High-Density QCD and Cosmic-Ray Air Showers

We discuss particle production in the high-energy, small-$x$ limit of QCD where the gluon density of hadrons is expected to become nonperturbatively large. Strong modifications of the phase-space distribution of produced particles as compared to leading-twist models are predicted, which reflect in the properties of cosmic-ray induced air showers in the atmosphere. Assuming hadronic primaries, our results suggest a light composition near Greisen-Zatsepin-Kuzmin cutoff energies. We also show that cosmic-ray data are sensitive to various QCD evolution scenarios for the rate of increase of the gluon density at small $x$, such as fixed-coupling and running-coupling Balitsky-Fadin-Kuraev-Lipatov evolution. There are clear indications for a slower growth of the gluon density as compared to RHIC and HERA, due, e.g., to running-coupling effects.