Calibration of EEMC Towers using pi⁰ --> gamma gamma

Analysis Details

• Two cluster invariant mass spectra for were accumulated for the most energetic seed tower in each event.
• All cluster pairs which contained the high tower in the event were studied.
• EHT1 triggers were used for calibration. EHT1, EHT2 and MINBIAS triggers were separately binned.
• For EHT1 and EHT2 events, pi0's with less than 4.0 GeV energy were discarded to reduce background of "untriggered" pions.
• 25 background events were mixed for each real event.
• An approximate Z vertex was determined from BBC E-W timing information.
• The Monte Carlo was used to correct for systematic effects in the mass of the neutral pions due to the poor granularity of the detector coupled to the highly asymmetric decays.
• Monoenergetic pions were generated at 2, 4, 6 and 8 GeV.
• Invariant masses were fit in each eta bin.
• The mean energy of the background-subtracted pions in the data was used to interpolate between the different expected Monte Carlo pi0 masses.

Overview

For EHT1 events which contain two or more clusters we calculated the invariant mass of the two clusters. The mass was binned in histograms corresponding to the tower which fired the high-tower trigger (assumed to be the most energetic tower in the event, and required to be > 4.0 GeV). The combinatoric background was calculated by mixing uncorrelated clusters randomly selected from previous events with one of the two clusters from the real event.

The background-subtracted mass spectra in each tower/eta bin were then fit with gaussians to determine the pi0 mass. These were then compared with the Monte Carlo predictions for each eta bin to extract a gain correction:

h = M2 / Mpi2= 4 E1E2 sin phi / 2 / Mpi2
h = gcorrected / g

Iterated gain corrections

First iteration set439e was based on an initial set of calibrations, i.e. Piotr's MIP analysis a.k.a. set430. The plot shows the mass spectra accumulated in each eta bin, the raw gain corrections for each eta bin (top right) and the monte-carlo adjusted gain corrections for each eta bin (center right). The smaller data points in the center-right plots show the gain corrections for each tower, extracted from tower-by-tower fits which can be found in this directory. Subsector 5A seems to have the best statistics of any of the plots, subsector 7E is one of the worst.

The gain corrections were applied to obtain a calibration which I called set439e. The pi0 finder was run a second time to obtain set439f, with individual tower fits in this directory.

At some point in all of this, I decided that we lacked statistics to make definitive statements about eta bins 11 and 12 (near eta = 1). I attempted to filter these towers out of set439g (tower fits) so as not to introduce systematic uncertainties in the bins at larger eta.

Set set439h (tower fits) is about the best we can do for eta bins #1-8, I think. The poor-quality of the fits available in eta bins (10), 11 and 12 couple into bins (7), 8 and 9, increasing systematic uncertainties in those bins.

On the next iteration, I attempted to merge set439h with the MIPS, and include eta bins 11 and 12 in the analysis again. set439i was the result (tower fits). One more iteration was attempted to try to retrieve any information near eta = 1.0, fixing eta bins 1-8 to the set439h values. This resulted in set439j (tower fits). I think we've found the point of diminishing returns.

Systematic uncertainties

• Estimate 3% from uncertainties in the fits
• sector5a
• sector6a
• sector7a
• sector8a
• Estimate 5% from uncertainty in Monte Carlo correction, by looking at the pi0 masses from the MINBIAS data using calibration set 439h
minbias calibration estimate

Note from the minbias systematic uncertainty plot, it is clear that the EHT1 data gets the normalization wrong by on the order of 15-20%.

Older stuff below saved for my reference... please ignore

Gain Corrections

Below you will see the "standard" set of gain correction plots using pi0's. Invariant mass spectra are shown in each eta bin on the left. On the right, the extracted gain corrections ("h" in the above equations) are shown. The top plot shows the gain raw gain corrections in each eta bin from the data, and the expected result from the Monte Carlo.

The plot below this shows the ratio of the data to Monte Carlo corrections, i.e. the correction to the gains which we should apply to the data to reconstruct the "expected" (from Monte Carlo) mass of the pi0 in each eta bin. The smaller open square data points show the results individually for each tower.

The eta bin fit results in a calibration constant "k" equal to--