Statistical methods applied to composition studies of ultrahigh energy cosmic rays

The mass composition of high energy cosmic rays above 1017 eV is a crucial issue to solve some open questions in astrophysics such as the acceleration and propagation mechanisms. Unfortunately, the standard procedures to identify the primary particle of a cosmic ray shower have low efficiency mainly due to large fluctuations in the shower development. We present a statistical method for composition studies based on several measurable features of the longitudinal development of the CR shower such as Nmax, Xmax, asymmetry, skewness and kurtosis. Principal component analysis was used to evaluate the relevance of each parameter in the representation of the overall shower features and a linear discriminant analysis (LDA) was used to combine the different parameters to maximize the discrimination between different particle showers. LDA provides a separation between primary gammas, proton and iron nuclei better than the procedures based on Xmax only. The method proposed herein was successfully tested in the energy range from 1017 to 1020 eV even when limitations of shower track length were included in order to simulate the field of view of fluorescence telescopes.