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.

No abstract

No abstract

We provide a leading singularity analysis protocol in Baikov representation, for the searching of Feynman integrals with uniform transcendental (UT) weight. This approach is powered by the recent developments in rationalizing square roots and syzygy computations, and is particularly suitable for finding UT integrals with multiple mass scales. We demonstrate the power of our approach by determining the UT basis for a two-loop diagram with three external mass scales.