The FSI contribution to the observed $B_s$ decays into $K^{+}{K}^{-}$ and ${\pi }^{+}{K}^{-}$

Because at the tree level $B_s\to K^{+}{K}^{-}$ is Cabibbo-triple suppressed, so its branching ratio should be smaller than that of $B_s\to \pi^+ K^-$\mathrm{.}Themeasurementspresentareversedratioas$R=\mathcal B(B_s\rightarrow \pi^+K^-)/\mathcal B(B_s\rightarrow K^+ K^-)\sim{4.9/33}$. Therefore, It has been suggested that the transition $B_s\to K^{+}{K}^{-}$ is dominated by the penguin mechanism, which is proportional to $V_{cb}{V}_{cs}^{\ast }$. In this work, we show that an extra contribution from the final state interaction (FSI) to $B_s\to K^+K^-$viasequentialprocesses$B_s\to D^{()}_{(s)} \bar D_s^{()}\to K^+K^-$ is also substantial and should be superposed on the penguin contribution. Indeed, taking into account of the FSI effects, the theoretical prediction on $R$ is well consistent with the data.