Polarization Responses in Pion Electroproduction at the Delta Resonance

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Polarization Responses in Pion Electroproduction
at the Delta Resonance

• Mark Jones
• Jefferson Lab
• for the Jefferson Lab Hall A Collaboration

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Response Functions

• left/right asymmetry offers 1 unpolarized and 5
  polarized response functions
• OOP acceptance gives additional 7 polarized, 1
  unpolarized response functions

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Sensitivity to Phase
For two channels, Fermi-Watson requires resonant
amplitudes to carry common phase. Let Ari b
where r is resonant and b is background amplitude.
Thus, helicity-independent recoil polarization
offers access to relative phase.
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Kinematics and Beam Delivery
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W versus Q2 kinematic coverage
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Differential cross section
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Differential cross section
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Focal-Plane Polarimeter

• Helicity-dependent polarization from helicity
  difference, cancels false asymmetry
• Helicity-dependent polarization must be corrected
  for instrumental asymmetry
• Measure 22 components at FPP, but obtain 33
  components at target from variation of spin
  transport

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Maximum-likelihood method for polarization at
target

• eventwise likelihood accounts for variation of A,
  S, ?
• yields average polarization coefficients in bin
  of (W,Q2,?cm,f)
• spin transport Saß accounts for
• cm to lab transformation
• precession in spectrometer
• coordinate transformations to FPP
• small false asymmetries, ?a, depend primarily on d

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Preliminary
(R. Rochè)
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Preliminary
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Multipole Analysis
Represent each amplitude, real or imaginary part
of Mlj or Elj or Slj, as
where A(0) is taken from baseline model and dA is
a correction to be fitted to data.

• include all data (cross sections and
  polarizations or polarization response
  functions) for specified (W,Q2)
• vary appropriate subset of multipole amplitudes
  for low partial waves
• keep other amplitudes fixed at baseline values.

Typically fit 14 angular distributions using only
12 parameters!
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1 multipoles

• W dependence qualitatively consistent with
  models.
• Q2 dependence relatively small
• Im M1 smaller than predicted.

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Nonresonant amplitudes

• Strong correlation between E0 and S0 maybe
  Rosenbluth separation would help.
• Data favors DMT 1- amplitudes, which were fit in
  analysis of Hall C data.
• Still need to optimize selection of fitting
  parameters.

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Summary

• Polarization observables for electroproduction of
  pseudoscalar mesons sensitive to interference of
  nonresonant and nondominant resonances with
  dominant amplitudes
• Have measured angular distributions of recoil
  polarization in meson electroproduction for the
  first time
• Significant OOP coverage from boost

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• Multipole analysis
• preliminary analysis demonstrates consistent fits
  to many angular distributions simultaneously with
  relatively few parameters
• optimization requires further study
• plan to incorporate Hall B data also
• Future possibilities
• repeat with smaller e for Rosenbluth separation
• higher Q2 for ?
• higher W for Roper, etc.
• ? production near S11
• requires substantial investment in beam time and
  manpower