Annihilation Contributions and CP Asymmetries in $B^{+}\to {\pi }^{+}{K}^0,K^{+}{K}^0$ and $B^0\to K^0{\bar{K}}^0$

Abstract

Recently the branching ratios for $B^{+}\to K^{+}{\bar{K}}^0$ and $B^0\to K^0{\bar{K}}^0$ have been measured. Data indicate that the annihilation amplitudes in these decays are not zero. A non-zero annihilation amplitude plays an important role in CP violation for $B^{+}\to {\pi }^{+}{K}^0,K^{+}{\bar{K}}^0$. Using the measured branching ratios for these decays, we show that there is an absolute bound of 5% for the size of CP asymmetry in $B^{+}\to {\pi }^{+}{K}^0$ from a relation between the amplitudes of these decays. The size of CP asymmetry in $B^{+}\to K^{+}{\bar{K}}^0$ can, however, be as large as 90%. Future experimental data will test these predictions.

Comments: 9 pages, 3 figures; version added a few references and corrected a typo; the final version to appear at PRD