Search for two-neutrino double electron capture in $^{36}$Ar with the DarkSide-50 detector

Technical Summary: Search for Two-Neutrino Double Electron Capture in 36Ar with the DarkSide-50 Detector

Problem and Motivation
Two-neutrino double electron capture ($2EC_{2\nu}$) is a rare second-order weak-interaction process where an atomic nucleus simultaneously captures two electrons from the atomic shells, emitting two neutrinos. While the neutrinoless mode ($2EC_{0\nu}$) is a primary target for discovering physics beyond the Standard Model (specifically Majorana neutrinos and lepton number violation), the two-neutrino mode is a Standard Model-allowed process. Experimental measurement of the $2EC_{2\nu}$ half-life provides a critical test for nuclear matrix element (NME) calculations, which are essential for predicting the rates of the neutrinoless mode.

The isotope $^{36}\text{Ar}$ is a candidate for this process, with a theoretically predicted half-life of approximately $1.7 \times 10^{29}$ years. This prediction is significantly longer than that of $^{124}\text{Xe}$ (recently observed by XENON1T) due to the smaller decay energy ($Q \approx 433$ keV vs. $\approx 2.8$ MeV) and the "doubly magic" nature of the $^{36}\text{Ar}$ nucleus ($Z=N=18$), which suppresses the nuclear matrix element. Prior to this work, no experimental search for $2EC_{2\nu}$ in $^{36}\text{Ar}$ had been conducted. The challenge lies in detecting the low-energy atomic de-excitation signals (Auger electrons and X-rays) against a background of radioactive contaminants, requiring a detector with ultra-low radioactivity and a large exposure of argon.

Methodology
The study utilizes data from the DarkSide-50 experiment, located at the Laboratori Nazionali del Gran Sasso (LNGS) in Italy. The detector is a dual-phase liquid argon (LAr) time projection chamber (TPC) with an active mass of $(46.4 \pm 0.7)$ kg.

• Target Material: The experiment employed underground argon (UAr) extracted from a mine, which is depleted in the cosmogenic isotope $^{39}\text{Ar}$ compared to atmospheric argon. The isotopic abundance of $^{36}\text{Ar}$ in the UAr target was determined via inductively coupled plasma mass spectrometry (ICP-MS) to be $\eta_{\text{UAr}}^{36\text{Ar}} = (7.32 \pm 0.13) \times 10^{-3}\%$, representing a depletion factor of $45.6 \pm 0.8$ relative to atmospheric argon.
• Signal Characteristics: The $2EC_{2\nu}$ process in $^{36}\text{Ar}$ involves the capture of two electrons from the K-shell (KK-capture, $\sim74\%$ probability) or one from the K-shell and one from the L-shell (KL-capture, $\sim26\%$ probability). The resulting atomic vacancies lead to a cascade of Auger electrons and characteristic X-rays. The total energy release is approximately 4.8 keV, manifesting as ionization signals in the liquid argon.
• Data Selection: The analysis covers 633.5 live-days of data collected between December 2015 and December 2018, corresponding to a total exposure of $\approx 12.3$ ton-days. A fiducial mass of $(19.4 \pm 0.3)$ kg was defined to minimize external backgrounds. The region of interest (ROI) for the search corresponds to an ionization charge of $[27, 100]$ reconstructed electrons ($N_e$), equivalent to roughly 1–4 keV.
• Signal Modeling and Validation: The signal spectrum was modeled as a composite of two monoenergetic lines corresponding to the KK- and KL-capture channels, weighted by their transition probabilities. To validate the detector response to such complex, multi-electron cascades, the authors used the electron capture decay of $^{37}\text{Ar}$ (specifically the K-shell line at 2.829 keV) as a benchmark. A "total-energy" approach, treating the cascade energy release as a single interaction point, was found to reproduce the observed $^{37}\text{Ar}$ spectrum better than an independent-electron simulation. This validated approach was applied to the $^{36}\text{Ar}$ signal model.
• Statistical Analysis: A binned profile likelihood fit was performed using the RooFit/HistFactory package. The fit included nuisance parameters for background normalization and shape (dominated by $^{39}\text{Ar}$ and $^{85}\text{Kr}$ decays, and external gamma/X-ray backgrounds) and systematic uncertainties related to signal modeling.

Key Results

• Observation: No statistically significant excess of events was observed in the region of interest above the expected background.
• Upper Limit on Events: The 90% confidence level (C.L.) upper limit on the number of $2EC_{2\nu}$ events is $N_{2EC_{2\nu}} < 278$.
• Half-Life Limit: Using the measured exposure, the $^{36}\text{Ar}$ isotopic abundance, and the molar mass of argon, the authors set a lower limit on the half-life of the two-neutrino double electron capture in $^{36}\text{Ar}$:
  $$T_{1/2}^{2EC_{2\nu}} > 9.2 \times 10^{19} \text{ years} \quad (90\% \text{ C.L.})$$
• Systematics: The systematic uncertainty on the $^{36}\text{Ar}$ abundance ($\pm 1.8\%$) and the energy scale modeling were found to have a negligible impact on the final limit.

Significance and Claims
The paper claims this work as the first experimental search for two-neutrino double electron capture in $^{36}\text{Ar}$. While the established limit ($9.2 \times 10^{19}$ years) is several orders of magnitude below the theoretical prediction ($1.7 \times 10^{29}$ years), the result provides the first empirical constraint on this specific isotope.

The authors emphasize that the successful observation of $2EC_{2\nu}$ in $^{124}\text{Xe}$ by XENON1T validates the theoretical models (such as QRPA and shell models) used to calculate NMEs. Consequently, the lack of a signal in $^{36}\text{Ar}$ at current sensitivities is consistent with these models. The paper posits that any future positive detection of $2EC_{2\nu}$ in $^{36}\text{Ar}$ by next-generation experiments would be highly significant, potentially indicating a breakdown of the nuclear models for this specific isotope or the presence of new physics.

Future Projections
The paper evaluates the projected sensitivity of the upcoming DarkSide-20k experiment. With a fiducial mass of $\sim34$ tons of UAr (a $\sim1000\times$ increase over DarkSide-50), improved radiopurity (using SiPMs and PMMA walls), and enhanced background suppression (specifically $^{85}\text{Kr}$ removal), the sensitivity to $2EC_{2\nu}$ is expected to improve by a factor of $\sim100$ over a 10-year run. This would allow DarkSide-20k to probe half-lives up to $\sim 10^{22}$ years, bringing the experimental reach closer to the theoretical predictions.