Improved modeling of $β$ electronic recoils in liquid xenon using LUX calibration data

We report here methods and techniques for creating and improving a model that reproduces the scintillation and ionization response of a dual-phase liquid and gaseous xenon time-projection chamber. Starting with the recent release of the Noble Element Simulation Technique (NEST v2.0), electronic recoil data from the $\beta$ decays of ${}^3$H and ${}^{14}$C in the Large Underground Xenon (LUX) detector were used to tune the model, in addition to external data sets that allow for extrapolation beyond the LUX data-taking conditions. This paper also presents techniques used for modeling complicated temporal and spatial detector pathologies that can adversely affect data using a simplified model framework. The methods outlined in this report show an example of the robust applications possible with NEST v2.0, while also providing the final electronic recoil model and detector parameters that will used in the new analysis package, the LUX Legacy Analysis Monte Carlo Application (LLAMA), for accurate reproduction of the LUX data. As accurate background reproduction is crucial for the success of rare-event searches, such as dark matter direct detection experiments, the techniques outlined here can be used in other single-phase and dual-phase xenon detectors to assist with accurate ER background reproduction.