The performance of the track matching algorithm in Brunel v31r8 is discussed. An event weighted efficiency of $82.3 \%$ is found for a ghost rate of $8.9 \%$

Needham, M

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LHCb note 2007-129Performance of the track matchingM. NeedhamCERN ∗October 4, 2007AbstractThe performance of the track matching algorithm in Brunel v31r8is discussed. An event weighted efficiency of 82.3% is found for a ghostrate of 8.9%.∗Present Addresss: Laboratoire de Physique des Hautes Energies, Ecole PolytechniqueFe´de´rale de Lausanne .1 IntroductionThe track matching algorithm at the time of the DC’ 06 data challenge [1] isdescribed in [2]. Since then there have been improvements in the inputs tothe algorithm — the T seeds and the VELO tracks. This has led to a bettertrack matching algorithm with a lower ghost rate and higher efficiency. Therelevant changes to the T-seeds are as follows. First, the performance of theT-seeding has improved [3]. This led to an increase in the matching efficiencyby around 1 % whilst reducing the ghost rate by 0.7 %. Second, the quality ofthe Kalman fit that is performed on seed tracks after the pattern recognitionstep has been improved [4].The quality of the VELO tracks has also improved. The final step in theVELO pattern recognition is to fit a straight line to the VELO track candi-date. To account for multiple scattering in this procedure hits further awayfrom the interaction point are deweighted [5]. Consequently, the track pa-rameters, determined by this procedure, are not optimal at the exit of theVELO where the matching is performed. By reducing this de-weighting pa-rameter and performing the fit in the opposite sense a better estimate ofthe track parameters for the matching was obtained. This increased the ef-ficiency of the track matching increased by ∼ 1 % whilst reducing the ghostrate by 4 % [6]. Finally, a second pass VELO tracking algorithm, based onbuilding spacepoints has been implemented [7]. This algorithm increases theefficiency of the VELO track finding by 1 %. In particular the performancefor Ks decays products has been improved. The efficiency of the VELOtracking for tracks for tracks of this type is increased from ∼ 84 % to 91 %1.In addition, the speed of the algorithm has been improved [6] by:• Minimizing the number of track extrapolations.• Caching selected VELO candidates.• An improved selection procedure for the candidate matches.• Using the information in the non-bend plane to make a fast pre-selectionof good matches before making the full χ2 calculation.1This is still worse than the performance for tracks originating from the interactionpoint where an efficiency of ∼ 95 % is obtained.22 PerformanceThe performance of the algorithm has been studied using data generated forthe DC’ 06 production reconstructed with Brunel v31r8. The following datasamples were used:• A sample of 13000 Bd → J/ψ(µ+µ−)KS(pi+pi−) events generated at thedefault LHCb luminosity of 2× 1032 cm−2s−1.• A sample of 4000 Bd → J/ψ(e+e−)K∗ events generated at the defaultLHCb luminosity of 2× 1032 cm−2s−1.• Samples of 500 inclusive b events generated at luminosities of 5, 8, 10,2 0 ×1032 cm−2s−1.The majority of results were obtained with the first sample. From the contextit should be clear when this is not the case. The definitions of efficiency andghost rate are those given in [8]. The following efficiencies are determinedwith respect to those particles which are reconstructible as long tracks.The performance of the algorithm depends on the value of the χ2match that isused. In Fig. 1 the efficiency versus the ghost rate is plotted for various valuesof this variable. From this plot it can be seen that a cut at χ2match = 900is reasonable. Using this value an event-weighted efficiency of 82.3 % isobtained 2. This is 3% higher than the corresponding DC 06 number [2].The efficiency of the algorithm depends quite strongly on the track momenta.This can be seen in Fig. 2 where the efficiency is plotted as a function of thetrack momentum. For tracks with p > 20 GeV/c an efficiency of ∼ 91 %is found. Below 20 GeV/c the efficiency falls rapidly. This reflects the factthat low momentum tracks are penalized in the matching procedure becausethe effect of multiple scattering is ignored. In Fig. 3 the dependence of theefficiency on the pseudorapidity of the track is shown. Within the LHCbacceptance the efficiency is largely flat. However, there are dips at η ∼ 3.7and η ∼ 4.3. The latter is attributed to the material of the conical 25 mradsection of the beam pipe which lies within the acceptance of the detector.The origin of the former is not clear.The efficiency for reconstructing tracks that originate from B decays hasalso been investigated. The results are summarized in Table 1. For the2The corresponding track-weighted efficiency would be 80.6 %.3Efficiency 0.76 0.77 0.78 0.79 0.8 0.81 0.82 0.83 0.84Ghost rate 00.020.040.060.080.10.12 < 9002χGhost rate  < 9002χFigure 1: Track finding efficiency versus ghost rate for various cuts on theχ2match. The points from left to right correspond to cuts at 300, 500, 700, 900,1100, 1300, 1500, 1800, 2000.p/GeV0 20 40 60 80 100efficiency00.20.40.60.81Figure 2: Track finding efficiency as a function of the track momentum.case of muons from Bd → J/ψ(µ+µ−)KS(pi+pi−) and electrons from Bd →J/ψ(e+e−)K∗ the performance is comparable to that of the inclusive tracksample. The performance for pions from Bd → J/ψ(µ+µ−)KS(pi+pi−) isworse. This is explained by the worse VELO tracking performance for tracks4η1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6efficiency00.10.20.30.40.50.60.70.80.9Figure 3: Track finding efficiency as a function of the track pseudorapidityη.TrackTrack type p (GeV)efficiency (%)µ± from Bd → J/ψ(µ+µ−)KS(pi+pi−) 33 88.1± 0.3e± from Bd → J/ψ(e+e−)K∗ 23 84.3 ±0.3pi± from Bd → J/ψ(µ+µ−)KS(pi+pi−) 12 76.7± 0.4Table 1: Efficiencies for reconstructing tracks from specific B final states.The column labeled final state efficiency refers to the efficiency for recon-structing both tracks.of this type discussed in Section 1.An event-weighted ghost rate of 8.9 % is found3 with the default value ofthe χ2match cut. This value is 4.8 % lower than corresponding DC’06 number.Since this value is stored in the Track class [9] it is possible to reduce theghost rate at a later stage — though at the expense of some loss in efficiency.In Fig. 4 the distributions for four different variables are compared for realand ghost tracks. The four variables are:3The track-weighted ghost rate is 10.9 %.5• The weighted number of measurements on the track defined as:nmeas = nV ELO + nTT + nIT + 0.5× nOT ,where the weight of 0.5 takes accounts of the fact that the OT gives onaverage twice as many measurements per track as the IT.• The χ2/ndof.• The track pseudorapidity.• The track’s transverse momentum.Compared to real tracks ghost tracks have less measurements and a worseχ2/ndof. In addition, they tend to lie at high η and also around η = 4.34. Finally, it can be seen that ghost tracks have on average a lower pT thanreal tracks. Either one or a combination of these variables could be used toreduce the ghost rate. Studies in this direction are ongoing [10, 11].The origin of ghost tracks has been also studied using the tool described in[12]. The results are shown in Fig 5. It can be seen that the majority ofghost tracks are due to a ’random’ combination of a VELO track with anunrelated T seed being chosen. The second largest source of ghosts is due tocases where either the T or VELO part of the track is classified as a ghost.The performance as a function of the number of visible interactions as de-fined in [14] has also been investigated. Fig. 6 shows the dependence of theefficiency and ghost rate on this quantity. For each additional visible inter-action in the detector the efficiency decreases by 2.5 % whilst the ghost rateincreases by 4.2 %. This behaviour is similar to that found in the previousstudies [2]. If only the number of visible interactions in the event spill effectsthe performance of the track reconstruction then efficiencies and ghost ratesfor an arbitrary luminosity can be derived directly from Fig. 6. Such a proce-dure is only valid if other effects, for example, the increased spillover at highluminosity can be neglected. The performance of the long tracking systemfor luminosities up to 2× 1032 cm−2s−1 has been also been studied directly.The results are summarized in Fig. 7. In this plot the efficiency and ghostrate as a function of luminosity are shown together with predictions madebased on Fig. 6. The latter are referred to as the limited spillover efficiencyand ghost-rate. As can be seen the efficiency of the algorithm is robust upto a luminosity of 5 × 1032 cm−2s−1. Above this the performance degrades4This effect is also attributed to the 25 mrad cone of the beam pipe.6#meas10 15 20 25 30 35 40 45 50 550500100015002000250030003500400045002χ0 10 20 30 40 50 60 70 80 90 100110210310410510η1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 602004006008001000pt/GeV0 1 2 3 4 5 6 7 8 9 10020004000600080001000012000140001600018000Figure 4: Comparison of the properties of real (points) and ghost tracks(line). The four variables considered are: number of measurements, χ2/ndof,η, pT .linearly with increasing luminosity. The ghost-rate increases linearly withthe luminosity. Above 5 × 1032 cm−2s−1 the predicted values diverge fromthose found indicating that the effect of spillover is not small.Finally, it should be noted that at a luminosity of 2 × 1032 cm−2s−1 thealgorithm takes 6 ms per event on a 64-bit 3 GHz Intel Xeon processor.3 SummaryIn this note the performance of the track matching has been updated. Theimprovements in the VELO tracking and T-seeding since DC’ 06 has resultedin a noticeable improvement in performance. It should be noted that by fullyimplementing the program of work discussed in [2] it is expected that theperformance of the algorithm can be further improved.7InconsistantPartsEMConversionHadronicGhostParentNoneDecayInFlightSpilloverAndNoiseFromPhilllllllll0 10 20 30 40 50Figure 5: R dotchart [13] showing the composition of ghost tracks in %. Thedefinitions of the ghost classes are given in [12].References[1] Gauss v25r7, Boole v12r10, Brunel v30r14, XmlDDDB v30r14.[2] J. van Tilburg and M. Needham. Updated Performance of the TrackMatching. LHCb-note 2007-020.[3] R. Forty and M. Needham. Updated Performance of the T seeding.LHCb-note 2007-023.[4] M. Needham, Tracking News, T-Rec meeting, 2nd July 2007.[5] D. Hutchcroft et al. VELO Pattern Recognition. LHCb-note 2007-013.[6] M. Needham, Tracking and Alignment Workshop, Heidelberg, 22ndFebruary 2007.8# Interactions1 2 3 4 5 6efficiency00.050.10.150.20.25# Interactions1 2 3 4 5 6ghost rate00.10.20.30.40.50.60.70.8Figure 6: Efficiency (left) and ghost rate (right) versus the number of visibleinteractions.] -1s-2cm32Luminosity [ 102 4 6 8 10 12 14 16 18 20 %0102030405060708090EfficiencyEfficiency limited spilloverGhost rateGhost rate limited spilloverFigure 7: Track Matching performance versus luminosity.[7] D. Hutchcroft, New tracking algorithm to catch Velo Ks tracks after 3Dpattern recognition, T-Rec meeting, 2nd July 2007.9[8] M. Needham. Combined Long Tracking Performance. LHCb-Note 2007-019.[9] J. Hernando Morata and E. Rodrigues. Tracking event model. LHCb-note 2007-007.[10] M. Needham, Tracking and Alignment Workshop, Amsterdam, 31st Au-gust 2007.[11] A. Perieanu, Tracking and Alignment Workshop, Amsterdam, 31st Au-gust 2007.[12] M. Needham. Classification of Ghost Tracks. LHCb-Note 2007-128.[13] R Development Core Team. R: A Language and Environment for Sta-tistical Computing. R Foundation for Statistical Computing, Vienna,Austria, 2005. ISBN 3-900051-07-0.[14] The LHCb Collaboration. Reoptimized Detector Design and Perfor-mance. CERN/LHCC LHCC-2003-030.10

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