Sensitivity of the LUX detector to the possible neutrinoless double beta decay of $^{134}$Xe

The Large Underground Xenon (LUX) detector is a 370-kg liquid xenon (LXe) time-projection chamber designed primarily for the direct detection of weakly-interacting massive particles (WIMPs), a leading dark matter candidate. LUX operates on the 4850-foot level of the Sanford Underground Research Facility in Lead, SD. The unenriched xenon of LUX contains the natural 10.4\% abundance of the isotope $^{134}$Xe, a candidate for the lepton-number-violating process of neutrinoless double beta (0$\nu\beta\beta$) decay. If observed, this process would confirm the existence of massive Majorana neutrinos and would be a possible path to the measurement of neutrino mass and other studies of new weak-interaction physics. Given its xenon mass and the length of exposure for the LUX detector, there is an opportunity to improve upon the $T_{1/2} > 5.8 \times 10^{22}$ yr sensitivity of the 6.5-kg DAMA experiment (enriched to 17.1\% $^{134}$Xe) from 2002 (Bernabei, et al., Phys. Lett. B 527, 182-186, 2002.). Building upon previous LUX measurements of the energy resolution and signal yields up to 662~keV, this talk will go over the response of the LUX detector at 826 keV, the $^{134}$Xe $Q$-value, and the current status of the LUX $^{134}$Xe 0$\nu\beta\beta$ analysis.