THE RUNNING COUPLING FROM SU(3) GAUGE-THEORY

We present high precision results on the static qqBAR potential on 32(4) and smaller lattices, using the standard Wilson action at beta = 6.0, 6.2, 6.4, and 6.8 on the Connection Machine CM-2. Within our statistical errors (almost-equal-to 1%) we did not observe any finite size effects affecting the potential values, on varying the spatial lattice extent from 0.9 fm up to 3.3 fm. We find violations of asymptotic scaling in the bare coupling up to beta = 6.8. We demonstrate that scaling violations on the string tension can be considerably reduced by introducing effective coupling schemes, which allow for a safer extrapolation of LAMBDA(L) to its continuum value. We are also able to see and to quantify the running of the coupling from the interquark force. From this we extract the ratio square-root sigma/LAMBDA(L). Both methods yield consistent values for the LAMBDA-parameter: LAMBDA(MSBAR) = 0.558(-0.007)+0.017 x square-root sigma = 246(-3)+7MeV.