PHYSICAL REVIEW D 83, 052002 (2011)

Constraints on 13 from a three-flavor oscillation analysis of reactor antineutrinos at KamLAND
A. Gando,1 Y. Gando,1 K. Ichimura,1 H. Ikeda,1 K. Inoue,1,2 Y. Kibe,1,* Y. Kishimoto,1 M. Koga,1,2 Y. Minekawa,1
T. Mitsui,1 T. Morikawa,1 N. Nagai,1 K. Nakajima,1 K. Nakamura,1,2 K. Narita,1 I. Shimizu,1 Y. Shimizu,1 J. Shirai,1
F. Suekane,1 A. Suzuki,1 H. Takahashi,1 N. Takahashi,1 Y. Takemoto,1 K. Tamae,1 H. Watanabe,1 B. D. Xu,1
H. Yabumoto,1 H. Yoshida,1 S. Yoshida,1 S. Enomoto,2,† A. Kozlov,2 H. Murayama,2,3 C. Grant,5 G. Keefer,4,‡
A. Piepke,2,4 T. I. Banks,3 T. Bloxham,3 J. A. Detwiler,3 S. J. Freedman,2,3 B. K. Fujikawa,2,3 K. Han,3 R. Kadel,3
T. O’Donnell,3 H. M. Steiner,3 D. A. Dwyer,5 R. D. McKeown,5 C. Zhang,5 B. E. Berger,6 C. E. Lane,7 J. Maricic,7
T. Miletic,7,x M. Batygov,8,k J. G. Learned,8 S. Matsuno,8 M. Sakai,8 G. A. Horton-Smith,2,9 K. E. Downum,10 G. Gratta,10
Y. Efremenko,2,11 O. Perevozchikov,11,{ H. J. Karwowski,12 D. M. Markoff,12 W. Tornow,12K. M. Heeger,2,13 and M. P. Decowski2,3,14(The KamLAND Collaboration)
1

Research Center for Neutrino Science, Tohoku University, Sendai 980-8578, Japan
Institute for the Physics and Mathematics of the Universe, Tokyo University, Kashiwa 277-8568, Japan3
Physics Department, University of California, Berkeley,and Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
4
Department of Physics and Astronomy, University of Alabama, Tuscaloosa, Alabama 35487, USA
5
W. K. Kellogg Radiation Laboratory, California Institute of Technology, Pasadena, California 91125, USA
6
Department of Physics, Colorado State University, Fort Collins, Colorado 80523, USA
7
Physics Department, Drexel University, Philadelphia, Pennsylvania 19104, USA
8
Department of Physics and Astronomy, University of Hawaii at Manoa, Honolulu, Hawaii 96822, USA
9
Department of Physics, Kansas State University, Manhattan, Kansas 66506, USA
10
Physics Department, Stanford University, Stanford, California 94305, USA
11
Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996, USA
12
Triangle Universities Nuclear Laboratory and Physics Departments, Duke University, Durham, North Carolina 27708, USA;
North Carolina Central University, Durham, North Carolina 27707, USA;and the University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599, USA
13
Department of Physics, University of Wisconsin, Madison, Wisconsin 53706, USA
14
Nikhef, Science Park 105, 1098 XG Amsterdam, the Netherlands(Received 25 September 2010; published 4 March 2011)2

We present new constraints on the neutrino oscillation parameters m221 , 12 , and 13 from a threeflavor analysis of solar and KamLAND data. The KamLAND data set includes data acquired following aradiopurity upgrade and amounts to a total exposure of 3:49  1032 target-proton-year. Under theassumption of CPT invariance, a two-flavor analysis (13 ¼ 0) of the KamLAND and solar data yields
þ0:19
2
5
eV2 ; a three-flavor analysis withthe best-fit values tan2 12 ¼ 0:444þ0:036
0:030 and m21 ¼ 7:500:20  10
2
þ0:0355eV2 ,13 as a free parameter yields the best-fit values tan 12 ¼ 0:4520:033 , m221 ¼ 7:50þ0:19
0:20  10
2
þ0:016and sin 13 ¼ 0:0200:016 . This 13 interval is consistent with other recent work combining the CHOOZ,
atmospheric and long-baseline accelerator experiments. We also present a new global 13 analysis,
incorporating the CHOOZ, atmospheric, and accelerator data, which indicates sin2 13 ¼ 0:009þ0:013
0:007 .
A nonzero value is suggested, but only at the 79% C.L.
DOI: 10.1103/PhysRevD.83.052002

PACS numbers: 14.60.Pq, 26.65.+t, 28.50.Hw, 91.35.x

I. INTRODUCTION
Neutrino flavor oscillation is by now well established by
the convergence of results from experiments involving

solar, reactor, atmospheric, and accelerator neutrinos.
Central to any discussion of neutrino oscillation phenomenology is the Pontecorvo-Maki-Nakagawa-Sakata (PMNS)*Present address: Department of Physics, Tokyo Institute of Technology, Tokyo 152-8551, Japan†
Also at Center for Experimental Nuclear Physics and Astrophysics, University of Washington, Seattle, Washington 98195, USA‡
Present address: Lawrence Livermore National Laboratory, Livermore, California 94550, USA
x
Present address: Department of Physics and Astronomy, Rowan University, 201 Mullica Hill Road, Glassboro, New Jersey 08028,
USAk
Present address: SNOLAB, Lively, ON P3Y 1N2, Canada{
Present address: Department of Physics, University of South Dakota, 414 E. Clark St., Vermillion, South Dakota 57069, USA

1550-7998= 2011=83(5)=052002(11)052002-1

Ó 2011 American Physical Society

PHYSICAL REVIEW D 83, 052002 (2011)

A. GANDO et al.

mixing matrix which describes neutrino mixing in analogy
to the Cabibbo-Kobayashi-Maskawa (CKM) matrix of thequark sector [1]. Although the possibility of more than
three neutrino mass states, motivated in part by [2], is not
excluded, our notation and discussion is restricted to theassumption of three neutrino mass states. In this case, thethree-flavor eigenstates ðe ;  ;  Þ can be expressed as alinear combination of the three mass eigenstatesð1 ; 2 ; 3 Þ:j i ¼

3
X

Ui ji ið ¼ e; ; Þ:

i¼1

Ignoring possible Majorana phases which are irrelevant tooscillation phenomenology, the PMNS matrix U isparametrized by three mixing angles, 12 , 23 , 13 , and a
CP-violating phase . U may be written as
1
0
10
1
0
0
c13
0 s13 eiC@
U ¼ @ 0 c23 s23 AB
01
0 A
0 s23 c23
s13 ei 0
c13
01
c12 s12 0 @ s12 c12 0 A;
(1)
0
0 1
where sij ¼ sinij and cij ¼ cosij .
The mass-squared splittings (m2ij  m2i  m2j ) between the neutrino mass states are described by two independent parameters, m221 and m232 . At the currently
achieved sensitivity, mixing between 1 and 2 (1 -2
mixing) can explain the KamLAND data [3] and also,with addition of Mikheyev-Smirnov-Wolfenstein (MSW)
enhancement [4,5], the solar results [6–13]. Atmospheric[14], K2K [15], and MINOS [16] data can be accommodated by 2 -3 mixing. As of yet, there is no experimental
evidence of 1 -3 mixing (i.e., a nonzero 13 ) with highstatistical significance.
Probing the value of 13 is a subject of intense on
going activity. The most stringent limit to date, fromthe 1-km-baseline CHOOZ reactor experiment [17], issin2 13 < 0:04 at the 90% C.L. Next-generation accelerator experiments (T2K [18] and NOA [19]) and reactor
experiments (Double Chooz [20], Daya Bay [21], and
RENO [22]) aim to significantly improve the sensitivity
to this parameter and may definitively determine the valueof 13 . If 13 is nonzero, future oscillation experiments may
explore leptonic CP violation (parametrized by ) andprobe the neutrino mass hierarchy (i.e., the sign ofm232 ). The feasibility of such experiments and the pathforward depend critically on the magnitude of 13 .
This article presents an updated KamLAND data set andfocuses on new constraints on 12 , m221 , and 13 based ona three-flavor combined analysis of KamLAND andsolar data. As motivated by [23], we also present a
global analysis including the CHOOZ, accelerator, andatmospheric oscillation experiments in order to explore
possible hints of nonzero 13 .
II. APPROXIMATE THREE-FLAVOR NEUTRINO
OSCILLATION FORMALISM
Previous KamLAND results [3] were based on a
two-flavor (1 -2 ) oscillation formalism which assumes
13 ¼ 0. For the length scales relevant to reactor neutrino
oscillation at KamLAND and solar neutrino oscillation in
the LMA-MSW solution, the dependence of the moregeneral three-flavor phenomenology on the larger 1 -3
mass splitting (jm231 j  jm232 j  m221 ) averages out
and the three-flavor survival probability (P3ee ), including
matter effects, may be approximated as
4
4
~2
P3
ee ¼ cos 13 Pee þ sin 13 :

(2)

P~2
ee has the same form as the survival probability inmatter for 1 -2 mixing but with the electron density(Ne ) modified: N~ e ¼ Ne cos2 13 [24]. Since sin2 13  1,
the survival probability can be further approximated as
2
~2
P3
ee  ð1  2sin 13 ÞPee . Thus, for KamLAND and thesolar experiments, 1 -3 mixing would give rise to anenergy-independent suppression of the survival probability relative to the 13 ¼ 0 case.
For solar neutrino oscillation in the LMA-MSW solution, coherent mixing can be safely ignored due to the long
distance between the Sun and the Earth. The two-neutrino
survival probability is simply expressed as


P~ 2
ee ¼ P1 P1e þ P2 P2e ;(3)

where Pi and Pie are, respectively, the probability of thee ! i transition in the Sun and the probability of the
i ! e transition in the Earth with the modified electron~ e . Neutrino propagation in the Sun and Earth isdensity N
calculated following the analytical procedure of [25,26],
and the resulting survival probabilities agree well withnumerical calculations.
For reactor antineutrinos studied at KamLAND, thematter effect in the Earth is not as large as for solar
neutrinos. Assuming a constant rock density (2:7 g=cm3 ),the two-neutrino survival probability is given by22
2 1:27m21M L
;
(4)
P~2
¼
1

sin
2
sin
12M
ee
E
where L is the electron antineutrino ( e ) flight distance inmeters from the source to the detector, E is the  e energy in
MeV, and m221 is in eV2 . 12M and m221M are the mattermodified mixing angle and mass splitting defined bysin 2 212M ¼

sin2 212;
ðcos212  A=m221 Þ2 þ sin2 212

(5)

qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
m221M ¼ m221 ðcos212  A=m221 Þ2 þ sin2 212 : (6)052002-2

PHYSICAL REVIEW D 83, 052002 (2011)

CONSTRAINTS ON 13 FROM A THREE-FLAVOR . . .

pﬃﬃﬃ~ e E, and has a negative sign for antineutriA ¼ 2 2GF N
nos; GF is the Fermi constant. The matter effect modifies
the expected reactor  e event rate by up to 3%, dependingon the oscillation parameters.
III. KAMLAND EXPERIMENTThe KamLAND detector is located in Kamioka mine,
Gifu, Japan. The primary target volume consists of 1 ktonof ultrapure liquid scintillator (LS). This inner detector(ID) of LS is shielded by a 3.2-kton water-Cherenkov outerdetector (OD). Scintillation light is viewed by 1325
17-inch and 554 20-inch photomultiplier tubes (PMTs)
providing 34% solid-angle coverage. A detailed overview
of the detector is given in [27].
The  e flux at KamLAND is dominated by 56 Japanese
nuclear power reactors. The flux-weighted average baseline to these reactors is 180 km. The reactor fluxes arecalculated precisely based on detailed operational data
including the thermal power variation and fuel replacement
and reshuffling records, provided for all Japanese commercial reactors by a consortium of Japanese electric powercompanies. The absolute thermal power, used to normalize
the fission rates, is measured to within 2% for each reactor.
This uncertainty is conservatively assumed to be correlated
across all reactors, though some potentially uncorrelated
components have been put forward in [28]. The data points
are typically provided at weekly frequency during regular
operations when the relative instability is of the order of
103 . When the operating parameters vary more quickly,
the data are provided at higher frequency, with a period
between 10 min and 1 h. The relative fission yields, averaged over the entire live-time period, for isotopes(235 U:238 U:239 Pu:241 Pu) are (0:571:0:078:0:295:0:056), respectively. The detailed reactor operation data are also
used for accurate tracking of the flux-weighted averagereactor baseline and spectrum shape change over thecourse of the experiment. The contribution from Korean
reactors, based on reported electric power generation, isestimated to be ð3:4  0:3Þ%. The contribution fromJapanese research reactors and the remainder of the global
nuclear power industry, estimated using reactor specifications from the International Nuclear Safety Center [29],is ð1:0  0:5Þ%. The  e spectra per fission provided in[30–32] are used, and the uncertainties are further constrained from [33]. In addition, the long-lived, out-ofequilibrium fission products 90 Sr, 106 Ru, and 144 Ce [34]are evaluated from the history of fission rates for eachisotope and are found to contribute only ð0:6  0:3Þ%.
Electron antineutrinos are detected in KamLAND via
the inverse beta-decay reaction,  e þ p ! eþ þ n. This
process has a delayed coincidence (DC) event pair signature which offers powerful background suppression. Theenergy deposited by the positron generates the DC pair’s
prompt event and is approximately related to the incident e energy by E ’ Ep þ E n þ 0:8 MeV, where Ep is theþ

sum of the e kinetic energy and annihilation  energies,
and E n is the average neutron recoil energy, Oð10 keVÞ.
The delayed event in the DC pair is generated by thecapture  produced when the neutron captures on a protonor 12 C nucleus. The mean neutron capture time is207:5  2:8 s [27].
In the previous KamLAND result [3] the largest background in the prompt energy region below 3.0 MeV camefrom 13 Cð; nÞ16 O reactions induced by -decays in the LS.
This affected the estimation of the flux of geologically
produced antineutrinos (geo- e ) expected between
0.9 MeV and 2.6 MeV from the decay chains of 238 U and232
Th in the Earth [35,36]. In 2007 the KamLAND collaboration started a campaign to purify the LS and ultimately
achieved a twentyfold reduction of 210 Po, the dominant-decay source. This reduction gives a better signal-tobackground ratio for the geo- e flux estimation and enhances sensitivity to reactor  e oscillations below 2.6 MeV.
We present an improved measurement of reactor  eoscillation based on data collected from March 9, 2002,
to November 4, 2009. This sample includes the previously
reported data set [3], denoted hereafter as DS-1, in addition
to data collected after LS purification commenced, designated as DS-2. The total live time is 2135 days after
removing periods of low data quality which occurred during LS purification, and after detector vetoes to reduce
cosmogenic backgrounds. The high-quality data selectedfrom DS-2 accounts for 30.41% of the total live time. The
number of target protons within the 6.0-m-radius sphericalfiducial volume is calculated to be ð5:98  0:12Þ  1031
for the combined data set, which corresponds to an exposure to  e of 3:49  1032 proton-years.
Physical quantities such as event vertex and energy arereconstructed based on the timing and charge distributionsof scintillation photons recorded by the ID PMTs. The
vertex and energy reconstructions are calibrated using
60 Co, 68 Ge, 203 Hg, 65 Zn, 241 Am9 Be, 137 Cs, and 210 Po13 C
radioactive sources. The observed vertex resolution ispﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
12 cm= E ðMeVÞ, and the energy resolution ispﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
6:4%= E ðMeVÞ. For DS-2, the resolutions are timedependent due to a light-yield reduction of up to 20%
relative to DS-1. The source calibrations are augmented
with studies of muon spallation products to monitor thedetector stability and to determine the nonlinearity of theenergy response due to LS quenching, Cherenkov light,
and dark hit contributions. The systematic uncertainty of
the absolute energy response over the full DS-1 and DS-2
data sets is less than 1.2%, and when propagated in thereactor  e spectrum produces a 1.8% uncertainty on m221
and a 1.3% uncertainty on the event rate above the analysis
threshold.
For DS-1, the systematic uncertainty on the fiducial
volume up to 5.5 m radius was determined to be 1.6%
with a full-volume calibration campaign [37]. The uncertainty in the volume between 5.5 m and 6.0 m radius was

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A. GANDO et al.

TABLE I. Estimated systematic uncertainties for the neutrino oscillation parameters m221 ,12 , and 13 for the earlier/later periods of measurement, denoted in the text as DS-1/DS-2. The
overall uncertainties are 4:1%=4:5% for DS-1/DS-2.
Detector-related (%)
1:8=1:8
1:8=2:5
1:1=1:30:7=0:80:2=0:2
2:3=3:0

estimated from the vertex uniformity of muon-induced 12 B
and 12 N; the combined uncertainty on the 6.0-m-radiusfiducial volume for DS-1 is 1.8%. To date there havebeen no full-volume calibrations for DS-2, so we rely onvertex uniformity of cosmogenic 12 B and 12 N events; inthis case, we assign a 2.5% uncertainty on the 6.0-m-radiusfiducial volume.
Table I summarizes the systematic uncertainties onm221 and the expected event rate of reactor  e ’s; theoverall rate uncertainties for DS-1 and DS-2 are 4.1%
and 4.5%, respectively.
IV. KAMLAND DATA REDUCTION AND
CANDIDATE EVENT SELECTION
Antineutrino DC-pair candidates are selected by performing the following series of first-level cuts: (i) prompt
energy: 0:9 < Ep ðMeVÞ < 8:5; (ii) delayed energy: 1:8 <Ed ðMeVÞ < 2:6 (capture on p), or 4:4 < Ed ðMeVÞ < 5:6(capture on 12 C); (iii) spatial correlation of prompt anddelayed events: R ðmÞ < 2:0; (iv) time separation between prompt and delayed events: 0:5 < T ðsÞ <1000; and (v) fiducial volume radii: Rp , Rd ðmÞ < 6:0.
In order to increase the ratio of signal to accidental
background, a second-level cut is performed using a likef e. Here f e and facc arelihood discriminator, L ¼ f þfacce
the probability density functions (PDFs) for  e DC pairs
and accidental DC pairs, respectively; both PDFs are functions of the 6 DC-pair parameters: Ep , Ed , R, T, Rp , Rd .
The PDF for accidental DC pairs can be evaluateddirectly from the data with an off-time cut; we use 10 ms <
T < 20 s. To utilize the variation in the accidental DC
rate with time, the full data set is divided into five periods
and the corresponding facc is computed for each. The PDF
for  e DC pairs is calculated with a Monte Carlo (MC)simulation. The systematic error in the simulated PDF isevaluated by comparing simulated calibration data to realcalibration data for the 68 Ge and 241 Am9 Be sources.
For each 0.1 MeV interval in prompt energy, we chooseS
Lcut ðEp Þ to maximize pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ, where S and Bacc are theSþBaccexpected number of  e and accidental DC pairs, respectively, with LðEp Þ > Lcut ðEp Þ. To exploit the time variation

 e -spectra [33] e -spectra
Reactor power
Fuel composition
Long-lived nuclei
Total

0:6=0:6
2:4=2:4
2:1=2:1
1:0=1:0
0:3=0:4
3:3=3:4of both the signal and background, the optimal Lcut ðEp Þ isdetermined for each of the five time periods. Finally, only
DC pairs with LðEp Þ > Lcut ðEp Þ are selected. The efficiency and uncertainty of the cut are evaluated for eachperiod using the MC; the Ep -dependent efficiency, averaged over the five time periods, is shown in the top panel ofFig. 1. A no-oscillation input spectrum is used to generatef e . The effect of using an oscillated  e spectrum waschecked with various trial values of ð12 ; m221 Þ and found
not to greatly affect the selection. The number of accidental DC pairs remaining after all cuts is determined to be

Efficiency (%)

Energy scale
Fiducial volume
Energy scale
Lcut ðEp Þ eff.
Cross section
Total

Rate

Reactor-related (%)

100
Selection efficiency

80
60

KamLAND datano-oscillation
best-fit osci.
accidental
16
13C(α,n) O
best-fit Geo νebest-fit osci. + BG
+ best-fit Geo νe350

Events/0.425MeV

m221

300
250
200
150
100
50
0
0

1

2

3

4

5

6

7

8

Ep (MeV)

FIG. 1 (color). Prompt energy spectrum of  e candidate events
above 0.9 MeV energy threshold (vertical dashed line). The data
together with the background and reactor  e contributions fitted
from an unbinned maximum-likelihood three-flavor oscillation
analysis are shown in the main panel. The number of geo- e ’s isunconstrained in the fit. The shaded background histograms are
cumulative. The top panel shows the energy-dependent selection
efficiency; each point is the weighted average over the five time
periods described in the text.

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PHYSICAL REVIEW D 83, 052002 (2011)

CONSTRAINTS ON 13 FROM A THREE-FLAVOR . . .
TABLE II.

Estimated backgrounds excluding geo- e after first- and second-level cuts.

Background
1
2
3
4
5
Total

Contribution
Accidental
9
Li=8 He
13
16
Cð; nÞ Og:s: ;np ! np
13 Cð; nÞ16 O ;12 Cðn; n0 Þ12 C (4.4 MeV )
g:s:
13 Cð; nÞ16 O, 1st e.s. (6.0 MeV eþ e )13 Cð; nÞ16 O, 2nd e.s. (6.13 MeV )
Fast neutron and atmospheric neutrino

102:5  0:1. The dominant contributors to these accidental
DC pairs are 2.6 MeV -rays from external 208 Tl -decays.
In addition to accidental background events, there areother processes which produce background DC pairs. The
13
Cð; nÞ16 O nuclear reaction in the LS is the largest suchbackground. The dominant  source is 210 Po, a long-lived
daughter nucleus of 222 Rn. This reaction produces neutrons
with energies up to 7.3 MeV, and mostly contributes DC
pairs with prompt energies below 2.6 MeV. By counting thequenched scintillation signals from the 5.3 MeV  particles, we find ð5:95  0:29Þ  109 -decays in full data set.
The rate of the 13 Cð; nÞ16 O background and its prompt
energy spectrum is estimated by simulation. The total crosssection and final-state partial cross sections for 16 O, i
(where i ¼ 0, 1, 2 for the ground, first, and second excitedstates of 16 O), are based on [38,39], but the relative normalizations of the i were tuned by an in situ calibration usinga 210 Po13 C source [40]. The data require 0 and 1 bescaled by 1.05 and 0.6, respectively, while no scaling isrequired for 2 . Including the uncertainty on the number of-decays, we assign an uncertainty of 11% for the groundstate and 20% for the excited states. We estimate that the
total number of 13 Cð; nÞ16 O DC pairs remaining in
the full data set after the first- and second-level cuts is198:6  23:0. DS-2, which benefited from reduced 210 Po
contamination due to LS purification, contributes only 7%of the 13 Cð; nÞ16 O events after all selection cuts.
Delayed-neutron beta emitters 9 Li and 8 He, which areproduced in the LS by cosmic-ray muons, also generate DC
pairs [27]. They are removed by a 2-s veto of the entire
fiducial volume after LS showering muons, which generate
more than 106 photoelectrons in the LS, and poorly reconstructed LS muons. In the case of nonshowering, wellreconstructed LS muons, the 2-s veto is applied only within
a 3-m-radius cylinder around the muon track in order tominimize the exposure loss from the veto. From a fit to thetime delay between prompt DC events and their preceding
LS muons, we estimate the background remaining after theveto and DC selection cuts is 24:8  1:6 events.
Fast neutrons and atmospheric neutrinos are also a possible source of DC pairs. Fast neutrons generated in thematerial outside the OD may scatter into the ID, andsubsequent coincidence signals in the LS from prompt

102:5  0:1
24:8  1:6
171:7  18:2
7:3  0:8
15:9  3:3
3:7  0:7
<12:3
325:9  26:1

neutron scatter and delayed capture sometimes pass the e DC signal selection criteria. Monte Carlo studies ofneutron generation outside the ID [27] indicate that fastneutrons are generated primarily by cosmic-ray muons. A
2-ms veto after OD-tagged muons mostly eliminates fastneutron DC pairs. The residual background due to the OD
tagging inefficiency and muons that pass nearby but do notenter the OD is estimated from simulation. Atmospheric
neutrino backgrounds are evaluated using the NUANCE
software [41] to simulate neutrino interactions and related
processes. Both atmospheric neutrino and fast neutron DC
pairs are assumed to have a flat prompt energy spectrum inthe energy range of the present analysis, and are estimatedto contribute less than 12.3 candidates in total after all
selection cuts.
Geo- e fluxes at Kamioka can be calculated based on areference Earth model [42] which assumes a radiogenic
heat production rate of 16 TW from the decay chains of U
and Th. Including neutrino oscillation effects, this model
predicts 85 and 21 events in the full data set from U and Th
decays, respectively. However, since the estimate of thegeo- e yield is highly dependent on the Earth model, theevent rates from the U and Th decay chains are not constrained in the oscillation analysis; only the prompt energy
spectrum shapes, which are independent of the Earthmodel, are used to constrain their contribution. A possible
background contribution from a hypothetical reactor- esource at the Earth’s center, motivated by [43] and investigated in [36], is neglected in this analysis.
After all selection cuts, we expect, in the absence of  edisappearance, 2879  118 events from reactor  e , and325:9  26:1 events from the backgrounds, as summarizedin Table II. The observed number is 2106 events.
V. OSCILLATION ANALYSISThe KamLAND data is analyzed based on an unbinned
maximum-likelihood method. The 2 is defined by
2052002-5

¼

geo
2
2
rate ð12 ; 13 ; m21 ; NBG1!5 ; NU;Th ; 1!4 Þgeo 2 lnLshape ð12 ; 13 ; m221 ; NBG1!5 ; NU;Th; 1!4 Þþ

2 ðN
BG1!5 Þ þ
BG

2 ð
1!4 Þ:syst(7)

PHYSICAL REVIEW D 83, 052002 (2011)

A. GANDO et al.
2

20
15
10
5

2σ
1σ

1.8

99% C.L.

99% C.L.

99.73% C.L.

99.73% C.L.

1.6

best-fit

best-fit

KamLAND+Solar
95% C.L.
99% C.L.

1.2

99.73% C.L.

1

best-fit

0.8
0.6

2

(b)

Solar

KamLAND

95% C.L.

95% C.L.

1.8

99% C.L.

99% C.L.

99.73% C.L.

99.73% C.L.

1.6

best fit

best fit

1.4

KamLAND+Solar
95% C.L.
99% C.L.

1.2

99.73% C.L.

1

best fit

0.8

θ13 free0.4

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

2σ
1σ

0.6

θ13 = 0

0.4

3σ

∆χ2

4σ

95% C.L.

4σ

3σ

KamLAND

20
15
10
5

2σ
1σ

Solar

4σ

(a)

95% C.L.

1.4

∆χ2

3σ

3σ

∆m221 (10-4eV2)

4σ

2σ
1σ

2

In our analysis of the solar neutrino data, we include therates in the chlorine [6] and gallium [9] experiments,
Borexino [13], SNO III [12], the zenith spectra in SuperKamiokande phase I [10], and the day-night spectra in
SNO phase I and II [11]. The measured fluxes are compared with the high-metallicity standard solar model predictions (GS98) [44].
For the three-flavor KamLAND-only analysis, without
any constraints on 13 from other oscillation experiments, the best-fit oscillation parameter values are5m221 ¼ 7:49þ0:20
eV2 ,tan2 12 ¼ 0:436þ0:102
0:20  10
0:081 ,þ0:0372and sin 13 ¼ 0:0320:037 (< 0:094 at the 90% C.L.).
The two-flavor oscillation treatment using Eq. (7), as presented previously in [3], is a special case of the three-flavor
treatment with 13 ¼ 0. For this case the best-fit oscillation
parameters from the KamLAND-only analysis are5 eV2 and tan2  ¼ 0:492þ0:086 .
m221 ¼ 7:50þ0:20
12
0:20  10
0:067In the KamLAND data, 13 is expected to contribute only
an energy-independent event rate suppression and we findalmost no effect on the m221 measurement when 13 isincluded as a free parameter. Figure 1 shows the prompt
energy spectrum of candidate events in KamLAND together with the best-fit background and reactor  e spectra
for the three-flavor fit to the KamLAND data. The fit
estimates 82 and 26 events from U and Th geo- e ’s,
respectively, in agreement with the reference model.
Figure 2 compares the allowed regions in theðtan2 12 ; m221 Þ plane from the two- and three-flavor oscillation analyses. We find [Fig. 2(a)] that the allowed
region from the solar data is in agreement with the
KamLAND data, and the small tension between the twoflavor best-fit values of 12 , discussed previously in∆m221 (10-4eV2)∆χ2

The terms are, in order: thecontribution for (i) the total
rate, (ii) the prompt energy spectrum shape, (iii) a penalty
term for backgrounds, and (iv) a penalty term for systematic uncertainties. NBG1!5 are the expected backgroundgeo
are the contributions
levels discussed in Sec. IV, and NU;Th
expected from U and Th geo- e ’s. NBG1!5 are allowed
to vary in the fit but are constrained with the penalty termgeoare(iii) using the estimates summarized in Table II. NU;Th
free parameters and are unconstrained to avoid any Earthmodel dependence. The 1!4 parametrize the uncertainties
on the reactor  e spectra and energy scale, the event rate,
and the energy-dependent efficiencies; these parameters
are allowed to vary in the analysis but are constrained byterm (iv). The background energy scale uncertainties are
estimated to contribute at most an additional 0.5% to theerror on the event rate and are neglected in this analysis.
The prompt energy spectrum shape likelihood term (ii) is
evaluated as a function of the candidate event time. The
detailed knowledge of the time evolution of the total
reactor  e spectrum and effective baseline, afforded by
the reactor fuel composition and power data provided by
the Japanese reactor operators, is thus fully utilized in theanalysis. Variations in the total observed spectrum shapewith time due to changes in the background levels—especially the 13 Cð; nÞ16 O reduction from the LS purification—are also exploited by this term. The spectrum
shape likelihood term allows an Earth-model-independent
constraint of the geo- e contribution since the U and Th
decay spectra are known independently of the Earth model.
A 2 scan of the ð12 ; 13 ; m221 Þ oscillation parameter
space is carried out, minimizing 2 with respect togeo, and 1!4 .
NBG1!5 , NU;Th

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. 2 (color). Allowed regions projected in the ðtan2 12 ; m221 Þ plane, for solar and KamLAND data from (a) the two-flavor
oscillation analysis (13 ¼ 0) and (b) the three-flavor oscillation analysis, where 13 is a free parameter. The shaded regions are from the
combined analysis of the solar and KamLAND data. The side panels show the  2 profiles projected onto the tan2 12 and m221 axes.

052002-6

PHYSICAL REVIEW D 83, 052002 (2011)

CONSTRAINTS ON 13 FROM A THREE-FLAVOR . . .

Solar

0.16
0.14

sin 2 θ13

95% C.L.

3

90% C.L.

LB
L

+S
ola
r

Ka
mL
AN
D

Glob
al
Atm
osp
her
ic +

4

lar

So

1

Kam

D

LAN

0
0

0.01 0.02 0.03 0.04 0.05 0.06 0.07

sin2θ13

FIG. 4 (color).  2 -profiles projected onto the sin2 13 axis fordifferent combinations of the oscillation data floating the undisplayed parameters ðtan2 12 ; m221 Þ.

a positive 13 , although the current statistical power ispoor. For a global analysis combining our updated
KamLAND þ solar analysis with the combined CHOOZ,
atmospheric, and LBL (appearance þ disappearance)
analysis from [46], we find sin2 13 ¼ 0:009þ0:013
0:007 . Our
global result is very similar to the global analysis carriedout by [46] with the previous KamLAND data set but thesignificance of nonzero 13 is reduced slightly to the
79% C.L.
VI. VISUALIZATION OF THE
SURVIVAL PROBABILITY
Figures 5 and 6 illustrate different aspects of the survival
probability for the KamLAND data. The data points in

1

KamLAND+Solar
95% C.L.
99% C.L.
99.73% C.L.
best-fit

0.1

5

2

95% C.L.
99% C.L.
99.73% C.L.
best-fit

0.12

CH
OO
Z+

6

KamLAND
95% C.L.
99% C.L.
99.73% C.L.
best-fit

0.18

8
7

Survival Probability

0.2

99.73% C.L.

9

∆χ 2

[23,45], has eased. Assuming CPT invariance, the twoneutrino oscillation parameter values from a combined
analysis of the solar and KamLAND data are tan2 12 ¼
þ0:19
2
5
eV2 . For the
0:444þ0:036
0:030 and m21 ¼ 7:500:20  10
three-flavor analysis combining the solar and KamLAND
data, the best-fit parameter values are tan2 12 ¼
þ0:0162
0:452þ0:035
0:033 and sin 13 ¼ 0:0200:016 ; the best-fit value
2for m21 is the same as for the two-flavor result. The
best-fit values for the different data combinations andanalysis approaches are summarized in Table III in
Appendix A.
Figure 3 shows the regions in the ðtan2 12 ; sin2 13 Þ planeallowed by 2 minimization with respect to m221 for eachanalysis. The reduction of the best-fit value of tan2 12 forthe three-flavor KamLAND-only analysis relative to thetwo-flavor KamLAND analysis (Fig. 2) follows the anticorrelation apparent in the KamLAND contours (Fig. 3).
The correlation between 12 and 13 in the solar data isslight and the difference between the best-fit values of 12from the two-flavor and three-flavor analyses of the solaronly data is small.
Figure 4 shows  2 -profiles projected onto the sin2 13
axis for different combinations of the data. The analysis of
the KamLAND data gives sin2 13 ¼ 0:032þ0:037
0:037 (< 0:094
at the 90% C.L.), and the combined analysis of the solar
and KamLAND data gives sin2 13 ¼ 0:020þ0:016
0:016 . The constraint on nonzero 13 from the combined KamLAND andsolar analysis is comparable to the constraint from the
combined analysis of CHOOZ, atmospheric, and longbaseline accelerator (LBL, i.e., K2K and MINOS) experiments presented in [46], which includes the recent eappearance result from MINOS [47]. In the solar þ
KamLAND analysis the preference for nonzero 13 comes
mostly from the KamLAND data. All oscillation data favor

10

0.08

0.8
0.6
0.4
0.2

3-ν best-fit oscillation

0.06

Data - BG - Geo νe2-ν best-fit oscillation

0

0.04

20

0.02

30

40

50

60

70

80

90

100

110

L0/Eν (km/MeV)
e

0
0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

tan2 θ12
FIG. 3 (color). Allowed regions from the solar and KamLAND
data projected in the ðtan2 12 ; sin2 13 Þ plane for the three-flavor
analysis.

FIG. 5 (color). Ratio of the observed  e spectrum to the
expectation for no-oscillation versus L0 =E for the KamLAND
data. L0 ¼ 180 km is the flux-weighted average reactor baseline.
The 2- and 3- histograms are the expected distributions basedon the best-fit parameter values from the two- and three-flavor
unbinned maximum-likelihood analyses of the KamLAND data.

052002-7

PHYSICAL REVIEW D 83, 052002 (2011)

A. GANDO et al.

Fig. 5 are the ratio of the observed reactor  e spectrum tothat expected in the case of no oscillation plotted as afunction of L0 =E, where L0 (L0 ¼ 180 km) is the fluxweighted average reactor baseline. The oscillatory structure arising from the sin2 ð1:27m221 L=EÞ term is clear, but
is distorted because the reactor sources are distributed
across multiple baselines. We also overlay in the figurexðEp ; tÞ ¼







reactors
X Z^ 221M Li
1
1
Si ðE; tÞ2 ^2 1:27m
P
dE
sin
2

sin
ðE
;
t;
EÞ
12M
R p
E
4 L2i
sin2 2^12 Nnoosc ðEp ; tÞ i

(8)




^ 221M L1
2 2^
2 1:27m
;
sin
sin
12M
E
sin2 2^12

(9)

where
Nnoosc ðEp ; tÞ ¼

reactorsX Z

dE PR ðEp ; t; EÞiSi ðE; tÞ
4 L2i

(10)

is the number of candidates with prompt energy Ep expected in the absence of neutrino oscillation from all
reactors at time t at KamLAND; the index i labels thereactor source; Li and Si ðE; tÞ are, respectively, the baseline and the neutrino spectrum at time t of reactor i; andPR ðEp ; t; EÞ is the probability that a  e with energy E will
be detected at KamLAND with prompt energy Ep . PR
includes the number of target protons, the inverse

Survival Probability

1
0.8
0.6
0.4
0.2
0

0

3-ν best-fit osci.

Data - BG - Geo ν e2-ν best-fit osci.

no-oscillation

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.91x ≡ 〈sin 2θ12Msin (1.27∆ m 221ML/Eν )〉/sin22θ12e
2the expected oscillation curves based on the best-fit
parameters from the two- and three-flavor unbinned
maximum-likelihood analyses discussed previously. The
suppression of the oscillation amplitude is slightly larger
for the nonzero 13 case.
To focus on 12 and 13 effects in the data, we introduce
a parameter xðEp ; tÞ defined by

2

FIG. 6 (color). Survival probability of reactor  e versus x 
hsin2 2^12M sin2 ð1:27m^ 221M L=EÞi=sin2 2^12 . The angle bracket
indicates the weighted average over reactor baseline (Li ) andoriginal neutrino energies (E). The points are the survival
probability for the KamLAND data. The 3- line and 1 C.L.
region are calculated using the unbinned maximum-likelihood fit
to the KamLAND data. The 2- line is calculated from the twoflavor unbinned maximum-likelihood KamLAND analysis. The
1 C.L. band for the 2- case is not shown but is similar inmagnitude to the no-oscillation case shown at P ¼ 1:0.

beta-decay cross section, and the time-dependent detector
response function. ð^12 ; m^ 221 Þ are the best-fit values fromthe two-flavor unbinned analysis, and ð^12M ; m^ 221M Þ are
the matter-modified oscillation parameters calculated withthose best-fit values. The angle bracket notation in Eq. (9)indicates the weighted average over reactor baselines Li
and neutrino emission energies E, written explicitly in
Eq. (8). For the region of ðm221 ; 12 ; 13 Þ parameter spaceclose to m^ 221 , all the information about the reactors,
detector-related effects, and matter modification is contained in the parameter x. With this definition, the survival
probability may be written as a linear functionof x, PðEp ; tÞ ¼ A  B xðEp ; tÞ, where A ¼ ðcos4 13 þ
sin4 13 Þ and B ¼ cos4 13 sin2 212 . 13 effects are predominantly encoded in A, whereas 12 effects dominate theslope B. This linear relationship is illustrated in Fig. 6.
The points there are the survival probability for
KamLAND events binned as a function of x. Also shown
are lines where A and B have been calculated using thebest-fit values from the two- and three-flavor unbinned
maximum-likelihood analyses of the KamLAND data.
The axis intercept at x ¼ 0 of the best-fit 3- line is lessthan one, illustrating the slight indication of positive 13from the unbinned likelihood analysis. Any further improvement in the significance of the 13 investigation
with KamLAND requires reduced systematic uncertainties
on the reactor flux and increased detector exposure.
A binned analysis based on the data points in Fig. 6 isoutlined in Appendix B.
VII. CONCLUSION
An updated KamLAND reactor  e data set was presented. The data set benefits from increased exposure andan improved background environment due to a radiopurity
upgrade of the LS. The analysis slightly hints at a nonzero
13 with the available oscillation data. In a two-flavor
analysis (13 ¼ 0) of the solar and KamLAND data, thebest-fit values for the oscillation parameters areþ0:19
2
5 eV2 .
tan2 12 ¼ 0:444þ0:036
0:030 and m21 ¼ 7:500:20  10052002-8

PHYSICAL REVIEW D 83, 052002 (2011)

CONSTRAINTS ON 13 FROM A THREE-FLAVOR . . .

In the three-flavor analysis, floating the value of 13 without
any constraints from the other oscillation experiments
gives the solar þ KamLAND best-fit values tan2 12 ¼
þ0:19
2
5
eV2 , and sin2 13 ¼
0:452þ0:035
0:033 , m21 ¼ 7:500:20  10
þ0:0162
0:0200:016 . The limits on m21 are the same for the twoand three-flavor analyses. All three oscillation parameters
derived from the KamLAND-only antineutrino data are ingood agreement with those from the solar-only neutrino
data and reveal no inconsistency with CPT invariance,
which was assumed for the joint fits. The upper limit we
obtain on sin2 13 is compatible with other recent work
combining CHOOZ, atmospheric, and accelerator experiments. More definitive information on the value of 13
should come from upcoming accelerator and reactor
experiments.
ACKNOWLEDGMENTS
The KamLAND experiment is supported by the Grantin-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. Departmentof Energy (DOE) Grants No. DE-FG03-00ER41138, DEAC02-05CH11231, and DE-FG02-01ER41166, as well asother DOE grants to individual institutions. The reactor
data are provided by courtesy of the following electricassociations in Japan: Hokkaido, Tohoku, Tokyo,
Hokuriku, Chubu, Kansai, Chugoku, Shikoku, andKyushu 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.

TABLE III. Summary of the best-fit values for tan2 12 andsin2 13 from two- and three-flavor neutrino oscillation analyses
of various combinations of experimental data.
Data set

Analysis method

tan2 12

sin2 13

KamLAND

two-flavor

0:492þ0:086
0:0670

two-flavor

0:444þ0:036
0:0300KamLAND

three-flavor

þ0:037
0:0320:037

KamLAND þ solar

three-flavor

Globalthree-flavor

0:436þ0:102
0:081
0:452þ0:035
0:0330:444þ0:039
0:027

KamLAND þ solar

TABLE IV. Survival probability for each bin in x [definedin Eq. (8)]. The first column indicates the bin range ofx  hsin2 2^12M sin2 ð1:27m^ 221M L=EÞi=sin2 2^12 . The weighted
average x is given in the second column. The observed survival
probability is shown in the third column. The uncertainties
include only the statistical and background estimation uncertainties, which are assumed to be uncorrelated. In addition, thesystematic uncertainty ( corr ¼ 4:1%) on the flux predictionneeds to be included for each bin as a fully correlated uncertainty.
x rangex

0.1–0.3
0.3–0.4
0.4–0.5
0.5–0.6
0.6–0.7
0.7–0.9

0.230
0.354
0.451
0.555
0.638
0.800

The best-fit values for the different data combinations
and analysis approaches are summarized in Table III.
APPENDIX B
We consider the unbinned maximum-likelihood method
presented in Sec. V to be the optimal approach to analyzing
the KamLAND data because it takes full advantage of all
the spectral and time information available. In this appendix we outline a binned oscillation analysis which we findreproduces very well the  2 contours in the ð12 ; 13 Þ
subspace for the unbinned likelihood KamLAND-only
analysis shown in Fig. 3. The binning parameter isthe parameter x introduced in Sec. VI and defined in
Eq. (8). Table IV lists the binned data. The binned 2 isdefined asXpi  i ð1 þ corr Þ 2  corr 2
2
¼
þ
;
(B1)
pi

þ0:0130:0090:007

Survival probability (p p)0:749  0:044
0:650  0:039
0:624  0:046
0:512  0:038
0:416  0:030
0:415  0:160

where

APPENDIX Aiþ0:0160:0200:016

corr

4
2
i ¼ cos 13 ð1  sin 212x i Þ þ sin4 13(B2)

and x i is the weighted average of x over bin i. The pairs
ðpi ; pi Þ are the observed survival probability, defined as
the ratio of the observed events to the expectation for no
oscillation, and its uncertainty for each bin i, and corr is afactor needed to account for the systematic uncertainty( corr ¼ 0:041) on the flux prediction. In Eq. (B2), thevacuum 12 should be used because matter corrections to12 and m221 are included in the calculation of x, as shownin Eq. (8). For a global analysis, the small dependence onm221 can be ignored and the binned 2 may be used for ascan over the ð12 ; 13 Þ oscillation parameter space.
Comparing the  2 map built using this method and thatfrom the full unbinned analysis shown in Fig. 3, the only
significant deviations appear far from the best-fit point athigh values of 12 where constraints from the solar neutrino experiments dominate.

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PHYSICAL REVIEW D 83, 052002 (2011)

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