  Cosmic Rays (CR) impinging on the terrestrial atmosphere provide a viable
opportunity to study new physics in hadron-nucleus collisions at energies
covering many orders of magnitude, including a regime well beyond LHC energies.
The permanent flux of primary CR can be used to estimate event rates for a
given type of new physics scenario. As a step to estimate the potential for
new-physics searches in CR-induced Extensive Air Showers (EAS), we here
determine the total luminosity, including the contribution stemming from the
cascade of secondaries in hadron-air interactions using Monte Carlo simulations
of the hadronic shower component with CORSIKA~8. We show results obtained for
single showers and discuss the interplay with the CR spectrum. Furthermore, we
discuss the possibility to study BSM phenomenology in EAS, focusing on
so-called large-multiplicity Higgs production as an explicit example and its
impact on EAS observables.
