1. Patricia Solvignon Temple University
Study of Quark-Hadron Duality on Neutron and 3He Spin Structure Functions
Patricia Solvignon
Temple University
Hall A Interview Seminar
Jefferson Lab, Newport News
March 24, 2006

2. Outlines Brief theoretical description of Quark-Hadron Duality
Experimental setup
Analysis steps
Preliminary results on the Spin Structure Functions
Preliminary test of Quark-Hadron Duality on Neutron and 3He

3. Inclusive Electron Scattering
Photon momentum transfer
Invariant mass squared
Bjorken variable

4. Inclusive Electron Scattering
Photon momentum transfer
Invariant mass squared
Bjorken variable {
Unpolarized
case

5. Inclusive Electron Scattering
Photon momentum transfer
Invariant mass squared
Bjorken variable {
Unpolarized
case {
Polarized case

6. Resonance region Q2
Low Q2 and W<2 GeV : coarse resolution  we don’t see partons.
The nucleon goes through different excited states: the resonances

7. Deep Inelastic ScatteringQ2 u d d
High Q2 and W>2GeV: fine resolution  we see partons
asymptotic freedom of
the strong interaction
Parton model: scaling
2004 Nobel Prize
D. J. Gross, H. D. Politzer and F. Wilczek

8. Scaling of F2 F2= 1990 Nobel Prize
Figure from: H. W. Kendall, Rev. Mod. Phys. 63 (1991) 597
1990 Nobel Prize
J. I. Friedman, H. W. Kendall and R. E. Taylor

9. Structure functions in the parton model
In the infinite-momentum frame:
no time for interactions between partons
Partons are point-like non-interacting particles: Nucleon = i i
No simple partonic distribution for g2(x,Q2)

10. First observed by Bloom and Gilman in the 1970’s on F2
Quark-hadron duality
First observed by Bloom and Gilman in the 1970’s on F2
Scaling curve seen at high Q2 is an accurate average over the resonance region at lower Q2
Global and Local duality are observed for F2
I. Niculescu et al., PRL 85 (2000) 1182

11. Theoretical interpretations
Lattice QCD
PT
Quark models
OPE
pQCD
Q2 =∞
Q2 =0
Operator Product Expansion (Rujula, Georgi, Politzer):
 Higher twist corrections are small or cancel.
pQCD (Carlson, Mukhopadhyay):
 Q2 dependence of transition form factors vs. x dependence of parton distribution functions
SU(6) symmetry breaking in the quark model (Close, Isgur and Melnitchouk):
 investigate several scenarios with suppression of:
spin-3/2
helicity-3/2
symmetric wave function

12. Scaling of g1 moments proton neutron
M. Amerian et al., PRL 859(2002)
R. Fatemi et al., PRL 91 (2003)

13. World data HERMES for A1p Jlab Hall B for g1p preliminary
A. Airapeian et al., PRL 90 (2003)
Jlab Hall B for g1p
From DIS 2005 proceedings
preliminary

14. World data
Indication of duality from Jlab Hall A for g13He

15. The experiment E01-012  Test of spin duality on the neutron (and 3He)
Ran in Jan.-Feb. 2003
Inclusive experiment:
Measured polarized cross section differences
Form g1 and g2
 Test of spin duality on the neutron (and 3He)

16. 3He as an effective neutron target

17. The E Collaboration
K. Aniol, T. Averett, W. Boeglin, A. Camsonne, G.D. Cates,
G. Chang, J.-P. Chen, Seonho Choi, E. Chudakov, B. Craver,
F. Cusanno, A. Deur, D. Dutta, R. Ent, R. Feuerbach,
S. Frullani, H. Gao, F. Garibaldi, R. Gilman, C. Glashausser,
O. Hansen, D. Higinbotham, H. Ibrahim, X. Jiang, M. Jones,
A. Kelleher, J. Kelly, C. Keppel, W. Kim, W. Korsch,K. Kramer,
G. Kumbartzki, J. LeRose, R. Lindgren, N. Liyanage, B. Ma,
D. Margaziotis, P. Markowitz, K. McCormick, Z.-E. Meziani,
R. Michaels, B. Moffit, P. Monaghan, C. Munoz Camacho,
K. Paschke, B. Reitz, A. Saha, R. Sheyor, J. Singh, K. Slifer,
P. Solvignon, V. Sulkosky, A. Tobias, G. Urciuoli, K. Wang,
K. Wijesooriya, B. Wojtsekhowski, S. Woo, J.-C. Yang,
X. Zheng, L. Zhu
and the Jefferson Lab Hall A Collaboration

18. Experimental setup Standard Hall A equipment:
Polarized electron beam
Standard Hall A equipment:
Both HRS in symmetric configuration
double the statistics
control the systematics
Particle ID = Cerenkov + EM calorimeter
 /e reduced by 104
Polarized 3He target

19. Electron Beam Polarization
Used Moller Polarimeter: measurements performed by E. Chudakov et al.
70 < Pbeam < 85% for production data

20. How to polarize 3He ? Two step process:
Rb vapor is polarized by optical pumping with circularly polarized light
Rb e- polarization is transferred to 3He nucleus by spin-exchange interaction
A small amount of N2 is added
for quenching

21. The polarized 3He target
Two chamber cell
Pressure ~ 14 atm under running conditions
High luminosity: 1036 s-1cm-2
Ltg ~ 40cm

22. The polarized 3He system
Longitudinal and transverse configurations
2 independent polarimetries:
NMR and EPR

23. Nuclear Magnetic Resonance
P3He = w S
w : from calibration with an identical target cell filled with water S
Apply perpendicular RF field
Ramp holding field (H0)
} flip the 3He spins under
AFP conditions

24. Electron Paramagnetic Resonance
2
P3He = epr 
Polarized 3He creates an extra magnetic field: B3He
Measure the Zeeman splitting frequency when B0 and B3He are aligned and anti-aligned.
epr : depend of cell density and holding field.

25. Target performance
Pavg~ 37%
Statistical errors only

26. Analysis scheme
Radiative
corrections

27. Pion asymmetries Statistical errors only 4GeV, 25o 3GeV, 25o 5GeV, 25o

28. The CO2 gas Cerenkov counter
Index of refraction:
n =
Knock-out e-
&
Low energy e-

29. Lead Glass Calorimeter
Cuts applied for electron efficiency > 99%

30. Unpolarized cross sections
4GeV, 25o
3GeV, 25o
5GeV, 25o
5GeV, 32o

31. Unpolarized cross sections
3GeV, 25o
4GeV, 25o
5GeV, 25o
5GeV, 32o

32. Unpolarized cross sections
3GeV, 25o
4GeV, 25o
5GeV, 25o
5GeV, 32o

33. Unpolarized cross sections
3GeV, 25o
4GeV, 25o
5GeV, 25o
5GeV, 32o

34. Unpolarized cross sections
3GeV, 25o
4GeV, 25o
5GeV, 25o
5GeV, 32o

35. Radiative corrections
At reaction point: E0 Ep
External

36. Radiative corrections
Internal
At reaction point: E0 Ep
External

37. Radiative corrections
Internal
At reaction point: E0 Ep
External

38. Radiative corrections
Internal
At reaction point: E0 Ep
External
Computation to get the real reaction

39. Radiative corrections
Used QFS model for o. Next will use E data for o:
Used E data as a model for radiative corrections at the lowest energy:

40. Unpolarized cross sections
3GeV, 25o
4GeV, 25o
5GeV, 25o
5GeV, 32o

41. Unpolarized cross sections
3GeV, 25o
4GeV, 25o
5GeV, 25o
5GeV, 32o

42. Asymmetries
3GeV, 25o
4GeV, 25o
5GeV, 25o
5GeV, 32o

43. Asymmetries Statistical errors only 3GeV, 25o 4GeV, 25o 5GeV, 25o

44. g13He at constant Q2

45. g13He at constant Q2

46. g13He at constant Q2

47. g13He at constant Q2

48. g13He at constant Q2

49. g13He at constant Q2

50. 1 in the resonance region
Extract the neutron from effective polarization equation:
Pn=86%
Pp=-2.8%
Statistical errors only

51. Test of Duality on Neutron and 3He
Used method defined by N. Bianchi, A. Fantoni and S. Liuti on g1p
Get g1 at constant Q2
Define integration range in the resonance region in function of W
Integrate g1res and g1dis over the same x-range and at the same Q2
PRD 69 (2004)
If  duality is verified

52. Test of duality on 3He
Statistical errors only

53. Test of duality on neutron
Statistical errors only

54. Spin asymmetries In the parton model:
 and  depend on kinematic variables
D and d depend on R=L/ T for 3He
In the parton model:
If Q2 dependence similar for g1 and for F1  weak Q2 dependence of A1

55. A13He

56. A13He

57. A13He
Statistical errors only

58. A13He
Statistical errors only

59. A13He
Statistical errors only

60. A13He
Statistical errors only

61. Summary
E provides precision data of Spin Structure Functions on neutron (3He) in the resonance region for 1.0<Q2<4.0(GeV/c)2
Direct extraction of g1 and g2 from our data
Overlap between E resonance data and DIS data
First precise test of Quark-Hadron Duality for neutron and 3He SSF
Global duality seems to work for g1 for all our Q2
Too early to draw conclusions on A1 behavior.
E data combined with proton data
test of spin and flavor dependence of duality
Our data can also be used to extract moments of SSF (e.g. Extended GDH Sum Rule, BC Sum Rule)

62. Jlab at 12 GeV

63. Extra Slides

64. Systematics Target density polarization 1.0-2.0% 3.0-4.0% Beam charge
energy
1.0%
3.0%
0.5%
N2 dilution %
Detector efficiencies
2.5%
Acceptance %
Radiative corrections ?

65. A23He

66. Particle identification performance
/e reduced by 104 and electron efficiency kept above 98%

67. NMR: water calibration
NMR analysis done by Vince Sulkosky

68. Elastic asymmetry
Check of the product:

69. Nitrogen cross sections
Modified the QFS model by adding energy dependence to the cross sections