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The calibration systematic uncertainty comes from the imperfectness of calibration, which can take different forms: absolute calibration uncertainty and relative uncertainty involving cell to cell difference, in-cell flat shift and in-cell shift as a function of cell length. In order to study the relative miscalibration effect, shifts are applied at the calibration step and the intentionally miscalibrated samples are then processed through the standard reconstruction and particle identification chains. The absolute miscalibration effect does not require to process new samples and is studied by applying the shift to the extrapolation spectra. The miscalibration effect in the two detectors is expected to cancel largely.

Absolute miscalibration: The uncertainty of the absolute calibration for the first analysis is determined as the data vs MC difference in the reconstructed energy of Michel electrons. The Michel electron produced in a muon decay presents an upper energy limit of 53 MeV

and is usually used as a standard candle to evaluate the calibration performance. Fig.7.7

shows the data/MC comparison for the calorimetric energy of Michel electrons in both ND and FD [108]. The miscalibration level is calculated as the percentage difference between the mean of the data and MC distributions, resulting in 1% for ND and 5% for FD. To take effect of the absolute calibration uncertainty into full consideration, 5% is chosen to be the shift in absolute calibration, which represents less than 1% of the total background and 6% of the signal prediction in the LID selected region.

(a) (b)

Figure 7.7: The data/MC comparison in the calorimetric energy of Michel electrons in ND (left) and FD (right).

Cell-to-cell difference: The cell-to-cell difference is refered to the different performance of

the attenuation calibration from cell to cell. Fig.7.8 shows the data vs MC comparison

in PECorr/cm variable for the calibrated hits [109]. In order to match the MC to data, the cell response in MC needs to be smeared by 8% which is then taken as the cell-to-cell difference. The uncertainty is applied to each cell as a 8% smearing on the attenuation

calibration constant. Fig.7.10 shows the comparison between the samples with nominal

and shifted calibrations for the events passing pre-selection in the ND and the ones passing cosmic rejection cuts in the FD. The figures present small differences for either ND or FD [110], [111]. The resulting differences in the total background and signal prediction are less than 1% in the LID selected region.

In-cell flat shift: After the in-cell calibration, ideally the response at any position along the cell should be normalized to the response at the center of the cell. However, due to the fluctuations in data and the uncertainties of the attenuation fit, difference exists. In order to evaluate the difference between data and simulation, a polynomial function is fitted to the data/MC ratio of the attenuation constant as a function of in-cell position

W (See Fig.7.9). The difference can be parameterized in two terms: flat shift which is

defined as the amount of data/MC difference at the center of the cell (W = 0) and slope shift which is the rest of the fitted polynomial function with the flat shift subtracted and

(a) (b)

Figure 7.8: The Data/MC comparison of the PECorr/cm distribution for the calibrated hits before (left) and after (right) MC smearing. In order to overlap the MC to data, MC is smeared by 8%, which is taken as the cell-to-cell difference.

contains the information of the difference in shape. In this part, only the former will be discussed and, according to the fit, the amount of the shift is 8%. Two sets of samples, one with attenuation constants shifted uniformly by 8% down and the other by 8% up, are

processed through the reconstruction and PID. Fig.7.11 and Fig.7.12 show the nominal

vs shifted comparison for 8% down and 8% up samples. Shifts in peaks can be clearly observed in both ND and FD for all the components. The overall uncertainty of the prediction is calculated as the average of the flat 8% down and flat 8% up samples. The effect on the final prediction is 4.22% of total background and 2.84% of signal predictions in LID region.

In-cell cell length dependent shift: The in-cell cell length dependent shift describes the difference in shape of the attenuation constant distributions between data and simulation. For the first analysis, the shift is applied as a linear function of W so that the shift in the attenuation constants is 8% at the two cell ends and is 0% the shift at W = 0. ”Slopeup” sample is the one with the constant shifted up at near end and down at far end by 8% so that the calibrated energy of hits at near end is overestimated and the ones at far

(a) (b)

Figure 7.9: The data to MC ratio of the attenuation constant as a function of W (black) and the polynomial fit (blue) for the X-view (left) and Y-view (right) cells in FD.

end is underestimated, while ”Slopedown” sample applies an incorrect increase in the

calibrated energy of hits at far end and a decrease in the ones at near end. Fig.7.13

and Fig.7.14 show the nominal to shifted comparison in the LID selected spectra for

Slopeup and Slopedown samples respectively. A small difference is observed as the slope of the attenuation constant distribution changes in both ND and FD. According to the

Table.7.5, the uncertainties are -3.21% for the total background and -1.51% for signal in

Slope 1.33 2.27 2.94 10.51 3.92

Total 7.58 4.44 15.10 21.78 13.35

LEM

% diff signal total bkg. νµ CC NC beam νe CC

Absolute 1.20 5.80 12.25 0.81 10.36 Relative 2.84 4.22 10.46 1.87 8.33 Random -1.33 -0.80 1.09 -0.42 1.43 Slope -1.51 -3.21 -4.35 1.06 6.45 Total 3.68 7.90 16.72 2.34 14.84 (a) (b)

Figure 7.10: Comparison between the LID selected spectra with norminal and shifted calibra- tion for ND (left) and FD (right).

(a) _(b)

Figure 7.11: Comparison between the LID selected spectra with norminal and flatdown by 8% calibration for ND (left) and FD (right).

(a)

(b)

Figure 7.12: Comparison between the LID selected spectra with norminal and flatup by 8% calibration for ND (left) and FD (right).

(a) _(b)

Figure 7.13: Comparison between the LID selected spectra with norminal and slopedown by 8% calibration for ND (left) and FD (right).

(a)

(b)

Figure 7.14: Comparison between the LID selected spectra with norminal and slopeup by 8% calibration for ND (left) and FD (right).