GPD and underlying spin structure of the Nucleon M. Wakamatsu and H. Tsujimoto (Osaka Univ.) 1. Introduction Still unsolved fundamental puzzle in hadron physics If intrinsic quark spin carries little of total nucleon spin what carries the rest of nucleon spin ? quark OAM : gluon polarization : Nucleon Spin Puzzle (EMC, 1988) gluon OAM :

axial anomaly of QCD ? Skyrme model (Ellis-Karliner-Brodsky, 1988) Chiral Quark Soliton Model (Wakamatsu-Yoshiki, 1991) no theoretical prediction for the magnitude of G. Altarelli and G.G. Ross, 1988 R.D. Carlitz, J.C. Collins and A.H. Mueller, 1988 A.V. Efremov and O.V. Teryaev, 1988 importance of quark orbital angular momentum possible importance of gluon polarization

It is meaningless to talk about the spin contents of the nucleon without reference to the energy scale of observation grows rapidly as increases, even though it is small at low energy scale decreases rapidly to compensate the increase of When we talk about nucleon spin contents naively, we think of it at low energy scale of nonperturbative QCD CQSM predicts important remark

The question is : only experiments can answer it ! (Compass,2004) direct measurement of Generalized Parton Distributions via DVCS & DVMP Ji’s quark angular momentum sum rules direct measurement of via photon-gluon fusion processes : small ? asymmetry of high hadron pairs

equal partition of momentum and total angular momentum ! 2. Generalized form factor and quark angular momentum total quark angular momentum (Ji’s sum rule) anomalous gravitomagnetic moment (AGM) seems to vanish

observation at low energy scale : Quark OAM carries about half of nucleon spin ! We are then necessarily led to the conclusion : (from polarized DIS)

natural decomposition in Breit frame corresponds to Sachs decomposition of electromagnetic F.F. 3. unpolarized GPD :

forward limit in QCSM I=0 part : J. Ossmann et al., Phys. Rev. D71 (2005) I=1 part : M. W. and H. Tsujimoto, Phys. Rev. D71 (2005) st and 2nd moment sum rules CQSM contains no gluon fields story of I = 0 part of

: (Ossmann et al.) Dirac sea valence

spin versus momentum distributions : (I=0 case) using Ji’s relation spin distribution momentum distribution important constraints difference of: not extremely large

: I = 0 part (Ossmann et al.)

story of I = 1 part of model expression 1st moment sum rule gives distribution of nucleon isovector magnetic moment in Feynman momentum x -space

a prominant feature of CQSM prediction for Since partons with are at rest in the longitudinal direction, The contribution of Dirac sea quarks has a large and sharp peak If one remembers the important role of the pion clouds in the isovector magnetic moment of the nucleon, the above transverse motion can be interpreted as simulating pionic quark-antiquark excitation with long-range tail its large contribution to must come from the around motion of quarks and antiquarks in the transverse plane.

proposed physical picture may be confirmed if one can experimentally determine the following observable Impact parameter dependent parton distribution M. Burkardt, Phys. Rev. D62 (2000) M. Burkardt, Int. J. Mod. Phys. A18 (2003) 173 J.P. Ralston and B. Pire, Phys. Rev. D66 (2002)

anticipated impact parameter-dependent distribution long range tail in direction in smaller x region

spin versus momentum distributions : (I=1 case) assuming Ji’s relation spin distribution momentum distribution big difference with I = 0 case difference of: fairly large

[Note ]

4. Summary and Conclusion There has been long-lasting dispute over this issue. Using the following information Ji’s sum rule : absence of flavor singlet quark AGM : empirical PDF information down to LE scale :

More definite conclusion will be obtained through direct experimental extraction of are interesting themselves, since they give distribution of anomalous magnetic moments in Feynman momentum x -space More detailed information would be obtained from impact-parameter dependent distributions origin of anomalous magnetic moment of composite particle Can we see Chiral Enhancement near or large ?

[Appendix]

H. Hagler et. al., Phys. Rev. D68 (2003)

[Addendum] chirally odd twist-3 distribution of the nucleon (I) QCD-based analysis where

consider chiral limit ( ), for simplicity contradicts CLAS observation ? H. Avakian et. al., Phys. Rev. D69 (2004) indicate except for singularity

(II) Chiral Quark Soliton Model 1st and 2nd moment sum rules proportional to dynamically generated quark mass M, which vanishes in the perturbative QCD vacuum Experimental confirmation of nontrivial structure of at tool to probe the role of nonperturbative QCD dynamics in DIS dynamically generated quark mass