parameterized within the string model already for $r\;\gsim\;0.4$ fm [@Necco:2001xg; @Luscher:2002qv]. In fact, we also do not see any signal for string breaking in the zero temperature QCD heavy quark potential. This is expected due to the fact that the Wilson loop operator used here for the calculation of the $T=0$ potential has only small overlap with states where string breaking occurs [@Bernard:2001tz; @Pennanen:2000yk]. Moreover, the distances for which we analyze the data for the QCD potential are below $r\;\lsim\;1.2$ fm at which string breaking is expected to set in at zero temperature and similar quark masses [@Pennanen:2000yk].

The coupling at $T=0$ {#couplt=0}
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Deviations from the string model and from the pure gauge potential, however, are clearly expected to become apparent in the 2-flavor QCD potential at small distances and may already be seen from the short distance part in Fig. \[peik\]. These deviations are expected to arise from an asymptotic weakening of the QCD coupling, [*i.e.*]{} $\alpha=\alpha(r)$, and to some extent also due to the effect of including dynamical quarks, [*i.e.*]{} from leading order perturbation theory one expects $$\begin{aligned}
\alpha(r) \simeq \frac{1}{8\pi} \frac{1}{\beta_0 \log \left(1/(r \Lambda_{\text{ QCD}})\right)}\;,
\label{runningcoupling}\end{aligned}$$ with $$\begin{aligned}
\beta_0 = \frac{33-2N_f}{48 \pi^2}\;,\end{aligned}$$ where $N_f$ is the 