Contributions of K 0 ∗ 1430 and K 0 ∗ 1950 in the Charmed Three-Body B Meson Decays

Abstract

In this work, we investigate the resonant contributions of $K_0^{\ast }\left(1430\right)$ and $K_0^{\ast }\left(1950\right)$ in the three-body $B_{\left(s\right)}⟶D_{\left(s\right)}K\pi$ within the perturbative QCD approach. The form factor $F_{k\pi }\left(s\right)$ is 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 $B^0⟶{\overline{D}}^0{K}_0^{\ast 0}\left(1430\right)⟶{\overline{D}}^0{K}^{+}{\pi }^{-}$ and $B_s^0⟶{\overline{D}}^0{\overline{K}}_0^{\ast 0}\left(1430\right)⟶{\overline{D}}^0{K}^{-}{\pi }^{+}$ is 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.