Reconstruction and particle identification for a DIRC system

We study the reconstruction and particle identification (PID) problem for Ring Imaging devices providing a good knowledge of the direction of the Cherenkov photons, as the DIRC system, on which we specialize. We advocate first the use of the stereographic projection as a tool allowing a suitable representation of the photon data, as it allows to represent the Cherenkov cone always as a circle. We set up an algorithm able to perform reliably a fit of circle arcs of small angular opening, by minimising a true chi(2) expression. The system we develop for PID relies on this algorithm and on a procedure able to remove background photons with a high efficiency. We thus show that, even when the background is large, it is possible to perform an efficient PID by means of a fit algorithm which finally provides all the circle parameters; these are connected with the charged track direction and its Cherenkov angle. It is shown that background effects can be dealt without spoiling significantly the reconstruction probability distributions. (C) 1999 Elsevier Science B.V. All rights reserved.