Integration-by-parts reductions of Feynman integrals using Singular and GPI-Space
Dominik Bendle (Department of Mathematics, Technische Universität Kaiserslautern, Kaiserslautern, 67663, Germany, Fraunhofer Institute for Industrial Mathematics ITWM, Fraunhofer-Platz 1, Kaiserslautern, 67663, Germany); Janko Böhm (Department of Mathematics, Technische Universität Kaiserslautern, Kaiserslautern, 67663, Germany); Wolfram Decker (Department of Mathematics, Technische Universität Kaiserslautern, Kaiserslautern, 67663, Germany); Alessandro Georgoudis (Department of Physics and Astronomy, Uppsala University, Uppsala, SE-75108, Sweden); Franz-Josef Pfreundt (Fraunhofer Institute for Industrial Mathematics ITWM, Fraunhofer-Platz 1, Kaiserslautern, 67663, Germany); et al - Show all 8 authors
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 Singular with the workflow management system GPI-Space, 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-Space. 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-Space to convert the basis of IBP reductions, and discuss the possible simplification of master-integral coefficients in a uni- formly transcendental basis.
