Contributions of <i>ρ</i> (770,1450)→ <i>ωπ</i> to Cabibbo-favored <i>D</i> → <i>hωπ</i> decays*

Abstract Recently, the BESIII Collaboration observed the three-body decays , , and . In this study, we investigate the contributions of the subprocesses in these Cabibbo-favored decays , with and , by introducing these subprocesses into the decay amplitudes of the relevant decay processes via the vector form factor , which has been measured in the related τ and processes. We provide the first theoretical predictions for the branching fractions of the quasi-two-body decays , , and . Our findings reveal that the contributions from the subprocess are significant in these observed three-body decays , , and , notwithstanding the contributions originating from the Breit-Wigner tail effect of . The numerical results of this study suggest that the dominant resonance contributions for the three-body decays and originate from the P -wave intermediate states , and their interference effects.