The performance of the track reconstruction for `Long Tracks' in DC'~06 is presented in detail. An event weighted efficiency of 89.4 % is found for a ghost rate of 16.7 %

Needham, M

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LHCb note 2007-019Combined Long TrackingPerformanceM. NeedhamCERNMarch 12, 2007AbstractThe performance of the track reconstruction for ‘Long Tracks’ inDC’ 06 is presented in detail. An event weighted efficiency of 89.4 %is found for a ghost rate of 16.7 %.1 IntroductionIn this note the performance of the tracking system at the time of DC ’06 [1] isdescribed. The layout of the LHCb detector is shown in Fig. 1. The trackingsystem consists of the Vertex Locator (VELO) [2], the Trigger Tracker (TT)[3] and three stations placed downstream of the magnet (T1-T3). Each ofthe T stations is further divided into an inner and outer part. The innerpart makes use of Silicon micro-strips [4] whilst the outer part is constructedusing straw-tubes [5]. The angular coverage of the system is 15 – 300 mradwhich corresponds to a range in pseudorapidity, η of 1.9 to 4.9.M1M3M2M4 M5RICH2HCALECALSPD/PSMagnetz5my5m10m 15m 20mTTT1T2T3VertexLocatorFigure 1: Side-view of the LHCb detector.The studies presented in this note are focused on the performance for tracksthat traverse the entire spectrometer. These so called ‘Long Tracks’ aremeasured with the highest precision and are the most important sub-set forthe reconstruction of B mesons. The reconstruction of Long Tracks proceedsas follows:VELO Tracking: A standalone search is made for straight line track seg-ments in the VELO [6].Forward Tracking: Continuations of the VELO tracks are searched for inthe T stations using an optical method [7, 8].Fit: The forward tracks are fitted using a Kalman filter algorithm whichproperly takes account of multiple scattering and energy loss within2the detector [9].Seeding: A standalone search is made for track segments in the T stations[10].Matching: The track segments found in the T stations are extrapolatedupstream to the VELO. The predicted track positions are compared tothose of the VELO track segments and a χ2 criterion is used to selectgood matches [11].Fit: The matched tracks are fitted using the Kalman filter.Clone Killing: The tracks found by the forward tracking and matching arecombined. As a final step a clone killing algorithm is run to select thebest track from among those that share many hits [12]. If two or moretracks are flagged as clones the one with the most hits is selected.In both the match and forward algorithms information from the TT stationis added only at the end of the pattern recognition step. In the case of theforward tracking it is used as one of several criteria to validate a candidatetrack.The performance studies were done using data generated for the DC’ 06production. For the reconstruction Brunel v30r14 and XmlDDDB versionv30r14 were used. Four data samples were used:• A sample of 25000 B+ → D0K+ events generated at the default LHCbluminosity of 2× 1032 cm−2s−1.• A sample of 2000 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−)KS(pi+pi−) events generated at thedefault LHCb luminosity of 2× 1032 cm−2s−1• A sample of 1000 Bd → J/ψ(µ+µ−)KS(pi+pi−) events generated at aluminosity of 5× 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.32 DefinitionsIt is first necessary to define performance indicators for Long tracks. Aparticle is defined to be in the LHCb acceptance if it satisfies the followingcriteria:• The particle momentum at its production vertex is more than 1 GeV/c.• Three reconstructed clusters in the r sensors of the VELO.• Three reconstructed clusters in the φ detectors of the VELO.• A reconstructed x and u hit in each of the tracking stations T1-T3.• It does not interact hadronically before the end of the T stations.The track reconstruction efficiency is then given by:efficiency = N(accepted ∩ track reconstructed)/N(accepted )For the efficiency calculation all particles except electrons satisfying the aboveacceptance criteria are used regardless of their origin. Electrons are excludedbecause the majority originate in secondary interactions such as photon con-versions. These have little physics interest but are more difficult to recon-struct due to subsequent bremsstrahlung in the detector material. To deter-mine whether a Monte Carlo has been reconstructed an association algorithmis needed. A track is said to be related to a true particle (MCParticle) ifmore than 70 % of the clusters in the VeLo come from that particle and morethan 70 % of the hits in the seeding region also come from that particle. Thechoice of these criteria is somewhat arbitary and will investigated further inSection 3.The other important indicator of the tracking performance is the ghost rate.The is defined as:ghost rate = N(rec tracks not related to a MCParticle)/N(rec tracks)Both the efficiency and the ghost rate can be calculated in two ways. The firstis to calculate these quantities on an event-by-event basis (’event weighted’).If values for the whole event sample are required the averages of the resultingdistributions are used. The alternative is simply to calculate the efficiencyand ghost rate on the whole sample of tracks ignoring which event the trackcame from (’track weighted’). Since there are large event-to-event fluctua-tions in the case of the ghost rate the first method is preferred and will beused for the majority of the results presented in this note.43 PerformanceOn average 33.7 tracks are reconstructed per event of which 59 % are offorward type and 41 % are of match type. The matched tracks that arechosen in place of the corresponding forward track by the clone killer are ofhigher quality. For example the momentum resolution of the best tracks is4.6 per mille compared to 4.7 per mille for forward tracks alone.Using the definition given in Section 2 an event weighted efficiency of 0.894is found 1. If only the Forward Tracking is run an efficiency of 0.86 is foundshowing that the track matching contributes noticeably to the overall effi-ciency. In Fig. 2 the dependence of the efficiency on the pseudorapidity of thetrack is given. Across the majority of the LHCb acceptance the efficiency isflat. However, there is a dip at a η ∼ 4.3. This is attributed to the materialof the 25 mrad section of the beam-pipe which lies within the acceptance ofthe detector. Fig. 3 shows the efficiency as a function of momentum. It canbe seen that:• Below ∼ 10 GeV/c the efficiency falls rapidly. This is because the size’sof search windows are typically dominated by the effect of multiplescattering in the detector which increases at lower momenta.• Above 10 GeV the efficiency reaches a plateau at around 0.95This performance is similar to what was achieved in the past [13]. Since boththe forward and matching algorithms use VeLo seeds as input the maximumperformance that can be achieved is limited to the efficiency of the VeLotracking algorithm which is ∼ 0.97 for high momentum tracksThe efficiency for reconstructing tracks that originate from B decays has alsobeen investigated. The results are summarized in Table 1. For the case ofmuons from Bd → J/ψ(µ+µ−)KS(pi+pi−) a comparable performance to thatobtained with the inclusive track sample is obtained. For the electron case theperformance is slightly worse reflecting the fact that bremsstrahlung in thematerial of the detector makes them harder to reconstruct. The performancefor pions from Bd → J/ψ(µ+µ−)KS(pi+pi−) where the pion’s give sufficienthits in the VeLo to be reconstructible as long tracks is poor — there is only a76% probability to reconstruct such a particle. This is partially attributed tothe worse performance of the VeLo track finding for particles that originatefar from the interaction point [6].1The corresponding track weighted number would be 0.885.5η1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6efficiency00.20.40.60.81LHCb AcceptanceFigure 2: Track finding efficiency as a function of the track pseudorapidityη.p/GeV0 10 20 30 40 50 60 70 80 90 100efficiency00.20.40.60.81Figure 3: Track finding efficiency as a function of the track momentum.The event weighted ghost rate is 0.17 2. This is worse than the value of 0.10achieved in the past [13]. The degradation in performance is attributed to2The corresponding track weighted number would be 0.21.6TrackTrack type p/GeVefficiency (%)µ± from Bd → J/ψ(µ+µ−)KS(pi+pi−) 33 94.2± 0.5e± from Bd → J/ψ(e+e−)KS(pi+pi−) 34 90.1± 0.4pi± from Bd → J/ψ(µ+µ−)KS(pi+pi−) 12 75.6± 2.2Table 1: Efficiencies for reconstructing tracks from specific B final states. Thecolumn labeled final state efficiency refers to the efficiency for reconstructingboth tracks.several factors. First, the occupancy in the T stations has increased by up to40% as a result of a more realistic beam-pipe design [14, 15] and the decisionto increase the size of the Outer Tracker readout gate from 50 ns to 75 ns[16]. In addition, the size of the magnetic field in the region of the TT stationis reduced. This makes the use of information from this station less effectivein identifying ghost tracks.In Fig. 4 the properties of ghost and real tracks are compared for four vari-ables: the weighted number of measurements on the track defined as:nmeas = nvelo + nTT + nIT + 0.5× nOT 3,the χ2/ndof the track pseudorapidity and finally the track’s transverse mo-mentum. Compared to real tracks ghost tracks have less measurements andhave a worse χ2/ndof. In addition, they tend to lie at high η and also aroundη = 4.3 4. Finally, it can be seen that ghost tracks have lower pt than realtracks. By cutting either on one of these variables or a combination of themthe ghost rate can be reduced at the cost of reduced efficiency. In the caseof the Match tracks the criteria used to select a good combination of VeLoand T-seeds is stored in the track and can be used to reduce the ghost rate[11].The simplest and most intuitive variable to use to reduce the ghost rate isthe χ2/ndof of the track fit. Fig. 5 shows the variation of the efficiency versusghost rate as a function of a cut on this quantity. From this plot it can beseen that by requiring χ2/ndof < 25 the ghost rate can be reduced to 0.14with negligible loss in efficiency. Such a cut also removes the majority of the3The weight of 0.5 takes accounts of the fact that the OT gives twice the number ofmeasurements per track to the IT.4This effect is also attributed to the effect of the 25 mrad cone of the beam-pipe.7#meas10 15 20 25 30 35 40 45 50 550200040006000800010000120001400016000180002χ0 50 100 150 200 250 300 350 400 450 50010210310410510η1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6010002000300040005000pt/GeV0 1 2 3 4 5 6 7 8 9 1010210310410510Figure 4: Comparison of the properties real (points) and ghost tracks(solid). The four variables considered are: number of measurements (topleft), χ2/ndof (top right), η (bottom left), pt (bottom right)ghosts with η > 5.3 which are outside the physical acceptance of the detector.This illustrates the fact that many of the variables that can be used to reducethe ghost are corelated. The ghost rate can be further reduced, with someloss in efficiency, by cutting harder on the χ2/ndof. Since the distribution ofthe χ2/ndof is broader at lower momentum this loss is more pronounced atlow momentum.It should also be noted that since in the standard LHCb software no link tothe Monte Carlo truth is stored for hits coming from spills other than theevent one, if a track from a previous spill were reconstructed it would beclassified as ghost. However, in dedicated studies it has been found the rateof such tracks is negligible.The quality of the reconstructed tracks is good. Fig 6 shows the purity, ie thefraction of correct hits of the reconstructed tracks. The average track purityis 0.985 and very few tracks have purities below 0.9. From this plot it canbe infered that similar results will be obtained if the criteria used to define aparticle as being reconstructed (Section 2) are varied. This has been tested8Efficiency 0.65 0.7 0.75 0.8 0.85 0.9Ghost rate 00.020.040.060.080.10.120.140.16Figure 5: Efficiency versus ghost rate as a function of a cut on the χ2/ndof.The points from left to right corresponds to cuts at 2, 2.5, 3, 4, 5, 10, 25, 50,100 and ∞.directly by studying how the efficiency and ghost rate vary if the associationcriteria are varied in the range 0.6 to 0.9 (Fig. 7). It can be seen that effectof varying the association requirements is small.purity0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1110210310410510Figure 6: Track Purity.The performance as a function of the number of visible interactions as defined9Purity Cut0.6 0.65 0.7 0.75 0.8 0.85 0.9%00.10.20.30.40.50.60.70.80.91EfficiencyGhost rateFigure 7: Event-weighted efficiency and ghost-rate as a function of cut onthe hit purity required to associate it to a Monte Carlo particle as describedin Section 2.in [3] has also been investigated. Fig. 8 shows the dependence of the efficiencyand ghost rate on this quantity. It can be seen that the dependence ofthe efficiency on the number of visible interactions is quite weak. For eachadditional visible interaction in the detector the efficiency decreases by ∼0.01. The ghost rate shows a clear dependence on the number of visibleinteractions in the detector. For each additional interaction the ghost rateincreases by ∼ 0.06.Finally, the performance with data generated at a luminosity of 5× 1032 cm−2s−1has been studied. In this case an efficiency of 0.88 and a ghost rate of 0.21 isfound. If only the number of visible interactions in the event spill effects theperformance of the track reconstruction then efficiencies and ghost rates foran arbitrary luminosity can be derived directly from Fig. 8. At a luminosityof 5 × 1032 cm−2s−1, on average there are two visible interactions per Bevent. From Fig. 8 the efficiency in this case would be expected to be 0.89and the ghost rate 0.20 — in good agreement with the observed values. Athigher luminosities this extrapolation will at some point break down due toincreased spillover that further increases occupancies and detector dead-time.10# Interactions1 2 3 4 5 6efficiency00.10.20.30.40.50.60.70.80.9# Interactions1 2 3 4 5 6ghost rate00.050.10.150.20.250.30.350.40.45Figure 8: Efficiency (left) and ghost rate (right) versus the number of visibleinteractions.4 Summary and OutlookIn this note the performance of the pattern recognition for finding long trackshas been described. An efficiency of ∼ 0.95 is achieved for particles above10 GeV/c. This is similar to that found in previous studies. However, due tothe more realistic description of the detector used the ghost rate has increasedfrom around 0.1 to 0.17.In the future a further reduction in the ghost rate is expected by combiningseveral variables such as the number of measurements and χ2/ndof of thetrack fit to give a single powerful discriminating variable. Such an approachis used in the Tsa seeding [10] where the number of hits on a track comparedto what is expected, the fit χ2 and kinematic information are combined into alikelihood. Alternatively, a discriminanting variable could be built from thisinformation. Such an approach would be similar to the information criteria:t = lnχ2 − 2× ndofproposed as a discriminating variable in [17].11References[1] Gauss v25r7, Boole v12r10, Brunel v30r14, XmlDDDB v30r14.[2] The LHCb Collaboration. Vertex Locater Technical Design Report.CERN/LHCC 2001-011.[3] The LHCb Collaboration. Reoptimized Detector Design and Perfor-mance. CERN/LHCC LHCC-2003-030.[4] The LHCb Collaboration. Inner Tracker Technical Design Report.CERN/LHCC 2002-029.[5] The LHCb Collaboration. Outer Tracker Technical Design Report.CERN/LHCC 2001-024.[6] D. Hutchcroft et al. Velo Pattern Recognition. LHCb-note 2007-013.[7] M. Benayoun and O. Callot. The forward tracking, an optical modelmethod. LHCb-note 2002-008.[8] O. Callot and S. Menzemer. Performance of the forward tracking. LHCb-note 2007-015.[9] E. Rodrigues . The LHCb Kalman Fit. LHCb-note 2007-014.[10] R. Forty and M. Needham. Standalone Track Reconstruction in theT-Stations. LHCb-note 2007-022.[11] M. Needham and J. van Tilburg. Performance of the Track Matching.LHCb-note 2007-020.[12] E. Rodrigues. Dealing with clones in the Tracking. LHCb-note 2006-065.[13] M. Needham. Status and Expected Performance of the LHCb TrackingSystem. Nuclear Physics B, (156):217–220, 2006.[14] M. Needham. Silcon Tracker Occupancies and Clustering. LHCb-note2007-024.[15] J. Amoraal. OT Simulation. LHCb-note, in preparation.[16] J. Nardulli. Outer Tracker Occupancy Studies. LHCb-Note 2005-092.[17] A. Strandlie and R. Fru¨hwirth. Reconstruction of charged tracks in thepresence of large amounts of background and noise. Nuclear Instrumentsand Methods A, 566:157–165, 2006.12

Combined Long Tracking Performance

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