Search for ν̄e from the Sun at Super-Kamiokande-I

arXiv:hep-ex/0212067 v1 30 Dec 2002

The Super-Kamiokande Collaboration
Y. Gandox , S. Fukudaa , Y. Fukudaa , M. Ishitsukaa , Y. Itowa , T. Kajitaa , J. Kamedaa,i , K. Kaneyukia ,K. Kobayashia, Y. Koshioa , M. Miuraa , S. Moriyamaa, M. Nakahataa , S. Nakayamaa, T. Nambaa ,Y. Obayashia, A. Okadaa , T. Ooyabua, C. Sajia , N. Sakuraia , M. Shiozawaa, Y. Suzukia , H. Takeuchia ,Y. Takeuchia , Y. Totsukaa,i , S. Yamadaa , S. Desaib , M. Earlb , E. Kearnsb, M.D. Messierb,∗ , J.L. Stoneb ,L.R. Sulakb , C.W. Walterb , M. Goldhaberc , T. Barszczakd, D. Casperd, W. Gajewskid , W.R. Kroppd, S. Mined ,D.W. Liud , M.B. Smyd , H.W. Sobeld , M.R. Vaginsd , A. Gagoe , K.S. Ganezere , J. Hille , W.E. Keige ,R.W. Ellsworthf , S. Tasakag , A. Kibayashih, J.G. Learnedh , S. Matsunoh , D. Takemorih, Y. Hayatoi ,A. K. Ichikawai, T. Ishiii , T. Kobayashii, T. Maruyamai,† , K. Nakamurai , Y. Oyamai , M. Sakudai ,M. Yoshidai , M. Kohamaj,‡ , T. Iwashitaj , A.T. Suzukij , T. Inagakik , I. Katok , T. Nakayak , K. Nishikawak ,T.J. Hainesl,d , S. Dazeleym , S. Hatakeyamam, R. Svobodam , E. Blaufussn , M.L. Chenn , J.A. Goodmann ,G. Guilliann , G.W. Sullivann , D. Turcann , K. Scholbergo , A. Habigp , M. Ackermannq , C.K. Jungq ,K. Martensq,§ , M. Malekq , C. Maugerq , C. McGrewq , E. Sharkeyq , B. Virenq,c , C. Yanagisawaq , T. Toshitor ,C. Mitsudas , K. Miyanos , T. Shibatas , Y. Kajiyamat, Y. Nagashimat , K. Nittat , M. Takitat , H.I. Kimu ,S.B. Kimu , J. Yoou , H. Okazawav , T. Ishizukaw , M. Etohx , T. Hasegawax, K. Inouex , K. Ishiharax , J. Shiraix ,A. Suzukix , M. Koshibay , Y. Hatakeyamaz , Y. Ichikawaz , M. Koikez , K. Nishijimaz , H. Ishinoaa , M. Moriiaa ,R. Nishimuraaa , Y. Watanabeaa , D. Kielczewskabb,d , H.G. Bernscc , S.C. Boydcc , A.L. Stachyracc, R.J. Wilkescc
aInstitute for Cosmic Ray Research, University of Tokyo, Kashiwa, Chiba 277-8582, Japanb Department of Physics, Boston University, Boston, MA 02215, USAc Physics Department, Brookhaven National Laboratory, Upton, NY 11973, USAd Department of Physics and Astronomy, University of California, Irvine, Irvine, CA 92697-4575, USAe Department of Physics, California State University, Dominguez Hills, Carson, CA 90747, USAf Department of Physics, George Mason University, Fairfax, VA 22030, USAg Department of Physics, Gifu University, Gifu, Gifu 501-1193, Japanh Department of Physics and Astronomy, University of Hawaii, Honolulu, HI 96822, USAi Institute of Particle and Nuclear Studies, High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305-0801, Japanj Department of Physics, Kobe University, Kobe, Hyogo 657-8501, Japank Department of Physics, Kyoto University, Kyoto 606-8502, Japanl Physics Division, P-23, Los Alamos National Laboratory, Los Alamos, NM 87544, USAm Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA 70803, USAn Department of Physics, University of Maryland, College Park, MD 20742, USAo Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USAp Department of Physics, University of Minnesota, Duluth, MN 55812-2496, USA
q Department of Physics and Astronomy, State University of New York, Stony Brook, NY 11794-3800, USAr Department of Physics, Nagoya University, Nagoya, Aichi 464-8602, Japans Department of Physics, Niigata University, Niigata, Niigata 950-2181, Japant Department of Physics, Osaka University, Toyonaka, Osaka 560-0043, Japanu Department of Physics, Seoul National University, Seoul 151-742, Korea
v Internatinal and Cultural Studies, Shizuoka Seika College, Yaizu, Shizuoka, 425-8611, Japanw Department of Systems Engineering, Shizuoka University, Hamamatsu, Shizuoka 432-8561, Japanx Research Center for Neutrino Science, Tohoku University, Sendai, Miyagi 980-8578, Japany The University of Tokyo, Tokyo 113-0033, Japanz Department of Physics, Tokai University, Hiratsuka, Kanagawa 259-1292, Japanaa Department of Physics, Tokyo Institute for Technology, Meguro, Tokyo 152-8551, Japan
bb Institute of Experimental Physics, Warsaw University, 00-681 Warsaw, Poland
cc Department of Physics, University of Washington, Seattle, WA 98195-1560, USA

We present the results of a search for low energy ν̄e from the Sun using 1496 days of data fromSuper-Kamiokande-I. We observe no significant excess of events and set an upper limit for theconversion probability to ν̄e of the 8 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 ν̄e for Eν̄e = 10MeV - 17MeV.
PACS numbers: 14.60.Pq,26.65.+t,96.40.Tv,95.85.Ry

Solar neutrino measurements at Super-Kamiokande [1]and SNO [2] 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 νe to some superposition ofνµ and ντ . However, measurements reported so far do
not rule out the possibility that some of the νe transformto antiparticles (ν̄µ , ν̄τ ). In the so-called “hybrid models” [3], spin flavor precession(SFP) and oscillation cantransform solar neutrinos to ν̄e if the neutrino is Majorana, it has large magnetic moment, and the Sun has alarge magnetic field. If the neutrino has a magnetic moment, there are two conversion scenarios: the neutrino isa Dirac particle or a Majorana particle. In the Dirac neutrino case, νeL changes to νeR by spin magnetic momenttransition. The νeR is a sterile neutrino. On the other
hand, in the case of the Majorana neutrino, SFP causes
νe → ν̄µ,τ . Neutrino oscillation then yields ν̄µ,τ → ν̄e .
Solar ν̄e could also originate from neutrino decay [4]. In
this paper, we present a search for ν̄e from the Sun.
The inverse beta decay process, ν̄e + p → n + e+ is predominant for ν̄e interaction in Super-Kamiokande (SK).
The positron energy is related to the neutrino energy by:Ee+ ≈ Eν̄e − 1.3 MeV. The positron angular distribution
relative to the incident ν̄e direction is nearly flat witha small energy dependent slope [5], which is in contrast
to the sharply forward peaked elastic scattering distribution. The difference between these distributions can beused to separate solar neutrino events from ν̄e events.
Super-Kamiokande is a 22.5kton fiducial volume water Cherenkov detector, located in the Kamioka mine in
Gifu, Japan. The 1496 live days of solar neutrino datafrom Super-Kamiokande-I were collected between May
31, 1996, and July 15, 2001. A detailed description of
SK can be found elsewhere [1, 6]. The dominant backgrounds to the solar neutrino signal are 222 Rn in thewater, external gamma rays and muon-induced spallation products. Background reduction is carried out inthe following steps: first reduction, spallation cut, second reduction, and external γ-ray cut. The first reduction removes events from electronic noise and other nonphysical sources, and events with poorly reconstructedvertices. The spallation cut removes events due to radioisotopes (X) produced by cosmic ray muon interactions
with water: µ +16 O → µ + X. These radio-isotopes
are called “spallation products.” The spallation products have lifetimes from 0.001 to 14 sec, and emit β andγ rays. We cut these events using likelihood functions
based on time, position, and muon pulse height. The
time and position likelihood functions are measures of theproximity of a candidate event to a muon track, while thepulse height likelihood function measures the likelihoodthat a muon produced a shower. These three likelihood
functions are used together to discriminate against spallation events [6]. The second reduction removes eventswith poor vertex fit quality and diffuse Cherenkov ringpatterns, both characteristics of low-energy background
events. The external γ-ray cut removes events due to γrays from the surrounding rock and PMTs etc.. Fig. 1
shows the energy spectrum after each reduction step.
At SK, a positron from inverse beta decay is indistin-

Number of events/day/22.5kt/0.5MeV

2

After 1st reduction
After spallation cut
After 2nd reduction
After gamma cut

10 4
10 3
10 2

–

νe SSM(BPB2001)

10

1

10

10

-1

-2

6

8

10

12

14

16
18
20
Energy (MeV)

FIG. 1: Energy spectrum after each reduction step. The solid
curve shows the expected ν̄e spectrum after application of all
cuts, assuming all neutrinos convert to ν̄e ’s.

guishable from an electron or gamma ray because thedelayed 2.2 MeV gamma ray from n + p → d + γ is below the detector’s energy threshold. In order to remove
elastic scattering events due to solar neutrinos, we cut
events with cosθsun ≥ 0.5, where θsun is the event direction with respect to the direction from the Sun. The region cos θsun < 0.5 would be occupied by solar ν̄e event,in addition 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 222 Rn). Spallation accounts for a small fraction of background events in thisregion. In contrast, for E & 8 MeV, most background
events are produced by spallation.
The spallation cut used in the data reduction efficiently
removes short-lifetime spallation products. This cut also
removes ∼90% of long-lifetime products such as 16
7 N (τ 12
11= 7.1 sec) and 4 Be (τ 12 = 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 such events tothe post-reduction data sample using a statistical subtraction technique. First, we made a time distribution ofmuon 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 is an average of ≈ 500 events foreach low energy event. If the low energy event is due toa long lifetime spallation product, its event time will becorrelated 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 thenumber of µ responsible for spallation events, we haveto subtract the number of µ which did not make spallation events from this distribution. In order to perform
this subtraction, we made a sample of artificial events

distributed randomly in space and time. We applied thespallation cut to the random events as in the actual data
sample in order to account for biases introduced by thiscut. The muon time distribution of the random sample is shown in Fig. 2(B). The dip near Delta-T = 0 isdue 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 issubtracted from distribution (A). The number of muon
events in the delta-T = 100 sec - 200 sec region is used asa normalization factor because the contamination frommuons which make spallation products is negligible inthis region. The number of spallation events is estimatedbyobserved
randomSpa = N0−50sec− N0−50sec
×

observed
N100−200sec
randomN100−200sec

4

entries(x 10 )observed
N0−50secis the number of muon events within 50 seconds
randompreceding the observed events, while N0−50sec
is the corobserved
responding number for random events. N100−200sec
andrandomN100−200sec are similarly defined, but with a timing window of 100 to 200 seconds preceding the events. For 8.020.0 MeV, and cos θsun ≤ 0.5, the number of estimatedspallation background events is (2.80 ± 0.20) × 104 . The
number of observed ν̄e candidate events is 29781, so theratio of spallation events to observed events is (93±7)%.
The spallation contamination in each energy bin is shownin Fig. 3.

11
10
9

0

20

40

60

80 100 120 140 160 180 200
Delta-T(sec)5entries(x 10 )(A) Final sample
58
54
50

0

20

40

60

80 100 120 140 160 180 200

2entries(x 10 )(B) Random sample Delta-T(sec)
40
20
0
0

20

40

60

80 100 120 140 160 180 200(C) (A) − Scaled(B) Delta-T(sec)

FIG. 2: (A): µ delta-T distribution before observed events(B): Before random events (C): The delta-T distribution of
events caused by spallation products (A)−scaled(B).

The energy spectrum of the solar ν̄e is not known because the mechanism for ν̄e creation is not known. Even

Spallation/Observed(%)

3
120

100

80

60

40

20

0

8

9

10

11

12

20

Ee (MeV)
FIG. 3: Spallation contamination in each energy bin. The
horizontal axis shows the total energy in MeV and the verticalaxis shows the ratio of spallation events to observed events inpercent.

if one assumes the SFP-oscillation hybrid model, the energy spectrum depends on µν × Bsolar , δm2 and sin2 (2θ),
none of which is known precisely, if at all. In order to deal
with this ambiguity, we have chosen two spectrum models: the 8 B neutrino spectrum [7] and monochromatic(spectrum independent analysis).
For the 8 B spectrum dependent analysis, we obtain an
upper limit on the solar ν̄e flux by comparing the observed number of events outside of the elastic scatteringpeak (cos θsun ≤ 0.5) with the expected number of ν̄eevents assuming that all 8 B neutrinos convert to ν̄e . The
expected number is obtained by Monte Carlo simulationof solar ν̄e interaction with the detector. The SSM 8 B
neutrino flux was assumed (5.05 ×106 /cm2 /sec). The
solid lines in Fig.4 show 90% C.L. limits on the ν̄e flux
before statistical spallation subtraction. The dashed lines
show the limits after statistical subtraction (only for E≥ 8 MeV). The combined upper limit for 8 MeV ≤ E ≤20 MeV is 0.8% of the SSM neutrino flux.
Some authors have indicated that the positron angular distribution may be useful for the search for ν̄e in the
SK data (e.g. [9, 10]). Taking θ as the opening angle
between the positron and neutrino momenta, cos θ is distributed as f(cos θ) = 0.5 × (1 + α × cos θ), where α isa monotonically increasing function of neutrino energy(except near threshold), and α ≤ 0 for Eν . 13 MeV
and ≥ 0 above this [5]. At the lowest neutrino energies,f(cos θ) has sufficient slope to be useful for the ν̄e search.
ν̄e events with the predicted cos θ distribution were input
to a detector simulator to obtain the expected positron
angular distribution. The resulting distribution has thesame form as above. The fitted value of α is -0.076 at
Etotal = 5 - 6 MeV, 0.107 at Etotal = 12 - 20 MeV, andcrosses 0 at ∼ 9 MeV.

4

N
cos
X
i=1

(

18

Nidata − Niel − Ni O − αNiν̄e − βNiBG (1 + γ cos θsun )σistat.

+γ
σisyst.

2

Ncos (= 30) is the number of angular bins for cos θsun ≤0.5, Nidata is the number of observed data events, σistat.
is the statistical error of the observed data, Niel is the18
expected number of elastic scattering events, Ni O is the18
expected number of events from the O(νe ;e)18 F reaction, Niν̄e is the number of ν̄e events, NiBG is the numberof all other background events that are uncorrelated in18
direction with the Sun. Niel and Ni O are both . 2%of Nidata , and the systematic errors of these terms are
negligible. σisyst. is the systematic error of the shape ofthe background and γ is the parameter that takes this
into account. β parameterizes the amount of such background events. We selected β and γ which minimizes χ2
for each α. A 1-parameter χ2 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.
The analysis above assumes that the ν̄e ’s originate
from 8 B solar neutrinos. We also generalized our searchby assuming a monochromatic ν̄e source at each energy
and set a conservative ν̄e flux upper limit. The interaction of such ν̄e with the detector was simulated, andstandard data reduction cuts were applied. The positron
spectrum is well described by a Gaussian. We thencounted the number of events in the data in the ± 1σ
range of this Gaussian. We took this number to be thenumber of events due to monochromatic ν̄e , and we 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 lim-

its after statistical subtraction of long lifetime spallation
events. The 90% C.L. limits are shown in Fig5.
νe/SSM ν e (%)

10 2

–

Solar neutrino elastic scattering is one of the backgrounds for this analysis. Almost all such events havecos θsun > 0.5, so events with cos θsun > 0.5 are cut. We
also subtract the small amount of spill-over into cos θsun
≤ 0.5 using Monte Carlo simulation (∼5% for 5-20MeV).
Another background is due to 18 O(νe ;e)18 F [11]. Thereis only a small number of events from this source (0.03%∼ 2%, depending on energy), but electrons from this process, like the low-energy ν̄e , have negative slope in theirangular distribution. So they are subtracted from thedata. The νe flux is taken as the charged current flux
value from SNO, 1.76 × 106 /cm2 /sec [12].
A ν̄e upper limit is obtained using a probability testwith the slope of the cos θ distribution serving as aconstraint. This test is based on a χ2 test with χ2
defined as follows:

10

)2

1
5

6

7

8

9

10

11

12

20
Ee(MeV)

FIG. 4: Summary of ν̄e limits. The horizontal axis shows total
positron energy in MeV and the vertical axis shows the 90%
C.L. ν̄e rate normalize to the SSM νe rate. The solid lines
show the 90% C.L. limit ratio. The dashed lines show thelimit after statistical subtraction of the spallation background.
The dotted lines show the result from the angular distribution
analysis.

In summary, a search for ν̄e flux from the Sun was
performed using all 1496 live days of solar neutrino datafrom Super-Kamiokande-I. Using the 8 B and monochromatic energy spectra, 90% C.L. upper limits were set forthe solar ν̄e flux. For the 8 B spectrum, the upper limit
to the flux was 0.8% of the SSM νe flux prediction for
Etotal = 8.0-20.0MeV. This can be compared with the
Kamiokande result of 4.5% [13]. For ν̄e fluxes with various monochromatic energies, the resulting upper limits
are shown in Fig. 5.

Acknowledgments

The authors acknowledge the cooperation of the
Kamioka Mining and Smelting Company. The SuperKamiokande has been built and operated from fundingby 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 andTechnology.

52

νe flux(/cm /sec)

10 6

–

10 5

10 4

10 3

10 2

9

10

11

12

13

14

15

16
17
18
–
νe energy(MeV)

FIG. 5: ν̄e flux 90% C.L. upper limit for each monochromaticν̄e . The horizontal axis shows neutrino energy in MeV andthe vertical axis shows the flux limit (in /cm2 /sec). The black
circles show the limits before spallation subtraction while theblack stars show the limits after subtraction. The two highestenergy bins have insufficient number of events for statisticalsubtraction.

[∗] 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 351-0198, Japan[§] Present address: Department of Physics, University of
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