Contributions of $K_0^{\ast }(1430)$ and $K_0^{\ast }(1950)$ in the charmed three-body $B$ meson decays

Abstract

In this work, we investigate the resonant contributions of $K_0^{\ast }(1430)$ and $K_0^{\ast }(1950)$ in the three-body $B_{(s)}\to D_{(s)}K\pi$ within the perturbative QCD approach. The form factor $F_{k\pi }(s)$ are adopted to describe the nonperturbative dynamics of the S-wave $K\pi$ system. The branching ratios of all concerned decays are calculated and predicted to be in the order of $10^{-10}$ to $10^{-5}$. The ratio $R$ of branching fractions between $B^0\to {\bar{D}}^0{K}_0^{\ast 0}(1430)\to {\bar{D}}^0{K}^{+}{\pi }^{-}$ and $B_s^0\to {\bar{D}}^0{\bar{K}}_0^{\ast 0}(1430)\to {\bar{D}}^0{K}^{-}{\pi }^{+}$ are predicted to be 0.0552, which implies the discrepancy for the LHCb measurements. We expect that the predictions in this work can be tested by the future experiments, especially, to resolve $R$ ratio discrepancy.