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

Abstract

We study the resonances $\varphi (1020)$ and $\varphi (1680)$ contributions for the three-body decays $B^{+}\to D_s^{+}K\bar{K}$ in the perturbative QCD approach. The branching ratios for $B^{+}\to D_s^{+}\varphi (1020)\to D_s^{+}{K}^{+}{K}^{-}$ and $B^{+}\to D_s^{+}\varphi (1020)\to D_s^{+}{K}^0{\bar{K}}^0$ are predicted to be $(1.53\pm 0.23)\times 10^{-7}$ and $(1.02_{-0.13}^{+0.19})\times 10^{-7}$, respectively. The decay $B^{+}\to D_s^{+}\varphi (1680)$ with $\varphi (1680)$ decays into $K^{+}{K}^{-}$ or $K^0{\bar{K}}^0$, has the branching fraction $(6.94_{-2.02}^{+1.83})\times 10^{-9}$, which is about $5\%$ of the result for $B^{+}\to D_s^{+}\varphi (1020)\to D_s^{+}{K}^{+}{K}^{-}$.

Comments: 5 pages and 1 figure; Some modifications, matching the published version