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arXiv · 2602.04371

Canonical differential equations beyond polylogs

Claude Duhr·Sara Maggio·Christoph Nega·Benjamin Sauer·Lorenzo Tancredi·Fabian J. Wagner
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Abstract

Feynman integrals whose associated geometries extend beyond the Riemann sphere, such as elliptic curves and Calabi-Yau varieties, are increasingly relevant in modern precision calculations. They arise not only in collider cross-section calculations, but also in the post-Minkowskian expansion of gravitational-wave scattering. A powerful approach to compute integrals of this type is via differential equations, particularly when cast in a canonical form, which simplifies their $\varepsilon$-expansion and makes analytic properties manifest. In these proceedings, we will present a method to systematically construct canonical differential equations even for integrals that evaluate beyond multiple polylogarithms. The discussion is kept as light as possible, focusing on the two-loop sunrise integral, deferring the technical details to the original publications.

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Claude Duhr, Sara Maggio, Christoph Nega, Benjamin Sauer, Lorenzo Tancredi, Fabian J. Wagner. 2026-02-04. Canonical differential equations beyond polylogs. https://arxiv.org/abs/2602.04371

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