generalized form factors, generalized patron distributions, and spin contents of the nucleon with y....
TRANSCRIPT
Generalized Form Factors, Generalized Patron Distributions, and Spin Contents of the Nucleon
with Y. Nakakoji (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 ?
Nucleon Spin Puzzle : ( EMC measurement, 1988 )
It is meaningless to talk about the spin contents of the nucleon
without reference to the energy scale of observation
When we talk about nucleon spin contents naively, we should regard
that we are thinking of it at low energy scale of nonperturbative QCD
• grows rapidly as increases, even though it is
small at low energy scale
• decreases rapidly to compensate the increase of
(I) Scale dependence of polarized PDF
two cautions when discussing nucleon spin contents
(II) Factorization scheme dependence of polarized PDF
2 popular factorization schemes for longitudinally polarized PDF
Nonperturbative aspect is totally left unknown !
- arising from axial-anomaly of QCD -
Perturbative aspect of axial-anomaly is fully understood
no predictive power for the magnitude of
Compatible with Naïve Quark Model ?
See, however, the recent COMPASS measurement !
Empirical PDF fits based on the two factorization schemes
Relation between the scheme and the AB scheme
MSbar scheme
AB scheme
In fact, COMPASS group pointed out that, based on
around , a value of of about 3 would be
required to obtain the expected of the order of 0.6.
incompatible with the recent COMPASS data !
• “Gluon polarization in the nucleon from quasi-real photoproduction
of high- hadron pairs”, hep-ex / 0511028
What about ?
“Evidence for the Absence of Gluon Orbital Angular Momentum
in the Nucleon”, S.J. Brodsky and S. Gardner, hep-ph / 0608219.
• The Sivers mechanism for the single-spin asymmetry in the
unpolarized lepton scattering from a transversely polarized nucleon
is driven by the OAM of quarks and gluons.
• They claim that small single-spin asymmetry measured by
the COMPASS collaboration on the deuteron target is an
indication of small gluon OAM !.
What remains is alone ?
• 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 hegdehog M.F.
dominance of quark OAM
- chiral soliton picture of the nucleon -
• CQSM well reproduces and
at
at the leading order QCD
assuming
• CQSM predicts at model energy scale around
• SU(2) : M. W. and T. Kubota, Phys. Rev. D60 (1999) 034022
• SU(3) : M. Wakamatsu, Phys. Rev. D67 (2003) 034005
New compass data (2005)
We repeat the question again :
only experiments can settle the despute !
appearing in high-energy DVCS & DVMP processes
Ji’s angular momentum sum rules
Recent noteworthy development is
possibility of direct measurement of
through Generalized Parton Distributions (GPDs)
2. Generalized form factors and Ji’s angular momentum sum rule
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)
and are well determined from empirical PDF fits
(Example) MRST004 or CTEQ5
since
fundamentally important to know !
: total nucleon AGM identically vanishes ! important observation
two possibilities
The 1st possibility, i.e. the absence of the net quark contribution to
the anomalous magnetic moment of the nucleon :
seems to be favored by
LHPC & QCDSF lattice simulations ( as well as CQSM )
CQSM
LHPC
AGM form factor
AGM
natural spin decomposition in Breit frame
corresponds to Sachs decomposition of electromagnetic F.F.
3. Relation of GFF with unpolarized GPDs
Mellin moment sum rules relevant to our discussion
(1) 1st moment (magnetic moment) sum rule
(2) 2nd moment (angular momentum) sum rule
unintegrated Ji’s sum rule
canonical part anomalous part
familiar unpolarized PDF
and its canonical part in CQSM
and its canonical part in CQSM
anomalous part
no Dirac sea contribution
small valence contribution to
Dirac sea contribution valence contribution
cancel !
model independet prediction for nucleon spin contents
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.
• The quark- and gluon-momentum fractions, and ,
are empirically well determined.
(ex) MRST2004 , CTEQ5 PDF fits
• The above proportionality relations holds scale-independently,
since the evolution equations for and
are exactly the same !
[Reason] forming spatial moments of and does not
change the short-distance singularity of the oparotors !
Important facts
• There also exist phenomenological fits for the longitudinally
polarized PDF, which contains information on and ,
although with larger uncertainties, compared with unpolarized case.
These are enough to determine quark and gluon OAM as function of energy scale, through the relations :
(ex) LSS2005 , DNS2005, GRSV2000, AAC PDF fits
The nucleon spin contents at
If evolved down to low energy model scale
increasing increasing slowly increasing
Nearly half of nucleon spin comes from quark OAM !
around
4. Summary and Conclusion
: long-lasting dispute over this issue.
Based only upon
• Ji’s sum rule :
Empirical PDF information evolved down to LE scale around 600MeV
- model independent conclusion -
• absence of flavor singlet quark AGM :
• For obtaining more definite conclusion, 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 parton distributions
origin of AMM & AGM & OAM of composite particle
in Feynman momentum x-space
[ Addendum ]
A conjecture on the net quark contribution to nucleon AGM
Note that, in CQSM
small !
probably small !
Dirac sea
valence
CQSM prediction for isosinglet
CQSM prediction for isovector GPD
Pionic interpretation of central peak due to polarized Dirac sea
may be confirmed by investigating dependence of
Further support may be obtained by investigating the canonical part
of
NMC observation
Scale dependencies of
decreasing
increasing
increasing
Scale dependencies of