Combined Analysis of Neutrino and Antineutrino Oscillations at T2K

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.

Figure 1

The leptonic $CP$ asymmetry, $A_{CP}=[P({\nu }_{\mu }\to {\nu }_e)-P({\overline{\nu }}_{\mu }\to {\overline{\nu }}_e)]/[P({\nu }_{\mu }\to {\nu }_e)+P({\overline{\nu }}_{\mu }\to {\overline{\nu }}_e)]$, as a function of energy for maximal $CP$-violation hypotheses (top) and the ${\nu }_{\mu }$ (${\overline{\nu }}_{\mu }$) and ${\nu }_e+{\overline{\nu }}_e$ components of the unoscillated neutrino flux in neutrino and antineutrino modes (bottom).

Figure 2

The FGD2 data, prefit predictions and postfit predictions binned in $p_{\mu }$ (left) and $\cos {\theta }_{\mu }$ (right) for the neutrino mode $\mathrm{CC}0\pi$ (top), antineutrino mode CC 1-track ${\mu }^{+}$ (middle) and antineutrino mode CC 1-track ${\mu }^{-}$ (bottom) categories. The overflow bins are integrated out to $10000\mathrm{MeV}/c$ for $p_{\mu }$ and $-1.0$ for $\cos {\theta }_{\mu }$ respectively.

Figure 3

The reconstructed lepton momentum and angle relative to the beam at the far detector for the ${\overline{\nu }}_e$ sample signal (left) and background (right) expectation with the data overlaid (blue points).

Figure 4

The reconstructed neutrino energy at the far detector for the ${\nu }_e$ (left) and ${\overline{\nu }}_e$ (right) candidate samples is shown together with the expected distribution without oscillation (blue histogram) and the best fit (red histogram).

Figure 5

The 68% (90%) constant $-2\mathrm{\Delta }\ln L$ confidence regions for the ${\sin }^2{\theta }_{23}-|\mathrm{\Delta }{m}_{32}^2|$ plane assuming normal ordering, alongside $\mathrm{NO}\nu \mathrm{A}$ [43], MINOS+[44], SK [45], and IceCube [46] confidence regions.

Figure 6

The 68% (90%) constant $-2\mathrm{\Delta }\ln L$ confidence regions in the ${\delta }_{CP}-{\sin }^2{\theta }_{13}$ plane are shown by the dashed (continuous) lines, computed independently for the normal (black) and inverted (yellow) mass ordering. The best-fit point is shown by a star for each mass-ordering hypothesis. The 68% confidence region from reactor experiments on ${\sin }^2{\theta }_{13}$ is shown by the yellow vertical band.

Figure 7

$-2\mathrm{\Delta }\ln \mathcal{L}$ as a function of ${\delta }_{CP}$ for the normal (black) and inverted (yellow) mass ordering. The vertical lines show the corresponding allowed 90% confidence intervals, calculated using the Feldman-Cousins method. ${\sin }^2{\theta }_{13}$ is marginalized using the reactor measurement as prior probability.