Third- and all- order results for semi-inclusive QCD hard processes

In this thesis we present third-order corrections to heavy-quark production in photonexchange deep-inelastic scattering (DIS) and we study the resummation of leading and sub-leading contributions to DIS and other QCD hard processes at large values of the Bjorken variable x. We provide approximate next-to next-to-leading order (NNLO) corrections for the heavy-quark contribution to the structure function F2 in photon-exchange DIS. This is achieved by extending and combining the available NNLO information from different kinematic limits. In particular, we predict the full logarithmic behaviour of the coefficient functions near the threshold of heavy-quark production applying soft-gluon exponentiation (SGE). We utilize available all order-result in the high-energy limit to derive an analytic NNLO expression for the dominant contributions in this limit. Finally from known even integer Mellin moments of the heavy-quark operator matrix elements, as well as from the already mentioned high-energy behaviour, we construct an approximation for the heavy-quark coefficient functions at asymptotically large values of the exchanged momentum squared Q2. By combining these individual results we construct NNLO coefficient functions for heavy-quark DIS which, while still being approximate, represent the most comprehensive results possible at this point. The resulting improvement of the prediction, as well as the low-Q2 small-x limitations of the present NNLO results, are then illustrated in a phenomenological study. In the second part of this thesis we address the all-order resummation of QCD quantities in the large-x limit for which SGE is not applicable. After reviewing the resummation method that will be employed and the already available results for inclusive DIS (for which we will provide a closed analytic formula at next-to-next-to-leading logarithmic (NNLL) accuracy for the first time), we apply this method to electronpositron semi-inclusive annihilation (SIA). Also in this case, closed analytic formulae for the resummed time-like splitting and coefficient functions at NNLL accuracy are presented. This resummation method is then applied to the off-diagonal partonic cross sections in Drell-Yan lepton pair production and in Higgs hadro-production, for which we are able to resum only the leading logarithmic (LL) contributions