On a procedure to derive ϵ-factorised differential equations beyond polylogarithms
Abstract In this manuscript, we elaborate on a procedure to derive ϵ-factorised differential equations for multi-scale, multi-loop classes of Feynman integrals that evaluate to special functions beyond multiple polylogarithms. We demonstrate the applicability of our approach to diverse classes of pr...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2023-07-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP07(2023)206 |
| _version_ | 1797647473155506176 |
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| author | Lennard Görges Christoph Nega Lorenzo Tancredi Fabian J. Wagner |
| author_facet | Lennard Görges Christoph Nega Lorenzo Tancredi Fabian J. Wagner |
| author_sort | Lennard Görges |
| collection | DOAJ |
| description | Abstract In this manuscript, we elaborate on a procedure to derive ϵ-factorised differential equations for multi-scale, multi-loop classes of Feynman integrals that evaluate to special functions beyond multiple polylogarithms. We demonstrate the applicability of our approach to diverse classes of problems, by working out ϵ-factorised differential equations for single- and multi-scale problems of increasing complexity. To start we are reconsidering the well-studied equal-mass two-loop sunrise case, and move then to study other elliptic two-, three- and four-point problems depending on multiple different scales. Finally, we showcase how the same approach allows us to obtain ϵ-factorised differential equations also for Feynman integrals that involve geometries beyond a single elliptic curve. |
| first_indexed | 2024-03-11T15:18:02Z |
| format | Article |
| id | doaj.art-537d6ffe506e4262bb281a3cfe3cbe73 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-03-11T15:18:02Z |
| publishDate | 2023-07-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-537d6ffe506e4262bb281a3cfe3cbe732023-10-29T12:08:23ZengSpringerOpenJournal of High Energy Physics1029-84792023-07-012023715210.1007/JHEP07(2023)206On a procedure to derive ϵ-factorised differential equations beyond polylogarithmsLennard Görges0Christoph Nega1Lorenzo Tancredi2Fabian J. Wagner3Technical University of Munich, TUM School of Natural Sciences, Physics DepartmentTechnical University of Munich, TUM School of Natural Sciences, Physics DepartmentTechnical University of Munich, TUM School of Natural Sciences, Physics DepartmentTechnical University of Munich, TUM School of Natural Sciences, Physics DepartmentAbstract In this manuscript, we elaborate on a procedure to derive ϵ-factorised differential equations for multi-scale, multi-loop classes of Feynman integrals that evaluate to special functions beyond multiple polylogarithms. We demonstrate the applicability of our approach to diverse classes of problems, by working out ϵ-factorised differential equations for single- and multi-scale problems of increasing complexity. To start we are reconsidering the well-studied equal-mass two-loop sunrise case, and move then to study other elliptic two-, three- and four-point problems depending on multiple different scales. Finally, we showcase how the same approach allows us to obtain ϵ-factorised differential equations also for Feynman integrals that involve geometries beyond a single elliptic curve.https://doi.org/10.1007/JHEP07(2023)206Higher-Order Perturbative CalculationsScattering AmplitudesDifferential and Algebraic Geometry |
| spellingShingle | Lennard Görges Christoph Nega Lorenzo Tancredi Fabian J. Wagner On a procedure to derive ϵ-factorised differential equations beyond polylogarithms Journal of High Energy Physics Higher-Order Perturbative Calculations Scattering Amplitudes Differential and Algebraic Geometry |
| title | On a procedure to derive ϵ-factorised differential equations beyond polylogarithms |
| title_full | On a procedure to derive ϵ-factorised differential equations beyond polylogarithms |
| title_fullStr | On a procedure to derive ϵ-factorised differential equations beyond polylogarithms |
| title_full_unstemmed | On a procedure to derive ϵ-factorised differential equations beyond polylogarithms |
| title_short | On a procedure to derive ϵ-factorised differential equations beyond polylogarithms |
| title_sort | on a procedure to derive ϵ factorised differential equations beyond polylogarithms |
| topic | Higher-Order Perturbative Calculations Scattering Amplitudes Differential and Algebraic Geometry |
| url | https://doi.org/10.1007/JHEP07(2023)206 |
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