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

TL;DR

This paper explores two gauge-invariant decompositions of the nucleon spin and momentum, clarifying their differences, physical meanings, and implications for the evolution of orbital angular momenta and momentum fractions.

Contribution

It clarifies the physical interpretation of potential angular momentum and compares the evolution equations of two nucleon spin decompositions.

Findings

The two decompositions are physically nonequivalent.

Potential angular momentum's physical meaning is clarified.

Differences in evolution equations impact predictions of quark and gluon momentum fractions.

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.