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

## TL;DR

This paper investigates how fluctuations in muon numbers in ultra-high-energy cosmic ray air showers are influenced by high-x neutral pion production in initial proton-Air interactions, with implications for future detector analyses.

## Contribution

It demonstrates that the low-muon tail in shower distributions is governed by high-x neutral pion production, highlighting the importance of the first interaction in muon fluctuation studies.

## Key findings

- Fluctuations are dominated by the first interaction.
- Low-N_mu tail is linked to high-x neutral pion production.
- Implications for future UHECR detector analyses.

## Abstract

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-$N_{\mu}$ tail of the shower-to-shower distribution of the number of muons is determined by the high-$x_{\rm L}$ region of the production cross-section of neutral pions in the first interaction.