Algorithmic transformation of multi-loop master integrals to a canonical basis with CANONICA

Abstract The integration of differential equations of Feynman integrals can be greatly facilitated by using a canonical basis . This paper presents the Mathematica package CANONICA , which implements a recently developed algorithm to automatize the transformation to a canonical basis. This represents the first publicly available implementation suitable for differential equations depending on multiple scales. In addition to the presentation of the package, this paper extends the description of some aspects of the algorithm, including a proof of the uniqueness of canonical forms up to constant transformations. Program summary Program Title: CANONICA Program Files doi: http://dx.doi.org/10.17632/fmwnmmhn77.1 Licensing provisions: GNU General Public License version 3 Programming language: Wolfram Mathematica, version 10 or higher Nature of problem: Computation of a rational basis transformation of master integrals leading to a canonical form of the corresponding differential equation. Solution method: The transformation law is expanded in the dimensional regulator. The resulting differential equations for the expansion coefficients of the transformation are solved with a rational ansatz.

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