Fixation of theoretical ambiguities in the improved fits to $xF_3$ CCFR data at the next-to-next-to-leading order and beyond

Abstract

Using the results for the NNLO QCD corrections to anomalous dimensions of odd $xF_3$ Mellin moments and N$^3$LO corrections to their coefficient functions we improve our previous analysis of the CCFR'97 data for $xF_3$. The possibility of extracting from the fits of $1/Q^2$-corrections is analysed using three independent models,including infrared renormalon one. Theoretical quetion of applicability of the renormalon-type inspired large-$\beta_0$ approximation for estimating corrections to the coefficient functions of odd $xF_3$ and even non-singlet $F_2$ moments are considered. The comparison with [1/1] Pad\'e estimates is given. The obtained NLO and NNLO values of $\alpha_s(M_Z)$ are supporting the results of our less definite previous analysis and are in agreement with the world average value $\alpha_s(M_Z)\approx 0.118$. We also present first N$^3$LO extraction of $\alpha_s(M_Z)$. The interplay between higher-order perturbative QCD corrections and $1/Q^2$-terms is demonstrated. The results of our studies are compared with those obtained recently using the NNLO model of the kernel of DGLAP equation and with the results of the NNLO fits to CCFR'97 $xF_3$ data, performed by the Bernstein polynomial technique.