Measurements of atmospheric neutrinos and antineutrinos in the MINOS far detector

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 ν_μ and ν_μ interactions, and 701 contained-vertex showers, composed mainly of charged-current νₑ and νₑ 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 ν_μ and ν_μ events. The observed ratio of ν_μ to ν_μ events is compared with the Monte Carlo (MC) simulation, giving a double ratio of ${R}_{{{ν}}/{ν}}ᵈᵃᵗᵃ/{R}_{{{ν}}/{ν}}MC=1.03±{}0.08(stat)±{}0.08(syst)$. The ${{ν}}_{{μ}}$ and ${{{ν}}}_{{μ}}$ 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 $|{Δ}{m}²|=(1.9±{}0.4)×{}{10}^{{-}3} {eV}²$ and ${sin}²2{θ}>0.86$. The fit is extended to incorporate separate ${{ν}}_{{μ}}$ and ${{{ν}}}_{{μ}}$ oscillation parameters, returning 90% confidence limits of $|{Δ}{m}²|{-}|{Δ}{m̄}²|={0.6}_{{-}0.8}+2.4×{}{10}^{{-}3} {eV}²$ on the difference between the squared-mass splittings for neutrinos and antineutrinos.