Ananthanarayan, B and Banik, S and Bera, S and Datta, S (2024) Automated Evaluation of Feynman Integrals Using GKZ Hypergeometric Systems. In: 25th DAE-BRNS High Energy Physics Symposium, HEPS 2022, 12 December 2022through 16 December 2022, IISER Mohali, pp. 124-127.
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Feynman integrals at any order of perturbation, in the Lee-Pomeransky representation, could be realised as a subset of Euler-Mellin integrals. Such integrals satisfy the Gelfand-Kapranov-Zelevinsky (GKZ) system of partial differential equations. In an ongoing collaboration, we automate the derivation of the associated GKZ system for a given Feynman diagram from either its Lee-Pomeransky representation or its Mellin-Barnes representation. We also present the automation of two mathematically equivalent techniques, namely the Gröbner deformation method and the method of triangulations of point configurations to solve this system. We have implemented these in the Mathematica package FeynGKZ 1, which is the first public proof-of-concept software that evaluates Feynman integrals in the GKZ framework. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024.
| Item Type: | Conference Paper |
|---|---|
| Publication: | Springer Proceedings in Physics |
| Publisher: | Springer Science and Business Media Deutschland GmbH |
| Additional Information: | The copyright for this article belongs to Springer Science and Business Media Deutschland GmbH |
| Keywords: | Automated evaluation; Feynman diagrams; Feynman integrals; Hypergeometric; Mathematica packages; Point configurations; Proof of concept; Systems of partial differential equations |
| Department/Centre: | Division of Physical & Mathematical Sciences > Centre for High Energy Physics |
| Date Deposited: | 06 Sep 2024 11:16 |
| Last Modified: | 06 Sep 2024 11:16 |
| URI: | http://eprints.iisc.ac.in/id/eprint/86038 |
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