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We propose a new renormalization scheme of the running coupling constant ingeneral gauge theories using the Wilson loops. The renormalized couplingconstant is obtained from the Creutz ratio in lattice simulations and thecorresponding perturbative coefficient at the leading order. The latter can becalculated by adopting the zeta-function resummation techniques. We perform abenchmark test of our scheme in quenched QCD with the plaquette gauge action.The running of the coupling constant is determined by applying the step-scalingprocedure. Using several methods to improve the statistical accuracy, we showthat the running coupling constant can be determined in a wide range of energyscales with relatively small number of gauge configurations.

A new scheme for the running coupling constant in gauge theories using Wilson loops