THE AXIAL CURRENT AND ITS DIVERGENCE

In the Standard Model, the axial current is not conserved due to fermion masses and the axial anomaly. In this work, we employ perturbative quantum chromodynamics to evaluate the matrix elements of the local and non-local axial currents for a gluon target, providing insights into their relation with the axial anomaly. Our analysis revisits well-established results related to the nucleon spin sum rule, along with recent developments in off-forward kinematics. A significant aspect of our approach is the use of an infrared regulator, with a particular focus on the non-zero quark mass. We observe important cancellations between the contributions from the axial anomaly and the quark mass term, and we discuss how these cancellations are linked to the conservation of angular momentum.