Scaling Study of Pure Gauge Lattice QCD by Monte Carlo Renormalization Group Method

Abstract

The scaling behavior of pure gauge SU(3) in the region $\beta =5.85-7.60$ is examined by a Monte Carlo Renormalization Group analysis. The coupling shifts induced by factor 2 blocking are measured both on 32${}^4$ and 16${}^4$ lattices with high statistics. A systematic deviation from naive 2-loop scaling is clearly seen. The mean field and effective coupling constant schemes explain part, but not all of the deviation. It can be accounted for by a suitable change of coupling constant, including a correction term $\mathcal{O}(g^7)$ in the 2-loop lattice $\beta$-function. Based on this improvement, $\sqrt{\sigma }/{\Lambda }_{\overline{MS}}^{n_f=0}$ is estimated to be $2.2(\pm 0.1)$ from the analysis of the string tension $\sigma$.

Comments: 4 pages of A4 format including 7-postscript figures