Progress Toward A $2\nu\beta\beta$ Measurement For The Majorana Demonstrator

The MAJORANA DEMONSTRATOR is a $^{76}$Ge-based neutrinoless double-beta decay ($0\nu\beta\beta$) experiment. Staged at the 4850 ft level of the Sanford Underground Research Facility, the DEMONSTRATOR operates an array of high-purity p-type point contact Ge detectors deployed within a graded passive shield and an active muon veto system. The present work concerns the two-neutrino double-beta decay mode ($2\nu\beta\beta$) of $^{76}$Ge. For Ge detectors, having superior energy resolution (0.1%), this mode poses negligible background to the $0\nu\beta\beta$ mode, even for a ton-scale experiment. However, the measurement of the $2\nu\beta\beta$ mode allows for careful systematics checks of active detector mass, enrichment fraction, and pulse shape discrimination cuts related to both the $0\nu\beta\beta$ and $2\nu\beta\beta$ decay modes. A precision measurement of the $2\nu\beta\beta$ shape also allows searches for spectral distortions, possibly indicative of new physics, including $0\nu\beta\beta\chi$. Work is underway to construct a full experimental background model enabling a Bayesian fit to the measured energy spectrum and extraction of a precise $2\nu\beta\beta$ spectrum and half-life.