Inspired by the significant virtual contributions of the subprocesses $D^{*}/B^{*}\to D\pi$ and $\rho \to \omega \pi /K\overline{K}$ in the three-body hadronic $B$ meson decays, we study the off-shell effects of the resonance $K^{*}$ decaying into the $K^{*}\pi$ or $K\rho$ system in the decays $B\to K^{*}\pi h$ and $B\to K\rho h$ (with $h=\pi ,K$) within the perturbative QCD approach. The strong coupling constants $g_{K^{*}{K}^{*}\pi }$ and $g_{K^{*}K\rho }$ involved in this work are derived from the coupling constant $g_{\rho \omega \pi }$ under the flavor SU(3) symmetry. The $CP$ averaged branching fractions for the quasi-two-body decays $B\to K^{*}[\to K^{*}\pi ]h$ and $B\to K^{*}[\to K\rho ]h$ are predicted to be on the order of ${10}^{-9}$ to ${10}^{-7}$ in this study. And the branching fractions for the decays $B\to K^{*}[\to K\rho ]h$ are found to be around half of the corresponding results for the $B\to K^{*}[\to K^{*}\pi ]h$ channels, mainly due to the phase space difference between the $K\rho$ and $K^{*}\pi$ pairs originating from the intermediate state $K^{*}$. Experimental data for the $K^{*}$ decaying into the final states $K^{*}\pi$ and $K\rho$ in the $B$ meson decays is expected to be obtained by the LHCb and Belle-II experiments in the near future.

Close

PrevNext

Reuse & PermissionsView figure in article

• 
• 

• Branching fraction
• Hadronic decays
• Particle decays
• Particle phenomena
• Perturbative QCD
• Bottom mesons