T2K measurements of muon neutrino and antineutrino disappearance using $3.13\times 10^{21}$ protons on target

We report measurements by the T2K experiment of the parameters $\theta_23$ and $\Delta m^2_{32}$ which govern the disappearance of muon neutrinos and antineutrinos in the three-flavor PMNSneutrino oscillation model at T2K's neutrino energy and propagation distance. Utilizing the ability of the experiment to run with either a mainly neutrino or a mainly antineutrino beam, muon-like events from each beam mode are used to measure these parameters separately for neutrino and antineutrino oscillations. Data taken from $1.49\times 10^{21}$ protons on target (POT) in neutrino mode and $1.64\times 10^21$ POT in antineutrino mode are used. Assuming the normal neutrino mass ordering the best-fit values obtained by T2K were $\sin^2\theta_{23}=0.51^{+0.06}_{-0.07}$ $(0.43^{+0.21}_{-0.05})$ and $\Delta m^2_{32}=2.47^{+0.08}_{-0.09} (2.50^{+0.18}_{-0.13})$ $eV^2/c^4$. for neutrinos (antineutrinos). No significant differences between the values of the parameters describing the disappearance of muon neutrinos and antineutrinos were observed. An analysis using an effective two-flavour neutrino oscillation model where the sine of the mixing angle is allowed to take non-physical values larger than 1 is also performed to check the consistency of our data with the three-flavor model. Our data were found to be consistent with a physical value for the mixing angle.