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Solar 8B and hep Neutrino Measurements from 1258 Days of Super-Kamiokande Data

Solar neutrino measurements from 1258 days of data from the Super-Kamiokande detector are presented. The measurements are based on recoil electrons in the energy range 5.0-20.0MeV. The measured solar neutrino flux is 2.32 +- 0.03(stat.) +0.08-0.07(sys.)*10^6cm^{-2}s^{-1}, which is 45.1+-0.5(stat.)+1.6-1.4(sys.)% of that predicted by the BP2000 SSM. The day vs night flux asymmetry is 0.033+-0.022(stat.)+0.013-0.012(sys.). The recoil electron energy spectrum is consistent with no spectral distortion (\chi^2/d.o.f. = 19.0/18). The seasonal variation of the flux is consistent with that expected from the eccentricity of the Earth's orbit (\chi^2/d.o.f. = 3.7/7). For the hep neutrino flux, we set a 90% C.L. upper limit of 40 *10^3cm^{-2}s^{-1}, which is 4.3 times the BP2000 SSM prediction.

Solar neutrino measurements from 1258 days of data from the Super-Kamiokande detector are presented [? ]. The measurements are based on recoil electrons in the energy range 5.0-20.0 MeV. The measured solar neutrino flux is 2.32 ± 0.03 (stat.) +0.08 −0.07 (sys.) ×10 6 cm −2 s −1 , which is 45.1 ± 0.5 (stat.) +1. 6 −1.4 (sys.)% of that predicted by the BP2000 SSM. The day vs night flux asymmetry (Φn − Φ d )/Φaverage is 0.033 ± 0.022 (stat.) +0.013 −0.012 (sys.). The recoil electron energy spectrum is consistent with no spectral distortion (χ 2 /d.o.f. = 19.0/18). The seasonal variation of the flux is consistent with that expected from the eccentricity of the Earth's orbit (χ 2 /d.o.f. = 3.7/7). For the hep neutrino flux, we set a 90% C.L. upper limit of 40 × 10 3 cm −2 s −1 , which is 4.3 times the BP2000 SSM prediction. Solar neutrinos have been detected using chlorine-, gallium-, and water-based detectors [1,2,3,4,5]; all have measured significantly lower solar neutrino flux than predicted by Standard Solar Models (SSMs) [6,7,8]. This disagreement between the measured and expected solar neutrino flux, known as the "solar neutrino problem", is generally believed to be due to neutrino flavor oscillations. Signatures of neutrino oscillations in Super-Kamiokande (SK) might include distortion of the recoil electron energy (E recoil ) spectrum, difference between the night-time solar neutrino flux relative to the day-time flux, or a seasonal variation in the neutrino flux. Observation of these effects would be strong evidence in support of solar neutrino oscillations independent of absolute flux calculations. Conversely, non-observation would constrain oscillation solutions to the solar neutrino problem. We describe here solar neutrino measurements from 1258 days of SK data.
SK, located at Kamioka Observatory, Institute for Cosmic Ray Research, University of Tokyo, is a 22.5 kton fiducial volume water Cherenkov detector that detects solar neutrinos via the elastic scattering of neutrinos off atomic electrons. The scattered recoil electron is detected via Cherenkov light production, allowing both the direction and total energy to be measured. These quantities are related to the original neutrino direction and energy. Detailed descriptions of SK can be found elsewhere [5,9,10,11].
The 1258-day solar neutrino data were collected in four periods with different trigger thresholds between May 31, 1996 and October 6, 2000 (table I). The analysis threshold has been at 5.0 MeV except for the first 280 days where the data were analyzed with a threshold of 6.5 MeV. The analysis threshold is determined by the level of irreducible background events and the event trigger threshold. An event is triggered when the sum of PMTs registering a hit in a 200 nsec time window (N hit ) is above a threshold (table I). This threshold should be sufficiently low that the trigger efficiency at the analysis threshold is nearly 100%. The lowering of the trigger threshold in periods 2-4 was made possible by the addition of a software filter to the data acquisition system that removes a large portion of background events. This removal is accomplished by reconstructing the event vertex and rejecting events with vertices within 2 m of the inner detector wall, most of which are due to external radioactivity. Each lowering of the trigger threshold in the course of the experiment was made possible by increasing the number of computers that run the filter program.
There are 2.0×10 9 events in the raw data sample before background reduction. After removing cosmic ray muon events, the sample in the 22.5 kton fiducial volume with numerical values that were omitted from the PRL draft.  The dominant background sources in the low-energy region (E < ∼ 6.5 MeV) are 222 Rn in the water and external radioactivity; in the high-energy region (E > ∼ 6.5 MeV), radioactive decay of muon-induced spallation products accounts for most of the background. Background reduction takes place in the following steps: first reduction, spallation cut, second reduction, and external gammaray cut. The first reduction includes cuts that remove events due to electronic noise and arcing PMTs. In addition, a cut on the goodness of the reconstructed vertex is used to remove obvious background events originating from various non-physical sources. The number of remaining events after the first reduction is 1.5 × 10 7 . The spallation cut has been improved compared to that used in earlier publications [5,10,11]. We have improved the likelihood functions used in removing spallation events and introduce a new cut for 16 N events that originate from absorption of cosmic ray stopped µ − on 16 O. The number of events in the high-energy region (6.5-20 MeV) before and after spallation cut is 1.6 × 10 6 and 3.3 × 10 5 , respectively. The spallation cut is 79% efficient for solar neutrino events. The second reduction removes events with poor vertex fit quality or with blurred Cherenkov ring patterns, characteristics of low-energy background events and external gamma rays. This newly introduced reduction step has improved the signal-to-noise ratio in the low-energy region by almost an order of magnitude. The number of events before and after the second reduction in the 5.0-6.5 MeV region are 1.0 × 10 7 and 1.4 × 10 6 events, respectively. In addition, the gamma-ray cut, which removes external events, has been tightened for those events with E < 6.5 MeV. The combined efficiency of the first reduction, second reduction, and the external gamma ray cut for solar neutrino events is ∼ 73% for E ≥ 6.5 MeV, and ∼ 52% for E < 6.5 MeV. After these reduction steps, 236,140 events remain in the fiducial volume above 5 MeV, with S/N ≈ 1 in the solar direction.
The SK detector simulation is based on GEANT 3.21 [12]. The energy scale was measured using a larger sample of data from an in situ electron linear accelerator [9] (LINAC) compared to that used in earlier results.
The detector simulation's reliability was tested using the well-known β decay of 16 N, which is produced in situ by an (n, p) reaction on 16 O. Fast neutrons for this reaction are produced using a portable deuterium-tritium neutron generator (DTG) [13]. The energy scale measured by the DTG agrees with that from the LINAC within ±0.3%. The total systematic uncertainty in the absolute energy scale, including possible long term variation and direction dependence, is ±0.6%.
We compare our solar neutrino measurements against reference fluxes and neutrino spectra in order to search for signatures of neutrino oscillations. For E recoil ≥ 5.0 MeV, solar neutrinos are expected to come almost exclusively from the β decay of 8 B, with a slight admixture of neutrinos from 3 He-proton (hep) fusion. For the absolute flux of 8 B and hep neutrinos, we take the BP2000 [6] SSM as our reference. The β decay spectrum of the 8 B neutrinos is dominated by the transition to a broad excited state of 8 Be, which decays immediately to two α particles. Bahcall et al. [14] use a neutrino spectrum deduced from a comparison of world data on 8 Be α decay [15,16,17] with the direct measurement of the positron spectrum from 8 B decay measured by Napolitano, Freedman, and Camp [18]. Energy-dependent systematic errors are deduced from a combination of experimental uncertainties and the theoretical uncertainties in radiative and other corrections that must be made to convert the charged particle data into a neutrino spectrum [14]. Recently, Ortiz et al. [19] have made an improved measurement of the 8 B spectrum based on 8 Be α decay in which some of the major sources of systematic errors present in previous measurements were reduced or eliminated. We have adopted the neutrino spectral shape and experimental uncertainties from this measurement. These experimental uncertainties were then added in quadrature with the theoretical uncertainties given by Bahcall et al. [14].
The solar neutrino signal is extracted from the data using the cos θ sun distribution (Fig. 1). The angle θ sun is that between the recoil electron momentum and the vector from the sun to the Earth. The solar neutrino flux is obtained by a likelihood fit of the signal and background shapes to the cos θ sun distribution in data. The signal shape is obtained from the known angular distribution and detector simulation, while the background shape is nearly flat in cos θ sun . In the 8 B flux measurement, the data are subdivided into 19 energy bins in the range 5.0-20.0 MeV (binning as in Fig. 3). The likelihood function is defined as follows: S is the total number of signal events, while N j , B j , and Y j represent the number of observed events, the number of background events, and the expected fraction of signal events in the j-th bin, respectively. likelihood function is maximized with respect to S and B j . For the energy spectrum measurement, each term in the product over bins is maximized separately.
The total systematic error is +3.5% −3.0% , with the largest sources coming from the reduction cut efficiency ( +2.2% −1.7% ), energy scale and resolution (±1.4%), systematic shifts in the event vertex (±1.3%), and the angular resolution of the recoil electron momentum (±1.2%). Fig. 2 shows the solar neutrino flux as a function of the solar zenith angle θ z (the angle between the vertical axis at SK and the vector from the sun to the Earth). Numerical values are shown in Table II. The day-time solar neutrino flux Φ d is defined as the flux of events when cos θ z ≤ 0, while the night-time flux Φ n is that when cos θ z > 0. The measured fluxes are: Φ d = 2.28 ± 0.04 (stat.) +0.08 −0.07 (sys.) × 10 6 cm −2 s −1 Φ n = 2.36 ± 0.04 (stat.) +0.08 −0.07 (sys.) × 10 6 cm −2 s −1 Some neutrino oscillation parameters predict a non-zero difference between Φ n and Φ d due to the matter effect in the Earth's mantle and core [20]. The degree of this difference is measured by the day-night asymmetry, defined as A = (Φ n −Φ d )/Φ average , where Φ average = 1 2 (Φ n +Φ d ). We find: in the day-night asymmetry measurement. The largest sources of error in the asymmetry are the energy scale and resolution ( +0.012 −0.011 ) and the non-flat background shape of the cos θ sun distribution (±0.004). Fig. 3 shows the measured recoil electron energy spectrum relative to the Ortiz et al. spectrum normalized to BP2000. (See Table III  error (shown in Fig. 3 as a band around the total flux) is due to uncertainties that could cause a systematic shift in the energy spectrum. The sources of this error are uncertainties in the energy scale, resolution, and the reference 8 B spectrum against which the data are compared. The seasonal dependence of the solar neutrino flux is shown in Fig. 4. (See Table IV for numerical values.) The points represent the measured flux, and the curve shows the expected variation due to the orbital eccentricity of the Earth (assuming no neutrino oscillations, and normalized to the measured total flux). The data are consistent with the expected annual variation (χ 2 /d.o.f. = 3.7/7). Systematic errors are included in the calculation of χ 2 . The total systematic error on the relative flux values in each seasonal bin is ±1.3%, the largest sources coming from energy scale and resolution ( +1.2% −1.1% ) and reduction cut efficiency (±0.6%).
The hep neutrino flux given by BP2000 is 9.3 × 10 3 cm −2 s −1 [6], which is three orders of magnitude smaller than the 8 B neutrino flux. Although the theoretically calculated hep flux is highly uncertain because of many delicate cancellations in calculating the astrophysical S factor, a recent calculation by Marcucci, et al. [21] shows that the flux is unlikely to be drastically larger than the value given in BP2000. The effect of hep neutrinos on solar neutrino measurements at SK is expected to be small. However, since the end-point of the hep neutrino spectrum is 18.77 MeV compared to about 16 MeV for the 8 B spectrum, the high energy end of the E recoil spectrum should be relatively enriched with hep neutrinos. An unexpectedly large hep flux may distort the E recoil spectrum. In our measurement of the hep flux, we extract the number of events in the window E recoil = 18-21 MeV from a cos θ sun distribution like the one shown in Fig. 1. This window was chosen because it optimizes the significance of the hep flux measurement in MC as- suming BP2000 8 B and hep fluxes. We find 1.3 ± 2.0 events in the chosen window. Assuming that all of these events are due to hep neutrinos, the 90% confidence level upper limit of the hep neutrino flux is 40 × 10 3 cm −2 s −1 (4.3 times the BP2000 prediction). Fig. 5 shows the expected energy spectra with various hep contributions.
In summary, SK has lowered the analysis energy threshold to 5.0 MeV, collected more than twice the data previously reported, and reduced systematic errors through refinements in data analysis and extensive detector calibrations. With those improvements, and with the 18,464 observed solar neutrino events, SK provides very precise measurements of the recoil electron energy spectrum, day-night flux asymmetry, and the absolute solar neutrino flux. The measured flux is 45.1 ± 0.5 (stat.) +1.6 −1.4 (sys.)% of the BP2000 prediction. We found no statistically significant energy spectrum distortion (χ 2 /d.o.f. = 19.0/18 relative to the predicted 8 B spectrum), and the day-night flux difference of 3.3% of the average flux is 1.3 σ from zero. However, the precision of these measurements should provide strong and important constraints on the neutrino oscillation parameters. The seasonal dependence of the flux shows the expected 7% annal variation due to the eccentricity of the Earth's orbit. This is the first neutrino-based observation of the Earth's orbital eccentricity. A stringent limit on the hep neutrino flux (Φ hep < 40 × 10 3 cm −2 s −1 ) was obtained, which corresponds to 4.3 times the predicted value from BP2000.  IV: Numerical results of the seasonal analysis. The time period (1st column), the ratio of observed and expected number of events without eccentricity correction (2nd column), the ratio of observed and expected number of events with eccentricity correction (3rd column), and 1σ error of systematic error (4th column). Systematic errors are relative. Energy range is 5.0-20.0MeV.