Hyper-Kamiokande consists of two identical water-Cherenkov detectors of total 520 kt, with the first one in Japan at 295 km from the J-PARC neutrino beam with 2.5|$^\circ$| off-axis angles (OAAs), and the second one possibly in Korea at a later stage. Having the second detector in Korea would benefit almost all areas of neutrino oscillation physics, mainly due to longer baselines. There are several candidate sites in Korea with baselines of 1000–1300 km and OAAs of 1|$^\circ$|–3|$^\circ$|⁠. We conducted sensitivity studies on neutrino oscillation physics for a second detector, either in Japan (JD |$\times$| 2) or Korea (JD + KD), and compared the results with a single detector in Japan. Leptonic charge–parity (CP) symmetry violation sensitivity is improved, especially when the CP is non-maximally violated. The larger matter effect at Korean candidate sites significantly enhances sensitivities to non-standard interactions of neutrinos and mass ordering determination. Current studies indicate the best sensitivity is obtained at Mt. Bisul (1088 km baseline, |$1.3^\circ$| OAA). Thanks to a larger (1000 m) overburden than the first detector site, clear improvements to sensitivities for solar and supernova relic neutrino searches are expected.

The three major unknown neutrino oscillation parameters at the present juncture are the mass hierarchy, the octant of the mixing angle ${\theta }_{23}$ and the $CP$ phase ${\delta }_{CP}$. It is well known that the presence of hierarchy-${\delta }_{CP}$ and octant degeneracies affects the unambiguous determination of these parameters. In this paper, we show that a comprehensive way to study the remaining parameter degeneracies is in the form of a generalized hierarchy-${\theta }_{23}\text{−}{\delta }_{CP}$ degeneracy. This is best depicted as contours in the test (${\theta }_{23}-{\delta }_{CP}$) plane for different representative true values of parameters. We show that the wrong-hierarchy and/or wrong-octant solutions can be further classified into eight different solutions depending on whether they occur with the wrong or right value of ${\delta }_{CP}$. These eight solutions are different from the original eightfold degenerate solutions and can exist, in principle, even if ${\theta }_{13}$ is known. These multiple solutions, apart from affecting the determination of the true hierarchy and octant, also affect the accurate estimation of ${\delta }_{CP}$. We identify which of these eight different degenerate solutions can occur in the test (${\theta }_{23}-{\delta }_{CP}$) parameter space, taking the long-baseline experiment $\mathrm{NO}\nu \mathrm{A}$ running in the neutrino mode as an example. The inclusion of the $\mathrm{NO}\nu \mathrm{A}$ antineutrino run removes the wrong-octant solutions appearing with both right and wrong hierarchy. Adding T2K data to this resolves the wrong hierarchy-right octant solutions to a large extent. The remaining wrong-hierarchy solutions can be removed by combining $\mathrm{NO}\nu \mathrm{A}+\mathrm{T}2\mathrm{K}$ with atmospheric neutrino data. We demonstrate this using ICAL@INO as the prototype atmospheric neutrino detector. We find that the degeneracies can be resolved at the $2\sigma$ level by the combined data set, for the true parameter space considered in the study.

If the flavor-dependent nonstandard interactions (NSIs) in neutrino propagation exist, then the matter effect is modified, and the modification is parametrized by the dimensionless parameter ${\epsilon }_{\alpha \beta }$ ($\alpha$, $\beta =e$, $\mu$, $\tau$). In this paper, we discuss the sensitivity of the T2HKK experiment, the possibility of which is now seriously discussed as a future extension of the T2K experiment, to such NSIs. On the assumption that ${\epsilon }_{\alpha \mu }=0$ ($\alpha =e$, $\mu$, $\tau$) and ${\epsilon }_{\tau \tau }=|{\epsilon }_{e\tau }|/(1+{\epsilon }_{ee})$, which are satisfied by other experiments to a good approximation, we find that, among the possible off-axis flux configurations of 1.3°, 1.5°, 2.0°, and 2.5°, the case of the off-axis angle 1.3° gives the highest sensitivity to ${\epsilon }_{ee}$ and $|{\epsilon }_{e\tau }|$. Our results show that the 1.3° off-axis configuration can exclude NSIs for $|{\epsilon }_{ee}|\gtrsim 1$ or $|{\epsilon }_{e\tau }|\gtrsim 0.2$ at $3\sigma$. We also find that in the presence of NSIs T2HKK (for the off-axis angle 1.3°) has better sensitivity to the two $CP$ phases [${\delta }_{CP}$ and arg(${\epsilon }_{e\tau }$)] than DUNE. This is because of the synergy between the two detectors, i.e., one in Kamioka and one in Korea. T2HKK has better sensitivity to the $CP$ phases than the atmospheric neutrino experiment at Hyper-Kamiokande in inverted hierarchy, but in normal hierarchy, the atmospheric neutrino experiment has the best sensitivity to the $CP$ phases.

The octant of the leptonic mixing angle θ23 and the CP phase δCP are the two major unknowns (apart from neutrino mass hierarchy) in neutrino oscillation physics. It is well known that the precise determination of octant and δCP is interlinked through the octant-δCP degeneracy. In this paper we study the proficiency of the DUNE experiment to determine these parameters scrutinizing, in particular, the role played by the antineutrinos, the broadband nature of the beam and the matter effect. It is well known that for Pμe and Pμ¯e¯ the octant-δCP degeneracy occurs at different values of δCP, combination of neutrino and antineutrino runs help to resolve this. However, in regions where neutrinos do not have octant degeneracy adding antineutrino data is expected to decrease the sensitivity because of the degeneracy and reduced statistics. However we find that in case of DUNE baseline, the antineutrino runs help even in parameter space where the antineutrino probabilities suffer from degeneracies. We explore this point in detail and point out that this happens because of the (i) broad-band nature of the beam so that even if there is degeneracy at a particular energy bin, over the whole spectrum the degeneracy may not be there; (ii) the enhanced matter effect due to the comparatively longer baseline which creates an increased tension between the neutrino and the antineutrino probabilities which raises the overall χ2 in case of combined runs. This feature is more prominent for IH since the antineutrino probabilities in this case are much higher than the neutrino probabilities due to matter effects. The main role of antineutrinos in enhancing CP sensitivity is their ability to remove the octant-δCP degeneracy. However even if one assumes octant to be known the addition of antineutrinos can give enhanced CP sensitivity in some parameter regions due to the tension between the neutrino and antineutrino χ2s

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 $ 5 \sigma$ (8 $\sigma$) C.L. for any value of true $\delta_{CP}$. With T2HK+HK+DUNE the significance of the mass hierarchy increases to almost 15 $\sigma$ for the unfavorable value of $\delta_{CP}$. For these combined setup, octant can be resolved except $43.5^\circ < \theta_{23} < 48^\circ$ at $5\sigma$ C.L for both the hierarchies irrespective of the value of $\delta_{CP}$. The significance of CP violation is around 10 $\sigma$ C.L. for $\delta_{CP} \sim \pm 90^\circ$. Apart from that these combined facility has the capability to discover CP violation for at least $68\%$ fraction of the true $\delta_{CP}$ values at $5 \sigma$ for any value of true $\theta_{23}$. We also find that, with combination of all these three, the precision of $\Delta m^2_{{\rm eff}}$, $\sin^2\theta_{23}$ and $\delta_{CP}$ becomes 0.3%, 2% and 20% respectively. We also clarify how the octant degeneracy occurs in the HK atmospheric neutrino experiment.Comment: 28 pages, 11 figures, 2 tables, Version accepted for publication in Nucl. Phys.