Measurements of the branching fractions of $Ξ_{c}^{0}\toΞ^{0}π^{0}$, $Ξ_{c}^{0}\toΞ^{0}η$, and $Ξ_{c}^{0}\toΞ^{0}η^{\prime}$ and asymmetry parameter of $Ξ_{c}^{0}\toΞ^{0}π^{0}$
We present a study of $Ξ_{c}^{0}\toΞ^{0}π^{0}$, $Ξ_{c}^{0}\toΞ^{0}η$, and $Ξ_{c}^{0}\toΞ^{0}η^{\prime}$ decays using the Belle and Belle~II data samples, which have integrated luminosities of 980~$\mathrm{fb}^{-1}$ and 426~$\mathrm{fb}^{-1}$, respectively. We measure the following relative branching fractions $${\cal B}(Ξ_{c}^{0}\toΞ^{0}π^{0})/{\cal B}(Ξ_{c}^{0}\toΞ^{-}π^{+}) = 0.48 \pm 0.02 ({\rm stat}) \pm 0.03 ({\rm syst}) ,$$ $${\cal B}(Ξ_{c}^{0}\toΞ^{0}η)/{\cal B}(Ξ_{c}^{0}\toΞ^{-}π^{+}) = 0.11 \pm 0.01 ({\rm stat}) \pm 0.01 ({\rm syst}) ,$$ $${\cal B}(Ξ_{c}^{0}\toΞ^{0}η^{\prime})/{\cal B}(Ξ_{c}^{0}\toΞ^{-}π^{+}) = 0.08 \pm 0.02 ({\rm stat}) \pm 0.01 ({\rm syst}) $$ for the first time, where the uncertainties are statistical ($\rm stat$) and systematic ($\rm syst$). By multiplying by the branching fraction of the normalization mode, ${\mathcal B}(Ξ_{c}^{0}\toΞ^{-}π^{+})$, we obtain the following absolute branching fraction results $(6.9 \pm 0.3 ({\rm stat}) \pm 0.5 ({\rm syst}) \pm 1.3 ({\rm norm})) \times 10^{-3}$, $(1.6 \pm 0.2 ({\rm stat}) \pm 0.2 ({\rm syst}) \pm 0.3 ({\rm norm})) \times 10^{-3}$, and $(1.2 \pm 0.3 ({\rm stat}) \pm 0.1 ({\rm syst}) \pm 0.2 ({\rm norm})) \times 10^{-3}$, for $Ξ_{c}^{0}$ decays to $Ξ^{0}π^{0}$, $Ξ^{0}η$, and $Ξ^{0}η^{\prime}$ final states, respectively. The third errors are from the uncertainty on ${\mathcal B}(Ξ_{c}^{0}\toΞ^{-}π^{+})$. The asymmetry parameter for $Ξ_{c}^{0}\toΞ^{0}π^{0}$ is measured to be $α(Ξ_{c}^{0}\toΞ^{0}π^{0}) = -0.90\pm0.15({\rm stat})\pm0.23({\rm syst})$.