Analysis of three-body charmless $B$-meson decays under the factorization-assisted topological-amplitude approach

We analyze quasi-two-body charmless $B$ decays $B_{(s)} \to P_1 V \to P_1 P_2 P_3$ with $V$ representing a vector resonant, and $P_{1,2,3}$ as a light pseudo-scalar meson, pion, kaon or $\eta^{(\prime)}$. The intermediate processes $B_{(s)} \to P_1 V $ are calculated in the factorization-assisted topological-amplitude approach and the vector resonant effects are described by the Breit-Wigner propagator, which successively decay to $P_1 P_2$ via strong interaction. Taking into account of all vector resonances in ground state, $\rho, K^*, \omega, \phi$, we present the related branching fractions, and calculate the virtual effects for $B_{(s)} \to \pi, K (\rho ,\omega \to) KK$. We also predict direct $\it{CP}$ asymmetries of three body B decay modes with $\rho, K^*$ resonances as intermediate states. Our predicted branching fractions of decay modes dominated by the color-favored tree diagram or the color-favored penguin diagram are consistent with the perturbative QCD approach's predictions as well as QCD factorization approach. While for those nonperturbative contribution dominated decay modes, the branching ratios in this work are in better agreement with current experimental data than the PQCD predictions and the QCD factorization results due to their shortage of the nonperturbative contributions or $1/m_b$ power corrections. Many of the decays channels, especially for direct $\it{CP}$ asymmetries, are waiting for the future experiments.