Does the Gluon Spin Contribute in A Gauge Invariant Way to Nucleon Spin?

TL;DR

This paper investigates the gauge invariance of the gluon spin contribution to nucleon spin, revealing it is not gauge invariant under general transformations and proposing a method to relate calculations across gauges.

Contribution

It demonstrates the non-invariance of the gluon spin matrix element under general gauge transformations and provides a way to convert results between different gauges.

Findings

Gluon spin matrix element is gauge dependent.

A simple method exists to relate gauge-specific calculations.

Gauge invariance does not hold for the gluon spin operator in general.

Abstract

Although the matrix element of the gluon spin operator in nucleon helicity states is known to be independent of some special choices of gauge, we show that it is not invariant under a general gauge transformation. We find that there exists a simple means of obtaining the matrix element in a different choice of gauge from a calculation made in one specific gauge. Similar conclusions hold for other manifestly gauge-dependent operators present in the QCD angular momentum operator.