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Extraction of GEn at Q2=1 (GeV/c)2 by
Measurements of
May 1, 2011
Ge JinUniversity of Virginia
)'e,e(He3
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Abstract
GEn was extracted for the first time by inclusive polarized
measurements of Getting the ratio of asymmetries in longitudinal and
transverse target polarization; separating the electric and magnetic form factor contributions
Proton and neutron contributions calculated in PWIA New technique, confirms previous measurements;
uncertainty: ~18%, largely statistical
)',e(He3 e
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Previous measurements and extraction of GE
n
Rosenbluth separation Polarization transfer d(e,e’n)p Polarized scattering, neutron tagging Polarized inclusive quasi-elastic
scattering
)n'e,e(He3
)'e,e(He3
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Previous extractions of GE by
Uncertainties comparable to measured quantity
)'e,e(He3
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Detectors and kinematics of this measurement Detectors:
HRS-R: detect electrons, placed at 170
Kinematics: Beam energy: 3.6 GeV Q2: 1 (GeV/c)2
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Polarized 3He target
Room-temperature gaseous (10 atm) target
Rb-K hybrid optical pumping and spin exchange
Average polarization ~55%
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Analysis in asymmetries
Beam polarization: by Hall A Möller measurements Target polarization: by run-by-run NMR calibration Dilution factor: by N2 pressure curve Radiative correction: by formalism of Mo and Tsai, peaking
approximation of Steil, et al. Code used in JLab E94010 for inelastic 3He scattering
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Transverse-longitudinal asymmetry ATL’
(target polarization perpendicular to q)
Near quasi-elastic peak 0.9<xBj<1.1,
ATL’=(-0.55±0.09 (stat)±0.04 (syst))%
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Transverse asymmetry AT’
(target polarization parallel to q)
Near quasi-elastic peak 0.9<xBj<1.1,
AT’ =(3.12±0.10 (stat)±0.21 (syst))%
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Helicity asymmetry in electron scattering
THe
TLHe
L
THe
TTLHe
TL
RvRv
RvRvA 33
33
'''' *cos*cos*sin
where R’s are response functions and v’s are kinematics factors
T. D. Donnelly and A. S. Raskin, Ann. Phys 169, 247 (1986)
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Ratio of asymmetries
''
''
'
'
'''
'''
3
3
33
3
33
3
asymmetry allongitudin-e transvers,0* and 2/*when
asymmetry se transver,0*when
THe
T
TLHe
TL
T
TL
THe
TLHe
L
TLHe
TLTL
THe
TLHe
L
THe
TT
Rv
Rv
A
A
RvRv
RvA
RvRv
RvA
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3He inclusive response functions near quasi-elastic peak in PWIA
Transverse-
longitudinal:
Transverse:
where H’s are calculated by momentum distribution and nucleon polarization in 3He
A. Kievsky, E. Pace, G. Salme’ and M. Viviani, PRC 56 (1997) p.64
Neutron: HnProton: Hp
T’
Proton: HpTL’
])()(2[2
]2[2
'2
'2
2
'
'''
3
3
Tnn
MTpp
MTHe
TLnn
MnETL
ppM
pETL
He
HGHGqM
QR
HGGHGGR
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3He spin structure
Spin-1/2 particle, 3 spin-1/2 nucleons (protons and neutron)
Angular Momentum l=0 l=0 l=2 ~90% ~1-2% ~8%
EffectiveNeutronTarget
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The ratio of asymmetries as functions of form factors
]))()(2[2
(
])2[2(
'2
'2
2
'
'''
'
'
Tnn
MTpp
MT
TLnn
MnETL
ppM
pETL
T
TL
HGHGqMQ
v
HGGHGGv
A
A
By measuring ATL’/AT’ and using GEp, GM
n, and GMn
as known parameters can one extract GEn
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Final result of GEn at Q2=0.95 (GeV/c)2
Results: GE
n/GD=0.226±0.041 (stat)±0.016 (syst)
GEn=0.0414±0.0077 (stat)±0.0032 (syst)
Conclusion Our unprecedented method of measuring GE
n (ratio of asymmetries in ) gave results in agreement with world data
)'e,e(He3
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Comments and Outlook
Further theoretical support (near quasi-elastic peak)
Advantages: Single arm (HRS) detector calibration At higher Q2, GE
n contributes more strongly to ATL’ than the other form factors.
Big saving of beam time: 18% accuracy in 3-day run Ratio-of-asymmetry method insensitive to systematic
error (beam and target polarization, dilution factor, radiative correction partly cancel)
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Graduate StudentsG. Jin, University of Virginia
E. Long, Kent State UniversityM. Mihovilovič, Jožef Stefan Institute
Y. Zhang, Lanzhou University
Run CoordinatorsA. Camsonne, Jefferson Lab
P. Monaghan, Hampton UniversityS. Riordan, University of VirginiaB. Sawatzky, Temple UniversityR. Subedi, University of Virginia
V. Sulkosky, MITY. Qiang, Duke University
B. Zhao, College of William and Mary
S. Golge
O. Hansen
T. Holmstrom
J. Huang
H. Ibrahim
E. Jensen
M. Jones
H. Kang
J. Katich
C. W. Kees
P. King
J. LeRose
R. Lindgren
H. Lu
W. Luo
K. Allada
B. Anderson
J. R. M. Annand
W. Boeglin
P. Bradshaw
M. Canan
C. Chen
R. De Leo
X. Deng
A. Deur
C. Dutta
L. El Fassi
D. Flay
F. Garibaldi
H. Gao
R. Gilman
P. Markowitz
M. Meziane
R. Michaels
B. Moffit
N. Muangma
H. P. Khanal
K. Pan
D. Parno
E. Piasetzky
M. Posik
A. J. R. Puckett
X. Qian
X. Qui
A. Saha
Thanks to the Hall A Quasi-Elastic
Family ExperimentsSpokespersons
T. Averett, College of William and Mary (E05-015, E08-05)
J. P. Chen, Jefferson Lab (E05-015)
S. Gilad, MIT (E05-102)
D. Higinbotham, Jefferson Lab (E05-102, E08-005)
X. Jiang, Rutgers University (E05-015)
W. Korsch, University of Kentucky (E05-102)
B. E. Norum, University of Virginia (E05-102)
S. Sirca, University of Ljubljana (E05-102)
V. Sulkosky, MIT (E08-005)
E05-015,E08-005,and E05-102
CollaborationF. Salvatore
M. ShabestariA. ShahinyanB. Shoenrock
J. St. JohnA. Tobias
W. TiremanG. M. Urciuoli
D. WangK. WangJ. Watson
B. WojtsekhowskiZ. Ye
X. ZhanX. Zheng
L. Zhu
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Four nucleon form factors
J. J. Kelly, PRC 068202, 2004
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Ratio of Inclusive Asymmetry ATL’/AT’
Longitudinal:
Transverse:
Asymmetry ratio:
Where v’s are kinematics factors
By measuring ATL’/AT’ and using GEp , GM
n , GMn
as known parameters can one extract GEn
ctiond_cross_seunpolarize
)*cos*cos*(sin
]))()(2[2
(
])2[2(
ctiond_cross_seunpolarize
ctiond_cross_seunpolarize
'''''
'2
'2
2
'
'''
'
'
'''
'''
33
3
3
THe
TTLHe
TLMottTL
Tnn
MTpp
MT
TLnn
MnETL
ppM
pETL
T
TL
THe
TMottT
TLHe
TLMottTL
RvRvA
HGHGqMQ
v
HGGHGGv
A
A
RvA
RvA
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Asymmetry Results
Kinematics: 3 pass beam, HRS-R 170, Q2=0.95 GeV2
Analysis: Asymmetry in 0.9<x<1.1 Yawei Zhang’s target and dilution factor
analysis Karl Slifer’s radiative correction code radcor.f
Results: ATL’=-0.55±0.09(stat)±0.04(syst)% AT’ =3.12±0.10(stat)±0.21(syst)%
Error: Stat error dominates ATL’ Syst error contributed by beam and target
polarization, and dilution factor
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Analysis on the ratio of asymmetries Ratio:
ATL’/AT’ =-0.18±0.03(stat)±0.01(syst)
Statistical uncertainty dominates Systematic
Beam polarization: <3% Dilution factor cancels Target polarization: ~0.6% contributed by the frequency reading
Δν in EPR calibration Radiative correction: <5%