We present constraints on weakly interacting massive particles (WIMP)-nucleus scattering from the 2013 data of the Large Underground Xenon dark matter experiment, including $1.4\times10^{4}\;\mathrm{kg\; day}$ 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% C.L. upper limit has a minimum of 0.6 zb at 33 $\mathrm{GeV}\,c^{-2}$ WIMP mass.
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