Analysis of three-body charmed $B$ meson decays $B\to D(V^{\ast }\to )VP$

Abstract

We systematically analyze the decays $B_{(s)}\to D_{(s)}(V^{\ast }\to )VP$, where $V^{\ast }$ represents a vector resonance ($\ddot{I},\ddot{I}‰$ or $K^{\ast }$), and $VP$ denotes the final-state meson pairs $\ddot{I}‰\ddot{I}€$, $\ddot{I}\ddot{I}€$ and $\ddot{I}K$. The intermediate subprocesses $B_{(s)}\to D_{(s)}{V}^{\ast }$ are calculated in the factorization-assisted topological-amplitude approach, while the intermediate resonant states $V^{\ast }$ are modeled using a relativistic Breit-Wigner distribution, subsequently decaying into $VP$ through strong interactions. We predict the off-shell effects of the ground-state resonances ($\ddot{I},\ddot{I}‰,K^{\ast }$) in $B_{(s)}\to D_{(s)}(V^{\ast }\to )VP$. Our results show that the virtual contributions from $\ddot{I}\to \ddot{I}‰\ddot{I}€$, $\ddot{I}‰\to \ddot{I}\ddot{I}€$, and $K^{\ast }\to \ddot{I}K$ are crucial for these three-body decays, $B_{(s)}\to D_{(s)}VP$. In particular, the branching fractions arising from the $\ddot{I}$ and $\ddot{I}‰$ virtual effects can be comparable to the total decay rates of $B_{(s)}\to D_{(s)}\ddot{I}‰\ddot{I}€$ and $B_{(s)}\to D_{(s)}\ddot{I}\ddot{I}€$, respectively. Decays with branching fractions of order $10^{-6}-10^{-4}$ are expected to be measurable at Belle II and LHCb. Compared with previous perturbative QCD predictions for $B_{(s)}\to D_{(s)}(\ddot{I}\to )\ddot{I}‰\ddot{I}€$, our results are consistent but exhibit higher precision.

25 pages, 2 figures