Search for Double Beta Decays of $^{134}$Xe with EXO-200 Phase II

EXO-200 was a leading double beta decay experiment consisting of a single-phase, enriched liquid xenon time projection chamber filled with an admixture of 80.672% $^{136}$Xe and 19.098% $^{134}$Xe. The detector operated at WIPP between 2010 and 2018 and was designed to search for double beta decay of $^{136}$Xe. Data was acquired in two phases separated by a period of detector upgrades. We report on the search for $0νββ$ and $2νββ$ decay of $^{134}$Xe with Phase II EXO-200 data, with median 90% C.L. exclusion sensitivity $T_{1/2}^{0ν} \geq 3.7\times 10^{23}$ yr and $T_{1/2}^{2ν} \geq 2.6 \times 10^{21}$ yr, respectively. No statistically significant signal is observed for either decay mode. We set a world-leading lower limit on the half-life of the neutrinoless decay mode of $^{134}$Xe of $T_{1/2}^{0ν} \geq 8.7\times10^{23}$ (90% C.L.) and the second strongest constraint on the two-neutrino decay of $T_{1/2}^{2ν} \geq 2.9\times10^{21}$ (90% C.L.), a 3-fold improvement over the EXO-200 Phase I measurement. New constraints are also set for the $2νββ$ and $0νββ$ decays of $^{134}$Xe to the lowest excited state of $^{134}$Ba.