We report on measurements of neutrino oscillation using data from the T2K long-baseline neutrino experiment collected between 2010 and 2013. In an analysis of muon neutrino disappearance alone, we find the following estimates and 68% confidence intervals for the two possible mass hierarchies: $\text{normal hierarchy}:{\sin }^2{\theta }_{23}=0.514_{-0.056}^{+0.055}$ and $\mathrm{\Delta }{m}_{32}^2=(2.51\pm 0.10)\times 10^{-3}{\mathrm{eV}}^2/c^4$ and $\text{inverted hierarchy}:{\sin }^2{\theta }_{23}=0.511\pm 0.055$ and $\mathrm{\Delta }{m}_{13}^2=(2.48\pm 0.10)\times 10^{-3}{\mathrm{eV}}^2/c^4$. The analysis accounts for multinucleon mechanisms in neutrino interactions which were found to introduce negligible bias. We describe our first analyses that combine measurements of muon neutrino disappearance and electron neutrino appearance to estimate four oscillation parameters, $|\mathrm{\Delta }{m}^2|$, ${\sin }^2{\theta }_{23}$, ${\sin }^2{\theta }_{13}$, ${\delta }_{CP}$, and the mass hierarchy. Frequentist and Bayesian intervals are presented for combinations of these parameters, with and without including recent reactor measurements. At 90% confidence level and including reactor measurements, we exclude the region ${\delta }_{CP}=[0.15,0.83]\pi$ for normal hierarchy and ${\delta }_{CP}=[-0.08,1.09]\pi$ for inverted hierarchy. The T2K and reactor data weakly favor the normal hierarchy with a Bayes factor of 2.2. The most probable values and 68% one-dimensional credible intervals for the other oscillation parameters, when reactor data are included, are ${\sin }^2{\theta }_{23}=0.528_{-0.038}^{+0.055}$ and $|\mathrm{\Delta }{m}_{32}^2|=(2.51\pm 0.11)\times 10^{-3}{\mathrm{eV}}^2/c^4$.

The T2K experiment measures muon neutrino disappearance and electron neutrino appearance in accelerator-produced neutrino and antineutrino beams. With an exposure of $14.7(7.6)\times {10}^{20}$ protons on target in the neutrino (antineutrino) mode, 89 ${\nu }_e$ candidates and seven anti-${\nu }_e$ candidates are observed, while 67.5 and 9.0 are expected for ${\delta }_{CP}=0$ and normal mass ordering. The obtained $2\sigma$ confidence interval for the $CP$-violating phase, ${\delta }_{CP}$, does not include the $CP$-conserving cases (${\delta }_{CP}=0$, $\pi$). The best-fit values of other parameters are ${\sin }^2{\theta }_{23}=0.526_{-0.036}^{+0.032}$ and $\mathrm{\Delta }{m}_{32}^2={2.463}_{-0.070}^{+0.071}\times {10}^{-3}{\mathrm{eV}}^2/c^4$.

T2K reports its first results in the search for $CP$ violation in neutrino oscillations using appearance and disappearance channels for neutrino- and antineutrino-mode beams. The data include all runs from January 2010 to May 2016 and comprise $7.482\times 10^{20}$ protons on target in neutrino mode, which yielded in the far detector 32 $e$-like and $135\mu$-like events, and $7.471\times 10^{20}$ protons on target in antineutrino mode, which yielded 4 $e$-like and $66\mu$-like events. Reactor measurements of ${\sin }^{2}2{\theta }_{13}$ have been used as an additional constraint. The one-dimensional confidence interval at 90% for the phase ${\delta }_{CP}$ spans the range ($-3.13$, $-0.39$) for normal mass ordering. The $CP$ conservation hypothesis (${\delta }_{CP}=0$, $\pi$) is excluded at 90% C.L.

This paper reports on the search for heavy neutrinos with masses in the range $140<M_N<493\mathrm{MeV}/{\mathrm{c}}^2$ using the off-axis near detector ND280 of the T2K experiment. These particles can be produced from kaon decays in the standard neutrino beam and then subsequently decay in ND280. The decay modes under consideration are $N\to {\ell }_{\alpha }^{\pm }{\pi }^{\mp }$ and $N\to {\ell }_{\alpha }^{+}{\ell }_{\beta }^{-}\stackrel{(-)}{\nu }(\alpha ,\beta =e,\mu )$. A search for such events has been made using the Time Projection Chambers of ND280, where the background has been reduced to less than two events in the current dataset in all channels. No excess has been observed in the signal region. A combined Bayesian statistical approach has been applied to extract upper limits on the mixing elements of heavy neutrinos to electron-, muon- and tau- flavored currents ($U_e^2$, $U_{\mu }^2$, $U_{\tau }^2$) as a function of the heavy neutrino mass, e.g., $U_e^2<{10}^{-9}$ at 90% C.L. for a mass of $390\mathrm{MeV}/{\mathrm{c}}^2$. These constraints are competitive with previous experiments.

The T2K experiment reports an updated analysis of neutrino and antineutrino oscillations in appearance and disappearance channels. A sample of electron neutrino candidates at Super-Kamiokande in which a pion decay has been tagged is added to the four single-ring samples used in previous T2K oscillation analyses. Through combined analyses of these five samples, simultaneous measurements of four oscillation parameters, $|\mathrm{\Delta }{m}_{32}^2|$, ${\sin }^2{\theta }_{23}$, ${\sin }^2{\theta }_{13}$, and ${\delta }_{\mathrm{CP}}$ and of the mass ordering are made. A set of studies of simulated data indicates that the sensitivity to the oscillation parameters is not limited by neutrino interaction model uncertainty. Multiple oscillation analyses are performed, and frequentist and Bayesian intervals are presented for combinations of the oscillation parameters with and without the inclusion of reactor constraints on ${\sin }^2{\theta }_{13}$. When combined with reactor measurements, the hypothesis of $CP$ conservation (${\delta }_{\mathrm{CP}}=0$ or $\pi$) is excluded at 90% confidence level. The 90% confidence region for ${\delta }_{\mathrm{CP}}$ is $[-2.95,-0.44]$ ($[-1.47,-1.27]$) for normal (inverted) ordering. The central values and 68% confidence intervals for the other oscillation parameters for normal (inverted) ordering are $\mathrm{\Delta }{m}_{32}^2=2.54\pm 0.08(2.51\pm 0.08)\times {10}^{-3}{\mathrm{eV}}^2/c^4$ and ${\sin }^2{\theta }_{23}=0.55_{-0.09}^{+0.05}$ ($0.55_{-0.08}^{+0.05}$), compatible with maximal mixing. In the Bayesian analysis, the data weakly prefer normal ordering (Bayes factor 3.7) and the upper octant for ${\sin }^2{\theta }_{23}$ (Bayes factor 2.4).

This paper reports measurements of final-state proton multiplicity, muon and proton kinematics, and their correlations in charged-current pionless neutrino interactions, measured by the T2K ND280 near detector in its plastic scintillator (${\mathrm{C}}_8{\mathrm{H}}_8$) target. The data were taken between years 2010 and 2013, corresponding to approximately $6\times {10}^{20}$ protons on target. Thanks to their exploration of the proton kinematics and of imbalances between the proton and muon kinematics, the results offer a novel probe of the nuclear-medium effects most pertinent to the (sub-)GeV neutrino-nucleus interactions that are used in accelerator-based long-baseline neutrino oscillation measurements. These results are compared to many neutrino-nucleus interaction models which all fail to describe at least part of the observed phase space. In case of events without a proton above a detection threshold in the final state, a fully consistent implementation of the local Fermi gas model with multinucleon interactions gives the best description of the data. In the case of at least one proton in the final state, the spectral function model agrees well with the data, most notably when measuring the kinematic imbalance between the muon and the proton in the plane transverse to the incoming neutrino. Within the models considered, only the existence of multinucleon interactions are able to describe the extracted cross section within regions of high transverse kinematic imbalance. The effect of final-state interactions is also discussed.