SVT Track-Hit matching - Year 1

Introduction:

The purpose of this study is to evaluate the SVT hit reconstruction using the TPC reconstructed tracks. Three main aspects were/will be considered here:

Selecting and Projecting TPC tracks:

The TPC recosntructed tracks were taking from a DST file from production P00he. The requirements to accept a track as a good one are:

In addition, the event itself must have a valid vertex at z position between -20.0 and +50.0 cm.

The projection is performed using the StHelix object from Star Class Library. The helix is projected to the plane xz at y=10.4 cm.

Reconstructing the SVT hits:

The reconstruction of the SVT hits is perfromed using the code in CVS. It's a transcription of the code used for the E896 experiment. Therefore, some tunning to the STAR environment still needs to be done.

The cluster finder reports the hit position in local wafer coordinates, i.e., anode and time bin number. In order to compare these positions to the track extrapolations, they need to be transformed to STAR global coordinates. The transformation equation is given by the expression:

Therefore, three quantities are necessary to perform such transformation:

For the results presented bellow, just 2 wafers were used (the best ones): 5 and 7. The values used for the quatities described above are:

The first test one can perform about the aproach used to get the clusters and the tracks extrapolated to the ladder is to correlate the number of clusters found in each hybrid with the number of tracks extrapolated to the hybrid. This comparison is shown in Figure 1.

Figure 1: Number of tracks extrapolated to the hybrid (X-axis) versus the number of hits in the same hybrid (Y-axis). The top left correspond to wafer = 5, hybrid = 1, the top right to wafer = 5, hybrid = 2, the bottom left correspond to wafer = 7, hybrid = 1 and the bottom right to wafer = 7, hybrid = 2.

Residuals:

The residuals are given by the difference between the hit postion and the position where the reconstructed TPC track hits the ladder. Therefore, it folds both the SVT hit position resolution AND the track extrapolation resolution.

A hit and a track are "matched" when the distance between them is the smallest possible. In order to avoid any bias during the track-hit matching, the process was unfolded in the two independent directions x and z, i.e., when the track-hit matching is performed in the z direction, only residuals in the x direction are considered, and vice-versa.

Figure 2 shows the residual in the z direction, but taking the distance of closest approach in the same direction (therefore, biased). Figure 3 shows the residual in the x direction, but taking the distance of closest approach in the z direction (in principle, not biased).

Figure 2: "biased" residuals in z direction expressed in cm. The bias comes from the demanding of matching between hits and tracks in the same direction. The top left correspond to wafer = 5, hybrid = 1, the top right to wafer = 5, hybrid = 2, the bottom left correspond to wafer = 7, hybrid = 1 and the bottom right to wafer = 7, hybrid = 2.
Figure 3:residuals in x direction expressed in cm. The matching between hits and tracks is performed in the z direction. The top left correspond to wafer = 5, hybrid = 1, the top right to wafer = 5, hybrid = 2, the bottom left correspond to wafer = 7, hybrid = 1 and the bottom right to wafer = 7, hybrid = 2.

The peak at the origin in Figure 2 should not be considered as a proper match (as will be stressed later). However, the peak in Figure 3 (the indepent direction from the match direction) is a clear evidence of real matching between hits and tracks. It also shows a ~+0.5 cm displacement of the ladder in x direction.

The same exercise can be done demanding the match in the x direction, instead of z. Figures 4 and 5 show the residuals in x and z directions, respectively. Once again, the peak at zero in the z-residuals distribution confirms the real matching between tracks and hits.

Figure 4: "biased" residuals in x direction expressed in cm. The bias comes from the demanding of matching between hits and tracks in the same direction. The top left correspond to wafer = 5, hybrid = 1, the top right to wafer = 5, hybrid = 2, the bottom left correspond to wafer = 7, hybrid = 1 and the bottom right to wafer = 7, hybrid = 2.
Figure 5:residuals in z direction expressed in cm. The matching between hits and tracks is performed in the x direction. The top left correspond to wafer = 5, hybrid = 1, the top right to wafer = 5, hybrid = 2, the bottom left correspond to wafer = 7, hybrid = 1 and the bottom right to wafer = 7, hybrid = 2.

Once we get confidence in the matching procedure (through the exercises described above), the next step corresponds to perform the matching taking in account both directions, i.e., calculating the distance of closest approach in R, where: R = sqrt(dx**2 + dz**2).

The residuals obtained from such procedure can be visualized in Figures 6 and 7.

Figure 6:residuals in x direction expressed in cm. The matching between hits and tracks is performed in the r direction. The top left correspond to wafer = 5, hybrid = 1, the top right to wafer = 5, hybrid = 2, the bottom left correspond to wafer = 7, hybrid = 1 and the bottom right to wafer = 7, hybrid = 2.
Figure 7:residuals in z direction expressed in cm. The matching between hits and tracks is performed in the r direction. The top left correspond to wafer = 5, hybrid = 1, the top right to wafer = 5, hybrid = 2, the bottom left correspond to wafer = 7, hybrid = 1 and the bottom right to wafer = 7, hybrid = 2.

From these figures, one can conclude that the folded SVT position resolution and the reconstructed TPC track extrapolation resolution, consists of:

  • x direction : ~0.1 cm
  • z direction : ~0.3 cm

Probing the procedure:

In order to make sure that the matching procedure used is not creating some "bogus" peaks and correlating tracks and hits that do not correspond to the same particle, two tests were performed.

The first one corresponds to a event mismatch approach. Reconstructed tracks from one event are taken, and the match procedure is applied to clusters from another event. The expectation is to get no peaks whatsoever in the residuals plots, since there is no real track-hit matching in the sample.

Figure 8 shows the correlation between the number of tracks extrapolating to the ladder versus the number of hits in the ladder. It's already clear from this plot the total absence of any correlation between these two quantities.

Figure 8: Number of tracks extrapolated to the hybrid (X-axis) versus the number of hits in the same hybrid (Y-axis). The top left correspond to wafer = 5, hybrid = 1, the top right to wafer = 5, hybrid = 2, the bottom left correspond to wafer = 7, hybrid = 1 and the bottom right to wafer = 7, hybrid = 2.

Figure 9 and 10 show the residuals in x and z directions obtained when performing the matching in x direction. A peak is obtained in the x direction, since the procedure is "forcing" it. But, in the z direction, no peak can be visualized, showing the lack of correlation between tracks and hits.

Figure 9: residuals in x direction expressed in cm, using the same direction to demand matching. The top left correspond to wafer = 5, hybrid = 1, the top right to wafer = 5, hybrid = 2, the bottom left correspond to wafer = 7, hybrid = 1 and the bottom right to wafer = 7, hybrid = 2.
Figure 10: residuals in z direction expressed in cm, using the x direction to demand matching. The top left correspond to wafer = 5, hybrid = 1, the top right to wafer = 5, hybrid = 2, the bottom left correspond to wafer = 7, hybrid = 1 and the bottom right to wafer = 7, hybrid = 2.

The next test is more subtle. Instead of mismatching events, I just shift the ladder by +0.5 cm in the x direction, and perfrom the matching in this same direction. Figures 11 and 12 show the results obtained for the residuals in x and z directions, respectively. Once again, a peak is obtained in x (the matching direction), however, a spread distribution is obtained in z (the independent direction).

Figure 11: residuals in x direction expressed in cm, using the same direction to demand matching. The top left correspond to wafer = 5, hybrid = 1, the top right to wafer = 5, hybrid = 2, the bottom left correspond to wafer = 7, hybrid = 1 and the bottom right to wafer = 7, hybrid = 2.
Figure 12: residuals in z direction expressed in cm, using the x direction to demand matching. The top left correspond to wafer = 5, hybrid = 1, the top right to wafer = 5, hybrid = 2, the bottom left correspond to wafer = 7, hybrid = 1 and the bottom right to wafer = 7, hybrid = 2.

These two tests give great confidence about the procedure used in the track-hit matching, taking to the conclusion that the peaks at zero obtained in the residuals distribution, indeed correspond to a real track-hit matching between the TPC and the SVT.

Efficiency and Ghost Hits:

The next step corresponds to the calculation of the efficiency obtained with our cluster finder and the evaluation of ghost hits. The procedure used for this study is the same as before, using the distance of closest approach in R(=sqrt(dx**2+dz**2)).

The following studies were performed using tracks satisfying the following criteria:

  • primary track, i.e., points to the main vertex (dca < 3 cm), refit including the main vertex;
  • flag > 0;
  • number of fit points > 10;
Figure 13 shows the R distribution obtained for the sample.
Figure 13: distribution of distance of closest aproach between tracks and hits. The top left correspond to wafer = 5, hybrid = 1, the top right to wafer = 5, hybrid = 2, the bottom left correspond to wafer = 7, hybrid = 1 and the bottom right to wafer = 7, hybrid = 2.

The efficiency is given by the ratio between the number of tracks associated to a hit divided by the total number of tracks extrapolated to a given hybrid. A track is associated to a hit when the distance R is less than 0.8 cm.

Figure 14 shows the efficiency obtained for the 3484 events of run 1183020 as a function of the transversal momentum of the track. Figures 15 and 16 show the efficiency as a function of x and z position in the hybrid, respectively.

Figure 14: efficiency as function of transversal momentum (GeV/c). The top left correspond to wafer = 5, hybrid = 1, the top right to wafer = 5, hybrid = 2, the bottom left correspond to wafer = 7, hybrid = 1 and the bottom right to wafer = 7, hybrid = 2.
Figure 15: efficiency as function of x position (in cm, hybrid local coordinates). The top left correspond to wafer = 5, hybrid = 1, the top right to wafer = 5, hybrid = 2, the bottom left correspond to wafer = 7, hybrid = 1 and the bottom right to wafer = 7, hybrid = 2.
Figure 16: efficiency as function of z position (in cm, hybrid local coordinates). The top left correspond to wafer = 5, hybrid = 1, the top right to wafer = 5, hybrid = 2, the bottom left correspond to wafer = 7, hybrid = 1 and the bottom right to wafer = 7, hybrid = 2.

Next, one can check the fraction of clusters that are associated to a track. This fraction must reflect the probability of producing a ghost hit (1-fraction). In this case, instead of using well reconstructed primary tracks, global tracks were used. As the residuals for global tracks is worse than primary tracks, the track-hit association is considered when dca < 1.3 cm. Figures 17 and 18 show the cluster efficiency as a function of the cluster position in x and z directions, respectively.

Figure 17: fraction of associated clusters as function of x position (in cm, hybrid local coordinates). The top left correspond to wafer = 5, hybrid = 1, the top right to wafer = 5, hybrid = 2, the bottom left correspond to wafer = 7, hybrid = 1 and the bottom right to wafer = 7, hybrid = 2.
Figure 18: fraction of associated clusters as function of z position (in cm, hybrid local coordinates). The top left correspond to wafer = 5, hybrid = 1, the top right to wafer = 5, hybrid = 2, the bottom left correspond to wafer = 7, hybrid = 1 and the bottom right to wafer = 7, hybrid = 2.

Visual Inspection:

 In addition to all quantitative procedures described above, one can visually inspect the track-hit association, drawing the track and hit distributions for each event in the same graphic. Figures 19, 20 and 21 show three examples of such visual inspection. These plots can be obtained for each hybrid using the SVT online code, clicking on "Tracks Projected to Hybrids - Anode vs Time" and "Clusters - Anode vs Time" from the View option in the menu bar. For the time being, this option requires a dst file as input, instead of recosntructing the tracks from raw data.
Figure 19: tracks projected to the hybrids (crosses) and clusters (circles) plotted in x versus z local position.
Figure 20: tracks projected to the hybrids (crosses) and clusters (circles) plotted in x versus z local position.
Figure 21: tracks projected to the hybrids (crosses) and clusters (circles) plotted in x versus z position.
Figure 22: 3D representation of tracks (and their hits) that project to wafer 5, hybrid 1 (same event and hybrid as Figure 21).
Figure 23: 3D representation of tracks (and their hits) that project to wafer 5, hybrid 1 (same event and hybrid as Figure 21, zoom from Figure 22).

Using the hit-track matching:

The matching of reconstructed TPC tracks to SVT hits might be a useful tool to study and tune:

  • the time zero;
  • the drift velocity;
  • the cluster finder;

As a first exercise, one can verify how sensitive these results are to a more realistic model of the drift velocity. A first guess corresponds to a parametrized drift velocity obtained through bench measurements using the laser. The expression for the drift distance is given by (see Jun's page):

  • Drift distance (mm) = scaling_factor*(0.1481+2.7114*dt+1.7508*dt^2-0.3355*dt^3+0.0263*dt^4)
where dt is the drift time in microseconds. The scaling factor depends on various conditions, like temperature. It might be possible to get it from the calibration runs we have, since several injection lines were identified there. For the time being, it was set to unit.

Figure 24 shows the residuals in x (drift) direction obtained using the formula above for the drift distance. The sigma of the Gaussian fit is actually worse than the results obtained with a constant drift velocity (Figure 6).

Figure 24: residuals in x direction expressed in cm. The matching between hits and tracks is performed in the r direction. The top left correspond to wafer = 5, hybrid = 1, the top right to wafer = 5, hybrid = 2, the bottom left correspond to wafer = 7, hybrid = 1 and the bottom right to wafer = 7, hybrid = 2.

One can thus examine the residuals as a function of the drift distance, looking for any pattern that might reveal any important information. Figure 25 shows such plot for the procedure described above, while Figure 26 shows the same plot, but the residuals were obtained using a constant drift velocity.

Figure 25: residuals in x direction expressed in cm versus the drift distance (also in cm). The drift distance is calculated using a drift velocity parametrized by bench measurements. The top left correspond to wafer = 5, hybrid = 1, the top right to wafer = 5, hybrid = 2, the bottom left correspond to wafer = 7, hybrid = 1 and the bottom right to wafer = 7, hybrid = 2.
Figure 26: residuals in x direction expressed in cm versus the drift distance (also in cm). The drift distance is calculated using a constant drift velocity. The top left correspond to wafer = 5, hybrid = 1, the top right to wafer = 5, hybrid = 2, the bottom left correspond to wafer = 7, hybrid = 1 and the bottom right to wafer = 7, hybrid = 2.

Clearly, one can see a "funny" shape in Figure 25 (parametrized drift distance) that does not show up in Figure 26. That might be the result of the missing scaling factor. This shape is reflected in the tail of the residuals distribution. The hybrids 1 have the tail on the negative side, while hybrids 2 have it on the positive side (residual = track position - cluster position).

One can conclude from this exercise that the hit-track matching is a useful tool to examine things like this. More to come...

  

  Please send comments and sugestions to: munhoz@rhic.physics.wayne.edu.

(Last update: September 09, 1999)