Four-loop QCD analysis of the Bjorken sum rule

We study the polarized Bjorken sum rule (BSR) at low momentum transfers in the range 0.22 < Q < 1.73 GeV with the four-loop (NLO)-L-3 expression for the coefficient function C-Bj(alpha(s)) in the framework of the common QCD perturbation theory (PT) and the singularity-free analytic perturbation theory (APT). The analysis of the PT series for C-Bj(alpha(s)) gives a hint to its asymptotic nature manifesting 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 similar to 300 MeV and gives a possibility for reliable extraction of the higher twist (HT) corrections. At the same time, above Q similar to 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. (C) 2011 Elsevier B.V. All rights reserved.