Complementarity between Hyperkamiokande and DUNE in determining neutrino oscillation parameters

In this work we investigate the sensitivity to the neutrino mass hierarchy, the octant of the mixing angle ${\theta }_{23}$ and the CP phase ${\delta }_{CP}$ in the future long baseline experiments T2HK and DUNE as well as in the atmospheric neutrino observation at Hyperkamiokande (HK). We show for the first time that the sensitivity is enhanced greatly if we combine these three experiments. Our results show that the hierarchy sensitivity of both T2HK and HK are limited due to the presence of parameter degeneracy. But this degeneracy is removed when T2HK and HK are added together. With T2HK + HK (DUNE), the neutrino mass hierarchy can be determined at least at 5σ (8σ) C.L. for any value of true ${\delta }_{CP}$. With T2HK + HK + DUNE the significance of the mass hierarchy increases to almost 15σ for the unfavorable value of ${\delta }_{CP}$. For this combined setup, octant can be resolved except $43.5°<{\theta }_{23}<48°$ at 5σ C.L. for both the hierarchies irrespective of the value of ${\delta }_{CP}$. The significance of CP violation is around 10σ C.L. for ${\delta }_{CP}\sim \pm 90°$. Apart from that this combined facility has the capability to discover CP violation for at least $68\text{\%}$ fraction of the true ${\delta }_{CP}$ values at 5σ for any value of true ${\theta }_{23}$. We also find that, with combination of all these three, the precision of $\Delta m_{\mathrm{eff}}^2$, ${\sin }^2{\theta }_{23}$ and ${\delta }_{CP}$ becomes 0.3%, 2% and 20% respectively. We also clarify how the octant degeneracy occurs in the HK atmospheric neutrino experiment.