Quasi-two-body decays $B_{(s)}\to P{D}_0^{\ast }(2400)\to PD\pi$ in the perturbative QCD approach

Abstract

We study the quasi-two-body decays $B\to P{D}_0^{\ast }(2400)\to PD\pi$ with $P=(\pi ,K,\eta ,{\eta }^{\prime })$ in the perturbative QCD factorization approach. The predicted branching fractions for the considered decays are in the range of $10^{-9}$-$10^{-4}$. The strong Cabibbo-Kobayashi-Maskawa (CKM) suppression factor $R_{CKM}\approx {\lambda }^4({\bar{\rho }}^2+{\bar{\eta }}^2)\approx 3\times 10^{-4}$ results in the great difference of the branching ratios for the decays with $D_0^{\ast }$ and ${\bar{D}}_0^{\ast }$ as the intermediate states. The ratio $R_{{\bar{D}}_0^{\ast 0}}$ between the decays $B^0\to {\bar{D}}_0^{\ast 0}{K}^0\to D^{-}{\pi }^{+}{K}^0$ and $B^0\to {\bar{D}}_0^{\ast 0}{\pi }^0\to D^{-}{\pi }^{+}{\pi }^0$ is about $0.091_{-0.005}^{+0.003}$, consistent with the flavour-$SU$(3) symmetry result. The ratio for the branching fractions is found to be $1.10_{-0.02}^{+0.05}$ between $\mathcal{B}(B_s^0\to D_0^{\ast +}{K}^{-}\to D^0{\pi }^{+}{K}^{-})$ and $\mathcal{B}(B^0\to D_0^{\ast +}{\pi }^{-}\to D^0{\pi }^{+}{\pi }^{-})$ and to be $1.03_{-0.07}^{+0.06}$ between $\mathcal{B}(B_s^0\to {\bar{D}}_0^{\ast 0}{\bar{K}}^0\to D^{-}{\pi }^{+}{\bar{K}}^0)$ and $2\mathcal{B}(B^0\to {\bar{D}}_0^{\ast 0}{\pi }^0\to D^{-}{\pi }^{+}{\pi }^0)$. The predictions in this work can be tested by the future experiments.

Comments: minor corrections, to appear in PRD