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 ͑1͒ even in the helicity eigenstates the gauge-dependent spin and orbital angular momentum operators do not have gauge-independent matrix element, ͑2͒ 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 ͑3͒ 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 ⌬g(x). ͓S0556-2821͑99͒02207-9͔ PACS number͑s͒: 12.38.Aw, 14.20.Dh E ជ a ϭϪٌ ជ A 0a Ϫ ‫ץ‬A ជ ‫ץ‬t Ϫgf abc A ជ b A 0c .

Exploring the polarization of gluons in the nucleon

“…G µν is the QCD field strength tensor, andG µν its dual. The integral of ∆g(x, Q 2 ) over all momentum fractions x becomes a local operator only in A + = 0 gauge and then coincides with ∆G(Q 2 ) [2,7]. The COMPASS experiment at CERN and the HERMES experiment at DESY attempt to access ∆g(x, Q 2 ) in charm-or high-p T hadron final states in photon-gluon fusion γ * g → qq.…”

Leading Chiral Contributions to the Spin Structure of the Proton

“…[16], the quark and gluon angular momentum distributions are found to be J q (x) = x(Σ(x)+E q (x, 0, 0))/2 and J g (x) = x(g(x)+E g (x, 0, 0))/2, where Σ(x) and g(x) are unpolarized (singlet) quark and gluon distributions and E q,g (x, 0, 0) are generalized parton distributions [17]. The moments of these distributions are related to the form factors of the twist-two operators [8].…”

Orbital Angular Momentum: How to Define it and How to Measure it

“…contrary to claim of Hoodbhoy, Ji and Lu [18]. The results in the latter paper depend on discarding an infinite number of surface terms, each arising from integrating a divergence term, and this is almost certainly unjustified.…”