Octant Ambiguity in the Presence of Non-isotropic Lorentz Invariance Violation

Global analyses of neutrino data suggest that the mixing angle $\theta_{23}$ is likely to be nonmaximal with two closely matched solutions emerging: one representing a smaller angle ($\theta_{23}$ < $\pi/4$) and the other a larger angle ($\theta_{23}$ > $\pi/4$). This ambiguity, known as the octant ambiguity of $\theta_{23}$, presents a significant challenge in neutrino research and is a primary objective of future long-baseline experiments. In this study, for the first time, we explore how non-isotropic Lorentz violation affects measurements of mixing angle $\theta_{23}$, with a particular emphasis on sidereal effects in the Deep Underground Neutrino Experiment. Our findings reveal that ability of DUNE to resolve the octant ambiguity is significantly compromised in the presence of the $c^{xy}_{e \tau}$ parameter. Furthermore, we demonstrate that LIV exacerbates the degeneracy between the Dirac CP-phase $\delta_{cp}$ and $\theta_{23}$.