Probing hadronic interaction models with the hybrid data of the Pierre Auger Observatory

Presently large systematic uncertainties remain in the description of hadronic interactions at ultra-high energies and a fully consistent description of air-shower experimental data is yet to be reached. The amount of data collected by the Pierre Auger Observatory using simultaneously the fluorescence and surface detectors in the energy range $10^{18.5}-10^{19.0}$ eV has provided opportunity to perform a multi-parameter test of model predictions. We apply a global method to simultaneously fit the mass composition of cosmic rays and adjustments to the simulated depth of shower maximum ($X_\text{max}$), and hadronic signals at ground level ($R_\text{Had}$). The best description of hybrid data is obtained for a deeper scale of simulated $X_\text{max}$ than predicted by hadronic interaction models tuned to the LHC data. Consequently, the deficit of the simulated hadronic signal at ground level, dominated by muons, is alleviated with respect to the unmodified hadronic interaction models. Because of the size of the adjustments $\Delta X_\text{max}$ and $R_\text{Had}$ and the large number of events in the sample, the statistical significance of these assumed adjustments is large, greater than 5$\sigma_\text{stat}$, even for the combination of the systematic experimental shifts within 1$\sigma_\text{sys}$ that are the most favorable for the models.