Contributions of the subprocess $K_0^{\ast }(1430)\to K{\eta }^{\prime }$ in the charmless three-body $B$ meson decays

Abstract

We study the contributions for $K{\eta }^{\prime }$ pair originating from the scalar intermediate state $K_0^{\ast }(1430)$ in the three-body decays $B\to K{\eta }^{\prime }h$ ($h=\pi ,K$) within the perturbative QCD approach. The contribution of $K_0^{\ast }(1430)\to K{\eta }^{\prime }$ is described by the Flatt$\acute{\mathrm{e}}$ formula with coupled channels $K\pi$, $K\eta$ and $K{\eta }^{\prime }$. The strong coupling constants $g_{K_0^{\ast }K{\eta }^{(\prime )}}$ are extracted from $g_{K_0^{\ast }K\pi }$ within flavor SU$(3)$ symmetry. In spite of the strong depression by phase space near the threshold of $K{\eta }^{\prime }$, the $CP$ averaged branching fractions for the $B\to K_0^{\ast }(1430)h\to K{\eta }^{\prime }h$ decays are predicted to be on the order of $10^{-8}$ to $10^{-5}$, which are non-negligible for the corresponding three-body $B$ decays. Since the K$\eta$ system is almost decoupled from the even-spin strange mesons under flavor SU$(3)$ symmetry, those quasi-two-body $B$ decays with subprocess $K_0^{\ast }(1430)\to K\eta$ shall have quite small branching ratios and are not taken into account in this work. We also estimate that the branching fraction for $K_0^{\ast }(1430)\to K{\eta }^{\prime }$ is about one fifth of that for $K_0^{\ast }(1430)\to K\pi$. The predictions for the relevant decays are expected to be tested by the LHCb and Belle-II experiments in the future.

Comments: 10 pages, 2 figures and 4 tables. Matching the published version in PRD