Measurements of neutrino oscillation parameters from the T2K experiment using $3.6\times10^{21}$ protons on target

The T2K experiment presents new measurements of neutrino oscillation parameters using $19.7(16.3)\times 10^{20}$ protons on target (POT) in (anti-)neutrino mode at the far detector (FD). Compared to the previous analysis, an additional $4.7\times 10^{20}$ POT neutrino data was collected at the FD. Significant improvements were made to the analysis methodology, with the near-detector analysis introducing new selections and using more than double the data. Additionally, this is the first T2K oscillation analysis to use NA61/SHINE data on a replica of the T2K target to tune the neutrino flux model, and the neutrino interaction model was improved to include new nuclear effects and calculations. Frequentist and Bayesian analyses are presented, including results on $\sin ^2\theta _{13}$ and the impact of priors on the $\delta _{\textrm{CP}}$ measurement. Both analyses prefer the normal mass ordering and upper octant of $\sin ^2\theta _{23}$ with a nearly maximally CP-violating phase. Assuming the normal ordering and using the constraint on $\sin ^2\theta _{13}$ from reactors, $\sin ^2\theta _{23}=0.561^{+0.021}_{-0.032}$ using Feldman–Cousins corrected intervals, and $\varDelta {}m^2_{32}=2.494_{-0.058}^{+0.041}\times 10^{-3}~\text {eV}^2$ using constant $\varDelta \chi ^{2}$ intervals. The CP-violating phase is constrained to $\delta _{\textrm{CP}}=-1.97_{-0.70}^{+0.97}$ using Feldman–Cousins corrected intervals, and $\delta _{\textrm{CP}}=0,\pi $ is excluded at more than 90% confidence level. A Jarlskog invariant of zero is excluded at more than $2\sigma $ credible level using a flat prior in $\delta _{\textrm{CP}},$ and just below $2\sigma $ using a flat prior in $\sin \delta _{\textrm{CP}}.$ When the external constraint on $\sin ^2\theta _{13}$ is removed, $\sin ^2\theta _{13}=28.0^{+2.8}_{-6.5}\times 10^{-3},$ in agreement with measurements from reactor experiments. These results are consistent with previous T2K analyses.