Difference: ArOverview (9 vs. 10)

Revision 102009-05-06 - SaraKnaack

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-- SaraKnaack - 11 Feb 2009
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  • Both the T_0 scan and the background multiplicity correction improve the fit probability, separately, by ~2%.
  • There will be more studies necessary to get a handle on the T_0 effect, especially to limit and significant systematics due to this effect, eg. outside information.

T0 Extraction

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In order to extract the t0 offset time for the electron time spectrum data I used the high time-resolution histograms in MTA and an error function to apply a fit to the data to obtain a t0 result. In this scan of fits the data has been broken up into groups of 10 or fewer MuCap data "runs."
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In order to extract the t0 offset time for the electron time spectrum data I used the high time-resolution histograms in MTA and an error function to apply a fit to the data to obtain a t0 result. In the scan of fits below the data has been broken up into groups of 10 or fewer MuCap data "runs." The transition of the time spectrum at early times is described by an error function, properly parameterized for the amplitude of the early transition in the data.
 
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In red are the fit results to the -50 - -30 ns time window, the green points are associated with the -50 - -38 ns time window, and the results in blue are for the -38 - -30 ns fit window condition. The chi-squares of these fits show the same pattern which the three full statistics fit show. The full -50 to -30 ns fit window yields fits which clearly don't fully agree with the data, while the fit to the data in the -50- -38 ns and -38 - -30 ns data are more or less believable, but which yield differing results that are, following the statistics of the fit, fairly consistent insofar as the errors assigned don't indicate that the results are entirely overlapping for either t0 or the spread in the transition time.
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TF1 *F = new TF1("F","([2]/2)*(TMath::Erf(((x-[0])/[1]))+1)+[3]",-100,50);

The following three plots are fits to the full statistics data with 1.25 ns time bins, in the early -50 - -30 ns , -50 - -38 ns, and -38 - -30 ns fit windows, respectively.

  ElT0Scan_Results.gif
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ElT0Scan_Results.gif
 ElT0Scan_Results.gif
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ElT0Scan_Results.gif
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In red are the fit results to the -50 - -30 ns time window, the green points are associated with the -50 - -38 ns time window, and the results in blue are for the -38 - -30 ns fit window condition. The chi-squares of these fits show the same pattern which the three full statistics fit show. The full -50 to -30 ns fit window yields fits which clearly don't fully agree with the data, while the fit to the data in the -50- -38 ns and -38 - -30 ns data are more or less believable, but which yield differing results that are, following the statistics of the fit, fairly inconsistent insofar as the errors assigned don't indicate that the results are overlapping for either t0 or the spread in the transition time.
  ElT0Scan_Results.gif

The first conclusion is that the fit results change little over the groups of data by run, which is also to say that the time t0 offset changes little over the entire data-set. The width of the transition seems to be no wider than + or - 3 ns, as shown in the upper right panel of the plot. Furthermore the fit results for t0 vary little for a given fit time window, but even across time windows the fit results show little spread outside the -38.5 +- 1.5ns. Since the spread in the transition time is greater than the actual variation in the t0 parameter it makes sense to choose a central value in the range of values obtained for t0 (-38), and to assign an uncertainty to that value which covers the expected range of the transition time, ~ 3 ns. In this way we have a reasonable central value, which the data reflects, and an uncertainty which covers the possible range of values in the t0 offset. Following these considerations a -38 +- 3 ns result for t0 seems appropriate for the data, and accounts for the systematic difficulties in obtaining this result.

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While the fits in the full -50 to -30 ns fit window show unacceptable chi squares, it's also true that the fit results for the early and late parts of the transition in the data show emphasize that the distortions to this simple transition picture are not of a magnitude that prohibit a reasonable determination of the t0 offset for the analysis. By comparing the fit results for different time windows and noting the stability of these results through-out the data set, it makes sense that a -38 +- 3 ns result for t0 will safely account for the uncertainty due to these effects in the time spectrum.
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While the fits in the full -50 to -30 ns fit window show unacceptable chi squares, it's also true that the fit results for the early and late parts of the transition in the data show emphasize that the distortions to this simple transition picture are not of a magnitude that prohibit a reasonable determination of the t0 offset for the analysis. By comparing the fit results for different time windows and noting the stability of these results through-out the data set, it seems to make sense that a -38 +- 3 ns result for t0 will safely account for the uncertainty due to these effects in the time spectrum.
 

5/6/09 Update - T0 correction and El-Capture time spectrum comparison

ElT0Scan_Quality.gif
 
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