Synthetic Running Coupling of QCD

Abstract.Based on a study of the analytic running coupling obtained from the standard perturbation-theory results up to four-loop order, the QCD “synthetic” running coupling αsyn is built. In so doing the perturbative time-like discontinuity is preserved and nonperturbative contributions not only remove the nonphysical singularities of the perturbation theory in the infrared region but also decrease rapidly in the ultraviolet region. In the framework of the approach, on the one hand, the running coupling is enhanced at zero and, on the other hand, the dynamical gluon mass mg arises. Fixing the parameters which characterize the infrared enhancement corresponding to the string tension σ and normalization, say, at Mτ completely define the synthetic running coupling. In this case the dynamical gluon mass appears to be fixed and the higher-loop stabilization property of mg is observed. For σ = (0.42 GeV)2 and αsyn(Mτ2) = 0.33 ± 0.01 it is obtained that mg = 530 ± 80 MeV.