Static quark-antiquark potential: Scaling behavior and finite-size effects in SU(3) lattice gauge theory.

Abstract

We present results on the static $q\overline{q}$ potential from high-statistics simulations on ${16}^{4}$, ${24}^{3}$\ifmmode\times\else\texttimes\fi{}32, and ${32}^{4}$ lattices, using the standard Wilson action at $\ensuremath{\beta}=6.0,6.2, \mathrm{and} 6.4$ on the Connection Machine CM2. To decrease noise and increase accuracy, we applied a suitable local smoothing technique on the spatial parts of Wilson loop operators. As a result, we find a violation of asymptotic scaling of the string tension, as signaled by $\frac{\sqrt{\ensuremath{\sigma}}}{{\ensuremath{\Lambda}}_{L}}=96.7(1.6)(2.6),86.4(1.0)(1.9),82.3(0.8)(1.7)$, for the three $\ensuremath{\beta}$ values, with statistical and systematic errors. We observe a linear confining potential up to distances of 2 fm. A volume of ${(1.5\phantom{\rule{0ex}{0ex}}\mathrm{f}\mathrm{m})}^{3}$ appears to be sufficient to avoid finite-size effects within our statistical accuracy (\ensuremath{\cong} 1%).