March 2006Nikolas Meitanis

Outline Theoretical Framework Experimental Apparatus Data Analysis Results and Conclusion

THEORETICAL FRAMEWORK

MotivationImportance 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.

Electron-Nucleon Elastic ScatteringUnpolarized target: Rosenbluth cross sectionMott cross section: (spin electron, spinless+structureless nucleon)Polarized target:

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

Electron-Deuteron Elastic ScatteringUnpolarized Cross SectionPolarized Cross SectionDeuteron Properties: Simplest nuclear system in natureSpin 1, Isospin 0Proton and Neutron loosely bound, spins alignedGround state: admixture of S and D

Electrodisintegration QE: Special case of electrodisintegration QE: Electron scatters off single nucleon PWBA: No excited states, no FSIPolarized cross sectionBeam-target vector asymmetryEXCLUSIVE: both scattered electron and hadron detected.Scattering off either proton or neutron.Quasi-Elastic

Inclusive Electron-Deuteron Quasi-elastic ScatteringBeam-target vector asymmetry10 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 GMn in the inclusive electro-disintegration reaction of polarized electrons and polarized deuterium.NEW MEASUREMENT.

Sensitivity to GMnASYMMETRIESNOTE: 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

Sensitivity to GMn (2)Same sensitivity across W spectrum.

Sensitivity to GMn (3)The ratio enhances sensitivity to the form factor. The form factor enters the ratio squared.RATIO OF ASYMMETRIES

Calculation by H. ArenhovelIncorporated in Monte Carlo.

Friedrich & Walcher form factors forproton, 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.

Friedrich&Walcher ParametrizationExpressed form factors as smooth part plus bumpsmoothbump

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

Previous GMn Measurements Unpolarized electron-deuteron quasi-elastic. Inclusive. Proton contributions subtracted (model dependent).

Ratio of cross sections D(e,en) and D(e,ep) 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

Worlds Data for GMn Holzwarth B1, B2: Soliton Simula: CQM Lomon: VMD model Miller: Cloudy Bag model FW: Friedrich & Walcher par. Faessler: ChPT THEORETICAL CALCULATIONS

EXPERIMENTALAPPARATUS

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

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

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

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

RF DissociatorCritical parameters for optimizing performance:Nozzle temperatureGas through-putVacuumMatching Network RF powerOxygen AdmixtureDissociates molecules into atomsConsists of an RF coil, connected to an RF power supply and wrapped around a glass tube.

Dissociation ResultsHYDROGENDEUTERIUM

Sextupole System24 segments glued together.Create radial field.RAYTRACE simulations used tooptimize location / opening of apertures, location of sextupoles.Used to focus atoms with pos. atomic electron spin and de-focus the rest.

Hyperfine StructureDEUTERIUMHYDROGENQuantum mechanics of spin - spin system.Two Zeeman multiplets:Symmetric triplet, anti-symmetric singlet.Spin 1 spin system:Quadruplet + Doublet.

RF Transition UnitsMFT UNITDEUTERIUM TRANSITIONSTo induce transitions between the hyperfine states.

Storage CellTo 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:RecombinationSpin Relaxation

Other ComponentsTarget 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.

Polarization ResultsBeam:Average Pol. 65%Measured with Compton Pol.Target Vector Pol. 85% (deuterium)From (e,ep) analysis off deuterium.Target Tensor Pol. 80% (deuterium)From ed-elastic analysis.

DATA ANALYSIS

Data Sets

Inclusive Electron Selection1. 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 Q2 bins.

Inclusive Electron SelectionData from 3 triggersTrigger 1 : (e,ep), (e,ed)Trigger 2: (e,en)Trigger 7: (e,e) singles prescaled by 3INCLUSIVE: ADD TRIGGERSNOTE: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.

Data SpectraSample of experimental spectra for first Q2 bin and 2004 data.Bin 1Bin 2Bin 2Bin 3Bin 3Bin 4Bin 4Bin 1

Data Spectra (2)Sample of experimental spectra for first Q2 bin and 2004 data.Bin 1Bin 2Bin 2Bin 1Bin 4Bin 3Bin 4Bin 3

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

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

QEelastic

Electron-Deuteron Elastic EventsThe contamination was accounted for in the MC.

Extraction of GMnThe following analysis process was performed for each data set independently: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.Q2 = 0.189 (GeV/c)2

Extraction of GMn (2)2. Divide the asymmetries to form the ratio. Q2 = 0.189 (GeV/c)2Vary GMn value wrt the dipole form factor in the Monte Carlo.4. Obtain 2 for each calculation.20042005

Extraction of GMn (3)Q2 = 0.189 (GeV/c)2Find minimum of 2 for each Q2 bin using a parabolic shape. 6. Calculate error by varying 2 for each Q2 bin by 1. 20042005

Systematic Uncertainties

Target polarization angle uncertainty

Uncertainty in GEnA 20% uncertainty in GEn contributes 0.5% uncertainty in GMn .

False AsymmetriesNegligible Effect.

RESULTS & CONCLUSION

Final Results

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.