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

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Christoph Dlapa (Max Planck for Physics)

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 Höschele 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 twoloop five-point integrals. A Mathematica implementation of our algorithm is made available together with this paper.

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