UvA-DARE (Digital Academic Repository) KamLAND's precision neutrino oscillation measurements

The KamLAND experiment started operation in the Spring of 2002 and is operational to this day. The experiment observes signals from electron antineutrinos from distant nuclear reactors. The program, spanning more than a decade, allowed the determination of LMA-MSW as the solution to the solar neutrino transformation results (under the assumption of CPT invariance) and the measurement of various neutrino oscillation parameters. In particular, the solar mass-splitting (cid:2)m 221 was determined to high precision. Besides the study of neutrino oscillation, KamLAND started the investigation of geologically produced antineutrinos (geo-ν e ). The collaboration also reported on a variety of other topics related to particle and astroparticle physics. © 2016 The Author. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP 3 .


Introduction
Japan began operation of its first commercial nuclear power plant in the mid-1960s. The country invested heavily in nuclear reactors to generate electricity in the subsequent decades and by the year 2000 about 50 nuclear reactors provided 30% of the country's electricity. Besides producing electricity, nuclear reactors also emit electron antineutrinos (ν e ) isotropically in the decay of neutron-rich radioactive products of the fission process. These well-defined sources of ν e 's give the opportunity to study neutrino properties. The Kamioka Liquid Scintillator Anti-Neutrino Detector (KamLAND) experiment was proposed in 1994 [1,2] and was approved by the Japanese government in 1997. In the following years, groups from Japan and the U.S. built the experiment in the old Kamiokande [3] cavity in the Kamioka Mine (Gifu Prefecture, Japan). The initial goals of KamLAND were the search for neutrino oscillation, the first observation of neutrinos originating from radioactive decays in the Earth's mantle (so-called geo-neutrinos) and the possible detection of galactic Supernovae. The KamLAND experiment was completed in early 2002. After a brief detector commissioning phase, regular scientific data recording started on March 9, 2002.
The location of the Kamioka Mine in relation to the Japanese nuclear power reactors provided a flux-weighted average distance of ∼180 km. About 80% of the neutrino flux in 2002 came from 26 reactors within a distance range of 138-214 km, see Fig. 1. The 180 km baseline, together with the emitted ν e spectrum peaking at ∼4 MeV, made KamLAND primarily sensitive to the neutrino oscillation solutions of the 'solar neutrino problem' for solar mass-splitting values of m 2 21 > 10 −5 eV 2 . This review summarizes the KamLAND results obtained in five neutrino-oscillation-related data-releases between 2002 and 2013 [4][5][6][7][8].

The KamLAND detector
The KamLAND detector is located in the Kamioka Mine under Mount Ikenoyama at a depth of ∼2700 m water-equivalent. The primary volume consists of 1 kton of ultra-pure liquid scin- tillator (LS), which provides the neutrino interaction target, see Fig. 2. The LS consists of 80% dodecane and 20% pseudocumene by volume and (1.36 ± 0.03) g/liter PPO 1 as a fluor. The LS is contained in a 13-m-diameter spherical balloon made of 135-µm-thick transparent nylon/EVOH 2 composite film. The balloon is suspended in non-scintillating purified mineral oil (so-called buffer oil). The inner detector (ID) is inside an 18-m-diameter stainless steel spherical tank. Bolted to the inside of the tank are 1325 fast 20-inch-diameter photo multiplier tubes (PMTs), masked to 17-inch diameter, and 554 20-inch-diameter PMTs viewing the inside volume of the ID. The PMT coverage is 34%. The ID is surrounded by a 3.2 kton water-Cherenkov outer detector (OD) that serves as a cosmic-ray muon veto and provides additional shielding from external sources of radioactivity.
KamLAND is sensitive to ν e 's through the inverse β-decay reaction, ν e + p → e + + n, with a reaction threshold of 1.8 MeV. This process has a delayed coincidence event pair signature which provides strong radioactive background suppression. The positron carries most of the energy of the incoming antineutrino from the reaction and is annihilated quickly, providing a prompt event. An approximation of the incident ν e energy is given by E ν e E p + E n + 0.8 MeV, where E p , the prompt energy, is the sum of the positron kinetic and annihilation energies. E n is the average neutron recoil energy and is of order tens of keV. The delayed event of the delayed coincidence event pair is produced by the capture-γ when the neutron captures on either a proton or a 12 C nucleus in the LS, with a mean capture time of 207.5 ± 2.8 µs [9].
The event vertex and energy reconstruction algorithms are based on the timing and charge distribution of scintillation photons recorded by the 17-inch and 20-inch PMTs. These algorithms were tuned with a wide variety of radioactive sources over the lifetime of the experiment. The sources that have been deployed are: 60 Co, 65 Zn, 68 Ge, 137 Cs, 203 Hg, 210 Po 13 C, 241 Am 9 Be, spanning a variety of energies and particles. Deployments were routinely done through the central calibration system at the top of the detector [10], see Fig. 2, but a full-volume campaign was also performed [11]. The vertex resolution is ∼12 cm/ √ E(MeV), and the energy resolution, using both the 17-inch and 20-inch PMTs, is 6.4%/ √ E(MeV). The conversion between the deposited energy and KamLAND's prompt energy scale is non-linear and particle-dependent. We use a model that includes Birk's quenching and Cherenkov-light emission with parameters constrained by the calibration data to make the conversion. The systematic uncertainties in this model, estimated at 1.8%, is the largest contribution to the uncertainty on m 2 21 . The event vertex information is used in order to limit the search for candidate ν e events to a central fiducial volume, where the signal-to-background is estimated to be highest. The initial publication [4] used 5.0 m as the radius defining the spherical fiducial volume in the KamLAND detector, this was later expanded to 5.5 m [12]. Radioactive backgrounds near the surface of the balloon can cause accidental backgrounds (see Section 4). As the understanding of the backgrounds on the balloon grew, it became possible to model them and increase the fiducial-volume-radius to 6.0 m [6] through the use of a likelihood discriminator to suppress these accidental backgrounds.
The KamLAND detector was modified in September 2011 to accommodate the KamLAND-Zen neutrinoless double beta-decay experiment [13]. The initial phase of KamLAND-Zen used about 300 kg of 136 Xe loaded into 13 tons of liquid scintillator, all contained in a 3-m-diameter balloon at the center of the detector. The KamLAND and KamLAND-Zen phases continue to coexist.

Reactor signal
To calculate the expected ν e -signal from nuclear reactors, the collaboration uses detailed reactor operation records, which are provided by a consortium of Japanese electric power companies. These include the thermal power variation as well as refueling and fuel rearrangement data from all Japanese commercial reactors. The absolute thermal power, used to normalize the fission rates, is measured to within 2% for each reactor [14]. The data points are typically provided weekly, or more often, with a period of 1 h or even 10 min when the operating parameters vary more quickly. This information, combined with publicly available world reactor data, is used to calculate the instantaneous fission rates using a reactor model. Only four fission isotopes contribute significantly to the ν e spectrum. The ratios of the fission yields averaged over the entire livetime period up to the latest data-release in 2013, are (0.567 : 0.078 : 0.298 : 0.057) for ( 235 U : 238 U : 239 Pu : 241 Pu). Although their contribution is small, long-lived, out-of-equilibrium fission products 90 Sr, 106 Ru and 144 Ce are also included in the calculations. The emitted ν e energy spectrum is calculated using ν e spectra from [15,16]. Neutrino oscillation effects distort the ν e spectrum as the ν e 's travel from the reactors to KamLAND. Observation of this effect is therefore direct evidence for neutrino oscillation. The time evolution of the expected and observed detection rates at KamLAND is shown in Fig. 3.
When the neutrino fluxes were highest, roughly 95% of the ν e flux at KamLAND came from Japanese power reactors, ∼3.5% came from Korean reactors and about 1% came from reactors around the world. The total ν e flux and these ratios changed dramatically following the Fukushima nuclear accident in March 2011. All Japanese nuclear reactors were shutdown by September 2013 due to a review of nuclear safety. The absence of a ν e -signal from Japanese reactors at KamLAND lasted until August 2015, when one of the reactors was put back into operation.

Backgrounds
The delayed coincidence event pair technique to identify the ν e -candidates through the inverse β-decay reaction, described in Section 2, strongly suppresses backgrounds from radioactivity. Nevertheless, a number of backgrounds are important in the analysis of KamLAND data.
The rate of accidental coincidences increases in the outer region of the fiducial volume. This background can be accurately estimated through the pairing of random single events. Below 2.6 MeV prompt energy, the reactor-ν e background is expected to be dominated by geologically produced antineutrinos or geo-ν e . These are antineutrinos from the decay chains of 238 U and 232 Th in the Earth. While they are a background to KamLAND's neutrino oscillation measurements, they are also an interesting signal in their own right, providing a glimpse into the Earth's interior [17,18]. The geo-ν e background can be avoided by requiring a 2.6 MeV E p -threshold for the neutrino oscillation studies.
One unexpected background was the discovery of a correlated background due to 13 C(α, n) 16 O reactions from α-decay of 210 Po, a daughter of 222 Rn introduced into the LS during construction. This was the main background until May 2007 (Period 1 in Fig. 3), when the collaboration embarked on a liquid scintillator purification campaign. The purification campaign reduced the 13 C(α, n) 16 O decays by a factor of ∼20, effectively removing the background in subsequent years.
Above 2.6 MeV, neutrons, atmospheric neutrinos and long-lived delayed-neutron β-emitters are sources of correlated backgrounds. Roughly 3000 neutrons per kton-day are produced through spallation processes, but these are eliminated by a 2 msec full-volume veto after a passing muon. The remaining fast neutrons come from muons missed by the OD or interacting in the rock just outside of it, but these are also suppressed by several layers of absorbers. The surviving neutrons can scatter and capture in the LS, mimicking the ν e signal. We also expect backgrounds from atmospheric neutrinos, but their number is relatively small. Finally, the cosmogenically produced delayed-neutron β-emitters 8 He (T 1/2 = 119 msec) and 9 Li (T 1/2 = 178 msec) also contribute to the background. They are predominately produced in so-called "showering muons", muons that deposit a large amount of energy in the liquid scintillator. We suppress them by requiring a 2-sec veto of the entire volume after a showering muon or a 2-sec veto of a 3-m-radius volume around a muon track. See Ref. [9] for a detailed discussion of the cosmogenically produced backgrounds in KamLAND.

Results
The first KamLAND results were released in December 2002 [4], shortly after the first SNO measurement of solar neutrino flavor transformation [19]. The initial KamLAND results showed evidence for reactor antineutrino disappearance. Assuming CPT invariance, this result eliminated all but the LMA-MSW oscillation solution as the explanation of the solar neutrino flavor transformation. In the subsequent decade, KamLAND was able to report on more and more precise neutrino oscillation parameters in the solar sector.

Neutrino oscillation results
Details of the ν e -candidate selection cuts can be found elsewhere [4][5][6][7][8]. The most recent data release of 2013 identified 2611 candidate ν e 's, with an expected background (excluding geo-ν e ) of 364.1 ± 30.5 events. Fig. 4 shows the prompt energy ν e -candidate spectra separately for the three periods when the KamLAND detector was in distinct running conditions. As discussed in Section 4, Period 1 was dominated by the significant background from 13 C(α, n) 16 O, which was substantially reduced during a purification campaign starting in 2007. Period 3 starts after the inner-balloon for the KamLAND-Zen [13] experiment was installed in September 2011. This period coincides with the low reactor neutrino flux following the Fukushima nuclear accident in March 2011.
The energies of reactor antineutrinos and the average baseline of ∼180 km allowed KamLAND to analyze the first years of data in a two-neutrino framework (i.e., assuming θ 13 = 0). By the time of the data-release in 2010, the data-set was sufficiently large to extend this to a three-neutrino analysis with Earth-matter effects. This in turned allowed not only the measurement of m 2 21 and θ 12 , but also the possibility to constrain θ 13 . Fig. 5 shows the evolution of the allowed solar neutrino oscillation parameter regions, from 2002 up until the latest KamLAND data-release in 2013. The first data in 2002 [4] allowed, under the assumption of CPT invariance, to restrict the solar neutrino oscillation parameter space to m 2 21 > ∼10 −5 eV 2 . However, several regions of m 2 21 were still allowed at 95% C.L. (blue shaded regions in Fig. 5). The 2004 data-release [5] reduced the allowed parameter space to three distinct m 2 21 parameter regions at 95% C.L. By 2008 the shape-distortion effects in the reactor spectrum allowed to shrink m 2 21 to one parameter region. Table 1 lists the 2013 KamLAND neutrino oscillation parameter results under various combinations of experimental data. m 2 21 is now one of the most precisely determined neutrino oscillation parameters. The allowed region contours in the panels in Fig. 5 also show the complementarity between the KamLAND results and the solar results: the solar results allow a precision measurement of θ 12 , while KamLAND provides a measurement of m 2 21 . Finally, Fig. 6 provides an illustration of the oscillatory nature of the signal measured by KamLAND. The data points in Fig. 6 are the ratio of the observed reactor ν e spectrum to that expected in the case of no-oscillation shown as a function of L 0 /E ν e , where L 0 is the flux- Fig. 4. Prompt energy spectrum of ν e -candidate events for each data taking period (see Fig. 3), the inset shows the prompt spectrum with a finer binning for low-energy events. KamLAND suffered from a large radioactive background in the first period of data taking. This was significantly reduced after a purification campaign (Period 2). Period 3 is after the installation of an inner-balloon for the KamLAND-Zen experiment in September 2011. It coincides with a low reactor neutrino flux period following the Fukushima reactor accident. Figure adapted from [8]. Table 1 Summary of the fit values for m 2 21 , tan 2 θ 12 and sin 2 θ 13 from three-flavor neutrino oscillation analyses with various combinations of experimental data. These results come from the latest KamLAND data-release [8]  term in the ν e survival probability expression. The shape is somewhat distorted due to multiple reactor baselines and the fact that ν e 's are emitted in a spectrum of energies.

Other results
While the primary focus of the KamLAND experiment has been the search for, and precision measurement of, neutrino oscillation effects, the experiment has also provided a number of other important measurements. The KamLAND Collaboration performed the first experimental study Fig. 6. Illustration of the neutrino oscillation effect. The ratio of the observed ν e spectrum to the expectation for nooscillation as a function of L 0 /E ν e is shown for the KamLAND data. L 0 = 180 km is the effective flux-weighted average reactor baseline. The histogram and curve show the expectation accounting for the distances to the individual reactors and time-dependent ν e flux variations and includes the 3-ν best-fit oscillation parameters listed on the last line of Table 1. of geo-neutrinos [17], significantly improving the results later [18,8]. The collaboration studied astrophysical sources of neutrinos such as solar-7 Be [20] and 8 B [21], and extraterrestrial antineutrino sources [12,22]. The experiment has also been used to set limits on the invisible decay of neutrons [23] and proton decay [24].

Conclusions
The KamLAND experiment has been operational since the beginning of 2002. The experiment has monitored the ν e flux from more than 50 Japanese nuclear reactors over more than a decade. The KamLAND results have allowed to establish the LMA-MSW neutrino oscillation mechanism as the solution to the solar neutrino flavor transformation. The large collection of reactor ν e events coming from an average baseline of 180 km enable a precise determination of the m 2 21 neutrino oscillation parameter. Although the KamLAND detector has been modified to study neutrinoless double beta decay in 136 Xe in September 2011, the experiment also continues to be used to monitor reactor antineutrinos and other sources of (anti-)neutrinos.