Track Reconstruction Algorithm Research Articles

The derivation of Jacobian matrices for the propagation of track parameter uncertainties in the presence of magnetic fields and detector material

In high-energy physics experiments, the trajectories of charged particles are reconstructed using track reconstruction algorithms. Such algorithms need to both identify the set of measurements from a single charged particle and to fit the parameters by propagating tracks along the measurements. The propagation of the track parameter uncertainties is an important component in the track fitting to get the optimal precision in the fitted parameters. The error propagation is performed at intersections between the track and local coordinate frames defined on detector components by calculating a Jacobian matrix corresponding to the local-to-local frame transport. This paper derives the Jacobian matrix in a general manner to harmonize with numerical integration methods developed for inhomogeneous magnetic fields and materials. The Jacobian and transported covariance matrices are validated by simulating the propagation of charged particles between two frames and comparing with the results of numerical methods.

CNN-based track reconstruction study for gamma-ray pair telescope

MeV Gamma-ray Telescope (MGT) is a conceptual mission aimed at improving the detection sensitivity of gamma-ray astronomy in the MeV energy range. It consists of three sub-detectors: Gamma-ray Conversion silicon tracker, CALOrimeter and Anti-Coincident Detector. In this paper, a track reconstruction algorithm based on Convolutional Neural Networks (CNN) is developed for MGT. In order to train and test the model, Geant4 simulation is used and generates a large number of gamma-ray events at nine energy points in the energy band from 0.5 GeV to 10 GeV. Finally, the reconstruction results of angular resolution, position resolution and acceptance are shown. The testing results indicate that the angular resolution of MGT significantly improves in the 0.5∼10 GeV range compared with Fermi-LAT.

The position resolution of the Gas Microchannel plate Pixel Detector

The Gas Microchannel plate Pixel Detector (GMPD) is purposefully designed and manufactured for astrophysical X-ray polarization detection, slated for use in various space missions such as the Cosmic X-ray Polarization Detector (CXPD) CubeSat, Low Energy Polarimeter Detector (LPD/POLAR-2), and the Chasing All Transients Constellation Hunters (CATCH). Past research has explored the polarization and spectral performance of GMPD. This study, for the first time, experimentally investigates its imaging characteristics to validate its imaging capabilities. Utilizing a deconvolution method, we measured the position resolution of GMPD, revealing distinctions in the detector's imaging capabilities for X-rays of varying energies and in orthogonal directions. These research findings will provide targeted insights for optimizing the photoelectron track reconstruction algorithm and correcting systematic effects in polarization measurements for future applications of GMPD.

The future of X-ray polarimetry towards the 3-dimensional photoelectron track reconstruction

The development of the first X-ray polarimeter, based on the photoelectric effect 20 years ago and implemented thanks to advances in gas amplification structures and readout techniques, had a significant impact in opening a new window for X-ray polarimetry. This system measures the X-ray polarization by reconstructing the initial direction of the photoelectron, emitted by the interaction of an incident photon with an atomic electron, in a gas mixture from an ionization track collected on a two-dimensional plane. However, actual X-ray polarimeters, are still requiring relatively long exposure time and cannot coupled with high effective area mirrors or concentrators. In this context, the high yield polarimetry experiment in X-rays (Hype-X) project is currently underway, aiming to improve the sensitivity of the next generation X-ray polarimetry detectors taking advantage of the recent advancements in imaging techniques for high-resolution time projection chambers. In particular, we are evaluating the use of TIMEPIX3 to be applied for the read-out of a gas detector, which will allow us to obtain a three-dimensional image of the photoelectron track. To evaluate the improvement achievable by using a 3D track reconstruction, in this paper, we have reproduced a three-dimensional photoelectron track from a `Geant4' Monte Carlo simulation and examined the sensitivity of X-ray polarimetry using a new three-dimensional track reconstruction algorithm. We report the improvement of the modulation factor with three-dimensional track reconstruction as ∼5% (relative) in the 2–8 keV range and ∼17% (relative) in the 2–4 keV range compared to the current two-dimensional polarimetry system. This is equivalent to add a further telescope to the three-telescope systems now employed in space on board the IXPE mission.

Potentiality of automatic parameter tuning suite available in ACTS track reconstruction software framework

Particle tracking is among the most sophisticated and complex part of the full event reconstruction chain. A number of reconstruction algorithms work in a sequence to build these trajectories from detector hits. Each of these algorithms use many configuration parameters that need to be fine-tuned to properly account for the detector/experimental setup, the available CPU budget and the desired physics performance. Few examples of such parameters include the cut values limiting the search space of the algorithm, the approximations accounting for complex phenomena or the parameters controlling algorithm performance. The most popular method to tune these parameters is hand-tuning using brute-force techniques. These techniques can be inefficient and raise issues for the long-term maintainability of such algorithms. The opensource track reconstruction software framework known as “A Common Tracking Framework (ACTS)” offers an alternative solution to these parameter tuning techniques through the use of automatic parameter optimization algorithms. ACTS come equipped with an auto-tuning suite that provides necessary setup for performing optimization of input parameters belonging to track reconstruction algorithms. The user can choose the tunable parameters in a flexible way and define a cost/benefit function for optimizing the full reconstruction chain. The fast execution speed of ACTS allows the user to run several iterations of optimization within a reasonable time bracket. The performance of these optimizers has been demonstrated on different track reconstruction algorithms such as trajectory seed reconstruction and selection, particle vertex reconstruction and generation of simplified material map, and on different detector geometries such as Generic Detector and Open Data Detector (ODD). We aim to bring this approach to all aspects of trajectory reconstruction by having a more flexible integration of tunable parameters within ACTS.

BESIII track reconstruction algorithm based on machine learning

Track reconstruction is one of the most important and challenging tasks in the offline data processing of collider experiments. For the BESIII detector working in the tau-charm energy region, plenty of efforts were made previously to improve the tracking performance with traditional methods, such as template matching and Hough transform etc. However, for difficult tracking tasks, such as the tracking of low momentum tracks, tracks from secondary vertices and tracks with high noise level, there is still large room for improvement. In this contribution, we demonstrate a novel tracking algorithm based on machine learning method. In this method, a hit pattern map representing the connectivity between drift cells is established using an enormous MC sample, based on which we design an optimal method of graph construction, then an edgeclassifying Graph Neural Network is trained to distinguish the hit-on-track from noise hits. Finally, a clustering method based on DBSCAN and RANSAC is developed to cluster hits from multiple tracks. Track fitting algorithm based on GENFIT2 is also studied to obtain the track parameters, where deterministic annealing filter are implemented to deal with ambiguities and potential noises. The preliminary results on BESIII MC sample presents promising performance, showing potential to apply this method to other trackers based on drift chamber as well, such as the CEPC and STCF detectors under pre-study.

KinKal: A Kinematic Kalman filter Track Fitting Package for the Mu2e Experiment

Many current physics experiments require precision reconstruction of low-energy particles. One example is the Mu2e experiment, which requires reconstructing an isolated 105 MeV electron with better than 500 KeV/c momentum resolution. Mu2e uses a low-mass straw tube tracker, and a CsI crystal calorimeter, to reconstruct tracks. In this paper, we present the design and performance of a track reconstruction algorithm optimized for Mu2e’s unusual requirements. The algorithm is based on the KinKal [1] kinematic Kalman filter track fit package. KinKal supports multiple track parameterizations, including one optimized for looping tracks, such as Mu2e signal tracks, and others optimized for straight or slightly-curved tracks, such as the high-momentum (>1 GeV/c) cosmic ray muons used to calibrate and align the Mu2e detectors. All KinKal track parameterizations include the track origin time, to correctly model correlations arising from measurements that couple time and space, such as the straw drift time or the calorimeter cluster time. KinKal employs magnetic field inhomogeneity and material effect correction algorithms with 10−4 fractional precision. The Mu2e fit uses Artificial Neural Net functions to discriminate background hits from signal hits, and to resolve the straw tube hit left-right ambiguity, while iterating the extended Kalman filter. The efficiency, accuracy, and precision of the Mu2e track reconstruction, as tested on detailed simulations of Mu2e data, are presented.

Quantum Algorithms for Charged Particle Track Reconstruction in the LUXE Experiment

The LUXE experiment is a new experiment in planning in Hamburg, which will study quantum electrodynamics at the strong-field frontier. LUXE intends to measure the positron production rate in this unprecedented regime using, among others, a silicon tracking detector. The large number of expected positrons traversing the sensitive detector layers results in an extremely challenging combinatorial problem, which can become computationally expensive for classical computers. This paper investigates the potential future use of gate-based quantum computers for pattern recognition in track reconstruction. Approaches based on a quadratic unconstrained binary optimisation and a quantum graph neural network are investigated in classical simulations of quantum devices and compared with a classical track reconstruction algorithm. In addition, a proof-of-principle study is performed using quantum hardware.

A quantum algorithm for track reconstruction in the LHCb vertex detector

High-energy physics is facing increasingly demanding computational challenges in real-time event reconstruction for the near-future high-luminosity era. Using the LHCb vertex detector as a use case, we explore a new algorithm for particle track reconstruction based on the minimisation of an Ising-like Hamiltonian with a linear algebra approach. The use of a classical matrix inversion technique results in tracking performance similar to the current state-of-the-art but with worse scaling complexity in time. To solve this problem, we also present an implementation as a quantum algorithm, using the Harrow-Hassadim-Lloyd (HHL) algorithm: this approach can potentially provide an exponential speedup as a function of the number of input hits over its classical counterpart, in spite of limitations due to the well-known HHL Hamiltonian simulation and readout problems. The findings presented in this paper shed light on the potential of leveraging quantum computing for real-time particle track reconstruction in high-energy physics.

Towards a muon scattering tomography system for both low-Z and high-Z materials

Muon scattering tomography (MST) is a non-destructive technique to image various materials by utilizing cosmic ray muons as probes. A typical MST system with a two-fold track detectors is particularly effective in detecting high-Z materials (e.g. nuclear materials), but difficult to recognize low-Z materials (e.g. explosive materials). In this work, we present a concept of MST system to discriminate both low-Z and high-Z materials by extra measuring momentum of low-energy muons with a Cherenkov detector. A toy Monte Carlo simulation to describe detector responses and multiple scatterings of a muon tracking through materials is developed for statistical tests. Based on momentum-dependent track reconstruction and image reconstruction algorithm, we evaluate separation powers of different materials in the system. The results show that momentum measurement of low-energy muons and accurate track reconstruction can improve separation power of low-Z materials significantly. This may enable the MST system to detect both low-Z and high-Z materials with cosmic ray muons in the whole energy range.

Studying quantum algorithms for particle track reconstruction in the LUXE experiment

The LUXE experiment (LASER Und XFEL Experiment) is a new experiment in planning at DESY Hamburg, which will study Quantum Electrodynamics (QED) at the strong-field frontier. In this regime, QED is non-perturbative. This manifests itself in the creation of physical electron-positron pairs from the QED vacuum. LUXE intends to measure the positron production rate in this unprecedented regime by using, among others, a silicon tracking detector. The large number of expected positrons traversing the sensitive detector layers results in an extremely challenging combinatorial problem, which can become computationally very hard for classical computers. This paper presents a preliminary study to explore the potential of quantum computers to solve this problem and to reconstruct the positron trajectories from the detector energy deposits. The reconstruction problem is formulated in terms of a quadratic unconstrained binary optimisation. Finally, the results from the quantum simulations are discussed and compared with traditional classical track reconstruction algorithms.

The Mu2e experiment — Searching for charged lepton flavor violation

The Mu2e experiment will search for a Standard Model violating rate of neutrinoless conversion of a muon into an electron in the presence of an aluminum nucleus. Observation of this charged lepton flavor violating process would be an unambiguous sign of new physics. Mu2e will improve upon previous searches for this process by four orders of magnitude. This requires the world’s highest-intensity muon beam, a detector system capable of efficiently reconstructing the 105 MeV/c conversion electron signal, and minimizing sensitivity to background events. A pulsed 8 GeV proton beam strikes a target, producing pions that decay into muons. Beam outside the pulse must be suppressed to <10−10 to reduce beam-related backgrounds. The muon beam is guided from the production target along the transport system and onto the aluminum stopping target. Conversion electrons leave the stopping target and propagate inside a solenoidal magnetic field to the tracker and electromagnetic calorimeter. The tracker is a system of straw tube panels filled with Ar/CO2 at 1 atm that tracks particles inside of a solenoidal B-field and measures their momenta with ∼100 keV/c resolution to resolve signal events from decay-in-orbit backgrounds. The CsI calorimeter provides E/p and is used to seed the track reconstruction algorithm with σE/E∼10% and σt<500ps. Additionally, a novel cosmic ray veto with greater than 99.99% efficiency brings the expected number of background events to fewer than one over three years of running. To normalize the experiment, the stopping target monitor measures the rate of capture photons from muons incident on the stopping target by using a system of high-purity germanium and lanthanum bromide scintillators.

An exploratory study of machine learning techniques applied to therapeutic energies particle tracking in microdosimetry using the novel hybrid detector for microdosimetry (HDM)

In this work we present an advanced random forest-based machine learning (ML) model, trained and tested on Geant4 simulations. The developed ML model is designed to improve the performance of the hybrid detector for microdosimetry (HDM), a novel hybrid detector recently introduced to augment the microdosimetric information with the track length of particles traversing the microdosimeter. The present work leads to the following improvements of HDM: (i) the detection efficiency is increased up to 100%, filling not detected particles due to scattering within the tracker or non-active regions, (ii) the track reconstruction algorithm precision. Thanks to the ML models, we were able to reconstruct the microdosimetric spectra of both protons and carbon ions at therapeutic energies, predicting the real track length for every particle detected by the microdosimeter. The ML model results have been extensively studied, focusing on non-accurate predictions of the real track lengths. Such analysis has been used to identify HDM limitations and to understand possible future improvements of both the detector and the ML models.

Reconstruction of a muon bundle in the JUNO central detector

The Jiangmen Underground Neutrino Observatory (JUNO) is a multi-purpose neutrino experiment. One of the main goals is to determine the neutrino mass ordering by precisely measuring the energy spectrum of reactor antineutrinos. For the detection of reactor antineutrinos, cosmogenic backgrounds, such as 9Li/8He and fast neutrons induced by cosmic muons, should be rejected carefully by applying muon veto cuts, which require good muon track reconstruction. With a 20-kton liquid scintillator detector, the simulation shows the proportion of muon bundles (muon multiplicity ≥ 2) to be approximately 8% in JUNO, whereas its reconstruction has been rarely discussed in previous experiments. This study proposes an efficient algorithm for muon track reconstruction based on the charge response of a photomultiplier tube array. This is the first reconstruction of muon bundles in a large-volume liquid scintillator detector. In addition, the algorithm shows good performance and potential for reconstruction for both a single muon and double muons (muon multiplicity = 2). The spatial resolution of a single-muon reconstruction was 20 cm, and the angular resolution was 0.5°. For double-muon reconstruction, the spatial and angular resolutions could be 30 cm and $$1.0^\circ$$ , respectively. Moreover, this paper also discusses muon classification and the veto strategy.

A Common Tracking Software Project

The reconstruction of the trajectories of charged particles, or track reconstruction, is a key computational challenge for particle and nuclear physics experiments. While the tuning of track reconstruction algorithms can depend strongly on details of the detector geometry, the algorithms currently in use by experiments share many common features. At the same time, the intense environment of the High-Luminosity LHC accelerator and other future experiments is expected to put even greater computational stress on track reconstruction software, motivating the development of more performant algorithms. We present here A Common Tracking Software (ACTS) toolkit, which draws on the experience with track reconstruction algorithms in the ATLAS experiment and presents them in an experiment-independent and framework-independent toolkit. It provides a set of high-level track reconstruction tools which are agnostic to the details of the detection technologies and magnetic field configuration and tested for strict thread-safety to support multi-threaded event processing. We discuss the conceptual design and technical implementation of ACTS, selected applications and performance of ACTS, and the lessons learned.

Machine learning for track reconstruction at the LHC

The planned upgrade of the LHC to its High-Luminosity counterpart (HL-LHC) circa 2027 will bring about a drastic increase in instantaneous luminosity, pileup, and trigger rates. Currently, most LHC experiments use Kalman filter based track reconstruction algorithms which exhibit outstanding physics performance but scale poorly with the amount of data produced per bunch crossing. Therefore, the high energy physics community is currently performing intensive R&D to commission new or improved algorithms for this crucial data reconstruction task. This article presents many approaches such as running existing Kalman filter algorithms on accelerated hardware and overhauling the current approaches with machine learning techniques. A new algorithm testbed for research in track reconstruction, ACTS, is also discussed.

Search by triplet: An efficient local track reconstruction algorithm for parallel architectures

Millions of particles are collided every second at the LHCb detector placed inside the Large Hadron Collider at CERN. The particles produced as a result of these collisions pass through various detecting devices which will produce a combined raw data rate of up to 40 Tbps by 2021. These data will be fed through a data acquisition system which reconstructs individual particles and filters the collision events in real time. This process will occur in a heterogeneous farm employing exclusively off-the-shelf CPU and GPU hardware, in a two stage process known as High Level Trigger.The reconstruction of charged particle trajectories in physics detectors, also referred to as track reconstruction or tracking, determines the position, charge and momentum of particles as they pass through detectors. The Vertex Locator subdetector (VELO) is the closest such detector to the beamline, placed outside of the region where the LHCb magnet produces a sizable magnetic field. It is used to reconstruct straight particle trajectories which serve as seeds for reconstruction of other subdetectors and to locate collision vertices. The VELO subdetector will detect up to 109 particles every second, which need to be reconstructed in real time in the High Level Trigger.We present Search by triplet, an efficient track reconstruction algorithm. Our algorithm is designed to run efficiently across parallel architectures. We extend on previous work and explain the algorithm evolution since its inception. We show the scaling of our algorithm under various situations, and analyse its amortized time in terms of complexity for each of its constituent parts and profile its performance. Our algorithm is the current state-of-the-art in VELO track reconstruction on SIMT architectures, and we qualify its improvements over previous results.

Towards a realistic track reconstruction algorithm based on graph neural networks for the HL-LHC

The physics reach of the HL-LHC will be limited by how efficiently the experiments can use the available computing resources, i.e. affordable software and computing are essential. The development of novel methods for charged particle reconstruction at the HL-LHC incorporating machine learning techniques or based entirely on machine learning is a vibrant area of research. In the past two years, algorithms for track pattern recognition based on graph neural networks (GNNs) have emerged as a particularly promising approach. Previous work mainly aimed at establishing proof of principle. In the present document we describe new algorithms that can handle complex realistic detectors. The new algorithms are implemented in ACTS, a common framework for tracking software. This work aims at implementing a realistic GNN-based algorithm that can be deployed in an HL-LHC experiment.

Deep ensemble analysis for Imaging X-ray Polarimetry

We present a method for enhancing the sensitivity of X-ray telescopic observations with imaging polarimeters, with a focus on the gas pixel detectors (GPDs) to be flown on the Imaging X-ray Polarimetry Explorer (IXPE). Our analysis determines photoelectron directions, X-ray absorption points and X-ray energies for 1-9keV event tracks, with estimates for both the statistical and model (reconstruction) uncertainties. We use a weighted maximum likelihood combination of predictions from a deep ensemble of ResNet convolutional neural networks, trained on Monte Carlo event simulations. We define a figure of merit to compare the polarization bias–variance trade-off in track reconstruction algorithms. For power-law source spectra, our method improves on the current planned IXPE analysis (and previous deep learning approaches), providing ∼45% increase in effective exposure times. For individual energies, our method produces 20%–30% absolute improvements in modulation factor for simulated 100% polarized events, while keeping residual systematic modulation within 1σ of the finite sample minimum. Absorption point location and photon energy estimates are also significantly improved. We have validated our method with sample data from real GPD detectors.

A fast and efficient SIMD track reconstruction algorithm for the LHCb upgrade 1 VELO-PIX detector

The upgraded CERN LHCb detector, due to start data taking in 2021, will have to reconstruct 4 TB/s of raw detector data in real time using commodity processors. This is one of the biggest real-time data processing challenges in any scientific domain. We present an intrinsically parallel reconstruction algorithm for the vertex detector of the LHCb experiment designed to optimally exploit multi-core general purpose architectures. We evaluate the algorithm on two high-end architectures from two different vendors and discuss in detail the impact of different SIMD Instruction Set Architecture extensions on the performance. We further compare the algorithm to current state-of-the-art scalar pattern recognition algorithms. We show a factor 2 speedup while achieving similar or better levels of physics performance.