Measurement of neutrino oscillation with KamLAND: evidence of spectral distortion.

Abstract

We present results of a study of neutrino oscillation based on a 766 ton/year exposure of KamLAND to reactor antineutrinos. We observe 258 nu (e) candidate events with energies above 3.4 MeV compared to 365.2+/-23.7 events expected in the absence of neutrino oscillation. Accounting for 17.8+/-7.3 expected background events, the statistical significance for reactor nu (e) disappearance is 99.998%. The observed energy spectrum disagrees with the expected spectral shape in the absence of neutrino oscillation at 99.6% significance and prefers the distortion expected from nu (e) oscillation effects. A two-neutrino oscillation analysis of the KamLAND data gives Deltam(2)=7.9(+0.6)(-0.5)x10(-5) eV(2). A global analysis of data from KamLAND and solar-neutrino experiments yields Deltam(2)=7.9(+0.6)(-0.5)x10(-5) eV(2) and tan((2)theta=0.40(+0.10)(-0.07), the most precise determination to date.

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Lawrence Berkeley National Laboratory
Title:
Measurement of neutrino oscillation with Kamland: Evidence of spectral distortion
Author:
Araki, T.
Eguchi, K.
Enomoto, S.
Furuno, K.
Ichimura, K.
Ikeda, H.
Inoue, K.
Ishihara, K.
Iwamoto, T.
Kawashima, T.
Kishimoto, Y.
Koga, M.
Koseki, Y.
Maeda, T.
Mitsui, T.
Motoki, M.
Nakajima, K.
Ogawa, H.
Owada, K.
Ricol, J.-S.
Shimizu, I.
Shirai, J.
Suekane, F.
Suzuki, A.
Tada, K.
Tajima, O.
Tamae, K.
Tsuda, Y.
Watanabe, H.
Busenitz, J.
Classen, T.
Djurcic, Z.
Keefer, G.
McKinny, K.
Mei, D.-M.
Piepke, A.
Yakushev, E.
Berger, B.E.
Chan, Y.D.
Decowski, M.P.
Dwyer, D.A.
Freedman, S.J.

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Fu, Y.
Fujikawa, B.K.
Goldman, J.
Gray, F.
Heeger, K.M.
Lesko, K.T.
Luk, K.-B.
Murayama, H.
Poon, A.W.P.
Steiner, H.M.
Winslow, L.A.
Horton-Smith, G.A.
Mauger, C.
McKeown, R.D.
Vogel, P.
Lane, C.E.
Miletic, T.
Gorham, P.W.
Guillian, G.
Learned, J.G.
Maricic, J.
Matsuno, S.
Pakvasa, S.
Dazeley, S.
Hatakeyama, S.
Rojas, A.
Svoboda, R.
Dieterle, B.D.
Detwiler, J.
Gratta, G.
Ishii, K.
Tolich, N.
Uchida, Y.
Batygov, M.
Bugg, W.
Efremenko, Y.
Kamyshkov, Y.
Kozlov, A.
Nakamura, Y.
Gould, C.R.
Karwowski, H.J.
Markoff, D.M.
Messimore, J.A.
Nakamura, K.
Rohm, R.M.
Tornow, W.
Wendell, R.
Young, A.R.
Chen, M.-J.
Wang, Y.-F.
Piquemal, F.
Publication Date:
06-13-2004

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Publication Info:
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arXiv:hep-ex/0406035 v1 13 Jun 2004
Measurement of Neutrino Oscillation with KamLAND:
Evidence of Spectral Distortion
T. Araki,1K. Eguchi,1S. Enomoto,1K. Furuno,1K. Ichimura,1H. Ikeda,1K. Inoue,1K. Ishihara,1, ∗T. Iwamoto,1, †
T. Kawashima,1Y. Kishimoto,1M. Koga,1Y. Koseki,1T. Maeda,1T. Mitsui,1M. Motoki,1K. Nakajima,1H. Ogawa,1
K. Owada,1J.-S. Ricol,1I. Shimizu,1J. Shirai,1F. Suekane,1A. Suzuki,1K. Tada,1O. Tajima,1K. Tamae,1Y. Tsuda,1
H. Watanabe,1J. Busenitz,2T. Classen,2Z. Djurcic,2G. Keefer,2K. McKinny,2D.-M. Mei,2, ‡A. Piepke,2E. Yakushev,2
B.E. Berger,3Y.D. Chan,3M.P. Decowski,3D.A. Dwyer,3S.J. Freedman,3Y. Fu,3B.K. Fujikawa,3J. Goldman,3
F. Gray,3K.M. Heeger,3K.T. Lesko,3K.-B. Luk,3H. Murayama,3, §A.W.P. Poon,3H.M. Steiner,3L.A. Winslow,3
G.A. Horton-Smith,4C. Mauger,4R.D. McKeown,4P. Vogel,4C.E. Lane,5T. Miletic,5P.W. Gorham,6G. Guillian,6
J.G. Learned,6J. Maricic,6S. Matsuno,6S. Pakvasa,6S. Dazeley,7S. Hatakeyama,7A. Rojas,7R. Svoboda,7
B.D. Dieterle,8J. Detwiler,9G. Gratta,9K. Ishii,9N. Tolich,9Y. Uchida,9, ¶M. Batygov,10W. Bugg,10Y. Efremenko,10
Y. Kamyshkov,10A. Kozlov,10Y. Nakamura,10C.R. Gould,11H.J. Karwowski,11D.M. Markoff,11J.A. Messimore,11
K. Nakamura,11R.M. Rohm,11W. Tornow,11R. Wendell,11A.R. Young,11M.-J. Chen,12Y.-F. Wang,12and F. Piquemal13
(The KamLAND Collaboration)
1Research Center for Neutrino Science, Tohoku University, Sendai 980-8578, Japan
2Department of Physics and Astronomy, University of Alabama, Tuscaloosa, Alabama 35487, USA
3Physics Department, University of California at Berkeley and
Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
4W. K. Kellogg Radiation Laboratory, California Institute of Technology, Pasadena, California 91125, USA
5Physics Department, Drexel University, Philadelphia, Pennsylvania 19104, USA
6Department of Physics and Astronomy, University of Hawaii at Manoa, Honolulu, Hawaii 96822, USA
7Department of Physics and Astronomy, Louisiana State University, Baton Rouge, Louisiana 70803, USA
8Physics Department, University of New Mexico, Albuquerque, New Mexico 87131, USA
9Physics Department, Stanford University, Stanford, California 94305, USA
10Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996, USA
11Triangle Universities Nuclear Laboratory, Durham, North Carolina 27708, USA and
Physics Departments at Duke University, North Carolina State University, and the University of North Carolina at Chapel Hill
12Institute of High Energy Physics, Beijing 100039, People’s Republic of China
13CEN Bordeaux-Gradignan, IN2P3-CNRS and University Bordeaux I, F-33175 Gradignan Cedex, France
(Dated: June 13, 2004)
We present an improved measurement of the oscillation between the first two neutrino families based on a
766.3 ton-year exposure of KamLAND to reactor anti-neutrinos. KamLAND observes 258 events with νe en-
ergies above 3.4MeV compared to 365.2 events expected in the absence of neutrino oscillation. The confidence
level for reactor νedisappearance is now 99.995%. The observed energy spectrum disagrees with the expected
spectral shape in the absence of neutrino oscillation at the 99.9% confidence level but agrees with the distortion
expected from νeoscillation effects. A two-neutrino oscillation analysis of the KamLAND data gives a best-fit
point at ∆m2= 8.3×10−5eV2and tan2θ =0.41. A global analysis of data from KamLAND and solar neutrino
experiments yields ∆m2=8.2+0.6
−0.5×10−5eV2and tan2θ=0.40+0.09
−0.07, the most precise determination to date.
PACS numbers: 14.60.Pq, 26.65.+t, 28.50.Hw
The first measurement of reactor anti-neutrino disappear-
ance by KamLAND [1] suggested that solar neutrino flavor
transformation through the Mikheyev-Smirnov-Wolfenstein
(MSW) [2] matter effect has a direct correspondence to
anti-neutrino oscillation in vacuum. KamLAND and solar-
neutrino experiments have restricted the oscillation parame-
ter space for the first two families, eliminating all but the
large-mixing-angle (LMA-MSW) solution. The LMA solu-
tion was confined to two small regions conventionally named
“LMA I” and “LMA II” [3] for the lower ∆m2∼7×10−5eV2
and higher ∆m2∼2×10−4eV2bands respectively. A com-
bined analysis [4] of the latest results from SNO, other solar
neutrino experiments, and the previous KamLAND result dis-
favored LMA II at greater than 99% C.L. This Letter reports
on new results based on a factor of three longer exposure time
andanalysisimprovementsallowinga33%largerfiducialvol-
ume. There were large variations in the reactor power produc-
tion in Japan in 2003, providing an opportunity to study the
anti-neutrino flux modulation at the KamLAND site.
The KamLAND experiment consists of 1kton of ultra-pure
liquid scintillator (LS) contained in a transparent nylon-based
balloon suspended in non-scintillating oil. The balloon is sur-
rounded by an array of 1879 photomultiplier tubes (PMT’s)
mounted on the inner surface of an 18-m-diameter spherical
stainless-steel containment vessel. Electron anti-neutrinos are
detected via the inverse β-decay reaction, νe+ p → e++ n,
with a 1.8MeV νeenergy threshold. The prompt scintillation
light from the e+gives an estimate of the incident νeenergy,

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Eνe= Eprompt+ En+ 0.8MeV, where Epromptis the prompt
event energy including the positron kinetic energy and the an-
nihilationenergy,andEnis the averageneutronrecoil energy.
The ∼ 200µs delayed 2.2MeV γ-ray from neutron capture
on hydrogen is a powerful tool for reducing backgrounds. A
3.2kton water-Cherenkovdetector surrounds the containment
sphere,absorbingγ-raysandneutronsfromtheenclosingrock
and tagging cosmic-ray muons. This outer detector (OD) is
more than 92% efficient for muons passing through the fidu-
cial volume.
KamLAND is surrounded by 53 power reactor units in
Japan. The reactor operation data, including thermal power
generation, fuel burn up, fuel exchange and enrichment
records, are provided by all Japanese commercial power reac-
tors and are used to calculate the time dependent fission rate
of each isotope. The averaged relative fission yields through-
out the reported run period were235U:238U:239Pu:241Pu =
0.563:0.079:0.301:0.057. The expected νe flux is calcu-
lated using the fission rates and anti-neutrino spectra taken
from the literature [5]. The νecontribution from Japanese
research reactors and reactors outside of Japan is 4.5%. We
assume that these reactors have the same average fuel com-
position as the Japanese commercial reactors for this contri-
bution. The total integrated thermal power flux of all reactors
over the detector livetime was 701Joule/cm2.
We report on data collected between March 9, 2002 and
January11,2004,includingareanalysisofthedatareportedin
Ref. [1]. The PMT array in the central detector was upgraded
on February 27, 2003 by commissioning 554 20-inch tubes,
increasing the photo-cathode coverage from 22% to 34% and
improving the energy resolution from 7.3%/?E(MeV) to
6.2%/?E(MeV). The trigger threshold of 200 hit 17-inch
PMT’s corresponds to about 0.7MeV at the detector center.
The location of particle interactions inside the detector is
determined from PMT hit timing, and the detected energy
is obtained from the number of observed photo-electrons af-
ter corrections for position and gain variations. Position and
time dependence of the energy estimation are monitored pe-
riodically by deploying γ-ray and neutron sources along the
central vertical axis (z-axis) of the scintillator volume. Trace
contaminants on the balloon and in the scintillator are also
exploited for detector calibrations.
tainty in the energy scale at the 2.6MeV prompt event energy
(Eνe≃3.4MeV) analysis threshold is 2.0%, corresponding
to a 2.3% uncertainty in the number of events in an unoscil-
lated reactor νespectrum.
The radial fiducial volume cut is increased from 5m [1] to
5.5m in the present analysis, expanding the fiducial mass to
543.7tons, which corresponds to 4.61×1031free target pro-
tons. The radial positions of the prompt and delayed event
are both required to be less than 5.5m. The 1.2m cylindri-
cal cut along the z-axis previously used to exclude low en-
ergy backgrounds from thermometers is not applied. The
event selection cuts for the time difference (∆T) and posi-
tion difference (∆R) between the positron and delayed neu-
tron are 0.5µs< ∆T <1000µs and ∆R <2m, respectively.
The systematic uncer-
The delayed event energy is required to be within 1.8MeV<
Edelayed <2.6MeV and 2.6MeV< Eprompt <8.5MeV to
avoid backgrounds. The event selection efficiency of all cuts
is (89.8±1.5)%.
The total volume of the KamLAND liquid scintillator
is 1171±25m3, as measured by flow meters during de-
tector filling. The “nominal” 5.5-m-radius fiducial volume
(4
ume. The actual fiducial volume is defined by the cuts on
the radial positions of the reconstructed event vertices. We
calibrate the vertex reconstruction with data from radioac-
tive sources deployed along the z-axis of the detector. At
present, only z-axis calibrations are available, so we as-
sess the systematic uncertainty in the total fiducial volume
by studying uniformly-distributed muon spallation products,
identified as delayed coincidences following detected muons.
We measure the position distribution of the β-decays of
12B (Q=13.4MeV, τ1/2=20.2ms) and12N (Q=17.3MeV,
τ1/2=11.0ms), which are producedby muon spallation at the
rate of about 8012B/12N events/kton-day. Fits to the en-
ergy distribution of these events indicate that our sample is
mostly12B; the relative contributionof12N is only ∼1%. The
number of12B/12N events reconstructed in the fiducial vol-
ume compared to the total number in the entire LS volume is
0.607±0.006(stat)±0.006(syst), where the systematic error
arises from events near the balloon edge that deposit a frac-
tion of their energy outside the LS. In a similar study of spal-
lation neutrons, which we identify via the 2.2MeV capture
γ-ray, we find the ratio 0.587±0.013(stat). However, con-
cerns about reconstruction of low energy events close in time
with larger muon signals lead us to use the spallation-induced
neutron capture events only as a consistency check.
The12B/12N events typically have higher energy than our
anti-neutrino candidates, so we include an additional system-
atic error to account for the possible variation of fiducial vol-
ume with energy. We constrain this variation to 2.7% by com-
paring the prompt and delayed event positions of delayed-
neutron β-decays of9Li (Q=13.6MeV, τ1/2=178ms) and
8He (Q=10.7MeV, τ1/2=119ms).
from the LS volume measurements, the12B/12N volume ra-
tio calibration, and the constraints on energy dependence, we
obtain a 4.7% systematic error on the fiducial volume.
Accidental coincidences increase in the outer region of
the fiducial volume, since most of this background is due to
sources external to the liquid scintillator. This background is
estimated with a 10ms to 20s delayed-coincidence window,
bypairingrandomsinglesevents,orbysimply“swapping”[6]
the prompt and delayedselection criteria. These methodsgive
consistent accidental backgroundestimates of 2.69±0.02 for
events abovethe 2.6MeV threshold. Below this threshold, the
accidental background is much higher and there is a potential
contribution from geo-neutrinos from U and Th in the Earth.
Future extraction of the geo-neutrino signal will require dif-
ferent analysis cuts.
Above the 2.6MeV prompt event energy analysis thresh-
old, spallation-produced neutrons and long-lived delayed-
3πR3) corresponds to 0.595±0.013 of the total LS vol-
Combining the errors

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TABLE I: Estimated systematic uncertainties (%).
Fiducial Volume
Energy threshold
Efficiency of cuts
Livetime
Total systematic error
4.7
2.3
1.6
0.06
Reactor power
Fuel composition 1.0
νespectra [5]
Cross section [7] 0.2
2.1
2.5
6.5
neutron β-emitters are the largest potential backgrounds in
KamLAND. The ∼3000 spallation neutrons per kton-day are
effectively eliminated with a 2ms veto of the entire detec-
tor following a detected muon. The remaining neutron back-
ground comes from muons missed by the OD or interacting
in the rock just outside it. This background is suppressed
strongly by the high OD tagging efficiency and multiple lay-
ers of absorbers: the OD itself, the 2.5m of non-scintillating
oil surrounding the LS, and the 1m of LS outside the fiducial
volume. We estimate this background contributes fewer than
0.89 events to our data sample.
The12B/12N spallation events are effectively suppressed
by the delayed-coincidence requirement. However, the ∼1.5
events/kton-day in the delayed-neutron branches of9Li and
8He mimic the anti-neutrino signal. From fits to the decay-
time and β-energy spectra we see mostly9Li decays; the con-
tribution of8He relative to9Li is less than 15% at 90% C.L.
For single, well-tracked muons passing through the detector,
we apply a 2s veto within a 3m radius cylinder around the
track. We veto the entire volume for 2s after one in ∼30
muons, those that produce more than ∼106photo-electrons
above minimum ionization or muons tracked with poor re-
liability. We estimate that 4.8±0.99Li/8He events remain
after these cuts are applied. The deadtime introduced by all
muon cuts is 9.7%; the total livetime including spallation cuts
is 515.1days. The total backgroundis 7.5±1.3 events, where
the fast neutron contribution has been included in the error.
In the absence of anti-neutrino disappearance, we ex-
pect 365.2±23.7(syst) events above 2.6MeV for the entire
data set, where the systematic uncertainty is detailed in Ta-
ble I.We observe 258 events, confirming νe disappear-
ance at the 99.995% C.L. The average νesurvival probabil-
ity is 0.686±0.044(stat)±0.045(syst). Theeffectivebaseline
varies with the actual power output of the reactor sources in-
volved, so the survival probabilities for different time periods
are not directly comparable. The new analysis procedure ap-
plied to the data previously reported (March 2002 to October
2002) gives 0.582±0.069(stat)±0.039(syst), in agreement
with 0.611±0.085(stat)±0.041(syst) reported in Ref. [1].
After September 2002, a large number of Japanese nuclear
reactors were off, as shown in Fig. 1a. This change decreased
the expected νeflux at KamLAND by more than a factor of
two, in the absence of νeoscillation. In Fig. 1b the signal
counts in KamLAND are plotted in bins of approximately
equal νeflux as determined from the total reactor power. For
∆m2and tan2θ determined below and the known distribu-
rate (events/day)
e ν
no-osc
0 0.20.40.60.81 1.2
rate (events/day)
e ν
observed
0
0.2
0.4
0.6
0.8
1
1.2
Data
Background
distance (km)
0 250500750 1000
(events)
e ν
no-osc
0
50
100
150
09 Mar ’0219 Oct ’02 31 May ’0311 Jan ’04
rate (ev/d)
e ν
no-osc
0.3
0.6
0.9
1.2
(a)
(b)
FIG. 1: (a) Estimated time variation of the reactor νe flux at
KamLAND with no anti-neutrino oscillation. (b) Observed νeevent
rate versus no-oscillation reactor νe flux. Data points correspond to
intervals of approximately equal νeflux. The dashed line is the best
linear fit, the gray region is the associated 90% C.L. The solid line
shows a fit constrained to the expected background at zero reactor
anti-neutrino flux. The inset shows the reactor distance distribution
for νeevents in the absence of oscillations.
tions of reactor power level and distance, the expected oscil-
lated νerate is well approximatedby a straight line. The slope
can be interpreted as the reactor-correlated signal and the in-
tercept as the reactor-independent constant background rate.
Fig. 1b shows a straightline fit to the data and its 90% C.L. re-
gion. Theinterceptis consistent with knownbackgrounds,but
substantially larger backgrounds cannot be excluded; hence
this fit does not usefully constrain speculative sources of anti-
neutrinos such as a geo-reactor at the Earth’s core [8]. The
predicted KamLAND rate for typical 3TW geo-reactor sce-
narios is comparable to our expected backgroundof 7.5±1.3
events and would have minimal impact on the analysis of the
reactor power signal. In the following we consider contribu-
tions only from known anti-neutrino sources.
Fig. 2a shows the correlation of the prompt and delayed
event energy after all selection cuts except for the Edelayed
cut. The prompt energy spectrum above 2.6 MeV is shown
in Fig. 2b. The data are evaluated with an unbinned maxi-
mum likelihood fit to two-flavor neutrino oscillation as was
done previously [1]. In the present analysis, the back-
ground parameters are changed to include only9Li and ac-
cidental backgrounds since the8He contribution is found

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4
(MeV)
delayed
E
2
3
4
5
Fri Jun 11 11:43:30 2004
(MeV)
prompt
E
012345678
Events / 0.425 MeV
0
20
40
60
80
no-oscillation
best-fit oscillation
accidentals
KamLAND data
(a)
(b)
FIG. 2: (a) The correlation of energies between the prompt and de-
layed events after cuts. The three events with Edelayed ∼ 5MeV are
events in which the delayed neutron was captured on carbon. (b)
Prompt event energy spectrum of the νecandidate events along with
the spectrum of accidental backgrounds. The shaded band indicates
the systematic error in the best-fit reactor spectrum above 2.6MeV.
to be small, while the accidental background is larger be-
cause of the larger fiducial volume. The best-fit spectrum is
shown in Fig. 2b; the best-fit values for ∆m2and tan2θ are
8.3×10−5eV2and 0.41 respectively. A shape-only analysis
gives ∆m2=8.3×10−5eV2and tan2θ =0.78.
Taking account of the spallation background, the Baker-
Cousins χ2[9] for the best fit is rather poor, 19.6 (11 DOF).
The χ2is significantly worsened by the data bin at 8MeV.
To test the goodness-of-fit level of several hypotheses we fol-
low the statistical techniques described in Ref. [10]. First,
we fit the data to a hypothesis to find the best-fit parame-
ters. Next, we bin the energy spectrum of the data into 20
equal-probability bins and calculate the Pearson-χ2statistic
(χ2
on the hypothesis in question using the parameters fit from
the data and calculate χ2
confidence level of the data is the fraction of simulated
spectra with a higher χ2
For our best-fit oscillation pa-
rameters, the goodness-of-fit is 42% with χ2
The goodness-of-fit of the scaled no-oscillation spectrum
where the normalization was fit to the data was only 0.1%
(χ2
To illustrate oscillatory behavior of the data, we plot
in Fig. 3 the L0/E distribution, where the data and the
best-fit spectra are divided by the expected no-oscillation
spectrum.Two alternative hypotheses for neutrino disap-
pearance, neutrino decay [11] and decoherence [12], give
different L0/E dependences.
sis, we survey the parameter spaces and find the best-fit
p) for the data. We then simulate 10,000 spectra based
pfor each generated spectrum. The
p.
p/DOF=18.3/18.
p/DOF=43.4/19).
As in the oscillation analy-
2030 40 50607080
0
0.2
0.4
0.6
0.8
1
1.2
1.4
(km/MeV)
e
ν
/E
0
L
Ratio
2.6 MeV prompt
analysis threshold
KamLAND data
best-fit oscillation
best-fit decay
best-fit decoherence
FIG. 3: Ratio of the observed anti-neutrino spectrum to the expec-
tation for no-oscillation versus L0/E. The curves show the expecta-
tion for the best-fit oscillation, best-fit decay and best-fit decoher-
ence models taking into account the individual time-dependent flux
variations of all reactors and detector effects. The data points and
models are plotted with L0=180km, as if all anti-neutrinos detected
in KamLAND were due to a single reactor at this distance.
pointsat (sin2θ, m/cτ) = (1.0,0.011MeV/km)fordecayand
(sin22θ, γ0) = (1.0,0.028MeV/km) for decoherence, using
the notation of the references. Applying the goodness-of-fit
proceduredescribedabove,wefindthatdecayhasagoodness-
of-fit of only 5% (χ2
a goodness-of-fit of 6% (χ2
The ∆χ2contours in ∆m2-tan2θ parameter space, includ-
ing small matter effects [13], are shown in Fig. 4a. The best
fit point is in the LMA I region. Maximal mixing for values
of ∆m2consistent with LMA I is allowed at the 79% C.L.
Due to the spectral distortions in the data, the LMA II re-
gion is disfavored at the 99.6% C.L., as are larger values of
∆m2previously allowed by KamLAND. The allowed region
at lower ∆m2is only disfavored at the 94% C.L., but this
region is inconsistent with the LMA region determined from
solar neutrino experiments assuming CPT invariance.
A two-flavor global analysis of the KamLAND data includ-
ing detailed reactor information, the observed solar neutrino
fluxes [14], and the assumption of CPT invariance restricts
the allowed ∆m2-tan2θ parameter space to the region shown
in Fig. 4b. The sensitivity in ∆m2is dominated by the ob-
serveddistortionintheKamLANDspectrum,whilesolarneu-
trino data provide the best constraint on θ. The best fit point
for the combinedanalysis is at ∆m2=8.2+0.6
tan2θ=0.40+0.09
The conclusion that the LMA II region is excluded is
strengthened by the present result. The significantly distorted
spectral shape supports the conclusion that the observation of
reactor νedisappearance is due to neutrino oscillation. Statis-
tical uncertaintiesin the KamLAND data are now on the same
level as systematics. Current efforts to perform full-volume
source calibrations and a reevaluation of reactor power uncer-
tainties will reduce systematic errors.
p/DOF=30.1/18), while decoherence has
p/DOF=28.6/18).
−0.5×10−5eV2and
−0.07.

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5
)
2
(eV
2
m
∆
-5
10
-4
10
θ
2
tan
-1
10
1 10
KamLAND
95% C.L.
99% C.L.
99.73% C.L.
KamLAND best fit
Solar
95% C.L.
99% C.L.
99.73% C.L.
solar best fit
θ
2
tan
0.20.30.40.5 0.60.70.8
)
2
(eV
2
m
∆
KamLAND+Solar fluxes
95% C.L.
99% C.L.
99.73% C.L.
global best fit
-5
10
×
4
-5
10
×
6
-5
10
×
8
-4
10
×
1
-4
10
×
1.2
a) b)
FIG. 4: (a) Allowed regions of neutrino oscillation parameters from KamLAND anti-neutrino data (shaded regions) and solar neutrino ex-
periments (lines) [4]. (b) Result of a combined two-neutrino oscillation analysis of KamLAND and the observed solar neutrino fluxes under
the assumption of CPT invariance. The best-fit point is ∆m2=8.2+0.6
parameter range.
−0.5×10−5eV2and tan2θ =0.40+0.09
−0.07including the allowed 1-sigma
The KamLAND experiment is supported by the COE pro-
gram under grant 09CE2003 of the Japanese Ministry of Ed-
ucation, Culture, Sports, Science and Technology, and un-
der the United States Department of Energy grant DEFG03-
00ER41138. The reactor data are provided by courtesy of the
following electric associations in Japan: Hokkaido, Tohoku,
Tokyo, Hokuriku, Chubu, Kansai, Chugoku, Shikoku and
Kyushu Electric Power Companies, Japan Atomic Power Co.
and Japan Nuclear Cycle Development Institute. Kamioka
Mining and Smelting Company has provided service for ac-
tivities in the mine.
∗Present address: Kamioka Observatory, ICRR, University of
Tokyo, Gifu, Japan
†Present address: ICEPP, University of Tokyo, Tokyo, Japan
‡Present address: LANL, Los Alamos, NM 87545, USA
§Present address: School of Natural Sciences, Institute for Ad-
vanced Study, Princeton, NJ 08540, USA
¶Present address: Imperial College London, UK
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