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

We study the next-to-next-to-leading order (NNLO) evolution of favour singl et parton densities and structure functions in massless perturbative QCD, P resent information on the corresponding three-loop splitting functions is u sed to derive parametrizations of these quantities, including Bjorken-x dep endent estimates of their residual uncertainties. Compact expressions are a lso provided for the exactly known, but in part rather lengthy two-loop sin glet coefficient functions. The size of the NNLO corrections and their effe ct on the stability under variations of the renormalization and mass-factor ization scales are investigated. Except for rather low values of the scales , the residual uncertainty of the three-loop splitting functions does not l ead to relevant effects for x > 10(-3). Inclusion of the NNLO contributions considerably reduces the theoretical uncertainty of determinations of the quark and gluon densities from deep-inelastic structure functions. (C) 2000 Elsevier Science B.V. All rights reserved.