JHEP01(2021)190 a a k b j s,d d 2 7 j t d,h, o, Springer k t July 28, 2020 : k H.P. Lima I. Bekman, V. Sinev, D. Hellwig, January 28, 2021 December 4, 2020 n k G. Mention, k December 16, 2020 4 : : o J. Busenitz, F. Suekane, : 8 k, o A. Givaudan, u, w M. Kuze, M. Kaneda, M. Vivier, h Received d B. Reinhold, r f,q Revised 13 O. Corpace, Published b, J. Haser, Accepted 3 D. Navas-Nicolás, C. Buck, B. Lubsandorzhiev, V. Sibille, D. Lhuillier, m e, A. Oralbaev, q t p J.C. Barriere, h 10 k D. Kryn, v k, r K. Kale, B. Viaud, 6 d, k f T. Matsubara, L.F.F. Stokes, I. Gil-Botella, b r s T. Hara, Published for SISSA by https://doi.org/10.1007/JHEP01(2021)190 c S. Appel, P. Chimenti, A. Onillon, T. Brugière, C. Lastoria, e A. Minotti, f C. Jollet, d g J. Reichenbacher, J.M. LoSecco, R. Sharankova, 7 k,d w I. Stancu, i, and F. Yermia k 12 13 C. Veyssiere, J. Martino, H. Furuta, a H. de Kerret, r, h, 14 7 7 n y i, c, b, E. Blucher, M.C. Goodman, L. Scola, A. Stahl, j E. Chauveau, J. Jochum, y T. Lasserre, o R. Milincic, Y. Sun, M. Obolensky, G. Yang J.C. dos Anjos, a i 5 h E. Kemp, 9 G. Pronost, u t, v o a A. Etenko, i, l J. Maricic, e c z . 3 P. Soldin, C.E. Lane, J.M. López-Castaño, L. Bezrukov, n M. Cerrada, o T. Miletic, 1 w I.M. Pepe, r, Z. Djurcic, 2 The Authors. H. Almazan, L. Oberauer, M. Ishitsuka, f T. Sumiyoshi, C. Wiebusch, T. Kawasaki, S. Schoppmann, C. Mariani, L.F.G. Gonzalez, h d c 4

d v 11 n e,d d, , d,aa, d,e h, d,k u,m M. Lindner, Now at Physics Department,Now Arcadia at University, 450 LAPP, S. CNRS/IN2P3, Easton 74940Now at Road, Annecy-le-Vieux, Instituto Glenside, France. de PANow 19038, Física at U.S.A. Corpuscular, Kamioka IFIC Observatory, (CSIC/UV), ICRR,Now 46980 University at Paterna, of South Spain. Tokyo, Dakota Kamioka, School Gifu 506-1205, of Japan. MinesNow & at Technology, 501 State E. University of Saint New Joseph York St. at Rapid Stony City, Brook, SD Stony 57701, Brook, NY, 11755, U.S.A. Now at IJC Laboratory,Now CNRS/IN2P3, at Université Universidade Paris-Saclay, Orsay, Estadual France. Now de at Londrina, Massachusetts 86057-970 Institute Londrina,Now of Brazil. at Technology, Cambridge, Tokyo Massachusetts University 02139, ofDeceased. U.S.A. Science, Noda, Chiba,Now Japan. at Physics &Now Astronomy at Department, High University of Energy Hawaii Accelerator at Research Manoa, Organization Honolulu, (KEK), Hawaii, Tsukuba, U.S.A. Ibaraki, Japan. Now at Department of Physics and Astronomy, University of Sussex, Falmer, Brighton, United Kingdom. e 9 3 4 5 6 7 8 1 2 10 11 12 13 14 Open Access Article funded by SCOAP U.S.A. S. Schönert, M. Skorokhvatov, S. Sukhotin, S. Wagner, Jr., J. Maeda, A. Meregaglia, P. Novella, C. Palomares, J.V. Dawson, H. Gomez, A. Hourlier, M. Karakac, T. Lachenmaier, The Double Chooz collaboration T. Abrahão, T.J.C. Bezerra, A. Cabrera, Reactor rate modulation oscillationdetectors analysis in with Double two Chooz JHEP01(2021)190 , 017 . 0 ± 094 . interactions up e ¯ ν ) = 0 and the total back- 13 θ 13 θ (2 2 Li decays. The background- 9 [email protected] , oscillation analysis based on the observed antineutrino rates at the Dou- 13 θ A [email protected] E-mail: Physik Department, Technische Universität München,Kepler 85748 Center Garching, for Germany Astro andUniversidade Particle Estadual Physics, de Universität Campinas-UNICAMP, Tübingen, Campinas,Center 72076 SP, for Tübingen, 13083-970, Neutrino Germany Brazil Physics, VirginiaLNCA Tech, Underground Blacksburg, Laboratory, Virginia CNRS/IN2P3-CEA, 24061, Chooz, U.S.A. France University of Notre Dame, NotreIPHC, Dame, CNRS/IN2P3, Indiana Université 46556, de U.S.A. Strasbourg,SUBATECH, 67037 CNRS/IN2P3, Strasbourg, Université France de Nantes,Research Center IMT-Atlantique, 44307 for Nantes, Neutrino France Science,Department Tohoku of University, Physics, Sendai Tokyo 980-8578, Institute Japan Department of of Technology, Physics, Tokyo, 152-8551, Tokyo Metropolitan Japan University, Tokyo, 192-0397, Japan IRFU, CEA, Université Paris-Saclay, 91191Department of Gif-sur-Yvette, Physics, France Kitasato University,Department Sagamihara, of 252-0373, Physics, Japan Kobe University,NRC Kobe, Kurchatov 657-8501, Institute, Japan 123182 Moscow,Max-Planck-Institut Russia für Kernphysik, 69117 Heidelberg, Germany The Enrico Fermi Institute, TheCentro University de of Investigaciones Chicago, Energéticas, Chicago, Medioambientales28040, Illinois y Madrid, Tecnológicas, 60637, CIEMAT, Spain U.S.A. Department of Physics, Drexel University,Institute Philadelphia, of Pennsylvania Nuclear 19104, Research of U.S.A. the Russian Academy of Sciences, Moscow 117312, Russia Department of Physics andTuscaloosa, Astronomy, Alabama University 35487, of U.S.A. Alabama, Argonne National Laboratory, Argonne, IllinoisAPC, 60439, Université U.S.A. de Paris, CNRS,Centro Brasileiro Astroparticule et de Cosmologie, Pesquisas F-75006, Físicas,Université Paris Rio de de Bordeaux, Janeiro, CNRS/IN2P3, RJ, CENBG, 22290-180, F-33175 Brazil Gradignan, France III. Physikalisches Institut, RWTH Aachen University, 52056 Aachen, Germany l i t b c j s e q r o z p g d v y a k h f u n w m background model considering fast-neutrons interactionsmodel-independent and determination of thebeing mixing the best-fit angle total yieldsmodel. background sin rates A fully second consistent with oscillationrates the to analysis cosmogenic the is background cosmogenic also background performed estimates. constraining While the the total central background value is not significantly ground rates without relying onThe any assumptions analysis on comprises the 865 specific daystor background of in contributions. data operation. collected The in oscillationof both results reactor-off detectors are data with enhanced in at by the leastto the far one use a (near) reac- of visible detector. 24.06 energy days The (12.74 of analysis days) considers 8.5 MeV, the using the events at higher energies to build a cosmogenic Abstract: ble Chooz far andapproach near provides detectors a for so different reactor far power unique conditions simultaneous is determination presented. of This aa JHEP01(2021)190 to 0.015. Along with 13 θ 2007.13431 Neutrino Detectors and Telescopes (experiments), Oscillation ArXiv ePrint: the addition of the backgroundthe model oscillation reduces results, the the uncertainty normalizationcision on of of 0.86%, the reducing anti-neutrino rate the is 1.43% measured uncertainty associated with to aKeywords: the pre- expectation. modified due to the consistency between the reactor-off data and the background estimates, JHEP01(2021)190 e ¯ ν ], respec- ] are based 5 9 , – 4 6 ), and one phase 2 31 m ∆ , 2 21 ) with the flavor eigenstates . Double Chooz, Daya Bay 3 m 13 ν ). After the observation of the , θ ], relying on the observation of ∆ 2 9 ν – , CP 6 1 δ [ ν 13 θ 5 ] and atmospheric sectors [ 2 ) generated in nuclear reactors at typical 3 e , ¯ ν 2 , reactor neutrino experiments have recently ) 9 – 1 – 2 31 7 m ∆ value offered by reactor experiments is used as an ]). As a consequence, reactor neutrino experiments , 23 10 13 θ θ ( 13 is derived from the observed energy-dependent deficit of and 13 ) θ ]. The oscillations among the three active neutrino species are 2 21 1 m -violation in the leptonic sector ( ∆ , CP 12 1 θ (see for instance [ ( CP ), two independent mass square differences ( interaction, usually referred to as inverse beta decay (IBD). The time and δ 13 n θ + ). The 3-flavor neutrino oscillations are described by means of three mixing angles , e and background measurements τ selection and expected backgrounds 23 ν , θ e 13 µ → Double Chooz and other reactor experiments detect the electron antineutrinos via the , ¯ ν θ ν , p e 12 e ν θ ¯ on background models built assuming a numberspectrum of background of sources. each The ratereactor-on background and energy periods, contribution and is incorporatedthese to estimated background the from models, total the background expectation.with data respect Accounting collected for to a during MC-based null-oscillation expectation or the unoscillated flux measured ν spatial coincidence of thea prompt positron large signal-to-background and ratio. thefast delayed However, neutron neutrons accidental capture and and signals cosmogenic correlatedbecoming yields radio-nuclides events non-negligible induced can backgrounds. by mimic The oscillation the analyses characteristic presented in IBD [ signature, the disappearance of electronflight antineutrinos distances ( of 1–2external constraint km. in current and The futuresurement accelerator-based of experiments aiming at theplay mea- a major role in the search for the leptonic CP-violation. responsible for the dominant oscillations in thetively so-called driven by solar [ observed the oscillation inducedand by RENO the have last provided precise mixing measurements angle, of In the lastoscillation few experiments decades, [ neutrinosnow have well established, been connecting proven the( mass to eigenstates be ( massive( particles in several 6 Summary and conclusions 1 Introduction 3 Reactor-on and reactor-off data4 samples Reactor rate modulation analysis 5 Contents 1 Introduction 2 JHEP01(2021)190 13 13 θ θ 400 ∼ candi- or NT) e L ¯ ν ], providing 9 follows with the 4 of Gd-unloaded scin- 3 neutrino target describes the reactor-on and the total background 3 13 θ rate in absence of oscillations e ¯ ν with and without the background ], reducing its associated uncertainty. 5 12 describes the selection of the 2 – 2 – . concludes with an overview. 13 6 θ or GC). This second volume was originally meant to fully contain candidates with respect to the expected m, respectively. Both detectors are identical and yield effectively identical of Gd-loaded (0.1%) liquid scintillator inside a transparent acrylic vessel. ], which uses only the far detector of the Double Chooz experiment, to a e ¯ ν 3 11 1050 ∼ gamma-catcher selection and expected backgrounds flux generated at the two reactors (B1 and B2, with a thermal power of 4.25 GW L e e ¯ This paper is organized as follows. Section In this paper, an alternative background-model-independent oscillation analysis is pre- ν ¯ ν contains 10 m This volume is surrounded bytillator another ( acrylic vessel filled withthe 23 energy m deposition ofannihilation gamma in rays the from target the region. neutron capture The on Gd GC and is the in positron turn contained within a third volume each) of the Chooz Bdistances nuclear between power the plant, far operated (FD)m by and and Électricité near de (ND) detectors France. andresponses The the average after reactor calibration, cores thus are leadinguncertainties in to the a oscillation major analyses. reductionders of and The the detectors an correlated consist outer systematic of muon a veto set on of the concentric top. cylin- The innermost volume ( 2 The setup of thethe Double Chooz experiment consists of two identical detectors measuring dates and the corresponding expected backgrounds,and while reactor-off section data samplesdefinition used of for the the RRM oscillationoscillation approach analysis. analysis and results Section the aremodel systematic constraint, presented uncertainties and in involved. section section Finally, the 2017, which offer aBG constraint model. to the Beyond BG theobserved rate neutrino rate and oscillation, of serves the as IBD analysistineutrino independent also interactions. flux yields validation normalization The of a provided value by the measurement Bugey-4 is of [ found the to be fully consistent with the an- is improved by incorporatingalso to the a analysis consistency a testdescribed background for in model [ the based model onmulti-detector [ setup itself. considering both Thisalso the paper incorporates near extrapolates and for far the the detectors. first RRM time The analysis the oscillation reactor-off analysis data collected by both detectors during is performed for differentpower. reactor This operation allows for conditions arate, ranging simultaneous without determination from of making zero both anytechnique to is consideration full particularly about thermal competitive thefrom in individual the only background Double two Chooz sources. nuclearis experiment, cores. also This as obtained it In collects following addition, data the a same background-model-dependent RRM result procedure. on In this case, the precision on dependent and the uncertainty onimpact the on background the expectations uncertainty may of have a non-negligible sented: the Reactor Rate Modulationserved (RRM). rate of In this approach, the comparison of the ob- at a near detector. As a consequence, the oscillation analyses are background-model- JHEP01(2021)190 : - ]. e of β 9 ¯ ν 96% . 99 inner muon ]. In Double C spallation > 30 m for the 9 candidates by ∼ 12 e ¯ ν Li and accidental 9 Li undergoes a 9 B) are estimated to 12 100 m and ∼ ] is the range of the visible energy 9 ]). While the fast-neutron twofold 15 decay at rest or µ – 3 – (ID). The ID is surrounded by the ]), C and Gd. This implies that IBD detection volume He is reported in [ 14 , 8 13 ) is directly related to the energy of the interacting inner detector ) and a delayed trigger (neutron capture). The energy of the + e ] for details), a time and spatial correlation between the prompt and 9 ] for details). The energy windows considered for the prompt and de- 14 visible energy s, while the distance between the vertexes is imposed to be below 120 cm. µ ], where the prompt energy signal is extended to 20 MeV to better constraint ). As discussed below, the IBD candidates above this energy are used to infer 9 e ¯ ν 8 MeV), the so-called Total Neutron Capture (TnC) selection approach accounts + 0.78 MeV. While the Double Chooz detectors were originally designed to ∼ Li, as no indication of + 9 e ) made of stainless steel and filled with non-scintillating mineral oil. The surface of E (IV), a 50 cm thick liquid scintillator volume equipped with 78 8-inch PMTs. Finally, s and 800 The physical events mimicking the IBD signature have been discussed in [ The IBD candidates selection in the RRM analysis follows the lines described in [ ≈ µ 0.5% in the FD and 0.1% in the ND). The reactor-on-based background model adopted e ¯ ν < buffer a non-negligible contamination in thethe IBD accidental candidates background samples. contribution However, relying the( estimation on of the rate ofin single the events current is analysis veryevents. is precise The built only with difference the with respect contributions to of the fast-neutrons, model in [ correspond mostly to fast-neutrons(mainly and unstable isotopessignature produced is upon due ton a decay. proton Other recoilbe cosmogenic on negligible. backgrounds H (like followed Apartradioactivity by events from and the the neutron n-capture, captures correlated (hereafter, backgrounds, accidental background) random also coincidences become of natural the reactor a background expectation. Chooz, given the small overburdenFD of and the ND, detectors respectively), (depths of the muon-induced cosmogenic backgrounds dominate. These delayed correlation to set an-H cut events reducing (see the [ ratelayed of signals random coincidences, are especially 1.0–8.5 MeV inpresented and the in 1.3–10.0 [ MeV, respectively. Unlikethe in background the shapes, IBD in selection this analysis it is restricted to be below 8.5 MeV ( almost a factor of 3.and After OV a data series of (see muon-induceddelayed [ background signals vetoes is based on required. the0.5 ID, The IV time difference betweenIn the addition, signals an is artificial neural comprised network between (ANN) has been developed relying on the prompt- E exploit the large neutrongammas capture ( cross-section in Gdfor and neutron captures the in characteristic H de-excitation (seeconsiders [ both the NT and the GC, boosting the statistical sample of the interactions and to alloware for devoted the to event the vertex suppression and and energy rejection reconstruction, of the backgrounds. The IV selection and OV reliesing on a the prompt triggerprompt twofold-coincidence ( signature signal of ( the IBD process, provid- the buffer is coveredand with buffer an tank array defineveto of the 390 low backgroundthe 10-inch upper PMTs. part The ofscintillator NT, the strips GC detectors grouped is in covered different by modules. an While outer the muon ID veto is (OV), meant made to of detect the plastic IBD ( JHEP01(2021)190 Li Li 9 9 Visible Energy (MeV) 62 18 004 . . . 1 Antineutrino candidatescandidatescandidatescandidates Antineutrino Antineutrino Antineutrino Antineutrino expectationexpectationexpectationexpectation Fast•neutron Fast•neutron Fast•neutron Fast•neutron 0 0 ± ± ± 09 89 . . 110 . 020 3 . 10 12 14 16 18 20 Li and accidental backgrounds are 0 9 ± 0

600 500 400 300 200 100 Entries / MeV / Entries 30 14 03 8 320 . . . 0 0 %). Given that the spectral shape of the ± ± – 4 – 30 09 009 . . Li decays which is used to extrapolate the total rate %). This number allows to extrapolate the total , offers a direct measurement of the number of 010 4 . 9 . 2 1 5 0 . 0 1 0 ± ± ± 7 . 030 ], the fraction of the spectrum below (above) 8.5 MeV is 930 . . 0 10 3 15 Li contribution from the candidates observed in the 8.5 MeV ) FD (SD) FD (MD) ND (MD) 9 Visible Energy (MeV) %( 1 5 . Antineutrino candidatescandidatescandidatescandidates Antineutrino Antineutrino Antineutrino Antineutrino expectationexpectationexpectationexpectation Fast•neutron Fast•neutron Fast•neutron Fast•neutron − 0 . The background estimates are quoted separately for the first phase ± 1 3 . Li isotope 89 Accidental 9 ]. This noise has been suppressed in the ND covering the PMT bases with contribution is Fast-neutron Rate (day e 16 ¯ ν Li decays in the 1.0–8.5 MeV energy window considered for the RRM oscillation 9 10 12 14 16 18 20 . IBD candidates (black dots) as a function of the visible energy above 8.5 MeV, extracted . Background expectation in the 1.0–8.5 MeV window. The accidental, fast-neutron and 0

50

300 250 200 150 100 Entries / MeV / Entries Li decay contributions to the background model are derived from reactor-on IBD candidates. accidental rate between bothdescribed periods in is [ due toa the radioupure increase polyester of film, yielding theFD. a light reduction The noise in background increase thesample in accidental of rate the random with FD coincidences respect accidental used to rate to the estimate uncertainty this is background due in to the the MD phase. smaller statistical computed to be number of analysis. The expectedsummarized in rates table forof the the fast-neutron, experiment (single-detector,phase hereafter (multi-detector, SD), hereafter operating MD) with only both the detectors FD, running. and The the increase second in the FD to 12.0 MeV energy window.events The tagged fast-neutron rate by and the energy8.5–12.0 IV MeV spectrum range, up is as to measured shown from in 20decays MeV. figure (the Subtracting theprompt fast-neutron contribution signal in is the well known [ Table 1 9 and the estimation of the Figure 1 from reactor-on data inneutrons the is FD shown (left) with8.5–12 and MeV dashed range the line provides ND and thebelow (right). yellow 8.5 number MeV. The error of expected band. contribution The from fast- fast-neutron subtraction in the JHEP01(2021)190 . ]. 6 2 ] data Pu iso- 12 241 s is applied after µ Pu, and flux is small but not 239 ]. The time evolution e ¯ flux during the reactor- ν 20 U, e ¯ ν 235 decays from fission products keep β ) is fully correlated between the FD plus background contributions) in the e 4% ¯ ν . ]. While the 1 ], the oscillation analysis presented in this can be estimated either by means of Monte 9 e 18 which vanishes with time. Since the reactor- , U is predicted from [ ¯ ν e – 5 – ¯ 17 ν 238 candidates (actual e , where the days with one (1-Off) and two (2-On) reactors in ¯ ν 2 flux changes significantly during the reactor refuelling periods, when e ¯ reactor-based oscillation experiments, Double Chooz is unique in ob- ν 13 θ ]), the contribution from 19 , the number of 2 Among the fluxes from 6 different cores, they have been so far unable to collect data when all of e ¯ tineutrinos. After the nucleartaking reactors place are generating turned a off, off residual periods flux of are shortnegligible. in However, the time, amount the ofCarlo contribution residual simulations, from or by the performing residual a relative comparison of the rates observed at different livetimes and number of IBDIn candidates order in to each period reduceeach detected and the muon. detector cosmogenic Thus, are the backgrounds, listedduring corresponding the in a livetimes MD table time differ period in due vetosites. the to of the near Applying different and 1.25 overburdens far the and detectors the muon selection rates different cuts in backgrounds, to the regardless experimental the of reactor-off their origin, data with provides a an contribution inclusive from sample residual of an- taining reactor-off data (2-Off) whenrefuelling the or two maintenance. cores Since of theν the Daya Chooz Bay site and are RENO broughtthem experiments down are are for exposed off. to Double the samples Chooz in has 2011 taken and reactor-off 2012) data samples and during MD both (two the samples SD in (two 2017) periods. The corresponding ulation still accounts for thebetween Bugey4-based the normalization SD in and orderanalysis to MD precision keep flux as the expectations. consistency theand Bugey-4 the This ND, uncertainty choice and ( does therefore suppressed not to impact a the negligible oscillation level in a multi-detector analysis. for instance [ of the fission fractionsdone are in past accounted Double for Choozhave using publications been where dedicated used the Chooz as ND a was reactorAlthough not this virtual simulations. available, is near Bugey4 not detector As [ required to in define oscillation analyses the with absolute MD flux data, normalization the in associated SD. flux sim- samples is shown inoperation figure are clearly visible.on periods A prediction has of beenThe the carried reactor unoscillated out flux as modeltopes described is contributions in adopted are previous from derived Double [ from Chooz the publications Institut [ Laue-Langevin (ILL) reactor data (see only the FD was available, andFD between and January the 2015 ND and April werein 2016 simultaneously section (384 collecting days), data. when According the single-detector to period the is selection 47351, described the while FD in and the 206981 multi-detector in period the is ND. respectively The 42054 time in evolution of the candidates rate for the MD data The Double Chooz dataparticular, have the been total taken underonly different one reactor of operating the conditions.position, cores In is thus in evolving operation. inwork In time. comprises addition, the the As flux data done depends in taken on [ between the April cores 2011 fuel com- and January 2013 (481 days), when 3 Reactor-on and reactor-off data samples JHEP01(2021)190 ] has in SD 21 e ¯ ν 63 53 . . , without con- . In order to 1 1 ], an evolution 2 2 ± ± 22 09 91 . . , in good agreement 400 . 1 Day since data taking start − 2 candidates samples. e day ¯ ν 30 26 69 29 . . 0 0 07 . ± ± 1 ± 71 99 . . 38 300 . 7 . Once subtracted to the observed rate 30 7 05 7 ] to estimate the total background rate . . 1 0 1 − 21 ± ± rate according to the reactor-on simulation. The day e ¯ 32 96 ν . . – 6 – 7 7 18 . 0 200 ) ± 1 ] database. The expected rate of residual − ) 58 1 18 . − 0 100 . e ¯ ν Live time (day) 7.16 16.90 12.74 Detector (period) FD (SD) FD (MD) ND (MD) IBD Candidates (day 0 0 100 200 300 400 Expected background (day . IBD candidates rate for FD (top) and ND (bottom) as a function of the day of data 50 . Reactor-off data samples during SD and MD. The last row shows the total background

800 600 400 200 250 200 150 100

1000

ND IBD candidates rate (day rate candidates IBD ND FD IBD candidates rate (day rate candidates IBD FD ) )

•1 •1 The SD reactor-off data has been used in [ code predicting the isotopecomputed inventory in using the the reactor BESTIOLE cores.reactor-off period [ The is neutrino found spectrumof to is events, be then the measured inclusivewith background the rate expectation is from the background model defined in section in previous Doublecorresponding Chooz background IBD models. selection Inthe procedures, this current as analysis, IBD well the selection,estimate as data yielding the residual have to the neutrino been rate contribution, confront reprocessed the ofbeen it Monte-Carlo with adopted. approach candidates with described A quoted in dedicated the [ simulation in has been table performed with FISPACT [ sidering the residual baselines. Thereby once the residuala neutrinos direct are measurement estimated, of the the reactor-off total data allow background for remaining in the Table 2 expectation between 1.0 and 8.5 MeV according to the model described in section significant rate difference in thebaselines various between 1-Off the periods detector for and each the detector two corresponds reactors. to the different Figure 2 taking during thedashed MD red line period. shows the expected Empty unoscillated circles show the observed rate of candidates, while the JHEP01(2021)190 , being the 2 Li decaysLi decaysLi decaysLi decaysLi decays 99999 Reactor•Off ND data data data data data Reactor•Off NDReactor•Off NDReactor•Off NDReactor•Off NDReactor•Off ND AccidentalsAccidentalsAccidentalsAccidentalsAccidentals Fast•neutronsFast•neutronsFast•neutronsFast•neutronsFast•neutrons Visible Energy (MeV) Li decays. Li estimates up to 9 9 ]. The null-oscillation 9 in the ND, consistently 1 in the ND is significantly − e ¯ ν 5 10 15 20 ) day 28 . 5 determination becomes background- ± 13 .

θ 10 33

. Entries / 0.25 MeV 0.25 / Entries 1 9 – 7 – in reactor experiments relies on the comparison of 13 (R+S) analysis, as done in [ θ 3.0 MeV. This discrepancy corresponds to the presence ∼ in the FD and ( 1 Li decaysLi decaysLi decaysLi decaysLi decays 99999 Reactor•Off FD data data data data data Reactor•Off FDReactor•Off FDReactor•Off FDReactor•Off FDReactor•Off FD AccidentalsAccidentalsAccidentalsAccidentalsAccidentals Fast•neutronsFast•neutronsFast•neutronsFast•neutronsFast•neutrons − Visible Energy (MeV) ), the contribution of the residual 7 ) day rate plus shape 49 ∼ . 1 ], considering accidental coincidences, fast-neutrons and 9 Li estimations following the analysis described in section 2 ND ± 9 52 /L . flux, a R+S background model in each detector is also considered, assuming a 5 10 15 20 0 e 2 FD ¯ ν L . Reactor-off IBD candidates as a function of the visible energy during the MD period. , superimposed to the background model. The expectation reproduces the data at 3 1

10 ]. The energy spectra of the reactor-off IBD candidates in the FD and ND are shown in The larger reactor-off statistical sample in the MD period, especially in the ND, allows Entries / 0.25 MeV 0.25 / Entries 9 at a short baselineBesides (near the detector), where thecertain oscillation number effect of background is sources. smallmodel-dependent Thus, or and the still the negligible. from associated the uncertainty background model. contains a non-negligible contribution The measurement of the mixing angle the observed prompt energy spectrumthe with deficit the in expectation the in observedare absence number of accounted of oscillation. candidates for and in Both theexpectation a distortion comes of either from the a energy reactor spectrum flux simulation or from the measurement of the flux 8.5 MeV are ( with the reactor-on expectations quoted in table 4 Reactor rate modulation analysis of the residualinvolved neutrinos, parent whose isotopes. spectrum Accordingdetectors is to ( known the to differentlarger vanish geometrical than above acceptance between 3 in MeV the used the due to FD. to perform the only The difference observed that reactor-off no IBD candidates interactions above are 8.5 expected. MeV have The been obtained for detailed comparisons within the [ background model adoptedfigure in this workhigh and energies, described but deviates below Figure 3 The observed candidates in themodel FD described (left) in and [ the ND (right) are superimposed to the background JHEP01(2021)190 ) ]. 23 = 2 and 4.1 ) for (4.1) r : 13 d N exp θ ) in the B flux have R ) data due e osc ND ν ¯ ν η r ( R , where is evaluated for 2 i = osc FD bin, by means of η ν /L exp d ∗ th R i , th R P ν d P r R is the expected rate of N i  and between the reactor cores ν P R L osc , although only the normal- d obs d η = ) ] and further discussed in [ R exp d 6 ∗ 13 th , the average R θ P 3 (2 2 ) with the expected one ( sin obs and the total background rate, is the average disappearance coefficient, R − ) 1 13  osc θ from the B1 and B2 cores differ. According . As the accidental background rate is known η + d (2 ]) and the distance e – 8 – 2 d B ¯ ν ) value in the MD reactor-on period is computed 24 B sin ([ osc ND = and 2 η ( ) conditions. As the signal-to-background ratio varies ) coefficient is computed, for each m exp d th 13 ∆ (RO) determination of the mixing angle is implemented θ osc R FD P osc ) in the MD reactor-off period. This ensures a precise η (2 η ν + r 2 d ]. The same values apply to R 9 B flux increases with the thermal power while the background refers to all background sources but the accidental one (in short, e = d ¯ ν rate-only stands for either the FD or the ND, B obs d d R .A , which differs between reactor-on and reactor-off ( (the i energy spectrum. This relation between ) 13 e e θ th ¯ ν ¯ ν P E 4 background). The estimation. L/ ν 2 r m R (∆ The systematic uncertainties related to the IBD detection and the reactor The RRM technique exploits the correlation of the expected and observed rates, which As an alternative approach, the RRM analysis offers a background-model-independent 2 in bins of the total baseline-adjusted thermal power ( e sin ¯ (0.56) since the relativeto contributions the of residual neutrinoreactor-off period spectrum is discussed 0.86 in (0.21). section been described in detail in [ consequence, hereafter cosmogenic simulations as the integrationby of the the oscillation normalized effect antineutrino drivenand by energy the spectrum detectors. multiplied Theto average be 0.55 (0.11). The FD coefficient obtained for the SD reactor-on period is slightly larger data taken at variousν reactor conditions, grouping theis IBD the candidates number and ofyields the the cores). expected determination of A sin with fit a of precision these below 1%, data the points fit to is the performed model with accidental-subtracted expressed samples. in As eq. a ( where the subindex antineutrinos in absence ofh oscillation, and to the different determination of the total background ratefor which the does not rely on Monte-Carlo simulations follows a linear model parametrized by technique, using reactor-on and reactor-off datain collected R+S with analyses, both the the systematic FD uncertainties andcomparison are the highly ND. suppressed of by As means the ofthe the observed relative comparison flux of at thethe different measurements residual detectors. at neutrino both rate detectors Beyond ( also the provides error a suppression, determination of the total (inclusive) background rate,Relying independently on of rate-only information, the these number estimations of(with are background not respect affected sources. to by the the energy predictedThe distortion spectrum) simple first experimental reported setup inboosts [ of the Double precision of Chooz,total the background. collecting RRM The 2-On, results current 1-Off by analysis implements offering and for a the 2-Off powerful first data, time lever a arm multi-detector to RRM constrain the measurement of by comparing the observeddifferent reactor rate thermal of power ( candidatesdepending ( on rate remains constant), the RRM analysis provides a simultaneous estimation of JHEP01(2021)190 2 6= χ r flux , (5.1) e ¯ ν ν FD(SD) 2 α   d B (only for MD), a − ν ) r  d R ) for both B1 and B2 α ν σ + is treated as fully uncor-  ) yields 1.43%, considering and ν φ σ for each bin in the detector ), and 3) reactor-off d ν d,r . These values are computed σ ν 2 d B α σ is negligible. In the MD period, χ , are the nuisance parameters ac- d,r is conservatively treated as fully ) th w  d ν 13 P  θ σ α depends on the thermal power itself. (2 B2 , 2 . with th 4 X P ν =B1 , and r σ is fully correlated in the two data samples. ν d,r + ]. For the MD samples, no error is considered , respectively. As α account for the relative fraction of antineutri- φ d  flux prediction ( bin in each detector is based on a standard – 9 – FD ,  21 σ α φ σ e parameters are used in both periods: d,r ∗ th ¯ ν α ν d w P is treated as a free parameter in the oscillation fit. in the FD and the ND ( α and (1 + ν φ ν r σ exp d R , R function consists of reactor-on and reactor-off terms, which φ and detected in the detector σ 2 ), respectively. Since the far detector has the same perfor- − are introduced in order to account for the different flux and r χ ¯ bin is computed according to the same procedure. However, α ND  obs d ], the uncertainty on σ R ∗ th . The weights 11   P ), 2) reactor-on ν r  2 α σ ! ≡ r 1 , stat d σ ). In turn, these errors can be decomposed into their correlated and uncor- ν ND ν

r α is the statistical error and is set to 30% as estimated in [ ) and 0.22% ( σ = = ν is defined as: r d error in each FD  , r and background measurements , σ stat d σ d 2 on σ th χ 13 P Assuming Gaussian-distributed errors, the reactor-on θ is fully correlated among the two detectors, while in reactor-off periods is treated differently in the SD and MD samples. For the SD ν FD(MD) ν e ¯ where counting for the uncertainties related between SD and MD,α specific nos generated in the reactor sample set of nuisance parameters detection uncertainties. The in turn are divided intosamples. individual terms In for addition, the penalty FD orparameters (SD), pull to FD terms the (MD) are uncertainties and added ND quoted to detector constrain in data each section one of the nuisance 5 The fit of theminimization. observed rates Apart for from each the free parameters sin in the expected reactor-on IBDthe flux correlated detection and reactorν uncertainties. Finally, the uncertaintysample, on the residual as the IBD rate normalization of The as more of 90%reactors of being the in operation), reactor-on the dataσ dependence are of taken at fulluncorrelated reactor between power the (either SD with and 1 the or MD 2 data. The total correlated normalization error mance during the SDConcerning and the reactor-on MD flux periods, uncertainty,fission only rates the (0.78%) thermal are power (0.47%) consideredtive and to approach. fractional be This fully implies uncorrelated that the amongby total reactors, the correlated in reactor Bugey4 a error normalization), conserva- iscores. 1.41% while (fully the dominated As uncorrelated discussed is in 0.91% [ ( detection efficiency ( prediction ( related contributions among the detectorsefficiency and error the in reactor the cores.0.39% FD The ( and correlated the detection ND is 0.25%, while the uncorrelated uncertainties are ization uncertainties need to be accounted for. These can be divided in three groups: 1) JHEP01(2021)190 . 2 = χ ν r FD (5.5) (5.4) (5.2) (5.3) bins, α FD ∗ × th B 2 function P , ! ! 2 2 ND χ obs 017 d ]. The values /L . ν 9 r 0 N ) has been set is the expected σ 2 FD ν b r FD(MD) − ± , in terms of the L N ] α , respectively, with ν exp 4 . The background- r d =

1 094 N α parameters according . 14 + ν / 2 ¯ α r ND + 0 ! 2 function used for the fit . α  d r , ! 2 α : χ d ) = 0 ν ND L is the number of cosmogenic = 11 2 pull 13 σ B θ distribution: [1 + χ ν FD(SD) C 2 (2 ND B − + α at 90% C.L. 2 exp χ d σ 1 /dof

  is the parameter accounting for the N 2 exp ND − d r , r ν χ B + N r d ], the SD data is divided in 6 X 2 off d α

+ χ 11 C 2 2 day + .  + 4 + ) fit are shown in figure 2 i ν r ν , , with ] ! d σ α 1 < , ν ND ), and r d −  the reactor-off live time), 2 on – 10 – B α T FD ν r χ r ND r , T B N + day × X b R i 4 1  d ND − N B FD . . + X 2 α 2 σ exp B   +1 −  and exp R , FD 1 . is consistent with all previous results form Double Chooz, ) obs d d 1 B , being  ND X ND  [1 + = incorporates Gaussian pulls for the 13 − N 13 σ α

T θ 2 θ = exp  d χ = 27 (2 × exp = 2 2 N + χ N 2 B can be improved by introducing the constraint of the cosmogenic 64 day expectation. While in the SD reactor-off data this parameter is ND 2 BG  + . 0 χ d = B e 13 ¯ ν  FD FD  θ C < C σ α ln  and , in the MD reactor-off it is left free, but correlated between the FD and ν r FD ν obs + r 1 d R 2 σ − N !

φ φ is the number of observed IBD candidates, σ α

obs = 2 39 day . Li and fast-neutron background expectations quoted in table d = 0 N , 9 2 off ± The precision on The results of the (sin The number of reactor-on bins considered for each data sample ( 2 pull χ χ 75 . background estimates into the fit.as two The extra background Gaussian constraint priors: is added to the being the precision competitive with theof one achieved the by the total R+S analysis cosmogenic inof backgrounds [ the in the FDsimilar and associated ND errors. are The alsolimit best-fit consistent of for with 0, the the with residual sum neutrinos is brought to the physical observed versus the expected(C.L.) rate, regions. and of The3 the RRM 68.4%, yields 95.5%independent best-fit and determination of values 99.7% of confidence sin level can then be expressed as: according to the available statistics.while As the done MD in data [ in 4 bins for both detectors. The overall constrained by the ND according toFinally, the The ratio last term of of reactor-averaged the to baselines their associated uncertainties: where background events ( number of antineutrinos ( error on the residual Due to the low statisticsin in the the sample reactor-off of periods, selected speciallyis events in then is the defined considered SD as to one, be binned the Poisson-distributed. Poisson uncertainty likelihood The following reactor-off a according to the Monte Carlo simulation considering the reactor powers and the baselines. JHEP01(2021)190 ) and •1 1 •1 − •1 day +1.4 •2.1 0.4 day ± 0.017 (stat+sys) ± 28 day . 0 ) in the FD (ND). Expected rate (day ± ) = 0.094 13 θ 4% . 48 (2 . 2 0 result. However, the . The results of the 1 FD Cosmogenic rate: 3.8 sin ND Cosmogenic rate: 27.1 ∼ − 13 ( = 0 =1.0 θ 2 χ ∆ ν /dof=11/14)/dof=11/14) r FD 1% 22 2 χχ χ R ∆ ∼ 55 day . 1 5 4 3 2 0 5 10 30 25 20 15 5.5 4.5 3.5 2.5 ND dataND data 90% CL90% CL Best fit (Best fit ( ± 0 200 400 600 800 1000 error defined as . The fit yields a best-fit value of σ 57 1 Accidentals subtracted 99.7% C.L. 95.5% C.L. 68.3% C.L. Best•fit . 5 . As expected due to the consistency 0

16

800 600 400 200

Observed rate (day rate Observed ) 1000

/ •1 = 22 5 . ) 13 θ exp ND Li determinations with reactor-on and reactor- (2 9 2 ) – 11 – B = 13 •1 sin ) fit results. The upper plots show the observed rates •1 •1 and day /dof ND 1 0.4 day +1.4 •2.1 2 ± B − χ 0.017 (stat+sys) , . ± 0.04 0.06 0.08 0.1 0.12 0.14 0.16 2 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.04 0.06 0.08 0.1 0.12 0.14 0.16 FD χ B ∆ Expected rate (day

5 0 ) = 0.094

5 4 3 2 29 day

10 ∆

χ , 30 25 20 15 .

13

5.5 4.5 3.5 2.5 , with

2

)

θ

FD Cosmogenic rate (day rate Cosmogenic FD ) 0 fit are presented in figure ) (day rate Cosmogenic ND

(2 •1 2 •1 13 ) θ ± 015 FD Cosmogenic rate: 3.8 ND Cosmogenic rate: 27.1 sin . 13 (2 0 stand for the central value and uncertainty of the background ex- =1.0 θ 2 2 33 χ . ∆ ± (2 B /dof=11/14)/dof=11/14) 2 22 σ χχ = 3 095 . ) and the combination of the and exp FD DC•I FD dataDC•I FD data DC•II FD dataDC•II FD data 90% CL90% CL Best fit (Best fit ( 1 B 0 20 40 60 80 100 120 140 error defined as . RRM (sin σ ) = 0 exp 1 Accidentals subtracted B 13 0 θ

80 60 40 20

140 120 100

Observed rate (day rate Observed

) (2 •1 2 sin between the background estimatesnificantly and modified the with reactor-off respectcombination data, to of the the the central background-independent background valueprecise model is determination of not and the sig- the residual reactor-off neutrinos, yielding information now allows for a more where pectations. These aredata (table built considering theoff fast-neutron data: determination fromcorresponding reactor-on sin versus the expected rates(dashed in line). the The FD statistical (left)The errors, and bottom not the visible, plot ND are shows (right), at theone-dimensional superimposed the 68.4%, projections level to 95.5% of of and the 99.7% best-fit C.L. model regions for the three parameters and the Figure 4 JHEP01(2021)190 . ], 2 9 ND ) χ and •1 B •1 •1 FD and the B ) 1.4 day ± 0.2 day ± 13 θ 0.015 (stat+sys) ± (2 2 with respect to Expected rate (day ) = 0.095 13 13 θ θ (2 2 FD Cosmogenic rate: 3.4 sin ND Cosmogenic rate: 23.5 7% higher than the one =1.0 2 ∼ χ 1.55 1.40 1.33 , respectively) are slightly ∆ /dof=14/16)/dof=14/16) 1 22 ± ± ± χχ − ), the larger best-fit value of ND dataND data 90% CL90% CL Best fit (Best fit ( 40 day . 4 0 200 400 600 800 1000 error defined as σ 1 1 Accidentals subtracted ± 0

0.29 22.57 0.24 23.49 0.25 21.86 is found to be

800 600 400 200 Observed rate (day rate Observed

) 1000

± ± ± 49 •1 ) in the FD (ND). The parameters . ND , a summary of the background expectations 23 4% B . 3 0 ). ) – 12 – ∼ ) FD ND •1 and ( 1 1 014 •1 − . •1 − 0 1% in the 1.0–8.5 MeV energy range). This difference is 1.4 day ± ± 0.2 day 1 ∼ ± − 0.015 (stat+sys) ± 24 day 105 . . 0 Expected rate (day ) = 0.095 ± 13 33 day θ . Expectation 3.33 R+S Best-fit 3.43 ) = 0 . According to these non-vanishing values, the best-fit parame- fit results. The observed rates versus the expected rates in the FD (left) RRM Best-fit 3.37 (2 1 37 2 1 . ) 13 − FD Cosmogenic rate: 3.4 ND Cosmogenic rate: 23.5 sin 3 θ ± ( 13 Background (day θ =1.0 (2 2 χ 86 2 (2 ∆ . ND 2 /dof=14/16)/dof=14/16) 22 χχ 85 day B 21 . 1 ]( 9 ± and can be left free in the fit by removing the corresponding pull term in the DC•I FD dataDC•I FD data DC•II FD dataDC•II FD data 90% CL90% CL Best fit (Best fit ( φ 18 0 20 40 60 80 100 120 140 error defined as . FD σ . RRM sin α 1 Accidentals subtracted . Cosmogenic background expectations and best-fit values in the FD and the ND. For B 0 = 3

80 60 40 20

are constrained by the estimates obtained from reactor-on data.

140 120 100

Finally, in order to provide a measurement of the IBD rate normalization, the pa- Although fully consistent, the best fit of ) (day rate Observed •1 ν r ND ND Figure 5 and the ND (right)errors, are not shown visible, superimposed areB at to the the level best-fit of model (dashed line). The statistical rameter Since the correlated detectionthis efficiency parameter is provides known effectivelyvalue the with of relative a the normalization negligible reactor-on with uncertainty flux respect (0.25%), simulation. to This the central central value is defined by the mean cross- considered in the R+S analysisand yet. the In best-fit table values isbackground presented. in Due the to ND the (visible anti-correlationobtained in between in sin bottom the plot current ofthe RRM figure R+S analysis result pulls (sin down the central value of R ters of reduced with respect to the background-model-independent fit results. obtained in [ mostly driven by the background constraint and the use of the new MD reactor-off data, not Table 3 comparison purposes, therestricted last to the row 1.0–8.5 MeV shows energy the window. best-fit values obtained in the R+S analysis [ JHEP01(2021)190 ] , 1 9 − FD B , ) , as well 39 day ) . 13 θ 0 13 θ (2 ± 2 measurement, (2 2 75 . , thus being fully 13 θ = 3 86% . function consisting of 0 FD ± 2 B χ 04 . 0 is not significantly modified. ) 13 which is consistent with previ- and the total background rates. θ . The precision achieved by the yields 13 (2 13 2 θ θ φ 017 α . 0 interactions in data samples collected at e ± ¯ ν 094 . , measured by Bugey-4. Once corrected for the – 13 – i f σ h ) = 0 13 θ . The limited reduction on the error is due to the domi- reactor experiments, Double Chooz is the only one with oscillation analyses implemented in reactor experiments, (2 2 13 13 015 . The best-fit value of θ . θ 0 ± ), relying on a reactor-on background model. The best fit values , are also consistent with the background estimates. Thus, these flux errors cancel out, while the uncorrelated flux uncertainty 1 ] for details), fission e 9 − / ¯ 014 ν 095 . 2 . 0 day cm ± 4 1 . . 2 43 ) = 0 +1 − − 105 13 1 . . θ 10 (2 × 2 . According to this result, the best-fit of sin ) = 0 = 27 φ 08) . 13 σ 0 θ ND ± (2 ) fit yields a background-independent value of B The RRM oscillation fit relies on the minimization of a In this work, a multi-detector RRM analysis is implemented for the first time. As in 2 75 . ND and expectations can be added toresults: the sin RRM in ordernant to role improve of the the precisionthe of detection the and background-model-dependent oscillation reactor R+S flux and systematic the uncertainties. RRM The results, compatibility as of well as the consistency tection efficiency and theB reactor flux normalization uncertainties.ous The Double (sin ChoozRRM results: analysis sin is(sin competitive with thatof the one total obtained cosmogenic in background the rates in R+S the fit FD presented and in ND, [ available reactor-off samples, thus offering a unique cross-check of thereactor-on background and models. reactor-off terms,rameters as accounting well for as therors penalty systematic considered terms uncertainties in constraining to the the their fit nuisance estimated pa- are values. those The impacting er- the expected IBD rates, namely, the de- is significantly suppressed.the Apart multi-detector measurement from of boosting theobserved IBD IBD the rate interactions normalization. precision allows The in for currentreactor-off oscillation a the data analysis determination also samples uses of for for the the boththe first backgrounds. the time FD Among and the ND, offering a powerful handle to constrain estimating the corresponding rates and energy spectra from reactor-onR+S data. analyses, the relative comparisona of major the reduction rates of observeddetection at the and different involved baselines reactor systematic leads uncertainties. to In particular, the correlated Carlo expectations provides a background-independentas measurement inclusive of background sin ratespriori in assumptions the far on and thedifferent near from individual detectors the background which usual sources. R+S dowhich no are This depend based approach of on is any background intrinsically a models considering a number of background sources and 6 Summary and conclusions The simple experimental setup ofreactors, Double allows Chooz, for consisting a ofThe simultaneous only RRM analysis two determination relies detectors of on and thedifferent two rate total of reactor observed powers. The comparison of such rates with the null-oscillation Monte specific averaged fuel compositions of(5 the Double Chooz reactor cores,consistent it with the is expectation computed but to reducing be ization the 1.43% uncertainty on the IBD rate normal- section per fission (see [ JHEP01(2021)190 13 θ (2018) ]. 98 ]. deviation with SPIRE IN ]. (2015) 074] ][ 86% . 02 (2002) 011301 SPIRE 0 IN SPIRE ± Phys. Rev. D 89 ][ IN , 04 ][ . 0 Erratum ibid. hep-ex/0404034 [ [ result, the RRM fit is used to measure Phys. Rev. Lett. hep-ex/0212021 , [ 13 hep-ex/0411038 (EDF); the European fund FEDER; the θ [ (2014) 086 10 (2004) 101801 – 14 – Review of Particle Physics 93 Evidence for an oscillatory signature in atmospheric (2003) 021802 JHEP Improved measurements of the neutrino mixing angle , (2005) 081802 90 ), which permits any use, distribution and reproduction in 94 ]. ]. First results from KamLAND: Evidence for reactor anti-neutrino collaboration, Electricité de France SPIRE SPIRE collaboration, Phys. Rev. Lett. IN IN Direct evidence for neutrino flavor transformation from neutral current Evidence for muon neutrino oscillation in an accelerator-based , collaboration, ][ ][ CC-BY 4.0 ]. Phys. Rev. Lett. This article is distributed under the terms of the Creative Commons , collaboration, rate normalization. The best-fit value yields a Phys. Rev. Lett. , e SPIRE ¯ ν IN [ collaboration, collaboration, arXiv:1406.7763 nucl-ex/0204008 neutrino oscillation K2K experiment Double CHOOZ with the Double CHOOZ[ detector interactions in the Sudbury[ Neutrino Observatory KamLAND disappearance Super-Kamiokande Particle Data Group 030001 SNO [5] [6] [3] [4] [1] [2] References Physics (RENAFAE) in Brazil. Open Access. Attribution License ( any medium, provided the original author(s) and source are credited. Spain; the Department ofof Energy Energy and in the the Nationaland United the States; Science Russian the Foundation Foundation Russian and for Academyof Department Basic of Science, Research Science, (RFBR) Technology the and in Kurchatov(FINEP), Russia; Innovation Institute the the (MCTI), Conselho Brazilian Nacional the Ministry de FinanciadoraSão Desenvolvimento Científico de Paulo e Estudos Tecnológico Research (CNPq), e Foundation the Projetos (FAPESP) and the Brazilian Network for High Energy orative Research Center TR27, the excellence clusterand “Origin and the Structure Maier-Leibnitz-Laboratorium of the Garching Universe” Culture, in Sports, Germany; Science and the TechnologyPromotion Ministry of of Japan of Science (MEXT) Education, (JSPS) anditividad in the Japan; (SEIDI-MINECO) Japan the Society under Ministerio for grants de the FPA2016-77347-C2-1-P Economía, and Industria MdM-2015-0509 y Compet- in We thank theRégion company de Champagne-Ardenne;de the Département Communes des Ardenne Ardennes;CNRS/IN2P3, Rives the and computer de centre the CC-IN2P3 Communauté Meuse.Planck and Gesellschaft, LabEx the UnivEarthS Deutsche in Forschungsgemeinschaft We DFG, France; the the acknowledge Transregional Max Collab- the support of the CEA, Double Chooz oscillation analyses.the Beyond observed the respect to the flux normalization predicted by Bugey-4,Acknowledgments thus being fully consistent. between the reactor-off data and the background models, confirms the robustness of the JHEP01(2021)190 ] 83 ] ]. ]. 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