We report on a new analysis of neutrino oscillations in MINOS using the complete set of accelerator and atmospheric data. The analysis combines the $ u_{mu}$ disappearance and $ u_{e}$ appearance data using the three-flavor formalism. We measure $|De
lta m^{2}_{32}|=[2.28-2.46]times10^{-3}mbox{,eV}^{2}$ (68% C.L.) and $sin^{2}theta_{23}=0.35-0.65$ (90% C.L.) in the normal hierarchy, and $|Delta m^{2}_{32}|=[2.32-2.53]times10^{-3}mbox{,eV}^{2}$ (68% C.L.) and $sin^{2}theta_{23}=0.34-0.67$ (90% C.L.) in the inverted hierarchy. The data also constrain $delta_{CP}$, the $theta_{23}$ octant degeneracy and the mass hierarchy; we disfavor 36% (11%) of this three-parameter space at 68% (90%) C.L.
This paper reports measurements of atmospheric neutrino and antineutrino interactions in the MINOS Far Detector, based on 2553 live-days (37.9 kton-years) of data. A total of 2072 candidate events are observed. These are separated into 905 contained-
vertex muons and 466 neutrino-induced rock-muons, both produced by charged-current $ u_{mu}$ and $bar{ u}_{mu}$ interactions, and 701 contained-vertex showers, composed mainly of charged-current $ u_{e}$ and $bar{ u}_{e}$ interactions and neutral-current interactions. The curvature of muon tracks in the magnetic field of the MINOS Far Detector is used to select separate samples of $ u_{mu}$ and $bar{ u}_{mu}$ events. The observed ratio of $bar{ u}_{mu}$ to $ u_{mu}$ events is compared with the Monte Carlo simulation, giving a double ratio of $R^{data}_{bar{ u}/ u}/R^{MC}_{bar{ u}/ u} = 1.03 pm 0.08 (stat.) pm 0.08 (syst.)$. The $ u_{mu}$ and $bar{ u}_{mu}$ data are separated into bins of $L/E$ resolution, based on the reconstructed energy and direction of each event, and a maximum likelihood fit to the observed $L/E$ distributions is used to determine the atmospheric neutrino oscillation parameters. This fit returns 90% confidence limits of $|Delta m^{2}| = (1.9 pm 0.4) times 10^{-3} eV^{2}$ and $sin^{2} 2theta > 0.86$. The fit is extended to incorporate separate $ u_{mu}$ and $bar{ u}_{mu}$ oscillation parameters, returning 90% confidence limits of $|Delta m^{2}|-|Delta bar{m}^{2}| = 0.6^{+2.4}_{-0.8} times 10^{-3} eV^{2}$ on the difference between the squared-mass splittings for neutrinos and antineutrinos.
This paper outlines a method for improving the precision of atmospheric neutrino oscillation measurements. One experimental signature for these oscillations is an observed deficit in the rate of $ u_{mu}$ charged-current interactions with an oscillat
ory dependence on $L_{ u}/E_{ u}$, where $L_{ u}$ is the neutrino propagation distance, and $E_{ u}$ is the neutrino energy. For contained-vertex atmospheric neutrino interactions, the $L_{ u}/E_{ u}$ resolution varies significantly from event to event. The precision of the oscillation measurement can be improved by incorporating information on $L_{ u}/E_{ u}$ resolution into the oscillation analysis. In the analysis presented here, a Bayesian technique is used to estimate the $L_{ u}/E_{ u}$ resolution of observed atmospheric neutrinos on an event-by-event basis. By separating the events into bins of $L_{ u}/E_{ u}$ resolution in the oscillation analysis, a significant improvement in oscillation sensitivity can be achieved.
