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# Double Chooz θ13 measurement via total neutron capture detection

## Abstract

Neutrinos were assumed to be massless particles until the discovery of the neutrino oscillation process. This phenomenon indicates that the neutrinos have non-zero masses and the mass eigenstates (ν1, ν2, ν3) are mixtures of their flavour eigenstates (νe, νμ, ντ). The oscillations between different flavour eigenstates are described by three mixing angles (θ12, θ23, θ13), two differences of the squared neutrino masses of the ν2/ν1 and ν3/ν1 pairs and a charge conjugation parity symmetry violating phase δCP. The Double Chooz experiment, located near the Chooz Electricité de France reactors, measures the oscillation parameter θ13 using reactor neutrinos. Here, the Double Chooz collaboration reports the measurement of the mixing angle θ13 with the new total neutron capture detection technique from the full data set, yielding sin2(2θ13) = 0.105 ± 0.014. This measurement exploits the multidetector configuration, the isoflux baseline and data recorded when the reactors were switched off. In addition to the neutrino mixing angle measurement, Double Chooz provides a precise measurement of the reactor neutrino flux, given by the mean cross-section per fission 〈σf〉 = (5.71 ± 0.06) × 10−43 cm2 per fission, and reports an empirical model of the distortion in the reactor neutrino spectrum.

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## Data availability

All data that support the plots within this paper and other findings of this study are available from the corresponding authors (C.B. and A.C.) upon reasonable request.

## Code availability

Most of the data analysis code is ROOT-based and custom developed by the DC collaboration and is available from the corresponding authors (C.B. and A.C.) upon reasonable request.

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## Acknowledgements

This publication is dedicated to our colleague Hervé de Kerret. We thank the company EDF (‘Electricity of France’), the European fund FEDER, the Région Grand Est (formerly known as the Région Champagne-Ardenne), the Département des Ardennes and the Communauté de Communes Ardenne Rives de Meuse. We acknowledge the support of the CEA, CNRS/IN2P3, the computer centre CC-IN2P3 and LabEx UnivEarthS in France; the Max Planck Gesellschaft, the Deutsche Forschungsgemeinschaft DFG, the Transregional Collaborative Research Centre TR27, the excellence cluster ‘Origin and Structure of the Universe’ and the Maier-Leibnitz-Laboratorium Garching in Germany; the Ministry of Education, Culture, Sports, Science and Technology of Japan (MEXT) and the Japan Society for the Promotion of Science (JSPS) in Japan; the Ministerio de Economía, Industria y Competitividad (SEIDI-MINECO) under grants FPA2016-77347-C2-1-P and MdM-2015-0509 in Spain; the Department of Energy and the National Science Foundation in the United States; the Russian Academy of Science, the Kurchatov Institute and the Russian Foundation for Basic Research (RFBR) in Russia and the Brazilian Ministry of Science, Technology and Innovation (MCTI), the Financiadora de Estudos e Projetos (FINEP), the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), the São Paulo Research Foundation (FAPESP) and the Brazilian Network for High Energy Physics (RENAFAE) in Brazil.

## Author information

### Contributions

The DC detectors were designed, constructed and commissioned by the DC collaboration. Simulations and data analyses were performed by the DC members as well. All authors contributed to the work presented in this manuscript, which was subjected to an internal collaboration-wide review process.

### Corresponding authors

Correspondence to C. Buck or A. Cabrera.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Peer review information Nature Physics thanks Juan Jose Gomez Cadenas and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Extended data

### Extended Data Fig. 1 Reactor Flux Systematic Uncertainties on the Signal Normalisation.

The 1σ uncertainty stands for 68% frequentist probability. Both rate and shape flux uncertainties are treated via covariance matrices as predicted by the data-driven reactor flux model31,32,36 used by Double Chooz. The Bugey4 experiment provides an independent rate constraint via its 〈σf〉 and therefore extra precision via the cancellation of the common spectrum terms. The uncertainty coming from the reactor–detector baselines is negligible (< 0.01%). The unknown inter-reactor correlations are assumed to be correlated for the reactor power (Pth) and the fission fractions (αf) in the single detector (SD) case and uncorrelated for any multi detector (MD) configuration in general (combined uncertainty of Pth and αf is 0.83%). These assumptions are made to minimise the θ13 sensitivity to be conservative. In the Double Chooz case with two reactors the uncertainties on Pth and αf are reduced by about a factor of $$\sqrt{2}$$. Only the uncorrelated terms are relevant for the specific MD case in Double Chooz (ND/FD-I and ND/FD-II).

### Extended Data Fig. 2 Detection Systematic Uncertainties.

The 1σ uncertainty stands for 68% frequentist probability. The central column shows the uncertainties on the signal normalisation for the single detector (SD) case. The multi detector (MD) case in the column on the right shows the uncertainty on the ratio of the signal rates (FD/ND). The total systematics is dominated by the uncertainty of the number of protons for IBD interactions (mainly the GC). This is to be re-measured upon future detector dismantling. The total neutron capture selection reduces systematics as compared to the element dependent detection, since it is not sensitive to the knowledge of the Gd/H fraction of neutron captures. Boundary systematics rely on the modelling of spill-in/out events at volume interfaces with the simulation are assumed fully correlated between detectors. The selection systematics rely on an IBD data-driven method, thus inclusively accounting and averaging over selection and energy scale (stability, uniformity and linearity) variations. The vetoes play a negligible role as they were optimised to maximise the selection efficiency while adding a negligible systematic.

### Extended Data Fig. 3 sin22θ13 Measurement Uncertainties Breakdown.

The match between the θ13 uncertainty from data (0.0139) and the predicted sensitivity (0.0141) allows for a MC uncertainty breakdown. The 1σ uncertainty stands for 68% frequentist probability for the total contribution. In the central column the fractional uncertainties of the different systematics (x) are given. They were calculated from the sensitivity assuming just one systematic contribution in addition to the statistical uncertainty. The statistical part was then subtracted in quadrature. The total is larger than the square root of the sum of the individual squared uncertainties because of correlations. The difference corresponds to a (0.0065)2 term. The column on the right shows the total uncertainty when the corresponding single systematics is removed. The impact of background and in particular of the energy scale on the sensitivity is higher than one might expect from the values given in the central column. Again, this is due to the correlations.

### Extended Data Fig. 4 Total Neutron Capture Selection Criteria & Background Rejection.

The complete total neutron capture selection definition is here detailed, including selection criteria and background vetoes. The type of background rejected by each cut is also highlighted.

### Extended Data Fig. 5 TnC Selection Artificial Neural Network Definition.

The near detector (ND, left) and far detector (FD, right) Artificial Neural Network (ANN) cut definition are shown. Each plot shows full data (black-solid) and accidental background only (blue-solid) curves. The remaining data upon background subtraction is shown (black-points) represents correlated events, which are signal IBD-like. The 1σ uncertainty stands for 68% frequentist probability: statistics only (error bar). The IBD MC (solid red), with no backgrounds, is contrasted against the data. Sizeable differences between the FD and the ND ANN output are dominated by the different signal to background contamination of each detector. The ND has ~ 10 × better signal to accidental background. The FD has lower statistics. The MC exhibits excellent agreement to data across the entire dynamic for both detectors. A similar ANN definition had been demonstrated for FD-I data13. The ANN per detector cut was optimised to reduce the FD background and to match a slight prompt spectral distortion in both detectors (not shown explicitly). The latter is key to ensure an unbiased rate+shape θ13 measurement. Such a distortion is known to arise from the Δrprompt–delay variable slightly dependent on the prompt energy. Hence, the indicated ANN cut are slightly different for ND (0.86) and FD (0.85). This causes a 1.3% difference in rate normalisation, corroborated with data to a few per mille precision.

### Extended Data Fig. 6 TnC Efficiency & Background Rejection.

The evolution of the total neutron capture (TnC) selection is illustrated in terms of IBD selection efficiency (solid lines), total background rejection (dotted lines) and the accidental background rejection (dashed lines). The estimation of the total background rejection uses 17 days of 0-reactor data. The average singles rate per detector is ~ 10 s−1. The first criterion corresponds to a time of [0.5,800]μs as a ‘loose’ coincidence with a [1.0,20.0] MeV prompt and the [1.3,10.0] MeV delayed triggers. The rates are 2291 day−1 (far detector) and 2375 day−1 (near detector), which imply a rejection factor of ~ 375 relative to singles. These numbers provide an absolute scale to the all other shown below. The Δrprompt–delay ≤1.2 m condition yields some important reduction. However, major accidental background rejection is only obtained by the ANN with a ~ 400 rejection factor. After the ANN, the challenging correlated cosmogenic background dominates the total background rate, as expected due to the shallow overburden. The far detector is better shielded. Extra rejection uses the cosmogenic vetoes. The overall rejection factors are ~ 193 (far detector) and ~ 34 (near detector) relative to the loose coincidence.

### Extended Data Fig. 7 Scrutiny of the θ13 Measurement.

The nominal θ13 measurement (top) can be decomposed into a) the rate-only and shape-only contributions, b) FD-I (no ND) and FD-II (isoflux) contributions. A measurement without marginalising over $$| \Delta {m}_{ee}^{2}|$$ as (2.484 ± 0.036) × 10−3eV2 is also shown. These numbers demonstrate that the nominal θ13 measurement is dominated by the rate-only information (systematics limited) of the best FD-II isoflux data sample. Furthermore, releasing the constraint on $$| \Delta {m}_{ee}^{2}|$$ does not impact the measured central value of θ13. Two alternative θ13 measurements are also shown for comparison: a) the Data-to-Data and b) the Reactor Rate Modulation (RRM). Both are expected to be immune to the reactor model spectrum distortion while excellent agreement is found (details in text). Last, the FD-I+FD-II single detector θ13 measurements are also shown using two uncertainty prescriptions. The new data-driven prescription uses an increased 4σ reactor model shape uncertainty. The standard reactor model prescription is also shown, indicating a bias on the result. The agreement of the single and multi detector, with the more conservative uncertainty and the much better χ2/d.f., suggests the new prescription provides a better treatment of the data. The previous FD-I only SD θ13 measurement12 (blue) is shown for reference. Bugey4 must be used in all single detector measurements to protect the rate normalisation. The 1σ uncertainty stands for 68% frequentist probability: both statistics (red error bar) and total (black error bar, including systematics).

### Extended Data Fig. 8 Shape-Only Reactor Spectral Distortion.

The data to prediction spectral ratio for the latest Double Chooz near detector (black), Daya Bay29 (blue), RENO10 (red) and NEOS45 (green) results are shown, exhibiting a common dominant pattern predominantly characterised by the 5 MeV excess. Small differences across experiments are still possible but unresolved so far. The Bugey341 (not shown) is the only experiment known not to reproduce this structure. This remains an issue. The RENO and NEOS normalisation has been modified relative to publications to ensure the shape-only condition (average R = 1) is met. The 1σ uncertainty stands for 68% frequentist probability: both statistics (error bars) and the common reactor model prediction shape-only uncertainty (grey shaded). The shape-only is significantly smaller than the dominant rate-only uncertainties. Since the same reactor model prediction is used, this uncertainty is expected to remain a representative guideline to all experiments. The 5 MeV excess is compensated by a deficit region [1.5,4.0] MeV for all experiments due to the shape-only condition. A good agreement is found between Double Chooz and Daya Baya data throughout the entire energy range. The non-trivial match among different experiments suggests that most detector and part of the reactor effects are accurately reproduced by the simulation, thus cancelling across in R. This implies that the common reactor prediction model inaccuracies are expected to dominate the observed distortion. This is consistent with the fact that all other experiments use the same prediction strategy.

### Extended Data Fig. 9 Near Detector 〈σf〉 Uncertainty Breakdown.

The 1σ uncertainty stands for 68% frequentist probability. With a total uncertainty of about 1%, the mean cross section per fission measured with the near detector (ND) is the most precise measurement to date. The total uncertainty is dominated by the uncertainty on the proton number and on the reactor thermal power. The proton-number uncertainty could still improve during DC detectors dismantling operations while the reactor thermal power uncertainty is expected to be irreducible.

## Supplementary information

### Supplementary Information

Supplementary text.

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The Double Chooz Collaboration. Double Chooz θ13 measurement via total neutron capture detection. Nat. Phys. 16, 558–564 (2020). https://doi.org/10.1038/s41567-020-0831-y

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