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

TL;DR

This paper analyzes three-body $B$ meson decays involving intermediate vector resonances, emphasizing off-shell effects and virtual contributions, and provides precise predictions for branching fractions relevant for experiments like Belle II and LHCb.

Contribution

It introduces a systematic analysis of $B o D V^* o D V P$ decays considering off-shell effects and virtual contributions, improving prediction accuracy over previous models.

Findings

Virtual effects of $ ho$, $ ext{omega}$, and $K^*$ are crucial in these decays.

Branching fractions from virtual effects can be comparable to total decay rates.

Predicted decay rates are within measurable range at Belle II and LHCb.

Abstract

We systematically analyze the decays $B_{(s)} \to D_{(s)} (V^* \to)\, V\, P$, where $V^*$ represents a vector resonance ($\rho, \, \omega$ or $K^*$), and $V P$ denotes the final-state meson pairs $ \omega\, \pi$, $ \rho\, \pi$ and $ \rho \, 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 ($\rho,\, \omega, \, K^*$) in $B_{(s)} \to D_{(s)} (V^* \to )V P$. Our results show that the virtual contributions from $\rho \to \omega \, \pi$, $\omega \to \rho\, \pi$, and $K^* \to \rho\, K$ are crucial for these three-body decays, $B_{(s)} \to D_{(s)} V\, P$. In particular, the branching fractions arising from the $\rho$ and $\omega$ virtual effects can be comparable to the total decay rates of $B_{(s)} \to D_{(s)} \omega\, \pi$ and $B_{(s)} \to D_{(s)} \rho\, \pi$, 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 $B_{(s)} \to D_{(s)} (\rho \to)\, \omega\, \pi$, our results are consistent but exhibit higher precision.