Measurements of atmospheric neutrinos and antineutrinos in the MINOS far detector

P. Adamson et al. (The MINOS Collaboration)

Phys. Rev. D 86, 052007 – Published 17 September 2012

Abstract

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

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Received 17 August 2012

DOI:https://doi.org/10.1103/PhysRevD.86.052007

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Vol. 86, Iss. 5 — 1 September 2012

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Figure 1
The simulated atmospheric neutrino energy spectrum in the MINOS Far Detector for 2553 live-days of data. Separate distributions are plotted for contained-vertex neutrino interactions and neutrino-induced rock-muons showing the predictions for the case of no oscillations, and for oscillations with $Δ m^{2} = 2.32 \times 10^{- 3} {eV}^{2}$ and ${sin }^{2} 2 θ = 1.0$ . The contained-vertex neutrino interactions are generated in the range 0.2–50 GeV, with a median value of 2 GeV; the neutrino-induced rock-muons range up to neutrino energies of 10 TeV, with a median value of 50 GeV. The effect of $ν_{μ} \to ν_{τ}$ oscillations is visible for neutrino energies below 100 GeV.
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Figure 2
Distributions of the trace variable, $Δ_{Z}$ , for contained-vertex tracks. This estimates the distance in $z$ traveled by a cosmic-ray muon inside the detector before first entering the scintillator. The hatched histogram shows the simulated prediction for the atmospheric neutrino signal; the solid line shows the predicted total rate, given by the sum of the signal and the cosmic-ray muon background; the points show the observed data. The background distribution is peaked towards low values of $Δ_{Z}$ , and the arrow indicates the selection applied to reduce the background.
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Figure 3
Distributions of the pulse height at the upper end of the track ( $Q_{vtx}$ ), plotted against the $z$ component ( $\cos θ_{z}$ ) and $y$ component ( $\cos θ_{y}$ ) of the downward track direction. The distributions are plotted for contained-vertex muons that pass the trace and topology requirements and span fewer than 25 planes. The plots on the left show simulated atmospheric neutrinos; those on the right show the cosmic-ray muon background. The background events are associated with large pulse heights and directions parallel to the vertically aligned scintillator planes. The hatched area is the region rejected by the pulse height and direction selection criteria as part of the topology requirements. Note that the requirement of a track spanning $\geq 8$ planes causes the acceptance to drop to zero as $| \cos θ_{z} |$ approaches 0, and as $\cos θ_{y}$ approaches $- 1$ .
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Figure 4
Distribution of $1 / β$ normalized velocity variable, demonstrating the purity of the track direction identification. The $1 / β$ variable is the gradient of a linear fit to the measured times as a function of distance along each track. The distribution is plotted for all tracks that pass the topology and timing selections. The peak at $- 1.0$ corresponds to downward-going muons; the peak at $+ 1.0$ to upward-going muons. A good separation is achieved between the upward-going neutrino-induced signal, and downward-going cosmic-ray muon background.
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Figure 5
Distribution of reconstructed zenith angle for muons with good timing and topology. In the range $\cos θ_{z} > 0.10$ , the observed rate of muons is dominated by the cosmic-ray background and falls steeply as the mean rock overburden increases rapidly. For $\cos θ_{z} < 0.10$ , the distribution flattens, as the cosmic-ray muon flux falls below that of neutrino-induced muons. To minimize the background from cosmic-ray muons, events are required to satisfy $\cos θ_{z} < 0.05$ .
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Figure 6
Distributions of the trace variable, $Δ_{Z}$ , for contained-vertex showers. This variable estimates the distance in $z$ traveled by a cosmic-ray muon inside the detector before entering the scintillator. The hatched histogram shows the simulated prediction for the atmospheric neutrino signal. The solid line gives the predicted total rate, dominated by the cosmic-ray muon background. The points show the observed data. The background is peaked towards low values of $Δ_{Z}$ , since cosmic-ray muons typically travel a small distance in $z$ before entering the scintillator. The arrow indicates the selection applied on $Δ_{Z}$ to reduce the background.
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Figure 7
Distributions of mean and rms shower pulse height per scintillator plane observed for contained-vertex showers that pass the fiducial and trace cuts. The hatched histogram shows the simulated prediction for the atmospheric neutrino signal. The solid line gives the total prediction, dominated by the cosmic-ray muon background. The points show the observed data. The arrows indicate the selection applied to reduce the background.
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Figure 8
Distributions of reconstructed neutrino energy, plotted for selected contained-vertex showers. The dotted line shows the prediction for no oscillations; the solid line shows the prediction for $Δ m^{2} = 2.32 \times 10^{- 3} {eV}^{2}$ and ${sin }^{2} 2 θ = 1.0$ ; the shaded histogram shows the predicted cosmic-ray muon background; the points with errors show the observed data. The $ν_{μ} + {\bar{ν}}_{μ}$ CC component is small and hence the total prediction does not depend strongly on the oscillation parameters.
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Figure 9
Distributions of track fit uncertainty, $(q / p) / σ_{q / p}$ , and track straightness variable, $χ_{line}^{2} / dof$ , used to select events with well-measured muon charge sign. The distributions are plotted for contained-vertex muons (left panels), and neutrino-induced rock-muons (right panels). In each plot, the dashed line indicates the total prediction in the absence of oscillations; the solid line shows the prediction for oscillations with $Δ m^{2} = 2.32 \times 10^{- 3} {eV}^{2}$ and ${sin }^{2} 2 θ = 1.0$ ; the shaded histogram shows the cosmic-ray muon background; and the points show the observed data. In addition, the hatched histograms show the component with misidentified charge sign. The arrows indicate the selections used to identify events with well-measured charge sign.
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Figure 10
Distributions of reconstructed zenith angle, for contained-vertex muons (left), and neutrino-induced rock-muons (right). In each plot, the dashed line gives the nominal prediction for the case of no oscillations; the shaded histogram shows the cosmic-ray muon background; and the points with errors show the observed data. The solid line shows the best fit to the data, which combines the best fit oscillation and systematic parameters.
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Figure 11
Distributions of reconstructed ${log }_{10} (L / E)$ , for contained-vertex muons (left), and neutrino-induced rock-muons (right). In each plot, the dashed line gives the nominal prediction for the case of no oscillations; the shaded histogram shows the cosmic-ray muon background; and the points with errors show the observed data. The solid line shows the best fit to the data, which combines the best fit oscillation and systematic parameters.
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Figure 12
Distributions of reconstructed ${log }_{10} (L / E)$ , plotted for selected neutrinos and antineutrinos in the contained-vertex muon sample (left panels) and neutrino-induced rock-muon sample (right panels). In each case, the dashed line gives the nominal prediction in the absence of oscillations; the shaded histogram shows the cosmic-ray muon background; and the points with errors show the observed data. The solid line indicates the best fit to the data, which combines the best fit oscillation and systematic parameters.
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Figure 13
Distributions showing the calculated $L / E$ resolution for the high resolution sample of contained-vertex muon, which have well-measured propagation direction. The dashed histogram indicates the nominal prediction in the absence of oscillations; the solid histogram indicates the prediction for the best fit oscillation parameters presented in this paper; the shaded histogram shows the cosmic-ray muon background; and the points with error bars represent the observed data. The vertical dashed lines correspond to the partitions used to divide the selected events into four bins of $L / E$ resolution.
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Figure 14
Ratios of the predicted ${log }_{10} (L / E)$ distributions with oscillations to those without oscillations in the four bins of $L / E$ resolution. The predictions with oscillations are generated using input parameters of $Δ m^{2} = 2.32 \times 10^{- 3} {eV}^{2}$ and ${sin }^{2} 2 θ = 1.0$ . The oscillations are most sharply defined in the bin of highest resolution. Here, a clear oscillation dip can be seen at ${log }_{10} (L / E) \approx 2.7$ , corresponding to the peak oscillation probability. The ratio then rises to a maximum at ${log }_{10} (L / E) \approx 3$ , and a second dip is visible before the ratio averages to $1 - \frac{1}{2} {sin }^{2} 2 θ = 0.5$ , as the frequency of oscillations becomes rapid.
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Figure 15
Distributions of ${log }_{10} (L / E)$ observed in each bin of $L / E$ resolution for contained-vertex muons, and in each bin of muon momentum for neutrino-induced rock-muons. For each of the panels, the dashed line gives the nominal prediction in the absence of oscillations; the shaded histogram shows the cosmic-ray muon background; and the points represent the data. The solid line indicates the best fit to the data, combining the best fit oscillation and systematic parameters.
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Figure 16
Confidence limits on the parameters $| Δ m^{2} |$ and ${sin }^{2} 2 θ$ , assuming equal oscillations for neutrinos and antineutrinos. The solid line gives the 90% contour obtained from this analysis, with the best fit parameters indicated by the star. For comparison, the dashed line shows the 90% contour given by the MINOS oscillation analysis of neutrinos from the NuMI beam [12], with the best fit point indicated by the triangle. The dotted line shows the 90% contour from the Super-Kamiokande atmospheric neutrino zenith angle analysis (from [21]), with the best fit point indicated by the circle.
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Figure 17
Confidence limits on neutrino (left) and antineutrino (right) oscillation parameters. The solid lines show the 90% contours obtained from this analysis. The two-parameter contours for neutrinos and antineutrinos are calculated by profiling the four-parameter likelihood surface. The best fit parameters are indicated by the stars. For comparison, the dashed lines in each plot show the 90% contours from the MINOS analysis of beam data in neutrino mode [12] and antineutrino mode [15], with the best fit points indicated by the triangles. The dotted lines show the 90% contours from the Super-Kamiokande analysis of atmospheric neutrinos and antineutrinos (from [21]), with the best fit points indicated by the circles.
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Figure 18
Comparisons of the observed and predicted 90% contours. The left plot shows the contours for the two-parameter oscillation fit, where neutrinos and antineutrinos take the same oscillation parameters. The right two plots, labeled $ν$ and $\bar{ν}$ , show the contours obtained for neutrinos and antineutrinos, respectively, resulting from the four-parameter oscillation fit, where neutrinos and antineutrinos take different oscillation parameters. In each case, the predicted contours are generated by inputting the best fit parameters from the observed data into the simulation, and running the full oscillation fit, including the 12 systematic parameters.
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Figure 19
Confidence limits obtained for the oscillation parameters $| Δ m^{2} |$ and $| Δ {\bar{m}}^{2} |$ , representing the mass splittings for neutrinos and antineutrinos, respectively. At each point in parameter space, the negative log-likelihood function has been minimized with respect to the mixing parameters ${sin }^{2} 2 θ$ and ${sin }^{2} 2 \bar{θ}$ . The 68%, 90%, and 99% contours are indicated by the dotted, solid, and dashed curves, respectively, and the best fit parameters are indicated by the star. The diagonal dashed line indicates the line of $| Δ m^{2} | = | Δ {\bar{m}}^{2} |$ .
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