Final Result of the MAJORANA DEMONSTRATOR's Search for Neutrinoless Double-$\beta$ Decay in $^{76}$Ge

Abstract

The MAJORANA DEMONSTRATOR searched for neutrinoless double-$\beta$ decay ($0\nu\beta\beta$) of $^{76}$Ge using modular arrays of high-purity Ge detectors operated in vacuum cryostats in a low-background shield. The arrays operated with up to 40.4 kg of detectors (27.2 kg enriched to $\sim$88\% in $^{76}$Ge). From these measurements, the DEMONSTRATOR has accumulated 64.5 kg yr of enriched active exposure. With a world-leading energy resolution of 2.52 keV FWHM at the 2039 keV $Q_{\beta\beta}$ (0.12\%), we set a half-life limit of $0\nu\beta\beta$ in $^{76}$Ge at $T_{1/2}>8.3\times10^{25}$ yr (90\% C.L.). This provides a range of upper limits on $m_{\beta\beta}$ of $(113-269)$ meV (90\% C.L.), depending on the choice of nuclear matrix elements.