Contributions of $\rho(770,1450)\to \omega\pi$ for the Cabibbo-favored $D \to h\omega\pi$ decays

TL;DR

This paper investigates the role of $ ho(770,1450)^+$ resonances in specific three-body $D$ meson decays, providing theoretical predictions that highlight the significance of these subprocesses in observed decay channels.

Contribution

It introduces the contributions of $ ho(770,1450)^+$ subprocesses into decay amplitudes, offering the first theoretical predictions for related branching fractions in $D$ meson decays.

Findings

$ ho(770)^+$ contributions are significant in observed decays.

Interference effects between $ ho(770)^+$ and $ ho(1450)^+$ are important.

Dominant contributions come from P-wave intermediate states.

Abstract

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