Two-neutrino double electron capture of ${}^{124}$Xe in the first LUX-ZEPLIN exposure

The broad physics reach of the LUX-ZEPLIN (LZ) experiment covers rare phenomena beyond the direct detection of dark matter. We report precise measurements of the extremely rare decay of ${}^{124}$Xe through the process of two-neutrino double electron capture (2$\nu$2EC), utilizing a $1.39\mathrm{k}\mathrm{g}\times \mathrm{y}\mathrm{r}$ isotopic exposure from the first LZ science run. A half-life of $T_{1\mathrm{/}2}^{2\nu 2\mathrm{E}\mathrm{C}}=(1.09\pm {0.14}_{\text{stat}}\pm {0.05}_{\text{sys}})\times {10}^{22}\mathrm{y}\mathrm{r}$ is observed with a statistical significance of $8.3\sigma$, in agreement with literature. First empirical measurements of the KK capture fraction relative to other K-shell modes were conducted, and demonstrate consistency with respect to recent signal models at the $1.4\sigma$ level.