On the model uncertainties for the predicted maximum depth of extensive air showers

Abstract: A quantitative analysis of model uncertainties for calculations of the maximum depth of proton-initiated extensive air showers (EAS) has been performed. Staying within the standard physics picture and using the conventional approach to the treatment of high energy interactions, we found that present uncertainties on the energy dependence of the inelastic cross section, the rate of diffraction, and the inelasticity of hadronic collisions allow one to increase the predicted average EAS maximum depth by about 10 g/cm$^2$. Invoking more exotic assumptions regarding a potentially significant modification of the parton hadronization procedure by hypothetical collective effects, we were able to change drastically the predicted energy dependence of the inelasticity of proton-air interactions and to increase thereby the predicted EAS maximum depth by up to $\simeq 30$ g/cm$^2$. However, those latter modifications are disfavored by the data of the LHCf experiment, regarding forward neutron production in proton-proton collisions at the Large Hadron Collider, and by measurements of the muon production depth by the Pierre Auger Observatory.