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

Abstract

We systematically analyze the decays $B_{(s)} \to D_{(s)} (V^* \to)\, V\, P$, where $V^*$ represents a vector resonance ($ρ, \, ω$ or $K^*$), and $V P$ denotes the final-state meson pairs $ ω\, π$, $ ρ\, π$ and $ ρ\, K$. The intermediate subprocesses $B_{(s)} \to D_{(s)} V^*$ are calculated in the factorization-assisted topological-amplitude approach, while the intermediate resonant states $V^*$ 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 ($ρ,\, ω, \, K^*$) in $B_{(s)} \to D_{(s)} (V^* \to )V P$. Our results show that the virtual contributions from $ρ\to ω\, π$, $ω\to ρ\, π$, and $K^* \to ρ\, K$ are crucial for these three-body decays, $B_{(s)} \to D_{(s)} V\, P$. In particular, the branching fractions arising from the $ρ$ and $ω$ virtual effects can be comparable to the total decay rates of $B_{(s)} \to D_{(s)} ω\, π$ and $B_{(s)} \to D_{(s)} ρ\, π$, 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 $B_{(s)} \to D_{(s)} (ρ\to)\, ω\, π$, our results are consistent but exhibit higher precision.