Extracting the best physics sensitivity from T2HKK: A study on optimal detector volume

T2HK is an upcoming long-baseline experiment in Japan which will have two water Cherenkov detector tanks of 187 kt volume each at distance of 295 km from the source. An alternative project, T2HKK is also under consideration where one of the water tanks will be moved to Korea at a distance of 1100 km. The flux at 295 km will cover the first oscillation maximum and the flux at 1100 km will mainly cover the second oscillation maximum. As physics sensitivity at the dual baseline rely on variation in statistics, dependence of systematic uncertainty, effect of second oscillation maximum and matter density, 187 kt detector volume at 295 km and 187 kt detector volume at 1100 km may not be the optimal configuration of T2HKK. Therefore, we have tried to optimize the ratio of the detector volume at both the locations by studying the interplay between the above mentioned parameters. For the analysis of neutrino mass hierarchy, octant of $\theta_{23}$ and CP precision, we have considered two values of $\delta_{\rm{CP}}$ as 270$^\circ$ and $0^\circ$ and for CP violation we have considered the value of $\delta_{\rm CP}= 270^\circ$. These values are motivated by the current best-fit values of this parameter as obtained from the experiments T2K and NO$\nu$A. Interestingly we find that if the systematic uncertainty is negligible then the T2HK setup i.e., when both the detector tanks are placed at 295 km gives the best results in terms of hierarchy sensitivity at $\delta_{\rm CP}= 270^\circ$, octant sensitivity, CP violation sensitivity and CP precision sensitivity at $\delta_{\rm CP}= 0^\circ$. For current values of systematic errors, we find that neither T2HK, nor T2HKK setup is giving better results for hierarchy, CP violation and CP precision sensitivity. The optimal detector volume which is of the range between 255 kt to 345 kt at 1100 km gives better results in those above mentioned parameters.