Running Coupling and the Lambda-Parameter from SU(3) Lattice Simulations

TL;DR

This paper uses lattice QCD simulations to measure the running coupling and Lambda-parameter in SU(3), providing precise estimates and methods to reduce scaling violations for better continuum extrapolation.

Contribution

It introduces effective coupling schemes to minimize scaling violations and accurately determine the Lambda-parameter from lattice simulations.

Findings

Consistent Lambda_MSbar value of 0.558 with small errors.

Measured alpha(5 GeV) = 0.150(3).

No finite size effects observed in potential values.

Abstract

We present new results on the static qq-potential from high statistics simulations on 32^4 and smaller lattices, using the standard Wilson beta = 6.0, 6.4, and 6.8. Within our statistical errors we do not observe any finite size effects affecting the potential values, on varying the spatial lattice extent from 0.9fm up to 3.3fm. We are able to see and quantify the running of the coupling from the Coulomb behaviour of the interquark force. From this we extract the ratio \sqrt{sigma}/Lambda_L. We demonstrate that scaling violations on the string tension can be considerably reduced by introducing effective coupling schemes, which allow for a safe extrapolation of \Lambda_L to its continuum value. Both methods yield consistent values for Lambda: Lambda_MSbar = 0.558_{-0.007}^{+0.017}\sqrt{sigma} = 246_{-3}^{+7}MeV. At the highest energy scale attainable to us we find alpha(5 GeV) = 0.150(3)