The $Q^2$ Dependence of the Sum Rules for Structure Functions of Polarized $e(\mu)N$ Scattering

The nonperturbative $Q^2$- dependence of the sum rules for the structure functions of polarized $e(\mu)N$ scattering is discussed. The determination of twist-4 corrections to the structure functions at high $Q^2$ by QCD sum rules is reviewed and critically analyzed. It is found that in the case of the Bjorken sum rule the twist-4 correction is small at $Q^2 > 5 GeV^2$ and does not influence the value of $\alpha_s$ determined from this sum rule. However, the accuracy of the today experimental data is insufficient to reliably determine $\alpha_s$ from the Bjorken sum rule. For the singlet sum rule -- $p+n$ -- the QCD sum rule gives only the order of magnitude of twist-4 correction. At low and intermediate $Q^2$ the model is presented which realizes a smooth connection of the Gerasimov-Drell-Hearn sum rules at $Q^2 = 0$ with the sum rules for $\Gamma_{p,n}(Q^2)$ at high $Q^2$. The model is in a good agreement with the experiment.