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Generalized Form Factors, Generalized Patron Distributions, and Spin Contents of the Nucleon

Generalized Form Factors, Generalized Patron Distributions, and Spin Contents of the Nucleon. with Y. Nakakoji (Osaka Univ.). 1. Introduction. Nucleon Spin Puzzle. : ( EMC measurement, 1988 ). - Still unsolved fundamental puzzle in hadron physics -.

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Generalized Form Factors, Generalized Patron Distributions, and Spin Contents of the Nucleon

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  1. Generalized Form Factors, Generalized Patron Distributions, and Spin Contents of the Nucleon with Y. Nakakoji (Osaka Univ.) 1. Introduction Nucleon Spin Puzzle : ( EMC measurement, 1988 ) - Still unsolved fundamental puzzle in hadron physics - If intrinsic quark spin carries little of total nucleon spin What carries the rest of nucleon spin ?

  2. grows rapidly as increases, even though it is • small at low energy scale • decreases rapidly to compensate the increase of two cautions when discussing nucleon spin contents (I)Scale dependence of polarized PDF 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 should regard that we are thinking of it at low energy scale of nonperturbative QCD

  3. no predictive power for the magnitude of (II)Factorizationscheme dependence of polarized PDF - arising from axial-anomaly of QCD - Perturbative aspect of axial-anomaly is fully understood 2 popular factorization schemes for longitudinally polarized PDF Nonperturbative aspect is totally left unknown !

  4. Empirical PDF fits based on the two factorization schemes Relation between the scheme and the AB scheme MSbar scheme AB scheme Compatible with Naïve Quark Model ? See, however, the recent COMPASS measurement !

  5. around , a value of of about 3 would be required to obtain the expected of the order of 0.6. • “Gluon polarization in the nucleon from quasi-real photoproduction • of high- hadron pairs”, hep-ex / 0511028 In fact, COMPASS group pointed out that, based on incompatible with the recent COMPASS data !

  6. What about ? “Evidence for the Absence of Gluon Orbital Angular Momentum in the Nucleon”, S.J. Brodsky and S. Gardner, hep-ph / 0608219. • The Sivers mechanism for the single-spin asymmetry in the • unpolarized lepton scattering from a transversely polarized nucleon • is driven by the OAM of quarks and gluons. • They claim that small single-spin asymmetry measured by • the COMPASS collaboration on the deuterontarget is an • indication of small gluon OAM !. What remains is alone ?

  7. 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 hegdehog M.F.

  8. CQSM predicts at model energy scale around at assuming • CQSM well reproduces and at the leading order QCD

  9. SU(2) : M. W. and T. Kubota, Phys. Rev. D60 (1999) 034022 • SU(3) : M. Wakamatsu, Phys. Rev. D67 (2003) 034005

  10. New compass data (2005)

  11. possibility of direct measurement of We repeat the question again : only experiments can settle the despute ! Recent noteworthy development is through Generalized Parton Distributions (GPDs) appearing in high-energy DVCS & DVMP processes Ji’s angular momentum sum rules

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

  13. and are well determined from empirical PDF fits :total nucleon AGM identically vanishes ! important observation (Example) MRST004 or CTEQ5 fundamentally important to know ! since

  14. two possibilities The 1st possibility, i.e. the absence of the net quark contribution to the anomalous magnetic moment of the nucleon : seems to be favored by LHPC & QCDSF lattice simulations ( as well as CQSM )

  15. AGM form factor LHPC AGM CQSM

  16. 3. Relation of GFF with unpolarized GPDs natural spin decomposition in Breit frame corresponds to Sachs decomposition of electromagnetic F.F.

  17. Mellin moment sum rules relevant to our discussion (1) 1st moment (magnetic moment) sum rule (2) 2nd moment (angular momentum) sum rule unintegrated Ji’s sum rule familiar unpolarized PDF canonical part anomalous part

  18. and its canonical part in CQSM

  19. and its canonical part in CQSM

  20. anomalous part noDirac sea contribution Dirac sea contribution to cancel ! smallvalence contribution valence contribution

  21. Not only CQSM but also LHPC & QCDSF lattice simulations • indicate smallness of quark AGM model independet prediction for nucleon spin contents • In the following, we assume smallness of • and set them 0, for simplicity. We are then led to surprisingly simple relations :

  22. The quark- and gluon-momentum fractions, and , • are empirically well determined. [Reason] forming spatial moments of and does not change the short-distance singularity of the oparotors ! Important facts (ex) MRST2004 , CTEQ5 PDF fits • The above proportionality relations holds scale-independently, • since the evolution equations for and • are exactly the same !

  23. There also exist phenomenological fits for the longitudinally • polarized PDF, which contains information on and , • although with larger uncertainties, compared with unpolarized case. (ex) LSS2005 , DNS2005, GRSV2000, AAC PDF fits These are enough to determine quark and gluon OAM as function of energy scale, through the relations :

  24. The nucleon spin contents at

  25. around If evolved down to low energy model scale increasing increasing slowly increasing Nearly half of nucleon spin comes from quark OAM !

  26. Ji’s sum rule : • absence of flavor singlet quark AGM : 4. Summary and Conclusion : long-lasting dispute over this issue. Based only upon Empirical PDF information evolved down to LE scale around 600MeV - model independent conclusion -

  27. For obtaining more definite conclusion, 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 parton distributions origin of AMM & AGM & OAM of composite particle

  28. [ Addendum ] A conjecture on the net quark contribution to nucleon AGM small ! probably small ! Note that, in CQSM

  29. CQSM prediction for isosinglet Dirac sea valence

  30. CQSM prediction for isovector GPD

  31. Pionic interpretation of central peak due to polarized Dirac sea may be confirmed by investigating dependence of

  32. Further support may be obtained by investigating the canonical part of NMC observation

  33. Scale dependencies of decreasing increasing increasing

  34. Scale dependencies of

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