5.3.1 Testing condition
As described in section 4.2, a tentative optical transmission protocol which halves the lane rate is developed for the cosmic ray test.
Besides, at the time of this test, the encoder of the TSF still had unresolved issues. Therefore, alternative TSF and 2D tracker firmwares which sends and re-ceives track segment hit map without encoding were made specifically for the test.
Because the entire hit map has to be sent through the optical transmission, there is no enough bandwidth left for the extra information attached to the track seg-ment. Thus, the 2D Tracker maps the track segment hits using all the 3 priority wire positions. Track segment information other than ID are filled with dummy data in the output.
In addition, the version of the Track Segment Finder only sent TS hits in half of the 𝑟-𝜙 plane. As a result, there will be some “dead zone” near the edge of the 𝜙 acceptance, which is shown in Fig. 5.5.
4Events with more than 4 tracks in a quarter should be triggered anyway, so it doesn’t matter which track are reconstructed by the 2D tracker.
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Figure 5.5: TS acceptance of the 2D tracker with partial hit map input. The shaded area is the partial input from the TSF. The missing TS input are shown in red.
5.3.2 Output of the 2D tracker
Several cosmic ray data sets were taken after July 4 2017. The output from the 2D tracker that accepts tracks with azimuthal angle ranging from 46.125∘ to 138.375∘was recorded. The raw data from the Belle2Link readout were converted, and the events were plotted on the geometrical plane for verification. The possible region of the reconstructed track were also plotted on the geometrical plane to aid examination.
Figure 5.6 is an event in which the 2D tracker found a single track. Some ob-served characteristics call for more explanation:
1. The reconstructed 𝜙0 seems biased. The region between the real lines are left (have a smaller 𝜙) to all the chosen track segments.
The reconstruction is not biased. The clustering uses all the input track seg-ments (including the grey track segseg-ments in the plot). The real problem is that the selection of the track segment is biased. According to the method
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r :−0.0212 φ : 78.8◦
Figure 5.6: A single-track cosmic ray event. Each grey hourglass shape is an input track segment hit to the 2D tracker. The colored hourglass shapes are the track segments associated to the found track. The real lines cover the possible region of the reconstructed track. The region between the dashed lines includes the track segments that may contribute to the cluster. The parameters (𝑟, 𝜙) are synonyms of (𝜔, 𝜙0).
specified in section 4.6.2, the rightmost track segment with a first priority (central cell) hit within the range chosen. Ideally, only the track segments in the middle will be a first priority hit, but since the priority position is miss-ing in this test, the track segment selection is degraded. The bias analysis will be performed after the 2D tracker receive the complete track segment information. If the Track Segment Finder send multiple first priority hits, or multiple second priority hits without a first priority hit, the output of the 2D tracker would still be biased. Then, depending on the impact to the 3D tracker, it might be desirable to change the current track segment selection scheme of the 2D tracker.
2. The input track segment hit in superlayer 0 is missing
Its cause in this event is simple: This is a cosmic track with a large impact parameter 𝑑0. The incident angle in the innermost superlayer exceeds the acceptance range of the Track Segment Finder. Thus, no track segment is
.. found. Other than large 𝑑0, the efficiency to find a track segment in the inner superlayers will also be lower for cosmic tracks with large 𝑧0, since the length is shorter for the inner sense wire.5
Another single-track event is shown in Figure 5.7. In this event, track segments from all 5 axial superlayers are present, and the selection is also not biased.
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r :−0.0106 φ : 66.4◦
Figure 5.7: Another single-track cosmic ray event
Perhaps more eyebrow-raising are the events in which the 2D tracker found multiple tracks. In Figure 5.8, a cosmic ray with large 𝑑0 passed through the CDC, and the 2D tracker found 3 “jets.” In the first jet, there were 3 tracks with 𝜔 = −0.0097 cm−1 found with the track segments in the 4 outer superlayers. The second jet contains 4 tracks with 𝜔 from −0.0159 cm−1to − 0.0176 cm−1, found with track segments in superlayer 0, 2, 6, and 8. The third jet contains the 2 tracks with the largest curvature given by hits in the 4 inner superlayers.
A closer look at its input revealed that these clones are cause by the timing of the input track segments. In Figure 5.9, the incoming hits in clock 280 produces
5In principle, the 2D tracker is designed to be inefficient to the tracks with large impact param-eters, which are dominated by the cosmic rays and the secondary tracks produced by the beam backgrounds. While the 2D tracker is in principle not sensitive to 𝑧0, the track segment hit in the innermost superlayer might provide additional discriminating power to veto tracks with large 𝑧0. The option to make it mandatory for all tracks to have a hit in superlayer 0 is under evaluation.
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Figure 5.8: A multi-track cosmic ray event from a single source
the initial track at clock 290. The subsequent hits from clock 282 to 285 changed the cluster shape, and thus the 2D tracker gave new outputs to account for the possible updates from the Track Segment Finder. The cause of 2 or 3 output tracks in a same clock cycle is either because the cluster size exceeded the 9 × 9 cells specified in the algorithm, or there were disconnected clusters in this event.
What’s worse, starting from clock 296, some hits appeared again in the input to the 2D tracker. These secondary hits would make the 2D tracker find more clones after 10 clocks. The main reason that they didn’t show up is because we were not expecting such TSF response, so the Belle2Link was configure to take data within only 24 clock cycles.
Two additional events with “multi-jet” output are displayed in Figure 5.10and Figure 5.11.