Three-loop beta function and non-perturbative $α_s$ in asymmetric momentum scheme

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Abstract
We determine the three-loop coefficient of the beta function in the asymmetric momentum subtraction scheme in Landau gauge. This scheme is convenient for lattice studies of \alpha_s, the running coupling constant of QCD. We present high statistics lattice results for \alpha_s in the SU(3) Yang-Mills theory without quark, compare with the three-loop running and extract the value of the corresponding \Lambda_\msbar parameter. We estimate the systematic error coming from four-loop terms. We obtain the result: \Lambda_\msbar = 295 (5) (15) {a^{-1}(\beta=6.0) \over 1.97 GeV} MeV.

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