Perturbative results of matrix elements of the axial current and their relation with the axial anomaly

TL;DR

This paper uses perturbative QCD to compute matrix elements of the axial current for a gluon target, clarifying their connection with the axial anomaly and revisiting classic nucleon spin results.

Contribution

It provides a detailed perturbative analysis of axial current matrix elements, emphasizing the role of quark mass and infrared regulation in relation to the axial anomaly.

Findings

Cancellations between axial anomaly and quark mass contributions.

Clarification of the axial current's non-conservation in the Standard Model.

Insights into off-forward kinematics and nucleon spin sum rule.

Abstract

In the Standard Model of particle physics, the axial current is not conserved, due both to fermion masses and to the axial anomaly. Using perturbative quantum chromodynamics, we calculate matrix elements of the local and non-local axial current for a gluon target, clarifying their connection with the axial anomaly. In so doing, we also reconsider classic results obtained in the context of the nucleon spin sum rule as well as recent results for off-forward kinematics. An important role is played by the infrared regulator, for which we put a special emphasis on the nonzero quark mass. We highlight cancellations that take place between contributions from the axial anomaly and the quark mass, and we elaborate on the relation of those cancellations with the conservation of angular momentum.