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

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.