Numerical evaluation of the general massive 2-loop 4-denominator self-mass master integral from differential equations

2003/12/15 by M. Caffo, H. Czyż, H. Czyz +3 · 16 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Diagram #Differential (mechanical device) #Differential equation #First-order partial differential equation #Integral equation #Integro-differential equation #Invariant (physics) #Loop (graph theory) #Mathematical analysis #Mathematical physics #Mathematics #Numerical analysis #Particle physics theoretical and experimental studies #Physics #Quantum Chromodynamics and Particle Interactions #hep-ph

paper · pdf · doi:10.1016/j.nuclphysb.2004.01.019

published in Nuclear Physics B 681(1-2), 230-246 (Elsevier BV) · Latex, 20 pages, 7 figures

arxiv created 2003/12/15 · openalex publication_date 2004/02/02 · arxiv updated 2010/04/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

The differential equation in the external invariant p² satisfied by the master integral of the general massive 2-loop 4-denominator self-mass diagram is exploited and the expansion of the master integral at p²=0 is obtained analytically. The system composed by this differential equation with those of the master integrals related to the general massive 2-loop sunrise diagram is numerically solved by the Runge-Kutta method in the complex p² plane. A numerical method to obtain results for values of p² at and close to thresholds and pseudo-thresholds is discussed in details.

Citations

• Algebraic-numerical evaluation of Feynman diagrams: two-loop self-energies
• Integration by parts: The algorithm to calculate β-functions in 4 loops
• Numerical evaluation of the general massive 2-loop sunrise self-mass master integrals from differential equations
• Two-point functions at two loops in three flavour chiral perturbation theory
• Calculation of master integrals by difference equations
• The pseudothreshold expansion of the 2-loop sunrise selfmass master amplitudes

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