Electron energy spectra, fluxes, and day-night asymmetries of ${}^8$B solar neutrinos from measurements with NaCl dissolved in the heavy-water detector at the Sudbury Neutrino Observatory

Results are reported from the complete salt phase of the Sudbury Neutrino Observatory experiment in which NaCl was dissolved in the ${}^2\mathrm{H}$${}_2\text{O}$ (“${\text{D}}_2\text{O}$”) target. The addition of salt enhanced the signal from neutron capture as compared to the pure ${\text{D}}_2\text{O}$ detector. By making a statistical separation of charged-current events from other types based on event-isotropy criteria, the effective electron recoil energy spectrum has been extracted. In units of ${10}^6{\text{cm}}^{-2}{\text{s}}^{-1}$, the total flux of active-flavor neutrinos from ${}^8\mathrm{B}$ decay in the Sun is found to be ${4.94}_{-0.21}^{+0.21}{\text{(stat)}}_{-0.34}^{+0.38}\text{(syst)}$ and the integral flux of electron neutrinos for an undistorted ${}^8\mathrm{B}$ spectrum is ${1.68}_{-0.06}^{+0.06}{\text{(stat)}}_{-0.09}^{+0.08}\text{(syst)}$; the signal from (${\nu }_x,e$) elastic scattering is equivalent to an electron-neutrino flux of ${2.35}_{-0.22}^{+0.22}{\text{(stat)}}_{-0.15}^{+0.15}\text{(syst)}$. These results are consistent with those expected for neutrino oscillations with the so-called large mixing angle parameters and also with an undistorted spectrum. A search for matter-enhancement effects in the Earth through a possible day-night asymmetry in the charged-current integral rate is consistent with no asymmetry. Including results from other experiments, the best-fit values for two-neutrino mixing parameters are $\Delta m^2=({8.0}_{-0.4}^{+0.6})\times {10}^{-5}$ eV${}^2$ and $\theta =33.9_{-2.2}^{+2.4}$ degrees.

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Figure 1

(Color) Reduction of the data set as successive cuts are applied. The PMT instrumental, external light and pickup cuts remove instrumental backgrounds originating from the detector hardware. The high-level cuts (Sec. 7) further reduce the instrumental backgrounds by rejecting events that do not possess the characteristics of Cherenkov light emission from single or multiple βs. The fiducial volume cut, which selects events reconstructed with $\rho <0.77$, removes most of the radioactive background events that originate outside the ${\text{D}}_2\text{O}$ target. Note that the relationship between electron kinetic energy and total number of PMT hits per event is approximately 0.12 MeV/PMT hit and the analysis region is between 46 and 167 PMT hits.

Figure 2

(Color) Signal loss as a function of energy for CC electrons assuming an undistorted ${}^8\mathrm{B}$ spectrum. Signal loss uncertainties are divided into two classes: uncorrelated (error bars) and correlated (error bands). Correlated uncertainties arise from systematic uncertainties in the measurement of signal loss and uncorrelated uncertainties arise from statistical uncertainties in the calibration data used in this measurement.

Figure 3

(Color) Attenuation coefficients of (a) ${\text{D}}_2\text{O}$ and (b) ${\text{H}}_2\text{O}$ as a function of date for 369- and 420-nm pulsed laser scans. The data points are correlated by systematics that are common to each of the measurements. Note that the ${\text{H}}_2\text{O}$ values are determined by subtracting the acrylic vessel ex situ measured attenuation coefficients from the measured ${\text{H}}_{2}O+$acrylic values.

Figure 4

(Color) Measured angular response curves for PMT-reflector assemblies from three optical scans taken at 385 nm during the salt phase of operation. The incident angle for photons originating from the fiducial volume ($\rho <0.77$) is confined to less than 35 degrees. The average response from all the laser scans is used as the input to the MC simulation. Note that the y axis zero is suppressed.

Figure 5

(Color) PMT time-residual spectrum for a ${}^{16}\mathrm{N}$ run taken with the source positioned at the center of the detector. The time residual is calculated without any walk correction to the PMT hit time. Only hit PMTs with time residuals within the 20-ns “prompt window” centered at the “prompt peak” are used to estimate the energy of an event.

Figure 6

(Color) $N_{\mathrm{corrected}}$ distributions for data (points) and MC (histogram) for a ${}^{16}\mathrm{N}$ run taken with the source positioned at the center of the detector. The dashed line corresponds to the energy threshold cut of $T_{\mathrm{eff}}=5.5$ MeV.

Figure 7

(Color) (a) Mean $N_{\mathrm{corrected}}$ and (b) mean $T_{\mathrm{eff}}$ versus date for data and MC high-rate ${}^{16}\mathrm{N}$ calibrations runs with the source at the center of the detector. Note that the full y-axis ranges are $~4\%$ and $~2\%$ of the average $N_{\mathrm{corrected}}$ and $T_{\mathrm{eff}}$ values respectively. Error bars are statistical only, and the spread of the variation between data and Monte Carlo provides the measure of the energy scale uncertainty arising from temporal variations in detector response.

Figure 8

(Color) (a) Data and MC mean energy versus ρ distributions and (b) the run-by-run ratio of data to MC mean energy versus ρ are shown for ${}^{16}\mathrm{N}$ calibration runs. The dashed vertical line corresponds to the fiducial volume cut at $R=550$ cm. Points at the same value of ρ can have differing energy response in data or Monte Carlo because of local point-to-point nonuniformities in detector response.

Figure 9

(Color) Difference between mean reconstructed (a) x, (b) y, and (c) $z$ coordinates and the coordinates of the deployed ${}^{16}\mathrm{N}$ source versus ρ. The ${}^{16}\mathrm{N}$ source was deployed along the central ($z$) axis for the data shown in this figure. From these data, systematic uncertainties on x- and y-coordinate vertex reconstruction are evaluated to be 2 cm and the uncertainty on $z$-coordinate vertex reconstruction is evaluated to be 6 cm.

Figure 10

(Color) Data and MC distributions of the cosine of the angle between generated event direction and reconstructed direction for a ${}^{16}\mathrm{N}$ source located at the center of the detector are shown. The events are selected such that the reconstructed vertex is at least 120 cm away from the source position.

Figure 11

(Color) ${\beta }_{14}$ isotropy distributions for ${}^{252}\mathrm{Cf}$ data and MC, ${}^{16}\mathrm{N}$ data and MC, and simulated CC events.

Figure 12

(Color) ${\beta }_{14}$ isotropy distributions of (a) ${}^{252}\mathrm{Cf}$ data and MC width versus ρ and (b) ${}^{16}\mathrm{N}$ data and MC mean versus ρ. Systematic effects observable in the distributions are attributed to temporal and spatial nonuniformities in detector response and give the estimates on the ${\beta }_{14}$ systematic uncertainties.

Figure 13

(Color) Neutron energy response during the ${\text{D}}_2\text{O}$ (dashed) and salt (solid) running periods. The vertical line represents the analysis energy threshold of $T_{\mathrm{eff}}=5.5$ MeV in the salt period. For the ${\text{D}}_2\text{O}$ period the analysis energy threshold was $T_{\mathrm{eff}}=5.0$ MeV. The distributions shown here are normalized to the neutron detection efficiency in the two phases for $R<550$ cm.

Figure 14

(Color) Neutron capture efficiency versus radial position of the ${}^{252}\mathrm{Cf}$ source for the pure ${\text{D}}_2\text{O}$ and salt phase. The solid line is a fit of the salt phase data to Eq. (10), and the dotted line is a fit of the ${\text{D}}_2\text{O}$ phase data to a neutron diffusion model.

Figure 15

(Color) Comparison of neutron detection efficiency ($T_{\mathrm{eff}}>5.5$ MeV) for MC simulated NC events (data points) and that derived from ${}^{252}\mathrm{Cf}$ calibration data (shaded band) as a function of volume-weighted radius ρ. The band represents the statistical and systematic uncertainties summarized in Table 9. An additional 1.0% radial reconstruction uncertainty that is assigned to the solar neutrino flux is also included in the band. The volume-weighted NC MC efficiency is within the systematic uncertainty assigned to the ${}^{252}\mathrm{Cf}$ measurement.

Figure 16

(Color) The distribution of high-level cut parameters for instrumental backgrounds and neutrino candidates. The two cut parameters are the isotropy ${\beta }_{14}$ and the fraction of PMT hits within the prompt time window. The ${}^{16}\mathrm{N}$ calibration source was used to generate the sample “neutrino candidate” events and thereby establish the signal window for Cherenkov events and to calibrate the cut efficiency.

Figure 17

(Color) In situ determination of the low-energy background in the ${\text{D}}_2\text{O}$. The data points represent low-energy events selected by the criteria described in the text. The data isotropy (${\beta }_{14}$) distribution is fit to a combination of ${}^{208}\mathrm{Tl}$ and ${}^{214}\mathrm{Bi}$ distributions. Also shown are the ${}^{24}\mathrm{Na}$ background and solar neutrino contributions that were constrained in the fit. The fit result is shown as the sum histogram.

Figure 18

(Color) (a) Thorium and (b) uranium backgrounds (equivalent equilibrium concentrations) in the ${\text{D}}_2\text{O}$ deduced by in situ and ex situ techniques. The ${\text{MnO}}_x$ and HTiO radiochemical assay results, the Rn assay results, and the in situ Cherenkov signal determination of the backgrounds are presented for the period of this analysis on the left-hand side of panels (a) and (b). The right-hand side shows time-integrated averages, including an additional sampling systematic uncertainty for the ex situ measurement. The weighted average of the ex situ Th measurements is decreased by $0.65\times {10}^{-15}$ to allow for the effect of source terms in the piping external to the acrylic vessel, as discussed in the text. The large ${}^{222}\mathrm{Rn}$ excess near day 580 is the decay of Rn that was added for calibration purposes and was excluded in calculating the mean ex situ results. The weighted average of the ex situ ${}^{222}\mathrm{Rn}$ measurements appear as an upper limit only. This is because of intermittent backgrounds appearing in the radon extraction process.

Figure 19

(Color) Fitted MC prediction to the radon spike data, with the steeply falling background Cherenkov spectrum and neutron peaks shown separately.

Figure 20

(Color) Maximum likelihood fit of the data ρ distribution (data points) to the PDFs constructed from Th or U calibration sources. Because the external Cherenkov backgrounds are small for the solar neutrino analysis threshold ($T_{\mathrm{eff}}>5.5$ MeV) and fiducial volume ($\rho <0.77$), this fit is performed for $T_{\mathrm{eff}}>4.5$ MeV in the region $1.1<\rho <2.5$ to enhance the statistics. Contributions of these backgrounds are then obtained from extrapolating the fit results to the solar neutrino signal window. The band represents the systematic uncertainties in this analysis.

Figure 21

(Color) Day-night asymmetries of selected muon-induced neutron properties and background rates. The day-night asymmetries for the muon-induced neutron properties are calculated for events in the full day and night data sets. The day-night asymmetries of the background rates are determined by combining the calculated asymmetry of each individual data run. Each data run lasted for less than 24 hr.

Figure 22

(Color) (a) ${\beta }_{14}$ and (b) $\cos {\theta }_{\odot }$ distributions for CC, ES, NC, and external neutron events. Where internal and external neutron distributions are identical the distribution is simply labeled neutrons. Note that the distribution normalizations are arbitrary and chosen to allow the shape differences to be seen clearly.

Figure 23

(Color) (a) $T_{\mathrm{eff}}$ and (b) ρ distributions for CC, ES, NC, and external neutron events. Where internal and external neutron distributions are identical the distribution is simply labeled neutrons. Note that the distribution normalizations are arbitrary and chosen to allow the shape differences to be seen clearly. The CC energy spectrum shape corresponds to an undistorted ${}^8\mathrm{B}$ model. The highest-energy bin in (a) represents the average number of events per 0.5 MeV for the range 13.5–20 MeV.

Figure 24

(Color) Data $T_{\mathrm{eff}}$ spectrum with statistical uncertainties. Included are MC spectra for neutron, CC, ES, and external neutron distributions. Note that an undistorted ${}^8\mathrm{B}$ spectral shape has been assumed and each MC contribution has been normalized to the number of corresponding fit events measured by the energy-constrained signal extraction. The highest-energy bin represents the average number of events per 0.5 MeV for the range 13.5–20 MeV.

Figure 25

(Color) (a) Extracted CC $T_{\mathrm{eff}}$ spectrum. Systematic uncertainties have been combined in quadrature and include only the effect of PDF shape change. (b) Extracted CC $T_{\mathrm{eff}}$ spectrum with statistical error bars compared to predictions for an undistorted ${}^8\mathrm{B}$ shape with combined systematic uncertainties, including both shape and acceptance components. The systematic error bands represent the fraction of the total uncertainty attributable to the given quantity. The highest-energy bin represents the average number of events per 0.5 MeV for the range 13.5–20 MeV.

Figure 26

(Color) (a) Extracted ES $T_{\mathrm{eff}}$ spectrum. Systematic uncertainties have been combined in quadrature and include only the effect of PDF shape change. (b) Extracted ES $T_{\mathrm{eff}}$ spectrum with statistical error bars compared to predictions for an undistorted ${}^8\mathrm{B}$ shape with combined systematic uncertainties, including both shape and acceptance components. The systematic error bands represent the fraction of the total uncertainty attributable to the given quantity. The highest-energy bin represents the average number of events per 0.5 MeV for the range 13.5–20 MeV.

Figure 27

(Color) (a) PDF shape change contributions and (b) total contributions from energy-related systematic energy uncertainties to the extracted CC spectrum assuming an underlying, undistorted ${}^8\mathrm{B}$ shape.

Figure 28

(Color) Distribution of (a) ${\beta }_{14}$, (b) $\cos {\theta }_{\odot }$ and (c) volume-weighted radius ρ. Points with error bars represent data, whereas the MC predictions for CC, ES, NC+internal, and external-source neutron events, all scaled to the energy-unconstrained fit results, are as indicated in the legend. The dark solid lines represent the summed components. The (a) and (b) distributions are for events with $T_{\mathrm{eff}}\ge 5.5$ MeV and $R_{\mathrm{fit}}\le 550$ cm and are averaged assuming an undistorted ${}^8\mathrm{B}$ spectrum. The same energy cut has been applied for (c) but events are shown out to $\rho <1.6$, where $\rho =1.0$ is the edge of the heavy water volume. The dashed vertical line represents the 550-cm fiducial volume cut.

Figure 29

(Color) Flux of $\mu +\tau$ neutrinos versus flux of electron neutrinos. CC, NC, and ES flux measurements are indicated by the filled bands. The total ${}^8\mathrm{B}$ solar neutrino flux predicted by the standard solar model [12] is shown as dashed lines and that measured with the NC channel is shown as the solid band parallel to the model prediction. The narrow band parallel to the SNO ES result correponds to the Super-Kamiokande result in Ref. [8]. The intercepts of these bands with the axes represent the $\pm 1\sigma$ uncertainties. The nonzero value of ${\varphi }_{\mu \tau }$ provides strong evidence for neutrino flavor transformation. The point represents ${\varphi }_e$ from the CC flux and ${\varphi }_{\mu \tau }$ from the NC-CC difference with 68, 95, and 99% C.L. contours included.

Figure 30

(Color) Comparison of phase I (306 days) and phase II (391 days) flux results. For each case the inner error bar represents the statistical uncertainty, whereas the full error bar represents the combined statistical and systematic uncertainty.

Figure 31

(Color) Day-night asymmetries on each CC energy bin as a function of electron energy. Panel (a) shows the case in which no constraint is made on $A_{\mathrm{NC}}$. Panel (b) shows the case in which $A_{\mathrm{NC}}$ is constrained to zero. Uncertainties are statistical only. The horizontal lines in each figure show the expectation for $\Delta m^2=7\times {10}^{-5}$ eV${}^2$ and $\tan {}^2\theta =0.40$.

Figure 32

(Color) Joint probability contours for $A_{\mathrm{NC}}$ versus $A_{\mathrm{CC}}$ (as %), statistical uncertainties only. The points indicate the results when $A_{\mathrm{NC}}$ is allowed to float and when it is constrained to zero.

Figure 33

(Color) (a) Day and night extracted CC energy spectra with statistical uncertainties only. Bin values are expressed in units of equivalent ${}^8\mathrm{B}$ flux, normalized such that the sum of the flux bin values above 5.5 MeV equals the total integral ${}^8\mathrm{B}$ neutrino flux above 0 MeV, as determined for the day and night integral fluxes quoted in Sec. 12d (see Appendix). (b) Differences between night and day spectra. In both figures, the final bin extends to 20 MeV.

Figure 34

(Color) SNO-only neutrino oscillation analysis, including pure ${\text{D}}_2\text{O}$ phase day and night spectra, and salt-extracted CC spectra, NC and ES fluxes, day and night. The ${}^8\mathrm{B}$ flux was free in the fit; hep solar neutrinos were fixed at $9.3\times {10}^3$ cm${}^{-2}$ s${}^{-1}$[9]. The star is plotted at the best-fit parameters from the ${\chi }^2$ analysis, listed in Table 28.

Figure 35

(Color) (a) Global neutrino oscillation analysis using only solar neutrino data and (b) including KamLAND 766-ton-year data. The solar neutrino data included SNO's pure ${\text{D}}_2\text{O}$ phase day and night spectra, SNO's salt phase extracted day and night CC spectra and ES and NC fluxes, the rate measurements from the Cl, SAGE, Gallex/GNO, and SK-I zenith spectra. The ${}^8\mathrm{B}$ flux was free in the fit; hep solar neutrinos were fixed at $9.3\times {10}^3$ cm${}^{-2}$ s${}^{-1}$. The stars are plotted at the best-fit parameters from the ${\chi }^2$ analysis, listed in Table 28.

Figure 36

(Color) Extracted CC $T_{\mathrm{eff}}$ spectrum compared to that predicted with the best-fit LMA parameters. Only statistical uncertainties are shown in the data spectrum. The band on the undistorted ${}^8\mathrm{B}$ model shape represents the 1σ uncertainty determined from detector systematic uncertainties. The predicted spectrum is normalized to the same number of counts as the data spectrum. Note that the data points, especially the first three points, are statistically correlated as well as having correlated systematics as indicated by the error band.