On the measurement of the proton-air cross section using cosmic ray data

Cosmic ray data may allow the determination of the proton-air cross section at ultra-high energy. For example, the distribution of the first interaction point in air showers reflects the particle production cross section. As it is not possible to observe the point of the first interaction $X_{\rm 1}$ of a cosmic ray primary particle directly, other air shower observables must be linked to $X_{\rm 1}$. This introduces an inherent dependence of the derived cross section on the general understanding and modeling of air showers and, therfore, on the hadronic interaction model used for the Monte Carlo simulation. We quantify the uncertainties arising from the model dependence by varying some characteristic features of high-energy hadron production.