This paper presents a comprehensive study on the reconstruction of vertex positions and particle tracks using heavy ion collision data from the Large Hadron Collider (LHC). Nonlinear particle trajectories, background noise, and scattering effects complicate accurate vertex prediction and trajectory reconstruction in real particle detectors. The solution proposed in this paper is integrating geometric methods with the DBSCAN density clustering algorithm to overcome these issues. This method effectively improves the precision of vertex finding and particle track reconstruction. In the meantime, a geometrical technique and probabilistic quantization are employed to predict the motion radius of the particle more accurately. This framework has been independently confirmed in an analysis of >10,000 collision points, which proves the frameworks robustness. Compared with the benchmark method, the framework only relies on the coordinates of the hit point recorded by the detector, which not only improves the universality of the algorithm application but also reduces the requirements on the equipment and the complexity of implementation and effectively improves the precision of vertex and trajectory reconstruction. The results are for the vertexing accuracy (0.005 cm) and average tracking search precision (95.40%) with a radius determination error of 0.5 cm. The proposed method also stands valid when these results are evaluated.
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