Canonical differential equations beyond genus one
Abstract We discuss for the first time canonical differential equations for hyperelliptic Feynman integrals. We study hyperelliptic Lauricella functions that include in particular the maximal cut of the two-loop non-planar double box, which is known to involve a hyperlliptic curve of genus two. We c...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2025-02-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP02(2025)014 |
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| author | Claude Duhr Franziska Porkert Sven F. Stawinski |
| author_facet | Claude Duhr Franziska Porkert Sven F. Stawinski |
| author_sort | Claude Duhr |
| collection | DOAJ |
| description | Abstract We discuss for the first time canonical differential equations for hyperelliptic Feynman integrals. We study hyperelliptic Lauricella functions that include in particular the maximal cut of the two-loop non-planar double box, which is known to involve a hyperlliptic curve of genus two. We consider specifically three- and four-parameter Lauricella functions, each associated to a hyperelliptic curve of genus two, and construct their canonical differential equations. Whilst core steps of this construction rely on existing methods — that we show to be applicable in the higher-genus case — we use new ideas on the structure of the twisted cohomology intersection matrix associated to the integral family in canonical form to obtain a better understanding of the appearing new functions. We further observe the appearance of Siegel modular forms in the ε-factorized differential equation matrix, nicely generalizing similar observations from the elliptic case. |
| format | Article |
| id | doaj-art-9f168f9a4f2048898e1d5fa2a9471fc6 |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-9f168f9a4f2048898e1d5fa2a9471fc62025-02-09T12:08:36ZengSpringerOpenJournal of High Energy Physics1029-84792025-02-012025215710.1007/JHEP02(2025)014Canonical differential equations beyond genus oneClaude Duhr0Franziska Porkert1Sven F. Stawinski2Bethe Center for Theoretical Physics, Universität BonnBethe Center for Theoretical Physics, Universität BonnBethe Center for Theoretical Physics, Universität BonnAbstract We discuss for the first time canonical differential equations for hyperelliptic Feynman integrals. We study hyperelliptic Lauricella functions that include in particular the maximal cut of the two-loop non-planar double box, which is known to involve a hyperlliptic curve of genus two. We consider specifically three- and four-parameter Lauricella functions, each associated to a hyperelliptic curve of genus two, and construct their canonical differential equations. Whilst core steps of this construction rely on existing methods — that we show to be applicable in the higher-genus case — we use new ideas on the structure of the twisted cohomology intersection matrix associated to the integral family in canonical form to obtain a better understanding of the appearing new functions. We further observe the appearance of Siegel modular forms in the ε-factorized differential equation matrix, nicely generalizing similar observations from the elliptic case.https://doi.org/10.1007/JHEP02(2025)014Scattering AmplitudesDifferential and Algebraic GeometryHigher-Order Perturbative Calculations |
| spellingShingle | Claude Duhr Franziska Porkert Sven F. Stawinski Canonical differential equations beyond genus one Journal of High Energy Physics Scattering Amplitudes Differential and Algebraic Geometry Higher-Order Perturbative Calculations |
| title | Canonical differential equations beyond genus one |
| title_full | Canonical differential equations beyond genus one |
| title_fullStr | Canonical differential equations beyond genus one |
| title_full_unstemmed | Canonical differential equations beyond genus one |
| title_short | Canonical differential equations beyond genus one |
| title_sort | canonical differential equations beyond genus one |
| topic | Scattering Amplitudes Differential and Algebraic Geometry Higher-Order Perturbative Calculations |
| url | https://doi.org/10.1007/JHEP02(2025)014 |
| work_keys_str_mv | AT claudeduhr canonicaldifferentialequationsbeyondgenusone AT franziskaporkert canonicaldifferentialequationsbeyondgenusone AT svenfstawinski canonicaldifferentialequationsbeyondgenusone |