A close look on 2-3 mixing angle with DUNE in light of current neutrino oscillation data

Recent global fit analyses of oscillation data show a preference for normal mass ordering (NMO) at 2.5$\sigma$ and provide 1.6$\sigma$ indications for lower $\theta_{23}$ octant and leptonic CP violation. A high-precision measurement of $\theta_{23}$ is pivotal to convert these hints into discoveries. In this work, we study in detail the capabilities of DUNE to establish the deviation from maximal $\theta_{23}$ and to resolve its octant at high confidence levels. We exhibit the possible correlations and degeneracies among $\sin^2\theta_{23}$, $\Delta m^2_{31}$, and $\delta_{CP}$ in disappearance and appearance oscillation channels at the probability and event levels. Introducing for the first time, a bi-events plot in the plane of total $\nu$ and $\bar\nu$ disappearance events, we discuss the impact of $\sin^2\theta_{23}$ - $\Delta m^2_{31}$ degeneracy in establishing non-maximal $\theta_{23}$ and show how this degeneracy can be resolved by exploiting the spectral shape information in $\nu$ and $\bar\nu$ disappearance events. A 3$\sigma$ (5$\sigma$) determination of non-maximal $\theta_{23}$ is possible in DUNE in total 7 years if $\sin^2\theta_{23} \lesssim 0.465~(0.450)$ or $\sin^2\theta_{23} \gtrsim 0.554~(0.572)$ for any value of $\delta_{CP}$ and NMO. We study the individual contributions from appearance and disappearance channels, impact of systematic uncertainties and marginalization over oscillation parameters, importance of spectral analysis and data from both $\nu$ and $\bar\nu$ runs, while analyzing DUNE's sensitivity to establish non-maximal $\theta_{23}$. DUNE can resolve the octant of $\theta_{23}$ at 4.2$\sigma$ (5$\sigma$) using 7 (10) years of run assuming $\sin^2\theta_{23}$ = 0.455, $\delta_{CP}$ = $223^\circ$, and NMO. DUNE can improve the current relative 1$\sigma$ precision on $\sin^2\theta_{23}$ ($\Delta m^2_{31}$) by a factor of 4.4 (2.8) using 7 years of run.