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 ${\nu }_{\mu }({\bar{\nu }}_{\mu })\to {\nu }_e({\bar{\nu }}_e)$ appearance samples, rather than the ${\nu }_{\mu }({\bar{\nu }}_{\mu })\to {\nu }_{\mu }({\bar{\nu }}_{\mu })$ 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.