In an attempt to confirm the findings made by Adam Kocoloski (see here), to perhaps determine where time-dependency is occurring in the BEMC (assuming that there is any localization), and to extend the analysis to 2008 data, we have created and applied analysis tools to off-line EMC calibration data, analyzing ADC tower response with regard to time.  This work directly extends the analysis tools developed by Matthew Walker, and uses the EMC off-line calibration data that he maintains.

A sample of our results is shown below for 2006 data:

Originally, we had intended to examine every tower on every run and attempt to track tower gains individually, creating histograms for mip position at each pairing.  We tried this first with the 2008 data, but this proved unworkable as there simply were not enough events to analyze tower/run gains individually.  We found, however, that if we accumulated histograms for eta bins over fills, occupancy was much better and analysis could be performed.  This technique was extended to the 2006 data.

Once histogram creation was complete, for each eta bin/fill histogram we then attempted to apply a Gaussian fit across ADC tower responses.  We discovered a number of irregularities in attempting to apply this fit, so many so that we abandoned the legacy Gaussian fit methodology and instead used a Landau fit.  This appeared to give far fewer errors during the fit process, and also appeared to fit the ADC tower response histograms better than a Gaussian fit.  However, this fit did not work perfectly, both because there were histograms with too few events to even attempt a Landau fit, and because the fit applied incorrectly to some histograms.  Histograms that could not be fit appeared to have three to five events, probably corresponding to three or fewer bins with occupancy.  When a fit was attempted for these histograms, zero or fewer degrees of freedom were reported by root.  We eliminated these bin/fill histograms from our consideration since they could not yield statistically significant results.  We were able to correct the fits in the second category somewhat.  If a naive Landau fit gave a peak result of less than zero, which is not a reasonable fit since it fails to reflect any physical phenomenon, we attempted to correct that fit by eliminating bins over 100 ADC tower response in the fit.   Note that this correction was only applied to 2006 data.  Out of 220 known bad fits (fits with ADC tower response less than zero), 60 fits could be corrected in this way.  This left 160 towers with less than zero ADC tower response.  A table of low occupancy bin/fill histograms and known bad bin/fill histograms can be found at the end of this post.

The histograms with their associated Landau fits for 2006 data can be found here, and for 2008 data can be found here.  Examining these histograms will reveal that the 2008 data has events well below zero in many of the histograms.  The 2006 histograms also display negative events, but this is not nearly as prevalent in the 2006 data as in the 2008 data.  These negative ADC responses are apparently due to a zero ADC tower response in the calibration data which then has a pedestal correction applied.  Our analysis suggested that the 2006 data is successfully filtering out most towers that would give rise to negative events, but the 2008 data is not.  The method for filtering events has not changed from the 2006 data set to the 2008 data set (we use status tables as our primary filtering mechanism), and we are uncertain why this problem is occurring.  Also, please note that there is a relatively low-occupancy "zero" fill present in the 2006 data.  This fill number was included in the off-line calibration data, and we are uncertain at this time as to the correct fill number(s) for this data.  Finally, in the 2006 fits, histograms that were re-fit with ADC tower response bins over 100 eliminated from the fit will appear with a red fit line rather than a yellow fit line.

The final results of this analysis gives us mip peaks over time.  Plots of the mip peaks over time for the each eta bin for the 2006 off-line calibration data are available here.  One of these plots can be seen in Figure 1 for the 9th eta bin.

For each of these plots, eta bin 1 corresponds to eta = -1, eta = 0 occurs between eta bins 20 and 21, and eta bin 40 corresponds to eta = 1 (fill number mappings are provided at the end of this article).  On each plot the Landau peak error is also shown, calculated using GetParError(1).  In green, the mip mean values and associated errors are also ploted for comparison.  Finally, a constant linear fit has been applied to each graph.

Once these plots were created, we calculated the chi^2 for each eta bin.  The chi^2 per eta bin is plotted in Figure 2 and included in the 2006 data analysis results file.  There appears to be significant deviation from the fit in Figure 1, as well as in the graphs of the other eta bins, suggesting that there is a time dependence in the information captured by the BEMC.  This is further supported by the large chi^2 values in Figure 2.  For clarity, a weighted average of every 4 fills was calculated and plotted and a constant linear fit applied.  These results are included in the data analysis results file, and an example can be seen in Figure 3 for eta bin 9.  Finally, for completeness, the chi^2 for the graphed weighted averages was calculated.  This plot can be seen in Figure 4.

This same process was repeated for the 2008 data:

There was significantly less usable 2008 data, and while weighted averaging was completed, it was not necessary to see trends in the data.  There does appear to be some significant time-related deviation in the first four fills, but overall time-dependence in the 2008 data is not nearly so pronounced as in the 2006 data.

For a complete set of mip position fits, data graphs, and chi^2 graphs, including the weighted average graphing for the 2008 data, see the following two PDF files:

gainsOverTimeRebin2006(2).pdf

gainsOverTimeRebin2008(2).pdf

It is possible, from the archived postscript files linked above to determine the mapping from actual fill numbers to the "Fill Time" on the individual eta bin mip position graphs.  However, for ease of use, a table of mappings is provided here:

2006 Fills

The complete code used to generate these graphs and histograms can be found here.

2006 Chi^2 Information for Non-Weighted Average Plots

Below are 3D graphs of the bin/fill mip peak deviations and weighted deviations from the mean, both corrected by elimination of the known bad and low occupancy points, and without those corrections.

Row 1:  Starting with the unweighted, uncorrected peak deviations from the mean (calculated using the formula (peak-mean)/mean):

Row 2: Next, the uncorrected weighted deviations (calculated using the formula (peak-mean)/error):

Row 3: Next, the corrected peak deviations from the mean (calculated using the formula (peak-mean)/mean):

Row 4: Finally, the corrected weighted deviations (calculated using the formula (peak-mean)/error):

Most Significant High/Low Deviation Fills per Eta

Low Statistic Eta-Fills

Known Bad Fit Eta-Fills