Gauge-invariant decomposition of nucleon spin

Abstract

We investigate the relation between the known decompositions of the nucleon spin into its constituents, thereby clarifying in what respect they are common and in what respect they are different essentially. The decomposition recently proposed by Chen et al. can be thought of as a nontrivial generalization of the gauge-variant Jaffe-Manohar decomposition so as to meet the gauge-invariance requirement of each term of the decomposition. We however point out that there is another gaugeinvariant decomposition of the nucleon spin, which is closer to the Ji decomposition, while allowing the decomposition of the gluon total angular momentum into the spin and orbital parts. After clarifying the reason why the gauge-invariant decomposition of the nucleon spin is not unique, we discuss which decomposition is more preferable from an experimental viewpoint.

Wilson lines and orbital angular momentum

“…In order to unambiguously define what is meant by gluon spin and orbital angular momentum, Chen et al proposed to split the gauge field into a pure-gauge term and a physical term [2][3][4][5] A μ (x) = A pure μ (x) + A phys μ (x) (1) satisfying specific gauge transformation laws…”

Recent Developments in Nucleon Spin Decomposition

“…which is precisely (16). Similarly, I can define the canonical gluon OAM density L g can (x) and analyze its twist structure.…”

Recent Developments in Nucleon Spin Decomposition

“…The idea to use the 'physical part' of the gauge field was originally due to Chen et al 6 (see also Ref. 7), and the notations A phys and D pure are borrowed from their work. However, the explicit form (7) is different from theirs.…”