Matrix Elements of the Axial Current and the Axial Anomaly in perturbative QCD

In the Standard Model, the axial current is not conserved due to fermion masses and the axial anomaly. We calculate the perturbative matrix elements of local and non-local axial currents for a gluon target, clarifying their connection to the axial anomaly. This work revisits classical results on the nucleon spin sum rule and recent findings in off-forward kinematics, particularly focusing on the so-called "anomaly poles." We highlight the role of quark mass as a crucial infrared regulator and identify cancellations between contributions from the axial anomaly and quark mass, emphasizing their relation to the conservation of angular momentum. This study enhances our understanding of axial currents in high-energy particle interactions.