Abstract
We consider a definition of the QCD running coupling constant α(μ) related to Wilson loops of size r× t with arbitrary fixed t r . 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 t r ; in the t r → ∞ limit, the “ q 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 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.
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