Improved calculation of F2 in electroproduction and x F3 in neutrino scattering to NNLO and determination of αS

We improve the existing calculations of deep inelastic scattering to next-to-next-to-leading order in the following manner. First, we use the recently calculated values of the anomalous dimensions for moments with index n = 10, 12 in ep scattering. Second, we use also recently calculated anomalous dimensions for n = 1, 3,..., 13 for xF(3) in nuN scattering, to extend the calculation to this process. Lastly, we use the determinantal constraints on the moments that follow from positivity of the structure functions to stabilize the fits. We find substantial improvement over previous results, getting the following numbers: Lambda (n(f) = 4, 3 loop) = 274 +/- 20 MeV. alpha (3loop)(S)(M-Z(2)) = 0.1166 +/- 0.0013, x(2)/d.o.f. = 92/(153 - 18) from ep and, from nuN, Lambda (n(f) = 4, 3 loop) = 255 +/- 72 MeV alpha (3loop)(S)(M-Z(2)) = 0.1153 +/- 0.0063, x(2)/d.o.f. = 0.335/(64 - 7). The errors take into account experimental errors and higher twist effects among other estimated theoretical errors. We can also extrapolate the fit, made originally for the range 3.5 less than or equal to Q(2) less than or equal to 230 GeV2 to higher momenta. obtaining very good reproduction of experimental data up to Q(2) similar or equal to 5000 GeV2. The fitted value of the coupling is now, int;luding the data at high Q(2), alpha (3loop)(S)(M-Z(2)) = 0.1163 +/- 0.0014. (C) 2001 Elsevier Science B.V. All rights reserved.