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 α_{syn} 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 m_g arises. Fixing the parameter which characterize the infrared enhancement corresponding to the string tension σand normalization, say, at M_τcompletely define the synthetic running coupling. In this case the dynamical gluon mass appears to be fixed and the higher loop stabilization property of m_g is observed. For σ= (0.42 GeV)^2 and α_{syn}(M^2_τ) = 0.33 \pm 0.01 it is obtained that m_g = 530 \pm 80 MeV.