It has been pointed out that the mixing of an eV-scale sterile neutrino with active flavors can lead to a loss of sensitivity to the ${\theta }_{23}$ octant (sign of ${\sin }^2{\theta }_{23}-1/2$) in long baseline experiments, because the main oscillation probability $P_0=4{\sin }^2{\theta }_{23}{\sin }^2{\theta }_{13}{\sin }^2{\mathrm{\Delta }}_{31}$ can be degenerate with the sum of the interferences with the solar oscillation amplitude and an active-sterile oscillation amplitude in both neutrino and antineutrino oscillations, depending on the $CP$ phases. In this paper, we show that the above degeneracy is resolved by measuring the same beam at different baseline lengths. We demonstrate that the Tokai-to-Hyper-Kamiokande-to-Korea (T2HKK) experiment (one 187 kton fiducial volume water Cerenkov detector is placed at Kamioka, $L=295\mathrm{km}$, and another detector is put in Korea, $L\sim 1000\mathrm{km}$) exhibits a better sensitivity to the ${\theta }_{23}$ octant in those parameter regions where the experiment with the two detectors at Kamioka is insensitive to it. Therefore, if a hint of sterile-active mixings is discovered in short baseline experiments, T2HKK is a better option than the plan of placing two detectors at Kamioka. We also consider an alternative case where one detector is placed at Kamioka and a different detector is at Oki Islands, $L=653\mathrm{km}$, and show that this configuration also leads to a better sensitivity to the ${\theta }_{23}$ octant.

• Received 14 May 2019
• Accepted 27 March 2020

DOI:https://doi.org/10.1103/PhysRevD.101.075034

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Published by the American Physical Society