An automatized algorithm to compute infrared divergent multi-loop integrals

2000/04/30 by T. Binoth, Gudrun Heinrich, G. Heinrich · 12 citations
Engineering · Mathematics · Physics and Astronomy · #Algorithm #Combinatorics #Computer science #Electromagnetic Scattering and Analysis #Infrared #Loop (graph theory) #Mathematics #Optics #Particle Accelerators and Free-Electron Lasers #Particle physics theoretical and experimental studies #Physics #hep-ph

paper · pdf · doi:10.1016/s0550-3213(00)00429-6

published as Nucl.Phys. B585 (2000) 741-759 · 14 pages, 5 eps figures. Replaced by slightly extended, published version, typos corrected

openalex publication_date 2000/10/01 · arxiv created 2001/07/17 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We describe a constructive procedure to separate overlapping infrared divergences in multi-loop integrals. Working with a parametric representation in D=4-2*epsilon dimensions, adequate subtractions lead to a Laurent series in epsilon, where the coefficients of the pole- and finite terms are sums of regular parameter integrals which can be evaluated numerically. We fully automatized this algorithm by implementing it into algebraic manipulation programs and applied it to calculate numerically some nontrivial 2-loop 4-point and 3-loop 3-point Feynman diagrams. Finally, we discuss the applicability of our method to phenomenologically relevant multi--loop calculations such as the NNLO QCD corrections for e⁺e^- --> 3 jets.

Citations

• Integration by parts: The algorithm to calculate β-functions in 4 loops
• On Nielsen's generalized polylogarithms and their numerical calculation
• Differential Equations for Two-Loop Four-Point Functions
• A short note on two-loop box functions
• Calculating three-loop diagrams in heavy quark effective theory with integration-by-parts recurrence relations

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