Running coupling constant and correlation length from Wilson loops

TL;DR

This paper introduces a new way to define the QCD running coupling constant and correlation length using Wilson loops, enabling precise calculations at high momentum scales with finite-size scaling techniques.

Contribution

It proposes novel definitions of the QCD running coupling and correlation length based on Wilson loops, closely related to the $ar{ ext{MS}}$ scheme and suitable for Monte Carlo evaluations.

Findings

Defined a Wilson loop-based running coupling close to $ar{ ext{MS}}$ scheme

Introduced a correlation length definition applicable to large momentum scales

Demonstrated finite-size scaling techniques for Monte Carlo evaluations

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 for all values of $t/r$; in the $t/r\to\infty$ limit, the ``$q\bar q$ force'' scheme is recovered. We propose a definition of correlation length, also related to Wilson loops, which can be applied to the Monte Carlo evaluation of $\alpha(\mu)$ up to very large momentum scales by use of finite-size scaling techniques.