Exploring QCD Factorization at Moderate Energy Scales

Asymptotic freedom in QCD facilitates the use of partonic degrees of freedom over short distances, but physical processes are sensitive to a wide range of scales. Thus, it is necessary in QCD calculations to utilize a factorization scheme to separate a process into perturbative and non-perturbative factors. This separation relies on an assumption that one energy scale is infinitely larger than the other scales involved in the process. However, much experimental research in areas such as nucleon structure and quark-hadron duality occur at more moderate energy scales where that basic assumption may not be true but perturbative calculations should still be useful. Thus, an exploration of the limits of factorization at more moderate energy scales is needed. This dissertation examines various aspects of factorization at these energy scales First by applying the necessary approximations to a simple model where exact calculations are possible and so the effects of these approximations can be quantified This is followed by examining areas where corrections are known to be needed. First is an exploration of target mass corrections (TMCs) in the case of deep inelastic scattering (DIS), including a discussion of what large corrections imply about the target structure. Second, is a general examination of PDFs and FFs at moderate scales. Third, I will discuss how this fits into the long-term effort to study the transition between small transverse momentum (generated non-perturbatively) and large transverse momentum (generated in the hard process)