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Nuclear Instruments and Methods in Physics Research A 566 (2006) 85–88

www.elsevier.com/locate/nima

Event reconstruction in the CBM experiment

I. Kisel�,1

Kirchhoff Institute for Physics, University of Heidelberg, 69120 Heidelberg, Germany

Available online 27 June 2006

Abstract

A typical central Au+Au collision in the CBM experiment (GSI, Germany) will produce up to 700 tracks in the inner tracker. The

large track density together with the presence of a non-homogeneous magnetic field make reconstruction of events complicated.

A cellular automaton method is used to reconstruct tracks in the inner tracker. Track and vertex fitting is done using the Kalman filter

technique. A special analytic formula has been derived for fast track extrapolation in a non-homogeneous magnetic field. A standalone

ring finding in the RICH detector is based on the elastic net method. Results of tests of the reconstruction procedure are presented.

r 2006 Elsevier B.V. All rights reserved.

PACS: 07.05.Kf; 07.05.Mh; 29.40.Gx; 29.40.Ka; 29.85.+c

Keywords: Event reconstruction; Track finding; Track fitting; Cellular automaton; Kalman filter; Elastic net; CBM

1. CBM experiment

CBM [1] is a dedicated heavy-ion experiment toinvestigate the properties of highly compressed baryonicmatter as it is produced in nucleus–nucleus collisions at theFacility for Antiproton and Ion Research (FAIR) inDarmstadt, Germany.

The scientific goal of the research program of the CBMexperiment is to explore the phase diagram of stronglyinteracting matter in the region of highest baryon densities.New states of matter beyond the deconfinement and chiraltransition at high net baryon densities and moderatetemperatures may be within reach of the experiment. Theproposed experimental program includes: the study of in-medium properties of hadrons; the search for the chiral anddeconfinement phase transition at high baryon densities;the search for the critical point of strongly interactingmatter; the study of the nuclear equation of state ofbaryonic matter at high densities (as it exists in the interior

e front matter r 2006 Elsevier B.V. All rights reserved.

ma.2006.05.040

21 549817; fax: +49 6221 549809.

ess: ikisel@kip.uni-heidelberg.de.

he European Community-Research Infrastructure Activity

‘‘Structuring the European Research Area’’ program

, contract number RII3-CT-2004-506078).

of neutron stars); the search for new states of matter athighest baryon densities.The experiment aims for a comprehensive study of

hadrons, electrons and photons emitted in heavy-ioncollisions. Its main experimental objective is the measure-ment of extremely rare signals in an environment typicalfor heavy-ion collisions. This requires the collection of ahuge number of events which can only be obtained by veryhigh reaction rates and long data taking periods. Reactionrates are up to 10MHz (minimum bias) which correspondsto a beam intensity of 109 beam particles per second with a1% interaction target. The rare signals are embedded in alarge background of charged particles.The experimental setup has to fulfill the following

requirements: identification of electrons which requires apion suppression factor of the order of 105; identificationof hadrons with large acceptance; determination of theprimary and secondary vertices (accuracy of 30 mm); highgranularity of the detectors; fast detector responseand readout; very short detector dead time; fast triggerand data acquisition; radiation hard detectors andelectronics and tolerance towards d-electrons. Fig. 1 depictsthe present layout of the CBM experimental setup.Inside the dipole magnet gap are the target and a seven

plane Silicon Tracking System (STS) consisting of pixel andstrip detectors. The Ring Imaging Cherenkov detector

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Fig. 1. Geometry of the CBM experiment.

6 5 4 3 2 1

1

12

Collect tracks Creat tracklets

Fig. 2. A simple illustration of the cellular automaton algorithm. It

creates tracklets, links and numbers them as possibly situated on the same

trajectory, and collects tracklets into track candidates.

I. Kisel / Nuclear Instruments and Methods in Physics Research A 566 (2006) 85–8886

(RICH) used for electron detector. The Transition RadiationDetector (TRD) arrays measure electrons with momentumabove 1GeV. The TOF stop detector consists of ResistivePlate Chambers (RPC). The Electromagnetic Calorimeter(ECAL) measures electrons, photons and muons.

The CBM setup is optimized for heavy-ion collisions inthe beam energy range from about 8 to 45AGeV.

Large track densities (on average 500 tracks in the innertracker in a typical central Au+Au collision) together withthe presence of a non-homogeneous magnetic field makethe reconstruction of events complicated. Therefore, thecollaboration performs an extensive study of differenttrack recognition methods in order to better understandthe geometry of the detector and to investigate specificfeatures of accepted events [1].

2. Cellular automaton-based track finding

One of the methods under study is based on a cellularautomaton [2]. This method creates short track segments(tracklets) in neighboring detector planes and links theminto tracks (see a simple illustration in Fig. 2).

First, using all groups of neighboring chambers thealgorithm generates a set of tracklets. A set of cuts, whichreflect a geometrical acceptance of the detector system (e.g.forward tracks with minimum 4 hits and momentum largerthan 200MeV/c), is applied to possibly create onlytracklets corresponding to tracks with enough hits to bereconstructed. Since hits in the detector chambers aresorted, tracklets are generated in groups with the sameleftmost hit (due to inserted loops over chambers). There-fore, every hit stores two pointers: to the first and the lasttracklets of his group. Each tracklet has a counter meaningits possible position on a track (initially set to 1).

In the next step, the tracklets are extrapolated to the nextlayer in the target direction. Usually tracklets are createdstarting from the most downstream chamber and going

back in the direction of the target. Therefore, duringgeneration of the next portion of tracklets (one or twochambers closer to the target) the algorithm applies a trackmodel to the tracklets with a common point (simpleselection of the tracklets using the already stored pointers)in order to find neighbors.Then, for all tracklets the algorithm finds neighbors

(possible track continuations according to the trackmodel) and increases the counters of the tracklets. Ifneighbors are found, a counter of the current tracklet isincremented with respect to a neighbor with the largestcounter (counter ¼ countermaxneighb þ 1).After proceeding these three steps for all chambers, the

algorithm builds track candidates out of the tracklets. Itstarts with the tracklets having the largest counter(countermax ¼ 6 in Fig. 2), for each of them takes a neighbor(at the right) which has a counter ¼ countermax � 1,continues further following the counters (e.g. goes from 4to 3, but not 2), makes branches, but no empty layers, andfinally keeps the best (w2) track for each initial tracklet withthe largest counter.Then, a competition between the track candidates is

necessary to select only tracks satisfying some qualitycriteria. After the previous step a set of track candidateswith the same number of hits has been created, therefore,w2 is a well suitable criterion to sort them. After sorting thealgorithm starts with the best (in terms of w2) track andflags all hits of the track as used. It continues with the nexttrack (with higher w2), checks if the number of used hits isless than Nmax (parameter, depends on track density) andflags his hits as used or deletes the track. Then it proceedswith the next track candidate, etc.The algorithm repeats collecting tracks with decremen-

ted max_counter until the shortest tracks are collected.After finding all tracks, in case of a significant detector

inefficiency the algorithm merges short tracks (clones) intolong tracks using the track model.

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Table 1

Track reconstruction efficiency for different sets of tracks

Track category Efficiency (%)

Reference set 99.45

All set 96.98

Extra set 89.46

Clone 0.01

Ghost 0.61

I. Kisel / Nuclear Instruments and Methods in Physics Research A 566 (2006) 85–88 87

Finally, the algorithm applies additional cuts to killghost tracks which are mostly short tracks.

Being essentially local and parallel, the cellular auto-maton method avoids exhaustive combinatorial searches,even when implemented on conventional computers. Sincethe cellular automaton algorithm operates with highlystructured information, the amount of data to be processedin the course of the track search is significantly reduced.Employing possibly the simplest track model leads toutmost computational simplicity and a fast algorithm.

For evaluation purposes all simulated and reconstructedtracks are subdivided into several categories: a referenceset of tracks, an all set, an extra set, and clone and ghosttracks [1].

By definition, a track from the all set of tracks shouldintersect the sensitive regions of at least four stations. Areference track should have a momentum greater than1GeV/c in addition. The reference set of tracks can alsoinclude tracks of particular physics interest: secondarytracks from interesting decays; primary tracks comingfrom the target region. In addition to these tracks, an extraset of tracks, containing low-momentum tracks, is alsoconsidered.

A reconstructed track is assigned to a generated particle,if at least 70% of its hits have been caused by this particle.A generated particle is regarded as found, if it has beenassigned to at least one reconstructed track. If the particleis found more than once, all additionally reconstructedtracks are regarded as clones. A reconstructed track iscalled a ghost, if it is not assigned to any generated particle(70% criteria).

Efficiency of track reconstruction for particles detectedin at least four stations is presented in Fig. 3 and Table 1.Tracks of high momentum particles are reconstructed verywell with efficiencies of 99.45%, while multiple scattering indetector material leads to a lower reconstruction efficiencyof 89.46% for slow particles from the extra set of tracks.

The reconstruction efficiency for reference primarytracks is almost 100%, while the efficiency of all referencetracks is slightly lower because of the presence of secondary

Momentum, GeV/c0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Effi

cien

cy, %

0

10

20

30

40

50

60

70

80

90

100

Fig. 3. Track reconstruction efficiency as a function of momentum.

tracks, originating far downstream from the target region.The total efficiency for all tracks with a large fraction ofsoft secondary tracks is 96.98%. The clone rate of thealgorithm is 0.01% and the ghost rate 0.61%.

3. Track and vertex fitting

Track and vertex fitting have been done with a Kalmanfilter-based procedure [1].Propagation of tracks in non-homogeneous magnetic

field is based on a specially developed analytic formula [3].The formula has been derived under very general assump-tions on the magnetic field. Therefore, the precision of theextrapolation does not depend on the shape of themagnetic field. The extrapolated track parameters areexpanded in a power series of the magnetic fieldcomponents as a small parameter, therefore, one can cutoff the higher-order terms in the series. The quality of theresults obtained with the formula up to third order is foundto be equivalent to those achieved with a fourth orderRunge–Kutta method. In the power series terms of thesame order are found to differ significantly from eachother. This leads to an efficient realization of the analyticformula where one keeps only a few major terms within thesame order.The mean relative momentum resolution for all tracks is

0.69%. Secondary tracks from D0 decay being longer haveslightly better momentum resolution of 0.67%. After theprimary vertex is reconstructed, tracks identified asprimary can be refitted with an additional constraint tothe primary vertex position. This improves their averagetrack momentum resolution to 0.63%.The primary vertex was determined from all tracks

reconstructed in the STS excluding those which formedwell detached vertices like K0

S and L decays. The Kalmanfilter-based algorithm reconstructs the primary vertex withthe accuracy of 4 mm for the longitudinal and better than1mm for transversal components of the primary vertexposition.The precision of the secondary vertex parameters

obtained in the geometrical vertex fit can be improved bytaking into account several assumptions on tracks asso-ciated to the vertex. Two types of constraints have beenincluded into the secondary vertex fit: a mass constraintand a topological constraint. The mass constraint is usuallyapplied in the case of one or several combinations ofparticles in the vertex are known to originate from a

ARTICLE IN PRESSI. Kisel / Nuclear Instruments and Methods in Physics Research A 566 (2006) 85–8888

narrow width mass state. The topological constraint is usedto point a mother particle to the (already reconstructed)primary vertex. The final accuracy is 44:4mm for thelongitudinal and 1:7mm for transversal components of thesecondary vertex position for the D0 decay.

4. Standalone RICH ring finder

Standalone finding of rings in the RICH detector isbased on the elastic neural net (see Ref. [4] with the sourcecode of the algorithm). The method does not require anyprior track information and can be used for triggering.Application of the method to the RICH detector of theCBM experiment shows an efficiency of 94.3% and highspeed (5.4ms per event with about 1400 hits in the RICHdetector). Due to its computational simplicity and highspeed, the algorithm is considered to be further implemen-ted in hardware which can increase the speed by anotherfew orders of magnitude.

5. Summary

A track finding algorithm based on the cellularautomaton method is developed for the reconstruction oftracks in the inner tracker of the CBM experiment.Comprehensive tests of the algorithm have shown highreconstruction efficiency and low ghost rate. The algorithmhas a reasonable behavior of the CPU time consumption

and robustness with respect to large track densities. Thealgorithm is intrinsically parallel and therefore suitable forimplementation on multiprocessor systems like the STI cellprocessor. It is also possible to implement the most timeconsuming combinatorial part of the algorithm in hard-ware, for instance FPGAs, thus speeding the algorithm bya few orders of magnitude. From experience in the HERA-B and LHCb experiments we expect that the cellularautomaton algorithm will work reliably with more realisticsimulated and the real data of the CBM experiment.Track and vertex fitting procedures are based on a

Kalman filter approach. Propagation of tracks in non-homogeneous magnetic field is based on a speciallydeveloped analytic formula.A standalone RICH ring finder is based on the elastic net

method. It has demonstrated a good ring finding efficiencyand a high speed.

References

[1] Compressed Baryonic Matter Experiment, Technical Status Report,

GSI, Darmstadt, 2005.

[2] I. Abt, D. Emeliyanov, I. Kisel, S. Masciocchi, Nucl. Instr. and Meth

A 489 (2002) 389.

[3] S. Gorbunov, I. Kisel, An analytic formula for track extrapolation in

an inhomogeneous magnetic field, CBM-SOFT-note-2005-001, 18

March 2005.

[4] S. Gorbunov, I. Kisel, Elastic net for standalone RICH ring finding,

CBM-SOFT-note-2005-002, 22 September 2005.