Updated QCD Analysis of the Bjorken Sum Rule Based on the Analytic Perturbation Theory

We present an updated analysis of the Bjorken sum rule for the difference between the first moments of the spin-dependent structure function $${{g}_{1}}$$ of the proton and neutron in the low-momentum-transfer region, $${{Q}^{2}} < 1$$ GeV2. Our theoretical description is based on singularity-free analytic perturbation theory and an original method for matching the large- and low- $${{Q}^{2}}$$ regions. After fixing the QCD parameters at large $${{Q}^{2}}$$ , we extend the description to the lowregion by using the Gerasimov–Drell–Hearn sum rule as a boundary condition. In this way, we avoid the divergence problem of the higher-twist representation written as an expansion in inverse powers of $$1{\\kern 1pt} /{\\kern 1pt} {{Q}^{2}}$$ as $${{Q}^{2}} \\to 0$$ . We investigate the stability of our theoretical predictions and their agreement with new Jefferson Lab experimental data on the nucleon spin structure at values of $${{Q}^{2}}$$ very close to zero.