Searches forB0Decays to Combinations of Two Charmless Isoscalar Mesons

We search for $B$ meson decays into two-body combinations of $\eta ,{\eta }^{\prime },\omega$, and $\varphi$ mesons from $89\times {10}^6$ $B\overline{B}$ pairs collected with the BABAR detector at the PEP-II asymmetric-energy $e^{+}{e}^{-}$ collider at SLAC. We find the branching fraction $\mathcal{B}(B^0\to \eta \omega )=({4.0}_{-1.2}^{+1.3}\pm 0.4)\times {10}^{-6}$ with a significance of $4.3\sigma$. For the other decay modes we set the following 90% confidence level upper limits on the branching fractions, in units of ${10}^{-6}$: $\mathcal{B}(B^0\to \eta \eta )<2.8$, $\mathcal{B}(B^0\to \eta {\eta }^{\prime })<4.6$, $\mathcal{B}(B^0\to {\eta }^{\prime }{\eta }^{\prime })<10$, $\mathcal{B}(B^0\to {\eta }^{\prime }\omega )<2.8$, $\mathcal{B}(B^0\to \eta \varphi )<1.0$, $\mathcal{B}(B^0\to {\eta }^{\prime }\varphi )<4.5$, and $\mathcal{B}(B^0\to \varphi \varphi )<1.5$.