The role of orbital angular momentum
in the internal spin structure of the nucleon
based on collaboration with Y. Nakakoji, H. Tsujimoto
1. Current status of nucleon spin problem
2. Role of CQSM in nucleon structure function physics
3. CQSM analysis of unpolarized GPD
4. Model independent analysis of nucleon spin contents
5. Flavor decomposition of nucleon spin (model dependent)
6. Summary
Plan of Talk
M. Wakamatsu (Osaka University) : PACSPIN-07
Early stage proposals to explain very small quark spin fraction
(I) Gluon spin hypothesis
(A) naive claim
(B) axial-anomaly of QCD
(II) Quark orbital angular momentum hypothesis
(III) Gluon orbital angular momentum hypothsis
no serious consideration until recently !
OK if The question remains why !
1. Current status of nucleon spin problem
unfavored ? is small, because is large !
but need very large !
Two remarkable recent progresses :
(1) New COMPASS & HERMES analyses
(2) COMPASS, PHENIX, STAR analyses
• Precise measurements of deuteron spin-dependent structure function 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
Still totally unknown are and !
Recent interesting observation concerning
“Evidence for the Absence of Gluon Orbital Angular Momentum
in the Nucleon”, S.J. Brodsky and S. Gardner, Phys. Let. B643
The Sivers mechanism for the single-spin asymmetry in the
unpolarized lepton scattering from a transversely polarized nucleon
is driven by the orbital angular momentum of quarks and gluons.
They argued that small single-spin asymmetry on the deuteron
target measured by the COMPASS collaboration is an
indication of small gluon OAM !.
If true, what remains is alone ?
Skyrme model (Ellis-Karliner-Brodsky, 1988)
Chiral Quark Soliton Model (Wakamatsu-Yoshiki, 1991)
Importance of quark orbital angular momentum
Collective quark motion generating rotating M.F. of hedgehog shape
In particular, since the latter is an effective quark theory
- Large chiral soliton picture of the nucleon -
Spin S.R
appearing in high-energy DVCS & DVMP processes
Ji’s angular momentum sum rule
new recent development
through Generalized Parton Distributions (GPDs)
We need more direct empirical information on
possibility of direct measurement of
Factorization
Hard part :
Soft part :
Perturbative QCD
Nonpurturbative QCD
Lattice QCD Effective models of QCD
• most promising in the long run
- still at incomplete stage -
• continuum limit & chiral limit ?
• only lower moments of PDF
• physical interpretation ?
So many !
Necessary condition of good model,
which has predictive power ?
• able to explain many observables
with less parameters !
2. Role of CQSM in nucleon structure function (DIS) physics
Black Box
Advantages of Chiral Quark Soliton Model
parameter-free predictions for PDFs
• a nucleon is a composite of valence quarks and infinitely many
Dirac sea quarks moving in a slowly rotating M.F. of hedgehog shape
• field theoretical nature of the model (proper inclusiuon of polarized
Dirac-sea quarks) enables reasonable estimation of antiquark dist.
Default
Lack of explicit gluon degrees of freedom
• only 1 parameter of the model (dynamical quark mass ) was
already fixed from low energy phenomenology
How to use predictions of this low energy model for parton distributions ?
We follow the spirit of
* M. Glueck, E. Reya, and A. Vogt, Z. Phys. C67 (1995) 433
They start the QCD evolution at the extraordinary low energy scales like
Even at such low energy scales, their PDF fit turns out to need
nonperturbatively generated sea-quarks (and some gluons)
which may be connected with the effects of
meson clouds
Our general strategy
• use predictions of CQSM as initial-scale distributions of DGLAP eq.
for flavor SU(2) CQSM
for flavor SU(3) CQSM
• initial energy scale is fixed to be
pQCD is barely applicable ?
On the Applicability of pQCD ?
NLO
Parameter free predictions of the CQSM : 3 twist-2 PDFs
Transversities [3rd twist-2 PDF]
• Totally different behavior of Dirac-sea contributions in different PDFs !
Isoscalar unpolarized PDF
positivity
sea-like soft component
Isovector unpolarized PDF
Isoscalar longitudinally polarized PDF
New COMPASS data
CQSM
New COMPASS and HERMES fits for in comparison with CQSM prediction
[old]
Isovector longitudinally polarized PDF
CQSM predicts
This means that antiquarks gives sizable positive contribution to Bjorken S.R.
denied by the HERMES analysis of semi-inclusive DIS data
However, HERMES analysis also denies negative strange-quark polarization
favored by the global-analysis heavily depending on inclusive DIS data !
We need more complete understanding of
spin-dependent fragmentation mechanism
• HERMES Collabotation, Phys. Rev. D71 (2005) 012003
Transversities vs. longitudinally polarized PDF : CQSM predictions
• M. Wakamatsu, arXiv:0705.2917 [hep/ph]
not so small
[global fit] M. Anselmino et. al., Phys. Rev. D75 (2007) 054032.
global fit
global fit
natural spin decomposition in Breit frame
corresponds to Sachs decomposition of electromagnetic F.F.
3. CQSM analyses of unpolarized GPDs
magnetic moment desity
in Feynman x-space
angular momentum density
in Feynman x-space
canonical part anomalous part
canonical part anomalous part
quark number dist.
quark momentum dist.
1st and 2nd moment sum rules
CQSM predictions for GPDs
(A) Isovector channel
(B) Isoscalar channel
• M.W. and H. Tsujimoto, Phys. Rev. D71 (2005) 074001
• J. Ossmann et. al., Phys. Rev D70 (2005) 034011
forward limit of GPDs
forward limit of GPDs
So far, only the forward limit was calculated.
• M.W. and Y. Nakakoji, Phys. Rev. D74 (2006) 054006
• See also M.W. and Y. Nakakoji above
magnetic moment dist.
in Feynman x-space
(A) Isovector magnetic moment distribution :
a prominent feature of CQSM prediction for
The contribution of deformed Dirac sea quarks has a large
and sharp peak around Since this large Dirac-sea contribution to
is nearly symmetric with respect to , it gives a
significant contribution to the 1st moment
but no contribution to the 2nd moment
Since partons with are at rest in the longitudinal direction
its large contribution to the first moment must come
from transverse motion of quarks and antiquarks
If one remembers the important role of 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
Interpretation of sharp peak of around
in the transverse direction
validity of claimed picture may be confirmed by investigating
dependence of
positivity of antiquark dist.
(B) Isoscalar magnetic moment distribution :
anomalous part
no net Dirac sea contribution
small valence contribution to
Dirac sea contribution valence contribution
cancel !
two possibilities
total nucleon anomalous gravitomagnetic moment (AGM) vanishes !
important observation (it is a sound fact)
It follows from
4. Model independent prediction for nucleon spin contents
anomalous gravitomagnetic form factor
CQSMLHPC2005
Lattice QCD
within the CQSM
LHPC2005
QCDSF2004
1st important observation
We are then led to surprisingly simple relations :
Not only CQSM but also LHPC & QCDSF lattice simulations
indicate smallness of quark AGM
In the following, we assume smallness of
and set them 0, for simplicity.
• O.V. Teryaev, hep-ph/0004376 ; hep-ph/0612205
2nd important observation
(I) The quark- and gluon- momentum fractions, and ,
are empirically fairly precisely determined.
In fact, MRST2004 & CTEQ5 QCD fits give almost the same
numbers for these quantities below
[Reason] forming spatial moments of and does not
change the short-distance singularity of the operators !
(II) The above proportionality relations holds scale-independently,
since the evolution equations for and
are exactly the same !
The above evolution equations at NLO may be used to estimate
and at lower energy scales !
Evolve down
MRST2004 evolved down to
Gluons carry about 20% of linear and total angular momentum
fraction even at this low energy scale of nonperturbative QCD ! We conjecture that this comes from gluon OAM not from !
This statement is not inconsistent with the recent observation by
Brodsky and Gardener, since what would be related to Sivers
mechanism is the anomalous part of gluon OAM.
On the other hand, our postulated identity, implies
that gluon OAM comes totally from its canonical orbital motion,
not from the anomalous contribution related to GPD
Nucleon spin contents extracted from
cross over around
CQSM
5. Flavor decomposition of nucleon spin (model dependent)
Ji’s angular momentum sum rule
known known
known
Key quantity is quark AGM :
unknown
sensitive to models !
LHPC2005
QCDSF2004
CQSM2006
LHPC2007 (new)
ChPT extrapolation
Lattice and CQSM predictions for Isovector AGM :
Most recent LHPC results on
• Ph. Hagler et. al., arXiv : 0705.429 [hep-lat]
Main conclusion at
[Cf.] MRST & New COMPASS, HERMES with
Assuming
Transverse target-spin asymmetry of exclusive production on proton
• Hermes Collaboration, arXiv:0707.2486 [hep-ex]
far from conclusive yet !
6. Summary and Conclusion
: long-lasting dispute over this issue.
Based only upon
smallness of flavor singlet quark AGM :
model independent estimate for nucleon spin contents !
Around , there is a crossover where
but
• Flavor decomposition cannot be performed quantitatively yet, since it
depend on highly model-dependent quantity
Still we can conclude that
As increases, decreases rapidly, but the magnitude of
remains large such that even around the
a scale of few GeV.
• This peculiar property of the quark OAMs comes from the way of
their defintion through Ji’s angular momentum as well as the relation
are interesting themselves,
since they give distributions of anomalous magnetic moments
anomalous magnetic moment distribtion may also be related to
Sivers function measured by SSA of semi-inclusive reactions ?
origin of AMM & AGM & OAM of composite particle
in Feynman momentum x-space
We hope rapid progress of experimental GPD studies !
[Appendix]
Intimate relation between Sivers function and anomalous magnetic distribution ?
• Z. Lu and I. Schmidt, hep-ph / 0611158
within the diquark model in the light-front formalism
anomalous magnetic moment distribution
• scalar diquark
• final state interation necessary for Sivers mechanism is one-gluon-exchange
Sivers function and its lowest -moment
Main assumptions
LO evolution equation
Request for future Lattice QCD studies
More refined check of the relation
A) Larger lattice space, higher statistics, etc.
B) Stability againt the variation of pion mass, ……
More reliable evaluation of
A) Simulation with smaller pion mass
or
B) Reliable chiral extrapolation ( ex., by using chiral PT )
On the pion mass dependence of observables
with
and
After obtaining self-consistent soliton solutions for several values of
, we calculate nucleon observables in question.
Basic model laglangian
New COMPASS QCD fits at NLO
New HERMES QCD fits at NLO
s-quark polarization
Remember that
small !
probably smaller !
Reasoning to show smallness of