Testing Model Predictions of Depth of Air-Shower Maximum and Signals in Surface Detectors using Hybrid Data of the Pierre Auger Observatory

We present a method for testing the predictions of hadronic interaction models and improving their consistency with observed two-dimensional distributions depth shower maximum, $X_\text{max}$, signal at ground level as function zenith angle. The relies on assumption that mass composition is same all angles, while atmospheric development attenuation depend in correlated way. In work, each three leading LHC-tuned models, we allow global shift $\Delta X_\text{max}$ predicted which every energy, rescaling $R_\text{Had}$ component constant apply analysis to 2297 events reconstructed both fluorescence surface detectors Pierre Auger Observatory energies $10^{18.5-19.0}$ eV angles below 60$^\circ$. Given modeling assumptions made this analysis, best fit reaches its optimum value when shifting $X_\text{max}$ deeper values increasing signal. This change scale alleviates previously identified model deficit (commonly called muon puzzle) but does not fully remove it. Because size adjustments large number sample, statistical significance need these large, greater than 5$\sigma_\text{stat}$, even combination systematic experimental shifts within 1$\sigma_\text{sys}$ are most favorable models.