Chiral Quark Soliton Model and Nucleon Spin Structure Functions

1. Chiral Quark Soliton Model and Nucleon Spin Structure Functions M. Wakamatsu, Osaka Univ., July 2009, Bled Plan of talk • Introduction • Basics of Chiral Quark Soliton Model • CQSM and Parton Distribution Functions • On the role and achievements of CQSM in the DIS physics • Chiral-odd twist-3 distribution function • Nucleon spin problem revisited : current status • Generalized Parton Distributions and Ji’s angular momentum sum rule • Semi-empirical analysis of the nucleon spin contents

2. 1. Introduction What is Chiral Quark Soliton Model like ? What is (or was) Skyrme model ? Bohr’s collective model in baryon physics! Bohr’s model of rotational nuclei Skyrme model microscopic basis Deformed Hartree theory Cranking quantization CQSM

3. nucleon spin sum rule : importance of • discovery of novel correction missing in corresponding Skyrme model Compressed history of CQSM [1988] D. Diakonov, V. Petrov, and P.Pobylitsa • proposal of the model based on instanton picture of QCD vacuum (Skyrme model, Hybrid chiral bag model, …… ) [1991] M. W. and H. Yoshiki • numerical basis for nonperturbative evaluation of nucleon observables including vacuum polarization effects ( based on the workby Kahana-Ripka-Soni, 1984 ) [1993] M. W. and T. Watabe - resolution of - problem - [1996 - ] D. Diakonov et al., H. Weigel et al., M. Wakamatsu et al. • application to Parton Distribution Functions of the nucleon

4. 2. Basics of Chiral Quark Soliton Model Basic lagrangian effective meson action derivative expansion

5. Energy of Soliton construction without derivative expansion M.F. Dirac equation breaks rotational symmetry Hartree condidion

6. 1. Cranked iso-rotation of hedgehog M.F. induces Coriolis coupling slow collective rotation 　　　　　　　　　　and fast internal motion ! Quark hedgehog state Spin-isospin projection using cranking method (linear response theory) in the rotating or body-fixed intrinsic frame 2. Evaluate changes of intrinsic quark w.f. and associate changes of observables by treating this Coriolis coupling as an external perturbation 3. Canonically quantize iso-rotational motion Underlying dynamical assumption here is the validity of adiabatic treatment

7. Final formula for evaluating nucleon observables with and diagonal sum over occupied states ( = valence + Dirac sea )

8. double sum virtual transitions from occupied to nonoccupied states

9. Noteworthy achievements of CQSM for low energy baryon observables (1) reproduce small quark spin fraction of N consistent with EMC observation ! (2) reproduce large sigma term ! (3) resolve problem of the Skyrme model ! • Still, most low energy baryon observables are insensitive to low energy models ! • We demonstrate that the potential ability of CQSM manifestsmost clearly in its predictions for internal partonic structure of the nucleon (or baryons) !

10. 3. CQSM and Parton Distribution Functions Field theoretical definition of quark distribution functions - nucleon matrix element of quark bilinear operator with light-cone separation - We take account of this nonlocalityin space and time in path-integral formalism Answer in schematic form where

12. Remark on the antiquark distributions (unpolarized distribution) where one can prove for longitudinally polarized distribution we have

13. 4. On the role and achievement of CQSM in Deep-Inelastic-Scattering physics • Standard approach to DIS physics Factorization theorem PDFs Soft part is treated as a black box, which should be determined via experiments ! reasonable strategy ! We however believe that, even if this part is completely fixed by experiments, one still wants to know why those PDFs take the form so determined ! • Nonstandard but complementary approach to DIS physics is necessary here to understand hidden chiral dynamics of soft part, based on models or lattice QCD

14. Merits of CQSM over many other effective models of baryons • it is a relativistic mean-field theory of quarks, consistent with • field theoretical nature of the model (nonperturbative inclusion of polarized • Dirac-sea quarks) enables reasonable estimation of antiquark distributions. • only 1 parameter of the model (dynamical quark mass M) was already fixed • from low energy phenomenology parameter-free predictions for PDFs Default Lack of explicit gluon degrees of freedom

15. How should we use predictions of CQSM ? Follow the spirit of empirical PDF fit by Glueck-Reya-Vogt (GRV) • They start the QCD evolution at the extraordinary low energy scales like • They found that, even at such low energy scales, one needs nonperturbatively • generated sea-quarks, which may be connected with effects of meson clouds. Our general strategy • use predictions of CQSM as initial-scale distributions of DGLAP equation • initial energy scale is fixed to be (similarly to the GRVPDF fitting program)

16. QCD running coupling constant at next-to-leading order (NLO) pQCD is barely applicable !

17. Parameter free predictions of CQSM for 3 twist-2 PDFs • unpolarized PDFs • longitudinally polarized PDFs • transversities (chiral-odd) totally different behavior of the Dirac-sea contributions in different PDFs !

18. Isoscalar unpolarized PDF sea-like soft component positivity

19. Isovector unpolarized PDF - NMC observation -

20. ratio in comparison with Fermi-Lab. Drell-Yan data NA51 old fits FNAL E866 / NuSea CQSM parameter free prediction new fit parameter free prediction

21. Longitudinally polarized structure functions for p, n, D : (data before 2003) SU(2) : M. W. and T. Kubota, Phys. Rev. D60 (1999) 034022SU(3) : M. Wakamatsu, Phys. Rev. D67 (2003) 034005

22. New compass data (2005)

23. New COMPASS and HERMES fits for together with CQSM prediction CQSM New data Old data

24. CQSM predicts A proposal to measure and via polarized Drell-Yanat JPark Isovector longitudinally polarized PDF This means that antiquarks gives sizable positive contribution to Bjorken S.R. contradict the HERMES analysis of semi-inclusive DIS data • HERMES Collaboration, Phys. Rev. D71 (2005) 012003 However, HERMES analysis also denies negative strange-quark polarization favored by most global-analysis heavily depending on inclusive DIS data ! A recent new global fit including polarized pp data at RHIC • D. Florian, R. Sassot, M. Strattmann, W. Vogelsang, hep-ph/0804.0422

25. 5. Chiral-odd twist-3 distribution function chiral-odd Why is it interesting ? pQCD M.Burkardt and Y.Koike (2002) What is the physical origin of this delta-function singularity ?

26. general definition of measures light-cone correlation of scalar type existence of delta-function singularity in indicates disentangling the origin of delta-function singularity in with long-range (infinite-range) correlation of scalar type

27. Within the CQSM, we can analytically confirm this fact M.W. and Y.Ohnishi, Phys. Rev. D67 (2003) 114011 P. Schweitzer, Phys. Rev. D67 (2003) 114010 existence of this infinite-range correlation is inseparably connected with nontrivial vacuum structure of QCD spontaneous cSB and nonvanishing vacuum quark condensate Why does vacuum property come into a hadron observable ? connected with extraordinary nature of scalar quark density in the nucleon

28. total valence Dirac sea CQSM prediction for the scalar quark density of the nucleon

29. Nonvanishing quark condensate as a signal of the spontaneous cSB of the QCD vacuum is the physical origin of 　-type singularity in This in turn dictates that We thus conclude that

30. Sophisticated numerical method to treat containing Y. Ohnishi and M.W., Phys. Rev D69 (2004) 114002 We find that where with

31. 1st moment sum rule for isoscalar dominant with this gives Favors fairly large sigma term numerically

32. Isovector part of total valence Dirac sea no singularity at

33. Combining isoscalar- and isovector-part of 　 , we can get any of Comparison with CLAS semi-inclusive data extracted by Efremov and Schweitzer

34. (1) delta-function singularity in chiral-odd twist-3 distribution is violation of sigma-term sum rule of need more precise experimental information on this quantity in wider range of especially in small region To sum up this part manifestation of nontrivial vacuum structure of QCD in hadron observable (2) Existence of this singularity will be observed as

35. fairly precisely determined ! likely to be small, but still with large uncertainties ! 6. Nucleon spin problem revisited : current status two remarkable recent progresses : (1) New COMPASS & HERMES analyses • Precise measurements of deuteron spin-dependent structure function with 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

36. The remaining 70 % of nucleon spin should be carried by , from Lattice QCD from direct measurements by RHIC et al. from Brodsky-Gardner’s argument What is our current understanding of thenucleon spin ? safe statement ! However, we are in a quite confusing situation concerning the separation of the remaining part. What carry the rest of the nucleon spin ? Interesting possibility is to get direct empirical information on through Generalized Parton Distributions (GPDs) appearing in high-energy DVCS & DVMP processes

37. lower part of Handbag Diagram contains information on nonpertubative quark-gluon structure of the nucleon, parametrized by 4 GPDs depending on 3 kinematical variables 7. Generalized Parton Distributions and Ji’s angular momentum sum rule DVCS and DVMP amplitude dominant in Bjorken limit Handbag diagram

38. Generalized form factors of the nucleon Dirac F.F. Pauli F.F. electromagnetic current coupled to photon energy momentum tensor coupled to graviton

39. quark and gluon contribution to the nucleon anomalous gravitomagnetic moment (AGM) Ji’s angular momentum sum rule where - momentum fraction carried by quarks and gluons - is a measurable quantity, since it is the 2nd moment of GPD

40. Since the momentum fractions are already well determined phenomenologically, we are left with two empirically unknowns 8. Semi-empirical analysis of nucleon spin contents • M.W. and Y. Nakakoji, Phys. Rev. D77 (2008) 074011/1-15. • Phys. Rev. D74 (2006) 054006/1-27. We start with Ji’s angular momentum sum rule where with the constraint We also need the isovector combination for flavor decomposition

41. theoretical information on isovector satisfactory agreement between the predictions of CQSM and lattice QCD Old Lattice New Lattice

42. theoretical information on In the following, we treat as an unknown quantity within this range ! Lattice QCD • QCDSF-UKQCD (2007) • LHPC (2007) : covariant BchPT : HBChPT very sensitive to the chiral extrapolation method ! CQSM only a reasonable bound can be given (due to lack of gluon field)

43. The quark- and gluon- momentum fractions, and , are for those between asymptotic limit with 1st important observation ( of our semi-empirical analysis ) scale-dependent quantities, but they are empirically fairly precisely known. In fact, MRST2004 & CTEQ5 QCD fits give almost the same numbers [Ex.] well-known solution of LO evolution equation

44. Scale dependencies of quark and gluon momentum fraction at NLO evolve down to low-energy scale using NLO evolution eq.

45. [Reason] forming spatial moments of and does not change the short-distance singularity of the operators ! 2nd important observation ( due to Xiangdong. Ji ) and obey exactly the same evolution equation ! The evolution equations at NLO may be used to estimate as well as at any energy scale !

46. Scale dependencies of quark and gluon total angular momentum proportionality !

47. we conjecture that here comes from gluon OAM not from ! total angular momentum fraction at the nonperturbative scale • quarks and gluons respectively carry about 80% and 20% of total angular (and linear) momentum of the nucleon • quarks and gluons respectively carry about 65% and 35% of total angular momentum of the nucleon The truth would lie between these two limiting cases !

48. Once is known, we can determine the quark OAM through Since is approximately scale independent, we use here central fit of HERMES analysis : is a rapidly decreasing functions of ! One observes that

49. flavor decomposition of quark total angular momentum small is consistent with lattice QCD prediction !

50. Information on quark OAM, can be obtained by subtracting the known information on intrinsic quark polarizations Neglecting error bars, for simplicity, we have at scale indep. prominent features isovector dominance of quark OAM !