Prospects for observing the missing $2D$ and $1F$ charmonium states around 4 GeV

Abstract

Our understanding of high-lying states within the charmonium family remains incomplete, particularly in light of recent observations of charmonium states at energies around 4 GeV. In this study, we investigate the spectroscopic properties of several high-lying charmonia, focusing on the $2D$ and $1F$ states. A mass spectrum analysis is conducted, incorporating the unquenched effects. We then present a detailed study of the strong decay properties, including partial decay widths for two-body strong decays permitted by the Okubo-Zweig-Iizuka (OZI) rule. Additionally, we explore the primary radiative decay channels associated with these states. Finally, we discuss the radiative transitions of the $2D$ and $1F$ states via $e^+e^-$ annihilation. Theoretical predictions provided here aim to guide future experimental searches for high-lying charmonium states at facilities such as BESIII, Belle II, LHCb, and the future STCF.

Figures (5)

• Figure 1: The mass spectrum of charmonium family, the experimental data and $S$-$D$ mixing scheme of vector charmonia.
• Figure 2: Strong decay widths of the $D$-wave charmonium states near their open-flavor thresholds. Figures (a), (b), and (c) display the partial widths as a function of mass for the $\eta_{c2}(4137)$, $\psi_2(4137)$, and $\psi_3(4144)$ states, respectively. The horizontal axis spans $\pm 150$ MeV around the nominal mass of each state. Decay channels with partial widths below 5 MeV are omitted for clarity but are included in the total width sums. The yellow band marks the $\pm 30$ MeV region around our calculated central mass values, and the red dashed line indicates the precise calculated mass.
• Figure 3: Strong decay widths of the $F$-wave charmonium states near their open-flavor thresholds. Figures (a), (b), (c), and (d) display the partial widths as a function of mass for the $h_{c3}(4074)$, $\chi_{c2}(4070)$, $\chi_{c3}(4075)$ and $\chi_{c4}(4076)$ states, respectively. The horizontal axis spans $\pm 150$ MeV around the nominal mass of each state. Decay channels with partial widths below 5 MeV are omitted for clarity but are included in the total width sums. The yellow band marks the $\pm 30$ MeV region around our calculated central mass values, and the red dashed line indicates the precise calculated mass.
• Figure 4: The allowed diagrams of the $e^+e^- \to \psi(4230) \to \gamma X$, including the $\psi(4230) \to \gamma \eta_{c2}(2D)$, $\psi(4230) \to \gamma \chi_{c2}(1F)$, and $\psi(4230) \to \gamma \chi_{c3}(1F)$ processes in the frame of hadronic loop mechanism.
• Figure 5: The numerical results for the process $e^+e^- \to \psi(4230) \to \gamma X$. The left, middle, and right columns depict the partial widths, branching ratios (among all $\psi(4230)$ decay modes), and production cross sections, respectively, for each final state $X$. In the right column, the cross sections are plotted for three typical values of the parameter $\alpha$: 1.5, 1.75, and 2, distinguished by different line styles.