Calculation of massless Feynman integrals using harmonic sums

2005/05/31 by Stefan Bekavac · 2 citations
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Mathematical functions and polynomials #Particle physics theoretical and experimental studies #hep-ph

paper · pdf · doi:10.1016/j.cpc.2006.02.004

published as Comput.Phys.Commun. 175 (2006) 180-195 · 30 pages, 6 figures; Minor typos corrected, references added. Published in Computer Physics Communications

openalex publication_date 2006/04/18 · arxiv created 2006/07/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A method for the evaluation of the epsilon expansion of multi-loop massless Feynman integrals is introduced. This method is based on the Gegenbauer polynomial technique and the expansion of the Gamma function in terms of harmonic sums. Algorithms for the evaluation of nested and harmonic sums are used to reduce the expressions to get analytical or numerical results for the expansion coefficients. Methods to increase the precision of numerical results are discussed.

Citations

• New features of FORM
• Integration by parts: The algorithm to calculate β-functions in 4 loops
• Analytic two-loop results for self-energy- and vertex-type diagrams with one non-zero mass
• Analysis of PSLQ, an integer relation finding algorithm

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