True Transition Probability
5.5 Far Detector Data
Figure 5.18 shows the Far Detector data spectrum along with the prediction based on Near Detector data without oscillations, the prediction with the same oscillation parameters measured for neutrinos in [77], and the predicted background spectrum. 42 events were observed with an unoscillated expectation of 66.6±8.2(stat)±5.0(syst) and an oscillated expectation of 60.3±7.8(stat)±4.6(syst) assuming the neutrino oscillation parameters as above. The two-sigma deficit is at high energies so it is not associated with previously observed oscillations [63, 65, 66, 77]. In order to be sure there is not a problem with selection, comparisons between Far Detector data and simulation in the selection variables are shown in Figures 5.19-5.21. The deficit is limited to the signal region in the CC/NC separation parameter and appears at low (q/p)/ σq/p since the deficit is at higher energies (higher energy tracks have poorer charge-determination). There is no evidence of an excess of events being inadvertently removed by a problem with the selection. Also shown are the track vertex and end positions in Figure 5.22. The vertex plots show an apparent asymmetry with no event vertices in the right-most section of the detector, but, as described in the next section, there is no evidence of a detector problem in this region and fake data studies show that such an asymmetry is reasonably likely with so few events.
Energy (GeV) ν
µReconstructed
Events / 4 GeV
0 5 10 15
Energy (GeV) ν
µReconstructed
Events / 4 GeV
0 5 10 15
0 5 10 15 20 30 40 50
Far Detector Data No Oscillations CPT Conserving Systematic Error Background (CPT) MINOS Preliminary
Low Energy Beam Far Detector
20 POT
×10 3.2
Figure 5.18: Far Detector ¯νµdata spectrum (black points) compared to predictions with no oscillations (solid red histogram) and with theνµoscillation parameters from [77] (dashed blue histogram). The background is also displayed (gray shaded histogram).
Event Classification Parameter
-1 -0.5 0 0.5 1 1.5
Events
0 10 20 30 40
Dataνµ Oscillations No
eV2
10-3
=2.5× m2
Δ MINOS PRELIMINARY Far Detector
Low Energy Beam
20 PoT
× 10 3.2
Figure 5.19: CC/NC separation parameter (DpID) is shown in the Far Detector in data (black points), oscillated simulation (solid red line) and unoscillated simulation (dashed red line). All other selection cuts have been applied. The line and arrow mark the region removed by the cut. The deficit appears only in the signal region and does not appear to be due to a mismodeling of the CC/NC separator.
94 Antineutrinos in a Neutrino Beam
(q/p) (q/p)/σ
0 10 20 30 40 50
Events
0 5 10 15 20
Dataνµ Oscillations No
eV2
10-3
=2.5× m2
Δ
MINOS PRELIMINARY Far Detector
Low Energy Beam
20 PoT
× 10 3.2
Figure 5.20: Charge-sign selection variable (q/p)/ σq/pis shown in the Far Detector in data (black points), oscillated simulation (solid red line) and unoscillated simulation (dashed red line). All other selection cuts have been applied. The deficit appears largest at low values since this variable is correlated with energy:
higher energy tracks have poorer charge-determination. The line and arrow mark the region removed by the cut.
/|
|Relative Angle ï
0 1 2 3
Events
0 10 20 30
Dataiµ Oscillations No
eV2
10ï3
=2.5× m2
6
MINOS PRELIMINARY Far Detector
Low Energy Beam
20 PoT
× 10 3.2
Figure 5.21: Charge-sign selection variable|Relative Angle−π|is shown in the Far Detector in data (black points), oscillated simulation (solid red line) and unoscillated simulation (dashed red line). All other selection cuts have been applied. The line and arrow mark the region removed by the cut. There appear to be no missing events at lower relative angles, as might be expected if there were a problem with this selector.
Event Vertex X Position (m)
-4 -2 0 2 4
Event Vertex Y Position (m) -4 -2 0 2 4
MINOS PRELIMINARY
20 PoT
× 10 Far Detector: 3.2 Low Energy Beam
Event End X Position (m)
-4 -2 0 2 4
Event End Y Position (m)-4 -2 0 2 4
MINOS PRELIMINARY
20 PoT
× 10 Far Detector: 3.2 Low Energy Beam
Figure 5.22: Selected antineutrino event vertex (left) and end (right) positions in the Far Detector as a function ofx- andy-coordinates. The apparent asymmetry in vertexxpositions was shown to be consistent with statistical fluctuations (p >0.05 compared to distributions from pseudo-experiments), given the number of events observed.
5.5.1 Cross-checks
After the box was opened, several cross-check studies were undertaken. The first step was to un- derstand how unlikely it was to observe so large a deficit. Figure 5.23 shows the distribution of the number of selected events in 10,000 fake experiments, including systematic shifts. The probability of seeing 42 events or below was 2.4%, but the probability of being as far from the mean (high or low) as observed was 5.1%. The likelihood of the left-right vertex asymmetry was also exam- ined and found to be consistent with statistical fluctuations: comparisons with pseduo-experiment distributions gavep-values>0.05 for the values measured in the data.8
A study was also undertaken to see what effect a mismodeling of precisely which events the selection cuts remove in the Near Detector might produce. This effect was modeled by changing the selection cuts up and down in only the Near Detector and seeing the size of this effect on the Far Detector prediction. The ratios of the shifted to nominal predictions are shown in Figure 5.24 and the changes are extremely small between 5 GeV and 30 GeV where the majority of the antineutrino spectrum is.
The event rate over time was also examined. If the deficit were concentrated in a single time period it would suggest a beam or detector problem. Figure 5.25 shows the number of Far Detector antineutrino events per proton-on-target in 4-month blocks. There is no evidence of a single time period being responsible for the deficit – it appears constant over time. Figure 5.26 shows the Near Detector antineutrino event rate. An excess of Near Detector events could cause an apparent deficit at the Far Detector, but the Near Detector event rate appears stable over time, as well.
8I performed the pseudo-experiment studies of the event counts and vertex asymmetry.
96 Antineutrinos in a Neutrino Beam
Number of Events
0 20 40 60 80 100
Pseudo Experiments
0 1000 2000 3000 4000 5000
Mean = 58.3
Low Energy Beam
20 POT
×10 3.2
Far Detector Simulated
MINOS Preliminary
42) = 2.4%
P(N ≤ P(N ≥ 75)
= 2.7%
Figure 5.23: The distribution of the number of selected events in 10,000 fake experiments. In addition to randomly selected events, each experiment also has a random set of systematic shifts so the effects of systematic errors are included. Our mean experiment had 58.3 events and our actual experiment had 42 events. The probability of getting 42 events or below is 2.4% and the probability of being as far from the mean as observed is 5.1%.
Energy (GeV) ν
µReconstructed
0 10 20 30 40 50
Nominal / Modified
0.8 0.9 1 1.1 1.2
dp ID low (Q/P) low (Q/P)/σ
rel Ang low
dp ID high (Q/P) high (Q/P)/σ
rel Ang high MINOS Preliminary Far Detector Prediction
Low Energy Beam
Figure 5.24: Ratio of the nominal Far Detector prediction to the modified predictions with higher and lower cuts on the individual selection variables. The high and low cut values are chosen such that the efficiency×purity of each modified selection is 3% lower than the maximum. None of these changes can reproduce the deficit seen in the Far Detector.
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