5.3 Simulated Performance
5.3.1 First Stage Simulation and Performance
The pattern-matching performance is studied for the configuration with one pixel and seven strip layers. For strip layers, a TSP SSsize of 40 strips is chosen. Pixels are also ganged together into
SSs that are long in the z coordinate (403 pixels, corresponding to half of the sensor), so that not so many patterns are spent finding tracks that are very similar inz. To maintain a relatively small
SSarea in the pixel layer, theSSis selected to be 33 pixels wide in the bending coordinate.
TSP pattern banks are produced with this configuration from a large set of single muons (up to a few billion). In the gHTT scenario, a final AM bank of 3.75 million patterns per 0.2×0.2 region inη×φis foreseen to reconstruct tracks withpT>1 GeV. To ensure high efficiency in this region, patterns are generated from muons in a slightly larger region of phase space, corresponding to 0.24×0.24 inη×φandpT>800 MeV. TheRMSof the beamspot inzis foreseen to be 5 cm, so the target fiducial region is selected to be|z|<3σ= 15 cm. Tracks are considered withd0<2 mm. The training sample of single muons is drawn with flat priors on the particlez0,d0,η,φ, and 1/pT in the ranges specified. For each muon with hits in all 8−NWClayers, theSSIDof each hit is stored as a pattern in the bank. The number of independent muons producing the same pattern is also recorded, so that only the most ‘popular’ patterns can be used for the final bank if desired.
A second strategy for pattern bank generation is also possible, instead of the one using fully- simulated single muons described above. The ‘fast inversion’ strategy uses the constants from the linear track fit (mapping 9-dimensional track coordinate space to 5-dimensional helix parameter
7In the results presented below, this is the “Step 2.2” geometry used in the pixel detectorTDR[120], in which
5. Hardware Tracking for the Trigger 70
space) to generate hit coordinates from random track parameters. In this method, five helix param- eters are randomly chosen in the specified range and the sector corresponding to these parameters is selected (with the most popular sector selected in the case of multiple matches). The corresponding fit constants are used along with 9−5 = 4 random Gaussian constraints to produce pseudo-track coordinates which are converted toSSIDs and then a pattern. Both strategies are compared, with the latter having the advantage of being significantly less computationally intensive, as muons are only needed to generate fit constants and not each pattern.
To produce the finalAMbank these (O(100 M))TSPpatterns are combined by settingDCbits to produce a bank of 3.75 million patterns. Up to two SSs may be combined for the pixel layer withDCbits in each dimension, while three are allowed in the strip layers. The maximum number ofDC bits set per pattern allowed is scanned, with the optimal number found to be small enough so that the per-layer maximum number ofDC bits has little impact. AM patterns are produced with an iterative procedure consideringTSPpatterns ranked by the number of (pseudo-)tracks that have produced each pattern. The most popularTSPpattern is added to theAMbank. Subsequent
TSP patterns are combined with existing patterns in the bank by settingDC bits in existing AM
patterns if possible, else new patterns are added to the bank. Once theAMbank contains the full 3.75 million patterns, still-to-be-consideredTSP patterns can no longer be added to the bank, but may still be used to set further DC bits in the existing AM patterns, so long as the per-pattern limits on the total and per-layer number ofDC bits is respected.
Figure 5.10 shows the single muon efficiency versus the average number of matched patterns (roads) per event in a minimum-bias sample for a variety of configurations. Banks are compared which have been produced using the fast inversion technique as well as the fully-simulated single muon patterns. The fast inversion generally does not perform as well, but the procedure should continue to be studied and tuned in order to perform its performance relative to the fully-simulated bank. The performance is also compared for banks produced with either one or twoWCs, and for matching criteria that requires only six or seven out of eight matching hits. A requirement that hits are present in all eight layers was found not to give acceptable efficiency for all configurations. For all configurations, the relative volume of patterns in the bank is varied by scanning the maximum number of DC bits allowed per pattern. A high efficiency (> 98%) is obtained for a number of configurations, with the full-simulation muon bank with two WCs, seven-of-eight logic, and a maximum of five DC bits per pattern yielding the lowest number of roads per event (220 roads, 98.6% efficient).
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Figure 5.10: The efficiency to find muon tracks is compared to the number of matched patterns (roads) as a function of the pattern bank and matching logic. Banks are compared where theTSP
bank has been produced using fully simulated single muon events as well as ‘fast inversion’ pseudo- tracks produced from the eight-layer fit constants. Banks with one and twoWCsare compared, as well as matching logic requiring six- or seven-of-eight hits. For each of these configurations (denoted by distinct colors) the number of maximum DC bits per pattern is scanned, with more DC bits giving both higher efficiency as well as a larger number of matched patterns.
5. Hardware Tracking for the Trigger 72
May 15, 2019 C. Herwig (Penn) — HTT
chi2 effect on 1st stg. efficiency
10 0 5 10 15 20 25 30 35 40 chi2/nDoF cut 0.95 0.96 0.97 0.98 0.99
1st stage eff wrt truth
eff1truth
0.989 0.99 0.991 0.992 0.993 First stage efficiency wrt truth 65 70 75 80 85 90 95
Mean 1st stage tracks
2WC.7of8.3of5.5MaxDC 5 10 15 20 25 30 35 40 chi2/nDoF cut 65 70 75 80 85 90 95
Mean 1st stage tracks
2WC.7of8.3of5.5MaxDC
Loosening could recover some efficiency.
Depending on HW details, may come 'for free'
This study done with:
2WC, 7/8, full-sim bank, max 2 DC bits
95.4% eff., 75 roads, 8.5 1st stg. tracks
Tracks with in-
road HW only
Tracks with in-
road HW only
(a) 0 20 40 60 80 100 [GeV] T p 0 0.2 0.4 0.6 0.8 1 Efficiency single muon single pion single electron (b)Figure 5.11: At left, the efficiency is shown for single muon events as a function of theχ2/nDOF requirement. The default requirement of 40 is very loose, nominally to ensure a high signal efficiency for tracks extrapolated into the second stage, and could be tightened upon further optimization. At right, efficiencies are compared for single muon, pion, and electron samples. Efficiencies are poorest for electrons due to bremsstrahlung energy losses leading to ‘kinked’ tracks, but could be mitigated by incorporating additional particle species into the sample of training events.
given by the product of hit multiplicities over each layer of the road. A loose requirement on the fit quality (χ2 divided by thenumber of degrees of freedom (nDOF)less than 40) is made andHW logic is set to retain tracks which have at least three unique hits. Overlaps are resolved by selecting tracks with more hit coordinates and a lowerχ2/nDOF. Figure5.11ashows the change in efficiency as a function of the χ2/nDOF cut for single muon events. The relative efficiency of single muons, pions, and electrons is shown in Figure5.11bfor a benchmark configuration requiring seven-of-eight matches, oneWC at most fourDC bits per pattern, and a full-simulationTSPbank.
The dependence of the number of first-stage tracks on the number of matched patterns is shown for a number of configurations in Figure 5.12a. The rate of fake tracks is further quantified in Figure5.12busing truth information associated to each track. Each hit is assigned the an identifying ‘barcode’ denoting which truth particle in the event record deposited a plurality of the hit’s charge. The ‘barcode fraction’ of a reconstructed track gives the fraction of hits originating from the same truth particle, maximized over all truth particles. For example, an eight-layer track with barcode 0.25 would have only two hits originating from the same truth particle, with the other four coming from random hits from other tracks. A requirement on the barcode fraction (often above 70% or 80%) may be used as a sensible definition of fake tracks.
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7of8, 1WC, Fast Inversion 6of8, 1WC, Fast Inversion 7of8, 1WC, full-sim 6of8, 1WC, full-sim 7of8, 2WC, full-sim 6of8, 2WC, full-sim (a) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Barcode fraction of Match 0 200 400 600 800 1000 N Tracks (b)
Figure 5.12: At left, the relation between the number of matched patterns (roads) and first-stage tracks is shown for the same variety of configurations considered in Figure 5.10. At right, the barcode fraction for the set of accepted first-stage tracks is shown for the optimal previously selected in Figure 5.10 (using the full-simulation muon bank with two WCs, seven-of-eight logic, and a maximum of fiveDC bits per pattern yielding 220 roads and 13 tracks). The entry corresponding to tracks with 100% barcode fraction is suppressed, with 36% of first-stage tracks found to have a barcode fraction of less than 70%.