Detailed studies of 100 Mo two-neutrino double beta decay in NEMO-3

This is a self-archived version of an original article. This version may differ from the original in pagination and typographic details. Author(s): Title: Year: Version: Copyright: Rights: Rights url: Please cite the original version: CC BY 4.0 https://creativecommons.org/licenses/by/4.0/ Detailed studies of 100 Mo two-neutrino double beta decay in NEMO-3 © The Author(s) 2019. Published version NEMO-3 Collaboration NEMO-3 Collaboration. (2019). Detailed studies of 100 Mo two-neutrino double beta decay in NEMO-3. European Physical Journal C, 79(5), Article 440. https://doi.org/10.1140/epjc/s10052019-6948-4 2019 Eur. Phys. J. C (2019) 79:440 https://doi.org/10.1140/epjc/s10052-019-6948-4 Regular Article - Experimental Physics Detailed studies of 100Mo two-neutrino double beta decay in NEMO-3 R. Arnold1, C. Augier2, A. S. Barabash3, A. Basharina-Freshville4, S. Blondel2,S.Blot 5, M. Bongrand2, D. Boursette2, V. Brudanin6,7,J.Busto 8,A.J.Caffrey 9,S.Calvez 2,M.Cascella 4,C.Cerna 10,J.P.Cesar 11,A. Chapon12,E.Chauveau10,A.Chopra4,L.Dawson4,D.Duchesneau13,D. Durand12,R.Dvornický6,19,V.Egorov6,G. Eurin2,4,J.J.Evans 5,L.Fajt 14, D. Filosofov6, R. Flack4, X. Garrido2, C. Girard-Carillo2, H. Gómez2, B. Guillon12, P. Guzowski5, R. Hodák14, A. Huber10, P. Hubert10, C. Hugon10, S. Jullian2, O. Kochetov6,S.I.Konovalov 3, V. Kovalenko6, D. Lalanne2,K.Lang 11,Y.Lemière 12, T. Le Noblet13,Z.Liptak 11,X.R.Liu 4, P. Loaiza2,G. Lutter10, M. Macko10,14, C. Macolino2, F. Mamedov14, C. Marquet10, F. Mauger12, A. Minotti13, B. Morgan15, J. Mott4,27, I. Nemchenok6, M. Nomachi16, F. Nova11, F. Nowacki1, H. Ohsumi17,G.Oliviéro 12, R. B. Pahlka11, C. Patrick4, F. Perrot10,A.Pin 10, F. Piquemal10,18, P. Povinec19,P.Pˇridal14, Y. A. Ramachers15,A.Remoto 13,J. L. Reyss20,C.L.Riddle 9, E. Rukhadze14, R. Saakyan4, A. Salamatin6, R. Salazar11, X. Sarazin2, J. Sedgbeer21, Yu. Shitov6,L.Simard 2,22,F.Šimkovic 6,19, A. Smetana14,K.Smolek 14,A.Smolnikov 6, S. Söldner-Rembold5,B. Soulé10,I.Štekl 14, J. Suhonen23,C.S.Sutton 24, G. Szklarz2, H. Tedjditi8, J. Thomas4,V.Timkin 6, S. Torre4,Vl.I. Tretyak25, V. I. Tretyak6,a,V.I.Umatov 3, I. Vanushin3, C. Vilela4, V. Vorobel26, D. Waters4,F.Xie 4, A. Žukauskas26 1IPHC, ULP, CNRS/IN2P3, 67037 Strasbourg, France 2LAL, Université Paris-Sud, CNRS/IN2P3, Université Paris-Saclay, 91405 Orsay, France 3NRC “Kurchatov Institute”, ITEP, 117218 Moscow, Russia 4UCL, London WC1E 6BT, UK 5University of Manchester, Manchester M13 9PL, UK 6JINR, 141980 Dubna, Russia 7National Research Nuclear University MEPhI, 115409 Moscow, Russia 8Aix Marseille Université, CNRS, CPPM, 13288 Marseille, France 9Idaho National Laboratory, Idaho Falls, ID 83415, USA 10 CENBG, Université de Bordeaux, CNRS/IN2P3, 33175 Gradignan, France 11 University of Texas at Austin, Austin, TX 78712, USA 12 LPC Caen, ENSICAEN, Université de Caen, CNRS/IN2P3, 14050 Caen, France 13 LAPP, Université de Savoie, CNRS/IN2P3, 74941 Annecy-le-Vieux, France 14 Institute of Experimental and Applied Physics, Czech Technical University in Prague, 12800 Prague, Czech Republic 15 University of Warwick, Coventry CV4 7AL, UK 16 Osaka University, 1-1 Machikaneyama Toyonaka, Osaka 560-0043, Japan 17 Saga University, Saga 840-8502, Japan 18 Laboratoire Souterrain de Modane, 73500 Modane, France 19 FMFI, Comenius University, 842 48 Bratislava, Slovakia 20 LSCE, CNRS, 91190 Gif-sur-Yvette, France 21 Imperial College London, London SW7 2AZ, UK 22 Institut Universitaire de France, 75005 Paris, France 23 Jyväskylä University, 40351 Jyvaskyla, Finland 24 MHC, South Hadley, MA 01075, USA 25 Institute for Nuclear Research, Kiev 03028, Ukraine 26 Faculty of Mathematics and Physics, Charles University in Prague, 12116 Prague, Czech Republic 27 Present Address: Boston University, Boston, MA 02215, USA Received: 21 March 2019 / Accepted: 13 May 2019 © The Author(s) 2019 Abstract The full data set of the NEMO-3 experiment has been used to measure the half-life of the two-neutrino double beta decay of 100Mo to the ground state of 100Ru, ae-mail: [email protected] T1/2=6.81 ±0.01 (stat)+0.38 −0.40 (syst)×1018 year. The two-electron energy sum, single electron energy spectra and distribution of the angle between the electrons are presented with an unprecedented statistics of 5 ×105events and a 0123456789().: V,-vol 123 440 Page 2 of 11 Eur. Phys. J. C (2019) 79:440 signal-to-background ratio of ∼80. Clear evidence for the Single State Dominance model is found for this nuclear transition. Limits on Majoron emitting neutrinoless double beta decay modes with spectral indices of n =2,3,7, as well as constraints on Lorentz invariance violation and on the bosonicneutrinocontributiontothetwo-neutrinodoublebeta decay mode are obtained. 1 Introduction Spontaneous nuclear double beta decay is a second order weak interaction process that was theoretically considered for the first time by Goeppert-Mayer [1]. It can occur in some even-even nuclei when two bound neutrons simultaneouslyundergobeta decayand aretransformed into twobound protons emitting two electrons and two (anti)neutrinos. Twoneutrino double beta decay, 2νββ, is one of the rarestdirectly observed radioactive processes with half-lives ranging from 7×1018 to 2 ×1021 years [2,3]. The decay rate of 2νββ decay can be expressed as 1/T2ν 1/2=g4 AG2ν|M2ν|2,(1) where gAisthe axial-vector couplingconstant, G2νis aphase space factor, and M2νis a nuclear matrix element (NME). Measurement of the 2νββ half-life gives direct access to the value of the NME for this process and therefore provides experimental input into nuclear models that are used to evaluate NMEs. Moreover, 2νββ may provide answers to the question of gAquenching in nuclear matter that is currently being actively discussed [4–8]. Detailed studies of 2νββ may therefore be useful to improve NME calculations for the neutrinolessmode of doublebeta decay, 0νββ,the process which violates total lepton number and is one of the most sensitive probes of physics beyond the Standard Model. A recent review of the 0νββ NME calculation methods, challenges and prospects can be found in [9]. Previous measurements have shown that the 100Mo 2νββ half-life is shorter compared to other ββ isotopes [10–17], and it is therefore a promising nucleus for precise studies of the process. Here we present the most accurate to date study of 100Mo 2νββ decay including single electron energy andangular distributionsof the electrons emitted inthe decay withanunprecedentedstatisticsof 5×105events.Theimpact of the single electron energy spectra on nuclear models that are used to calculate the NME is also presented. Searchesformostcommonlydiscussed0νββ mechanisms (exchange of a light Majorana neutrino, right-handed currents, super-symmetry) with NEMO-3 have been reported earlierin[18,19].In this paperwepresentresults obtainedfor 100Mo 0νββ decay accompanied by the emission of Majoron bosons with spectral indices n≥2, as well as constraints on contributions from bosonic neutrinos and from Lorentz invariance violation to 2νββ spectra of 100Mo. 2 The NEMO-3 detector The NEMO-3 detector, its calibration and performance are described in detail in [20] and more recently in [19]. A combination of tracking and calorimetric approaches allows for a full reconstruction of ββ event topology. A tracking chamber is used to reconstruct electron tracks, their origin and end points. The electron energies and arrival times are measured with a plastic scintillator calorimeter. The cylindrical detector measuring 3 m in height and 5 m in diameter is made up of 20 wedge-shaped sectors of identical size. Each sector hosts 7 thin foil strips containing a ββ isotope. The source foils are positioned in the middle of the tracking detector at a radius of 1 m and have a height of 2.48 m. The tracking detector is based on a wire chamber made of 6180 open drift cells operating in Geiger mode with helium as the main working gas with the addition of ethanol (4%), argon (1%) and water vapour (0.15%). The wire cells are strung vertically parallel to the source foils and have average transverse and longitudinal resolutions of 0.5 mm and 0.8 cm (σ) respectively. The tracking volume is surrounded by a segmented calorimeter composed of 1940 optical modules made of 10 cm thick polystyrene scintillator blocks coupled tolowradioactivityphotomultipliertubes(PMT).Theenergy resolution of optical modules for 1 MeV electrons ranges from 5.8 to 7.2% and the time resolution is 250 ps (σ). The detector was calibrated by deploying 207Bi, 90Sr and 232U sources during the course of data collection. The stability of the PMT gains was monitored by a dedicated light injection system that was run every 12 hours. The NEMO-3 detector is supplied with a solenoid which generates a 25G magnetic field parallel to the tracking detector wires and provides charge identification by track curvature. The detector is surrounded by passive shielding consisting of a 19cm thick iron plates to suppress the external gamma ray flux, and of borated water, paraffin and wood to moderate and absorb environmental neutrons. One of the unique advantages of the NEMO-3 technology is the ability to unambiguously identify electrons, positrons, gammaand delayed alpha-particles. This approach leads to a strong suppression of backgrounds by eliminating events that do not exhibit a ββ topology. In addition, it allows for an efficient backgroundevaluation byselecting eventtopologies corresponding to specific background channels. An electron isidentifiedbyareconstructedprompttrackinthedrift chamber matching to a calorimeter deposit. Extrapolating the track to the foil plane defines the event vertex in the source. The track extrapolation to the calorimeter identifies the impact point of the electron track with the corresponding optical 123 Eur. Phys. J. C (2019) 79:440 Page 3 of 11 440 module and is used to correct the reconstructed energy of the electron deposited in the scintillator. The track curvature in the magnetic field is used to distinguish electrons from positrons. A γ-ray is identified as an energy deposit in the calorimeter without an associated track in the drift chamber. An α-particle is identified by a short straight track delayed with respect to the prompt electron in order to tag 214Bi → 214Po delayed coincidences. The NEMO-3 detector took data at the Modane Underground Laboratory (LSM) in the Frejus tunnel at a depth of 4800 m w.e. enabling the cosmic muon flux suppression by a factor of >106. The detector hosted source foils of 7 different ββ isotopes. The two isotopes with the largest mass were 100Mo (6.914 kg) [19] and 82Se (0.932 kg) [21] with smaller amounts of 48Ca, 96Zr, 116Cd, 130Te and 150Nd [22–26]. Two types of purified molybdenum foils were installed in NEMO-3, metallic and composite. Both foil types were enriched in 100Mo with the isotopic enrichment factor ranging from 95.14±0.05 to 98.95±0.05%. The average enrichment factor was 97.7% for metallic foils and 96.5% for composite foils. The metallic foils contained 2479±5gof100Mo. The mean metallic foil density is 58 mg/cm2with a total foil surface of 43,924 cm2. The composite foils contained 4435±13 g of 100Mo. They were produced by mixing a fine molybdenum powder with polyvinyl alcohol (PVA) glue and deposited between Mylar foils of 19 µm thickness. The average surface density of the composite foils is 66 mg/cm2and the total foil surface area is 84,410 cm2. Monte Carlo (MC) simulations are performed with a GEANT-3 based [27] program using the DECAY0 [28] event generator. The time-dependent status and performance of the detector are taken into account in modelling the detector response. The data presented here were collected between February 2003 and October 2010 with a live time of 4.96 years and a total exposure of 34.3 kg year of 100Mo. This is the same exposure as that used for 0νββ results published earlier [19]. 3 Background model Trace quantities of naturally-occurring radioactive isotopes can occasionally produce two-electron events and thus can mimicββ-decayevents.The largestcontributionscomefrom isotopes that are progenies of 238U( 234mPa, 214Pb, 214Bi, 210Bi) and of 232Th (228Ac, 212Bi, 208Tl), as well as 40K. The background is categorised as internal if it originates from radioactive decays inside the ββ source foils, see Fig. 1a. Two electrons can be produced via β-decay followed by a Møller scattering, β-decay to an excited state with the subsequent internal conversion or due to Compton scattering of the de-excitation photon. Fig. 1 Mechanisms of internal (a)andexternal(b) background production in the source foil Decays inside the tracking detector volume form a separate background category. The main source of this background is radon, 222Rn. The decay of radon progenies near the source foil can produce signal-like events in an analogous manner to internal background decays. The last background category is due to the external γ-ray flux produced by decay of radioactive isotopes in detector components, the surrounding area and due to neutron interactions in the shield and material of the detector. The PMT glass is the main source of these γ-rays. They can produce two-electron events due to e+e−pair creation in the source foil and subsequent charge misidentification, double ComptonscatteringorComptonscatteringfollowedbyMøllerscattering, see Fig. 1b. A detailed discussion of the NEMO-3 background model is presented in [29] and results of screening measurements can be found in [19,20,29]. Here we follow the same background model as that presented for the 100Mo 0νββ analysis [19]. However, radioactive isotopes contributing to the low energy region of the 100Mo 2νββ spectrum were not relevant for the 0νββ analysis in [19] and are therefore discussed in more detail below. The background in question comes from traces of β-decaying isotopes 210Bi, 40K and 234mPa in 100Mo foils. In addition, 100Mo 2νββ decay to the 0+ 1 excited state of 100Ru is also taken into account as a source 123 440 Page 4 of 11 Eur. Phys. J. C (2019) 79:440 Fig. 2 Single electron events energy spectra for metallic and composite molybdenum. The error bars correspond to statistical uncertainty only Table 1 100Mo source foil contamination activities measured with the NEMO-3 detector. Activities of 214Bi and 208Tl are from [19] Source 100Mo metallic 100Mo composite 214Bi internal, mBq/kg 0.060 ±0.019 0.305 ±0.038 214Bi mylar, mBq/kg −1.05 ±0.06 208Tl, mBq/kg 0.087 ±0.004 0.128 ±0.003 234mPa, mBq/kg 11.40 ±0.06 2.10 ±0.03 40K , mBq/kg 8.67 ±0.05 13.57 ±0.04 210Bi, mBq/m25.51 ±0.03 19.42 ±0.03 of internal background. The experimental half-life value of T1/2=6.7+0.5 −0.4×1020 years [3] is used to evaluate this contribution. The activities of β-emitters in 100Mo foils are determined from the fit to the electron energy distribution for a single electron event sample, which is shown in Fig. 2separately for metallic and composite foils. To disentangle the 210Bi contribution from the source foils and the surface of the tracker wires the activity measured in [29]isusedforthe latter. Figure 2shows the sum of both contributions. Secular equilibrium is assumed between 214Pb and 214Bi. The same is done between 228Ac, 212Bi and 208Tl, where the branching ratio of 35.94% is taken into account. There is sufficiently good agreement between data and MC for the single electron energy spectrum. The observed deviations of MC from data are within 6% and are not significant when the systematic uncertainty on the external background is taken into account. The results of the internal 100Mo foil contamination measurements carried out with the NEMO-3 detector are shown in Table 1. 4 Two-neutrino double beta decay of 100Mo Candidate ββ events are selected by requiring two reconstructed electron tracks, each associated with an energy deposited in an individual optical module. The energy deposited by the electron in a single optical module should be greater than 300 keV. Each PMT must be flagged as stable according to the light injection survey [19]. The tracks must both originate from the 100Mo source foil, and their points of intersection with the plane of the source foil must be within 4 cm transverse to and 8 cm along the direction of the tracker wires, in order to ensure that the two tracks are associated to a common event vertex. The track curvatures must be consistent with electrons moving outwards from the source foil. The timing and the path length of the electrons must be consistent with the hypothesis of simultaneous emission of two electrons from a common vertex in the 100Mo source foil [19]. There should be no γ-ray hits and α-particle tracks in the event. After the above event selection there are 501,534 100Mo two-electron candidate events, with 193,699 coming from the metallic foils and 307,835 from the composite foils. Table 2shows the number of expected background and candidate signal events in 100Mo foils. The number of 2νββ events is obtained from a binned log-likelihood fit to the two-electron energy sum distribution under the single state dominance (SSD) nuclear model, as detailed below. The average signal-to-background ratio is S/B=79, with S/B=63 for the metallic foils and S/B=94 for the composite foils. The detector acceptance and selection efficiency for 2νββ 100Mo events calculated using MC simulations is =(2.356 ±0.002)%, with met =(2.472 ± 0.003)% and com =(2.292 ±0.002)% for the metal123 Eur. Phys. J. C (2019) 79:440 Page 5 of 11 440 Table 2 Expected number of background events in the two-electron channel and the number of 100Mo 2νββ candidate events in molybdenum foils Source Metallic Composite Total 100Mo 228Ac,212Bi, 208Tl 49.5±0.5 142.3±1.3 191.8±1.4 214Pb,214Bi 14.2±0.1 177.2±0.7 191.3±0.7 40K 101.4±2.5 296.0±7.3 397.5±7.7 234mPa 1783.8±11.8 656.7±4.3 2440.5±12.5 210Bi 25.6±1.490.3±2.8 115.9±3.1 Radon 434.3±6.2 590.3±5.2 1024.6±8.1 Ext Bkg 562.7±9.7 1238.6±14.7 1801.3±17.6 ββ 0+ 148.6±0.871.1±1.0 119.7±1.3 Tot bkg 3020 ±17 3263 ±18 6283 ±25 ββ g.s. 190,683 ±117 304,571 ±144 495,254 ±186 Data 193,699 307,835 501,534 lic and composite molybdenum foils respectively. Using the above values gives the 100Mo 2νββ-decay half-life of T1/2=(6.65 ±0.02)×1018 year for the metallic foils and T1/2=(6.91 ±0.01)×1018 year for the composite foils. The difference between the two sample measurements may be explained by inaccuracy of the thin foil modelling and is taken into account in estimation of the systematic uncertainty in Sect. 4.2. We consider the mean value over the two data samples as the more reliable half-life estimation T1/2=(6.81 ±0.01)×1018 year.(2) The two-electron energy sum spectra and the distributions of cosine of the angle between two electrons emitted from 100Mo foil are shown in Fig. 3, separately for the metallic and composite foils as well as for the total 100Mo sample. Theelectron energy measured in the calorimeter is smaller than the energy at the point of origin due to energy losses in the foil and in the drift chamber. For instance in the case of 100Mo 2νββ decay the mean electron track length from the source foil to the calorimeter is 75 cm and the mean energy lossof electrons inthe driftchamber is43 keV.Thesingle and summed electron energy distributions are presented for the measured values of the electron kinetic energy Eeand sum of the measured electron kinetic energies ESU M, respectively, i.e., without correction for the energy loss. The angular distribution is corrected with the wellmeasureddistributionof theopeningangle betweentwoelectrons emitted in 207Bi decay. The MC distribution of the cosine of the angle between two electron tracks has been reweighted based on data collected in the regular energy calibration runs performed with 207Bi sources. The correction is biggest for small opening angles, and is at the level of 4% on average. 4.1 Role of intermediate nuclear states in 100Mo 2νββ transition The nuclear ββ decay (A,Z) →(A,Z+2) is realized via two subsequent virtual βtransitions through the complete set of states of intermediate nucleus (A,Z+1). In the case of 100Mo 2νββ transition between the ground states of the parent (100Mo) and daughter (100Ru) nuclei with spin-parity 0+the process is governed by two Gamow-Teller transitions through 1+states of 100Tc. Nuclear theory does not predict a priori whether there is a dominance of transition through the 1+ground state (SSD hypothesis [30–32]) or through higher lying excited states, namely from the region of the Gamow-Teller resonance (HSD hypothesis). The SSD versus HSD analysis is feasible as the ground state of 100Tc has spin-parity JP=1+and is lying close to the ground state of 100Mo. The evidence in favour of SSD in 100Mo 2νββ decay was already observed at the beginning of NEMO-3 data analysis [33]. Further hints for the SSD model in the 100Mo 2νββ decay were obtained in charge-exchange experiments by observing a strong Gamow-Teller transition to the 1+ ground state of 100Tc in the 100Mo(3He,t)100Tc reaction [34]. It was estimated that this transition could contribute as much as 80% to the total value of the 100Mo 2νββ matrix element. It was shown in [31,32] that SSD and HSD models can be directly distinguished by making high precision kinematics measurements of 2νββ decay products. The distribution of the individual electron energies was shown to have the most discriminating power, especially in the low energy part of the spectrum. Figure 4shows the individual electron energy spectra for three nuclear models, with SSD-3 being a modification of the SSD model where a finer structure of intermediate states is accounted for [35,36]. Figure 5shows the energy sum and angular distribution of the final state electrons where the data are fitted with the HSD model. The tension between the data and the model is evident already from these distributions with χ2/ndf =4.57 (pvalue =5.3×10−12) and χ2/ndf =1.98 (pvalue =0.007) for the energy sum and angular distributions respectively. However, the strongest evidence comes from the single electron energy distributions shown in Fig. 6 for the three models, HSD, SSD and SSD-3, fitted to the data. It is clear from the distributions and χ2values that the HSD model can be ruled out with high confidence while SSD and SSD-3 provide a fairly good description of the data. The difference between SSD and SSD-3 in describing the data is maximised with a cut on the electron energy sum of ESU M >1.4 MeV as shown in Fig. 7, which also increases the signal-to-background ratio. There is a slight preference of the SSD-3 model over SSD in this case, contrary to the results obtained without this cut demonstrated at Fig. 6.Due to systematic effects connected to the energy reconstruction 123 440 Page 6 of 11 Eur. Phys. J. C (2019) 79:440 ESUM (MeV) Residual(σ) -2 0 2 0 0.5 1 1.5 2 2.5 3 3.5 0 5000 10000 15000 20000 NEMO-3 100Mo metallic Events/0.1 MeV Data (193699) 2νββ 100Mo Tot bkg χ2/ndf= 13.5/21 = 0.64 Data/MC 0.95 1 1.05 cos(Θ) Residual(σ) -2 0 2 -1 -0.5 0 0.5 1 0 5000 10000 15000 20000 25000 NEMO-3 100Mo metallic Events Data (193699) 2νββ 100Mo Tot bkg χ2/ndf= 26.60/19 = 1.40 Data/MC 0.95 1 1.05 ESUM (MeV) Residual(σ) -2 0 2 0 0.5 1 1.5 2 2.5 3 3.5 0 5000 10000 15000 20000 25000 30000 35000 NEMO-3 100Mo composite Events/0.1 MeV Data (307835) 2νββ 100Mo Tot bkg χ2/ndf= 36.5/21 = 1.74 Data/MC 0.95 1 1.05 cos(Θ) Residual(σ) -2 0 2 -1 -0.5 0 0.5 1 0 10000 20000 30000 40000 NEMO-3 100Mo composite Events Data (307835) 2νββ 100Mo Tot bkg χ2/ndf= 15.41/19 = 0.81 Data/MC 0.95 1 1.05 ESUM (MeV) Residual(σ) -2 0 2 0 0.5 1 1.5 2 2.5 3 3.5 0 10000 20000 30000 40000 50000 NEMO-3 100Mo total Events/0.1 MeV Data (501534) 2νββ 100Mo Tot bkg χ2/ndf= 21.0/22 = 0.95 Data/MC 0.95 1 1.05 cos(Θ) Residual(σ) -2 0 2 -1 -0.5 0 0.5 1 0 10000 20000 30000 40000 50000 60000 NEMO-3 100Mo total Events Data (501534) 2νββ 100Mo Tot bkg χ2/ndf= 22.2/19 = 1.17 Data/MC 0.95 1 1.05 Fig. 3 Distributions of two-electron summed kinetic energy and the opening angle between two electron tracks in 100Mo foils after an exposure of 34.3 kg year. Data are compared to the MC prediction of the SSD model (see text), where the resulting event numbers are taken from a binned log-likelihood fit 123 Eur. Phys. J. C (2019) 79:440 Page 7 of 11 440 0 0.2 0.4 0.6 0.8 1 0 0.5 1 1.5 22.5 Te (MeV) dN/dTe (a.u.) HSD SSD SSD-3 Fig. 4 Theoretical distributions of the individual electron kinetic energy for three models of 100Mo 2νββ decay: HSD, SSD and SSD-3 and electron energy loss simulations discussed below these two models cannot be discriminated against each other. The SSD is chosen as the baseline model and is used to estimate the 100Mo 2νββ half-life (see Sect. 4and Fig. 3). We note that differences in the low energy part of the single electron spectra (Fig. 4) affect the selection efficiency of 100Mo 2νββ events. Consequently, the measured half-life for the SSD model is 14% shorter than the analogous result for the HSD model. The SSD-3 model would give a 1.8% shorter half-life than that of the SSD model. 4.2 Systematic uncertainties on 100Mo 2νββ half-life Apart from the statistical uncertainties on the fitted number of signal events, the measurement of the 2νββ decay half-life is subject to a number of systematic uncertainties. The uncertainty on the reconstruction and selection efficiency including the detector acceptance effects is evaluated by carrying out dedicated calibrations with 207Bi sources whose activities were known with a 5% uncertainty. Consequently, the systematic error on the signal efficiency is taken to be 5%. LimitedprecisionofMC simulation programinmodelling of multiple scattering processes and electron energy losses in molybdenum ββ source foils also contribute to the total systematic error. Corresponding uncertainty is evaluated as the difference between the mean half-life value and the values obtained with metallic (−2.3%) and composite (+1.5%) foils. The 1.8% half-life value difference between the SSD and SSD-3 nuclear models is taken as a systematic error due to the 100Mo 2νββ decay model. The uncertainty on the energy scale translates into an error on the half-life measurement of 0.6%. The100Momassuncertaintygivesdirectlythecorresponding uncertainty of the half-life value and is estimated to be 0.2%. The error on the activities of external backgrounds, radon and the foil contamination with 214Bi and 208Tl is 10% as shown in [19]. The uncertainty on the backgrounds from 40K in the source foils as well as from 210Bi is estimated to be 4%. The observed discrepancy in the 234mPa decay scheme reported in [37] and [38] lead to a 30% normalisation uncertainty on the activity from this isotope. The 7.5% error on therateofthe100Mo 2νββ decay to the excited states [3] is also taken into account. Overall, due to a high signal-tobackground ratio the uncertainty on all background contributions produces only a 0.2% systematic uncertainty on the 100Mo 2νββ half-life determination. Thesystematicuncertaintiesonthemeasured2νββ 100Mo half-life are summarised in Table 3. The individual sources of the systematic error are assumed to be uncorrelated and the total uncertainty is obtained to be [+5.6,−5.8]%. Thefinalvalue ofthehalf-lifefor the 2νββ decayof 100Mo under the SSD model is: T1/2=6.81 ±0.01 (stat)+0.38 −0.40 (syst)×1018 year.(3) This value is in good agreement with the world average value of (7.1±0.4)×1018 year [3] and with a recent result obtained using low-temperature scintillating bolometers(Li100 2MoO4),[6.90±0.15(stat)±0.37(syst)]×1018 year [17]. 5 Search for new physics with continuous 100Mo ββ energy spectra Deviations in the shape of the 2νββ energy spectra can provide hints of new physics. Below we report on results of searches for physics beyond the Standard Model that can modifythetwo-electronenergysumdistributionofthe100Mo 2νββ decaydue to emissionofMajoronbosons,theexistence of a bosonic component in the neutrino states and possible Lorentz invariance violation. The shape of the two-electron energy sum distribution in various types of decays is characterized by the spectral index n[39], being determined by the phase space G∼ (Qββ −T)n, where Qββ is the full energy released in the decay minus two electron masses and T is the sum of kinetic energies of two emitted electrons. The ordinary 2νββ decay has a spectral index of n=5. Any modification from this functional form can be an indication of new physics. A number of grand unification theories predict the existence of a massless or light boson which couples to the neutrino. Neutrinoless ββ decay can proceed with the emission of one or two Majoron bosons resulting in a continuous energy sum spectrum with spectral index n= 5. The decay accompanied by a single Majoron emission has n=1,2 and 3, while models with two Majoron emissions predict 123 440 Page 8 of 11 Eur. Phys. J. C (2019) 79:440 ESUM (MeV) Residual(σ) -2.5 0 2.5 0 0.5 1 1.5 2 2.5 3 3.5 0 10000 20000 30000 40000 50000 NEMO-3 100Mo total Events / 0.1 MeV Data (501534) 2νββ 100Mo HSD Tot bkg χ2/ndf= 100.5/22 = 4.57 Data/MC 0.95 1 1.05 cos(Θ) Residual(σ) -2 0 2 -1 -0.5 0 0.5 1 0 10000 20000 30000 40000 50000 60000 NEMO-3 100Mo total Events Data (501534) 2νββ 100Mo HSD Tot bkg χ2/ndf= 37.6/19 = 1.98 Data/MC 0.95 1 1.05 Fig. 5 Two-electron events. Energy sum and cosine of the angle between the two electrons for HSD model Ee (MeV) Residual (σ) -10 0 10 0 0.5 1 1.5 2 2.5 3 0 200 400 600 800 1000 1200 1400 x 10 2NEMO-3 100Mo N entries/0.075 MeV Data 2νββ 100Mo Tot bkg HSD χ2/ndf= 42.91 Ee (MeV) Residual (σ) -2 0 2 00.511.522.53 0 200 400 600 800 1000 1200 1400 x 10 2NEMO-3 100Mo N entries/0.075 MeV Data 2νββ 100Mo Tot bkg SSD χ2/ndf= 1.54 Ee (MeV) Residual (σ) -2 0 2 00.511.522.53 0 200 400 600 800 1000 1200 1400 x 10 2NEMO-3 100Mo N entries/0.075 MeV Data 2νββ 100Mo Tot bkg SSD-3 χ2/ndf= 1.84 Fig. 6 Distribution of individual electron kinetic energy in the ββ channel from 100Mo foils compared with MC spectra under the HSD, SSD and SSD-3 nuclear models. The HSD hypothesis is excluded (χ2/ndf =1159/27) while the data are consistent with the SSD and SSD-3 models (χ2/ndf =41.5/27 and χ2/ndf =49.7/27 respectively) Ee (MeV) Residual (σ) -10 0 10 0 0.5 1 1.5 2 2.5 3 0 5000 10000 15000 20000 25000 30000 35000 NEMO-3 100Mo, Esum > 1.4 MeV N entries/0.075 MeV Data 2νββ 100Mo Tot bkg HSD χ2/ndf= 55.86 Ee (MeV) Residual (σ) -2.5 0 2.5 00.511.522.53 0 5000 10000 15000 20000 25000 30000 35000 NEMO-3 100Mo, Esum > 1.4 MeV N entries/0.075 MeV Data 2νββ 100Mo Tot bkg SSD χ2/ndf= 1.45 Ee (MeV) Residual (σ) -2.5 0 2.5 00.511.522.53 0 5000 10000 15000 20000 25000 30000 35000 NEMO-3 100Mo, Esum > 1.4 MeV N entries/0.075 MeV Data 2νββ 100Mo Tot bkg SSD-3 χ2/ndf= 1.13 Fig. 7 Distribution of individual electron kinetic energy in the ββ channel from 100Mo foils with the cut on the summed electron energy ESU M >1.4 MeV to maximise the signal-to-background ratio. The data are compared with MC spectra under the HSD, SSD and SSD-3 nuclear models. The HSD hypothesis is excluded (χ2/ndf =1508/27) whilethedataareconsistentwiththeSSDandSSD-3models(χ2/ndf = 39/27 and χ2/ndf =30.6/27 respectively) 123