1 March 2006 Nikolas Meitanis

2 Outline  Theoretical Framework  Experimental Apparatus  Data Analysis  Results and Conclusion

3 THEORETICAL FRAMEWORK

4 Motivation Importance of Nucleon Form Factors  Fundamental quantities: describe electro-magnetic structure  Tests of theoretical calculations  Necessary for parity-violation experiments NOTE: Due to the absence of free neutron targets: Neutron form factors known less precisely compared to proton.

5 Electron-Nucleon Elastic Scattering Unpolarized target: Rosenbluth cross section Mott cross section: (spin ½ electron, spinless+structureless nucleon) Polarized target:

6 Electron-Nucleon Elastic Scattering Forming asymmetries: Asymmetry in terms of Sachs form factors: ( θ *, φ * ) : Angles between the target polarization and the momentum transfer vector. θ* = 0 deg. : parallel kinematics θ* = 90 deg. : perpendicular kinematics.

7 Electron-Deuteron Elastic Scattering Unpolarized Cross Section Polarized Cross Section Deuteron Properties: Simplest nuclear system in nature Spin 1, Isospin 0 Proton and Neutron loosely bound, spins aligned Ground state: admixture of S and D

8 Electrodisintegration  QE: Special case of electrodisintegration  QE: Electron scatters off single nucleon  PWBA: No excited states, no FSI Polarized cross section Beam-target vector asymmetry EXCLUSIVE: both scattered electron and hadron detected. Scattering off either proton or neutron. Quasi-Elastic

9 Inclusive Electron-Deuteron Quasi-elastic Scattering Beam-target vector asymmetry 10 Structure Functions remaining after integration. Only electron detected. Cross section derived from integral of exclusive structure functions over n-p phase space. This asymmetry exhibits sensitivity to G M n in the inclusive electro- disintegration reaction of polarized electrons and polarized deuterium. NEW MEASUREMENT.

10 Sensitivity to G M n ASYMMETRIES NOTE: Asymmetries vary with opposite sign in the two sectors. This can be exploited in a linear combination of the two. Polarized deuteron: Incoherent sum of pol. neutron and pol. proton

11 Sensitivity to G M n (2) Same sensitivity across W spectrum.

12 Sensitivity to G M n (3) The ratio enhances sensitivity to the form factor. The form factor enters the ratio squared. RATIO OF ASYMMETRIES

13 Calculation by H. Arenhovel Incorporated in Monte Carlo. Friedrich & Walcher form factors for proton, Galster form factor for GEn. Incorporates: 1. Final State Interactions (FSI) 2. Meson Exchange Currents (MEC) 3. Isobar Configurations (IC) 4. Relativistic Corrections (RC) A model of Deuteron structure using the Bonn potential.

14 Friedrich&Walcher Parametrization Expressed form factors as “smooth“ part plus “bump” smooth bump

15 F&W Parametrization (2) The effect of changing the proton form factors from dipole to the FW parametrization. The Galster parametrization is used for Gen and the dipole for GMn.

16 Previous G M n Measurements  Unpolarized electron-deuteron quasi-elastic. Inclusive. Proton contributions subtracted (model dependent).  Ratio of cross sections D(e,e’n) and D(e,e’p) in QE kinematics. Less sensitive to nuclear structure. Needed to know neutron detection efficiency.  Quasi-elastic scattering of polarized electrons off polarized Helium-3. Inclusive. Nuclear structure model an issue

17 World’s Data for G M n  Holzwarth B1, B2: Soliton  Simula: CQM  Lomon: VMD model  Miller: Cloudy Bag model  FW: Friedrich & Walcher par.  Faessler: ChPT THEORETICAL CALCULATIONS

18 EXPERIMENTAL APPARATUS

19 MIT-Bates Linear Accelerator Siberian Snakes  Polarized Source  Linac  Recirculator  South Hall Ring (SHR)  Siberian Snakes  BLAST detector in SHR  ABS: BLAST target embedded in the beamline

20 The BLAST Detector  ABS target  Wire Chambers  Cerenkov Counters  TOFs  Neutron Counters  Magnetic Coils

21 The BLAST Detector + Coils  ABS target  Wire Chambers  Cerenkov Counters  TOFs  Neutron Counters  Magnetic Coils

22 Atomic Beam Source (ABS)  RF Dissociator  Sextupole System  RF Transition Units  Storage Cell  Breit-Rabi Polarimeter

23 RF Dissociator Critical parameters for optimizing performance: Nozzle temperature Gas through-put Vacuum Matching Network – RF power Oxygen Admixture Dissociates molecules into atoms Consists of an RF coil, connected to an RF power supply and wrapped around a glass tube.

24 Dissociation Results HYDROGENDEUTERIUM

25 Sextupole System 24 segments glued together. Create radial field. RAYTRACE simulations used to optimize location / opening of apertures, location of sextupoles. Used to focus atoms with pos. atomic electron spin and de-focus the rest.

26 Hyperfine Structure DEUTERIUM HYDROGEN Quantum mechanics of spin ½ - spin ½ system. Two Zeeman multiplets: Symmetric triplet, anti-symmetric singlet. Spin 1 – spin ½ system: Quadruplet + Doublet.

27 RF Transition Units MFT UNIT DEUTERIUM TRANSITIONS To induce transitions between the hyperfine states.

28 Storage Cell To limit de-polarization: Cooled to 100 K. Coated with Dryfilm. Used to increase target thickness for internal target. 60 cm long, 15 mm diameter, Al. De-polarization effects: Recombination Spin Relaxation

29 Other Components Target Holding Field : To maintain and control the orientation of the target polarization. Electromagnet with two pairs of coils. Covers ± 20 cm of the cell. Breit-Rabi Polarimeter (BRP) : To monitor transitions. A dipole magnet with a gradient field for electron-spin separation.

30 Polarization Results Beam: Average Pol. ≈ 65% Measured with Compton Pol. Target Vector Pol. ≈ 85% (deuterium) From (e,e’p) analysis off deuterium. Target Tensor Pol. ≈ 80% (deuterium) From ed-elastic analysis.

31 DATA ANALYSIS

32 Data Sets Running period June-OctoberMarch-June Total Charge320 kC550 kC Target pol. angle 32 deg.47 deg. Ave. Beam current 100 mA180 mA Cell length60 cm Target thickness 6x10 31 cm -2

33 Inclusive Electron Selection 1. Particles with inbending Wire-Chamber Track (negative charge). 2. Correlated TOF – Cerenkov signals. 3. Invariant mass cuts: essentially limit events to QE regime. 4. The data were divided into four Q 2 bins.

34 Inclusive Electron Selection Data from 3 triggers Trigger 1 : (e,e’p), (e,e’d) Trigger 2: (e,e’n) Trigger 7: (e,e’) singles prescaled by 3 INCLUSIVE: ADD TRIGGERS NOTE: In forming the inclusive cross section, the individual detection efficiencies cancel out when trigger 7 is taken into account. Electron detection efficiency is not crucial when forming asymmetries.

35 Data Spectra Sample of experimental spectra for first Q 2 bin and 2004 data. Bin 1Bin 2 Bin 3 Bin 4 Bin 1

36 Data Spectra (2) Sample of experimental spectra for first Q 2 bin and 2004 data. Bin 1Bin 2 Bin 1 Bin 4Bin 3 Bin 4 Bin 3

37 Experimental Background  Empty target background From cell-wall scattering etc. Uniform across W spectrum, 1-3% Dilutes individual sector asymmetries  Pion contamination Only past pion-threshold (high-W edge) Expected to be negligible  Electro-deuteron elastic scattering Only at low-W edge Varies between 1-5% Sizeable effect on asymmetries and ratio

38 Electron-Deuteron Elastic Events  Monte Carlo of ed elastic versus disintegration events. Resolution convolutes peaks Mostly at low-Q2 Only at low-W edge Varies between 1-5% Effect on asymmetries and ratio QE elastic

39 Electron-Deuteron Elastic Events The contamination was accounted for in the MC.

40 Extraction of G M n The following analysis process was performed for each data set independently: 1.Divide the data into the Q2 bins and form the asymmetries in both perpendicular and parallel kinematics. Within each Q2 bin, divide the data in W bins. Correct the asymmetries for empty target background. Q 2 = (GeV/c) 2

41 Extraction of G M n (2) 2. Divide the asymmetries to form the ratio. Q 2 = (GeV/c) 2 3.Vary G M n value wrt the dipole form factor in the Monte Carlo. 4. Obtain χ 2 for each calculation

42 Extraction of G M n (3) Q 2 = (GeV/c) 2 5.Find minimum of χ 2 for each Q 2 bin using a parabolic shape. 6. Calculate error by varying χ 2 for each Q 2 bin by

43 Systematic Uncertainties Uncertainty Source % GMn err % GMn err Target Polarization Angle2.5%1.5% 2.Cuts, Recon & Resolution1.5% 3.Value of GEn0.5% 4.Radiative Effects0.5%

44 Target polarization angle uncertainty

45 Uncertainty in G E n A 20% uncertainty in G E n contributes 0.5% uncertainty in G M n.

46 False Asymmetries Negligible Effect.

47 RESULTS & CONCLUSION

48 Final Results

49 Final Results (2) 1. New measurement technique. 2. Includes full deuteron structure. 3. Consistent with recent polarization and other data. 4. Provides a tighter fit to form factor in the low Q2 region.