1. Spin Asymmetries of the Nucleon Experiment ( E07-003) Anusha Liyanage Hall C User Meeting (January 25, 2013) Analysis Updates Proton Form Factor Ratio, G P E /G P M From Double Spin Asymmetries

2. Outline Introduction Physics Motivation Experiment Setup Polarized Target Elastic Kinematic Data Analysis & MC/SIMC Simulation Conclusion 2

3. The four-momentum transfer squared, Introduction Nucleon Elastic Form Factors Defined in context of single-photon exchange. Describe how much the nucleus deviates from a point like particle. Describe the internal structure of the nucleons. Provide the information on the spatial distribution of electric charge (by electric form factor,G p E ) and magnetic moment ( by magnetic form factor, G p M ) within the proton. Can be determined from elastic electron-proton scattering. They are functions of the four-momentum transfer squared, Q 2 3

4. At low Fourier transforms of the charge, and magnetic moment, distributions in Breit Frame At General definition of the nucleon form factor is Sachs Form Factors ; ; F 1 – non-spin flip (Dirac Form Factor) describe the charge distribution F 2 – spin flip (Pauli form factor) describe the magnetic moment distribution 4

5. Form Factor Ratio Measurements 1.Rosenbluth separation method. Measure the electron - unpolarized proton elastic scattering cross section at fixed Q 2 by varying the scattering angle, θ e. Strongly sensitive to the radiative corrections. Y = m X + C The gradient =, The Intercept =, E - Incoming electron energy E / - Outgoing electron energy θ e - Outgoing electron’s scattering angle M p - Proton mass 5

6. 2.Polarization Transfer Technique. Measure the recoil proton polarization components from elastic scattering of polarized electron-unpolarized proton. Ratio insensitive to absolute polarization, analyzing power. Less sensitive to radiative correction. Polarization along q Polarization perpendicular to q (in the scattering plane) Polarization normal to scattering plane. E - Incoming electron energy E / - Outgoing electron energy θ e– Outgoing electron’s scattering angle M P - Proton mass 6

7. 3.Double-Spin Asymmetry. Measure the double asymmetry between even (++, --) and odd (+-, -+) combinations of electron and proton polarization. Different systematic errors than Rosenbluth or proton recoil polarization methods. The sensitivity to the form factor ratio is similar to that of the Polarization Transfer Technique. r = G p E /G p M a, b, c = kinematic factors, = pol. and azi. Angles between and A p = The beam - target asymmetry Here, 7

8. Dramatic discrepancy between Rosenbluth and recoil polarization technique. Multi-photon exchange considered the best candidate for the explanation Double-Spin Asymmetry is an independent technique to verify the discrepancy Physics Motivation Dramatic discrepancy ! RSS (Jlab) Q 2 = 1.50 (GeV/c) 2 5.176.25 SANE 2.06 Q 2 (GeV/c) 2 8

9. Elastic (e, e’p) scattering from a polarized NH 3 target using a longitudinally polarized electron beam (Data collected from Jan – March, 2009) HMS for scattered proton or electron detection Central angles are 22.3° and 22.0° Solid angle ~10 msr Hall C at Jefferson Lab BETA for coincidence electron detection Central scattering angle: 40 ° Over 200 msr solid angle coverage Experiment Setup 9

10. Polarized Target The Polarized Target Assembly C, CH 2 and NH 3 Dynamic Nuclear Polarization (DNP) polarized the protons in the NH 3 target up to 90% at 1 K Temperature 5 T Magnetic Field Temperature is maintained by immersing the entire target in a liquid He bath Used microwaves to excite spin flip transitions (55 GHz - 165 GHz) Polarization measured using NMR coils To maintain reasonable target polarization, the beam current  was limited to 100 nA and  uniformly rastered. 10

11. Used only perpendicular magnetic field configuration for the elastic data Average target polarization is ~ 70 % Average beam polarization is ~ 73 % Θ B = 180° Θ B = 80° ( 80 and 180 deg ) Polarized Target Magnetic Field 11

12. Run DatesBeam EnergyMagnet Orientation Run Hours/ Proposed PAC hours Average Beam Polarization Spectrometer mode Coincidence Single Arm HMS Detects Proton Electron E Beam GeV 4.725.89 P HMS GeV/c 3.584.174.40 Θ HMS (Deg) 22.3022.0015.40 Q 2 (GeV/c) 2 5.176.262.06 Total Hours (h) ~40 (~44 runs) ~155 (~135 runs) ~12 (~15 runs) Elastic Events~113~1200~5x10 4 Elastic Kinematics ( From HMS Spectrometer ) 12

13. Electrons in HMS E’ E Θ e - p By knowing, the incoming beam energy,, scattered electron energy, and the scattered electron angle, Data Analysis 13

14.  Momentum Acceptance The elastic data are outside of the usual delta cut +/- 8% Use -8% < <10% P -Measured momentum in HMS P c -HMS central momentum Invariant Mass, W (GeV/c 2 ) hsdelta (%) & Use 10% < <12% 14

15. Extract the electrons Here, - Total measured shower energy of a chosen electron track by HMS Calorimeter - Detected electron momentum/ energy at HMS - Relative momentum deviation from the HMS central momentum Used only Electron selection cuts. # of Cerenkov photoelectrons > 2 - Cerenkov cut -8% < < 10% and 10% < <12% - HMS Momentum Acceptance cuts > 0.7 - Calorimeter cut 3.5 x 10 4 1.5 x 10 4 -8% < < 10% 10% < < 12% 15

16. Extracted the Asymmetries ….. The raw asymmetry, A r N + / N - = Charge and live time normalized counts for the +/- helicities ∆A r = Error on the raw asymmetry -8% < < 10%10% < <12% 16

17. Extracted the Asymmetries ….. Need dilution factor, f in order to determine the physics asymmetry, and G p E /G p M (at Q 2 =2.2 (GeV/c) 2 ) P B P T = Beam and target polarization N c = A correction term to eliminate the contribution from quasi-elastic scattering on polarized 14 N under the elastic peak (negligible in SANE) Use MC/DATA comparison for NH 3 target to extract the dilution factor….. 17

18. Srast x offset=-0.4 cm Srast y offset=0.1 cm MC for C run 18

19. MC with NH3  Generated N, H and He separately.  Added Al coming from target end caps and 4K shields as well.  Calculated the MC scale factor using the data/MC luminosity ratio for each target type.  Added all targets together by weighting the above MC scale factors.  Used 60% packing fraction.  Adjusted acceptance edges in Y and Y’ by adjusting the horizontal beam position.  Adjusted the vertical beam position to bring the elastic peak to GeV. srast x = -0.40 cm srast y = 0.10 cm 19

20. Determination of the Dilution Factor What is the Dilution Factor ? The dilution factor is the ratio of the yield from scattering off free protons(protons from H in NH 3 ) to that from the entire target (protons from N, H, He and Al) Invariant Mass, W (GeV/c 2 ) Each target type contributions (Top target) 20 Invariant Mass, W (GeV/c 2 ) Dilution Factor, -8% < < 10%

21.  MC Background contributions (Only He+N+Al)  Calculate the ratio of Yield Data /Yield MC for the region 0.7 < W <0.85 and MC is normalized with this new scaling factor.  Used the polynomial fit to N+ He+Al in MC and  Subtract the fit function from data 21 Invariant Mass, W (GeV/c 2 )

22. Each target type contributions (Top target) Invariant Mass, W (GeV/c 2 ) 10% < < 12% Invariant Mass, W (GeV/c 2 ) 22

23.  The relative Dilution Factor Dilution Factor, We have taken data using both NH3 targets, called NH3 top and NH3 bottom. NH3 crystals are not uniformly filled in each targets which arise two different packing fractions and hence two different dilution factors. Invariant Mass, W (GeV/c 2 ) The relative dilution factor for two different targets, top and bottom for two different delta regions, -8% < < 10% and 10% < <12% 23

24. Beam /Target Polarizations COIN data Single arm electron data 24

25.  The Physics Asymmetry -8% < < 10% 10% < < 12% Invariant Mass, W (GeV/c 2 ) Phys. Asym., A P 25

26.  The beam - target asymmetry, A p From the HMS kinematics, r 2 << c  Error propagation from the experiment r = G E /G M a, b, c = kinematic factors, = pol. and azi. Angles between and Here, Where, μ – Magnetic Moment of the Proton=2.79 26

27. Preliminary ….. -8 < < 1010 < < 12 Top Ap±eAp-0.212±0.022-0.150±0.032 Bot Ap±eAp-0.216±0.027-0.161±0.040 Avg. Ap±eAp-0.213±0.017-0.154±0.025 (Deg)45.68 (Deg)190.49 Q 2 (GeV/c) 2 2.21.927 μ G E /G M 0.477±0.1900.928±0.279 Pred. μ G E /G M 0.750.775 Pred. Ap-0.188-0.174 Q 2 (GeV/c) 2 2.06 Wei. Avg. μ G E /G M 0.62±0.157 27

28. ΘPΘP Xclust Yclust e e’e’ P Definitions : X/Yclust - Measured X/Y positions on the BigCal X = horizontal / in-plane coordinate Y = vertical / out – of – plane coordinate Eclust - Measured electron energy at the BigCal By knowing the energy of the polarized electron beam, E B and the scattered proton angle, Θ P We can predict the X/Y coordinates - X_HMS, Y_HMS and ( Target Magnetic Field Corrected) The Energy - E_HMS of the coincidence electron on the BigCal Coincidence Data (Electrons in BETA and Protons in HMS) 28

29. Run DatesBeam EnergyMagnet Orientation Run Hours/ Proposed PAC hours Average Beam Polarization Spectrometer mode Coincidence Single Arm HMS Detects Proton Electron E Beam GeV 4.725.89 P HMS GeV/c 3.584.174.40 Θ HMS (Deg) 22.3022.0015.40 Q 2 (GeV/c) 2 5.176.262.06 Total Hours (h) ~40 (~44 runs) ~155 (~135 runs) ~12 (~15 runs) e-p Events~113~1200~5 x 10 4 Elastic Kinematics ( From HMS Spectrometer ) 29

30. Fractional momentum difference P HMS – Measured proton momentum by HMS P cal - Calculated proton momentum by knowing the beam energy, E and the proton angle, Θ P cent – HMS central momentum Data MC 30

31. X/Y position difference Data MC X position difference X_HMS-Xclust/ cm Y_HMS-Yclust/ cm Y position difference 31

32. Applied the coincidence cuts X_HMS-Xclust/ cm Y_HMS-Yclust/ cm Abs( )<0.02 abs(X_HMS-Xclust)<7 abs(Y_HMS-Yclust)<10 32

33. Elastic Events X_HMS-Xclus/ cmt Y_HMS-Yclust/ cm 4.72 GeV data Raw # of Yields Run Number 5.89 GeV data X_HMS-Xclus/ cmt Y_HMS-Yclust/ cm Run Number Raw # of Yields 33

34. Extract the Raw Asymmetries Need dilution factor, f in order to determine the physics asymmetry, and G p E /G p M Raw yields are normalized with Total Charge charge average +/- life times 34

35. Determine The Dilution Factor Estimate The Background Get the ratio of data/SIMC_C for the region of 0.03 < < 0.08. (ratio=2.73893) Normalized the SIMC_C with that ratio (2.73893) for the region of -0.1 < < 0.1 and added SIMC_H3 to it. Compare with the data. Data/SIMC(H3+2.73893*C) = 0.991536 Used the Gaussian fit for the SIMC_C (normalized with 2.73893) and subtract it from the data Get the relative dilution factor by taking the ratio of SIMC_C substracted data to data. the relative df. = (data-SIMC_C)/data 35

36. Get The Relative Dilution Factor Two different target cups (NH 3 Top and NH 3 Bottom) Two different packing fractions Need Two different dilution factors 36

37. The Relative Dilution Factors For Top Target Bottom Target 37

38. The Relative Dilution Factor (Used the Integration Method) Because of the low statistics, It is hard to correct the raw asymmetry for the df as a function of Just integrate over the region of +/- 0.02 for the top and bottom. The relative D.F = (data-SIMC_C)_top/data_top = 606-130/606 = 0.785 = (data-SIMC_C)_bot/data_bot = 541-92/541 = 0.830 Top TargetBottom Target Similarly, the relative D.F for 4.72 GeV beam energy is 0.816 38

39. Beam and Target Polarizations Used the runs of beam polarization > 60 % and abs(target polarization) > 55 % Used the charge average target and beam polarizations to calculate the physics asymmetries 39

40. Extract the Physics Asymmetries Beam Energy(GeV) 4.725.89 Ap±eAp0.184±0.136-0.006±0.077 Dilution Factor, f 0.816Top (0.785) Bot. (0.830) (Deg)102 (Deg)00 Q 2 (GeV/c) 2 5.176.26 μ G E /G M -0.032±0.6680.875±0.424 Q 2 (GeV/c) 2 5.72 Wei. Avg. μ G E /G M 0.614±0.358 40

41. Extract the Proton Form Factor Ratio, G p E /G p M Q 2 (GeV/c) 2 2.065.72 μ G E /G M 0.620± 0.157 0.614± 0.358 Q 2 (GeV/c) 2 41 Preliminary …..

42. Measurement of the beam-target asymmetry in elastic electron- proton scattering offers an independent technique of determining the G p E /G p M ratio. This is an ‘exploratory’ measurement, as a by-product of the SANE experiment. Extraction of the G p E /G p M ratio from single-arm electron and coincidence data are shown. The preliminary data point at Q 2 =2.06 (GeV/c) 2 is very consistent with the recoil polarization data. The preliminary weighted average data point of the coincidence data at Q 2 =5.72 (GeV/c) 2 has large error due to the lack of elastic events. Conclusion 42

43. SANE Collaborators: Argonne National Laboratory, Christopher Newport U., Florida International U., Hampton U., Thomas Jefferson National Accelerator Facility, Mississippi State U., North Carolina A&T State U., Norfolk S. U., Ohio U., Institute for High Energy Physics, U. of Regina, Rensselaer Polytechnic I., Rutgers U., Seoul National U., State University at New Orleans, Temple U., Tohoku U., U. of New Hampshire, U. of Virginia, College of William and Mary, Xavier University of Louisiana, Yerevan Physics Inst. Spokespersons: S. Choi (Seoul), M. Jones (TJNAF), Z-E. Meziani (Temple), O. A. Rondon (UVA)

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45. Packing Fraction. Packing fraction is the actual amount of target material normalized the nominal amount expected for the target volume. Determined by taking the ratio of data to MC as a function of W. Need to determine the packing fractions for each of the NH3 loads used during the data taking. Hoyoung Kang’s work 45

46.  Determine the Packing Fraction Compared data to SIMC simulation for the NH3 target for 3 different Packing Fractions. Normalized MC_NH3 by 0.93 which is the factor that brings C data/MC ratio to 1. Pf (%)506070 Data/MC Ratio 1.000.880.78 Data/MC Ratio/0.93 1.0750.950.84 Determined the packing fraction which brings Data/MC ratio to 1 from the plot. Packing Fraction=56.3 % Consistent with Hoyoung kang’s packing fraction determinations !!!! 46