1. 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 measurement, 1988 ) gluon OAM :

2. Skyrme model (Ellis-Karliner-Brodsky, 1988) Chiral Quark Soliton Model (Wakamatsu-Yoshiki, 1991) importance of quark orbital angular momentum collective motion of quarks in rotating hegdhog M.F. dominance of quark OAM - chiral soliton picture of the nucleon -

3. axial anomaly of QCD ? 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 possible importance of gluon polarization Perturbative aspect  factorization scheme dependence of PDF Nonperturbative aspect  totally left unknown ! but

4. 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

5. 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

6. 2. Generalized form factor and quark angular momentum Ji’s angular momentum sum rule where - momentum fraction carried by quarks and gluons - quark and gluon contribution to the nucleon anomalous gravitomagnetic moment (AGM)

7. Origin of the terminology Anomalous Gravitomagnetic Moment energy momentum tensor coupled to graviton electromagnetic current coupled to photon Dirac F.F. Pauli F.F.

8. total nucleon anomalous gravitomagnetic moment (AGM) vanishes! three possibilities

9. recent lattice simulation by LHPC Collaboration support (2) net quark contribution to nucleon AGM vanishes ! but denies the possibility (3) ( O.V.Teryaev, hep-ph/9904376)

10. LHPC Collab., H. Hagler et. al., Phys. Rev. D68 (2003) 034505

12. equal partition of momentum and total angular momentum ! analysis of LHPC group strongly indicates Once accepting this postulate ( and remembering Ji’s sum rule ) net quark contribution to nucleon AGM vanishes ! ( Teryaev, hep-ph/9904376 & hep-ph/9803403 )

13. now we can reach more surprising conclusion, based only upon two already known observations at low energies quark and gluon fields shares about 70 % and 30 % of the total nucleon momentum at low energy scale (Ex.) GRV fit of unpolarized PDF at NLO observation (1)

14. This means, at low energy : quark OAM carries nearly half of nucleon spin ! We are inevitably led to the conclusion : observation (2) : just the EMC & subsequent experiments

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

16. forward limit in Chiral Quark Soliton Model I=0 part : J. Ossmann et al., Phys. Rev. D71 (2005)034001 I=1 part : M. W. and H. Tsujimoto, Phys. Rev. D71 (2005) 074001 1st and 2nd moment sum rules CQSM contains no gluon fields story of I = 0 part of

17. : (Ossmann et al.) Dirac sea valence

18. spin versus momentum distributions : (I=0 case) using Ji’s unintegrated sum rule spin distributionmomentum distribution important constraints for the anomalous part difference of: not extremely large

19. : I = 0 part (Ossmann et al.) momentum dist. spin dist.

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

22. a prominant feature of CQSM prediction for Since partons with are at rest in the longitudinal direction, The contribution of deformed Dirac sea quarks has a large and sharp peak around 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 motion of quarks and antiquarks in the transverse plane.

23. validity of the proposed physical picture may be confirmed if one can experimentally extract the following observable Impact parameter dependent parton distribution M. Burkardt, Phys. Rev. D62 (2000) 071503 M. Burkardt, Int. J. Mod. Phys. A18 (2003) 173 J.P. Ralston and B. Pire, Phys. Rev. D66 (2002) 111501

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

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

26. [Note ] spin dist. momentum dist.

27. 4. Summary and Conclusion : long-lasting dispute over this issue. Relying only upon Ji’s sum rule : empirical PDF information evolved down to LE scale : - model independent conclusion - absence of flavor singlet quark AGM :

28. For more definite conformation, experimental extraction of unpolarized spin-flip GPD (forward limit) is indispensable are interesting themselves, since they give distributions of anomalous magnetic moments 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 ? in Feynman momentum x -space

29. [ Addendum ]

31. especially significant for longitudinally polarized PDF in the flavor-singlet channel due to axial anomaly (Ex.) empirical PDF fit Factorization scheme dependence of PDF

32. AB scheme compatible with the naive NRQM ? puzzle is hidden in unknown mechanism of large gluon polarization is generally scale-dependent beyond L.O. but this dependence is fairly weak ! MSbar scheme