Study of the Perturbative QCD Series Structure to Order α4s

Abstract

We study the polarized Bjorken sum rule at low momentum transfers in the range 0.22 < Q < 1.73 GeV with the four-loop N3LO expression for the coefficient function CBj(ois) in the frame work of the common QCD perturbation theory (PT) and the sin-gularity-free analytic perturbation theory (APT). The analysis of the PT series for CAois) gives a hint to its asymptotic nature man ifesting itself in the region Q < 1 GeV. It relates to the observation that the accuracy of both the three- and four-loop PT predictions happens to be at the same 10% level. On the other hand, the usage of the two-loop APT allows one to describe the precise low energy. JLab data down to Q ~ 300 MeV and gives a possibility for reliable extraction of the higher twist (HT) corrections. At the same time, above Q ~ 700 MeV the APT two-loop order with HT is equivalent to the four-loop PT with HT compatible to zero and is adequate to current accuracy of the data.