Improved analysis of moments of F3 in neutrino-nucleon scattering using   the Bernstein polynomial method
  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. 
Paul M. Brooks and C.J. Maxwell