Search for double-$\beta$ decay of ${}^{76}\mathrm{Ge}$ to excited states of ${}^{76}\mathrm{Se}$ with the majorana demonstrator

The majorana demonstrator is a neutrinoless double-$\beta$ decay search consisting of a low-background modular array of high-purity germanium detectors, $\sim 2/3$ of which are enriched to 88% in ${}^{76}\mathrm{Ge}$. The experiment is also searching for double-beta decay of ${}^{76}\mathrm{Ge}$ to excited states (e.s.) in ${}^{76}\mathrm{Se}$. ${}^{76}\mathrm{Ge}$ can decay into three daughter states of ${}^{76}\mathrm{Se}$, with clear event signatures consisting of a $\beta \beta$-decay followed by the prompt emission of one or two $\gamma$ rays. This results with high probability in multi-detector coincidences. The granularity of the demonstrator detector array enables powerful discrimination of this event signature from backgrounds. Using 41.9 kg yr of isotopic exposure, the demonstrator has set world leading limits for each e.s. decay of ${}^{76}\mathrm{Ge}$, with 90% CL lower half-life limits in the range of $(0.75–4.0)\times {10}^{24}$ yr. In particular, for the $2\nu$ transition to the first $0^{+}$ e.s. of ${}^{76}\mathrm{Se}$, a lower half-life limit of $7.5\times {10}^{23}$ yr at 90% CL was achieved.

Figure 1

Level diagram of the $\beta \beta$ decay of ${}^{76}\mathrm{Ge}$ into ${}^{76}\mathrm{Se}$ [39].

Figure 2

Diagram of the majorana demonstrator showing each shield layer, the inserted cryostats with their detector arrays, and the module hardware outside of the shielding.

Figure 3

Comparison of fraction of events with different detector multiplicities from Monte Carlo simulations of backgrounds (red) and $2\nu \beta \beta$ to the $0_1^{+}$ e.s. (blue). Sensitivity can be significantly improved by focusing on events with multiplicity $>1$.

Figure 4

Multiplicity 2 energy spectrum produced by a simulation of $2\nu \beta \beta$ decay to the $0_1^{+}$ e.s. of ${}^{76}\mathrm{Se}$. The vertical and horizontal lines at energies 559 and 563 keV act as a clear detection signature for the decay and are used as a region of interest for this search

Figure 5

The datasets were further divided into 80 sub-datasets based on which detectors were active, and the isotopic exposure and detection efficiency for each $\beta \beta$ to e.s. mode were separately calculated for each one. Shown above is the distribution of detection efficiencies for the decay to the $0_1^{+}$ e.s.

Figure 6

Left: simulated multiplicity 2 background two-dimensional energy spectrum histogram. Vertical and horizontal lines correspond to events in which one hit has a fixed energy, while diagonal lines correspond to events with a fixed sum energy. Right: Scatter plot of all multiplicity 2 events, including all events in datasets used in this analysis. A Gaussian kernel density estimate with width 5 keV was used to achieve a similar color scale to the simulated spectrum.

Figure 7

Energy spectra demonstrating the effects of applying the sum- and coincident-energy cuts for the $2\nu \beta \beta$ decay to $0_1^{+}$ decay mode. All multiplicity 2 or greater events are included, with passing events in blue and cut events stacked atop these in red. Left: Energy spectrum for all BG (top) and e.s. (bottom) simulated hits in coincidence with a hit in the signal or BG ROI. Right: Sum energy spectrum for BG (top) and e.s. (bottom) simulated events including a hit in the signal or BG ROI. Figure 8 shows similar information, including only multiplicity 2 events and plotted over two dimensions; this includes the cyan and green events in that figure, projected along the single-hit or sum energies. Note in the BG spectra that narrow ranges around prominent peaks are cut, as intended.

Figure 8

Top: Simulated multiplicity 2 energy spectrum for the background model. The colors represent cut events (red), surviving events (blue), and events that pass all cuts in the signal ROI (green) and BG ROI (cyan). Figure 7 shows similar information, with the events in the green and cyan ROIs projected onto the single hit (vertical and horizontal) and sum energy (diagonal) axes. Bottom: scatter plot of multiplicity 2 events in data used in this analysis.

Figure 9

Top: Energy spectra recorded while the ${}^{56}\mathrm{Co}$ line source was inserted into the calibration track for Module 1 (left) and Module 2 (right). Spectra are shown for multiplicity 1 events and multiplicity 2 events in which the other detector hit fell within the 511 keV peak. The SEPs (red triangle) and DEPs (green x) that were fit and used for simulation validation are shown. Bottom: the ratio of peak amplitudes from the selected SEPs and DEPs for Module 1 (left) and Module 2 (right). The expected systematic error from the dead layer thickness for SEPs and DEPs is shown on top of the residuals.

Figure 10

Left: Simulated energy spectrum including $42\mathrm{kg}\mathrm{yr}$ of exposure from the background model and the $2\nu \beta \beta$ decay to $0_1^{+}$ e.s. peaks at 559 and 563 keV, assuming a half-life of ${10}^{24}$ y. The cuts optimized for this decay mode are included. Right: Measured data energy spectrum with the same cuts applied.

Figure 11

Energy spectra for each $\beta \beta$ decay to e.s. decay mode after applying optimized cuts. The signal and BG ROIs are highlighted in blue and red, respectively.