The Gauge-Invariant Angular Momentum Sum-Rule for the Proton

TL;DR

This paper develops a gauge-invariant framework for the proton's angular momentum sum-rule, expressing it through three form factors, clarifying their physical interpretation, and analyzing their scale dependence and experimental measurability.

Contribution

It introduces a gauge-invariant approach to decompose the proton's angular momentum into quark and gluon contributions using three form factors, with detailed renormalization analysis.

Findings

The axial charge cancels out of the sum-rule.

Derived one-loop scale dependence and mixing of form factors.

Connected theoretical form factors to experimental measurements.

Abstract

We give a gauge-invariant treatment of the angular momentum sum-rule for the proton in terms of matrix elements of three gauge-invariant, local composite operators. These matrix elements are decomposed into three independent form factors, one of which is the flavour singlet axial charge. The other two are interpreted as total quark and gluon angular momentum. We further show that the axial charge cancels out of the sum-rule. The general form of the renormalisation mixing of the three operators is written down and also determined to one loop from which the scale dependence and mixing of the form factors is derived. We relate these results to a previous parton model calculation by defining the parton model quantities in terms of the three form factors. We also mention how the form factors can be measured in experiments.