Proton-proton interactions at the Highest Energies: the Grey-Disk and the Core-Corona models

In this letter, the Grey-Disk and the Core-Corona models are combined in a scenario that aims to explain different unexpected features observed in the interactions of the highest energy particles in the Earth's atmosphere. In particular, the observed distributions of $X_{\rm max}$ and $N_\mu$ are explained, assuming that the ultra-high-energy cosmic ray spectrum is dominated by protons produced by a few extra-galactic sources with different injection spectra and maximum energy cutoffs. The compliance of this heterodox scenario with other relevant observations as the instep region in the energy spectrum, the event-by-event correlations between $X_{\rm max}$ and the detected signal at the ground and the absence of detection, so far, of UHE neutrinos or photons, are also briefly discussed. If confirmed, such a scenario would dramatically change the present understanding of the UHECR primary composition and, thus, the characteristics of their sources.