Running coupling constant and correlation length from Wilson loops

TL;DR

This paper introduces a new way to define the QCD running coupling constant using Wilson loops, connecting it to the quark-antiquark force, and discusses finite-size scaling for high-momentum evaluations.

Contribution

It proposes a Wilson loop-based scheme for the QCD coupling constant that closely matches the MS scheme and introduces a correlation length concept for large-scale computations.

Findings

The scheme approximates the MS scheme across all t/r ratios.

In the t/r→∞ limit, it recovers the quark-antiquark force scheme.

A feasible method for high-momentum coupling evaluation via finite-size scaling.

Abstract

We consider a definition of the QCD running coupling constant $\alpha(\mu)$ related to Wilson loops of size $r{\times}t$ with arbitrary fixed $t/r$. The schemes defined by these couplings are very close to the $\overline{\rm MS}$ scheme (i.e.\ the one-loop perturbative correction to the coupling is small) for all values of $t/r$; in the $t/r\to\infty$ limit, the ``$q\bar q$ force'' scheme is recovered, where the coupling constant is related to the quark-antiquark force. We discuss the possibility of applying finite-size scaling techniques to the Monte Carlo evaluation of $\alpha(\mu)$ up to very large momentum scales. We propose a definition of correlation length, also related to Wilson loops, which should make such a computation feasible.