1. H(e,e’p)n Analysis in BLAST2
Aaron Maschinot
Massachusetts Institute of Technology
Ph.D. Thesis Defense
09/02/05

2. Outline of Presentation
Physics Motivation and Theory
Overview of BLAST Project
BLAST Drift Chambers
Data Analysis
Results and Monte Carlo Comparison
Summary

3. Deuteron Wave Functions
(Bonn Potential)
NN interaction conserves only total angular momentum
Spin-1 nucleus lies in L = 0, 2 admixture state:
Tensor component must be present to allow L = 2
Fourier transform into momentum space:
L = 2 component is dominant at p ~ 0.3GeV
(Bonn Potential)

4. Deuteron Density Functions
Calculate density functions:
Straightforward form:
Possess azimuthal degree of symmetry
Famous “donut” and “dumbbell” shapes
In absence of tensor NN component, plots are spherical and identical

5. Donuts and Dumbbells

6. Deuteron Electrodisintegration
Loosely-bound deuteron readily breaks up
electromagnetically into two nucleons
cross section can be written as:
In Born approximation, Ae = AVd = ATed = 0
ATd vanishes in L = 0 model for deuteron (i.e. no L = 2 admixture)
Measure of L = 2 contribution and thus tensor NN component
Reaction mechanism effects (MEC, IC, RC) convoluted with tensor contribution
AVed provides a measure of reaction mechanisms
Also measure of L = 2 contribution
Provides measurement of beam-vector polarization product (hPZ)

7. Tensor Asymmetry in PWIA
In PWIA, ATd is a function of only the “missing momentum”:
ATd has a straightforward form:

8. The BLAST Project Bates Large Acceptance Spectrometer Toroid
Utilizes polarized beam and polarized targets
0.850 GeV longitudinally polarized electron beam
Vector/tensor polarized internal atomic beam source
(ABS) target
Large acceptance, left-right symmetric spectrometer
detector
Simultaneous parallel/perpendicular, in-plane/out-of-plane asymmetry measurements
Toroidal magnetic field
BLAST is ideally suited for comprehensive analysis of spin-dependent electromagnetic responses of few-body nuclei at momentum transfers up to 1(GeV/c)2
Nucleon form factors
Deuteron form factors
Study few body effects, pion production, …

9. Polarized Electron Beam at Bates
0.850 GeV longitudinally-polarized electron beam
0.500 GeV linac with recirculator
Polarized laser incident on GaAs crystal
25 minute lifetime at 200 mA ring current
Polarization measured via Compton polarimeter
Polarization ~ amount of back-scattered photons
Nondestructive measurement of polarization
Beam helicity flipped with each fill
Long-term beam polarization stability
Average beam polarization = 65% ± 4%

10. The BLAST Targets Internal Atomic Beam Source (ABS) target
Hydrogen and deuteron gas targets
Rapidly switch between polarization states
Hydrogen polarization in two-state mode
Vector : +Pz  -Pz
Deuteron polarization in three-state mode
(Vector, Tensor) :
(-Pz, +Pzz) ( +Pz, +Pzz)
(0, -2Pzz)
Flow = 2.6  1016 atoms/s
Density = 6.0  1013 atoms/cm2
Luminosity = 4.6  mA
Actual polarization magnitudes from data analysis
Pz = 86% ± 5%, Pzz = 68% ± 6%

11. The BLAST Spectrometer
Left-right symmetric detector
Simultaneous parallel and
perpendicular asymmetry
determination
Large acceptance
Covers 0.1(GeV/c)2 ≤ Q2 ≤ 0.8(GeV/c)2
Out-of-plane measurements
DRIFT CHAMBERS
momentum determination,
kinematic variables
CERENKOV COUNTERS
electron/pion discrimination
SCINTILLATORS
TOF, particle identification
NEUTRON COUNTERS
neutron determination
MAGNETIC COILS
3.8kG toroidal field
BEAM
DRIFT CHAMBERS
TARGET
CERENKOV
COUNTERS
BEAM
NEUTRON COUNTERS
SCINTILLATORS

12. Drift Chamber Theory
Charged particles leave stochastic trail of ionized electrons
Apply uniform electric field
Function of HV wire setup
Electrons “drift” to readout wires
Series of accelerations and decelerations
Electron amplification near readout wires (~105)
Pulses  TDCs  distances

13. Drift Chamber Design 3  2  3 = 18 hits per track
Three drift chambers in either detector sector
Each chamber consists of two layers of drift cells
Each drift cell consists of three sense wires
3  2  3 = 18 hits per track
~1000 total sense wires
~9000 total field wires

14. Drift Wire Tensioning Wire positions must be known accurately (~10 µm)
Wires strung under tension
Resist electromagnetism, gravity
Chambers pre-stressed before wiring
Tension must be measured
AC signal on HV DC level
Induces charge on nearby wires
Wires vibrate in E&M field
Stop generating signal
Only harmonic frequency remains after ~100 ms
Readout voltage info
FFT to get wire’s tension

15. Detector Performance All detectors operating at or near designed level
Drift chambers ~98% efficient per wire
TOF resolution of 300 ps
Clean event selection
Cerenkov counters 85% efficient in electron/pion discrimination
Neutron counters 10% (25-30%) efficient in left (right) sectors
Reconstruction resolutions good but still being improved
current
goal p 3% 2% 
0.5°
0.3° 
0.6°
0.5º z
1 cm

16. Deuteron Data Summary
Runs consist of multiple fills and all (beam, target) spin states
Beam helicity flipped every fill (~25 min)
Target (vector,tensor) state shuffled semi-randomly (~5 min)
All states in each run (~60 min)
Deuteron data set taken during June - October 2004
400 kC (150 pb-1) of data collected
5700k 2H(e,e’p)n events

17. Monte Carlo 2H(e,e’p)n Asymmetries
Based on theoretical model from H. Arenhövel
Emphasis on Bonn potential but others considered, too (e.g. Paris and V18)
Reaction mechanism effects considered (e.g. FSI, MEC, IC, RC)
Detector acceptance taken into account in Monte Carlo results
Target polarization vector, , set at 32º on left side
Can access different (i.e. parallel and perpendicular) asymmetry components
electron side
side
asymmetry component
left
right
perpendicular
parallel
32°

18. Kinematics: Monte Carlo Vs. Data
Compare electron and proton momenta
Polar angle, 
Azimuthal angle, 
Magnitude, p
Good agreement in polar and azimuthal angles
Momentum magnitudes show nonnegligible discrepancies

19. Momentum Magnitude Corrections
Nonnegligible discrepancies with momentum magnitudes
reconstruction errors
energy loss
Empirical fits needed to match-up data
Shift data peak to match MC for different Q2 bins:
Fit correction factors to polynomial function in Q2

20. Missing Mass Only scattered electron and proton are detected
Actually measure 2H(e,e’p)X
Need extra cuts to ensure that X = n
Define “missing” energy, momentum, and mass:
Demanding that mM = mn helps ensure that X = n

21. Missing Momentum Magnitude, pM

22. Background Contributions
Empty target runs provide a measure of background:
Negligible contribution at small pM , ~5% contribution at large pM
~1% contribution for all cos M
Beam collimator greatly reduces background
f vs pM
f vs cos M

23. Tensor Asymmetry Vs pM

24. Tensor Asymmetry Vs pM

25. Tensor Asymmetry Vs cos M

26. Tensor Asymmetry Vs cos M

27. Beam-Vector Asymmetry Vs pM

28. Beam-Vector Asymmetry Vs pM

29. Target Angle Systematic Error
Polarization set nominally at 32°
Variation with vertex position
Good agreement between holding field map and T20 calculations
Polarization angle known to ~1°
Uncertainty introduces asymmetry error
Studied via Monte Carlo perturbation
Negligible contribution to beam-vector asymmetries
Dominant contribution to tensor asymetries at high pM d z

30. Target Polarization Systematic Error
Polarization uncertainty leads to asymmetry error:
Dominant contribution to beam-vector asymmetries
Dominant contribution to tensor asymmetries at low pM
Contribution comparable to tensor asymmetry spin angle error at high pM

31. False Asymmetries
2H(e,e’p)n AVd, Ae, and ATed asymmetries are very small
All three vanish in PWIA
Inconsistency implies target polarization deviations
Nonequal PZ/PZZ magnitudes in different states
False asymmetries consistent with zero
AVd Ae
ATed

32. Determining hPZ
Need to determine beam-vector polarization product (hPZ)
Determination of GnE
Determination of beam-vector asymmetries
In QE limit, 2H(e,e’p)n is well understood:
reduces to H(e,e’p) with spectator n
<1% model error for pM < 0.15 GeV/c
Compare to Arenhovel’s deuteron model
uses dipole form factors
low-Q2 extraction is “most reliable”

33. Dipole Form Factor Corrections
Arenhovel uses dipole nucleon form factors:
Use elastic e-p beam-vector asymmetry:
Use more realistic parameterization
Friedrich and Walcher
[Eur. Phys. J. A17: (2003)]
Compute F&W to dipole asymmetry ratio:
r ~ 1.01 (1.02) for perp (para) kinematics

34. hPZ Results and Systematic Error
Dominant error from spin angle determination uncertainty
Overall, hPZ = ± 0.007
Target has PZ = 0.86 ± 0.05
SOURCE
CONTRIBUTION
Target Polarization Angle
0.004
Dipole Approximation
0.003
NN Potential Dependence
Missing Mass Cut
0.002
TOTAL
0.006
Perp Kine
Para Kine
hPZ DIPOLE
0.572
0.564
rDIPF&W
1.01
1.02
hPZ F&W
0.567
0.553
hPZ OVERALL
0.558 ± 0.009STAT ± 0.006SYST h
0.65 ± 0.04 PZ
0.86 ± 0.05

35. Summary and Conclusions
ATd reproduces Monte Carlo results well
Overall consistency with tensor component existence in Arenhovel’s representation of total NN potential
Evidence of D-state onset at slightly lower pM (~20MeV/c)
Importance of reaction mechanism effects
AVed has same basic form as Monte Carlo predictions
Unexplained rise in asymmetry above predictions
ABS target vector highly polarized at Pz  86%
Thank You Very Much!