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 fluctuations energy taken by neutral pions which emerge from first interaction cosmic ray atmosphere. We show that high-energy tail pion spectrum produced proton-air can be constrained, within uncertainties present experiments, through analysis shower-to-shower distribution showers, $P({N}_{\ensuremath{\mu}})$.