Reactor On-Off Antineutrino Measurement with KamLAND
A. Gando,1 Y. Gando,1 H. Hanakago,1 H. Ikeda,1 K. Inoue,1, 2 K. Ishidoshiro,1 H. Ishikawa,1 M. Koga,1, 2
R. Matsuda,1 S. Matsuda,1 T. Mitsui,1 D. Motoki,1 K. Nakamura,1, 2 A. Obata,1 A. Oki,1 Y. Oki,1
M. Otani,1 I. Shimizu,1 J. Shirai,1 A. Suzuki,1 Y. Takemoto,1 K. Tamae,1 K. Ueshima,1 H. Watanabe,1
B.D. Xu,1 S. Yamada,1 Y. Yamauchi,1 H. Yoshida,1 A. Kozlov,2 S. Yoshida,3 A. Piepke,2, 4 T.I. Banks,5B.K. Fujikawa,2, 5 K. Han,5 T. O’Donnell,5 B.E. Berger,6 J.G. Learned,7 S. Matsuno,7 M. Sakai,7 Y. Efremenko,2, 8
H.J. Karwowski,9 D.M. Markoff,9 W. Tornow,2, 9 J.A. Detwiler,10 S. Enomoto,2, 10 and M.P. Decowski2, 11(The KamLAND Collaboration)
1
Research Center for Neutrino Science, Tohoku University, Sendai 980-8578, Japan
Kavli Institute for the Physics and Mathematics of the Universe (WPI), University of Tokyo, Kashiwa, 277-8583, Japan
3
Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan
4
Department of Physics and Astronomy, University of Alabama, Tuscaloosa, Alabama 35487, USA
5
Physics Department, University of California, Berkeley, andLawrence Berkeley National Laboratory, Berkeley, California 94720, USA
6
Department of Physics, Colorado State University, Fort Collins, Colorado 80523, USA
7
Department of Physics and Astronomy, University of Hawaii at Manoa, Honolulu, Hawaii 96822, USA
8
Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996, USA
9
Triangle Universities Nuclear Laboratory, Durham, North Carolina 27708, USA; Physics Departments at Duke
University, Durham, North Carolina 27705, USA; North Carolina Central University, Durham, North Carolina
27701, USA and the University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599, USA
10
Center for Experimental Nuclear Physics and Astrophysics, University of Washington, Seattle, Washington 98195, USA
11
Nikhef and the University of Amsterdam, Science Park, Amsterdam, the Netherlands(Dated: March 21, 2013)arXiv:1303.4667v2 [hep-ex] 20 Mar 20132

The recent long-term shutdown of Japanese nuclear reactors has resulted in a significantly reduced reactor
ν e flux at KamLAND. This running condition provides a unique opportunity to confirm and constrain backgrounds for the reactor ν e oscillation analysis. The data set also has improved sensitivity for other ν e signals,
in particular ν e ’s produced in β-decays from 238 U and 232 Th within the Earth’s interior, whose energy spectrum overlaps with that of reactor ν e ’s. Including constraints on θ13 from accelerator and short-baseline reactor
neutrino experiments, a combined three-flavor analysis of solar and KamLAND data gives fit values for the os2+0.18−5cillation parameters of tan2 θ12 = 0.436+0.029
eV2 , and sin2 θ13 = 0.023+0.002−0.025 , ∆m21 = 7.53−0.18 × 10
−0.002 .
+28
238
U and 232 Th, corresponding toAssuming a chondritic Th/U mass ratio, we obtain 116−27 ν e events from6
−2 −1
s at the KamLAND location. We evaluate various bulk silicate Eartha geo ν e flux of 3.4+0.8−0.8 × 10 cmcomposition models using the observed geo ν e rate.
PACS numbers: 14.60.Pq, 28.50.Hw, 91.35.-x, 91.67.Qr

I.

INTRODUCTION

The Kamioka Liquid-scintillator Antineutrino Detector(KamLAND) demonstrated the oscillatory nature of neutrino
flavor transformation by observing electron antineutrinos (ν e )with energies of a few MeV from nuclear reactors typically
180 km away [1]. Following the Fukushima nuclear accident
in March 2011, the entire Japanese nuclear reactor industry,
which generates >97% of the reactor ν e flux at KamLAND,
has been subjected to a protracted shutdown due to a review
of nuclear safety standards. This unexpected situation allows
for a reactor on-off study of backgrounds for the KamLAND
neutrino oscillation analysis.
The reactor-off data also yield improved sensitivity forν e ’s produced by other sources. Previously, we used the
KamLAND data to search for geoneutrinos, ν e ’s producedin β-decays from primordial radioactivity within the Earth’s
interior. The 238 U and 232 Th decay chains emit ν e ’s with energies below 3.4 MeV, so reactor ν e events with similar energies pose a background for this signal. Despite having a highreactor ν e background, KamLAND performed the first exper-

imental study of geo ν e ’s from the decay chains of 238 U and232
Th [2]. Later the geo ν e signal at KamLAND was used
to estimate our planet’s radiogenic heat production and constrain composition models of the bulk silicate Earth (BSE, theEarth’s region outside its metallic core). In particular it was
found that fully-radiogenic Earth models are disfavored [3].
The Borexino experiment at Gran Sasso also reported a positive observation of geo ν e ’s [4].
In this article, we present improved reactor neutrino oscillation results and geo ν e flux measurements including the recent
reactor-off period. For the reactor ν e rate estimate, we also apply new evaluations of reactor antineutrino emission spectra,
as well as constraints on oscillation parameters from accelerator and short-baseline reactor neutrino oscillation measurements.

II.

NEUTRINO OSCILLATION

Neutrino oscillation is well established by experimental
studies of solar, reactor, atmospheric, and accelerator neutri-

2
nos. KamLAND observes ν e ’s from many reactors at a fluxweighted average distance of 180 km, providing optimal sensitivity for the LMA-MSW ν1 -ν2 mixing solution to the solar
neutrino problem. For the length scale relevant to reactor ν eoscillation at KamLAND, the three-flavor survival probability3ν
(Pee), including matter effects, may be approximated as

Chimney

Photomultiplier Tubes2ν
3ν
+ sin4 θ13 .
Pee= cos4 θ13 Peee(1)
Buffer Oil

2ν
The two neutrino survival probability Peee
has the same form
as the survival probability in matter for ν1 -ν2 mixing but with
ee = Ne cos2 θ13 [5]. It
the electron density (Ne ) modified: Nis given by2ν
Peee= 1 − sin2 2θ12M sin2

∆m221M L
4Eν

,

Xe-LS 13 ton

Outer Balloon(13 m diameter)
Inner Balloon(3.08 m diameter)

LS 1 kton(2)

where L is the distance from the source to the detector, Eν isthe ν e energy, and θ12M and ∆m221M are the matter-modified
mixing angle and mass splitting defined bysin2 2θ12, (3)(cos 2θ12 − A/∆m221 )2 + sin2 2θ12q∆m221M = ∆m221 (cos 2θ12 − A/∆m221 )2 + sin2 2θ12 .(4)Fiducial Volume(12 m diameter)

FIG. 1: Schematic diagram of the KamLAND detector. The shaded
region in the liquid scintillator indicates the volume for the ν e analysis after the inner balloon was installed.

sin2 2θ12M =√ee Eν has a negative sign for
The parameter A = ±2 2GF N
antineutrinos; GF is the Fermi coupling constant.
Recently, accelerator and short-baseline (∼1 km) reactor
experiments have demonstrated that θ13 is non-zero, and havemeasured it with high precision [6–10]. An analysis incorporating this new θ13 constraint will improve the determinationof the other oscillation parameters.

III.

GEONEUTRINO FLUX AT KAMLAND

While the mechanical properties of the Earth’s interior are
well established, its composition, including its radiochemical
content, remains uncertain. Decays of uranium (U), thorium(Th), potassium (K) and their progeny generate heat. Depending on their abundance and distribution within the Earth, these
decays may be an essential heat source for generating Earthdynamics. A leading BSE model [11] based on measured elemental abundances of chondritic meteorites and mantle peridotites predicts a radiogenic heat production of 8 TW fromthe 238 U decay chain, 8 TW from the 232 Th decay chain, and
4 TW from 40 K [12]. This would account for nearly half of theheat dissipation rate from the Earth’s surface, which a recent
analysis finds to be 47 ± 2 TW [13].
The energy spectrum of 40 K neutrinos falls entirely below
the 1.8 MeV energy threshold for the inverse β-decay reaction
by which KamLAND observes antineutrinos, rendering these
decays invisible to KamLAND. However, the 238 U and 232 Th
decay chain ν̄e ’s extend above this threshold with distinct energy distributions, making possible a direct measurement of
the individual 238 U and 232 Th contributions.

The geo ν e flux at the KamLAND detector can be calculated from the isotope abundances ai (r~′ ) for each isotope i atsource positions r~′ by integrating over the entire Earth,dΦ(Eν , ~r)dEν
X dni (Eν ) Z
ai (r~′ )ρ(r~′ )Pee (Eν , |~r − r~′ |)Ai=d3 r~′, (5)dEν
4π|~r − r~′ |2⊕iwhere ~r is the detector position, Ai is the decay rate per unit
mass, dni (Eν )/dEν is the ν e energy spectrum for each modeof decay, ai (r~′ ) is the isotope mass per unit rock mass, ρ(r~′ ) is
the rock density, and Pee (Eν , |~r − r~′ |) is the ν e survival probability given by Eq. (1) with L = |~r − r~′ |. Given the measured
values of neutrino oscillation parameters and the energy range
of detectable geo ν e ’s, the integration over the volume of the
Earth averages over the second sine function in Eq. (2), allowing the approximation,


1
2
3ν
4
(6)
Pee ≃ cos θ13 1 − sin 2θ12 + sin4 θ13 .
2
In Eq. (6) we have neglected matter effects, which modify
the survival probability by <1% [14]. From a global analysisof neutrino oscillation data involving solar, accelerator, andreactor neutrinos, including the present KamLAND data, we
obtain Pee = 0.551 ± 0.015. The less-than 3% uncertainty
in Pee is negligible compared to the statistical uncertainty of
KamLAND’s current geo ν e flux measurement.
IV.

THE KAMLAND EXPERIMENT

KamLAND is located in Gifu Prefecture, Japan, under
Mount Ikenoyama at a depth of ∼2700 m water-equivalent.

3
The primary volume consists of 1 kton of ultra-pure liquid
scintillator (LS), which comprises the neutrino interaction target (Fig. 1). The LS is contained in a 13-m-diameter spherical balloon made of 135-µm-thick transparent nylon/EVOH(ethylene vinyl alcohol copolymer) composite film. The balloon is suspended in non-scintillating purified mineral oil contained inside an 18-m-diameter stainless steel tank. The LS
consists of 80% dodecane and 20% pseudocumene (1,2,4trimethylbenzene) by volume, and 1.36 ± 0.03 g/liter PPO(2,5-diphenyloxazole) as a fluor. The scintillation light isviewed by an array of 1325 specially-developed fast 20-inchdiameter photomultiplier tubes (PMTs) masked to 17-inch
diameter, and 554 older unmasked 20-inch PMTs, providing 34% solid-angle coverage in total. This inner detector(ID) is surrounded by a 3.2 kton water-Cherenkov outer detector (OD) that serves as a cosmic-ray muon veto counter.
In September 2011, the KamLAND-Zen neutrinoless double beta-decay search was launched [15]. This search makes
use of KamLAND’s extremely low background and suspends
a ββ source, 13 tons of Xe-loaded liquid scintillator (Xe-LS),in a 3.08-m-diameter inner balloon (IB) at the center of thedetector, as shown in Fig. 1. To avoid backgrounds from the
IB and its support material, the ν e analysis reported here is
restricted to events occurring well outside the IB.
Electron antineutrinos are detected through the inverse βdecay reaction, ν e + p → e+ + n, which yields a delayed coincidence (DC) event pair signature that provides a powerful tool to suppress backgrounds. The prompt scintillation
light from the e+ gives a measure of the incident ν e energy,Eν ≃ Ep + E n + 0.8 MeV, where Ep is the sum of the e+
kinetic energy and annihilation γ energies, and E n is the average neutron recoil energy, O(10 keV). The mean time for
capture of the neutron in the LS is 207.5 ± 2.8 µs [16]. The
scintillation light from the capture γ constitutes the delayed
event of the DC pair.

V.

ANTINEUTRINO CANDIDATE EVENT SELECTION

The data reported here are based on a total live-time of2991 days, collected between March 9, 2002 and November 20, 2012. The data set is divided into three periods.
Period 1 (1486 days live-time) refers to data taken up to May
2007, at which time we embarked on a LS purification campaign that continued into 2009. Period 2 (1154 days livetime) refers to data taken during and after the LS purification campaign, and Period 3 (351 days live-time) denotes thedata taken after installing the IB. We removed periods of low
data quality and high dead time that occurred during LS purification and KamLAND-Zen IB installation. The LS purification reduced the dominant Period 1 background for ν̄e ’s,
13C(α, n)16 O decays, by a factor of ∼20. The high-quality
data taken after LS purification accounts for 50% of the total live-time. Using a spherical fiducial scintillator volume
with 6.0 m radius, the number of target protons is estimatedto be (5.98 ± 0.13) × 1031 , resulting in a total exposure of(4.90 ± 0.10) × 1032 target-proton-years. The reduced fiducial volume in Period 3 is accounted for in the detection ef-

ficiency; it contributes negligible additional fiducial volume
uncertainty for Period 3.
Event vertex and energy reconstruction is based on thetiming and charge distributions of scintillation photons
recorded by the ID PMTs. The reconstruction is calibrated with 60 Co, 68 Ge, 203 Hg, 65 Zn, 241 Am9 Be, 137 Cs, and210
Po13 C radioactive
p sources. The achieved vertex resolution is p
∼12 cm / E(MeV), and the energy resolution is
6.4% / E(MeV). The nonlinear, particle-dependent conversion between deposited (real) energy and KamLAND’s
prompt energy scale is performed with a model incorporating Birks quenching and Cherenkov emission. The model
parameters are constrained with calibration data, and contribute a 1.8% systematic uncertainty to the measured valueof ∆m221 . Using calibration data taken throughout the fiducial
volume during Period 1, we find that the deviation of reconstructed vertices from the actual deployment locations is lessthan 3 cm. Incorporating a study of muon-induced 12 B/12 N
decays [18], the fiducial volume uncertainties are 1.8% for the
pre-purification data and 2.5% for the post-purification data.
For the DC event pair selection, we apply the following
series of cuts: (i) prompt energy: 0.9 < Ep (MeV) < 8.5;(ii) delayed energy:
1.8 < Ed (MeV) < 2.6 (captureon p), or 4.4 < Ed (MeV) < 5.6 (capture on 12 C);(iii) spatial correlation of prompt and delayed events:∆R < 2.0 m; (iv) time separation between prompt anddelayed events: 0.5 < ∆T (µs) < 1000; (v) fiducial volume
radii: Rp , Rd < 6.0 m; (vi) and for Period 3, delayed vertex
position: Rd > 2.5 m and ρd > 2.5 m, Zd > 0 m (verticalcentral cylinder cut at the upper hemisphere) to eliminate
backgrounds from the KamLAND-Zen material. To maximize the sensitivity to ν e signals, we perform an additional
event selection designed to suppress accidental coincidence
backgrounds from radioactive contaminants in the detector
while maintaining high efficiency for ν e ’s. First, using a
combination of Monte Carlo, data-driven, and analyticalmethods, we constructed a probability density function (PDF)
for the ν e signal (fν e ) and accidental (facc ) coincidence
events. The PDF is based on the six cut parameters (Ep , Ed ,∆R, ∆T , Rp , Rd ). For each candidate pair, we calculate thefν eand determine a selection value,
discriminant L = fν +facce

S
Lcut (Ep ), to maximize the figure-of-merit √S+B
foracc
prompt energy intervals of 0.1 MeV. In the figure-of-merit,
S is the number of the expected signal events assuming anoscillation-free reactor spectrum and the geo ν e fluxes predicted by [17]. Bacc corresponds to the number of accidental
background events, as measured using an out-of-time delayedcoincidence window selection (10 ms < ∆T < 20 s). The
selection efficiency is calculated via Monte Carlo from theratio of selected ν e ’s to the total number of generated ν e ’s in
R < 6 m. The systematic uncertainty is evaluated using 68 Ge
and 241 Am9 Be source calibrations as discussed in [1]. The
total number of events passing all selection criteria is 2611.
The reactor fluxes can be predicted from reactor operation
records, which are provided to the KamLAND Collaboration
by a consortium of Japanese electric power companies, andinclude the thermal power variation as well as fuel exchange

4
TABLE I: Estimated backgrounds for ν e in the energy range between 0.9 MeV and 8.5 MeV after event selection cuts.
Background

Period 1(1486 days)
1 Accidental
76.1 ± 0.1
2 9 Li/8 He
17.9 ± 1.4 13C(α, n)16 Og.s. , elastic scattering
160.4 ± 16.4
3 13C(α, n)16 Og.s. , 12 C(n, n ′ )12 C∗ (4.4 MeV γ) 6.9 ± 0.7 13C(α, n)16 O∗ , 1st e.s. (6.05 MeV e+ e− )14.6 ± 2.9
4 13C(α, n)16 O∗ , 2nd e.s. (6.13 MeV γ)
3.4 ± 0.7
5 Fast neutron and atmospheric neutrino
< 7.7
Total
279.2 ± 22.1

Period 2(1154 days)
44.7 ± 0.1
11.2 ± 1.1
16.5 ± 3.8
0.7 ± 0.2
1.7 ± 0.5
0.4 ± 0.1
< 5.9
75.2 ± 7.6

Period 3(351 days)
4.7 ± 0.1
2.5 ± 0.5
2.3 ± 1.0
0.10 ± 0.04
0.21 ± 0.09
0.05 ± 0.02
< 1.7
9.9 ± 2.1

All Periods(2991 days)
125.5 ± 0.1
31.6 ± 1.9
179.0 ± 21.1
7.7 ± 0.9
16.5 ± 3.5
3.9 ± 0.8
< 15.3364.1 ± 30.5

Period 1

Period 2

Period 3

0.5
0.4
0.3
0.2
0.1
0

2002

2003

2004

2005

2006

2007

Rate (events/day)

2009

2010

2011

Period 2

Period 3

0.7
0.6
0.5
0.4

0.1
0

KamLAND data
Expected reactor ν e + backgrounds + geo ν eExpected reactor ν e + backgrounds
Expected reactor ν e

2002

2003

0.3
0.2
0.1
0

2004

2005

2006

2007

0.1

0.2

0.3

0.4

0.5

0.6

Expected Rate (events/day)

Period 1

0.2

0.4

2012

0.9
0.8

0.3

0.5

Year

(b) 2.6-8.5 MeV
1

2008

0.6

2008

2009

Year

2010

2011

2012

Observed Rate (events/day)Rate (events/day)

0.6

Observed Rate (events/day)(a) 0.9-2.6 MeV

1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Expected Rate (events/day)

FIG. 2: Time evolution of expected and observed rates at KamLAND for ν e ’s with energies between (a) 0.9 MeV and 2.6 MeV and (b)2.6 MeV and 8.5 MeV. The points indicate the measured rates in a coarse time binning, while the curves show the expected rate variation forreactor ν e ’s (black line), reactor ν e ’s + backgrounds (colored line), and reactor ν e ’s + backgrounds + geo ν e ’s (gray line). The geo ν e rates
are calculated from the reference model [17]. The vertical bands correspond to data periods not used in the analysis. In the right panel of (a),the data are grouped according to periods of similar expected reactor ν e + background rates, as denoted by the colored bands. The observed
event rate for each group is plotted at the exposure-weighted expected event rate within the group. The efficiency-corrected best-fit value ofthe geo ν e rate from the full spectral analysis (dashed line), its 1σ error (shaded region), and the model expectation (gray line) are drawn forcomparison. The contribution of geo ν e ’s in (b) is negligible. The oscillation parameters used to calculate the expected reactor ν e rate are the
+0.18
−5
2
eV2 , and sin2 θ13 = 0.023+0.002
best-fit values from the global oscillation analysis: tan2 θ12 = 0.436+0.029−0.002 .
−0.025 , ∆m21 = 7.53−0.18 × 10

and reshuffling data for all Japanese commercial reactors. The
thermal power generation used for the normalization of thefission rates is measured to within 2%. Only four isotopes
contribute significantly to the ν e emission spectra; the relative
fission yields, averaged over the entire live-time period for thisresult, are (0.567 : 0.078 : 0.298 : 0.057) for (235 U : 238 U :239
Pu : 241 Pu), respectively. A recent recalculation of the ν espectra per fission of these isotopes introduced a ∼3% upward

shift [19, 20] relative to the previous standard calculation [21,22], causing past measurements at short-baselines to appear
to have seen fewer ν̄e ’s than expected. It has been speculated
that this so-called Reactor Antineutrino Anomaly may be due
to some systematic uncertainty or bias, or could potentiallybe due to oscillation into a heavy sterile neutrino state with∆m2 ∼ 1 eV2 [23]. To make our analysis insensitive to theseeffects, the normalization of the cross section per fission forVI. ANTINEUTRINO MEASUREMENT AND
OSCILLATION ANALYSIS

To extract the neutrino oscillation parameters and geoneutrino fluxes, ν e candidates are analyzed with an unbinned
maximum-likelihood method incorporating the event rate andthe prompt energy spectrum shape, including their time variation, in the range 0.9 < Ep (MeV) < 8.5. The χ2 is definedbygeoχ2 = χ2rate (θ12 , θ13 , ∆m221 , NBG1→5 , NU,Th, α1→4 )geo−2 ln Lshape (θ12 , θ13 , ∆m221 , NBG1→5 , NU,Th, α1→4 )+χ2BG (NBG1→5 ) + χ2syst (α1→4 )+χ2osci (θ12 , θ13 , ∆m221 ) .

(8)

(a)
Period 1
Period 2
Period 360

0.16

Events/0.2MeV/day

40(b) Period 1

0.14
0.12
0.1
0.08

0.08
0.06
0.04
0.02
0
1

1.5

2

2.5

Ep (MeV)

0.06
0.04
0.02
0
0.16

Events/0.2MeV/day

where αi is the fractional fission rate of the isotope i. The
contribution from Korean reactors, based on reported electric power generation, is estimated to be (4.9 ± 0.5)%. The
contribution from Japanese research reactors and all other reactors around the world is (1.1 ± 0.6)%. The levels of thelong-lived, out-of-equilibrium fission products 90 Sr, 106 Ru,
and 144 Ce [25] are evaluated from the history of fission rates
for each isotope and are found to contribute an additional(0.7 ± 0.3)%. Applying the selection cut efficiency, we expect a total of 3564 ± 145 events from reactors in the absenceof ν e disappearance.
A calculation of the geo ν e flux at KamLAND based on
the reference Earth model of [17] gives an expected 109 and
27 geo ν e events from U and Th, respectively. Since the estimation of the geo ν e yield is highly model-dependent, theevent rates from the U and Th decay chains are not constrainedin the oscillation analysis. Only the prompt energy spectral
shapes, which are independent of the Earth model, are used toconstrain their contributions. A possible contribution from ahypothetical reactor-ν e source at the Earth’s center, motivatedby [26] and investigated in [4] and [3], is neglected as a background in the fit for the oscillation parameters and geoneutrino
fluxes, but is addressed briefly below as an independent signal.
In Period 1, the dominant background is the 13 C(α, n)16 O
reaction, generated from the α-decay of 210 Po in the LS.
The neutrons in this reaction are produced with energies
up to 7.3 MeV, but the visible energy is quenched to below 2.7 MeV. Accounting for the energy-dependent efficiency of the Lcut (Ep ) selection, the estimated number of
13
C(α, n)16 O background events is 207.1 ± 26.3 in the energy region 0.9 < Ep (MeV) < 8.5. The accidental background, which dominates in Periods 2 and 3, is measured withan out-of-time delayed coincidence window from 10 ms to
20 s to be 125.5 ± 0.1 events. Including smaller contributions
from cosmogenically produced radioactive isotopes, fast neutrons produced by cosmic-ray muons, and atmospheric neutrinos, the total background is estimated to be 364.1 ± 30.5
events. The backgrounds are detailed in Table I.

10080(c) Period 2

0.14
0.12
0.1
0.08

0.08
0.06
0.04
0.02
0
1

1.5

2

2.5

Ep (MeV)

0.06
0.04
0.02
0
0.16

(d) Period 3
KamLAND data
best fit osci.
accidental13
C(α, n)16O
Best-fit Geo νeBest-fit osci. + BG
+ best-fit Geo νe

0.14
0.12
0.1
0.08
0.06
0.04

Events/0.2MeV/dayi

Events/0.425MeV/day

each reactor is adjusted to reproduce the Bugey4 result [24]:X(αreac.
− αBugey4) hσii (7)hσireac. = hσiBugey4 +iiEfficiency (%)

5

0.03
0.02
0.01
0

1

1.5

2

2.5

Ep (MeV)

0.02
0

0

1

2

3

4

5

6

7

8

Ep (MeV)
FIG. 3: Prompt energy spectrum of ν e candidate events above the0.9 MeV energy threshold (vertical dashed line) for each data taking period. The background, reactor and geo ν e contributions are
the best-fit values from a KamLAND-only analysis. The prompt energy spectra of ν e candidate events in the low-energy region are also
shown in the inset panels with a finer binning. The top panel showsthe energy-dependent selection efficiency curves for each period.

The terms are, in order: the χ2 contribution for (i) the timevarying event rate, (ii) the time-varying prompt energy spectrum shape, (iii) a penalty term for backgrounds, (iv) a penalty
term for systematic uncertainties, and (v) a penalty term forgeo
the oscillation parameters. NU,Th
are the flux normalization
parameters for U and Th geo ν e ’s, and allow for an Earthmodel-independent analysis. NBG1→5 are the expected number of backgrounds, and are allowed to vary in the fit but are
constrained with the penalty term (iii) using the estimates described in the preceding section and listed, with the corresponding index, in Table I. α1→4 parametrize the uncertainties on the reactor ν e spectrum, the energy scale, the event
rate, and the energy-dependent detection efficiency; these parameters are allowed to vary in the analysis but are constrained

20
15
10
5

4σ

1

2σ
1σ
KamLAND+Solar KamLAND
95% C.L.

95% C.L.

99% C.L.

99% C.L.

99.73% C.L.

99.73% C.L.

best-fit

4σ

(a)

3σ

2.2
2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2

best-fit

Solar
95% C.L.
99% C.L.

0.4
0.2
3-ν best-fit oscillation

0
20

30

40

60

70

80

90

100

e

∆χ

20
15
10
5

50

Data - BG - Geo νe

L0/Eν (km/MeV)

θ13 freetan θ12∆χ 2

0.6

best-fit22

4σ

FIG. 5: Ratio of the observed ν e spectrum to the expectation for
no-oscillation versus L0 /E for the KamLAND data. L0 = 180 km
is the flux-weighted average reactor baseline. The 3-ν histogram isthe best-fit survival probability curve from the three-flavor unbinned
maximum-likelihood analysis using only the KamLAND data.

3σ
2σ
1σ
95% C.L.

99% C.L.

99% C.L.

99.73% C.L.

99.73% C.L.

best-fit

4σ

95% C.L.

3σ(b)

KamLAND+Solar KamLAND

2σ
1σ

2
∆m21
(10-4eV 2)0.8

99.73% C.L.

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 5 10 15 20

2.2
2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2

Survival Probability

3σ

2σ
1σ

2
∆m21
(10-4eV 2)

∆χ 2

6

best-fit

Solar
95% C.L.
99% C.L.
99.73% C.L.
best-fitθ13 constrained

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 5 10 15 20

tan2 θ12∆ χ2

FIG. 4: Allowed regions projected in the (tan2 θ12 , ∆m221 ) plane,
for solar and KamLAND data from the three-flavor oscillation analysis for (a) θ13 free and (b) θ13 constrained by accelerator and shortbaseline reactor neutrino experiments. The shaded regions are fromthe combined analysis of the solar and KamLAND data. The sidepanels show the ∆χ2 -profiles projected onto the tan2 θ12 and ∆m221
axes.

by term (iv). Table II summarizes the systematic uncertainties
on ∆m221 and the expected event rate of reactor ν e ’s. The
overall rate uncertainties for Period 1 and for Periods 2 and 3
are 3.5% and 4.0%, respectively. Systematic uncertainties
are conservatively treated as being fully correlated across alldata taking periods. The penalty term (v) optionally provides
a constraint on the neutrino oscillation parameters from solar [27–31], accelerator (T2K [6], MINOS [7]), and shortbaseline reactor neutrino experiments (Double Chooz [8],Daya Bay [9], RENO [10]).

Figure 2 plots the time variation for the rates of reactor ν e ’s,
geo ν e ’s, and backgrounds for the three data taking periods,
assuming the best-fit oscillation parameters, and geo ν e fluxes
from the reference model of [17]. Also drawn are the correlations between the measured and expected best-fit event rates,
which should fit to a line with unit slope and zero offset in theabsence of geo ν e ’s. The vertical displacement of the trend
for events below 2.6 MeV is attributed to the contribution ofgeo ν e ’s.
Figure 3 shows the prompt energy spectra of ν e candidate
events for each period. The reduction of the 13 C(α, n)16 O
background in Period 2 and of reactor ν e ’s in Period 3 canclearly be seen. For the three-flavor KamLAND-only analysis (χ2osci = 0), the fit oscillation parameter values are−5∆m221 = 7.54+0.19
eV2 , tan2 θ12 = 0.481+0.092−0.18 × 10
−0.080 ,+0.0332and sin θ13 = 0.010−0.034. The contours are nearly symmetric about tan2 θ12 = 1, but the best-fit values for tan2 θ12 > 1
are slightly disfavored over those for tan2 θ12 < 1, with
∆χ2 = 0.8. Assuming CPT invariance, the oscillation parameter values from a combined analysis including constraints

TABLE II: Contributions to the systematic uncertainty in the neutrino
oscillation parameters ∆m221 , θ12 , and θ13 for the earlier / later periods of measurement, denoted in the text as Period 1 / Period 2 & 3.
The overall uncertainties are 3.5% / 4.0% for Period 1 / Period 2 & 3.
∆m221
Rate

Detector-related (%)
Energy scale
1.8 / 1.8

Reactor-related (%)ν e -spectra [32]0.6 / 0.6

Fiducial volume
Energy scale
Lcut (Ep ) eff.
Cross section
Total

ν e -spectra [24]Reactor power
Fuel composition
Long-lived nuclei
Total

1.8 / 2.5
1.1 / 1.3
0.7 / 0.8
0.2 / 0.2
2.3 / 3.0

1.4 / 1.4
2.1 / 2.1
1.0 / 1.0
0.3 / 0.4
2.7 / 2.8

250

100
80
60

Selection efficiency
Data - BG - best-fit reactor νe40

U contribution
Th contribution

20
0Best-fit reactor νe
Accidental

KamLAND data

180

(a)

200

68.3%

Reference geo νe95.4%

N U + N Th

Efficiency (%)

7

99.7%

150
100

Events / 0.2MeV

160

50

140
120
100

0
-1

80

13

60

Best-fit geo νe40Best-fit reactor νe + BG
+ best-fit geo νeC(α, n) O

20

16

25

-0.5
0
0.5
(NU - NTh) / (NU + NTh)

1

(b)

0
1

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

20

Ep (MeV)4σ∆χ 2

FIG. 6: Prompt energy spectrum of the ν e events in the low-energy
region for all data taking periods. Bottom panel: data together withthe best-fit background and geo ν e contributions. The fit incorporates
all available constraints on the oscillation parameters. The shaded
background and geo ν e histograms are cumulative. Middle panel:observed geo ν e spectrum after subtraction of reactor ν e ’s and otherbackground sources. The dashed and dotted lines show the best-fit
U and Th spectral contributions, respectively. The blue shaded curveshows the expectation from the geological reference model of [17].
Top panel: the energy-dependent selection efficiency.

15
10

3σ

5

2σ
1σ

0
from solar neutrino experiments are tan2 θ12 = 0.437+0.029−0.026 ,+0.19
2+0.0152
2−5∆m21 = 7.53−0.18 × 10 eV , and sin θ13 = 0.023−0.015 .
A global analysis including also constraints on θ13 from accelerator and short-baseline reactor neutrino experiments yields
+0.18
2
−5
tan2 θ12 = 0.436+0.029
eV2 ,−0.025 , ∆m21 = 7.53−0.18 × 10
and sin2 θ13 = 0.023+0.002−0.002 . The fit values for the different
combinations are summarized in Table III. Figure 4 shows theextracted confidence intervals in the (tan2 θ12 , ∆m221 ) planewith and without the θ13 constraint.

TABLE III: Summary of the fit values for ∆m221 , tan2 θ12 andsin2 θ13 from three-flavor neutrino oscillation analyses with various
combinations of experimental data.
Data combination∆m221
tan2 θ12+0.19
KamLAND
7.54−0.18 0.481+0.092−0.080+0.029
KamLAND + solar
7.53+0.19−0.18 0.437−0.026+0.029
KamLAND + solar + θ13 7.53+0.18−0.18 0.436−0.025

sin2 θ13
0.010+0.033−0.0340.023+0.015−0.0150.023+0.002−0.002

0

50

100
150
N U + NTh

200

250

FIG. 7: (a) Confidence level (C.L.) contours for the observed numberof geo ν e events. The small shaded region represents the predictionof the reference model of [17]. The vertical dashed line represents
the value of (NU − NTh )/(NU + NTh ) expected for a Th/U mass
ratio of 3.9 derived from chondritic meteorites. (b) ∆χ2 -profile fromthe fit to the total number of geo ν e events, fixing the Th/U mass ratio
at 3.9. The grey band represent the geochemical model prediction,
assuming a 20% uncertainty in the abundance estimates.

The KamLAND data illustrates the oscillatory shape of reactor ν e ’s arising from neutrino oscillation. The ratio of the
background- and geo-ν e -subtracted reactor ν e spectrum to theno-oscillation expectation is shown in Fig. 5 as a function of
L0 /E, where L0 = 180 km is the flux-weighted average reactor baseline. The improved determination of the geo ν e flux
resulting from the addition of the reactor-off data makes thesecond peak at L0 /E = 70 km/MeV more evident than inprevious analyses.

8

VII.

CONSTRAINTS ON EARTH MODELS

While the mantle is the most massive layer of the Earth’s
interior, its chemical composition is still uncertain. A quantitative estimate of the heat production by radiogenic components is of particular importance for understanding dynamic
processes such as mantle convection. Indeed, precisely how
the mantle convects is still not fully understood, and controversy remains as to whether two-layer convection or wholevolume convection provides a more accurate description. In
this work, we carry out a comparison of existing Earth models
using the KamLAND geo ν e data on the basis of simple but
appropriate assumptions.
The crustal contribution to the flux at KamLAND can be estimated from compositional data through rock sampling [17].
Since current Earth models predict that the lithophiles U and
Th are absent in the core, for a first approximation of the radiogenic heat, we attribute any excess above the crustal contribution to U and Th uniformly distributed throughout the mantle.
Under these generic assumptions, the measured KamLAND
geo ν e flux translates to a total radiogenic heat production of
11.2+7.9−5.1 TW from U and Th. This calculation accounts forcrustal uncertainties of 17% and 10% for U and Th, respectively, including correlated errors as suggested in [34]. To

Geodynamicalνe Flux (× 106 cm-2s-1)

For the geo ν e flux measurement we incorporate all available constraints on the oscillation parameters. The insets in
Fig. 3 detail the observed spectra in the low-energy region foreach data taking period. Figure 6 shows the measured geo
ν e event spectrum after subtracting the best-fit reactor ν e andbackground spectra. The best-fit to the unbinned data yields
116 and 8 geo ν e ’s from U and Th decays, respectively. The
joint confidence intervals for the sum NU +NTh and the asymmetry factor (NU − NTh )/(NU + NTh ) are shown in Fig. 7.
This result agrees with the expectation from the geologicalreference model of [17]. We obtained an upper limit of <19(90% C.L.) in the Th/U mass ratio, indicating the separationof U and Th ν e ’s. Assuming a Th/U mass ratio of 3.9, as predicted by the geochemical model of [11] from the abundances
observed in chondritic meteorites, the total number of U and2
Th geo ν e events is 116+28−27 , with a ∆χ -profile as shown in
Fig. 7(b). This result corresponds to an (oscillated) ν e flux of
6−2 −1
3.4+0.8
s at KamLAND, or a total antineutrino−0.8 × 10 cm
6−2 −1
flux including all flavors of 6.2+1.5
s . From−1.5 × 10 cm
2
the ∆χ -profile (Fig. 7(b)), we find that the null hypothesis isdisfavored with a p-value of 2 × 10−6 .
The KamLAND data also tests the hypothesis of a natural
nuclear reactor in the Earth’s core [33] assuming a constant
power output over the duration of the experiment. The oscillation parameters are constrained from the solar, accelerator,
and reactor neutrino data, while the contributions from geological reactor ν e ’s and from U and Th geo ν e ’s are allowed
to vary. The fit gives a limit on the geological reactor powerof <3.1 TW at 90% C.L. (<3.7 TW at 95% C.L.), an improvement of a factor of 1.7 over the previous KamLAND result [3],due primarily to the reduction of the commercial reactor ν ebackground in Period 3.

6Geochemical
Cosmochemical

4
KamLAND 68.3% C.L.

2

0
0

10
20
30
238
232
Radiogenic Heat from U + Th (TW)

FIG. 8: Geo ν e flux versus radiogenic heat from the decay chains of
U and 232 Th. The measured geo ν e flux (gray band) is compared with the expectations for the different mantle models fromcosmochemical [36], geochemical [11], and geodynamical [37] estimates (color bands). The sloped band starting at 7 TW indicatesthe response to the mantle ν e flux, which varies between the homogeneous and sunken-layer hypotheses (solid lines), discussed in the
text. The upper and lower dashed lines incorporate the uncertainty inthe crustal contribution.
238

parameterize the planetary-scale energy balance, the fractionof the global heat production from radioactive decays, the socalled “Urey ratio”, is introduced. Allowing for mantle heat
contributions of 3.0 TW from other isotope decays [12, 35],
we find that the convective Urey ratio, the contribution to the
Urey ratio from just the mantle, is between 0.09 and 0.42 at
68% C.L. This range favors models that allow for a substantial but not dominant contribution from the Earth’s primordialheat supply.
Several established estimates of the BSE composition givedifferent geo ν e flux predictions. Reference [38] categorizes
the models into three groups: geochemical, cosmochemical,
and geodynamical. Geochemical models [11], such as thereference Earth model of [17], use primordial compositions
equal to those found in CI carbonaceous chondrites, but allow for elemental enrichment by differentiation, as deduced
from terrestrial samples. Cosmochemical models [36] assume
a mantle composition similar to that of enstatite chondrites,
and yield a lower radiogenic abundance. Geodynamical models [37], on the other hand, require higher radiogenic abundances in order to drive realistic mantle convection.
In Fig 8, the observed geo ν e flux at KamLAND is
compared with the expectations from these BSE compositional models assuming a common estimated crustal contribution [17]. The ν e flux predictions vary within the plottedvertical bands due to uncertainties in both the abundances ofradioactive elements in the mantle as well as their distributions. The spread of the slope reflects the difference between
two extreme radiochemical distributions: the “homogeneous
hypothesis” in which U and Th are assumed to be distributed

9
uniformly throughout the mantle, and the “sunken-layer hypothesis”, which assumes that all of the U and Th below thecrust collects at the mantle-core interface. While the statistical treatment of geological uncertainties is not straightforward, assuming Gaussian errors for the crustal contribution
and for the BSE abundances, we find that the geodynamical
prediction with the homogeneous hypothesis is disfavored at
89% C.L. However, due to the limited statistical power of thedata, all BSE composition models are still consistent within∼2σ C.L.
VIII. CONCLUSION

An updated KamLAND measurement of ν e ’s was presented. This data benefits from the significant reduction ofreactor ν e ’s due to the long-term shutdown of commercial nuclear reactors in Japan. The geo ν e flux estimate is significantly improved by the reactor-off data. Likewise, the reactor
neutrino oscillation parameters are also better determined dueto the reduction of uncertainties in the geo ν e flux and therates of other backgrounds. Including constraints on θ13 fromaccelerator and short-baseline reactor neutrino experiments, athree-flavor analysis of solar and KamLAND data gives fit values for the oscillation parameters of tan2 θ12 = 0.436+0.029−0.025 ,2+0.0022−5∆m221 = 7.53+0.18
×
10
eV
,
and
sin
θ
=
0.023
13
−0.18
−0.002 .

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ACKNOWLEDGMENTS

The KamLAND experiment is supported by the Grant-inAid for Specially Promoted Research under grant 21000001
of the Japanese Ministry of Education, Culture, Sports,
Science and Technology; the World Premier International
Research Center Initiative (WPI Initiative), MEXT, Japan;
Stichting FOM in the Netherlands; and under the US Department of Energy (DOE) Grant No. DE-AC02-05CH11231,
as well as other DOE grants to individual institutions. The
Kamioka Mining and Smelting Company has provided service for activities in the mine.

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