T.A. Trainor and D. Weerasundara
During the 1995 fall run NA49 collected nearly 0.7 million nucleus-nucleus collisions using the 158 GeV/nucleon lead beam at the CERN SPS accelerator. A preliminary production analyses of these data is in progress at CERN. We describe below a correlation analysis that we performed to determine the geometry of the Time Projection Chamber (TPC) system of the NA49 experiment.
It is crucial to physics analysis, namely particle momentum determination and reconstruction of decay vertices, to know the locations and orientations of the TPCs relative to the standard NA49 coordinate system quite accurately. The design parameters of the NA49 experiment require the determination of relative TPC positions and their angles with an accuracy of order 100 µm and 100 µrad within a system that covers an area of nearly 15m by 7m. We have achieved this goal by carrying out an analysis of TPC tracking data to determine the geometrical positions of the four TPCs relative to each other, to the beam and to the magnet system. Tracking data for this analysis were collected for two different multi-target configurations. In one configuration, data were obtained from the simultaneous placement of four targets along the beam line. In the second configuration, data were collected with a single target in place along the beam for each of the four different targets. In both configurations, with the magnetic field turned off, each TPC sees straight tracks coming from these beam-target interaction points. TPC tracks are parametrized by four quantities: two slopes and two intercepts, in the horizontal (bend) and vertical planes.
By a correlation analysis of these straight tracks in an appropriately defined space, the location of the beam-target interaction point can be precisely reconstructed in each TPC local reference frame. A comparison of these relative positions generates a common registration of all of the TPCs with the beam-target system.
For the purpose of the TPC alignment we define an intercept space
by 
where
i = -
zi · '.
zi
is the distance to target i from a TPC mid-plane,
and and ' =
d/dz
are the intercept and slope of a TPC track in the
(,z) plane
in the internal coordinate system of each TPC
(= x,y for bending and
vertical planes, respectively).
TPC tracks coming from a beam-target interaction form a straight-line correlation in this intercept space. Requiring the track correlation to be parallel to the track intercept axis determines the longitudinal (z) position, and the intercept of the correlation locates the transverse position of the beam-target interaction in the local coordinate system of each TPC. Simultaneous measurements of four of these beam-target interaction points uniquely determine the beam in each of the TPCs. Comparing the measured beam slopes and intercepts in each of the TPC local coordinate systems we are able to determine the relative positions and angles of the TPCs with the required accuracy.