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 propertiesfrom the distributions of two of the main observables of proton extensive airshowers: the depth of maximum shower development, $X_\mathrm{max}$, and thenumber of muons at the ground, $N_\mu$. We determine relevant parameters of thefirst and subsequent interactions of the cascade and analyse how they impact onthese observables. By training a universal neural network, we demonstrate thatwe can recover the most relevant parameters (fraction of energy going to thehadronic channel in the first interaction, first interaction multiplicity andeffective inelasticity) for different hadronic interaction models using onlythe observables $X_\mathrm{max}$ and $N_\mu$.