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We revisit the sensitivity study of the Tokai-to-Kamioka-and-Korea (T2KK) andTokai-to-Kamioka-and-Oki (T2KO) proposals where a water Cerenkov detector withthe 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 fordetermination 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 improvingtreatment 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 $10^{21}$POTwith the proton energy of 40 GeV), the mass hierarchy determination with themedian sensitivity of 3 - 5 $\sigma$ by the T2KK and 1 - 4 $\sigma$ by the T2KOexperiment are expected when $\sin^2\theta_{23} = 0.5$, depending on the masshierarchy pattern and CP phase. These sensitivities are enhanced (reduced) by$30\%$ - $40\%$ in $\Delta \chi^2$ when $\sin^2\theta_{23} = 0.6\, (0.4)$. TheCP phase is measured with the uncertainty of $20^\circ$ - $50^\circ$ by theT2KK and T2KO using the $\nu_\mu$ - $\bar{\nu}_\mu$ focusing beam ratio between3.5 : 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 T2KOexperiments to both the mass hierarchy determination and leptonic CP phasemeasurement simultaneously with the preferred beam ratio being between 3 : 2 -2.5 : 2.5 ($\times 10^{21}$POT).

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