LUX-ZEPLIN (LZ) is a next generation dark matter direct detection experiment that will operate 4850 feet underground at the Sanford Underground Research Facility (SURF) in Lead, South Dakota, USA. Using a two-phase xenon detector with an active mass of 7 tonnes, LZ will search primarily for low-energy interactions with Weakly Interacting Massive Particles (WIMPs), which are hypothesized to make up the dark matter in our galactic halo. In this paper, the projected WIMP sensitivity of LZ is presented based on the latest background estimates and simulations of the detector. For a 1000 live day run using a 5.6 tonne fiducial mass, LZ is projected to exclude at 90% confidence level spin-independent WIMP-nucleon cross sections above $1.6 times 10^{-48}$ cm$^{2}$ for a 40 $mathrm{GeV}/c^{2}$ mass WIMP. Additionally, a $5sigma$ discovery potential is projected reaching cross sections below the existing and projected exclusion limits of similar experiments that are currently operating. For spin-dependent WIMP-neutron(-proton) scattering, a sensitivity of $2.7 times 10^{-43}$ cm$^{2}$ ($8.1 times 10^{-42}$ cm$^{2}$) for a 40 $mathrm{GeV}/c^{2}$ mass WIMP is expected. With underground installation well underway, LZ is on track for commissioning at SURF in 2020.
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