Strong Coupling Constant to Four Loops in the Analytic Approach to QCD

Abstract.

 The QCD analytic running coupling α_an which has no nonphysical singularities for all Q ²>0 is considered for the initial perturbation-theory approximations up to four-loop order. The finiteness of the analytic coupling at zero is shown to be a consequence of the asymptotic freedom property of the initial theory. The nonperturbative contributions to the analytic coupling are extracted explicitly. For all Q>Λ they are represented in the form of an expansion in inverse powers of Euclidean momentum squared. The effective method for a precise calculation of the analytic running coupling is developed on the basis of the stated expansion. The energy-scale evolution of the analytic running coupling for the one- to four-loop cases is studied and the higher loop stability and low dependence on the quark-threshold matching conditions in comparison with the perturbative running coupling were found. Normalizing the analytic running coupling at the scale of the rest mass of the Z boson with the world-average value of the strong coupling constant, α_an(M _Z ²)=0.1181±0.002, one obtains as a result of the energy-scale evolution of the analytic running coupling α_an(M_τ ²)=0.2943^+0.0111 _−0.0106 that is notably lower than the estimations of the coupling strength available at the scale of the mass of the τ lepton.