Bridging Experiments, Narrowing Uncertainties: When DUNE Meets Hyper-K to unveil insights into 2–3 Oscillation Sector

A meticulous determination of $\Delta m^2_{31}$ and $\theta_{23}$ is indispensable for accurately evaluating the Earth's matter effect in long-baseline experiments, a key element in resolving the neutrino mass ordering conundrum and in measuring the CP phase in the $3\nu$ paradigm. By reviewing the footprints of previous and ongoing experiments and considering the anticipated sensitivities from the upcoming IceCube Upgrade and KM3NeT/ORCA, we examine the expected advancements in the precision of 2--3 oscillation parameters that the next-generation long-baseline experiments, DUNE and Hyper-K, are set to provide, either independently or in combination. We underscore the significance of the complementarity between these two experiments, which substantially enhances the sensitivity to deviations from maximal mixing in $\theta_{23}$, decisively excludes the wrong-octant solutions for $\theta_{23}$, and enables exceptionally refined measurements of the 2--3 oscillation parameters, surpassing the capabilities of each experiment when considered in isolation. Our analysis shows that, for the current best-fit values of the oscillation parameters and assuming normal mass ordering (NMO), the combination of DUNE and Hyper-K can confirm a non-maximal $\theta_{23}$ and exclude the wrong octant solution with a statistical significance of approximately $7\sigma$ with their nominal exposures. Furthermore, we find that DUNE and Hyper-K together can enhance the existing $1\sigma$ precision on $\sin^2\theta_{23}$ and $\Delta m^2_{31}$ by factors of 7 and 5, respectively, assuming NMO. Given the financial hurdles and the prolonged commitment required for the full 10-year operation of DUNE and Hyper-K, our study highlights that even with less than half of their nominal exposures, the collaboration between DUNE and Hyper-K can still achieve sensitivities in our phenomenological analyses that are on par with those expected from their full exposures individually. Finally, we highlight how the synergistic interplay between DUNE and Hyper-K can offer more stringent constraints on the ($\sin^2\theta_{23},\delta_{\mathrm{CP}}$) plane, outstripping the reach of the standalone experiments.