It was realized that while I had extented my fit range to lower mass, I hadn't updated the functional forms to fully represent the Monte Carlo histogram shapes.  For the following fits, I use

• Signal: two skewed Gaussion, but rather than using a common mean, I let one mean be near the main pi0 peak and one be near the low mass peak
• Combinatorial background: single skewed Gaussian as always
• Other background (i.e. combinatorics, etc.): single skewed Gaussian
• Fitting in 0.0 to 0.3 GeV

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Results

The results of fitting the template functions to Monte Carlo data is given in one attached PDF and the results of fitting the weights and energy scale factor to the data is given in the second PDF.  The first are the 5-6 GeV pT bin, and subsequent plots are higher pT bins.  The mean peak position and cross section are also given in the second PDF.

Note: it has been suggested that the label "pi0 signal" in these plots would be more accurately stated "pi0s", as 0.1 to 0.2 GeV is the "signal region" and the region from which data is used for computing the cross section and asymmetries.

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Conclusions

• The fits are not in general not too bad, and give resonable results.
• The previous statement that the MC was missing some of the low mass peak should have been more correctly stated that the functional form used for the pi0s was missing some of the low mass peak.  Some of this low mass peak due to signal is really in the MC histogram, but didn't get represented in the functional forms used before.  Note: the intention before was only to fit the MC signal distribution above 0.1 anyhow, so this was reasonable then, and this is a reasonable update now.
• The various methods and cuts tried last week are no longer needed.
• The cross section is a little higher in the lower pT bins, but this is not a major effect.  This means that the was a little "low mass" events that were not accounted for, and these were predominately signal.
• We seem to have a stable, reasonable, fit procedure.
• Recall: systematics from this step include
  • Uncertainty on the number of pi0 counts in 0.1 to 0.2
  • Uncertainty based on propagating all the uncertainties from all the fits---both the functional parameter fits and the overall weight fits.
  • Uncertainty based on fitting the residual from 0.1 to 0.2 to a constant