LHCb-PUB-2014-004 (v4) May 20, 2014 Upgrade tracking with the UT Hits P. Gandini 1, C. Hadjivasiliou 1, J. Wang 1 1 Syracuse University, USA LHCb-PUB-2014-004 20/05/2014 Abstract The performance of the LHCb tracking system for the upgrade on long tracks is evaluated in terms of efficiency and ghost rate reduction for several different sets of requirements. We find that the efficiency is quite high and that the ghost rate reduction is substantial. We also describe the current algorithm for adding UT hits to the tracks.
Contents 1 Introduction 1 1.1 The upgraded LHCb detector......................... 1 1.2 Track definitions................................ 2 1.3 Adding UT hits to long tracks......................... 3 2 Description of the algorithm 4 2.1 UT hits and track containers.......................... 4 2.2 Description of the algorithm.......................... 4 3 Performance 6 3.1 Useful definitions................................ 6 3.1.1 Ghost rates and efficiencies....................... 6 3.1.2 Momentum cuts............................. 6 3.1.3 Geometrical cuts............................ 7 3.2 Ghost rates................................... 7 3.3 Association efficiency for good tracks..................... 7 3.4 Hit efficiency and purity............................ 9 3.5 Requiring hits only in the acceptance of the UT detector.......... 11 3.6 Stress test.................................... 12 4 Conclusions 12 References 12
Figure 1: Schematic view of the LHCb upgrade detector. 1 Introduction 1.1 The upgraded LHCb detector The upgrade of the LHCb detector is detailed in Ref. [1]. The upgraded LHCb detector is shown in Figure 1. The upgraded LHCb Tracking system will have the same geometry of the current one, with major changes in each of its composing subdetectors. It will consist of a vertex locator (VELO) [2] placed around the interaction point, a silicon strip detector located upstream of the magnet (UT) [3] and planes of scintillating fibers placed downstream of the magnet (SciFi of T stations) [3]. This note is mostly related to the UT detector. The UT maintains the general concept of the TT (four planes organized in two separate stations), but with better performance and technology optimised for the upgraded conditions of the machine. The first and the last planes have vertical strips, while those in the center are tilted at a small stereo angle of ±5 respectively. The active area of the sensor is extended close to the beam pipe, with a circular aperture of 33.4 mm from the nominal beam pipe center. 1
1719 mm UTbX UTbV Z X Y UTaU UTaX 66.8 mm 1338 mm 1528 mm Figure 2: Schematic view of the UT detector geometry. 1.2 Track definitions Depending on the properties of their trajectories, tracks can be divided into different classes, as sketched in Figure 3: Upstream track T track Long track Velo Velo track TT Downstream track T1 T2 Figure 3: A schematic view of the different types of charged tracks in the LHCb detector. Tracks are classified according to the detectors involved in their reconstruction. T3 2
Long tracks They transverse the full tracking system, from the VELO to the last tracking station, leaving hits in all the subdetectors. These tracks have the most precisely determined momentum. Upstream tracks They transverse only the VELO and the TT stations. These low momentum tracks are bent out of the detector acceptance by the magnetic field and they don t reach the tracking stations T1, T2 and T3. The momentum resolution on these tracks is usually poor. Downstream tracks They originate outside the VELO and they have hits only in the UT and T stations. Those highly displaced tracks are usually produced in the decay of long-lived particles which decay outside the fiducial volume of the VELO, e.g. K 0 S and Λ0 hadrons. VELO tracks They exit the detector angular acceptance before the UT and have hits in the VELO detector only. Usually produced at low rapidity, they are useful for the reconstruction of the primary interaction vertices. T tracks They are only observed in the T stations In this note we will concentrate only on long tracks. 1.3 Adding UT hits to long tracks UT hits are added on long tracks with the PrAddUTHitsTool tool. This is a rewriting of the existing tool for the current detector PatAddTTCoord, documented elsewhere for the current detector [4]. The code has been reorganized to pick up the new UT geometry. No major changes were required to obtain a satisfactory performance, as most of the parameters involved in the pattern recognition algorithm only depend on the magnetic field, which have not changed (same magnet). A quick preliminary optimisation was performed on MC simulations, showing comparable performance compared to the current nominal setup, therefore it will not be documented here. A more detailed and careful optimisation of the algorithm (with changes on the grouping of the hits and their χ 2 evaluation) is foreseen in the immediate future, with the main goal of getting benefits from the finer segmentation in the inner part of the detector where the occupancy is higher and so is the expected ghost rate (and misassociation of the hits). 3
Number of tracks 4000 3500 3000 2500 3 10 2000 1500 1000 500 0 0 5 10 15 20 25 30 35 40 History of the track Figure 4: Origin of the long tracks in the best container: 2.5% of the tracks are coming from the match algorithm, the rest from the forward algorithm. 2 Description of the algorithm 2.1 UT hits and track containers UT hits are added at the later stage of both the forward and match algorithms which are forming long tracks [3]. A full description of the tracking chain is beyond the scope of this note, therefore only the basic principles will be explained here. Tracks from the forward and match containers are then compared, cleaned (e.g. a clone killing algorithm is run to remove tracks with many hits in common) and then passed to the so-called best container. The origin of the long tracks in the best container is shown in Fig. 4. Therefore, we will concentrate mainly on forward tracks, which play a crucial role in the trigger as well. 2.2 Description of the algorithm UT hits are added in the last stages of tracking algorithms (independently for forward and match). They are added before any clone killer algorithm and additional cuts on the quality of the track. We summarise here the main steps of the algorithm. Several quantities have been optimised on simulation. Prepare Hits All the UT hits are retrieved and passed to the algorithm. VELO Extrapolation in y direction All hits are considered in a loop. The VELO segment of the track is extrapolated in the y direction to the z coordinate of the considered hit. As the bending plane is horizontal, a linear extrapolation is performed. Fringe fields have negligible impact on the predicted y. The hit is accepted if the predicted y pred is compatible with the sensor active region plus a tolerance ytol: y pred y sensor center < y sensor /2 + ytol 4
VELO Extrapolation in x direction The VELO segment of the track is extrapolated in the x direction to the z coordinate of the hit. The magnetic field is considered here and is represented as a kick from the VELO straight line dependent on the momentum of the track. The trajectory is therefore described as two straight lines (the VELO part and the Fiber Tracker part) intersecting at a given focal plane zutfield. The predicted x pred position is calculated as follows ( z = z hit z Velo ): x pred = x EndVelo + z dx dz [Velo] ± ttparam q p (z hit zutfield) The plus/minus sign depends on the polarity of the magnet (up/down). Hits are selected if within a window x pred x hit < xtol. Multiple scattering Multiple Scattering (MS) is taken into account projecting x hit = x pred x hit into the middle of UT and inflating it allowing some possible scattering from the original predicted position: proj hit = x hit zutproj zmspoint z hit zmspoint Sort and select Hits are sorted in a vector by increasing projections and if there are less then three hits in the container the algorithm is aborted (no hits are added to the track). Grouping of the hits Hits are grouped in a progressive way. The first projection in the vector is taken and the remaining hits are grouped if they fulfill the following empirical criterion (circular cut in the space of the parameters): proj hit proj firsthit < maxaxproj 2 (1 proj firsthit minaxproj )2 The procedure is repeated for all the hits in the array, until all groups are formed. Linear fit and χ 2 For each set of hits a linear fit is performed using a Cholesky Decomposition. An outlier-removal procedure is applied to remove hits with a bad contribution to the total χ 2. This is done iteratively until the χ 2 is below a certain threshold or there are less than four hits remaining in the set. Adding the hits The set with the smallest χ 2 and the maximum number of hits (if any) is added to the long track. 5
3 Performance This section presents the performance of this algorithm on MC simulated events in the upgrade conditions. A sample of about 50k events of B 0 s φφ decays at a luminosity of L = 2 10 33 cm 2 s 1 is used to evaluate efficiencies and ghost rates. This sample has a mean number of interaction per crossing ν = 7.6 (at 25ns). The luminosity of L = 1 10 33 cm 2 s 1 (ν = 3.8) has been also investigated for comparison. 3.1 Useful definitions 3.1.1 Ghost rates and efficiencies We define here a couple of useful definitions used throughout the note. A ghost track is defined as a track that is not matched to any MC particles. If more than one track is associated to the same MC particle, those tracks are defined as clones. The association of a reconstructed track with a MC particle is defined in terms of hit matching (70%), i.e. n terms of the number of shared hits. Clones are considered good tracks in the definition of the ghost rate as they are the copy of the same good MC particle. The ghost rate is defined as: Ghost rate = N ghost tracks N total tracks UT hits are added on tracks and used to reduce the ghost rate, as ghost tracks coming from a wrong matching of the VELO and the Fiber Tracker parts are not supposed to have hits in the UT. A track is defined to have UT hits associated if at least three UT hits (on three different planes) have been assigned by the algorithm. It is possible to attach more than four hits to the same track if more strips (clusters) are fired on the same plane. The association efficiency for tracks, passing a defined set of cuts, is thus defined as: Association Efficiency = N tracks (with UT hits) N tracks For good (not ghost) track efficiency counters, we exclude reconstructed electrons and study the MC truth of the considered tracks, e.g. if they are coming from B meson decays (b-hadron daughters). 3.1.2 Momentum cuts Several momentum cuts have been investigated in the note. For ghost rates, we considered three different sets of cuts applied to all the long tracks considered: All tracks: All long tracks in the containers p > 5 GeV/c: All long tracks with p > 5 GeV/c Trigger-like: All long tracks with p > 3 GeV/c and p T > 0.5 GeV/c 6
3.1.3 Geometrical cuts We considered cuts on the pseudorapidity of the tracks and on the fiducial volume of the UT detector (e.g. excluding tracks outside the detector acceptance). The η ranges considered are: 0 < η < 2 < η < 5 Tracks are defined to be inside the Geometrical acceptance (later referred to as in Geom) if they don t fall inside the beam pipe and they cross the active area of each of the four UT planes. Tracks are fully propagated in the magnetic field to calculate their spacial position at each plane. 3.2 Ghost rates The ghost rates for the forward track container (see Sec. 2.1) is summarised in Tab. 1. Rates are shown as a function of transverse momentum and number of visible Primary Vertices (at least 4 VELO tracks used for the PV reconstruction) in Fig. 5. The effect of adding UT hits is also shown. L = 2 10 33 cm 2 s 1 (ν = 7.6) L = 1 10 33 cm 2 s 1 (ν = 3.8) Ghost rate (all tracks) with UT hits (all tracks) Ghost rate (all tracks) with UT hits (all tracks) 0 < η < All tracks 42.6% 24.7% (rel. 0.58 ) 24.8% 14.5% (rel. 0.59 ) p > 5 GeV/c 40.1% 19.6% (rel. 0.50 ) 23.0% 10.8% (rel. 0.47 ) Trigger-like 35.5% 10.3% (rel. 0.29 ) 14.2% 4.3% (rel. 0.30 ) 2 < η < 5 All tracks 38.7% 23.8% (rel. 0.61 ) 21.5% 14.1% (rel. 0.66 ) p > 5 GeV/c 35.7% 19.0% (rel. 0.53 ) 18.6% 10.4% (rel. 0.57 ) Trigger-like 34.0% 10.3% (rel. 0.30 ) 13.0% 4.3% (rel. 0.33 ) Ghost rate (in Geom) with UT hits (in Geom) Ghost rate (in Geom) with UT hits (in Geom) 0 < η < All tracks 38.8 % 23.4 % (rel. 0.60 ) 21.0 % 13.8 % (rel. 0.65 ) p > 5 GeV/c 34.8 % 18.3 % (rel. 0.52 ) 17.7 % 9.9 % (rel. 0.56 ) Trigger-like 33.6 % 10.2 % (rel. 0.30 ) 12.7 % 4.2 % (rel. 0.33 ) 2 < η < 5 All tracks 38.1 % 23.2 % (rel. 0.61 ) 20.9 % 13.8 % (rel. 0.66 ) p > 5 GeV/c 34.9 % 18.3 % (rel. 0.53 ) 17.8 % 10.0 % (rel. 0.56 ) Trigger-like 33.7 % 10.2 % (rel. 0.30 ) 12.8 % 4.2 % (rel. 0.33 ) Table 1: forward container: mean ghost rates for different requirements and samples. 3.3 Association efficiency for good tracks The reconstruction efficiency is measured using simulation by comparing the number of correctly reconstructed tracks (good tracks) with and without UT hits assigned. Tracks are defined to be correctly reconstructed if the Velo and T station parts of the track are 7
ghostrate 0.6 0.5 0.4 forward forward (with UT Hits) ghostrate 0.6 0.5 0.4 forward forward (with UT Hits) 0.3 0.3 0.2 0.2 0.1 0.1 0 0 1000 2000 3000 4000 5000 Pt [MeV/c] ghostrate 0.6 0.5 0.4 forward forward (with UT Hits) 0 10 0 20 40 60 80 100 P [MeV/c] 0.3 0.2 0.1 0 0 5 10 15 #PV Figure 5: Ghost rates as a function of momentum and number of visible Primary Vertices (forward container L = 2 10 33 cm 2 s 1 (ν = 7.6)). associated to the same MC particle. The UT hits are considered correctly reconstructed if he Velo and T station parts of the track are associated to the same MC particle and he added UT hits are associated to the same MC particle as well. UT hit efficiencies are calculated for different requirements and specific requests on the minimum number of layers which must be fired by the associated MC particle in order for the hits to be reconstructible by the algorithm itself. Results are presented in Tab. 2 and plotted in Fig. 6. Here are some useful definition to understand the tables: All: all good tracks are considered 2 < η < 5: this geometrical cut is applied on the tracks in Geom: tracks are defined to be inside the geometrical acceptance of the detector. Tracks are fully propagated in the magnetic field to calculate their spacial position at each plane. Tracks inside the beam pipe and outside the active area of each of the four UT planes are excluded. Minimum Hits: the MC particle associated to the track is required to have at least 3 digitalised hits in 3 different planes. If this is not the case, the algorithm cannot add UT hits by definition, therefore this requirement is supposed to show the performance of the pure pattern recognition part (no detector inefficiencies included). 8
L = 2 10 33 cm 2 s 1 (ν = 7.6) L = 1 10 33 cm 2 s 1 (ν = 3.8) All 2 < η < 5 in Geom Minimum Hits All 2 < η < 5 in Geom Minimum Hits long 92.5% 97.9% 99.0% 99.0% 92.5% 97.8% 99.0% 99.0% long [p > 5 GeV/c] 90.1% 97.2% 98.7% 98.7% 90.1% 97.2% 98.8% 98.8% long [Trigger-like] 94.8% 97.8% 98.7% 98.7% 95.0% 97.9% 98.8% 98.8% long fromb 96.3% 98.3% 98.9% 98.9% 96.2% 98.4% 99.1% 99.1% long fromb [p > 5 GeV/c] 95.8% 98.1% 98.8% 98.8% 95.7% 98.2% 99.0% 99.0% long fromb [Trigger-like] 96.9% 98.3% 98.8% 98.8% 96.9% 98.4% 99.0% 99.0% Table 2: forward container: association efficiencies for different requirements on η and the number of hits left by the MC particle. Efficiency of association 1.05 1 0.95 0.9 0.85 All long Long from B 0.8 0 1000 2000 3000 4000 5000 Pt [MeV/c] 1.05 Efficiency of association 1 0.95 0.9 0.85 All long Long from B Efficiency of association 1.05 1 0.95 0.9 0.85 All long Long from B 0.8 0 5 10 15 #PVs 0.8 10 0 20 40 60 80 100 P [MeV/c] Figure 6: Efficiency of association as a function of momentum and npv (for all tracks inside the geometrical acceptance) 3 3.4 Hit efficiency and purity In this section we investigate the quality of the hits added to both good and ghost tracks. The mean number of hits (and layers) added per track is shown in Tab. 3. The number of ghost tracks which pass the UT hit requirements (more than 3 layers) is also shown for the different cuts. The hit purity is defined as: Hit Purity = N true hits added N total added 9
while the single hit efficiency is defined as: Hit Efficiency = Those quantities are shown in Fig. 7. N true hits added N true generated hits <nut hits> added <nut layers> Ghosts with UT requirement All Ghost tracks 1.79 1.74 48.3% Ghosts [p > 5 GeV/c] 1.53 1.50 40.9% Ghosts [Trigger-like] 0.83 0.81 21.8% <nut hits> added <nut layers> Hit Purity Hit Efficiency All Good tracks 3.96 3.86 0.977 0.955 Good [p > 5 GeV/c] 3.93 3.85 0.985 0.960 Good [Trigger-like] 3.98 3.89 0.994 0.973 All Good fromb 4.00 3.90 0.990 0.972 Good fromb [p > 5 GeV/c] 3.99 3.90 0.993 0.975 Good fromb [Trigger-like] 4.01 3.91 0.996 0.979 Table 3: Statistics on the quality of the UT hits added on ghost and good tracks (with different requirements). The fraction of ghosts which has 3 or more UT layers is also shown/ Tracks are required to have 2 < η < 5 and are taken from the forward container. Luminosity is L = 2 10 33 cm 2 s 1 (ν = 7.6). Purity 1.05 1 Efficiency 1.05 1 0.95 0.95 0.9 0.9 0.85 All long 0.85 All long Long from B 0.8 0 1000 2000 3000 4000 5000 P [MeV/c] Long from B 0.8 0 1000 2000 3000 4000 5000 P [MeV/c] Figure 7: Hit Purities and Efficiencies versus transverse momentum. 10
3.5 Requiring hits only in the acceptance of the UT detector In this test we consider a more refined requirement on the tracks, requiring UT hits only on tracks which are inside the active area of the detector. E.g. tracks in the beam pipe don t have UT hits by definition, therefore no requirement should be applied concerning a possible UT confirmation. We apply this request: if a track is in the geometrical acceptance of the UT, a decision is made on the UT hits. The track is kept only if it has at least 3 planes fired. if the track is in the beam hole, or outside the planes, no decision is made and the track is always kept. Results are shown in Tab. 4 and 5. No cut on η is applied. The fraction of ghosts and good tracks is also presented in the table, showing that ghosts are mostly concentrated in the beam-hole region. The η distributions are shown in Fig. 8 Ghost rate Ghost rate (UT Hits, new requirement) Ghosts in Geom. Acceptance 2 < η < 5 All tracks 42.6 % 30.6 % (rel. 0.72 ) 78.9 % p > 5 GeV/c 40.1 % 28.2 % (rel. 0.70 ) 71.8 % Trigger-like 35.5 % 15.1 % (rel. 0.42 ) 87.7 % Table 4: forward container: mean ghost rates. L = 2 10 33 cm 2 s 1 (ν = 7.6). Overall Efficiency (UT Hits, new requirement) Good in Geom. Acceptance long 99.1% 92.4 % long [p > 5 GeV/c] 98.9% 89.9 % long [Trigger-like] 98.7% 95.6 % long fromb 99.0% 96.8 % long fromb [p > 5 GeV/c] 98.9% 96.4 % long fromb [Trigger-like] 98.9% 97.7 % Table 5: forward container: Efficiencies. L = 2 10 33 cm 2 s 1 (ν = 7.6). Fraction of good tracks 0.06 0.05 0.04 0.03 0.02 0.01 All long Long from B 0 0 2 4 6 η ghostrate 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 forward forward (with UT Hits) 0.1 0 0 2 4 6 η Figure 8: Distribution of Good tracks and ghost rates as a function of the pseudorapidity. 11
3.6 Stress test We use here a simulation with worse performance in the electronics of the UT detector [3]. We compare the tracks coming from the forward container. Stress Test Nominal electronics Ghost rate Ghost rate (UT Hits) Ghost rate Ghost rate (UT Hits) 2 < η < 5 All tracks 39.1 % 24.4 % (rel. 0.62 ) 38.8 % 24.3 % (rel. 0.63 ) p > 5 GeV/c 36.5 % 19.5 % (rel. 0.53 ) 36.2 % 19.6 % (rel. 0.54 ) Trigger-like 35.6 % 10.2 % (rel. 0.29 ) 35.1 % 10.3 % (rel. 0.29 ) Table 6: forward container: (1000evt) mean ghost rates for the stress test sample. L = 2 10 33 cm 2 s 1 (ν = 7.6). Stress Test Nominal electronics 2 < η < 5 Minimum Hits 2 < η < 5 Minimum Hits long 97.6% 98.9% 97.9% 99.0% long [p > 5 GeV/c] 96.8% 98.6% 97.1% 98.7% long [Trigger-like] 97.6% 98.6% 97.9% 98.7% long fromb 98.0% 98.8% 98.2% 98.8% long fromb [p > 5 GeV/c] 97.7% 98.6% 98.0% 98.7% long fromb [Trigger-like] 97.8% 98.6% 98.1% 98.7% Table 7: forward container: (1000evt) association efficiencies for the stress test sample. L = 2 10 33 cm 2 s 1 (ν = 7.6). 4 Conclusions The performance of the PrAddUTHitsTool algorithm has been presented. We investigated its use on tracks taken from the forward, match and best containers separately. UT hits are very useful to reduce ghost rates up to a factor of 4 (depending on the specific requirements), while maintaining very high efficiencies on interesting tracks useful for B-physics. Further optimisations of the algorithm are foreseen in the immediate future to improve the good-track efficiency and integrate this tool with the VeloUT [5] algorithm. We would like to thank the UT software and hardware groups, especially E. Bowen, B. Storaci, A. Davis and M. De Cian for their precious help in the work performed in this note. References [1] L. Collaboration, Framework TDR for the LHCb Upgrade: Technical Design Report, Tech. Rep. CERN-LHCC-2012-007. LHCb-TDR-12, CERN, Geneva, Apr, 2012. [2] L. Collaboration, LHCb VELO Upgrade Technical Design Report, Tech. Rep. CERN- LHCC-2013-021. LHCB-TDR-013, CERN, Geneva, Nov, 2013. 12
[3] L. Collaboration, LHCb Tracker Upgrade Technical Design Report, Tech. Rep. CERN- LHCC-2014-001. LHCB-TDR-015, CERN, Geneva, Feb, 2014. [4] O. Callot and S. Hansmann-Menzemer, The forward tracking: Algorithm and performance studies, Tech. Rep. LHCb-2007-015. CERN-LHCb-2007-015, CERN, Geneva, May, 2007. [5] E. Bowen and B. Storaci, VeloUT tracking software for the LHCb Upgrade, Tech. Rep. LHCb-PUB-2013-023. CERN-LHCb-PUB-2013-023. LHCb-INT-2013-056, CERN, Geneva, Dec, 2013. 13