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

TL;DR

This study investigates the scaling behavior of pure gauge SU(3) lattice QCD using Monte Carlo Renormalization Group methods, revealing deviations from naive scaling and proposing a refined coupling scheme to improve theoretical predictions.

Contribution

It provides a detailed analysis of scaling deviations in SU(3) lattice QCD and introduces a modified coupling scheme to better match observed data.

Findings

Deviation from naive 2-loop scaling observed

Modified coupling scheme improves agreement

Estimate of .2 for /_{\,}^n_f=0

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 ${\cal O}(g^7)$ 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 $\sigma$.