Joint Institute for Nuclear Research, Russia

The polarized Bjorken sum rule, defined as the difference between the first moments of the spin-dependent structure functions of the proton and neutron, plays an important role in studies of the nucleon spin structure. As the squared momentum transfer decreases, higher-twist contributions and nonperturbative QCD effects become increasingly important, making the description of the low-$Q^2$ region particularly relevant. To describe the Bjorken sum rule in different $Q^2$ regions, expansions can be constructed in parameters that are small in the corresponding limits: at large $Q^2$, such a parameter is $1/Q^2$, whereas at small $Q^2$ it is $Q^2$ itself. In particular, at large $Q^2$, the higher-twist contribution is represented as a series in inverse powers of $Q^2$. As $Q^2$ decreases, the terms of this series grow, and in the limit $Q^2 \to 0$ the series diverges, requiring a different description of the low-energy region. For the small-$Q^2$ region, a power expansion in the direct parameter is introduced, while the transition between the two regions is implemented using the analytic matching method. The dependence of the matching point $Q_0^2$ on the number of terms in the power series is investigated. This approach makes it possible to describe the Bjorken sum rule over the entire considered range of $Q^2$ within perturbation theory in the inverse parameter at large $Q^2$ and in the direct parameter at small $Q^2$, including the region beyond perturbative QCD.