Description of my LH Tracking Algorithm.  It could be used as a stand along tracking algo for the FGT, or as a seed track finder to combine with standard STAR tracking systems.  The LH stands for first fitting a line, and the secondly a helix.

Residual Definition

For this algorithm, the residual will be defined between point and a line, and is the distance in the (x,y) plane at the given z of the point.  The residual between a line and a set of lines is the square root of the sum of the squared residuals between the line and each point.

The Algorithm

The algo proceeds as follows:

1. Pairs of r and phi clusters are combined into points
2. All combinations of n points, with each point on a disctinct disc, are considered
3. A line is fit by minimizing the (x,y) plane residuals.  There exists a closed form solution, so this is quite fast.
4. Candiate tracks are formed for each line where the residual between the line and the n-points in the fit is below threshold.
5. For each track, associate the closest point on each disc, such that the residual between the line and the point is below some threshold.
6. Tracks with the number of associated points below some threshold are removed from the pool.
7. If multiple tracks share more associated points than some threshold, the tracks with the largest residuals are removed.
8. Tracks are refit using the associated points (which may be different points per disc and/ot a different number of points)
9. The points on each track can then either be fit to a helix to extract the charge, pT and pZ values, or used as seed points for some other tracking algorithm.  (This step is not yet implemented).

Note: one can also add the vertex into the list of required points.  In this case, the vertex is included as one of the n points for the initial line fits (thus using only n-1 points from the FGT), and the vertex is always used in refitting the line in step 8, regardless of the residual between the vertex and the line.

Thresholds

The current options considered is to require the number of points, n, to be 3, including the vertex (2 FGT points).  The thresholds for steps 4 and 5 are both 1 cm.  The threshold for step 7 is set to 1 point, i.e. tracks are not allowed to share points on the FGT.

Results

I have analyzed events in the file st_physics_13086088_raw_3020010, taken March 26th, during the pp500 GeV running.  The following data shows the number of events/triggers and tracks for various scenarios.  So far, the amount of data analyzed is to small to make fancy plots.  The amount of data analyzed will be increased soon.

Total      triggers:  7576
EHT0-nofgt triggers:   328
EHT0-fgt   triggers:   278

Total      events with FGT tracks: 83    Total      FGT tracks: 176
EHT0-nofgt events with FGT tracks: 74    EHT0-nofgt FGT tracks: 158
EHT0-fgt   events with FGT tracks: 71    EHT0-fgt   FGT tracks: 150

Now require the track to be aimed at the EEMC:
Total      events with FGT tracks: 23    Total      FGT tracks: 37
EHT0-nofgt events with FGT tracks: 23    EHT0-nofgt FGT tracks: 37
EHT0-fgt   events with FGT tracks: 22    EHT0-fgt   FGT tracks: 36

Now require a >3 signal in one of the preshowers, postshowers, or towers:
Total      events with FGT tracks:  8    Total      FGT tracks: 10
EHT0-nofgt events with FGT tracks:  8    EHT0-nofgt FGT tracks: 10
EHT0-fgt   events with FGT tracks:  8    EHT0-fgt   FGT tracks: 10

One sees that just over half of the EHT0-fgt triggers result in an FGT track.  Only about a quarter of these FGT tracks are actually aimed at the EEMC, and of those, only about 30% leave signals in the EEMC.  Thus the ratio of EHT0-fgt triggers to FGT tracks leaving signals in the EEMC is about 28 to 1.

The following table shows the pedestal subtracted ADC values for the EEMC tower layers, in units of pedestal sigma.

   TOWERS  PRESHOWER1  PRESHOWER2  POSTSHOWER   EVENT NUMBER
  -1.5750     -0.5915     15.8572      0.0870         868734
   0.1771      0.3971     34.4638      0.9559         902215
 120.6830     49.9701      1.3521     -1.0588         907701
   4.2000      1.6765     62.1912      2.3485         917726
  16.9291      3.1831     68.8676     -0.5588         917726
  -1.2020     -1.1324      5.3582     -0.0147         920472
  -1.6423      0.5217     37.0423     22.6377         937427
  11.2021     82.5882     35.9143     -0.5942         937427
   0.2936      1.7536      9.3188     -1.6338         952156
   2.9821      5.5821     41.6323    127.7100         969835

Nine of the ten tracks leaving signal in the EEMC left >3 sigma deposit in preshower 2, while the signals in the other layers are much more sparse among the 10 events.