Abstract
We present high precision results on the static q q potential on 32 4 and smaller lattices, using the standard Wilson action at β = 6.0, 6.2, 6.4, and 6.8 on the Connection Machine CM-2. Within our statistical errors (≈ 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 β = 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 Λ 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 √σ Λ L . Both methods yield consistent values for the Λ-parameter: Λ MS =0.558 +0.017 −0.007 × σ =246 +7 −3MeV .
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