Description and performance studies of the Forward Tracking for a scintilating fibre detector at LHCb

The $Forward$ $Tracking$ algorithm extends tracks reconstructed in the Vertex Locator to the three stations of the $Scintillating$ $Fibre$ $Tracker$. A Hough Cluster like algorithm is used to identify consistent fibre tracker hits. These hits are then combined with the input VELO tracks to so called long tracks, which is the main track type of physics analyses in LHCb. The algorithm consists of several steps which are described in detail. Its performance is studied on simulated $B^0_s \to \phi\phi$ samples for the running conditions expected in future data taking after the upgrade, namely a luminosity larger $\mathcal{L} = 2 \times 10^{33} cm^{-2}s^{1}$.