On the relation between QCD potentials in momentum and position space

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.