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FeynGKZ: A Mathematica package for solving Feynman integrals using GKZ hypergeometric systems

Ananthanarayan, B and Banik, S and Bera, S and Datta, S (2023) FeynGKZ: A Mathematica package for solving Feynman integrals using GKZ hypergeometric systems. In: Computer Physics Communications, 287 . ISSN 00104655

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Official URL: https://doi.org/10.1016/j.cpc.2023.108699


In the Lee-Pomeransky representation, Feynman integrals can be identified as a subset of Euler-Mellin integrals, which are known to satisfy Gel'fand-Kapranov-Zelevinsky (GKZ) system of partial differential equations. Here we present an automated package to derive the associated GKZ system for a given Feynman diagram and solve it in terms of hypergeometric functions using two equivalent algorithms, namely the triangulation method and the Gröbner deformation method. We present our code in the form of a Mathematica package FeynGKZ.wl which requires the softwares polymake, Macaulay2 and TOPCOM, and the packages AMBRE and Olsson.wl as dependencies. As applications of the package, we find series solutions to the GKZ systems of several one-loop and two-loop Feynman integrals. These are included in the file Examples.nb that can be downloaded along with the package from GitHub.

Item Type: Journal Article
Publication: Computer Physics Communications
Publisher: ELSEVIER
Additional Information: The copyright of this article belongs to the Authors.
Keywords: Feynman integrals, Multiloop Feynman integrals, Computer algebra, Multivariate hypergeometric functions, Analytic continuation
Department/Centre: Division of Physical & Mathematical Sciences > Centre for High Energy Physics
Date Deposited: 29 Mar 2023 11:06
Last Modified: 29 Mar 2023 11:06
URI: https://eprints.iisc.ac.in/id/eprint/81043

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