Algorithm for differential equations for Feynman integrals in general dimensions
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910493865672704 |
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| author | de la Cruz, Leonardo Vanhove, Pierre |
| author_facet | de la Cruz, Leonardo Vanhove, Pierre |
| contents | We present an algorithm for determining the minimal order differential equations associated to a given Feynman integral in dimensional or analytic regularisation. The algorithm is an extension of the Griffiths-Dwork pole reduction adapted to the case of twisted differential forms. In dimensional regularisation, we demonstrate the applicability of this algorithm by explicitly providing the inhomogeneous differential equations for the multiloop two-point sunset integrals: up to 20 loops for the equal mass case, the generic mass case at two- and three-loop orders. Additionally, we derive the differential operators for various infrared-divergent two-loop graphs. In the analytic regularisation case, we apply our algorithm for deriving a system of partial differential equations for regulated Witten diagrams, which arise in the evaluation of cosmological correlators of conformally coupled $ϕ^4$ theory in four-dimensional de Sitter space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_09908 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Algorithm for differential equations for Feynman integrals in general dimensions de la Cruz, Leonardo Vanhove, Pierre High Energy Physics - Theory High Energy Physics - Phenomenology Mathematical Physics We present an algorithm for determining the minimal order differential equations associated to a given Feynman integral in dimensional or analytic regularisation. The algorithm is an extension of the Griffiths-Dwork pole reduction adapted to the case of twisted differential forms. In dimensional regularisation, we demonstrate the applicability of this algorithm by explicitly providing the inhomogeneous differential equations for the multiloop two-point sunset integrals: up to 20 loops for the equal mass case, the generic mass case at two- and three-loop orders. Additionally, we derive the differential operators for various infrared-divergent two-loop graphs. In the analytic regularisation case, we apply our algorithm for deriving a system of partial differential equations for regulated Witten diagrams, which arise in the evaluation of cosmological correlators of conformally coupled $ϕ^4$ theory in four-dimensional de Sitter space. |
| title | Algorithm for differential equations for Feynman integrals in general dimensions |
| topic | High Energy Physics - Theory High Energy Physics - Phenomenology Mathematical Physics |
| url | https://arxiv.org/abs/2401.09908 |