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

I. J. Arnquist, F. T. Avignone III, A. S. Barabash, K. H. Bhimani, E. Blalock, B. Bos, M. Busch, Y. -D. Chan, J. R. Chapman, C. D. Christofferson, P. -H. Chu, C. Cuesta, J. A. Detwiler, Yu. Efremenko, H. Ejiri, S. R. Elliott, N. Fuad, G. K. Giovanetti, M. P. Green, J. Gruszko, I. S. Guinn, V. E. Guiseppe, R. Henning, E. W. Hoppe, R. T. Kouzes, A. Li, R. Massarczyk, S. J. Meijer, L. S. Paudel, W. Pettus, A. W. P. Poon, D. C. Radford, A. L. Reine, K. Rielage, D. C. Schaper, S. J. Schleich, D. Tedeschi, R. L. Varner, S. Vasilyev, S. L. Watkins, J. F. Wilkerson, C. Wiseman, C. -H. Yu

Published 2024-12-20Version 1

The Majorana Demonstrator was an ultra-low-background experiment designed for neutrinoless double-beta decay ($0\nu\beta\beta$) 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 half-life limits of $1.27\times10^{26}$ years (90\% confidence level) for $^{76}$Ge($ppp$) $\rightarrow$ $^{73}$Cu e$^+\pi^+\pi^+$ and $^{76}$Ge($ppn$) $\rightarrow$ $^{73}$Zn e$^+\pi^+$. The half-life limit for the invisible tri-proton decay mode of $^{76}$Ge is found to be $1.4\times10^{25}$ yr. Furthermore, we have updated limits for corresponding multi-nucleon decays.