Static quark-antiquark potential with renormalization-group-improved lattice action

The expectation values of Wilson loops are calculated with a renormalization-group (RG)-improved lattice action on a ${12}^4$ lattice for 2.1≤β≤2.7 with steps Δβ=0.1. Then the quark-antiquark static potential is calculated by a fitting procedure directly to the logarithms of the expectation values of Wilson loops rather than Creutz ratios. The inverse of the lattice spacing a at β=2.4 turns out to be $a^{\mathrm{-}1}$=1470(30) MeV by inputting the string tension σ=(420 MeV${)}^2$. This value is in remarkable agreement with the value $a^{\mathrm{-}1}$=1460(60) MeV which has been obtained from the meson spectrum calculated on an $8^3$×16 lattice at β=2.4 with the same RG-improved lattice action. The scaling behavior of the string tension and the problem of universality are also investigated.