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There are multiple techniques to determine the chemical composition of theultra-high-energy cosmic rays. While most of the methods are primarilysensitive to the average atomic mass, it is challenging to discriminate betweenthe two lightest elements: proton and helium. In this paper, theproton-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 theshower maximum $X_{\mathrm{max}}$. Using the exponential decay scale $\Lambda$measured by the Pierre Auger Observatory and the Telescope Array experiment wederive 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 $10^{18.3} < E < 10^{19.3}$ eVcorrespondingly. It is shown that the result is conservative with respect tothe admixture of heavier elements. We evaluate the impact of the hadronicinteraction model uncertainty. The implications for the astrophysical models ofthe origin of cosmic rays and the safety of the future colliders are discussed.

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