TY - JOUR

T1 - Relation between QCD potentials in momentum and position space

AU - Jezabek, M.

AU - Peter, M.

AU - Sumino, Y.

N1 - Funding Information:
This work is partly supported by KBN grant 2P03B08414, by BMBF grant POL-239-96 and by the Alexander von Humboldt Foundation.

PY - 1998/6/4

Y1 - 1998/6/4

N2 - We derive a formula which relates the QCD potentials in momentum space and in position space in terms of the β 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 mb 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 mb much below 100 MeV would not be achievable within perturbative QCD.

AB - We derive a formula which relates the QCD potentials in momentum space and in position space in terms of the β 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 mb 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 mb much below 100 MeV would not be achievable within perturbative QCD.

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U2 - 10.1016/S0370-2693(98)00418-3

DO - 10.1016/S0370-2693(98)00418-3

M3 - Article

AN - SCOPUS:0348116161

VL - 428

SP - 352

EP - 358

JO - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

JF - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

SN - 0370-2693

IS - 3-4

ER -