Analysis of Neutrino Oscillations at Current and Future Accelerator Neutrino Experiments

The T2K and Hyper-Kamiokande experiments are current and future long baseline off-axis neutrino oscillation experiments located in Japan. They monitor a primarily $\overset{(-)}{\nu}_{\mu}$ at two points, one 280 m from the beam source and the other 295 km from the source allowing for the measurement of the flavour content of the neutrino beam over a long distance. The Bayesian results from the T2K experiment using the data set from runs 1--11 are presented in this thesis. In addition this thesis presents future sensitivities studies from the Hyper-Kamiokande experiment and improvements to the Bayesian fitter.

When fitting with only T2K data for run 1--11 the best-fit oscillation parameters are $\sin^2\theta_{23}=0.48_{-0.077}^{+0.014}$, $\Delta m^{2}_{32}=2.51\times10^{-3}$ eV$^{2}$ $[2.44,2.57]\cup[-2.59,-2.51]$, $\sin^2\theta_{13}=0.024_{-0.003}^{+0.006}$, $\delta_{CP}=-1.84_{-0.92}^{+1.15}$. The $95.45\%$ credible interval for $\delta_{CP}$ excludes $[0.25, 2.51]$ and the $90\%$ credible interval excludes $[-0.13,2.89]$.

When fitting with T2K data with the PDG 2020 reactor constraint~\cite{PDG2021} on $\sin^{2}\theta_{13}$ for run 1--11 the best-fit oscillation parameters are $\sin^2\theta_{23}=0.552_{-0.053}^{+0.022}$, $\Delta m^{2}_{32}=2.51\times10^{-3}$ eV$^{2}$ $[2.42,2.58]\cup[-2.56,-2.54]$, $\sin^2\theta_{13}=0.0220\pm0.0007$, $\delta_{CP}=-1.59_{-0.98}^{+0.65}$. The $95.45\%$ credible interval for $\delta_{CP}$ excludes $[-0.25, 3.02]$ and the $90\%$ credible interval excludes $[-3.14,-3.02]\cup[-0.44, 3.14]$.