Automatic reduction of four-loop bubbles

2002/11/19 by York Schröder, Y. Schroder · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Combinatorics #Computational Physics and Python Applications #Computer science #Energy (signal processing) #Geometry #Loop (graph theory) #Mathematics #Particle physics #Particle physics theoretical and experimental studies #Physics #Quantum Chromodynamics and Particle Interactions #Quantum chromodynamics #Quantum mechanics #Reduction (mathematics) #Theoretical physics #Type (biology) #hep-ph

paper · pdf · doi:10.1016/s0920-5632(03)80208-6

published as Nucl.Phys.Proc.Suppl. 116 (2003) 402-406 · 5 pages. Talk presented at RADCOR/Loops and Legs 2002, Kloster Banz, Germany

arxiv created 2002/11/19 · openalex publication_date 2003/03/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We give technical details about the computational strategy employed in a recently completed investigation of the four-loop QCD free energy. In particular, the reduction step from generic vacuum bubbles to master integrals is described from a practical viewpoint, for fully massive as well as QED-type integrals.

Citations

• New features of FORM
• High-precision ϵ-expansions of massive four-loop vacuum bubbles
• Integration by parts: The algorithm to calculate β-functions in 4 loops
• Recurrence relations for three-loop prototypes of bubble diagrams with a mass
• Connection between Feynman integrals having different values of the space-time dimension

Cited by

• Pressure of hot QCD up tog6ln(1/g)
• Hypergeometric representation of a four-loop vacuum bubble