Recurrence relations for three-loop prototypes of bubble diagrams with a mass

1995/12/29 by L.V. Avdeev, Leo. V. Avdeev · 2 citations
Physics and Astronomy · #High-Energy Particle Collisions Research #Particle physics theoretical and experimental studies #Quantum Chromodynamics and Particle Interactions #hep-ph

paper · pdf · doi:10.1016/0010-4655(96)00090-2

published as Comput.Phys.Commun. 98 (1996) 15-19 · 9 pages in LaTeX

arxiv created 1995/12/29 · openalex publication_date 1996/10/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Recurrence relations derived via the Chetyrkin--Tkachov method of integration by parts are applied to reduce scalar three-loop bubble (vacuum) diagrams with a mass to a limited number of master integrals. The reduction is implemented as a package of computer programs for analytic evaluation in FORM. The algorithms are applicable to diagrams with any integer powers on the lines in an arbitrary dimension. A physical application is the evaluation of the three-loop QCD correction to the electroweak rho parameter.

Citations

• Integration by parts: The algorithm to calculate β-functions in 4 loops

Cited by

• Explicit solutions of the multi-loop integral recurrence relations and its application
• High-precision epsilon expansions of single-mass-scale four-loop vacuum bubbles