1 Introduction The challenges in tracking charged particles in the HERA-B experiment [5] arise mainly from the huge track density, the high cell occup

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1 Hera-B 99{111 Software 99{16 ranger { a Pattern Recognition Algorithm for the HERA-B Main Tracking System Part V: Compatibility Analysis Rainer Mankel 1 Institut fur Physik, Humboldt Universitat zu Berlin Invalidenstr 11, D{1115 Berlin, Germany and Alexander Spiridonov 2 3 DESY Zeuthen Platanenallee 6, D{15738 Zeuthen, Germany June 29, 1999 Abstract The solutions for track reconstruction in the HERA-B main tracking system introduced in previous works [1, 2, 3, 4] have been extended in severals ways. We have analyzed the rate of multiply reconstructed particles and developed and tested a compatibility analysis strategy to suppress such redundancies. We give eciencies and parameter resolutions after application of this method, where we now also include the silicon strip superlayer SI8, re-evaluate the cpu time requirements on a modern Intel processor and nally show results of rst investigations on an integration of main tracker and vertex detector track segments. 1 mankel@ifh.de 2 spiridon@ifh.de. 3 Permanent address: Institute for High Energy Physics, Protvino, Russia.

2 1 Introduction The challenges in tracking charged particles in the HERA-B experiment [5] arise mainly from the huge track density, the high cell occupancies which can range up to 2% in the \hottest" parts of the HERA-B outer tracker, the complexity of the tracker geometry which combines devices of dierent technologies, the large amount of material in the tracking area and the highly inhomogeneous magnetic eld. In previous works, a method for track reconstruction in the main tracking system has been devised which was found in detailed Monte Carlo based studies to meet the requirements above. The tracking strategy relies on the following steps: 1. straight-line track nding in the pattern tracker, which is located in the eld-free area between magnet and RICH 2. upstream propagation through the magnet tracker 3. downstream propagation to the tc area chambers 4. full iterative ret The individual steps have been implemented using largely the concept of Concurrent Track Evolution [1, 2, 3, 4] and the Kalman lter technique [6, 7, 8, 9] and the performance has been found adequate for the goals of a hadronic B factory. In order to achieve a smooth integration into the full HERA-B reconstruction, some additional steps are advisable. One aspect deserving attention is the possibility of multiple reconstruction of tracks. Since the initial seeding of track candidates is done in several places to compensate for hits lost because of detector ineciency of track overlap, multiple reconstruction can occur, in particular since multiple use of hits is not generally prohibited in the track nding procedure [1, 2, 3]. We will refer to such redundant reconstructions of a particle as clones. To preserve the highest possible reconstruction eciency, measures to eliminate clones are postponed to a late stage in the main tracker reconstruction, where a maximum of information on each track candidate is available. A natural place for this elimination is just before the matching with the vertex detector and hence before evaluation of the particle identication devices, since both types of operation may encounter complications if redundant reconstructions are not removed. An essential aspect of the matching with vertex detector segments is the resolution of track parameters at the rst point. We dedicate one section of this note to the track parameter residuals, where we also include now the silicon strip detector superlayer outside the vertex vessel, SI8, which had been excluded in earlier studies. Finally,we begin to study the integration with the vertex detector reconstruction, which is however still mimicked by an idealized track nding and matching. 1

3 2 Compatibility Analysis 2.1 Motivation Virtually every track reconstruction method needs to enforce at some point that patterns are not reconstructed more than once. The usual way is to insure that the basic entities of information, as detector hits, are not used by several patterns. In high occupancy experiments as HERA-B, however, this requirement cannot be exerted too strictly, because it is unavoidable that two or more particles can hit the same drift chamber cell, or produce nearby strip detector hits which merge into a single cluster. One basically has the choice to inhibit multiple use of information on the following levels: Hit level A very popular method is to keep a pool of available detector hits, and to remove hits of a reconstructed object from this list when the latter is stored. For a track following algorithm, this implies that the result will in general depend on the order in which the track candidates are seeded and propagated. The main danger is then through ghost tracks which absorb hits from other particles, which may then fail to be reconstructed. The nonnegligible ghost rates of eg. O(8%) on the pattern tracker level indicates the risc of reducing the single particle eciency, which is a crucial gure of merit for reconstruction of B mesons, eg. in the golden decay mode. Segment level An approach less dangerous to high occupancy tracking is the compatibility analysis (further explanation below) of the set of track segments after a reconstruction step, which could be performed eg. after the pattern tracker analysis. Such a procedure selects one of several incompatible track segments using quality criteria. On a preliminary stage, when eg. the momentum of the particle is not yet known, there may still be uncertainties in the quality of a track candidate which may lead to selection of a segment which will fail in the subsequent propagation or matching. Track level The track level is the same as the segment level when all information of the detector subsystem (here: the main tracker) is used. This is the most powerful stage for evaluation of track candidates, and we will use it in the following. 2.2 Method We have applied a still relatively simple compatibility analysis to the track candidate sample available after the propagation to the tc area chambers, but without a full ret, which we prefer to postpone to the nal track candidate, since this will include hits from the vertex detector and other systems. 2

4 The method loops over all pairs of track candidates and checks for each pair whether the two candidates are compatible. Two track candidates are called compatible if they share less than 5% of their hits 4. If two candidates are found to be incompatible, the superior candidate is kept and the inferior one is removed from the sample. Superiority is dened in the following way: if the number of hits in the two candidates dier by at least four, the track candidate containing more hits is always dened as superior. In the other case, a track quality is dened as Q = N Hits ; 2 and the superior track candidate is the one with the higher quality estimate. 2.3 Performance The evaluation of eciency and ghost rates was done in a similar way as de- ned in [2, 3], based on simulated interactions generated with FRITIOF and PYTHIA [1] passed through the full HERA-B detector simulation HBGEAN [11]. Compared to the earlier evaluations, however, some changes have been introduced: the framework of ARTE-1-8-r4 has been used the silicon strip detector superlayer SI8 has been integrated into the magnet propagation, which reinforces the inner tracking at the entrance of the magnet we assume that strip cluster reconstruction in the micro-strip gaseous chambers will allow to distinguish cases in which instead of a single particle, two or more particles pass closer than the double-track separation distance of 8 m. In this case we set the error of the hit coordinate invariably to 3 m. This is certainly only a crude approximation and should be updated with the behaviour of a real cluster algorithm which was not available at the time of this study. With these changes, we give rst an update on the performance without compatibility analysis, for events with one interaction containing the golden B decay in the muon channel, superimposed with on average four inelastic interactions. A typical prism event display [12] with 1+6 interactions is shown in g. 1. The results are shown in the left columns of tab. 1 and tab. 2. The eciencies and ghost rates are { within statistical errors { identical to the ones in the earlier notes, with perhaps some improvement in the magnet propagation eciency of the pions. 4 ie. if the intersection set contains less than half of each candidate's hits 3

5 (a) (b) + ; + ; Figure 1: (a) Display of an event with one interaction containing the golden B decay and six superimposed inelastic interactions, after ret of the combined magnet/pattern tracker and tc area segment. Both the Monte Carlo tracks (light grey) and the reconstructed tracks (thick dark lines) are shown (reconstructed hit points denoted by crosses). (b) Same event, with the display restricted to particles from the golden B decay. The innermost of these tracks have their rst reconstructed hits in superlayer SI8. 4

6 Particle ( pattern+magnet tracker) before compatibility after compatibility analysis analysis J= (96.7.4)% (96.7.4)% J=! + ; (93:4 1:)% (93:4 1:)% (95.3.6)% (95.3.6)% KS KS! + ; ( )% ( )% B! J= KS! + ; + ; ( )% ( )% X (p > 1GeV=c) ( )% ( )% Clones of X (p > 1 GeV=c) (33.1.2)% ( 1.3.5)% Ghosts (2.2.7)% ( )% Table 1: Eciencies for track nding in the pattern and magnet tracker. The ghost rates and the rates of redundant reconstructions (clones) are also shown. If several valid reconstructed objects are assigned to the same reference particle, the redundant reconstructions are called clones. We can then calculate the clone rate clone = N clone N ref for this class of particles. This clone rate is 33.1% for charged reference particles with momenta above 1 GeV (see tab. 1), which can lead to problems in the matching process. The average number of reconstructions per charged reference particle ( + clone ) is 1.2. It is sometimes more instructive to consider the mean reconstruction multiplicity m RC, which is dened as the mean number of valid reconstructions per reference particle for cases where at least one reconstruction exists. We can derive this multiplicity as m RC = + clone =1+ clone For charged reference particles with momenta above 1 GeV, the mean reconstruction multiplicity is then before compatibility analysis. The compatibility analysis reduces the number of clones drastically while keeping the pattern recognition eciency virtually unchanged (see tables 1 and 2). The clone rate for magnet tracker segments is reduced from 33.1% to 1.%. The mean reconstruction multiplicity m RC is reduced to As a side eect, the ghost rate for magnet segments is slightly reduced from 2% to 1.8%, in the tc area propagation the ghost rate is even more strongly reduced from 8% to 5.9%. This observation indicates clearly that part of the tc area ghosts are actually caused by unsuccessful propagation of clones. Postponing the compatibility analysis after the tc area propagation step has thus the clear advantage that the most successful tc area continuation is selected. 5

7 Particle ( tc area propagation) before compatibility after compatibility analysis analysis J= (98.3.3)% (98.3.3)% J=! + ; (97:2 :7)% (97:2 :7)% (95.6.6)% (95.6.6)% KS KS! + ; 1% 1% B! J= KS! + ; + ; ( )% ( )% X (p > 1GeV=c) ( )% ( )% Ghosts ( )% ( )% Table 2: Eciencies for tc area propagation before and after compatibility analysis. The remaining clone yield is smaller than the ghost rate and should, after matching with the vertex detector, be uncritical for all purposes. A further suppression of clones would, however, still be possible if needed, albeit with some compromises regarding the track nding eciency. Figure 2 shows the behaviour of track nding eciency for muons from the golden B decay, and the ghost and clone rates as a function of the number of inelastic interaction superimposed on the interaction which generates the b hadrons. The track nding eciencies in the patter/magnet tracker and the tc area stay on a high level over the full range, they should be multiplied if a tc area segment is required for analysis. The remaining clone rate is hardly increasing with the number of interactions, which shows that the compatibility analysis is quite eective also at high interaction multiplicities. 2.4 Speed In previous notes [2, 3], the computing time consumption of the tracking algorithms was determined on workstations as eg. the Silicon Graphics Challenge with the R44 processor and a clock rate of 15 MHz. Since the HERA-B L4 farm will use PCs with Intel processors, we have taken the opportunity to re-evaluate the performance on a PC with a 333 MHz Pentium II processor. Figure 3 shows the computing time per event for pattern/magnet tracker analysis, tc area propagation and the compatibility analysis as function of the number of inelastic interactions which are superimposed on the interaction which generates the b hadrons. At the nominal 1+4 interactions, the combined pattern/magnet/tc area analysis takes around 2s per event, while the additional eort for compatibility analysis is almost negligible. It should be noted that the PC nodes used for the farm will still have a somewhat higher clock rate. The original milestone for the event reconstruction time was 4s. 6

8 Efficiency µ ± (B ), pattern+magnet µ ± (B ), tc area ghosts, pattern+magnet ghosts, tc area clones N INEL Figure 2: Combined pattern and magnet tracker track nding eciency (full circles) and tc area propagation eciency (open circles) after the compatibility analysis, as a function of the number of superimposed inelastic interactions, for muons from the golden B decay, which satisfy the reference track criteria which are dened in [1, 2]. In the lower part of the gure, the ghost rates of both parts of the tracking system, and the rate of clone tracks are shown. 7

9 T CPU [s] 6 Pentium II CPU 333 MHz 5 4 pattern+magnet tc area weedout N INEL Figure 3: Computing time of combined pattern and magnet tracker analysis, tc area propagation and compatibility analysis (labelled weedout) as a function of the number of inelastic interactions which are superimposed on the interaction generating the golden B decay. 8

10 from the golden B decay σ=46 µm x [cm] σ= t x x σ=67 µm y [cm] σ= t y Figure 4: Distribution of residuals (see text for explanation) at the track point of lowest z in the magnet tracker, for the parameters x, y, t x and t y for muons from the golden B decay, after compatibility analysis. The solid points with error bars are directly obtained from the parameters delivered by the pattern recognition step, the shaded histogram is the result of an iterative ret which interpolates traversed material between the hits. The result of Gaussian ts to both distributions is also shown, and the standard deviation is quoted for the retted case. 9

11 from the golden B decay 25 2 x σ= y σ= t x σ= t y σ= Figure 5: Normalized residuals (see text for explanation) at the track point of lowest z in the magnet tracker, for the parameters x, y, t x and t y for muons from the golden B decay, after compatibility analysis. The solid points with error bars are directly obtained from the parameters delivered by the pattern recognition step. The result of a Gaussian t is also shown, and the standard deviation is quoted. 1

12 2.5 Update on Parameter Resolutions In the following we will give an update on the resolution at the main tracker entrance of track parameters for particles from the golden B decay, complementing the information given in [2]. Figure 4 shows the distribution of residuals for the parameters x, y, t x and t y at the lowest z point in the main tracker, for muons from the golden B decay, after compatibility analysis. The gures compare directly the quality of residuals obtained from the pattern recognition step (solid points) and after a full iterative ret with the method discussed in [4] (shaded histograms). Gaussian ts for both cases are superimposed. The accuracy of the parameter estimate is already quite good without ret, which suggests to postpone the ret until after the vertex detector matching step. The relative sizes of the impact parameter resolutions of 46 m inx and 67 m iny can be attributed to the 5 stereo angle. The track slope resolutions are of 1:1 1 ;4 in t x = tan x and 2:1 1 ;4 in t y = tan y dier less because of the approaching multiple scattering limit. The quality of the estimated covariance matrix is expressed in the normalized residuals X REC i ;X MC i C 1=2 ii which are shown in g. 5. These distributions show still some improvement with respect to the ones displayed in g. 9 of [2], which is related to the improved description of the coordinate error estimate for merged clusters in the inner tracker (see above). The corresponding distributions for pions from the golden B decay are shown in gs. 6 and 7. The parameter resolutions are slightly worse which is expected due to the smaller average momentum compared to the muons. 2.6 Integration with Vertex Detector Reconstruction For a discussion of the momentum resolution, it is interesting how the addition of the vertex detector segment of a track aects the momentum residual. As an optimized vertex detector pattern recognition program was not yet available in the full geometry reconstruction chain at the time of this study 5, we have produced the vertex detector segment by applying the track t [4] to the hits belonging to the same particle, which were located using the Monte Carlo truth. This procedure is sometimes called idealized pattern recognition. In the next step, these vertex detector segments were combined with corresponding valid reconstructions of the same particle in the main tracker,.ie. also the matching process was idealized using Monte Carlo information. The resulting combination 5 this note is based on work done during late autumn

13 from the golden B decay 3 25 σ=57 µm 3 25 σ=75 µm x [cm] y [cm] σ= σ= t x x t y Figure 6: Distribution of residuals (see text for explanation) at the track point of lowest z in the magnet tracker, for the parameters x, y, t x and t y for pions from the golden B decay, after compatibility analysis. The solid points with error bars are directly obtained from the parameters delivered by the pattern recognition step, the shaded histogram is the result of an iterative ret which interpolates traversed material between the hits. The result of Gaussian ts to both distributions is also shown, and the standard deviation is quoted for the retted case. 12

14 from the golden B decay x σ= y σ= t x σ= t y σ= Figure 7: Normalized residuals (see text for explanation) at the track point of lowest z in the magnet tracker, for the parameters x, y, t x and t y for pions from the golden B decay, after compatibility analysis. The solid points with error bars are directly obtained from the parameters delivered by the pattern recognition step. The result of a Gaussian t is also shown, and the standard deviation is quoted. 13

15 (a) (b) Figure 8: (a) Display of an event with one interaction containing the golden B decay and six superimposed inelastic interactions, after ret of the combined pattern recognition in magnet and pattern tracker, tc area propagation, compatibility analysis, idealized matching with vertex detector segments and iterative ret. (b) Same event, with the display restricted to particles from the golden B decay. The ; decays in ight after traversal of TC2. 14

16 was then passed through the full iterative ret [4]. A typical event display with the resulting reconstructed tracks is shown in g. 8. The resulting distribution of the relative momentum residual p=p for muons from the golden B decay is shown in g. 9. The distributions are well described by Gaussians except for some moderate tails. As detailed in tab. 3, the momentum precision delivered by the pattern recognition step in the magnet is already quite accurate (7:9 1 ;3 ) and only slightly improved by adding the hits from vertex detector and tc area and performing the full iterative ret, which is not surprising after the reasoning on contribution of dierent detector parts to the resolution in [4]. The resolution obtained with realistic main tracker pattern recognition is also only slightly (9%) worse than the one obtained with idealized pattern recognition applied to the whole tracking system. Method p=p magnet propagation (7.9.2) 1 ;3 magnet propagation + tc area propagation + SVD + ret (7.4.2) 1 ;3 ideal pattern recognition + t (6.8.2) 1 ;3 Table 3: Relative momentum resolution p=p determined by from tting a Gaussian to the central peak of the residual distribution. The resolution is given, rst, as directly obtained from the magnet propagation procedure, second, from a ret to the hits delivered by this procedure and the subsequent tc area propagation and, nally, from a t to the hits selected using Monte Carlo information (ideal pattern recognition + t). 3 Summary The frequency of redundant reconstructions (\clones") in the main tracker reconstruction chain has been investigated. A compatibility analysis method has been developed which was found to suppress the clone rate below the level of ghosts virtually without loss in track nding eciency. Another benet of this procedure is a further suppression of ghosts especially in the tc area propagation step. The speed of the track reconstruction algorithms has been re-evaluated on a modern Pentium processor, it was found to be at least a factor of three faster than on the workstations used before. The estimation of track impact parameters and slopes at the rst track point near the entrance of the magnet was found to be quite accurate after the propagation step so that it is hardly improved by the full ret. Application of the 15

17 35 3 σ=(7.4±.2) p / p Figure 9: Distribution of the relative momentum residual p=p for muons from the golden B decay. The solid points with error bars correspond to the parameter as it is delivered directly by the magnet propagation, the shaded histogram is the result of pattern and magnet tracker analysis, tc area propagation, compatibility analysis, matching with the vertex detector segment (idealized) and the iterative ret. The results of Gaussian ts to the central parts of both distributions are superimposed, where the standard deviation is quoted for the retted case. 16

18 latter gives covariance matrix estimates which lead to normalized residuals whose distributions have widths close to unity. The quality of the momentum estimate is close to the technical limit modelled by ideal pattern recognition. References [1] R. Mankel, A Concurrent Track Evolution Algorithm for Pattern Recognition in the HERA-B Main Tracking System, Nucl. Instr. and Meth. A 395 (1997) 169. R. Mankel, ranger { a Pattern Recognition Algorithm for the HERA-B Main Tracking System, Part I: The HERA-B Pattern Tracker, HERA-B Note (1997). [2] R. Mankel and A. Spiridonov, The Concurrent Track Evolution Algorithm: Extension for Track Finding in the Inhomogeneous Magnetic Field of the HERA-B Spectrometer, hep-ex/98921, Nucl. Instr. and Meth. A426 (1999) 268. R. Mankel and A. Spiridonov, ranger { a Pattern Recognition Algorithm for the HERA-B Main Tracking System, Part II: The HERA-B Magnet Tracker, HERA-B Note (1998). [3] R. Mankel and A. Spiridonov, ranger { a Pattern Recognition Algorithm for the HERA-B Main Tracking System, Part III: Tracking in the Trigger Chambers, HERA-B Note (1998). [4] R. Mankel, ranger { a Pattern Recognition Algorithm for the HERA-B Main Tracking System, Part IV: The Object-Oriented Track Fit, HERA-B Note (1998). [5] T. Lohse et al., An Experiment to Study CP Violation in the B System Using an Internal Target at the HERA Proton Ring (Proposal), DESY-PRC 94/2 (1994). [6] R.E. Kalman, Trans. ASME, J. Basic Engineering (196) R. Battin, Am. Rocket Soc. 32 (1962) 1681 R.E. Kalman and R.S. Bucy, Trans. ASME, J. Basic Engineering (1962) [7] R. Fruhwirth, Nuclear Instr. and Meth. A262 (1987) 444. [8] P. Billoir and S. Qian, Nuclear Instr. and Meth. A294 (199)

19 [9] R. Mankel, Application of the Kalman Filter Technique in the HERA-B Track Reconstruction, HERA-B Note (1995). [1] T.S. Sjostrand, CERN-TH (1992) B. Anderson, G. Gustafson and Hong Pi, Z. Phys. C57 (1993) 485. [11] S. Nowak, HBGEAN and HBRCAN, HERA-B Internal Note (1995). [12] R. Mankel, prism { the HERA-B Event Display and its Tcl/Tk User Interface, HERA-B Note 97-9 (1997). 18