Transforming differential equations of multi-loop Feynman integrals into canonical form

• Main Author: Christoph Meyer
• Format: Article
• Language: English
• Published: SpringerOpen 2017-04-01
• Series: Journal of High Energy Physics
• Subjects: QCD Phenomenology
• Online Access: http://link.springer.com/article/10.1007/JHEP04(2017)006

Abstract The method of differential equations has been proven to be a powerful tool for the computation of multi-loop Feynman integrals appearing in quantum field theory. It has been observed that in many instances a canonical basis can be chosen, which drastically simplifies the solution of the differential equation. In this paper, an algorithm is presented that computes the transformation to a canonical basis, starting from some basis that is, for instance, obtained by the usual integration-by-parts reduction techniques. The algorithm requires the existence of a rational transformation to a canonical basis, but is otherwise completely agnostic about the differential equation. In particular, it is applicable to problems involving multiple scales and allows for a rational dependence on the dimensional regulator. It is demonstrated that the algorithm is suitable for current multi-loop calculations by presenting its successful application to a number of non-trivial examples.