On the muon scale of air showers and its application to the AGASA data

TL;DR

This paper investigates the muon content in air showers, comparing experimental data from AGASA with simulations, revealing a persistent muon deficit in models at the highest energies.

Contribution

It introduces and analyzes two estimators for muon content, applying them to AGASA data to quantify the muon deficit in air shower simulations.

Findings

AGASA data shows a muon deficit compared to simulations.

The estimators effectively quantify muon content and its fluctuations.

Results support the existence of a muon deficit at ultra-high energies.

Abstract

Recently, several experiments reported a muon deficit in air shower simulations with respect to the data. This problem can be studied using an estimator that quantifies the relative muon content of the data with respect to those of proton and iron Monte Carlo air shower simulations. We analyze two estimators. The first one, based on the logarithm of the mean of the muon content, is built from experimental considerations. It is ideal for comparing results from different experiments as it is independent of the detector resolution. The second estimator is based on the mean of the logarithm of the muon content, which implies that it depends on shower-to-shower fluctuations. It is linked to the mean-logarithmic mass $\left \langle \ln A \right \rangle$ through the Heitler-Matthews model. We study the properties of the estimators and their biases considering the knowns and unknowns of typical experiments. Furthermore, we study these effects in measurements of the muon density at $1000\,$m from the shower axis obtained by the Akeno Giant Air Shower Array (AGASA). Finally, we report the estimates of the relative muon content of the AGASA data, which support a muon deficit in simulations. These estimates constitute valuable additional information of the muon content of air showers at the highest energies.