Difference: ArOverview (6 vs. 7)

Revision 72009-03-04 - SaraKnaack

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-- SaraKnaack - 11 Feb 2009
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ElFit_b120mm.gif
Csrtm_1mus_b120mm.gif
Csrtm_7mus_b120mm.gif

Muon Decay Rate Fit Scan

Work 2/23-3/3

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The Background multiplicity correction decreases the chi-square moderately by ~ .1

ElFit_b120mm_BMC.gif
  • A improvement in the definition of the pull histogram does not affect the over all chi-square, but better supports the quality of the fit
  • Compare to the previous result shown last week
ElFit_b120mm.gif
 

Scan of fits of MC pseudo-data generated from the fit result to the b<120 mm impact-parameter cut data.

  • 120 -15,000 ns
  • No background multiplicity correction was taken into account for the fit to the real data
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  • First I will show the normalized fit chi-square and probability for the 100 samples of pseudo-data
  • On the respective axes below the normalized chi-square and probability of the real fit are emphasized with the solid red lines for comparison to the MC fit results
ElFitMCScan_Quality.gif
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  • The important observation here is that the relative to the distribution of MC fit results, the chi-square, (while elevated at 1.12) of the fit to the real data is neither the highest, ~12% being equally or more aberrant in the >1 direction.
  • Like wise this fit to data is also not the least probable in comparison to the pseudo data fit results.
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  • The important observation here is that the relative to the distribution of MC fit results, the chi-square, (while elevated at 1.12) of the fit to the real data is neither the highest, ~10% being equally or more aberrant from 1 in the >1 direction.
  • Like wise the fit to data is also not the least probable in comparison to the pseudo data fit results.
 ElFitMCScan_Results.gif
  • Just to verify the fits, here are the fit results for the three physical parameters in the fit function, with their "truth values" indicated in read, again these are the values obtained in the fit to the data
  • Each parameter shows a random scattering around the truth values, as expected in fits to pseudo-data generated with the same function.
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  • Again, there was no background multiplicity correction applied to the errors, which would improve the chi-square by another small margine of ~2%, based on the T_0=0 comparison
  • First of all the quality of the fit remains at a very similar level, improving slightly in the direction of small negative values at ~ -30 ns.
  • I also observe a significant linear response, vs. the value of the T_0 constant, in the fit results of the three physical parameters.
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  • The shift from T_0=0 ns to T_0=-30 ns is an effect of ~1 sigma for the molecular formation rate, ~1.5 sigma for the argon transfer rate and between 2-3 sigma for the Ar capture rate.
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  • The shift from T_0=0 ns to T_0=-30 ns is an effect of ~1 sigma for the molecular formation rate and the p-to-argon transfer rate for the muon. Finally the shift is ~3 sigma for the Ar capture rate.
  • The chi-square and fit probability indicate that any values for T_0 outside of -100 to 100 ns are increasingly out of agreement with the data
 
  • In fact It is my understanding this brings these results in closer agreement with the capture fit results.
ElT0Scan_Quality.gif

ElT0Scan_Results.gif

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  • Finally the full panel of all the scan plots.
 ElT0Scan.gif
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Conclusions

  • A case is beginning to appear that the somewhat high chi-square may be a result of an improbable distribution which can occur at the ~10% level
  • 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.
 
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