An analytical solution to the problem of linear track segment reconstruction in drift tube chambers

Drift tube chambers are used for high resolution position measurements of charged particles in high energy physics. In the case of track reconstruction in two dimensions, for given geometry of a calibrated drift tube chamber, its output can be translated to a collection of triples, each one containing the coordinates of the wire of the drift tube crossed by a particle and the distance of the closest approach of a particle to the wire. The distance of the closest approach defines a drift circle which has the center at the wire and the radius equal to the distance of the closest approach. To reconstruct a linear segment of a track, a common tangent must be found to drift circles associated with that single track. In the study it is shown that this problem can be solved analytically.