We present constraints on WIMP-nucleus scattering from the 2013 data of the Large Underground Xenon (LUX) dark matter experiment, including $1.4\times10^{4}\,\mathrm{kg\cdot days}$ of search exposure. This new analysis incorporates several advances: single-photon calibration at the scintillation wavelength; improved event-reconstruction algorithms; a revised background model including events originating on the detector walls in an enlarged fiducial volume; and new calibrations from decays of an injected tritium $\beta$ source and from kinematically constrained nuclear recoils down to 1.1 keV. Sensitivity, especially to low-mass WIMPs, is enhanced compared to our previous results which modeled the signal only above a 3 keV minimum energy. Under standard dark matter halo assumptions and in the mass range above 4 $\mathrm{GeV}\,c^{-2}$, these new results give the most stringent direct limits on the spin-independent WIMP-nucleon cross section. The 90% CL upper limit has a minimum of 0.4 zb at 33 $\mathrm{GeV}\,c^{-2}$ WIMP mass.
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