Solar neutrino results in Super-Kamiokande-III

The results of the third phase of the Super-Kamiokande solar neutrino measurement are presented and compared to the first and second phase results. With improved detector calibrations, a full detector simulation, and improved analysis methods, the systematic uncertainty on the total neutrino flux is estimated to be $\pm 2.1\%$, which is about two thirds of the systematic uncertainty for the first phase of Super-Kamiokande. The observed ${}^8\mathrm{B}$ solar flux in the 5.0 to 20 MeV total electron energy region is $2.32\pm 0.04(\mathrm{stat})\pm 0.05(\mathrm{sys})\times {10}^6{\mathrm{cm}}^{-2}{\sec }^{-1}$ under the assumption of pure electron-flavor content, in agreement with previous measurements. A combined oscillation analysis is carried out using SK-I, II, and III data, and the results are also combined with the results of other solar neutrino experiments. The best-fit oscillation parameters are obtained to be ${sin}^2{\theta }_{12}={0.30}_{-0.01}^{+0.02}({tan}^2{\theta }_{12}={0.42}_{-0.02}^{+0.04})$ and $\Delta m_{21}^2={6.2}_{-1.9}^{+1.1}\times {10}^{-5}{\mathrm{eV}}^2$. Combined with KamLAND results, the best-fit oscillation parameters are found to be ${sin}^2{\theta }_{12}=0.31\pm 0.01({tan}^2{\theta }_{12}=0.44\pm 0.03)$ and $\Delta m_{21}^2=7.6\pm 0.2\times {10}^{-5}{\mathrm{eV}}^2$. The ${}^8\mathrm{B}$ neutrino flux obtained from global solar neutrino experiments is $5.3\pm 0.2(\mathrm{stat}+\mathrm{sys})\times {10}^6{\mathrm{cm}}^{-2}{\mathrm{s}}^{-1}$, while the ${}^8\mathrm{B}$ flux becomes $5.1\pm 0.1(\mathrm{stat}+\mathrm{sys})\times {10}^6{\mathrm{cm}}^{-2}{\mathrm{s}}^{-1}$ by adding KamLAND results. In a three-flavor analysis combining all solar neutrino experiments, the upper limit of ${sin}^2{\theta }_{13}$ is 0.060 at 95% C.L.. After combination with KamLAND results, the upper limit of ${sin}^2{\theta }_{13}$ is found to be 0.059 at 95% C.L.

Figure 1

Solid line shows the vertex resolution for SK-III as a function of the true total electron energy, while the dashed line shows that of SK-I.

Figure 2

Vertex shift of Ni calibration events. The origin of the arrows shows the true Ni source position and the direction indicates the averaged reconstructed position direction. The length of the arrow indicates the magnitude of the vertex shift. All vertex shifts are scaled by a factor of 20 to make them easier to see.

Figure 3

Definition of detector coordinate system.

Figure 4

Likelihood value for reconstruction of event direction as a function of the reconstructed total electron energy and opening angle between the reconstructed direction and the direction from vertex to each hit PMT.

Figure 5

The solid line shows the angular resolution of SK-III as a function of the true total electron energy, while the dashed line shows that of SK-I.

Figure 6

Relation between $N_{\mathrm{eff}}$ and the true total electron energy (MeV) obtained from MC simulation. The dotted line in the upper figure shows the fitted polynomial function. The lower figure shows the deviation of the reconstructed energy from the polynomial function.

Figure 7

Energy resolution function obtained by electron MC simulation. Black points show 1 standard deviation for a Gaussian fit of the MC simulation divided by the true total electron energy, while the red (dashed) line shows a fit to a polynomial function. The black (dotted) line shows SK-I energy resolution.

Figure 8

The $z$ dependence of the energy scale measured by LINAC calibration. The marker shows an average of (MC-DATA)/DATA over four energies at each data-taking point. The error bars show the root mean square of (MC-DATA)/DATA for four energies. The filled circle markers are for $R=4\mathrm{m}$ ($x=-4\mathrm{m}$, $y=0\mathrm{m}$) and the square markers are for $r=12\mathrm{m}$ ($x=-12\mathrm{m}$, $y=0\mathrm{m}$). The open circle markers show the $z$ dependence obtained by DT calibration. The dashed and dotted lines show $\pm 1$ and 0.5%, respectively. The edge of the fiducial volume is the same as the edge of the plot window (from $-1610\mathrm{cm}$ to 1610 cm).

Figure 9

The $\varphi$ dependence of the energy scale measured by DT calibration. The marker shows (MC-DATA)/DATA for each point and the error bars show statistical uncertainty. The circle, square, and triangle markers are for $z=+12\mathrm{m}$, 0 m, and $-12\mathrm{m}$, respectively. Zaverage is the average difference of energy scale between MC simulation and DT data obtained at the same $z$-position. The dashed and dotted lines show $\pm 1$ and 0.5%, respectively.

Figure 10

Energy scale difference between LINAC direction and other direction measured by DT calibration (LINAC direction range includes 76% of 7 MeV electrons). The solid and dotted lines show $\pm 1$ and 0.5%, respectively.

Figure 11

Energy resolution difference between MC simulation and data as a function of energy, obtained by LINAC calibration.

Figure 12

Trigger efficiency as a function of energy. Markers are ${}^{16}\mathrm{N}$ calibration data and the solid histogram is MC simulation. The vertical dashed line shows the analysis threshold, 5.0 MeV.

Figure 13

Wavelength dependence of the water coefficients: scattering and absorption combined (black, solid line), absorption (red, dashed line), Rayleigh scattering (green, dotted line) and Mie scattering (blue, dashed-dotted line). The absorption coefficient is a function of water transparency and the water transparency in this graph is 139 m.

Figure 14

The upper figure shows the time variation of the measured water transparency (weighted by the Cherenkov spectrum) during SK-III. The lower figure shows the stability of the peak energy of decay electrons in SK-III as a function of time.

Figure 15

Hit-rate difference, (MC-DATA)/DATA, for barrel (upper), top (left lower), and bottom (right lower). Black (dashed line) shows $\beta =0$. Red (solid line) shows the hit-rate difference with tuned $\beta$. This calibration data was taken in February 2008, the same period as the LINAC calibration.

Figure 16

Timing distribution of each hit PMT after tuning the MC simulation, for LINAC 5.1 MeV $(x,z)=(-4\mathrm{m},0\mathrm{m})$ data. The blue histogram with open circles shows data and the red dashed histogram shows MC simulation.

Figure 17

Distribution of cut variable for the small clustered hit cut. Blue (filled circle) shows background sample events which are selected from $r>12\mathrm{m}$ and $z>-3\mathrm{m}$. Red (open circle) shows the solar neutrino MC simulation and the same volume cut is applied. For both data and MC events, event selection cuts up to the external event cut are applied. The reconstructed energies of these samples are in 5.0–6.5 MeV.

Figure 18

Vertex distribution of 5.0–6.5 MeV energy region before and after the small cluster hits cut. The horizontal axis shows $r^2$ and the vertical axis shows the number of events. Events with $z>-7\mathrm{m}$ are selected to show background events in the barrel.

Figure 19

Vertex distribution of final data sample in the 5.0–6.5 MeV energy region (22.5 kton fiducial volume).

Figure 20

Number of events after each event reduction step as a function of energy. From the top, the markers show events after spallation cut, event quality cut, external event cut, ${}^{16}\mathrm{N}$ cut, and small clustered hit cut plus tight fiducial volume cut. The dashed histogram shows the number of events in the SK-I final sample.

Figure 21

Reduction efficiency for the solar neutrino MC simulation. The definition of each histogram is the same as for Fig. 20.

Figure 22

The vertex shift as a function of energy. The markers show the amount of vertex shift measured by Ni calibration at $x=15.2\mathrm{m}$ $y=-0.7\mathrm{m}$ and $z=12\mathrm{m}$. For the vertical axis, negative values mean vertex shifts inward towards the center of the detector.

Figure 23

The systematic uncertainty of the fiducial volume as a function of energy.

Figure 24

The difference of vertex resolution between MC simulation and data as a function of energy obtained by LINAC calibration. The dashed line and the dotted line show 1 cm and 2 cm difference, respectively.

Figure 25

Energy-correlated systematic uncertainties. The solid, dotted, and dashed lines show the uncertainties of the ${}^8\mathrm{B}$ spectrum, the energy scale, and the energy resolution, respectively.

Figure 26

The angular distribution of the solar neutrino final sample events. The dotted line seen under the peak in the solar direction represents background contributions.

Figure 27

Ratio of observed and expected energy spectra. The dashed line represents the SK-III average.

Figure 28

95% C.L. allowed region from SK-I, II, III combined analysis. The ${}^8\mathrm{B}$ flux is constrained by the SNO NC rate (LETA and phase-III).

Figure 29

Allowed region for all solar experiments at 95% C.L..

Figure 30

Allowed region for all solar experiments and KamLAND for two-flavor analysis at 95% C.L..

Figure 31

Allowed region for all solar experiments for two-flavor analysis at 95% C.L.. The light green contour and the yellow star show the result without SK-III, and the light blue contour and the black star show the result with SK-III, which is same as Fig. 29.

Figure 32

Allowed region in solar parameter space $({\theta }_{12},\Delta m^2)$ obtained by the three-flavor analysis. The thick lines and the star mark show the allowed regions and the best-fit point of the global solar analysis. The thin lines and the square mark show the allowed regions and the best-fit point of our KamLAND analysis. The filled areas and the filled circle mark show the allowed regions and the best-fit point of the combined analysis. For all regions, the innermost area (red), the middle area (green) and the outermost area (blue) show 68.3, 95, 99.7% C.L., respectively.

Figure 33

Allowed region in $({\theta }_{12},{\theta }_{13})$ space obtained by the three-flavor analysis. The definitions of marks and lines are same as in Fig.c 32.