Abstract

The main results of this thesis are the introduction of a new and systematic way to treat and resum logarithmic enhancements, to all orders in perturbation theory and to any desired logarithmic accuracy. The method developed is applied to the threshold logarithmic enhancements as well as to small transverse momentum distributions. We utilize an effective field theoretic approach to perform the resummation which turns out to be in complete agreement with the conventional approaches, though it is a much simpler one. This approach will be applied to deep inelastic scattering, Drell-Yan lepton pair production and the Standard Model Higgs production.

We have derived the functions $g_i(\alpha_s \ln {\overline N})$ for $i=1,2,3$ that resums threshold logarithms up to next-to-next-to leading logarithmic accuracy. Certain quantities (the $D^{(3)}$ for the Higgs production and the Drell-yan process and the $B^{(3)}$ for deep inelastic scattering) that contribute to the resummation at the NNNLL are also derived. Moreover, our method opens a door towards understanding the origin of the universality of the functions $f$ that contribute to anomalous dimensions of the quark and gluon form factors.

On the conceptual level, the effective approach to compute the perturbative coefficient functions of the factorization theorem(s) highlights the way these theorems could be viewed in terms of a multiple steps of integrating out momentum modes through a matching procedure. The remaining infrared divergences (at the factorization scale) are exactly the parton distribution functions.

In this work we also study exclusive processes. We will be mainly concerned with the nucleon to delta transition and how to utilize perturbative QCD to obtain a leading order factorization formula for such a process, and for similar ones. Based on this, we are able to make phenomenological predictions for certain transition form factors which can be verified experimentally.