-- SaraKnaack - 11 Feb 2009
# Electron Time Spectrum Results

## Consistency with world expectation values.

### Input Assumptions

### Electron fit results.

### Rate Results (Preliminary - subject to some reference checking and documentation)

## El Time Spectrum Scans

## El "nocut"

## El "b120mm"

## Muon Decay Rate Fit Scan

# Work 2/23-3/3

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

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

## A T_0 scan for the electron time distribution fit.

### A T_0 variable was added to the time distribution function, and fixed in a series of fits to the data while varied between - 100 to 100 ns.

### Conclusions

- phi = 0.0112 +/- .0001 (known to something like 1 % relative precision)
- C_Ar = 18.5 +/- .5 ppm

- R_ppmu = 1.999 (88) 10^-5 1/ns
- R_pAr_ = 4.468 (17) 10^-5 1/ns
- R_Ar = 1.423 (17) 10^-3 1/ns
- Chi-square currently 1.16, slightly high
- Subject to full consistency and understanding of the electron time spectrum and the assignment of appropriate cuts and systematic errors, mu-Ar-p kinetics and/or apparatus related.

- r_ppmu = R_ppmu/phi = 1.776 (80) 10^-3 1/ns (or )
- Compare to 2.34 (17) 10^-3 1/ns from Bystritsky
- Compare to 1.89 (20) 10^-3 1/ns from Blasser
- This is fairly consistent with a theoretical result ~ 1.8 (1) 10^-3 1/ns. (?)
- Or 2.3 (2) 10^-3 1/ns world average
- r_pAr = 2.156 (61) 10^2 1/ns
- Which is quite higher than the earlier result of 1.63 (9) 10^2 1/ns
- R_Ar = 1.423 (17) 10^-3 1/ns
- Compare to 1.40 (1)10^-3 1/ns (? must double check)

- 120-15000 ns fit window
- "nocut" impact parameter condition

- 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

- 120 -15,000 ns
- No background multiplicity correction was taken into account for the fit to the real data
- Question is, does this fit make sense and is it reliable?
- 100 pseudo-data spectra were generated using the fit function resulting from the fit to the data
- In the plots below, the real fit results are in the right most bin of the histograms.
- 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

- 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.

- 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.

- A T_0 offset can create a time-dependent effect in the fit to the time spectrum, causing a poorer chi-square in the fit.
- Here I have varied a T_0 parameter in the fit function at values from -100 to 100 ns, and fixed this in the fit.
- 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.
- 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.

- Finally the full panel of all the scan plots.

- 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.

Topic revision: r7 - 2009-03-04 - SaraKnaack

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