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Deriving canonical differential equations for Feynman integrals from a single uniform weight integral

MPS-Authors

Dlapa,  Christoph
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Henn,  Johannes
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Yan,  Kai
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

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Citation

Dlapa, C., Henn, J., & Yan, K. (2020). Deriving canonical differential equations for Feynman integrals from a single uniform weight integral. Journal of High Energy Physics, 05, 25. Retrieved from https://publications.mppmu.mpg.de/?action=search&mpi=MPP-2020-10.


Cite as: http://hdl.handle.net/21.11116/0000-0008-1C6F-E
Abstract
Differential equations are a powerful tool for evaluating Feynman integrals. Their solution is straightforward if a transformation to a canonical form is found. In this paper, we present an algorithm for finding such a transformation. This novel technique is based on a method due to Hoschele et al. and relies only on the knowledge of a single integral of uniform transcendental weight. As a corollary, the algorithm can also be used to test the uniform transcendentality of a given integral. We discuss the application to several cutting-edge examples, including non-planar four-loop HQET and non-planar two-loop five-point integrals. A Mathematica implementation of our algorithm is made available together with this paper.