Measurement of the $2\nu \beta \beta$ decay half-life and search for the $0\nu \beta \beta$ decay of ${}^{116}\mathrm{Cd}$ with the NEMO-3 detector

The NEMO-3 experiment measured the half-life of the $2\nu \beta \beta$ decay and searched for the $0\nu \beta \beta$ decay of ${}^{116}\mathrm{Cd}$. Using 410 g of ${}^{116}\mathrm{Cd}$ installed in the detector with an exposure of 5.26 y, ($4968\pm 74$) events corresponding to the $2\nu \beta \beta$ decay of ${}^{116}\mathrm{Cd}$ to the ground state of ${}^{116}\mathrm{Sn}$ have been observed with a signal to background ratio of about 12. The half-life of the $2\nu \beta \beta$ decay has been measured to be $T_{1/2}^{2\nu }=[2.74\pm 0.04(\text{stat})\pm 0.18(\text{syst})]\times 10^{19}\mathrm{y}$. No events have been observed above the expected background while searching for $0\nu \beta \beta$ decay. The corresponding limit on the half-life is determined to be $T_{1/2}^{0\nu }\ge 1.0\times 10^{23}\mathrm{y}$ at the 90% C.L. which corresponds to an upper limit on the effective Majorana neutrino mass of $⟨m_{\nu }⟩\le 1.4–2.5\mathrm{eV}$ depending on the nuclear matrix elements considered. Limits on other mechanisms generating $0\nu \beta \beta$ decay such as the exchange of R-parity violating supersymmetric particles, right-handed currents and majoron emission are also obtained.

Figure 1

Distribution of the total energy in the external $\gamma \text{−}e$ channel. The external background is modeled with ${}^{40}\mathrm{K}$, ${}^{214}\mathrm{Bi}$, ${}^{228}\mathrm{Ac}/{}^{212}\mathrm{Bi}/{}^{208}\mathrm{Tl}$, ${}^{210}\mathrm{Bi}$, ${}^{60}\mathrm{Co}$ and ${}^{234m}\mathrm{Pa}$ in the PMT, scintillator surface, iron structure, iron shield and the air surrounding the detector. The ratio of data events to the total Monte Carlo model and the residuals are shown in the bottom panels.

Figure 2

Distribution of the delayed $\alpha$ track length in the $1e1\alpha$ channel. The contribution of the radon progeny from the wires of the tracking chamber, the Mylar films which envelop the foils, and the foil surface are shown. The small contribution at small track lengths is consistent with ${}^{214}\mathrm{Bi}$ contained in the source foil bulk. The ratio of data events to the total Monte Carlo model and the residuals are shown in the bottom panels.

Figure 3

Distribution of the total energy in the $1e2\gamma$ channel which provides the most sensitive measure of ${}^{208}\mathrm{Tl}$. The contribution from the external background, radon progeny in the tracking chamber and from ${}^{214}\mathrm{Bi}$ are also considered. The ratio of data events to the total Monte Carlo model and the residuals are shown in the bottom panels.

Figure 4

Distribution of the track vertices on the source foil in the $1e$ channel. Three regions are defined based on the number of recorded events. The high activity regions, consistent with an excess of ${}^{234m}\mathrm{Pa}$ on the surface of the foil, are rejected from the analysis.

Figure 5

Distribution of the electron energy from the $1e$ channel. The dominant contribution at low energies is due to single-$\beta$ emitting isotopes: ${}^{40}\mathrm{K}$, ${}^{234m}\mathrm{Pa}$ and ${}^{210}\mathrm{Bi}$. At higher energies the radon progeny in the tracking chamber and the internal ${}^{214}\mathrm{Bi}$ become significant. There are subleading contributions from other internal and external backgrounds as well as from $2\nu \beta \beta$. The ratio of data events to the total Monte Carlo model and the residuals are shown in the bottom panels.

Figure 6

Distribution of the total electron energy (left) and the angle between the two electron tracks (right) in the two-electron channel. Background contributions are due to external events, radon progeny in the tracker chamber, internal ${}^{208}\mathrm{Tl}$, ${}^{214}\mathrm{Bi}$ and single-$\beta$ emitters. The ratio of data events to the total Monte Carlo model and the residuals are shown in the bottom panels.

Figure 7

Distribution of the single electron energy in the two electron channel under the SSD (left) and the HSD (right) hypothesis. Background contributions are due to external events, radon progeny in the tracker chamber, internal ${}^{208}\mathrm{Tl}$, ${}^{214}\mathrm{Bi}$ and single-$\beta$ emitters. The ratio of data events to the total Monte Carlo model and the residuals are shown in the bottom panels. In the SSD (HSD) hypothesis the p-value of the Kolmogorov-Smirnov test is 0.990 (0.726) while the p-value of the ${\chi }^2$ test is 0.193 (0.004). The results of the tests are in favor of the SSD hypothesis but there is not enough sensitivity to exclude the HSD hypothesis.

Figure 8

Comparison of the $2\nu \beta \beta$ half-life of ${}^{116}\mathrm{Cd}$ measured in this work with respect to previous measurement from Aurora [17], Solotvina [16], NEMO-2 [15] and ELEGANT-V [11]. The black bars show the statistical uncertainty while the colored bars show the total statistical and systematical error combined in quadrature.

Figure 9

Distribution of the output score of the BDT trained for the search of $0\nu \beta \beta$ decays via the exchange of a light Majorana neutrino. The open histogram stacked over the background model shows the 90% C.L. limits obtained on the $0\nu \beta \beta$ decay. The ratio of data events to the total Monte Carlo model and the residuals are shown in the bottom panels.

Figure 10

Distribution of the total electron energy in two-electron channel above 2 MeV. The four open histograms stacked over the background model show the 90% C.L. limits obtained on the $0\nu \beta \beta$ decay for different mechanisms (see text).