Charge-separated atmospheric neutrino-induced muons in the MINOS far detector

We found 140 neutrino-induced muons in 854.24 live days in the MINOS far detector, which has an acceptance for neutrino-induced muons of $6.91\times {10}^6{\mathrm{cm}}^2\mathrm{sr}$. We looked for evidence of neutrino disappearance in this data set by computing the ratio of the number of low momentum muons to the sum of the number of high momentum and unknown momentum muons for both data and Monte Carlo expectation in the absence of neutrino oscillations. The ratio of data and Monte Carlo ratios, $\mathcal{R}$, is $\mathcal{R}={0.65}_{-0.12}^{+0.15}(\mathrm{stat})\pm 0.09(\mathrm{syst})$, a result that is consistent with an oscillation signal. A fit to the data for the oscillation parameters ${sin}^{2}2{\theta }_{23}$ and $\Delta m_{23}^2$ excludes the null oscillation hypothesis at the 94% confidence level. We separated the muons into ${\mu }^{-}$ and ${\mu }^{+}$ in both the data and Monte Carlo events and found the ratio of the total number of ${\mu }^{-}$ to ${\mu }^{+}$ in both samples. The ratio of those ratios, ${\widehat{\mathcal{R}}}_{CPT}$, is a test of $CPT$ conservation. The result ${\widehat{\mathcal{R}}}_{CPT}={0.72}_{-0.18}^{+0.24}(\mathrm{stat}{)}_{-0.04}^{+0.08}(\mathrm{syst})$ is consistent with $CPT$ conservation.