Measurements of the Branching Fractions of the Singly-Cabibbo-Suppressed Decays $D^0toomegaeta$, $eta^{(prime)}pi^0$ and $eta^{(prime)}eta$

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 ${mathcal B}(D^0toomegaeta)=(2.15pm0.17_{rm stat.}pm0.15_{rm sys.})times 10^{-3}$, ${mathcal B}(D^0toetapi^0)=(0.58pm0.05_{rm stat.}pm0.05_{rm sys.})times 10^{-3}$, ${mathcal B}(D^0toeta^primepi^0)=(0.93pm0.11_{rm stat.}pm0.09_{rm sys.})times 10^{-3}$, ${mathcal B}(D^0toetaeta)=(2.20pm0.07_{rm stat.}pm0.06_{rm sys.})times 10^{-3}$ and ${mathcal B}(D^0toeta^primeeta)=(0.94pm0.25_{rm stat.}pm0.11_{rm sys.})times 10^{-3}$. We note that ${mathcal B}(D^0to omegaeta)$ is measured for the first time and that ${mathcal B}(D^0to etaeta)$ is measured with much improved precision.