Constraints on "Fixed Point" QCD from the CCFR Data on Deep Inelastic Neutrino-Nucleon Scattering

The results of LO {\it Fixed point} QCD (FP-QCD) analysis of the CCFR data for the nucleon structure function $~xF_3(x,Q^2)~$ are presented. The predictions of FP-QCD, in which $~\alpha_{s}(Q^2)~$ tends to a nonzero coupling constant $\alpha_{0}$ as $~Q^2\to \infty~,$ are in good agreement with the data. If $~\alpha_{0}~$ is a first order zero of the $~\beta~$ function, constraints for the possible values of the $~\beta~$ function parameter $~b~$ regulating how fast $~\alpha_ s(Q^2)~$ tends to its asymptotic value $~\alpha_{0}~$ are found from the data. The corresponding values of $~\alpha_{0}~$ are also determined. Having in mind the recent QCD fits to the same data we conclude that in spite of the high precision and the large $~(x,Q^2)~$ kinematic range of the CCFR data they cannot discriminate between QCD and FP-QCD predictions for $~xF_3(x,Q^2)~$. PACS: 12.38.Qk; 19.90+b; 13.60 Hb