Calculation of electroproduction to NNLO and precision determination of alpha(s)

We use the known values of the two-loop Wilson coefficients and the three-l oop anomalous dimension matrix gamma(n) to perform a next-to-next-to leadin g order (NNLO) calculation of ep deep inelastic scattering. Because gamma(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 par ameters: the QCD mass Lambda, and 11 initial values for the moments of the structure functions. The data points spread in the range of momenta 2.5 GeV 2 less than or equal to Q(2) less than or equal to 230 GeV2. The chi(2)/d.o .f. decreases substantially when going from LO to NLO, and also from NLO to NNLO (although only a little now) to chi(2)/d.o.f. = 79.2/(102 - 12). The favoured value of Lambda is Lambda(n(f) = 4,3 loop) = 282.7 +/- 35.1 MeV, c orresponding to the value of the coupling at the Z mass of alpha(s)(( 3 loo p))(M-Z(2)) = 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. (C) 1999 Elsevier Science B.V. All rights reserved.