We discuss the interplay between higher orders of the perturbative QCD expansion and higher-twist contributions in the analysis of recent Jefferson Lab data on the lowest moments of spin-dependent proton and neutron structure functions À p;n 1 ðQ 2 Þ and Bjorken sum rule function À pÀn 1 ðQ 2 Þ at 0:05 < Q 2 < 3 GeV 2 . We demonstrate that the values of the higher-twist coefficients p;n 2k extracted from the mentioned data by using the singularity-free analytic perturbation theory provide a better convergence of the highertwist series than with the standard perturbative QCD. From the high-precision proton data, we extract the value of the singlet axial charge a 0 ð1 GeV 2 Þ ¼ 0:33 AE 0:05. We observe a slow Q 2 dependence of fitted values of the twist coefficient 4 and a 0 when going to lower energy scales, which can be explained by the well-known renormalization group evolution of 4 ðQ 2 Þ and a 0 ðQ 2 Þ. As the main result, a good quantitative description of all the Jefferson Lab data sets down to Q ' 350 MeV is achieved.

We provide here all the procedures in Mathematica which are needed for the computation of the analytic images of the strong coupling constant powers in Minkowski (Ā ν (s; n f ) and A glob ν (s)) and Euclidean (Ā ν (Q 2 ; n f ) and A glob ν (Q 2 )) domains at arbitrary energy scales (s and Q 2 , correspondingly) for both schemes -with fixed number of active flavours n f = 3, 4, 5, 6 and the global one with taking into account all heavy-quark thresholds. These singularity-free couplings are inevitable elements of Analytic Perturbation Theory (APT) in QCD [1-3], and its generalization -Fractional APT [4][5][6], needed to apply the APT imperative for renormalization-group improved hadronic observables.Computer for which the program is designed and others on which it is operable: Any work-station or PC where Mathematica is running.Operating system or monitor under which the program has been tested: Windows XP, Mathematica (versions 5 and 7).No. of bytes in distributed program including test data etc.: 47 kB (main module FAPT.m) and 4 kB (interpolation module FAPT Interp.m); 21 kB (notebook FAPT Interp.nb showing how to use the interpolation module); 10 888 kB (interpolation data files: AcalGlob i.dat and UcalGlob i.dat with = 1, 2, 3, 3P, and 4) 1 Distribution format: ASCIINature of physical problem: The values of analytic imagesĀ ν (Q 2 ) andĀ ν (s) of the QCD running coupling powers α ν s (Q 2 ) in Euclidean and Minkowski regions, correspondingly, are determined through the spectral representation in the QCD Analytic Perturbation Theory (APT). In the program FAPT we collect all relevant formulas and various procedures which allow for a convenient evaluation ofĀ ν (Q 2 ) andĀ ν (s) using numerical integrations of the relevant spectral densities. Method of solution:FAPT uses Mathematica functions to calculate different spectral densities and then performs numerical integration of these spectral integrals to obtain analytic images of different objects.Restrictions on the complexity of the problem: It could be that for an unphysical choice of the input parameters the results are out of any meaning.Typical running time: For all operations the running time does not exceed a few seconds. Usually numerical integration is not fast, so that we advice to use arrays of precalculated data and apply then the routine Interpolate (as shown in supplied example of the program usage, namely in the notebook FAPT Interp.nb).

We study the polarized Bjorken sum rule at low momentum transfers in the range 0.22 < Q < 1.73 GeV with the four-loop N 3 LO expression for the coefficient function C Bj (α 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 (α 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 ∼ 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.

No abstract

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 Q 2 scales based on analysis of recent accurate data on the Bjorken sum rule and available now four-loop expression for the coefficient-function CBj (Q 2 ). We demonstrate that the standard perturbative series for CBj (Q 2 ) gives a hint to its asymptotic nature manifesting itself in the region Q 2 1 GeV 2 . It is confirmed by the considered integral model for the perturbative QCD correction. We extract a value of highertwist µ4 coefficient 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.