Summary of TR2 studies

TR2 Studies

A number of problems with the TR2 counters went undectected during the FOCUS data taking period. Here we explore those problems and their implications.

Nominal TR2 Geometry

The TR2 counter consisted of 4 separate scintillators and PMT's whose signals were OR'ed together to form the TR2 trigger input. The nominal arrangement of the counters was as shown in the following figure. Each scintillator was 4.25" high, 4.25" wide and 1/16" thick. Each had a piece cut off on the middle corner in order to avoid creating regions of thick material where three or four counters overlapped.

The actual arrangement of the counters varied during the run since TR2-1 was replaced during the 1996 christmas shutdown. This replacement resulted in a gap being created between Tr2-2 and Tr2-1 which was not present in the initial arrangement. The post-christmas arrangement is shown in the diagram below.

TR2 Run Periods

In terms of TR2 efficiency four distinct run periods have been identified.

Run < 7882: Tr2-1 was inefficient during the early data taking period. This was situation was improved on Nov 21, 1996 (run 7882) by raising voltages and adjusting thresholds.
7881 < Run < 9000: Despite the voltage adjustments TR2-1 continued to degrade until it was replaced in January 1997.
9000 < Run < 10950: Unfortunately, it was not put back properly and a gap between TR2-1 and TR2-2 was created. The last "photon" run before the TR2-1 counter was run 8754 taken on Dec 23, 1996 and the first "photon" run taken with the repaired counter was run 9055 taken on Jan 20, 1997.
Run > 10950: The last significant adjustment to the counters occurred on April 11, 1997 (run ~10950) when all the TR2 signals were amplified and the discriminator thresholds were readjusted.

These effects can be clearly seen in the following scatter plots and projection plots in which the X and Y coordinate of SSD tracks extrapolated to the Z location of TR2 (as measured in the SSD coordinate system) are plotted for events containing a single reconstructed SSD track. The events were all collected using the pre-scaled TR2 trigger and so the tracks are most from likely pair conversions of photons.

Y vs X Scatter Plots Y and X Projections

The projection plots above can be used to estimate the counter efficiencies. First we define the following quantities ..

P_G = Trigger probability when the pair track is projected into the "good" region.
P_B = Trigger probability when the pair track is projected into the "bad" region.
X₁ = P_G / P_B (run>9000)
X₁ = [1-(1-P_G).(1-P_B)] / P_B (run<9000)
This is the scale factor which when applied to the events in the "bad" region, produces continuous projection plots.
X₂ = P_G / [1-(1-P_G)²]
This is the scale factor which when applied to the events in the overlap region between TR2-2 and TR2-3, produces continuous projection plots.

By measuring X₁ and X₂ we can calculate P_G and P_B for each run period. The reults of these measurements are shown below ...

Run Period	P_G	P_B
Run < 7882	0.80 +/- 0.06	0.67 +/- 0.05
7881 < Run < 9000	0.89 +/- 0.05	0.83 +/- 0.06
9000 < Run < 10950	0.77 +/- 0.06	0.43 +/- 0.04
Run > 10950	0.95 +/- 0.03	0.65 +/- 0.02

To demonstrate that we have properly calculated both the efficiencies and the counter geometries we reproduce the scatter and projection plots weighted by the inverse of the position dependent efficiency.

Weighted Y vs X Scatter Plots Weighted Y and X Projections