Discriminant analysis based on spectral statistics applied to TeV cosmic γ/proton separation

It has been shown that spectral statistics techniques, based on random matrix theory, can be applied to study correlations at ground level between the secondary particles of simulated extensive air showers. The statistical description of shower fronts provided by appropriate spectral measures makes it possible to separate them into different classes depending on the type of the primary cosmic ray. Using a suitable combination of spectral statistics in the framework of discriminant analysis, we introduce a new statistic which separates shower fronts according to the primary type with improved efficiency.

► Hits on the detector are identified with complex eigenvalues of a random matrix.
► Two spectral statistics are constructed from the ensemble of random matrices.
► The statistics are properly combined in an algorithm for gamma-proton separation.
► Quality factors have been quite improved and computational efforts have been reduced.