Disentangling data contributions to the precision measurement of the largest leptonic mixing angle

Abstract

This study examines the precise measurement of the largest leptonic mixing angle $\theta_{23}$ through the analysis of neutrino oscillation data samples. Our findings indicate that, contrary to common understanding, the ${\nu}_{\mu}(\bar{\nu}_{\mu})\rightarrow {\nu}_{e}(\bar{\nu}_{e})$ appearance samples, rather than the ${\nu}_{\mu}(\bar{\nu}_{\mu})\rightarrow \nu_{\mu}(\bar{\nu}_{\mu})$ disappearance samples, are sensitive to test the hypothesis of maximal mixing $\theta_{23}=\pi/4$, particularly if $\theta_{23}$ resides in the higher octant and $\sin^2\theta_{23}<0.54$. The former serves as the primary source for determining the octant of the $\theta_{23}$ mixing angle; however, the latter remains relevant if $\theta_{23}$ is indeed in the lower octant with $\sin^2\theta_{23}<0.42$. In a joint T2HK and DUNE analysis, utilizing only appearance sub-samples can exclude the maximal-mixing and determine the actual octant for about 60\% of the currently allowed range of the $\theta_{23}$ angle. We argue that, despite the presence of parameter degeneracy, the precise measurement of $\theta_{23}$ exhibits minimal dependence on other unknown factors, including the CP-violation phase and neutrino mass ordering.