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7.6 Reconstruction Efficiency and Background Rejection
To distinguish between background and signal events a X2 cut can be applied. The effects of this cut are explained in detail and compared for both techniques. To find a good trade-off between high track reconstruction efficiency and low background acceptance, both parameters are plotted as a function of theX2for different scenarios.
In Figure 7.6 the track reconstruction efficiency for the DESY and PSI conditions assuming two tracks per frame is shown.
For the DESY conditions, the performance of both techniques is comparable as the scattering is relatively low. Therefore the difference due to ignoring the scattering for the simple tracking is small. Under PSI conditions, this is different: The shape of the efficiency as function ofX2 for the tracking with correlations is similar to the
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(a) Tracking with correlations for DESY conditions.
(b) Tracking with correlations for PSI conditions.
(c) Simple tracking for DESY con-ditions.
(d) Simple tracking for PSI condi-tions.
Figure7.6: Reconstruction efficiency as function ofX2cut value for the two methods for different amount of background hits and for both DESY and PSI conditions, assuming two hits per frame: Top plots show the tracking with correlations and the
bottom ones show the simple tracking.
DESY conditions, but their absolute efficiency is lower. This can be explained by the increased mean scattering, which leads to a higher probability of two tracks crossing each other and being misinterpreted as two different tracks. In addition a background hit at one of the planes can result in a better track candidate than the real track hit due to the scattering. In the simple tracking algorithm the reconstruction efficiency reaches a slightly higher absolute value of up to 96.5 % compared to the 94.8 % for the tracking with correlations. The shape of the efficiency curve changes strongly, which is also expected: Assuming a straight track, ignoring the scattering at the planes leads to larger residuals for more scattering and this leads per definition to a higherX2value.
Therefore the efficiency increases slower inX2 for larger mean scattering angles.
The absolute efficiency reaches never 100 % even for X2 going to infinity, if one has two or more tracks per frame. This is caused by the possibility of having two scattered tracks, which cross each other. This can result in lowerX2values another combination of the eight hits from the initial tracks.
The second relevant value to look at is the number of reconstructed fake tracks, either coming from pure background combinations or track hits combined with noise hit. In this case the normalization is not well defined. Therefore the background is normalized to the complete number of reconstructed tracks, because it gives a measure for the impurity of the track sample and the results are plotted in Figure 7.7. All plots show the
84 Chapter7 Simulations same behavior: The more noise/background hits are created, the larger the probability to fit a fake track. For lowX2values, the background is coming from reconstructed tracks, consisting of a mixture of real track hits and noise hits, while the highX2values are coming from pure background distributions.
2
(a) Tracking with correlations for DESY conditions.
(b) Tracking with correlations for PSI conditions.
(c) Simple tracking for DESY con-ditions.
(d) Simple tracking for PSI condi-tions.
Figure7.7: Background accaptance as function of theX2cutvaue for differ-ent numbers of background hits and tracks per frame assuming the DESY
and PSI conditions.
For the DESY conditions, the difference for both techniques is again very small and the overall background acceptance stays below 1 % which is a very low background acceptance. In contrast, for PSI conditions, the background acceptance for the simple tracking increases to over 6 % for the analyzed range, which can be explained: Fake tracks can be created either by pure background hits, combinations of background and track hits or wrongly assigned track hits. The probability to create these fake tracks increases with increasing scattering. The tracking with correlations shows a much faster rising background acceptance as function of theX2cut. This has to be put into perspective of the faster rising signal efficiency curve, already saturated at around 20 compared to the simple tracking, which saturates around 100.
Figure 7.6 also shows, that the absolute reconstruction efficiency of the simple tracking algorithm is higher than the one for the tracking with correlations while the background acceptance for the simple tracking is smaller compared to the other method (see Figure 7.7).
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Optimal X
2Values
The optimalX2 strongly depends on the settings. In the case of the DESY conditions, a cut value of 15 makes sense for the tracking with correlations, because the signal reconstruction efficiency is saturated and the background acceptance is below 1% for single track frames and 2% for two track frames.
For the simple track fitting, the best value is 40 for the DESY conditions, resulting in comparable signal efficiency and background acceptance.
For the PSI setup, the ideal cut value for tracking with correlations can be determined with the same arguments: The background acceptance for X2 smaller than 15 is again acceptable small and stays below 15 % and the efficiency is again saturated at up to 95 %. For the simple tracking, the cut value should be set around 100, leading to a high efficiency of up to 95 % and an acceptably background acceptance of below 6 %.
Those results depend on the amount of scattering and the geometrical properties of the setup and therefore have to be reevaluated for every setup. The tracking with correlations is stable under changes of scattering in terms of reconstruction efficiency, while the simple tracking method varies strongly with the scattering and geometry. The background acceptance is slightly lower for the simple tracking, which can be explained by the way the tracks are selected: The simple tracking minimizes the squared distances while the tracking with correlations starts at a reference plane and accepts hits with larger distances at higher plane numbers. So in the latter case it becomes more likely to pick up a noise hit on one of the last planes, which fits better than the hit corresponding to the track.