Chiral Quark Soliton Model and Nucleon Spin Structure Functions M. Wakamatsu, Osaka Univ., July 2009, Bled 1.Introduction 2.Basics of Chiral Quark Soliton Model 3.CQSM and Parton Distribution Functions 4.On the role and achievements of CQSM in the DIS physics 5.Chiral-odd twist-3 distribution function 6.Nucleon spin problem revisited : current status 7.Generalized Parton Distributions and Ji’s angular momentum sum rule 8.Semi-empirical analysis of the nucleon spin contents Plan of talk

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 CQSM microscopic basis Deformed Hartree theory Cranking quantization

[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, …… ) numerical basis for nonperturbative evaluation of nucleon observables including [1991] M. W. and H. Yoshiki [1993] M. W. and T. Watabe vacuum polarization effects ( based on the work by Kahana-Ripka-Soni, 1984 ) - resolution of - problem - discovery of novel correction missing in corresponding Skyrme model [ ] D. Diakonov et al., H. Weigel et al., M. Wakamatsu et al. application to Parton Distribution Functions of the nucleon Compressed history of CQSM nucleon spin sum rule : importance of

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

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

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 1. Cranked iso-rotation of hedgehog M.F. induces Coriolis coupling slow collective rotation and fast internal motion !

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

virtual transitions from occupied to nonoccupied states double sum

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 manifests most clearly in its predictions for internal partonic structure of the nucleon (or baryons) !

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 nonlocality in space and time in path-integral formalism Answer in schematic form where

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

Factorization theorem Standard approach to DIS physics Soft part is treated as a black box, which should be determined via experiments ! 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 reasonable strategy ! 4. On the role and achievement of CQSM in Deep-Inelastic-Scattering physics PDFs

Merits of CQSM over many other effective models of baryons parameter-free predictions for PDFs Default Lack of explicit gluon degrees of freedom only 1 parameter of the model (dynamical quark mass M) was already fixed from low energy phenomenology 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.

use predictions of CQSM as initial-scale distributions of DGLAP equation initial energy scale is fixed to be (similarly to the GRV PDF fitting program) 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. How should we use predictions of CQSM ? Our general strategy

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

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 !

Isoscalar unpolarized PDF positivity sea-like soft component

Isovector unpolarized PDF - NMC observation -

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

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

New compass data (2005)

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

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 CQSM predicts However, HERMES analysis also denies negative strange-quark polarization favored by most global-analysis heavily depending on inclusive DIS data ! HERMES Collaboration, Phys. Rev. D71 (2005) A recent new global fit including polarized pp data at RHIC D. Florian, R. Sassot, M. Strattmann, W. Vogelsang, hep-ph/ A proposal to measure and via polarized Drell-Yan at JPark

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

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

Within the CQSM, we can analytically confirm this fact M.W. and Y.Ohnishi, Phys. Rev. D67 (2003) existence of this infinite-range correlation is inseparably connected with nontrivial vacuum structure of QCD spontaneous  SB 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 P. Schweitzer, Phys. Rev. D67 (2003)

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

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

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

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

Dirac sea valence total Isovector part of no singularity at

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

To sum up this part manifestation of nontrivial vacuum structure of QCD in hadron observable (2) Existence of this singularity will be observed as (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

two remarkable recent progresses : (1) New COMPASS & HERMES analyses (2) COMPASS, PHENIX, STAR analyses Precise measurements of deuteron spin-dependent structure function with 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 fairly precisely determined ! 6. Nucleon spin problem revisited : current status likely to be small, but still with large uncertainties !

What is our current understanding 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 The remaining 70 % of nucleon spin should be carried by, However, we are in a quite confusing situation concerning the separation of the remaining part. from Lattice QCD from direct measurements by RHIC et al. from Brodsky-Gardner’s argument What carry the rest of the nucleon spin ? safe statement !

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

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

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

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

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

theoretical information on 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) In the following, we treat as an unknown quantity within this range !

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

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

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

Scale dependencies of quark and gluon total angular momentum proportionality !

quarks and gluons respectively carry about 80% and 20% of total angular (and linear) momentum of the nucleon total angular momentum fraction at the nonperturbative scale 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 ! we conjecture that here comes from gluon OAM not from !

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

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

prominent features isovector dominance of quark OAM ! scale indep. 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 dependence of quark OAM

Note that is a decreasing (increasing) function of, since decreasing func.scale indep. Since from evolution equation, we then find that This is really an surprising conclusion, since it means that the isovector combination of quark OAM in the asymptotic limit is solely determined by the neutron beta-decay coupling constant ! Why ? This mysterious conclusion is an inevitable consequence of the following two theoretical postulates : The definition of via Ji’s angular momentum sum rule : The observation that and obey the same evolution equation.

F. Ellinghaus et. al., Eur. Phys. J. C46 (2006) 729. F. Ellinghaus, arXiv: HERMES Collaboration hard exclusive production on the transversely polarized hydrogen target JLab Hall A Collaboration M. Mazous et. al., Phys. Rev. Lett. 99 (2007) analysis of DVCS and Bethe-Heitler processes on the deuteron Z. Ye, hep-ex/ Comparison with obtained from GPD analyses

GPD extraction of our semi-empirical estimate

Summary on nucleon spin problem Accepting the observation that the intrinsic quark spin carries only about 1/3 of the total nucleon spin, what carry the rest of it ? message from our analysis The answer drastically depends on the energy scale of observation ! At the relatively high-energy scale around The decomposition of into and is gauge-dependent, and has large uncertainties. Still, our phenomenological analysis indicates that relatively large at high energy is a consequence of partial cancellation of large and positive and negative with moderate magnitudes.

At the low energy scale of nonperturbative QCD around, we get a very different picture : Importance of quark OAM is consistent with the nucleon picture of CQSM ! Unexpected finding is concerned with flavor decomposition of the quark OAM in the asymptotic limit : we have found that A precise determination of and, especially their scale dependencies is of vital importance to check our scenario on the nucleon spin contents, since and are basically scale-independent and already known ! beta-decay coupling const.

[Backup Slides]

Isoscalar longitudinally polarized PDF New COMPASS data deuteron sign change in low region ! nonlocality correction !

Recently, Anselmino et al., succeeded to get a first empirical information on the transversities from the combined global analysis of the azimuthal asymmetries in semi-inclusive DIS scatterings measured by HERMES and COMPASS groups, and those in processes by the Belle Collaboration. Brief comment on transversities Their results, although with large uncertainties, already indicates a remarkable qualitative difference between transversities and longitudinally polarized PDFs such that No (or less) spin crisis in the tensor channel ! Our theoretical analysis indicates that the cause of this feature can be traced back to the relation

auxiliary field method with nonlinear constraint (by hand) reparametrization relation with NJL model