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

We compute the full three-loop coefficient functions for the structure functions F2 and FL in massless perturbative QCD. The results for FL 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 αs from scaling violations. The three-loop corrections to FL are larger than those for F2. Especially for the latter quantity the expansion in powers of αs is very stable, for photon virtualities Q2≫1GeV2, over the full x-range accessible to fixed-target and collider measurements.