Multiloop calculations in HQET

2002/11/21 by Andrey Grozin, A. G. Grozin · 3 citations
Mathematics · Physics and Astronomy · #Applied mathematics #Basis (linear algebra) #Combinatorics #Diagram #Geology #Geometry #High-Energy Particle Collisions Research #Inversion (geology) #Loop (graph theory) #Mathematical physics #Mathematics #Particle physics #Particle physics theoretical and experimental studies #Physics #Propagator #Quantum Chromodynamics and Particle Interactions #Quantum chromodynamics #Quark #hep-ph

paper · pdf · doi:10.1016/s0168-9002(03)00519-9

published in Nuclear Instruments and Methods in Physics Research Section A Accelerators Spectrometers Detectors and Associated Equipment 502(2-3), 610-612 (Elsevier BV) · Talk at ACAT'2002 (Moscow)

arxiv created 2002/11/21 · openalex publication_date 2003/04/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Recently, algorithms for calculation of 3-loop propagator diagrams in HQET and on-shell QCD with a heavy quark have been constructed and implemented. These algorithms (based on integration by parts recurrence relations) reduce an arbitrary diagram to a combination of a finite number of basis integrals. Here I discuss various ways to calculate non-trivial bases integrals, either exactly or as expansions in epsilon. Some integrals of these two classes are related to each other by inversion, which provides a useful cross-check.

Citations

• Integration by parts: The algorithm to calculate β-functions in 4 loops
• Heavy quark effective theory beyond perturbation theory: renormalons, the pole mass and the residual mass term
• The three-loop relation between the and the pole quark masses
• Calculating three-loop diagrams in heavy quark effective theory with integration-by-parts recurrence relations