Lower limit on the ultra-high-energy proton-to-helium ratio from the measurements of the tail of $X_{\mathrm{max}}$ distribution

Understand

There are multiple techniques to determine the chemical composition of the ultra-high-energy cosmic rays.

• While most of the methods are primarily sensitive to the average atomic mass, it is challenging to discriminate between the two lightest elements: proton and helium.
• In this paper, the proton-to-helium ratio in the energy range $10^{18.0} \mbox{eV}$ to $10^{19.3} \mbox{eV}$ is estimated using the tail of the distribution of the depth of the shower maximum $X_{\mathrm{max}}$.
• Using the exponential decay scale $\Lambda$ measured by the Pierre Auger Observatory and the Telescope Array experiment we derive the 68\%\,CL constraints on the proton-to-helium ratio $\mathrm{p}/\mathrm{He} > 7.3 $ and $\mathrm{p}/\mathrm{He} > 0.43 $ for $10^{18.0} < E < 10^{18.5}$ eV and $10^{18.3} < E < 10^{19.3}$ eV correspondingly.