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We use recently calculated next-to-next-to-leading order (NNLO) anaomalous dimension coefficients for the moments of the xF_3 structure function in neutrino- nucleon scattering, together with the corresponding three-loop Wilson coefficients, to obtain improved QCD predictions for both odd and even moments. To investigate the issue of renormalization scheme dependence the Complete Renormalization Group Improvement (CORGI) approach is used, in which all dependence on renormalization or factorization scales is avoided by a complete resummation of RG-predictable scale logarithms. We also consider predictions using the method of effective charges and compare with the standard ``physical scale'' choice. The Bernstein polynomial method is used to construct experimental moments from the xF_3 data of the CCFR collaboration insensitive to the data in the region of x which is inaccessible experimentally. Direct fits for \Lambda^(5)MSbar (\alpha_s(M_Z)) are performed. The CORGI fits including target mass corrections give a value \alpha_s(M_Z)=0.119+/-0.002, nicely consistent with the world average. The effective charge and physical scale fits give slightly smaller values which are still consistent within the errors., Comment: 33 pages, 8 figures, typos corrected, discussion of effects of correlations on \chi^2 analysis

For the GLS and Bjorken DIS sum rules we compare fixed-order NNLO perturbative QCD estimates, and all-orders resummed estimates, with the available data, in order to assess the reliability of fixed-order perturbation theory at rather small Q^2 values. Fits are also performed for non-perturbative power corrections using a recently proposed model., Comment: 16 pages, 6 figures

We consider the leading one-chain term in a skeleton expansion for QCD observables and show that for energies Q^2>\Lambda^2, where Q^2=\Lambda^2 is the Landau pole in the coupling, the skeleton expansion result is equivalent to the standard Borel integral representation, with ambiguities related to infrared (IR) renormalons. For Q^2<\Lambda^2 the skeleton expansion result is equivalent to a previously proposed modified Borel representation where the ambiguities are connected with ultraviolet (UV) renormalons. We investigate the Q^2-dependence of the perturbative corrections to the Adler D function, the GLS sum rule, and the polarized and unpolarized Bjorken sum rules. In all these cases the one-chain result changes sign in the vicinity of Q^2=\Lambda^2, and then exhibits freezing behaviour, vanishing at Q^2=0. Finiteness at Q^2=\Lambda^2 implies specific relations between the residues of IR and UV renormalons in the Borel plane. These relations, only one of which has previously been noted (though it remained unexplained) are shown to follow from the continuity of the characteristic function in the skeleton expansion. By considering the compensation of non-perturbative and perturbative ambiguities we are led to a result for the Q^2 dependence of these observables at all Q^2, in which there is a single undetermined non-perturbative parameter, and which involves the skeleton expansion characteristic function. The observables freeze to zero in the infrared. We briefly consider the freezing behaviour of the Minkowskian R_{e+e-} ratio., Comment: 26 pages, 6 figures, correction of typos, additional references, amended discussion of Minkowskian freezing