  Weakly Interacting Massive Particles (WIMPs) are a leading candidate for dark
matter and are expected to produce nuclear recoil (NR) events within liquid
xenon time-projection chambers. We present a measurement of the scintillation
timing characteristics of liquid xenon in the LUX dark matter detector and
develop a pulse shape discriminant to be used for particle identification. To
accurately measure the timing characteristics, we develop a template-fitting
method to reconstruct the detection times of photons. Analyzing calibration
data collected during the 2013-16 LUX WIMP search, we provide a new measurement
of the singlet-to-triplet scintillation ratio for electron recoils (ER) below
46~keV, and we make a first-ever measurement of the NR singlet-to-triplet ratio
at recoil energies below 74~keV. We exploit the difference of the photon time
spectra for NR and ER events by using a prompt fraction discrimination
parameter, which is optimized using calibration data to have the least number
of ER events that occur in a 50\% NR acceptance region. We then demonstrate how
this discriminant can be used in conjunction with the charge-to-light
discrimination to possibly improve the signal-to-noise ratio for nuclear
recoils.
