Searching for low-mass dark matter particles with a massive Ge bolometer operated above ground

The EDELWEISS Collaboration has performed a search for dark matter particles with masses below the GeV scale with a 33.4-g germanium cryogenic detector operated in a surface lab. The energy deposits were measured using a neutron-transmutation-doped Ge thermal sensor with a 17.7 eV (rms) baseline heat energy resolution leading to a 60 eV analysis energy threshold. Despite a moderate lead shielding and the high-background environment, the first sub-GeV spin-independent dark matter limit based on a germanium target has been achieved. The experiment provides the most stringent, nuclear-recoil-based, above-ground limit on spin-independent interactions above $600\mathrm{MeV}/{\mathrm{c}}^2$. The experiment also provides the most stringent limits on spin-dependent interactions with protons and neutrons below $1.3\mathrm{GeV}/{\mathrm{c}}^2$. Furthermore, the dark matter search results were studied in the context of strongly interacting massive particles, taking into account Earth-shielding effects, for which new regions of the available parameter space have been excluded. Finally, the dark matter search has also been extended to interactions via the Migdal effect, resulting for the first time in the exclusion of particles with masses between 45 and $150\mathrm{MeV}/{\mathrm{c}}^2$ with spin-independent cross sections ranging from ${10}^{-29}$ to ${10}^{-26}{\mathrm{cm}}^2$.

Figure 1

Left: Hourly averaged noise power spectral densities (PSDs) (black curves), detector signal bandwidth (black dashed line), and resulting optimal filter transfer functions (red curves) as a function of frequency, for the six days of data acquisition. The 137 separate PSDs and transfer functions are overlayed. Right: Example of a 200 eV pulse: unfiltered raw trace (gray solid line) and output of the optimal filter (red solid line). The trigger level at $3\sigma$ is shown as the blue dotted line. The result of the pulse fitting procedure, with a ${\chi }^2/\mathrm{ndf}=1.03$, is shown as the black long-dashed line.

Figure 2

Left: Event energy distribution between 5 and 8 keV as a function of time. The horizontal bands at 5.90 and 6.49 keV correspond to the $K_{\alpha }$ and $K_{\beta }$ x-ray lines, respectively, of Mn emitted by the ${}^{55}\mathrm{Fe}$ source. The data have been corrected for the measured time evolution of the detector gain as a function of time, shown as the red line, and corresponding to the right-hand axis. Right: Baseline heat energy resolution (rms) in eV as a function of time. The gray dots are the values derived from a fit to the energy distributions of the noise event selection, and the black squares are those derived from the ratio of the signal and noise PSDs. The corresponding trigger rates in hertz are shown as red dots. Each data point corresponds to one hour. The gray shaded region in both panels corresponds to the interval of the blinded dataset.

Figure 3

Left: Distribution of ${\chi }_{\text{Normal}}^2$ as a function of energy for the events in the blinded dataset. The events passing all $\mathrm{\Delta }{\chi }^2$ cuts are shown as black dots while those rejected are shown as gray dots. The expected region where different pulse populations are expected is shown in purple (events with normal pulse shape), blue (fast pulses), red (slow pulses) and green (single-sample spikes). Right: Signal efficiency as a function of heat energy for $10^6$ simulated events injected in the data stream with energies uniformly selected between 0 and 2.5 keV, shown from 0 to 2 keV corresponding to the region of interest. Gray points: Trigger plus live-time efficiency as a function of the input energy, together with a fit with an error function (gray line). Black points and line: Trigger plus live-time efficiency as a function of the energy resulting from the ${\chi }^2$ fit of a pulse to the data in the frequency domain. Blue points and line: The same, but after applying all $\mathrm{\Delta }{\chi }^2$ cuts. Red points and line: The final efficiency obtained after applying the additional cut on ${\chi }_{\text{Normal}}^2$. In both panels, the gray area corresponds to energies below the analysis cut.

Figure 4

Energy spectrum recorded in the blinded day of the DM search data, after all cuts. The calibration lines from the ${}^{55}\mathrm{Fe}$ source at 5.90 and 6.49 keV are clearly visible, and they exhibit an energy dispersion of 34 eV (rms). The data are normalized in events per kilogram per day and per keV and are not corrected for efficiency. The bin size is 10 eV. The inset shows an enlargement of this distribution between 40 and 200 eV (black dots), as well as the energy spectrum observed in the simulated noise streams after all cuts (red dots). The blue squares are the difference between the two spectra.

Figure 5

Comparison of the energy spectrum after all cuts for the blinded data set (black dots) with the background model derived from the five-day nonblinded dataset (black dashed line). Also shown are the spectra for three excluded WIMP signals. The solid colored lines are the unsmeared WIMP spectra, while colored points are the spectra that incorporate resolution effects and all cuts. Left: Standard elastic nuclear recoil spectra that are excluded for WIMPs with masses of 0.7 (red), 2 (blue) and $10\mathrm{GeV}/{\mathrm{c}}^2$ (green). Right: Inelastic Migdal spectra that are excluded for WIMPs with masses of 0.05 (magenta), 0.1 (cyan) and $1.0\mathrm{GeV}/{\mathrm{c}}^2$ (yellow).

Figure 6

The 90% C.L. limits on the cross section for spin-independent interaction between a DM particle and a nucleon as a function of the particle mass obtained in the present work. The thick solid red line corresponds to the result from the standard WIMP analysis. The associated red contour is obtained from the SIMP analysis, taking into account the slowing of the DM particle flux through the material above the detector. The thick dashed line and its accompanying red contour are obtained in the Migdal analysis. These results are compared to those of other experiments (see text). Other results using the Migdal effect are shown as dashed lines. The other shaded contours correspond to the SIMP analyses of the CRESST 2017 surface run [31, 32, 53] (blue contour), the XQC rocket [55, 57] (gray contour with full line) and the CMB [58] (gray contour with dashed line).

Figure 7

The 90% C.L. limits on the cross section for spin-dependent interactions assuming a dark matter coupling only to neutrons (left panel) and to protons (right panel) as a function of the particle mass obtained in the present work. The thick red lines and contours correspond to the presented surface dark matter search taking into account Earth-shielding effects and the so-called Migdal effect (dashed line) which is only relevant for the neutron SD coupling. These results are compared to those of other direct detection experiments shown as solid lines: LUX [71] (purple), XENON1T [72] (green), PICO-60-II [73] (brown), CDMSLite [74] (pink), and PANDAX-II [75] (blue). The other shaded contours correspond to the SIMP analyses from the XQC rocket [55, 57, 59] (black solid line), the RRS balloon experiment [59], and the CMB [58] (gray contour with dashed line).

Figure 8

Comparison of pulse simulations and analytic detector response. Left: Density function for the output energy $E_{\mathrm{out}}$ at a given input energy $E_{\mathrm{in}}$ estimated from pulse simulations after applying cuts. Right: Analytic density function described in Eq. (a3), including optimal filter resolution and efficiency cuts. We use bins of 2.5 eV in both $E_{\mathrm{in}}$ and $E_{\mathrm{out}}$.