Hadronic Form Factor Uncertainties

1
Hadronic Form Factor Uncertainties

• J. Martin, U. Winnipeg
• M. Pitt, Va Tech

2
Physics

• The usual form factors GE?, GM? are known.
• By measuring at very low Q2 and very forward
  angles, we attempt to isolate the first term,
  which to zeroth order in Q2 is just proportional
  to QWp

• However, there are still corrections due to
  unknown terms
• GEs, GMs, GAe
• For example, at our experiments kinematics, the
  2nd and 3rd terms (only weakly dependent on QWp)
  contribute about 30. So, to measure QWp at the
  2 level, these must be controlled at 5 relative
  level.
• Also there are EW rad cor we take these to be
  known.

3
Procedure to Estimate Uncertainties due to GEs,
GMs

• Use asymmetry data from previous experiments.
• Assume a reasonable empirical form for GEs, GMs
  with some unknown parameters (typically the
  strangeness radius and the strangeness magnetic
  moment).
• Use fitting to determine the errors in those
  parameters.
• Calculate the error induced on the asymmetry to
  be measured by the Qweak experiment and hence on
  the extraction of QWp.

4
Example the empirical model known as linear

• P1?s P2?s
• SAMPLE, HAPPEX, PVA4, G0FWD proton included.
• Relative uncertainty on Qwp is

• Result

5
Example the empirical model known as Galster

• P1?s P2?s
• SAMPLE, HAPPEX, PVA4, G0FWD proton included.
• Relative uncertainty on Qwp is

• Result

6
Additional studies

• Tried eight different empirical forms, fitted
  over all data and over restricted Q2lt0.25 range.
• Tried fixing ?s (motivated by Leinweber et al).
• Tried three parameter fit
• Include Qweak as just another experiment
• Fit ?s, ?s, and QWp directly.
• Advantage Unified description of QWp from all
  PV electron experiments.
• Disadvantage statistical and systematic
  uncertainties of Qweak and all the other
  experiments are rolled into final answer for QWp.

7
Example three parameter fit with Galster

• P1?s
• P2?s
• P3QWp
• SAMPLE, HAPPEX, PVA4, G0FWD. and Qweak proton
  included.
• TOTAL Relative uncertainty on Qwp is displayed on
  graph.

• Result

fair agreement with other method
8
Results
9
For PAC Jeopardy

• results of 2-par fit for linear (fit to all
  data) and super simple (fit to Q2lt0.25).
• Although fit to all experiments, plot contains
  experiments which are at roughly the same beam
  energy (HAPPEX and G0).

10
Conclusions and Remaining Work

• For two of the reasonable models considered, the
  answer is within the error envelope. These
  models are definitely justifiable.
• However, uncertainty appears to depend on
  empirical form assumed for strangeness form
  factors.
• Remaining to do
• include more data G0BACK, PVA4 backward,
  deuterium, HAPPEX-He.
• Q2 binning for Qweak.
• effect of lowering average Q2 of Qweak.
• Mark will now talk more about use of these
  results and axial piece.