Antineutrino science by KamLAND.

KamLAND measured the ν̄ e's flux from distant nuclear reactors, and found fewer events than expected from standard assumptions about ν̄ e propagation at the 99.998% confidence level (C.L.). The observed energy spectrum disagrees with the expected spectral shape at 99.6% C.L., and prefers the distortion from neutrino oscillation effects. A two-flavor oscillation analysis of the data from KamLAND and solar neutrino experiments with CPT invariance, yields [Formula: see text] eV(2) and [Formula: see text]. All solutions to the solar neutrino problem except for the large mixing angle (LMA) region are excluded. KamLAND succeeded in detecting geoneutrinos produced by the decays of (238)U and (232)Th within the Earth. The total observed number of 4.5 to 54.2, assuming a Th/U mass concentration ratio of 3.9 is consistent with 19 predicted by geophysical models. This detection allows better estimation of the abundances and distributions of radioactive elements in the Earth, and of the Earth's overall heat budget.

Introduction

The existence of neutrinos was first proposed in 1930, to explain an anomaly seen in experiments on the radioactive β-decay of atomic nuclei. But we don’t know many things about neutrinos. Neutrinos are fundamental particles similar to electrons, but much lighter and with no electric charge, interact only weakly with normal matter, and can penetrate the Earth with negligible attenuation. It is often says that neutrino physics is largely an art of learning a great deal by observing nothing. However the neutrino became a little less mysterious. In 1998 Super-Kamiokande obtained the evidence of atmospheric neutrino oscillations.[1)] This was the first discovery of a finite neutrino mass. The relation between neutrino oscillations and neutrino masses is in the following. Neutrinos participating in the charged current weak interactions are characterized by the flavor (e, μ, τ). But the neutrinos of definite flavor are not necessarily states of a definite mass. Instead, they are generally coherent superpositions of such states. There is good evidence, from a variety of experiments, that only two of the three mass eigenstates contribute significantly. For instance the states, |νe>, |ν mix with the mass states |ν1>, |ν2> as:

Neutrino flavor oscillations are a fundamental consequence of two assumptions: that the neutrino has a finite rest mass and that the neutrino flavor eigenstates mix in the mass eigenstates. If a neutrino is initially created in a state of |νe>, then the transition probability to |ν>, at a distance L from the source is where is the mass squared difference, and the angle θ is known as the vacuum mixing angle. Super-Kamiokande supports the conclusion that the observed effect is due to the ν→ν oscillations.

The KamLAND (1000 ton Kamioka Liquid Scintillator Anti-Neutrino Detector) project was proposed in 1994 for further studies of neutrino oscillations. The principal goal of KamLAND[2)] is a search for the oscillation of ν̄e’s emitted from distant power reactors. There are two accidental lucks in this experiment. One is in the neutrino source. KamLAND is surrounded with a number of powerful reactors with a total of ∼70GW (109 watt) which is nearly equal to ∼ 7% of the world nuclear power generation. On top of that these reactors are located at about the same distance of ∼ 180 km. This means that the effects of oscillations will add up rather than average out between the different reactors. The second luck is in its long baseline, typically 180 km. This distance enables KamLAND to approach the smallest Δ m2 down to 105 eV2 among experiments using artificially produced neutrinos, and also addresses one of oscillation solutions to the “solar neutrino deficit problem”[3)] with ν̄e’s under laboratory conditions. Additionally, KamLAND is the first detector sensitive enough to measure the geoneutrinos, ν̄e’s produced in the Earth from the 238U and 232Th decay chains. One of basic factors in the interior dynamics and the evolution of the present Earth is the radiogenic heat, ∼ 90% of which comes from the decay of 238U and 232Th. Consequently the first detection of geoneutrinos may provide a new window for the exploration of the Earth.

The success of the experiment depends heavily on how much the background can be suppressed and how many background events can be identified. It is not enough to make the detector radioactively ultrapure. To minimize background events, the design must include a high-light-emission liquid scintillator and large aperture photomultiplier tubes (PMT’s) with state-of-the-art time and energy response. After proposing the KamLAND project, detector R&D works immediately started in particular for developing 17-inch PMT’s with high quality timing and energy responses and a plastic balloon filled with 1000 tons of liquid scintillator. In 1997 the full budget was funded by the Center Of Excellence (COE) program sponsored by Japan Society for the Promotion of Science (JSPS). In 1999 13 US institutes joined in the KamLAND project. Since then, the project was performed by the Japan-US collaboration. KamLAND launched into taking data in January 22, 2002. The data-taking is quite stable since March 2002. In this Report the reactor antineutrino detection and the first result of geoneutrino detection are discussed.

KamLAND detector

KamLAND is a large neutrino detector built in the Kamioka mine beneath the mountains of Japanese Alps, about 200km west of Tokyo. The underground laboratory is located 1000 m below the summit of Mt. Ikenoyama. The detector sits at the site of the old Kamiokande, the 3000 m3 water Cerenkov detector which played a leading role in the study of neutrinos produced via cosmic rays and also helped to pioneer the subject of neutrino astronomy. After dismantling the Kamiokande detector, the rock cavity was enlarged to be 20 m in diameter and 20 m in height. The KamLAND detector consists of a series of concentric spherical shells. Fig. 1 shows a conceptual drawing of the detector. The neutrino detector/target is 1000 tons of ultra-pure liquid scintillator located at the center of the detector. The KamLAND liquid scintillator is a chemical cocktail of 80% dodecane, 20% pseudocumene (1,2,4-trimethylbenzene) and 1.52 g/liter of PPO (2,5-diphenyloxazole) as a fluor. The scintillator is housed in a 13 m-diameter spherical balloon made of 3-layers of nylon with a total thickness of 135 μm and supported by a cargo net structure at the top of the stainless steel vessel. This balloon system hangs inside the 18 m-diameter stainless-steel spherical vessel. A buffer mixture of dodecane and isoparaffin oils fills the volume between the stainless steel vessel and the balloon. Its density is 0.04% lighter than that of the liquid scintillator to reduce a mechanical load on the balloon. The entire inner surface of the vessel (Inner Detector: ID) is covered by an array of a total of 1879 photomultiplier tubes (PMT’s), 1325 of which are specially developed 17-inch and 554 of which are the old Kamiokande 20-inch devices. The total photocathode coverage is 34%. A 3-mm-thick acrylic barrier at 16.6 m diameter prevents radon emanating from PMT glasses from entering the liquid scintillator. This central detector stands in the cylindrical rock cavity. The volume between the sphere vessel and the cavity is filled with ∼ 3200 m3 of pure water in which 225 Kamiokande PMT’s are placed to detect cosmic-ray muons by their Cerenkov light. This outer detector (OD) absorbs γ-rays and neutrons from the surrounding rock and provides a tag for cosmic-ray μ’s. Each PMT signal in ID is recorded, using the analog-transient-waveform-digitizer (ATWD). The ATWD’s are self launching with a threshold ∼ 1/3 photoelectrons and operated with 3 different gains allowing a dynamic range of ∼ 1 mV to 1 V. There are 128 samples per waveform with a sampling time of 1.5 nsec. A pair of 2 ATWD’s for each PMT is equipped to reduce detector dead time. The primary ID trigger is set at 200 PMT hits, corresponding to about 0.7 MeV. This threshold is lowered to 120 hits for 1 msec after the primary trigger to detect lower energy delayed signals.

Fig. 1

Schematic view of the KamLAND detector.

The detector performance is investigated, using laser and LED light-sources, radioactive sources and cosmic-ray μ-induced events of spallation-products, neutrons and γ’s. Cosmic-ray μ-induced events provide a monitor to examine the position dependence and the time variation of detector performance, since these events distribute uniformly in space and time. The energy dependence of the position resolution is estimated to ∼30 cm/ for energy up to ∼8 MeV. The systematic uncertainty in the energy scale at the 2.6 MeV analysis threshold is 2.0%. The energy resolution is 6.2%/ . Radioactive materials inside the liquid scintillator are possible background sources for reactor antineutrino and geoneutrino events. A Monte Carlo study requires that the concentrations of 238U, 232Th and 40K in the liquid scintillator should be lowered to 10−13g/g, 10−13g/g and 10−14g/g. Detecting the sequential chain-decays of 214Bi→214Po→210Pb and 212Bi→212Po→208Pb are used to evaluate the 238U and 232Th concentrations. The results are (3.4 ± 0.4) × 10−18g/g for 238U and (5.2 ± 0.8) × 10−17g/g for 232Th. The upper limit of 40K concentration is given to be 2.7 × 10−16g/g. These results tell us that the contaminations of 238U, 232Th and 40K inside the liquid scintillator are extremely below the requirements.

Reactor antineutrino detection

Since nuclear reactors are very intense sources of ν̄e produced through β-decays of neutron rich fission fragments. Studying neutrino oscillations is to look for a deficit of the neutrino flux and observe a deformation in the energy spectrum characterized by oscillation parameters, (Δ m2, sin2 2θ). The Kam-LAND detector is exposed to a large flux of ν̄e’s produced by 52 local reactors in 18 Japanese commercial power-stations. The 26 reactors located at distances of 140–210 kilometers away from Kamioka generate ∼70GW which corresponds to ∼7% of the world nuclear power generation. With such desirable conditions as a huge reactor power, an extremely long and definite base-line (∼180 km), and the relatively low neutrino energy, KamLAND improves a Δ m2 detection sensitivity by more than 2 order of magnitudes for the previous reactor experiments, and is accessible to the large mixing angle (LMA[3)]) oscillation parameter region to solve the solar νe deficit problem.

To determine the reactor ν̄e flux, the information of instantaneous thermal power, fuel burn-up, exchange and enrichment records for all Japanese power reactors is required. The fission rate for each fissile element is calculated, combining all above data. The thermal power generation is checked with the independent records of electric power generation. Figs. 2 (a) and 2 (b) show one example of thermal power data and the corresponding fission-rate calculations for fissile elements of 235,238U and 239,241Pu of which elements contribute to 99.9% of the ν̄e flux generation. The time-integrated fission flux at Kamioka given by these fuel elements in units of fission number/cm2 is plotted in Fig. 2 (c) as a function of the distance. More than 79% of the total fission flux arises from 26 reactors within the distance of ∼180 km from Kamioka. This relatively narrow band of distances allows KamLAND to be sensitive to spectral distortions for certain oscillation parameters. The contribution to the ν̄e flux from Korean reactors is estimated to be (2.46 ± 0.25)% based on the reported electric power generation rates. That from other reactors around the world is (0.70± 0.35)% as an average. Once the fission rates of fissile isotopes are obtained, the expected ν̄e flux is calculated using the measurements of ν̄e energy spectrum per fission.[4)]

Fig. 2

Examples of instantaneous thermal power (a) and fuel burn-up (b) records for one of Japanese commercial reactors. (c) is the fission yields at Kamioka from 4 fissile nuclei. The accumulation period is the same as the data-taking interval of March 9, 2002 to January 11, 2004. These data are provided according to the special agreement between Tohoku Univ. and the Japanese nuclear power-reactor organization.

Upon entering the detector, ν̄e is captured by a free proton and an inverse β-decay reaction occurs, ν̄e +p → e++n. The positron deposits its energy and then annihilates, yielding two γ-rays (each 511 keV). The neutron is thermalized in (211.2 ± 2.6) μsec. and then captured by a proton in the following reaction, n + p → d + γ (2.22 MeV). Thus the inverse β-decay reaction provides a clear sequential signature of the prompt e+ and delayed γ with the definite time- and close space-correlations. The incident ν̄e energy is given by E ∼ E+ + 0.8 MeV, neglecting the small neutron recoil. Although the need to prevent any signals mimicking neutrino events is imperative, these signal correlations give a high rejection-power for background events. Nevertheless we can’t escape from the geoneutrino background. KamLAND has the first chance to search for geoneutrinos which are ν̄e’s originated from the U/Th decays inside the Earth. The radiogenic heat by the U/Th decays makes a dominant role in the energy generation of the Earth. We evaluated the detection rate of geoneutrinos in KamLAND, using various geophysical and geochemical models.[5)] In Fig. 3 a smooth broad histogram is the expected visible energy spectrum of positrons produced by reactor neutrinos, and 2 sharp peaks in the energy below 2.5 MeV are expected by geoneutrinos. In the reactor neutrino oscillation analysis, positrons with energies above 2.6 MeV are used to escape from the geoneutrino pollution.

Fig. 3

Expected energy spectra of positrons produced by the reactor neutrinos and geoneutrinos.[5)]

Reactor data analysis

So far KamLAND demonstrated “First Results from KamLAND: Evidence for Reactor Antineutrino Disappearance”, using the first period data sample taken in 4 March 2002 to 6 October 2002 (ANA-I), [6)] and “Measurement of Neutrino Oscillation with KamLAND: Evidence of Spectral Distortion”, using the second period data sample taken in 9 March 2002 to 11 January 2004 (ANA-II).[7)] These data samples correspond to a total exposure time of 162.2 ton-yr for ANA-I and 766.3 ton-yr for ANA-II, respectively. The selection cuts for ν̄e events in ANA-I are in the following: (i) fiducial volume (R < 5 m), (ii) time correlation (0.5 μsec < ΔT < 660 μsec), (iii) vertex correlation (ΔR < 1.6 m), (iv) delayed energy (1.8 MeV < Edelayed< 2.6 MeV), and (v) a requirement from the delayed vertex position to be more than 1.2 m from the central vertical axis to eliminate background from LS monitoring thermometers. Antineutrinos emitted through the 238U and 232Th decays in the Earth, geoneutrinos contribute lowenergy events with Eprompt< 2.49 MeV. To avoid ambiguities from geoneutrinos (vi) a prompt energy cut of Eprompt> 2.6 MeV is applied. In ANA-II more elaborate selection cuts are used: R < 5.5 m corresponding to the fiducial mass of 543.7 ton and the target-free protons of 4.61 × 1031, 0.5 μsec < ΔT < 1000 μsec, ΔR < 2 m and 2.6 < Eprompt< 8.5 MeV. The efficiency of ν̄e event selection is improved from (78.3±1.6)% for ANA-I to (89.8±1.5)% for ANA-II. The overall systematic error is 6.5% for Eprompt>2.6 MeV. The cosmic μ-induced spallation events are eliminated, using the time and space correlations between μ’s with the energy deposit of E> 3 GeV and prompt events. The correlation of prompt and delayed energies for the ANA-II ν̄e candidates before applying Edelayed cut is plotted in Fig. 4. A clear event-isolation in the delayed energy window can be seen. Events concentrated in Edelayed ∼ 1 MeV are expected to be accidental backgrounds. The event rate of Edelayed ∼ 5 MeV is consistent with the expected neutron radiative capture rate on 12C. These events are not used at present due to very low statistics.

Fig. 4

Scatter plot of Eprompt and Edelayed for the ν̄e candidate events.

Background events passing through the above event-selection criteria and thus embedding inside the inverse β-decay candidates come dominantly from the reactions of 13C(α, n)16O* and 12C(n,n′)12C* induced by α particles of the radon daughter 210Po in the liquid scintillator. The μ-induced spallation-products of 9Li/8He emit a β and a neutron, thus mimicking the inverse β-decay events. Contributions from the accidental backgrounds and fast neutrons are small. Table 1 summarizes the number of the observed ν̄e candidate-events, the number of the expected reactor ν̄e events and the number of the expected background events for ANA-I and ANA-II. This table also shows the ratio of the observed ν̄e events minus background events to the expected reactor events. This ratio is 0.611 ± 0.085(stat) ± 0.041(syst) for ANA-I, and 0.658 ± 0.044(stat) ± 0.047(syst) for ANA-II. Kam-LAND observed the first evidence for reactor antineutrino disappearance with 99.95% C.L. in ANA-I and reconfirmed it with 99.998% C.L. in ANA-II. The time variations of the observed and expected reactor ν̄e event rates are plotted at the 6 data-taking-time-periods in Fig. 5. The rate of reactor antineutrino disappearance is almost constant in each time-interval.

Table 1

Event Summary

	ANA-I	ANA-II
data sample	162.2 ton·yr	766.3 ton·yr
observed ev.	54	258
expected ev.	86.8±5.6	365.2± 23.7
background ev.	2.8±1.7	17.8±7.3
(9Li, 8He)	(0.94±0.85)	(4.8±0.9)
(13C(α, n)16O*)	(1.9±1.3)	(10.3±7.1)
(others)	(0±0.5)	(2.69±0.02)
N_obs−N_BGN_expected	0.601±0.069(stat)±0.042(sys)	0.686±0.044(stat)±0.045(sys)

Fig. 5

Time dependence of the observed and expected reactor event rates.

The prompt energy spectrum above 2.6 MeV is shown in Fig. 6, comparing with the spectra estimated from the reactor ν̄e events, and the accidental and 13C(α, n)16O backgrounds. The observation definitely deviates from the reactor neutrino shape in the energy below 4 MeV. Even in making the normalization free, the best fit of the scaled reactor spectrum shown also in Fig. 6 disagrees with the observation, being excluded at the 99.6% C.L. Here the spectral distortion due to the systematic uncertainties for the backgrounds is considered in the following: for the 13C(α, n)16O background, a free-scale uncertainty around 6 MeV and a 32% scale uncertainty of the estimated rate around 2.6 and 4.4 MeV are applied to fitting. KamLAND gives the first evidence of the spectrum distortion in neutrino experiments with the confidence level of ∼ 3σ. The reactor neutrino anomaly defined as the combined effect of the rate disappearance and spectrum distortion is found at the high confidence level of 99.999995%.

Fig. 6

Prompt energy spectrum of ν̄e candidate events with associated background spectra. The no-oscillation, the best-fit scaled no-oscillation and the best-fit oscillation spectra are compared to the data.

Fig. 7 shows the ratio of measured to expected flux for KamLAND (ANA-I) as well as previous reactor experiments as a function of the average distance from the source. Earlier measurements have seen no trace of anomaly. But the first data from KamLAND gives a lower ratio, exactly as expected by LMA, one of solar neutrino oscillation solutions. The dotted curve drawn with sin2 2θ = 0.833 and Δ m2 = 5.5×10−5eV2, is representative of a best-fit LMA prediction. Thus the reactor neutrino anomaly prefers the effect expected from neutrino oscillations.

Fig. 7

The ratio of measured to expected ν̄e flux from reactor experiments. The solid circle is the KamLAND result plotted at a flux-weighted average distance of ∼ 180 km. The shaded region indicates the range of flux predictions corresponding to the 95% C.L. LMA region from a global analysis of the solar neutrino data.

Neutrino oscillation analysis of reactor data

A two-flavor oscillation analysis for the Kam-LAND event rate and spectrum shape data is carried out, accounting for the 9Li spallation accidental, and the 13C(α, n)16O, background rates with the same manner as the best fit of the scaled reactor spectrum. The best-fit oscillation spectrum together with the backgrounds is shown also in Fig. 6; the best-fit parameters are Δ m2 = 7.9 × 10−5 eV2 and tan2θ = 0.46. The allowed and excluded regions of the oscillation parameters are shown in Fig. 8. The allowed region of the large mixing angle (LMA) solution of solar neutrino experiment[8)] is also shown in this figure. At the 3σ confidence KamLAND squeezes the allowed Δ m2 into 3 narrow bands named LMA-0, LMA-I and LMA-II. However LMA-0 is disfavored at the 97.5% C.L. and LMA-II at 98.0% C.L. The best fit stands at LMA-I, which is consistent with the solar neutrino result, assuming CPT invariance. A global analysis of data from KamLAND and solar neutrino experiments gives an stringent constraint to the oscillation parameter as shown in Fig. 9, where the best fit parameter is eV2 and . The Δχ2 distributions in this figure tell that the sensitivity in Δ m2 is dominated by the observed distortion in the KamLAND spectrum, while solar neutrino data provide the best constraint on θ. This result gives the most precise determination of Δ m2 to date.

Fig. 8

Excluded regions for the rate analysis and allowed regions for the combined rate and shape analysis at several confidence levels.

Fig. 9

Allowed region obtained by the global analysis combined the KamLAND data and solar neutrino fluxes. Δχ2 profiles on sin2 2θ and Δ m2 are also shown.

To test the goodness of the oscillation hypothesis, the ratio of observed ν̄e spectrum to the expected for no-oscillation as a function of L0/E is compared with the prediction from the neutrino oscillation with the best-fit values of Δ m2 and sin2 2θ. The constant L0 chooses 180 km, as if a single reactor at this distance contributes to KamLAND. Two alternative hypothesis for neutrino disappearance, neutrino decay[9)] and decoherence[10)] give different L0/E. Fig. 10 shows the data and best-fits of oscillation, decay and decoherence. The neutrino oscillation is much favored with more than 99% C.L., while the decay and decoherence are excluded at the 95% and 94% C.L. The KamLAND results strengthen that the observed flux disappearance and the distortion of the spectral shape prove the evidence of reactor antineutrino oscillations. A two-flavor oscillation analysis of the data gives that the LMA region is the only remaining oscillation solution to the solar neutrino deficit problem, assuming the CPT invariance.

Fig. 10

Ratio of the observed ν̄e spectrum to the expectation for no-oscillation versus L0/E with L0 =180 km. The histogram is the expectation for the best-fit oscillation, and the curves show the energy dependence for the best-fit decay and best-fit decoherence.

Geoneutrino detection

Thanks to a 1000 ton large target volume, KamLAND has a first chance to search for the geoneutrinos (ν̄e’s) produced from the 238U and 232Th decay chains.[5)] Radiogenic heat dominantly from decays of 238U, 232Th and 40K is supposed to contribute approximately half of the total measured heat dissipation rate from the Earth which is 44.2 ± 1.0 TW (1012 watt) or 31 ± 1 TW, depending on an analysis procedure.[11), 12)] Another 1/2 is believed to come from the primordial energy of planetary accretion and latent heat of core solidification. Heat generation of the Earth is the basic factor to understand the interior dynamics of plate tectonics, mantle convection and terrestrial magnetism. More fundamentally why such heat exists at the present Earth asks how our Earth was born and has been evolving. Detecting geoneutrinos from radioactive elements in the Earth is expected to bring direct insight from the deep Earth and is essential to study the above fundamental subjects.

The 238U and 232Th decays via a series of well established α and β processes emit 6 and 4 ν̄e’s, respectively. The 40K decays through two branching modes, 89.28% of a β decay and 10.72% of an electron capture, accompanying ν̄e or νe. The expected ν̄e energy distributions of these decay chains are shown in Fig. 11. KamLAND detects ν̄e’s with E > 1.8 MeV due to the reaction threshold energy of the inverse β-decay, resulting to be sensitive to ν̄e’s from 238U and 232Th.

Fig. 11

Energy distributions of the expected ν̄e’s from 238U, 232Th and 40K decay chains. The vertical dotted line indicates E = 1.8 MeV,the threshold energy of inverse β-decay.

To estimate geoneutrino flux at the Earth surface, we constructed a reference Earth model including the current available geophysical and geochemical knowledge.[13)] Seismic data provides the structural feature of the inner Earth which divides the Earth into sediment, crust, mantle and core. These regions are further sub-divided as listed in Table 2. The seismological analysis also yields the thickness maps of sediment and crust at 2° × 2° resolution and the global thicknesses of core and mantle. Each sub-region has different 238U and 232Th concentrations. The bulk chemical composition of the Earth is studied based on the analysis of chondritic meteorite which is thought to be close to the Earth ingredients, and then the bulk silicate Earth model (BSE model[14)]) was constructed. Our reference Earth model completely follows the BSE model. Table 2 summarizes the 238U and 232Th concentrations of our reference Earth model.

Table 2

238U and 232Th concentrations from our reference Earth model,[13)] and geoneutrino fluxes at Kamioka in units of cm−2sec−1

		U (ppm)	U series ν̄e	Th (ppm)	Th series ν̄e
Sediment	continental	2.8	6.11×104	10.7	5.07×104
	oceanic	1.68	1.35×104	6.91	1.20×104
Continental Crust	upper	2.8	1.15×106	10.7	9.57×105
	middle	1.6	4.31×105	6.1	3.57×105
	lower	0.2	5.25×104	1.2	6.85×104
Oscanic Crust		0.10	9.04×103	0.22	4.33×103
Mantle	upper	0.012	2.20×105	0.048	1.91×105
	lower	0.012	4.03×105	0.048	3.51×105
Core	outer	0	0	0	0
	inner	0	0	0	0

One can see the 232Th/238U mass ratio distributes between 2.2 and 4.0 in each region. The present model assumes that the ratio of chemical composition, 232Th/238U at each region is uniform, and 238U and 232Th are absent inside the core. The expected geoneutrino flux from each region at KamLAND (36.42°N, 137.31°E), including a suppression factor of 0.59 due to neutrino oscillations is also shown in Table 2. A total geoneutrino flux is 4.33×106 cm−2s−1 in which the sediment, crust and mantle contributions are 3%, 70% and 27%, respectively. The effect of local geology and specific structure of Japan Island Arc was found to be less than 10% error on the total expected flux.

Geoneutrino data analysis

The data sample based on a total detector live-time of 749.1±0.5 days taken in 7 March 2002 to 30 October 2004, is used to search for geoneutrinos. [15)] The ν̄e event cuts are almost the same as the reactor ν̄e cuts. However to reduce accidental co-incidence events, the fiducial volume was squeezed to 5 m spherical radius. Also to qualify the inverse β-decay events, the stringent time and space correlations between the prompt and delayed events, 0.5 μsec < ΔT < 500 μsec and ΔL < 100 cm were applied as shown in Fig. 12. The overall efficiency for detecting geoneutrino candidates with energies between 1.7 and 3.4 MeV in the fiducial volume is estimated to be 0.687 ± 0.007. The energy range reaches below the inverse β-decay threshold of 1.8 MeV owing to the detector energy resolution.

Fig. 12

(a) ΔL - ΔT plot, and (b) the prompt and delayed energy correlation of ν̄e candidate events. Points inside the dotted red boxes are used for the geoneutrino analysis.

The energy spectra of ν̄e candidate events and associated background events are shown in Fig. 13. A total of 152 candidate events are observed. On the other hand backgrounds are dominated by reactor ν̄e’s, and by α-particle induced neutron backgrounds from the 13C(α, n)16O reaction. The energy spectrum of reactor ν̄e’s in this energy region is determined by analyzing ν̄e’s with energies greater than 3.4 MeV, where there is no signal from the geoneutrinos. Using the reactor neutrino oscillation parameters, the number of reactor ν̄e background events is estimated to be 80.4±7.2. The number of α-particle induced neutron background events is 42 ± 11. Including other small contribution from random coincidences, the total background is 127±13 events (1 σ error). Thus geoneutrino candidates from the 238U and 232Th decay chains are extracted. This result is consistent with the 19 events predicted by our reference Earth model.

Fig. 13

(a) ν̄e energy spectra of the candidate events (data), the total expectation (thin solid black line), the total backgrounds (thick solid black line), the expected 238U signals (dot-dashed red line), the expected 232Th signals (dotted green line), and the backgrounds due to reactor ν̄e (dashed blue line), 13C(α, n)16O reactions (dotted brown line) and random coincidences (dot-dashed blue line). (b) ν̄e energy spectra of the candidate events subtracted by the total backgrounds.

An un-binned maximum likelihood analysis of the ν̄e energy spectrum is carried out as a cross-check of extracting the number of geoneutrino events. Here the reactor neutrino oscillation parameters are allowed to take the values of the best-fit ±1σ. The confidence intervals for the number of geoneutrinos are shown in Fig. 14 (a). The best fit gives 3 238U and 18 232Th geoneutrinos shown by the dark circle. Although this result is somehow contradict with that of our reference Earth model indicated by the rectangular box in Fig. 14 (a), even 68.3% C.L. contour covers this box. Based on a study of chondritic meteorites, the Th/U mass ratio in the Earth is believed to be between 3.7 and 4.1, and is known better than either absolute concentration. Hence we investigate the χ2 behavior, assuming a Th/U ratio of 3.9, which corresponds to the χ2 distribution along the dotted line in Fig. 14 (a). With the 90% C.L. the total number of 238U and 232Th geoneutrinos are 4.5 to 54.2, as shown in Fig. 14 (b). The central value of 28.0 is consistent with 25 obtained the above rate-only analysis. The 99% confidence upper limit of the total 238U and 232Th geoneutrino flux at Kam-LAND is 1.62 × 107 cm−2s−1 which corresponds to an upper limit on radiogenic power of 60 TW for our reference Earth model. There is currently a program underway to reduce the 210Pb content of the detector. This should help to reduce the substantial systematic error due to the 13C(α, n)16O background. Further background reduction will require a new detector location, far away from nuclear reactors. The reported investigation of geoneutrinos should pave the way to future and more accurate measurements, which may provide a new window for the exploration of the Earth.

Fig. 14

Confidence intervals of geoneutrinos. (a) Dark circle and rectangular area stand for the best-fit and the prediction of our reference model. (b) The vertical dotted line and gray band give the constraint from our reference model.

Conclusions

KamLAND demonstrated the reactor ν̄e disappearance at long baselines and high confidence level (99.998% C.L.) for the first time. The observed distortion of the spectral shape supports the conclusion that the observation of reactor ν̄e disappearance is due to neutrino oscillation. With the assumption of CPT invariance, the LMA region is the only remaining oscillation solution consistent with the KamLAND result. Furthermore, because the antineutrinos are created in nuclear reactors rather than in the core of the Sun, several alternative possible solutions to the solar neutrino deficit, for instance, the neutrino magnetic moment and unknown neutrino interactions inside the Sun, are swept away. The all caveats about solar neutrino measurements are eliminated in one stroke of KamLAND. This means that the solar neutrino deficit problem which had been continuing for almost 30 years was finally solved.

The first experimental study of antineutrinos from the Earth’s interior was performed, using KamLAND. The present measurement is consistent with current geophysical models. The KamLAND results show that measuring the flux of Earth’s geoneutrinos could provide scientists with an assay of our planet’s total amount of radioactivity, and could also serve as a deep probe for studying portions of the planet that are otherwise inaccessible to us. Furthermore a whole network of the KamLAND-type detectors could reveal unprecedented views of three-dimensional features of the planet’s interior. The KamLAND experiment heralds the dawn of a new science, neutrino geoscience.