Contributions of the kaon pair from $\rho (770)$ for the three-body decays $B\to DK\bar{K}$

Abstract

We study the contributions of the kaon pair originating from the resonance $\rho (770)$ for the three-body decays $B\to DK\bar{K}$ by employing the perturbative QCD approach. According to the predictions in this work, the contributions from the intermediate state $\rho (770{)}^0$ are relatively small for the three-body decays such as $B^0\to {\bar{D}}^0{K}^{+}{K}^{-}$, $B_s^0\to {\bar{D}}^0{K}^{+}{K}^{-}$, and $B^{+}\to D_s^{+}{K}^{+}{K}^{-}$, while about $20\%$ of the total three-body branching fraction for $B^{+}\to {\bar{D}}^0{K}^{+}{\bar{K}}^0$ could possibly come from the subprocess $\rho (770{)}^{+}\to K^{+}{\bar{K}}^0$. We also estimate the branching fractions for $\rho (770{)}^{\pm }$ decay into the kaon pair to be about $1\%$, and that for the neutral $\rho (770)$ decay into $K^{+}{K}^{-}$ or $K^0{\bar{K}}^0$ to be about $0.5\%$, which will be tested by future experiments.

Comments: 12 pages, 3 figures and 4 tables. Some modifications, matching the published version