H(e,e’p)n Analysis in BLAST 2 Aaron Maschinot Massachusetts Institute of Technology Ph.D. Thesis Defense 09/02/05

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

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)

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

Donuts and Dumbbells

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)

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

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, …

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%

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%

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

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

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

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

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

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

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°

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

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

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

Missing Momentum Magnitude, pM

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

Tensor Asymmetry Vs pM

Tensor Asymmetry Vs pM

Tensor Asymmetry Vs cos M

Tensor Asymmetry Vs cos M

Beam-Vector Asymmetry Vs pM

Beam-Vector Asymmetry Vs pM

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

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

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

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”

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

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 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

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!