Measuring the deviation of the 2–3 lepton mixing from maximal with atmospheric neutrinos

The measurement of the deviation of the 2–3 leptonic mixing from maximal, $D_{23}\equiv 1/2-{sin}^2{\theta }_{23}$, is one of the key issues for understanding the origin of the neutrino masses and mixing. In the $3\nu$ context we study the dependence of various observables in the atmospheric neutrinos on $D_{23}$. We perform the global $3\nu$-analysis of the atmospheric and reactor neutrino data taking into account the effects of both the oscillations driven by the solar parameters ($\Delta m_{21}^2$ and ${\theta }_{12}$) and the 1–3 mixing. The departure from the one-dominant mass scale approximation results into the shift of the 2–3 mixing from maximal by $\Delta {sin}^2{\theta }_{23}\approx 0.04$, so that $D_{23}\sim 0.04\pm 0.07$ $(1\sigma )$. Though the value of the shift is not statistically significant, the tendency of the allowed region to move towards smaller values of ${sin}^2{\theta }_{23}$ is robust. The shift is induced by the excess of the $e$-like events in the sub-GeV sample. We show that future large scale water Cherenkov detectors can determine $D_{23}$ with accuracy of a few percent, comparable with the sensitivity of future long-baseline experiments. Moreover, the atmospheric neutrinos will provide unique information on the sign of the deviation (octant of ${\theta }_{23}$).