PrimEx - analysis of PbWO4 test data

Pedestals

Here's a note on the gain-matching algorithm.

Summary of Dave's Analysis

I need to point out that much work was done analyzing this data by Carlos Salgado, Dennis Weygand and Mina Nozer. While the analyses I present here was done independantly, it includes ideas from many discussions with them as well as others at the weekly PrimEx meetings.

The data exhibited some clearly non-linear behavior with respect to the tagger energy. This is shown here in a plot of tagger energy vs. adc value for crystal 8 (the crystal in the center of the 9 chinese_new). The band at higher ADC values comes from data when the beam was centered on this crystal. The other overlapping bands come from when the beam was centered on neighboring crystals.

The non-linearity was only evident in whichever crystal the beam was centered on (i.e. when the phototube saw lots of light). Here, plots of tagger energy vs. (pedestal subtracted) ADC value are shown for when the beam was centered on crystal 8 (top) and a neighbor (bottom). The blue lines are drawn from 0,0 to demonstrate the extent of the non-linearity(linearity) of the top(bottom) plot.

The non-linearity w.r.t. the tagger energy was removed by fitting a piece-wise function to data from beam-centered and beam-centered-on-neighbor conditions. This was done for each crystal independantly. A few examples are shown here. Since the average fraction of the shower seen by the crystal with the beam centered at different positions is not known precisely, a parameter K was included in the function and allowed to vary in the fit. The parameter K represents the ratio of the energy fraction seen by the crystal with the beam centered on it and that seen by the crystal with the beam centered on the neighbor. The curve is linear up to the "transition point" (another parameter varied in the fit) where it then changed into a 3rd order polynomial. The two functions were required to be continuous and smoothly varying at the transition point (after scaling the ploynomial by the factor K.

Here is an example of the non-linearity correction function. In this case, crystal 14. The Y-axis is in arbitrary units, but is proportional to what a linear response would be given the actual response on the X-axis. The line helps show how much the response deviates from linearity.

Here now is a plot of the tagger energy vs. the non-linearity-corrected ADC value for crystal 14. The linear response w.r.t. the tagger energy is typical for all crystals in the array.

Once the non-linearities were all removed, attempts were made to gain match the crystals. In short, this was never accomplished in a satisfactory way due to significant cross-talk between crystals. I'm not going to go into details of the evidence for this here. Sufficed to say that even with the non-linearity corrections, the central crystal only contributed about 40-45% to the calorimeter sum when it is known through simulation and literature that it should contribute more like 80% for the given geometry.

In an attempt to make a comparison between the different crystals, the resolution of each crystal was measured from data taken while the beam was centered on it. The resolution as a function of incident photon energy was determined for each crystal independantly. The table shown here lists the weighted averages of of these for incident photon energies bewteen 1 and 5 GeV. Note that these values do not have the contribution due to the energy bin widths removed. The point of this exercise ,however, is to make a relative comparison between the different crystal types.

The detailed plots from which the above values were taken can be seen by clicking on the links in the following table

Xtal 1 EPS	Xtal 2 EPS	Xtal 3 EPS	Xtal 4 EPS	Xtal 5 EPS	Xtal 6 EPS
Xtal 7 EPS	Xtal 8 EPS	Xtal 9 EPS	Xtal 10 EPS	Xtal 11 EPS	Xtal 12 EPS
Xtal 13 EPS	Xtal 14 EPS	Xtal 15 EPS	Xtal 16 EPS	Xtal 17 EPS	Xtal 18 EPS
Xtal 19 EPS	Xtal 20 EPS	Xtal 21 EPS	Xtal 22 EPS	Xtal 23 EPS	Xtal 24 EPS
Xtal 25 EPS	Xtal 26 EPS	Xtal 27 EPS	Xtal 28 EPS	Xtal 29 EPS	Xtal 30 EPS
Xtal 31 EPS	Xtal 32 EPS	Xtal 33 EPS	Xtal 34 EPS	Xtal 35 EPS	Xtal 36 EPS

Here is a summary of the energy resolution of the PbWO4 array for individual crystals. The lines indicate weighted averages for the different crystal types.

Conclusions

Two significant problems existed with this PbWO4 data:
1. Non-linear response (in all probability due to phototubes/bases)
2. Large cross-talk due to light leakage
Both of these problems can be addressed at some level using bench tests. The fact that virtually no cross-talk was observed in the data taken last November with a different, but very similar PbWO4 array indicates how sensitive the cross-talk is to packaging and wrapping techniques.
The individual crystal resolutions appear flat as functions of photon energy. This indicates a small contribution to sigma/E from the linear term.
The only crystal type showing a significant difference is the china_old. This is not surprising since the manufacturer claimed the new ones are made using improved techniques.

This data was sufficiently problematic that a precsise and accurate comparison between the crystal types is not likely in the time frame with which a decision is needed. Another few months of analysis might yield better results. In the short term, however, the resolution of individual crystals is the best indicator that could be extracted.

The results of comparing the individual crystal resolutions for the different crystal types at least shows no large difference in their performance. There is no indication here that one vendor produces crystals of such an improved quality as to make a large improvment in the precision of the final experiment. The primary weights used in choosing a vendor should therefore fall to things such as price and delivery schedule.

David Lawrence
davidl@jlab.org
Thu Sep 14 15:55:39 EDT 2000