Faraway algorithm to reconstruct and trigger vertices from Long-Living Particles at LHCb

The Standard Model and many new physics scenarios predict the existence of long-lived particles (LLPs), with lifetimes larger than 100 ps. However, the reconstruction and selection of these particles are very challenging at the Large Hadron Collider (LHC) due to their significantly displaced decay point. Because of the recently upgraded LHCb detector and the new GPU-based first High-Level Trigger (HLT1) it became possible to develop brand-new algorithms for fast track reconstruction without the usage of the hits from the first two trackers (VErtex LOcator and Upstream Tracker). The Faraway track reconstruction algorithm, developed in the framework of this master thesis work, uses only hits in the new large Scintillating Fibre Tracker (SciFi) to reconstruct secondary vertices formed by LLPs. The algorithm utilises a new procedure for fast extrapolation of the tracks through the LHCb magnetic field. In addition, it uses a fully connected single-layer Neural Network (NN) for fake vertex rejection. The algorithm is validated using mass distributions of $K_s^0$ and $\Lambda$ hadrons from the real data collected during the 2024 LHCb operation. It is expected that the Faraway reconstruction algorithm will extend the LHCb physics potential during future data-taking periods.