How to analyze the Al and Cl 8-step data

David Bowman9/28/12

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 detectorto detector.

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?

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 yieldOver some time window.

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

Average (over 2000 runs) transients

Transients for 48 detectors

The transients for different detectors are differentThe average transient is not exponential.

Fits to 48 detector yields vs k

• Trial function

Fit asymmetries to glr, gud, and ring offsets

• Results for ring 1

Aud = -0.7 +/- 3.6 +/- 8.0Alr = -5.6 +/- 3.6 +/- 8.0The systematic error is obtained from the normalized Chi2

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