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\subsection{SiTrack}
The SiTrack LVL2 algorithm adopts a combinatorial pattern recognition
approach to reconstruct tracks starting from SPs formed in the ID
silicon detectors.

\par In order to perform SP combinations, these are first of all grouped into sets from which
the entries of each combination will be then extracted; the grouping is implemented in SiTrack,
using the idea of ``logical layers''. These correspond to a list of physical detector layers,
i.e. barrel layers and end-cap disks, and are labeled with increasing numbers moving away from
the beam line. The same physical layer can be included in more logical layers, to increase the
robustness of the track finding process. To provide a tangible example, the first logical layer
adopted for the reconstruction of high $p_T$ isolated leptons includes the innermost two pixel
barrel layers and the innermost pixel end-cap disk.

\par Once the SP have been associated to the logical layers they belong to, the track reconstruction
algorithm proceeds through the following five steps:
\begin{itemize}
\item track seeds formation;
\item optional primary vertex reconstruction along the beam line;
\item track seeds extension;
\item extended seeds merging;
\item clone removal.
\end{itemize}
The formation of track seeds corresponds to a combinatorial pairing of SP coming from the
innermost two logical layers. For each seed, the extrapolation to the beam line is evaluated,
using a straight line approximation; this process is depicted in Fig. \ref{fig_sitrack_rphi}.
\begin{figure}[htb]
\begin{center}
\ifpdf
\includegraphics[width=0.4\textwidth]{figures/lvl2_sitrack_rphi12.pdf}
\includegraphics[width=0.4\textwidth]{figures/lvl2_sitrack_rphi23.pdf}
\else
\includegraphics[width=0.4\textwidth]{figures/lvl2_sitrack_rphi12.eps}
\includegraphics[width=0.4\textwidth]{figures/lvl2_sitrack_rphi23.eps}
\fi
\end{center}
\caption{\label{fig_sitrack_rphi} Pictorial scheme of the SiTrack combinatorial strategy for
track seeds formation (left) and track seeds extension (right).}
\end{figure}
At this point a cut on the transverse impact parameter is applied. This cut, meant to reduce
the number of seeds to be further processed, is particularly important, as it fixes the lowest
reconstructible track $p_T$ value.

\par The subsequent step is the reconstruction of the position of the primary interaction vertex
along the beam line, used to reject tracks not coming from the primary interaction. The vertex
reconstruction is performed filling a histogram with the longitudinal impact parameter of the
seeds and searching for histogram maxima; more vertex candidates can be retained and seeds not
pointing to any of the reconstructed vertexes are discarded. This step is optional and,
as an example, is used for jet tracks reconstruction, while it is skipped in case of low
multiplicity event topologies, e.g. for the reconstruction of single isolated leptons.
Each retained seed is extended, as depicted in Fig. \ref{fig_sitrack_rphi}, extrapolating it to
the outer logical layers and forming one or more SP triplets for each seed; extensions are
selected applying a cut on the distance between the outer SP and the extrapolated seed. Each
extended seed is then fitted by a straight line in the longitudinal plane and parametrized as a
circle in the transverse plane.

\par At this point, all the extensions found for each seed must be merged into a single full track,
grouping the triplets having similar track parameters after the fit. The full track is thus
defined as formed by the union of the SP from all the merged extensions. All the triples not
involved in the merging process are discarded, while track parameters are re-evaluated for the
full track, fitting it with a straight line in the longitudinal plane and a circle in the
transverse one.

\par Two full tracks obtained from different track seeds may still share most of their SP; these
tracks are defined as clones. To eliminate these ambiguous cases, only the clone track containing
the largest number of SP is retained; in case more clone tracks contain the same number of space
points, the one with the lowest $\chi^2$ value prevails. The retained full tracks are finally
refit using one of the available common fit tool.