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We consider computational problems in the framework of non­ power Analityc Perturbation Theory and Fractional Analytic Per­turbation Theory that are the generalization of the standard QCD perturbation theory. The singularity-free, finite couplings Av(Q2), v ( s) appear in these approaches as analytic images of the standard QCD coupling powers avs(Q2) in the Euclidean and Minkowski do­mains, respectively. We provide a package "FAPT" based on the system Mathematica for QCD calculations of the images Av(Q2), v(s) u p t o N3LO of renormalization group evolution. Application of these approaches to Bjorken sum rule analysis and Q2 -evolution of higher twist µ p-n is considered.

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.

We present progress in the QCD analysis of the Bjorken sum rule at low momentum transfers. We study asymptotic structure of the perturbative QCD expansion at low Q2 scales based on analysis of recent accurate data on the Bjorken sum rule and available now four-loop expression for the coefficient-function CBj(Q2). We demonstrate that the standard perturbative series for CBj(Q2) gives a hint to its asymptotic nature manifesting itself in the region Q2. 1 GeV2. It is confirmed by the considered integral model for the perturbative QCD correction. We extract a value of higher-twist µ4coefficient and study the interplay between higher orders and higher-twist contributions. Results of other approaches to the description of Bjorken sum rule data are discussed.