An assay-based background projection for the MAJORANA DEMONSTRATOR using Monte Carlo Uncertainty Propagation

The background index is an important quantity which is used in projecting and calculating the half-life sensitivity of neutrinoless double-beta decay ($0νββ$) experiments. A novel analysis framework is presented to calculate the background index using the specific activities, masses and simulated efficiencies of an experiment’s components as distributions. This Bayesian framework includes a unified approach to combine specific activities from assay. Monte Carlo uncertainty propagation is used to build a background index distribution from the specific activity, mass and efficiency distributions. This analysis method is applied to the MAJORANA DEMONSTRATOR, which deployed arrays of high-purity Ge detectors enriched in $^{76}$Ge to search for $0νββ$. The framework projects a mean background index of $\left[8.95 \pm 0.36\right] \times 10^{-4}$cts/(keV kg yr) from $^{232}$Th and $^{238}$U in the DEMONSTRATOR’s components.

💡 Research Summary

The paper presents a comprehensive Bayesian framework for projecting the background index (BI) of neutrinoless double‑beta decay (0νββ) experiments, with a specific application to the MAJORANA DEMONSTRATOR. The BI, defined as counts per keV·kg·yr in the region of interest, directly determines the half‑life sensitivity of a 0νββ search. Traditional BI estimates often summed component contributions using point estimates of specific activities and detection efficiencies, treating assay upper limits as hard caps and ignoring statistical uncertainties in simulation efficiencies. This approach can underestimate uncertainties, especially when many assay results are upper limits or when simulated efficiencies are near zero.

The authors introduce a unified method to combine multiple assay measurements, including both measured activities with uncertainties and upper limits. Measured activities are weighted by the inverse square of their uncertainties (standard weighted least‑squares), while the most stringent 90 % confidence upper limit is converted into a “truncated‑at‑zero Gaussian” with a mean of zero and a standard deviation derived from the limit. Only one upper limit per isotope‑component pair is included to avoid artificial reduction of uncertainty. After computing the weighted average activity, a χ² per degree‑of‑freedom test assesses consistency; if χ²/(Nₐ−1) exceeds unity, the combined uncertainty is inflated by the factor Σ = √