Probing the $π^0$ spectrum at high-$x$ in proton-Air interactions at ultra-high energies

The average number of muons in air showers and its connection with shower development has been studied extensively in the past. With the upcoming detector upgrades, UHECR observatories will be able to probe higher moments of the distribution of the number of muons. Here a study of the physics of the fluctuations of the muon content is presented. In addition to proving that the fluctuations must be dominated by the first interactions, we show that low-$N_μ$ tail of the shower-to-shower distributi...