The Running Coupling from SU(3) Gauge Theory

TL;DR

This paper provides high-precision lattice QCD results on the static quark-antiquark potential, demonstrating the running of the coupling and estimating the Lambda parameter with reduced scaling violations.

Contribution

It introduces effective coupling schemes to reduce scaling violations and accurately extract the QCD Lambda parameter from lattice data.

Findings

No finite size effects observed up to 3.3 fm

Scaling violations in the string tension can be reduced with effective couplings

Consistent determination of the Lambda parameter as approximately 246 MeV

Abstract

We present high precision results on the static quark-antiquark-potential on 32^4 and smaller lattices, using the standard Wilson action at BETA = 6.0, 6.2, 6.4, and 6.8 on the Connection Machine CM-2. Within our statistical errors (1%) we did not observe any finite size effects affecting the potential values, on varying the spatial lattice extent from 0.9 fm up to 3.3 fm. We find violations of asymptotic scaling in the bare coupling up to BETA = 6.8. We demonstrate that scaling violations on the string tension can be considerably reduced by introducing effective coupling schemes, which allow for a safer extrapolation of LAMBDA_Lattice to its continuum value. We are also able to see and to quantify the running of the coupling from the interquark force. From this we extract the ratio \sqrt{SIGMA}/LAMBDA_L. Both methods yield consistent values for the LAMBDA-parameter: LAMBDA_MSbar = 0.558(-0.007+0.017)\sqrt{SIGMA} = 246(-3+7) MeV.