Discriminant Analysis Results

In order to test the discrimination power of the DF one set of PISA output data at each energy was used for calculating the values of and . The other set of output data was then used for calculating the DF.

We find that the DF produces very good discrimination between muons and pions of known equal (or sufficiently close) momenta. However, the results depend on the ``bias'' that is chosen. For a large negative bias, all pions are correctly identified but all muons are incorrectly identified as pions. For large positive bias the reverse is true. As the bias is varied from negative to positive values around zero, the fraction of correctly identified muons increases and the fraction of correctly identified pions decreases. We present our results in a format that shows this variation with changing bias. The results of the Discriminant Analysis for the three schemes shown in Fig. 2 are summarized in Figs. 3, 4, and 5.

  
Figure 3: Discrimination efficiency for pad layout described in the PHENIX CDR (Case 1 in Fig. 2).

  
Figure 4: Discrimination efficiency for pad layout shown for Case 2 in Fig. 2.

  
Figure 5: Discrimination efficiency for pad layout shown for Case 3 in Fig. 2.

Each of these shows plots of the fraction of muon tracks correctly identified as muons (``Muon ID efficiency'') versus the fraction of pion tracks incorrectly identified as muons (``Fake Pion ID efficiency''). In all cases five discriminant variables were used:

1. Last plane hit
2. Total hits
3. Total hits divided by the number (1-6) of the last plane to register any hits
4. Ratio of total hits in first plane to register any hits to total hits in last plane to register any hits.
5. Angle between the beam axis and the straight-line fit to the road.

This set of discriminant variables is not exactly the same as used by Saskia Mioduszewski [3] but the results are very insensitive to the choice of variables. Roughly speaking, any three or four variables are sufficient and the use of more than four or five does not improve the discrimination power.

As indicated in the figures, the discrimination power is nearly perfect for all the incident particle momenta above 2.25 GeV/c. The abrupt degradation in performance below that momentum can be explained on the basis of the fact that, at about this momentum, some of the muons are not able to completely penetrate all six layers of the muon identifier. At 1.5 GeV/c none of the muons reaches beyond plane 5. At momenta for which the muons are able to penetrate all six layers, muons and pions are easily distinguished from each other. At these momenta there is no need to closely match the momentum of the particles used to produce the training data with the momentum of the test particles. For example, the results for 5 GeV/c are equally good if either 3 GeV/c or 8 GeV/c training data are used for calculating and .