Integration-by-parts reductions of Feynman integrals using Singular and GPI-Space

• Published in: The journal of high energy physics 2020-02, Vol.2020 (2), p.1-34, Article 79
• Main Authors: Bendle, Dominik, Böhm, Janko, Decker, Wolfram, Georgoudis, Alessandro, Pfreundt, Franz-Josef, Rahn, Mirko, Wasser, Pascal, Zhang, Yang
• Format: Article
• Language: English
• Subjects: Classical and Quantum Gravitation; Computer algebra; Differential and Algebraic Geometry; Elementary Particles; High energy physics; Integrals; Interpolation; Linear algebra; Multiscale analysis; Parallel processing; Petri nets; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; Scattering Amplitudes; Software; String Theory; Workflow management systems
• ISSN: 1029-8479; 1126-6708; 1029-8479
• DOI: 10.1007/JHEP02(2020)079

A bstract We introduce an algebro-geometrically motived integration-by-parts (IBP) re- duction method for multi-loop and multi-scale Feynman integrals, using a framework for massively parallel computations in computer algebra. This framework combines the com- puter algebra system S ingular with the workflow management system GPI-S pace , which are being developed at the TU Kaiserslautern and the Fraunhofer Institute for Industrial Mathematics (ITWM), respectively. In our approach, the IBP relations are first trimmed by modern tools from computational algebraic geometry and then solved by sparse linear algebra and our new interpolation method. Modelled in terms of Petri nets, these steps are efficiently automatized and automatically parallelized by GPI-S pace . We demonstrate the potential of our method at the nontrivial example of reducing two-loop five-point non- planar double-pentagon integrals. We also use GPI-S pace to convert the basis of IBP reductions, and discuss the possible simplification of master-integral coefficients in a uni- formly transcendental basis.