M. Wakamatsu

Is gauge-invariant complete decomposition of the nucleon spin possible?

Is gauge-invariant complete decomposition of the nucleon spin possible? Although it is a difficult theoretical question which has not reached a complete consensus yet, a general agreement now is that there are at least two physically inequivalent gauge-invariant decompositions (I) and (II) of the nucleon. In these two decompositions, the intrinsic spin parts of quarks and gluons are just common. What discriminate these two decompositions are the orbital angular momentum parts. The orbital angular momenta of quarks and gluons appearing in the decomposition (I) are the so-called mechanical orbital angular momenta, while those appearing in the decomposition (II) are the generalized (gauge-invariant) canonical ones. By this reason, these decompositions are also called the mechanical and canonical decompositions of the nucleon spin, respectively. A crucially important question is which decomposition is more favorable from the observational viewpoint. The main objective of this concise review is to try to answer this question with careful consideration of recent intensive researches on this problem.

Chiral symmetry and the nucleon spin structure functions

We carry out a systematic investigation of twist-two spin dependent structure functions of the nucleon within the framework of the chiral quark soliton model (CQSM) by paying special attention to the role of chiral symmetry of QCD. The importance of chiral symmetry is illustrated through the good reproduction of the recent SLAC data for the neutron spin structure function

Polarized structure function g2(x) in the chiral quark soliton model

{g}_{1}^{n}{(x,Q}^{2}).

Chiral odd distribution functions in the chiral quark soliton model

We also observe a substantial difference between the predictions of the longitudinally polarized distribution functions and those of the transversity distribution functions. That the chiral symmetry may be responsible for this difference is seen in the isospin dependence of the corresponding first moments, i.e., the axial and tensor charges. The CQSM predicts

Do we expect light flavor sea quark asymmetry also for the spin dependent distribution functions of the nucleon

{g}_{A}^{(0)}{/g}_{A}^{(3)}ensuremath{simeq}0.25

Spin and orbital angular momentum distribution functions of the nucleon

for the ratio of the isoscalar to isovector axial charges, while

On the chiral quark soliton model with Pauli-Villars regularization

{g}_{T}^{(0)}{/g}_{T}^{(3)}ensuremath{simeq}0.46

QUARK–ANTIQUARK ASYMMETRY OF THE NUCLEON STRANGE SEA

for the ratio of the isoscalar to isovector tensor charges, which should be compared with the prediction

Quark-antiquark asymmetry of the nucleon strange sea

{g}_{A}^{(0)}{/g}_{A}^{(3)}{=g}_{T}^{(0)}{/g}_{T}^{(3)}=3/5

Solving the nucleon spin puzzle based on the chiral quark soliton model

of the constituent quark model or of the naive MIT bag model without proper account of chiral symmetry. Another prominent prediction of the CQSM is the opposite polarization of the