Octant of ${\theta }_{23}$ in danger with a light sterile neutrino

Present global fits of world neutrino data hint towards non-maximal ${\theta }_{23}$ with two nearly degenerate solutions, one in the lower octant (${\theta }_{23}<\pi \mathrm{/}4$), and the other in the higher octant ($\theta_{23}

\pi/4$)\mathrm{.}Thisoctantambiguityof$\theta_{23}$ is one of the fundamental issues in the neutrino sector, and its resolution is a crucial goal of next-generation long-baseline (LBL) experiments. In this letter, we address for the first time, the impact of a light eV-scale sterile neutrino towards such a measurement, taking the Deep Underground Neutrino Experiment (DUNE) as a case study. In the so-called 3+1 scheme involving three active and one sterile neutrino, the ${\nu }_{\mu }\to {\nu }_e$ transition probability probed in the LBL experiments acquires a new interference term via active-sterile oscillations. We find that this novel interference term can mimic a swap of the ${\theta }_{23}$ octant, even if one uses the information from both neutrino and antineutrino channels. As a consequence, the sensitivity to the octant of ${\theta }_{23}$ can be completely lost and this may have serious implications in our understanding of neutrinos from both the experimental and theoretical perspectives.