Importance of theKηandKη′Decay Modes in Understanding Charmed and Other Meson Decays

The $D^0\to {\overline{K}}^0\eta$ decay mode is shown to be suppressed by a large factor insensitive to $\eta -{\eta }^{\prime }$ mixing and SU(3)-symmetry breaking in all transitions via intermediate states with flavor quantum numbers of a $q\overline{q}$ pair, e.g., SU(3) octet, but to be roughly equal to the ${\overline{K}}^0{\pi }^0$ and ${\overline{K}}^0{\eta }^{\prime }$ when produced via exotic $\mathrm{qq}\overline{q}\overline{q}$ channels. The relative decay rates to ${\overline{K}}^0\eta$, ${\overline{K}}^0{\eta }^{\prime }$, and ${\overline{K}}^0{\pi }^0$ distinguish between models producing the additional $q\overline{q}$ pair in weak or strong vertices.