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How to analyze the Al and Cl 8-step data

How to analyze the Al and Cl 8-step data. David Bowman 9/28/12. Mark McCrea’s data and analysis of voltage sources into ADC’s. Mark’s analysis. Trial function. Both the amplitude and time constant vary from detector to detector. The transients produce a false asymmetry.

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How to analyze the Al and Cl 8-step data

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  1. How to analyze the Al and Cl 8-step data David Bowman 9/28/12

  2. Mark McCrea’s data and analysis of voltage sources into ADC’s

  3. Mark’s analysis Trial function Both the amplitude and time constant vary from detector to detector.

  4. The transients produce a false asymmetry • In the + - - + - + + - spin sequence the large transient in step 1 produces a false asymmetry of order 10-6(10-5/8). • The false asymmetry is large compared to our goal statistical uncertainty for Al (3 10-8). • What procedure can be used to extract the asymmetry for the 8-step data? • We need to analyze the imperfect Al data in order to get an NPDGamma asymmetry before the LH data are complete. • What is the statistical uncertainty? • What is the systematic uncertainty caused by the transient?

  5. Factors affecting statistical error • The polarization is approximately constant wrt time. • The fluctuations in the data are caused by counting statistics • The optimal estimator for the polarization is The smallest uncertainty is obtained by summing the yield Over some time window.

  6. Averaging procedure • Form yields integrated over a time window for each spin sequence and each run • Calculate counting statistics from fluctuations in detector-pair ratios • Calculate fluctuations from intensity and c. s. from fluctuations in individual detectors • Calculate counting statistics weighted 8-step yields averaged over all (2000) runs. 48 8-step yields vs k=1, 2, 3,…,8 with counting statistics errors • The results that follow are from Tim’s analysis of Al data

  7. Average (over 2000 runs) transients Transients for 48 detectors The transients for different detectors are different The average transient is not exponential.

  8. Fits to 48 detector yields vs k • Trial function

  9. Fit asymmetries to glr, gud, and ring offsets • Results for ring 1 Aud = -0.7 +/- 3.6 +/- 8.0 Alr = -5.6 +/- 3.6 +/- 8.0 The systematic error is obtained from the normalized Chi2

  10. Conclusions • We can determine the Al asymmetry with a statistical uncertainty of ~4 10-8 and a systematic uncertainty of ~ 8 10-8 • We still need to do so using cleaned data • The uncertainty in the transient function is the cause of the large systematic uncertainty

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