Determination of high-energy hadronic interaction properties from observables of proton initiated extensive air showers

We propose a method to extract high-energy hadronic interaction properties from the distributions of two of the main observables of proton extensive air showers: the depth of maximum shower development, $X_\mathrm{max}$, and the number of muons at the ground, $N_\mu$. We determine relevant parameters of the first and subsequent interactions of the cascade and analyse how they impact on these observables. By training a universal neural network, we demonstrate that we can recover the most relevant parameters (fraction of energy going to the hadronic channel in the first interaction, first interaction multiplicity and effective inelasticity) for different hadronic interaction models using only the observables $X_\mathrm{max}$ and $N_\mu$.