Search for $CP$ Violation in Neutrino and Antineutrino Oscillations by the T2K Experiment with $2.2\times {10}^{21}$ Protons on Target

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 $\mathrm{\Delta }{m}_{32}^2={2.463}_{-0.070}^{+0.071}\times {10}^{-3}{\mathrm{eV}}^2/c^4$.

Figure 1

FGD2 data and model predictions prior to and after the ND280 data fit, binned in $p_{\mu }$ for the $\nu$ beam mode $\mathrm{CC}0\pi$ sample. The prediction after the ND280 data fit is separated by type of interaction.

Figure 2

Reconstructed neutrino energy distributions at the far detector for the ${\nu }_{\mu }$ CCQE (left) and ${\overline{\nu }}_{\mu }$ CCQE (right) -enriched samples with the total predicted event rate shown in red. Ratios to the predictions under the no oscillation hypothesis are shown in the bottom figures.

Figure 3

Reconstructed neutrino energy distributions at the far detector for the ${\nu }_e$ CCQE (top left), ${\nu }_e$ $\mathrm{CC}1{\pi }^{+}$ (bottom left), and ${\overline{\nu }}_e$ CCQE (bottom right) -enriched samples. Predictions under the no oscillation hypothesis are shown in blue and best-fit spectra in red.

Figure 4

The 68% (90%) constant $-2\mathrm{\Delta }\ln \mathcal{L}$ confidence regions in the $|\mathrm{\Delta }{m}^2|-{\sin }^2{\theta }_{23}$ plane for normal (black lines) and inverted (red lines) ordering using the reactor measurement prior on ${\sin }^2(2{\theta }_{13})$.

Figure 5

The 68% (90%) constant $-2\mathrm{\Delta }\ln \mathcal{L}$ confidence regions in the ${\sin }^2{\theta }_{13}-{\delta }_{CP}$ plane using a flat prior on ${\sin }^2(2{\theta }_{13})$, assuming normal (black lines) and inverted (red lines) mass ordering. The 68% confidence region from reactor experiments on ${\sin }^2{\theta }_{13}$ is shown by the yellow vertical band.

Figure 6

$1\mathrm{D}-2\mathrm{\Delta }\ln \mathcal{L}$ as a function of ${\delta }_{CP}$ for normal (black) and inverted (red) mass ordering using the reactor measurement prior on ${\sin }^2(2{\theta }_{13})$. The vertical lines show the corresponding allowed $2\sigma$ confidence intervals, calculated using the Feldman-Cousins method instead of the constant $-2\mathrm{\Delta }\ln \mathcal{L}$ method.