Adjustments to Model Predictions of Depth of Shower Maximum and Signals at Ground Level using Hybrid Events of the Pierre Auger Observatory

Abstract

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