Module Intersection for the Integration-by-Parts Reduction of Multi-Loop Feynman Integrals
Year: 2020
Type: other
Abstract: In this manuscript, which is to appear in the proceedings of the conference "MathemAmplitude 2019" in Padova, Italy, we provide an overview of the module intersection method for the the integration-by-parts (IBP) reduction of multi-loop Feynman integrals. The module intersection method, based on computational algebraic geometry, is a highly efficient way of getting IBP relations without double propagator or with a bound on the highest propagator degree. In this manner, trimmed IBP systems which are much shorter than the traditional ones can be obtained. We apply the modern, Petri net based, workflow management system GPI-Space in combination with the computer algebra system Singular to solve the trimmed IBP system via interpolation and efficient parallelization. We show, in particular, how to use the new plugin feature of GPI-Space to manage a global state of the computation and to efficiently handle mutable data. Moreover, a Mathematica interface to generate IBPs with restricted propagator degree, which is based on module intersection, is presented in this review.
Institutions: University of Kaiserslautern, University of Science and Technology of China, Centre National de la Recherche Scientifique, Université Paris Sciences et Lettres, École Normale Supérieure - PSL, Sorbonne Université, Sorbonne Paris Cité, Institut de Physique Théorique, Université Paris Diderot
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4298857728