On Precision of the Leptonic Mixing Angle ${\theta }_{23}$ and its Implications for the Flavor Models

Among three leptonic mixing angles, ${\theta }_{23}$ angle, which characterizes the fractional contribution of two flavor eigenstates ${\nu }_{\mu }$ and ${\nu }_{\tau }$ to the third mass eigenstate ${\nu }_3$, is known to be the largest but the least precisely measured. The work investigates possible reach of ${\theta }_{23}$ precision with two upcoming gigantic accelerator-based long-baseline neutrino experiments, namely Hyper-Kamiokande and DUNE experiments as well as a possible joint analyses of future neutrino facilities. Our simulation yields that each experiment will definitely establish the octant of ${\theta }_{23}$ angle for all values within 1$\sigma$ parameter interval, while considering the current limitation. However, if the actual value is $0.48\le {\sin }^2{\theta }_{23}\le 0.54$, it becomes challenging for these two experiments to reject the maximal (${\theta }_{23}=\pi \mathrm{/}4$) hypothesis and conclude its octant. This octant-blind region can be further explored with the proposed facilities ESSnuSB and a neutrino factory. Accurate determination of the mixing angle ${\theta }_{23}$, as well as the accuracy of ${\delta }_{CP}$, is crucial for examining a certain category of discrete non-Abelian leptonic flavor models. Specifically if CP is conserved in leptonic sector, the combined analysis of Hyper-K and DUNE will rule out the majority of these models. However, if the CP is maximally violated, higher precision of ${\delta }_{CP}$ is necessary for testing these flavor models.