Running coupling constant of background perturbation theory and lattice interquark interaction

The conventional parametrizations of lattice static interquark force are shown to produce a mismatch of coupling constant near the matching point R_m \approx 0.2 fm. The running coupling constant of the background perturbation theory yields instead a selfconsistent description of lattice data over all interval of distances, 0.05 fm \la R \la 1.1.fm, and is an analytic function with the property of asymptotic freedom at small R and it is freezing at large R.