Search for from the Sun at SuperKamiokandeI
Abstract
We present the results of a search for low energy from the Sun using 1496 days of data from SuperKamiokandeI. We observe no significant excess of events and set an upper limit for the conversion probability to of the B solar neutrino. This conversion limit is 0.8% (90% C.L.) of the standard solar model’s neutrino flux for total energy = 8 MeV  20 MeV. We also set a flux limit for monochromatic for = 10MeV  17MeV.
pacs:
14.60.Pq,26.65.+t,96.40.Tv,95.85.RySolar neutrino measurements at SuperKamiokande SK1500 and SNO SNOCC have established that the solar neutrino problem is explained by the transformation of electron neutrinos to other active neutrinos. The mechanism for this transformation is generally assumed to be via neutrino flavor oscillations from to some superposition of and . However, measurements reported so far do not rule out the possibility of spin flavor precession(SFP) in which some of the transform to antiparticles (, ). In the socalled “hybrid models” VVO , SFP and oscillation can transform solar neutrinos to if the neutrino is Majorana, it has a large magnetic moment, and the Sun has a large magnetic field. If the neutrino has a magnetic moment, there are two possibilities: (1) the neutrino is a Dirac particle ; (2) it is a Majorana particle. In the Dirac neutrino case, changes to by the spin magnetic moment transition. The is a sterile neutrino. On the other hand, in the Majorana neutrino scenario, SFP causes . Neutrino oscillation then yields . Solar could also originate from neutrino decay decay . In this paper, we present a search for from the Sun.
The inverse beta decay process, , is predominant for interactions in SuperKamiokande (SK). The cross section for this process is two orders of magnitude greater than that for elastic scattering, and therefore SK has good sensitivity for the detection of solar . The positron energy is related to the neutrino energy by MeV. The positron angular distribution relative to the incident direction is nearly flat with a small energy dependent slope Vogel , which is in contrast to the sharply forward peaked elastic scattering distribution. The difference between these distributions can be used to separate solar neutrino events from events.
SuperKamiokande is a 22.5 kton fiducial volume water Cherenkov detector, located in the Kamioka mine in Gifu, Japan. The data used for the search were collected in 1496 live days between May 31, 1996 and July 15, 2001. A detailed description of SK can be found elsewhere SK1500 ; SK . Dominant backgrounds to the solar neutrino signal are Rn in the water, external gamma rays and muoninduced spallation products. Background reduction is carried out in the following steps: first reduction, spallation cut, second reduction, and external ray cut. The first reduction removes events from electronic noise and other nonphysical sources, and events with poorly reconstructed vertices. The spallation cut removes events due to radioisotopes (X) produced by cosmic ray muon interactions with water: . These radioisotopes are called “spallation products.” The spallation products emit beta and gamma rays and have lifetimes ranging from 0.001 to 14 sec. We cut these events using likelihood functions based on time, position, and muon pulse height. The time and position likelihood functions are measures of the proximity of a candidate event to a muon track, while the pulse height likelihood function measures the likelihood that a muon produced a shower. These three likelihood functions are used together to discriminate against spallation events SK . The second reduction removes events with poor vertex fit quality and diffuse Cherenkov ring patterns, both characteristics of lowenergy background events. The external ray cut removes events due to rays from the surrounding rock, photomultipliers(PMTs), etc.. Fig. 1 shows the energy spectrum after each reduction step.
At SK, a positron from inverse beta decay is indistinguishable from an electron or a gamma ray because the delayed 2.2 MeV gamma ray from n + p d + is below the detector’s energy threshold. In order to remove elastic scattering events due to solar neutrinos, we cut events with cos 0.5, where is the event direction with respect to the direction from the Sun. The region 0.5 would be occupied by solar events, in addition to events due to known background sources which could not be removed by the standard data reduction. For E 8 MeV, most background events are due to radioactivity in the detector materials (such as Rn). Spallation accounts for a small fraction of background events in this region. In contrast, for E 8 MeV, most background events are produced by spallation.
The spallation cut used in the data reduction efficiently removes shortlifetime spallation products. This cut also removes 90% of longlifetime products such as N ( = 7.1 sec) and Be ( = 13.8 sec). Event by event removal of the remaining 10% of these events is impractical because this introduces large dead time. However, we can estimate the contribution of these events to the postreduction data sample using a statistical subtraction technique. First, we made a time distribution of muon events preceding each low energy event by up to 200 seconds (Fig. 2(A)). Since the average muon rate at SK is 2.5 Hz, there are, on average, 500 events for each low energy event. If the low energy event is due to a long lifetime spallation product, its event time will be correlated with one of the 500 preceding muon events. If this is not the case, then its event time will be uncorrelated with all of the muon events. To estimate the number of responsible for spallation events, we have to subtract the number of which did not make spallation events from the total number of . In order to perform this subtraction, we made a sample of simulated events distributed randomly in space and time. We applied the spallation cut to this sample as in the actual data sample in order to account for biases introduced by this cut. The muon time distribution of the random sample is shown in Fig. 2(B). The dip near DeltaT = 0 is due to the accidental loss of events by the spallation cut. To estimate the number of muons which made spallation products, distribution (B) with suitable normalization is subtracted from distribution (A); the result of this subtraction is shown in Fig. 2(C). The number of muon events in the deltaT = 100 sec  200 sec region is used to calculate the normalization factor because the contamination from muons which make spallation products is negligible in this region. The number of spallation events is obtained as
is the number of muon events within 50 seconds preceding the observed events, while is the corresponding number for random events. and are similarly defined, but with a timing window of 100 to 200 seconds preceding the events. For 8.020.0 MeV, and , the number of spallation background events obtained by this method is (2.77 0.20) 10. The number of observed candidate events is 29781, so the ratio of spallation events to observed events is (937)%. The spallation contamination in each energy bin is shown in Fig. 3.
The energy spectrum of the solar is not known because the mechanism for creation is not known. Even if one assumes the SFPoscillation hybrid model, the energy spectrum depends on B, and , none of which are known precisely, if at all. In order to deal with this ambiguity, we have chosen two spectrum models: the B neutrino spectrum ortiz and monochromatic spectrum (spectrum independent analysis).
For the B spectrum dependent analysis, we obtain an upper limit on the solar flux by comparing the observed number of events outside of the elastic scattering peak () with the expected number of events assuming that all B neutrinos convert to . The expected number is obtained by Monte Carlo simulation of solar interaction with the detector. The dependence was simulated , and the effect of this dependence on the efficiency is taken into account. The standard solar model(SSM) B neutrino flux was assumed (5.05 /cm/sec) BPB2001 . Through the rest of this paper, electron neutrino spectrum and flux refer to the unoscillated quantities at the Sun. The solid lines in Fig.4 show 90% C.L. limits on the flux before statistical spallation subtraction. The dashed lines show the limits after statistical subtraction (only for E 8 MeV). By combining the statistics for 8 MeV E 20 MeV, we obtained a global upper limit of 0.8% of the SSM neutrino flux.
Some authors have indicated that the positron angular distribution may be useful for the search for in the SK data (e.g. ang0 ; Lujan ). is distributed as f() = 0.5 (1 + ), where is a monotonically increasing function of neutrino energy (except near threshold), and 0 for MeV and 0 above this Vogel . The angular information is useful for the search at the lowest neutrino energies where f() has sufficient slope and the event statistics are large. events with the predicted distribution were input to a detector simulator to obtain the expected positron angular distribution. The resulting distribution has the same form as above. The fit value of is 0.076 at = 5  6 MeV, 0.107 at = 12  20 MeV, and crosses 0 at 9 MeV.
Solar neutrino elastic scattering is one of the backgrounds for this analysis. Almost all such events have 0.5, so events with 0.5 are cut. We also subtract the small amount of spillover into 0.5 using Monte Carlo simulation (5% for 520MeV). Another background is due to O(;)F o18 . There is only a small number of events from this source (0.03% 2%, depending on energy), but electrons from this process, like the lowenergy , have negative slope in their angular distribution. So they are subtracted from the data. The flux is taken as the charged current flux value from SNO, /cm/sec SNO .
A flux upper limit is obtained using
a probability test with the slope of the
distribution serving as a constraint.
This test is based on a test with
defined for each energy as follows:
is the index for the bins ( 0.5, = 30), is , is the number of observed data events, is the statistical error of the observed data, is the expected number of elastic scattering events, is the expected number of events from the O(;)F reaction, is the number of events assuming all SSM convert to (the number in each bin depends on the slope ), and is the shape for all other background events that are almost uncorrelated in direction with the Sun (this background is essentially flat). and are both 2% of , and the systematic errors of these terms are negligible. (= 0.5%) is the systematic error of the slope of the background shape and is the parameter that takes this into account. parameterizes the amount of such background events. We divided the parameter space for into a grid, and minimized with respect to and at each grid point. The resulting and indicated good fits to the data. as a function obtained in this way is input to a probability function. From this analysis, we set a 90% C.L. upper limit for each energy bin. The dotted lines in Fig. 4 show the result. It should be noted that the spallation background subtratction is not applied in this analysis for two reasons. First, for E 8 MeV, spallation subtraction is ineffective because spallation events form a small subset of the total background. Second, for E 8 MeV, there are insufficient statistics after spallation subtraction to perform an angular analysis of the data.
The analysis described so far assume that the originate from B solar neutrinos. We also generalized our search by assuming a monochromatic source at various energies and set conservative flux upper limits. The interaction of such with the detector was simulated, and standard data reduction cuts were applied. The positron spectrum is well described by a Gaussian. We then counted the number of events in the data in the 1 range of this Gaussian. We took this number to be the number of events due to monochromatic and obtained an upper limit. This upper limit is very conservative because we do not take account of the large spillover from lower energy bins that is implied by the sharply falling spectrum seen in the data. We also obtained limits after statistical subtraction of long lifetime spallation events. The 90% C.L. limits are shown in Fig5.
In summary, a search for flux from the Sun was performed using all 1496 live days of solar neutrino data from SuperKamiokandeI. Using the B and monochromatic energy spectra, 90% C.L. upper limits were set for the flux. For the B spectrum dependent analysis, the upper limit to the flux was 0.8% of the SSM flux prediction for E = 8.020.0MeV. This can be compared with the Kamiokande result of 4.5% KID . For fluxes with various monochromatic energies, the resulting upper limits are shown in Fig. 5.
Acknowledgements.
The authors acknowledge the cooperation of the Kamioka Mining and Smelting Company. The SuperKamiokande has been built and operated from funding by the Japanese Ministry of Education, Culture, Sports, Science and Technology, the U.S. Department of Energy, and the U.S. National Science Foundation. This work was partially supported by the Korean Research Foundation (BK21) and the Korea Ministry of Science and Technology.References
 (1)
 (*) Present address: Harvard University, Cambridge, MA 02138, USA
 (†) Present address: Enrico Fermi Institute, University of Chicago, Chicago, IL 6063 7, USA
 (‡) Present address: The Institute of Physical and Chemical Reasearch (RIKEN), Wako, Saitama 3510198, Japan
 (§) Present address: Department of Physics, University of Utah, Salt Lake City, UT 8 4112, USA
 (6) S.Fukuda et al., Phys. Lett. B 539 (2002) 179
 (7) Q.R.Ahmad et al., Phys. Rev. Lett. 87 (2001) 071301

(8)
C.S.Lim and W.J.Marciano, Phys. Rev. D37 (1988) 1368;
E.Kh.Akhmedov, Phys. Lett. B 213 (1988) 64; Sov. Phys. JETP 68 (1989) 690.
J.Barranco et al., arXiv:hepph/0207326  (9) Z.Berezhiani, G.Fiorentini, M.Moretti and A.Rossi, JETP Lett. 55 (1992) 151; A.Acker, A.Joshipura and S.Pakvasa, Phys. Lett. B 285 (1992) 371; R.S.Raghavan, XG.He, S.Pakvasa, Phys. Rev. D 38 (1988) 1317.; J.F.Beacom and N.F.Bell Phys. Rev. D 65 (2002) 113009.
 (10) P.Vogel and J.F.Beacom, Phys. Rev. D. 60 (1999) 053003.

(11)
Y. Fukuda et al., Phys. Rev. Lett. 81 1158 (1998).
M. Nakahata et al., Nucl. Instrum. Methods Phys. Res. Sect. A 421, 113 (1999).
Y. Fukuda et al., Phys. Rev. Lett. 82, 2430 (1999).
Y. Fukuda et al., Phys. Rev. Lett. 82, 1810 (1999). S.Fukuda et al., Phys. Rev. Lett. 86 (2001) 5651  (12) C.E.Ortiz et al., Phys. Rev. Lett. 85, 2909 (2000).
 (13) J.N.Bahcall et al., Astrophys. J. 555 (2001) 9901012.
 (14) G.Fiorentini, M.Moretti, and F.L.Villante, Phys. Lett. B 413, 378 (1997)
 (15) E.TorrenteLujan, Phys. Lett. B 494, 255 (2000).
 (16) W.C. Haxton and R.G.H. Robertson, Phys. Rev. C 59(1999)515
 (17) Q.R.Ahmad et al., Phys. Rev. Lett. 89 (2002) 011301
 (18) K.Inoue, Ph.D. Thesis, University of Tokyo (1993).