Generalized Form Factors, Generalized Patron Distributions, and Spin Contents of the Nucleon
description
Transcript of Generalized Form Factors, Generalized Patron Distributions, and Spin Contents of the Nucleon
![Page 1: Generalized Form Factors, Generalized Patron Distributions, and Spin Contents of the Nucleon](https://reader037.fdocuments.in/reader037/viewer/2022110103/56814533550346895db1fd38/html5/thumbnails/1.jpg)
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 )
![Page 2: Generalized Form Factors, Generalized Patron Distributions, and Spin Contents of the Nucleon](https://reader037.fdocuments.in/reader037/viewer/2022110103/56814533550346895db1fd38/html5/thumbnails/2.jpg)
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
![Page 3: Generalized Form Factors, Generalized Patron Distributions, and Spin Contents of the Nucleon](https://reader037.fdocuments.in/reader037/viewer/2022110103/56814533550346895db1fd38/html5/thumbnails/3.jpg)
(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
![Page 4: Generalized Form Factors, Generalized Patron Distributions, and Spin Contents of the Nucleon](https://reader037.fdocuments.in/reader037/viewer/2022110103/56814533550346895db1fd38/html5/thumbnails/4.jpg)
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
![Page 5: Generalized Form Factors, Generalized Patron Distributions, and Spin Contents of the Nucleon](https://reader037.fdocuments.in/reader037/viewer/2022110103/56814533550346895db1fd38/html5/thumbnails/5.jpg)
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
![Page 6: Generalized Form Factors, Generalized Patron Distributions, and Spin Contents of the Nucleon](https://reader037.fdocuments.in/reader037/viewer/2022110103/56814533550346895db1fd38/html5/thumbnails/6.jpg)
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 ?
![Page 7: Generalized Form Factors, Generalized Patron Distributions, and Spin Contents of the Nucleon](https://reader037.fdocuments.in/reader037/viewer/2022110103/56814533550346895db1fd38/html5/thumbnails/7.jpg)
• 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 -
![Page 8: Generalized Form Factors, Generalized Patron Distributions, and Spin Contents of the Nucleon](https://reader037.fdocuments.in/reader037/viewer/2022110103/56814533550346895db1fd38/html5/thumbnails/8.jpg)
• CQSM well reproduces and
at
at the leading order QCD
assuming
• CQSM predicts at model energy scale around
![Page 9: Generalized Form Factors, Generalized Patron Distributions, and Spin Contents of the Nucleon](https://reader037.fdocuments.in/reader037/viewer/2022110103/56814533550346895db1fd38/html5/thumbnails/9.jpg)
• SU(2) : M. W. and T. Kubota, Phys. Rev. D60 (1999) 034022
• SU(3) : M. Wakamatsu, Phys. Rev. D67 (2003) 034005
![Page 10: Generalized Form Factors, Generalized Patron Distributions, and Spin Contents of the Nucleon](https://reader037.fdocuments.in/reader037/viewer/2022110103/56814533550346895db1fd38/html5/thumbnails/10.jpg)
New compass data (2005)
![Page 11: Generalized Form Factors, Generalized Patron Distributions, and Spin Contents of the Nucleon](https://reader037.fdocuments.in/reader037/viewer/2022110103/56814533550346895db1fd38/html5/thumbnails/11.jpg)
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)
![Page 12: Generalized Form Factors, Generalized Patron Distributions, and Spin Contents of the Nucleon](https://reader037.fdocuments.in/reader037/viewer/2022110103/56814533550346895db1fd38/html5/thumbnails/12.jpg)
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)
![Page 13: Generalized Form Factors, Generalized Patron Distributions, and Spin Contents of the Nucleon](https://reader037.fdocuments.in/reader037/viewer/2022110103/56814533550346895db1fd38/html5/thumbnails/13.jpg)
and are well determined from empirical PDF fits
(Example) MRST004 or CTEQ5
since
fundamentally important to know !
: total nucleon AGM identically vanishes ! important observation
![Page 14: Generalized Form Factors, Generalized Patron Distributions, and Spin Contents of the Nucleon](https://reader037.fdocuments.in/reader037/viewer/2022110103/56814533550346895db1fd38/html5/thumbnails/14.jpg)
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 )
![Page 15: Generalized Form Factors, Generalized Patron Distributions, and Spin Contents of the Nucleon](https://reader037.fdocuments.in/reader037/viewer/2022110103/56814533550346895db1fd38/html5/thumbnails/15.jpg)
CQSM
LHPC
AGM form factor
AGM
![Page 16: Generalized Form Factors, Generalized Patron Distributions, and Spin Contents of the Nucleon](https://reader037.fdocuments.in/reader037/viewer/2022110103/56814533550346895db1fd38/html5/thumbnails/16.jpg)
natural spin decomposition in Breit frame
corresponds to Sachs decomposition of electromagnetic F.F.
3. Relation of GFF with unpolarized GPDs
![Page 17: Generalized Form Factors, Generalized Patron Distributions, and Spin Contents of the Nucleon](https://reader037.fdocuments.in/reader037/viewer/2022110103/56814533550346895db1fd38/html5/thumbnails/17.jpg)
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
![Page 18: Generalized Form Factors, Generalized Patron Distributions, and Spin Contents of the Nucleon](https://reader037.fdocuments.in/reader037/viewer/2022110103/56814533550346895db1fd38/html5/thumbnails/18.jpg)
and its canonical part in CQSM
![Page 19: Generalized Form Factors, Generalized Patron Distributions, and Spin Contents of the Nucleon](https://reader037.fdocuments.in/reader037/viewer/2022110103/56814533550346895db1fd38/html5/thumbnails/19.jpg)
and its canonical part in CQSM
![Page 20: Generalized Form Factors, Generalized Patron Distributions, and Spin Contents of the Nucleon](https://reader037.fdocuments.in/reader037/viewer/2022110103/56814533550346895db1fd38/html5/thumbnails/20.jpg)
anomalous part
no Dirac sea contribution
small valence contribution to
Dirac sea contribution valence contribution
cancel !
![Page 21: Generalized Form Factors, Generalized Patron Distributions, and Spin Contents of the Nucleon](https://reader037.fdocuments.in/reader037/viewer/2022110103/56814533550346895db1fd38/html5/thumbnails/21.jpg)
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.
![Page 22: Generalized Form Factors, Generalized Patron Distributions, and Spin Contents of the Nucleon](https://reader037.fdocuments.in/reader037/viewer/2022110103/56814533550346895db1fd38/html5/thumbnails/22.jpg)
• 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
![Page 23: Generalized Form Factors, Generalized Patron Distributions, and Spin Contents of the Nucleon](https://reader037.fdocuments.in/reader037/viewer/2022110103/56814533550346895db1fd38/html5/thumbnails/23.jpg)
• 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
![Page 24: Generalized Form Factors, Generalized Patron Distributions, and Spin Contents of the Nucleon](https://reader037.fdocuments.in/reader037/viewer/2022110103/56814533550346895db1fd38/html5/thumbnails/24.jpg)
The nucleon spin contents at
![Page 25: Generalized Form Factors, Generalized Patron Distributions, and Spin Contents of the Nucleon](https://reader037.fdocuments.in/reader037/viewer/2022110103/56814533550346895db1fd38/html5/thumbnails/25.jpg)
If evolved down to low energy model scale
increasing increasing slowly increasing
Nearly half of nucleon spin comes from quark OAM !
around
![Page 26: Generalized Form Factors, Generalized Patron Distributions, and Spin Contents of the Nucleon](https://reader037.fdocuments.in/reader037/viewer/2022110103/56814533550346895db1fd38/html5/thumbnails/26.jpg)
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 :
![Page 27: Generalized Form Factors, Generalized Patron Distributions, and Spin Contents of the Nucleon](https://reader037.fdocuments.in/reader037/viewer/2022110103/56814533550346895db1fd38/html5/thumbnails/27.jpg)
• 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
![Page 28: Generalized Form Factors, Generalized Patron Distributions, and Spin Contents of the Nucleon](https://reader037.fdocuments.in/reader037/viewer/2022110103/56814533550346895db1fd38/html5/thumbnails/28.jpg)
![Page 29: Generalized Form Factors, Generalized Patron Distributions, and Spin Contents of the Nucleon](https://reader037.fdocuments.in/reader037/viewer/2022110103/56814533550346895db1fd38/html5/thumbnails/29.jpg)
[ Addendum ]
A conjecture on the net quark contribution to nucleon AGM
Note that, in CQSM
small !
probably small !
![Page 30: Generalized Form Factors, Generalized Patron Distributions, and Spin Contents of the Nucleon](https://reader037.fdocuments.in/reader037/viewer/2022110103/56814533550346895db1fd38/html5/thumbnails/30.jpg)
![Page 31: Generalized Form Factors, Generalized Patron Distributions, and Spin Contents of the Nucleon](https://reader037.fdocuments.in/reader037/viewer/2022110103/56814533550346895db1fd38/html5/thumbnails/31.jpg)
Dirac sea
valence
CQSM prediction for isosinglet
![Page 32: Generalized Form Factors, Generalized Patron Distributions, and Spin Contents of the Nucleon](https://reader037.fdocuments.in/reader037/viewer/2022110103/56814533550346895db1fd38/html5/thumbnails/32.jpg)
CQSM prediction for isovector GPD
![Page 33: Generalized Form Factors, Generalized Patron Distributions, and Spin Contents of the Nucleon](https://reader037.fdocuments.in/reader037/viewer/2022110103/56814533550346895db1fd38/html5/thumbnails/33.jpg)
Pionic interpretation of central peak due to polarized Dirac sea
may be confirmed by investigating dependence of
![Page 34: Generalized Form Factors, Generalized Patron Distributions, and Spin Contents of the Nucleon](https://reader037.fdocuments.in/reader037/viewer/2022110103/56814533550346895db1fd38/html5/thumbnails/34.jpg)
Further support may be obtained by investigating the canonical part
of
NMC observation
![Page 35: Generalized Form Factors, Generalized Patron Distributions, and Spin Contents of the Nucleon](https://reader037.fdocuments.in/reader037/viewer/2022110103/56814533550346895db1fd38/html5/thumbnails/35.jpg)
Scale dependencies of
decreasing
increasing
increasing
![Page 36: Generalized Form Factors, Generalized Patron Distributions, and Spin Contents of the Nucleon](https://reader037.fdocuments.in/reader037/viewer/2022110103/56814533550346895db1fd38/html5/thumbnails/36.jpg)
Scale dependencies of