Forward hadron production in proton-air collisions above LHC energies through the fluctuations of extensive air showers

Primary proton-air interactions at ultra-high energies leave a physically interpretable imprint on the correlated fluctuations of the depth of shower maximum and the muon content in extensive air showers. This imprint reflects the stochasticity in the partition of the primary energy among secondary particles in the first interaction. We show that these fluctuations can be accessed through a probabilistic description that isolates sensitivity to hadronic physics in the initial collision, while treating the subsequent shower development as effectively universal. The uncertainties resulting from this universality are smaller than the spread among current hadronic interaction models and comparable to current experimental uncertainties. Consequently, the joint observable space defined by these two quantities provides a new probe of hadron production in kinematic regimes far beyond the reach of human-made accelerators.