Stringent constraint on $CPT$ violation with the synergy of T2K-II, $\mathrm{NO}\nu \mathrm{A}$ extension, and JUNO

Neutrino oscillation experiments have measured precisely at few percent levels the mass-squared differences ($\mathrm{\Delta }{m}_{21}^2$, $\mathrm{\Delta }{m}_{31}^2$) of three neutrino mass eigenstates, and the three leptonic mixing angles (${\theta }_{12}$, ${\theta }_{13}$, ${\theta }_{23}$) by utilizing both neutrino and antineutrino oscillations. The possible $CPT$ violation may manifest itself in the difference of neutrino and antineutrino oscillation parameters, making these experiments promising tools for testing $CPT$ invariance at unprecedented precision. We investigate empirically the sensitivity of the $CPT$ test via the difference in mass-squared splittings ($\mathrm{\Delta }{m}_{31}^2-\mathrm{\Delta }{\overline{m}}_{31}^2$) and in leptonic mixing angles (${\sin }^2{\theta }_{23}-{\sin }^2{\overline{\theta }}_{23}$) with the synergy of T2K-II, $\mathrm{NO}\nu \mathrm{A}$ extension, and JUNO experiments. If the $CPT$ symmetry is found to be conserved, the joint analysis of the three experiments will be able to establish limits of $|\mathrm{\Delta }{m}_{31}^2-\mathrm{\Delta }{\overline{m}}_{31}^2|<5.3\times {10}^{-3}{\mathrm{eV}}^2$ and $|{\sin }^2{\theta }_{23}-{\sin }^2{\overline{\theta }}_{23}|<0.10$ at $3\sigma$ confidence level (CL) on the possible $CPT$ violation, extending substantially the current bound of these parameters. We find that with ($\mathrm{\Delta }{m}_{31}^2-\mathrm{\Delta }{\overline{m}}_{31}^2$), the dependence of the statistical significance on the relevant parameters to exclude the $CPT$ conservation is marginal, and that, if the difference in the best-fit values of $\mathrm{\Delta }{m}_{31}^2$ and $\mathrm{\Delta }{\overline{m}}_{31}^2$ measured by $\mathrm{MINOS}(+)$ and $\mathrm{NO}\nu \mathrm{A}$ persists as the true, the combined analysis will rule out the $CPT$ conservation at $4\sigma$ CL. With the (${\sin }^2{\theta }_{23}-{\sin }^2{\overline{\theta }}_{23}$), the statistical significance to exclude $CPT$ invariance depends strongly on the true value of ${\theta }_{23}({\overline{\theta }}_{23})$ mixing angle. In the case of maximal mixing of ${\theta }_{23}$, as indicated by the current T2K and $\mathrm{NO}\nu \mathrm{A}$ measurements, the $CPT$ conservation will be excluded at $3\sigma$ CL or higher if the difference in the best-fit values of ${\theta }_{23}$ and ${\overline{\theta }}_{23}$ remains as the true.

Figure 1

$CPT$ asymmetries in disappearance channels for T2K baseline $\mathrm{L}=295\mathrm{km}$ (left) and $\mathrm{NO}\nu \mathrm{A}$ baseline $\mathrm{L}=810\mathrm{km}$ (right). The differences in solid lines and dashed lines indicate extrinsic $CPT$ effects caused by matter.

Figure 2

The $3\sigma$ CL regions of $\mathrm{\Delta }{m}_{31}^2$ and $\mathrm{\Delta }{\overline{m}}_{31}^2$ (left), ${\sin }^2{\theta }_{23}$ and ${\sin }^2{\overline{\theta }}_{23}$ (right). The black, red, and blue lines are for an analysis with T2K-II only, a joint of T2K-II and $\mathrm{NO}\nu \mathrm{A}\text{−}\mathrm{II}$, and a joint of T2K-II, $\mathrm{NO}\nu \mathrm{A}\text{−}\mathrm{II}$, and JUNO, respectively.

Figure 3

The bounds on possible $CPT$ violation manifested in the asymmetries of the mass-squared splittings $|{\delta }_{\nu \overline{\nu }}(\mathrm{\Delta }{m}_{31}^2)|$ (left) and of the leptonic mixing angles $|{\delta }_{\nu \overline{\nu }}({\sin }^2{\theta }_{23})|$ (right). The black, red, and blue lines correspond to an analysis with T2K-II only, a joint of T2K-II and $\mathrm{NO}\nu \mathrm{A}\text{−}\mathrm{II}$, and a joint of T2K-II, $\mathrm{NO}\nu \mathrm{A}\text{−}\mathrm{II}$, and JUNO, respectively.

Figure 4

Statistical significance to exclude $CPT$ is computed as a function of true ${\delta }_{\nu \overline{\nu }}(\mathrm{\Delta }{m}_{31}^2)$ under various scenarios of the involved parameters. The left plot is when $\mathrm{\Delta }{m}_{31}^2$ is examined at three different true values, while ${\sin }^2{\theta }_{23}={\sin }^2{\overline{\theta }}_{23}=0.51$ is assumed to be true. The right plot presents the $CPT$ sensitivity of ${\delta }_{\nu \overline{\nu }}(\mathrm{\Delta }{m}_{31}^2)$ at different true values of ${\sin }^2{\theta }_{23}$ and ${\sin }^2{\overline{\theta }}_{23}$ while $\mathrm{\Delta }{m}_{31}^2=2.55\times {10}^{-3}{\mathrm{eV}}^2$ is assumed to be true.

Figure 5

Statistical significance to exclude $CPT$ is computed as function of true ${\delta }_{\nu \overline{\nu }}({\sin }^2{\theta }_{23})$ under various scenarios of the involved parameters. The left is when ${\sin }^2{\theta }_{23}$ is examined at three different true values while $\mathrm{\Delta }{m}_{31}^2=\mathrm{\Delta }{\overline{m}}_{31}^2=2.55\times {10}^{-3}{\mathrm{eV}}^2$ is assumed. The right presents the $CPT$ sensitivity of ${\delta }_{\nu \overline{\nu }}({\sin }^2{\theta }_{23})$ at different true values of $\mathrm{\Delta }{m}_{31}^2$ and $\mathrm{\Delta }{\overline{m}}_{31}^2$ while ${\sin }^2{\theta }_{23}=0.51$ is assumed to be true.

Figure 6

Statistical significance to exclude $CPT$ is computed as a function of true ${\delta }_{\nu \overline{\nu }}({\sin }^2{\theta }_{23})$ under various scenarios of the involved parameters. Both muon (anti)neutrino disappearance samples and electron (anti)neutrino appearance samples from T2K-II and $\mathrm{NO}\nu \mathrm{A}\text{−}\mathrm{II}$ are used. The sensitivity is examined at three different true values of ${\sin }^2{\theta }_{23}$ values while $\mathrm{\Delta }{m}_{31}^2=\mathrm{\Delta }{\overline{m}}_{31}^2=2.55\times {10}^{-3}{\mathrm{eV}}^2$ is assumed to be true.