1. Possible studies of structure functions at JLab
Shunzo Kumano
High Energy Accelerator Research Organization (KEK)
Graduate University for Advanced Studies (GUAS)
Our codes are available for
Nuclear PDFs:
Polarized PDFs:
Fragmentation functions:
Q2 evolutions:
Workshop on the Jefferson Laboratory Upgrade to 12 GeV
Sept Nov. 20, 2009, INT, Seattle, USA
November 5, 2009 1

2. Outline Three different topics. I will stop when time runs out.
1. Nuclear modifications of R = FL / FT at large x
We (M. Ericson and SK) insist that
nuclear modifications of R = FL / FT should exist at large x.
2. From nucleon-spin crisis to tensor-structure crisis (?)
Tensor structure functions of spin-1 hadrons (b1, b2, …).
3. ∆ g(x) determination by accurate g1 measurements
Accurate g1 by JLab E07-011
 NLO gluon term in g1 could be determined.

3. Nuclear modifications of R = FL / FT at large x
Ref. M. Ericson and SK, Phys. Rev. C 67 (2003)

4. ' Nuclear effect on R = FL / FT by HERMES L, T X p RA /RD Q2 (GeV2)
HERMES, K. Ackerstaff el al., PL B 475 (2000) 386;
Erratum, PL B567 (2003) 339 [hep-ex/ ; hep-ex/ ]. p X '
L, T
(2000) (2003)
Q2 (GeV2)
RA /RD

5. Nuclear effects on R by CCFR/NuTeV
U.-K. Yang et al., PRL 87 (2001)
CCFR
HERMES
SLAC
note
No significant deviation is measured
from the nucleon case ( ).
No large nuclear modification
of R is observed in +Fe !
(note: CCF/NuTeV target is Fe)

6. M. Ericson and SK, Phys. Rev. C 67 (2003) 022201
 Submitted (Nov. 30, 2002) just after the HERMES correction paper (Oct. 31, 2002).
 Nuclear modifications of transverse-longitudinal ratio
do exist in medium and large-x regions,
although the modifications do not seem to exist at small x
within experimental errors according to the revised
HERMES paper.
 Mechanisms
(1) Transverse nucleon motion
 T-L admixture of nucleon structure functions.
(2) Binding and Fermi-motion effects in the spectral function.

7. Formalism Projection operators of W1A and W2A
Longitudinal and transverse components

8. Formalism (continued)

9. Results R x x admixture effects 10 GeV Q = 100 10 GeV Q = 100
0.1
0.2
0.3
0.4
0.6
0.8 1 x R 14 N 10
GeV 2 Q =
100
0.95 1
1.05
1.1
0.2
0.4
0.6
0.8 x
without L-T mixing 10
GeV 2 Q =
100
admixture effects

10. After the HERMES (CCFR/NuTeV)
re-analysis, people tend to lose interest
in the nuclear effect on R.
However, we claim that nuclear
modification should exist in medium
and large-x regions.
Physical origins
 transverse-longitudinal admixture
due to the transverse Fermi motion
 binding and Fermi motion effects
in the spectral function
In the kinematical region of
our prediction, data does not
exist.
Need future experimental
investigations at
JLab, EIC,  factory, …

11. Almost same for p an d, but at 0.04 < x < 0.32.
JLab measurements in 2007
• V. Tvaskis et al., PRL 98 (2007)
• Lingyan Zhu (Hampton Univ),
personal communications (2009).
Badelek, Kwiecinski, Stasto (1997)
E99-118
MRST-2004
GRV-1995
Almost same for p an d, but at 0.04 < x < 0.32.
In any case, nuclear modifications
should be small for the deuteron.
Importance of future JLab measurements
for heavier nuclei, especially at large x (>0.4).

12. From nucleon-spin crisis to tensor-structure crisis (?)
Refs. F. E. Close and SK, Phys. Rev. D 42 (1990) 2377,
M. Hino and SK, Phys. Rev. D 59 (1999) ;
D 60 (1999) ,
SK and M. Miyama, Phys. Lett. B 497 (2000) 149,
T.-Y. Kimura and SK, Phys. Rev. D 78 (2008)

13. References on tensor structure function b1
Theoretical formalism for polarized electron-deuteron
deep inelastic scattering
P. Hoodbhoy, R. L. Jaffe, and A. Manohar, NP B312 (1989) 571.
[ L. L. Frankfurt and M. I. Strikman, NP A405 (1983) 557. ]
HERMES experimental result
A. Airapetian et al., Phys. Rev. Lett. 95 (2005)
Our works
Sum rule for b1
F. E. Close and SK, Phys. Rev. D 42 (1990) 2377.
Projections to F1, F2, g1, g2, b1, …, b4 from W 
T.-Y. Kimura and SK, Phys. Rev. D 78 (2008)

14. Motivation  Spin structure of the spin-1/2 nucleon
Nucleon spin puzzle: This issue is not solved yet,
but it is rather well studied theoretically and experimentally.
 Spin-1 hadrons (e.g. deuteron)
Tensor-structure puzzle (???)
There are some theoretical studies especially on tensor structure
in electron-deuteron deep inelastic scattering.
 HERMES experimental results
A few investigations have been done for polarized
proton-deuteron processes.
 J-PARC, COMPASS, U70, GSI-FAIR, RHIC … experiment ?

15. Structure function b1 in a simple example
Spin-1 particles (deuteron, mesons)
b1 = 0
b1  0: New field of high-energy spin physics
with orbital angular momenta.
only in S-wave
The b1 probes a dynamical aspect of hadron structure
beyond simple expectations of a naive quark model.
Description of tensor structure
by quark-gluon degrees of freedom

16. Electron scattering from a spin-1 hadron
P. Hoodbhoy, R. L. Jaffe, and A. Manohar, NP B312 (1989) 571.
[ L. L. Frankfurt and M. I. Strikman, NP A405 (1983) 557. ]

17. Projections to F1, F2, …, b4 from W
T.-Y. Kimura and SK,
PRD 78 (2008)

18. Structure
Functions
Parton
Model

19. Sum rule for b1 Elastic amplitude in a parton model F.E.Close and SK,
PRD42, 2377 (1990).
Elastic amplitude in a parton model

20. Macroscopically If the sum-rule violation is shown by experiment,
it suggests antiquark
tensor polarization.

21. HERMES results on b1 deuteron positron 27.6 GeV/c
A. Airapetian et al. (HERMES), PRL 95 (2005)
deuteron
positron
27.6 GeV/c
Drell-Yan experiments probe
these antiquark distributions.

22. Actual experimental proposals at J-PARC: P04, P24
Antiquark
distributions
 +
 –  q
E866
E906
J-PARC
 It should be possible to use polarized proton-deuteron Drell-Yan processes
to measure the tensor polarized distributions.

23. References for tensor structure in Drell-Yan
• General formalism for polarized Drell-Yan processes
with spin-1/2 and spin-1 hadrons
M. Hino and SK, Phys. Rev. D59 (1999)
• Parton-model analysis of polarized Drell-Yan processes
M. Hino and SK, Phys. Rev. D60 (1999)
• An application: Possible extraction of polarized
light-antiquark distributions from Drell-Yan
SK and M. Miyama, Phys. Lett. B497 (2000) 149.
Comments on the situation
• There was a feasibility study for polarized deuteron beam at RHIC:
E. D. Courant, BNL-report (1998).
• No actual experimental progress with hadron facilities.
• Future: J-PARC, COMPASS, U70, GSI-FAIR, RHIC, …

24. Spin asymmetries in the parton model
Unpolarized cross section
Spin asymmetries

25. Possibly, opening of tensor-structure crisis at JLab!?
Possible JLab measurements
HERMES (2005)
See P. Hoodbhoy et al.,
NP B312 (1989) 571.
Possible JLab measurements
in this x region.
• HERMES data have large errors
 Important contribution from JLab.
See also a theoretical model by G. A. Miller,
in Topical Conference on Electronuclear physics
with Internal Targets, edited by R. G. Arnold
(World Scientific, 1990).
Possibly, opening of tensor-structure crisis at JLab!?

26. Determination of gluon polarization by accurate g1 measurements
Refs. AAC (Asymmetry Analysis Collaboration),
Y. Goto et al., Phys. Rev. D 62 (2000) ;
M. Hirai, SK, N. Saito, Phys. Rev. D 69 (2004) ;
74 (2006) ;
M. Hirai, SK, Nucl. Phys. B 813 (2009) 106.

27. Nucleon Spin Nucleon Spin: Naïve Quark Model QCD
Sea-quarks and gluons?
Orbital angular momenta ?
Electron / muon scattering
Almost none of nucleon spin
is carried by quarks!
Recent data indicate
DG is small at x ~ 0.1.
Future experiments
Nucleon Spin:

28. F. Kunne (COMPASS), AIP Conf. Proc. 1149 (2009) 321.
Gluon polarization from lepton scattering
F. Kunne (COMPASS), AIP Conf. Proc (2009) 321.

29. Gluon polarization from RHIC π0 production
(Torii’s talk at Pacific-Spin05)
Parton distribution functions
Parton interactions
Fragmentation functions
Gluonic processes dominate.
Determination of ∆g
however with uncertainties of
gluon fragmentation functions.
Uncertainty range of
gluon fragmentation functions in LO.
(See the next page.)
In the NLO, the range is smaller.

30. Comparison of fragmentation functions in pion
(KKP) Kniehl, Kramer, Pötter
(AKK) Albino, Kniehl, Kramer
(HKNS) Hirai, Kumano, Nagai, Sudoh
(DSS) de Florian, Sassot, Stratmann
NLO
• Gluon and light-quark
fragmentation functions have
large uncertainties, but they
are within the uncertainty bands.
The functions of KKP, Kretzer,
AKK, DSS, and HKNS are
consistent with each other.
All the parametrizations agree
in charm and bottom functions.
M. Hirai, SK, T.-H. Nagai, K. Sudoh,
PRD75 (2007)
A code is available at

31. AAC codes for polarized PDFs: http://spin.riken.bnl.gov/aac/
Global analyses of polarized PDFs: Asymmetry Analysis Collaboration (AAC)
AAC codes for polarized PDFs:
2000 version (AAC00) Y. Goto et al., PRD 62 (2000)
- Q2 dependence of A1, positivity
- q at small and large x   issue
2004 version (AAC03) M. Hirai, SK, N. Saito, PRD 69 (2004)
- uncertainty estimation
(very large g uncertainty, impact of accurate g1p (E155))
- error correlation between g and q
2006 version (AAC06) M. Hirai, SK, N. Saito, PRD 74 (2006)
- include RHIC-Spin 0 (g uncertainty is significantly reduced)
- g at large x ? (from Q2 difference between HERMES and COMPASS)
- g < 0 solution
2008 version (AAC08) M. Hirai, SK, NPB 813 (2009) 106.
- impact of g by JLab E ?
(g uncertainty could be significantly reduced.)
Today’s talk

32. General method for determining polarized PDFs
Leading Order (LO)
Next to Leading Order (NLO)
Unpolarized PDFs

33. Constraint on ∆ g(x) from current g1 data

34. Gluon polarization at large x
AAC, PRD74 (2006) :
Analysis without higher-twist effects
NLO
This term is terminated.
CG=0
x=0.001
x=0.3
x=0.05

35. However, it may be higher-twist effect.
LSS, PRD73 (2006)
Leading Twist (LT)
Higher Twist (HT)
LT fit
LT+HT fit
LT+HT fit,
only LT term is shown
At this stage, we cannot conclude that the difference between
the HERMES and COMPASS data should be 100% HT or
HT+g(large x)>0, or 100% g(large x)>0 effects.

36. Obtained polarized PDFs by AAC06
Gluon polarization tends to
be positive at large x.

37. Constraint on ∆ g(x) from future g1 data: Effects of E07-011 at JLab 12 GeV

38. 3 data sets for global analyses of polarized PDFs
Current
DIS (g1)
RHIC
p0 (run 5)
JLab
E (g1) A
Included — B C
Expected E data
Set A: Only DIS data for the determination
of polarized PDFs [Dg(x)]
Set B: Effects of collider data sets
p0 production [Run-5 PHENIX,
PRD76, R (2007)]
Set C: Effect of DIS accurate g1 data
by JLab E
g1 measurements [E. Brash, et al.,
JLab experiment E07-011;
X. Jiang, personal communications.] 38

39. Effects of expected JLab E07-011 data
“positive”
“node” x
Two initial functions for∆ g(x): positive, node
Positive
Node
Gluon
Reduction of
uncertainties
for ∆ g(x)
by E07-011
Antiquark

40. ∆ g(x) with PHENIX run-5 or JLab E07-011 data
Note: π0 data are from run-5 although it may not be a good idea to compare future data with past ones.
Significant improvements
JLab-E is comparable
to RHIC run-5 π0
in determining ∆ g(x)
if gluon fragmentation errors
are neglected.

41. Why such a large improvement of ∆ g(x) by E07-011 data?

42. The End
The End