Work

Canonical differential equations beyond polylogs

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2602.04371

Authors: Duhr, Claude, Maggio, Sara, Nega, Christoph, Sauer, Benjamin, Tancredi, Lorenzo, Wagner, Fabian J.

Institutions: University of Bonn, Max Planck Institute for Gravitational Physics, Technical University of Munich, Humboldt-Universität zu Berlin

Topic: Particle physics theoretical and experimental studies

Subfield: Nuclear and High Energy Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

Funders: European Commission, Deutsche Forschungsgemeinschaft

Awards: G1897041155, G4066435496, EXC 2094: ORIGINS: Vom Ursprung des Universums bis zu den ersten Bausteinen des Lebens, G7658987431, G7832817051, GRK 2575: Überdenken der Quantenfeldtheorie

OpenAlex ID: W7128000910

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