N Alt = r Alt nc · N LE nc + r Alt cc · N LE cc , (3) 10 N LE cc = ( N Alt − r Alt nc · N $^{LE}$)/( r Alt cc − r Alt nc ) N LE nc = N Alt − r Alt cc · N r Alt nc − r Alt cc (4) N LE = N LE nc + N LE cc (2) R ≡ N$_{Data}$ − B$_{CC}$ S$_{NC}$ , (5) VII. SEARCH FOR ACTIVE NEUTRINO DISAPPEARANCE ergy ; (ii) relative calibration of the hadronic energy be- tween the two detectors; (iii) relative normalization be- tween the two detectors; (iv) charged-current background in selected neutral-current events; and (v) uncertainties due to the near-detector selection requirements in the near-detector event counts. Monte Carlo studies have been performed where, for each single uncertainty, the Monte Carlo spectrum is varied by ± 1 standard devia- tion independently, in order to estimate the effect of each on the extrapolated spectrum. Beam and cross section uncertainties that are common to the two detectors ef- fectively cancel when using the F/N extrapolation. of selected neutral-current events may be written as where r Alt nc = N Alt nc / N LE nc and r Alt cc = N Alt cc / N LE cc are determined from the Monte Carlo simulation. Equa- tions (2) and (3) can be solved to yield the solutions: The final estimate on the N LE cc background number re- sults from the weighted average of the three different so- lutions of Eq. (4) when the LE beam data is compared with each of the other beam configurations. The un- certainty on the N LE cc background number is 12% ± 2%. Therefore, the uncertainty in the number of charged- current background events is conservatively taken to be 15% at all energies at the near and far-detectors. The absolute hadronic energy scale has an uncertainty of 12%. This value is a combination of the uncer- tainty in the hadronization model and intranuclear ef- fects (10%) and uncertainty of the detector response to single hadrons (6%). An uncertainty of 3% on the relative energy scale between the two detectors was determined from cross-calibration studies using stopping muons [4]. The relative normalization between the two detectors has an uncertainty of 4%. This is a combination of the uncer- tainties due to fiducial mass, live time, and reconstruc- tion differences between the two detectors. To evaluate the uncertainties due to the near-detector selection, the requirement that the total number of recon- structed strips in an event is at least four was shifted by ± 1 strip. The effects on the reconstructed energy spec- trum were determined for each shift. The uncertainty has been estimated to be 15.2% for E$_{reco}$ < 0.5 GeV, 2.9% for 0.5 < E$_{reco}$ < 1 GeV, 0.4% for 1 < E$_{reco}$ < 1.5 GeV and is negligible for higher visible energies. The uncertainty in the number of charged-current background events is determined using near-detector data taken in several different beam configurations, namely, (i) horns-off , in which there was no current in the magnetic horns; (ii) medium energy , in which the target is moved upstream from the first horn by 100 cm; and (iii) high energy , in which the target is moved upstream from the first horn by 250 cm. For each of these beam configurations, described in further detail in Ref. [4], the charged-current background component has a consider- ably different spectrum from the one obtained in the low- energy (LE) configuration. The charged-current back- ground component in the neutral-current spectrum can thus be determined by using the observed differences in energy spectrum between the low-energy beam configura- tion and each of the other beam configurations along with information from Monte Carlo simulation of each config- uration. In the low-energy configuration, the number of selected near-detector neutral-current events N LE can be written as the sum of true neutral-current events and background charged-current events in that beam config- uration: The data collected in the near and far-detectors have been classified as either neutral-current or charged- current events using the selections described in the pre- vious sections. A total of 388 data events are selected as neutral-current in the far-detector. The measured and predicted E$_{reco}$ spectra at the far-detector are shown in Fig. 9. The prediction assumes that oscillations occur only among the three active flavors and uses the values of | Δ m 2 $_{32}$| and θ$_{23}$ previously measured by MINOS [10]. The agreement between the observed and predicted neutral-current spectra is quantified using a statistic, R : where, within a given energy range, N$_{Data}$ is the observed event count, B$_{CC}$ is the extrapolated charged-current For an alternate beam configuration “Alt”, the number Although the present analysis is not capable of isolat- ing an electron neutrino appearance signal, it must take ν$_{µ}$ → ν$_{e}$ oscillations into account because the classifica- tion criteria of this analysis include ν$_{e}$ charged-current interactions in the neutral-current enriched sample with nearly 100% efficiency. This accounting is done by com- paring the observed neutral-current spectrum to two pre- dictions, one that assumes null ν$_{e}$ appearance, and an- other that assumes an upper limit for the ν$_{e}$ appear- ance rate in the far-detector calculated with the normal neutrino-mass hierarchy, θ$_{13}$ = 12 ◦ and δ = 3 π/ 2. The choice of θ$_{13}$ corresponds to the 90% confidence level upper limit established by the CHOOZ reactor experi- ment [31] for the | Δ m 2 $_{32}$| value measured by MINOS [10]; the choice of δ maximizes the ν$_{e}$ appearance for the cho- sen value of θ$_{13}$ . As seen in Fig. 9, the observed spectrum matches the prediction based on oscillations among the three active flavors very well over the full range of allowed values of θ$_{13}$ .