Gauge invariance and hadron structure

TL;DR

This paper demonstrates that despite their gauge dependence, gluon spin and orbital angular momentum operators have gauge-invariant expectation values in hadron states, ensuring a gauge-independent nucleon spin decomposition.

Contribution

It proves the gauge invariance of expectation values for gauge-dependent operators in hadron states with definite momentum and polarization, clarifying nucleon spin structure.

Findings

Gauge-dependent operators have gauge-invariant expectation values in hadron states.

Conventional nucleon spin decomposition is gauge independent.

Results extend to quark momentum and kinetic energy operators.

Abstract

We prove that the {\em gauge dependent} gluon spin, gluon and quark orbital angular momenta operators have {\em gauge invariant} expectation values on hadron states with {\em definite} momentum and polarization, therefore the conventional decomposition of nucleon spin into contributions from the spin and orbital angular momentum of quark and gluon is {\em gauge independent}. Similar conclusions apply to the {\em gauge dependent} quark momentum and kinetic energy operators, and accordingly nucleon momentum and mass structures.