The third-order QCD corrections to deep-inelastic scattering by photon exchange

We compute the full three-loop coefficient functions for the structure functions F-2 and F-L in mass-less perturbative QCD. The results for F-L complete the next-to-next-to-leading order description of unpolarized electromagnetic deep-inelastic scattering. The third-order coefficient functions for F2 form, at not too small values of the Bjorken variable x, the dominant part of the next-to-next-to-next-to-leading order corrections, thus facilitating improved determinations of the strong coupling alpha s from scaling violations. The three-loop corrections to F-L are larger than those for F-2. Especially for the latter quantity the expansion in powers of as is very stable, for photon virtualities Q(2) >> 1 GeV2 over the full x-range accessible to fixed-target and collider measurements. (c) 2005 Elsevier B.V. All rights reserved.