We test the predictions of hadronic interaction models regarding the depth of maximum of air-shower profiles, $X_{\max }$, and ground-particle signals in water-Cherenkov detectors at 1000 m from the shower core, $S(1000)$, using the data from the fluorescence and surface detectors of the Pierre Auger Observatory. The test consists of fitting the measured two-dimensional ($S(1000)$, $X_{\max }$) distributions using templates for simulated air showers produced with hadronic interaction models epos-lhc, qgsjet-ii-04, sibyll 2.3d and leaving the scales of predicted $X_{\max }$ and the signals from hadronic component at ground as free-fit parameters. The method relies on the assumption that the mass composition remains the same at all zenith angles, while the longitudinal shower development and attenuation of ground signal depend on the mass composition in a correlated way. The analysis was applied to 2239 events detected by both the fluorescence and surface detectors of the Pierre Auger Observatory with energies between ${10}^{18.5}\mathrm{eV}$ to ${10}^{19.0}\mathrm{eV}$ and zenith angles below 60°. We found, that within the assumptions of the method, the best description of the data is achieved if the predictions of the hadronic interaction models are shifted to deeper $X_{\max }$ values and larger hadronic signals at all zenith angles. Given the magnitude of the shifts and the data sample size, the statistical significance of the improvement of data description using the modifications considered in the paper is larger than $5\mathrm{<ruby><rb>\sigma </rb><rt>しぐま</rt></ruby>}$ even for any linear combination of experimental systematic uncertainties.

• Received 22 December 2023
• Accepted 15 February 2024

DOI:https://doi.org/10.1103/PhysRevD.109.102001

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Published by the American Physical Society