# Report on Tests and Measurements of Hadronic Interaction Properties with Air Showers

## TL;DR

This paper summarizes recent experimental tests of hadronic interactions via air shower measurements, highlighting a persistent muon deficit in simulations at ultra-high energies and cross-calibrating data from multiple experiments.

## Contribution

It provides a combined analysis of air shower data from eight experiments, revealing a significant muon deficit in simulations at energies above 10 PeV, with implications for hadronic interaction models.

## Key findings

- Muon deficit increases with energy in simulations.
- Significant discrepancy (8 sigma) for EPOS-LHC and QGSJet-II.04 models.
- Data from multiple experiments are unified using the z-scale.

## Abstract

We present a summary of recent tests and measurements of hadronic interaction properties with air showers. This report has a special focus on muon density measurements. Several experiments reported deviations between simulated and recorded muon densities in extensive air showers, while others reported no discrepancies. We combine data from eight leading air shower experiments to cover shower energies from PeV to tens of EeV. Data are combined using the z-scale, a unified reference scale based on simulated air showers. Energy-scales of experiments are cross-calibrated. Above 10 PeV, we find a muon deficit in simulated air showers for each of the six considered hadronic interaction models. The deficit is increasing with shower energy. For the models EPOS-LHC and QGSJet-II.04, the slope is found significant at 8 sigma.