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Constraining the energy spectrum of neutral pions in ultra-high-energy proton-air interactions

Fluctuations in the muon content of extensive air showers are anticorrelated to the fluctuations of the energy taken by the neutral pions which emerge from the first interaction of the cosmic ray in the atmosphere. We show that the high-energy tail of the neutral pion spectrum produced in the first proton-air interaction can be constrained, within the uncertainties of present cosmic ray experiments, through the analysis of the shower-to-shower distribution of the muon content of the air showers, $P(N_μ)$.