Reactor Neutrinos

Abstract

We review the status and the results of reactor neutrino experiments. Short-baseline experiments have provided the measurement of the reactor neutrino spectrum, and their interest has been recently revived by the discovery of the reactor antineutrino anomaly, a discrepancy between the reactor neutrino flux state of the art prediction and the measurements at baselines shorter than one kilometer. Middle and long-baseline oscillation experiments at Daya Bay, Double Chooz, and RENO provided very recently the most precise determination of the neutrino mixing angle 𝜃₁₃. This paper provides an overview of the upcoming experiments and of the projects under development, including the determination of the neutrino mass hierarchy and the possible use of neutrinos for society, for nonproliferation of nuclear materials, and geophysics.

1. Introduction: 80 Years of Reactor Neutrino Physics

Invented by Pauli [1] in 1930, named by Amaldi in 1934, and later modeled in the Fermi theory of beta decay [2]. The weakly coupling neutrino was first searched for by Reines and Cowan. Starting at the Hanford nuclear reactor (Washington), they later moved to the new Savannah River Plant (South Carolina) to perform their definitive and ground-breaking experimental detection. This breakthrough had two important consequences: resolving and clarifying the unsatisfactory situation of a fundamental particle needed for the consistency of theory, but first thought to be unobservable, and demonstrating the possibility of using neutrinos as a sensitive probe of particle physics. Indeed, several years after the completion of the pioneering, Reines and Cowan's work neutrinos were beginning to be used regularly to investigate the weak interactions, the structure of nucleons, and the properties of their constituent quarks.

In the first crude experiment of 1953 [3], Reines and Cowan's goal was to demonstrate unambiguously a reaction caused in a target by a neutrino produced elsewhere. The experiment pioneered the delayed coincidence technique to search for the reaction: 𝜈_𝑒+𝑝→𝑒⁺+𝑛, where an electron antineutrino from the Hanford nuclear reactor interacted with a free proton in a large tank filled with cadmium-loaded liquid scintillator. The positron and the resultant annihilation gamma rays are detected as a prompt signal, while the neutron is thermalized in the liquid scintillator and subsequently captured by the cadmium. The excited nucleus then emits gamma radiation which is detected as the delayed signal. The first result, at two standard deviations, was followed in 1956 and 1958 by more precise experiments [4–6], where the significance improved to over four standard deviations. In addition to the detection, the reaction cross-section was measured to be 11±2.6×10⁻⁴⁴ cm² [6]. Nowadays, reactor neutrinos like Daya Bay, KamLAND, or Double Chooz are still detected through similar experimental methods.

2. Nuclear Reactors and Neutrinos

Nuclear reactors are very intense sources of neutrinos that have been used all along the neutrino’s history, from its discovery up to the most recent oscillation studies. With an average energy of about 200 MeV released per fission and 6 neutrinos produced along the 𝛽-decay chains of the fission products, one expects about 2×10²⁰ 𝜈/𝑠 emitted in a 4𝜋 solid angle from a 1 GW reactor (thermal power). Since unstable fission products are neutron-rich nuclei, all 𝛽 decays are of 𝛽⁻ type, and the neutrino flux is actually pure electronic antineutrinos (𝜈_𝑒).

The neutrino oscillation search at a reactor is always based on a disappearance measurement, using the powerful inverse beta decay (IBD) detection process to discriminate the neutrino signal from backgrounds. The observed neutrino spectrum at a distance 𝐿 from a reactor is compared to the expected spectrum. If a deficit is measured, it can be interpreted in terms of the disappearance probability which, in the two neutrino mixing approximation, reduces to 𝑃_𝑒𝑒=1−sin²2𝜃sin²Δ𝑚²𝐿,4𝐸 (1) where Δ𝑚² is the difference between the squared masses of the two neutrino states and 𝜃 is the mixing angle fixing the amplitude of the oscillation.

Here, we will especially consider reactor antineutrino detector at short distances below 100 m from the reactor core, in particular ILL-Grenoble, Goesgen, Rovno, Krasnoyarsk, Savannah River, and Bugey [7–15]. These experiments have played an important role in the establishment of neutrino physics, and especially neutrino oscillations, over the last fifty years. Unlike modern long-baseline reactor experiments motivated by the measurement of the last unknown mixing angle 𝜃₁₃ [16–18], which measure 𝑃_𝑒𝑒 by comparing the event rate and spectrum in two detectors at different distances, the aforementioned short baseline experiments can only employ one detector and therefore depend on an accurate theoretical prediction for the emitted 𝜈_𝑒 flux and spectrum to measure 𝑃_𝑒𝑒.

Until late 2010, all data from reactor neutrino experiments appeared to be fully consistent with the mixing of 𝜈_𝑒, 𝜈_𝜇, and 𝜈_𝜏 with three mass eigenstates, 𝜈₁, 𝜈₂, and 𝜈₃, with the squared mass differences |Δ𝑚²₃₁|≃2.410⁻³eV² and Δ𝑚²₂₁/|Δ𝑚²₃₁|≃0.032. The measured rate of 𝜈_𝑒 was found to be in reasonable agreement with that predicted from the “old” reactor antineutrino spectra [19–21], though slightly lower than expected, with the measured/expected ratio at 0.980±0.024, including recent revisions of the neutron mean lifetime, 𝜏_𝑛=881.5s, in 2011 (PDG).

In preparation for the Double Chooz reactor experiment [16], the Saclay reactor neutrino group reevaluated the specific reactor antineutrino flux for 235U, 239Pu, 241Pu, and 238U. In 2011, they reported their results [22], which correspond to a flux that is a few percent higher than the previous prediction. This also necessitates a reanalysis of the ratio of the observed event rate to the predicted rate for 19 published experiments at reactor-detector distances below 100 m.

2.1. Reference Antineutrino Spectra

Fission reactors release about 10²⁰𝜈_𝑒GW⁻¹s⁻¹, which mainly come from the beta decays of the fission products of 235U, 238U, 239Pu, and 241Pu. The emitted antineutrino spectrum is then given by: 𝑆_tot𝐸_𝜈=_𝑘𝑓_𝑘𝑆_𝑘𝐸_𝜈, (2) where 𝑓_𝑘 refers to the contribution of the main fissile nuclei to the total number of fissions of the kth branch and 𝑆_𝑘 to their corresponding neutrino spectrum per fission.

The distribution of the fission products of uranium or plutonium isotopes covers hundreds of nuclei, each of them contributing to 𝑆_𝑘(𝐸) through various 𝛽 decay chains. At the end the total antineutrino spectrum is a sum of thousands of 𝛽-branches weighted by the branching ratio of each transition and the fission yield of the parent nucleus. Despite the impressive amount of data available in nuclear databases, the ab initio calculation of the emitted antineutrino spectrum is difficult. Moreover, when looking at the detected spectrum through the IBD process, the 1.806 MeV threshold and the quadratic energy dependence of the cross-section enhance the contribution of transitions with large endpoints (𝐸₀>4 MeV). Systematic errors of the nuclear data and the contribution of poorly known nuclei become a real limitation for the high energy part of the antineutrino spectrum. Uncertainties below the 10% level seem to be out of reach with the ab initio approach, preventing any accurate oscillation analysis.

In order to circumvent this issue, measurements of total 𝛽 spectra of fissile isotopes were performed in the 1980s at ILL [19–21], a high flux research reactor in Grenoble, France. Thin target foils of fissile isotopes 235U, 239Pu and 241Pu, were exposed to the intense thermal neutron flux of the reactor. A tiny part of the emitted electrons could exit the core through a straight vacuum pipe to be detected by the high resolution magnetic spectrometer BILL [23]. The electron rates were recorded by a pointwise measurement of the spectrum in magnetic field steps of 50 keV, providing an excellent determination of the shape of the electron spectrum with subpercent statistical error. The published data were smoothed over 250 keV. Except for the highest energy bins with poor statistics, the dominant error was the absolute normalization, quoted around 3% (90% CL), with weak energy dependence.

In principle, the conversion of a 𝛽-spectrum into an antineutrino spectrum can be done using the energy conservation between the two leptons 𝐸_𝑒+𝐸_𝜈=𝐸_0, (3) with 𝐸₀, the endpoint of the 𝛽 transition. However this approach requires to know the contribution of all single branches in the ILL sectra and this information is not accessible from the integral measurement. Therefore a specific conversion procedure was developped using a set of 30 “virtual” 𝛽-branches, fitted on the data. The theoretical expression for the electron spectrum of a virtual branch was of the form 𝑆_virtual𝑍,𝐴,𝐸_𝑒=𝐾_Norm.×ℱ(𝑍,𝐴,𝐸_𝑒)_{Fermifunction}×𝑝_𝑒𝐸_𝑒(𝐸_𝑒−𝐸₀)²_Phasespace×1+𝛿𝑍,𝐴,𝐸_{𝑒Correction}, (4) where 𝑍 and 𝐴 are the charge and atomic number of the parent nucleus and 𝐸₀ is the endpoint of the transition. The origin of each term is described by the underbraces. The 𝛿 term contains the corrections to the Fermi theory. In the ILL papers, it included the QED radiative corrections as calculated in [24]. The 𝑍 dependence comes from the Coulomb corrections. Since a virtual branch is not connected to any real nucleus, the choice of the nuclear charge was described by the observed mean dependence of 𝑍 on 𝐸₀ in the nuclear databases 𝑍𝐸₀=49.5−0.7𝐸₀−0.09𝐸²₀,𝑍≤34. (5)

The 𝐴 dependence is weaker and linked to the determination of 𝑍 through global nuclear fits.

Once the sum of the 30 virtual branches is fitted to the electron data, each of them is converted to an antineutrino branch by substituting 𝐸_𝑒 by 𝐸₀−𝐸_𝜈 in (4) and applying the correct radiative corrections. The predicted antineutrino spectrum is the sum of all converted branches. At the end of this procedure, an extra correction term is implemented in an effective way as Δ𝑆_branch𝐸_𝜈≃0.65𝐸_𝜈−4.00%. (6) This term is an approximation of the global effect of weak magnetism correction and finite size Coulomb correction [25].

The final error of the conversion procedure was estimated to be 3-4% (90% CL), to be added in quadrature with the electron calibration error which directly propagates to the antineutrino prediction. From these reference spectra, the expected antineutrino spectrum detected at a reactor can be computed. All experiments performed at reactors since then relied on these reference spectra to compute their predicted antineutrino spectrum.

2.2. New Reference Antineutrino Spectra

Triggered by the need for an accurate prediction of the reactor antineutrino flux for the first phase of the Double Chooz experiment, with a far detector only, the determination of antineutrino reference spectra has been revisited lately [22]. In a first attempt, a compilation of the most recent nuclear data was performed for an up-to-date ab initio calculation of the antineutrino fission spectra. The asset of this approach is the knowledge of each individual 𝛽 branch, providing a perfect control of the conversion between electron and antineutrino spectra. As a powerful cross-check, the sum of all the branches must match the very accurate electron spectra measured at ILL. Despite the tremendous amount of nuclear data available, this approach failed to meet the required accuracy of few % for two main reasons as follows.(i)The majority of the 𝛽 decays are measured using 𝛽-𝛾 coincidences, which are sensitive to the so-called pandemonium effect [26]. The net result is an experimental bias of the shape of the energy spectra, with the high energy part being overestimated relative to the low energy part. New measurements are ongoing with dedicated experimental setups to correct for the pandemonium effect, but in the case of the reference spectra many unstable nuclei have to be studied. (ii)As mentioned above, an important fraction of the detected neutrinos has a large energy (>4 MeV). The associated 𝛽 transitions mostly come from very unstable nuclei with a large energy gap between the parent ground state and the nuclear levels of the daughter nucleus. Their decay scheme is often poorly known or even not measured at all.

A reference data set was constituted based on all fission products indexed in the ENSDF database [27]. All nuclei measured separtely to correct for the pandemonium effect were substituted when not in agreement with the ENSDF data (67 nuclei from [28] and 29 nuclei from [29]). A dedicated interface, BESTIOLE, reads the relevant information of this set of almost 10000 𝛽-branches and computes their energy spectrum based on (4). Then, the total beta spectrum of one fissioning isotope is built as the sum of all fission fragment spectra is weighted by their activity. These activities are determined using a simulation package called MCNP Utility for Reactor Evolution (MURE [30]). Following this procedure, the predicted fission spectrum is about 90% of the reference ILL 𝛽 spectra, as illustrated in Figure 2 for the ²³⁵U isotope. The missing contribution is the image of all unmeasured decays as well as the remaining experimental biases of the measurements. To fill the gap one can invoke models of the decay scheme of missing fission products. Reaching a good agreement with the ILL electron data remains difficult with this approach.

Another way to fill the gap is to fit the missing contribution in the electron spectrum with few virtual branches. The same ILL procedure can be used except that the virtual branches now rest on the base of physical transitions. This mixed approach combines the assets of ab initio and virtual branches methods as follows.(i)The prediction still matches accurately the reference electron data from the ILL measurements. (ii)90% of the spectrum is built with measured 𝛽 transitions with “true” distributions of endpoint, branching ratios, nuclear charges, and so forth. This suppresses the impact of the approximations associated with the use of virtual beta branches. (iii)All corrections to the Fermi theory are applied at the branch level, preserving the correspondence between the reference electron data and the predicted antineutrino spectrum.

The new predicted antineutrino spectra are found about 3% above the ILL spectra. This effect is comparable for the 3 isotopes (²³⁵U, ²³⁹Pu, and ²⁴¹Pu) with little energy dependence. The origin and the amplitude of this bias could be numerically studied in detail following a method initially developped in [31]. A “true” electron spectrum is defined as the sum of all measured branches. Since all the branches are known, the “true” antineutrino spectrum is perfectly defined as well, with no uncertainty from the conversion. Applying the exact same conversion procedure than in the eighties on this new electron reference confirms the 3% shift between the converted antineutrino spectrum and the “true” spectrum.

Further tests have shown that this global 3% shift is actually a combination of two effects. At high energy (𝐸>4 MeV), the proper distribution of nuclear charges, provided by the dominant contribution of the physical 𝛽-branches, induces a 3% increase of the predicted antineutrino spectrum. On the low energy side, it was shown that the effective linear correction of (6) was not accounting for the cancellations operating between the numerous physical branches when the correction is applied at the branch level (see Figure 1).

(a)

(b)

Figure 1 

Numerical tests of the conversion-induced deviations from a “true” spectrum built from a set of known branches (see text for details). (a) Effect of various 𝑍(𝐸) polynomials used in the formula of the virtual branches. (b) Deviation of converted spectra with the effective correction of (6) (solid line) or with the correction applied at the branch level.

Figure 2 

The effective nuclear charge 𝑍 of the fission fragments of 235U as a function of 𝐸0. The area of the each box is proportional to the contribution of that particular 𝑍 to the fission yield in that energy bin. The lines are fits of quadratic polynomials. Black color-ENSDF database; other colors illustrate the small sensitivity to different treatment of the missing isotopes.

Beyond the correction of these above biases, the uncertainty of the new fission antineutrino spectra couldn't be reduced with respect to the initial predictions. The normalisation of the ILL electron data, a dominant source of error, is inherent to any conversion procedure using the electron reference. Then, a drawback of the extensive use of measured 𝛽-branches in the mixed approach is that it brings important constraints on the missing contribution to reach the electron data. In particular, the induced missing shape can be difficult to fit with virtual branches, preventing a perfect match with the electron reference. These electron residuals are unfortunately amplified as spurious oscillations in the predicted antineutrino spectrum leading to comparable conversion uncertainties (see red curve in Figure 3). Finally, the correction of the weak magnetism effect is calculated in a quite crude way, and the same approximations are used since the eighties.

Figure 3 

Comparison of different conversions of the ILL electron data for 235U. Black curve: cross-check of results from [19] following the same procedure. Red curve: results from [22]. Green curve: results from [32] using the same description of 𝛽 decay as in [22]. Blue curve: update of the results from [22], including corrections to the Fermi theory as explained in the text. The thin error bars show the theory errors from the effective nuclear charge 𝑍 and weak magnetism. The thick error bars are the statistical errors.

In the light of the above results, the initial conversion procedure of the ILL data was revisited [32]. It was shown that a fit using only virtual branches with a judicious choice of the effective nuclear charge could provide results with minimum bias. A mean fit similar to (5) is still used, but the nuclear charge of all known branches is now weighted by its contribution in the total spectrum, that is, the associated fission yield. As shown in Figure 2, the result is quite stable under various assumptions for the weighting of poorly known nuclei. The bias illustrated in the left plot of Figure 1 is corrected.

The second bias (Figure 1(b)) is again corrected by implementing the corrections to the Fermi theory at the branch level rather than using effective corrections as in (6). Using the same expression of these corrections than in [22], the two independent new predictions are in very good agreement (Figure 3), confirming the 3% global shift. Note that the spurious oscillations of the Mueller et al. spectra are flattened out by this new conversion because of the better zeroing of electron residuals.

A detailed review of all corrections to the Fermi theory is provided in [32] including finite size corrections, screening correction, radiative corrections, and weak magnetism. To a good approximation, they all appear as linear correction terms as illustrated in Figure 4 in the case of a 10 MeV endpoint energy. This refined study of all corrections leads to an extra increase of the predicted antineutrino spectra at high energy as illustrated by the blue curve in Figure 3. The net effect is between 1.0% and 1.4% more detected antineutrinos depending on the isotope (see Table 1).

Table 1 

Relative change of the new predicted events rates with respect to the ILL reference (in %). The relative change of the emitted flux is always close to 3%, dominated by the few first bins because the energy spectra are dropping fast.

Figure 4 

Shown is the relative size of the various corrections to the Fermi theory for a hypothetical 𝛽 decay with 𝑍=46, 𝐴=117, and 𝐸0=10 MeV. The upper panel shows the effect on the antineutrino spectrum, whereas the lower panel shows the effect on the 𝛽 spectrum. 𝛿WM: weak magnetism correction; 𝐿0, C: Coulomb and weak interaction finite size corrections: S screening correction; 𝐺𝜈,𝛽: radiative corrections.

The corrections of Figure 4 are known with a good relative accuracy except for the weak magnetism term. At the present time, a universal slope factor of about 0.5% per MeV is assumed, neglecting any dependence on nuclear structure [25]. Accurate calculation for every fission product is out of reach. Using the conserved vector current hypothesis, it is possible to infer the weak magnetism correction from the electromagnetic decay of isobaric analog states. Examples of the slope factors computed from the available data are shown in Table I of [32]. While most examples are in reasonable agreement with the above universal slope, some nuclei with large value of log𝑓𝑡 have a very large slope factor. Moreover, a review of the nuclear databases [33] shows that 𝛽 transitions with log𝑓𝑡>7 contribute between 15 and 30% to the total spectrum. Still the data on the weak magnetism slopes are scarce, and none of them corresponds to fission products. At this stage, it is difficult to conclude if the uncertainty of the weak magnetism correction should be inflated or not. The prescription of the ILL analysis, 100%, corresponds to about 1% of the detected neutrino rate. The best constraints could actually come from shape analysis of the reactor neutrino data themselves. The Bugey and Rovno data are accurate altough detailed information on the detector response might be missing for such a detailed shape analysis. The combination of the upcoming Daya Bay, Double Chooz, and RENO data should soon set stringent limits on the global slope factor.

The error budget of the predicted spectra remains again comparable to the first ILL analysis. The normalization error of the electron data is a common contribution. The uncertainties of the conversion by virtual branches have been extensively studied and quantified based on the numerical approach. The uncertainty induced by the weak magnetism corrections is, faute de mieux, evaluated with the same 100% relative error. The final central values and errors are summarized in table [22].

2.3. Off-Equilibrium Effects

For an accurate analysis of reactor antineutrino data, an extra correction to the reference fission spectra has to be applied. It is often of the order of the percent. It comes from the fact that the ILL spectra were acquired after a relatively short irradiation time, between 12 hours and 1.8 days depending on the isotopes, whereas in a reactor experiment the typical time scale is several months. A nonnegligible fraction of the fission products have a lifetime of several days. Therefore, the antineutrinos associated with their 𝛽 decay keep accumulating well after the “photograph at 1 day” of the spectra taken at ILL. Very long-lived isotopes correspond to nuclei close to the bottom of the nuclear valley of stability. Hence, one naively expects these 𝛽 transitions to contribute at low energy. For a quantitative estimate of this effect, the same simulations developed in [22] for the ab initio calculation of antineutrino spectra were used. The sensitivity to the nuclear ingredients is suppressed because only the relative changes between the ILL spectra and spectra of longer irradiations at commercial reactors were computed. The corrections to be applied are summarized in [22]. As expected, they concern the low energy part of the detected spectrum and vanish beyond 3.5 MeV. The corrections are larger for the ²³⁵U spectrum because its irradiation time, 12 h, is shorter than the others. The uncertainty was estimated from the comparison between the results of MURE and FISPAC codes as well as from the sensitivity to the simulated core geometry. A safe 30% relative error is recommended.

2.4. ²³⁸U Reference Spectrum

The ²³⁸U isotope is contributing to about 8% of the total number of fissions in a standard commercial reactor. These fissions are induced by fast neutrons therefore, their associated 𝛽-spectrum could not be measured in the purely thermal flux of ILL. A dedicated measurement in the fast neutron flux of the FRMII reactor in Munich has been completed and should be published in the coming months [34].

Meanwhile the ab initio calculation developed in [22] provides a useful prediction since the relatively small contribution of ²³⁸U can accommodate larger uncertainties in the predicted antineutrino spectrum. An optimal set of 𝛽-branches was tuned to match the ILL spectra of fissile isotopes as well as possible. The base of this data set consists of the ENSDF branches corrected for the pandemonium effect as described in Section 2.2. Missing 𝛽 emitters are taken from the JENDL nuclear database [35], where they are calculated using the gross-theory [36]. Finally, the few remaining nuclei were described using a model based on fits of the distributions of the endpoints and branching ratios in the ENSDF database, then extrapolated to the exotic nuclei.

The comparison with the reference ²³⁵U ILL data showa that the predicted spectrum agrees with the reference at the ±10% level.

Then, this optimal data set is used to predict a ²³⁸U spectrum. Again the activity of each fission product is calculated with the evolution code MURE. The case of an N4 commercial reactor operating for one year was simulated. After such a long irradiation time, the antineutrino spectrum has reached the equilibrium. The results are summarized in [22]. The central values are about 10% higher than the previous prediction proposed in [37]. This discrepancy might be due to the larger amount of nuclei taken into account in the most recent work. Nevertheless, both results are comparable within the uncertainty of the prediction, roughly estimated from the deviation with respect to the ILL data and the sensitivity to the chosen data set.

2.5. Summary of the New Reactor Antineutrino Flux Prediction

In summary, a reevaluation of the reference antineutrino spectra associated to the fission of ²³⁵U, ²³⁹Pu, and ²⁴¹Pu isotopes [22] has revealed some systematic biases in the previously published conversion of the ILL electron data [19–21]. The net result is a ≃+3% shift in the predicted emitted spectra. The origin of these biases was not in the principle of the conversion method but in the approximate treatment of nuclear data and corrections to the Fermi theory. A complementary work [32] confirmed the origin of the biases and showed that an extra correction term should be added increasing further the predicted antineutrino spectra at high energy. These most recent spectra are the new reference used for the analysis of the reactor anomaly in the next section. The prediction of the last isotope contributing to the neutrino flux of reactors, ²³⁸U, is also updated by ab initio calculations.

The new predicted spectra and their errors are presented in [22]. The deviations with respect to the old reference spectra are given in Table 1.

3. Investigating Neutrino Oscillations

3.1. Exploring the Solar Oscillation

The sun is a well-defined neutrino source to provide important opportunities of investigating nontrivial neutrino properties because of the wide range of matter density and the great distance from the sun to the earth. Precise measurement of solar neutrinos is a direct test of the standard solar model (SSM) that is developed from the stellar structure and evolution.

Solar neutrinos have been observed by several experiments: Homestake with a chlorine detector, SAGE, GALLEX and GNO with gallium detectors, Kamiokande and Super-Kamiokande with water Cherenkov detectors, and SNO with a heavy water detector. Most recently, Borexino has successfully observed low energy solar neutrinos with their energy spectrum using a liquid scintillator detector of ultra low radioactivity.

The first observation of solar neutrinos by the Homestake experiment demonstrated the significantly smaller measured flux than the SSM prediction, known as “the solar neutrino puzzle” at that time. SAGE, GALLEX, and GNO are sensitive to the most abundant 𝑝𝑝 solar neutrinos, and also observed the deficit. Kamiokande-II and Super-Kamiokande succeeded in real-time and directional measurement of solar neutrinos in a water Cherenkov detector. The solar neutrino problem was solved by SNO through the flavor-dependent measurement using heavy water. In 2001, the initial SNO charged current result combined with the Super-Kamiokande's high-statistics 𝜈𝑒 elastic scattering result provided direct evidence for flavor conversion of solar neutrinos. The later SNO neutral current measurements further strengthened the conclusion. These results are consistent with those expected from the large mixing angle (LMA) solution of solar neutrino oscillation in matter with Δ𝑚²_sol∼5×10⁻⁵ eV² and tan²𝜃_sol∼0.45.

The KamLAND reactor neutrino experiment at a flux-weighted average distance of ∼180 km obtained a result of reactor antineutrino disappearance consistent with the LMA solar neutrino solution. The current solar neutrino and KamLAND data suggest that Δ𝑚²₂₁=(7.50±0.20)×10⁻⁵eV² with a fractional error of 2.7% and sin²2𝜃₁₂=0.857±0.024 with a fractional error of 2.8%.

3.2. Exploring the Atmospheric Oscillation

The Super-Kamiokande obtained the first convincing evidence for the neutrino oscillation in the observation of the atmospheric neutrinos, in 1998. A clear deficit of atmospheric muon neutrino candidate events was observed in the zenith-angle distribution compared to the no-oscillation expectation. The distance-to-energy 𝐿/𝐸 distribution of the Super-Kamiokande data demonstrated 𝜈_𝜇↔𝜈_𝜏 oscillations and completely ruled out some of exotic explanations of the atmospheric neutrino disappearance such as neutrino decay and quantum decoherence.

Accelerator experiments can better measure the value of |Δ𝑚²_atm| than the atmospheric neutrino observation due to a fixed baseline distance and a well-understood neutrino spectrum. K2K is the first long-baseline experiment to study 𝜈_𝜇 oscillations in the atmospheric Δ𝑚² region with a neutrino path length exceeding hundreds of kilometers. MINOS is the second long-baseline experiment for the atmospheric neutrino oscillation using a 𝜈_𝜇 beam. The MINOS finds the atmospheric oscillation parameters as |Δ𝑚²_atm|=(2.32^+0.12_−0.08)×10⁻³eV² and sin²2𝜃_atm>0.90 at 90% C.L. OPERA using the CNGS 𝜈_𝜇 beam reported observation of one 𝜈_𝜏 candidate. T2K began a new long-baseline experiment in 2010, and is expected to measure |Δ𝑚²_atm| and sin²𝜃_atm even more pricisely. No𝜈a is expected to be in operation soon for the accurate measurement of atmospheric neutrino oscillation parameters.

The current atmospheric neutrino and accelerator data suggest that Δ𝑚²₃₂₍₃₁₎=(2.32^+0.12_−0.08)×10⁻³ eV² with a fractional error of 4.3% and sin²2𝜃₂₃=0.97±0.03 with a fractional error of 3.1%.

3.3. Measuring the Last and Smallest Neutrino Mixing Angle 𝜃₁₃

In the presently accepted paradigm to describe the neutrino oscillations, there are three mixing angles (𝜃₁₂, 𝜃_23, and 𝜃₁₃) and one phase angle (𝛿) in the Pontecorvo-Maki-Nakagawa-Sakata matrix [38–40]. It was until 2012 that 𝜃₁₃ is the most poorly known and smallest mixing angle.

Measurements of 𝜃₁₃ are possible using reactor neutrinos and accelerator neutrino beams. Reactor measurements have the property of determining 𝜃₁₃ without the ambiguities associated matter effects and CP violation. In addition, the detector for a reactor measurement is not necessarily large, and the construction of a neutrino beam is not needed. The past reactor measurement had a single detector which was placed about 1 km from the reactors. The new generation reactor experiments, Daya Bay, Double Chooz, and RENO, using two detectors of 10∼40 tons at near (300∼400 m) and far (1∼2 km) locations have significantly improved sensitivity for 𝜃₁₃ down to the sin²(2𝜃₁₃)∼0.01 level. With 𝜃₁₃ determined and measurements of 𝜈_𝜇→𝜈_𝑒 and 𝜈_𝜇→𝜈_𝑒 oscillations using accelerator neutrino beams impinging on large detectors at long baselines will improve the knowledge of 𝜃₁₃ and also allow access to matter or CP violation effects.

Previous attempts at measuring 𝜃₁₃ via neutrino oscillations have obtained only upper limits [41–43]; the CHOOZ [41, 42] and MINOS [44] experiments set the most stringent limits: sin²2𝜃₁₃<0.15 (90% C.L.). In 2011, indications of a nonzero 𝜃₁₃ value were reported by two accelerator appearance experiments, T2K [45] and MINOS [46], and by the Double Chooz reactor disappearance experiment [47, 48]. Global analyses of all available neutrino oscillation data have indicated central values of sin²2𝜃₁₃ that are between 0.05 and 0.1 (see e.g., [49, 50]). In 2012, Daya Bay and RENO reported definitive measurements of the neutrino oscillation mixing angle, 𝜃₁₃, based on the disappearance of electron antineutrinos emitted from reactors. The 𝜃₁₃ measurements by the three reactor experiments are presented in the following sections.

4. Daya Bay

The Daya Bay collaboration announced on March 8, 2012, the discovery of a nonzero value for the last unknown neutrino mixing angle 𝜃₁₃ [51], based on 55 days of data taking. It is consistent with previous and subsequent measurements [45–48, 52]. An improved analysis using 139 days of data is reported at international conferences, and a paper is now under preparation [53].

4.1. The Experiment

The Daya Bay nuclear power complex is located on the Southern coast of China, 55 km to the northeast of Hong Kong and 45 km to the East of Shenzhen. A detailed description of the Daya Bay experiment can be found in [54]. As shown in Figure 5, the nuclear complex consists of six pressurized water reactors grouped into three pairs with each pair referred to as a nuclear power plant (NPP). All six cores are functionally identical pressurized water reactors of 2.9 GW thermal power [55]. Three underground experimental halls (EHs) are connected with horizontal tunnels. Two antineutrino detectors (ADs) are located in EH1, two (only one installed at this moment) in EH2, and four (only three installed) ADs are positioned near the oscillation maximum in EH3 (the far hall). The baselines from six ADs to six cores are listed in Table 2. They are measured by several different techniques and cross-checked by independent groups, as described in [53]. The overburdens, the simulated muon rate, and average muon energy are also listed in Table 2.

Table 2 

Vertical overburden, muon rate 𝑅_𝜇, and average muon energy 𝐸_𝜇 of the three EHs and baselines from antineutrino detectors AD1-6 to reactors D1, D2, and L1-4 in meters.

Figure 5 

Layout of the Daya Bay experiment. The dots represent reactors, labeled as D1, D2, L1, L2, L3 and L4. Six ADs, AD1–AD6, are installed in three EHs.

The 𝜈_𝑒s are detected via the inverse 𝛽 decay (IBD) reaction, 𝜈_𝑒+𝑝→𝑒⁺+𝑛, in a gadolinium-doped liquid scintillator (Gd-LS) [56–58]. Each AD has three nested cylindrical volumes separated by concentric acrylic vessels as shown in Figure 6. The innermost volume holds 20 t of 0.1% by weight Gd-LS that serves as the antineutrino target. The middle volume is called the gamma catcher and is filled with 21 t of undoped liquid scintillator (LS) for detecting gamma rays that escape the target volume. The outer volume contains 37 t of mineral oil (MO) to provide optical homogeneity and to shield the inner volumes from radiation originating, for example, from the photomultiplier tubes (PMTs) or the stainless steel containment vessel (SSV). There are 192 8-inch PMTs (Hamamatsu R5912) mounted on eight ladders installed along the circumference of the SSV and within the mineral oil volume. To improve uniformity, the PMTs are recessed in a 3 mm thick black acrylic cylindrical shield located at the equator of the PMT bulb.

Figure 6 

Schematic diagram of the Daya Bay detectors.

Three automated calibration units (ACU-A, ACU-B, and ACU-C) are mounted at the top of each SSV. Each ACU is equipped with a LED, a 68Ge source, and a combined source of ²⁴¹Am-¹³C and 60Co. The Am-C source generates neutrons at a rate of 0.5 Hz. The rates of the 60Co and 68Ge sources are about 100 Hz and 15 Hz, respectively.

The muon detection system consists of a resistive plate chamber (RPC) tracker and a high-purity active water shield. The water shield consists of two optically separated regions known as the inner (IWS) and outer (OWS) water shields. Each region operates as an independent water Cherenkov detector. In addition to detecting muons that can produce spallation neutrons or other cosmogenic backgrounds in the ADs, the pool moderates neutrons and attenuates gamma rays produced in the rock or other structural materials in and around the experimental hall. At least 2.5 m of water surround the ADs in every direction. Each pool is outfitted with a light tight cover with dry nitrogen flowing underneath.

Each water pool is covered with an overlapping array of RPC modules [59] each with a size of 2m×2m. There are four layers of bare RPCs inside each module. The strips have a “zigzag” design with an effective width of 25 cm and are stacked in alternating orientations providing a spatial resolution of ∼8 cm.

Each detector unit (AD, IWS, OWS, and RPC) is read out with a separate VME crate. All PMT readout crates are physically identical, differing only in the number of instrumented readout channels. The front-end electronics board (FEE) receives raw signals from up to sixteen PMTs, sums the charge among all input channels, identifies over-threshold channels, records timing information on over-threshold channels, and measures the charge of each over-threshold pulse. The FEE in turn sends the number of channels over threshold and the integrated charge to the trigger system. When a trigger is issued, the FEE reads out the charge and timing information for each over-threshold channel, as well as the average ADC value over a 100 ns time-window immediately preceding the over-threshold condition (pre-ADC).

Triggers are primarily created internally within each PMT readout crate based on the number of over-threshold channels (Nhit) as well as the summed charge (E-Sum) from each FEE. The system is also capable of accepting external trigger requests, for example, from the calibration system.

4.2. Data, Monte Carlo Simulation, and Event Reconstruction

The data used in this analysis were collected from December 24, 2011 through May 11, 2012.

The detector halls operated independently, linked only by a common clock and GPS timing system. As such, data from each hall were recorded separately and linked offline. Simultaneous operation of all three detector halls is required to minimize systematic effects associated with potential reactor power excursions.

Triggers were formed based either on the number of PMTs with signals above a ∼0.25 photoelectron (pe) threshold (Nhit triggers) or the charge sum of the over-threshold PMTs (E-Sum trigger).

A small number of AD PMTs, called flashers, spontaneously emit light, presumably due to a discharge within the base. The visible energy of such events covers a wide range, from sub-MeV to 100 MeV. Two features were typically observed when a PMT flashed. The observed charge for a given PMT was very high with light seen by the surrounding PMTs, and PMTs on the opposite side of the AD saw light from the flasher.

To reject flasher events, a flasher identification variable (FID) was constructed. Figure 7 shows the discrimination of flasher events for the delayed signal of IBD candidates. The inefficiency for selection was estimated to be 0.02%. The uncorrelated uncertainties among ADs were estimated to be 0.01%. The contamination of the IBD selection was evaluated to be <10⁻⁴.

Figure 7 

Discrimination of flasher events and IBD-delayed signals in the neutron energy region. The delayed signals of IBDs have the same distribution for all six Ads, while the flashers are different.

The AD energy response has a time dependence, a detector spatial dependence (nonuniformity), and a particle species and energy dependence (nonlinearity). The goal of energy reconstruction was to correct these dependences in order to minimize the AD energy scale uncertainty. The LEDs were utilized for PMT gain calibration, while the energy scale was determined with a 60Co source deployed at the detector center. The sources were deployed once per week to check for and correct any time dependence.

A scan along the z-axis utilizing the 60Co source from each of the three ACUs was used to obtain nonuniformity correction functions. The nonuniformity was also studied with spallation neutrons generated by cosmic muons and alphas produced by natural radioactivity present in the liquid scintillator. The neutron energy scale was set by comparing 60Co events with neutron capture on Gd events from the Am-C source at the detector center. Additional details of energy calibration and reconstruction can be found in [54]. Asymmetries in the mean of the six ADs’ response are shown in Figure 8. Asymmetries for all types of events in all the ADs fall within a narrow band, and the uncertainty is estimated to be 0.5%, uncorrelated among ADs.

Figure 8 

Asymmetry values for all six ADs. The sources 68Ge, 60Co, and Am-C were deployed at the detector center. The alphas from polonium decay and neutron capture on gadolinium from IBD and spallation neutrons were uniformly distributed within each detector. Differences between these sources are due to spatial nonuniformity of detector response.

A Geant4 [60] based computer simulation (Monte Carlo, MC) of the detectors and readout electronics was used to study detector response and consisted of five components: kinematic generator, detector simulation, electronics simulation, trigger simulation, and readout simulation. The MC is carefully tuned, by taking measured parameters of the materials properties, to match observed detector distributions, such as PMT timing, charge response, and energy nonlinearity. An optical model is developed to take into account photon absorption and reemission processes in liquid scintillator.

4.3. Event Selection, Efficiencies, and Uncertainties

Two preselections were completed prior to IBD selection. First, flasher events were rejected. Second, triggers within a (−2𝜇s, 200 μs) window with respect to a water shield muon candidate (𝜇_WS) were rejected, where a 𝜇_WS was defined as any trigger with Nhit >12 in either the inner or outer water shield. This allowed for the removal of most of the false triggers that followed a muon, as well as triggers associated with the decay of spallation products. Events in an AD within ±2 μs of a 𝜇_WS with energy >20 MeV or >2.5 GeV were classified as AD muons (𝜇_AD) or showering muons (𝜇_sh), respectively.

Within an AD, only prompt-delayed pairs separated in time by less than 200 μs (1<𝑡_𝑑−𝑡_𝑝<200𝜇s, where 𝑡_𝑝 and 𝑡_𝑑 are time of the prompt and delayed signal, resp.,) with no intervening triggers and no 𝐸>0.7 MeV triggers within 200 𝜇s before the prompt signal or 200 𝜇s after the delayed signal were selected (referred to as the multiplicity cut). A prompt-delayed pair was vetoed if the delayed signal is in coincidence with a water shield muon (−2𝜇s<𝑡_𝑑−𝑡_𝜇W𝑆<600 μs) or an AD muon (0<𝑡_𝑑−𝑡_𝜇AD<1000𝜇s) or a showering muon (0<𝑡_𝑑−𝑡_𝜇sh<1s). The energy of the delayed candidate must be 6.0MeV<𝐸_𝑑<12.0MeV, while the energy of the prompt candidate must be 0.7MeV<𝐸_𝑝<12.0 MeV. The prompt energy, the delayed energy and the capture time distributions for data and MC are shown in Figures 9, 10, and 11, respectively.

Figure 9 

The prompt energy spectrum from AD1. IBD selection required 0.7<𝐸𝑝<12.0MeV. Accidental backgrounds were subtracted, where the spectrum of accidental background was estimated from the spectrum of all >0.7 MeV triggers.

Figure 10 

The delayed energy spectrum from AD1. IBD selection required 6.0<𝐸𝑑<12.0MeV. Accidental backgrounds were subtracted, where the spectrum of accidental background was estimated from the spectrum of single neutrons.

Figure 11 

The neutron capture time from AD1. IBD selection required 1<𝑡𝑑−𝑡𝑝<200 𝜇s. In order to compare data with MC, a cut on prompt energy (𝐸𝑝>3MeV) was applied to reject accidental backgrounds.

The data are generally in good agreement with the MC. The apparent difference between data and MC in the prompt energy spectrum is due to nonlinearity of the detector response; however, the correction to this nonlinearity was not performed in this analysis. Since all ADs had similar nonlinearity (as shown in the bottom pannel of Figure 8), and the energy selection cuts cover a larger range than the actual distribution, the discrepancies introduced negligible uncertainties to the rate analysis.

For a relative measurement, the absolute efficiencies and correlated uncertainties do not factor into the error budget. In that regard, only the uncorrelated uncertainties matter. Extracting absolute efficiencies and correlated errors were done in part to better understand our detector, and it was a natural consequence of evaluating the uncorrelated uncertainties. Efficiencies associated with the prompt energy, delayed energy, capture time, Gd capture fraction, and spill-in effects were evaluated with the Monte Carlo. Efficiencies associated with the muon veto, multiplicity cut, and livetime were evaluated using data. In general, the uncorrelated uncertainties were not dependent on the details of our computer simulation.

Table 3 is a summary of the absolute efficiencies and the systematic uncertainties. The uncertainties of the absolute efficiencies were correlated among the ADs. No relative efficiency, except 𝜖_𝜇𝜖_𝑚, was corrected. All differences between the functionally identical ADs were taken as uncorrelated uncertainties. Detailed description of the analysis can be found in [53].

Table 3 

Summary of absolute efficiencies and systematic uncertainties. For our relative measurement, only the uncorrelated uncertainties contribute to the final error in our relative measurement.

4.4. Backgrounds

Backgrounds are actually the main source of systematic uncertainties of this experiment; even though the background to signal ratio is only a few percent. Extensive studies show that cosmic-ray-induced backgrounds are the main component, while AmC neutron sources installed at the top of our neutrino detector for calibration contribute also to a significant portion. Although the random coincidence background is the largest, its uncertainty is well under control. Table 4 lists all the signal and background rates as well as their uncertainties. A detailed study can be found in [53].

Table 4 

Signal and background summary. The background and IBD rates were corrected for the 𝜖_𝜇𝜖_𝑚 efficiency.

The accidental background was defined as any pair of otherwise uncorrelated triggers that happen to satisfy the IBD selection criteria. They can be easily calculated based on textbooks, and their uncertainties are well understood. When calculating the rate of accidental backgrounds listed in Table 4, A correction is needed to account for the muon veto efficiency and the multiplicity cut efficiency. An alternate method, called the off-windows method, was developed to determine accidental backgrounds. This result was also validated by comparing the prompt-delayed distance of accidental coincidences selected by the off-windows method with IBD candidates. The relative differences between off-windows method results and theoretical calculation of 6 ADs were less than 1%.

Energetic neutrons entering an AD aped IBD by recoiling off a proton before being captured on Gd. The number of fast neutron background events in the IBD sample is estimated by extrapolating the prompt energy (𝐸_𝑝) distribution between 12 and 100 MeV down to 0.7 MeV. Two different extrapolation methods were used; one is a flat distribution, and the other one is a first-order polynomial function. The fast neutron background in the IBD sample was assigned to be equal to the mean value of the two extrapolation methods, and the systematic error was determined from the sum of their differences and the fitting uncertainties. As a check, the fast neutrons prompt energy spectrum associated with tagged muons validates our extrapolation method.

The rate of correlated background from the 𝛽-n cascade of 9Li/8He decays was evaluated from the distribution of the time since the last muon and can be described by a sum of exponential functions with different time constant [61]. To reduce the number of minimum ionizing muons in these data samples, we assumed that most of the 9Li and 8He production was accompanied with neutron generation. The muon samples with and without reduction were both prepared for 9Li and 8He background estimation. By considering binning effects and differences between results with and without muon reduction, we assigned a 50% systematical error to the final result.

The ¹³C (𝛼𝑛)16O background was determined by measuring alpha decay rates in situ and then by using MC to calculate the neutron yield. We identified four sources of alpha decays, the 238U, 232Th, ²²⁷Ac decay chains, and 210Po taking into account half lives of their decay chain products, 164.3 𝜇s, 0.3 𝜇s, and 1.781 ms, respectively. Geant4 was used to model the energy deposition process. Based on JENDL [62] (𝛼n) cross-sections, the neutron yield as a function of energy was calculated and summed. Finally, with the in-situ measured alpha decay rates and the MC determined neutron yields, the 13C(𝛼𝑛)16O rate was calculated.

During data taking, the Am-C sources sat inside the ACUs on top of each AD. Neutrons emitted from these sources would occasionally ape IBD events by scattering inelastically with nuclei in the shielding material (emitting gamma rays) before being captured on a metal nuclei, such as Fe, Cr, Mn, or Ni (releasing more gamma rays). We estimated the neutron-like events from the Am-C sources by subtracting the number of neutron-like singles in the 𝑍<0 region from the 𝑍>0 region. The Am-C correlated background rate was estimated by MC simulation normalized using the Am-C neutron-like event rate obtained from data. Even though the agreement between data and MC is excellent for Am-C neutron-like events, we assigned 100% uncertainty to the estimated background due to the Am-C sources to account for any potential uncertainty in the neutron capture cross-sections used by the simulation.

4.5. Side-By-Side Comparison in EH1

Relative uncertainties were studied with data by comparing side-by-side antineutrino detectors. A detailed comparison using three months of data from ADs in EH1 has been presented elsewhere [54]. An updated comparison of the prompt energy spectra of IBD events for the ADs in EH1 using 231 days of data (Sep. 23, 2011 to May 11, 2012) is shown in Figure 12 after correcting for efficiencies and subtracting background. A bin-by-bin ratio of the AD1 and AD2 spectra is also shown. The ratio of total IBD rates in AD1 and AD2 was measured to be 0.987±0.004(stat.)±0.003(syst.), consistent with the expected ratio of 0.982. The difference in rates was primarily due to differences in baselines of the two ADs in addition to a slight dependence on the individual reactor on/off status. It was known that AD2 has a 0.3% lower energy response than AD1 for uniformly distributed events, resulting in a slight tilt to the distribution shown in Figure 12(b). The distribution of open circles was created by scaling the AD2 energy by 0.3%. The distribution with scaled AD2 energy agrees well with a flat distribution.

(a)

(b)

Figure 12 

The energy spectra for the prompt signal of IBD events in AD1 and AD2 (a) are shown along with the bin-by-bin ratio (b). Within (b), the dashed line represents the ratio of the total rates for the two ADs, and the open circles show the ratio with the AD2 energy scaled by +0.3%.

4.6. Reactor Neutrino Flux

Reactor antineutrinos result primarily from the beta decay of the fission products of four main isotopes, 235U, 239Pu, 238U, and 241Pu. The 𝜈_𝑒 flux of each reactor (𝑆(𝐸)) was predicted from the simulated fission fraction 𝑓_𝑖 and the neutrino spectra per fission (𝑆_𝑖) [19–22, 32, 37] of each isotope [63], 𝑆(𝐸)=𝑊_th∑_𝑘𝑓_𝑘𝐸_𝑘𝑖𝑓_𝑖𝑆_𝑖(𝐸), (7) where 𝑖 and 𝑘 sum over the four isotopes, 𝐸_𝑖 is the energy released per fission, and 𝑊_th is the measured thermal power.

The thermal power data were provided by the power plant. The uncertainties were dominated by the flow rate measurements of feedwater through three parallel cooling loops in each core [63–65]. The correlations between the flow meters were not clearly known. We conservatively assume that they were correlated for a given core but were uncorrelated between cores, giving a maximal uncertainty for the experiment. The assigned uncorrelated uncertainty for thermal power was 0.5%.

A simulation of the reactor cores using commercial software (SCIENCE [66, 67]) provided the fission fraction as a function of burnup. The fission fraction carries a 5% uncertainty set by the validation of the simulation software. The 3D spatial distribution of the isotopes within a core was also provided by the power plant, although simulation indicated that it had a negligible effect on acceptance. A complementary core simulation package was developed based on DRAGON [68] as a cross-check and for systematic studies. The code was validated with the Takahama-3 benchmark [69] and agreed with the fission fraction provided by the power plant to 3%. Correlations among the four isotopes were studied using the DRAGON-based simulation package, and agreed well with the data collected in [70]. Given the constraints of the thermal power and correlations, the uncertainties of the fission fraction simulation translated into a 0.6% uncorrelated uncertainty in the neutrino flux.

The neutrino spectrum per fission is a correlated uncertainty that cancels out for a relative measurement. The reaction cross-section for isotope 𝑖 was defined as 𝜎_𝑖=∫𝑆_𝑖(𝐸_𝜈)𝜎(𝐸_𝜈)𝑑𝐸_𝜈, where 𝑆_𝑖(𝐸_𝜈) is the neutrino spectra per fission and 𝜎(𝐸_𝜇) is the IBD cross-section. We took the reaction cross-section from [10] but substituted the IBD cross-section with that in [71]. The energy released per fission and its uncertainties were taken from [72]. Nonequilibrium corrections for long-lived isotopes were applied following [22]. Contributions from spent fuel [73, 74] (∼0.3%) were included as an uncertainty.

The uncertainties in the baseline and the spatial distribution of the fission fractions in the core had a negligible effect to the results.

Figure 13 presents the background-subtracted and efficiency-corrected IBD rates in the three experimental halls. Predicted IBD rate from reactor flux calculation and detector Monte Carlo simulation are shown for comparison. The dashed lines have been corrected with the best-fit normalization parameter 𝜀 in (10) to get rid of the biases from the absolute reactor flux uncertainty and the absolute detector efficiency uncertainty.

Figure 13 

The daily average measured IBD rates per AD in the three experimental halls are shown as a function of time along with predictions based on reactor flux analyses and detector simulation.

4.7. Results

The 𝜈_𝑒rate in the far hall was predicted with a weighted combination of the two near hall measurements assuming no oscillation. A ratio of measured-to-expected rate is defined as 𝑀𝑅=^𝑓𝑁_𝑓=𝑀_𝑓𝛼𝑀_𝑎+𝛽𝑀_𝑏, (8) where 𝑁_𝑓 and 𝑀_𝑓 are the predicted and measured rates in the far hall (sum of AD 4–6) and 𝑀_𝑎 and 𝑀_𝑏 are the measured IBD rates in EH1 (sum of AD 1-2) and EH2 (AD3), respectively. The values for 𝛼 and 𝛽 were dominated by the baselines and only slightly dependent on the integrated flux of each core. For the analyzed data set, 𝛼=0.0439 and 𝛽=0.2961. The residual reactor-related uncertainty in 𝑅 was 5% of the uncorrelated uncertainty of a single core. The deficit observed at the far hall was as follows: 𝑅=0.944±0.007(stat)±0.003syst. (9)

The value of sin²2𝜃₁₃ was determined with a 𝜒² constructed with pull terms accounting for the correlation of the systematic errors [75] as follows: 𝜒²=⁶_𝑑=1𝑀_𝑑−𝑇_𝑑1+𝜀+∑_𝑟𝜔^𝑑_𝑟𝛼_𝑟+𝜀_𝑑+𝜂_𝑑²𝑀_𝑑+𝐵_𝑑+_𝑟𝛼²_𝑟𝜎²_𝑟+⁶_𝑑=1𝜀²_𝑑𝜎²_𝑑+𝜂²_𝑑𝜎²_𝐵, (10) where 𝑀_𝑑 is the measured IBD events of the 𝑑th AD with backgrounds subtracted, 𝐵_𝑑 is the corresponding background, 𝑇_𝑑 is the prediction from neutrino flux, MC, and neutrino oscillations, and 𝜔^𝑑_𝑟 is the fraction of IBD contribution of the 𝑟th reactor to the 𝑑th AD determined by baselines and reactor fluxes. The uncorrelated reactor uncertainty is 𝜎_𝑟 (0.8%), as shown in Table 5. 𝜎_𝑑 (0.2%) is the uncorrelated detection uncertainty, listed in Table 8. 𝜎_𝐵 is the background uncertainty listed in Table 4. The corresponding pull parameters are (𝛼_𝑟, 𝜀_𝑑, and 𝜂_𝑑). The detector- and reactor-related correlated uncertainties were not included in the analysis; the absolute normalization 𝜀 was determined from the fit to the data.

Table 5 

Reactor-related uncertainties.

The survival probability used in the 𝜒² was 𝑃_sur=1−sin²2𝜃₁₃sin²1.267Δ𝑚²₃₁𝐿𝐸−cos⁴𝜃₁₃sin²2𝜃₁₂sin²1.267Δ𝑚²₂₁𝐿𝐸, (11) where Δ𝑚²₃₁=2.32×10⁻³eV², sin²2𝜃₁₂=0.861^+0.026_−0.022, and Δ𝑚²₂₁=7.59^+0.20_−0.21×10⁻⁵eV². The uncertainty in Δ𝑚²₃₁ had negligible effect and thus was not included in the fit.

The best-fit value is sin²2𝜃₁₃=0.089±0.010(stat.)±0.005syst. (12) with a 𝜒²/NDF of 3.4/4. All best estimates of pull parameters are within its one standard deviation based on the corresponding systematic uncertainties. The no-oscillation hypothesis is excluded at 7.7 standard deviations. Figure 14 shows the measured number of events in each detector, relative to those expected assuming no oscillation. A ∼1.5% oscillation effect appears in the near halls. The oscillation survival probability at the best-fit values is given by the smooth curve. The 𝜒² versus sin²2𝜃₁₃ is shown in the inset.

Figure 14 

Ratio of measured versus expected signal in each detector, assuming no oscillation. The error bar is the uncorrelated uncertainty of each AD. The expected signal was corrected with the best-fit normalization parameter. The oscillation survival probability at the best-fit value is given by the smooth curve. The AD4 and AD6 data points were displaced by −30 and +30 m for visual clarity. The 𝜒2 versus sin22𝜃13 is shown in the inset.

The observed 𝜈_𝑒spectrum in the far hall was compared to a prediction based on the near hall measurements 𝛼𝑀_𝑎+𝛽𝑀_𝑏 in Figure 15. The distortion of the spectra is consistent with the expected one calculated with the best-fit 𝜃₁₃ obtained from the rate-only analysis, providing further evidence of neutrino oscillation.

(a)

(b)

Figure 15 

(a) Measured prompt energy spectrum of the far hall (sum of three ADs) compared with the no-oscillation prediction from the measurements of the two near halls. Spectra were background subtracted. Uncertainties are statistical only. (b) The ratio of measured and predicted no-oscillation spectra. The red curve is the best-fit solution with sin22𝜃13=0.089 obtained from the rate-only analysis. The dashed line is the no-oscillation prediction.

5. Double Chooz

The Double Chooz detector system (Figure 16) consists of a main detector, an outer veto, and calibration devices. The main detector comprises four concentric cylindrical tanks filled with liquid scintillators or mineral oil. The innermost 8 mm thick transparent (UV to visible) acrylic vessel houses the 10m³𝜈-target liquid, a mixture of n-dodecane, PXE, PPO, bis-MSB, and 1 g gadolinium/l as a beta-diketonate complex. The scintillator choice emphasizes radiopurity and long-term stability. The 𝜈-target volume is surrounded by the 𝛾-catcher, a 55 cm thick Gd-free liquid scintillator layer in a second 12 mm thick acrylic vessel, used to detect 𝛾-rays escaping from the 𝜈-target. The light yield of the 𝛾-catcher was chosen to provide identical photoelectron (pe) yield across these two layers. Outside the 𝛾-catcher is the buffer, a 105 cm thick mineral oil layer. The buffer works as a shield to 𝛾-rays from radioactivity of PMTs and from the surrounding rock and is one of the major improvements over the CHOOZ detector. It shields from radioactivity of photomultipliers (PMTs) and of the surrounding rock, and it is one of the major improvements over the CHOOZ experiment. 390 10-inch PMTs are installed on the stainless steel buffer tank inner wall to collect light from the inner volumes. These three volumes and the PMTs constitute the inner detector (ID). Outside the ID, and optically separated from it, is a 50 cm thick inner veto liquid scintillator (IV). It is equipped with 78 8-inch PMTs and functions as a cosmic muon veto and as a shield to spallation neutrons produced outside the detector. The detector is surrounded by 15 cm of demagnetized steel to suppress external 𝛾-rays. The main detector is covered by an outer veto system. The readout is triggered by custom energy sum electronics. The ID PMTs are separated into two groups of 195 PMTs uniformly distributed throughout the volume, and the PMT signals in each group are summed. The signals of the IV PMTs are also summed. If any of the three sums is above a set energy threshold, the detector is read out with 500 MHz flash-ADC electronics with customized firmware and a dead time-free acquisition system. Upon each trigger, a 256 ns interval of the waveforms of both ID and IV signals is recorded. Having reduced the ambient radioactivity enables us to set a low trigger rate (120 Hz) allowed the ID readout threshold to be set at 350 keV, well below the 1.02 MeV minimum energy of an IBD positron, greatly reducing the threshold systematics. The experiment is calibrated by several methods. A multiwavelength LED-fiber light injection system (LI) produces fast light pulses illuminating the PMTs from fixed positions. Radio-isotopes 137Cs, 68Ge, 60Co, and 252Cf were deployed in the target along the vertical symmetry axis and, in the gamma catcher, through a rigid loop traversing the interior and passing along boundaries with the target and the buffer. The detector was monitored using spallation neutron captures on H and Gd, residual natural radioactivity, and daily LI runs. The energy response was found to be stable within 1% over time.

Figure 16 

A cross-sectional view of the Double Chooz detector system.

5.1. Chooz Reactor Modeling

Double Chooz's sources of antineutrinos are the reactor cores B1 and B2 at the Électricité de France (EDF) Centrale Nucléaire de Chooz, two N4 type pressurized water reactor (PWR) cores with nominal thermal power outputs of 4.25GW_th each. The instantaneous thermal power of each reactor core 𝑃^𝑅_th is provided by EDF as a fraction of the total power. It is derived from the in-core instrumentation with the most important variable being the temperature of the water in the primary loop. The dominant uncertainty on the weekly heat balance at the secondary loops comes from the measurement of the water flow. At the nominal full power of 4250 MW, the final uncertainty is 0.5% (1 𝜎 C.L.). Since the amount of data taken with one or two cores at intermediate power is small, this uncertainty is used for the mean power of both cores.

The antineutrino spectrum for each fission isotope is taken from [22, 32], including corrections for off-equilibrium effects. The uncertainty on these spectra is energy dependent but is on the order of 3%. The fractional fission rates 𝛼_𝑘 of each isotope are needed in order to calculate the mean cross-section per fission. They are also required for the calculation of the mean energy released per fission for reactor 𝑅: ⟨𝐸_𝑓⟩_𝑅=_𝑘𝛼_𝑘⟨𝐸_𝑓⟩_𝑘. (13) The thermal power one would calculate given a fission is relatively insensitive to the specific fuel composition since the ⟨𝐸_𝑓⟩_𝑘 differ by <6%; however, the difference in the detected number of antineutrinos is amplified by the dependence of the norm and mean energy of 𝑆_𝑘(𝐸) on the fissioning isotope. For this reason, much effort has been expended in developing simulations of the reactor cores to accurately model the evolution of the 𝛼_𝑘.

Double Chooz has chosen two complementary codes for modeling of the reactor cores: MURE and DRAGON [30, 76–78]. These two codes provide the needed flexibility to extract fission rates and their uncertainties. These codes were benchmarked against data from the Takahama-3 reactor [79]. The construction of the reactor model requires detailed information on the geometry and materials comprising the core. The Chooz cores are comprised of 205 fuel assemblies. For every reactor fuel cycle, approximately one year in duration, one-third of the assemblies are replaced with assemblies containing fresh fuel. The other two-thirds of the assemblies are redistributed to obtain a homogeneous neutron flux across the core. The Chooz reactor cores contain four assembly types that differ mainly in their initial 235U enrichment. These enrichments are 1.8%, 3.4%, and 4%. The data set reported here spans fuel cycle 12 for core B2 and cycle 12 and the beginning of cycle 13 for B1. EDF provides Double Chooz with the locations and initial burnup of each assembly. Based on these maps, a full core simulation was constructed using MURE for each cycle. The uncertainty due to the simulation technique is evaluated by comparing the DRAGON and MURE results for the reference simulation leading to a small 0.2% systematic uncertainty in the fission rate fractions 𝛼_𝑘. Once the initial fuel composition of the assemblies is known, MURE is used to model the evolution of the full core in time steps of 6 to 48 hours. This allows the 𝛼_𝑘’s, and therefore the predicted antineutrino flux, to be calculated. The systematic uncertainties on the 𝛼_𝑘’s are determined by varying the inputs and observing their effect on the fission rate relative to the nominal simulation. The uncertainties considered are those due to the thermal power, boron concentration, moderator temperature and density, initial burnup error, control rod positions, choice of nuclear databases, choice of the energies released per fission, and statistical error of the MURE Monte Carlo. The two largest uncertainties come from the moderator density and control rod positions.

In far-only phase of Double Chooz, the rather large uncertainties in the reference spectra limit the sensitivity to 𝜃₁₃. To mitigate this effect, the normalization of the cross-section per fission for each reactor is anchored to the Bugey-4 rate measurement at 15 m [10]: ⟨𝜎_𝑓⟩_𝑅=⟨𝜎_𝑓⟩^Bugey+_𝑘𝛼^𝑅_𝑘−𝛼^Bugey_𝑘⟨𝜎_𝑓⟩_𝑘, (14) where 𝑅 stands for each reactor. The second term corrects the difference in fuel composition between Bugey-4 and each of the Chooz cores. This treatment takes advantage of the high accuracy of the Bugey-4 anchor point (1.4%) and suppresses the dependence on the predicted ⟨𝜎_𝑓⟩_𝑅. At the same time, the analysis becomes insensitive to possible oscillations at shorter baselines due to heavy Δ𝑚²∼1eV² sterile neutrinos. The expected number of antineutrinos with no oscillation in the 𝑖th energy bin with the Bugey-4 anchor point becomes as follows: 𝑁_𝑖^exp,𝑅=𝜖𝑁_𝑝14𝜋𝐿_𝑅²𝑃^𝑅_th⟨𝐸_𝑓⟩_𝑅×⟨𝜎_𝑓⟩_𝑅∑_𝑘𝛼^𝑅_𝑘⟨𝜎_𝑓⟩_𝑘𝑘𝛼^𝑅_𝑘⟨𝜎_𝑓⟩^𝑖_𝑘, (15) where 𝜖 is the detection efficiency, 𝑁_𝑝 is the number of protons in the target, 𝐿_𝑅 is the distance to the center of each reactor, and 𝑃^𝑅_th is the thermal power. The variable ⟨𝐸_𝑓⟩_𝑅 is the mean energy released per fission defined in (13), while ⟨𝜎_𝑓⟩_𝑅 is the mean cross-section per fission defined in (14). The three variables 𝑃^𝑅_th, ⟨𝐸_𝑓⟩_𝑅, and ⟨𝜎_𝑓⟩_𝑅 are time dependent with ⟨𝐸_𝑓⟩_𝑅 and ⟨𝜎_𝑓⟩_𝑅 depending on the evolution of the fuel composition in the reactor and 𝑃^𝑅_th depending on the operation of the reactor. A covariance matrix 𝑀^exp_𝑖𝑗=𝛿𝑁_𝑖^exp𝛿𝑁_𝑗^exp is constructed using the uncertainties listed in Table 6.

Table 6 

The uncertainties in the antineutrino prediction. All uncertainties are assumed to be correlated between the two reactor cores. They are assumed to be normalization and energy (rate and shape) unless noted as normalization only.

The IBD cross-section used is the simplified form from Vogel and Beacom [71]. The cross-section is inversely proportional to the neutron lifetime. The MAMBO-II measurement of the neutron lifetime [80] is being used, leading to 𝐾=0.961×10⁻⁴³cm²MeV⁻².

5.2. Modeling the Double Chooz Detector

The detector response uses a detailed Geant4 [81, 82] simulation with enhancements to the scintillation process, photocathode optical surface model, and thermal neutron model. Simulated IBD events are generated with run-by-run correspondence of MC to data, with fluxes and rates calculated as described in the previous paragraph. Radioactive decays in calibration sources and spallation products were simulated using detailed models of nuclear levels, taking into account branching ratios and correct spectra for transitions [83–85]. Optical parameters used in the detector model are based on detailed measurements made by the collaboration. Tuning of the absolute and relative light yield in the simulation was done with calibration data. The scintillator emission spectrum was measured using a Cary Eclipse Fluorometer [86]. The photon emission time probabilities used in the simulation are obtained with a dedicated laboratory setup [87]. For the ionization quenching treatment in our MC, the light output of the scintillators after excitation by electrons [88] and alpha particles [89] of different energies was measured. The nonlinearity in light production in the simulation has been adjusted to match these data. The finetuning of the total attenuation was made using measurements of the complete scintillators [87]. Other measured optical properties include reflectivities of various detector surfaces and indices of refraction of detector materials.

The readout system simulation (RoSS) accounts for the response of elements associated with detector readout, such as from the PMTs, FEE, FADCs, trigger system and DAQ. The simulation relies on the measured probability distribution function (PDF) to empirically characterize the response to each single PE as measured by the full readout channel. The Geant4-based simulation calculates the time at which each PE strikes the photocathode of each PMT. RoSS converts this time per PE into an equivalent waveform as digitized by FADCs. After calibration, the MC and data energies agree within 1%.

A set of Monte Carlo 𝜈_𝑒 events representing the expected signal for the duration of physics data taking is created based on the formalism of (16). The calculated IBD rate is used to determine the rate of interactions. Parent fuel nuclide and neutrino energies are sampled from the calculated neutrino production ratios and corresponding spectra, yielding a properly normalized set of IBD-progenitor neutrinos. Once generated, each event-progenitor neutrino is assigned a random creation point within the originating reactor core. The event is assigned a weighted random interaction point within the detector based on proton density maps of the detector materials. In the center-of-mass frame of the 𝜈−𝑝 interaction, a random positron direction is chosen, with the positron and neutron of the IBD event given appropriate momenta based on the neutrino energy and decay kinematics. These kinematic values are then boosted into the laboratory frame. The resulting positron and neutron momenta and originating vertex are then available as inputs to the Geant4 detector simulation. Truth information regarding the neutrino origin, baseline, and energy are propagated along with the event, for use later in the oscillation analysis.

5.3. Event Reconstruction

The pulse reconstruction provides the signal charge and time in each PMT. The baseline mean (𝐵_mean) and rms (𝐵_rms) are computed using the full readout window (256 ns). The integrated charge (𝑞) is defined as the sum of digital counts in each waveform sample over the integration window, once the pedestal has been subtracted. For each pulse reconstructed, the start time is computed as the time when the pulse reaches 20% of its maximum. This time is then corrected by the PMT-to-PMT offsets obtained with the light injection system.

Vertex reconstruction in Double Chooz is not used for event selection but is used for event energy reconstruction. It is based on a maximum charge and time likelihood algorithm which utilizes all hit and no-hit information in the detector. The performance of the reconstruction has been evaluated in situ using radioactive sources deployed at known positions along the 𝑧-axis in the target volume, and off-axis in the guide tubes. The sources are reconstructed with a spatial resolution of 32 cm for ¹³⁷Cs, 24 cm for ⁶⁰Co, and 22 cm for ⁶⁸Ge.

Cosmic muons passing through the detector or the nearby rock induce backgrounds which are discussed later. The IV trigger rate is 46s⁻¹. All muons in the ID are tagged by the IV except some stopping muons which enter the chimney. Muons which stop in the ID and their resulting Michel 𝑒 can be identified by demanding a large energy deposition (roughly a few tens of MeV) in the ID. An event is tagged as a muon if there is >5 MeV in the IV or >30 MeV in the ID.

The visible energy (𝐸_vis) provides the absolute calorimetric estimation of the energy deposited per trigger. 𝐸_vis is a function of the calibrated 𝑃𝐸 (total number of photoelectrons): 𝐸_vis=𝑃𝐸^𝑚𝜌,𝑧,𝑡×𝑓^𝑚_𝑢𝜌,𝑧×𝑓^𝑚_𝑠(𝑡)×𝑓^𝑚_MeV, (16) where 𝑃𝐸=∑_𝑖𝑝𝑒_𝑖=∑_𝑖𝑞_𝑖/gain_𝑖(𝑞_𝑖). Coordinates in the detector are 𝜌 and 𝑧, 𝑡 is time, 𝑚 refers to data or Monte Carlo (MC), and 𝑖 refers to each good channel. The correction factors 𝑓_𝑢, 𝑓_𝑠, and 𝑓_MeV correspond, respectively, to the spatial uniformity, time stability, and photoelectron per MeV calibrations. Four stages of calibration are carried out to render 𝐸_vis linear, independent of time and position, and consistent between data and MC. Both the MC and data are subjected to the same stages of calibration. The sum over all good channels of the reconstructed raw charge (𝑞_𝑖) from the digitized waveforms is the basis of the energy estimation. The 𝑃𝐸 response is position dependent for both MC and data. Calibration maps were created such that any 𝑃𝐸 response for any event located at any position (𝜌, 𝑧) can be converted into its response as if measured at the center of the detector (𝜌=0, 𝑧=0): 𝑃𝐸^𝑚_⨀=𝑃𝐸^𝑚(𝜌,𝑧)×𝑓^𝑚_𝑢(𝜌,𝑧). The calibration map's correction for each point is labeled 𝑓^𝑚_𝑢(𝜌,𝑧). Independent uniformity calibration maps 𝑓^𝑚_𝑢(𝜌,𝑧) are created for data and MC, such that the uniformity calibration serves to minimize any possible difference in position dependence of the data with respect to MC. The capture peak on H (2.223 MeV) of neutrons from spallation and antineutrino interactions provides a precise and copious calibration source to characterize the response nonuniformity over the full volume (both NT and GC).

The detector response stability was found to vary in time due to two effects, which are accounted for and corrected by the term 𝑓^𝑚_𝑠(𝑡). First, the detector response can change due to variations in readout gain or scintillator response. This effect has been measured as a +2.2% monotonic increase over 1 year using the response of the spallation neutrons capturing on Gd within the NT. Second, few readout channels varying over time are excluded from the calorimetry sum, and the average overall response decreases by 0.3% per channel excluded. Therefore, any response 𝑃𝐸_⨀(𝑡) is converted to the equivalent response at 𝑡₀, as 𝑃𝐸^𝑚_⨀𝑡0=𝑃𝐸^𝑚_⨀(𝑡)×𝑓^𝑚_𝑠(𝑡). The 𝑡₀ was defined as the day of the first Cf source deployment, during August 2011. The remaining instability after calibration is used for the stability systematic uncertainty estimation.

The number 𝑃𝐸_⨀𝑡0 per MeV is determined by an absolute energy calibration independently, for the data and MC. The response in 𝑃𝐸_⨀𝑡0 for H capture as deployed in the center of the NT is used for the absolute energy scale. The absolute energy scales are found to be 229.9𝑃𝐸_⨀𝑡0/MeV and 227.7𝑃𝐸_⨀𝑡0/MeV, respectively, for the data and MC, demonstrating agreement within 1% prior to this calibration stage.

Discrepancies in response between the MC and data, after calibration, are used to estimate these uncertainties within the prompt energy range and the NT volume. Table 7 summarizes the systematic uncertainty in terms of the remaining nonuniformity, instability, and nonlinearity. The relative nonuniformity systematic uncertainty was estimated from the calibration maps using neutrons capturing on Gd, after full calibration. The rms deviation of the relative difference between the data and MC calibration maps is used as the estimator of the nonuniformity systematic uncertainty, and is 0.43%. The relative instability systematic error, discussed above, is 0.61%. A 0.85% variation consistent with this nonlinearity was measured with the 𝑧-axis calibration system, and this is used as the systematic error for relative nonlinearity in Table 7. Consistent results were obtained when sampling with the same sources along the GT.

Table 7 

Energy scale systematic errors.

Table 8 

Cuts used in the event selection and their efficiency for IBD events. The OV was working for the last 68.9% of the data.

5.4. Neutrino Data Analysis. Signals and Backgrounds

The 𝜈_𝑒 candidate selection is as follows. Events with an energy below 0.5 MeV, where the trigger efficiency is not 100%, or identified as light noise (𝑄_max/𝑄_tot>0.09 or rms(𝑡_start)>40ns), are discarded. Triggers within a 1 ms window following a tagged muon are also rejected in order to reduce the correlated and cosmogenic backgrounds. The effective veto time is 4.4% of the total run time. Defining Δ𝑇≡𝑡_delayed−𝑡_prompt, further selection consists of 4 cuts: (1)time difference between consecutive triggers (prompt and delayed): 2𝜇s<Δ𝑇<100𝜇s, where the lower cut reduces correlated backgrounds and the upper cut is determined by the approximately 30𝜇s capture time on Gd; (2)prompt trigger: 0.7MeV<𝐸_prompt<12.2MeV; (3)delayed trigger: 6.0MeV<𝐸_delayed<12.0MeV and 𝑄_max/𝑄_tot<0.055; (4)multiplicity: no additional triggers from 100𝜇s preceding the prompt signal to 400𝜇s after it, with the goal of reducing the correlated background.

The IBD efficiencies for these cuts are listed in Table 8.

A preliminary sample of 9021 candidates is obtained by applying selections (1–4). In order to reduce the background contamination in the sample, candidates are rejected according to two extra cuts. First, candidates within a 0.5 s window after a high energy muon crossing the ID (𝐸_𝜇>600 MeV) are tagged as cosmogenic isotope events and are rejected, increasing the effective veto time to 9.2%. Second, candidates whose prompt signal is coincident with an OV trigger are also excluded as correlated background. Applying the above vetoes yields 8249 candidates or a rate of 36.2±0.4 events/day, uniformly distributed within the target, for an analysis livetime of 227.93 days. Following the same selection procedure on the 𝜈_𝑒 MC sample yields 8439.6 expected events in the absence of oscillation.

The main source of accidental coincidences is the random association of a prompt trigger from natural radioactivity and a later neutron-like candidate. This background is estimated not only by applying the neutrino selection cuts described, but also using coincidence windows shifted by 1 s in order to remove correlations in the time scale of n-captures in H and Gd. The radioactivity rate between 0.7 and 12.2 MeV is 8.2 s⁻¹, while the singles rate in 6–12 MeV energy region is 18h⁻¹. Finally, the accidental background rate is found to be 0.261±0.002 events per day.

The radioisotopes 8He and 9Li are products of spallation processes on 12C induced by cosmic muons crossing the scintillator volume. The 𝛽-n decays of these isotopes constitute a background for the antineutrino search. 𝛽-n emitters can be identified from the time and space correlations to their parent muon. Due to their relatively long lifetimes (9Li: 𝜏=257 ms, 8He: 𝜏=172 ms), an event-by-event discrimination is not possible. For the muon rates in our detector, vetoing for several isotope lifetimes after each muon would lead to an unacceptably large loss in exposure. Instead, the rate is determined by an exponential fit to the Δ𝑡_𝜇𝜈≡𝑡_𝜇−𝑡_𝜈 profile of all possible muon-IBD candidate pairs. The analysis is performed for three visible energy 𝐸^vis_𝜇 ranges that characterize subsamples of parent muons by their energy deposition, not corrected for energy nonlinearities, in the ID as follows. (1)Showering muons crossing the target value are selected by 𝐸^vis_𝜇>600 MeV, and feature, they an increased probability to produce cosmogenic isotopes. The Δ𝑡_𝜇𝜈 fit returns a precise result of 0.95±0.11 events/day for the 𝛽-n-emitter rate. (2)In the 𝐸^vis_𝜇 range from 275 to 600 MeV, muons crossing GC and target still give a sizable contribution to isotope production of 1.08±0.44 events/day. To obtain this result from a Δ𝑡_𝜇𝜈 fit, the sample of muon-IBD pairs has to be cleaned by a spatial cut on the distance of closest approach from the muon to the IBD candidate of 𝑑_𝜇𝜈<80 cm to remove the majority of uncorrelated pairs. The corresponding cut efficiency is determined from the lateral distance profile obtained for 𝐸^vis_𝜇>600 MeV. The approach is validated by a comparative study of cosmic neutrons that show an almost congruent profile with very little dependence on 𝐸^vis_𝜇 above 275 MeV. (3)The cut 𝐸^vis_𝜇<275 MeV selects muons crossing only the buffer volume or the rim of the GC. For this sample, no production of 𝛽-n emitters inside the target volume is observed. An upper limit of <0.3 events/day can be established based on a Δ𝑡_𝜇𝜈 fit for 𝑑_𝜇𝜈<80 cm. Again, the lateral distribution of cosmic neutrons has been used for determining the cut efficiency.

The overall rate of 𝛽𝑛 decays found is 2.05^+0.62_−0.52 events/day.

Most correlated backgrounds are rejected by the 1 ms veto time after each tagged muon. The remaining events arise from cosmogenic events whose parent muon either misses the detector or deposits an energy low enough to escape the muon tagging. Two contributions have been found: fast neutrons (FNs) and stopping muons (SMs). FNs are created by muons in the inactive regions surrounding the detector. Their large interaction length allows them to cross the detector and capture in the ID, causing both a prompt trigger by recoil protons and a delayed trigger by capture on Gd. An approximately flat prompt energy spectrum is expected; a slope could be introduced by acceptance and scintillator quenching effects. The time and spatial correlations distribution of FN are indistinguishable from those of 𝜈_𝑒 events. The selected SM arise from muons entering through the chimney, stopping in the top of the ID, and eventually decaying. The short muon track mimics the prompt event, and the decay Michel electron mimics the delayed event. SM candidates are localized in space in the top of the ID under the chimney and have a prompt-delayed time distribution following the 2.2 μs muon lifetime. The correlated background has been studied by extending the selection on 𝐸_prompt up to 30 MeV. No IBD events are expected in the interval 12MeV≤𝐸_prompt≤30MeV. FN and SM candidates were separated via their different correlation time distributions. The observed prompt energy spectrum is consistent with a flat continuum between 12 and 30 MeV, which extrapolated to the IBD selection window provideing a first estimation of the correlated background rate of ≈0.75 events/day. The accuracy of this estimate depends on the validity of the extrapolation of the spectral shape. Several FN and SM analyses were performed using different combinations of IV and OV taggings. The main analysis for the FN estimation relies on IV tagging of the prompt triggers with OV veto applied for the IBD selection. A combined analysis was performed to obtain the total spectrum and the total rate estimation of both FN and SM, (0.67±0.20) events/day summarized, in Table 9.

Table 9 

Summary of observed IBD candidates, with corresponding signal and background predictions for each integration period before any oscillation fit results have been applied.

There are four ways that can be utilized to estimate backgrounds. Each independent background component can be measured by isolating samples and subtracting possible correlations. Second, we can measure each independent background component including spectral information when fitting for 𝜃₁₃ oscillations. Third, the total background rate is measured by comparing the observed and expected rates as a function of reactor power. Fourth, we can use the both-reactor-off data to measure both the rate and spectrum. The latter two methods are used currently as cross-checks for the background measurements due to low statistics and are described here. The measured daily rate of IBD candidates as a function of the no-oscillation expected rate for different reactor power conditions is shown in Figure 17. The extrapolation to zero reactor power of the fit to the data yields 2.9±1.1 events per day, in excellent agreement with our background estimate. The overall rate of correlated background events that pass the IBD cuts is independently verified by analyzing 22.5 hours of both-reactors-off data [48]. The expected neutrino signal is <0.3 residual 𝜈_𝑒 events.

Figure 17 

Daily number of 𝜈𝑒 candidates as a function of the expected number of 𝜈𝑒. The dashed line shows the fit to the data, along with the 90% C L band. The dotted line shows the expectation in the no-oscillation scenario.

Calibration data taken with the 252Cf source were used to check the Monte Carlo prediction for any biases in the neutron selection criteria and estimate their contributions to the systematic uncertainty.

The fraction of neutron captures on gadolinium is evaluated to be 86.5% near the center of the target and to be 1.5% lower than the fraction predicted by simulation. Therefore, the Monte Carlo simulation for the prediction of the number of 𝜈_𝑒 events is reduced by factor of 0.985. After the prediction of the fraction of neutron captures on gadolinium is scaled to the data, the prediction reproduces the data within 0.3% under variation of selection criteria.

The 252Cf is also used to check the neutron capture time, Δ𝑇. The simulation reproduces the efficiency (96.2%) of the Δ𝑡_𝑒+𝑛 cut with an uncertainty of 0.5% augmented with sources deployed through the NT and GC.

The efficiency for Gd capture events with visible energy greater than 4 MeV to pass the 6 MeV cut is estimated to be 94.1%. Averaged over the NT, the fraction of neutron captures on Gd accepted by the 6.0 MeV cut is in agreement with calibration data within 0.7%.

The Monte Carlo simulation indicates that the number of IBD events occurring in the GC with the neutron captured in the NT (spill-in) slightly exceeds the number of events occurring in the target with the neutron escaping to the gamma catcher (spill-out), by 1.35%±0.04% (stat) ± 0.30%(sys). The spill-in/out effect is already included in the simulation, and therefore no correction for this is needed. The uncertainty of 0.3% assigned to the net spill-in/out current was quantified by varying the parameters affecting the process, such as gadolinium concentration in the target scintillator and hydrogen fraction in the gamma-catcher fluid within its tolerances. Moreover, the parameter variation was performed with multiple Monte Carlo models at low neutron energies.

5.5. Oscillation Analysis

The oscillation analysis is based on a combined fit to antineutrino rate and spectral shape. The data are compared to the Monte Carlo signal and background events from high-statistics samples. The same selections are applied to both signal and background, with corrections made to Monte Carlo only when necessary to match detector performance metrics. The oscillation analysis begins by separating the data into 18 variably sized bins between 0.7 and 12.2 MeV. Two integration periods are used in the fit to help separate background and signal fluxes. One set contains data periods, where one reactor is operating at less than 20% of its nominal thermal power, according to power data provided by EDF, while the other set contains data from all other times, typically when both reactors are running. All data end up in one of the two integration periods. Here, we denote the number of observed IBD candidates in each of the bins as 𝑁_𝑖, where 𝑖 runs over the combined 36 bins of both integration periods. The use of multiple periods of data integration takes advantage of the different signal/background ratios in each period, as the signal rate varies with reactor power, while the backgrounds remain constant in time. This technique adds information about background behavior to the fit. The distribution of IBD candidates between the two integration periods is given in Table 9. A prediction of the observed number of signal and background events is constructed for each energy bin, following the same integration period division as the following data: 𝑁^𝑝red_𝑖=^Reactors_𝑅=1,2𝑁_𝑖^𝜈,𝑅+^Bkgnds._𝑏𝑁^𝑏_𝑖, (17) where 𝑁_𝑖^𝜈,𝑅=𝑃(𝜈_𝑒→𝜈_𝑒)𝑁_𝑖^exp,𝑅, 𝑃_{𝜈𝑒→𝜈𝑒} is the neutrino survival probability from the well-known oscillation formula, and 𝑁_𝑖^exp,𝑅 is given by (16). The index 𝑏 runs over the three backgrounds: cosmogenic isotope; correlated; and accidental. The index 𝑅 runs over the two reactors, Chooz B1 and B2. Background populations were calculated based on the measured rates and the livetime of the detector during each integration period. Predicted populations for both null-oscillation signal and backgrounds may be found in Table 9.

Systematic and statistical uncertainties are propagated to the fit by the use of a covariance matrix 𝑀_𝑖𝑗 in order to properly account for correlations between energy bins. The sources of uncertainty 𝐴 are listed in Table 10 as follows: 𝑀_𝑖𝑗=𝑀^sig._𝑖𝑗+𝑀^det._𝑖𝑗+𝑀^stat._𝑖𝑗+𝑀^eff._𝑖𝑗+^Bkgnds._𝑏𝑀^𝑏_𝑖𝑗. (18)

Table 10 

Summary of signal and background normalization uncertainties in this analysis relative to the total prediction.

Each term 𝑀^𝐴_𝑖𝑗=cov(𝑁^pred_𝑖,𝑁^pred_𝑗)_𝐴 on the right-hand side of (18) represents the covariance of 𝑁^pred_𝑖 and 𝑁^pred_𝑗 due to uncertainty 𝐴. The normalization uncertainty associated with each of the matrix contributions may be found from the sum of each matrix; these are summarized in Table 10. Many sources of uncertainty contain spectral shape components which do not directly contribute to the normalization error but do provide for correlated uncertainties between the energy bins. The signal covariance matrix 𝑀^sig._𝑖𝑗 is calculated taking into account knowledge about the predicted neutrino spectra. The 9Li matrix contribution contains spectral shape uncertainties estimated using different Monte Carlo event generation parameters. The slope of the FN/SM spectrum is allowed to vary from a nearly flat spectrum. Since accidental background uncertainties are measured to a high precision from many off-time windows, they are included as a diagonal covariance matrix. The elements of the covariance matrix contributions are recalculated as a function of the oscillation and other parameters (see below) at each step of the minimization. This maintains the fractional systematic uncertainties as the bin populations vary from the changes in the oscillation and fit parameters.

A fit of the binned signal and background data to a two-neutrino oscillation hypothesis was performed by minimizing a standard 𝜒² function: 𝜒²=³⁶_𝑖,𝑗𝑁_𝑖−𝑁^pred_𝑖×𝑀_𝑖𝑗⁻¹𝑁_𝑗−𝑁^pred_𝑗^𝑇+𝜖_FN/SM−1²𝜎²_FN/SM+𝜖_9Li−1²𝜎²_9Li+𝛼_𝐸−1²𝜎²_𝛼𝐸+Δ𝑚²₃₁−Δ𝑚²_31MINOS²𝜎²_MINOS. (19)

The use of energy spectrum information in this analysis allows additional information on background rates to be gained from the fit, in particular because of the small number of IBD events between 8 and 12 MeV. The two fit parameters 𝜖_FN/SM and 𝜖_9Li are allowed to vary as part of the fit, and they scale the rates of the two backgrounds (correlated and cosmogenic isotopes). The rate of accidentals is not allowed to vary since its initial uncertainty is precisely determined in-situ. The energy scale for predicted signal and 9Li events is allowed to vary linearly according to the 𝛼_𝐸 parameter with an uncertainty 𝜎_𝛼𝐸=1.13%. A final parameter constrains the mass splitting Δ𝑚²₃₁ using the MINOS measurement [90] of Δ𝑚²₃₁=(2.32±0.12)×10⁻³eV², where we have symmetrized the error. This error includes the uncertainty introduced by relating the effective mass-squared difference observed in a 𝜈_𝜇 disappearance experiment to the one relevant for reactor experiments and the ambiguity due to the type of the neutrino mass hierarchy; see for example [91]. Uncertainties for these parameters, 𝜎_FN/SM, 𝜎_9Li, and 𝜎_MINOS, are listed as the initial values in Table 11. The best fit gives sin²2𝜃₁₃=0.109±0.030(stat.)±0.025(syst) at Δ𝑚²₃₁=2.32×10⁻³ eV², with a 𝜒²/NDF=42.1/35. Table 11 gives the resulting values of the fit parameters and their uncertainties. Comparing the values with the ones used as input to the fit in Table 9, we conclude that the background rate and uncertainties are further constrained in the fit, as well as the energy scale.

Table 11 

Parameters in the oscillation fit. Initial values are determined by measurements of background rates or detector calibration data. Best-fit values are outputs of the minimization procedure.

The final measured spectrum and the best-fit spectrum are shown in Figure 18 for the new and old data sets, and for both together in Figure 19.

Figure 18 

Measured prompt energy spectrum for each integration period (data points) superimposed on the expected prompt energy spectrum, including backgrounds (green region), for the no-oscillation (blue dotted curve) and best-fit (red solid curve), backgrounds at sin22𝜃13=0.109 and Δ𝑚231=2.32×10−3eV2. Inset: stacked spectra of backgrounds. Bottom: differences between data and no-oscillation prediction (data points) and differences between best-fit prediction and no-oscillation prediction (red curve). The orange band represents the systematic uncertainties on the best-fit prediction.

Figure 19 

Sum of both integration periods plotted in the same manner as Figure 18.

An analysis comparing only the total observed number of IBD candidates in each integration period to the expectations produces a best fit of sin²2𝜃₁₃=0.170±0.052 at 𝜒²/NDF=0.50/1. The compatibility probability for the rate-only and rate+shape measurements is about 30% depending on how the correlated errors are handled between the two measurements.

Confidence intervals for the standard analysis were determined using a frequentist technique [92]. This approach accommodates the fact that the true 𝜒² distributions may not be Gaussian and is useful for calculating the probability of excluding the no-oscillation hypothesis. This study compared the data to 10,000 simulations generated at each of 21 test points in the range 0≤sin²2𝜃₁₃≤0.25. A Δ𝜒² statistic, equal to the difference between the 𝜒² at the test point and the 𝜒² at the best fit, was used to determine the region in sin²2𝜃₁₃ where the Δ𝜒² of the data was within the given confidence probability. The allowed region at 68% (90%) CL is 0.068(0.044)<sin²2𝜃₁₃<0.15 (0.17). An analogous technique shows that the data exclude the no-oscillation hypothesis at 99.9% (3.1𝜎).

6. RENO

The reactor experiment for neutrino oscillation (RENO) has obtained a definitive measurement of the smallest neutrino mixing angle of 𝜃₁₃ by observing the disappearance of electron antineutrinos emitted from a nuclear reactor, excluding the no-oscillation hypothesis at 4.9𝜎. From the deficit, the best-fit value of sin²2𝜃₁₃ is obtained as 0.113±0.013(stat.)±0.019(syst.) based on a rate-only analysis.

Consideration of RENO began in early 2004, and its proposal was approved by the Ministry of Science and Technology in Korea in May 2005. The company operating the Yonggwang nuclear power plant, KHNP, has allowed us to carry out the experiment in a restricted area. The project started in March 2006. Geological survey was completed in 2007. Civil construction began in middle 2008 and was completed in early 2009. Both near and far detectors are completed in early 2011, and data taking began in early August 2011. RENO is the first experiment to measure 𝜃₁₃ with two identical detectors in operation.

6.1. Experimental Setup and Detection Method

RENO detects antineutrinos from six reactors at Yonggwang Nuclear Power Plant in Korea. A symmetric arrangement of the reactors and the detectors, as shown in Figure 20, is useful for minimizing the complexity of the measurement. The six pressurized water reactors with each maximum thermal output of 2.8GW_th (reactors 3, 4, 5, and 6) or 2.66 GW_th (reactors 1 and 2) are lined up in roughly equal distances and span ∼1.3 km.

Figure 20 

A schematic setup of the RENO experiment.

Two identical antineutrino detectors are located at 294 m and 1383 m, respectively, from the center of reactor array to allow a relative measurement through a comparison of the observed neutrino rates. The near detector is located inside a resticted area of the nuclear power plant, quite close to the reactors to make an accurate measurement of the antineutrino fluxes before their oscillations. The far (near) detector is beneath a hill that provides 450 m (120 m) of water-equivalent rock overburden to reduce the cosmic backgrounds.

The measured far-to-near ratio of antineutrino fluxes can considerably reduce systematic errors coming from uncertainties in the reactor neutrino flux, target mass, and detection efficiency. The relative measurement is independent of correlated uncertainties and helps to minimize uncorrelated reactor uncertainties.

The positions of two detectors and six reactors are surveyed with GPS and total station to determine the baseline distances between detector and reactor to an accuracy of less than 10 cm. The accurate measurement of the baseline distances finds the reduction of reactor neutrino fluxes at detector to a precision of much better than 0.1%. The reactor-flux-weighted baseline is 408.56 m for the near detector and 1443.99 m for the far detector.

6.2. Detector

Each RENO detector (Figure 21) consists of a main inner detector (ID) and an outer veto detector (OD). The main detector is contained in a cylindrical stainless steel vessel that houses two nested cylindrical acrylic vessels. The innermost acrylic vessel holds 18.6 m³ (16.5 t) ∼0.1% Gadolinium-(Gd-) doped liquid scintillator (LS) as a neutrino target. An electron antineutrino can interact with a free proton in LS, 𝜈_𝑒+𝑝→𝑒⁺+𝑛. The coincidence of a prompt positron signal and a delayed signal from neutron capture by Gd provides the distinctive signature of inverse 𝛽 decay.

Figure 21 

A schematic view of the RENO detector. The near and far detectors are identical.

The central target volume is surrounded by a 60 cm thick layer of LS without Gd, useful for catching 𝛾-rays escaping from the target region and thus increasing the detection efficiency. Outside this 𝛾-catcher, a 70 cm thick buffer layer of mineral oil provides shielding from radioactivity in the surrounding rocks and in the 354 10-inch photomultipliers (PMTs) that are mounted on the inner wall of the stainless steel container.

The outermost veto layer of OD consists of 1.5 m of highly purified water in order to identify events coming from outside by their Cherenkov radiation and to shield against ambient 𝛾-rays and neutrons from the surrounding rocks.

The LS is developed and produced as a mixture of linear alkyl benzene (LAB), PPO, and bis-MSB. A Gd-carboxylate complex using TMHA was developed for the best Gd loading efficiency into LS and its long-term stability. Gd-LS and LS are made and filled into the detectors carefully to ensure that the near and far detectors are identical.

6.3. Data Sample

In the 229 day data-taking period between 11 August 2011 to 26 March 2012, the far (near) detector observed 17102 (154088) electron antineutrino candidate events or 77.02±0.59 (800.8±2.0) events/day with a background fraction of 5.5% (2.7%). During this period, all six reactors were mostly on at full power, and reactors 1 and 2 were off for a month each because of fuel replacement.

Event triggers are formed by the number of PMTs with signals above a ∼0.3 photoelectron (pe) threshold (NHIT). An event is triggered and recorded if the ID NHIT is larger than 90, corresponding to 0.5∼0.6 MeV well below the 1.02 MeV as the minimum energy of an IBD positron signal or if the OD NHIT is larger than 10.

The event energy is measured based on the total charge (𝑄_tot) in pe, collected by the PMTs and corrected for gain variation. The energy calibration constant of 250 pe per MeV is determined by the peak energies of various radioactive sources deployed at the center of the target.

6.4. Background

In the final data samples, uncorrelated (accidentals) and correlated (fast neutrons from outside of ID, stopping muon followers and 𝛽-n emitters from 9Li/8He) background events survive selection requirements. The total background rate is estimated to be 21.75±5.93 (near) or 4.24±0.75(far) events per day and summarized in Table 12.

Table 12 

Event rates of the observed candidates and the estimated background.

The uncorrelated background is due to accidental coincidences from random association of a prompt-like event due to radioactivity and a delayed-like neutron capture. The remaining rate in the final sample is estimated to be 4.30±0.06(near) or 0.68±0.03(far) events per day.

The 9Li/8He 𝛽-n emitters are mostly produced by energetic muons because their production cross-sections in carbon increase with muon energy. The background rate in the final sample is obtained as 12.45±5.93(near) or 2.59±0.75 (far) events per day from a fit to the delay time distribution with an observed mean decay time of ∼250 ms.

An energetic neutron entering the ID can interact in the target to produce a recoil proton before being captured on Gd. Fast neutrons are produced by cosmic muons traversing the surrounding rock and the detector. The estimated fast neutron background is 5.00±0.13(near) or 0.97±0.06(far) events per day.

6.5. Systematic Uncertainty

The combined absolute uncertainty of the detection efficiency is correlated between the two detectors and estimated to be 1.5%. Uncorrelated relative detection uncertainties are estimated by comparing the two identical detectors. They come from relative differences between the detectors in energy scale, target protons, Gd capture ratio, and others. The combined uncorrelated detection uncertainty is estimated to be 0.2%.

The uncertainties associated with thermal power and relative fission fraction contribute to 0.9% of the 𝜈_𝑒 yield per core to the uncorrelated uncertainty. The uncertainties associated with 𝜈_𝑒 yield per fission, fission spectra, and thermal energy released per fission result in a 2.0% correlated uncertainty. We assume a negligible contribution of the spent fuel to the uncorrelated uncertainty.

6.6. Results

All reactors were mostly in steady operation at the full power during the data-taking period, except for reactor 2 (R2), which was off for the month of September 2011, and reactor 1 (R1), which was off from February 23 2012 for fuel replacement. Figure 22 presents the measured daily rates of IBD candidates after background subtraction in the near and far detectors. The expected rates assuming no oscillation, obtained from the weighted fluxes by the thermal power and the fission fractions of each reactor and its baseline to each detector, are shown for comparison.

Figure 22 

Measured daily-average rates of reactor neutrinos after background subtraction in the near and far detectors as a function of running time. The solid curves are the predicted rates for no oscillation.

Based on the number of events at the near detector and assuming no oscillation, RENO finds a clear deficit, with a far-to-near ratio 𝑅=0.920±0.009(stat.)±0.014syst.. (20)

The value of sin²2𝜃₁₃ is determined from a 𝜒² fit with pull terms on the uncorrelated systematic uncertainties. The number of events in each detector after the background subtraction has been compared with the expected number of events, based on the reactor neutrino flux, detection efficiency, neutrino oscillations, and contribution from the reactors to each detector determined by the baselines and reactor fluxes.

The best-fit value thus obtained is sin²2𝜃₁₃=0.113±0.013(stat.)±0.019syst., (21) and it excludes the no-oscillation hypothesis at the 4.9 standard deviation level.

RENO has observed a clear deficit of 8.0% for the far detector and of 1.2% for the near detector, concluding a definitive observation of reactor antineutrino disappearance consistent with neutrino oscillations. The observed spectrum of IBD prompt signals in the far detector is compared to the non oscillation expectations based on measurements in the near detector in Figure 23. The spectra of prompt signals are obtained after subtracting backgrounds shown in the inset. The disagreement of the spectra provides further evidence of neutrino oscillation.

(a)

(b)

Figure 23 

Observed spectrum of the prompt signals in the far detector compared with the nonoscillation predictions from the measurements in the near detector. The backgrounds shown in the inset are subtracted for the far spectrum. The background fraction is 5.5% (2.7%) for far (near) detector. Errors are statistical uncertainties only. (b) The ratio of the measured spectrum of far detector to the non-oscillation prediction.

In summary, RENO has observed reactor antineutrinos using two identical detectors each with 16 tons of Gd-loaded liquid scintillator and a 229 day exposure to six reactors with total thermal energy of 16.5 GW_th. In the far detector, a clear deficit of 8.0% is found by comparing a total of 17102 observed events with an expectation based on the near detector measurement assuming no oscillation. From this deficit, a rate-only analysis obtains sin²2𝜃₁₃=0.113±0.013 (stat.) ±0.019 (syst.). The neutrino mixing angle 𝜃₁₃ is measured with a significance of 4.9 standard deviation.

6.7. Future Prospects and Plan

RENO has measured the value of sin²2𝜃₁₃ with a total error of ±0.023. The expected sensitivity of RENO is to obtain ±0.01 for the error based on the three years of data, leading to a statistical error of 0.006 and a systematic error of ∼0.005.

The fast neutron and 9Li/8He backgrounds produced by cosmic muons depend on the detector sites having different overburdens. Therefore, their uncertainties are the largest contribution to the uncorrelated error in the current result, and change the systematic error by 0.017 at the best-fit value.

RENO makes efforts on further reduction of backgrounds, especially by removing the 9Li/8He background by a tighter muon veto requirement and a spectral shape analysis to improve the systematic error. A longer-term effort will be made to reduce the systematic uncertainties of reactor neutrino flux and detector efficiency.

7. The Reactor Antineutrino Anomaly-Thierry

7.1. New Predicted Cross-Section per Fission

Fission reactors release about 10²⁰𝜈_𝑒GW⁻¹s⁻¹, which mainly come from the beta decays of the fission products of 235U, 238U, 239Pu, and 241Pu. The emitted antineutrino spectrum is then given by 𝑆_tot(𝐸_𝜈)=∑_𝑘𝑓_𝑘𝑆_𝑘(𝐸_𝜈), where 𝑓_𝑘 refers to the contribution of the main fissile nuclei to the total number of fissions of the kth branch and 𝑆_𝑘 to their corresponding neutrino spectrum per fission. Antineutrino detection is achieved via the inverse beta-decay (IBD) reaction 𝜈_𝑒+¹H→𝑒⁺+𝑛. Experiments at baselines below 100 m reported either the ratios (𝑅) of the measured to predicted cross-section per fission, or the observed event rate to the predicted rate.

The event rate at a detector is predicted based on the following formula: 𝑁^Pred_𝜈𝑠⁻¹=14𝜋𝐿²𝑁_𝑝𝑃_th𝐸_𝑓𝜎^pred_𝑓, (22) where the first term stands for the mean solid angle and 𝑁_𝑝 is the number of target protons for the inverse beta-decay process of detection. These two detector-related quantities are usually known with very good accuracy. The last two terms come from the reactor side. The ratio of 𝑃_th, the thermal power of the reactor, over ⟨𝐸_𝑓⟩, the mean energy per fission, provide the mean number of fissions in the core. 𝑃_th can be known at the subpercent level in commercial reactors, somewhat less accurately at research reactors. The mean energy per fission is computed as the average over the four main fissioning isotopes, accounting for 99.5% of the fissions 𝐸_𝑓=_𝑘𝐸_𝑘,𝑘=²³⁵U,²³⁸U,²³⁹Pu,²⁴¹Pu. (23)

It is accurately known from the nuclear databases and study of all decays and neutron captures subsequent to a fission [72]. Finally, the dominant source of uncertainty and by far the most complex quantity to compute is the mean cross-section per fission defined as 𝜎^pred_𝑓=^∞₀𝑆_tot𝐸_𝜈𝜎_V−A𝐸_𝜈𝑑𝐸_𝜈=_𝑘𝑓_𝑘𝜎^pred_𝑓,𝑘, (24) where the 𝜎^pred_𝑓,𝑘 is the predicted cross-sections for each fissile isotope, 𝑆_tot is the model dependent reactor neutrino spectrum for a given average fuel composition (𝑓_𝑘), and 𝜎_V−A is the theoretical cross-section of the IBD reaction: 𝜎_V−A𝐸_𝑒cm²=857×10⁻⁴³𝜏_𝑛[s]𝑝_𝑒[MeV]×𝐸_𝑒[MeV]1+𝛿_rec+𝛿_wm+𝛿_rad, (25) where 𝛿_rec, 𝛿_wm, and 𝛿_rad are, respectively, the nucleon recoil, weak magnetism, and radiative corrections to the cross-section (see [22, 93] for details). The fraction of fissions undergone by the kth isotope, 𝑓_𝑘, can be computed at the few percent level with reactor evolution codes (see for instance [79]), but their impact in the final error is well reduced by the sum rule of the total thermal power, accurately known from independent measurements

Accounting for new reactor antineutrino spectra [32] the normalization of predicted antineutrino rates, 𝜎^pred_𝑓,𝑘, is shifted by +3.7%, +4.2%, +4.7%, and +9.8% for 𝑘=²³⁵U, 239Pu, 241Pu, and 238U, respectively. In the case of 238U, the completeness of nuclear databases over the years largely explains the +9.8% shift from the reference computations [22].

The new predicted cross-section for any fuel composition can be computed from (24). By default, the new computation takes into account the so-called off-equilibrium correction [22] of the antineutrino fluxes (increase in fluxes caused by the decay of long-lived fission products). Individual cross-sections per fission per fissile isotope are slightly different, by +1.25% for the averaged composition of Bugey-4 [10], with respect to the original publication of the reactor antineutrino anomaly [93] because of the slight upward shift of the antineutrino flux consecutive to the work of [32] (see Section 2.2 for details).

7.2. Impact of the New Reactor Neutrino Spectra on Past Short-Baseline (<100 m) Experimental Results

In the eighties and nineties, experiments were performed with detectors located a few tens of meters from nuclear reactor cores at ILL, Goesgen, Rovno, Krasnoyarsk, Bugey (phases 3 and 4), and Savannah River [7–15]. In the context of the search of 𝒪(eV) sterile neutrinos, these experiments, with baselines below 100 m, have the advantage that they are not sensitive to a possible θ₁₃-, Δ𝑚²₃₁-driven oscillation effect (unlike the Palo Verde and CHOOZ experiments, for instance).

The ratios of observed event rates to predicted event rates (or cross-section per fission), 𝑅=𝑁_obs/𝑁_pred, are summarized in Table 13. The observed event rates and their associated errors are unchanged with respect to the publications; the predicted rates are reevaluated separately in each experimental case. One can observe a general systematic shift more or less significantly below unity. These reevaluations unveil a new reactor antineutrino anomaly (http://irfu.cea.fr/en/Phocea/Vie_des_labos/Ast/ast_visu.php?id_ast=3045) [93], clearly illustrated in Figure 24. In order to quantify the statistical significance of the anomaly, one can compute the weighted average of the ratios of expected-over-predicted rates, for all short-baseline reactor neutrino experiments (including their possible correlations).

Table 13 

𝑁_obs/𝑁_pred ratios based on old and new spectra. Off-equilibrium corrections have been applied when justified. The err column is the total error published by the collaborations including the error on 𝑆_tot, and the corr column is the part of the error correlated among experiments (multiple baseline or same detector).

Figure 24 

Short-baseline reactor antineutrino anomaly. The experimental results are compared to the prediction without oscillation, taking into account the new antineutrino spectra, the corrections of the neutron mean lifetime, and the off-equilibrium effects. Published experimental errors and antineutrino spectra errors are added in quadrature. The mean-averaged ratio including possible correlations is 0.927±0.023. As an illustration, the red line shows a 3 active neutrino mixing solution fitting the data, with sin2(2𝜃13)=0.15. The blue line displays a solution including a new neutrino mass state, such as |Δ𝑚2new,𝑅|≫2eV2 and sin2(2𝜃new,𝑅) = 0.12, as well as sin2(2𝜃13)=0.085.

In doing so, the authors of [93] have considered the following experimental rate information: Bugey-4 and Rovno91, the three Bugey-3 experiments, the three Goesgen experiments and the ILL experiment, the three Krasnoyarsk experiments, the two Savannah River results (SRP), and the five Rovno88 experiments. ^→𝑅 is the corresponding vector of 19 ratios of observed-to-predicted event rates. A 2.0% systematic uncertainty was assumed, fully correlated among all 19 ratios, resulting from the common normalization uncertainty of the beta spectra measured in [19–21]. In order to account for the potential experimental correlations, the experimental errors of Bugey-4 and Rovno91, of the three Goesgen and the ILL experiments, the three Krasnoyarsk experiments, the five Rovno88 experiments, and the two SRP results were fully correlated. Also, the Rovno88 (1I and 2I) results were fully correlated with Rovno91, and an arbitrary 50% correlation was added between the Rovno88 (1I and 2I) and the Bugey-4 measurement. These latest correlations are motivated by the use of similar or identical integral detectors.

In order to account for the non-Gaussianity of the ratios 𝑅 a Monte Carlo simulation was developed to check this point, and it was found that the ratios distribution is almost Gaussian, but with slightly longer tails, which were taken into account in the calculations (in contours that appear later, error bars are enlarged). With the old antineutrino spectra, the mean ratio is 𝜇=0.980±0.024.

With the new antineutrino spectra, one obtains 𝜇=0.927±0.023, and the fraction of simple Monte Carlo experiments with 𝑟≥1 is 0.3%, corresponding to a −2.9𝜎 effect (while a simple calculation assuming normality would lead to −3.2𝜎). Clearly, the new spectra induce a statistically significant deviation from the expectation. This motivates the definition of an experimental cross-section 𝜎^ano_𝑓^,2012=0.927×𝜎^pred,new_𝑓. With the new antineutrino spectra, the minimum 𝜒² for the data sample is 𝜒²_min,data=18.4. The fraction of simple Monte Carlo experiments with 𝜒²_min<𝜒²_min,data is 50%, showing that the distribution of experimental ratios in ^→𝑅 around the mean value is representative given the correlations.

Assuming the correctness of 𝜎^pred,new_𝑓, the anomaly could be explained by a common bias in all reactor neutrino experiments. The measurements used different detection techniques (scintillator counters and integral detectors). Neutrons were tagged either by their capture in metal-loaded scintillator, or in proportional counters, thus leading to two distinct systematics. As far as the neutron detection efficiency calibration is concerned, note that different types of radioactive sources emitting MeV or sub-MeV neutrons were used (Am-Be, 252Cf, Sb-Pu, and Pu-Be). It should be mentioned that the Krasnoyarsk, ILL, and SRP experiments operated with nuclear fuel such that the difference between the real antineutrino spectrum and that of pure 235U was less than 1.5%. They reported similar deficits to those observed at other reactors operating with a mixed fuel. Hence, the anomaly can be associated neither with a single fissile isotope nor with a single detection technique. All these elements argue against a trivial bias in the experiments, but a detailed analysis of the most sensitive of them, involving experts, would certainly improve the quantification of the anomaly.

The other possible explanation of the anomaly is based on a real physical effect and is detailed in the next section. In that analysis, shape information from the Bugey-3 and ILL-published data [7, 8] is used. From the analysis of the shape of their energy spectra at different source-detector distances [8, 9], the Goesgen and Bugey-3 measurements exclude oscillations with 0.06<Δ𝑚²<1eV² for sin²(2𝜃)>0.05. Bugey-3's 40 m/15 m ratio data from [8] is used as it provides the best limit. As already noted in [94], the data from ILL showed a spectral deformation compatible with an oscillation pattern in their ratio of measured over predicted events. It should be mentioned that the parameters best fitting the data reported by the authors of [94] were Δ𝑚²=2.2eV² and sin²(2𝜃)=0.3. A reanalysis of the data of [94] was carried out in order to include the ILL shape-only information in the analysis of the reactor antineutrino anomaly. The contour in Figure14 of [7] was reproduced for the shape-only analysis (while for the rate-only analysis discussed above that of [94] was reproduced, excluding the no-oscillation hypothesis at 2𝜎).

7.3. The Fourth Neutrino Hypothesis (3+1 Scenario)

7.3.1. Reactor Rate-Only Analysis

The reactor antineutrino anomaly could be explained through the existence of a fourth nonstandard neutrino, corresponding in the flavor basis to a sterile neutrino 𝜈_𝑠 with a large Δ𝑚²_new value.

For simplicity, the analysis presented here is restricted to the 3+1 four-neutrino scheme in which there is a group of three active neutrino masses separated from an isolated neutrino mass, such that |Δ𝑚²_new|≫10⁻²eV². The latter would be responsible for very short-baseline reactor neutrino oscillations. For energies above the IBD threshold and baselines below 100 m, the approximated oscillation formula 𝑃_𝑒𝑒=1−sin²2𝜃_newsin²Δ𝑚²_new𝐿4𝐸_𝜈𝑒 (26) is adopted, where active neutrino oscillation effects are neglected at these short baselines. In such a framework, the mixing angle is related to the 𝑈 matrix element by the relation: sin²2𝜃_new=4𝑈_𝑒4²1−𝑈_𝑒4². (27)

One can now fit the sterile neutrino hypothesis to the data (baselines below 100 m) by minimizing the least-squares function 𝑃_𝑒𝑒−^→𝑅^𝑇𝑊⁻¹𝑃_𝑒𝑒−^→𝑅, (28) assuming sin²(2𝜃₁₃)=0. Figure 25 provides the results of the fit in the sin²(2𝜃_new)−Δ𝑚²_new plane, including only the reactor experiment rate information. The fit to the data indicates that |Δ𝑚²_new,𝑅|>0.2 eV² (99%) and sin²(2𝜃_new,𝑅)∼0.14. The best-fit point is at |Δ𝑚²_new,𝑅|=0.5eV² and sin²(2𝜃_new,𝑅)∼0.14. The no-oscillation analysis is excluded at 99.8%, corresponding roughly to 3𝜎.

(a)

(b)

Figure 25 

(a) Allowed regions in the sin2(2𝜃new)−Δ𝑚2new plane obtained from the fit of the reactor neutrino data, without any energy spectra information, to the 3+1 neutrino hypothesis, with sin2(2𝜃13)=0. The best-fit point is indicated by a star. (b) Allowed regions in the sin2(2𝜃new)−Δ𝑚2new plane obtained from the fit of the reactor neutrino data, without ILL-shape information, but with the stringent oscillation constraint of Bugey-3 based on the 40 m/15 m ratios to the 3+1 neutrino hypothesis, with sin2(2𝜃13)=0. The best-fit point is indicated by a star.

7.3.2. Reactor Rate+Shape Analysis

The ILL experiment may have seen a hint of oscillation in their measured positron energy spectrum [7, 94], but Bugey-3’s results do not point to any significant spectral distortion more than 15 m away from the antineutrino source. Hence, in a first approximation, hypothetical oscillations could be seen as an energy-independent suppression of the 𝜈_𝑒 rate by a factor of (1/2)sin²(2𝜃_new,𝑅), thus leading to Δ𝑚²_new,𝑅>1eV² and accounting for the Bugey-3 and Goesgen shape analyses [8, 9]. Considering the weighted average of all reactor experiments, one obtains an estimate of the mixing angle, sin²(2𝜃_new,𝑅)∼0.15. The ILL positron spectrum is thus in agreement with the oscillation parameters found independently in the reanalyses mainly based on rate information. Because of the differences in the systematic effects in the rate and shape analyses, this coincidence is in favor of a true physical effect rather than an experimental anomaly. Including the finite spatial extension of the nuclear reactors and the ILL and Bugey-3 detectors, it is found that the small dimensions of the ILL nuclear core lead to small corrections of the oscillation pattern imprinted on the positron spectrum. However, the large extension of the Bugey nuclear core is sufficient to wash out most of the oscillation pattern at 15 m. This explains the absence of shape distortion in the Bugey-3 experiment. We now present results from a fit of the sterile neutrino hypothesis to the data including both Bugey-3 and ILL original results (no-oscillation reported). With respect to the rate only parameters, the solutions at lower |Δ𝑚²_{new,𝑅+𝑆}| are now disfavored at large mixing angle because they would have imprinted a strong oscillation pattern in the energy spectra (or their ratio) measured at Bugey-3 and ILL. The best fit point is moved to |Δ𝑚²_{new,𝑅+𝑆}|=2.4eV², whereas the mixing angle remains almost unchanged, at sin²(2𝜃_{new,𝑅+𝑆})∼0.14. The no-oscillation hypothesis is excluded at 99.6%, corresponding roughly to 2.9𝜎. Figure 25 provides the results of the fit in the sin²(2𝜃_new)−Δ𝑚²_new plane, including both the reactor experiment rate and shape (Bugey-3 and ILL) data.

7.4. Combination of the Reactor and the Gallium Anomalies

It is also possible to combine the results on the reactor antineutrino anomaly with the results on the gallium anomaly. The goal is to quantify the compatibility of the reactor and the gallium data.

For the reanalysis of the Gallex and Sage calibration runs with 51Cr and 37Ar radioactive sources emitting ∼1 MeV electron neutrinos [95–100], the methodology developed in [101] is used. However, in the analysis shown here, possible correlations between these four measurements are included. Details are given in [93]. This has the effect of being slightly more conservative, with the no-oscillation hypothesis disfavored at 97.7% C.L. Gallex and Sage observed an average deficit of 𝑅_𝐺=0.86±0.06(1𝜎). The best-fit point is at |Δ𝑚²_gallium|=2.4eV² (poorly defined), whereas the mixing angle is found to be sin²(2𝜃_gallium)∼0.27±0.13. Note that the best-fit values are very close to those obtained by the analysis of the rate+shape reactor data.

Combing both the reactor and the gallium data, The no-oscillation hypothesis is disfavored at 99.97% C.L (3.6𝜎). Allowed regions in the sin²(2𝜃_new)−Δ𝑚²_new plane are displayed in Figure 26, together with the marginal Δ𝜒² profiles for |Δ𝑚²_new| and sin²(2𝜃_new). The combined fit leads to the following constraints on oscillation parameters: |Δ𝑚²_new|>1.5eV² (99% C.L.) and sin²(2𝜃_new)=0.17±0.04 (1𝜎). The most probable |Δ𝑚²_new| is now rather better defined with respect to what has been published in [93], at |Δ𝑚²_new|=2.3±0.1eV².

Figure 26 

Allowed regions in the sin2(2𝜃new)−Δ𝑚2new plane from the combination of reactor neutrino experiments, the Gallex and Sage calibration sources experiments, and the ILL and Bugey-3-energy spectra. The data are well fitted by the 3+1 neutrino hypothesis, while the no-oscillation hypothesis is disfavored at 99.97% C.L (3.6𝜎).

7.5. Status of the Reactor Antineutrino Anomaly

The impact of the new reactor antineutrino spectra has been extensively studied in [93]. The increase of the expected antineutrino rate by about 4.5% combined with revised values of the antineutrino cross-section significantly decreased the normalized ratio of observed-to-expected event rates in all previous reactor experiments performed over the last 30 years at distances below 100 m [7–15]. The new average ratio, updated early 2012, is now 0.927±0.023, leading to an enhancement of reactor antineutrino anomaly, now significant at the 3𝜎 confidence level. The best-fit point is at |Δ𝑚²_{new,𝑅+𝑆}|=2.4eV² whereas the mixing angle is at sin²(2𝜃_{new,𝑅+𝑆})∼0.14.

This deficit could still be due to some unknown in the reactor physics, but it can also be analyzed in terms of a suppression of the 𝜈_𝑒 rate at short distance as could be expected from a sterile neutrino, beyond the standard model, with a large |Δ𝑚²_new|≫|Δ𝑚²₃₁|. Note that hints of such results were already present at the ILL neutrino experiment in 1981 [94].

Considering the reactor 𝜈_𝑒 anomaly and the gallium 𝜈_𝑒 source experiments [95–101] together, it is interesting to note that in both cases (neutrinos and antineutrinos) comparable deficits are observed at a similar 𝐿/𝐸. Furthermore, it turns out that each experiment fitted separately leads to similar values of sin²(2𝜃_new) and similar lower bounds for |Δ𝑚²_new| but without a strong significance. A combined global fit of gallium data and of short-baseline reactor data, taking into account the reevaluation of the reactor results discussed here, as well as the existing correlations, leads to a solution for a new neutrino oscillation, such that |Δ𝑚²_new|>1.5eV² (99% C.L.) and sin²(2𝜃_new)=0.17±0.04 (1𝜎), disfavoring the no-oscillation case at 99.97% C.L (3.6𝜎). The most probable |Δ𝑚²_new| is now at |Δ𝑚²_new|=2.3±0.1eV². This hypothesis should be checked against systematical effects, either in the prediction of the reactor antineutrino spectra or in the experimental results.

8. Reactor Monitoring for Nonproliferation of Nuclear Weapons

In the past, neutrino experiments have only been used for fundamental research, but today, thanks to the extraordinary progress of the field, for example, the measurement of the oscillation parameters, neutrinos could be useful for society.

The International Atomic Energy Agency (IAEA) works with its member states to promote safe, secure, and peaceful nuclear technologies. One of its missions is to verify that safeguarded nuclear material and activities are not used for military purposes. In a context of international tension, neutrino detectors could help the IAEA to verify the treaty on the non-proliferation of nuclear weapons (NPT), signed by 145 states around the world.

A small neutrino detector located at a few tens of meters from a nuclear core could monitor nuclear reactor cores nonintrusively, robustly, and automatically. Since the antineutrino spectra and relative yields of fissioning isotopes 235U, 238U, 239Pu, and 241Pu depend on the isotopic composition of the core, small changes in composition could be observed without ever directly accessing the core itself. Information from a modest-sized antineutrino detector, coupled with the well-understood principles that govern the core's evolution in time, can be used to determine whether the reactor is being operated in an illegitimate way. Furthermore, such a detector can help to improve the reliability of the operation, by providing an independent and accurate measurement, in real time, of the thermal power and its reactivity at a level of a few percent. The intention is to design an “optimal” monitoring detector by using the experience obtained from neutrino physics experiments and feasibility studies.

Sands is a one cubic meter antineutrino detector located at 25 meters from the core of the San Onofre reactor site in California [102]. The detector has been operating for several months in an automatic and nonintrusive fashion that demonstrates the principles of reactor monitoring. Although the signal-to-noise ratio of the current design is still less than two, it is possible to monitor the thermal power at a level of a few percent in two weeks. At this stage of the work, the study of the evolution of the fuel seems difficult, but this has already been demonstrated by the Bugey and Rovno experiments.

The NUCIFER experiment in France [103], a 850 liters Gd-doped liquid scintillator detector installed at 7 m from the Osiris nuclear reactor core at CEA-Saclay. The goal is the measurement of its thermal power and plutonium content. The design of such a small volume detector has been focused on high detection efficiency and good background rejection. The detector is being operated to since May 2012, and first results are expected in 2013.

The near detectors of Daya Bay, RENO, and Double Chooz will be a research detector with a very high sensitivity to study neutrino oscillations. Millions of events are being detected in the near detectors (between 300 and 500 m away from the cores). These huge statistics could be exploited to help the IAEA in its safeguards missions. The potential of neutrinos to detect various reactor diversion scenario’s can be tested.

A realistic reactor monitor is likely to be somewhere between the two concepts presented above.

9. Future Prospects

Reactors are powerful neutrino sources for free. It is a well understood source since the precision of the neutrino flux and energy spectrum is better than 2%. With a near detector, this uncertainty can be reduced to 0.3%. Clearly, this is much better than usual neutrinos sources such as accelerators, solar, and atmospheric neutrinos. If a detector is placed at different baseline, an experiment with different motivation can be planned.

9.1. Mass Hierarchy

With the discovery of the unexpected large 𝜃₁₃, mass hierarchy and even the CP phase become accessible with nowadays technologies. A number of new projects are now proposed based on different neutrino sources and different types of detectors.

It is known that neutrino mass hierarchy can be determined by long-baseline (more than 1000 km) accelerator experiment through matter effects. Atmospheric neutrinos may also be used for this purpose using a huge detector. Neutrino mass hierarchy can in fact distort the energy spectrum from reactors [104, 105], and a Fourier transformation of the spectrum can enhance the signature since mass terms appear in the frequency regime of the oscillation probability [106].

It is also shown that by employing a different Fourier transformation as the following: FCT(𝜔)=^𝑡max_𝑡min𝐹(𝑡)()(𝜔)=cos𝜔𝑡d𝑡,FST^𝑡max_𝑡min𝐹(𝑡)sin(𝜔𝑡)d𝑡, (29) the signature of mass hierarchy is more evident, and it is independent of the precise knowledge of Δ²₂₃ [107].

The normal hierarchy and inverted hierarchy have very different shapes of the energy spectrum after the Fourier transformation. A detailed Monte Carlo study [108] shows that if sin²2𝜃₁₃ is more than (1-2)%, a (10–50), kt liquid scintillator at a baseline of about 60 km with an energy resolution better than (2-3)% can determine the mass hierarchy at more than 90% C L In fact, with sin²2𝜃₁₃=0.1, the mass hierarchy can be determined up to the 3𝜎 level with a nominal detector size of 20 kt and a detector energy resolution of 3%.

The group at the Institute of High Energy Physics in Beijing proposed such an experiment in 2008. Fortunately, at a distance of 60 km from Daya Bay, there is a mountain with overburden more than 1500 MWE, where an underground lab can be built. Moreover, this location is 60 km from another nuclear power plant to be built, as shown in Figure 27. The total number of reactors, 6 operational and 6 to be built, may give a total thermal power of more than 35 GW.

Figure 27 

The new site for a long-baseline reactor neutrino experiment.

A conceptual design of the detector is shown in Figure 28. The detector is 30 m in diameter and 30 m high, filled with 20 kt liquid scintillator. The oil buffer will be 6 kt and water buffer is 10 kt. The totally needed number of 20′′ PMTs is 15000, covering 80% of the surface area.

Figure 28 

A conceptual design of a large liquid scintillator detector.

There are actually two main technical difficulties for such a detector. The attenuation length of the liquid scintillator should be more than 30 m, and the quantum efficiency of PMTs should be more than 40%. R&D efforts are now started at IHEP, and results will be reported in the near future.

There is another proposed project to construct an underground detector of RENO-50 [109]. It consists of 5,000 tons of ultralow-radioactivity liquid scintillator and photomultiplier tubes, located at roughly 50 km away from the Yonggwang nuclear power plant in Korea, where the neutrino oscillation due to 𝜃₁₂ takes place at maximum. RENO-50 is expected to detect neutrinos from nuclear reactors, the sun, supernova, the earth, any possible stellar object, and a J-PARC neutrino beam. It could be served as a multipurpose and long-term operational detector including a neutrino telescope. The main goal is to measure the most accurate (1%) value of 𝜃₁₂ and to attempt determination of the neutrino mass hierarchy.

9.2. Precision Measurement of Mixing Parameters

A 20 kt liquid scintillator can have a long list of physics goals. In addition to neutrino mass hierarchy, neutrino mixing parameters including 𝜃₁₂, Δ𝑚²₁₂ and Δ𝑚²₂₃ can be measured at the ideal baseline of 60 km to a precision better than 1%. Combined with results from other experiments for 𝜃₂₃ and 𝜃₁₃, the unitarity of the neutrino mixing matrix can be tested up to 1% level, much better than that in the quark sector for the CKM matrix. This is very important to explore the physics beyond the standard model, and issues like sterile neutrinos can be studied.

In fact, for this purpose, there is no need to require extremely good energy resolution and huge detectors. Some of the current members of the RENO group indeed proposed a 5 kt liquid scintillator detector exactly for this purpose [109]. If funding is approved, they can start right away based on the existing technology.

9.3. Others

A large liquid scintillator detector is also ideal for supernova neutrinos since it can determine neutrino energies for different flavors, much better than flavor-blind detectors. Geoneutrinos can be another interesting topic, together with other traditional topics such as atmospheric neutrinos, solar neutrinos, and exotic searches.

10. Conclusions and Outlook

Three reactor experiments have definitively measured the value of sin²2𝜃₁₃ based on the disappearance of electron antineutrinos. Based on unprecedentedly copious data, Daya Bay and RENO have performed rather precise measurements of the value. Averaging the results of the three reactor experiments with the standard Particle Data Group method, one obtains sin²2𝜃₁₃=0.098±0.013 [110]. It took 14 years to measure all three mixing angles after the discovery of neutrino oscillation in 1998.

The exciting result of solving the longstanding secret provides a comprehensive picture of neutrino transformation among three kinds of neutrinos and opens the possibility of searching for CP violation in the lepton sector. The surprisingly large value of 𝜃₁₃ will strongly promote the next round of neutrino experiments to find CP violation effects and determine the neutrino mass hierarchy. The relatively large value has already triggered reconsideration of future long-baseline neutrino oscillation experiments. The successful measurement of 𝜃₁₃ has made the very first step on the long journey to the complete understanding of the fundamental nature and implications of neutrino masses and mixing parameters.