True Transition Probability
POT 20 Events / 10
6.3 Systematics
There are a number of systematic uncertainties with the potential to affect the oscillation measure- ment. They fall into a few general categories: energy reconstruction, backgrounds, and extrapolation.
Thanks to the two-detector design of the MINOS experiment, none of these systematic uncertainties is significant in comparison to the statistical uncertainty from the size of the antineutrino data set.
6.3.1 Energy Reconstruction Systematics
Track energy scale
Track energy as measured by range has a systematic uncertainty of 2% determined using CalDet (see Section 3.4). Track energy as measured by curvature has an ad- ditional 1% uncertainty, determined by comparing range and curvature momentum measurements for stopping tracks. These uncertainties are taken as fully correlated between the two detectors.
Relative shower energy scale
The relative shower energy systematics come from uncertainties in the energy cali- bration procedure using cosmic ray muons. Data-simulation differences in the vari- ous calibration steps are added in quadrature and give an uncertainty of 1.85% in the Near Detector and 1.05% in the Far Detector [153]. The errors are uncorrelated between the detectors.
Absolute shower energy scale
The absolute shower energy systematic uncertainty is taken as fully correlated be- tween the two detectors and has two major components. The first component stems from uncertainties in the detector response to single hadrons as measured in CalDet at the CERN test beam and is 5.7% at all energies (see Section 3.4). The second
2I had a central role in adapting the extrapolation procedure for the antineutrino beam.
112 Antineutrinos in an Antineutrino Beam Systematic Uncertainty
Steel Thickness 0.2%
Scintillator Thickness 0.2%
FD Live Time 0.32%
ND Fiducial Bias (z) 0.43%
ND Fiducial Bias (y) 0.14%
ND Fiducial Bias (x) 0.53%
N/F Selection Bias 1.3%
Table 6.1: Components of the Near-to-Far normalization systematic uncertainty.
component is energy-dependent and encapsulates uncertainties in hadron produc- tion and intranuclear effects. It is 8.2% at the lowest energies, dropping off to 3%
above 10 GeV [154]. The final systematic has the energy-dependent form
σshw= 6.6% + (3.5%)×e1.44 GeV−Eshw (6.4) which is taken as fully correlated bin-to-bin.
6.3.2 Background Systematics
Neutral current background
The neutral current background systematic was evaluated by comparing data and Monte Carlo in an NC-dominated sample of events below a cut value of 0.3 inRoID, giving a systematic uncertainty of 20% on the amount of NC background.
Charged current νµ background
As with the NC background, the CCνµ background was evaluated by comparing data and Monte Carlo in a wrong sign-enhanced sample with (q/p)/(σq/p)>2.3,3 giving a systematic uncertainty of 30% on the amount of wrong-sign background.
6.3.3 Extrapolation Systematics
Near-to-Far normalization
The 1.54% normalization systematic incorporates several systematic uncertainties, all of which change the number of events expected at the two detectors per POT.
It is dominated by a 1.3% uncertainty on the difference in selection efficiency in the two detectors, evaluated by hand-scanning events in both detectors in data and Monte Carlo. Also included are uncertainties in the fiducial mass of the detectors,
3This variable is used in the neutrino-mode selection and is described in Section 5.1.
the spatial uniformity of the detector acceptances, and the live time of the Far Detector. All the components are tabulated in Table 6.1.
Cross-sections
A number of uncertainties are evaluated, both on the overall cross section and on various NEUGEN interaction model parameters. Some affect both neutrinos and antineutrinos and others are specific to antineutrinos. While the majority of the cross section uncertainty cancels between the two detectors, some residual uncertainty remains because of the spectral differences between the detectors.
Flux modeling
The flux modeling uncertainty encapsulates a number of sources of error, including hadron production, beam optics (horn positions, currents, etc.), the position of the target, and the amount of material in the beamline. The flux errors are evaluated by moving around the fit parameters in the beam tuning fit within their uncertainties and observing the effect on the flux. Again, the majority of the errors cancel between the two detectors, but some residual uncertainty remains because the two detectors do not see identical fluxes.
6.3.4 Effect on the Analysis
As with the neutrino-mode analysis (see Section 5.4), the effect of each systematic uncertainty on the oscillation results is estimated using the Monte Carlo simulation. Systematic shifts are applied to Monte Carlo events to produce shifted Near and Far Detector spectra. The shifts are applied both positively and negatively, producing two sets of spectra. The total systematic uncertainty can then be examined several ways.
Figure 6.7 shows the Far Detector systematic error band constructed from all the systematic uncertainties summed in quadrature. The correlation in the systematics between the two detectors, which generally leads to cancellation, needs to be taken into account. The systematically shifted Near Detector spectrum is extrapolated to the Far Detector, producing a systematically shifted prediction. The shift in the systematically shifted Far Detector spectrum is then divided out of the shifted prediction, approximating the cancellation that occurs when fitting.
An oscillation analysis is also performed (see Section 6.5) for each systematic shift using the systematically shifted Near and Far Detector spectra as fake data. The amount the best fit moves compared to using the nominal Monte Carlo shows the size of that systematic effect on the oscillation result. The sizes of these shifts, which are approximately an order of magnitude smaller than the statistical uncertainty, can be seen in the colored lines in Figure 6.8.
114 Antineutrinos in an Antineutrino Beam
Figure 6.7: Total systematic error band on the Far Detector prediction. The band is obtained by adding the effect of each individual systematic shift on the FD predicted energy spectrum in quadrature, taking into account the cancellation from extrapolation.
θ )
2
(2 sin
0.845 0.85 0.855 0.86 0.865 0.87 0.875
)
2eV
-3|(10
2m Δ |
3.30 3.32 3.34 3.36 3.38 3.40 3.42
NC Background WS CC Background Track energy Relative normalisation Relative hadronic energy FD Relative hadronic energy ND Overall hadronic energy Beam
Cross sections 20 POT
×10 MINOS Preliminary: 1.71
running νµ
MINOS
Figure 6.8: The shifts to the best fit oscillation parameters induced by the application of systematic shifts to the fake data. The cross section systematic is the sum in quadrature of all the component cross section sys- tematics. The systematic uncertainties are approximately an order of magnitude smaller than the statistical uncertainty.