Module Intersection for the Integration-by-Parts Reduction of Multi-Loop Feynman Integrals
| Autor: | Yang Zhang, Janko Boehm, Dominik Bendle, Wolfram Decker, Alessandro Georgoudis, Franz-Josef Pfreundt, Mirko Rahn |
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| Přispěvatelé: | Publica, Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Institut de Physique Théorique - UMR CNRS 3681 (IPHT), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Sorbonne Université (SU)-Université Paris Diderot - Paris 7 (UPD7) |
| Rok vydání: | 2020 |
| Předmět: |
High Energy Physics - Theory
loop integral [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th] Feynman graph review mathematical methods FOS: Physical sciences High Energy Physics - Phenomenology High Energy Physics - Phenomenology (hep-ph) computer: algebra High Energy Physics - Theory (hep-th) [PHYS.HPHE]Physics [physics]/High Energy Physics - Phenomenology [hep-ph] interface propagator algebraic geometry |
| Zdroj: | PoS MathemAmplitudes 2019: Intersection Theory and Feynman Integrals MathemAmplitudes 2019: Intersection Theory and Feynman Integrals, Dec 2019, Padova, Italy. pp.004, ⟨10.22323/1.383.0004⟩ MathemAmplitudes 2019: Intersection Theory and Feynman Integrals, Dec 2019, Padova, Italy |
| DOI: | 10.48550/arxiv.2010.06895 |
| Popis: | 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. Comment: 19 pages, 5 figures. To appear in the proceedings of "MathemAmplitudes 2019: Intersection Theory & Feynman Integrals", held in Padova 18-20 December 2019 |
| Databáze: | OpenAIRE |
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