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 measurement, 1988 )

gluon OAM :

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

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

importance of quark orbital angular momentum

collective motion of quarks

in rotating hegdhog M.F.

dominance of quark OAM

- chiral soliton picture of the nucleon -

axial anomaly of QCD ?

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

possible importance of gluon polarization

Perturbative aspect factorization scheme dependence of PDF

Nonperturbative aspect totally left unknown !

but

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

2. Generalized form factor and quark angular momentum

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)

Origin of the terminology Anomalous Gravitomagnetic Moment

energy momentum tensor coupled to graviton

electromagnetic current coupled to photon

Dirac F.F.

Pauli F.F.

total nucleon anomalous gravitomagnetic moment (AGM) vanishes!

three possibilities

recent lattice simulation by LHPC Collaboration support (2)

net quark contribution to nucleon AGM vanishes !

but

denies the possibility (3)

( O.V.Teryaev, hep-ph/9904376)

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

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

equal partition of momentum and total angular momentum !

analysis of LHPC group strongly indicates

Once accepting this postulate ( and remembering Ji’s sum rule )

net quark contribution to nucleon AGM vanishes !

( Teryaev, hep-ph/9904376 & hep-ph/9803403 )

now we can reach more surprising conclusion, based only upon

two already known observations at low energies

quark and gluon fields shares about 70 % and 30 % of

the total nucleon momentum at low energy scale

(Ex.) GRV fit of unpolarized PDF at NLO

observation (1)

This means, at low energy :

quark OAM carries nearly half of nucleon spin !

We are inevitably led to the conclusion :

observation (2) : just the EMC & subsequent experiments

natural spin decomposition in Breit frame

corresponds to Sachs decomposition of electromagnetic F.F.

3. unpolarized GPD :

forward limit in Chiral Quark Soliton Model

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 unintegrated sum rule

spin distribution momentum distribution

important constraints for the anomalous part

difference of : not extremely large

: I = 0 part (Ossmann et al.)

momentum dist.

spin dist.

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 deformed Dirac sea quarks has a large

and sharp peak around

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

motion of quarks and antiquarks in the transverse plane.

validity of the proposed physical picture may be confirmed if one can experimentally extract 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

in smaller x region

long range tail in direction

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]

spin dist.

momentum dist.

4. Summary and Conclusion

: long-lasting dispute over this issue.

Relying only upon

• Ji’s sum rule :

• empirical PDF information evolved down to LE scale :

- model independent conclusion -

• absence of flavor singlet quark AGM :

• For more definite conformation, experimental extraction of

unpolarized spin-flip GPD (forward limit) is indispensable

• are interesting themselves,

since they give distributions of anomalous magnetic moments

• 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 ?

in Feynman momentum x-space

[ Addendum ]

especially significant for longitudinally polarized PDF

in the flavor-singlet channel due to axial anomaly

(Ex.)

empirical PDF fit

Factorization scheme dependence of PDF

AB scheme

compatible with the naive NRQM ?

puzzle is hidden in unknown mechanism of large gluon polarization

is generally scale-dependent beyond L.O.

but this dependence is fairly weak !

MSbar scheme