Calculation of electroproduction to NNLO and precision determination of αs O

We use the known values of the two-loop Wilson coefficients and the three-loop anomalous dimension matrix γ(n) to perform a next-to-next-to leading order (NNLO) calculation of ep deep inelastic scattering. Because γ(n) is only known for a few values of n, the method of average reconstruction has to be used, which leaves 102 effective experimental points, for 12 parameters: the QCD mass Λ, and 11 initial values for the moments of the structure functions. The data points spread in the range of momenta 2.5 GeV2⩽Q2⩽230 GeV2. The χ2/d.o.f. decreases substantially when going from LO to NLO, and also from NLO to NNLO (although only a little now) to χ2/d.o.f.=79.2/(102−12). The favoured value of Λ is Λ(nf=4,3 loop)=282.7±35.1 MeV, corresponding to the value of the coupling at the Z mass of α(3 loop)s(MZ2)=0.1172±0.0024. The calculation, which constitutes a very precise test of QCD, includes target mass corrections; the error takes into account experimental errors and higher twist effects among other estimated theoretical errors.