Running coupling constant and correlation length from Wilson loops

We consider a definition of the QCD running coupling constant α(μ) related to Wilson loops of size r×t with arbitrary fixed tr. The schemes defined by these couplings are very close to the MS scheme (i.e. the one-loop perturbative correction to the coupling is small) for all values of tr; in the tr → ∞ limit, the “qq 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 α(μ) 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.