High-precision ϵ-expansions of massive four-loop vacuum bubbles

2002/10/24 by S. Laporta, Stefano Laporta · 83 citations
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Black Holes and Theoretical Physics #Bubble #Combinatorics #Computer science #Elliptic integral #Expression (computer science) #Loop (graph theory) #Mathematical analysis #Mathematical physics #Mathematics #Mechanics #Numerical analysis #Particle physics theoretical and experimental studies #Physics #Transcendental equation #Transcendental number #hep-ph

paper · pdf · doi:10.1016/s0370-2693(02)02910-6

published in Physics Letters B 549(1-2), 115-122 (Elsevier BV) · 7 pages, 2 figures, LaTex, to be published in Physics Letters B

arxiv created 2002/10/24 · openalex publication_date 2002/11/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

In this paper we calculate at high-precision the expansions in e=(4-D)/2 of the master integrals of 4-loop vacuum bubble diagrams with equal masses, using a method based on the solution of systems of difference equations. We also show that the analytical expression of a related on-shell 3-loop self-mass master integral contains new transcendental constants made up of complete elliptic integrals of first and second kind.

Citations

• Integration by parts: The algorithm to calculate β-functions in 4 loops
• Asymptotic expansion of Feynman integrals near threshold

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