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Extraction of G E n at Q 2 =1 (GeV/c) 2 by Measurements of May 1, 2011 Ge Jin University of Virginia

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Abstract G E n 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

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Previous measurements and extraction of G E n Rosenbluth separation Polarization transfer d(e,en)p Polarized scattering, neutron tagging Polarized inclusive quasi-elastic scattering

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Previous extractions of G E by Uncertainties comparable to measured quantity

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Detectors and kinematics of this measurement Detectors: HRS-R: detect electrons, placed at 17 0 Kinematics: Beam energy: 3.6 GeV Q 2 : 1 (GeV/c) 2

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Polarized 3 He 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 N 2 pressure curve Radiative correction: by formalism of Mo and Tsai, peaking approximation of Steil, et al. Code used in JLab E94010 for inelastic 3 He scattering

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Transverse-longitudinal asymmetry A TL (target polarization perpendicular to q) Near quasi-elastic peak 0.9<x Bj <1.1, A TL =(-0.55±0.09 (stat)±0.04 (syst))%

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Transverse asymmetry A T (target polarization parallel to q) Near quasi-elastic peak 0.9<x Bj <1.1, A T =(3.12±0.10 (stat)±0.21 (syst))%

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Helicity asymmetry in electron scattering where Rs are response functions and vs are kinematics factors T. D. Donnelly and A. S. Raskin, Ann. Phys 169, 247 (1986)

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Ratio of asymmetries

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3 He inclusive response functions near quasi-elastic peak in PWIA Transverse- longitudinal: Transverse: where Hs are calculated by momentum distribution and nucleon polarization in 3 He A. Kievsky, E. Pace, G. Salme and M. Viviani, PRC 56 (1997) p.64 Neutron: H n Proton: H p T Proton: H p TL

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3 He 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% Effective Neutron Target

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The ratio of asymmetries as functions of form factors By measuring A TL /A T and using G E p, G M n, and G M n as known parameters can one extract G E n

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Final result of G E n at Q 2 =0.95 (GeV/c) 2 Results: G E n /G D =0.226±0.041 (stat)±0.016 (syst) G E n =0.0414±0.0077 (stat)±0.0032 (syst) Conclusion Our unprecedented method of measuring G E n (ratio of asymmetries in ) gave results in agreement with world data

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Comments and Outlook Further theoretical support (near quasi-elastic peak) Advantages: Single arm (HRS) detector calibration At higher Q 2, G E n contributes more strongly to A TL 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 Students G. Jin, University of Virginia E. Long, Kent State University M. Mihovilovič, Jožef Stefan Institute Y. Zhang, Lanzhou University Run Coordinators A. Camsonne, Jefferson Lab P. Monaghan, Hampton University S. Riordan, University of Virginia B. Sawatzky, Temple University R. Subedi, University of Virginia V. Sulkosky, MIT Y. 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 Experiments Spokespersons 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 Collaboration F. Salvatore M. Shabestari A. Shahinyan B. Shoenrock J. St. John A. Tobias W. Tireman G. M. Urciuoli D. Wang K. Wang J. Watson B. Wojtsekhowski Z. Ye X. Zhan X. 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 A TL /A T Longitudinal: Transverse: Asymmetry ratio: Where vs are kinematics factors By measuring A TL /A T and using G E p, G M n, G M n as known parameters can one extract G E n

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Asymmetry Results Kinematics: 3 pass beam, HRS-R 17 0, Q 2 =0.95 GeV 2 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: A TL =-0.55±0.09(stat)±0.04(syst)% A T =3.12±0.10(stat)±0.21(syst)% Error: Stat error dominates A TL Syst error contributed by beam and target polarization, and dilution factor

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Analysis on the ratio of asymmetries Ratio: A TL /A T =-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%

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