Track Finding Algorithm Research Articles

A new track finding algorithm based on a multi-dimensional extension of the Hough Transform

We introduce a new pattern recognition algorithm for track finding in High Energy Physics Experiments based on an extension of the Hough Transform to multiple dimensions. A remarkable property of this algorithm is that the execution time is simply proportional to the total number of the hits to be processed, making it particularly attractive for high occupancy situations. The algorithm needs to be trained using a sufficiently large set of simulated tracks. The same track finding algorithm can be used for very different detector geometries and only the set of simulated tracks used for training needs to be changed. The particular structure of the algorithm also lends itself naturally to parallel hardware implementations which, combined with its intrinsic flexibility, should provide a most powerful tool for triggering at future colliders.

Reconstruction of Large Radius Tracks with the Exa.TrkX pipeline

Particle tracking is a challenging pattern recognition task at the Large Hadron Collider (LHC) and the High Luminosity-LHC. Conventional algorithms, such as those based on the Kalman Filter, achieve excellent performance in reconstructing the prompt tracks from the collision points. However, they require dedicated configuration and additional computing time to efficiently reconstruct the large radius tracks created away from the collision points. We developed an end-to-end machine learning-based track finding algorithm for the HL-LHC, the Exa.TrkX pipeline. The pipeline is designed so as to be agnostic about global track positions. In this work, we study the performance of the Exa.TrkX pipeline for finding large radius tracks. Trained with all tracks in the event, the pipeline simultaneously reconstructs prompt tracks and large radius tracks with high efficiencies. This new capability offered by the Exa.TrkX pipeline may enable us to search for new physics in real time.

Machine learning predictor for ‘measurement-to-track’ association for the ATLAS Inner Detector trigger

The track finding algorithm adopted for the LHC Run-2 data taking period is based on combinatorial track following, where the number of seeds scales non-linearly with the number of hits. The corresponding CPU time increase, close to cubical, creates huge and ever-increasing demand for computing power. This is particularly problematic for the silicon tracking detectors, where the hit occupancy is the largest. Therefore, it is essential that resource use is reduced, whilst maintaining the ability to reconstruct tracks with minimal loss in efficiency. This paper briefly summarises the work that has been done to optimise the HLT ID track seeding software for ATLAS Run-3 and beyond, in order to reduce the number of fake seeds constructed. An ML-based algorithm has been developed to predict if a pair of hits belong to the same track given input hit features, focusing on cluster width and inverse track inclination. The implementation of the trained predictor in the form of Look-Up Tables is presented, along with performance results in terms of tracking efficiency and speed-up factor using simulated data.

Modeling of Solid State Detectors Using Advanced Multi-Threading: The TCoDe and TFBoost Simulation Packages

Particle tracking for future experiments at colliders is an incredible challenge in terms of sensor technology and readout. Simulation tools are a crucial ingredient to investigate new layouts able to cope with harsh radiation conditions and, at the same time, provide valuable timing information for track finding algorithms. Detailed and numerous simulations of energy deposits as well as sensor and front-end electronics responses imply a heavy usage of computing resources. In this paper, we present two software packages that, via massive parallelization and dedicated algorithms, allow for a significant speed-up in simulation time.

Track finding algorithm using the track road method for the PANDA Forward Tracker

In this study, we present an algorithm for 3D track finding in the Forward Tracker of the PANDA experiment. This tracker is based on straw tube detectors and is designed to measure the deflection of particles in the magnetic field of the PANDA dipole magnet in order to determine their momenta. The algorithm uses the track road method for selecting track candidates. The applied track model in the projection onto the bending plane in the region before, inside and after the dipole magnet gap consists of line, circle and line, respectively. In the non-bending plane, a track projection is represented by a straight line. The algorithm was tested using simulated tracks of muons and obtained results for the track finding efficiency and for the momentum resolution are presented.

A Generalized Approach to Longitudinal Momentum Determination in Cylindrical Straw Tube Detectors

The upcoming PANDA experiment at FAIR will be among a new generation of particle physics experiments to employ a novel event filtering system realised purely in software, i.e. a software trigger. To educate its triggering decisions, online reconstruction algorithms need to offer outstanding performance in terms of efficiency and track quality. We present a method to reconstruct longitudinal track parameters in PANDA’s Straw Tube Tracker, which is general enough to be easily added to other track finding algorithms that focus on transversal reconstruction. For the pattern recognition part of this method, three approaches are employed and compared: a combinatorial path finding approach, a Hough transformation, and a recursive annealing fit. In a systematic comparison, the recursive annealing fit was found to outperform the other approaches in every category of quality parameters and reaches a reconstruction efficacy of 95% and higher. Due to its computational simplicity, the recursive annealing fit was also found to have faster execution times compared to the other algorithms.

Track Finding for the PANDA Detector Based on Hough Transformations

The PANDA experiment at FAIR (Facility for Antiproton and Ion Research) in Darmstadt is currently under construction. In order to reduce the amount of data collected during operation, it is essential to find as many true tracks as possible and to be able to distinguish them from false tracks. Part of the preparation for the experiment is the development of a fast online track finder. This work presents an online track finding algorithm based on Hough transformations, which is comparable in quality and performance to the currently best offline track finder in PANDA. In contrast to most track finders the algorithm can handle the challenge of extended hits delivered by PANDA’s central Straw Tube Tracker and thus benefit from its precise spatial resolution. Furthermore, optimization methods are presented that improved the ghost ratio as well as the speed of the algorithm by 70 %. Due to further development potential in terms of track finding for secondary particles and speed optimization on GPUs, this algorithm promises to exceed the quality and speed of other track finders developed for PANDA.

Track finding at Belle II

This paper describes the track-finding algorithm that is used for event reconstruction in the Belle II experiment operating at the SuperKEKB B-factory in Tsukuba, Japan. The algorithm is designed to balance the requirements of a high efficiency to find charged particles with a good track parameter resolution, a low rate of spurious tracks, and a reasonable demand on CPU resources. The software is implemented in a flexible, modular manner and employs a diverse selection of global and local track-finding algorithms to achieve an optimal performance.

Particle Track Reconstruction with Quantum Algorithms

Accurate determination of particle track reconstruction parameters will be a major challenge for the High Luminosity Large Hadron Collider (HL-LHC) experiments. The expected increase in the number of simultaneous collisions at the HL-LHC and the resulting high detector occupancy will make track reconstruction algorithms extremely demanding in terms of time and computing resources. The increase in number of hits will increase the complexity of track reconstruction algorithms. In addition, the ambiguity in assigning hits to particle tracks will be increased due to the finite resolution of the detector and the physical “closeness” of the hits. Thus, the reconstruction of charged particle tracks will be a major challenge to the correct interpretation of the HL-LHC data. Most methods currently in use are based on Kalman filters which are shown to be robust and to provide good physics performance. However, they are expected to scale worse than quadratically. Designing an algorithm capable of reducing the combinatorial background at the hit level, would provide a much “cleaner” initial seed to the Kalman filter, strongly reducing the total processing time. One of the salient features of Quantum Computers is the ability to evaluate a very large number of states simultaneously, making them an ideal instrument for searches in a large parameter space. In fact, different R&D initiatives are exploring how Quantum Tracking Algorithms could leverage such capabilities. In this paper, we present our work on the implementation of a quantum-based track finding algorithm aimed at reducing combinatorial background during the initial seeding stage. We use the publicly available dataset designed for the kaggle TrackML challenge.

On the initial approximation of charged particle tracks in detectors with linear sensing elements

The search for charged particle tracks in detectors with linear sensing elements, such as wire chambers, strip silicon detectors etc., starts with identification of straight track segments. The latter are deduced by constructing all possible combinations of activated detector elements. In the high multiplicity environment, with many activated detector elements, this causes large combinatorics and significantly reduces the performance of the track finding algorithms. In this report we trace this problem back to determination of the parameters of a straight line build from a number of skew lines (sensing elements of a detector) in space. Based on the intersection points of two hyperbolas, we demonstrate an analytic solution in the case of four skew detector elements.The procedure can also be applied as a first approximation to the more general case of curved track finding.

Characterisation of different stages of hadronic showers using the CALICE Si-W ECAL physics prototype

A detailed investigation of hadronic interactions is performed using $\pi^-$-mesons with energies in the range 2--10 GeV incident on a high granularity silicon-tungsten electromagnetic calorimeter. The data were recorded at FNAL in 2008. The region in which the $\pi^-$-mesons interact with the detector material and the produced secondary particles are characterised using a novel track-finding algorithm that reconstructs tracks within hadronic showers in a calorimeter in the absence of a magnetic field. The principle of carrying out detector monitoring and calibration using secondary tracks is also demonstrated.

Hardware demonstrator of a compact first-level muon track trigger for future hadron collider experiments

Single muon triggers are crucial for the physics programmes at hadron collider experiments. To be sensitive to electroweak processes, single muon triggers with transverse momentum thresholds down to 20 GeV and dimuon triggers with even lower thresholds are required. In order to keep the rates of these triggers at an acceptable level these triggers have to be highly selective, i.e. they must have small accidental trigger rates and sharp trigger turn-on curves. The muon systems of the LHC experiments and experiments at future colliders like FCC-hh will use two muon chamber systems for the muon trigger, fast trigger chambers like RPCs with coarse spatial resolution and much slower precision chambers like drift-tube chambers with high spatial resolution. The data of the trigger chambers are used to identify the bunch crossing in which the muon was created and for a rough momentum measurement while the precise measurements of the muon trajectory by the precision chambers are ideal for an accurate muon momentum measurement. A compact muon track finding algorithm is presented, where muon track candidates are reconstructed using a binning algorithm based on a 1D Hough Transform. The algorithm has been designed and implemented on a System-On-Chip device. A hardware demonstration using Xilinx Evaluation boards ZC706 has been set-up to prove the concept. The system has demonstrated the feasibility to reconstruct muon tracks with a good angular resolution, whilst satisfying latency constraints. The demonstrated track-reconstruction system, the chosen architecture, the achievements to date and future options for such a system will be discussed.

A track finding algorithm for the inner tracking system of MPD/NICA

An inner tracking system (ITS) based on silicon pixel sensors is currently considered as one of the possible MPD upgrade steps. The main purpose of the new detector is to provide a better precision of the primary and secondary vertex reconstruction and improve track reconstruction in MPD in the region close to the interaction point. To study the ITS performance a new track finding algorithm was developed, which better takes into account the new system’s advantages. In this paper the new algorithm is described and first results obtained on simulated data are presented.

Hadrons in the CALICE silicon-tungsten electromagnetic calorimeter

A detailed study of hadronic interactions is presented using data recorded with the highly granular CALICE silicon-tungsten electromagnetic calorimeter. The predictions of several Monte Carlo Geant4 models are compared with experimental data, taken at FNAL in 2008. The contribution recaps results published in 2015 and a set of new results available since the beginning of 2016. The published results present a detailed analysis of hadronic showers in terms of radial and longitudinal hit and energy distributions. For the most recent analysis a simple track-finding algorithm was developed to study tracks left by secondary particles, emerging from hadronic interactions in the highly granular electromagnetic calorimeter prototype. Present Monte Carlo simulations provide a good description of the experimental data in terms of new observables, available through the detailed analysis of secondary particles; the Monte Carlo predictions are within 20% of the data, and for many observables much closer.

New track finding based on cellar automaton for AMS-02 detector

We present a new track reconstruction algorithm based on cellular automaton for AMS-02 experiment. This algorithm has already become one of the standard method in AMS-02 Monte Carlo simulation and data production. The performance of new track finding is shown in terms of CPU time, track efficiency, fake rate and charge confusion. With the new track finding algorithm, track reconstruction efficiency of 99% is achieved for both electron Monte Carlo simulation and ISS data. A comparison of new track finding and previous track finding for nuclei and γ event sample is shown as well.

The track finding algorithm of the Belle II vertex detectors

The Belle II experiment is a high energy multi purpose particle detector operated at the asymmetric e + e − - collider SuperKEKB in Tsukuba (Japan). In this work we describe the algorithm performing the pattern recognition for inner tracking detector which consists of two layers of pixel detectors and four layers of double sided silicon strip detectors arranged around the interaction region. The track finding algorithm will be used both during the High Level Trigger on-line track reconstruction and during the off-line full reconstruction. It must provide good efficiency down to momenta as low as 50 MeV/c where material effects are sizeable even in an extremely thin detector as the VXD. In addition it has to be able to cope with the high occupancy of the Belle II detectors due to the background. The underlying concept of the track finding algorithm, as well as details of the implementation are outlined. The algorithm is proven to run with good performance on simulated ϒ(4S ) → BB events with an efficiency for reconstructing tracks of above 90% over a wide range of momentum.

FPGA-Based Tracklet Approach to Level-1 Track Finding at CMS for the HL-LHC

During the High Luminosity LHC, the CMS detector will need charged particle tracking at the hardware trigger level to maintain a manageable trigger rate and achieve its physics goals. The tracklet approach is a track-finding algorithm based on a road-search algorithm that has been implemented on commercially available FPGA technology. The tracklet algorithm has achieved high performance in track-finding and completes tracking within 3.4 $\mu$s on a Xilinx Virtex-7 FPGA. An overview of the algorithm and its implementation on an FPGA is given, results are shown from a demonstrator test stand and system performance studies are presented.

Hardware Demonstrator of a Level-1 Track Finding Algorithm with FPGAs for the Phase II CMS Experiment

At the HL-LHC, proton bunches collide every 25 ns, producing an average of 140 pp interactions per bunch crossing. To operate in such an environment, the CMS experiment will need a Level-1 (L1) hardware trigger, able to identify interesting events within a latency of 12.5 μs. This novel L1 trigger will make use of data coming from the silicon tracker to constrain the trigger rate. Goal of this new track trigger will be to build L1 tracks from the tracker information.The architecture that will be implemented in future to process tracker data is still under discussion. One possibility is to adopt a system entirely based on FPGA electronic.The proposed track finding algorithm is based on the Hough transform method. The algorithm has been tested using simulated pp collision data and it is currently being demonstrated in hardware, using the “MP7”, which is a μTCA board with a powerful FPGA capable of handling data rates approaching 1 Tb/s.Two different implementations of the Hough transform technique are currently under investigation: one utilizes a systolic array to represent the Hough space, while the other exploits a pipelined approach.

FPGA-Based Approach to Level-1 Track Finding at CMS for the HL-LHC

The high luminosity upgrade of the LHC is expected to deliver luminosities of 7.5 × 10 34 cm −2 s −1 , with an average of 140–200 overlapping proton-proton collisions in each bunch crossing at a frequency of 40 MHz. To maintain manageable trigger rates under these conditions track reconstruction will be incorporated in the all-hardware first level of the CMS trigger. A track-finding algorithm based on seed tracklets has been developed and implemented on commercially available FPGAs for this purpose. An overview of the algorithm is presented, results are shown of its expected performance from simulations, and an implementation of the algorithm in a Xilinx Virtex-7 FPGA for a hardware demonstrator system is discussed.

L1 track finding for a time multiplexed trigger

At the HL-LHC, proton bunches will cross each other every 25ns, producing an average of 140 pp-collisions per bunch crossing. To operate in such an environment, the CMS experiment will need a L1 hardware trigger able to identify interesting events within a latency of 12.5μs. The future L1 trigger will make use also of data coming from the silicon tracker to control the trigger rate. The architecture that will be used in future to process tracker data is still under discussion. One interesting proposal makes use of the Time Multiplexed Trigger concept, already implemented in the CMS calorimeter trigger for the Phase I trigger upgrade. The proposed track finding algorithm is based on the Hough Transform method. The algorithm has been tested using simulated pp-collision data. Results show a very good tracking efficiency. The algorithm will be demonstrated in hardware in the coming months using the MP7, which is a μTCA board with a powerful FPGA capable of handling data rates approaching 1Tb/s.