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, $Δm^2_{31}$ and $Δ\overline{m}^2_{31}$, using on-going JUNO and future DUNE and Hyper-Kamiokande experiments. Our study focuses on the discrepancy $δ_{ν\overlineν}(Δm^2_{31}) = Δm^2_{31} - Δ\overline{m}^2_{31}$, 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 $3σ$ confidence level, representing a $60\%$ improvement over the joint T2K-NO$ν$A-JUNO analysis. These results highlight the crucial role of multi-experiment synergies in testing fundamental symmetries of nature.