Systematic analysis of the D-wave charmonium states with the QCD sum rules

We systematically study the 1D charmonium spin-triplet (with the $J^{PC}=1^{--}, 2^{--}, 3^{--}$) and spin-singlet (with the $J^{PC}=2^{-+}$) via the QCD sum rules in comparison with the recent experimental results. The predicted mass $M_{\psi_1}=3.77\pm{0.09}\,\rm {GeV}$ supports identifying the $\psi_1$ as the $\psi(3770)$, the value $M_{\psi_2}=3.82\pm{0.09}\,\rm {GeV}$ is consistent with the reported observation of the $\psi_2(3823)$, the prediction $M_{\psi_3}=3.84\pm{0.08}\,\rm {GeV}$ supports identifying the $\psi_3$ as the $\psi_3(3842)$. Additionally, we estimate the unobserved $\eta_{c2}$ state lies at $3.83\pm{0.09}\,\rm {GeV}$, and suggest detection prospects in the future. More experimental data will help us to unravel the mass spectrum of the charmonium states near the open-charm thresholds.