| Summary: | This thesis describes theoretical and numerical investigations into the resummation of soft singularities in some perturbative QCD cross sections. The form of the quark <i>MS</i> splitting functions and coefficient function that resums all soft singularities in DIS and Drell-Yan is obtained. After obtaining the DIS and Drell-Yan quark coefficient functions that resum leading logarithms and next to leading logarithms, PDF's and higher twist are fitted with and without resummation to the DIS CCFR, BCDMS, SLAC and H1 data sets. These PDF's are then used to determine the effect of resummation on predictions of Tevatron and future LHC Drell-Yan cross sections. Variation of the renormalization and factorization scales is performed to determine if the dependence on these two quantities is reduced in the case that resummation is used, both in the fits to DIS data and in the Drell-Yan predictions. Independently, an improved treatment of heavy quarks in the calculation of <i>F</i><sub>2</sub> is investigated. A major simplification of the VFNS is described, and shown theoretically to be as perturbatively good as the VFNS. A fit of PDF's and higher twist to BCDMS and SLAC data is performed with variations of the threshold scales, to determine whether there is less threshold scale dependence in the VFNS than in the ZM-VFNS.
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