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.