  We present the results of the next-to-next-to-leading order QCD analysis of
the recently revised experimental data of the CCFR collaboration for the $xF_3$
structure function using the Jacobi polynomial expansion method. The effects of
the higher twist contributions are included into the fits following the
infrared renormalon motivated model. The special attention is paid to the
checks of the predictive abilities of the infrared renormalon model and to the
independent extraction of the $x$-shape of the twist-4 contributions to the
$xF_3$ structure function in the process of the leading order, next-to-leading
order and next-to-next-to-leading order fits of the revised CCFR data. We
stress that at the next-to-next-to-leading order the results for
$\alpha_s(M_Z)$ turn out to be almost nonsensitive to the higher-twist terms.
We obtain the following result $\alpha_s(M_Z)^{NNLO}=0.117 \pm 0.002(stat) \pm
0.005 (syst)\pm 0.003 (theory)$. The comparison of the outcomes of our
next-to-leading order and next-to-next-to-leading order analysis indicate that
the theoretical QCD uncertainties were underestimated in the process of the
next-to-leading order determination of $\alpha_s(M_Z)$, made recently by the
CCFR collaboration itself.

High Energy Physics - Phenomenology;High Energy Physics - Experiment