Implications of Color Gauge Symmetry for Nucleon Spin Structure

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; 3) the complete evolution of the gauge-dependent orbital angular momenta appears intractable in the lightcone gauge. We define a new gluon orbital angular momentum distribution Lg(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 ∆g(x). Typeset using REVTEX 1 The spin structure of the nucleon has been a subject of intense debate for about ten years. Much progress has been made in both experimental and theoretical frontiers [1]. However, some of the fundamental theoretical issues remain unsettled, as exemplified by a number of recent works in the literature. In particular, in analyzing the spin structure of the nucleon, color gauge invariance is still the cause of some confusion. In this paper, we intend to explore several important and relevant issues in detail. To set the stage, let us briefly recall the forms of angular momentum operator in quantum chromodynamics (QCD). In Ref. [2], a natural gauge-invariant expression is introduced ~ JQCD = ~ Jq + ~ Jg , (1) where ~ Jq = ∫