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

TL;DR

The study tackles how subresonant processes $\rho^+\to\omega\pi^+$ contribute to Cabibbo-favored three-body $D$ decays $D_s^+\to \eta\omega\pi^+$, $D^+\to K_S^0\omega\pi^+$, and $D^0\to K^-\omega\pi^+$. It employs a quasi-two-body framework that models $\rho\to\omega\pi$ via the vector form factor $F_{\omega\pi}(s)$, constrained by data from $\tau$ decays and $e^+e^-$ processes, and includes both $\rho(770)$ and $\rho(1450)$ with their interference, using the form $F_{\omega\pi}(s) = (g_{\rho\omega\pi}/f_\rho)\sum_{\rho_i} A_i e^{i\phi_i} m_{\rho_i}^2 / D_{\rho_i}(s)$. The authors provide the first theoretical predictions for the quasi-two-body branching fractions of $D_s^+\to \eta[\rho^+\to]\omega\pi^+$, $D^+\to K_S^0[\rho^+\to]\omega\pi^+$, and $D^0\to K^-[\rho^+\to]\omega\pi^+$, and analyze the impact of the subthreshold $\rho(770)^+$ tail and interference effects. Numerically, $g_{\rho\omega\pi}\approx 16.0$ GeV$^{-1}$ and $A_1\approx 0.171$, together with the measured resonance parameters, indicate that $\rho(770)^+$ contributions are sizable and that interference with $\rho(1450)^+$ amplifies the $P$-wave $\omega\pi$ production, offering insight into resonance structure and guiding future amplitude analyses of these 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.

Figures (3)

• Figure 1: Schematic view of the cascade decay $D_s^+\to \eta \rho^+\to \eta \omega\pi^+$, where $\rho^+$ stands for the intermediate states $\rho(770,1450)^+$ which decay into $\omega\pi^+$ in this work.
• Figure 2: Typical topological diagrams for the concerned decays at quark level, where $\rho$ stands for the intermediate states $\rho(770,1450)^+$, $h$ for $\eta, K^0_S$ or $K^-$, and the symbol $\otimes$ stands for the weak vertex in this work.
• Figure 3: The differential branching fractions for the quasi-two-body decays $D_s^+\to\eta [\rho^+\to]\omega\pi^+$, with the intermediate $\rho^+= \{\rho(770)^+, \rho(1450)^+, \rho(770)^+\&\rho(1450)^+\}$.