Track Finding Problem Statement
David Adams
December 17, 1996

In particle physics experiments a particle beam collides with another
beam or a fixed target and usually produces new particles.  Some of
the particles then pass through a detector system and leave signals
behind.  The goal of track-finding is to use these signals to
reconstruct the trajectories of these particles.

The peformance of a track-finding system may be characterized by
the following:

1. Efficiency - what fraction of tracks passing through the detector
   are found?

2. Misreconstructed fraction - what fraction of these are poorly
   reconstructed, i.e. have reconstructed parameters far from
   the true values?

3. Fake rate - what is the relative number of reconstructed tracks
   which do not correspond to any real track?

4. CPU performance - How much time is required to find the tracks?


Here is a rough sketch of the algorithm we use to address the
above problem:

The clustered hits for each subdetector (silicon, scifi, ...) are
combined to find tracks.  These clusters are initially assigned to layers.
The layers are particular to the problem of track-finding but are
closely related to the surfaces which make up the detector geometry.
The instructions for track finding are provided by paths.  Each path
is an ordered list of layers with instructions at each layer indicating 
whether and how to search for and add hits from the surface.
The path information at each layer includes:
1) Does track cross this layer and if not, how does it miss?
2) If crossed, should the full cluster information or only some subset
   be used?
3) What algorithm should be used to identify nearby clusters.
   (This is important for optimization.)
4) What algorithm should be used to add cluster information.
5) Criteria to evaluate whether the fit quality is acceptable.
Tracks pick up zero, one or more hits at each crossed layer.