A Kalman Filter for track reconstruction in very large time projection chambers

This study introduces a Kalman Filter tailored for homogeneous gas Time Projection Chambers (TPCs), adapted from the algorithm utilized by the ALICE experiment. In order to describe semi-circular paths in the plane perpendicular to the magnetic field, we introduce a novel mirror rotation technique into the Kalman Filter algorithm, enabling effective tracking of trajectories of varying lengths, including those with multiple circular paths within the detector, also known as "loopers". Demonstrated relative improvements of up to 80\% in electron momentum resolution and up to 50\% in muon and pion momentum resolution underscore the significance of this enhancement. Such advancements hold promise not only for the future of the ALICE TPC but also for neutrino high-pressure gas TPCs, where loopers become significant owing to the randomness of production points and their relatively low energies in neutrino interactions.
Comment: 37 pages, 22 figures