Resonances $\phi(1020)$ and $\phi(1680)$ contributions for the three-body decays $B^+ \to D_s^+K\bar K$

Abstract

We study the resonances $\phi(1020)$ and $\phi(1680)$ contributions for the three-body decays $B^+ \to D_s^+K\bar K$ in the perturbative QCD approach. The branching ratios for $B^+ \to D_s^+\phi(1020) \to D_s^+ K^+K^-$ and $B^+ \to D_s^+\phi(1020) \to D_s^+ K^0\bar{K}^0$ are predicted to be $(1.53\pm0.23) \times 10^{-7}$ and $(1.02^{+0.19}_{-0.13} )\times 10^{-7}$, respectively. The decay $B^+ \to D_s^+\phi(1680)$ with $\phi(1680)$ decays into $K^+K^-$ or $K^0\bar{K}^0$, has the branching fraction $(6.94^{+1.83}_{-2.02})\times 10^{-9}$, which is about $5\%$ of the result for $B^+ \to D_s^+\phi(1020) \to D_s^+ K^+K^-$.