Implications of color gauge symmetry for nucleon spin structure

Abstract

We study the chromodynamical gauge symmetry in relation to the internal spin structure of the nucleon. We show that (1) even in the helicity eigenstates the gauge-dependent spin and orbital angular momentum operators do not have gauge-independent matrix element, (2) the evolution equations for the gluon spin take very different forms in the Feynman and axial gauges, but yield the same leading behavior in the asymptotic limit, and (3) the complete evolution of the gauge-dependent orbital angular momenta appears intractable in the light-cone gauge. We define a new gluon orbital angular momentum distribution ${L}_{g}(x)$ which is an experimental observable and has a simple scale evolution. However, its physical interpretation makes sense only in the light-cone gauge just like the gluon helicity distribution $\ensuremath{\Delta}g(x).$