Determination of the proton-to-helium ratio in cosmic rays at ultra-high energies from the tail of the $X_{\max }$ distribution

Abstract

We present a method to determine the proton-to-helium ratio in cosmic rays at ultra-high energies. It makes use of the exponential slope, $\Lambda$, of the tail of the $X_{\max }$ distribution measured by an air shower experiment. The method is quite robust with respect to uncertainties from modeling hadronic interactions and to systematic errors on $X_{\max }$ and energy, and to the possible presence of primary nuclei heavier than helium. Obtaining the proton-to-helium ratio with air shower experiments would be a remarkable achievement. To quantify the applicability of a particular mass-sensitive variable for mass composition analysis despite hadronic uncertainties we introduce as a metric the `analysis indicator' and find an improved performance of the $\Lambda$ method compared to other variables currently used in the literature. The fraction of events in the tail of the $X_{\max }$ distribution can provide additional information on the presence of nuclei heavier than helium in the primary beam.

Added journal reference

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• Depth of Maximum of Air-Shower Profiles at the Pierre Auger Observatory: Measurements at Energies above 10^17.8 eV
• One-dimensional Hybrid Approach to Extensive Air Shower Simulation
• Measurement of the proton-air cross-section at $\sqrt{s}=57$ TeV with the Pierre Auger Observatory
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Cited by in corpus (1)

• On the efficiency of the evaluation of the primary cosmic ray composition using lateral distributions of air shower electromagnetic component