More on the relation between the two physically inequivalent decompositions of the nucleon spin and momentum

Abstract

In a series of papers, we have established the existence of two gauge-invariant decompositions of the nucleon spin, which are physically nonequivalent. The orbital angular momenta of quarks and gluons appearing in these two decompositions are gauge-invariant dynamical orbital angular momenta and "generalized" canonical orbital angular momenta with gauge-invariance, respectively. The key quantity, which characterizes the difference between these two types of orbital angular momenta is what-we-call the {\it potential angular momentum}. We argue that the physical meaning of the potential angular momentum in the nucleon can be made more transparent, by investigating a related but much simpler example from electrodynamics. We also make clear several remaining issues in the spin and momentum decomposition problem of the nucleon. We clarify the relationship between the evolution equations of orbital angular momenta corresponding to the two different decompositions above. We also try to answer the question whether the two different decompositions of the nucleon momentum really lead to different evolution equations, thereby predicting conflicting asymptotic values for the quark and gluon momentum fractions in the nucleon.

The version to appear in Physical Review D, LaTeX, 47 pages, 4 figures

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• Is gauge-invariant complete decomposition of the nucleon spin possible ?
• Inclusive double-helicity asymmetries in neutral pion and eta meson production in $\vec{p}+\vec{p}$ collisions at $\sqrt{s}=200$ GeV
• Parton Orbital Angular Momentum and Final State Interactions
• Geometrical approach to the proton spin decomposition
• Physics of Gluon Helicity Contribution to Proton Spin
• On the Observability of the Quark Orbital Angular Momentum Distribution
• Quark tensor charge and electric dipole moment within the Schwinger-Dyson formalism
• Gluon Spin, Canonical Momentum, and Gauge Symmetry
• Novel twist-three transverse-spin sum rule for the proton and related generalized parton distributions
• Quark scalar, axial, and pseudoscalar charges in the Schwinger-Dyson formalism
• Unravelling the physical meaning of the Jaffe-Manohar decomposition of the nucleon spin
• Gauge Invariant Descriptions of Gluon Polarizations
• On the two remaning issues in the gauge-invariant decomposition problem of the nucleon spin
• Measurements of double-helicity asymmetries in inclusive $J/\psi$ production in longitudinally polarized $p+p$ collisions at $\sqrt{s}=510$ GeV
• Are there infinitely many decompositions of the nucleon spin ?
• Proton spin after 30 years: what we know and what we don't?
• Double longitudinal-spin asymmetries in $J/\psi$ production at RHIC
• Are there infinitely many decompositions of the nucleon spin ?