Track and vertex reconstruction in particle detectors

The goal of experimental particle physics is the investigation of the smallest building blocks of our matter and their interactions. A frequent, but not exclusive, approach is the use of particle accelerators in which particles are accelerated to high energies and then brought to collision with other particles. At the moment, the most famous accelerator is probably the LHC (Large Hadron Collider) at CERN in Geneva. In the LHC, two proton beams circulating in opposite directions are stored in two evacuated beam tubes, accelerated to an energy never reached before, and finally brought to collision at four underground locations. Large experiments are set up in these places, which observe the collisions with the help of various types of particle detectors. Because up to 29 million collisions of proton bunches per second can occur, a strict selection with regard to the physical relevance of the collisions or events must take place, so that detector data are recorded only for a small fraction of all collisions. In this way, in 2012 the Higgs boson was discovered by two experiments at CERN. Extremely short-lived particles such as the Higgs boson or the W and Z bosons discovered at CERN in 1983 can only be identified and measured via their decay products. These decay products, which are often unstable particles themselves, are not observed directly, but must be reconstructed from the signals they leave behind in the various detector components. This book describes and explains the most im- portant mathematical and statistical methods that have been specially developed for the reconstruction of charged particles. The reconstruction is usually carried out in two main steps. In the first step, the pattern recognition or track finding, the signals from the track detectors are combined into track candidates. In the second step, the track parameter estimation, location, direction and momentum of the track candidate are estimated using statistical methods. At the same time the hypothesis is checked that all signals in a track candidate were actually produced by the same particles. If necessary, the assignment of the signals to the track candidates can be corrected. A problem which is closely related to the reconstruction of charged particles is the reconstruction of the collision points in the accelerator and the reconstruction of the decay points of unstable particles. The reconstruction of collision or decay points usually also takes place in two steps, namely pattern recognition and estima- tion. While the pattern recognition mostly uses algorithms that are tailored to the problem, the statistical methods for estimating the position of the collision or decay point are very similar to those applied in track reconstruction. The book concludes with two chapters in which the application of the previously described methods in the four LHC experiments and in two other experiments in Japan and Germany is summarized.