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The role of orbital angular momentum in the internal spin structure of the nucleon based on collaboration with Y. Nakakoji, H. Tsujimoto 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 Plan of Talk M. Wakamatsu (Osaka University) : PACSPIN-07

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

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Two remarkable recent progresses : (1) New COMPASS & HERMES analyses (2) COMPASS, PHENIX, STAR analyses Precise measurements of deuteron spin-dependent structure function high statistics, especially at lower x region 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 COMPASS : quasi-real photoproduction of high- hadron pairs Still totally unknown are and !

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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 ?

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

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

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

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Advantages of Chiral Quark Soliton Model 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 only 1 parameter of the model (dynamical quark mass ) was already fixed from low energy phenomenology

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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

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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

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

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

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

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Isoscalar unpolarized PDF positivity sea-like soft component

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Isovector unpolarized PDF

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Isoscalar longitudinally polarized PDF New COMPASS data

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

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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 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 HERMES Collabotation, Phys. Rev. D71 (2005) 012003

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

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

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

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

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

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

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a prominent feature of CQSM prediction for The contribution of deformed Dirac sea quarks has a large and sharp peak around 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

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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 Interpretation of sharp peak of around in the transverse direction

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validity of claimed picture may be confirmed by investigating dependence of

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

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anomalous part no net Dirac sea contribution small valence contribution to Dirac sea contribution valence contribution cancel !

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

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

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

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

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[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 ! The above evolution equations at NLO may be used to estimate and at lower energy scales ! Evolve down

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MRST2004 evolved down to

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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 of gluon OAM. 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

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Nucleon spin contents extracted from cross over around CQSM

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

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LHPC2005 QCDSF2004 CQSM2006 LHPC2007 (new) ChPT extrapolation Lattice and CQSM predictions for Isovector AGM :

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

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Assuming

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

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

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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 Jis angular momentum as well as the relation

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are interesting themselves, since they give distributions of anomalous magnetic moments 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 in Feynman momentum x -space We hope rapid progress of experimental GPD studies !

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[Appendix]

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

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LO evolution equation

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

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

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New COMPASS QCD fits at NLO New HERMES QCD fits at NLO s-quark polarization

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Remember that small ! probably smaller ! Reasoning to show smallness of

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