0.195(1)$ which is again smaller than the value for the QCD coupling but quite comparable to $\alpha_{\text{str}}$. In earlier studies of the heavy quark potentials in pure gauge theories and full QCD even larger values for the couplings were reported [@Glassner:1996xi; @Allton:1998gi; @Aoki:1998sb; @Bali:2000vr; @AliKhan:2001tx; @Aoki:2002uc]. To avoid here any confusions concerning the value of $\alpha$ we should stress that $\alpha$ should not be mixed with some value for the QCD coupling constant $\alpha_{QCD}$, it simply is a fit parameter indicating the ’average strength’ of the Coulomb part in the Cornell potential. The QCD coupling could be identified properly only in the entire perturbative distance regime and will be a running coupling, [*i.e.*]{} $\alpha_{\text{QCD}}=\alpha_{\text{QCD}}(r)$.

When approaching the short distance perturbative regime the Cornell form will overestimate the value of the coupling due to the perturbative logarithmic weakening of the latter, $\alpha_{\text{QCD}}=\alpha_{\text{QCD}}(r)$. To analyze the short distance properties of the QCD potential and the coupling in more detail, [*i.e.*]{} for $r\;\lsim\;0.4$ fm, and to firmly establish here the onset of its perturbative weakening with decreasing distance, it is customary to do so using non-perturbative definitions of running couplings. Following the discussions on the running of the QCD coupling [@Bali:1992ru; @Peter:1997me; @Schroder:1998vy; 