Liquid xenon two-phase time projection chamber (TPC) is one of the most promising technologies for WIMP dark matter direct detection. By using this technology, the LUX, XENON1T, and PANDAX-II collaborations established the most stringent limits on WIMP-nucleus cross section above 10 GeV. For WIMP searches, the expected signal is composed of nuclear recoils (NR), while our background is composed by both electron recoils (ER) and NR. The limits on the WIMP-nucleus cross section are extracted using a Profile Likelihood Ratio (PLR). The usage of the PLR requires a precise knowledge of signal and background models. In the first section, I will focus on the improvement of the detector response modeling and the re-analysis of the background model for LUX Run4 analyses. The LUX Run4 represents a challenge for the modeling of the detector response as several experimental parameters vary as a function of time. Then I will present a new detector response model based on the NEST yield model to consider those variations. This new model has been tuned on Run4 calibration data across many electric fields. After the decommissioning of the LUX experiment, some parts of the detector have been re-assayed to reevaluate the activity of the contaminants. I’m developing a new background model based on a Monte-Carlo simulation of the detector and those new measurements. Once achieved, this background model will be used in future analyses. I used the new detector response model to test the impact of the electric field and the light collection efficiency on detector sensitivity for several dark matter models.