- Email: [email protected]
KamLAND Results
Nuclear Physics B (Proc. Suppl.) 188 (2009) 84–89 www.elsevierphysics.com
KamLAND Results I. Shimizua for the KamLAND Collaboration a
Research Center for Neutrino Science, Tohoku University, Aramaki Aoba, Aoba, Sendai, Miyagi 980-8578, Japan KamLAND, designed to explore the neutrino oscillation of ν¯e ’s from reactors, showed the improved results with enhanced statistics of 2881 ton-yr data set, added data lowering the energy threshold, and suppressed systematic uncertainties. As a result, a scaled reactor spectrum with no distortion is excluded at more than 5σ, and the −5 best-fit of oscillation parameters gives Δm221 = 7.58+0.21 eV2 and tan2 θ12 = 0.56+0.14 −0.20 × 10 −0.09 . The improved analysis measured the mass-square difference of neutrino oscillation parameters at a precision of 2.8%, and also observed two cycles of oscillatory shape expected from neutrino oscillation. The geo neutrino flux, measured at the same time, is consistent with expectation based on an earth model within the statistical uncertainty.
1. Introduction The primary goal of the KamLAND experiment is a search for electron anti-neutrino oscillation. Previously, we showed a significant deficit of ν¯e ’s and excluded all solar neutrino solutions but the LMA solution assuming CPT invariance [1]. This result was followed by direct evidence of spectral distortion above the neutrino energy 3.4 MeV [2], and the data covers almost one cycle of oscillatory shape. In the previous results, the primary systematic error sources were the fiducial volume uncertainty on the mixing angle measurement, the energy scale uncertainty on the neutrino mass-square difference, and the 13 C(α, n)16 O rate uncertainty on the background estimation. In this report, we have extended the analysis down to the energy threshold of inverse β-decay (¯ νe + p → e+ + n), and suppressed the systematic and background uncertainties with the new calibration data. The exposure to reactor ν¯e ’s is almost 4 times over previous results. The precise measurement of neutrino oscillation parameters was achieved owe to those improvements. 2. Event selection Electron anti-neutrinos are detected via the inverse β-decay reaction, and the target event is selected by the delayed coincidence. Prompt scin0920-5632/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.nuclphysbps.2009.02.020
tillation light from the e+ has a high correlation with the incident ν¯e energy, Eν¯e Ep + E n + 0.8 MeV, where Ep is the prompt event energy including the positron kinetic energy and the annihilation energy, and E n is the average neutron recoil energy. The neutron is thermalized in the liquid scintillator through elastic scatterings from protons, and its capture reaction on hydrogen emits a 2.2 MeV γ-ray with ∼ 200 μs delay. Thus its reaction makes the delayed coincidence signal, which can be a powerful tool for reducing backgrounds. The detection efficiency and its uncertainties are evaluated with MC simulations. The ν¯e selecfν¯e tion is based on the discriminator L = fν¯ +f , acc e where fν¯e and facc are probability density function (PDF) for ν¯e signals and accidental backgrounds, as a function of prompt and delayed energies, space and time correlation, radial distances from the detector center (Ep , Ed , ΔR, ΔT , Rp , Rd ). For the discrimination of accidental backgrounds, we determined a selection value Lcut (Ep ) to get the maximal figure of merit √ S for each prompt energy interval of 0.1 S+Bacc MeV. Comparing MC simulations with the 68 Ge and 241 Am9 Be calibration data, the selection efficiency error was evaluated to be 0.6%.
85
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4 3
KamLAND data
1st excited state
ground state
2nd excited state
−
3
6129.9 keV(2nd excited state)
+
0
2
+
γ
−
²¹⁰Po¹³C source
+
0
0.0 keV(ground state) 16
O
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Adhesive seal
Derlin
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4438.9 keV
0 0
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6049.4 keV(1st excited state)
e+e
1
²¹⁰Po¹³C source
12 * γ C(n,n) C
4 5 Evisible (MeV)
6
7
8
Figure 1. Prompt energy spectrum of 210 Po13 C source data and the level scheme of 16 O. The cross sections were evaluated to fit the data by scaling for each state. The cross section uncertainties were evaluated to be 10% and 20% for the ground state and the excited states. Table 1 Estimated systematic uncertainties on the expected event rate of reactor ν¯e ’s. Detector-related (%) Fiducial volume Energy scale L-selection eff. Cross section Total
1.8 1.5 0.6 0.2 2.4
3. Calibration In KamLAND, various radioactive sources and a light source are deployed to calibrate the detector response. Previously, we had source calibration data only along the central axis (”z-axis”). However we couldn’t confirm the vertex reconstruction performance in ”off-axis” region, then we used the uniformly distributed 12 B events generated by cosmic-ray muons. The systematic uncertainty on the fiducial volume, 4.7% evaluated from the 12 B uniformity, was the dominant systematic error source. In order to reduce its error, we performed the ”off-axis” calibration (4π
Reactor-related (%) ν¯e -spectra Reactor power Fuel composition Long-lived nuclei Total
2.4 2.1 1.0 0.3 3.3
calibration) with the new source deployment system. We found the reconstruction vertex bias was less than 3 cm, corresponding to 1.8% of the volume uncertainty. Thus the systematic uncertainty on the expected event rate of reactor ν¯e ’s was reduced, and the overall uncertainty is 4.1% as given in Table 1. The dominant background source in the ν¯e analysis is the 13 C(α, n)16 O reaction which originates from the 210 Po α-decay. There are three final states, the ground state, the 1st excited state, and the 2nd excited state, and each has its own unique reaction. In the previous result [2], the cross section error for each state was assigned to
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I. Shimizu / Nuclear Physics B (Proc. Suppl.) 188 (2009) 84–89
Table 2 Estimated backgrounds to ν¯e ’s after selection efficiencies. Background Accidentals 9 Li/8 He Fast neutron & Atmospheric ν 13 C(α, n)16 Ogs , np → np 13 C(α, n)16 Ogs , 12 C(n, n )12 C∗ (4.4 MeV γ) 13 C(α, n)16 O 1st exc. state (6.05 MeV e+ e− ) 13 C(α, n)16 O 2nd exc. state (6.13 MeV γ) Total
the systematic uncertainty. Based on an old experimental data [3], its error for the ground state was 20%. However, for the excited state, there was only theoretical data [4] without any experimental cross-check, so its error was assumed to be 100% conservatively. For the precise evaluation of the (α, n) background, we used the following data, • quenching data of proton scintillation signal in the neutron beam experiment • total cross section data in the recent experiment [5] •
210
Po13 C source calibration data in KamLAND [6]
In order to convert the emitted neutron energies to the visible energies, the proton quenching factor was studied by an intense neutron source facility (OKTAVIAN) at Osaka University. Then its energy scale uncertainty is suppressed within 2%. Moreover, the total cross section uncertainty was also suppressed within 4% owe to the recent experimental data of 13 C(α, n)16 O reaction [5]. However, this data don’t give the cross section for each state. Therefore the new 210 Po13 C source [6], which consists of 210 Po α source and 13 C target nuclei, was prepared and measured 13 C(α, n)16 O reaction directly with the KamLAND detector. Fig. 1 shows the prompt energy spectrum of 210 Po13 C source data. The ground state makes a
Contribution 80.5 ± 0.1 13.6 ± 1.0 < 9.0 157.2 ± 17.3 6.1 ± 0.7 15.2 ± 3.5 3.5 ± 0.2 276.1 ± 23.5
proton recoil by a neutron, or a gamma-ray emission (4.4 MeV) from an excitation of 12 C, the 1st excited state generates annihilation gamma-rays from an internal pair creation (2 × 0.511 MeV), and the 2nd excited state results in a gamma-ray emission (6.1 MeV). We notes short range particles don’t contribute to the light output because most of their energies are deposited in the source or its container. The cross section for each state was determined by comparing the energy spectrum of the data and MC based on the cross sections from [5,4]. Each scaling factor is 1.05, 0.6, and 1.0 for the ground, 1st excited, and 2nd excited state. Including the 210 Po decay-rate, we assigned an uncertainty of 11% for the ground state and 20% for the excited states. 4. Results The analyses presented here are based on data collected from March 9, 2002 through May 12, 2007, including the reanalysis of the data used in earlier results [1,2]. In the absence of ν¯e disappearance, we expect 2179 ± 89(syst) events from all reactors, however, we observed only 1609 events. The estimated backgrounds to the ν¯e signal are summarized in Table 2. The total backgrounds is 276.1 ± 23.5 events without geo neutrino contributions from U and Th-decays. In the oscillation analysis, geo neutrino fluxes were unconstrained to avoid uncertainties from geology, i.e. they are free parameters in fitting. The expected no oscillation spectrum and the
87
100 80 60 40
1 KamLAND data no oscillation best-fit osci. accidental 13 16 C(α,n) O best-fit Geo νe best-fit osci. + BG + best-fit Geo νe
Events / 0.425 MeV
250 200 150 100
0.8 0.6 0.4 0.2
50 0 0
Data - BG - Geo νe Expectation based on osci. parameters determined by KamLAND
Efficiency
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Efficiency (%)
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0 1
2
3
4 5 Ep (MeV)
6
7
8
20
30
40
50 60 70 80 L0/Eν (km/MeV)
90
100
e
Figure 2. Energy spectrum of the observed prompt events, along with the expected no oscillation spectrum and best-fit including neutrino oscillations. The detection efficiency has an energy dependence as shown in the top panel.
Figure 3. Ratio of the observed ν¯e spectrum to the expectation for no oscillation versus L0 /E. Observed energies are converted with a fixed L0 = 180 km. The histogram and curve show the expectation for the best-fit oscillation accounting for the distances to the individual reactors, timedependent flux variations, and efficiencies.
best fit of oscillation spectrum are shown in fig. 2. The oscillation analysis is based on the maximum likelihood method considering background and systematic uncertainties. From the χ2 test in 0.9 < Ep < 8.5 MeV, a scaled reactor spectrum with no distortion is excluded at more than 5σ. In neutrino oscillations, the best-fit gives Δm221 = −5 7.58+0.21 eV2 and tan2 θ12 = 0.56+0.14 −0.20 × 10 −0.09 if tan2 θ12 < 1. To illustrate oscillatory behavior of the data, the L0 /E distribution is shown in fig. 3. The two alternate hypotheses for neutrino disappearance, neutrino decay [7] and neutrino decoherence [8], give different L0 /E dependence. The minimum χ2 of decay and decoherence are 34.5 and 45.1 larger than neutrino oscillation, strongly indicating the neutrino oscillation is the most favored hypothesis. In this updated result, we showed 2 cycles of oscillatory shape expected from neutrino oscillation. Fig. 4 shows the allowed region of neutrino oscillation parameters. From the KamLAND data, the most favored solution is the so-called LMA I (at Δm221 ∼ 7.6 × 10−5 eV2 ), and other so-
lutions at higher or lower Δm221 are disfavored at more than 4σ. For three-neutrino oscillation analysis, the uncertainty for tan2 θ12 is slightly larger, but we get the same result for Δm221 . If we assume CPT invariance, the allowed region, especially for tan2 θ12 , is more constrained with the global oscillation analysis combining the solar data [9,10]. For the global analysis, the −5 best-fit gives Δm221 = 7.59+0.21 eV2 and −0.21 × 10 +0.06 tan2 θ12 = 0.47−0.05 . The calculated geo neutrino fluxes, based on a geological reference model, are 2.24×106 cm−2 s−1 (56.6 events) and 1.90×106 cm−2 s−1 (13.1 events) from U and Th-decay chains assuming a 16 TW radiogenic heat generation, including a suppression factor of 0.57 due to neutrino oscillation. From the ν¯e analysis including the oscillation constraint on reactor ν¯e ’s by the solar data, the measured geo neutrino flux is (4.4±1.6)×106 cm−2 s−1 (73 ± 27 events) fixing the Th/U mass ratio to 3.9 from planetary data [12]. The measured flux is consistent with the reference model prediction.
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reactor flux. KamLAND 95% C.L. 99% C.L. 99.73% C.L. best fit
(a)
The next goal of the KamLAND experiment is the observation of low energy solar neutrinos. Before the solar phase, the dominant background below 1 MeV was caused by the radioactive impurities, such as 85 Kr and daughters of 210 Pb as shown in Fig 5. Therefore, we constructed the distillation system to purify the liquid scintillator. After the radioactive background reduction in KamLAND, we will measure the 7 Be, pep and CNO ν fluxes. Recently, the solar ν flux calculation was improved because of both the precise determination of the nuclear-fusion cross section [14,15] and the neutrino oscillation parameters. Then the measurement of low energy solar ν’s is of gaining importance in the solar model [16]. The observation of 7 Be and CNO ν’s is considered to be very useful to test the uncertain heavy element abundance in the sun.
Δm 221 (eV2)
10-4
5. Future
Solar 95% C.L. 99% C.L. 99.73% C.L. best fit
10-1
1
tan θ12 2
(b)
7 KamLAND + Solar 95% C.L. 99% C.L. 99.73% C.L. best fit
6
5 0.2
0.3
0.4
0.5
0.6
0.7
0.8
tan θ12 2
Figure 4. (a) Allowed region for neutrino oscillation parameters from KamLAND and Solar. (b) Result of a global two-neutrino oscillation analysis of KamLAND and Solar under the assumption of CPT invariance. The best-fit gives Δm221 = −5 7.59+0.21 eV2 and tan2 θ12 = 0.47+0.06 −0.21 × 10 −0.05 with marginalized errors.
The KamLAND data constrains hypothetical ν¯e sources such as a nuclear reactor at the Earth’s core [13]. A fit with constraints on oscillation parameters from the solar neutrino data sets an upper limit of 6.2 TW (90% C.L.) for the geo
Events/MeV/s
Δm 221 (10-5 eV2)
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104 103 102 10 1 10-1 10-2 10-3 10-4 10-5 10-60
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Bi
pp ν 7
Be ν
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pep ν 7
Be
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2
Figure 5. Visible energy spectra in low energy region for a 4 m radius fiducial volume. Expected spectra of solar neutrinos (no oscillation), radioactive impurities (red dashed line), and spallation isotopes (black solid line) are also shown.
In the first purification campaign, we circulated the liquid scintillator from May 1, 2007 through
I. Shimizu / Nuclear Physics B (Proc. Suppl.) 188 (2009) 84–89
August 1, 2007. The total volume of the processed liquid scintillator was 1,699 m3 . That volume corresponds to 1.4 times of the full volume (∼ 1,200 m3 ), but the background reduction was not sufficient to observe the solar ν’s [17]. So we need some improvements in the purification. In the first campaign, the density fluctuation caused the mixing of the purified and original liquid scintillator with convection that results in inefficient reduction. Thus, we need more precise control of the liquid scintillator density and temperature to keep the boundary of the liquid scintillator. In addition, we fixed some leakage points at the PPO distillation tower and near top of the detector, and we upgraded the distillation system in the PPO tower to get the better purification performance with low pressure distillation. Then, we started the second purification campaign from June 16, 2008. At the end of August, the total processed volume was 1,200 m3 , and we found the boundary of the liquid scintillator was kept well, and the 85 Kr background was reduced by almost two order of magnitude. For the observation of 7 Be ν, we may need a few more cycle of the purification. The ν¯e analysis can be also improved by the purification, because the largest background source is (α, n) reaction which originates from the 210 Po α-decay. The (α, n) background is focused mainly in the lower energy region as shown in fig. 2. Therefore, we expect the improvement of the geo neutrino flux measurement after the purification.
6. Summary We reported the improved measurement of neutrino oscillations in KamLAND. The new full volume calibration data and 210 Po13 C data contributed to the reduction of systematic uncertainties. The incorporated analysis above the energy threshold of inverse β-decay enhanced sensitivity to both neutrino oscillations and geo neutrino fluxes. Those improvements result in the precise measurement of neutrino oscillation parameters. Currently, we are operating the distillation system to purify the liquid scintillator for the observation of low energy solar neutrinos.
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REFERENCES 1. K. Eguchi et al. (KamLAND Collaboration), Phys. Rev. Lett. 90, 021802 (2003). 2. T. Araki et al. (KamLAND Collaboration), Phys. Rev. Lett. 94, 081801 (2005). 3. K. K. Sekharan et al., Phys. Rev. 156, 1187 (1967). 4. JENDL, the Japanese Evaluated Nuclear Data Library available at http://wwwndc.tokaisc.jaea.go.jp/jendl/jendl.html (2005). 5. S. Harissopulos et al., Phys. Rev. C72, 062801 (2005). 6. D. W. McKee et al., Nucl. Inst. Meth. A527, 272 (2008). 7. V.D. Barger et al., Phys. Rev. Lett. 82, 2640 (1999). 8. E. Lisi et al., Phys. Rev. Lett. 85, 1166 (2000). 9. B. Aharmim et al. (SNO Collaboration), Phys. Rev. C72, 055502 (2005). 10. J. N. Bahcall, A. M. Serenelli and S. Basu, Astrophys. J. 621, L85 (2005). 11. S. Enomoto, E. Ohtani, K. Inoue and A. Suzuki, Earth Planet Sci. Lett. 258, 147 (2007). 12. A. Rocholl and K. P. Jochum, Earth Planet. Sci. Lett. 117, 265 (1993). 13. P. Ball, Nature News, 822 (2008). 14. F. Confortola et al., Phys. Rev. C75, 065803 (2007). 15. A. Lemut et al., Phys. Lett. B634, 483 (2006). 16. C. P. Garay, talk at the conference Neutrino Telescopes 2007, available at http://neutrino.pd.infn.it/conference2007/ (2007). 17. Y. Kishimoto, J. Phys.: Conf. Ser. 120, 052010 (2008).
KamLAND Results I. Shimizua for the KamLAND Collaboration a
Research Center for Neutrino Science, Tohoku University, Aramaki Aoba, Aoba, Sendai, Miyagi 980-8578, Japan KamLAND, designed to explore the neutrino oscillation of ν¯e ’s from reactors, showed the improved results with enhanced statistics of 2881 ton-yr data set, added data lowering the energy threshold, and suppressed systematic uncertainties. As a result, a scaled reactor spectrum with no distortion is excluded at more than 5σ, and the −5 best-fit of oscillation parameters gives Δm221 = 7.58+0.21 eV2 and tan2 θ12 = 0.56+0.14 −0.20 × 10 −0.09 . The improved analysis measured the mass-square difference of neutrino oscillation parameters at a precision of 2.8%, and also observed two cycles of oscillatory shape expected from neutrino oscillation. The geo neutrino flux, measured at the same time, is consistent with expectation based on an earth model within the statistical uncertainty.
1. Introduction The primary goal of the KamLAND experiment is a search for electron anti-neutrino oscillation. Previously, we showed a significant deficit of ν¯e ’s and excluded all solar neutrino solutions but the LMA solution assuming CPT invariance [1]. This result was followed by direct evidence of spectral distortion above the neutrino energy 3.4 MeV [2], and the data covers almost one cycle of oscillatory shape. In the previous results, the primary systematic error sources were the fiducial volume uncertainty on the mixing angle measurement, the energy scale uncertainty on the neutrino mass-square difference, and the 13 C(α, n)16 O rate uncertainty on the background estimation. In this report, we have extended the analysis down to the energy threshold of inverse β-decay (¯ νe + p → e+ + n), and suppressed the systematic and background uncertainties with the new calibration data. The exposure to reactor ν¯e ’s is almost 4 times over previous results. The precise measurement of neutrino oscillation parameters was achieved owe to those improvements. 2. Event selection Electron anti-neutrinos are detected via the inverse β-decay reaction, and the target event is selected by the delayed coincidence. Prompt scin0920-5632/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.nuclphysbps.2009.02.020
tillation light from the e+ has a high correlation with the incident ν¯e energy, Eν¯e Ep + E n + 0.8 MeV, where Ep is the prompt event energy including the positron kinetic energy and the annihilation energy, and E n is the average neutron recoil energy. The neutron is thermalized in the liquid scintillator through elastic scatterings from protons, and its capture reaction on hydrogen emits a 2.2 MeV γ-ray with ∼ 200 μs delay. Thus its reaction makes the delayed coincidence signal, which can be a powerful tool for reducing backgrounds. The detection efficiency and its uncertainties are evaluated with MC simulations. The ν¯e selecfν¯e tion is based on the discriminator L = fν¯ +f , acc e where fν¯e and facc are probability density function (PDF) for ν¯e signals and accidental backgrounds, as a function of prompt and delayed energies, space and time correlation, radial distances from the detector center (Ep , Ed , ΔR, ΔT , Rp , Rd ). For the discrimination of accidental backgrounds, we determined a selection value Lcut (Ep ) to get the maximal figure of merit √ S for each prompt energy interval of 0.1 S+Bacc MeV. Comparing MC simulations with the 68 Ge and 241 Am9 Be calibration data, the selection efficiency error was evaluated to be 0.6%.
85
10-7events/50keV/α-decay
I. Shimizu / Nuclear Physics B (Proc. Suppl.) 188 (2009) 84–89
4 3
KamLAND data
1st excited state
ground state
2nd excited state
−
3
6129.9 keV(2nd excited state)
+
0
2
+
γ
−
²¹⁰Po¹³C source
+
0
0.0 keV(ground state) 16
O
1
2
3
Adhesive seal
Derlin
12
4438.9 keV
0 0
Weld
6049.4 keV(1st excited state)
e+e
1
²¹⁰Po¹³C source
12 * γ C(n,n) C
4 5 Evisible (MeV)
6
7
8
Figure 1. Prompt energy spectrum of 210 Po13 C source data and the level scheme of 16 O. The cross sections were evaluated to fit the data by scaling for each state. The cross section uncertainties were evaluated to be 10% and 20% for the ground state and the excited states. Table 1 Estimated systematic uncertainties on the expected event rate of reactor ν¯e ’s. Detector-related (%) Fiducial volume Energy scale L-selection eff. Cross section Total
1.8 1.5 0.6 0.2 2.4
3. Calibration In KamLAND, various radioactive sources and a light source are deployed to calibrate the detector response. Previously, we had source calibration data only along the central axis (”z-axis”). However we couldn’t confirm the vertex reconstruction performance in ”off-axis” region, then we used the uniformly distributed 12 B events generated by cosmic-ray muons. The systematic uncertainty on the fiducial volume, 4.7% evaluated from the 12 B uniformity, was the dominant systematic error source. In order to reduce its error, we performed the ”off-axis” calibration (4π
Reactor-related (%) ν¯e -spectra Reactor power Fuel composition Long-lived nuclei Total
2.4 2.1 1.0 0.3 3.3
calibration) with the new source deployment system. We found the reconstruction vertex bias was less than 3 cm, corresponding to 1.8% of the volume uncertainty. Thus the systematic uncertainty on the expected event rate of reactor ν¯e ’s was reduced, and the overall uncertainty is 4.1% as given in Table 1. The dominant background source in the ν¯e analysis is the 13 C(α, n)16 O reaction which originates from the 210 Po α-decay. There are three final states, the ground state, the 1st excited state, and the 2nd excited state, and each has its own unique reaction. In the previous result [2], the cross section error for each state was assigned to
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Table 2 Estimated backgrounds to ν¯e ’s after selection efficiencies. Background Accidentals 9 Li/8 He Fast neutron & Atmospheric ν 13 C(α, n)16 Ogs , np → np 13 C(α, n)16 Ogs , 12 C(n, n )12 C∗ (4.4 MeV γ) 13 C(α, n)16 O 1st exc. state (6.05 MeV e+ e− ) 13 C(α, n)16 O 2nd exc. state (6.13 MeV γ) Total
the systematic uncertainty. Based on an old experimental data [3], its error for the ground state was 20%. However, for the excited state, there was only theoretical data [4] without any experimental cross-check, so its error was assumed to be 100% conservatively. For the precise evaluation of the (α, n) background, we used the following data, • quenching data of proton scintillation signal in the neutron beam experiment • total cross section data in the recent experiment [5] •
210
Po13 C source calibration data in KamLAND [6]
In order to convert the emitted neutron energies to the visible energies, the proton quenching factor was studied by an intense neutron source facility (OKTAVIAN) at Osaka University. Then its energy scale uncertainty is suppressed within 2%. Moreover, the total cross section uncertainty was also suppressed within 4% owe to the recent experimental data of 13 C(α, n)16 O reaction [5]. However, this data don’t give the cross section for each state. Therefore the new 210 Po13 C source [6], which consists of 210 Po α source and 13 C target nuclei, was prepared and measured 13 C(α, n)16 O reaction directly with the KamLAND detector. Fig. 1 shows the prompt energy spectrum of 210 Po13 C source data. The ground state makes a
Contribution 80.5 ± 0.1 13.6 ± 1.0 < 9.0 157.2 ± 17.3 6.1 ± 0.7 15.2 ± 3.5 3.5 ± 0.2 276.1 ± 23.5
proton recoil by a neutron, or a gamma-ray emission (4.4 MeV) from an excitation of 12 C, the 1st excited state generates annihilation gamma-rays from an internal pair creation (2 × 0.511 MeV), and the 2nd excited state results in a gamma-ray emission (6.1 MeV). We notes short range particles don’t contribute to the light output because most of their energies are deposited in the source or its container. The cross section for each state was determined by comparing the energy spectrum of the data and MC based on the cross sections from [5,4]. Each scaling factor is 1.05, 0.6, and 1.0 for the ground, 1st excited, and 2nd excited state. Including the 210 Po decay-rate, we assigned an uncertainty of 11% for the ground state and 20% for the excited states. 4. Results The analyses presented here are based on data collected from March 9, 2002 through May 12, 2007, including the reanalysis of the data used in earlier results [1,2]. In the absence of ν¯e disappearance, we expect 2179 ± 89(syst) events from all reactors, however, we observed only 1609 events. The estimated backgrounds to the ν¯e signal are summarized in Table 2. The total backgrounds is 276.1 ± 23.5 events without geo neutrino contributions from U and Th-decays. In the oscillation analysis, geo neutrino fluxes were unconstrained to avoid uncertainties from geology, i.e. they are free parameters in fitting. The expected no oscillation spectrum and the
87
100 80 60 40
1 KamLAND data no oscillation best-fit osci. accidental 13 16 C(α,n) O best-fit Geo νe best-fit osci. + BG + best-fit Geo νe
Events / 0.425 MeV
250 200 150 100
0.8 0.6 0.4 0.2
50 0 0
Data - BG - Geo νe Expectation based on osci. parameters determined by KamLAND
Efficiency
Survival Probability
Efficiency (%)
I. Shimizu / Nuclear Physics B (Proc. Suppl.) 188 (2009) 84–89
0 1
2
3
4 5 Ep (MeV)
6
7
8
20
30
40
50 60 70 80 L0/Eν (km/MeV)
90
100
e
Figure 2. Energy spectrum of the observed prompt events, along with the expected no oscillation spectrum and best-fit including neutrino oscillations. The detection efficiency has an energy dependence as shown in the top panel.
Figure 3. Ratio of the observed ν¯e spectrum to the expectation for no oscillation versus L0 /E. Observed energies are converted with a fixed L0 = 180 km. The histogram and curve show the expectation for the best-fit oscillation accounting for the distances to the individual reactors, timedependent flux variations, and efficiencies.
best fit of oscillation spectrum are shown in fig. 2. The oscillation analysis is based on the maximum likelihood method considering background and systematic uncertainties. From the χ2 test in 0.9 < Ep < 8.5 MeV, a scaled reactor spectrum with no distortion is excluded at more than 5σ. In neutrino oscillations, the best-fit gives Δm221 = −5 7.58+0.21 eV2 and tan2 θ12 = 0.56+0.14 −0.20 × 10 −0.09 if tan2 θ12 < 1. To illustrate oscillatory behavior of the data, the L0 /E distribution is shown in fig. 3. The two alternate hypotheses for neutrino disappearance, neutrino decay [7] and neutrino decoherence [8], give different L0 /E dependence. The minimum χ2 of decay and decoherence are 34.5 and 45.1 larger than neutrino oscillation, strongly indicating the neutrino oscillation is the most favored hypothesis. In this updated result, we showed 2 cycles of oscillatory shape expected from neutrino oscillation. Fig. 4 shows the allowed region of neutrino oscillation parameters. From the KamLAND data, the most favored solution is the so-called LMA I (at Δm221 ∼ 7.6 × 10−5 eV2 ), and other so-
lutions at higher or lower Δm221 are disfavored at more than 4σ. For three-neutrino oscillation analysis, the uncertainty for tan2 θ12 is slightly larger, but we get the same result for Δm221 . If we assume CPT invariance, the allowed region, especially for tan2 θ12 , is more constrained with the global oscillation analysis combining the solar data [9,10]. For the global analysis, the −5 best-fit gives Δm221 = 7.59+0.21 eV2 and −0.21 × 10 +0.06 tan2 θ12 = 0.47−0.05 . The calculated geo neutrino fluxes, based on a geological reference model, are 2.24×106 cm−2 s−1 (56.6 events) and 1.90×106 cm−2 s−1 (13.1 events) from U and Th-decay chains assuming a 16 TW radiogenic heat generation, including a suppression factor of 0.57 due to neutrino oscillation. From the ν¯e analysis including the oscillation constraint on reactor ν¯e ’s by the solar data, the measured geo neutrino flux is (4.4±1.6)×106 cm−2 s−1 (73 ± 27 events) fixing the Th/U mass ratio to 3.9 from planetary data [12]. The measured flux is consistent with the reference model prediction.
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reactor flux. KamLAND 95% C.L. 99% C.L. 99.73% C.L. best fit
(a)
The next goal of the KamLAND experiment is the observation of low energy solar neutrinos. Before the solar phase, the dominant background below 1 MeV was caused by the radioactive impurities, such as 85 Kr and daughters of 210 Pb as shown in Fig 5. Therefore, we constructed the distillation system to purify the liquid scintillator. After the radioactive background reduction in KamLAND, we will measure the 7 Be, pep and CNO ν fluxes. Recently, the solar ν flux calculation was improved because of both the precise determination of the nuclear-fusion cross section [14,15] and the neutrino oscillation parameters. Then the measurement of low energy solar ν’s is of gaining importance in the solar model [16]. The observation of 7 Be and CNO ν’s is considered to be very useful to test the uncertain heavy element abundance in the sun.
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Solar 95% C.L. 99% C.L. 99.73% C.L. best fit
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Figure 4. (a) Allowed region for neutrino oscillation parameters from KamLAND and Solar. (b) Result of a global two-neutrino oscillation analysis of KamLAND and Solar under the assumption of CPT invariance. The best-fit gives Δm221 = −5 7.59+0.21 eV2 and tan2 θ12 = 0.47+0.06 −0.21 × 10 −0.05 with marginalized errors.
The KamLAND data constrains hypothetical ν¯e sources such as a nuclear reactor at the Earth’s core [13]. A fit with constraints on oscillation parameters from the solar neutrino data sets an upper limit of 6.2 TW (90% C.L.) for the geo
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Figure 5. Visible energy spectra in low energy region for a 4 m radius fiducial volume. Expected spectra of solar neutrinos (no oscillation), radioactive impurities (red dashed line), and spallation isotopes (black solid line) are also shown.
In the first purification campaign, we circulated the liquid scintillator from May 1, 2007 through
I. Shimizu / Nuclear Physics B (Proc. Suppl.) 188 (2009) 84–89
August 1, 2007. The total volume of the processed liquid scintillator was 1,699 m3 . That volume corresponds to 1.4 times of the full volume (∼ 1,200 m3 ), but the background reduction was not sufficient to observe the solar ν’s [17]. So we need some improvements in the purification. In the first campaign, the density fluctuation caused the mixing of the purified and original liquid scintillator with convection that results in inefficient reduction. Thus, we need more precise control of the liquid scintillator density and temperature to keep the boundary of the liquid scintillator. In addition, we fixed some leakage points at the PPO distillation tower and near top of the detector, and we upgraded the distillation system in the PPO tower to get the better purification performance with low pressure distillation. Then, we started the second purification campaign from June 16, 2008. At the end of August, the total processed volume was 1,200 m3 , and we found the boundary of the liquid scintillator was kept well, and the 85 Kr background was reduced by almost two order of magnitude. For the observation of 7 Be ν, we may need a few more cycle of the purification. The ν¯e analysis can be also improved by the purification, because the largest background source is (α, n) reaction which originates from the 210 Po α-decay. The (α, n) background is focused mainly in the lower energy region as shown in fig. 2. Therefore, we expect the improvement of the geo neutrino flux measurement after the purification.
6. Summary We reported the improved measurement of neutrino oscillations in KamLAND. The new full volume calibration data and 210 Po13 C data contributed to the reduction of systematic uncertainties. The incorporated analysis above the energy threshold of inverse β-decay enhanced sensitivity to both neutrino oscillations and geo neutrino fluxes. Those improvements result in the precise measurement of neutrino oscillation parameters. Currently, we are operating the distillation system to purify the liquid scintillator for the observation of low energy solar neutrinos.
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