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.

Figure 1

Distribution of the r.m.s. deviations of the measured hit times from the calculated hit times for calibration tracks. The resolution of the system is the mean of a Gaussian fit to the distribution, $2.31\pm 0.03\mathrm{ns}$.

Figure 2

Input momentum distribution for neutrino-induced ${\mu }^{-}$ and ${\mu }^{+}$ calculated with the Nuance simulation package. The distributions in the MINOS far detector without oscillations and with the Super-Kamiokande determined values of ${sin}^{2}2{\theta }_{23}$ and $\Delta m_{23}^2$ are shown. The oscillation affects mostly muons with low momenta.

Figure 3

A typical cosmic ray muon in the MINOS far detector. The top panel shows the timing information for the hits along the track with a straight line fit superposed. The legend gives $\Delta T/\Delta S=1/\beta$ and the ${\chi }_{1/\beta }^2/\mathrm{ndf}$ of the fit for this muon. The bottom panel shows the $(x,y)$ hit positions of this track. The resolution of the positions is the 4 cm width of the strips.

Figure 4

Distribution of ${\chi }_{1/\beta }^2/\mathrm{ndf}$ values from the $1/\beta$ determinations for data and cosmic ray muon Monte Carlo events. In this figure, the Monte Carlo distribution has been normalized to the same area as the data distribution. Events with ${\chi }_{1/\beta }^2/\mathrm{ndf}<3$ are used in the analysis.

Figure 5

Distribution of $1/\beta$ for upward-going neutrino-induced muons, with a peak at 1, and downward-going cosmic ray muons, with a peak at $-1$. The vertical lines at 0.7 and 1.3 bracket the events included in the upward-going muon sample.

Figure 6

Distributions of $\Delta T/\Delta S$ as in Fig. 3. The left panel shows a typical upward-going muon and the right panel shows a muon excluded by the $1/\beta$ cut from the upward-going sample.

Figure 7

The $\cos \theta$ distribution for all incoming muons. The data are fit to an exponential between $0.1\le \cos \theta \le 0.2$ to estimate the background of cosmic ray muons in the horizontal neutrino-induced muon signal region. The fit is shown in the figure. As indicated, we select muons coming from directions with $\cos \theta <0.05$.

Figure 8

Comparison of the ${\chi }_{\mathrm{line}}^2/\mathrm{ndf}$ distributions for stopping muons in the cosmic ray data (points), in the cosmic ray Monte Carlo simulation (boxes), and in the neutrino-induced Monte Carlo simulation (line). The number of events in each bin for the cosmic ray Monte Carlo simulation is shown by the location of the center of the box for the bin, and the vertical extent of the box indicates the statistical uncertainty in the bin.

Figure 9

Purity of the charge-sign determination for neutrino-induced muons as a function of ${\chi }_{\mathrm{line}}^2/\mathrm{ndf}$. Events with ${\chi }_{\mathrm{line}}^2/\mathrm{ndf}>10$ have well-determined charge sign and momentum.

Figure 10

Momentum resolution for Monte Carlo neutrino-induced muons as a function of ${\chi }_{\mathrm{line}}^2/\mathrm{ndf}$. The line at ${\chi }_{\mathrm{line}}^2/\mathrm{ndf}=10$ shows the cut used in the analyses.

Figure 11

Distribution of energies for neutrinos producing neutrino-induced muons observed in the MINOS detector as determined by the Monte Carlo simulation. The neutrinos producing low momentum muons are shown by the solid line, those producing high momentum muons are shown by the dashed line, and those producing unknown momentum muons are shown by open circles. Neutrinos producing muons detected by MINOS have energies $\gtrsim 2\mathrm{GeV}$.

Figure 12

Comparison of the ${\chi }_{\mathrm{line}}^2/\mathrm{ndf}$ distributions for neutrino-induced muon data and unoscillated Monte Carlo simulation.

Figure 13

Distribution of fit momenta for events in the combined low momentum and high momentum data samples. The Monte Carlo expectation for no oscillations is shown by the solid line. The unknown momentum muons are not included in this figure.

Figure 14

The intensity of neutrino-induced muons as a function of $\cos \theta$. The data are shown by the points, the best fit is shown by the solid line, and the null oscillation hypothesis is shown by the dotted line. The prediction using the MINOS result with the NuMI neutrino beam is shown by the dashed line. The top left panel shows the events with $1<p_{\mathrm{fit}}<10\mathrm{GeV}/c$ ($L$), the top right shows the events with $10\le p_{\mathrm{fit}}<100\mathrm{GeV}/c$ ($H$), and the bottom left shows events with unknown momentum ($U$).

Figure 15

The 68% (dotted line) and 90% (solid line) confidence intervals for the oscillation parameter fit. The best-fit point is indicated by the star. Also shown is the 90% confidence interval for the MINOS contained vertex analysis (dashed line) based on the first 418 days of data taking with the far detector.