Searching for Two-Neutrino and Neutrinoless Double Beta Decay of ¹³⁴Xe with the PandaX-4T Experiment

¹³⁴Xe is a candidate isotope for neutrinoless double beta decay~($0νββ$) search. In addition, the two-neutrino case ($2νββ$) allowed by the Standard Model of particle physics has not yet been observed. Utilizing the 10.4% of ¹³⁴Xe in the natural xenon in the PandaX-4T detector and its first 94.9-day exposure, we have established the most stringent constraints on $2νββ$ and $0νββ$ of ¹³⁴Xe half-lives, with limits of 2.8×10²² yr and 3.0×10²³ yr at 90% confidence level, respectively. The $2νββ$ ($0νββ$) limit surpasses the previously reported best result by a factor of 32 (2.7), highlighting the potential of large monolithic natural xenon detectors.