Measurements of the Branching Fractions of the Singly-Cabibbo-Suppressed Decays $D^0\toωη$, $η^{(\prime)}π^0$ and $η^{(\prime)}η$

By analyzing a data sample of 2.93 fb$^{-1}$ collected at $\sqrt s=$ 3.773 GeV with the BESIII detector operated at the BEPCII storage rings, we measure the branching fractions ${\mathcal B}(D^0\toωη)=(2.15\pm0.17_{\rm stat.}\pm0.15_{\rm sys.})\times 10^{-3}$, ${\mathcal B}(D^0\toηπ^0)=(0.58\pm0.05_{\rm stat.}\pm0.05_{\rm sys.})\times 10^{-3}$, ${\mathcal B}(D^0\toη^\primeπ^0)=(0.93\pm0.11_{\rm stat.}\pm0.09_{\rm sys.})\times 10^{-3}$, ${\mathcal B}(D^0\toηη)=(2.20\pm0.07_{\rm stat.}\pm0.06_{\rm sys.})\times 10^{-3}$ and ${\mathcal B}(D^0\toη^\primeη)=(0.94\pm0.25_{\rm stat.}\pm0.11_{\rm sys.})\times 10^{-3}$. We note that ${\mathcal B}(D^0\to ωη)$ is measured for the first time and that ${\mathcal B}(D^0\to ηη)$ is measured with much improved precision.