Search for Double Beta Decay of ${}^{136}$Xe to the $0_1^{+}$ Excited State of ${}^{136}$Ba with PandaX-4T

Abstract

We perform a search of double beta decay of ${}^{136}$Xe to the excited state, $0_1^{+}$, of ${}^{136}$Ba (2$\hat{I}½{\hat{I}}^2{\hat{I}}^2$-0${}_1^{+}$), using the dual-phase xenon detector of PandaX-4T with the first 94.9-day commissioning data. The multi-site events are reconstructed up to the MeV energy scale, which helps to improve the background model significantly. The background contribution from the stainless steel platform outside PandaX-4T cryostat is evaluated for the first time. No significant evidence for 2$\hat{I}½{\hat{I}}^2{\hat{I}}^2$-$0_1^{+}$ is observed, resulting in a lower limit on half-life of $7.5\times 10^{22}$ yr at the 90% confidence level. This is the first experimental limit on such a rare decay in a natural xenon-based detector.