Revisiting T2KK and T2KO physics potential and $\nu_\mu$ - $\bar{\nu}_\mu$ beam ratio

We revisit the sensitivity study of the Tokai-to-Kamioka-and-Korea (T2KK) and Tokai-to-Kamioka-and-Oki (T2KO) proposals where a water Cerenkov detector with the 100 kton fiducial volume is placed in Korea ($L = 1000$ km) and Oki island ($L = 653$ km) in Japan, respectively, in addition to the Super-Kamiokande for determination of the neutrino mass hierarchy and leptonic CP phase ($\delta_{CP}$). We systematically study the running ratio of the $\nu_\mu$ and $\bar{\nu}_\mu$ focusing beams with dedicated background estimation for the $\nu_e$ appearance and $\nu_\mu$ disappearance signals, especially improving treatment of the neutral current $\pi^0$ backgrounds. Using a $\nu_\mu$ - $\bar{\nu}_\mu$ beam ratio between 3 : 2 and 2.5 : 2.5 (in unit of $10^{21}$POT with the proton energy of 40 GeV), the mass hierarchy determination with the median sensitivity of 3 - 5 $\sigma$ by the T2KK and 1 - 4 $\sigma$ by the T2KO experiment are expected when $\sin^2\theta_{23} = 0.5$, depending on the mass hierarchy pattern and CP phase. These sensitivities are enhanced (reduced) by $30\%$ - $40\%$ in $\Delta \chi^2$ when $\sin^2\theta_{23} = 0.6\, (0.4)$. The CP phase is measured with the uncertainty of $20^\circ$ - $50^\circ$ by the T2KK and T2KO using the $\nu_\mu$ - $\bar{\nu}_\mu$ focusing beam ratio between 3.5 : 1.5 and 1.5 : 3.5. These findings indicate that inclusion of the $\bar{\nu}_\mu$ focusing beam improves the sensitivities of the T2KK and T2KO experiments to both the mass hierarchy determination and leptonic CP phase measurement simultaneously with the preferred beam ratio being between 3 : 2 - 2.5 : 2.5 ($\times 10^{21}$POT).