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

TL;DR

Addressing the long-standing muon-production discrepancy in extensive air showers, the paper compiles muon-density measurements from eight experiments across PeV–EeV energies and reinterprets them on a common z-scale. After cross-calibrating energy scales, electromagnetic shower data largely agree with post-LHC hadronic models up to ~10^16 eV, while muon densities reveal an energy-dependent deficit in simulations, increasing with energy and significant for EPOS-LHC and QGSJet-II.04 (8σ). The approach highlights the importance of cross-calibration for inter-experiment comparisons and suggests that current hadronic-interaction models inadequately describe high-energy muon production. The work provides a framework for diagnosing model deficiencies and guiding future hadronic-interaction refinements.

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.

Figures (10)

• Figure 1: Mass composition of cosmic rays quantified by $\langle \ln\!A \rangle$ as a function of cosmic-ray energy $E$. Model predictions (markers and lines) are compared to data bands, all taken from the review by Kampert and Unger Kampert:2012mx. Vertical arrows at the sides indicate the instrumental error achieved by leading experiments at low and high energies. The figure is discussed in the text.
• Figure 2: Air shower experiments have measured the muon density at ground under various conditions, which are shown here. Points and lines indicate a measurement in a narrow bin of the parameter, while boxes indicate integration over a parameter range. Left: Zenith angle of air showers versus shower energy. Middle: Lateral distance of the muon density measurement versus shower energy. Right: Energy threshold for the muons that are counted in the experiment. Some experiments measure muons below a shielding, which increases the muon energy threshold.
• Figure 3: Relative cross-calibration of the energy scales of the Pierre Auger Observatory and Telescope Array by matching flux measurements, as presented by the Spectrum Working Group. Shown are the adjusted fluxes.
• Figure 4: Global spline fit (GSF) of cosmic-ray data (lines) and energy-scale adjusted data (points) Dembinski:2017zsh. The GSF treats energy-scale offsets as soft-constrained free parameters and produces energy-scale adjustment factors as a fit result.
• Figure 5: All-particle flux from GSF Dembinski:2017zsh and NEVOD-DECOR Bogdanov:2018sfw models, and a preliminary update of the Yakutsk spectrum (see Pravdin et al. for the last publication Pravdin:2009xah), which was adjusted by an energy-scale factor 1.15 to match the GSF.