Three-loop beta function and non-perturbative ${\alpha }_s$ in asymmetric momentum scheme

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.

Comments: 9 pages, LaTeX with two figures. The final analysis has been revisited to include an estimation of the systematic error coming from higher-order terms