| This thesis presents a study of how the idea of factorization can be used to understand the origins of nucleon spin within Quantum Chromodynamics (QCD). Beginning with a general overview of QCD as a quantum field theory in Chapter 1, I then move on to study Deep-Inelastic Scattering (DIS) in Chapter 2.; The original research presented here concerns Deeply-Virtual Compton Scattering (DVCS), a process closely related to DIS. The special kinematics of DVCS allow one to measure new hadronic parton distributions. As explained in Chapter 3, these distributions contain information on the origins of nucleon spin that DIS cannot provide. We calculate the one-loop coefficient functions of these new distributions as they appear in DVCS and show that the soft physics inherent to this process can be separated from the hard at this order. We then argue that this property persists to all orders in the strong coupling, using the methods of Chapter 2. Using our result, we calculate a operator product expansion for the product of two electromagnetic currents that is valid for a certain class of off-diagonal matrix elements. This constitutes a generalization of the expansion first considered by Wilson in 1969 which has been used extensively in the past thirty years.; Chapter 4 is devoted to the complications associated with transversely polarized DIS. We discuss the special circumstances that arise here due to the introduction of a transverse direction. In particular, the gauge-invariance of QCD demands that these effects be inseparable from multiparton correlations within the nucleon. Among other things, this fact complicates the scale evolution of the relevant distributions. We show that these complications are removed at the one-loop level by taking the limit of large-Nc. Although this simplification has been known for several years, its origins have remained a mystery. Our new approach to the calculation allows us to understand these origins. We discuss the possibility of similar simplifications at the higher loop level and for other important distributions. |
