Atmospheric Mass-Squared Splitting at Sub-Percent Precision as a $CPT$ Symmetry Probe

In this paper, we present an improved test of $CPT$ symmetry in the neutrino sector by analyzing the atmospheric mass-squared splittings, $\Delta m^2_{31}$ and $\Delta \overline{m}^2_{31}$, using on-going JUNO and future DUNE and Hyper-Kamiokande experiments. Our study focuses on the discrepancy $\delta_{\nu\overline{\nu}}(\Delta m^2_{31}) = \Delta m^2_{31} - \Delta \overline{m}^2_{31}$, achieving unprecedented precision by exploiting the high statistics and reduced systematic uncertainties of these facilities. The combined analysis yields a sensitivity to $CPT$ violation at the level of $2\times 10^{-5}~\text{eV}^2$ at $3\sigma$ confidence level, representing a $60\%$ improvement over the joint T2K-NO$\nu$A-JUNO analysis. These results highlight the crucial role of multi-experiment synergies in testing fundamental symmetries of nature.