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

Neutrino oscillation experiments have measured precisely the mass-squared differences of three neutrino mass eigenstates, and three leptonic mixing angles by utilizing both neutrino and anti-neutrino oscillations. The possible CPT violation may manifest itself in the difference of neutrino and anti-neutrino oscillation parameters, making these experiments promising tools for testing CPT invariance. We investigate empirically the sensitivity of the CPT test via the difference in mass-squared splittings ($\Delta m^2_{31} - \Delta \overline{m}^2_{31}$) and in leptonic mixing angles ($\sin^2\theta_{23} - \sin^2\overline{\theta}_{23}$) with the synergy of T2K-II, NO$\nu$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 $|\Delta m^2_{31} - \Delta \overline{m}^2_{31}|$ < $5.3\times 10^{-3} \text{eV}^2$ and $|\sin^2\theta_{23} - \sin^2\overline{\theta}_{23}|$ < $0.10$ at 3$\sigma$ C. L. on the possible CPT violation. We find that with ($\Delta m^2_{31} - \Delta \overline{m}^2_{31}$), 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 $\Delta m^2_{31}$ and $\Delta \overline{m}^2_{31}$ measured by MINOS(+) and NO$\nu$A persists as the true, the combined analysis will rule out the CPT conservation at 4$\sigma$ C. L.. 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 $\theta_{23}(\overline{\theta}_{23})$. In case of maximal mixing of $\theta_{23}$, the CPT conservation will be excluded at 3$\sigma$ C. L. or more if the difference in the best-fit values of $\theta_{23}$ and $\overline{\theta}_{23}$ remains as the true.