Using the microstrip detectors described in spec:mstrip, we take advantage of the fact that charmed particles travel a short distance in the spectrometer before they decay. This means we can reconstruct two distinct vertices in the event: the primary or production vertex and the secondary or decay vertex. A diagram of a decay and its vertices is shown in select:charm_decay. By reconstructing the two vertices, we obtain several quantities on which we can cut to reduce non-charm backgrounds.
For the analyses presented in this thesis, we use a candidate driven vertexing algorithm called . To reconstruct a decay candidate, we find three separate tracks that match our requirements for being a proton, kaon, and pion respectively. We then use the vertexing algorithm to form a vertex from these three tracks. Assuming a valid vertex can be found, we point the momentum vector of the candidate back towards its origin and select additional tracks that form a good vertex with the candidate. These tracks and the momentum vector form the primary vertex.
This method has been shown to be more efficient  at extracting fully reconstructed charm decays than methods which form well separated vertices without any knowledge of the decay topology being searched for. There are several reasons that this candidate driven algorithm is superior. First, there is no default separation required between vertices. Second, primary tracks may pass through the secondary, but can be excluded from it. Finally, including additional tracks in the secondary will affect the point-back of the charm candidate, causing it to miss the primary.