High-precision epsilon expansions of single-mass-scale four-loop vacuum bubbles

2005/03/21 by York Schröder, Y. Schroder, Aleksi Vuorinen +1 · 1 citation
Physics and Astronomy · #Black Holes and Theoretical Physics #Particle physics theoretical and experimental studies #Quantum Chromodynamics and Particle Interactions #hep-ph

paper · pdf · doi:10.1088/1126-6708/2005/06/051

published as JHEP0506:051,2005 · 25 pages, uses axodraw.sty

arxiv created 2005/03/21 · openalex publication_date 2005/06/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article we present a high-precision evaluation of the expansions in \e=(4-d)/2 of (up to) four-loop scalar vacuum master integrals, using the method of difference equations developed by S. Laporta. We cover the complete set of `QED-type' master integrals, i.e. those with a single mass scale only (i.e. m<sub>i</sub>∈\0,m\) and an even number of massive lines at each vertex. Furthermore, we collect all that is known analytically about four-loop `QED-type' masters, as well as about \em all single-mass-scale vacuum integrals at one-, two- and three-loop order.

Citations

• New features of FORM
• High-precision evaluation of four-loop vacuum bubbles in three dimensions
• Integration by parts: The algorithm to calculate β-functions in 4 loops
• Recurrence relations for three-loop prototypes of bubble diagrams with a mass
• Analysis of PSLQ, an integer relation finding algorithm
• On the enumeration of irreducible k-fold Euler sums and their roles in knot theory and field theory

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• Four-loop singlet contribution to the electroweak ρ parameter