1. Nucleon Form Factors and the BLAST Experiment at MIT-Bates
Probing Nucleon Structure with Spin-Dependent Electron Scattering at Low Q2
Introduction/Motivation
BLAST Experiment
Results and Discussion
May 18, 2006
R. PAV06

2. Spin 1/2: Elastic electron scattering from nucleons
t = Q2/4M2
e = [1+2(1+t)tan2(q /2)]-1
Sach’s ff’s:
charge
GEp(0) = 1, GEn(0) = 0
magnetism
GMp(0) =
GMn(0) = –1.91

3. Polarized e-N scattering
Polarized beam + polarized target:
Donnelly + Raskin, Ann. Phys. 169 (1986)247 p n p
 neutron charge ff n
 neutron magnetic ff
Polarized beam + polarization of recoil nucleon:
neutron charge ff
proton GE/GM
Akhiezer+Rekalo, Sov.JPN 3 (1974) 277
Arnold,Carlson+Gross, PRC 21 (1980) 1426

4. Why study hadron form factors?
They give us the ground state properties of (all visible) matter:
size and shape
charge and magnetism distributions
spin and angular momentum
They are required for knowledge of many other things:
structure of nuclei at short distances
Proton charge radius and Lamb shift
precision tests of Weak interaction at low Q2
They should give clues on how to connect QCD to the NN force
cPT
pQCD
form factors
quarks/gluons
p cloud
lattice
QCD
They can be measured NOW with high precision!

5. Scientific Motivation for BLAST
Comprehensive study of spin observables from few-body nuclei at low Q2.
Nucleon form factors provide basic information on nucleon structure.
Low-Q2 region is a testing ground for QCD and pion-cloud inspired and other effective nucleon models.
GnE is the least known among the nucleon form factors, with errors of typically 15-20%.
GnE related to neutron charge distribution.
Precise knowledge of GnE is essential for parity violation experiments.

6. MIT-Bates Linear Accelerator Center
Linac: 2500 MeV
Beam: 850 MeV / Imax = 225 mA / Pe = 65 %
SHR: Siberian Snake + Compton Polarimeter
Target: Internal Target = Atomic Beam Source

7. Internal Target Physics at MIT-Bates
Ee  1 GeV, Pe= % Im= 200 mA,   10 min
pure species
thin
high polarization
thin cell
low holding field
South Hall Ring
L = atoms cm-2 s-1
Novosibirsk, AmPS, HERMES, IUCF, COSY

8. Atomic Beam Source Isotopically pure H or D
Vector Polarized H
Vector and Tensor D
Target Thickness/Luminosity
Flow 2.2 x 1016 atoms/s
Density 6 x 1013 atoms/cm2
Luminosity 6 x 1031 cm-2s-1
Target Polarization typically 70-80%

9. Atomic Beam Source

10. Atomic Beam Source Quasielastic Beam-Target Asymmetry
Aved(exp) = h·Pz ·Aved(th)
<hPz> = ± 0.006
<Pz> = 0.85 ± 0.04
<h> = 0.67 ± 0.04

11. Bates Large Acceptance Spectrometer Toroid
Left-Right symmetry
Large Acceptance
0.1 < Q2/(GeV/c)2 < 1.0
Coils: B = 3.8 kG
Drift Chambers
PID,tracking
 ≈ 0.5º,
Cerenkov Counters
e,  separation
Scintillators
TOF, PID, trigger
Neutron Counters
Neutron ToF

13. The BLAST Collaboration

14. Experimental Program
High quality data for nucleon and deuteron structure
by means of spin-dependent electron scattering
Pol. H
Inclusive
GpE/GpM
N-∆: C2/M1
Vect-Pol. D
GnM
D-state
GnE
Te11
Tens-Pol. D
T20

15. Event Selection

16. Neutron: Invariant Mass and Time of Flight
Very clean quasi-elastic 2H(e,e’n)p spectrum
Highly efficient proton veto (Wire Chambers)

17. Neutron: Invariant Mass and Time of Flight
Very clean quasi-elastic 2H(e,e’n)p spectrum
Highly efficient proton veto (Wire Chambers)

18. Target Spin Orientation

19. Target Spin Orientation
nucleons
Electron - Right Sector
“Parallel” Kinematics
* ≈ 0
electrons

20. Target Spin Orientation
Neutrons
electrons
Electron - left sector
“Perpendicular” Kinematics
* ≈ 90
nucleons
electrons

21. Kinematics and Observables
Electrodisintegration of the Deuteron
Quasi-elastic 2H(e,e’n)
Beam + Target Polarized

22. BLAST Data Collection

23. BLAST Data Collection

24. BLAST Data Collection

25. Nucleon Form Factors Parameterizations
However, the slope at Q^{2} predicted by the neutron charge radius is under predicted. The BLAST fit uses the same form with the slope at Q^{2}=0 fixed to the charge radius as such.

26. Proton Form Factors

27. Neutron Magnetic Form Factor GMn

28. Neutron Magnetic Form Factor GMn

29. Neutron Magnetic Form Factor GMn
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.

30. Preliminary BLAST GMn Data
N. Meitanis

31. Extraction of GnE Quasielastic
Full Monte Carlo Simulation of the BLAST experiment
Deuteron Electrodisintegration cross section calculations
by H. Arenhövel
Accounted for FSI, MEC, IC, RC
Spin-perpendicular beam-target asymmetry AedV(90º,0º) shows high sensitivity to GnE

32. Extraction of GnE Quasielastic
Full Monte Carlo Simulation of the BLAST experiment
Deuteron Electrodisintegration cross section calculations
by H. Arenhövel
Accounted for FSI, MEC, IC, RC
Spin-perpendicular beam-target asymmetry AedV(90º,0º) shows high sensitivity to GnE
Compare measured AedV with BLASTMC, varying GnE

33. Systematic Errors Uncertainty of target spin angle 5%
12% per degree
Beam-target polarization product %
Radiative effects <1.0%
Small helicity dependency
Uncertainty of GnM %
Model dependency <3%
Effect of potential negligible
Final state interaction reliable
Total: %

34. PRELIMINARY GnE World Plot
This shows the calculated Gen result obtained from measuring the vector asymmetry of quasi-elastic neutron scattering.
Only 60% of the existing data are included in this calculation so the uncertainties should still come down. Also many systematics still have to be checked. The error bars include statistical and systematic errors.
To extract Gen we have used Arenhovel’s calculations to calculate GMn and also to determine the effect of varying contributions of Gen.
Will eventually use BLAST measurements of GMn and other results in a global fit.
Hopefully we will be able to provide some useful results at low Q**2 to check the bump and for details of the pion cloud.

35. PRELIMINARY GnE World Plot V. Ziskin and E. Geis Preliminary result
Only 50% of data, final data should reach 0.5 (GeV/c)2
Use Arenhovel’s calculations for GnM and contribution of GnE
Need to combine with other BLAST measurements for global fit
Provide low Q2 data
Check bump
Pion cloud
PRELIMINARY
This shows the calculated Gen result obtained from measuring the vector asymmetry of quasi-elastic neutron scattering.
Only 60% of the existing data are included in this calculation so the uncertainties should still come down. Also many systematics still have to be checked. The error bars include statistical and systematic errors.
To extract Gen we have used Arenhovel’s calculations to calculate GMn and also to determine the effect of varying contributions of Gen.
Will eventually use BLAST measurements of GMn and other results in a global fit.
Hopefully we will be able to provide some useful results at low Q**2 to check the bump and for details of the pion cloud.
V. Ziskin and E. Geis

36. BLAST Fit to World Polarization Data
Remarkable consistency of all modern polarization experiments!
Here, I plot the contribution to the total value of GeN from the smooth dipole part in green and the bump part in blue. At low momentum transfer the parameterization is dominated by the bump part. At show distances the dipole part dominates, thus preserving pQCD scaling predictions. The gray bend around the total value of one sigma uncertainty of the fit, plotted here explicitly in percentage of the value of GeN. The uncertainty at Q^{2} is the uncertainty in charge radius measurement.
Global fit determines GEn to better than ±7%

37. Nucleon Models Dispersion theory gives the best description
Here, I plot the contribution to the total value of GeN from the smooth dipole part in green and the bump part in blue. At low momentum transfer the parameterization is dominated by the bump part. At show distances the dipole part dominates, thus preserving pQCD scaling predictions. The gray bend around the total value of one sigma uncertainty of the fit, plotted here explicitly in percentage of the value of GeN. The uncertainty at Q^{2} is the uncertainty in charge radius measurement.
Dispersion theory gives the best description
No theory describes GnE at low and high Q2 simultaneously

38. Conclusions & Outlook
BLAST at MIT-Bates has measured at low Q2 the nucleon form factors using polarized electrons from vector-polarized hydrogen/deuterium.
Very small systematic errors
GnE overall known to ≈ 5% at Q2 < 1 (GeV/c)2
Dispersion theory gives the best description
No theory describes GnE at low and high Q2 simultaneously
Evidence for enhancement at low Q2 - role of pion cloud?
With new precision data of T20 from BLAST and with improved A(Q2) new attempt to GnE determine from GQ
ed elastic analysis: Mainz-Saclay discrepancy 8% in A  factor of 2 in GnE
New measurements of A(Q2) at JLab (E ) and MAMI
Extension of GnE at high Q2 < 3.5 (GeV/c)2 (E-02-13)
Proposal of
Measure GnE for Q2 = (GeV/c)2 with both vector-polarized 2H and polarized 3He