Precision Constraints for Three-Flavor Neutrino Oscillations from the Full $\mathrm{MINOS}+$ and MINOS Dataset

We report the final measurement of the neutrino oscillation parameters $\mathrm{\Delta }{m}_{32}^2$ and ${\sin }^2{\theta }_{23}$ using all data from the MINOS and $\mathrm{MINOS}+$ experiments. These data were collected using a total exposure of $23.76\times {10}^{20}$ protons on target producing ${\nu }_{\mu }$ and ${\overline{\nu }}_{\mu }$ beams and 60.75 kt yr exposure to atmospheric neutrinos. The measurement of the disappearance of ${\nu }_{\mu }$ and the appearance of ${\nu }_e$ events between the Near and Far detectors yields $|\mathrm{\Delta }{m}_{32}^2|=2.40_{-0.09}^{+0.08}(2.45_{-0.08}^{+0.07})\times {10}^{-3}{\mathrm{eV}}^2$ and ${\sin }^2{\theta }_{23}=0.43_{-0.04}^{+0.20}(0.42_{-0.03}^{+0.07})$ at 68% C.L. for normal (inverted) hierarchy.

Figure 1

The $k$-NN discriminant used in $\mathrm{MINOS}+$ data to separate CC ${\nu }_{\mu }$ and ${\overline{\nu }}_{\mu }$ interactions from the background of NC interactions. The discriminant is shown for data and MC in the ND, where the MC has been corrected using the beam tuning described in the text. The red band is the systematic uncertainty on the MC prediction yielding a ${\chi }^2/\mathrm{d}.\mathrm{o}.\mathrm{f}.$ of (32.85/79) for the data and MC comparison. Interactions in both detectors with the discriminant value above 0.3 are selected by the analysis.

Figure 2

Top: The reconstructed energy spectra for MINOS and $\mathrm{MINOS}+$ events selected within the Far Detector fiducial volume for data (black points) adjusted for bin size, and the best fit MC predictions for MINOS (red hatched histogram), $\mathrm{MINOS}+$ (blue hatched histogram) and the sum (cyan line). The prediction at the FD with no oscillations is shown as the orange line. Bottom: The ratios of the data and the oscillated prediction to the no oscillation prediction for MINOS and $\mathrm{MINOS}+$ combined.

Figure 3

Confidence limits on $\mathrm{\Delta }{m}_{32}^2$ and ${\sin }^2{\theta }_{23}$ in the normal hierarchy for MINOS and $\mathrm{MINOS}+$ shown separately for the beam and atmospheric data. Contours are shown at 90% C.L. and at 68% C.L. Best fit points are shown for the beam data (triangle) and for the atmospheric fit (star).

Figure 4

The top figures show the 1D likelihood profiles as functions of $\mathrm{\Delta }{m}_{32}^2$ and ${\sin }^2{\theta }_{23}$ for each hierarchy. The bottom figure displays 90% confidence limits on $\mathrm{\Delta }{m}_{32}^2$ and ${\sin }^2{\theta }_{23}$ for the normal mass hierarchy, comparing $\mathrm{MINOS}+$, IceCube, $\mathrm{NO}\nu \mathrm{A}$, Super-K, and T2K [5, 7, 8, 11].