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

TL;DR

This paper introduces a robust method using the exponential slope of the $X_{ m max}$ tail to determine the proton-to-helium ratio in ultra-high-energy cosmic rays, overcoming modeling uncertainties.

Contribution

It proposes a new analysis technique based on the tail slope of $X_{ m max}$ to accurately measure the proton-helium ratio in cosmic rays.

Findings

The $ m extit{Lambda}$ method outperforms other variables in mass composition analysis.

The tail fraction of $X_{ m max}$ provides insights into heavier nuclei presence.

The method is robust against hadronic interaction uncertainties.

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 $X_{\rm max}$ 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 $X_{\rm max}$ 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 $X_{\rm max}$ distribution can provide additional information on the presence of nuclei heavier than helium in the primary beam.