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GPD and underlying spin structure of the Nucleon

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

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GPD and underlying spin structure of the Nucleon

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

  2. no theoretical prediction for the magnitude of importance of quark orbital angular momentum • Skyrme model (Ellis-Karliner-Brodsky, 1988) • Chiral Quark Soliton Model (Wakamatsu-Yoshiki, 1991) 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

  3. 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

  4. 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

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

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

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

  8. forward limit in QCSM 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 1st and 2nd moment sum rules CQSM contains no gluon fields

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

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

  11. : I = 0 part (Ossmann et al.)

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

  13. a prominant feature of CQSM prediction for • The contribution of 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

  14. 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) 071503 • M. Burkardt, Int. J. Mod. Phys. A18 (2003) 173 • J.P. Ralston and B. Pire, Phys. Rev. D66 (2002) 111501

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

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

  17. [Note]

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

  19. Can we see Chiral Enhancement near or large ? • 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

  20. [Appendix]

  21. H. Hagler et. al., Phys. Rev. D68 (2003) 034505

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

  23. consider chiral limit ( ), for simplicity indicate except for singularity contradicts CLAS observation ? H. Avakian et. al., Phys. Rev. D69 (2004) 112004

  24. Experimental confirmation of nontrivial structure of at (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 nonperturbative QCD dynamics in DIS tool to probe the role of dynamically generated quark mass

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