Effects of Final-state Interactions on Mixing-induced CP Violation in Penguin-dominated B Decays

Motivated by the recent indications of the possibility of sizable deviations of the mixing-induced CP violation parameter, $S_f$, in the penguin-dominated $b\to sq\bar{q}$ transition decays such as $B^0\to (\phi,\omega,\rho^0,\eta’,\eta,\pi^0,f_0)K_S$from$\sin 2\beta$ determined from $B\to J\mathrm{/}\psi K_S$, we study final-state rescattering effects on their decay rates and CP violation. Recent observations of large direct CP asymmetry in modes such as $B^0\to K^{+}{\pi }^{-},{\rho }^{-}{\pi }^{+}$ means that final state phases in 2-body B decays may not be small. It is therefore important to examine these long-distance effects on penguin-dominated decays. Such long-distance effects on $S_f$ are found to be generally small [i.e. $\mathcal{O}(1-2$] or negligible except for the $\omega K_S$ and ${\rho }^0{K}_S$ modes where $S_f$ is lowered by around 15% for the former and increased by the same percentage for the latter. However, final-state rescattering can enhance the $\omega K_S, \phi K_S, \eta’K_S, \rho^0K_S$and$\pi^0K_S$ rates significantly and flip the signs of direct CP asymmetries of the last two modes. Direct CP asymmetries in $\omega K_S$and$\rho^0K_S$channelsarepredictedtobe$\A_{\omega K_S}\approx -0.13$and$\A_{\rho^0K_S}\approx 0.47$, respectively. However, direct CP asymmetry in all the other $b\to s$ penguin dominated modes that we study is found to be rather small (a few percents), rendering these modes a viable place to search for the CP-odd phases beyond the standard model.