RPC and DTBX Trigger Response and Resolutions

The trigger system has to be versatile in various respects. Therefore besides the knowledge of deficiencies, the trigger response as a function of the kinematical variables , and of the simulated muons has to be studied. In fig. 4 we compare the output of the RPC and DTBX trigger systems with respect to the reconstructed values of , and . In contrast to fig. 4, fig. 5 shows the kinematical regions where the two systems were unable to reconstruct a single muon.

  
Figure 4: Reconstructed , and of reconstructed muons.

  
Figure 5: Generated , and of not identified muons.

The discrete nature of the trigger output is clearly visible as well as the non linear binning, which therefore leads to non-uniform occupancies. The binnings may be later changed to different values if necessary. For DTBX could have higher precision by using more information bits, whereas could be more fine-grained by using more DTBX detector elements e.g. the third superlayer. One should notice that at this stage of the analysis and are given at the point of reconstruction (which may be at different chamber positions in space and NOT at the vertex position like the respective values of the generated muons). In the different trigger philosophies of the two systems are evident. The trigger philosophy of RPC - not to miss a high track and reconstruct a certain value with at least 90% probability - is strongly reflected in the high rate of tracks with of 100 GeV/c. In contrast the DTBX trigger will give the reconstructed values for as a distribution around the nominal trigger input value. Changes of the assignment in this respect will require another choice of bit patterns of hits for RPC or another functional dependence of the azimuthal angle difference between two stations for DTBX.

  
Figure 6: resolution for DTBX and RPC.

  
Figure 7: resolution for RPC and DTBX. Branches correspond to different charges.

In fig. 6 we display the resolution in . The shapes and the RMS values of these distributions are different (the latter being 0.06 and 0.08 units for RPC and DTBX respectively). Moreover the resolution also varies as a function of .

The resolution in (fig. 7) seems to be influenced by the fact, that and are generally measured at different reference points. The two ``branches'' of fig. 7 are related to differently charged tracks. They are narrower for tracks with higher .

Due to the quantization it is very difficult to quote a resolution . We have analyzed the distributions for several intervals. The distributions have in general more than one maximum and the widths and the mean values change with .

  
Figure 8: resolution (RMS) for RPC and DTBX.

Therefore in fig. 8 we give, only as an indication, the RMS values of these distributions depending on , as to show how the resolution evolves with increasing for the two trigger systems. Not surprisingly we also observe an dependence of the assigned value. In the crack regions the resolution is rather coarse, which also happens, if less than 3 stations are used by DTBX to reconstruct the muon.