Cosmic ray studies with the KM3NeT neutrino telescope

The origin, propagation, and interaction of high-energy Cosmic Rays (CRs) with the atmosphere are not yet fully understood. In particular, we lack precise measurements of the CR hadronic interactions in the very forward region. This work focuses on the investigation of the CR secondary particle properties via the study of high-energy atmospheric muons. Muon detection is performed underwater with the KM3NeT neutrino telescopes. In this work, the simulation of atmospheric muons for the KM3NeT experiment was performed. This simulation was compared with KM3NeT data from the partially deployed detectors already taking data underwater. The simulation included the most recent models available: Sibyll 2.3d for the high-energy hadronic interaction and GSF for CR flux. During my PhD, I contributed to the development of atmospheric muon simulation software for the Cherenkov neutrino telescopes. In particular, I developed an alternative code for the muon propagation in water that allowed to cross-check the standard KM3NeT software and resolve the issues it was affected by. I developed a framework to tune the parameters of the fast muon generator MUPAGE on the CORSIKA full MC simulations that includes the recent models mentioned above. The framework results demonstrated that the tuned MUPAGE represents the CORSIKA results and can be used as a fast alternative to the full MC simulations. The fast generation allows the simulation of muons with the same statistics as in the real data. This goal is not achievable with the full simulations and the CPU resources available. Then, I performed studies on systematic uncertainties. The uncertainties include that on CR flux and its composition, high-energy hadronic interaction model, light attenuation length in seawater, and detector response simulation. Finally, I compared the KM3NeT data with the MC simulations including all systematic uncertainties mentioned above. The comparison revealed the discrepancy between the real data and the MC predictions for the underwater muon flux. There are ∼40% more muons in the data with respect to MC. Hence, the mismatch is of the same order as for the GeV muons at sea level (the muon puzzle). Muons detected with KM3NeT originate from the very first interactions of CRs in the atmosphere, while GeV muons at sea level are mostly originate in the lower parts of the atmosphere after several steps of the EAS cascade development. Thus, the measurement performed in this work provides new insights and the test-bench for possible solutions to the muon puzzle. The KM3NeT detectors are rapidly growing. The detector performance for the atmospheric muon detection grows both in terms of statistics, but also, what is more important for this study, it improves in the quality of the muon track reconstruction. More energy is absorbed in the detector volume and more light is emitted, which allows better direction and energy reconstruction. The framework developed during my thesis is provided to the Collaboration as the internally available code with all necessary documentation. This allows this work to be continued in the near future by the collaborators in order to extend the analysis for the larger and better KM3NeT detectors. The main KM3NeT goals are related to the neutrinos detection and, in this aspect, the atmospheric muons are only background. Its precise knowledge improves, however, the systematics of the main physics analysis. Also atmospheric muons are the most copious events and, thus, they provide a facility for the reconstruction code tests and the detector response studies. Therefore, better knowledge about true flux of these events allows to tune the other detector properties.