Results of the search for neutrinoless double-$\beta$ decay in ${}^{100}\mathrm{Mo}$ with the NEMO-3 experiment

The NEMO-3 detector, which had been operating in the Modane Underground Laboratory from 2003 to 2010, was designed to search for neutrinoless double-$\beta$ ($0\nu \beta \beta$) decay. We report the final results of a search for $0\nu \beta \beta$ decays with 6.914 kg of ${}^{100}\mathrm{Mo}$ using the entire NEMO-3 data set with a detector live time of 4.96 yr, which corresponds to an exposure of $34.3\mathrm{kg}·\mathrm{yr}$. We perform a detailed study of the expected background in the $0\nu \beta \beta$ signal region and find no evidence of $0\nu \beta \beta$ decays in the data. The level of observed background in the $0\nu \beta \beta$ signal region [2.8–3.2] MeV is $0.44\pm 0.13\mathrm{counts}/\mathrm{yr}/\mathrm{kg}$, and no events are observed in the interval [3.2–10] MeV. We therefore derive a lower limit on the half-life of $0\nu \beta \beta$ decays in ${}^{100}\mathrm{Mo}$ of $T_{1/2}(0\nu \beta \beta )>1.1\times 10^{24}\mathrm{yr}$ at the 90% confidence level, under the hypothesis of decay kinematics similar to that for light Majorana neutrino exchange. Depending on the model used for calculating nuclear matrix elements, the limit for the effective Majorana neutrino mass lies in the range $⟨m_{\nu }⟩<0.33–0.62\mathrm{eV}$. We also report constraints on other lepton-number violating mechanisms for $0\nu \beta \beta$ decays.

Figure 1

A schematic view of the NEMO-3 detector, showing the double-$\beta$ source foils, the tracking chamber, the calorimeter composed of scintillator blocks and PMTs, the magnetic coil and the shield.

Figure 2

Energy spectrum of a typical scintillator block, measured with the ${}^{207}\mathrm{Bi}$ calibration sources and summed over all the calibration runs. The data points are compared to a histogram of the energy spectrum calculated by the MC simulation. The peaks correspond to the energies of electrons from the main 482, 976, and 1682 keV internal conversion $K$ lines of ${}^{207}\mathrm{Bi}$.

Figure 3

Average energy resolution ${\sigma }_E/E$ measured at $E=1\mathrm{MeV}$ for the different types of scintillator blocks and sizes of PMTs as a function of NEMO-3 running time. Here, IN refers to the calorimeter blocks with 3-inch PMTs located in the central tower (inner wall of the calorimeter), L1, L2 and L3 refer to 3-inch PMTs located on the upper and lower end caps, EC and EE refer to 5-inch PMTs located on the external wall, and L4 to 5-inch PMTs on the upper and lower end caps of the calorimeter (see Fig. 3 in [4] for the exact location of the different types of scintillator).

Figure 4

Fraction of dead PMTs (in %) as a function of NEMO-3 running time for 3- and 5-inch PMTs, and for all PMTs.

Figure 5

Distribution of the laser correction factors calculated for all laser runs and for all stable PMTs used in the analysis.

Figure 6

Energy spectrum of electrons from $\beta$ decay of ${}^{214}\mathrm{Bi}$ measured using BiPo events inside the tracking detector, without laser survey [(a) and (b)] and after laser survey [(c) and (d)] for Phase I [(a) and (c)] and Phase II [(b) and (d)]. The data are compared to a MC simulation. The excess of electrons observed at $E_e>3.4\mathrm{MeV}$ in data are caused by PMTs with unstable gains. They are rejected by the laser correction (see Table 1).

Figure 7

Distributions of the difference $\mathrm{\Delta }T$ between the measured and expected time differences of scintillator hits for the internal hypothesis (a) and the internal probability $P_{\text{int}}$ (b) for two-electron events. The superimposed shaded histogram shows events with $P_{\text{int}}>1\%$.

Figure 8

Transverse and longitudinal view of a reconstructed double-$\beta$ data event. Tracks are reconstructed from a single vertex in the source foil, with an electronlike curvature in the magnetic field, and are each associated to an energy deposit in a calorimeter block.

Figure 9

Schematic view of the different components of the two-electron background: the external background produced by an external $\gamma$ ray, the internal background produced by internal ${}^{214}\mathrm{Bi}$ and ${}^{208}\mathrm{Tl}$ contaminations in the ${}^{100}\mathrm{Mo}$ source foil, and the radon contamination inside the tracking detector.

Figure 10

The two event topologies used to measure the external background: external $(\gamma ,e^{-})$ events and crossing-electron events.

Figure 11

Result of the fit of the external background to data for the total ${}^{100}\mathrm{Mo}$ exposure of $34.3\mathrm{kg}·\mathrm{yr}$, for the electron energy $E_e$ of external $(\gamma ,e^{-})$ events [(a) and (c)] and the energy $E_e^{\text{out}}$ measured in the last scintillator block hit in crossing-electron events [(b) and (d)]. The distributions are shown separately for Phases I [(a) and (b)] and II [(c) and (d)]. SC K40 corresponds to ${}^{40}\mathrm{K}$ impurities inside the scintillators. The lower panels show residuals between data and expected background, normalized to the Poisson error, ignoring bins with 0 events.

Figure 12

Distribution of $E_{\text{tot}}$ for $e^{+}{e}^{-}$ pair events consistent with being emitted from ${}^{100}\mathrm{Mo}$ foils for the entire data set. The data are compared to the sum of the expected background from external neutrons, $2\nu \beta \beta$ events, and the other background components.

Figure 13

Time distribution of delayed $\alpha$ tracks, measured for BiPo decays emitted inside the tracking detector, for Phase I [(a) and (b)] and Phase II [(c) and (d)], and for single delayed Geiger hit [(a) and (c)] or multiple delayed Geiger hits [(b) and (d)]. The distributions are fitted by the sum of an exponential function with $T_{1/2}$ set to the ${}^{214}\mathrm{Po}$ half-life of $T_{1/2}=164\mu \mathrm{s}$ and a constant term accounting for random coincidences.

Figure 14

The spatial distribution (vertical coordinate $z$ versus sector number) of the emission vertex of detected ${}^{214}\mathrm{Bi}\text{−}{}^{214}\mathrm{Po}$ decay cascade events emitted inside the tracking detector close to the source foils for Phase II. The left (right) corresponds to events with an emission vertex on the internal (external) side of the source foil. (a) and (b) correspond to a vertex on the foil or on the wires of the first layer of Geiger cells close to the foil, (c) and (d) correspond to a vertex on the wires of the second layer of Geiger cells, and (e) and (f) correspond to a vertex on the wires of the third layer of Geiger cells. The external side of sector 13 is not represented because of noise observed for Geiger cells in this zone.

Figure 15

Distributions of the energy of the electron, $E_{e^{-}}$, the energy sum $\sum E_{\gamma }$, and $E_{e^{-}}+\sum E_{\gamma }$ using $(e^{-},\gamma \gamma )$ and $(e^{-},\gamma \gamma \gamma )$ events for the combined ${}^{100}\mathrm{Mo}$ data set. The top panels show the composite and the bottom panels the metallic foils. The data are compared to the sum of the expected background from MC simulations and the fitted ${}^{208}\mathrm{Tl}$ activity inside the ${}^{100}\mathrm{Mo}$ foils.

Figure 16

Distribution of the total energy of two electrons $E_{\text{tot}}$ in the $(e^{-}{e}^{-},N\gamma )$ channel for the ${}^{100}\mathrm{Mo}$ data set compared to the expected background from ${}^{208}\mathrm{Tl}$ contamination inside the foils and to the total expected background. The normalizations of the different background components are not fitted, but set to the measured values. No event is observed for $E_{\text{tot}}>3.7\mathrm{MeV}$.

Figure 17

Distribution of the lengths of delayed $\alpha$ tracks for composite ${}^{100}\mathrm{Mo}$ foils for Phase II: (a) and (c) for electron and $\alpha$ tracks on the same side of the foils, (b) and (d) for electron and $\alpha$ tracks on opposite sides of the foils, (a) and (b) for $\alpha$ tracks on the inner side of the foils, (c) and (d) for $\alpha$ tracks on the outer side of the foils. The data are compared to the simulated background with a normalization determined by the fit of the different components of ${}^{214}\mathrm{Bi}$ background. “SW” corresponds to the ${}^{214}\mathrm{Bi}$ deposition on the surface of the wires, and “SF” to the deposition on the surface on the foil, where “IN” and “OUT” correspond to the components from the wires and surfaces inside and outside relative to the position of the foil. “Internal” ${}^{214}\mathrm{Bi}$ contamination originates inside the ${}^{100}\mathrm{Mo}$ foils, and the “Mylar” contamination from inside the Mylar.

Figure 18

Distribution of the delayed $\alpha$ track length for metallic ${}^{100}\mathrm{Mo}$ foils (see the Fig. 17 caption for further details).

Figure 19

Distribution of $E_{\text{tot}}$ for two-electron events with $E_{\text{tot}}>2\mathrm{MeV}$ for the copper, ${}^{130}\mathrm{Te}$, and natural tellurium foils [(a), (c), and (e)], and for ${}^{100}\mathrm{Mo}$ foils [(b), (d), and (f)], for Phase I [(a) and (b)] and Phase II [(c) and (d)], and combined [(e) and (f)]. The combined data correspond to an exposure of $13.5\mathrm{kg}·\mathrm{yr}$ for the copper, ${}^{130}\mathrm{Te}$, and natural tellurium foils, and $34.3\mathrm{kg}·\mathrm{yr}$ for the ${}^{100}\mathrm{Mo}$ foils. The data are compared to the sum of the expected background from $2\nu \beta \beta$ decays of ${}^{100}\mathrm{Mo}$, radon, external backgrounds, and from internal ${}^{214}\mathrm{Bi}$ and ${}^{208}\mathrm{Tl}$ contaminations inside the foils. Only the $2\nu \beta \beta$ background contribution is fitted to the data, while the other background components are set to the measured values given in Sec. 5. The lower panels show residuals between data and expected background, normalized to the Poisson error, ignoring bins with 0 events.

Figure 20

The 90% C.L. lower limits on $T_{1/2}(0\nu \beta \beta )$ for the light Majorana neutrino mass mechanism and upper limits on the effective Majorana neutrino mass $⟨m_{\nu }⟩$ using the same NME calculations [16, 17, 18, 19, 20] and recent phase space calculations [21, 22]. The shaded regions correspond to the ranges from using different NME calculations. The hatched area corresponds to the expected range for $⟨m_{\nu }⟩$, calculated from the neutrino oscillation parameters and assuming the inverted neutrino mass hierarchy.