Detailed studies of $^{100}$Mo two-neutrino double beta decay in NEMO-3

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 $^{100}$Mo to the ground state of $^{100}$Ru, $T_{1/2} = \left[ 6.81 \pm 0.01\,\left(\mbox{stat}\right) ^{+0.38}_{-0.40}\,\left(\mbox{syst}\right) \right] \times10^{18}$ y. The two-electron energy sum, single electron energy spectra and distribution of the angle between the electrons are presented with an unprecedented statistics of $5\times10^5$ events and a 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 bosonic neutrino contribution to the two-neutrino double beta decay mode are obtained.


Introduction
Spontaneous nuclear double beta decay is a second order weak interaction process that was theoretically considered for the first time by M. Goeppert-Mayer in 1935 [1]. It can occur in some even-even nuclei when two bound neutrons simultaneously undergo beta decay and are transformed into two bound protons emitting two electrons and two (anti)neutrinos. Two-neutrino double beta decay, 2νββ, is one of the rarest directly observed radioactive processes with half-lives ranging from 7×10 18 to 2×10 21 years [2,3].
The decay rate of 2νββ decay can be expressed as where g A is the axial-vector coupling constant, G 2ν is a phase space factor, and M 2ν is 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 g A quenching in nuclear matter that is currently being actively discussed [4][5][6][7]. Detailed studies of 2νββ may therefore be useful to improve NME calculations for the neutrinoless mode of double beta 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 [8].
Previous measurements have shown that the 100 Mo 2νββ half-life is shorter compared to other ββ isotopes [9][10][11][12][13][14][15][16], and it is therefore a promising nucleus for precise studies of the process. Here we present the most accurate to date study of 100 Mo 2νββ decay including single electron energy and angular distributions of the electrons emitted in the decay with an unprecedented statistics of 5 × 10 5 events. The impact of the single electron energy spectra on nuclear models that are used to calculate the NME is also presented.
Searches for most commonly discussed 0νββ mechanisms (exchange of a light Majorana neutrino, right-handed currents, super-symmetry) with NEMO-3 have been reported earlier in [17,18]. In this paper we present results obtained for 100 Mo 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 100 Mo.

The NEMO-3 detector
The NEMO-3 detector, its calibration and performance are described in detail in [19] and more recently in [18]. 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, Correspondence to: tretyak@jinr.ru 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 to low radioactivity photomultiplier tubes (PMT). The energy 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 207 Bi, 90 Sr and 232 U 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 25 G 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 19 cm 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, gamma-and 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 background evaluation by selecting event topologies corresponding to specific background channels. An electron is identified by a reconstructed prompt track in the drift 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 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 214 Bi → 214 Po delayed coincidences.
Two types of purified molybdenum foils were installed in NEMO-3, metallic and composite. Both foil types were enriched in 100 Mo 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 ± 5 g of 100 Mo. The mean metallic foil density is 58 mg/cm 2 with a total foil surface of 43924 cm 2 . The composite foils contained 4435 ± 13 g of 100 Mo. 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/cm 2 and the total foil surface area is 84410 cm 2 .
Monte Carlo (MC) simulations are performed with a GEANT-3 based [26] program using the DECAY0 [27] 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 y and a total exposure of 34.3 kg·y of 100 Mo. This is the same exposure as that used for 0νββ results published earlier [18].

Background model
Trace quantities of naturally-occurring radioactive isotopes can occasionally produce two-electron events and thus can mimic ββ-decay events. The largest contributions come from isotopes that are progenies of 238 U ( 234m Pa, 214 Pb, 214 Bi, 210 Bi) and of 232 Th ( 228 Ac, 212 Bi, 208 Tl), as well as 40 K.
The background is categorised as internal if it originates from radioactive decays inside the ββ source foils, see Fig. 1(a). 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. Decays inside the tracking detector volume form a separate background category. The main source of this background is radon, 222 Rn. 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 Compton scattering or Compton scattering followed by Møller scattering, see Fig. 1

(b).
A detailed discussion of the NEMO-3 background model is presented in [28] and results of screening measurements can be found in [18,19,28]. Here we follow the same background model as that presented for the 100 Mo 0νββ analysis [18]. However, radioactive isotopes contributing to the   [18] and are therefore discussed in more detail below. The background in question comes from traces of β-decaying isotopes 210 Bi, 40 K and 234m Pa in 100 Mo foils. In addition, 100 Mo 2νββ decay to the 0 + 1 excited state of 100 Ru is also taken into account as a source of internal background. The experimental halflife value of T 1/2 = 6.7 +0.5 −0.4 × 10 20 y [3] is used to evaluate this contribution.
The activities of β-emitters in 100 Mo foils are determined from the fit to the electron energy distribution for a single electron event sample, which is shown in Fig. 2 separately for metallic and composite foils. To disentangle the 210 Bi contribution from the source foils and the surface of the tracker wires the activity measured in [28] is used for the latter. Fig. 2 shows the sum of both contributions. Secular equilibrium is assumed between 214 Pb and 214 Bi. The same is done between 228 Ac, 212 Bi and 208 Tl, 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 100 Mo foil contamination measurements carried out with the NEMO-3 detector are shown in Table 1.  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 [18]. The tracks must both originate from the 100 Mo source foil, and their points of intersection with the plane of the source foil must be within 4cm transverse to and 8cm 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 100 Mo source foil [18]. There should be no γ-ray hits and α-particle tracks in the event.
After the above event selection there are 501534 100 Mo two-electron candidate events, with 193699 coming from the metallic foils and 307835 from the composite foils. Table 2 shows the number of expected background and candidate signal events in 100 Mo 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 100 Mo events calculated using MC simulations is = (2.356 ± 0.002)%, with met = (2.472 ± 0.003)% and com = (2.292 ± 0.002)% for the metallic and composite molybdenum foils respectively. Using the above values gives the 100 Mo 2νββ-decay half-life of T 1/2 = (6.65 ± 0.02) × 10 18 y for the metallic foils and T 1/2 = (6.91 ± 0.01) × 10 18 y 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 Section 4.2. We consider the mean value over the two data samples as the more reliable half-life estimation The two-electron energy sum spectra and the distributions of cosine of the angle between two electrons emitted from 100 Mo foil are shown in Fig. 3, separately for the metallic and composite foils as well as for the total 100 Mo sample.
The electron 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 100 Mo 2νββ decay the mean electron track  length from the source foil to the calorimeter is 75 cm and the mean energy loss of electrons in the drift chamber is 43 keV. The single and summed electron energy distributions are presented for the measured values of the electron kinetic energy E e and sum of the measured electron kinetic energies E SU M , respectively, i.e., without correction for the energy loss. The angular distribution is corrected with the wellmeasured distribution of the opening angle between two electrons emitted in 207 Bi 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 207 Bi sources. The correction is biggest for small opening angles, and is at the level of 4% on average.

Role of intermediate nuclear states in 100 Mo 2νββ transition
The nuclear ββ decay (A,Z) → (A,Z+2) is realized via two subsequent virtual β transitions through the complete set of states of intermediate nucleus (A,Z+1). In the case of 100 Mo 2νββ transition between the ground states of the parent ( 100 Mo) and daughter ( 100 Ru) nuclei with spinparity 0 + the process is governed by two Gamow-Teller transitions through 1 + states of 100 Tc. Nuclear theory does not predict a priori whether there is a dominance of transition through the 1 + ground state (SSD hypothesis [29,30]) 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 100 Tc has spin-parity J P = 1 + and is lying close to the ground state of 100 Mo.
The evidence in favour of SSD in 100 Mo 2νββ decay was already observed at the beginning of NEMO-3 data analysis [31]. Further hints for the SSD model in the 100 Mo 2νββ decay were obtained in charge-exchange experiments by observing a strong Gamow-Teller transition to the 1 + ground state of 100 Tc in the 100 Mo( 3 He,t) 100 Tc reaction [32]. It was estimated that this transition could contribute as much as 80% to the total value of the 100 Mo 2νββ matrix element.
It was shown in [30] 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. Fig 4 shows 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 [33].   5 shows 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 χ 2 /ndf=4.57 (p-value=5.3·10 −12 ) and χ 2 /ndf=1.98 (p-value=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 χ 2 values 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 E SU 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 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 100 Mo 2νββ half-life (see Section 4 and Fig. 3). We note that differences in the low energy part of the single electron spec-tra (Fig. 4) affect the selection efficiency of 100 Mo 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.

Systematic uncertainties on 100 Mo 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 207 Bi sources whose activities were known with a 5% uncertainty. Consequently, the systematic error on the signal efficiency is taken to be 5%.
Limited presision of MC simulation program in modelling 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 100 Mo 2νββ decay model.
The uncertainty on the energy scale translates into an error on the half-life measurement of 0.6%.
The 100 Mo mass uncertainty gives directly the corresponding 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 214 Bi and 208 Tl is 10% as shown in [18]. The uncertainty on the backgrounds from 40 K in the source foils as well as from 210 Bi is estimated to be 4%. The observed discrepancy in the 234m Pa decay scheme reported in [34] and [35] lead to a 30% normalisation uncertainty on the activity from this isotope. The 7.5% error on the rate of the 100 Mo 2νββ decay to the excited states [3] is also taken into account. Overall, due to a high signal-to-background ratio the uncertainty on all background contributions produces only a 0.2% systematic uncertainty on the 100 Mo 2νββ half-life determination.
The systematic uncertainties on the measured 2νββ 100 Mo 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]%. The final value of the half-life for the 2νββ decay of 100 Mo under the SSD model is:  The shape of the two-electron energy sum distribution in various types of decays is characterized by the spectral index n [36], being determined by the phase space G ∼ (Q ββ − T ) n , where Q ββ is the 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 n = 3 and 7 (see [37] and references therein). The results for the neutrinoless ββ decay with the emission of a Majoron corresponding to the spectral index n = 1 have already been published in [17,18]. The Majoronaccompanied 0νββ decay modes with spectral indices n = 2, 3 and 7 are considered here.
It was noted in [38] that violation of the Pauli exclusion principle resulting in a bosonic component in the neutrino states can be tested by looking at the shape of the energy and angular distributions of the electrons emitted in ββ decay. For the two-electron energy sum distribution the corresponding index would be n = 6.
Lorentz invariance is a fundamental symmetry. However, new physics at very high energies close to the Planck scale can manifest itself in small effects at low energies, including Lorentz invariance violation. Consequently, searches for non-Lorentz invariant effects have attracted active theoretical and experimental effort [39][40][41][42]. The possibility to test Lorentz invariance with ββ decay was discussed   in [43,44]. In case of 2νββ decay the Lorentz invariance violation may be manifested as a modification of the conventional electron sum spectrum due to an additional contribution of the Lorentz-violating perturbation with a spectral shape of n = 4. ; shape of the perturbation to the standard 2νββ decay due to Lorentz invariance violation 2ν-LIV (n = 4) and spectrum for 2νββ decay with bosonic neutrino 2ν-Boson (n = 6).
The theoretical distributions of the two-electron energy sum for different modes of 100 Mo ββ decay discussed above are shown in Fig 8. The difference in the shape of the distributions due to different spectral indices n is used to evaluate possible contributions from physics beyond the Standard Model. No significant deviations from the expected 100 Mo 2νββ spectral shape (n = 5) have been observed and therefore limits on new physics parameters have been set using the full energy sum spectrum of the full 100 Mo data set. The contributions of the ββ decay modes with spectral indices n = 2, 3, 6, 7 are constrained with a modified frequentist CL s method [45] using a profile likelihood fitting technique (COLLIE software package [46]). A profile likelihood scan is used for the distribution with the spectral index n = 4 in order to explore possibility of negative as well as positive Lorentzviolating perturbation.
The systematic uncertainties on background contributions discussed in Section 4.2, the 5% uncertainty on the detector acceptance and selection efficiency for signal, a possible distortion in the shape of the two-electron energy sum spectrum due to the energy calibration accuracy, as well as a 5% error on the modelling of the energy loss of electrons are taken into account in limit setting without imposing a constraint on the normalization of standard 2νββ contribution.
The limits on the half-lives for different 0νββ modes with Majoron(s) emission, and for the bosonic neutrino admixture obtained with the CL s method are given in Table 4. The half-life limits on the Majoron 0νββ modes Table 4: Lower bounds on half-lives (×10 21 y) at 90% C.L. from 0νββ searches with Majoron emission (spectral indices n = 2, 3, 7), and searches for the bosonic neutrino admixture. The ranges in the expected half-life limits are from the ±1σ range of the systematic uncertainties on the background model, signal efficiency and distortions in the shape of the energy spectrum. are translated into the upper limits on the lepton number violating parameter g ee , which is proportional to the coupling between the neutrino and the Majoron boson, using the relation, where G is the phase space (which includes the axialvector coupling constant g A ), M is the nuclear matrix element, and m = 2(4) is the mode with the emission of one (two) Majoron particle(s). The M and G values are taken from [47]. For the single Majoron emission and n = 3, M and G are taken from [48]. There are no NME and phase space calculations available for n = 2. The upper limits on the Majoron-neutrino coupling constant g ee are shown in Table 5. One can see that the NEMO-3 results presented here are the current best limits for n = 3 and the single Majoron emission mode and are comparable with the world's best results from the EXO-200 [49] and GERDA [50] experiments for the other two modes.  The contribution of bosonic neutrinos to the 2νββdecay rate can be parametrised as [38]: where W f and W b are the weights in the neutrino wavefunction expression corresponding to the two fermionic and two bosonic antineutrino emission respectively. The purely fermionic, T f 1/2 , and purely bosonic, T b 1/2 , half-lives are calculated under the SSD model to be [38] : T f 1/2 (0 + g.s.) = 6.8 · 10 18 y, T b 1/2 (0 + g.s.) = 8.9 · 10 19 y. (6) Using the NEMO-3 half-life limit of T b 1/2 (0 + g.s.) > 1.2 · 10 21 y (Table 4) an upper limit on the bosonic neutrino contribution to the 100 Mo 2νββ decay to the ground state can be evaluated as: Although this limit is stronger than the bound obtained earlier in [38], the 2νββ transition of 100 Mo to the ground state is not very sensitive to bosonic neutrino searches due to a small value of the expected bosonic-to-fermionic decay branching ratio r 0 (0 + g.s.) = 0.076. The 100 Mo 2νββ decay to the first excited 2 + 1 state has a branching ratio of r 0 (2 + 1 ) = 7.1 [38] and is therefore potentially more promising despite a lower overall decay rate. The current best experimental limit for this process is T 1/2 (2 + 1 ) > 2.5 · 10 21 y [51]. This bound is still an order of magnitude lower than the theoretically expected half-life value of T b 1/2 (2 + 1 ) = 2.4 · 10 22 y for purely bosonic neutrino, and two orders of magnitude lower than the corresponding expected value for purely fermionic neutrino, T f 1/2 (2 + 1 ) = 1.7 · 10 23 y [38].
The Standard Model Extension (SME) provides a general framework for Lorentz invariance violation (LIV) [39]. In this model, the size of the Lorentz symmetry breakdown is controlled by SME coefficients that describe the coupling between standard model particles and background fields. Experimental limits have been set on hundreds of these SME coefficients from constraints in the matter, photon, neutrino and gravity sectors [39]. The first search for LIV in 2νββ decay was carried out in [52]. The twoelectron energy sum spectrum of 136 Xe was used to set a limit on the parameterå (3) of , which is related to a time-like component of this LIV operator. The value of this parameter was constrained to be −2.65 × 10 −5 GeV <å (3) of < 7.6×10 −6 GeV by looking at deviations from the predicted energy spectrum of 136 Xe 2νββ decay [52].
In this work we adopt the same method, using the phase space calculations from [53], and perform a profile likelihood scan over positive and negative contributions of LIV to two-electron events by altering the 100 Mo 2νββ energy sum spectrum with positive and negative values of a (3) of . The result of this scan is shown in Fig. 9.
The minimum of the profile log-likelihood function corresponds to −135 counts and is not statistically significant even at 1σ level. The 90% CL exclusion limit is shown in Fig. 9 with the dashed line and gives −1798 and 1527 events for negative and positive contributions to the deviation from the 100 Mo 2νββ energy sum spectrum respectively. The corresponding constraint onå (3) of is calculated using equations (2)- (6) in [52]. The result for 100 Mo obtained with a full set of NEMO-3 data is

Summary
The results of the 2νββ decay of 100 Mo with the full data set of the NEMO-3 experiment corresponding to a 34.3 kg·y exposure are presented. The summed energy of two electrons, the single electron energy and the angular distributions between the two electrons have been studied with an unprecedented statistical precision (5 × 10 5 events). The single electron energy distribution has been used to discriminate between different nuclear models providing direct experimental input into NME calculations. The HSD model is excluded with high confidence, while the SSD model is consistent with the NEMO-3 data. The corresponding half-life for the 2νββ decay of 100 Mo is found to be T 1/2 = 6.81 ± 0.01 (stat) +0.38 −0.40 (syst) × 10 18 y. (9) Deviations from the expected shape of the 100 Mo 2νββ energy sum spectrum have been studied to obtain constraints on parameters for physics beyond the Standard Model. The most stringent upper limit to date has been obtained for the Majoron-neutrino coupling parameter g ee for the decay mode with a single Majoron particle emission and the spectral index n = 3. For other 0νββ modes with two Majoron bosons emission a comparable sensitivity with the world's best limits has been achieved. The most stringent constraints on the bosonic neutrino admixture and Lorentz invariance violation in 2νββ decay have been set.