The role of orbital angular momentum in the internal spin structure of the nucleon

1. The role of orbital angular momentum in the internal spin structure of the nucleon M. Wakamatsu (Osaka University) : PACSPIN-07 based on collaboration with Y. Nakakoji, H. Tsujimoto Plan of Talk 1. Current status of nucleon spin problem 2. Role of CQSM in nucleon structure function physics 3. CQSM analysis of unpolarized GPD 4. Model independent analysis of nucleon spin contents 5. Flavor decomposition of nucleon spin (model dependent) 6. Summary

2. 1. Current status of nucleon spin problem Early stage proposalsto explain very small quark spin fraction (I) Gluon spin hypothesis (A) naive claim The question remains why ！ OK if (B) axial-anomaly of QCD but need very large ! (II) Quark orbital angular momentum hypothesis unfavored ? is small, because is large ! (III) Gluon orbital angular momentum hypothsis no serious consideration until recently！

3. Two remarkable recent progresses : (1) New COMPASS & HERMES analyses • Precise measurements of deuteron spin-dependent structure function high statistics, especially at lower x region (2) COMPASS, PHENIX, STAR analyses • COMPASS : quasi-real photoproduction of high- hadron pairs • PHENIX : neutral pion double longitudinal spin asymmetry in the p-p collisions • STAR : double longitudinal spin asymmetry in inclusive jet production • in polarized p-p collision Still totally unknown are and !

4. Recent interesting observation concerning “Evidence for the Absence of Gluon Orbital Angular Momentum in the Nucleon”, S.J. Brodsky and S. Gardner, Phys. Let. B643 • The Sivers mechanism for the single-spin asymmetry in the unpolarized lepton scattering from a transversely polarized nucleon is driven by the orbital angular momentum of quarks and gluons. • They argued that small single-spin asymmetry on the deuteron target measured by the COMPASS collaboration is an indication of small gluon OAM !. If true, what remains is alone ?

5. Importance of quark orbital angular momentum - Large chiral soliton picture of the nucleon - • Skyrme model (Ellis-Karliner-Brodsky, 1988) • Chiral Quark Soliton Model (Wakamatsu-Yoshiki, 1991) In particular, since the latter is an effective quark theory Spin S.R Collective quark motion generating rotating M.F. of hedgehog shape

6. We need more direct empirical information on new recent development possibility of direct measurement of through Generalized Parton Distributions (GPDs) appearing in high-energy DVCS & DVMP processes Ji’s angular momentum sum rule

7. 2. Role of CQSM in nucleon structure function (DIS) physics Hard part : Perturbative QCD Factorization Black Box Soft part : Nonpurturbative QCD Lattice QCD Effective models of QCD So many ! • most promising in the long run • - still at incomplete stage - Necessary condition of good model, which has predictive power? • continuum limit & chiral limit ? • only lower moments of PDF • physical interpretation ? • able to explain many observables • with less parameters !

8. Advantages of Chiral Quark Soliton Model • only 1 parameter of the model (dynamical quark mass ) was • already fixed from low energy phenomenology parameter-free predictions for PDFs • a nucleon is a composite of valence quarks and infinitely many • Dirac sea quarks moving in a slowly rotating M.F. of hedgehog shape • field theoretical nature of the model (proper inclusiuon of polarized • Dirac-sea quarks) enables reasonable estimation of antiquark dist. Default Lack of explicit gluon degrees of freedom

9. How to use predictions of this low energy model for parton distributions ? We follow the spirit of * M. Glueck, E. Reya, and A. Vogt, Z. Phys. C67 (1995) 433 They start the QCD evolution at the extraordinary low energy scales like Even at such low energy scales, their PDF fit turns out to need nonperturbatively generated sea-quarks (and some gluons) which may be connected with the effects of meson clouds

10. Our general strategy • use predictions of CQSM as initial-scale distributions of DGLAP eq. for flavor SU(2) CQSM for flavor SU(3) CQSM • initial energy scale is fixed to be

11. On the Applicability of pQCD ? NLO pQCD is barely applicable ?

12. Parameter free predictions of the CQSM : 3 twist-2 PDFs

13. Transversities [3rd twist-2 PDF] • Totally different behavior of Dirac-sea contributions in different PDFs !

14. Isoscalar unpolarized PDF sea-like soft component positivity

15. Isovector unpolarized PDF

16. Isoscalar longitudinally polarized PDF New COMPASS data

17. New COMPASS and HERMES fits for in comparison with CQSM prediction CQSM [old]

18. Isovector longitudinally polarized PDF CQSM predicts This means that antiquarks gives sizable positive contribution to Bjorken S.R. denied by the HERMES analysis of semi-inclusive DIS data • HERMES Collabotation, Phys. Rev. D71 (2005) 012003 However, HERMES analysis also denies negative strange-quark polarization favored by the global-analysis heavily depending on inclusive DIS data ! We need more complete understanding of spin-dependent fragmentation mechanism

19. Transversities vs. longitudinally polarized PDF : CQSM predictions • M. Wakamatsu, arXiv:0705.2917 [hep/ph] not so small

20. global fit global fit [global fit] M.Anselmino et. al., Phys. Rev. D75 (2007) 054032.

21. 3. CQSM analyses of unpolarized GPDs natural spin decomposition in Breit frame corresponds to Sachs decomposition of electromagnetic F.F.

22. 1st and 2nd moment sum rules magnetic moment desity in Feynman x-space canonical part anomalous part quark number dist. angular momentum density in Feynman x-space canonical part anomalous part quark momentum dist.

23. CQSM predictions for GPDs So far, only the forward limit was calculated. (A) Isovector channel forward limit of GPDs • M.W. and H. Tsujimoto, Phys. Rev. D71 (2005) 074001 • M.W. and Y. Nakakoji, Phys. Rev. D74 (2006) 054006 (B) Isoscalar channel forward limit of GPDs • J. Ossmann et. al., Phys. Rev D70 (2005) 034011 • See also M.W. and Y. Nakakoji above

24. (A) Isovector magnetic moment distribution : magnetic moment dist. in Feynman x-space

25. The contribution of deformed Dirac sea quarks has a large and sharp peak around a prominent feature of CQSM prediction for • Since this large Dirac-sea contribution to is nearly symmetric with respect to , it gives a significant contribution to the 1st moment but no contribution to the 2nd moment

26. Interpretation of sharp peak of around • Since partons with are at rest in the longitudinal direction its large contribution to the first moment must come from transverse motion of quarks and antiquarks If one remembers the important role of 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 in the transverse direction

27. validity of claimed picture may be confirmed by investigating dependence of

28. (B) Isoscalar magnetic moment distribution : positivity of antiquark dist.

29. anomalous part no net Dirac sea contribution Dirac sea contribution cancel ! to smallvalence contribution valence contribution

30. 4. Model independent prediction for nucleon spin contents important observation (it is a sound fact) total nucleon anomalous gravitomagnetic moment (AGM) vanishes ! It follows from two possibilities

31. anomalous gravitomagnetic form factor within the CQSM Lattice QCD LHPC2005 CQSM LHPC2005 QCDSF2004

32. Not only CQSM but also LHPC & QCDSF lattice simulations indicate smallness of quark AGM 1st important observation • In the following, we assume smallness of and set them 0, for simplicity. We are then led to surprisingly simple relations : • O.V. Teryaev, hep-ph/0004376 ; hep-ph/0612205

33. (I) The quark- and gluon- momentum fractions, and , are empirically fairly precisely determined. 2nd important observation In fact, MRST2004 & CTEQ5 QCD fits give almost the same numbers for these quantities below

34. The above evolution equations at NLO may be used to estimate and at lower energy scales ! [Reason] forming spatial moments of and does not change the short-distance singularity of the operators ! (II) The above proportionality relations holds scale-independently, since the evolution equations for and are exactly the same ! Evolve down

35. MRST2004 evolved down to

36. On the other hand, our postulated identity, implies that gluon OAM comes totally from its canonical orbital motion, not from the anomalous contribution related to GPD • Gluons carry about 20% of linear and total angular momentum fraction even at this low energy scale of nonperturbative QCD ! • We conjecture that this comes from gluon OAM not from ! • This statement is not inconsistent with the recent observation by Brodsky and Gardener, since what would be related to Sivers mechanism is the anomalous part ofgluon OAM.

37. Nucleon spin contents extracted from cross over around CQSM

38. 5. Flavor decomposition of nucleon spin (model dependent) Key quantity is quark AGM : sensitive to models ! known unknown known known Ji’s angular momentum sum rule

39. Lattice and CQSM predictions for IsovectorAGM : LHPC2005 ChPT extrapolation LHPC2007 (new) QCDSF2004 CQSM2006

40. Most recent LHPC results on • Ph. Hagler et. al., arXiv : 0705.429 [hep-lat] Main conclusion at [Cf.] MRST & New COMPASS, HERMES with

41. Assuming

42. Transverse target-spin asymmetry of exclusive production on proton • Hermes Collaboration, arXiv:0707.2486 [hep-ex] far from conclusive yet!

43. smallness of flavor singlet quark AGM : 6. Summary and Conclusion : long-lasting dispute over this issue. Based only upon model independent estimate for nucleon spin contents ! Around , there is a crossover where but

44. Flavor decomposition cannot be performed quantitatively yet, since it • depend on highly model-dependent quantity Still we can conclude that As increases, decreases rapidly, but the magnitude of remains large such that even around the a scale of few GeV. • This peculiar property of the quark OAMs comes from the way of • their defintion through Ji’s angular momentum as well as the relation

45. are interesting themselves, since they give distributions of anomalous magnetic moments in Feynman momentum x-space • anomalous magnetic moment distribtion may also be related to Sivers function measured by SSA of semi-inclusive reactions ? origin of AMM & AGM & OAM of composite particle We hope rapid progress of experimental GPD studies !

46. [Appendix]

47. Intimate relation between Sivers function andanomalous magnetic distribution ? • Z. Lu and I. Schmidt, hep-ph / 0611158 Sivers function and its lowest -moment within the diquark model inthe light-front formalism anomalous magnetic moment distribution Main assumptions • scalar diquark • final state interation necessary for Sivers mechanism is one-gluon-exchange

48. LO evolution equation

49. Request for future Lattice QCD studies • More refined check of the relation • Larger lattice space, higher statistics, etc. • Stability againt the variation of pion mass, …… • More reliable evaluation of • Simulation with smaller pion mass • or • Reliable chiral extrapolation ( ex., by using chiral PT )

50. On the pion mass dependence of observables Basic model laglangian with and After obtainingself-consistent soliton solutions for several values of , we calculate nucleon observables in question.