On convergence of the perturbative series in QCD

Abstract

We study the convergence properties of the polarized Bjorken sum rule amplitude with the four-loop expression for the coefficient function, CBj(αs), in the framework of the common QCD perturbation theory and the singularity-free analytic perturbation theory. By using the model for the multiloop QCD correction, we tested the convergence properties of the coefficient function. Our analysis of the PT series for this function gives a hint to its asymptotic nature manifesting itself in the region Q < 1 GeV. Besides, the related values of the higher twists coefficients turn out to be highly unstable with respect to the PT order. On the contrary, the APT approach allows us to describe accurately the whole bulk of the JLab data down to Q ∼ 300 MeV and gives a possibility for reliable extraction of stable values for the higher twists coefficients providing accuracy of theoretical predictions higher then accuracy of current data.