Quantum Chromodynamics (QCD) is the fundamental theory of the strong interaction, yet many aspects of the structure of strongly interacting particles that can be observed (hadrons) are not well understood. A central theoretical tool in this context is QCD factorization for high-energy scattering, which separates short-distance, perturbative dynamics from long-distance, nonperturbative information encoded in parton correlation functions for hadrons. This thesis presents a perturbative study of local and non-local twist-two quark currents between gluon states, with the goal of shedding new light on recent discussions about the behavior of off-forward matrix elements and their forward limit. These matrix elements are relevant for the QCD factorization theorems of deep inelastic lepton-nucleon scattering (DIS) and deeply virtual Compton scattering (DVCS), both of which are of crucial importance for hadron structure studies. We analyze both the flavor-singlet axial current, whose nonconservation arises from quark masses and the axial anomaly, and the flavor-singlet vector current. A key aspect of our approach is the treatment of infrared physics: We use a nonzero quark mass and dimensional regularization as infrared regulators. We identify cancellations between anomaly and mass contributions and relate them to the conservation of angular momentum, and we compute the corresponding parton distribution functions (PDFs) and generalized parton distributions (GPDs) at one-loop accuracy, including Mellin-moment relations to local operators. A particular emphasis of the analysis is on the forward limit. Overall, our results provide a consistent picture of the forward limit in the perturbative setting considered here and support the standard QCD factorization framework used to extract PDFs and GPDs from DIS and DVCS, respectively.
Ignacio Castelli (Thu,) studied this question.