Data Sets and Histograms

Pythia events were catagorized according to this blog, and the histogram of the invariant mass distribution for each type is computed.  All available Pythia data from the Pythia QCD background production was used, with the individual runs weighted by 1/(lumi for the run).

For the data, 51 runs from 2006 were used.  The varying luminosity per run has not yet been taken into account.

Cuts

The following cuts were applied to both data and Monte Carlo:

• Both photon's in the pi0 candidate must have
  
  • energy > 1.5 GeV (IU), 2.0 GeV (TSIU) or 2.5 GeV (TSP)

  • energy in preshower 1 < 40 MeV

  • energy in SMD clusters (u+v) / photon energy > 0.006

•  mass of pi0 candidate < 0.6 GeV

The events are all seperated into the usual pT bins.

Fitting Procedure

Each of the three templates are normalized to have integral of unity so that the parameters represent the weight of each contribution.  The Monte Carlo templates were all shifted down by one bin, as 1) the peak position looks to high and 2) the sampling fraction study suggests the mass is too high by about 4 MeV (bin width is 6 MeV).  Root's TH1::Fit() function is used with option "MELNR".  All three weights are allowed to be free in the fit, but each time the function (equal to the weighted sum of the three templates) is evaluated, the weights are set to be the parameters being varied scaled such that the overall integral matches the integral of the data.  The fit (and integrals for normalizing) is preformed in the mass range 0.1 to 0.6 GeV.

Results

The attached log files from Root show the relative weights of the templates (in order signal, conversions, other background) before the fit (i.e. as present in Pythia) and after the fit.  The chisq, number of degrees of freedom, and the amount of signal (absolute and relative) are also given.  An attached PDF shows the templates vs. data before the fit, and another pdf shows the results after the fit.

Commentary

The Monte Carlo does not seem to fit the data well at pT < 7 GeV, and pT in 7 to 8 GeV it only fits marginally well.  Above pT of 8 GeV the agreement seems to be fairly good.  A major descrepancy is the shoulder.  Further studies (documented below) demonstrate the shoulder is due to events with either 1 u cluster and 2 v clusters or 2 u clusters and 1 v clusters.  A pT-dependant distrance cut can remove the shoulder so that (by eye) the agreement between MC and data looks better, the actual reduced chisq (now over 0.05-0.6 GeV since there is no shoulder to avoid) is not improved.  

Quick Shoulder Study

The following study did not use the preshower or SMD energy cuts.  The invariant mass distribution from data is divided into two samples (per each pT bin): one where both photons in the pi0 candidates share a u or v cluster (du or dv = 0), and the other sample being the contrary case (du != 0 and dv != 0).  The results are attached.  While at low pT, the shoulder occurs with du or dv = 0 (false cluster splitting), at higher pT the signal tends to have du or dv = 0, as the photons are generall too close to have the clusters be sufficiently seperated in both layers.

Removing the Shoulder

Plotting the distance between photons (D) vs pT shows that a cut of (D-4.0)^2 + (pT - 5.5)^2 < 4 is an effective cut at removing the shoulder.  The resulting log file and templates (before and after the fit) are attached.  Note, the chisq is not signficantly effected.  For easy reference, below is the table of chisq values, left column is without this extra cut (fit starting at 0.1 GeV), right column is with this cut (fit starting at 0.05 GeV).

Chi^2/NDF = 414.277 / 80 = 5.17847      Chi^2/NDF = 460.341 / 80 = 5.75426
Chi^2/NDF = 770.101 / 80 = 9.62626      Chi^2/NDF = 802.416 / 89 = 9.01592
Chi^2/NDF = 362.733 / 80 = 4.53416      Chi^2/NDF = 382.198 / 89 = 4.29436
Chi^2/NDF = 195.9 / 80 = 2.44875        Chi^2/NDF = 205.531 / 89 = 2.30934
Chi^2/NDF = 150.127 / 80 = 1.87659      Chi^2/NDF = 190.486 / 89 = 2.14029
Chi^2/NDF = 114.185 / 80 = 1.42731      Chi^2/NDF = 123.297 / 89 = 1.38536
Chi^2/NDF = 127.134 / 80 = 1.58918      Chi^2/NDF = 141.269 / 89 = 1.58729
Chi^2/NDF = 171.594 / 80 = 2.14493      Chi^2/NDF = 181.939 / 89 = 2.04426

Limiting the Amount of Material

Since low pT events are corelated with the vertex position being upstream, an additional cut is introduced requring the vertex position > -50 cm.  The farther upstream particles pass through more material not only because they start farther upstream, but also becaues of the angle with which they pass through the material.  E.g. particles produced at a vertex more downstream may miss the SVT and/or pass through its cables at a less oblique angle.  Results are attached, and the reduced chi^2 is listed below.  Note: the agreement between data and MC is much improved.

Chi^2/NDF = 283.12 / 80 = 3.539
Chi^2/NDF = 287.038 / 80 = 3.58798
Chi^2/NDF = 228.861 / 80 = 2.86077
Chi^2/NDF = 145.791 / 80 = 1.82238
Chi^2/NDF = 124.509 / 80 = 1.55637
Chi^2/NDF = 93.005 / 80 = 1.16256
Chi^2/NDF = 120.36 / 80 = 1.5045
Chi^2/NDF = 207.536 / 80 = 2.5942

For comparison, the comparable background fits for the preliminary results are in Weihong He's thesis, figures 5.25 through 5.31.  Reduced chi^2 values are typically in the 1-4 range, with some as high as 6 or 7.  There is not a perfect correlation, but it seems this last set of reduced chi^2 is often lower than those in the thesis, and the worse case here is much better than the worse case there.