Pattern Recognition, Tracking and Vertex Reconstruction in Particle Detectors (Particle Acceleration and Detection)

✍ Scribed by Rudolf Frühwirth, Are Strandlie

• Publisher: Springer
• Year: 2021
• Tongue: English
• Leaves: 208
• Category: Library

✦ Synopsis

This open access book is a comprehensive review of the methods and algorithms that are used in the reconstruction of events recorded by past, running and planned experiments at particle accelerators such as the LHC, SuperKEKB and FAIR. The main topics are pattern recognition for track and vertex finding, solving the equations of motion by analytical or numerical methods, treatment of material effects such as multiple Coulomb scattering and energy loss, and the estimation of track and vertex parameters by statistical algorithms. The material covers both established methods and recent developments in these fields and illustrates them by outlining exemplary solutions developed by selected experiments. The clear presentation enables readers to easily implement the material in a high-level programming language. It also highlights software solutions that are in the public domain whenever possible. It is a valuable resource for PhD students and researchers working on online or offline reconstruction for their experiments.

✦ Table of Contents

Preface
Scope
Content
Audience
Acknowledgements
A Note on the References
Typesetting and Notation
Contents
List of Figures
List of Tables
Part I Introduction
1 Tracking Detectors
1.1 Introduction
1.2 Gaseous Tracking Detectors
1.2.1 Multi-wire Proportional Chamber
1.2.2 Planar Drift Chamber
1.2.3 Cylindrical Drift Chamber
1.2.4 Drift Tubes
1.2.5 Time Projection Chamber
1.2.6 Micro-pattern Gas Detectors
1.3 Semiconductor Tracking Detectors
1.3.1 Silicon Strip Sensors
1.3.2 Hybrid Pixel Sensors
1.3.3 Silicon Drift Sensors
1.4 Scintillating Fiber Trackers
1.5 Alignment
1.6 Tracking Systems
1.6.1 Detectors at the LHC
1.6.1.1 ALICE
1.6.1.2 ATLAS
1.6.1.3 CMS
1.6.1.4 LHCb
1.6.2 Belle II and CBM
1.6.2.1 Belle II
1.6.2.2 CBM
References
2 Event Reconstruction
2.1 Trigger and Data Acquisition
2.1.1 General Remarks
2.1.2 The CMS Trigger System
2.1.3 The LHCb Trigger System
2.2 Track Reconstruction
2.3 Vertex Reconstruction
2.4 Physics Objects Reconstruction
2.4.1 Particle ID by Dedicated Detectors
2.4.2 Particle and Object ID by Tracking and Calorimetry
References
3 Statistics and Numerical Methods
3.1 Function Minimization
3.1.1 Newton–Raphson Method
3.1.2 Descent Methods
3.1.2.1 Line Search
3.1.2.2 Steepest Descent
3.1.2.3 Quasi-Newton Methods
3.1.2.4 Conjugate Gradients
3.1.3 Gradient-Free Methods
3.2 Statistical Models and Estimation
3.2.1 Linear Regression Models
3.2.2 Nonlinear Regression Models
3.2.3 State Space Models
3.2.3.1 Linear State Space Models and the Kalman Filter
3.2.3.2 Nonlinear State Space Models and the Extended Kalman Filter
3.3 Clustering
3.3.1 Hierarchical Clustering
3.3.2 Partitional Clustering
3.3.3 Model-Based Clustering
References
Part II Track Reconstruction
4 Track Models
4.1 The Equations of Motion
4.2 Track Parametrization
4.3 Track Propagation
4.3.1 Homogeneous Magnetic Fields
4.3.2 Inhomogeneous Magnetic Fields
4.3.2.1 Runge–Kutta Methods
4.3.2.2 Approximate Analytical Formula
4.4 Error Propagation
4.4.1 Homogeneous Magnetic Fields
4.4.1.1 Transformation from One Curvilinear Frame to Another
4.4.1.2 Transformations Between Curvilinear and Local Frames at a Fixed Point on the Particle Trajectory
4.4.1.3 Transformations Between Global Cartesian and Local Frames
4.4.2 Inhomogeneous Magnetic Fields
4.5 Material Effects
4.5.1 Multiple Scattering
4.5.1.1 The Distribution of the Scattering Angle
4.5.1.2 Multiple Scattering in Track Propagation
4.5.2 Energy Loss by Ionization
4.5.2.1 Mean Energy Loss
4.5.2.2 Ionization Energy Loss in Track Propagation
4.5.3 Energy Loss by Bremsstrahlung
4.5.3.1 Mean and Distribution of the Energy Loss
4.5.3.2 Approximation by Gaussian Mixtures
References
5 Track Finding
5.1 Basic Techniques
5.1.1 Conformal Transformation
5.1.2 Hough Transform
5.1.3 Artificial Retina
5.1.4 Legendre Transform
5.1.5 Cellular Automaton
5.1.6 Neural Networks
5.1.6.1 Hopfield Network
5.1.6.2 Recurrent Neural Network
5.1.6.3 Graph Neural Network
5.1.7 Track Following and the Combinatorial Kalman Filter
5.1.8 Pattern Matching
5.2 Online Track Finding
5.2.1 CDF Vertex Trigger
5.2.2 ATLAS Fast Tracker
5.2.3 CMS Track Trigger
5.2.3.1 Time Multiplexing
5.2.3.2 Pattern Matching
5.3 Candidate Selection
References
6 Track Fitting
6.1 Least-Squares Fitting
6.1.1 Least-Squares Regression
6.1.2 Extended Kalman Filter
6.1.3 Regression with Breakpoints
6.1.4 General Broken Lines
6.1.5 Triplet Fit
6.1.6 Fast Track Fit by Affine Transformation
6.2 Robust and Adaptive Fitting
6.2.1 Robust Regression
6.2.2 Deterministic Annealing Filter
6.2.3 Gaussian-Sum Filter
6.3 Linear Approaches to Circle and Helix Fitting
6.3.1 Conformal Mapping Method
6.3.2 Chernov and Ososkov's Method
6.3.3 Karimäki's Method
6.3.4 Riemann Fit
6.3.5 Helix Fitting
6.4 Track Quality
6.4.1 Testing the Track Hypothesis
6.4.2 Detection of Outliers
6.4.3 Kink Finding
References
Part III Vertex Reconstruction
7 Vertex Finding
7.1 Introduction
7.2 Primary Vertex Finding in 1D
7.2.1 Divisive Clustering
7.2.2 Model-Based Clustering
7.2.3 EM Algorithm with Deterministic Annealing
7.2.4 Clustering by Deterministic Annealing
7.3 Primary Vertex Finding in 3D
7.3.1 Preclustering
7.3.2 Greedy Clustering
7.3.3 Iterated Estimators
7.3.4 Topological Vertex Finder
7.3.5 Medical Imaging Vertexer
References
8 Vertex Fitting
8.1 Least-Squares Fitting
8.1.1 Straight Tracks
8.1.1.1 Exact Fit
8.1.1.2 Simplified Fit
8.1.2 Curved Tracks
8.1.2.1 Nonlinear Regression
8.1.2.2 Extended Kalman Filter
8.1.2.3 Fit with Perigee Parameters
8.2 Robust and Adaptive Vertex Fitting
8.2.1 Vertex Fit with M-Estimator
8.2.2 Adaptive Vertex Fit with Annealing
8.2.3 Vertex Quality
8.3 Kinematic Fit
References
9 Secondary Vertex Reconstruction
9.1 Introduction
9.2 Decays of Short-Lived Particles
9.3 Decays of Long-Lived Particles
9.4 Photon Conversions
9.5 Hadronic Interactions
References
Part IV Case Studies
10 LHC Experiments
10.1 ALICE
10.2 ATLAS
10.3 CMS
10.4 LHCb
References
11 Belle II and CBM
11.1 Belle II
11.2 CBM
References
A Jacobians of the Parameter Transformations
Transformation from One Curvilinear Frame to Another
Transformations Between a Local Frame and the Curvilinear Frame
Transformations Between the Intermediate Cartesian Frame and the Local Frame
B Regularization of the Kinematic Fit
Reference
C Software
FairRoot
ACTS: A Common Tracking Software
GBL: General Broken Lines
GENFIT
RAVE
References
Glossary and Abbreviations
Index