Running coupling constant and correlation length from Wilson loops

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 $\overline{\mathrm{MS}}$ 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.

Comments: 3 pages, compressed uuencoded PostScript, Contribution to Lattice 95