The Large Underground Xenon (LUX) dark matter experiment aims to detect rare low-energy interactions from Weakly Interacting Massive Particles (WIMPs). The radiogenic backgrounds in the LUX detector have been measured and compared with Monte Carlo simulation. Measurements of LUX high-energy data have provided direct constraints on all background sources contributing to the background model. The expected background rate from the background model for the 85.3 day WIMP search run is $(2.6pm0.2_{textrm{stat}}pm0.4_{textrm{sys}})times10^{-3}$~events~keV$_{ee}^{-1}$~kg$^{-1}$~day$^{-1}$ in a 118~kg fiducial volume. The observed background rate is $(3.6pm0.4_{textrm{stat}})times10^{-3}$~events~keV$_{ee}^{-1}$~kg$^{-1}$~day$^{-1}$, consistent with model projections. The expectation for the radiogenic background in a subsequent one-year run is presented.
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