Contributions of $ρ(770,1450)\to ωπ$ for the Cabibbo-favored $D \to hωπ$ decays

Abstract

Recently, the BESIII Collaboration has observed the three-body decays $D_s^+\to ηωπ^+$, $D^+\to K^0_Sπ^+ω$ and $D^0\to K^-π^+ω$. In this work, we investigate the contributions of the subprocesses $ρ^+\to ωπ^+$ in these Cabibbo-favored decays $D \to hωπ$, with $ρ^+= \{ρ(770)^+, ρ(1450)^+, ρ(770)^+\&ρ(1450)^+\}$ and $h=\{ η, K^0_S, K^-\}$, by introducing these subprocesses into the decay amplitudes of relevant decay processes via the vector form factor $F_{ωπ}$ which has measured in the related $τ$ and $e^+e^-$ processes; we provide the first theoretical predictions for the branching fractions of the quasi-two-body decays $D_s^+\toη[ρ^+\to]ωπ^+$, $D^+\to K^0_S[ρ^+\to]ωπ^+$ and $D^0\to K^-[ρ^+\to]ωπ^+$. Our findings reveal that the contributions from the subprocess $ρ(770)^+\toωπ^+$ are significant in these observed three-body decays $D_s^+\toηωπ^+$, $D^+\to K^0_S ωπ^+$ and $D^0\to K^- ωπ^+$, notwithstanding the contributions originating from the Breit-Wigner tail effect of $ρ(770)^+$. The numerical results of this study suggest that the dominant resonance contributions for the three-body decays $D_s^+\toηωπ^+$ and $D^+\to K^0_S ωπ^+$ are originated from the $P$-wave intermediate states $ρ(770)^+$, $ρ(1450)^+$ and their interference effects.