Improved Calculation of F2 in Electroproduction and xF3 in Neutrino Scattering to NNLO and Determination of alpha_s

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Abstract
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 xF3 in neutrino N 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 loops)= 274 \pm 20 MeV, alpha_s^{3 loops}(M_Z^2)=0.1166 \pm 0.0013 and chi^2/dof= 92/(153-18) from ep and, from \nu N, Lambda(n_f=4, 3 loops)=255 \pm 72 MeV, alpha_s^{3 loops}(M_Z^2)=0.1153 \pm 0.0063 and chi^2/dof=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 < Q^2 < 230 GeV^2 to higher momenta, obtaining very good reproduction of experimental data up to Q^2=5000 GeV^2. From this, in particular, we can exclude supersymmetric partners (squarks or gluinos) for masses up to some 60 GeV. The fitted value of the coupling is now, including the data at high Q^2, alpha_s^{3 loops}(M_Z^2)=0.1163 \pm 0.0014.

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