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) anomalous dimension coefficients for the moments of the xF3 structure function in νN scattering, together with the corresponding three-loop Wilson coefficients, to obtain improved QCD predictions for both odd and even moments of F3. To investigate the issue of renormalization scheme dependence, the Complete Renormalization Group Improvement (CORGI) approach is used, in which all dependence on renormalization and 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 xF3 data of the CCFR Collaboration) that are insensitive to the value of xF3 in the region of x which is inaccessible experimentally. Direct fits for ΛMS-bar(5) (αs(MZ)) are then performed. The CORGI fits including target mass corrections give a value αs(MZ)=0.1189-0.0019+0.0019, consistent with the world average. The effective charge and physical scale fits give slightly smaller values, which are still consistent within the errors