Pi0's in Eta bins (take 2)

To recap, pions were reconstructed using Jan's pi0 cluster finder, cuts, etc... See here. A nominal 50 ch/GeV overall scale factor was used in this analysis. High tower and minbias data were treated separately. On this web page we extend the previous analysis, using the Monte Carlo to correct for the (geometric) bias in the high-tower triggers... at least to the extent that Monte Carlo generated with Epi = 6.0 GeV models the response of the trigger...

High tower pi0 energy distributions
MC (Epi = 6.0 GeV) energy distributions

The Procedure

The procedure for extracting calibrations from the pi0 mass spectra was previously outlined/attempted here.

Since M2 = 4 E1E2 sin phi / 2,

M2 / M2pi = gactual / gnow... gives us information on the gain of the towers used to reconstruct the event. Singling out the tower which contains the most energy, we can show that (to a reasonable approximation) the other towers average out, and this ratio of squared-masses vs. eta tells us about the eta-dependent (and with enough statistics, tower-by-tower) calibration.

Geometric effects distort the pi0 mass spectrum as a function of eta, however. This is much more pronounced in the high tower triggers than min bias. Thus, one needs to use the Monte Carlo to remove these geometric effects from the (high tower) data before interpreting the mass-squared ratios as calibration changes.


Uniterated pi0 analysis

Starting with the current set of calibrations in the database, pi0's were reconstructed and binned versus eta (using the eta of the most energetic tower in the two clusters). The table below shows the mean masses of pi0's reconstructed from the data (minbias and high tower triggers) and Monte Carlo data samples which roughly reproduce the key features of the data samples. The scale factors (what Piotr refers to as "k" on his calibration pages) implied by each sample are also shown.


trigger Mass(data) Mass(MC) k=(M_data/M_mc)2
minbias 0.1373 GeV 0.1350 GeV 51.7 ch/GeV
high tower 0.1638 GeV 0.1539 GeV 56.6 ch/GeV

In the top two panels of the following plot we show the squared-ratios of the measured pi0 mass in each eta bin to the mean mass (averaged over all eta bins) for the data (black circles) and Monte Carlo (red squares). The left panels show high-tower data, the right minbias.

The bottom two panels in the show the eta dependence of the data corrected for the eta dependence of the Monte Carlo (i.e. the ratio of the black and red points in the upper plots). To the extent that the Monte Carlo models any geometric bias in reconstructing the mass, the lower two plots represent the eta dependence of the actual gains to what is currently in the database.


See also high tower mass spectra and monte carlo mass spectra for MC events generated w/ Epi = 6.0 GeV.
See also high tower mass spectra and monte carlo mass spectra for MC events generated w/ Epi = 2.0 GeV.


The following table shows the relative gains extracted from the high-tower data. Different mass ranges were used in the fits when extracting these numbers... so they don't match the plot exactly. These relative gains were used to correct the high tower and minbias data samples in the "first iteration" below.


eta binrelative calibration
0 0.889412
1 0.877985
2 0.874139
3 0.929342
4 0.945187
5 1.00713
6 1.07473
7 1.05375
8 1.0762
9 1.19415
10 1.04559
11 0.939646

1st iteration

Applying the relative gain corrections in the table above to the data we obtain the following results:


trigger Mass(data) Mass(MC) k=(M_data/M_mc)2
minbias 0.13788 GeV 0.13496 GeV 52.3 ch/GeV
high tower 0.16810 GeV 0.15386 GeV 59.7 ch/GeV

Again, plotting the ratios of masses-squared vs. eta bin,...

See also high tower mass spectra and monte carlo mass spectra for MC events generated w/ Epi = 6.0 GeV.
See also high tower mass spectra and monte carlo mass spectra for MC events generated w/ Epi = 2.0 GeV.


Summary

The fact that the eta dependence of the high-tower data DOES NOT degrade the quality of the minbias data suggests that this algorithmn is not insane. (Hope I didn't oversell the point there).


Jason C. Webb
Last modified: Tue Jul 22 19:37:35 EDT 2003