Accurate Scale Determinations for the Wilson Gauge Action

Abstract

Accurate determinations of the physical scale of a lattice action are required to check scaling and take the continuum limit. We present a high statistics study of the static potential for the SU(3) Wilson gauge action on coarse lattices ($5.54\le \beta \le 6.0$). Using an improved analysis procedure we determine the string tension and the Sommer scale $r_0$ (and related quantities) to 1% accuracy, including all systematic errors. Combining our results with earlier ones on finer lattices, we present parameterizations of these quantities that should be accurate to about 1% for $5.6\le \beta \le 6.5$. We estimate the $\text{La}$-parameter of quenched QCD to be ${\text{La}}_{\text{MSb}}=247(16)$ MeV.

Comments: 18 pages, LaTeX, 5 ps files (corrected typo in table 5, updated references)