Solar neutrino measurements in Super-Kamiokande-I

J. Hosaka et al. (Super-Kamiokande Collaboration)

Phys. Rev. D 73, 112001 – Published 1 June 2006

Abstract

The details of Super-Kamiokande-I’s solar neutrino analysis are given. Solar neutrino measurement in Super-Kamiokande is a high statistics collection of ${}^{8}B$ solar neutrinos via neutrino-electron scattering. The analysis method and results of the 1496 day data sample are presented. The final oscillation results for the data are presented also.

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Received 30 August 2005

DOI:https://doi.org/10.1103/PhysRevD.73.112001

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Vol. 73, Iss. 11 — 1 June 2006

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Figure 1
Coordinates of the Super-Kamiokande detector. The $Z$ axis is defined as the upward direction, pointing away from the center of the earth.
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Figure 2
(a) The average dark noise rate of the PMT’s used in SK-I. The dashed lines show the acceptable range for use in the solar neutrino analysis. (b) Number of dead PMT’s in SK-I. Note that sometimes repairs were possible, usually involving the replacement of broken high voltage supplies, leading to sudden drops in the number of dead PMT’s.
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Figure 3
Trigger efficiency as a function of energy. The left plot shows the efficiency as a function of reconstructed energy (see Sec. 4c for the details of reconstructed energy). The May 1997 LE triggers (black circles with black line) and SLE triggers (white circles with red line) were calculated using a $Ni (n, γ) Ni$ gamma source, while the SLE triggers on September 1999 (triangles with green line) and September 2000 (stars with blue line) were calculated using ${}^{16}N$ events from a DT generator. The right plot shows the efficiency as a function of true electron total energy obtained by a Monte Carlo simulation. Identically colored lines represent the same calibration data samples in both plots.
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Figure 4
(a) Input distributions of ${}^{8}B$ (solid line) and hep (dashed line) solar neutrino energies. (b) The cross section of the interaction for $ν_{e}$ (solid line) and $ν_{μ, τ}$ (dashed line) with electrons as a function of neutrino energy. (c) The spectrum of recoil electrons scattered by ${}^{8}B$ and hep solar neutrinos.
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Figure 5
Wavelength dependence of the water parameter coefficients: absorption (solid line), Rayleigh scattering (dashed line) and Mie scattering (dotted line). The absorption coefficient is also a function of water transparency. The filled region shows the range of this parameter as water transparency is changed, where the two solid lines define the SK-I minimum (73 m) and maximum (98 m) values.
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Figure 6
Translation of the water transparency parameter into a short wavelength absorption coefficient. Absorption is taken to be proportional to $λ^{- 4}$ for these wavelengths. Light scattering is assumed to be constant. The lower panel shows the energy deviation as a function of input momentum. The inner error bar of each point is the statistical uncertainty, while the outer error bar represents the spread of the six samples using 5, 6, 8, 10, 12, and $15 MeV / c$ as the input momenta.
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Figure 7
Search grid for the vertex reconstruction in the $x y$ plane (left figure) and in $z$ (right figure). The shaded area is the SK inner detector volume. The dashed line indicates the fiducial volume. The white stars (left) and white lines (right) are the grid points used by the standard vertex reconstruction. The circles in the $x y$ plane are the points used by the second vertex reconstruction.
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Figure 8
Timing constraint for pairs of hits. From the triangle relation $c t_{i} + Δ x > c t_{j} = c t_{i} + Δ c t_{i j}$ follows $Δ t_{i j} < Δ x / c = | {\vec{h}}_{i} - {\vec{h}}_{j} | / c$ .
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Figure 9
Search grid for the fast fit. 18 points around the input vertex are tested, the orientation is fixed. The grid size is adjusted between 1 and 8 m (see Table 2).
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Figure 10
Distance from reconstructed to correct vertex for ${}^{8}B$ Monte Carlo events with total recoil electron energy above 4.5 MeV. The inserted panel magnifies the distributions near zero on a linear scale.
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Figure 11
Vertex resolution (68.2% of reconstructed events reconstruct inside a sphere of radius $σ$ from correct vertex) of ${}^{8}B$ Monte Carlo events as a function of total recoil electron energy. The curves on the right-hand side show the fraction of reconstructed events as a function of total recoil electron energy.
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Figure 12
The distribution of the opening angle between the direction of the generated particle and the vector from the reconstructed vertex to the hit PMT position. This plot is made for 10 MeV electron MC events.
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Figure 13
The directional resolution’s dependence on energy, determined using Monte Carlo events.
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Figure 14
Function of the effective photo coverage’s dependence on the incident angle to a PMT.
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Figure 15
The energy resolution’s dependence on energy as determined using Monte Carlo events.
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Figure 16
Performance of the muon fitter. Left (right) figure shows the vertex (angular) correlation between generated and reconstructed Monte Carlo muon tracks. The area to the left of the dashed line in both plots shows the $1 - σ$ ( $= 68 %$ ) included region.
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Figure 17
(a) Time variation of the measured water transparency during SK-I. (b) Stability of the SK-I energy scale as a function of time. Each point represents the mean $N_{eff}$ value for 28 days of $μ_{e}$ decay events. The solid line represents the average $N_{eff}$ for all $μ_{e}$ decay events in SK-I; the dashed and dotted lines represent, respectively, $\pm 0.5 %$ and $\pm 1.0 %$ deviations from the average.
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Figure 18
The LINAC system at SK. The dotted line represents the fiducial volume of the detector and the letters (A to H) indicate the positions where LINAC data were taken.
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Figure 19
The relative difference between the reconstructed energy of LINAC data and the corresponding MC. (a) The results are shown for all positions and beam momenta. (b) Averaged over all positions. The dashed lines show $\pm 0.5 %$ . See Fig. 18 for the positions.
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Figure 20
The reconstructed energy resolution from LINAC data and MC. (a) shows the deviation of the resolution in each energy and position in LINAC calibration between data and MC; (b) averaged over all positions. The dashed lines show $\pm 2.5 %$ . See Fig. 18 for the positions.
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Figure 21
The deviation between data and MC for the volume-averaged DT energy scale as a function of time. The DT generator was available for the last two years of SK-I, starting in July, 1999. The dashed line shows the $\pm 0.64 %$ of energy scale uncertainty, which is estimated by LINAC calibration as discussed in Sec. 5b1.
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Figure 22
Directional dependence of energy scale by DT calibration. Upper figure shows $R_{down} - R$ as a function of time, lower figure shows the same for $R_{up} - R$ . Note that $R_{up} \approx - R_{down}$ .
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Figure 23
The differences of vertex resolution between data and MC in LINAC. The dashed lines show $\pm 5 cm$ . (a) The deviation of the resolution in each position as a function of energy. The LINAC position symbols in this plot are defined in Fig. 18. (b) All the data are averaged over all positions.
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Figure 24
The reconstructed angular resolution from LINAC data and MC. (a) shows the deviation of the resolution in each energy and position in LINAC calibration between data and MC. (b) is averaged over all positions. The dashed lines show $\pm 0.5 \deg$ . See Fig. 18 for the positions.
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Figure 25
Typical vertex distribution of the low energy events before the Intelligent Trigger selection. The analysis energy threshold for this plot is 5.0 MeV. The dashed line shows the fiducial volume edge.
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Figure 26
The relation between max charge and the number of hit PMT’s in a $5 \times 5$ patch surrounding the PMT with the maximum charge. At most 24 tubes in this patch (plus the one at the center) can be activated. The upper plot shows a typical distribution including active flasher events, and the lower plot shows a typical good data set. The cut region is the area above the line in the upper figure.
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Figure 27
$Δ L$ distribution for each $Q_{res}$ ranges, (1) $Q_{res} < 2.4 \times 10^{4} p . e .$ , (2) $2.4 \times 10^{4} < Q_{res} < 4.8 \times 10^{4} p . e .$ , (3) $4.8 \times 10^{4} < Q_{res} < 9.7 \times 10^{4} p . e .$ , (4) $9.7 \times 10^{4} < Q_{res} < 4.8 \times 10^{5} p . e .$ , (5) $4.8 \times 10^{5} < Q_{res} < 9.7 \times 10^{5} p . e .$ , (6) $9.7 \times 10^{5} p . e . < Q_{res}$ . The solid line shows the data, and the dashed line shows the random sample.
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Figure 28
$Δ T$ distribution for each time range, (1) $0.0 < Δ T < 0.1 \sec$ , (2) $0.1 < Δ T < 0.8 \sec$ , (3) $0.8 < Δ T < 4.0 \sec$ , (4) $4.0 < Δ T < 15 \sec$ , (5) $15 < Δ T < 100 \sec$ , (6) $0 < Δ T < 100 \sec$ . Cross marks are data and lines are fitted likelihood function $L_{spa}^{Δ T} (Δ T)$ .
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Figure 29
(a) $Q_{res}$ distribution for the spallation candidate events (solid line) and the noncandidate events (dashed line). (b) Cross marks show the result of subtracting dashed from solid line in (a), and dotted line shows the likelihood function $L_{spa}^{Q_{res}} (Q_{res})$ .
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Figure 30
The maximum likelihood value distribution for success [left figure, defined in Eq. (7.1)] and failure [right figure, defined in Eq. (7.2)] of muon track reconstruction. (See Sec. 4d for details.) The unshaded histogram shows all data while the hatched histogram shows the so-called random sample, in which the data is shuffled in time and position.
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Figure 31
Position dependence of the spallation cut’s dead time. The horizontal axis shows the distance from the barrel (left), and the minimum distance from the top or bottom (right).
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Figure 32
$R_{grid}$ distribution for data (solid line) and MC (dashed line). The normalization is done by scaling to the first bin. The dotted line shows the reduction criterion.
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Figure 33
The likelihood value distribution defined in Eq. (7.4) for data (solid line) and MC (dashed line). The dotted line shows the reduction criteria. Events with a likelihood of less than $- 1.85$ are rejected.
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Figure 34
The distance from the wall distribution using the second vertex reconstruction for data (solid line) and MC (dashed line). The normalization of MC is done by the total number of events. The dotted line shows the reduction criteria.
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Figure 35
Effective distance ( $d_{eff}$ ) of $E \geq 6.5 MeV$ (left) and $5.0 MeV \leq E < 6.5 MeV$ (right). Blank histogram shows data and hatched area shows solar neutrino MC.
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Figure 36
Vertex distribution before (blank) and after (hatched) applying the gamma ray cut. The left plots are $R^{2}$ for $| Z | < 1000 cm$ , and the right ones are $Z$ for $| R | < 1000 cm$ . The upper plots show $E \geq 6.5 MeV$ , and lower ones show $5.0 MeV \leq E < 6.5 MeV$ .
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Figure 37
Directional distribution (x, y, z) before (blank) and after (hatched) applying the gamma ray cut. The upper plots show $E \geq 6.5 MeV$ , and the lower plots show $5.0 MeV \leq E < 6.5 MeV$ .
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Figure 38
Summary of the reduction efficiencies on MC.
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Figure 39
Summary of the data reduction steps.
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Figure 40
Angular distribution of solar neutrino event candidates. The shaded area indicates the elastic scattering peak. The dotted area is the contribution from background events.
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Figure 41
The solar zenith angle dependence of the solar neutrino flux (error bars show statistical error). The width of the night time bins was chosen to separate solar neutrinos that pass through the Earth’s dense core (the rightmost Night bin) from those that pass through the mantle. The horizontal line shows the flux for all data.
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Figure 42
Solar neutrino flux as a function of time. The binning of the horizontal axis is 1.5 months. The curve shows the expected flux time variance. The wavy shape comes from the eccentricity in the Earth’s orbit around the Sun.
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Figure 43
The seasonal variation of the solar neutrino flux. The solid line is the prediction based on the eccentricity of the Earth’s orbit.
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Figure 44
Energy spectrum of the solar neutrino signal. The horizontal axis is the total energy of the recoil electrons. The vertical axis is the event rate of the observed solar neutrino signal events. The error bars are a quadrature of the statistical and uncorrelated errors. The reduction efficiencies in Fig. 38 are corrected. BP2004 SSM flux values are used for the ${}^{8}B$ and hep MC fluxes in this plot. The dashed line shows the contribution of only ${}^{8}B$ .
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Figure 45
Integral energy distributions for the hep solar neutrino analysis. The horizontal axis is the energy threshold of the recoil electrons. The integration is up to 21.0 MeV. Upper plot: the vertical axis is the expected number of events in SK-I’s 1496 day final data sample after all cuts. The solid and dashed lines correspond to the hep solar neutrino only and the ${}^{8}B + hep$ 90% C.L. upper limit. Lower plot: the ratio of the two histograms in the upper plot (dashed line/solid line).
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Figure 46
Energy spectrum of recoil electrons in the high energy region. The points show data with statistical error bars. The curves show expected spectra with various hep contributions to the best-fit ${}^{8}B$ spectrum. The unit of the fluxes for the curves are $/ {cm}^{2} / s$ . The dotted and dashed curves show the spectrum with 73 and 0 ( $\times 10^{3} / {cm}^{2} / s$ ) hep fluxes, respectively.
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Figure 47
The Sun’s electron density profile from the standard solar model [7] (SSM) as a function of the distance to the center (top panel), and Earth’s mass density profile (bottom panels). The left plot shows the density as a function of the distance to the Earth’s center. The right plot shows the minimum (dashed horizontal line), average (solid line), and maximum density (dashed line) a solar neutrino of zenith angle $θ_{z}$ encounters on its path through the Earth. The electron density is obtained from this by multiplying by $0.497 mol / {cm}^{3}$ for the mantle and $0.468 mol / {cm}^{3}$ for the core.
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Figure 48
Survival probability for ${}^{8}B$ solar neutrinos. The top plot displays contours of equal probability as a function of $Δ m^{2} / E$ and ${tan }^{2} θ$ . The middle panel shows the same probability as a function of $Δ E / m^{2}$ only where a particular (small) mixing angle has been selected. The shaded area contrasts the difference between neutrinos passing through the core of the Earth (which has the highest matter density) with neutrinos arriving directly from the Sun. The bottom panel shows a large mixing case. The line above the shaded area depicts the average probability for neutrinos passing through the Earth. Superimposed on these two lower panels are the locations of three neutrino branches ( $p p$ -dotted, ${}^{7}{Be}$ -dashed, and ${}^{8}B$ -solid) for the SMA, LMA, LOW, VAC, and quasi-VAC solutions.
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Figure 49
Expected SK day/night asymmetry (left) and spectral distortion (right) in the MSW region. The scale of the contours of equal asymmetry (distortion) is logarithmic. The spectral distortion is measured in terms of a $χ^{2}$ using the SK spectrum uncertainties (but not the values of the SK spectrum). The gray shaded areas correspond to the LMA, SMA, and LOW solutions.
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Figure 50
Expected SK summer/winter asymmetry (left) and spectral distortion (right) in the vacuum oscillation region. The scale of the contours of equal asymmetry (distortion) is logarithmic. The spectral distortion is measured in terms of a $χ^{2}$ using the SK spectrum uncertainties (but not the values of the SK spectrum). The gray shaded areas correspond to the VAC solutions.
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Figure 51
Distortion of the recoil electron spectrum using 21 (upper panel) and 8 (lower panel) bins. The measured event rates in each bin are divided by the event rates expected from MC assuming a ${}^{8}B$ $ν$ flux of $5.076 \times 10^{6} / {cm}^{2} s$ and a hep $ν$ flux of $32 \times 10^{3} / {cm}^{2} s$ . Overlaid is a typical LMA solution (red) and a LOW solution (green), where the assumed neutrino fluxes were fit to best describe the data.
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Figure 52
Dependence of data/MC on solar zenith angle. The MC assumes a ${}^{8}B$ $ν$ flux of $5.076 \times 10^{6} / {cm}^{2} s$ and a hep $ν$ flux of $32 \times 10^{6} / {cm}^{2} s$ . The six panels correspond to the energy ranges 5.5–6.5 MeV, 6.5–8.0 MeV, 8.0–9.5 MeV, 9.5–11.5 MeV, 11.5–13.5 MeV, and 13.5–16.0 MeV. Overlaid is a typical LMA solution (red) and a LOW solution (green), where the assumed neutrino fluxes were fit to best describe the data.
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Figure 53
Predicted solar zenith angle variation assuming a typical LMA solution, $Δ m^{2} = 6.3 \times 10^{- 5} {eV}^{2}$ and ${tan }^{2} θ = 0.52$ (which is the best fit to the SK energy spectrum, rate, and day/night variation).
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Figure 54
Left: excluded regions from the SK spectrum (red), SK rate time variations (green), and both combined (solid line) at 95% C.L. Right: excluded regions from the SK zenith spectrum (green) compared to the SK spectrum combined with the time-variation likelihood (red) at 95% C.L.
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Figure 55
Allowed areas from the rate-constrained SK unbinned time-variation analysis (left) and the SK zenith spectrum (right) at 95% C.L. The graphs at the top (and right) show the $χ^{2}$ difference as a function of ${tan }^{2} θ$ ( $Δ m^{2}$ ) alone where the $Δ m^{2}$ ( ${tan }^{2} θ$ ) is chosen to minimize $χ^{2}$ . The lines inside the contours show which $Δ m^{2}$ ( ${tan }^{2} θ$ ) is chosen.
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Figure 56
(a) Allowed area at 95% C.L. from the combination of SK and SNO. Overlaid is the area allowed by KamLAND data. The graphs at the top (right) show the $χ^{2}$ difference as a function of only ${tan }^{2} θ$ ( $Δ m^{2}$ ); the solid line is the SK/SNO fit, the dotted line is based on KamLAND [20] data. (b) Allowed area at 95% C.L. from the combination of SK/SNO (gray) and all solar data (dark gray) with KamLAND results. The lines inside the contours show the best-fit $Δ m^{2}$ ( ${tan }^{2} θ$ ) given a particular ${tan }^{2} θ$ ( $Δ m^{2}$ ). Note the linear scale on both axes. Only LMA-I remains allowed.
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Figure 57
Day/Night amplitude fit depending on $Δ m^{2}$ . The fit depends only very weakly on the mixing angle which is assumed to be ${tan }^{2} θ = 0.44$ . Overlaid (red line) is the expected amplitude and (blue lines) the $2 σ$ boundaries of the amplitude fit.
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Physical Review D

covering particles, fields, gravitation, and cosmology

Solar neutrino measurements in Super-Kamiokande-I

J. Hosaka et al. (Super-Kamiokande Collaboration)

Phys. Rev. D 73, 112001 – Published 1 June 2006

Abstract

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Physical Review D

covering particles, fields, gravitation, and cosmology

Solar neutrino measurements in Super-Kamiokande-I

J. Hosaka et al. (Super-Kamiokande Collaboration)

Phys. Rev. D 73, 112001 – Published 1 June 2006

Abstract

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