Short track reconstruction with VELO and TT

This note describes an algorithm for the reconstruction of tracks which pass through the VELO and TT stations but do not reach the T stations. The algorithm first collects all track segments which are found by the VELO tracking algorithm and are not assigned to any long track. For each VELO segment, a combination of TT hits consistent with an extrapolation of the segment is searched for and at least three TT hits are required for a successful match. The VELO segment and the matched TT hits are used to form an upstream track whose trajectory is refitted with a Kalman Filter fit. The performance of the algorithm is checked. An efficiency of about 75% for tracks with p > 1GeV is obtained for the re-optimized LHCb detector, with a corresponding ghost rate of ~15% and momentum resolution of ~ 15%.