The Jacobi polynomials QCD analysis of the CCFR data for xF$_{3}$ and the Q$^{2}$-dependence of the Gross - Llewellyn Smith sum rule

We present the results of our QCD analysis of the recent CCFR data for the structure function $xF_3 (x,Q^2)$ of the deep-inelastic neutrino--nucleon scattering. The analysis is based on the Jacobi polynomials expansion of the structure functions. The concrete results for the parameter $\Lambda_{\overline {MS}}^{(4)}$ and the shape of quark distributions are determined. At the reference scale $|Q_0 ^2|$=3 $GeV^2$ our results are in satisfactory agreement with the ones obtained by the CCFR group with the help of another method. The $Q_0^{2}$-dependence of the experimental data for the Gross--Llewellyn Smith sum rule is extracted in the wide region of high-momentum transfer. Within systematical experimental uncertainties the results obtained are consistent with the perturbative QCD predictions. We reveal the effect of the discrepancy between our results and the analysed perturbative QCD predictions at the level of the statistical error bars. The importance of taking account, in our procedure, of a still unknown next-next-to-leading approximation of the moments of the structure function $xF_3 (x,Q^2)$ is stressed.