Results of the two-dimensional particle identification analysis applied for the RICH in the DELPHI experiment

The Cherenkov radiation is fully described by two variables Θ and φ, polar and azimuthal angles, respectively. In all published methods the azimuthal angle φ is completely neglected. We want to suggest that one can profit using the φ angle as additional aid in the particle identification procedure. For the first time, two-dimensional analysis results, taking into account not only both angles but also their errors, are presented. The two-dimensional method based on the Lagrange technique couples together the constraint equation and the minimization function and leads to the correct probability estimation. The principles and advantages of the proposed method are presented.