GPD and underlying spin structure of the nucleon

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

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

3. no theoretical prediction for the magnitude of possible importance of gluon polarization axial anomaly of QCD ? • 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 Perturbative aspect  factorization scheme dependence of PDF but Nonperturbative aspect  totally left unknown !

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

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

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 electromagnetic current coupled to photon Dirac F.F. Pauli F.F. energy momentum tensor coupled to graviton

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

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

12. analysis of LHPC group strongly indicates net quark contribution to nucleon AGM vanishes ! Once accepting this postulate ( and remembering Ji’s sum rule ) equal partition of momentum and total angular momentum ! ( 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 observation (1) 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

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

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

16. story of I = 0 part of 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 forward limit in Chiral Quark Soliton Model 1st and 2nd moment sum rules CQSM contains no gluon fields

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

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

19. : I = 0 part (Ossmann et al.) spin dist. momentum 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 • The contribution of deformed Dirac sea quarks has a large • and sharp peak around • Since partons with are at rest in the longitudinal direction, its large contribution to must come from the motion of quarks and antiquarks in the transverse plane. 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

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

25. 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

26. spin dist. [Note] momentum dist.

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

28. Can we see Chiral Enhancement near or large ? • 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 in Feynman momentum x-space • More detailed information would be obtained from • impact-parameter dependent distributions origin of anomalous magnetic moment of composite particle

29. [ Addendum ]

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

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