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

Abstract

Because at the tree level $B_s\to K^{+}{K}^{-}$ is Cabibbo-triple suppressed, so its branching ratio should be smaller than that of $B_s\to {\pi }^{+}{K}^{-}$. The measurements present a reversed ratio as $R=\mathcal{B}(B_s\to {\pi }^{+}{K}^{-})/\mathcal{B}(B_s\to K^{+}{K}^{-})\sim 4.9/33$. 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 $B_s\to K^{+}{K}^{-}$ via sequential processes $B_s\to D_{(s)}^{(\ast )}{\bar{D}}_s^{(\ast )}\to K^{+}{K}^{-}$ 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.

Comments: 9 pages, 1 figures, 3 tables. Accepted by PRD