Numerical evaluation of the general massive 2-loop sunrise self-mass master integrals from differential equations

2002/03/27 by M. Caffo, H. Czyż, H. Czyz +1 · 41 citations
Mathematics · Physics and Astronomy · #Differential equation #Feynman diagram #Feynman integral #Graph #Numerical analysis #Numerical integration #Numerical methods for differential equations #Particle physics theoretical and experimental studies #Quantum chaos and dynamical systems #Sunrise #hep-ph

paper · pdf · doi:10.1016/s0550-3213(02)00315-2

published in Nuclear Physics B 634(1-2), 309-325 (Elsevier BV) · 1+21 pages, Latex, 5 ps-figures

arxiv created 2002/03/27 · openalex publication_date 2002/07/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

The system of 4 differential equations in the external invariant satisfied by the 4 master integrals of the general massive 2-loop sunrise self-mass diagram is solved by the Runge-Kutta method in the complex plane. The method, whose features are discussed in details, offers a reliable and robust approach to the direct and precise numerical evaluation of Feynman graph integrals.

Citations

• Integration by parts: The algorithm to calculate β-functions in 4 loops
• The pseudothreshold expansion of the 2-loop sunrise selfmass master amplitudes

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• BOKASUN: A fast and precise numerical program to calculate the Master Integrals of the two-loop sunrise diagrams
• Numerical evaluation of the general massive 2-loop 4-denominator self-mass master integral from differential equations
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