Studies on algorithms for the reconstruction of tracking particles in 4D for the sub-detector VELO

The second Upgrade of the LHCb experiment will implemented in subsequent years around 2030. Thus, the VELO detector will have to an upgrade with a pos- sible new technology that permits us to measure the positions and travel time of charged particles simultaneously. With this in mind, it is necessary to make previ- ous studies to see what kind of resolution will have this new detector. In particular, this study examines the potential algorithms that can be used, like for example, DB- SCAN(global algorithm) and Search by Triplet(local algorithm) to reconstruct the trajectory of particles. We make a detailed study on the Search by Triplet algorithm adding the time information. A interpretative study was done at the time informa- tion of the particles. It is found that the efficiency, fake rate, and clone rate of our algorithm can reach until 94%, 8%, 0.7%, respectively, using the Search by Triplet algorithm and the time information.