Master thesis defense by Tetiana Kozynets

Title: Angular distributions of atmospheric leptons via two-dimensional matrix cascade equations

Abstract: Hadronic interactions of cosmic rays in the atmosphere induce rich cascades of daughter particles, including atmospheric neutrinos and muons.

The atmospheric neutrino flux constitutes the main signal for neutrino oscillation measurements in experiments such as IceCube, KM3NeT, and Super-Kamiokande, and an accurate prediction of the flux expected prior to oscillations is crucial. This requires comprehensive modelling of the evolution of hadronic cascades in the atmosphere, which is unfeasible to do analytically. The Monte Carlo simulations, on the other hand, remain computationally expensive and lack flexibility when it comes to the investigation of systematic uncertainties.

These complications are mitigated in the numerical Matrix Cascade Equations (MCEq) code, which solves the system of coupled differential equations for particle production, interaction, and decay at extremely low computational costs. Previously, the MCEq framework included longitudinal-only development of air showers, which is a sufficient approximation for modelling neutrino fluxes at energies of 10 GeV and above. However, the mentioned experiments are expected to be sensitive to neutrino energies of a few GeV and below within the next decade, following the deployment of the IceCube-Upgrade, KM3NeT/ORCA, and Hyper-Kamiokande, respectively. Since the lateral component of hadronic cascades becomes important at these low energies, three-dimensional calculation schemes are required for precision calculations of atmospheric neutrino angular distributions. 

The necessary transition step between the one-dimensional and the three-dimensional treatments is a two-dimensional calculation, which takes into account the angular development of the air showers due to the deflection of the cascade secondaries from the primary cosmic ray axis. In this thesis, we develop a novel numerical technique for the combined longitudinal and angular evolution of the air showers using the MCEq code. By comparing our numerical solutions to those obtained with the standard Monte Carlo code CORSIKA, we show that our tool (dubbed ``2D MCEq'') is fast and accurate. This work is therefore providing a compelling alternative to the Monte Carlo codes and pushing the atmospheric neutrino flux calculations to the frontier of computational performance and precision.