Year: 2020
Type: article
Abstract: 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.
Source: Journal of High Energy Physics
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: diamond
Funders: National Science Foundation, European Commission, Deutsche Forschungsgemeinschaft, Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung, National Natural Science Foundation of China, Knut och Alice Wallenbergs Stiftelse, Mainz Institute for Theoretical Physics, Johannes Gutenberg University Mainz
Awards: G1394709509, G1574205601, G1871477277, Multi-loop Scattering Amplitudes via Algebraic Geometry, G2041291795, G251152387, G332579857, G434337789, G4430097687, Tagungen im Centro Stefano Franscini, Monte Verità, Ascona, 1996 / 1997, G501349349, G5607711389, G5608225264, G7490222812, G7936379390, Kavli Institute for Theoretical Physics, G8539495592, G87478678
OpenAlex ID: W2969015475