Eur. Phys. J. C manuscript No.(will be inserted by the editor)

Search for Signatures of Sterile Neutrinos with Double Chooz

T. Abrahao5,4, H. Almazan15, J.C. dos Anjos5, S. Appel22, J.C. Barriere11, I. Bekman1,T.J.C. Bezerra18,a, L. Bezrukov10, E. Blucher7, T. Brugiere17, C. Buck15, J. Busenitz2,A. Cabrera4,26,b, M. Cerrada8, E. Chauveau6, P. Chimenti5,c, O. Corpace11,J.V. Dawson4, Z. Djurcic3, A. Etenko14, H. Furuta19, I. Gil-Botella8, A. Givaudan4,H. Gomez4,11, L.F.G. Gonzalez24, M.C. Goodman3, T. Hara13, J. Haser15, D. Hellwig1,A. Hourlier4,d, M. Ishitsuka20,e, J. Jochum23, C. Jollet6, K. Kale6,17, M. Kaneda20,M. Karakac4, T. Kawasaki12, E. Kemp24, H. de Kerret4,f, D. Kryn4, M. Kuze20,T. Lachenmaier23, C.E. Lane9, T. Lasserre11,4, C. Lastoria8, D. Lhuillier11, H.P. LimaJr5, M. Lindner15, J.M. Lopez-Castano8,m, J.M. LoSecco16, B. Lubsandorzhiev10,J. Maeda21,13, C. Mariani25, J. Maricic9,g, J. Martino18, T. Matsubara21,h, G. Mention11,A. Meregaglia6, T. Miletic9,i, R. Milincic9,g, A. Minotti11,j, D. Navas-Nicolas4,8,b,P. Novella8,k, L. Oberauer22, M. Obolensky4, A. Onillon11, A. Oralbaev14,C. Palomares8, I.M. Pepe5, G. Pronost18,l, J. Reichenbacher2,m, B. Reinhold15,g,S. Schonert22, S. Schoppmann15, L. Scola11, R. Sharankova20, V. Sibille11,d, V. Sinev10,M. Skorokhvatov14, P. Soldin1, A. Stahl1, I. Stancu2, L.F.F. Stokes23, F. Suekane19,4,S. Sukhotin14, T. Sumiyoshi21, Y. Sun2,g, C. Veyssiere11, B. Viaud18, M. Vivier11,S. Wagner4,5, C. Wiebusch1,o, G. Yang3,n, F. Yermia18

1 III. Physikalisches Institut, RWTH Aachen University, 52056 Aachen, Germany2Department of Physics and Astronomy, University of Alabama, Tuscaloosa, Alabama 35487, USA3Argonne National Laboratory, Argonne, Illinois 60439, USA4APC, Universite de Paris, CNRS, Astroparticule et Cosmologie, F-75006, Paris5Centro Brasileiro de Pesquisas Fısicas, Rio de Janeiro, RJ, 22290-180, Brazil6Universite de Bordeaux, CNRS/IN2P3, CENBG, F-33175 Gradignan, France7The Enrico Fermi Institute, The University of Chicago, Chicago, Illinois 60637, USA8Centro de Investigaciones Energeticas, Medioambientales y Tecnologicas, CIEMAT, 28040, Madrid, Spain9Department of Physics, Drexel University, Philadelphia, Pennsylvania 19104, USA10Institute of Nuclear Research of the Russian Academy of Sciences, Moscow 117312, Russia11IRFU, CEA, Universite Paris-Saclay, 91191 Gif-sur-Yvette, France12Department of Physics, Kitasato University, Sagamihara, 252-0373, Japan13Department of Physics, Kobe University, Kobe, 657-8501, Japan14NRC Kurchatov Institute, 123182 Moscow, Russia15Max-Planck-Institut fur Kernphysik, 69117 Heidelberg, Germany16University of Notre Dame, Notre Dame, Indiana 46556, USA17IPHC, CNRS/IN2P3, Universite de Strasbourg, 67037 Strasbourg, France18SUBATECH, CNRS/IN2P3, Universite de Nantes, IMT-Atlantique, 44307 Nantes, France19Research Center for Neutrino Science, Tohoku University, Sendai 980-8578, Japan20Department of Physics, Tokyo Institute of Technology, Tokyo, 152-8551, Japan21Department of Physics, Tokyo Metropolitan University, Tokyo, 192-0397, Japan22Physik Department, Technische Universitat Munchen, 85748 Garching, Germany23Kepler Center for Astro and Particle Physics, Universitat Tubingen, 72076 Tubingen, Germany24Universidade Estadual de Campinas-UNICAMP, Campinas, SP, 13083-970, Brazil25Center for Neutrino Physics, Virginia Tech, Blacksburg, Virginia 24061, USA26LNCA Underground Laboratory, IN2P3/CNRS - CEA, Chooz, FranceReceived: date / Accepted: date

aNow at Department of Physics and Astronomy, University of Sussex,Falmer, Brighton, United KingdombNow at IJC Laboratory, CNRS/IN2P3, Universite Paris-Saclay, Orsay,FrancecNow at Universidade Estadual de Londrina, 86057-970 Londrina,BrazildNow at Massachusetts Institute of Technology, Cambridge, Mas-sachusetts 02139, USA

eNow at Tokyo University of Science, Noda, Chiba, JapanfDeceased.gNow at Physics & Astronomy Department, University of Hawaii atManoa, Honolulu, Hawaii, USAhNow at High Energy Accelerator Research Organization (KEK),Tsukuba, Ibaraki, JapaniNow at Physics Department, Arcadia University, Glenside, PA 19038

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Abstract We present a search for signatures of neutrinomixing of electron anti-neutrinos with additional hypothet-ical sterile neutrino flavors using the Double Chooz exper-iment. The search is based on data from 5 years of opera-tion of Double Chooz, including 2 years in the two-detectorconfiguration. The analysis is based on a profile likelihood,i.e. comparing the data to the model prediction of disappear-ance in a data-to-data comparison of the two respective de-tectors. The analysis is optimized for a model of three activeand one sterile neutrino. It is sensitive in the typical massrange 5×10−3 eV2 . ∆m2

41 . 3×10−1 eV2 for mixing an-gles down to sin2 2θ14 & 0.02. No significant disappearanceadditionally to the conventional disappearance related to θ13is observed and correspondingly exclusion bounds on thesterile mixing parameter θ14 as a function of ∆m2

41 are ob-tained.

Keywords sterile neutrino · neutrino mixing · reactorneutrino · Double Chooz

PACS 14.60.St · 13.15.+g · 95.55.Vj · 28.41.Ak

Mathematics Subject Classification (2010) 62F03 ·62P35 · 65C60

1 Introduction

The standard model of particle physics includes three flavorsof neutrinos that interact through the weak force with otherparticles [52]. The neutrino flavors are identified by the cor-responding charged lepton in charged current interactions.With the discovery [15, 35] of neutrino oscillations [45, 48],it became clear that neutrinos have mass. Currently the ma-jority of observations is consistent with the standard pictureof three mass eigenstates (ν1,ν2,ν3) mixing with the flavoreigenstates (νe,νµ ,ντ). The mixing is described by a 3× 3unitary matrix (PNMS matrix), parametrized by three mix-ing angles θ12, θ13, θ23 as well as a CP violating phase δ andtwo Majorana phases if neutrinos are Majorana particles.

The neutrino experiments Double Chooz, Daya Bay, andRENO contributed to the field by establishing the third oscil-lation mode that is related to the mixing angle θ13 [3, 16, 20].These experiments observe the disappearance of νe from nu-clear reactors by measuring the flux at different distances.

jNow at LAPP, CNRS/IN2P3 , 74940 Annecy-le-Vieux, FrancekNow at Instituto de Fısica Corpuscular, IFIC (CSIC/UV), 46980 Pa-terna, SpainlNow at Kamioka Observatory, ICRR, University of Tokyo, Kamioka,Gifu 506-1205, JapanmNow at South Dakota School of Mines & Technology, 501 E. SaintJoseph St. Rapid City, SD 57701nNow at State University of New York at Stony Brook, Stony Brook,NY, 11755, USAoCorresponding author, e-mail: wiebusch@physik.rwth-aachen.de

The concept of multiple identical detectors has proven cru-cial in controlling and reducing systematic uncertainties. To-day, the oscillation angle θ13 is the most precisely measuredoscillation parameter [52].

There have been speculations about the existence ofadditional neutrinos that are non-interacting with matter,see e.g. [1]. These thoughts are supported by experimentalanomalies reported by the LSND [13] and MiniBooNE [14]neutrino-beam experiments as well as the so-called reactor[46] and gallium [2, 9, 38] anomalies, where the observedνe and νe fluxes are roughly 5 % to 10 % less than the the-oretical predictions. However, the uncertainty of those pre-dictions remains an open question and our latest results [40]indicate a possible underestimation of the reactor flux pre-diction. Though this deficit is marginally compatible withthe uncertainty of the flux prediction, it could be also in-terpreted as disappearance due to oscillation with additionalneutrino states. Recently, the Neutrino-4 collaboration hasreported [51] indications of a spectral distortion at shortbaseline to the reactor that would be consistent with the os-cillation hypothesis. This result is subject of ongoing dis-cussions [23, 30, 50]. Particularly it has been reviewed in[27] considering the validity of the Wilks’ theorem, thus re-sulting in a reduced significance. Note that in this paper wereport a very similar effect of reduced significance with re-spect to Wilks’ theorem in our measurement. From a phe-nomenological perspective it is important to emphasize thatconsistency of all today’s global data within a single simplesolution remains an unsettled open debate, see e.g. [32].

The simplest extension of the standard oscillation pic-ture is a 3+1 model [1]. Though this model cannot consis-tently explain all experimental anomalies, its few parame-ters make it well suited as a benchmark model in the follow-ing discussions. Here, one additional sterile, i.e. not weaklyinteracting, neutrino mixes with the three active neutrinostates. This results in an additional mass state m4 and anextension of the mixing matrix to 4× 4 with the additionalparameters θ14, θ24, θ34, and additional CP violating phases.

In this picture, a non-zero mixing of reactor νe with asterile neutrino will result in a disappearance, superimposedto the standard oscillation related to θ13. Assuming smallmixing and baselines relevant for the Double Chooz experi-ment, only the parameters θ14 and the difference of squaredmasses ∆m2

41 ≡ m24−m2

1 are relevant [42], and the survivalprobability of νe as a function of distance L and energy Ecan be approximated by

Pνe→νe (E,L) ≈ 1−sin2 (2θ13)sin2(

1.267MeVeV2m

· ∆m2eeL

E

)− sin2 (2θ14)sin2

(1.267

MeVeV2m

· ∆m241L

E

)(1)

The first sine term corresponds to the disappearance relatedto the standard θ13 mixing while the second sine term de-

3

Fig. 1 Survival probability of reactor νe as a function of the energy forthe baselines of the ND (top) and FD (bottom) for different benchmarkoscillation parameters θ14 and ∆m2

41. The dotted line corresponds tothe no-sterile case, where the survival probability is governed by theconventional θ13 oscillation. The dashed and solid lines show two dif-ferent examples of sterile mixing.

scribes the additional disappearance due to the mixing withthe sterile neutrino state. The term ∆m2

ee is a shorthand forcos2 θ12 ∆m2

31 + sin2θ12 ∆m2

32.The effect is displayed in Fig. 1 for baselines of 400 m

and 1050 m corresponding to the average distances of thenuclear reactors to the two Double Chooz detectors. The ex-istence of sterile neutrinos with non-zero mixing leads tothe additional disappearance superimposed on the conven-tional oscillation. The amplitude of this oscillation is givenby the parameter sin2 (2θ14). The oscillation frequency seenin the energy-dependence is proportional to the difference ofsquared masses. For mass differences of ∆m2

41 � 0.1eV2,oscillations become fast. Given the experimental energyresolution, they become eventually indistinguishable froma global normalization change. Similarly, for small mass-square differences ∆m2

41 ≈ ∆m2ee ' 2.5×10−3 eV2 the dis-

appearance becomes indistinguishable from the conven-tional oscillation with θ13. Note, that the above approxima-tion is only used for illustrative purposes and for all numer-ical calculations in this analysis we use the full four-flavorpropagation code nuCraft [54].

The position of the two Double Chooz detectors hasbeen optimized for the measurement of θ13 assuming ∆m2≈2.5×10−3 eV2. For an energy range of detected reactor neu-trinos between about from 1 MeV to 8 MeV and the twobaselines of 400 m and 1050 m, the probed L/E range forthe disappearance of νe is approximately 50 m/MeV to1000 m/MeV. For larger mass differences, shorter baselinesare desirable in order to observe the un-oscillated flux witha near detector. This is realized by short-baseline experi-ments, Bugey-3 [31] and more recently DANSS [17], NEOS[41], Neutrino-4 [51], PROSPECT [25], SoLID [8], and

STEREO [18, 19], that target mass-square differences on theeV2 scale. The probed L/E range for these experiments istypically 1 m/MeV to 20 m/MeV. Therefore the here pre-sented search is complementary in probed L/E as well aslower probed mass-square differences below 0.1 eV2; seealso [33].

2 Experimental setup

The Double Chooz experiment consists of two nearly iden-tical gadolinium-doped liquid scintillator detectors [24] lo-cated close to the Chooz-B nuclear power plant, see Fig. 2.The power plant consists of two nuclear reactors of type N4,165 m apart with a thermal power of about 4.25 GW each.The far (near) detector is located underground with an over-burden of about 300 m (120 m) water equivalent at a distanceof 1115 m and 998 m (469 m and 355 m) to the reactor cores.

Fig. 2 The Double Chooz experiment. Left: arrangement of the twodetectors far and near with respect to the nuclear reactors. Right: De-sign of a Double Chooz detector. Figure modified from [40].

Details of the detectors are described in [3, 4, 6, 40].The detectors are constructed in an onion-like structure witha central detector made of four concentric cylindrical tanks.The innermost acrylic vessel contains 10.3 m3 gadoliniumloaded liquid scintillator called the ν-target. The ν-target issurrounded by the γ-catcher, filled with 22.5 m3 liquid scin-tillator without gadolinium loading. Both central volumesserve as the neutrino target. A neutrino interacting in the tar-get by inverse beta decay (νe + p→ e++ n) [53] producesthe characteristic signature of a delayed coincidence wellknown since the early days of neutrino experiments [28].

4

This is formed by a prompt signal from the positron and itsannihilation and then the delayed signal from the captureof the thermalized neutron by either gadolinium or hydro-gen. Though increasing the rate of accidental backgroundevents, the use of both types of captures in a combined dataset greatly enlarges the sensitive volume and thus the statis-tics of detected neutrinos as well as reducing some of thesystematic uncertainties. This technique, called total neutroncapture, has been developed by the Double Chooz experi-ment for the most recent θ13 analysis [40] and is appliedalso for this analysis.

The central target volumes are surrounded by a buffervolume filled with mineral oil, shielding the inner volumefrom radioactivity, partly from 390 10-inch PMTs that areinstalled on the inner wall of the stainless steel buffer tankand observe the target. Optically separated from these innervolumes is the inner veto. That is a 50 cm thick cylindricalvolume filled with liquid scintillator and equipped with 78 8-inch PMTs. It actively shields the inner detector by taggingcosmic-ray induced muons, gammas, and neutrons from out-side the detector. Shields of 15 cm thick demagnetized steel(1 m water) surround the inner veto of the far (near) detec-tor, suppressing external gamma rays. A chimney in the topcenter allows deploying radioactive sources for calibration.Above the detector is the outer veto detector that adds tothe shielding and allows for evaluating the efficiency of theinner veto detector.

Several key aspects of the Double Chooz experiment areimportant to this analysis. A main goal is avoiding depen-dencies on absolute predictions of the neutrino flux from thereactors as well as detection efficiencies. Therefore we per-form a direct comparison of the event rates measured in thetwo identical detectors, in the following referred to as data-to-data approach. This results in the cancellation of mostreactor flux related uncertainties as well as detection effi-ciencies and some of the background uncertainties in themeasurement of νe disappearance. Furthermore, due to thepresence of only two, relatively close reactor cores, the ge-ometry constitutes well defined baselines from the reactorsto the detectors which is important for testing faster oscilla-tion modes than the θ13 oscillation (see Fig. 1). The two de-tectors are situated close to the so-called iso-flux line, wherethe ratio of neutrino fluxes from the two reactors is the samefor both detectors, i.e. the relative contribution from the tworeactors is very similar in the two detectors, further reduc-ing the reactor uncertainty. Another important aspect is thatwe include measurements when one of the reactors or evenboth reactors were switched off. These data allow for di-rectly measuring the backgrounds and their spectral proper-ties [5, 39]. In this analysis, the data from these off-reactorphases are used to construct templates of the energy distri-bution of backgrounds as well as the uncertainties of these

templates for the fit to data. Additionally, the total rate isused to constrain the background rates.

Experimental backgrounds include uncorrelated back-grounds, where a single event appears in a random coinci-dence with another event, as well as correlated backgroundsthat mimic both the prompt and the delayed event. The dom-inant sources of uncorrelated backgrounds are natural ra-dioactivity and instrumental noise such as spontaneous lightemission in the PMT bases of the far detector [7]. Corre-lated backgrounds are mostly caused by secondary productsfrom cosmic ray air induced atmospheric muons that passclose or through the detectors. Muons reaching the detectorare detected with high efficiency and cause an active veto of1.25 ms duration. However, background events arise by (i)fast neutrons from interactions in the rock close to the de-tector entering the neutrino target, (ii) long lived isotopes,in particular 9Li [39], that undergo β -decays followed byneutron emission, and (iii) low energy stopping muons thatenter the detector through the chimney and decay by emis-sion of a Michel electron. All these backgrounds are consid-erably reduced during the data selection and the remainderare measured with specific methods and in dedicated cam-paigns, e.g. during reactor-off phases.

The data of this analysis are identical to the selectiondescribed in [40] and are separated into three data sets. Thefirst (FD-I) has been collected with the far detector prior tocommissioning of the near detector and consists of 455.21days of dead and down-time corrected livetime, collectedbetween April 2011 and January 2013. The second set (FD-II) has been collected with the far detector during operationof both detectors and consists of 362.97 days of livetime col-lected between January 2015 and April 2016. The third set(ND) are the data collected during the same period with thenear detector and corresponds to 257.96 days of livetime.Note that the effective livetime of the ND data is reducedwith respect to the FD-II data, because the larger muon ratein the near detector causes a larger dead-time due to vetoing.While the previously described data has been collected dur-ing operation of at least one reactor, additionally 7.16 daysof livetime with both reactors switched off during the FD-I phase are used to determine the total rate of backgroundevents.

3 Analysis Method

The analysis is based on a profile likelihood ratio (see e.g.G. Cowan in [52]) that has already been exploited by Dou-ble Chooz for a measurement of θ13 in [49] and has alsobeen used internally to confirm the result in [40]. The teststatistic is defined as the ratio of maximum likelihoods fortested model parameters~η = {sin2 2θ14,∆m2

41} with respectto the globally largest likelihood value which is found for

5

the parameters ~η = { ˆsin2 2θ14,ˆ

∆m241}. This defines the test

statistic for the given data set~x and model parameters ~η

λ (~x,~η) =−2 · ln supL (~x|~η ,~ξ )

supL (~x|~η ,~ξ )=−2∆ ln(L ) (2)

In addition to the two model parameters ~η that describe asterile neutrino signal, the reactor fluxes, detector responses,systematic uncertainties and backgrounds are modeled by atotal number of 298 additional and partly correlated param-eters ~ξ (see below for details). These parameters are treatedas nuisance parameters in the fit. They are optimized sep-arately for each respective signal hypothesis with ~ξ repre-senting those nuisance parameters that maximize the locallikelihood for the tested ~η .

For the test of a potential oscillation signal from ster-ile neutrinos, we compare the best-fit standard 3-flavormodel (null hypothesis, ~η0), described by the two parame-ters sin2 2θ14 = 0 and ∆m2

41 = 0, to the globally best fit 3+1sterile neutrino model (signal hypothesis) for the parame-ters ~η that maximize the likelihood of the data ~x. Note thatspecifically the null hypothesis~η0 is degenerate with respectto the two parameters ~η because only one of them fixed tozero is sufficient to model a no-oscillation signal. Further-more,~η0 is a special case, nested within the parameter spaceof the signal hypothesis resulting in λ (~x,~η0)≥ 0.

The likelihood itself is implemented as a product of mul-tiplicative terms with the Poissonian likelihoods P(ni,µi)

of the observed number of events ni in the energy bin i in allthree data sets d ∈ {ND,FD− I,FD− II} multiplied withGaussian prior functions G on external nuisance parameters

L (~x|~η ,~ξ ) = ∏d∈{ND,FD−I,FD−II}

∏i∈[Emin...Emax]

P(nd,i,µd,i(~η ,~ξ ))

·P(no f f ,µo f f (~ξ ))

·∏a∈~ξ

(G (a,a0,σa))

·∏~b∈~ξ

(G ((~b−~b0)

T V−1b (~b−~b0))

)(3)

Here µd,i(~η ,~ξ ) denotes the summed bin expectations of sig-nal and backgrounds as a function of the model parameters.The second term is the Poisson probability of the observedevent number during the reactor-off phases for the back-ground expectation as a function of the nuisance parame-ters. The third term describes Gaussian priors for all single,uncorrelated nuisance parameters a with the expectation a0and the uncertainty σa. The fourth term describes Gaussianpriors for all nuisance parameters~b that are correlated, de-scribed by the expectation~b0 and the covariance matrix Vb.

The data are binned for each of the three sets in 38 binsbetween 1 MeV to 20 MeV with custom bin sizes. The re-gion up to 8 MeV which is dominated by measured reac-tor νe has 28 bins of 0.25 MeV size. Above 8 MeV, binsare background dominated but are included in the fit asthey allow for constraining the background rates. Due tothe lower statistics, larger bin sizes are used. These are 4bins of 0.5 MeV size between 8 MeV to 10 MeV, where rareisotopes (9Li) dominate and 4 bins of 2 MeV size between12 MeV to 20 MeV, where fast neutrons dominate. In the in-termediate region 10 MeV to 12 MeV, 2 bins of 1 MeV sizeare used.

Systematic uncertainties are modeled by the followingnuisance parameters~ξ in the analysis (more details are givenin [36]):

– The normalizations of the reactor flux expectation foreach energy bin are free fit parameters. This approachis independent of existing reactor flux predictions andthe normalizations are only constrained by the data-to-data comparison of rate and shape of the data in eachdetector. This way, known discrepancies of reactor fluxmodels [22, 40, 41, 43], being independent of the base-line, do not bias the fit, however, at the price of a slightlyreduced sensitivity. The basis of the above approach is alarge correlation in the observed reactor flux for the threedata sets FD-I, FD-II, ND. Because of different runningtimes, this assumption is only approximate, (99.75 %for FD-II and ND, 93.20 % for FD-I and FD2, 93.10 %for FD-I and ND). Therefore, we model additional con-straints on the normalization of each energy bin of thethree data sets with a total of 3× 41 reactor flux pa-rameters between 1 MeV to 11.25 MeV. The number ofparameters is determined by the greatest common divi-sor of the bin widths to create a uniform binning. Thesebins form the basis of an area conserving spline, whichis energy corrected and later integrated over in the orig-inal binning. These parameters are correlated betweenthe data sets with the above correlation factors and addi-tionally we allow for uncorrelated shape deviations witha 41×41 covariance matrix for each data set, that is de-termined from the reactor flux prediction.

– The conventional oscillation parameters sin2 2θ13 and∆m2

ee are free parameters. While ∆m2ee is seeded with

the global best value from [47] and is constrained witha prior corresponding to its uncertainty, sin2 2θ13 is leftunconstrained. The latter ensures that assumptions aboutthe value, which has itself been largely determined in re-actor neutrino experiments, cannot introduce a bias. Bythis, sin2 2θ13 can acquire a different best-fit value forθ14 6= 0.

– Backgrounds are modeled with free parameters for rateand shape. The shape of the contribution from rare iso-topes (9Li) is assumed identical between the three data

6

sets. It has been determined experimentally by a ded-icated selection of events correlated in time and spacewith tagged muon events [6] and it is modeled with 38shape parameters. The rate is assumed identical for FD-Iand FD-II but is different for ND. Both total rates are notconstrained by a prior but are determined by the data asfree parameters during the fit.The rates and shapes of accidental backgrounds havebeen determined by time-scrambled experimental datafor each data set and are individually modeled by 38 pa-rameters for the shape and one parameter for the rate.These parameters are assumed uncorrelated for the threedata sets, to account for changes in data taking over timeand differences in the detectors but are constrained witha prior that reflects the uncertainty in the determinationof the rates.The fast neutron and stopping muon backgrounds aremodeled as R(E)=R0(a ·E+b ·exp(−λ ·E). Here, R0 isthe total rate and the three shape parameters λ , a, and bare further constrained by the normalization. The shapesare assumed to be fully correlated between the data sets,while the rates are the same for for FD-I and FD-II butindependent for ND.A special case is the small constant rate of νe fromthe reactor fuel that has been determined during FD-Ireactor-off phases to (0.58±0.17) d−1. As these neutri-nos undergo the same oscillation, this is modeled in thefit with the nominal oscillated shape expectation for νeand the rate is constrained by a prior corresponding tothis reactor-off rate.

– The uncertainties in the detector response are modelledidentically to [40] by second order polynomials. Theytake into account the non-linearity of the visible energyresponse of the scintillator, the non-uniformity withinthe detector, and the charge non-linearity of the photo-multiplier and electronics response. After analyzing thecorrelations of these effects where we assume the en-ergy response of the scintillator to be fully correlatedbut the other effects to be uncorrelated between the data-sets, the 9 polynomial coefficients can be expressed by7 independent parameters. In addition to the energy re-sponse, the total detection efficiency is subject to uncer-tainty, dominated by the uncertainty of the total targetmass. This is modeled by a total of three constrained andpartly correlated parameters.

The resulting expectations of reactor νe as well as the back-grounds for the default model are shown in Fig. 3 in com-parison to the experimental data for all three data sets. Inaddition to the above parameters we have tested additionaluncertainties but their effect was found to be negligible. Inparticular it was shown that the choice of mass ordering hasno relevant impact on the analysis.

5 10 15 20Visible Energy (MeV)

10

210

310

410

Eve

nts

/ 0.2

5 M

eV

Double Chooz IV: ND (258 live-days)

ND Data

MC (no oscillations)

Accidentals

Li9

Fast Neutrons

5 10 15 20Visible Energy (MeV)

1

10

210

310E

vent

s / 0

.25

MeV

Double Chooz IV: FD2 (363 live-days)

FD-II Data

MC (no oscillations)

Accidentals

Li9

Fast Neutrons

5 10 15 20Visible Energy (MeV)

1

10

210

310

Eve

nts

/ 0.2

5 M

eV

Double Chooz IV: FD1 (455 live-days)

FD-I Data

MC (no oscillations)

Accidentals

Li9

Fast Neutrons

Fig. 3 Visible energy distributions of the prompt events in the finaldata set. The ND (top) data is plotted with blue triangles and the FD-II (middle) and FD-I data are displayed as black squares. The differ-ent background model contributions are shown as stacked histogramswhere green indicates the long-lived isotopes (lithium) background,blue the accidental background and gray the fast neutron and stoppingmuon background. The red line indicates the total prediction from re-actor models assuming no oscillations including the backgrounds.

7

The above fit has been extensively tested. These tests in-clude a detailed validation of the θ13 fit in the absence of asterile signal that was found in good agreement to the pub-lished standard analyses of Double Chooz. Here, the relativeimpact of each systematic uncertainty has been evaluatedby performing fits excluding the corresponding nuisance pa-rameter (N-1) or fits including exclusively this parameter ontop of statistical uncertainties (stat+1). All resulting uncer-tainties have been found in good agreement with the stan-dard analysis [40].

For the validation of the detection of a sterile signal,studies of pseudo experiments with injected signal and blinddata-challenges have been performed. Furthermore, the im-pact of each systematic parameter and other experimentaleffects, such as the spectral distortion at 5 MeV have beentested. Here, it was verified that the fit results in an unbiasedestimation of the parameters sin2 2θ14 and ∆m2

41.

4 Test Statistic

The maximum likelihood is numerically obtained by min-imizing the negative log(L ). However, finding the globalminimum and ~η is numerically challenging because the fitdoes not converge for arbitrary combinations of initial signaland nuisance parameters to the global minimum. Therefore,the full phase space of signal parameters ~η is scanned byperforming a numerical fit of the parameters ~ξ for each scanpoint. The result of such a scan is shown in Fig. 4 for an Asi-mov data set [29] based on Monte Carlo simulations of thenull hypothesis of only standard oscillations. As the Asimovdata set represents the mean expectation for this hypothesis,we thus find λ (~x) = 0 for sin2(2θ14) = 0 corresponding tothe injected null hypothesis.

As noted above, the null hypothesis is a special casenested within the more general signal hypothesis. The teststatistic thus allows for a hypothesis test for a sterile sig-nal i.e. non-zero ~η with respect to the no-sterile case ~η0 =~0based on the likelihood ratio. If applied, Wilks’ theorem [55]would predict that the test statistic T S = λ (~x,~η0) follows aχ2 distribution with two degrees of freedom correspondingto the difference in degrees of freedom of the signal andnull hypotheses. However, the preconditions for Wilks’ the-orem are not fulfilled. First, the two parameters sin2 2θ14and ∆m2

41 are degenerate in case of the null hypothesis. Anycombination of these with one of the two parameters equal tozero is sufficient for fulfilling the null hypothesis even if theother parameter has a non-zero value. In many practical ap-plications one can accommodate the problem by introducingan effective degree of freedom 1 ≤ ne f f ≤ 2 and the valueof ne f f can be estimated by pseudo experiments with themethod introduced by Feldman and Cousins [34]. Secondly,the expectation value of partial derivatives with respect to

0.000 0.025 0.050 0.075 0.100 0.125 0.150 0.175sin2(2 14)

10 2

10 1

m2 41

/eV2

95% AW sens.68% AW sens.

0

2

4

6

8

10

(x,

)

Fig. 4 Test statistic λ (~x,~η) for an Asimov data set~x of the null hypoth-esis for a scan of the signal parameter space. All values of sin2 2θ14=0represent the null hypothesis of no-sterile oscillations and correspond-ingly λ = 0 for the Asimov data set. The color scale is clipped atλ = 10. The lines represent the 68 % and 95% sensitivity (see text)for constraining sin2 2θ14 as a function of ∆m2

41.

the parameters ||〈 ∂ 2L (~x|~η)∂ηi ∂η j

〉|| should form a positively def-inite matrix. Due to the oscillatory structure of the signalhypothesis, this is not the case here. A data fluctuation inany of the energy bins can be better described by some sig-nal hypotheses that correspond to such an oscillatory patternin the detectors. As a matter of fact, multiple, very differentsignal parameters can lead — within the experimental res-olutions — to similar patterns. In an illustrative picture, fora statistical fluctuation of the experimental data bins in en-ergy, multiple different combinations of signal parametersallow for a slightly improved description of the data withrespect to the null hypothesis. As a result, multiple minimaof the test statistic can be found within the signal parame-ter space. However, the existence of several minima impliesthat the above matrix of derivatives is zero in some points ofthe parameter space.

As verification of the above discussion, Fig. 5 showsan example analysis for a pseudo data set that was gener-ated from a Monte Carlo simulation of the null hypothesis.The occurrence of multiple minima of the test statistic iswell visible. As apparent features, these minima are hori-zontally elongated and thus correspond to a fixed value of∆m2

41. Repeated pseudo experiments show similar featureswith, however, different number of minima and locationsin each experiment. This supports the interpretation that foreach possible statistical representation of the null hypothe-sis, multiple signal hypotheses can be found that describethe observed data slightly better than the average expecta-tions from the null hypothesis. Each such solution requiresa fixed oscillation length and is usually found close to thesensitivity-line beyond the region where a stronger signalwould likely cause a more significant observation. More de-tails on these observations can be found in [36]. We note

8

0.000 0.025 0.050 0.075 0.100 0.125 0.150 0.175sin2(2 14)

10 2

10 1

m2 41

/eV2

95% AW sens.

0

2

4

6

8

10

(x,

)Fig. 5 Example analysis of a pseudo data set representing the null hy-pothesis. The data set was generated with Poissonian fluctuations froma Monte Carlo data set. The blue line represent the 95% sensitivity (asdefined in the text) for constraining sin2 2θ14 as a function of ∆m2

41.

that this has been independently discussed in [12] for short-baseline sterile neutrino searches and very recently in [27].

0.0 2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0TS

0.00

0.05

0.10

0.15

0.20

0.25

0.30

Norm

alize

d en

tries best fit from experimental data

2(dof=1)2(dof=2)

ndof = 1.79 ± 0.44, M = 7.52 ± 3.02, 2/dof = 1.23ndof = 2, M = 6.22 ± 0.34, 2/dof = 1.15ndof = 1, M = 18.82 ± 1.23, 2/dof = 1.45pseudo exp.

Fig. 6 Expected distribution of test statistic values as obtained from390 pseudo experiments of the null hypothesis. Also shown is the ex-pectation for a χ2-distribution with one and two degrees of freedomand various modified distribution functions (see text).

As a consequence, the distribution of the test statis-tic values T S = λ (~x,~η0) cannot be approximated by a χ2-distribution but has to be derived from an ensemble study ofpseudo experiments. Due to the huge computational effortfor scanning the full parameter space, this has been possibleonly for limited statistics of a few hundred pseudo experi-ments. The resulting test statistic values T S when compar-ing the global minimum to the null hypothesis are shown inFig. 6. It can be clearly seen that the test statistic stronglydeviates from χ2-distributions of one and two degrees offreedom. Motivated by the fact, that the choice of the bestof several random minima in the parameter space intro-duces a selection with trials (often called look-elsewhereeffect), we introduce a trial factor in three versions of a

modified approximation of the test statistic. For this, we cal-culate the probability distribution fM(x) of the largest χ2

value x from an ensemble M trials. This results to fM(x) =M · χ2(x,ndo f ) ·

(∫ x0 χ2(y,ndo f )dy

)M−1 where χ2(x,ndo f ) isthe p.d.f. of a single trial. Three versions of this approxi-mation with M as a free parameter are fitted to the pseudoexperiments, using χ2 distributions of one, two, and a fitteddegree of freedom ndo f . All three versions describe the ob-served test statistic reasonably well. Particularly the case ofndo f = 2 results in a fitted M ' 6 which agrees well with theobservations in pseudo experiments.

0 1 2 3 4 5

TS

0.00

0.25

0.50

0.75

1.00

1.25

1.50

1.75

2.00

Norm

alize

d en

tries

2(dof = 1)pseudo exp. sin22 true

14 = 0.000, m241 = 0.080 eV2

pseudo exp. sin22 true14 = 0.072, m2

41 = 0.280 eV2

Fig. 7 Test statistic for fixed values of ∆m241. Shown are the results

from 1999 pseudo experiments when fitting sin2 2θ14 for 100 discretevalues of ∆m2

41 for the injected null hypothesis. For comparison, theexpectation from a χ2 distribution of one degree of freedom is shown.Additionally the test statistic for 1997 pseudo experiments of an in-jected signal is shown. Here the median of the fit sin2 2θ med

14 has beendetermined for each of the 100 tested ∆m2

41 values. The test statisticis then evaluated with sin2 2θ med

14 instead of sin2 2θ14 = 0 as the nullhypothesis. All distributions are found to be consistent.

The situation becomes simpler, when taking into accountthat multiple values of ∆m2

41 can cause a minimum in thetest statistic. In a modified hypothesis, we can define thesensitivity as the ability to test values of sin2 2θ14 as a func-tion of ∆m2

41. When analyzing the pseudo experiments in araster scan for distinct fixed values of ∆m2

41 and varying onlysin2 2θ14 [34], a distribution that is well compatible with theexpectation from a χ2 distribution with one degree of free-dom is found as shown in Fig. 7. Also for an injected sig-nal, the test statistic with respect to the median expectationof the null hypothesis is consistent and also described bythe same χ2 distribution. This is a good confirmation of ourassumption that the observed trials are only related to dif-ferent degenerated oscillation lengths. This test shows thatin this case the test statistic can be well described with aχ2-distribution of one degree of freedom in agreement withWilks’ theorem.

9

5 Sensitivity

We define the sensitivity, in the following denoted asAsimov-Wilks’ (AW) sensitivity, by the boundary valuesin2 2θ14 as a function of ∆m2

41 where the test statistic of theAsimov data set has a value 〈λ (~x)〉 ≥ 3.84 (or 〈λ (~x)〉 ≥ 1).This corresponds to the boundary of the median signal ex-pectation where in case of absence of a signal 95 % (or 68 %)of experiments obtain a smaller value of sin2 2θ14. Thischoice marks the region, where larger values of sin2 2θ14 areexpected to lead to indications of a signal on the level of two(or one) standard deviations but is also closely related to theability of constraining sin2 2θ14 in the absence of a signal.These sensitivities are shown as lines in Fig. 4 and Fig. 5.The statistical coverage of the AW sensitivity as well as theunbiased estimation of the model parameters sin2 2θ14 and∆m2

41 have been verified with ensembles of pseudo data in[36].

For small values of ∆m241 . 5×10−3 eV2, the sensitivity

becomes weaker as the disappearance becomes ambiguouswith conventional oscillations whose energy dependenceis given by ∆m2

ee. The free nuisance parameter sin2 2θ13becomes degenerate with sin2 2θ14 and the sensitivity de-creases. Also towards large values of ∆m2

41 & 0.3eV2 thesensitivity decreases, because oscillations become fast, andthe disappearance turns into an overall deficit for both de-tectors. For the data-data fit approach as implemented here,an oscillation signal would thus become increasingly indis-tinguishable from an overall change of the reactor flux nor-malization. We have tested that by additionally constrain-ing the fit with a flux prediction. The sensitivity above∆m2

41 & 0.3eV2 would strongly improve but also becomestrongly model dependent. An interesting observation is thedip in sensitivity at ∆m2

41 ' 5×10−2 eV2. The effect is re-lated to the interference of maximum and minimum disap-pearance for neutrinos from the two reactor cores to the twodetectors, whose baselines differ by about∼100 m. A strongdisappearance for signals of one of the reactor is counter-acted by no disappearance for the other reactor. We havetested that the effect disappears when simulating the base-line of only one reactor core.

The effect of the aforementioned spectral distortions ofreactor flux models has been studied with two Asimov datasets. One of them included a bump-like distortion at 5 MeVusing a double-Gaussian approximation of the measurementin [22]. The resulting sensitivity is only marginally impactedas shown in Fig. 8.

6 Experimental result

The result of the scan of the test statistic λ (~x) for the exper-imental data is shown in Fig. 9.

Fig. 8 Sensitivity (95% C.L.) of the analysis as obtained from Asimovdata sets with and without a spectral distortion at 5 MeV.

0.000 0.025 0.050 0.075 0.100 0.125 0.150 0.175sin2(2 14)

10 2

10 1

m2 41

/eV2

global best fit95% AW sens.

0

2

4

6

8

10

(x,

)

Fig. 9 Likelihood scan of the experimental data.

The global best fit minimum is found for the valuesˆsin2 2θ14 = 0.043 and ˆ

∆m241 = 0.028eV2. The nuisance pa-

rameters converged to values within their reasonable range.In particular the best fit value sin2 2θ13 = 0.108+0.016

−0.017 ofthe null hypothesis is found in agreement with the nom-inal value 0.105±0.014 that has been obtained from thesame data set [40]. The difference to that result is expectedfrom the differences of the fit method and has been verifiedin a detailed comparison of the fit methods. Also the valuesin2 2θ13 = 0.1077 obtained for the global best fit η is veryclose to the null hypothesis and thus does not indicate a pullon the best fit.

The value of the test statistic of the best fit with respectto the null hypothesis of no sterile mixing is λ (~xexp) = 6.15.From 388 performed pseudo experiments of the null hypoth-esis in Fig. 6, a total of 96 have a larger or equal value of λ .The corresponding p-value is (24.7±2.2)%. This p-valuedoes not depend on details of the modeling of the test statis-tic. When using the three approximations of the test statisticdistributions in Fig. 6, very similar p-values between 22 % to26 % are obtained. Therefore, the experimental result is fully

10

consistent with the null hypothesis of no mixing with sterileneutrinos and no evidence for a signal can be reported.

The location of the best-fit point is not within the regionof good sensitivity but close to the estimated sensitivity line,see Figs. 8 and 4. This is, as discussed above, an expectedfeature of statistical background fluctuations that are beingpicked up by a signal model.

0.8

1.0

1.2 FD-I

no-sterilesteriledata

0.8

1.0

1.2

NIB

DAs

imov

spec

trum

FD-II

no-sterilesteriledata

1 2 3 4 5 6 7 8 9 10Evis / MeV

0.8

1.0

1.2 ND

no-sterilesteriledata

Fig. 10 Experimental residuals for the three consistently fitted datasets FD-I, FD-II, and ND. The data are normalized to the nominal re-actor expectation [37] adapted to the Double Chooz reactors includingconventional oscillations with parameters taken from an independentmeasurement [11]. The experimental data are plotted as red dots. Theglobal best fit is shown as a solid line while for comparison the best-fitnull hypothesis is shown as a dashed line. As the fit optimizes system-atic uncertainties to the data, only statistical error bars are displayed.

Figure 10 shows the fit residuals normalized to the num-ber of events expected for the nominal reactor-model includ-ing conventional oscillations. Also shown are the best fit ofthe null (non-sterile) and best-fit sterile hypothesis. All threedata sets are consistently described by both models with agenerally good agreement, including the observed bump at5 MeV and other spectral features, as expected from the im-plementation of the fit. No particular difference is observedbetween the three data sets that would hint to a mismod-eled detector responses. Note that due to the use of a freebut global normalization for each energy bin, the fit doesnot depend on the assumed shape and normalization of theinitial reactor flux model but only on the consistency ofthe measured experimental data in the three data sets. Thesterile model achieves a marginally better description. Thedifference can be quantified by Pearson’s χ2-test [52]. Thesummed χ2 values of the three data distributions of Fig. 10

are 78.17 for the best-fit no-sterile model and 71.91 for thebest-fit sterile model, respectively. With a rough estimationof the number of degrees of freedom of 76, i.e. the numberof data points corrected for the free overall normalizations ofeach energy bin, this indicates an acceptable goodness of fitfor both models. The difference ∆ χ2 = 6.25 shows no sys-tematic trend and is largely driven by a few fluctuating datapoints, i.e. the two energies 4.1 MeV and 5.6 MeV dominatethe difference with a summed contribution of ∆ χ2 = 5.5.As discussed above, this is an expected behavior also for theno-sterile case where for each statistical fluctuation of dataa matching sterile hypothesis can be constructed. No gen-eral trend in the data supporting a sterile signal is observed,which is consistent with the observation of an insignificantp-value as reported above.

7 Discussion

The experimental data has been tested over the full range ofthe two-dimensional signal parameter space. The globallyfound minimum does not constitute a significant observationof a signal but is well compatible with the null hypothesis ofno mixing with sterile neutrinos.

In response to the limited computing resources that donot permit the evaluation of the test statistic with pseudoexperiments at every point in the two-dimensional param-eter space with sufficiently accurate coverage, we have de-cided for a more robust limit-setting strategy which is alsoknown under the term raster-scan [44]. Here, we calculateone-dimensional exclusion limits on the maximum allowedvalue of sin2 2θ14 as a function of ∆m2

41. These limits arecalculated with a frequentist approach based on Wilks’ theo-rem comparing the local test statistic with respect to the bestfit at the probed ∆m2

41 and using the χ2 probability with onedegree of freedom. The statistical coverage of the approachhas been verified with pseudo experiments of injected signalas shown above.

Alternatively a two dimensional approach could be pur-sued, where the test statistic is compared to the globallyfound maximum likelihood. Such a strategy has been fol-lowed e.g. for the analysis in Daya Bay [22]. Here the ex-clusion would correspond to the probability of the combina-tion of sin2 2θ14 and ∆m2

41. However, pseudo experimentswith an injected signal have revealed that our test statis-tic strongly depends on the injected value of sin2 2θ14. Forsmall values of sin2 2θ14 it is close to the test statistic thatwe have observed for the null hypothesis (see Fig. 4) whileit gradually crosses over into a χ2-distribution of two de-grees of freedom for larger values. Because the determi-nation of limits with correct statistical coverage would re-quire the simulation of a very large number of pseudo ex-periments throughout the entire parameter space, we have

11

chosen the raster-scan approach. Within the available com-puting resources this resulted in limits of more accurate cov-erage. We note that this strategy applies only to the settingof limits but not to the p-value of the analysis that has beenobtained in a full two-dimensional approach.

0.00 0.05 0.10 0.15 0.20 0.25 0.30sin22 14

10 2

10 1m2 41

/eV2

experimental best fit95% data CL95% AW sens.

Fig. 11 Upper limit (dotted blue line) at 95 % C.L. for sin2 2θ14 as afunction of ∆m2

41. The black dot indicates the position of the globalbest fit. The green solid line corresponds to the AW sensitivity.

The resulting exclusion limits are shown in Fig. 11. Theobtained limits are generally close to the AW-sensitivity. Formasses ∆m2

41, where the best fit results in the null hypothesissin2 2θ14 = 0, the upper limit coincides with the median ex-pected sensitivity. Due to statistical fluctuations in the dataone expects variations around this median sensitivty, de-pending whether excesses or deficits in the prediction matchthese fluctuations better. As the allowed parameter space isbounded to positive values of sin2 2θ14, we expect roughlyfor 50 % of probed ∆m2

41 values fits with a non-zero valueof sin2 2θ14 resulting in less constraining limits than the av-erage sensitivity and similarly a roughly equal number ofmore constraining limits.

As discussed above, both experiments Daya Bay andRENO probe a similar range of L/E values and have pub-lished exclusion limits for a similar range of ∆m2

41 for sterileneutrino mixing in the 3+1 model [21, 26]. A comparison ofthese results is shown in Fig. 12. We note, that a detailedquantitative comparison is difficult, because, unlike DoubleChooz and as discussed above, the two other experimentsprovide two-dimensional limits. Furthermore, their analysisassumptions differ, in particular, the Daya Bay results in-cludes a reactor flux model and constraints on θ13. We havetested that such assumptions would also increase the sensi-tivity of this analysis. The statistics of νe candidates usedin Daya Bay and RENO is roughly four times the statisticsused here. In addition, the figure shows limits obtained bythe Bugey-3 collaboration and limits from combining cos-mological observations. The Double Chooz result based on

10-2 10-1 100

sin22θ14

10-2

10-1

|∆m

2 41|/

eV2

Double Chooz this analysis 95% CLDouble Chooz full data (expected) 95% CLDaya Bay 95% C.L. RENO 95% C.L.Cosmology 95% C.L.Bugey 3 90% C.L.Neos 90% C.L.

Fig. 12 Comparison of the upper exclusion limits provided by thisanalysis (Double Chooz) with results from other measurements: DayaBay [21], RENO [26], Bugey-3 [31] Neos [41], and cosmologicallimits [10] based on the combination of observations of the cosmicmicrowave background, gravitational lensing and baryon-acoustic os-cillations. Additionally displayed is the expected average sensitivityof Double Chooz with the full data statistics from the multi-detectorphase.

the here used data is less constraining than Daya Bay but iscompetitive to the other presented results.

The result has been obtained under the assumption of a3+1 model. An extension to a 3+2 model would require theextension of the 3×3 PMNS Matrix to 5 dimensions with 7additional mixing angles plus additional CP phases and theoscillations would also involve additional mass differences.In the simplest approximation, equation (1) would includean additional term −sin2 2θ15 sin2

∆m251L/(4E). This leads

to additional oscillations, which potentially interfere withthe 4-1 oscillation if ∆m2

41 ≈ ∆m251. As a result of test stud-

ies [36], we find that the here presented limits of the mixingangle as a function of ∆m2 are largely valid also for 3+2models with largely different mass difference and in partic-ular if ∆m2

51 & 0.3eV2. In case both mass-square differencesfall into the sensitive region of this analysis, the oscillationof the respective larger ∆m2 is largely washed out and re-sults in a global normalization offset, to which the data-to-data fit of this analysis is insensitive. In summary, thoughdifferent in statistical coverage, the test for a 3+1 model isalso sensitive for a signal of a more complicated model.

The relative impact of systematic uncertainties has beentested in terms of sensitivity for the null hypothesis and forrelatively strong signals of sin2 2θ14 = 0.1 and varying val-ues of ∆m2

41. It is found that the relative impact of systematicuncertainties on the total error increases towards smaller val-ues ∆m2

41. E.g. for determining the value sin2 2θ14 = 0.1 therelative error changes from σstat

σtot= 99% for ∆m2

41 = 0.1eV2

to σstatσtot

= 55% for ∆m241 = 7.3×10−3 eV2. Among the dif-

ferent systematic parameters, the uncertainty of the energy

12

scale and the unconstrained parameter θ13 show the largestimpact on the total uncertainty. As the current analysis islimited by statistics, it will benefit from the full data set ofDouble Chooz. Figure 12 shows the expected median sen-sitivity for the full duration of multiple detector operation,corresponding to an increase in statistics by roughly a fac-tor 2.4. In addition, we expect improvements by the off-reactor data set, that is enlarged from 7 to 32 days, resultingin reduced uncertainties in background modeling and fur-thermore the planned improved measurement of the protonnumber of the neutrino target.

8 Summary

We have presented an initial search for oscillations of elec-tron anti-neutrinos with additional sterile neutrino flavorswith the Double Chooz experiment. The search uses datafrom five years of operation of Double Chooz, includingtwo years in the two-detector configuration. The analysismethod is based on a profile likelihood, searching for thedisappearance due to oscillations in a data-to-data compar-ison of the two respective detectors. The analysis is opti-mized for a 3+1 model and is sensitive in the mass range5×10−2 eV2 . ∆m2

41 . 3×10−1 eV2. No significant disap-pearance signal additionally to the conventional oscillationsrelated to θ13 is observed in a full 2-d scan of the model pa-rameters. Correspondingly exclusion bounds on the sterilemixing parameter are determined in form of a raster-scan ofθ14 as a function of ∆m2

41. The result is competitive to simi-lar searches in this mass range. An update to the full data setfrom Double Chooz is planned.

Acknowledgements We thank the EDF (”Electricity of France”)company; the European fund FEDER; the Region Grand Est (formerlyknown as the Region Champagne-Ardenne); the Departement des Ar-dennes; and the Communaute de Communes Ardenne Rives de Meuse.We acknowledge the support of the CEA, CNRS/IN2P3, the computercentre CC-IN2P3 and LabEx UnivEarthS in France; the Max PlanckGesellschaft, the Deutsche Forschungsgemeinschaft DFG, the Tran-sregional Collaborative Research Center TR27, the excellence clus-ter ”Origin and Structure of the Universe” and the Maier-Leibnitz-Laboratorium Garching in Germany; the Ministry of Education, Cul-ture, Sports, Science and Technology of Japan (MEXT) and the JapanSociety for the Promotion of Science (JSPS) in Japan; the Ministe-rio de Economıa, Industria y Competitividad (SEIDI-MINECO) un-der grants FPA2016-77347-C2-1- P and MdM-2015-0509 in Spain;the Department of Energy and the National Science Foundation; theRussian Academy of Science, the Kurchatov Institute and the RussianFoundation for Basic Research (RFBR) in Russia; the Brazilian Min-istry of Science, Technology and Innovation (MCTI), the Financiadorade Estudos e Projetos (FINEP), the Conselho Nacional de Desenvolvi-mento Cientıfıco e Tecnologico (CNPq), the Sao Paulo Research Foun-dation (FAPESP) and the Brazilian Network for High Energy Physics(RENAFAE) in Brazil.

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