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We present a method to determine the proton-to-helium ratio in cosmic rays atultra-high energies. It makes use of the exponential slope, $\Lambda$, of thetail of the $X_{\rm max}$ distribution measured by an air shower experiment.The method is quite robust with respect to uncertainties from modeling hadronicinteractions and to systematic errors on $X_{\rm max}$ and energy, and to thepossible presence of primary nuclei heavier than helium. Obtaining theproton-to-helium ratio with air shower experiments would be a remarkableachievement.  To quantify the applicability of a particular mass-sensitive variable formass composition analysis despite hadronic uncertainties we introduce as ametric 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 $X_{\rm max}$ distribution canprovide additional information on the presence of nuclei heavier than helium inthe primary beam.

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