NNLO evolution of deep-inelastic structure functions: the non-singlet case

We study the next-to-next-to-leading order (NNLO) evolution of flavour non- singlet quark densities and structure functions in massless perturbative QC D. Present information on the corresponding three-loop splitting functions is used to derive parametrizations of these quantities, including Bjorken-x dependent estimates of their residual uncertainties. Compact expressions a re also provided for the exactly known, but rather involved two-loop coeffi cient functions. The size of the NNLO corrections and their effect on the s tability under variations of the renormalization scale are investigated. Th e residual uncertainty of the three-loop splitting functions does not lead to appreciable effects for x >10(-2). Inclusion of the NNLO contributions r educes the main theoretical uncertainty of alpha(s) determinations from non -singlet scaling violations by more than a factor of two. (C) 2000 Elsevier Science B.V. All rights reserved.