Elong-13-06-03

Including Drift by Bin

Dustin's work on the drift has given a different value depending on the spectrometer setting, which are shown in the table below.

<math>x_{\mathrm{Spectrometer}}</math>	<math>dA_{zz}^{drift}</math>
0.15	0.0046
0.30	0.0037
0.45	0.0028
0.55	0.0021

For the plots using the spectrometer settings as bins, where <math>A_{zz}</math> and <math>b_1</math> are in blue and red, these are included as an additional systematic uncertainty.

For the rebinned plots, where <math>A_{zz}</math> and <math>b_1</math> are in pink, each of the drift uncertainties are added as a weighted average. The weights are the number of events that each spectrometer contributes to the rebinned statistics.

That's to say,

<math>dA_{zz}^{Ave. Drift} = \frac{\sum \left( dA_{zz}^{drift}N_{Spec} \right)}{N_{Total}}</math>

where <math>dA_{zz}^{drift}</math> is shown in the table above for each spectrometer setting, <math>N_{Spec}</math> is the number of events from a particular spectrometer setting that go into this x bin, and <math>N_{Total}</math> is the total number of events, from all spectrometer settings, that go into this x bin.

Conservative Estimates

If we apply these with a conservative estimate, with <math>P_{zz}=20\%</math> and <math>dA_{zz}^{(Rel. Sys)} = 12\%</math>, we can estimate both the full spectrometer bins:

We can then use a weighted average for <math>dA_{zz}^{drift}</math>, where the weights are number of events that each spectrometer setting contributes to a particular <math>x</math> bin. The rebinned estimate is then:

Same as above, but if we split the systematic uncertainty into bars, we get:

Optimistic Estimates

If we apply these with an optimistic estimate, with <math>P_{zz}=40\%</math> and <math>dA_{zz}^{(Rel. Sys)} = 9\%</math>, we can estimate both the full spectrometer bins:

We can then use a weighted average for <math>dA_{zz}^{drift}</math>, where the weights are number of events that each spectrometer setting contributes to a particular <math>x</math> bin. The rebinned estimate is then:

Same as above, but if we split the systematic uncertainty into bars, we get:

--E. Long 20:58, 3 June 2013 (UTC)