Final Results of GERDA on the Two-Neutrino Double-$\beta$ Decay Half-Life of ${}^{76}$Ge

Abstract

We present the measurement of the two-neutrino double-$\beta$ decay rate of ${}^{76}$Ge performed with the GERDA Phase II experiment. With a subset of the entire GERDA exposure, 11.8 kg$\cdot$yr, the half-life of the process has been determined: $T_{1/2}^{2\nu }=(2.022\pm 0.018_{stat}\pm 0.038_{sys})\times 10^{21}$ yr. This is the most precise determination of the ${}^{76}$Ge two-neutrino double-$\beta$ decay half-life and one of the most precise measurements of a double-$\beta$ decay process. The relevant nuclear matrix element can be extracted: $M_{\text{eff}}^{2\nu }=(0.101\pm 0.001).$

7 pages, 4 figures, 2 tables

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