Rare multi-nucleon decays with the full data sets of the Majorana Demonstrator

Abstract

The Majorana Demonstrator was an ultra-low-background experiment designed for neutrinoless double-beta decay ($0\hat{I}½{\hat{I}}^2{\hat{I}}^2$) investigation in ${}^{76}$Ge. Located at the Sanford Underground Research Facility in Lead, South Dakota, the Demonstrator utilized modular high-purity Ge detector arrays within shielded vacuum cryostats, operating deep underground. The arrays, with a capacity of up to 40.4 kg (27.2 kg enriched to $\sim 88\%$ in ${}^{76}$Ge), have accumulated the full data set, totaling 64.5 kg yr of enriched active exposure and 27.4 kg yr of exposure for natural detectors. Our updated search improves previously explored three-nucleon decay modes in Ge isotopes, setting new partial lifetime limits of $1.83\times 10^{26}$ years (90\% confidence level) for ${}^{76}$Ge($ppp$) $\to$ ${}^{73}$Cu e${}^{+}\ddot{I}{€}^{+}\ddot{I}{€}^{+}$ and ${}^{76}$Ge($ppn$) $\to$ ${}^{73}$Zn e${}^{+}\ddot{I}{€}^{+}$. The partial lifetime limit for the fully inclusive tri-proton decay mode of ${}^{76}$Ge is found to be $2.1\times 10^{25}$ yr. Furthermore, we have updated limits for corresponding multi-nucleon decays.