Analysis of $D^0\to K\overline{K}X$ decays

Using data taken with the CLEO II detector, we have studied the decays of the $D^0$ to $K^{+}{K}^{-}$, $K^0{\overline{K}}^0$, $K_S^0{K}_S^0{K}_S^0$, $K_S^0{K}_S^0{\pi }^0$, $K^{+}{K}^{-}{\pi }^0$. We present significantly improved results for $B(D^0\to K^{+}{K}^{-})=(0.454\mathrm{}\pm 0.028\pm 0.035)\%$, $B(D^0\to K^0{\overline{K}}^0)=(0.054\mathrm{}\pm 0.012\pm 0.010)\%$, and $B(D^0\to K_S^0{K}_S^0{K}_S^0)=(0.074\mathrm{}\pm 0.010\pm 0.015)\%$, where the first errors are statistical and the second errors are the estimate of our systematic uncertainty. We also present a new upper limit $B(D^0\to K_S^0{K}_S^0{\pi }^0)<\mathrm{}0.059\%$ at the 90% confidence level and the first measurement of $B(D^0\to K^{+}{K}^{-}{\pi }^0)=(0.14\mathrm{}\pm 0.04)\%$.