This short note will describe simulations and results obtained for the VPD Trigger detector. The STAR VPD will consist of two identical elements, each located on opposite sides of the beam vertex. Each detector will consist of 24 segments arranged in two rings around the beam pipe, with eight segments in the inner ring and sixteen segments in the outer ring. Each segment will consist of a 1/4 " thick lead Cerenkov converter with 1/4" thick quartz radiator coupled to a photomultiplier tube. The current plan is to place the two VPD elements behind the XTP which will be located approximately 420 cm from the vertex, placing the VPD approximately 500 cm from the vertex. The motivation for the following simulations was to see what the affect of placing the VPD behind the XTP would be to the vertex resolution.
The following simulations were all run with the full STAR GEANT geometries and unless otherwise noted, they were also run with the XTP in front of the VPD. The XTP geometry file used was obtained from Lynn Wood of UC Davis, and included an iron layer as well as aluminum shell, i.e full XTP geometry. The XTP was centered at 420 cm from vertex, which would place the VPD at about 500 cm from vertex. The following event files were used for the first set of simulations: 100 Au + Au events, 200 Si + Si events, and 1000 p + p events.
The three sets of events were all run at 200 GeV using FRITIOF. The timing resolution of the VPD segments were assumed to be 75 ps and an ideal start time was assumed. The following figures show the results of the vertex resolution for the three event types, Au + Au, Si + Si and p + p where all the plots show the difference between calculated vertex and Monte Carlo vertex. The Au + Au and Si + Si cases show reasonable results, with the RMS value of the difference being about 0.5 and 0.7 respectively. But the value jumps up to 6.5 for p + p with calculated vertices differing by as much as 100 cm from the Monte Carlo vertex. The RMS value can be reduced to about 1.7 by requiring the calculated vertex to be less than 5 cm from the center. This also reduces the number of events from 602 to 308. (There are 602 of the 1000 events that have particles hitting both VPD elements, + and - z.) Another way to compare the ability to calculate the vertex is to look at plots of the calculated vertex vs. the Monte Carlo vertex for Au + Au and for p + p.
In an attempt to understand the results for p + p, the following plots were made showing the distribution of minimum times of the VPD elements for Au + Au for negative z and positive z and for p + p for negative z and positive z. While for Au + Au, the minimum times are no greater than about 17 ns, p + p can have minimum times as large as 25 ns. It should also be pointed out that statistically, there are 922 hits per side per event for Au + Au as compared to 3.9 for p + p, on average.
To see if there was a way of improving the results, 1000 p + p FRITIOF Events were run through GEANT at 500 GeV, with identical geometric configuration as before. While there is improvement from the previous result of the vertx resolution, the result is the same when applying the additional constraint of having the calculated vertex less than 5 cm from center.
There were two additional simulations done with 500 GeV p + p. In both cases, the XTP was moved behind the VPD (650 cm from vertex) and the VPD was moved closer to the vertex. The following figures show the resolution for the VPD at 400 cm from vertex and for 300 cm. The constraint applied above was also applied for the 400 cm case and the 300 cm case. A slight improvement is seen in the RMS value, but nothing significant. A summary of the simulation runs is shown in the table below, where the first column shows the colliding ions, the second the energy, the VPD distance from the center, the XTP distance from the center, the number of hits per side per event, the number of events where both sides are hit (using the constraint that the calculated vertex be less than 5 cm from the center) and the RMS value of the vertex resolution, where for the p + p cases, the same constraint is applied.
The simulations described here show that the VPD is adequate for use in heavy ion collisions, for the beams tested here, Au + Au and Si + Si. For p + p there are problems due to the low multiplicity of photons per collision which in turn leads to a large fluctuation in the minimum times for particles hitting the VPD elements.
In the event that funding were not available on day 1 for the full VPD, a simulation was carried out to determine the effect a partial VPD would have on determining the vertex position for Au-Au collisions. The simulation used 97 Au-Au events at 200 GeV with the VPD array located 3 meters from center on either side of the vertex. No FTPC was used in these simulations. The VPD configurations used were full VPD with 24 elements per side, a VPD with four elements per side, and a VPD with two elements per side. The results show that there is no serious effect on determining the vertex, however there are 5-10% fewer events that are selected based on the criteria that both sides of the vertex register a hit. Thus, for at least Au-Au collisions, no serious drawback is seen for a scaled down VPD, however the effect this would have on other beam species, such as Si-Si, or Au-Au at lower energies is unknown at this point. It is a reasonable assumption that the performance would get worse due to lower multiplicities in those collisions.