Deep-learning based measurement of the mass composition of ultra-high energy cosmic rays using the surface detector of the Pierre Auger Observatory

Ultra-high energy cosmic rays (UHECRs) are the most energetic particles found in nature. The search for their origin and the determination of their mass composition is still one of the biggest challenges of astroparticle physics. When penetrating the Earth’s atmosphere, UHECRs induce extensive air showers, which experiments like the Pierre Auger Observatory can measure. The atmospheric depth of the maximum of such showers, $X_{\mathrm{max}}$, contains valuable information about the mass of the UHECR and can be observed using Fluorescence Detectors (FDs), which feature a limited duty cycle of roughly $15\%$. In contrast, the Surface Detector (SD) of the Pierre Auger Observatory features a duty cycle of roughly $100\%$, but can not directly observe the shower maximum like the FD, making the reconstruction a challenging task. In this thesis, a measurement of the UHECR composition using the SD was performed. For that, an algorithm for the reconstruction of $X_{\mathrm{max}}$ using the time-dependent signals measured by the SD was developed. The algorithm relies on deep learning, the state-of-the-art machine learning approach using deep neural networks and associated techniques. The performance of the developed algorithm was extensively studied on simulations, including various hadronic interaction models. Additionally, the reconstruction of the method was verified and calibrated using Auger hybrid data. Subsequently, the energy evolution of $\langle X_{\mathrm{max}} \rangle$ was measured from $3~\mathrm{EeV}$ to beyond $100~\mathrm{EeV}$. The measurement is in excellent agreement with the results obtained using the SD-based delta method and composition analyses performed using the FD. The findings indicate a constant transition from a lighter to a heavier composition with an elongation rate of $D_{10}=25.8\pm 1.2~\mathrm{g/cm^{2}/decade}$. For the first time, the energy evolution of $\sigma(X_{\mathrm{max}})$, which is sensitive to the composition mix, was determined from $3~\mathrm{EeV}$ to beyond $100~\mathrm{EeV}$. In the common energy range at lower energies, the results of the new method are in remarkable agreement with the FD. At higher energies, the obtained results indicate an increasingly heavy and pure composition. This suggests that the observed cutoff in the energy spectrum is caused by the fact that the cosmic-ray accelerators reach their maximum energy