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arXiv · 2504.17757

On canonical differential equations for Calabi-Yau multi-scale Feynman integrals

Sara Maggio·Yoann Sohnle
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Abstract

We generalise a method recently introduced in the literature, that derives canonical differential equations, to multi-scale Feynman integrals with an underlying Calabi-Yau geometry. We start by recomputing a canonical form for the sunrise integral with all unequal masses. Additionally, we compute for the first time a canonical form for the three-loop banana integral with two unequal masses and for a four-loop banana integral with two unequal masses. For the integrals we compute, we find an $\epsilon$-form whose connection has at most simple poles. We motivate our construction by studying the Picard-Fuchs operators acting on the integrals considered. In the appendices, we give a constructive explanation for why our generalisation works.

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Sara Maggio, Yoann Sohnle. 2025-04-24. On canonical differential equations for Calabi-Yau multi-scale Feynman integrals. https://doi.org/10.1007/jhep10(2025)202

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