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

We compute the full three-loop coefficient functions for the structure functions image and image in massless perturbative QCD. The results for image complete the next-to-next-to-leading order description of unpolarized electromagnetic deep-inelastic scattering. The third-order coefficient functions for image 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 image from scaling violations. The three-loop corrections to image are larger than those for image. Especially for the latter quantity the expansion in powers of image is very stable, for photon virtualities image, over the full x-range accessible to fixed-target and collider measurements.