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 ${\bar{\nu }}_{\mu }\to {\bar{\nu }}_e$. 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.