A joint oscillation analysis of atmospheric neutrinos at Super-Kamiokande (SK) and accelerator neutrinos at Tokai-to-Kamioka (T2K) is in preparation. The atmospheric oscillation probability calculation is one of the most time-consuming parts of the fit and demands precision due to direct impact on oscillation parameter constraints. As an alternative to the existing method of pre-computing probabilities for a large number of simulated events, we develop new methods that allow real-time calculation with continuous values of oscillation parameters. Special techniques are introduced to average over fast oscillations at low energies. Furthermore, the density profile along the trajectory can significantly affect the oscillation probabilities of neutrinos crossing the Earth, which allows the study of neutrino mass ordering. We study the impact of the Earth model and improved approximations for the matter effect calculation. These results are not only useful in the analysis of SK atmospheric data, but are directly applicable to current and future experiments measuring atmospheric neutrino oscillations, such as IceCube, Hyper-Kamiokande, and DUNE.
|Collaboration||SK + T2K Collaboration|