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Dark Matter Investigation Using Double Beta Decay Experiments^{ †}

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## Abstract

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^{76}Ge nucleus.

## 1. Introduction

## 2. Expected Energy Distribution

^{76}Ge target nuclei (Q = 2.039 MeV). The shape of the electron energy distributions depend on the amount of invisible energy carried away by the DM particle upscattering. When ${\mathrm{M}}_{\chi}\ll {m}_{e}$ (green line), the expected energy distribution is very similar to the one expected for the neutrinoless double beta decay with a Majoron emission, $0\nu \beta \beta M$ (n = 2) [14,15]. On the other hand, in the case of ${\mathrm{M}}_{\chi}\simeq {m}_{e}$ (magenta line), a distribution very similar to the one expected for the $0\nu \beta \beta M$ (n = 1) decay is evaluated, while, for ${\mathrm{M}}_{\chi}\gg {m}_{e}$, a much harder distribution is expected (blue line).

^{76}Ge as a function of ${M}_{\chi}$ is shown in Figure 3. It is important to note that a direct measurement of the DM particle mass in the range 100–10 MeV could, in principle, be feasible with this approach. In particular, this is due to the deformation of the electron energy distribution caused by the upscattering of the $\chi $ particle.

## 3. Conclusions and Outlooks

^{76}Ge) obtained in this analysis of the Gerda Phase-I golden data set are compared with the current upper limit on the DM–Ge nucleus scattering obtained by considering the “Migdal effect” in the CDMSlite experiment [18]. Despite a deeper comparison being required to detail the $\chi $–nucleus interaction model, the proposed approach could be very effective for the direct detection of a light fermion DM candidate by using the existing or future neutrinoless double beta decay experiments.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

DM | Dark Matter. |

SM | Standard Model. |

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**Figure 1.**A possible detection diagram for the Majorana DM fermion, $\chi $. The exchange of one or more Majoron fields $\varphi $ could stimulate a neutrinoless double beta decay of the nucleus (A,Z) to the daughter nucleus (A,Z+2). A part of the decay Q-value is lost due to the invisible kinetic energy of the upscattering $\chi $ particle. In principle, a measurement of the mass of the $\chi $ particle is possible by studying the distribution of the sum of the kinetic energy of the electrons.

**Figure 2.**Upper limits on Dark Matter signals allowed by the “golden data-set” 17.9 kg × day exposure collected by Gerda Phase-I (points). The maximum signal allowed at 90% C.L. is shown for ${\mathrm{M}}_{\chi}$ = 7 keV, 0.5 MeV, and 5 GeV (green, magenta, and blue lines), respectively.

**Figure 3.**Behaviour of the maximum of the detected energy distribution versus the Dark Matter particle mass inducing a neutrinoless double beta decay in

^{76}Ge.

**Figure 4.**Example of upper limits on the total Dark Matter–Germanium nucleus cross section, obtained in this work considering the 17.9 kg × day exposure collected by Gerda Phase-I golden data set (blue line). Dotted line shows, as a comparison, the upper limits for the Dark Matter–Germanium nucleus elastic scattering for the very low mass region accessible exploiting the “Migdal effect” [17,18].

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**MDPI and ACS Style**

Nozzoli, F.; Cernetti, C.
Dark Matter Investigation Using Double Beta Decay Experiments. *Phys. Sci. Forum* **2023**, *7*, 29.
https://doi.org/10.3390/ECU2023-14056

**AMA Style**

Nozzoli F, Cernetti C.
Dark Matter Investigation Using Double Beta Decay Experiments. *Physical Sciences Forum*. 2023; 7(1):29.
https://doi.org/10.3390/ECU2023-14056

**Chicago/Turabian Style**

Nozzoli, Francesco, and Cinzia Cernetti.
2023. "Dark Matter Investigation Using Double Beta Decay Experiments" *Physical Sciences Forum* 7, no. 1: 29.
https://doi.org/10.3390/ECU2023-14056