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

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

2012-04-13

arxiv.org/abs/1204.2860v1

Physics

High Energy Physics

High Energy Physics - Phenomenology

LaTeX, 44 pages, 5 figures

Scientific paper

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 nontrivial gauge-invariant extensions of canonical orbital angular momenta, 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 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.

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