Searches for new physics below twice the electron mass with GERDA

Abstract

A search for full energy depositions from bosonic keV-scale dark matter candidates of masses between 65 and 1021 keV has been performed with data collected during Phase II of the GERmanium Detector Array (Gerda) experiment. Our analysis includes direct dark matter absorption as well as dark Compton scattering. With a total exposure of 105.5 kg years, no evidence for a signal above the background has been observed. The resulting exclusion limits deduced with either Bayesian or Frequentist statistics are the most stringent direct constraints in the major part of the 140-1021 keV mass range. As an example, at a mass of 150 keV the dimensionless coupling of dark photons and axion-like particles to electrons has been constrained to ${\alpha }^{\text{'}}/\alpha <8.7\times {10}^{-24}$ and $g_{\text{ae}}<3.3\times {10}^{-12}$ at 90% credible interval (CI), respectively. Additionally, a search for peak-like signals from beyond the Standard Model decays of nucleons and electrons is performed. We find for the inclusive decay of a single neutron in $_{}^{76}$ Ge a lower lifetime limit of ${\tau }_{\text{n}}>1.5\times {10}^{24}$ years and for a proton ${\tau }_{\text{p}}>1.3\times {10}^{24}$ years at 90% CI. For the electron decay $e^{\text{-}}\to {\nu }_{\text{e}}\gamma$ a lower limit of ${\tau }_{\text{e}}>5.4\times {10}^{25}$ years at 90% CI has been determined.

Supplementary information: The online version contains supplementary material available at 10.1140/epjc/s10052-024-13020-0.

Fig. 1

Scheme of the $_{}^{75}$Ge ground state $\beta$-decay to $_{}^{75}$As and subsequent $\gamma$-decays, adapted from [16]. The $\beta$-decay (E$_{\beta }^{}$ = 912.6 keV) to the second excited $_{}^{75}$As state in coincidence with the 264.60 keV $\gamma$-ray is used to tag both the neutron and proton disappearance in $_{}^{76}$Ge. Level and $\gamma$-ray of interest are highlighted in red. The transition $_{}^{75}$Ga${\to }^{75}$Ge following $_{}^{76}$Ge proton decays is shown in blue

Fig. 2

The contributions from detector resolution (red) and the Doppler-broadening (green) of lines from electron decay in the different atomic shells of germanium and argon (see Sect. 4.1). The total expected line shape of the electron decay signal at 255.9 keV is shown in blue. All Gaussians are normalized to unit area. Indicated resolution values are given in FWHM

Fig. 3

Combined Gerda Phase II/II+ spectrum of event multiplicity 1 after quality, muon veto, and LAr cuts. The dominant background contributions from $_{}^{39}$Ar $\beta$ decay and $_{}^{76}$Ge $2\nu \beta \beta$ decay are indicated. The green dashed line separates the regions 65–195 keV and 196–1021 keV with exposure ${\mathcal{E}}_1=60.0$ kg years and ${\mathcal{E}}_2=105.5$ kg years, respectively (see Table 1). The blue dashed lines mark the energy range inspected for bosonic DM candidates, i.e. 65–1021 keV

Fig. 4

Histogram of multiplicity 2 (M2) events; see text for more details. The spectrum accounts for M2 events that survived quality cuts as well as muon and LAr vetoes. The inset shows the data in the $\gamma$-window (blue band) inspected for the nucleon decay signal, i.e. $E_{\gamma }\pm 12.5$ keV with $E_{\gamma }\sim 265.0$ keV (gray dashed line)

Fig. 5

Part of the M1 spectrum shown in Fig. 3 with an example of a Bayesian fit at 662 keV (vertical line). The empirical background contribution is shown in red, while the best-fit model is shown in blue. $N_0$ denotes the best-fit signal strength. The signal excess of 5.1$\sigma$ can be explained by the 661.7 keV $\gamma$-line from $_{}^{137}$Cs (see Table 3)

Fig. 6

Plot of the local p-values of all count strength amplitudes versus the tested energies for the DM search. Apart from the $3\sigma$ excess at 710 keV all other local excesses with $\ge 3\sigma$ can be attributed to known $\gamma$ transitions (see Table 3)

Fig. 7

Bayesian exclusion limits on bosonic DM couplings to electrons obtained from Gerda Phase II and Phase II+ data (light blue line). The limits were deduced by converting the upper count strength limits into physics constraints including in the interaction rate both the photoelectric-like absorption and the dark Compton scattering processes, see Eq. (15). The regions around identified $\gamma$-lines (see Table 3 and numerical data in Supplemental Material have been omitted. Left: Bayesian constraints at 90% CI on the kinetic mixing strength of DPs. Right: Bayesian constraints at 90% CI on the coupling strength of ALPs to electrons. Results from other direct detection experiments [–42] are shown, as well as the previous Gerda limits [2]. Note that in the COSINE-100 paper [42] the previous numerical factors of 1.2 and 4 have been used in eqs. 4 and 5. The dashed, dark red line indicates the region below which the interpretation as a DM candidate being stable on the scale of the age of the Universe is valid without further assumptions [9]. Indirect constraints from X-ray and $\gamma$-ray observations taken from Refs. [9, 43] are indicated by the dot-dashed, brown line. Constraints derived from red giant (RG, dot-dashed, gold line) and horizontal branch (HB, dot-dashed, purple line) star energy losses are discussed in [44]

Fig. 8

Part of the M2 spectrum shown in Fig. 4 with the Bayesian fit of the nucleon decay signal at $E_0\sim$ 265 keV. A 1st-order polynomial was used to model the continuous background

Fig. 9

Part of the M1 spectrum shown in Fig. 3 with the Bayesian fit of the electron decay at $E_{\text{0}}=255.9$ keV (continuous line). The background fit includes two significant $\gamma$s (dashed lines) at $E_{\gamma ,1}=$238.6 keV ($_{}^{212}$Pb) and $E_{\gamma ,2}=$295.2 keV ($_{}^{214}$Pb), see Table 3

Fig. 10

Top: empirical background fit model. The fit was performed with a tenth order polynomial and a $\beta$-modified $\beta$ distribution. The vertical dashed, blue lines denote the lowest probed DM mass of 65 keV, the data set transition value of 195 keV, and 1021 keV as the highest potential integer DM mass below $2m_{\text{e}}$. Middle, bottom: plots of the data (blue dots) and the model (black line) in the two different energy ranges, i.e. 53–207 keV and 184–1033 keV, with the respective residuals shown below each panel. Residuals are defined as the difference between expected counts and observed counts, normalized by the square root of expected counts

Fig. 11

Comparison of Bayesian limits at 90% CI for the dimensionless coupling constant of DPs to electrons, plotted as a function of the respective DM mass when evaluated by considering photoelectric-like absorption only (gold), Compton scattering only (red), and both interactions (blue). Regions around identified $\gamma$ lines (see Sect. 4.3, Table 3) were omitted

Fig. 12

Comparison of Bayesian (red) and frequentist median sensitivities (gold) for the dimensionless coupling constant of DPs, plotted as a function of the respective DM masses. Couplings here are evaluated considering photoelectric-like absorption and Compton scattering processes. The indicated blue bands correspond to the 1 and 2$\sigma$ range for the Bayesian limits, respectively. Regions around identified $\gamma$ lines (see Sect. 4.3, Table 3) were omitted