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
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