Measurement of the Decay $Ξ^{0}\toΛγ$ with Entangled $Ξ^{0}\barΞ^{0}$ Pairs

In this Letter, a systematic study of the weak radiative hyperon decay $\Xi^{0}\to\Lambda\gamma$ at an electron-positron collider using entangled $\Xi^{0}\bar{\Xi}^{0}$ pair events is presented. The absolute branching fraction for this decay has been measured for the first time, and is $\left(1.347 \pm 0.066_{\mathrm stat.}\pm0.054_{\mathrm syst.}\right)\times 10^{-3}$. The decay asymmetry parameter, which characterizes the effect of parity violation in the decay, is determined to be $-0.741 \pm 0.062_{\mathrm stat.}\pm 0.019_{\mathrm syst.}$. The obtained results are consistent with the world average values within the uncertainties, offering valuable insights into the underlying mechanism governing the weak radiative hyperon decays. The charge conjugation parity ($CP$) symmetries of branching fraction and decay asymmetry parameter in the decay are also studied. No statistically significant violation of charge conjugation parity symmetry is observed.