Tracking performance for long-lived particles at LHCb

The LHCb experiment is dedicated to the study of the $c$- and $b$-hadrons decays, including long living particles such as $K_s$ and strange baryons ($\Lambda$, $\Xi$, etc... ). These kind of particles are difficult to reconstruct from LHCb tracking systems since they escape the detection in the first tracker. A new method to evaluate the performance in terms of efficiency and throughput of the different tracking algorithms for long living particles have been developed. Special emphasis is laid on particles hitting only part of the tracking system of the new LHCb upgrade detector.