Title :

"Is a complete decomposition of the nucleon spin possible ?"

Masashi Wakamatsu, Osaka University


Abstract :

Since the landmark EMC measurement, which revealed that only
a small amount of the nucleon spin comes from the intrinsic
spin of quarks in the nucleon, to understand what carry the
rest of the nucleon spin is one of the fundamental problems
of QCD. To answer this question unambiguously, one cannot
avoid to clarify what is an exact definition of each term of
the nucleon spin decomposition ?

In a series of studies, we have established the fact that
there are actually two physically nonequivalent decompositions
of the nucleon spin. The decomposition (I) turned out to be
a kind of extension of the well-known Ji decomposition, but
different from the original Ji decomposition, it allows a
decomposition of the total gluon angular momentum into the
intrinsic spin and orbital angular momentum (OAM) parts.
On the other hand, the decomposition (II) is a nontrivial
gauge-invariant extension of the Jaffe-Manohar decomposition.
A crucial difference between the two decomposition lies in
the OAM parts of quarks and gluons. 
The difference between the OAMs of quarks and gluons in the
two decompositions is characterized by a quantity, which we
call the "potential angular momentum", because it is a
correspondent of the angular momentum carried by the
electromagnetic potential appearing in the famous Feynman
paradox of classical electrodynamics.

Since both decompositions are gauge-invariant, they may in
principle be related to observables. A clear relation to
observables was first obtained for the decomposition (I).
It was shown that the OAMs of quarks and gluons in this
decomposition can be extracted from the combined analyses
of the unpolarized GPDs and the longitudinally polarized PDFs.
On the other hand, Hatta recently suggested that the OAMs of
quarks and gluons appearing in the decomposition (II) can be
related to a certain moment of generalized transverse-momentum
distributions (GTMD), which is also called the Wigner distributions.
Combined with our previous results, this opens up a possibility of
complete decompositions of the nucleon spin, including an
isolation of what-we-call the "potential angular momentum" term
characterizing the difference of the two decompositions (I) and
(II) of the nucleon spin.