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

Abstract

Recently, the BESIII Collaboration has observed the three-body decays $D_s^{+}\to \eta \omega {\pi }^{+}$, $D^{+}\to K_S^0{\pi }^{+}\omega$ 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 $h=\{\eta ,K_S^0,K^{-}\}$, 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 $D_s^{+}\to \eta [{\rho }^{+}\to ]\omega {\pi }^{+}$, $D^{+}\to K_S^0[{\rho }^{+}\to ]\omega {\pi }^{+}$ 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 $D_s^{+}\to \eta \omega {\pi }^{+}$, $D^{+}\to K_S^0\omega {\pi }^{+}$ 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 $D^{+}\to K_S^0\omega {\pi }^{+}$ are originated from the $P$-wave intermediate states $\rho (770{)}^{+}$, $\rho (1450{)}^{+}$ and their interference effects.

Comments: 10 pages, 3 figures, accepted for publication in Chinese Physics C