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The Running Coupling from SU(3) Lattice Gauge Theory

The UKQCD Collaboration, S. P. Booth, D. S. Henty, A. Hulsebos, A. C. Irving, C. Michael, P. W. Stephenson

TL;DR

The paper addresses how to extract the QCD scale ΛMSbar from SU(3) lattice gauge theory by defining a nonperturbative running coupling from the static interquark potential. It computes V(R) on large-volume lattices, corrects for lattice artefacts, and derives α(R) from the force, comparing to two-loop perturbation to locate ΛMSbar. The results show perturbative running at small R and yield ΛMSbar ≈ 256(20) MeV with √K/ΛMSbar ≈ 1.72(13) for pure SU(3), demonstrating a β-independent method for scale setting beyond the bare coupling. This approach provides a robust framework for determining the coupling in lattice QCD and can be extended toward full QCD with dynamical quarks.

Abstract

{}From an accurate determination of the inter-quark potential, one can study the running coupling constant for a range of $R$-values and hence estimate the scale $Λ_{\msbar} $. Detailed results are presented for $SU(3)$ pure gauge theory.

The Running Coupling from SU(3) Lattice Gauge Theory

TL;DR

The paper addresses how to extract the QCD scale ΛMSbar from SU(3) lattice gauge theory by defining a nonperturbative running coupling from the static interquark potential. It computes V(R) on large-volume lattices, corrects for lattice artefacts, and derives α(R) from the force, comparing to two-loop perturbation to locate ΛMSbar. The results show perturbative running at small R and yield ΛMSbar ≈ 256(20) MeV with √K/ΛMSbar ≈ 1.72(13) for pure SU(3), demonstrating a β-independent method for scale setting beyond the bare coupling. This approach provides a robust framework for determining the coupling in lattice QCD and can be extended toward full QCD with dynamical quarks.

Abstract

{}From an accurate determination of the inter-quark potential, one can study the running coupling constant for a range of -values and hence estimate the scale . Detailed results are presented for pure gauge theory.

Paper Structure

This paper contains 4 sections, 8 equations, 1 figure, 4 tables.

Table of Contents

  1. Introduction
  2. Lattice potentials
  3. Running Coupling
  4. Conclusions

Figures (1)

  • Figure 1: The effective running coupling constant $\alpha(R)$ obtained from the force between static quarks at separation $R$. The scale is set by the string tension $K$. Data at $\beta=6.5$ are from table \ref{['alphat']} (diamonds) and at $\beta=6.2$ (triangles). The dotted error bars represent an estimate of the systematic error due to lattice artefact correction as described in the text. The curves are the two-loop perturbative expression with $a(6.5)\Lambda_R=0.060$ (dotted) and 0.070 (continuous).