Method
The first 4 layers (called A, B, C, and D) of the spectrometer consist of 8 silicon sensors which can provide 3-dimenzional hit positions. Sensor are located at near beam pipe with certain angles. The pad size is 1mm by 1mm in the local sensor coordinates, thus a hit on a single pad provides a precise 3 dimensional hit (angular resolution is roughly 0.01 radian).
Charged tracks passing through the 4 layers where the magnetic field is small can be regarded as straight lines when multiple scattering is small, or in case of high momentum tracks. One can then simply apply a straight line fit to find a track candidate.
According to the PHOBOS Front-end tracking condition, or track seed definition, a track having minimum 3 hits on different layers among the 4 layers should be found as a track seed. Thus a track seed means a track having 3 hits on the layers, A-B-C, A-B-D, A-C-D, B-C-B, or having 4 hits on the layers A-B-C-D.
Full 3 hit combinations are tested with straight line fit and only combinations with good probability survive and are considered as track seed candidates. The candidates then pass through a filter where the best candidate selection is done among the candidates having common shared hits. After the filter, all the track seed candidates consist of exclusive hit content.
All track seed candidates have at this moment 3 hits, i.e., have one missing hit from a layer. Each candidate tries to find the missing hit by adding a hit from the missing layer and doing straight line fit. The candidate choose a hit with which the chi2 probability is maximum and become a 4-hit track seed. After this step, some candidates become 4-hit track seeds but some remain as before. Once again the filtering step for non-hit sharing condition is neccessary because some candidates may have shared hits after the missing hit recovery.
more description for filtering...
Final track seeds, or straight lines are passed to a 3-D vertex fitter, where the sum of miss distances of the tracks from a vertex is minimized (miss distance = minimum distance between a track and a vertex). The resulting vertex is assumed as the event primary vertex.
Resolution
Central event with 2 spectrometers in the B field
The 3D vertex finding algorithm is tested with 200 Hijing central events. Track seeds are reconstructed with 2 spectrometer arms and passed to the 3DVertexFinder. The resulting vertex resolution is about 300 micro meter in x, y, and 400 micron in z. The resolution is very much dependent on how we filter the seeds.
Click here to see in PS format
Central event with 1 spectrometers in the B field
For the same events, the same test is done but with only a single spectrometer. As expected, the vertex resolution becomes worse because only a half number of tracks are invovled in the vertex finding.
Click here to see in PS format
Usage
// ... many lines not shown
TPh3DVertexFinder *v3d = new TPh3DVertexFinder(1); // argument >0 will print out a introduction message
while (event=data->GetNextEvent())
{
// ... some stuffs like copying hits to detector are not shown here
TPhSpecVertex *vtx=v3d->FitVertex(seeds,db); // db= debug level
}