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

Abstract: We analyze the quasi-two-body charmed $B$ decays $B^{+,0}_{(s)} \to D_{(s)}^* P_2 \to D_{(s)} P_1 P_2$ with $P_{1,2}$ as a pion or kaon. The intermediate processes $B_{(s)} \to D_{(s)}^* P_2 $ are calculated with the factorization-assisted topological-amplitude approach and the resonant effects are calculated with the Breit-Wigner formalism. Taking all p-wave resonance states $ \bar D_{(s)}^*$ into consideration, we present the related branching fractions, calculate the Breit-Wigner-Tail effects, and investigate the flavor $SU(3)$ breaking effects. Most of our branching fractions are consistent with the perturbative QCD approach's predictions as well as the current experimental data. With more precision calculation of the intermediate two body charmed B meson decays, our quasi-two-body B decays calculation has significantly less theoretical uncertainty than the perturbative QCD approach. Many of those channels without any experimental data will be confronted with the future more accurate experiment measurements. Our results of the Breit-Wigner-tail effects also agree with the experimental very well. In $B^0$ decays this effect can reach approximately to $5\%$. It is also found that the Breit-Wigner-tail effects are not sensitive to the widths of their corresponding resonances. The flavor $SU(3)$ symmetry breaking effect is also investigated.