Relation between QCD potentials in momentum and position space

1998/03/13 by M. Jezabek, M. Jeżabek, M. Peter +1 · 4 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/s0370-2693(98)00418-3

published as Phys.Lett. B428 (1998) 352-358 · 10 pages,2 eps-figures included; the complete paper, including figures, is also available at http://ttp.physik.uni-karlsruhe.de/preprints/ttp98-09/

arxiv created 1998/03/13 · openalex publication_date 1998/06/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We derive a formula which relates the QCD potentials in momentum space and in position space in terms of the beta-function of the renormalization-group equation for the potential. This formula is used to study the theoretical uncertainties in the potential and in particular in its application to the determination of the pole mass m_b when we use perturbative expansions. We demonstrate the existence of these uncertainties for the Richardson potential explicitly and then discuss the limited theoretical accuracy in the perturbative QCD potential. We conclude that a theoretical uncertainty of m_b much below 100 MeV would not be achievable within perturbative QCD.

Citations

• Tables of Integrals, Series, and Products
• Review of Particle Physics

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