Higher order QCD effects in inclusive annihilation and deep inelastic scattering

We present a parton model interpretation of the predictions of quantum chromodynamics in the process e⁺e^?→hadron + anything. We give thecomplete list of parameters needed for the study of the scaling violations of fragmentation functions up to the next-to-leading logarithmic approximation. This includes flavour non-singlet and flavour singlet anomalous dimensions up to order α² and coefficient functions up to order α. We also present results for the deep inelastic scattering e^?h→e^? + anything. We find that in e⁺e^? annihilation the ratio of scaling violations of second order to first order is in general bigger than the corresponding ratio for deep inelastic scattering. The Gribov-Lipatov relation is thus violated in second order. We also find that a modified Drell-Yan analytic continuation relation holds between the deep inelastic and annihilation structure functions for quarks and gluons. In x space we give detailed numerical evaluation of the QCD effects for non-singlet and singlet densities, in the space-like and time-like regions.