arXiv:1105.3516v1 [astro-ph.HE] 18 May 2011

A study of extraterrestrial antineutrino sources with the KamLAND detector
A. Gando, Y. Gando, K. Ichimura, H. Ikeda, K. Inoue1 , Y. Kibe2 , Y. Kishimoto, M. Koga1 ,Y. Minekawa, T. Mitsui, T. Morikawa, N. Nagai, K. Nakajima K. Nakamura1 , K. Narita,
I. Shimizu, Y. Shimizu, J. Shirai, F. Suekane, A. Suzuki, H. Takahashi, N. Takahashi,
Y. Takemoto, K. Tamae, H. Watanabe, B.D. Xu, H. Yabumoto, H. Yoshida, and S. Yoshida
Research Center for Neutrino Science, Tohoku University, Sendai 980-8578, Japan
S. Enomoto3 , A. Kozlov, and H. Murayama4
Institute for the Physics and Mathematics of the Universe, Tokyo University, Kashiwa 277-8568,
Japan
C. Grant, G. Keefer5 , and A. Piepke1
Department of Physics and Astronomy, University of Alabama, Tuscaloosa, Alabama 35487, USA
T.I. Banks, T. Bloxham, J.A. Detwiler, S.J. Freedman1 , B.K. Fujikawa1 , K. Han, R. Kadel,
T. O’Donnell, and H.M. Steiner
Physics Department, University of California, Berkeley and
Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
D.A. Dwyer, R.D. McKeown, and C. Zhang
W. K. Kellogg Radiation Laboratory, California Institute of Technology, Pasadena, California
91125, USA
B.E. Berger
Department of Physics, Colorado State University, Fort Collins, Colorado 80523, USA
C.E. Lane, J. Maricic, and T. Miletic6 ,Physics Department, Drexel University, Philadelphia, Pennsylvania 19104, USA
M. Batygov7 , J.G. Learned, S. Matsuno, and M. Sakai
Department of Physics and Astronomy, University of Hawaii at Manoa, Honolulu, Hawaii 96822,
USA
G.A. Horton-Smith1
Department of Physics, Kansas State University, Manhattan, Kansas 66506, USA
K.E. Downum and G. Gratta

–2–
Physics Department, Stanford University, Stanford, California 94305, USA
Y. Efremenko1 , Y. Kamyshkov, and O. Perevozchikov8 ,Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996,
USA
H.J. Karwowski, D.M. Markoff, and W. Tornow
Triangle Universities Nuclear Laboratory, Durham, North Carolina 27708, USA andPhysics Departments at Duke University, North Carolina Central University, and the Universityof North Carolina at Chapel Hill
K.M. Heeger1
Department of Physics, University of Wisconsin, Madison, Wisconsin 53706, USA
andM.P. Decowski1
Nikhef, Science Park, Amsterdam, the Netherlands
ABSTRACT
We present the results of a search for extraterrestrial electron antineutrinos (ν e ’s)in the energy range 8.3 MeV < Eν e < 30.8 MeV using the KamLAND detector. In an
exposure of 4.53 kton-year, we identify 25 candidate events. All of the candidate events
1

Also with the Institute for the Physics and Mathematics of the Universe, Tokyo University, Kashiwa 277-8568,
Japan
2

Present address: Department of Physics, Tokyo Institute of Technology, Tokyo 152-8551, Japan

3

Also with the Center for Experimental Nuclear Physics and Astrophysics, University of Washington, Seattle,
Washington 98195, USA
4

Also with the Physics Department, University of California, Berkeley and Lawrence Berkeley National Laboratory,
Berkeley, California 94720, USA
5

Present address: Lawrence Livermore National Laboratory, Livermore, California 94550, USA

6

Present address: Department of Physics and Astronomy, Rowan University, 201 Mullica Hill Road, Glassboro,
New Jersey 08028, USA
78

Present address: SNOLAB, Lively, ON P3Y 1M3, Canada

Present address: Louisiana State University Department of Physics & Astronomy Nicholson Hall, Tower Dr.
Baton Rouge, LA 70803-4001, USA

–3–
can be attributed to background, most importantly neutral current atmospheric neutrino interactions, setting an upper limit on the probability of 8 B solar νe ’s converting
into ν e ’s at 5.3 × 10−5 (90% C.L.). The present data also allows us to set more stringent
limits on the diffuse supernova neutrino flux and on the annihilation rates for light dark
matter particles.
Subject headings: neutrinos, diffuse flux, solar antineutrinos, light dark matter

1.

Introduction

Ambient electron antineutrinos (ν e ’s) of terrestrial origin include geoneutrinos (Araki et al.
2005; Bellini et al. 2010), which have energies below ∼3.4 MeV, and man-made reactor antineutrinos (Cowan et al. 1956; Vogel et al. 1981), which have energies below ∼8 MeV. Naturally produced
ν e ’s with higher energies must be of cosmic origin. The region above a few tens of MeV is dominatedby neutrinos generated from the decays of muons and pions produced by cosmic-ray interactions in
the atmosphere. For antineutrinos in the energy region between 8 MeV and 15 MeV, only diffuse
neutrino flux from old supernovae (Totani & Sato 1995) and exotic generation mechanisms, e.g.,conversion of solar neutrinos into antineutrinos (Okun et al. 1984) or light dark matter annihilation (Palomares-Ruiz & Pascoli 2008) are thought to be possible.

1.1.

Solar Antineutrinos

There is no direct production of ν e ’s in the Sun. However, if the neutrino has a non-zeromagnetic moment it could be converted into an antineutrino in the strong solar magnetic field. Thismechanism was originally proposed as a solution to the solar neutrino problem (Okun et al. 1984)
and was later revisited in (Akhmedov & Pulido 2003). A two-step process takes place, the firststep occurs deep inside the solar interior, where a νe converts into a ν µ via spin flavor precession.
The ν µ then oscillates into an ν e while propagating from the Sun to the Earth. The combined
probability for the two processes is−10

P (νeL → ν eR ) ≃ 1.8 × 102

sin 2θ12
BT (0.05R⊙ ) 2,
10−12 µB
10 kG
µ

(1)

where BT is the transverse solar magnetic field in the region of neutrino production, R⊙ is thesolar radius, and µ is the neutrino magnetic moment in Bohr magneton (µB ). Very little is
known about the magnitude of magnetic fields in the solar interior, but values up to 3 × 107 G
are permitted based on SOHO observations (Couvidat et al. 2003). The present best-limit forthe probability of neutrino-to-antineutrino conversion, from the Borexino experiment, is less than
1.3 × 10−4 (Bellini et al. 2011).

–4–
1.2.

Diffuse Supernova Neutrino Flux

A diffuse ν e background exists from past core-collapse supernovae. Only upper limits for the
diffuse supernova neutrino flux (DSNF) have been set by Super-Kamiokande and SNO for energies
above 19.3 MeV (Malek et al. 2003) and 22.9 MeV (Aharmim et al. 2006), respectively. Because
the diffuse ν e energy is lowered by redshift, the spectral shape is closely connected to the historyof star formation. Various supernova and cosmological models predict different shapes, and should
be confronted with data.

1.3.

Dark Matter Annihilation

Self-annihilation of light (MeV-range) dark matter in the universe could create a monoenergetic neutrino signal in the detector. The Super-Kamiokande data provides the best-limiton the rate of such annihilation for dark matter mass (mχ ) above 15 MeV. Assuming an annihilation model in the Galactic halo (Palomares-Ruiz & Pascoli 2008), the limit can be translated intoa velocity-dependent averaged cross section (hσA vi) for dark matter particles.

2.

The KamLAND Experiment

KamLAND is located ∼1 km under the peak of Mt. Ikenoyama (36.42◦ N, 137.31◦ E) near
Kamioka, Japan. The 2700 meters water equivalent (mwe) of vertical rock overburden reduces thecosmic ray muon flux by almost five orders of magnitude. A schematic diagram of KamLAND isshown in Fig. 1. The primary target volume consists of 1 kton of ultra-pure liquid scintillator (LS)contained in a 13-m-diameter spherical balloon made of 135-µm-thick transparent nylon-EVOH(ethylene vinyl alcohol copolymer) composite film. The LS consists of 80% dodecane and 20%
pseudocumene (1,2,4-trimethylbenzene) by volume, and 1.36 ± 0.03 g/liter of the fluor PPO (2,5diphenyloxazole). A buffer comprising 57% isoparaffin and 43% dodecane oils by volume, whichfills the region between the balloon and the surrounding 18-m-diameter spherical stainless-steel
outer vessel, shields the LS from external radiation. The specific gravity of the buffer oil (BO)is adjusted to be 0.04% lower than that of the LS. An array of photomultiplier tubes (PMTs)—
1325 specially developed fast PMTs masked to 17-in.-diameter and 554 older 20-in.-diameter PMTs
reused from the Kamiokande experiment (Kume et al. 1983)—are mounted on the inner surface ofthe stainless-steel, providing 34% photocathode coverage. This inner detector (ID) is shielded by
a 3.2-kton water-Cherenkov outer detector (OD).
Electron antineutrinos are detected in KamLAND via the inverse beta-decay reaction,
ν e + p → e+ + n.

(2)This process has a delayed-coincidence (DC) event-pair signature which offers powerful backgroundsuppression. The energy deposited by the positron, which generates the DC pair’s prompt event,–5–
is approximately related to the incident ν e energy by Eν e ≃ Ep + E n + 0.8 MeV, where Ep is thesum of the e+ kinetic energy and annihilation γ energies, and E n is the average neutron recoil
energy which is of O(100 keV) for Ep > 7.5 MeV. The delayed event in the DC pair is generated
by a 2.2 MeV γ-ray produced when the neutron captures on a proton. The mean neutron capture
time is (207.5 ± 2.8) µs (Abe et al. 2010) . The detector is periodically calibrated with γ sources
deployed from a glove box installed at the top of the chimney region. The radioactive sources
are 60 Co, 68 Ge, 203 Hg, 65 Zn, 241 Am9 Be, 137 Cs, and 210 Po13 C, providing energy calibration up to∼8 MeV along the central axis of the detector. In addition, capture of neutrons on hydrogen andcarbon provides energy calibration throughout the entire sensitive volume. The visible energy inthe detector is measured from the number of detected photoelectrons and is corrected for event
position, detector non-uniformity, and scintillator non-linearity from quenching and Cherenkov
p
light production. The overall vertex reconstruction resolution is ∼12 cm / E(MeV), and energypresolution is 6.4%/ E(MeV). Energy reconstruction of positrons with Ep > 7.5 MeV (i.e., Eν e >8.3 MeV) is verified using tagged 12 B β − -decays (τ = 29.1 ms, Q = 13.4 MeV) generated via muon
spallation (Abe et al. 2010).

3.

Event Selection

The present analysis includes data accumulated between March 5, 2002 and July 23, 2010, corresponding to 2343 live-days. For the present search the following criteria were used: the prompt energy is required to be 7.5 MeV < Ep < 30.0 MeV, and the delayed energy to be 1.8 MeV < Ed < 2.6 MeV;a fiducial volume cut of R < 6 m on both prompt and delayed events, a time correlation cut of
0.5 µs < ∆T < 1000 µs, and a spatial correlation cut of ∆R < 1.6 m, this cut is driven by the mean
free path of capture-γ in the LS rather than the diffusion distance of the neutron. Spallation cuts
were used to reduce backgrounds from long-lived isotopes, such as 9 Li (τ = 257 ms, Q = 13.6 MeV),
that are generated by cosmic muons passing through the scintillator: a 2 ms veto is applied to theentire detector volume after a non-showering muon for both prompt and delayed events, a 2 s vetois applied after a showering muon (i.e., muons depositing more than 3 GeV of energy above theirminimum ionizing contribution) or non-reconstructed muon, while a 2-s 3-m-radius cylindrical cut
is applied around well-reconstructed non-showering muons (Abe et al. 2010) for delayed events.
The overall selection efficiency of the candidates is 92%, which is evaluated from a Monte Carlo(MC) simulation.

4.

Background Calculations

4.1.

Random Coincidences

Two uncorrelated events in the detector may accidentally coincide in time, space, and energy so
as to pass the ν e selection cuts. To estimate the background contribution from random coincidences,

–6–
events were selected with the appropriate prompt and delayed energies but in an out-of-time intervalof 0.2 s to 1.2 s after the prompt event. This out-of-time window is 103 times longer than thetime interval used for the ν e selection, providing a high-statistics background measurement. The
time distribution between prompt and delayed events in the range between 0.2 s and 1.2 s shows nocorrelation between these events. The random coincidence background for the analysis is determined
to be 0.22 ± 0.01 DC-pairs.

4.2.

Reactor Antineutrinos

The location of the KamLAND detector was selected for the copious ν e flux from 56 Japanese
nuclear power plants in order to study neutrino oscillation (Gando et al. 2011). The reactor ν e flux
at KamLAND dominates all other ν e sources for Ep < 7.5 MeV. However, the tail of the reactor
neutrino energy distribution extends to higher energies. The ν e flux comes primarily from the betadecay of neutron-rich fragments produced in the fission of four isotopes: 235 U, 238 U, 239 Pu, and
241 Pu. For each reactor the appropriate operational records including thermal power generation,
fuel burn-up, shutdowns and fuel reload schedule were used to calculate the fission rates. The
resulting ν e spectrum was calculated using the model of (Schreckenbach et al. 1985; Hahn et al.
1989; Vogel et al. 1981). The same methodology was used for previous reactor ν e analyses andshowed excellent agreement over a wide energy range between expected and detected ν e events
when taking neutrino oscillations into account (Gando et al. 2011). The total number of reactor
ν e candidates having Ep > 7.5 MeV is calculated to be 2.2 ± 0.7 events.
4.3.

Radioactive Isotopes

Cosmic-ray muons interacting with carbon nuclei in the scintillator produce a variety of radioactive isotopes (Abe et al. 2010). Two of these isotopes, 8 He and 9 Li, have decay modes withelectrons and neutrons in the final state. Such decays create DC-pairs similar to inverse beta-decay
and therefore represent a background in the present study.
The combination of a 2-s veto of the detector after showering muons and a 2-s 3-m-radius
cylindrical cut after non-showering muons significantly reduces the contribution of this background,but cannot eliminate it completely. The 9 Li isotope, which has a higher end-point value, longer life
time and a higher production rate, generates the majority of these background events after cuts.
To determine the contribution from this background we selected 9 Li candidates using the same cutsthat were used for the selection of the ν e candidates, but the muon veto was not applied. The 9 Li
rate was evaluated from the distribution of the decay time relative to all previous muons, using awider energy window of 0.9 MeV< Ep < 15.0 MeV to reduce statistical errors. For a 6-m fiducial
volume, 2074 ± 49 events were found after showering muons and 454 ± 31 events in a 3-m-radius
cylinder around the muon track after non-showering muons. 20% of these events occur in the

–7–energy region of interest 7.5 MeV< Ep < 15.0 MeV. The 2-s cut reduces the 9 Li background fromshowering muons to less than 0.2 events for Ep > 7.5 MeV. As non-showering muons occur with arelatively high frequency (0.2 Hz), to avoid the drastic loss of exposure which would accompany a
2-s full-detector veto we take advantage of the fact that non-showering muons can be relatively welltracked in the LS and instead restrict the 2-s veto to a 3-m-radius cylinder around the muon track.
A 2-ms full volume veto after all tagged muons is also used to suppress any spallation neutrons. To
measure the efficiency of these cuts the distribution of neutron captures as a function of distancefrom the muon track was examined, and we found only 5.9% of neutrons survive the 3-m-radius
cylindrical cut. The resulting number of 9 Li from spallation background with Ep > 7.5 MeV andsurviving the 3-m-radius cylindrical cut and time cut is 4.0 ± 0.3 events.
4.4.

Fast Neutrons

Fast neutrons outside the inner detector may cause backgrounds in the fiducial volume. A fastneutron can scatter on protons or carbon nuclei in the LS producing a scintillation signal followed
by a neutron capture signal, mimicking an ν e coincidence. A MC simulation of fast neutrons reveals
that the dominant background contribution is caused by muon-induced cosmogenic neutrons. A
2-ms veto after OD-tagged muons mostly eliminates this background, while OD-untagged muonsand the OD inefficiency cause a residual background. The MC-based study estimates 3.2 ± 3.2
fast neutrons remain in the data set, where a conservative uncertainty of 100% for the simulated
neutron production rate by muons is assumed (Abe et al. 2010).

4.5.

Atmospheric Neutrino Interactions

Charged current (CC) and neutral current (NC) interactions of atmospheric neutrinos withcarbon atoms in the KamLAND scintillator are the most significant source of background. Atmospheric neutrino spectra from (Honda et al. 2007), calculated specifically for the KamLAND
location, were used to estimate the contribution from these backgrounds.
The CC reactions by atmospheric ν e ’s generate an irreducible background. The contribution
from atmospheric ν e ’s is estimated to be ∼0.06 events in the energy window 7.5 MeV< Ep <30.0 MeV. Atmospheric νµ ’s and ν µ ’s could react with both protons and carbon nuclei to produce
muons and neutrons. The amount of detectable energy is shifted lower for such reactions becausea large fraction of the neutrino’s initial energy is expended to produce the muon. On the other
hand, such reactions are followed by muon decay and therefore manifest themselves as a triple timecorrelation between the prompt event, muon decay and neutron capture. In the event selection, we
found one coincidence event accompanied by a muon decay signal in a decay time interval of 0.5-µs
to 10-µs, and excluded it from the candidates. To calculate the contribution from these reactions,the cross sections from (Athar et al. 2007) were employed. The resulting background levels for

–8–reactions with a neutron in the final state are listed in Tab. 1. We estimate 4.0 ± 0.9 events intotal. The tagging efficiencies of the muon-decay-coincidence signature are calculated to be 78.6%
and (77.5 ± 0.2)% from mean life times in carbon of positive and negative muons respectively. The
residual background, including an untagged contribution from (7.1±1.4)% of negative muons which
capture rather than decay, is 0.9 ± 0.2 events.
The most challenging background to estimate is that from the NC interactions of all neutrino
species with carbon. In these reactions the neutrino transfers only a fraction of its energy to the final
products. It can eject a neutron from the carbon nucleus, leaving it in an excited state with multiple
decay modes. We used the following procedure to calculate the contribution from this background:
we integrated the momentum transfer from a neutrino to a quasi-free neutron over the entire
atmospheric neutrino spectra (Honda et al. 2007) using cross sections from (Ahrens et al. 1987).
We then accounted for the neutron binding energies for P-shell (18.7 MeV) and S-shell (41.7 MeV)
configurations and the corresponding shell populations. We also assumed that the neutron wasremoved from the carbon atom, leaving it in an excited state. All de-excitation modes reportedin (Kamyshkov & Kolbe 2003) were taken into account. For each final product we converted theparticle energy to visible energy in the detector using an energy scale model that includes nonlinearities from scintillator quenching. We calculate the contribution from this background to be
16.4 events with an estimated systematic uncertainty of 29% which is driven by uncertainties in
the atmospheric neutrino flux and the cross section of NC neutrino interactions.
We also attempted to estimate the NC background using the NUANCE software tool (version3), which simulates neutrino interactions and related processes (Casper 2002). However, we foundthe code overestimates this background rate by a factor of ∼2 relative to the above calculation in
the energy region under study, mainly due to an inaccurate cross section for intra-nuclear nucleon
re-scattering and an unexpected ∼25 MeV offset of outgoing neutron energies. We therefore do not
use the NUANCE-based estimation in this analysis.

5.

Data Interpretation

We observe 25 events after the cuts described in Section 3. The estimated number of backgrounds for ν e detection summarized in Tab. 2 is 26.9 ± 5.7 events in the prompt energy window
7.5 MeV < Ep < 30.0 MeV. Fig. 2 shows the event distribution as a function of prompt energy.
The data set presented here contains 16 times more statistics than the first KamLAND publicationon this subject, allowing us to verify the expected background contribution in the analyzed energy
window. The data is analyzed using an unbinned maximum likelihood fit to the event spectrum.
The estimate for 9 Li and reactor ν e are rather robust, on the other hand, reliable data for neutral
current interactions in the energy range of interest do not exist and the method we used to calculate
this background contribution has large uncertainties. To avoid possible bias from modeling in the
NC background calculation, the normalization of the NC events is a free parameter in the spectral
fits.

–9–
From the unbinned maximum likelihood fit, the allowed region for the NC background andthe probability of solar neutrino conversion is shown in Fig. 3. For the NC-floated normalization
analysis, the upper limit for neutrino conversion is 5.3 × 10−5 at 90% C.L., which corresponds to asolar ν e flux of 93 cm−2 s−1 above the energy threshold (Eν e ≥ 8.3 MeV). This limit is a factor 2.5
improvement over the previous limit in (Bellini et al. 2011). The fitted NC background assuming
zero solar ν e events is 14.8+5.8−5.4 events, which is in good agreement with the calculation (16.4 ± 4.7
events) within the uncertainties.
The probability for solar neutrino conversion can be predicted by the models of spin flavor
precession and MSW-LMA oscillations in the Sun. If the conversion model for 8 B neutrinos ofEq. (1) is assumed, we obtain the following limit on the product of the neutrino magnetic moment(µ) and the transverse solar magnetic field in the region of neutrino production (BT ):µ10−12 µBT (0.05R⊙ )< 5.9 × 102 ,
10 kG
B

(3)

using the value of 34◦ for the mixing angle (Gando et al. 2011). The current best limit on theneutrino magnetic moment is from the GEMMA spectrometer, µν e < 3.2 × 10−11 µB at 90%
C.L. (Beda et al. 2010). Lack of knowledge of the value of BT limits KamLAND sensitivity to
the neutrino magnetic moment.
This data also tests other potential ν e sources. Assuming an energy spectrum from the reference model (Ando & Sato 2004), we found an upper limit for the diffuse supernova ν e flux of
139 cm−2 s−1 at 90% C.L. in the analyzed energy range. This limit is weaker than our solar ν eflux limit due to the strong anticorrelation between the signal and NC background events amplified by the similarity in their spectral shapes. This flux limit corresponds to about 36 times
the model prediction (Ando & Sato 2004), indicating poor statistical power in constraining thecosmological models using the current KamLAND data. The upper limit for the monochromatic
ν e flux at each energy can be translated to a limit for the dark matter annihilation cross section (Palomares-Ruiz & Pascoli 2008). The dark matter annihilation limit varies weakly over thedark matter mass range due to limited statistics. We obtain hσA vi < (1–3) ×10−24 cm3 s−1 at 90%
C.L. in the mass range 8.3 MeV < mχ < 30.8 MeV, as shown in Fig. 4. This is the most stringent
constraint on the annihilation cross section below 15 MeV.
Finally, we also present model-independent upper limits for ν e fluxes, as shown in Fig. 5.
The limits are given at 90% C.L. based on the rate analysis using the Feldman-Cousins approach (Feldman & Cousins 1998) with 1 MeV energy bins, including all the constraints on the
background estimates in Tab. 2. The KamLAND data provides the best limits in the presented
energy range 8.3 MeV < Eν e < 18.3 MeV, owing to the efficient ν e detection by the delayed coincidence method and large exposure. Given that data are background limited, mainly from theatmospheric neutrino NC interactions, accumulation of additional statistics is unlikely to improve
this limit significantly.
In conclusion, we report the spectrum of high-energy ν e candidates found in the KamLAND

– 10 –
data set accumulated over more than eight years of detector operation. The live time exposure
corresponds to 4.53 kton-year. In the energy range from 8.3 MeV to 30.8 MeV, no excess of ν eevents over the expected background consisting of mostly atmospheric neutrino NC interactions,cosmogenically induced radioactivity, and reactor neutrino was detected. The data allow significantly improved limits on solar ν e conversion probability, and on diffuse supernova neutrino flux andannihilation cross section of dark matter below 15 MeV. The present level of background indicates
limitations for future studies of ν e ’s in this energy range using KamLAND. While a better detector
location could eliminate 9 Li background and suppress reactor neutrino background, atmospheric
neutrino NC interactions will continue to present significant challenges for next-generation large
liquid scintillator detectors.
The KamLAND experiment is supported by the Grant-in-Aid for Specially Promoted Research under Grant No. 16002002 of the Japanese Ministry of Education, Culture, Sports, Science and Technology; the World Premier International Research Center Initiative (WPI Initiative),
MEXT, Japan; and under the U.S. Department of Energy (DOE) Grants No. DE-FG03-00ER41138,
DE- AC02-05CH11231, and DE-FG02-01ER41166, as well as other DOE grants to individual institutions. The reactor data are provided by courtesy of the following electric associations inJapan: Hokkaido, Tohoku, Tokyo, Hokuriku, Chubu, Kansai, Chugoku, Shikoku, and Kyushu
Electric Power Companies, Japan Atomic Power Company, and Japan Atomic Energy Agency.
The Kamioka Mining and Smelting Company has provided service for activities in the mine.

APPENDIX
The model-independent upper limits for ν e fluxes provided for each energy may be useful togive an estimate of upper limits for various ν e sources. For example, one can easily test one’s own
model with a certain energy spectrum by an appropriate data integration. Tab. 3 lists the 1 MeV
binned upper limits shown in Fig. 5. The binned χ2 is defined as
χ2 =

X
i

ν2
√i
(ui / 2.71)2(4)

where νi is the model expectation for each energy bin, ui is the KamLAND upper limit at 90%√
C.L., and 2.71 is the conversion factor of limits from 90% C.L. to 1σ C.L. This binned χ2analysis approximately reproduces the solar ν e flux limit which is based on the unbinned maximum
likelihood method including all background and systematic uncertainties. On the other hand, alimit for the diffuse supernova ν e flux based on Eq. (4) will be optimistic, because Tab. 3 data
include the constraints on the NC background estimate.

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This preprint was prepared with the AAS LATEX macros v5.2.

– 13 –

Calibration device
Chimney

Water-Cherenkov
outer detector

Buffer oil
Balloon(13 m diameter)

Containment vessel(18 m diameter)

Fiducial volume(12 m diameter)

Liquid scintillator(1 kton)Outer detector
Photomultiplier tube

Fig. 1.— Schematic diagram of the KamLAND detector.

Photomultipliertube

– 14 –

12
KamLAND data
accidental
fast-neutron
atmospheric ν CC
atmospheric ν NC
spallation
reactor νe
BG + solar νe(90% C.L. upper limit)

Events / MeV

10
8
6
4
2
0

10

15

20
Ep (MeV)25

30

Fig. 2.— Prompt energy distribution of selected ν e candidates together with the best-fit backgrounds (filled areas) and 90% C.L. upper limit of solar ν e ’s (red dashed line). The backgroundhistograms are cumulative.

– 15 –

Atmospheric ν NC (Events)

4030

68.3% C.L.
90.0% C.L.
95.4% C.L.
99.7% C.L.

20

10

0
0

5
10
Conversion Probability

×10-5
15

Fig. 3.— Allowed region, with the best-fit point, for the unconstrained neutral current (NC)background and the probability of solar neutrino conversion from the KamLAND data in theenergy range of 8.3 MeV < Eν e < 30.8 MeV. The confidence level (C.L.) is shown for two degrees of
freedom. The gray shaded region indicates the ±1σ prediction from the NC background calculation.

– 16 –<σA v>90 (cm3 s-1)

10-22

10-23

10-24

10-25

10-26

10

15

20

25

30

mχ (MeV)Fig. 4.— Upper limits at 90% C.L. on the dark matter annihilation cross section from KamLAND(solid line) and Super-Kamiokande (dashed line) (Palomares-Ruiz & Pascoli 2008). The shaded
curve shows the natural scale of the annihilation cross section.

– 17 –KamLAND
Borexino
Super-Kamiokande
SNO

νe Flux (cm-2 s-1 MeV-1)

107
106
105
104
103
102
10
1
10-1
5

10

15

Eν (MeV)eFig. 5.— Model independent upper limits at 90% C.L. on the ν e flux from KamLAND (blue line),
Borexino (Bellini et al. 2011) (red line), SNO (Aharmim et al. 2004) (magenta line), and SuperKamiokande (Gando et al. 2003) (green line). The shaded curve shows the diffuse supernova ν eflux for the reference model prediction (Ando & Sato 2004).

– 18 –

Table 1.

Table 2.

Calculated backgrounds for atmospheric neutrino CC interactions with prompt energy
between 7.5 MeV and 30.0 MeV.
Reaction

Number of events

νµ +12 C→ µ− + n+11 N
ν µ +12 C→ µ+ + n+11 B+γ
ν µ +12 C→ µ+ + n+7 Li+α
ν µ +12 C→ µ+ + 2n+10 B
ν µ +12 C→ µ+ + n+11 B
ν µ + p → µ+ + n
Total

0.4
0.4
0.4
0.02
0.7
2.1
4.0 ± 0.9

Summary of the estimated backgrounds with prompt energy between 7.5 MeV and
30.0 MeV.
BackgroundNumber of events

Random coincidences
Reactor ν e
9 Li
Atmospheric ν (CC)
Atmospheric ν (NC)Fast-neutron
Total

0.22 ± 0.01
2.2 ± 0.7
4.0 ± 0.3
0.9 ± 0.2
16.4 ± 4.7
3.2 ± 3.2
26.9 ± 5.7

– 19 –

Table 3.

Model independent upper limit on the ν e flux for each energy bin from KamLAND, as
shown in Fig. 5.
Energy Range (MeV)

Upper Limit at 90% C.L. (cm−2 s−1 )8.3-9.3
9.3-10.3
10.3-11.3
11.3-12.3
12.3-13.3
13.3-14.3
14.3-15.3
15.3-16.3
16.3-17.3
17.3-18.3

56.2
67.1
83.8
14.0
25.8
32.2
18.9
24.1
14.5
13.0