Studying the mass sensitivity of air-shower observables using simulated cosmic rays

Using CORSIKA simulations, we investigate the mass sensitivity of cosmic-ray air-shower observables for sites at the South Pole and Malargüe, Argentina, the respective locations of the IceCube Neutrino Observatory and the Pierre Auger Observatory. Exact knowledge of observables from air-shower simulations was used to study the event-by-event mass separation between proton, helium, oxygen,
and iron primary cosmic rays with a Fisher linear discriminant analysis. Dependencies on the observation site as well as the energy and zenith angle of the primary particle were studied in the ranges from 10 $^{16.0}$–10$^{18.5}$ eV and 0° to 60°; they are mostly weak and do not change the qualitative results. Promising proton-iron mass separation is achieved using combined knowledge of all studied observables, also when
typical reconstruction uncertainties are accounted for. However, even with exact measurements, event-by-event separation of intermediate-mass nuclei is challenging and better methods than the Fisher discriminant
and/or the inclusion of additional observables will be needed. As an individual observable, high-energy muons (> 500 GeV) provide the best event-by-event mass discrimination, but the combination of muons of
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any energy and X$_{max}$ provides already a high event-by-event separation between proton-iron primaries at both sites. We also confirm that the asymmetry and width parameters of the air-shower longitudinal profile, R and L, are mass sensitive. Only R seems to be suitable for event-by-event mass separation, but L can potentially be used to statistically determine the proton-helium ratio. Overall, our results motivate the coincident measurement of several air-shower observables, including at least X$_{max}$ and the sizes of the muonic and electromagnetic shower components, for the next generation of air-shower experiments.