Till now all tests of the templates vere done for fixed vertex with Z=0. This is the first study of the dependence of acceptance of tracks on the difference of the track origin and the template vertex.
The calculations are analogical to the previous study on total momentum and theta grid, but ptot is substituted by Z of the vertex.
Single templates for several momentum and theta values were generated.
Then the particles with close momenta were simulated and the chi2
for the appropriate template were calculated. The plots of accepted
tracks and their probabilities are shown in the following pictures:
pi -, 200 MeV/c, theta=60
pi -, 1 GeV/c, theta=30
pi -, 1 GeV/c, theta=50
First scatter plot on each figure shows the arrea, where the tracks were accepted.
On the second scatter plot the central area is shown.
Third and fourth plots show the probability values - on the last we can
see the black area for accepted tracks and small dots depicting the probablility
for "rejected" track candidates.
There is a strong correlation between Z and theta of the accepted particles, obviously if after changing Z of the vertex we modify theta so that the particle hits the first plane in the same or neighbour pad, there is a big chance that the track will be still acceptable for the template calculated for different Z vertex.
The width of the acceptance region in Z is small, especially for higher momentum particles. For unmodified theta it ranges from about 0.2 cm at 200 MeV/c to only about 0.05 cm at 1 GeV/c (theta=30). This is exactly the half width of the pad in the first layer (0.1 cm pads).
To be able to reconstruct particles with momenta > 1 GeV/c we will have to prepare templates separated in Z-vertex no more than 0.05 cm. The full range of vertex positions (+10, -20 cm) corresponds thus to 600 sets of templates. Of course not for all of them covariance tables have to be calculated and may be even some interpolations of the particle trajectories will be possible.