integrals into $ε$-factorized form and to solve them in terms of a well controlled function space, as we demonstrate in the 5PM-1SF sector. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_07899 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Calabi-Yau periods for black hole scattering in classical general relativity Klemm, Albrecht Nega, Christoph Sauer, Benjamin Plefka, Jan High Energy Physics - Theory Algebraic Geometry The high-precision description of black hole scattering in classical general relativity using the post-Minkowskian (PM) expansion requires the evaluation of single-scale Feynman integrals at increasing loop orders. Up to 4PM, the scattering angle and the impulse are expressible in terms of polylogarithmic functions and Calabi-Yau (CY) two-fold periods. As in QFT, periods of higher dimensional CY n-folds are expected at higher PM order. We find at 5PM in the dissipative leading order self-force sector (5PM-1SF) that the only non-polylogarithmic functions are the K3 periods encountered before and the ones of a new hypergeometric CY three-fold. In the 5PM-2SF sector further CY two- and three-fold periods appear. Griffiths transversality of the CY period motives allows to transform the differential equations for the master integrals into $ε$-factorized form and to solve them in terms of a well controlled function space, as we demonstrate in the 5PM-1SF sector. |
| title | Calabi-Yau periods for black hole scattering in classical general relativity |
| topic | High Energy Physics - Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2401.07899 |