H(e,e’p)n Analysis in BLAST

1. H(e,e’p)n Analysis in BLAST 2 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  1031 /cm2/s @ 160mA • 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 • 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

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 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. A17:607-623 (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 = 0.558 ± 0.007 • Target has 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 • Importance of reaction mechanism effects • ABS target vector highly polarized at Pz 86% Thank You Very Much!