Measurement of the ${\ensuremath{\nu}}_{e}$ and total ${}^{8}$B solar neutrino fluxes with the Sudbury Neutrino Observatory phase-III data set

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Measurement of the $ν_{e}$ and total $^{8}$ B solar neutrino fluxes with the Sudbury Neutrino Observatory phase-III data set

B. Aharmim et al. (SNO Collaboration)

Phys. Rev. C 87, 015502 – Published 18 January 2013

Abstract

This paper details the solar neutrino analysis of the 385.17-day phase-III data set acquired by the Sudbury Neutrino Observatory (SNO). An array of $^{3}$ He proportional counters was installed in the heavy-water target to measure precisely the rate of neutrino-deuteron neutral-current interactions. This technique to determine the total active $^{8}$ B solar neutrino flux was largely independent of the methods employed in previous phases. The total flux of active neutrinos was measured to be $5 . 54_{- 0.31}^{+ 0.33} {(stat.)}_{- 0.34}^{+ 0.36} (syst.) \times 10^{6}$ cm $^{- 2}$ s $^{- 1}$ , consistent with previous measurements and standard solar models. A global analysis of solar and reactor neutrino mixing parameters yielded the best-fit values of $Δ m^{2} = 7 . 59_{- 0.21}^{+ 0.19} \times 10^{- 5} {eV}^{2}$ and $θ = 34 . 4_{- 1.2}^{+ 1.3} degrees$ .

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Received 14 July 2011

DOI:https://doi.org/10.1103/PhysRevC.87.015502

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Vol. 87, Iss. 1 — January 2013

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Figure 1
Side view of the SNO detector in phase III. The center of the AV is the origin of the Cartesian coordinate system used in this paper. The NCD counter strings were arranged on a square grid with 1-m spacing (shown in Fig. 2). Each string was made up of three or four individual 5-cm-diameter counters that were laser welded together. Weld joints are depicted along the length of the strings in this figure. Only the first row of NCD strings from the $y - z$ plane are displayed in this figure.
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Figure 2
The positions of the strings in the NCD array projected onto the plane of the AV equator ( $x - y$ plane). The array was anchored on a square lattice with a 1-m grid constant. The strings labeled with the same letter denote strings of the same length and distance from the center of the AV. Strings I2, I3, I6, and I7 contained $^{4}$ He instead of $^{3}$ He. The outer circle is the AV equator and the inner circle is the neck of the AV, through which the NCD strings were deployed. The NCD string markers are not drawn to scale.
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Figure 3
Energy dependence of fractional signal loss of NCD array data owing to instrumental background cuts, as measured with $^{252}$ Cf and Am-Be neutron calibration data. The abscissa is the event energy recorded by the shaper-ADC system. The neutron signal, as shown in Fig. 22 peaks at the $Q$ value of 764 keV. The fractional signal loss was sub- $1 %$ near the neutron peak.
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Figure 4
An example of NCD string position reconstruction from the data of one of the laserball scans at 500 nm. The contours represent the $68 %$ and $99 %$ CL of the fitted position of NCD string M1. Also shown in this figure is the nominal position of the string. The difference between the fitted position and the nominal position is $\sim$ 2 cm in this case.
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Figure 5
Angular response curves at 386 nm for the PMT-reflector assembly generated by the MC simulation both before and after the optimizations discussed in the text, in comparison to the optical scan in the preparatory phase in October 2003. Note that the $y$ axis zero is suppressed. Details on the design specifications and angular response of the PMT light concentrator can be found in Ref. [20].
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Figure 6
PMT relative angular response at 421 nm.
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Figure 7
(a) D $_{2}$ O and (b) H $_{2}$ O inverse attenuation lengths as a function of time at 421 nm. The lines show the linear fits covering the commissioning and data-taking periods of phase III. In each optical scan, the inverse attenuation length for the two media were fitted simultaneously with other optical parameters, as discussed in the text.
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Figure 8
Difference between data and MC vertex shifts in the three axis directions as a function of source position for scans along the main axes of the detector. Panels (a)–(c) represent the shifts in $x$ , $y$ , and $z$ coordinates, respectively.
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Figure 9
Difference between data and MC fitted vertex width in (a) $x$ , (b) $y$ , and (c) $z$ coordinates as a function of the position of the source ( $z_{src}$ ) for $^{16} N$ runs taken along the $z$ axis of the detector.
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Figure 10
Relative photon-collection efficiency of selected $^{16}$ N calibration runs as a function of time. The dashed line represents $δ_{drift}$ that was scaled to unity on September 27, 2005. The error bars show only the statistical uncertainties. The impact owing to systematic effects is explained in the text, which takes the drift and the difference between the calibrated MC and the $^{16} N$ calibration data into account.
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Figure 11
The mean effective electron kinetic energy of selected central $^{16}$ N calibrations (solid points) and MC simulation (open points).
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Figure 12
Panel (a) shows the mean effective kinetic energy $T_{eff}$ versus volume-weighted radius $ρ$ for the $^{16}$ N source deployed throughout the detector. Panel (b) shows the fractional difference between data and MC [the ratio (data-MC)/data] for the $^{16}$ N source deployed throughout the detector. The dashed line at $ρ = 0.77$ represents the edge of the fiducial volume at 550 cm. Points at the same value of $ρ$ could have different energy response in data or MC because of local point-to-point variation in detector response. The AV neck and the NCD array accentuated the variations at large $ρ$ .
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Figure 13
Temporal variation of the relative gain in (a) the shaper-ADC (top) and (b) MUX channels for string N1. In these plots the gain measured from each monthly extended electronic calibration was normalized to the mean gain. The data shown here extended from the commissioning (prior to run 50 000) to the completion of phase III data taking ( $\sim$ run 67 000).
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Figure 14
Temporal variation of the shaper-ADC channel threshold for string N1. In the threshold calibration, pulses from the pulser were attenuated by 30 dB. The channel threshold was determined by finding the attenuated pulser amplitude at which half of the expected events were observed. The data shown here extended from the commissioning (prior to run 50 000) to the completion of phase-III data taking ( $\sim$ run 67 000).
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Figure 15
The results of the brine source strength measurements in (a) 2005 and (b) 2006. The vertical axis in each frame shows the source strength $A_{^{24} Na}$ (in neutrons per second) in the SNO detector, deduced from the three different sample source strength $A_{samp}$ measurements (horizontal axis), at a reference time [see text and Eq. (15) for details]. This reference time ( $t = 0$ ) was defined as the beginning of the first run when the brine was judged to be well mixed. The error bars show combined statistical and systematic uncertainties. The line through the data points is the result of the best fit, while the band shows the uncertainty of the fit.
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Figure 16
Neutron capture rate in the NCD array as a function of time from the $^{24}$ Na spike in 2005. The vertical axis is in units of neutron events per second, while the horizontal axis is time in units of $^{24}$ Na mean lifetimes (one lifetime $=$ 21.58 h). The exponentially decaying points are the actual measured rate $R (t_{i})$ , while the data with the flat trend [ $R_{i} (0)$ ] is the rate after correcting for the exponential decay factor. The line through the points at time $>$ 0 is the best fit to the data. Time $t = 0$ was 4.53 $^{24}$ Na mean lifetimes after the spike was added.
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Figure 17
Ratio of the brine concentration as observed by reconstructed Cherenkov events in 2006 to that in 2005, as a function of detector coordinates. (a) $R =$ reconstructed radial distance from the center of SNO; (b) $z$ ; (c) $x$ ; and (d) $y$ .
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Figure 18
D $_{2}$ O radioactivity measurements by ex situ assays are shown for $^{222}$ Rn (top), $^{224}$ Ra (middle), and $^{226}$ Ra (bottom). The dashed lines are the bounds for different SNO detector configurations (from periods A to J, as indicated): A, phase-I (unadulterated D $_{2}$ O) commissioning; B, phase-I operation; C, salination; D, phase-II (salt) operation; E, desalination; F, preparation for NCD array installation; G, NCD array deployment; H, NCD array commissioning; I, phase-III (NCD array) operation; and J, removal of the NCD array. Periods highlighted in yellow were times with reduced access to the underground laboratory. For the radon data, color represents different sampling points: red is at the top (near the chimney-sphere interface), purple one-third of the way down and blue at the bottom of the AV. The radon level was well below target for essentially the whole duration of the experiment, except for the high level at the beginning of the experiment, a large calibration spike in phase II, and during the deployment of the NCD array (when the cover gas protection was temporarily turned off). For the radium data, color indicates the technique used: red is for HTiO and blue for MnO $_{x}$ . Radium assays sampled the heavy water either from the top or the bottom of the AV. Again the initial higher concentrations quickly went below target. It should be noted that the data shown in this plot were not the only input to determining the radiopurity of the D $_{2}$ O target.
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Figure 19
Probability distribution functions of (a) $β_{14}$ and (b) the volume-weighted position $ρ = R_{fit} / R_{AV}$ for different background sources in the in situ measurement of D $_{2}$ O and NCD array backgrounds.
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Figure 20
Comparison of pulse shape variables in $^{24}$ Na neutron calibration data (data points) and the NCD array MC (histogram) in the neutron energy window, 0.4 to 1.2 MeV, with statistical uncertainties only. The purpose of these figures is to compare different pulse-shape variables and moments of their distributions between simulation and data. The background rate during this calibration was negligible. (a) Fraction of events as a function of pulse amplitude, (b) time-axis mean of the pulse, (c) $10 %$ – $90 %$ rise time, and (d) full width at half maximum. All distributions are normalized to unit area.
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Figure 21
(a) Fractional first derivatives vs event energy (MeV) for two systematic variations (space charge and $α$ depth) of the simulation. (b) Number of events versus energy in the NCD array data analysis energy window, for data (black, with statistical uncertainties), neutron template from calibration data (purple, dashed), $α$ cocktail template from simulation (cyan), and total predicted number of events (gray, with systematic uncertainties) in the “open” data set (see Sec. 9). (c) Energy spectrum above the NCD array data analysis energy window, for data (black, with statistical uncertainties), alpha “cocktail” (gray, with systematic uncertainties), polonium (red), and bulk (blue dashed) simulation. The “cocktail” is a collection of simulated $α$ pulses with the appropriate mixture of NCD string cathode-surface polonium and bulk uranium and thorium $α$ events.
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Figure 22
One-dimensional projections of PMT array and NCD array data overlaid with best-fit results to signals. Instrumental background contributions from J3 and N4 are combined with the $α$ background in (d). The $χ^{2}$ values for the (a) $ρ$ , (b) $\cos θ_{⊙}$ , (c) $T_{eff}$ , and (d) shaper energy distributions are 7.3, 11.9, 0.3, and 17.0, respectively. Because these are one-dimensional projections in a multidimensional space, these $χ^{2}$ values are quoted as a qualitative demonstration of goodness-of-fit and cannot be simply evaluated.
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Figure 23
A comparison of the measured energy-unconstrained NC flux results in SNO's three phases. The horizontal band is the 1 $σ$ region of the expected total $^{8}$ B solar neutrino flux in the BS05(OP) model [65].
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Figure 24
After SNO-III. SNO-only neutrino oscillation confidence level contours published in Ref. [7]. This analysis includes the summed kinetic energy spectra from phase I (day and night); NC and ES fluxes, and CC kinetic energy spectra from phase II (day and night); and CC, NC, and ES fluxes from phase III. The best-fit point is at $Δ m^{2} = 4.57 \times 10^{- 5}$ eV $^{2}$ , $\tan^{2} θ = 0.447$ , $ϕ_{^{8} B} = 5.12 \times 10^{6}$ cm $^{- 2}$ s $^{- 1}$ . The $h e p$ neutrino flux was fixed at $7.93 \times 10^{3}$ cm $^{- 2}$ s $^{- 1}$ .
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Figure 25
After SNO-III. Neutrino oscillation parameters confidence level contours. (a) Global solar analysis including the rate measurements from Homestake, Gallex/GNO, SAGE, and Borexino; SK-I zenith-energy spectra from [62], summed kinetic energy spectra from SNO-I (day and night); NC and ES fluxes and CC kinetic energy spectra from SNO-II (day and night); and CC, ES, and NC fluxes from SNO-III. The best-fit point was at $Δ m^{2} = 4.90 \times 10^{- 5}$ eV $^{2}$ , $\tan^{2} θ = 0.437$ , $ϕ_{^{8} B} = 5.21 \times 10^{6}$ cm $^{- 2}$ s $^{- 1}$ . The $h e p$ neutrino flux was fixed at $7.93 \times 10^{3}$ cm $^{- 2}$ s $^{- 1}$ . (b) Including KamLAND data from [71], the best-fit point was at $Δ m^{2} = 7.59 \times 10^{- 5}$ eV $^{2}$ , $\tan^{2} θ = 0.468$ , $ϕ_{^{8} B} = 4.92 \times 10^{6}$ cm $^{- 2}$ s $^{- 1}$ .
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Figure 26
Examples of neutron signal and instrumental background pulses in the NCD array data. (a) A fork event, in which a small third reflection is seen in the tail of the pulse; (b) a flat trace. (c) an oscillatory pulse. (d) a neutron event.
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Physical Review C

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Measurement of the $ν_{e}$ and total $^{8}$ B solar neutrino fluxes with the Sudbury Neutrino Observatory phase-III data set

B. Aharmim et al. (SNO Collaboration)

Phys. Rev. C 87, 015502 – Published 18 January 2013

Abstract

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Physical Review C

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Measurement of the νe and total 8B solar neutrino fluxes with the Sudbury Neutrino Observatory phase-III data set

B. Aharmim et al. (SNO Collaboration)

Phys. Rev. C 87, 015502 – Published 18 January 2013

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Measurement of the $ν_{e}$ and total $^{8}$ B solar neutrino fluxes with the Sudbury Neutrino Observatory phase-III data set