GPD and underlying spin structure of the Nucleon

M. Wakamatsu and H. Tsujimoto (Osaka Univ.)

1. Introduction

Still unsolved fundamental puzzle in hadron physics

If intrinsic quark spin carries little of total nucleon spin

what carries the rest of nucleon spin ?

quark OAM : gluon polarization :

Nucleon Spin Puzzle (EMC, 1988)

gluon OAM :

axial anomaly of QCD ?

• Skyrme model (Ellis-Karliner-Brodsky, 1988)

• Chiral Quark Soliton Model (Wakamatsu-Yoshiki, 1991)

no theoretical prediction for the magnitude of

• G. Altarelli and G.G. Ross, 1988

• R.D. Carlitz, J.C. Collins and A.H. Mueller, 1988

• A.V. Efremov and O.V. Teryaev, 1988

importance of quark orbital angular momentum

possible importance of gluon polarization

It is meaningless to talk about the spin contents of the nucleon

without reference to the energy scale of observation

• grows rapidly as increases, even though it is small

at low energy scale

• decreases rapidly to compensate the increase of

When we talk about nucleon spin contents naively, we think of it

at low energy scale of nonperturbative QCD

CQSM predicts

important remark

The question is :

only experiments can answer it !

(Compass ,2004)

direct measurement of

Generalized Parton Distributions via DVCS & DVMP

Ji’s quark angular momentum sum rules

direct measurement of via photon-gluon fusion processes

: small ?

asymmetry of high hadron pairs

equal partition of momentum and total angular momentum !

2. Generalized form factor and quark angular momentum

total quark angular momentum (Ji’s sum rule)

anomalous gravitomagnetic moment (AGM) seems to vanish

observation at low energy scale :

Quark OAM carries about half of nucleon spin !

We are then necessarily led to the conclusion :

(from polarized DIS)

natural decomposition in Breit frame

corresponds to Sachs decomposition of electromagnetic F.F.

3. unpolarized GPD :

forward limit in QCSM

I=0 part : J. Ossmann et al., Phys. Rev. D71 (2005)034001

I=1 part : M. W. and H. Tsujimoto, Phys. Rev. D71 (2005) 074001

1st and 2nd moment sum rules

CQSM contains no gluon fields

story of I = 0 part of

: (Ossmann et al.)

Dirac sea

valence

spin versus momentum distributions : (I=0 case)

using Ji’s relation

spin distribution momentum distribution

important constraints

difference of : not extremely large

: I = 0 part (Ossmann et al.)

story of I = 1 part of

model expression

1st moment sum rule

gives distribution of nucleon isovector magnetic moment

in Feynman momentum x-space

a prominant feature of CQSM prediction for

• Since partons with are at rest in the longitudinal direction,

• The contribution of Dirac sea quarks has a large and sharp peak

If one remembers the important role of the 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

its large contribution to must come from the

around

motion of quarks and antiquarks in the transverse plane.

proposed physical picture may be confirmed if one can experimentally determine the following observable

Impact parameter dependent parton distribution

• M. Burkardt, Phys. Rev. D62 (2000) 071503

• M. Burkardt, Int. J. Mod. Phys. A18 (2003) 173

• J.P. Ralston and B. Pire, Phys. Rev. D66 (2002) 111501

anticipated impact parameter-dependent distribution

long range tail in direction

in smaller x region

spin versus momentum distributions : (I=1 case)

assuming Ji’s relation

spin distribution momentum distribution

big difference with I = 0 case

difference of : fairly large

[Note]

4. Summary and Conclusion

There has been long-lasting dispute over this issue.

Using the following information

• Ji’s sum rule :

• absence of flavor singlet quark AGM :

• empirical PDF information down to LE scale :

• More definite conclusion will be obtained through direct

experimental extraction of

• are interesting themselves,

since they give distribution of anomalous magnetic moments

in Feynman momentum x-space

• More detailed information would be obtained from

impact-parameter dependent distributions

origin of anomalous magnetic moment of composite particle

• Can we see Chiral Enhancement near 　 or large ?

[Appendix]

• H. Hagler et. al., Phys. Rev. D68 (2003) 034505

[Addendum] chirally odd twist-3 distribution of the nucleon

(I) QCD-based analysis

where

consider chiral limit ( ), for simplicity

contradicts CLAS observation ?

H. Avakian et. al., Phys. Rev. D69 (2004) 112004

indicate except for singularity

(II) Chiral Quark Soliton Model

1st and 2nd moment sum rules

proportional to dynamically generated quark mass M,

which vanishes in the perturbative QCD vacuum

Experimental confirmation of nontrivial structure of at

tool to probe the role ofnonperturbative QCD dynamics in DIS

dynamically generated quark mass