A FLUKA Study of $\beta$-delayed Neutron Emission for the Ton-size DarkSide Dark Matter Detector

In the published cosmogenic background study for a ton-sized DarkSide dark matter search, only prompt neutron backgrounds coincident with cosmogenic muons or muon induced showers were considered, although observation of the initiating particle(s) was not required. The present paper now reports an initial investigation of the magnitude of cosmogenic background from $\beta$-delayed neutron emission produced by cosmogenic activity in DarkSide. The study finds a background rate for $\beta$-delayed neutrons in the fiducial volume of the detector on the order of < 0.1 event/year. However, detailed studies are required to obtain more precise estimates. The result should be compared to a radiogenic background event rate from the PMTs inside the DarkSide liquid scintillator veto of 0.2 events/year.