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

Abstract

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. Significant improvements in the reconstruction efficiency for relatively short low momentum "looper" tracks are also shown. 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. In particular, an improvement in low energy electron reconstruction, for which the production of "looping" tracks is likely and the impact of the new algorithm is directly demonstrated, could significantly impact the quality of flux determination, which in accelerator neutrino experiments relies on the measurement of $\nu_e$ electron scatterings.