Measurements of Branching Fractions andCP-Violating Asymmetries inBMeson Decays to Charmless Two-Body States Containing aK0

We present measurements of branching fractions and $CP$-violating asymmetries in decays of $B$ mesons to two-body final states containing a $K^0$. The results are based on a data sample of approximately $88\times {10}^6$ ${\rm Y}(4S)\to B\overline{B}$ decays collected with the BABAR detector at the PEP-II asymmetric-energy $B$ Factory at SLAC. We measure $\mathcal{B}(B^{+}\to K^0{\pi }^{+})=(22.3\pm 1.7\pm 1.1)\times {10}^{-6}$, $\mathcal{B}(B^0\to K^0{\pi }^0)=(11.4\pm 1.7\pm 0.8)\times {10}^{-6}$, $\mathcal{B}(B^{+}\to {\overline{K}}^0{K}^{+})<2.5\times {10}^{-6}$, and $\mathcal{B}(B^0\to K^0{\overline{K}}^0)<1.8\times {10}^{-6}$, where the first uncertainty is statistical and the second is systematic, and the upper limits are at the $90\%$ confidence level. In addition, the following $CP$-violating asymmetries have been measured: ${\mathcal{A}}_{CP}(B^{+}\to K^0{\pi }^{+})=-0.05\pm 0.08\pm 0.01$ and ${\mathcal{A}}_{CP}(B^0\to K^0{\pi }^0)=0.03\pm 0.36\pm 0.11$.