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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 .

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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. Program summary: Program Title: FeynGKZ.wl, version 1.0 CPC Library link to program files: https://doi.org/10.17632/m8zds756vb.1 Developer's repository link: https://github.com/anant-group/FeynGKZ Licensing provisions: GNU General Public License 3 Programming language: Wolfram Mathematica version 13.0 or higher External routines/libraries: Macaulay2 version 1.20, TOPCOM version 0.17.8, polymake version 4.6, AMBRE version 2.1.1 and Olsson.wl Nature of problem: Deriving the GKZ system associated with a given Feynman integral, and solving it in terms of multivariate hypergeometric functions. Solution method: Automating the triangulation and Gröbner deformation methods for obtaining Γ-series solutions to the GKZ hypergeometric system associated with a given Feynman integral. References: [1] Wolfram Mathematica; proprietary software. [2] polymake, open-source software. [3] Macaulay2, open-source software. [4] TOPCOM, open-source software. [5] AMBREv2.1.1.m, open-source Mathematica package. [6] Olsson.wl, open-source Mathematica package. © 2023 Elsevier B.V.

Item Type: Journal Article
Publication: Computer Physics Communications
Publisher: Elsevier B.V.
Additional Information: The copyright for this article belongs to the Authors.
Keywords: Algebra; Iterative methods; Open systems; Triangulation, Analytic continuation; Computer algebra; Feynman integrals; Hypergeometric functions; Mathematica packages; Multiloop; Multiloop feynman integral; Multivariate hypergeometric function; Open-source softwares, Open source software
Department/Centre: Division of Physical & Mathematical Sciences > Centre for High Energy Physics
Date Deposited: 03 Apr 2023 09:34
Last Modified: 03 Apr 2023 09:34
URI: https://eprints.iisc.ac.in/id/eprint/81144

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