Proton-air interactions at ultra-high energies in muon-depleted air showers with different depths

TL;DR

This study links the steepness of muon distributions in ultra-high-energy air showers to the neutral pion energy spectrum, enabling probing of hadronic interactions and model differentiation using current detector capabilities.

Contribution

It introduces a method to relate shower maximum depth to the neutral pion spectrum, providing a new way to test hadronic interaction models at ultra-high energies.

Findings

The parameter Λ_μ evolves with X_max, reflecting hadronic activity.

X_max effectively probes the neutral pion energy spectrum.

Current detectors can statistically distinguish between models.

Abstract

The hardness of the energy spectrum of neutral pions produced in proton-air interactions at ultra-high energies, above $10^{18}$ eV, is constrained by the steepness of the shower-to-shower distribution of the number of muons in muon-depleted extensive air showers. In this work, we find that this steepness, quantified by the parameter $\Lambda_\mu$, evolves with the depth of the shower maximum, $X_{\max}$, assuming a universal value for shallow showers and an enhanced dependence on the high-energy hadronic interaction model for deep showers. We show that Xmax probes the so-called hadronic activity of the first interaction, thus allowing direct access to the energy spectrum of neutral pions in different regions of the kinematic phase space of the first interaction. We verify that the unbiased measurement of $\Lambda_\mu$ is possible for realistic mass composition expectations. Finally, we infer that the statistical precision in $\Lambda_\mu$ required to distinguish between hadronic interaction models can be achieved in current extensive air shower detectors, given their resolution and exposure.