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

Recently, the BESIII Collaboration has observed the three-body decays Dₛ⁺→ η ωπ⁺, D⁺→ K⁰Sπ⁺ω and D⁰→ K⁻π⁺ω. In this work, we investigate the contributions of the subprocesses ρ⁺→ ωπ⁺ in these Cabibbo-favored decays D → hωπ, with ρ⁺= \ρ(770)⁺, ρ(1450)⁺, ρ(770)⁺&ρ(1450)⁺\ and h=\ η, K⁰S, K⁻\, by introducing these subprocesses into the decay amplitudes of relevant decay processes via the vector form factor Fωπ 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 Dₛ⁺→η[ρ⁺→]ωπ⁺, D⁺→ K⁰S[ρ⁺→]ωπ⁺ and D⁰→ K⁻[ρ⁺→]ωπ⁺. Our findings reveal that the contributions from the subprocess ρ(770)⁺→ωπ⁺ are significant in these observed three-body decays Dₛ⁺→η ωπ⁺, D⁺→ K⁰S ωπ⁺ and D⁰→ 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 Dₛ⁺→η ωπ⁺ and D⁺→ K⁰S ωπ⁺ are originated from the P-wave intermediate states ρ(770)⁺, ρ(1450)⁺ and their interference effects. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Article funded by SCOAP3 and published under licence by Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Science and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd.