Electron neutrino and antineutrino appearance in the full MINOS data sample

We report on $\nu_e$ and $\bar{\nu}_e$ appearance in $\nu_\mu$ and $\bar{\nu}_\mu$ beams using the full MINOS data sample. The comparison of these $\nu_e$ and $\bar{\nu}_e$ appearance data at a 735 km baseline with $\theta_{13}$ measurements by reactor experiments probes $\delta$, the $\theta_{23}$ octant degeneracy, and the mass hierarchy. This analysis is the first use of this technique and includes the first accelerator long-baseline search for $\bar{\nu}_\mu\rightarrow\bar{\nu}_e$. Our data disfavor 31% (5%) of the three-parameter space defined by $\delta$, the octant of the $\theta_{23}$, and the mass hierarchy at the 68% (90%) C.L. We measure a value of 2sin$^2(2\theta_{13})$sin$^2(\theta_{23})$ that is consistent with reactor experiments.