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The Large Underground Xenon (LUX) experiment, a dual-phase xenon time-projection chamber operating at the Sanford Underground Research Facility (Lead, South Dakota), was cooled and filled in February 2013. We report results of the first WIMP search d ataset, taken during the period April to August 2013, presenting the analysis of 85.3 live-days of data with a fiducial volume of 118 kg. A profile-likelihood analysis technique shows our data to be consistent with the background-only hypothesis, allowing 90% confidence limits to be set on spin-independent WIMP-nucleon elastic scattering with a minimum upper limit on the cross section of $7.6 times 10^{-46}$ cm$^{2}$ at a WIMP mass of 33 GeV/c$^2$. We find that the LUX data are in strong disagreement with low-mass WIMP signal interpretations of the results from several recent direct detection experiments.
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