Algorithms and Software for Event Reconstruction in the RICH, TRD ...

Algorithms and Software for Event Reconstruction in the RICH, TRD and MUCH Detectors of the CBM Experiment Semen Lebedev1,2 , Claudia H¨ohne3 , Ivan Kisel1 , Andrey Lebedev1,2 , and Gennady Ososkov2 1

GSI Helmholtzzentrum f¨ ur Schwerionenforschung GmbH, Darmstadt, Germany Laboratory of Information Technologies, Joint Institute for Nuclear Research, Dubna, Russia 3 Justus Liebig-Universit¨ at Gießen, Germany

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Abstract. The Compressed Baryonic Matter (CBM) experiment at the future FAIR facility at Darmstadt will measure dileptons emitted from the hot and dense phase in heavy-ion collisions. Very fast event reconstruction is extremely important for CBM because of the huge amount of data which has to be handled. In this contribution the parallel event reconstruction algorithms in the Ring Imaging CHerenkov detector, Transition Radiation Detector and muon system are presented. Modern CPUs have two features, which enable parallel programming. First, the SSE technology allows using the SIMD execution model. Second, multi core CPUs enable to use multithreading. Both features were implemented in the reconstruction software. Simulation results show a significant speed up factor. Keywords: CBM experiment, event reconstruction, RICH, TRD, muon detector, Kalman filter, Hough Transform, parallel algorithm

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Introduction

The Compressed Baryonic Matter (CBM) [4] experiment will be a dedicated setup for the measurement of fixed target heavy ion collisions at the future FAIR accelerator at Darmstadt. It is being designed for the investigation of the properties of highly compressed baryonic matter [9]. High reaction rates (up to 10 MHz), events with large track multiplicity (about 800 charged particles per central Au + Au collision in the CBM detector acceptance) and high hit density are expected in the CBM experiment. This leads to special requirements for the event reconstruction software, which has to perform fast and stable in such an environment. Currently two different CBM setups are under investigation, one for electron and one for muon measurements [10]. In both cases CBM setup consists of several detectors including as main tracking device the silicon tracking system (STS), consisting of 8 silicon microstrip detector stations, located inside a large acceptance dipole magnet for track and vertex reconstruction and momentum determination.

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S. Lebedev, C. H¨ ohne, I. Kisel, A. Lebedev and G. Ososkov

The Transition Radiation Detector (TRD) is intended for tracking and electron identification for p > 1.5 GeV/c. TRD consists of 3 stations, each station consists of 4 identical layers. Each layer consists of a multilayer dielectric radiator, where transition radiation (TR) is produced by electrons, and of a gaseous detector (85%Xe+15%CO2 ) which measures deposited energy and TR. The muon system (MUCH) consists of 6 hadron absorber layers made of iron of variable thickness and detector stations in each of the gaps. The detector technology is still under discussion. GEM technology is the most promising candidate for regions with high hit density. For the outer parts at lower hit density, straw tubes are under discussion. For the measurement of muons from the decay of low-mass vector mesons (ρ, ω, ϕ) muons are required to pass only an iron absorber thickness of 125 cm (7.5 λI , with λI being the nuclear interaction length), whereas for muons from the decay of charmonia the full absorber length of 225 cm is used (total thickness of 13.4 λI ). The Ring Image CHerenkov (RICH) detector of CBM will serve for electron identification from lowest momenta up to 10 GeV/c [11, 12]. The current design of the RICH detector provides about 21 hits per electron ring, the ring radius of electrons is about 5 cm. As the photodetector can only approximately be placed in the focal plane, rings are typically distorted to ellipses with about 10% difference in the length of major and minor half axis. The dimensions of the sensitive pads for the photodetector are 0.58 × 0.58 cm2 . The ring and hit density on the photodetector plane are non-uniform and depend on the position on the photodetector. The inner part which is closer to the beam pipe has the highest ring densities.

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Track Reconstruction in the TRD and MUCH Detectors

The track reconstruction in the TRD and MUCH detectors is based on trackfollowing method using reconstructed tracks in STS as seeds. The track reconstruction in STS is based on the cellular automaton method [13] and STS track parameters are used as starting point for the following track prolongation. This track-following is based on the standard Kalman filter technique [14] and is used for the estimation of track parameters [5] and trajectory recognition. The track propagation algorithm estimates the trajectory and its errors in a covariance matrix while taking into account three physics effects which influence the trajectory, i.e., energy loss, multiple scattering and the influence of a magnetic field. The influence of the material on the track momentum is taken into account by calculating the expected average energy loss due to ionization (BetheBloch formula) and bremsstrahlung (Bethe-Heitler formula) [1]. The influence on the error, i.e., the covariance matrix due to multiple scattering is included by adding process noise in the track propagation. Here, a gaussian approximation using the Highland formula [1] is used to estimate the average scattering angle. The propagation of the trajectory is done according to the equation of motion. If the track passes a magnetic field the equation of motion for a charged particle

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is solved applying the 4th order Runge-Kutta method [20]. If passing a field free region a straight line is used for propagation and the transport matrix calculation. The transport matrix is calculated by integrating the derivatives along the so called zero trajectory [6]. A detailed description of the developed track propagation can be found in [15–17]. In the track finding algorithm tracks are prolongated subsequently from one detector station to the next adding additional hits in each detector. For the attachment of hits a validation gate is calculated, according to the chosen probability for rejecting the correct hit. A nearest neighbor approach is used to choose the hit to be assigned to a track, i.e., the algorithm attaches the nearest hit if lying in the validation region at all. After the hit is attached, track parameters are updated with the Kalman Filter. After track finding, so called clone tracks (consisting of a very similar set of hits) and ghost tracks (consisting of a set of hits from different tracks) have to be rejected while keeping correctly found tracks with high efficiency. The track selection algorithm works in two steps. First, tracks are sorted by their quality which is defined by the track length and χ2 . Then, starting from the highest quality tracks all hits belonging to a track are checked. In particular, the number of hits shared with other tracks is calculated and the track is rejected if more than 15% of the hits are shared.

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Ring Reconstruction in the RICH Detector

The developed ring recognition algorithm [18, 19] is standalone, i.e the input data is only an array of RICH hits. It consists of three steps. First, a local search of ring-candidates is performed which is based on the Hough Transform (HT) method. HT is a standard method for curve recognition in digital images [8], however, in its straight-forward realization for a multiparametric curve recognition it requires very large combinatorics which makes it too slow for the ring finding. Therefore instead of combining all possible hit triplets in the photodetector plane, we use the fact that the RICH rings have a maximum radius Rmax . Hit triplets are only combined in a local area of the ring-candidate (see Fig. 1, left). Hits are collected lying within a predefined region around the initial hit, which defines the preliminary position of the first ring. Then center and radius are calculated using HT equations from every triplet of selected hits and Hough histograms are filled. When the histograms are built, strong peaks in each histogram should correspond to the supposed positions of ring centers (2D histogram, see Fig. 1, right) and radii (1D histogram). If the peak is higher than a prescribed cut this ring-candidate is accepted and shifted to the ring-candidate array, otherwise rejected. The second step is a ring selection, in which mainly the quality of rings is determined using an artificial neural network. ANN has 6 input parameters (the number of hits in ring, ring radius, χ2 of the fit etc.), 12 hidden neurons and one output neuron. The output value of ANN corresponds to the ring quality. The

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S. Lebedev, C. H¨ ohne, I. Kisel, A. Lebedev and G. Ososkov

Fig. 1. Preliminary local hit selection in a region defined by the maximum ring diameter plus a safety margin (left). Schematic view of the 2D histogram of ring centers (right).

algorithm checks for shared hits for all ring-candidates. If the ring shares more than 25% of its hits with a better quality ring it is rejected. The third step is an ellipse fitting of found rings. An ellipse fitting algorithm based on the Taubin method [3] was implemented.

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Speedup of the tracking algorithm

In this section we discuss optimization and parallelization of the tracking algorithms using available features of modern processors. These features comprise a SIMD instruction set and multithreading. The first allows to pack several data items into one register and to operate on all of them in parallel thus achieving more operations per cycle. The second feature enables the routines to exploit all available CPU cores and hardware threads. The use of this modern CPU technologies allows to achieve a high calculation speed of the tracking algorithm. The Kalman Filter based track fit is in intensive use in the track reconstruction algorithm. Therefore, its speed is very critical for the track reconstruction. Following the developments of the SIMDized Kalman filter based track fit for the STS tracking in CBM [7], several modifications of the Kalman Filter based track fit algorithm were also investigated here for improved speed. The development is based on a tracking algorithm which has been developed using a double precision scalar version of the Kalman Filter [16]. In the following this is referred to as the ‘initial scalar version’. Profiling the scalar version of the track propagation procedure it was found that the bottleneck is the access to the field map. The reason is that for the application in CBM the algorithm uses a 70 MB large field map, therefore permanently accesses the main memory. It is obvious that running on a conventional computer the performance of an algorithm with data located in the main memory is significantly slower comparing to one working with the cache. The magnetic field of the CBM magnet is smooth and can be locally approximated by polynomials. It was found to be sufficient for the track propagator to use a

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polynomial of the seventh order to approximate the field in the planes of each station. The field behavior between stations is approximated by a parabola with coefficients calculated from the three closest stations. Track parameters taken with the polynomial approximation of the magnetic field are as precise as those calculated using the full magnetic field map. The initial scalar implementation of the track propagator uses a geometry navigation based on the ROOT geometry package. It is a very precise method for geometry navigation, however not efficient in terms of calculation speed. First, because it uses the detailed Monte-Carlo detector geometry. Second, because this algorithm is rather general and not optimized for the CBM setup. Thus, a simplified detector geometry and an optimized geometry navigation algorithm were developed. The simplified geometry is created by converting the detailed Monte-Carlo detector geometry into a reduced one, which only consists of planes perpendicular to the beam direction. The navigation in such a simplified geometry has been significantly optimized. In the initial serial scalar implementation of the tracking algorithm [16] tracks are propagated through the detector sequentially one by one, picking up the nearest hits on the detector stations. The use of such an approach does not allow to apply directly SIMDized track propagation and fitting routines. Thus, the track finder algorithm was significantly changed in order to be SIMDized. Since all tracks are independent and are propagated by the same algorithm, one can propagate four tracks in parallel after packing the correspondent four scalar track parameters from different tracks into vectors. This reduces the loop size four times. Finally, multithreading was implemented in the tracking. Since the parallel SIMDized propagation of each four tracks is independent from each other, each such track propagation can be executed concurrently in different threads. The number of threads depends on the number of CPU cores and the number of propagated tracks.

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Results

In order to test the developed algorithms, central Au+Au collisions at 25 AGeV beam energy were simulated with UrQMD [2] and propagated through the CBM setup using CBMROOT framework. These events were used to estimate the background in which the interesting signal (electrons or muons) from the primary vertex, were embedded. In order to enhance statistics 5 e+ (µ+ ) and 5 e− (µ− ) were embedded in each event at the primary vertex. The algorithm performance was tested for the computer with a 2×Core i7 processors at 2.66 GHz. The comparison of the initial serial scalar implementation and the parallel implementation of the MUCH tracking shows that on expense of a minor loss in the momentum integrated track reconstruction efficiency (from 94.7% to 94.0%) the parallel tracking algorithm is much faster. A speed up of 101 is achieved by optimization of the algorithm and the use of the optimized Kalman filter routines. SIMDization and multithreading give 1.5 and 3.3 speed up factors

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S. Lebedev, C. H¨ ohne, I. Kisel, A. Lebedev and G. Ososkov

correspondingly. In total, the parallel tracking algorithm is 487 times faster than the initial serial scalar algorithm (from 730 ms/event to 1.5 ms/event). The comparison of the initial serial scalar implementation and the parallel implementation of the ring finding shows that the reconstruction efficiency is the same for both versions and equals to 91%. Overall, typically 5% of the approximately 80 found rings are fake rings and 1% clone rings. A speed up of 74 is achieved by optimization of the algorithm. Using SIMDization and multithreading the speed of the algorithm was increased by a factor of 1.95. In total a speed up factor of 143 was achieved (from 357 ms/event to 2.5 ms/event) for the optimized parallel version in comparison to the initial algorithm.

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Summary

Next generation experiments as the CBM detector planned at FAIR aim at data recording rates not experienced so far. In order to perform efficient analysis, fast event reconstruction algorithms are essential. Advanced parallel algorithms and software for event reconstruction in the RICH, TRD and MUCH detectors of the CBM experiment were developed and passed comprehensive testing. The software is intensively used for the physics analysis and detector optimization studies.

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